THERMODYNAMIC MODELING OF AL AND NI BASED TERNARY ALLOY

BY HSIN-NING SU

MECHANICAL MATERIALS AND AEROSPACE ENGINEERING

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Material Science and Engineering in the Graduate College of the Illinois Institute of Technology

Approved _________________________ Adviser

Chicago, Illinois December 2004

ACKNOWLEDGEMENT I would like to express my deepest gratitude to my academic and research advisor Professor Philip Nash for his guidance and constant support in helping me to conduct and complete this work. I would like to thank Professor Kleppa, Dr. Qiti Guo and Dr. Susan Meschel who help me with the calorimetry experiment in University of Chicago. In addition, I need to thank Professor Sundman in Swedish Royal Institute of Technology and Professor Zi-Kui Liu in Pennsylvania State University for helping me in computational thermodynamics. Many thanks to all people I know in Illinois Institute of Technology. I will never forget about the friendship and companionship I have ever had in Chicago. Finally, I owe my family so much and I know I will never finish my research here without the understanding and the support from my family.

Hsin-Ning Su December 2004

iii

TABLE OF CONTENTS Page ACKNOWLEDGEMENT

.......................................................................................

iii

LIST OF TABLES

...................................................................................................

vii

LIST OF FIGURES

.................................................................................................

ix

LIST OF SYMBOLS

...............................................................................................

xii

.............................................................................................................

xv

ABSTRACT CHAPTER

1. INTRODUCTION

..............................................................................

1

1.1 Thermodynamic Property Measurement................................... 3 1.2 Phase Diagram Data Measurement........................................... 3 1.3 Thermodynamic Model of Gibbs Free Energy ......................... 5 1.4 Thermodynamic Model for Estimating Thermodynamic Prope rty .............................................................................................. 9 1.5 Enthalpy of Formation Measurement by Direct Synthesis Calo rimeter ....................................................................................... 17 1.6 Prospective of Ternary Al-Ni-X (X=Y, Fe, Ru) Super Alloy... 35 2. EXPERIMENTAL PROCEDURE

.....................................................

37

2.1 High Temperature Calorimeter Experiment ............................. 2.2 X-Ray Diffraction Experiment ................................................. 2.3 Differential Scanning Calorimeter............................................

37 46 54

3. RESULTS FOR Al-Ni-Y SYSTEM ........................................................

60

3.1 Al-Ni-Y System Overview ......................................................... 3.2 Summary of Enthalpy of Formation Result ................................ 3.3 Experimental Determination of Al-Ni-Y Isothermal Section at 650 °C .........................................................................................

60 71

4. ENTHALPY RESULT OF Al-Ni-Fe SYSTEM......................................

80

4.1 4.2 4.3 4.4

Literature Overview of Al-Ni-Fe System ................................... Experimental Procedure.............................................................. Enthalpy of Formation Calculation............................................. Wagner-Schottky Model............................................................. iv

73

80 81 82 83

4.5 Thermodynamic Modeling of B2 Phase ..................................... 4.6 Result and Discussion.................................................................

85 86

5. POINT DEFECTS IN B2 PHASE REGION OF Al-Ni-Fe SYSTEM ....

98

5.1 5.2 5.3 5.4 5.5 5.6

Point Defects in B2 Phase Overview.......................................... Experiment.................................................................................. Discussion................................................................................... Atomic Volume Calculation for Al0.40 Ni(0.60-x) Fex System........ Atomic Volume Calculation for Al0.33 Ni(0.67-x) Fex System ....... Excess Thermal Vacancy............................................................

98 99 100 102 106 110

6. ENTHAPY OF FORMATION IN Al-Ni-Ru SYSTEM.......................... 112 6.1 6.2 6.3 6.4 6.5 6.6

Point Defect in B2 Phase Overview ........................................... Experiment.................................................................................. Lattice Parameter Calculation..................................................... Prediction of Enthalpies of Formation........................................ Results......................................................................................... Three Dimensional Curve Fitting for Enthalpies of Formation Result .......................................................................................... 6.7 Lattice Parameter Result ............................................................. 6.8 Al-Ni-Ru Phase Equilibrium ...................................................... 6.9 Thermodynamic Modeling .........................................................

112 113 114 114 115 120 122 125 129

7. CONCLUSION........................................................................................ 133 APPENDIX A. MATERIAL SOURCE

....................................................................... 135

B. SPACE GROUP NUMBER AND SPACE GROUP SYMBOL ............. 137 C. COMPARISON BETWEEN EXPERIMENTAL PEAK INTENSITY AND CALCULATED PEAK INTENSITY FOR COMPUNDS IN AlNi-Fe SYSTEM ....................................................................................... 140 D. CROSS PLATFORM MIEDEMA’S SEMI-EMPIRICAL CALCULATI ON PROGRAM IN HTML AND JAVASCRIPT LANGUASPAC GRO UP NUMBER AND SPACE GROUP SYMBOL ................................... 160 E. CROSS PLATFORM MOLAR RATIO TO WEIGHT RATIO CONVE RTOR IN HTML AND JANASCRIPT LANGUAGE............................ 187 F. CROSS PLATFORM WEIGHT RATIO TO MOLAR RATIO CONVE RTOR IN HTML AND JANASCRIPT LANGUAGE............................ 217

v

G. CROSS PLATFORM ENTHALPY OF FORMATION CALCULATOR FOR DIRECT SYNTHESIS CALORIMETER IN HTML AND JAVA SCRIPT LANGUAGE............................................................................. 244 H. CROSS PLATFORM ENTHAPY MEASUREMENT ERROR CALCU LATOR FOR DIRECT SYNTHESIS CALORIMETER IN HTML AND JAVASCRIPT LANGUAGE .................................................................. 254 I. HIGH-TEMPERATURE DATA FOR CONDENSED PHASE Cu........ 259 BIBLIOGRAPHY

.................................................................................................... 262

vi

LIST OF TABLES Table

Page

1.1 Experimental Techniques and Measured Thermodynamic Properties............

3

1.2 Experimental Techniques and Obtained Phase Diagram Data........................

4

1.3 Thermodynamic Model Developed on Different Basis ..................................

9

1.4 The Definition of Parameters in Wagner-Schottky Model for a Ternary Com pound with B2 Structure ................................................................................. 13 1.5 High Temperature Calorimeter Experiments ..................................................

19

1.6 Comparison Between Kleppa Calorimeter and Jung Calorimeter ..................

33

2.1 Example of Parameter Settings in Data Acquisition Program ........................

43

2.2 Parameter Setting for X-ray Diffraction Experiment......................................

50

2.3 DSC Crucible Selection in Different Conditions ............................................

58

2.4 DSC Experiment Condition ............................................................................

59

3.1 High Compound Designations ........................................................................

63

3.2 Summary of High Temperature Reaction Calorimetry Results and Miedema's Semi-empirical Model Results ........................................................................ 65 3.3 Melting Points of Compounds in Al-Ni-Y System .........................................

66

3.4 Al-Ni-Y Intermetallic Compound Phase Crystal Structure Data ....................

72

3.5 Selected Sample Composition for Phase Equilibria Determination................

73

3.6 Comparison Between EDX and XRD Result..................................................

75

4.1 The Definitions of the Parameters in the Wagner-Schottky Model of the B2 Phase ...............................................................................................................

84

4.2 Summary of the High Temperature Reaction Calorimetry Results, Miedema’s Semi-empirical Model Results and Lattice Structure Results......................... 87 4.3 Enthalpy coefficients in the Wagner-Schottky Model of the B2 Phase in AlNi-Fe ............................................................................................................... vii

97

5.1 Summary of Crystal Structure and Lattice Parameter..................................... 101 5.2 Lattice Parameters Used in Calculation .......................................................... 103 5.3 Lattice Parameters Used in Calculation .......................................................... 107 5.4 Enthalpy of Formation of Selected Compounds in Al-Fe and Al-Ni.............. 111 6.1 Summary of High Temperature Reaction Calorimetry Results and Miedema's Semi-empirical Model Results ........................................................................ 116 6.2 Coefficients of Fitted Equation of Enthalpy of Formation ............................. 120 6.3 Comparison of Enthalpies of Formation Between Experimental Result and Fitted Result .................................................................................................... 121

viii

LIST OF FIGURES Figure

Page

1.1 Flowchart of the CALPHAD Method............................................................

8

1.2 Kohler Model for Predicting Ternary Thermodynamic Property..................

10

1.3 Muggianu Model for Predicting Ternary Thermodynamic Property.............

11

1.4 Toop Model for Predicting Ternary Thermodynamic Property.....................

12

1.5 Hillert Model for Predicting Ternary Thermodynamic Property...................

12

1.6 Schematic Diagram of The First High-temperature Reaction Calorimeter Built by O. J. Kleppa .....................................................................................

22

1.7 Schematic Diagram of the Calvet-type, Twin High Temperature Reaction Calorimeter for Temperatures Up to 500 ° C ................................................

23

1.8 Schematic Diagram of Calvet-type Twin Reaction Calorimeter for Temper atures Up to About 1100°C............................................................................

24

1.9 Schematic General View of High Temperature Calorimeter for 1400 K and Above.............................................................................................................

26

1.10 Shematic View of Calorimeter Section and Reference Section of the Kleppa -Topor Calorimeter ......................................................................................... 28 1.11 Schematic Diagram of the Kleppa-Topor Calorimeter Cell Assembly .........

29

1.12 The Principle Features of New Calorimeter Built by Jung............................

31

1.13 The Schematic Diagram of The Inner View of Thermopile and Cross-section of the Calorimeter Tube................................................................................. 32 2.1 Process of Assembling Liner .........................................................................

42

2.2 Schematic Temperature-Time Curve for Calorimeter ...................................

44

2.3 Structure of X-ray Diffractometer .................................................................

47

2.4 Calibration Curve for X-ray Diffraction Experiment ....................................

49

2.5 Lattice Parameter Obtained by Different Index Plan v.s. cos 2θ , Large Syst ematic Error and Small Random Error ..........................................................

53

ix

2.6 Lattice Parameter Obtained by Different Index Plan v.s. cos 2θ , Small Syst ematic Error and Large Random Error ..........................................................

53

2.7 Schematic Diagram of Heat Flux Type Differential Scanning Calorimetry .

55

2.8 Heat Flux Type DSC Rod..............................................................................

56

2.9 Setaram Setsys 1750 DSC .............................................................................

57

3.1 Partial Isothermal Section of the Al-Ni-Y System ........................................

62

3.2 Enthalpies of Formation in kJ/mole for Compounds in the Al-Ni-Y System

68

3.3 Measured and Predicted Enthalpies of Formation in AlxNi5-xY alloys .........

70

3.4 Measured and Predicted Enthalpies of Formation in Al2-xNixY alloys .........

71

3.5 Partial Isothermal Section of Al-Ni-Y at 650°C............................................

77

3.6 SEM Photo of Nominal Al9Ni3Y Alloy with 1) Al23Ni6Y4 Phase and 2) Al9 Ni3Y Phase.....................................................................................................

78

3.7 SEM Photo of Nominal Al3NiY Alloy with 1) Al3NiY Phase, 2) Al7Ni3Y2 Phase ..............................................................................................................

78

3.8 SEM Photo of Nominal Al4NiY Alloy with 1) Al4NiY Phase ......................

78

3.9 SEM Photo of Nominal Al16Ni3Y Alloy with 1) Al3NiY Phase, 2) Al9Ni3Y Phase and 3) Al phase ...................................................................................

79

3.10 SEM Photo of Nominal Al7Ni3Y2 Alloy with 1) Al4NiY Phase and 2) AlNi Phase ..............................................................................................................

79

3.11 SEM Photo of Nominal Al23Ni6Y4 Alloy with More Than 95% 1) Al23Ni6Y4 Phase and Less Than 5% 2) Al3Ni Phase...................................................... 79 4.1 Enthalpies of Formation of Compounds in the Al-Ni-Fe System Determined in This Work by High Temperature Reaction Calorimetry .......................... 88 4.2 Enthalpies of Formation of Solid B2 Al0.50 Ni(0.50-X) FeX ...............................

89

4.3 Enthalpies of Formation of Solid B2 Al0.40 Ni(0.60-X) FeX ...............................

90

4.4 Enthalpies of Formation of Solid B2 Al0.33 Ni(0.67-X ) FeX .............................

91

4.5 Comparison of Enthalpies of Formation for Selected Compounds ...............

93

x

4.6 Enthalpies of Formation of Solid B2 Al0.5 Ni(0.5-X) FeX Determined Experim enthalpy and Compared to Miedema and Thermocalc Values ......................

94

5.1 Lattice Parameter of Al0.50 Ni(0.50-X) FeX......................................................... 102 5.2 Lattice Parameter of Al0.40Ni (0.60-X)FeX ......................................................... 103 5.3 Lattice Parameter of Al0.33 Ni(0.67-x) Fex ......................................................... 107 5.4 Lattice Parameter of Al-Fe System................................................................ 111 6.1 Enthalpies of Formation in B2 Phase Field of Al-Ni-Ru System.................. 117 6.2 Enthalpies of Formation of Al0.45 Ni (0.55-X) RuX ............................................ 118 6.3 Enthalpies of Formation of Al0.50 Ni(0.50-X) RuX ............................................. 119 6.4 Lattice Parameters of Al0.50 Ni (0.50-X) RuX ..................................................... 123 6.5 Lattice Parameters of Al0.45 Ni (0.55-X) RuX ..................................................... 124 6.6 XRD Patterns of Al0.50 Ni(0.50-x) Rux ............................................................... 126 6.7 XRD Patterns of Al0.45 Ni(0.55-x) Rux ............................................................... 127 6.8 Schematic of Proposed Vertical Section of Al-Ni-Ru System at Constant 50 Atomic % Al .................................................................................................. 128 6.9 Schematic of Proposed Vertical Section of Al-Ni-Ru System at Constant 50 Atomic % Al .................................................................................................. 128 6.10 Experimental Liquidus Surface Projection for Al-Ni-Ru .............................. 130 6.11 Comparison of Calculated and Experimental Enthalpies of Formation for Compounds with Constant 50 at. % Al.......................................................... 132

xi

LIST OF SYMBOLS Symbol

H iSER reference

ideal

Gϕ

Definition Enthalpy of Formation Refered to Standard Element Reference Contribution of the Pure Components of the Phase to the Gibbs Energy

Gϕ

Ideal Mixing Contribution

Gϕ

Excess Gibbs Energy Corresponding to the Non-deal Interactions Between the Components

excess

υ ϕ

Binary Interaction parAmeter

∆G E

Ternary Gibbs Energy of Mixing

∆G ijE

Binary Gibbs Energy of Mixing

Li , j

Wij

Weight Probability

∆H f

Enthalpy of Formation of B2 Phase in A-B-C Ternary Compound

∆H*

Enthalpy of Formation of 1 Mole of the Ideally Stoichiometric B2 Phase

∆H12

Enthalpy of Formation of 1 Mole of B Antistructure Atoms in the β Sublattice

∆H13

Enthalpy of Formation of 1 Mole of C Antistructure Atoms in the β Sublattice

∆H 20

Enthalpy of Formation of 1 Mole of Vacancies in the α Sublattice

∆H 21

Enthalpy of Formation of 1 Mole of A Antistructure Atoms in the α Sublattice

∆H 23

Enthalpy of Formation of 1 Mole of C in the α Sublattice

x12

Concentration of B Antistructure Atoms In the Β Sublattice

xii

Symbol

Definition

x13

Concentration of C Antistructure Atoms in the β Sublattice

x 20

Concentration of Vacancies in the α Sublattice

x 21

Concentration of A Antistructure Atoms in the α Sublattice

x 23

Concentration of C Antistructure Atoms in the α Sublattice

∆H fAB

Enthalpy of Formation of 1 Mole of the Ideally Stoichiometric AB Compound

∆H fAC

Enthalpy of Formation of 1 Mole of the Ideally Stoichiometric AC Compound

i nWS

Electronic Charge Density Deffernece at the WignerSeitz Boundary

φ*

Experimental Work Function

Cis

Effective Surface Concentration

f BA

Degree of Surface Contact of an A Atom with B Neighbors

f CA

Degree of Surface Contact of an A Atom with C Neighbors

∆H inter

Interfacial Enthalpy

∆HReaction

Enthalpy of Reaction

∆HHeat Content

Enthalpy of Heat Content

VAl / Al

Atomic Size of Al in Al Sublattice

VNi / Al

Atomic Size of Ni in Al Sublattice

VNi / Ni

Atomic Size of Ni in Ni Sublattice

VFe / Al

Atomic Size of Fe in Al Sublattice

VFe / Ni

Atomic Size of Fe in Ni Sublattice

xiii

Symbol

Definition

∆V( Fe− Ni )α

Atomic Size Difference Between Fe and Ni in α Sublattice

∆V( Fe − Ni ) β

Atomic Size Difference Between Fe and Ni in β Sublattice

∆V( Fe − Al ) β

Atomic Size Difference Between Fe and Al in β Sublattice

∆V( Ni − Al ) β

Atomic Size Difference Between Ni and Al in β Sublattice

xiv

ABSTRACT Alloys involving Ni, Al and other elements are of interest for applications such as high temperature structural materials for gas turbines. Alloy development of such materials requires a thorough knowledge of the thermodynamic properties and phase equilibria in the binary, ternary and higher order alloy systems. Precise determinations of thermodynamic properties, especially enthalpy of formation, are valuable for obtaining an accurate thermodynamic model of a multicomponent system. In order to understand fundamental thermodynamic properties and the systematics between alloys, Al-Ni-Y, Al-Ni-Fe and Al-Ni-Ru were selected for studying enthalpy of formation, lattice parameter and also alloying behavior through correlations between the heat of formation and other physical properties. Partial isothermal section of Al-Ni-Y in a range of Y ≤ 0.33 at. % at 650°C was measured and Al3Ni2Y, Al7Ni3Y2, Al23Ni6Y4 have been confirmed to be the existing compounds. Site occupancy as well as atomic volume in B2 phase field of Al-Ni-Fe system have been studied in order to understand more about the alloying behavior. The existence of the miscibility gap between the B2 phase field across AlNi and AlRu in AlNi-Ru system has also been studied using enthalpy and lattice parameter results. Extended Miedema’s semi-empirical model has been used to predict enthalpy of formation of ternary compounds in selected ternary systems. The difference between the predicted and experimental results will be correlated to a factor which is required to be taken into consideration when upgrading the binary based Miedema model to ternary compound application.

xv

1 CHAPTER 1 INTRODUCTION The objectives of this research are to accurately determine heat of formation for aluminum-nickel-X ternary compounds and to use this data to develop thermodynamic models for ternary systems that are relevant to aluminum and nickel alloy processing and development. Heat of formation for aluminum-nickel-X ternary compounds can also be used in providing benchmarks for first principles calculations. The applicability of the Miedema model in its extended form for ternary compounds is examined by comparing it with our experimental data and several interpolation techniques for estimating ternary heats of formation. Applying Wagner-Schottky defect model to selected compound heats of formation together with density and x-ray data, will allow us to determine molar enthalpies of formation for various constitutional defects. Some phase equilibria data will also be generated in the course of the work and this will be used in conjunction with the thermodynamic data to develop a self-consistent Al-Ni-X thermodynamic database. Due to the fact that phase equilibria as well as phase diagrams are of great importance in diverse areas such as primary metal production, iron and steel-making, super alloys, nonferrous alloys, high-temperature structural ceramics, glass processing, semiconductors, superconductors, metal coatings, electric power industry, thermal energy storage technology, magneto hydrodynamics, etc, emphasis has been laid on the fact that industrial requirements for phase diagram information can not be met by presently available phase diagrams obtained by experiments. Experience has showed that conventional experimental study of systems with many components is very time-

2 consuming and expensive. It is therefore very important to develop a method for phase equilibria calculation and also utilize computers to facilitate the calculation. . Thermodynamic basis for the calculation of equilibria in multi-component systems has been established by van Laar [Laa08] since the beginning of the last century. During the last decade computer techniques have made a significant advance in the application of thermodynamic principles to the calculation of phase equilibria in complex systems. Several models describing thermodynamic properties have been developed explaining the equilibrium and phase relations in complex systems [Hil01] and are being increasingly used in actual industrial practice [Sun98].

3 1.1 Thermodynamic Property Measurement

The precision of a thermodynamic measurement is one of the most important factors to develop reliable thermodynamic models. There is a range of different experimental methods which are used for measuring thermodynamic properties. One single technique alone can not provide the whole picture of the thermodynamics of any system. Several experimental techniques for measuring thermodynamic properties are listed in Table 1.1.

Table 1.1. Experimental Techniques and Measured Thermodynamic Properties. Measuring Technique

Thermodynamic Property

Calorimeter

Enthalpy of formation Enthalpy of mixing Enthalpy of transformation

EMF, Knudsen cell

Chemical potential Activities

Partial pressure

Activities

Differential Scanning Calorimeter (DSC)

Enthalpy of transformation Melting Point

1.2 Phase Diagram Data Measurement

Phase diagram data is as important as thermodynamic property data when doing thermodynamic modeling. Phase identification is a major process in understating phase equilibria. Lattice parameter and site occupancy that are directly related to phase property are also measured in order to understand more about the system. Experimental techniques for phase diagram data measurement are, Differential Thermal Analysis (DTA), Optical

4 Microscope, Scanning Electron Microscopy (SEM), Energy Dispersive Spectroscopy (EDS), X-Ray diffraction (XRD), Neutron Diffraction), etc. The phase diagram data and corresponding experimental techniques are listed in Table 1.2. Since the thermodynamic data of multicomponent system is not easily available. Phase equilibria of binary or ternary systems become relatively important in order to build the thermodynamic model for predicting the phase diagram of multicomponent sytem. Therefore, reliable phase information of binary or ternary systems for large range of concentration and temperature have to be determined.

Table 1.2. Experimental Techniques and Obtained Phase Diagram Data. Measuring Technique

Phase Data

Differential Thermal Analysis

Phase transformation temperature Melting point

Optical Microscope

Phase identification Phase amount determination

Scanning Electron Microscopy (SEM)

Phase identification Phase amount determination

Energy Dispersive Spectroscopy (EDS)

Chemical element analysis

X-Ray Diffraction (XRD)

Phase identification Lattice parameter Site occupancy

Neutron Diffraction

Site occupancy

5 1.3 Thermodynamic Model of Gibbs Free Energy

Mathematical descriptions of the thermodynamic properties as a function of composition and temperature has been developed in order to estimate thermodynamic properties at different temperatures [Sau98]. The CALPHAD (CALculation of Phase Diagram) method is usually used for describing the Gibbs model for different condition.

1.3.1 Gibbs Free Energy Model of Pure Elements. The Gibbs energy of pure elements

i with the structure ϕ , refered to the enthalpy of its standard state element reference (SER) at 298.15K, H iSER , is described as a function of the temperature by the following equation: o

Giϕ − H iSER = a + bT + cT ln T + dT 2 + eT 3 + fT −1 + gT 7 + hT −9

This quantity is denoted GHSER i where the structure ϕ corresponds to SER. Values of the coefficients, a, b,…, h, are taken from the SGTE database [Din91]. The thermodynamic data for 78 pure elements used by SGTE (Scientific Group Thermodata Europe) were published and has been widely adopted within the international community as a basis for thermodynamic modeling of multi-component systems.

1.3.2 Gibbs Free Energy Model of Solid Solution. Solid solutions are described by a

random substitutional model and molar Gibbs energy is given by the general compound energy formalism:

Gϕ = where the Gibbs energy,

Gϕ + idealGϕ + excessGϕ

reference

Gϕ is the contribution of the pure components of the phase to the

reference

ideal

Gϕ is the ideal mixing contribution and

excess

Gϕ is the excess Gibbs

energy corresponding to the non-ideal interactions between the components.

6 The three terms are express by the following equations: reference

Gϕ = ∑ xi0Giϕ i

ideal

Gϕ = RT ∑ xi lnxi i

excess

Gϕ = xi x j ∑ υ Lϕi , j (xi − x j ) υ υ =0

where xi represents the modal fraction of components i and υ Lϕi , j is a binary interaction parameter: υ ϕ

Li , j = aυ + bυ T

1.3.3 Assessment of Gibbs Free Energy Model. The optimization of these parameters

can be done by means of the Parrot module of the ThermocalcTM program package [Sun85] which consists of sophisticated and generalized software for the calculation of chemical equilibria and phase diagrams [Jon90]. The criteria of the best estimation of the model parameters can be obtained from a statistical treatment of the errors associated with all experimental determinations of equilibrium states in the system. The most commonly used method in parameter evaluation is the least-square method [Jan84]. Figure 1.1 shows the flowchart of optimizing parameters using CALPHAD method [Har01]. Many more energy models other than those described above have been developed in order to describe thermodynamic properties of phases. The energy model has been developed step by step, taking into account various complicating aspects, and is now capable of describing the properties of many different types of phases. It is thus widely used in CALPHAD assessments. The energy model was reviewed by Mats Hillert [Hil01].

7

Figure 1.1. Flowchart of the CALPHAD Method [Har01]

8 1.4 Thermodynamic Model for Estimating Thermodynamic Property

In order to obtain an accurate phase diagram within a short time, precise measurement of thermodynamic property is necessary. The measurement is not easy if it is a multicomponent system and the problem cannot be solved easily due to the complexity of experiments in a multicomponent system. The calculation of thermodynamic properties has been playing an important role in developing phase diagrams. Different models have been developed to estimate different thermodynamic property, these model could be empirical, semi-empirical or based on first principles. Table 1.3 shows the several models used in recent thermodynamic calculations. Table 1.3. Thermodynamic Model Developed on Different Basis First principle

Semi-empirical

Empirical

Cluster variation method (CVM)

Miedema’s model for enthalpy prediction

Hillert model Kohler model

Density functional theory Toop model Muggianu model 1.4.1 Empirical Model for Estimating Thermodynamic Property.

Predicting

thermodynamic properties for ternary or multi-component system from binary ones is widely used because it is simple, effective and only requires information that can be easily calculated. The model that can express the ternary thermodynamic property in terms of its three binary systems can be a suitable one to calculate the particular thermodynamic property.

9 According to the method of choosing the binary composition, Hillert [Hil80] has classified these models into two categories: 1) Symmetric model: Kohler [Koh60], Colinet [Col67] and Muggianu [Mug75] 2) Asymmetric model: Bonnier [Bon60], Toop [Too65]and Hillert [Hil80] Ansara [Ans72, Ans70] and Hillert [Hil80, Hil83] have reviewed these models which can be summarized as:

E E E ∆G E =W12 ∆G12 +W31∆G 31 +W23∆G 23

∆G E is the ternary Gibbs energy of mixing, ∆G ijE is binary Gibbs energy of mixing. Wij is the weight probability.

Figure 1.2. Kohler Model for Predicting Ternary Thermodynamic Property x3  x1 x2  x2 E  2 E  ∆G E = ( x1 + x2 ) 2 + ∆G12 ; ; +   + ( x2 + x3 ) + ∆G 23   x1 + x2 x1 + x2   x2 + x3 x2 + x3  x3 x  E  ( x1 + x3 ) 2 + ∆G 31 ; 1    x1 + x3 x1 + x3 

10

Figure 1.3. Muggianu Model for Predicting Ternary Thermodynamic Property

∆G E =

4 x1 x2 E  1 + x1 − x2 1 + x2 − x1  ∆G12 ;  + (1 + x1 − x2 )(1 + x2 − x1 ) 2 2   4 x2 x3 E  1 + x2 − x3 1 + x3 − x2  ∆G12 ;  + (1 + x2 − x3 )(1 + x3 − x2 ) 2 2   4 x3 x1 E  1 + x3 − x1 1 + x1 − x3  ∆G12 ;   (1 + x3 − x1 )(1 + x1 − x3 ) 2 2  

11

Figure 1.4. Toop Model for Predicting Ternary Thermodynamic Property ∆G E =

 x x x  x2 E ∆G12 ( x1;1 − x1 ) + 3 ∆G13E ( x1;1 − x1 ) + ( x2 + x1 )2∆G E23  2 ; 3  (1 − x1 ) (1 − x1 )  x2 + x3 x2 + x3 

Figure 1.5. Hillert Model For Predicting Ternary Thermodynamic Property

∆G E =

x xx x2 E ∆G12 ( x1 ;1 − x1 ) + 3 ∆G13E ( x1;1 − x1 ) + 2 3 ∆G E23 ( v23 ; v32 ) (1 − x1 ) (1 − x1 ) v23v32

12 1.4.2 Wagner-Schottky Model for Describing Enthalpy. Thermodynamic treatments of

lattice defects in stoichiometric phase by Wagner and Schottky in 1930 [Wag30] and Olander in 1932 [Ola32] and of interstitial solutions by Johansson in 1937 [Joh37] has revealed that an adequate description of the properties of solution phases with sublattices must take the existence of the sublattices into account. The example for Wagner-Schottky model for describing an A-B-C compound with B2 phase crystal structure is shown below and the parameters are defined in Table 1.4.

∆H f = ∆H*(1+x 20 )+∆H12 x12 +∆H13 x13 +∆H 20 x 20 +∆H 21x 21 +∆H 23 x 23 ∆H* =x∆H fAB +(1-x)∆H fAC

13 Table 1.4. The Definition of Parameters in Wagner-Schottky Model for a Ternary Compound with B2 Structure Parameter

Definition

∆H f

Enthalpy of formation of B2 phase in A-B-C ternary compound

∆H*

Enthalpy of formation of 1 mole of the ideally stoichiometric B2 phase

∆H12

Enthalpy of formation of 1 mole of B antistructure atoms in the β sublattice

∆H13

Enthalpy of formation of 1 mole of C antistructure atoms in the β sublattice

∆H 20

Enhthalpy of formation of 1 mole of vacancies in the α sublattice

∆H 21

Enthalpy of formation of 1 mole of A antistructure atoms in the α sublattice

∆H 23

Enthalpy of formation of 1 mole of C in the α sublattice

x12

Concentration of B antistructure atoms in the β sublattice

x13

Concentration of C antistructure atoms in the β sublattice

x 20

Concentration of vacancies in the α Sublattice

x 21

Concentration of A antistructure atoms in the α sublattice

x 23

Concentration of C antistructure atoms in the α sublattice

∆H fAB

Enthalpy of formation of 1 mole of the ideally stoichiometric AB compound

∆H fAC

Enthalpy of formation of 1 mole of the ideally stoichiometric AC compound

14 1.4.3 Miedema’s Semi-empirical Model for Enthalpy Estimation. During the 1970s,

Miedema and co-workers developed a “semi-empirical” or “macroscopic-atom” model to predict the enthalpy of formation of binary metallic alloys in which at least one of the elements is a transition element [Boe88]. An extension of Pauling’s scheme was used for calculating enthalpy of formation of alloys and compounds in their standard state. In Pauling’s scheme, the heat of formation of simple molecules was proposed to be proportional to the summation of the squared electronegativity differences. But Pauling’s scheme only includes negative contribution to the enthalpy of formation. Miedema added a positive contribution which is proportional to the square of the cubic root of the i ) and also an electronic charge density difference at the Wigner-Seitz boundary ( nWS

experimental work function ( φ * ). In general Miedema’s expression for the enthalpy of formation of a binary intermetallic alloy is:

∆H (A CA BCB ) = ∆H '(A CA BCB ) + C A ∆H trans (A) + C B ∆H trans ( B )

(1)

∆H '(A CA BCB ) is constructed assuming the elements A and elements B are both metals:

∆H '(A CA BCB ) = fgP[−(∆φ * ) 2 +

Q R 2 (∆n1/3 ] WS ) − P P

The components in equation (2) are ∆φ * = ∆φA* − ∆φB* A 1/ 3 B 1/ 3 ∆n1/3 − (∆nWS ) WS = ( ∆nWS )

f = CSA CSB [1 + 8(CSA CSB ) 2 ]

(2)

15 g=

A −1/ 3 WS

(∆n )

2 B − (∆nWS ) −1/ 3

ci (Vi alloy ) 2 / 3 C = cA (VAalloy ) 2 / 3 + cB (VBalloy ) 2 / 3 s i

(Vi alloy ) 2 / 3 = Vi 2 / 3[1 + a

f (φi* − φ j* )] s Ci

i Here i and j denote A or B; the φi* are effective chemical potentials; nWS is the electron

density at the boundry of the Wigner-Seitz cell of parent metal I; Vi is the molar volume of i ; Ci is the concentration of i ; Vi alloy is the volume of i; the Cis is effective surface concentration [Her02].

The Miedema’s semi-empirical model was also extended to ternary systems [Bak98]. K , can be calculated from: The standard enthalpy of formation, ∆H 298 f

K i nter A inter C inter ∆H 298 = CA f BA ∆H (A in B) + CA f C ∆H (A in C) + CB f B ∆H (B in C) f

CA and CB are the molar ratios of A and B elements respectively in the corresponding compounds, f BA is the degree of surface contact of an A atom with B neighbors while f CA is the degree of surface contact of an A atom with C neighbors. ∆H inter is interfacial enthalpy.

16 1.5 Enthalpy of Formation Measurement by Direct Synthesis Calorimeter

Industrial application for new material development and metallurgical processes strongly rely on the development of phase diagrams and knowledge of thermodynamics. Instead of experimental determination of phase diagram, the development of computer technique leads the phase diagram calculation possible if reliable thermodynamic properties can be obtained. In the 80’s people believe the band theory of physical quantum mechanics is sufficient enough to provide a lot of ab-initio or semi-fitted data set. Unfortunately the relative phase stability in a multicomponent alloy depends on only some thousand of eV and the actual precision of the calculated cohesive energy will not attain 0.01 eV which is still too coarse [Her00]. Therefore, the experimental determination of thermodynamic property is still the most important process for phase diagram calculation. Numerous techniques such as EMF measurement, vapor pressure technique, high temperature calorimeter for thermodynamic measurement have been used for determining thermodynamic property experimentally. Among these, high temperature reaction calorimeter is a popular approach to obtain systematic thermodynamic information on alloy system. From 1927 to 1930, high temperature heat of mixing calorimeter for a large number of liquid alloys was measured in Japan [Kwa127, Kwa227]. An early venture into high temperature reaction calorimetry was made by Kubaschewski and Walter in Germany [Kub39]. O. J. Kleppa modified a commercial SETARAM calorimeter design to construct a direct synthesis calorimeter which is less expensive and a relatively simple microcalorimeter specifically for continuous operation at 1400K and above [Kle89].

17 Table 1.5 summarizes the types of experiments that can be done in a high temperature reaction calorimeter. A transposed temperature drop experiment consists of dropping a sample from room temperature into high temperature calorimeter without the presence of a solvent. If there is no phase change or chemical reaction, the heat content, H temperature

–H

room temperature

calorimeter

is measured, its temperature derivative gives the heat capacity.

If a phase transition takes places, the enthalpy of that change is included in the measurement. Measurements at several different calorimeter temperatures map out the heat capacity and enthalpy of transition. [Nav97]. Major developments in calorimeter design can be done in three ways: 1) To develop more sensitive and stable calorimeter capable of operation over a wide temperature range 2) To deal with a wider range of chemical compositions including volatile materials 3) To have better control and characterization of the structure and homogeneity of sample which leads to more sophisticated interpretation of the energetics obtained by calorimetry. Table 1.5 summarizes several types of high temperature calorimetry techniques [Nav97].

18 Table 1.5. High Temperature Calorimeter Experiments [Nav97] Calorimeter essentially isothermal Solvent present Solution calorimeter: sample equilibriated in hot calorimeter, then dissolved. Difference in heats of solution give heat of reaction at calorimeter T. Drop solution calorimeter: sample dropped from room T. Sample may be encapsulated in Au or Pt, pyrex or silica glass (which dissolves) or lead borate glass (same as solvent), or as unencapsulated pellets. Differences in heats of drop-solution give heat of reaction at room T. Solvent absent Transposed temperature drop calorimetry. No permanent changes in sample: heat content measurement, includes heat of any rapid and reversible phase change. Sample changes oxidation state: difference between first and second drop related to heat of redox reaction. Sample losses H2O, CO2 or other volatiles: difference related to heat of devolatization. Sample undergoes irreversible phase change: difference gives heats of transformation at room T. Sample undergoes change in degree of order or other structural parameters: difference gives ordering energy. Calorimeter changes temperature At constant rate Scanning calorimetry: measures heat capacity and phase change or decomposition In steps separated by isothermal periods Step scanning calorimetry: measures heat capacity and reversible phase transition enthalpies.

19 1.5.1 Calorimeters Developed by O. J. Kleppa. It has been more than 55 years that

Professor O. J. Kleppa has devoted to the measurement of enthalpy of formation in more than 200 binary systems and has published more than 224 papers up to Dec. 2004. He began his research on EMF measurement using liquid electrolyte since 1947 and finally he concluded two facts: 1) EMF method doesn’t allow reliable separation of measured Gibbs energy into appropriate enthalpy and entropy contribution, 2) EMF method requires a significant difference between the two components so it is not suitable for thermodynamic studies of a wide range of binary alloy system. [Kle01]. Kleppa also considered the possibility of using vapor pressure measurement which in principle can be applied to any solution systems. However, vapor pressure measurement requires experiment at very high working temperature which causes difficulties and also the experimental errors. Kleppa concluded that his experimental approach to the systematic study of the thermodynamics of binary alloys must be based on calorimetry, and more specifically on high-temperature mixing and reaction calorimetry. Calorimetric measurements would not provide all the desired thermodynamic information, but in most cases it would provide the leading term in the Gibbs energies of alloy formation. His experiences in using this method for nearly 50 years fully support this conclusion. [Kle02] The first calorimeter built by Kleppa in 1952 was a “conventional” or “quasiadabatic” design which was strongly influenced by Kubaschewski and Walter [Kub39]. That calorimeter was operated at temperatures up to 450°C for more than 10 years, Figure 1.6 [Kle94].

20 Kleppa was inspired by Calvet and Prat [Cal56] in 1959 and he built a high temperature twin microcalorimeter which was described in [Kle60]. Figure 1.7 gives the detail of the construction of the Calvet-type calorimeter [Kle60, Kle94]. This Calvet-type calorimeter allowed a wide range of different kinds of experiments to be performed, and it could be used for very much smaller samples. It was used extensively in studies of lowmelting molten salts. It also later provided the basis for pioneering work on solid solutions of hydrogen and deuterium in metals. The calorimeter was used for more than 20 years for innumerable calorimetric experiments on very many different kinds of materials. In order to obtain higher reaction temperature, Kleppa built a Calvet-type twin calorimeter suitable for operation up to 1100°C. It was constructed from a system of pure alumina cylinders which surrounded the central calorimetric. A schematic diagram of the calorimeter with the three heaters is shown in Fig. 1.8 [Kle94]. This unit was built in the early 1970s and was usually maintained at 800–1100°C.

21

Figure 1.6. Schematic Diagram of the First High-temperature Reaction Calorimeter Built by O. J. Kleppa [Kle94]

22

Figure 1.7. Schematic Diagram of the Calvet-type, Twin High Temperature Reaction Calorimeter for Temperatures Up to 500 ° C [Kle60, Kle94]

23

Figure 1.8. Schematic Diagram of Calvet-type Twin Reaction Calorimeter for Temperatures Up to About 1100°C [Kle94]

24 However, his most recent calorimeter (The kleppa-Topor calorimeter), developed in 1989, is based on the same principle as the commercial Setaram unit. Unlike the Setaram unit, it has a much larger internal diameter and it can be used continuously at temperatures up to about 1400 K, Figure 1.9 shows the schematic general view of this high temperature calorimeter for 1400 K and above [Kle94]. This calorimeter is maintained continuously at high temperature of 1373K to 1474K in a cylindrical furnace that is heated by a Pt40Rh heating element. This gives both the calorimeter and the furnace an acceptable lifetime [Kle94]. The current furnace has been in operation since 1993 and the latest calorimeter tube has been used since 1996. The fixed calorimeter temperature and the single function design of Kleppa’s calorimeter are to ensure a highly precise enthalpy measurement and also the long life of calorimeter. High stability and high precision have already proved that Kleppa’s calorimeter is one of the few successful ones among the world.

25

Figure 1.9. Schematic General View of High Temperature Calorimeter for 1400 K and above [Kle94]

26 A new single unit differential micro-calorimeter has been influenced in its design by the modified SETARAM calorimeter. The thermopile of the calorimeter is built into the wall of an alumina tube. Figure 1.10 shows a schematic view of calorimeter section (working section) and reference section of the Kleppa-Topor Calorimeter where twenty nine thermocouples are used in series in the thermopile [Kle94]. Reaction takes place in a small Boron Nitride crucible located inside a slightly larger Boron Nitride crucible which prevents the Pt20Rh liner from being contaminated by sputtered sample particles. The Pt20Rh liner and its components including Boron Nitride crucible, Boron Nitride protective cylinder, Boron Nitride protective crucible, Alumina protective cylinder, Zirconium getter and Stainless steel. Figure 1.11 shows schematic view of the Kleppa-Topor Calorimeter cell assembly showing part of the Pt20Rh liner, the boron nitride crucible, the boron nitride protective cylinder and stirrer, the alumina protective crucible and protective cylinders, as well as parts of the final gettering system for the argon gas [Kle94]. In order to prevent oxidation reaction which leads to errors in measurement, inert gas is introduced into the system and is vented at the point where sample is dropped. Zirconium getter and stainless steel sheet are also incorporated to enhance Oxygen removing efficiency.

27

Figure 1.10. Schematic View of Calorimeter Section and Reference Section of the Kleppa-Topor Calorimeter [Kle94]

28

Figure 1.11. Schematic Diagram of the Kleppa-Topor Calorimeter Cell Assembly [Kle94]

29 1.5.2 Recent Development of Kleppa-type High Temperature Direct Synthesis Calorimeter. W. G. Jung has recently built a Kleppa type calorimeter based on Kleppa’s

design in 2003 [Jun03], Figure 1.12. The purpose of the new calorimeter design by Jung is to increase the precision by two sets of thermopiles. The outer thermopile is the same as Kleppa’s thermopile arrangement shown in Figure 1.10, the inner thermopile as shown in Figure 1.13 [Jun03] is connected to the outer thermopile through a hole made in the calorimeter tube. Furthermore, the reaction tube is made of high purity quartz instead of expensive Pt20Rh used by Kleppa. Table 1.6 summaries the difference between kleppa and Jung’s calorimeter. The standard molar enthalpies of formation for NiSi and Ni3Al compounds were measured using this new Kleppa type calorimeter and the result show reasonably good agreement with other previously reported experimental results, which confirms the performance and stability of calorimeter.

30

Figure 1.12. The Principle Features of New Calorimeter Built by Jung [Jun03]

31

Figure 1.13. The Schematic Diagram of the Inner View of Thermopile and Cross-section of the Calorimeter Tube [Jun03]

32 Table 1.6. Comparison Between Kleppa Calorimeter and Jung Calorimeter O. J. Kleppa [kle98]

W. G. Jung [Jun03]

Reaction tube

Material: Pt20Rh Outer diameter: 22 mm Total length: 800 mm

Material: High purity quartz Outer diameter: 24 mm Inner diameter: 20 mm Total length: 900 mm

Calorimeter tube

Material: high purity Al2O3 Inner diameter: 23 mm Outer diameter: 29 mm Total length: 760 mm

Material: high purity Al2O3 Inner diameter: 25 mm Outer diameter: 31.7 mm Total length: 900 mm

Protecting gas getter

Ti granule Stainless steel sheet Zirconium

Ti granule Ti sheet silica gel P2O5 CaSO4

Data acquisition

Keithley 181 nanovoltmeter Volt-to-Frenquency conventer Computer

Keithley 2181 nanovoltmeter Chart Recorder Computer

Outer Thermopile

Pt-Pt13Rh thermocouple Pt-Pt13Rh thermocouple cemented into the grooves with cemented into the grooves with alumina cement alumina cement

Inner thermopile

None

Pt-Pt13Rh thermocouple cemented into the grooves with alumina cement

Specimen weight

0.1-0.12 g

1.0-1.5 g

33 1.5.3 Principle of Kleppa-type High Temperature Direct Synthesis Calorimeter. The

determination of enthalpy by Kleppa-type high temperature direct synthesis calorimeter is based on the Hess law. Enthalpy is a state function which means that the energy depends only on initial and final state of the reactant and product, and does not depend on the specific pathway taken to get from the reactants to the products. In high temperature calorimeter experiment, the overall reaction is carried out in a series of steps, 1) reaction experiment where elements react with each other and then form a compound, 2) heat content experiment where the compound is dropped from room temperature to calorimeter temperature. The enthalpy of formation for the compound will be equal to the sum of the enthalpy changes for the individual steps. The enthalpy of formation, ∆H f298K , of a binary compound XaYb is calculated from:

a X (s, 298K) + b Y (s, 298K)

=

XaYb (1373 K)

XaYb(s, 298 K) = XaYb (1373 K)

∆HReaction (1) ∆HHeat Content (2)

From reaction (1) and (2) we get a X(s, 298K) + b Y(s, 298K) = XaYb (s, 298 K) The standard enthalpy of formation is thus obtained. ∆H f298K = ∆HReaction - ∆HHeat Content ∆HReaction and ∆HHeat Content are molar enthalpy changes for reaction (1) and (2).

Procedures of obtaining enthalpy of formation , H f298K , of a ternary compound XaYbZc is calculated from:

34

a X (s, 298K) + b Y (s, 298K) + c Z (s, 298K)

=

XaYbZc (1373 K)

XaYbZc (s, 298 K) = ZaYbZc (1373 K)

∆HReaction (1) ∆HHeat Content (2)

From reaction (1) and (2) we get a X(s, 298K) + b Y(s, 298K) + c Z(s, 298K) = XaYbZc (s, 298 K) The standard enthalpy of formation is thus obtained. ∆H f298K = ∆HReaction - ∆HHeat Content ∆HReaction and ∆HHeat Content are molar enthalpy changes for reaction (1) and (2).

1.6 Prospective of Ternary Al-Ni-X (X=Y, Fe, Ru) Super Alloys

NiAl has a number of attractive properties for jet-engine applications, such as high melting point (1650°C), low density [Tay86], good thermal conductivity [Sin66], intrinsic oxidation resistance [Ait77]. It is possible to utilize alloying additions to NiAl to improve mechanical properties [Cot93]. With suitable alloying good strength properties at temperatures higher than 1000°C can be achieved. Also, the amorphous Al-based metallic glasses with high strength and high ductility have also been reported [Ino94, He94, Kim99]. Their high strength and good glass formability allows amorphous Albased metallic glasses to be high strength and low density material. The physical and mechanical properties of Nickel Aluminide were reviewed by [Noe92]. It would be very useful if we can exam the systematics of the alloying behavior through correlations between the heat of formation and other physical properties. The thermodynamic properties measured in this study are also valuable data for thermodynamic assessment of multicomponent system. Therefore, Al-Ni-Y, Al-Ni, Al-

35 Ni-Fe, Al-Ni-Ru alloy systems are selected for this study in order to understand the systematics to reduce the extensive experimental trial and error for developing alloys.

36

CHAPTER 2 EXPERIMENTAL PROCEDURE Since the nickel-based super alloys and Nickel Aluminide are of great interest for high-temperature structure and other application. Al-Ni-Y, Al-Ni-Fe, Al-Ni-Ru alloy systems have been selected for studying the systematics of alloy behavior using enthalpy of formation, melting point, lattice parameter and phase equlibria. The equipment used for this study includes a high temperature direct synthesis calorimeter, X-Ray Diffractometer, Differential Scanning Calorimeter, Scanning Electron Microscopy and Energy Dispersive X-Ray Spectroscopy. The information provided by each of the equipment is like a piece of puzzle and in order to make sense of the scrambled pieces of the puzzles, several of the equipments have been used to characterize the material and then obtain the whole picture of a jigsaw-puzzle.

2.1 High Temperature Calorimeter Experiment

The heats of formation were determined using a high temperature reaction calorimeter with a typical accuracy of ±1kJ/mole [Kle89]. The measurements were made with the calorimeter set at 1373±2K or 1473±2K and using a protective argon atmosphere. The calorimeter was calibrated using pure copper. Samples were produced by mixing elemental powders in a mortar in the required molar ratio and pressing them into small pellets. Typical sample weight was about 120 mg. The nickel and iron powders used were reduced in hydrogen prior to pressing in order to remove oxygen and carbon that would be a source of errors.

37 The enthalpy of reaction is measured in two steps. ∆HReaction is obtained first by dropping the pellet into the calorimeter from room temperature, with a minimum of six separate samples measured. The pellets were subsequently removed and again dropped from room temperature into the calorimeter to obtain the heat content of the compound, ∆HHeat Content. The difference between the two measurements yields the heat of formation at 298K. The results are averages of the six individual measurements. With the standard deviations from the reaction and heat content experiments designated as δ1 and δ2 and from the calibration as δ 3 the overall uncertainty in the measurements, δ, was determined from δ = (δ 12 + δ 22 + δ 32)1/2. In the case of alloys molten at the calorimeter temperature. Material from the reacted compound is used to obtain an x-ray diffraction pattern to confirm that the reacted sample is the desired compound.

2.1.1 Procedure of High Temperature Calorimeter Experiment. The calorimeter

experiment consists of three parts: sample preparation, liner assembly, and data acquisition. The detailed experimental procedure is described below: 1) Reduce sample elements which are possibly oxidized, detail procedure will be described in 2.1.2 2) Prepare liner and insert the liner into the calorimeter, detailed procedure will be described in 2.1.3. Wait at least 12 hours so the whole system is at equilibrium 3) Weigh element powder and mix them in a mortar. This has to be done gently to minimize possible weight loss that leads the prepared sample to be off stoichiometry.

38 4) Pour the powder mixture into the die and then compress it with a hydraulic press. Remove the compressed pellet from the die. Weigh the sample pellet. At least 6 sample pellets have to be prepared. 5) Run data acquisition program with proper parameters, detailed parameters will be described in 2.1.4 6) Reset nanovoltmeter 7) Drop the pellet into calorimeter and record heat effect with computer, repeat 5) to 7) till all the samples are finished 8) Calculate heat effect with previous determined calibration factor, detailed procedure of obtaining calibration factor will be described in 2.1.5 9) Material from the reacted compound is used to obtain an x-ray diffraction pattern to confirm that the reacted sample is the desired compound. Detailed procedure of obtaining x-ray diffraction pattern will be described in 2.2

2.1.2 Procedure of Reduction Prior to Sample Preparation. Elements which are easily

oxidized and reduced must be reduced in hydrogen prior to sample preparation in order to remove oxygen and carbon that would be a source of errors. The detailed procedure of the reduction process in a tube furnace is described below: 1) Place a few grams of metal powder into a clean porcelain boat. 2) Place the porcelain boat in the center of the oven with the aid of a wire hook. 3) Close the end of the tube by rubber stopper 4) Flow hydrogen gas over the sample for at least 0.5 hour before raising the temperature

39 5) Check if the gas is properly flowing by watching the water trap. 6) Set the temperature at about 873 K 7) Heat the sample for at least one hour 8) Turn off heat while maintaining the gas flow untill the sample cools completely 9) Turn off the gas and pull the sample out with the aid of the wire hook. This should be done immediately prior to mixing of powder for sample preparation.

2.1.3 Procedure of Assembling Liner. The liner comprises many components which

have to be assembled in correct order as described below: 1) Cut three stainless steel shim stock pieces to the size of the alumina tubes. Clean steel liners with acetone and then insert shim stock pieces into alumina tubes. 2) Add spacer. 3) Prepare two ceramic tubes with zirconium getters, one is new and the other is previously used once. Clean the alumina tubes with sandpaper and subsequently wipe with tissue. Insert zirconium getters to alumina tubes and make sure the top alumina contains the one day old zirconium getter. 4) Add two spacers. 5) Assemble the boron nitride sample container. Scrape out any remaining sample from the Boron nitride crucible with spatula. Place the clean crucible and the two boron nitride spacers into the long boron nitride outside crucible. Insert into the end of the lead-in tube.

40 6) Take a clean stainless steel rod and insert it into the liner to check that it is straight. Clean liner by inserting a long wire with Kleenex tissue attached at the end. The tissue is moistened with acetone. Air dry the liner with hose. 7) Grease the joint with small amount of vacuum grease. Put in the quartz insert with all the appropriate ceramic tubes and sample holder assembly. Turn the joint gently a few times to make sure that the grease is evenly distributed and there are no air bubbles. 8) Turn liner assembly to vertical position and shake it gently to make sure all the pieces are down at the bottom. Connect the side tube to the Argon gas cylinder. Stand by pressure is about 3-4 pressure units. 9) Before putting the liner into the calorimeter flush the liner with argon gas at 10-12 pressure units for at least half hour. Place liner with the clamp into the calorimeter about 6-8 inches at a time, waiting for fifteen minutes after each step. Advance slowly during the last few inches. The entire process should take about 1 hour and fifteen minutes. Figure 1.11 shows schematic view of the detailed cell assembly showing part of the Pt20Rh liner, the boron nitride crucible, the boron nitride protective cylinder and stirrer, the alumina protective crucible and protective cylinders, as well as parts of the final gettering system for the argon gas [Kle94]. Figure 2.1 shows the process of assembling liner.

41

1) Alumina tube 2) Pt20Rh liner 3) Shim stock inside alumina tube 4) Alumina spacer

5) Zirconia getter inside alumina tube 6) Boron nitride spacer 7) Boron nitride crucible 8) Boron nitride outside crucible

Insert 3)-8) to 1)

Insert all components to 2) Figure 2.1. Process of Assembling Liner

42 2.1.4 Parameter Setting in Data Acquisition program. The switch on the frequency to

voltage converter has to be switched to either endothermic or exothermic side so the computer can collect and integrate the heat effect signal properly. It is always endothermic for heat content measurement but it could be either endothermic or exothermic for reaction heat measurement. Therefore, it is necessary to guess whether the reaction heat is exothermic or endothermic for the very first sample of an unknown system. Parameters used for each experimental setup might be different. Table 2.1 is an example of parameter set used in most experiments. Table 2.1 Example of Parameter Settings in Data Acquisition Program Range from amplitude 0-1 Background time interval

60 second

Overall time interval

2200 second

Experimental time

350 second

Rating time

1100 second

For those parameters in Table 2.1, range from amplitude is always 0-1. Background time interval is the length of time the computer collects background signal and then averages it to obtain background signal as the baseline. Usually background signal is set to 60 seconds and is good enough for obtaining a reliable baseline even if the background signal is fluctuating. Overall time interval is the total time taken by the sample to generate any heat effect or the time sample reaches equilibrium with the calorimeter. The overall time has to be set properly to obtain precise total heat effect. Usually for a 100 mg sample it takes about 1000-2500 seconds for reaction heat measurement and 2000-2500

43 seconds for heat content measurement. The experimental time is the time before the curve in the temperature-time diagram reaches its maximum. Rating time is always half of the overall time. The typical temperature-time curve obtained after experiment is shown in Figure 2.2. Ideal baseline is a complete smooth line that can be seen in a sample with large heat effect. If the baseline is fluctuating instead of a straight line, it indicates the heat effect is relatively small. If the baseline is not a perfect horizontal line but drifting up or down, it indicates the power supplied to the furnace is not stable enough and large error of integrated total heat effect can be expected.

Figure 2.2. Schematic Temperature-Time Curve for Calorimeter

44 2.1.5 Calibrating Calorimeter. The sensitivity of the calorimeter decreases with time.

The way to maintain the experimental precision is to calibrate the calorimeter periodically. The calorimeter is usually calibrated by copper once every 6-8 weeks. Since the enthalpy of copper is a well known value (The enthalpy of Cu at various temperatures is listed in Appendix I), it is used as a standard material which is dropped into the calorimeter and the total heat effect is then obtained. The obtained heat effect is compared with the theoretical enthalpy difference of the copper standard between room temperature and calorimeter temperature. 1) Use silicon carbide paper to polish copper wire 2) Clean copper wire surface by acetone 3) Cut copper wire into sections, each section is around 100-120 mg 4) Place copper wire in the die and press it with hydraulic press to make copper pellet 5) Drop copper pellet into the calorimeter and record the heat effect with the computer

Correction factor (count/Joule) =

Heat Effect =

Heat Effect (count/g)*63.546 (g/mole) ∆H Cu T(K) (joule)

1 n A i (count) ∑ n i=1 Wi (g)

Ai is the area of the curve in temperature-time diagram (count) Wi is the sample weight (gram) n is total sample number

45

63.546 (g/mole) is the atomic weight of Cu

∆H Cu T(K) (joule) =32.7 * T (K) – 1737.2 can be used for describing enthalpy of liquid

phase Cu between 1357K (melting point) and 1500K, T is calorimeter temperature

Therefore, the equation can be written as: 1 n A i (count) *63.546 (g/mole) ∑ n i=1 Wi (g) Correction factor (count/Joule) = 32.7 * T (K) - 1737.2 (Joule)

2.2 X-Ray Diffraction Experiment

The ThermoARL X-ray diffractometry used in this study contains a vertical thetatheta goniometer, a convenient geometry for handling powder samples by facilitating the sample preparation and use of specialized sample holder. The goniometer features removable dual Soller slits and continuous variable micrometer-controlled slits for adjusting the width of both the incident and diffracted beams. The X-ray diffractometer is equipped with a Peltier cooled Si (Li) solid-state detector tuned for high count rate in order to minimize coincidence loss. It removes K-Beta and fluorescence radiation thus eliminating the need for filters and monochromators. Figure 2.3 shows the structure of Xray diffractometer.

46

Figure 2.3. Structure of X-ray Diffractometer

47 2.2.1

X-Ray Diffraction Software. The diffractometer is controlled using WINXRD, a

software running under Windows 2000 as a true multitasking 32-bit data collection and analysis package. The following is a listing of some of the available features for WinXRD. •

Background removal and smoothing

•

Peak finding and profile fitting

•

Data file manipulation for scaling, adding and subtracting

•

Qualitative and Quantitative analysis

•

Percent crystallinity determination

•

Crystallite size determination by Scherrer, Williamson-Hall and WarrenAverbach methods

•

Texture and residual stress analysis

•

Indexing and least squares unit cell determination

•

Retained austenite quantification.

48 2.2.2 Calibrating X-ray Diffraction Diffractometer. Calibration has to be done

periodically in order to obtain precise peak position as well as correct lattice parameter. The “1976 XRD Flat-Plate Intensity Standard” alumina purchased from NIST (National Institute of Standards and Technology) is used as the standard reference material for calibration. The standard reference material is scanned and peak positions are recorded and then compared with the alumina peak position obtained from JCPDS (Joint Committee on Powder Diffraction Standards) database. Figure 2.4 shows the calibration curve in the certified peak position-experimental peak position diagram.

certifiedl peak position (2 Theta)

140 120 100

y = 1.0468x - 0.832 R2 = 0.9999

80 60 40 20 0 0

20

40

60

80

100

120

experimental peak position (2 theta)

Figure 2.4. Calibration Curve for X-ray Diffraction Experiment Once the calibration curved is obtained, the peak position obtained from subsequent experiment has to be corrected by the equation of the calibrated curve.

corrected peak position (2θ) = 1.0468 * experimental peak position(2θ) – 0.832

49 2.2.3 Parameter Setting for X-Ray Diffraction Experiment. Parameters have to be

selected properly in order to obtain a reliable X-ray pattern. Table 2.2 shows the parameter setting for X-ray diffraction experiment.

Table 2.2. Parameter Setting for X-ray Diffraction Experiment X-ray Source: Cu Voltage: 45 kV Current: 40 mV Incident beam: Optic path: slits bloc Beam type: para-focalized Divergence: Fixed divergence: 1.2321 ° Minimum illumination: 5.38 mm Devergence slit width: 2.0 mm Scatter slit width: 4.00 mm Diffracted beam: Optic path: Slits Bloc Beam type: Para-Focalized Acceptance: Fixed acceptance: 1.2277 Minimum illumination length 5.36 mm Scatter slit width: 0.90 mm Resolution: 0.069 ° Receiving slit width: 0.30 mm Two theta range: Begin angle: 5 ° Eng angle: 120 ° Step size: 0.05 ° Preset time: 2 second

50 2.2.4

Accurate Determination of Lattice Parameter by X-ray Diffraction. A set of

index planes in an x-ray diffraction pattern have been used to determine the lattice parameter. Even though the lattice parameter calculated from different index planes should be the same, it always shows small variation with respect to θ value. Therefore, an extrapolation function has been used to obtain correct lattice parameter. The systematic error sources in d are: [Cul01] 1) Misalignment of the instrument 2) Use of a flat specimen instead of a specimen curved to conform to the focusing circle. 3) Absorption in the specimen. 4) Displacement of the specimen from the diffractometer axis. This is the larges error source which gives an error of: ∆d D cos 2θ =− d R sinθ D is the specimen displacement parallel to the diffraction-plane normal. R is diffractometer radius 5) Vertical divergence of the beam.

For 2) and 3)

For 4)

∆d varies as cos 2θ d

∆d cos 2θ varies as d sinθ

51 The Procedure to obtain correct lattice parameter of a cubic material is as following: 1. Align the instrument according to manufacturer’s instruction. cos 2θ 2. Fit a linear curve in lattice parameters vs or cos 2θ diagram, the lattice sinθ parameter where

cos 2θ or cos 2θ is 0 (θ = 90 °) is the lattice parameter without sinθ

systematic error. If Bradley-Jay method extrapolation function is used. For cubic material: ∆d ∆a a-a 0 cos 2θ = = =k1 d a0 a0 sinθ a=a 0 + a 0 k1

cos 2θ sinθ

If a Nelson-Riley extrapolation function is used. For cubic material:  cos 2θ cos 2θ  ∆d ∆a a-a 0 = = =k 2  +  d a0 a0 θ   sinθ  cos 2θ cos 2θ  + a=a 0 + a 0 k 2   θ   sinθ

For both Bradley-Jay method and Nelson-Riley method the systematic error is equal to 0 when θ is equal to 90 ° which means the systematic error can be eliminated by proper extrapolation. If we plot lattice parameter obtained by different index planes vs cos 2θ and then fit a linear curve as shown in Figure 2.5 and Figure 2.6, the intercept of the linear curve will be the lattice parameter where systematic error is 0 (when θ is equal to 90 °, cos 2θ =0)

52

Figure 2.5. Lattice Parameter Obtained by Different Index Plan v.s. cos 2θ , Large Systematic Error and Small Random Error

Figure 2.6. Lattice Parameter Obtained by Different Index Plan v.s. cos 2θ , Small Systematic Error and Large Random Error

53 The systematic error is a function of θ and the magnitude of the error is proportional to the slope of the fitted linear curve. The fitted curve in Figure 2.5 shows large negative slope indicating relatively large systematic error. Most of the data points are very close to the curve indicating small random error. However, those data points in Figure 2.6 have relatively similar lattice parameter indicate small systematic error but its scattering distribution indicates larger random error.

2.3 Differential Scanning Calorimeter Experiment

The change in physical properties of a substance subjected to a controlled temperature program as a function of temperature can be measured by DSC (Differential Scanning Calorimeter). Differential scanning calorimetry is a technique determining the variation in the heat flow given out or taken in by a sample when it undergoes temperature scanning in a controlled atmosphere. Any transformation taking place in a material is accompanied by an exchange of heat, DSC enables the temperature of this transformation to be determined and the heat from it to be quantified. Temperatures are measured in thin plates in contact, thereby measuring the difference in heat flow from the crucible. This gives a signal proportional to the difference in heat capacities between the sample and references. Figure 2.7 shows the schematic diagram of heat flux type differential scanning calorimetry. Figure 2.8 shows the heat flux type DSC rod with sample and reference pan used in this study.

54

Figure 2.7. Schematic Diagram of Heat Flux Type Differential Scanning Calorimetry

55

Figure 2.8. Heat Flux Type DSC Rod

The application of DSC can be used to determine physical properties such as transition temperatures, heat of fusion, heat capacity, heat of formation and sample purity. The purpose of DSC experiment in this study is to determine phase transformation temperature and the Setaram Setsys 1750 DSC is used, Figure 2.9. The Setaram Setsys 1750 DSC comprises a single structure including the controller, furnace, power, gas circuit and safety elements. It is designed as a modular structure that can integrate various measurements such as TG (Thermogravimetry), DTA (Differential Thermal Analysis),

56 DSC, TG-DTA, TD-DSC and TMA. A multitasking software package called “setsoft” provides programmable heating rate and easy to use interface.

Figure 2.9. Seteram Setsys 1750 DSC

57 2.3.1 Procedure of Differential Scanning Calorimeter Experiment. The three major

steps for running differential scanning calorimeter are setup equipment, select carrier gas and crucible, setup temperature program. Detailed procedure is described as following: 1) Select suitable rod and carrier gas, platinum rod is fine with inert gas such as argon and helium. If any of the reacting gas such as hydrogen is used, a tungsten rod has to be selected. Inert carrier gas: Platinum rod Reacting carrier gas: Tungsten rod 2) Select suitable crucible corresponding to conditions as shown in Table 2.3.

Table 2.3. DSC Crucible Selection in Different Conditions Crucible Condition Platinum

Nonmetalic sample

Alumina

Metallic sample

Tungsten

Reacting gas

Boron Nitride

Metallic sample

3) Assemble suitable module for corresponding rod and then install the electrical connection. 4) Prepare sample. The sample size has to be smaller than crucible dimension. 5) Place crucible with sample into the furnace chamber and then close the chamber. 6) Turn on the furnace gas. Open high carrier gas valve and low carrier gas valve and allow the gases to purge the whole system for 10 minutes

58 7) Close high carrier gas valve and wait for 10 minutes to allow the system to be stabilized. 8) Run the “setsoft2000” DSC controlling software and set the desired heating rate, starting temperature, final temperature. Start the experiment. 9) After the experiment is finished the chamber can only be opened to take the sample out after the furnace temperature is cooled down to below 200 °C.

The sample and crucible selection is important because sample should not react with crucible during the experiment. Also higher temperature might cause problems such as high sample vapor pressure, high sample diffusivity, shorten equipment lifetime. The experiment condition in this study is summarized in Table 2.4.

Table 2.4. DSC Experiment Condition Furnace gas Argon Carrier gas

Helium

Crucible

Boron Nitride/Alumina

Starting temperature

25 °C

Final temperature

1400 °C

Heating rate

10 °C/min

Rod

Pt/PtRh10%

59 CHAPTER 3 RESULTS FOR Al-Ni-Y SYSTEM Since the nickel-based superalloys, intermetallics based on Nickel Aluminide and some Al rich ternary alloys have interesting properties. Al-Ni-Y, Al-Ni-Fe, Al-Ni-Ru alloy systems have been selected for studying the systematics of alloy behavior through enthalpy of formation, melting point, lattice parameter, phase equlibria experimentally and Miedema’s semi-empirical calculation used for predicting the enthalpy of formation.

3.1 Al-Ni-Y System Overview

The enthalpies of formation of the ternary compounds Al4NiY, Al2NiY, Al2Ni6Y3, Al16Ni3Y, AlNiY, Al3Ni2Y, AlNi8Y3, Al7 Ni3Y2, and of the binary compounds Al2Y containing nickel and Ni5Y containing aluminum have been determined by high temperature reaction calorimetry. The enthalpy values measured are compared to previously published results where available as well as extended Miedema model predictions. The melting points of the compounds were determined by DTA and X-ray diffraction was used to confirm the crystal structures of the compounds. The enthalpies of formation of the ternary compounds show a maximum along the 50 atomic % Al section. The ternary compounds appear along lines of constant Y content consistent with binary compound solubility extensions. Alloys involving Ni, Al and other elements are of interest for applications such as high temperature structural materials. Alloy development of such materials requires a thorough knowledge of the phase equilibria in the binary, ternary and higher order alloy systems. To establish this knowledge experimentally requires a substantial amount of

60 time and effort. Thermodynamic modeling of phase diagrams provides an opportunity to approach the phase equilibria aspects of alloy development in a more efficient manner than experimentally determining the phase equilibria in large numbers of alloys at many temperatures. A number of computer programs exist for the calculation of multicomponent phase equilibria based on the Calphad method [Sau98]. The basic approach is to develop a thermodynamic description for the free energy of each phase as a function of composition and temperature and then to compute the minimum in free energy for a particular composition at a given temperature. In this way the phase diagram can be mapped in a matter of minutes or hours rather than the months involved with experimental methods of phase diagram determination. Of course, the accuracy of the computed diagram is dependent on the accuracy of the thermodynamic data used in the free energy descriptions of the phases. Such data are often not available resulting in estimations being used. We have embarked on a project to experimentally determine enthalpies of formation for alloys in the Ni-Al-X alloy systems, where X is a transition element, for use in thermodynamic modeling and validation of first principles calculations. The enthalpies of formation of intermetallic compounds in the Al-Ni-Y system as well as the binary compounds with significant solubility are determined in this study. The Ni-Al rich portion of the phase diagram of the Ni-Al-Y system was determined by Rykhal et al [Ryk77] and is shown in Figure 3.1. The Al-rich region was recently re-investigated [Rag00] and several additional compounds have been reported [Zar73, Gla92, Gla292, Gla93, Ryk72, Ryk272, Rom82, Ryk78]. Table 3.1 lists the standard crystallographic designations of the compounds in this system together with the mole fraction designations which are more convenient for thermodynamic considerations.

61

Figure 3.1. Partial Isothermal Section of the Al-Ni-Y System

62 Table 3.1. Compound Designations Crystallographic Mole Fraction Compound Designation

Compound Designation

AlNiY

Al0.33Ni0.33Y0.33

AlNi8Y3

Al0.08Ni0.67Y0.25

AlNi3Y2

Al0.17Ni0.5Y0.33

AlNi2Y2

Al0.20Ni0.40Y0.40

Al9Ni3Y

Al0.69Ni0.23Y0.08

Al7Ni3Y2

Al0.58Ni0.25Y0.17

Al4NiY

Al0.67Ni0.17Y0.16

Al3NiY

Al0.60Ni0.20Y0.20

Al3Ni2Y

Al0.50Ni0.33Y0.17

Al2-xNixY

Al0.53Ni0.14Y0.33

Al2-xNixY

Al0.60Ni0.07Y0.33

Al2NiY

Al0.50Ni0.25Y0.25

Al2Ni6Y3

Al0.18Ni0.55Y0.27

Al23Ni6Y4

Al0.70Ni0.18Y0.12

Al16Ni3Y

Al0.80Ni0.15Y0.05

AlxNi5-xY

Al0.25Ni0.58Y0.17

AlxNi5-xY

Al0.15Ni0.68Y0.17

AlxNi5-xY

Al0.05Ni0.78Y0.17

63 The enthalpies of formation of Al-Ni-Y compounds together with values calculated in this work based on Miedema’s model are listed in Table 3.2, calorimeter temperature set at 1473K except as noted. The melting point of Al-Ni-Y compounds are measured and listed in Table 3.3. The enthalpy of formation results are also plotted in Figure 3.2, together with binary compound enthalpy values from the literature. Values for the Ni-Y and Al-Ni systems are taken from references [Nas91] and [Nas291] respectively, except for AlNi which is from [Nas01]. Values for the Al-Y compounds are from references [Tim97, Jun91, Mes93, Tom01]. The Miedema model predictions show the correct trend but are in most cases significantly less exothermic than the measured values. The measured enthalpy values for AlxNi5-xY with increasing Al content show a significant increase from -34 kJ/mole for Ni5Y to -48 kJ/mole for Al0.34Ni4.66Y due to the Al-Y and Al-Ni interactions. The only enthalpy of formation value for a ternary phase in this system is for Al4NiY with a value of -60 kJ/mole [Ryk72]. This is considerably more exothermic than the value measured in this work, -54 kJ/mole. From Figure 3.2 it is clear that the highest heats of formation in this system occur along the section with constant 50 atomic % Al. This results from the fact that the Al-Y and Al-Ni bonds are stronger than Ni-Y bonds as indicated by the much lower enthalpy of formation of the binary NiY compared to AlNi and AlY.

64 Table 3.2. Summary of High Temperature Reaction Calorimetry Results and Miedema's Semi-empirical Model Results Miedema’s model ∆H formation (kJ/mole)

∆H Reaction (kJ/mole)

∆H Heat Content (kJ/mole)

Experimental ∆H formation (kJ/mole)

Al0.05Ni0.78Y0.17

-1.07 ± 1.08

35.07 ± 1.08

-36.14 ± 1.8

-30.1

Al0.08Ni0.67Y0.25

5.21 ± 1.5

43.1 ± 1.7

-37.9 ± 2.5

-39.2

Al0.15Ni0.68Y0.17

-11.13 ± 0.72

36.20 ± 0.35

-47.33 ± 1.1

-37.6

Al0.18Ni0.55Y0.27

0.0 ± 1.0

48.5 ± 0.8

-48.5 ± 1.5

-45.3

Al0.25Ni0.58Y0.17

-4.10 ± 0.8

44.19 ± 1.6

-48.3 ± 2.5

-42.3

Al0.33Ni0.33Y0.33

-6.96 ± 0.4

47.1 ± 0.3

-54.1 ± 0.9

-54. 5

Al0.50Ni0.25Y0.25

-31.6 ± 1.5

31.2 ± 0.2

-62.8 ± 1.5

-54.6

Al0.50Ni0.33Y0.17

-29.55 ± 1.2

32.87 ± 1.0

-62.8 ± 2.3

-49.2

Al0.53Ni0.14Y0.33†

-12.5 ± 1.9

39.0 ± 1.2

-

-58.6

Al0.58Ni0.25Y0.17

-33.4 ± 0.3

27.9 ± 0.6

-61.3 ± 1.0

-47.2

Al0.60Ni0.07Y0.33

-23.9 ± 1.0

32.8 ± 1.1

-56.7 ± 1.5

-59.8

Al0.60Ni0.20Y0.20

-20.3 ± 1.4

39.5 ± 0.8

-59.8 ± 1.3

-49

Al0.67Ni0.17Y0.16

-2.0 ± 0.5

52.0 ± 0.5

-54.0 ± 0.8

-44.8

Al0.67Ni0.17Y0.16

-0.5 ± 1.0

54.0 ± 0.3

-54.5 ± 1.2

-44.1

Al0.69Ni0.23Y0.08

-5.9 ± 0.9

41.1 ± 1.6

-47.0 ± 2.0

-36.2

Al0.70Ni0.18Y0.12

-14.0 ± 1.6

36.6 ± 0.4

-50.6 ± 1.8

-38.7

Al0.80Ni0.15Y0.05*

10.3 ± 0.5

46.1 ± 1.3

-35.7 ± 1.4

-25.4

Compound

* Calorimeter set at 1373K † Reacted sample was not predominantly single phase.

65

Table 3.3. Melting Points of Compounds in Al-Ni-Y System Compound

Melting Point

Al0.67Ni0.17Y0.16

1241K

Al0.50Ni0.25Y0.25

1418K

Al0.18Ni0.55Y0.27

1250K

Al0.80Ni0.15Y0.05* Al0.60Ni0.07Y0.33

1407K -

Al0.53Ni0.14Y0.33† Al0.33Ni0.33Y0.33

1421K

Al0.50Ni0.33Y0.17

1423K

Al0.25Ni0.58Y0.17

1426K

Al0.15Ni0.68Y0.17

1479K

Al0.05Ni0.78Y0.17

1569K

Al0.08Ni0.67Y0.25

-

Al0.58Ni0.25Y0.17

1408K

1413K

Measurements of the enthalpy of formation of amorphous Al-Ni-Y alloys [Ryk78] are consistently less exothermic than the corresponding crystalline compounds measured in this work. This is expected since the amorphous phase is less stable than the crystalline compounds. The binary compounds Al2Y and Ni5Y exhibit substantial solubility in the ternary system. Both of the compounds extend along lines of constant Y content indicating substitution of Ni for Al in Al2Y and Al for Ni in Ni5Y. This is confirmed by observations of simulated x-ray diffraction pattern peak intensities. In the case of Al2Y there is an analogous compound in the Ni-Y binary, Ni2Y, which has an identical crystal

66 structure. According to the published phase diagram [Ryk77] there is little solubility of Al in Ni2Y. The replacement of Al with Ni on the Al2Y lattice leads to an initial increase in the enthalpy of formation of the compound from -50 to -57 kJ/mole on adding 7 atomic % Ni. However further additions appears to lead to a decrease since the stability of the phase is limited. Unfortunately the Al2Y compound containing 14 atomic % Ni was not predominantly single phase and the enthalpy of formation has not been determined.

67

Ni

1.0

0.0

Ni17Y2 (-13) 0.9

0.1

AlXNi5-XY (-36)

0.2

AlNi3 (-38) 0.3

Al3Ni5 (-54) 0.4

0.7

Ni2Y (-31) 0.6

Al2Ni6Y3 (-48)

0.5

NiY (-35)

AlNi3Y2

Al3Ni2 (-59) 0.6

0.8

Ni3Y (-29)

AlXNi5-XY (-48) AlNi8Y3 (-38)

0.5

0.7

4

0.8 Ni Y (-28) 7 2

AlXNi5-XY (-47)

AlNi (-61)

Al3Ni (-38)

Ni5Y (-34) Ni Y (-25)

Al3Ni2Y (-63)

0.4

Ni2Y3 (-35)

AlNi2Y2 AlNiY (-54)

0.3

Al7Ni3Y2 (-61)

Al9Ni3Y (-47)

0.9

NiY3 (-33)

Al2NiY (-63) Al3NiY (-60) Al4NiY (-54)

Al23Ni6Y4 (-50)

0.2

AlNiY3 0.1

Al2-XNiXY (-57) 0.0

1.0

Al

0.0

0.1

0.2

0.3

0.4

Al3Y (-46) Al2Y (-50)

0.5

AlY (-76)

0.6

0.7

Al2Y3 (-47)

0.8

0.9

1.0

Figure 3.2. Enthalpies of Formation in kJ/mole for Compounds in the Al-Ni-Y System

Y

68 It is worth noting that the ternary compounds tend to occur along lines of constant Y content, consistent with the extensions of the binary compounds. This implies that Al and Ni can substitute for each other on the same sublattice but not on the Y sublattice. In Figure 3.3 the measured and predicted enthalpies of formation in AlxNi5-xY alloys are plotted as a function of Ni content across the section of constant Y content of 17 atomic %. It can be seen that the maximum negative heat of formation corresponds to the 50 atomic % Al composition. The Miedema model values are consistently smaller than the measured values, mainly due to the underestimation of the heats of formation of the binary compound Ni5Y by about -10 kJ/mole. However, they show the correct trend with a maximum negative value at 50 atomic % Al. For the Al2-xNixY alloys the data, shown in Figure 3.4, also indicate a maximum negative heat of formation at 50 atomic %Al in the section with constant Y content of 33 atomic %. However for this section the Miedema model predictions are mostly more negative which perhaps is the result of the over estimation of the heats for the binary compounds Al2Y and Ni2Y by about -10 kJ/mole. Based on the alloying behavior described above and the appearance of the binary phases, one might expect that ternary compounds with compositions AlNiY3 and AlNiY2 will exist in this system. The binary phases corresponding to these ratios will exhibit some solubility for the third element with the solubility extension occurring along constant Y contents of 60 atomic % and 50 atomic% respectively.

69

Figure 3.3. Measured and Predicted Enthalpies of Formation in AlxNi5-xY alloys

In most cases the x-ray diffraction patterns obtained from the reacted samples showed diffraction lines only from the compound being measured. Occasionally a few weak peaks corresponding to Y2O3 or other phases were observed. The results of the x-ray diffraction experiments are summarized in Table 3.4. In the case of Al0.53Ni0.14Y0.33 the xray diffraction pattern indicated that it consisted of Al2-x NixY, Al4NiY and another phase, consequently the heat of formation for this compound is not reported in Table 3.2.

70

Figure 3.4. Measured and Predicted Enthalpies of Formation in Al2-xNixY alloys 3.2 Summary of Enthalpy of Formation Result

The heats of formation of a number of Al-Ni-Y ternary compounds have been measured by direct synthesis drop calorimetry. The heats of formation exhibit maximum negative values in the section containing 50 atomic % Al. Miedema model predictions are generally less exothermic than the measured values. Ternary compounds appear mostly at a few fixed Y/(Ni+Al) ratios such as 1:5, 1:3 and 1:2. Based on this alloying behavior it is predicted that ternary compounds with compositions AlNiY3 and AlNiY2 will exist in this system and that the binary phases corresponding to these ratios will exhibit some solubility for the third element.

71 Table 3.4. Al-Ni-Y Intermetallic Compound Phase Crystal Structure Data Compound

Prototype

Pearson Spacegroup Spacegroup symbol No.

Lattice Parameter

Referen ce

Al0.67Ni0.17Y0.16

Al4NiY

oC24

Cmcm

63

[Zar73]

Al0.50Ni0.25Y0.25

BRe3

oC16

Cmcm

63

Al0.18Ni0.55Y0.27

Ag8Ca3

cI44

Im 3 m

229

a=4.059 b=15.192 c=6.643 a=4.259 b=10.215 c=6.824 a=8.948

Al0.80Ni0.15Y0.05

Al16Ni3Y

oC*

Cmcm

63

Al0.60Ni0.07Y0.33 Al0.53Ni0.14Y0.33 Al0.33Ni0.33Y0.33

Al2Y(Cu2Mg) Al2Y(Cu2Mg) Fe2P

cF24

Fd 3 m Fd 3 m

227

a=4.08 b=16.04 c=27.29 a=7.804

227

a=7.789

hP9

P 6 2m

189

Al0.50Ni0.33Y0.17

Al3Ni2Y

hP12

P6/mm

191

Al0.25Ni0.58Y0.17

Ni5Y(CaCu5)

hP6

P6/mm

191

Al0.15Ni0.68Y0.17

Ni5Y(CaCu5)

hP6

P6/mm

191

Al0.05Ni0.78Y0.17

Ni5Y(CaCu5)

hP6

P6/mm

191

Al0.08Ni0.67Y0.25

CeNi3

hP24

P63/mmc

194

a=7.050 c=3.794 a=9.015 c=4.070 a=5.033 c=4.052 a=4.940 c=4.205 a=4.915 c=4.147 a=5.138 b=16.34 a=17.841 b=4.219

cF24

Al0.58Ni0.25Y0.17 Al0.70Ni0.18Y0.12

Al23Ni6Y4

mC66

C2/m

12

Al0.69Ni0.23Y0.08

ErNi3Al9

hR78

R32

155

Al0.60Ni0.20Y0.20

Al3NiY

oP20

Pnma

62

Al0.40Ni0.40Al0.20

Mo2NiB2

oI10

Al0.17Ni0.50Y0.33

MgZn2

hP12

†

Lattice parameters from literature, see reference column

[Ryk77] [Ryk77] [Ryk277] [Ryk77]

†

[Ryk77] [Ryk77]

[Ryk78] [Ryk77]

†

[Gla277]

†

[Gla72]

a= 15.836 b=4.0681 c= 18.3110 β=112.97 a= 7.2894 c= 27.43

†

[Gla92]

†

[Rom82] [Ryk78]

a=8.156 b=4.0462 c=10.638 a=5.418 b=8.42 c=4.181

a=5.33† c=8.6

[Ryk72]

72 3.3 Experimental Determination of Al-Ni-Y Isothermal Section at 650°C

The phase diagram of Al-Ni-Fe has not been updated since 1977 [Ryk77]. Since several new compounds have been reported, it is necessary to confirm the existence of the compounds and also revise the phase diagram. Therefore, a series of compounds have been prepared in order to obtain the phase equilibria as well as the isothermal section. Table 3.5 shows the selected sample composition. Three element powder or ingots was mixed and heated to 1000 °C under vacuum furnace. Sample is maintained at 1000 °C for 10 minutes then cooled down to room temperature. Subsequently, samples are annealed at 650 °C for 7 days in tube furnace. Sample characterization is done by X-ray both diffractometer and SEM/EDS.

Table 3.5. Selected Sample Composition for Phase Equilibria Determination Nominal Alloy Composition Atomic Ratio Al(%) : Ni(%) : Al3NiY

60 : 20 : 20

Al4NiY

66 : 17 : 17

Al7Ni3Y2

58 : 25 : 17

Al9Ni3Y

69 : 23 : 8

Al16Ni3Y

80 : 15 : 5

Al23Ni6Y4

70 : 18 : 12

Al43Ni30Y27

43 : 30 : 27

Al55Ni30Y15

55 : 30 : 15

Al58Ni10Y32

58 : 10 : 32

Al60Ni31Y9

60 : 31 : 9

Al62Ni20Y18

62 : 20 : 18

Al65Ni30Y5

65 : 30 : 5

Al78Ni10Y12

78: 10: 12

73 As shown in Table 3.6, all samples consist 2 or 3 phases even if the nominal alloy composition is the same as proposed compound stoichoimetry such as Al7Ni3Y2, Al9Ni3Y, Al16Ni3Y and Al23Ni6Y4 which are supposed to be single phase. That is because the loss of vapor pressure while melting in the vacuum furnace. The final composition of a prepared sample could be off the nominal composition. Another possibility is the annealing time might not be long enough to fully anneal the sample. The phase data determined by SEM/EDX is sometimes not consistent as the result obtained from X-ray diffratometer due to the fact that the volume fraction of some phases might be too small to be detected.

74 Table 3.6. Comparison Between EDX and XRD Result EDX Result at. % EDX analysis comments and Phase found in XRD estimated phase fraction Al Ni Y

Nominal Alloy Composition Al3NiY 59 63

31 21

10 major, Al3NiY 16 minor, could be Al7Ni3Y2

Al4NiY

72

17

11 >98%, Al23Ni6Y4

Al7Ni3Y2

56 59 66 68 100 69 78

35 26 20 27

9 15 14 5

Al9Ni3Y Al16Ni3Y

Al23Ni6Y4 Al43Ni30Y27 Al55Ni30Y15 Al58Ni10Y32 Al60Ni31Y9 Al62Ni20Y18

100 66 71 75 44

56 56 62 64 70 53 53 56 61 66

25 17

20 20 19 30

31 44 28 20 2 34 47 34 23 20

30% >60%, Al7Ni3Y2 Al23Ni6Y4 around 70%, Al9Ni3Y Al 6 70% Al9Ni3Y 5 Al16Ni3Y

25% Al 14 >95%, Al23Ni6Y4 9 1% 6 1% 26

13 20%, Al3Ni2Y >60% NiAl 10 20% 16 30% Al4NiY 28 70% Al2Y 13 60%, Al3Ni2Y 40% AlNi 10 30% 16 60%, Al7Ni3Y2 14 5%, could be Al4NiY

Al65Ni30Y5

63 67

37 27

70% Al3Ni2 6 30%, Al9Ni3Y

Al78Ni10Y12

76 76

12 .

12 20% 24 80%

Al3NiY possible Al7Ni3Y2 Al2NiY Al23Ni6Y4 Al3Y Al7Ni3Y2 Al9Ni3Y Al Al9Ni3Y Al3Ni Al Al23Ni6Y4

AlNiY Al2NiY Al3Ni2Y Al7Ni3Y2 Al4NiY Al2Y Al3Ni2Y AlNi Al7Ni3Y2 Al9Ni3Y Al23Ni6Y4 Al3Ni2 Al9Ni3Y Al4NiY Al3Y

75 The result of the nominal Al60Ni31Y9 sample shows the equilibrium between Al3Ni2Y, NiAl. A tie line between Al3Ni2Y, NiAl can be confirmed. The nomrnal Al55Ni30Y15 sample shows a three phase (Al3Ni2Y, NiAl, Al7Ni3Y2) equilibrium which means a three phase triangle can be plotted between the three compositions. Nominal Al58Ni10Y32 sample shows a two phase equilibrium between Al4Ni2Y and Al2Y. From nominal Al62Ni20Y18 Sample and Al9Ni3Y sample, a three phase triangle can be expected between Al4NiY, Al9Ni3Y and Al23Ni6Y4. Nominal Al65Ni30Y5 sample shows three phase equilibrium between Al3Ni2, Al9Ni3Y and Al4NiY. Nominal Al16Ni3Y sample also shows three phase equilibrium between Al9Ni3Y, Al3Ni and Al. Nominal Al9Ni3Y sample shows three phase equilibrium between Al23Ni6Y4, Al9Ni3Y and Al. Nominal Al62Ni20Y18 sample shows equilibrium between Al7Ni3Y2 and Al4NiY. The nominal Al7Ni3Y2 sample shows equilibrium between Al7Ni3Y2 and AlNi. According to the above equilibrium observed by X-ray diffractometer or SEM/EDS, an isothermal section of Al-Ni-Y system at 650 °C can be plotted as Figure 3.5. The SEM photo of Al9Ni3Y, Al3NiY, Al4NiY, Al16Ni3Y, Al7Ni3Y2 and Al23Ni6Y4 is shown from Figure 3.6-Figure 3.11, respectively.

76

0.0

Ni

1.0

Ni17Y2 0.9

0.1

Ni5Y 0.2

AlXNi5-XY

AlNi3 0.3

Ni3Y

0.7

AlXNi5-XY

Al3Ni5

AlNi8Y3

0.4

AlXNi5-XY

AlNi

Ni4Y

0.8 Ni Y 7 2

Ni2Y 0.6

Al2Ni6Y3

0.5

0.5

NiY

AlNi3Y2

Al3Ni2

0.4

0.6

Al3Ni2Y

0.7

Al7Ni3Y2

Al3Ni 0.8

Al9Ni3Y

0.9

Al23Ni6Y4 0.0

0.1

0.2

NiY3 0.2

AlNiY3 0.1

Al2-XNiXY

1.0

Al

0.3

AlNiY

Al2NiY

Al3NiY Al4NiY

Ni2Y3

AlNi2Y2

Al3Y

0.3

Al2Y

0.4

0.0

AlY

0.5

Al2Y3

0.6

0.7

0.8

0.9

Figure 3.5. Partial Isothermal Section of Al-Ni-Y at 650°C

1.0

Y

77

Figure 3.6. SEM Photo of Nominal Al9Ni3Y Alloy with 1) Al23Ni6Y4 Phase and 2) Al9Ni3Y Phase

Figure 3.7. SEM Photo of Nominal Al3NiY Alloy with 1) Al3NiY Phase and 2) Al7Ni3Y2 Phase

Figure 3.8. SEM Photo of Nominal Al4NiY Alloy with 1) Al4NiY Phase

78

Figure 3.9. SEM Photo of Nominal Al16Ni3Y Alloy with 1) Al3NiY Phase, 2) Al9Ni3Y Phase and 3) Al phase

Figure 3.10. SEM Photo of Nominal Al7Ni3Y2 Alloy with 1) Al4NiY Phase and 2) AlNi Phase

Figure 3.11. SEM Photo of Nominal Al23Ni6Y4 Alloy with More Than 95% 1) Al23Ni6Y4 Phase and Less Than 5% 2) Al3Ni Phase

79 Chapter 4 ENTHALPY RESULTS OF Al-Ni-Fe SYSTEM The enthalpies of formation of Ternary compounds in the Al-Ni-Fe system have been determined by high temperature reaction calorimetry. The enthalpy values measured are compared to previously published results where available as well as extended Miedema model and Thermocalc predictions. The composition dependence of the enthalpy of formation and lattice parameter of the B2 phase was determined in the region of 0.33≤Al, mole fraction ≤0.5 and correlated with the defect structure. The results have been analyzed using a Wagner-Schottky model and the values of the parameters in the model determined.

4.1 Literature Overview of Al-Ni-Fe System

The Al-Ni-Fe system is of interest in the field of high temperature structural intermetallics because of the extensive B2 phase field extending from NiAl to FeAl. The available phase equilibria data indicate that the B2 phase field is quite extensive on the Al-deficient side of stoichiometry but very limited on the Al-rich side [Vil95]. The B2 structure can be visualized as an ordered bcc lattice. Unlike a bcc lattice one type of atom occupies the body-centered position and another type occupies the cube corners. This results in only one lattice point per unit cell and the lattice is therefore primitive cubic. When the composition deviates from stoichiometry constitutional defects must be introduced to preserve the crystal structure. The simple cubic lattice on which the Al atoms reside may be designated β and the corresponding transition metal lattice may be designated α . In NiAl it is well established that on the Al rich side of stoichiometry

80 vacancies are present on the α sublattice [Tay72]. On the Ni-rich side the excess Ni atoms occupy the β sublattice creating anti-structure defects. In the FeAl compound the constitutional defect structure is more controversial but appears to be analogous to that in NiAl [Jor03]. Recent work by Liu et al [Liu02] indicated an unexpected increase in the atomic size of Fe on addition to NiAl which was proposed to be due to a magnetic effect. Such an effect might be expected to result in unusual variation of the enthalpy of formation with composition. In the Calphad approach to modeling compound phases with broad composition ranges it is usual to use a Wagner-Schottky (W-S) model to describe the enthalpy of formation of the compound [Hua99]. Within that model there are several parameters related to the enthalpy of formation of specific types of defect. In order to determine the values of the W-S parameters we have measured the enthalpy of formation of the B2 phase in the Al-Ni-Fe system for the Al-deficient compositions.

4.2 Experimental Procedure

The heats of formation were determined using a high temperature reaction calorimeter with a typical accuracy of ±1kJ/mole [Kle89]. The measurements were made with the calorimeter set at 1373±2K, and using a protective argon atmosphere. The calorimeter was calibrated using pure copper. Samples were produced by mixing elemental powders in a mortar in the required molar ratio, and pressing them into a small pellet. Typical sample weight was about 120 mg. The nickel and iron powders used were reduced in hydrogen prior to preparation of the samples to remove oxygen and carbon which would be a source of errors.

81 The enthalpy of reaction is measured by two steps. ∆HReaction is obtained first by dropping the pellet into the calorimeter from room temperature. A minimum of six separate samples were measured. The pellets were subsequently removed and again dropped from room temperature into the calorimeter to obtain the heat content of the compound, ∆HHeat Content. The difference between the two measurements yields the heat of formation at 298K. The results are averages of the six individual measurements. With the standard deviations from the reaction and heat content experiments designated as δ1 and δ2 and from the calibration as δ 3 the overall uncertainty in the measurements, δ, was determined from δ = (δ 12 + δ 22 + δ 32)1/2. Material from the reacted compound is used to obtain an x-ray diffraction pattern to confirm that the reacted sample is the desired compound.

4.3 Enthalpy of Formation Calculation

By using direct synthesis, the standard enthalpy of formation, ∆Hf from:

298K

∆HReaction [1]

a Al (s, 298K) + b Ni (s, 298K) + c Fe (s, 298K) = AlaNibFec (1373 K) AlaNibFec (s, 298 K) = AlaNibFec(1373 K)

, is calculated

∆HHeat Content [2]

From reaction [1] and [2] we get a Al(s, 298K) + b Ni(s, 298K) + c Fe(s, 298K) = AlaNibFec (s, 298 K) The standard enthalpy of formation is thus obtained.

∆H f

298K

= ∆HReaction - ∆HHeat Content

∆HReaction and ∆HHeat Content are molar enthalpy changes for reaction [1] and [2].

82 4.4 Wagner-Schottky Model

Intermetallic compounds with B2 structure tend to be stable over a wide range of compositions. The wide homogeneity range is achieved by the incorporation of constitutional defects into the crystal structure.

The W-S model [Ryz00] has been

frequently used for describing the relationship between enthalpy of formation and composition over the B2 phase region of some alloy systems. Calorimetric measurements were made in this study to obtain the parameters for the W-S model, which can be used for enthalpy prediction in Calphad modeling of the system. The composition dependence of ∆H f of the B2 phase in Al-Ni-Fe using the W-S model is: ∆H f = ∆H*(1+x 20 )+∆H12 x12 +∆H13 x13 +∆H 20 x 20 +∆H 21x 21 +∆H 23 x 23 ∆H* =x∆H fAlNi +(1-x)∆H fAlFe

The definitions of the parameters in the above equations are given in Table 4.1.

83 Table 4.1. The Definitions of the Parameters in the Wagner-Schottky Model of the B2 Phase Parameter

Definition

∆H f

Enthalpy of formation of B2 phase in Al-Ni-Fe ternary compound

∆H*

Enthalpy of formation of 1 mole of the ideally stoichiometric B2 phase

∆H12

Enthalpy of formation of 1 mole of Ni antistructure atoms in the β sublattice

∆H13

Enthalpy of formation of 1 mole of Fe antistructure atoms in the β sublattice

∆H 20

Enhthalpy of formation of 1 mole of vacancies in the α sublattice

∆H 21

Enthalpy of formation of 1 mole of Al antistructure atoms in the α sublattice

∆H 23

Enthalpy of formation of 1 mole of Fe in the α sublattice

x12

Concentration of Ni antistructure atoms in the β sublattice

x13

Concentration of Fe antistructure atoms in the β sublattice

x 20

Concentration of vacancies in the α Sublattice

x 21

Concentration of Al antistructure atoms in the α sublattice

x 23

Concentration of Fe antistructure atoms in the α sublattice

∆H fAB

Enthalpy of formation of 1 mole of the ideally stoichiometric AlNi compound

∆H fAC

Enthalpy of formation of 1 mole of the ideally stoichiometric AlFe compound

84 4.5 Thermodynamic Modeling of the B2 Phase

By using Miedema's semi-empirical model extended for ternary alloys [Bak98], the standard enthalpy of formation, ∆H f

∆H f

298K

inter

= CA ƒBA∆H

298K

, can be calculated from:

inter

(A in B) + CA ƒCA ∆H

inter

(A in C) + CB ƒBC ∆H

(B in C)

CA and CB are the molar ratios of A and B elements respectively in the corresponding compounds, ƒBA is the degree of surface contact of an A atom with B neighbors while the inter

ƒCA is the degree of surface contact of an A atom with C neighbors. ∆H

is interfacial

enthalpy.

In the Calphad method the thermodynamic description of the bcc-A2 and bcc-B2 phases in the Al-Fe-Ni system is modeled with one Gibbs energy functions with a threesublattice model, i.e. (Al, Fe, Ni, Va)0.5(Al, Fe, Ni, Va)0.5(Va)3. It follows the model used in the Al-Ni binary system [Dup01], with Va standing for vacancy. When the mole fractions of Al, Fe and Ni in the first sublattice, often referred to as site fractions, are their mole fractions in the second sublattice, the phase becomes disordered, i.e. (Al, Fe, Ni, Va)(Va)3.

The models for the three constitutive binary systems are taken from the literature, i.e. Al-Ni [Dup01], Al-Fe [Sei94], and Fe-Ni [Fer88]. In the Al-Fe system, the bcc-B2 phase was modeled with the model (Al, Fe)0.5(Al, Fe)0.5(Va)3, so that Va needs to be added to

85 make the model compatible. Following a similar approach in the Al-Ni system [Dup01], the interaction parameter between Fe and Va in bcc-A2 was set to be 200 kJ/mole and the Gibbs energy of the end-members of (Fe)0.5(Va)0.5(Va)3 and (Va)0.5(Fe)0.5(Va)3 were set to be zero.

4.6 Result and Discussion

The enthalpies of formation of the B2 alloy compositions are compared in Figure 4.2Figure 4.5. By considering the heats of formation at various iso-concentrations one can determine the behavior in terms of the defect structure. The enthalpies of formation of the Al-Ni-Fe compounds are listed in Table 4.2, together with values calculated in this work based on Miedema’s model, calorimeter temperature was set at 1373K. The Miedema model predictions show the correct trend but in most cases are significantly less exothermic than the measured values.

86 Table 4.2. Summary of the High Temperature Reaction Calorimetry Results, Miedema's Semi-empirical Model Results and Lattice Structure Results

Compound

∆ Hf298K kJ/mole Experimental

Al0.82Ni0.09Fe0.09 -25.8±1.4 Al0.72Ni0.14Fe0.14 -36.7±1.6 Al0.18Ni0.75Fe0.07 -28.3±1.2 Al0.25Ni0.25Fe0.50 -27.9±1.4 Al0.25Ni0.50Fe0.25 -30.6±1.8 Al0.30Ni0.40Fe0.30 -34.2±1.1 Al0.33Ni0.10Fe0.57 -24.7±1.1 Al0.33Ni0.17Fe0.50 -32.3±1.8 Al0.33Ni0.33Fe0.33 -39.4±1.3 Al0.33Ni0.45Fe0.22 -41.2±1.2 Al0.33Ni0.50Fe0.17 -41.5±1.2 Al0.33Ni0.57Fe0.10 -43.8±1.3 Al0.40Ni0.10Fe0.50 -28.3±2.6 Al0.40Ni0.20Fe0.40 -32.8±2.7 Al0.40Ni0.30Fe0.30 -35.4±3.1 Al0.40Ni0.40Fe0.20 -42.8±1.9 Al0.40Ni0.50Fe0.10 -48.8±1.5 Al0.50Ni0.10Fe0.40 -29.8±1.9 Al0.50Ni0.25Fe0.25 -44.5±0.9 Al0.50Ni0.40Fe0.10 -47.7±1.2 Al0.33Fe0.67 -22.2±0.9 Al0.40Fe0.60 -25.9±1.2 Al0.50Fe0.50 -26.5±1.1 Al0.50Fe0.50* -25.1±1.1* † Al0.50Ni0.50 -61.8±1.1† Al0.40Ni0.60† -52† † obtained from [Nas91] * obtained from [Ryz00]

∆ Hf298K kJ/mole Miedema model

Crystal Structure

Phase

-15.8 -23.0 -22.8 -22.5 -25.3 -26.8 -28.3 -25.9 -29.3 -29.8 -31.6 -34.6 -28.1 -28.1 -31.2 -34.7 -36.9 -30.2 -31.4 -39.6 -26.8 -29.5 -32.7 -32.7 -49.7 -44.3

Al9Co2/mP22 /mC* AuCu3/CP4 ClCs/cP2 ClCs/cP2 ClCs/cP2 ClCs/cP2 ClCs/cP2 ClCs/cP2 ClCs/cP2 ClCs/cP2 ClCs/cP2 ClCs/cP2 ClCs/cP2 ClCs/cP2 ClCs/cP2 ClCs/cP2 ClCs/cP2 ClCs/cP2 ClCs/cP2 ClCs/cP2 ClCs/cP2 ClCs/cP2 ClCs/cP2 ClCs/cP2 ClCs/cP2

B2 B2 B2 B2 B2 B2 B2 B2 B2 B2 B2 B2 B2 B2 B2 B2 B2 B2 B2 B2 B2 B2 B2

Lattice Parameter (nm) 0.28893 0.28773 0.28929 0.28983 0.28943 0.28894 0.28876 0.28860 0.28738 0.29040 0.28955 0.28935 0.28879 0.28813 0.29033 0.28914 0.28764 0.28966 0.29051 0.29110 0.28870† -

87

Ni

: B2 Phase

1.0

0.0

: non B2 Phase Unit: kJ/mole

0.8

0.2

o At mi

(-52)

on c ti At o

0.6 (-47.7)

(-42.8)

0.4

(-39.4) (-27.9)

(-35.4)

0.8

(-32.8)

(-44.5)

Ni

cf

(-30.6) (-41.2) (-34.2)

(-48.5)

on

ra

(-41.5) (-61.8)

c ti

mi

0.6

(-43.8)

ra

0.4

cf

Al

(-28.3)

0.2

(-32.3)

(-36.7) (-24.7)

1.0

Al 0.0

(-25.8)

(-29.8)

0.2

0.4

(-26.5)

(-28.3)

0.0 (-25.9) (-22.2)

0.6

0.8

1.0

Fe

Atomic fraction Fe Figure 4.1. Enthalpies of Formation of Compounds in the Al-Ni-Fe System Determined in This Work by High Temperature Reaction Calorimetry

88

Enthalpy of formation of Al0.50Ni(0.50-x)Fex

Enthalpy for formation (kJ/mole)

-20

obtained from [Nas01] this study

-30

-40

-50

-60

-70 0.0

0.1

0.2

0.3

0.4

Fe, mole fraction

Figure 4.2. Enthalpies of Formation of Solid B2 Al0.50 Ni(0.50-X) FeX

0.5

89

Enthalpy of formation for Al0.40Ni(0.60-x)Fex

Enthalpy of formation (kJ/mole)

-25

extrapolated from [Nas01] this study

-30

-35

-40

-45

-50

-55 0.0

0.1

0.2

0.3

0.4

0.5

Fe, mole fraction

Figure 4.3. Enthalpies of Formation of Solid B2 Al0.40 Ni(0.60-X) FeX

0.6

90

-20

Enthalpy of formation of Al0.33Ni(0.67-x)Fex Enthalpy of formation (kJ/mole)

-25

extropolated from [Nas01] this study

-30

-35

-40

-45

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Fe, mole fraction

Figure 4.4. Enthalpies of Formation of Solid B2 Al0.33 Ni(0.67-X ) FeX

91 Selected comparisons of the results with the Calphad model calculated using Thermocalc are shown in Figure 4.5 and Figure 4.6. The results calculated from this model discussed in the previous section, are generally about 5 kJ/mole more exothermic than the experimental results determined in this work. This reflects the fact that the binary values from the database are of the order of 5 kJ/mole more exothermic than our measured values and that no ternary interaction parameters were used in the calculation. However, the slopes of the Thermocalc, Breuer [Bre01] data and the data from this work are identical. The solution calorimetry results of Breuer [Bre01] are generally 5 kJ/mole more exothermic than the data measured in this work by direct synthesis calorimeter. While our data are referred to 298K, the data of [Bre01] are referred to the calorimeter temperature 1073K. This would give a small difference of 1 to 2 kJ/mole bringing the two sets of data to within 3 to 4 kJ/mole. This would still seem to be outside of experimental error and we are investigating the reason for this.

92

Enthalpy of formation comparison Al0.40Fe0.60 Al0.50Ni0.40Fe0.10 Al0.50Ni0.10Fe0.40

Thermocalc Experiment Miedema

Al0.40Ni0.10Fe0.50 Al0.40Ni0.20Fe0.40 Al0.40Ni0.30Fe0.30 Al0.40Ni0.40Fe0.20 Al0.40Ni0.50Fe0.10 Al0.25Ni0.25Fe0.50 Al0.50Ni0.25Fe0.25 0

-10

-20

-30

-40

-50

-60

Enthalpy of formation (kJ/mole) Figure 4.5. Comparison of Enthalpies of Formation for Selected Compounds

93

Enthalpy of formation of Al0.5Ni(0.5-x)Fex -25

This work Breuer et al [Bre01] Miedema's calculation Thermocalc calculation

Enthalpy for formation (kJ/mole)

-30 -35 -40 -45 -50 -55 -60 -65 -70 0.0

0.1

0.2

0.3

0.4

Fe, mole fraction Figure 4.6. Enthalpies of Formation of Solid B2 Al0.5 Ni(0.5-X) FeX Determined Experimentally and Compared to Miedema and Thermocalc Values

0.5

94 The B2 phase in the Al-Ni-Fe system extends mostly in the Al deficient region. In this region it is known that the β sublattice contains Ni and/or Fe transition metal antistructure defects [And99]. The concentration of constitutional vacancy defects on the α sublattice is considered negligible (x20=0).

The W-S model equation corresponding to this composition region can then be modified to: f

*

∆H =∆H + ∆H12x12 + ∆H13x13 + ∆H23x23

In the case of constant 0.5 mole fraction of Al, no antistructure atoms or constitutional vacancies are formed, x12, x13, x20, x21=0, and the equation can be reduced further to: f

*

∆H =∆H + ∆H23x23

The enthalpies of formation of Al0.50 Ni(0.50-X) FeX compounds were fit with a linear f

*

curve as shown in Figure 4.2. This indicates that ∆H is essentially equal to ∆H , and

∆H23x23 is very close to zero for this concentration section. Similarly for the Al0.40 Ni(0.60X)

FeX section, Figure 4.3, the data do not show a clear trend beyond the experimental

error. The W-S formulation for the enthalpy across this section, constant Al = 0.4 (with x12, x13 = 0.1 and ∆H 12, ∆H 13 from Table 4.3).

f

*

∆H =∆H + ∆H 12x12 + ∆H 13x13 + ∆H 23x23

95

We conclude that ∆H23x23 is still quite small (0 to 2 kJ/mole). The enthalpies of formation for the section Al0.33 Ni(0.67-X) FeX are shown in Figure 4.4 where the data show a clear deviation from a linear fit based on the binary data. In this case the enthalpy of formation across this section (with x12, x13 =0.17) is:

f

*

∆H =∆H + ∆H12x12 + ∆H13x13

which means that ∆H23x23 has a significant value for this composition range. The data may be fit by two lines with different slopes intersecting at 0.33 Fe. The value of ∆H23x23 may be determined from the difference between the interpolated line from the binary data and the intersection point of the two fit lines at 0.33 Fe. The value of

∆H23 in this composition section is -15.8 kJ/mole. This may be compared with the value of ∆H23 = +6.1 kJ/mole in the Al-Ni-Co system obtained by Grün et al [Gru98], Table 4.3. The positive value of ∆H23 in the Al-Ni–Co system is consistent with the small positive enthalpy of mixing of Ni and Co [Nis91]. Similarly the negative value of ∆H23 in Al-NiFe is consistent with the negative enthalpy of mixing of Ni and Fe [Nis91].

96 Table 4.3. Enthalpy Coefficients in the Wagner-Schottky Model of the B2 Phase in AlNi-Fe Enthalpy kJ/mole Coefficients 97.5 (AlNi) [Nas01] ∆H12

∆H13

70.3 (AlFe) [Ryz00]

∆H23

-15.8 (Al0.33 Ni(0.67-X) FeX ) [This work]

∆H23

0 (Al0.50 Ni(0.50-X) FeX ) [This work]

∆H23

~ 0 (Al0.40 Ni(0.60-X) FeX ) [This work]

The W-S model provides a way to understand thermodynamic properties of phases with constitutional defect structures. However, as demonstrated in this work for the AlNi-Fe system it is likely that the enthalpy coefficients in the W-S formulation may be composition dependent in some cases.

97 CHAPTER 5 POINT DEFECTS IN B2 PHASE REGION OF Al-Ni-Fe SYSTEM The point defects in B2 phase region of the Al-Ni-Fe system have been investigated by measuring lattice parameters of alloys across the single B2 phase region between AlNi and AlFe. Atomic volumes of Al, Ni and Fe were determined and found to be in dependence of chemical composition and defect mechanism. The atomic size differences show Fe atom is more likely to occupy the Al sublattice than Ni atom.

5.1 Point Defects in B2 Phase Overview

The Al-Ni-Fe system is of interest in the field of high temperature structural intermetallics because of the extensive B2 phase field extending from NiAl to FeAl. The available phase equilibria data indicate that the B2 phase field is quite extensive on the Al-deficient side of stoichiometry but very limited on the Al-rich side [Vil95]. The B2 structure can be visualized as an ordered bcc lattice. Unlike a bcc lattice one type of atom occupies the body-centered position and another type occupies the cube corners. This results in only one lattice point per unit cell and the lattice is therefore primitive cubic. When the composition deviates from stoichiometry constitutional defects must be introduced to preserve the crystal structure. The simple cubic lattice on which the Al atoms reside may be designated α and the corresponding transition metal lattice may be designated α. In NiAl it is well established that on the Al rich side of stoichiometry vacancies are present on the α sublattice [Tay72]. On the Ni-rich side the excess Ni atoms occupy the β sublattice creating anti-structure defects. In the FeAl compound the constitutional defect structure is more controversial but appears to be analogous to that in

98 NiAl [Jor03]. Recent work by Liu et al [Liu02] indicated an unexpected increase in the atomic size of Fe on addition to NiAl which was proposed to be due to a magnetic effect. Such an effect might be expected to result in unusual variation of the enthalpy of formation with composition. In order to determine the atomic volume of Al, Ni and Fe in the B2 phase field, lattice parameters were measured across the single B2 phase region between AlNi and AlFe. The atomic volume can be obtained using lattice parameter as a function of composition of stoichiometry and defect mechanism.

5.2 Experiment

Twenty one alloys within the B2 phase field (0.33 ≤Al≤0.50) of the Al-Ni-Fe system were prepared by mixing elemental powders in a mortar in the required molar ratio, and pressing them into a small pellet. Typical sample weight was about 120 mg. The nickel and iron powders used were reduced in hydrogen prior to preparation of the samples to remove oxygen and carbon which would be a source of errors. Samples were dropped into the high temperature calorimeter [Kle89] at 1100°C for measuring enthalpy of formation and the results have been reported [Su03]. Finally the samples were furnace cooled to room temperature. X-ray diffraction was performed using Cu Kα radiation. Scans were taken over a 2θ range of 5° to 120°. A NIST standard reference alumina was used as a standard to correct d-spacing. The lattice parameter was calculated using 7–9 peaks. The NelsonRiley method was used for calculating systematic errors [Cul01].

99 5.3 Discussion

The lattice parameter result obtained in this study is shown in Table 5.1. It can be seen that lattice parameter is increased as the Fe content increase for the three systems Al0.50 Ni(0.50-X) FeX , Al0.40 Ni(0.60-X) FeX, and Al0.33Ni(0.67-X) FeX. Lattice parameters of Al0.50 Ni(0.50-X) FeX show completely different behavior from Al0.40 Ni(0.60-X) FeX and Al0.33 Ni(0.67-X) FeX. Figure 5.1 shows the lattice parameter of Al0.50 Ni(0.50-X) FeX can be fitted as a second order polynomial curve: y = 0.0116 x 2 - 0.00078 x + 0.2887 which indicates the atomic size of Ni and/or Fe is a function of Fe content. However, the fitted curve with changing slop is obtained in both Figure 5.2 and Figure 5.3. The slop changes at 10 at.% Fe in constant 40 at. % Al compounds and 17 at.% Fe in constant 33 at. % Al compounds suggest that antisite Fe atom preferentially occupies Al sublattices. Fe atoms go to Al sublattices first and after all Al sublattices are completely occupied (10 at. % Fe atoms in 40 at. % Al compound and 16 at. % Fe atoms in 33 at. % Al compound) Fe atoms start to occupy Ni sublattices. Due to the fact that the atomic size difference between Fe and Ni atoms in Al sublattices is not equal to the atomic size difference between Fe and Ni atoms in Ni sublattices, the change in slop is thus expected and also the atomic volume in different sublattices should be a single value which can be calculated for both Al0.40 Ni(0.60-X) FeX and Al0.33 Ni(0.67-X) FeX systems.

100 Table 5.1. Summary of Crystal Structure and Lattice Parameter Results in the Al-Ni-Fe System Compound

Crystal Structure

Phase

Lattice Parameter (nm)

Al0.25Ni0.25Fe0.50

ClCs/cP2

B2

0.2889

Al0.25Ni0.50Fe0.25

ClCs/cP2

B2

0.2877

Al0.30Ni0.40Fe0.30

ClCs/cP2

B2

0.2893

Al0.33Ni0.10Fe0.57

ClCs/cP2

B2

0.2898

Al0.33Ni0.17Fe0.50

ClCs/cP2

B2

0.2894

Al0.33Ni0.33Fe0.33

ClCs/cP2

B2

0.2889

Al0.33Ni0.45Fe0.22

ClCs/cP2

B2

0.2888

Al0.33Ni0.50Fe0.17

ClCs/cP2

B2

0.2886

Al0.33Ni0.57Fe0.10

ClCs/cP2

B2

0.2874

Al0.40Ni0.10Fe0.50

ClCs/cP2

B2

0.2904

Al0.40Ni0.20Fe0.40

ClCs/cP2

B2

0.2896

Al0.40Ni0.30Fe0.30

ClCs/cP2

B2

0.2894

Al0.40Ni0.40Fe0.20

ClCs/cP2

B2

0.2888

Al0.40Ni0.50Fe0.10

ClCs/cP2

B2

0.2881

Al0.50Ni0.10Fe0.40

ClCs/cP2

B2

0.2903

Al0.50Ni0.25Fe0.25

ClCs/cP2

B2

0.2891

Al0.50Ni0.40Fe0.10

ClCs/cP2

B2

0.2876

Al0.33Fe0.67

ClCs/cP2

B2

0.2897

Al0.40Fe0.60

ClCs/cP2

B2

0.2905

Al0.50Fe0.50

ClCs/cP2

B2

0.2911

Al0.50Ni0.50

ClCs/cP2

B2

0.2887

Al0.40Ni0.60

ClCs/cP2

B2

0.2865†

Al0.33Ni0.67

ClCs/cP2

B2

0.2851†

† Data taken or extrapolated from [Noe94]

101

0.2915

Pike et al. [Pik02], furnace cooled from 700°C Present work, furnace cooled from 1100°C

Lattice parameter (nm)

0.2910

0.2905

0.2900

0.2895

0.2890

0.2885 0.0

0.1

0.2

0.3

0.4

0.5

Fe, mole fraction Figure 5.1. Lattice Parameter of Al0.50 Ni(0.50-X) FeX

5.4. Atomic Volume Calculation for Al0.40 Ni(0.60-x) Fex System

The lattice parameter for compounds with constant 40 at. % Al obtained in present work is shown in Figure 5.2 where a1 is the lattice parameter of Al0.4 Ni0.6, a2 is the lattice parameter of Al0.40 Ni0.50 Fe

0.10, a3

is the lattice parameter of compound Al0.4 Fe0.6, a4 is

the lattice parameter of a hypothetical compound Al0.4 Ni0.6 where both Al and Ni atoms reside on Ni sublattices. Table 5.2 lists the selected lattice parameters and corresponding compound composition as well as the site occupancy, which will be used in the calculation.

102

0.298

a4 0.297 o

Present work, furnace cooled from 1100 C o Pike at al. [Pik02], quenched from 700 C o Pike et al. [Pik02], quenched from 1000 C

Lattice parameter (nm)

0.296 0.295 0.294 0.293 0.292

a3 0.291 0.290 0.289

a2 a1

0.288 0.287 0.0

0.1

0.2

0.3

0.4

0.5

Fe, mole fraction Figure 5.2. Lattice Parameter of Al0.40Ni (0.60-X)FeX

Table 5.2. Lattice Parameters Used in Calculation Coefficient Lattice parameter (nm) Composition 0.2887 (Al0.5) β ( Ni0.5) α a0 0.2865† (Al0.4 Ni0.1) β (Ni0.5) α a1

a2

0.2884

(Al0.4 Fe0.1) β (Ni0.5) α

a3

0.2906

(Al0.4 Fe0.1) β (Fe0.5) α

0.2979 (Al0.4) β (Fe0.6) β a4 † data taken from [Noe94], α and β represent different sublattices

0.6

103 For compound Al0.5 Ni0.5: 0.5 mole of Al atoms occupy Al sublattices and 0.5 mole of Ni atoms occupy Ni sublattices, a0 is the lattice parameter of Ni0.5 Al0.5:

a03 1 1 VAl / Al + VNi / Ni = 2 2 2

(1)

For compound A0.40 Ni0.60: 0.40 mole of Al atoms occupy Al sublattices, 0.10 mole of Ni atoms occupy Al sublattices and 0.5 mole of Ni atoms occupy Ni sublattices.

a3 4 1 1 VAl / Al + VNi / Al + VNi / Ni = 1 2 10 10 2

(2)

For compound Al0.40 Ni0.50 Fe 0.10: 0.40 mole of Al atoms occupy Al sublattices, 0.10 mole of Fe occupy Al sublattices and 0.5 mole of Ni occupy Ni sublattices.

a3 4 1 1 VAl / Al + VFe / Al + VNi / Ni = 2 2 10 10 2

(3)

For compound Al0.40 Fe0.60: 0.40 mole of Al atoms occupy Al sublattices, 0.10 mole of Fe occupy Al sublattices and 0.5 mole of Fe occupy Ni sublattices.

a33 4 1 1 VAl / Al + VFe / Al + VFe / Ni = 2 10 10 2

(4)

104 For the hypothetical compound of Al0.40 Fe0.60 (Both Al and Fe atoms are in Al sublattices): 0.40 mole of Al atoms occupy Al sublattices and 0.60 mole of Fe occupy Al sublattices. 4 6 a3 VAl / Al + VFe / Al = 4 2 10 10

(5)

By solving the above 5 equation (1)-(5) with 5 knowns, we are able to obtain the following atomic volume in Al0.40 Ni(0.60-x) Fex system with constant 0.40 mole fraction Al

VAl / Al = 0.0134 nm3 VNi / Al = 0.0107 nm3 VNi / Ni = 0.0106 nm3 VFe / Al = 0.0131 nm3 VFe / Ni = 0.0112 nm3

The atomic volume difference in Al and Ni sublattice can also be calculated:

∆V( Fe − Ni ) β =

VFe / Al − VNi / Al = 18 .1 % VFe / Al

∆V( Fe − Ni )α =

VFe / Ni − VNi / Ni = 5.1 % VFe / Ni

∆V( Fe − Al ) β =

VAl / Al − VFe / Al = 2.7 % VAl / Al

105

∆V( Ni − Al ) β =

VAl / Al − VNi / Al = 20.3 % VAl / Al

We can see the atomic size different between Fe and Al in Al sublattice (2.7%) is much smaller than the difference between Ni and Al in Al sublattices (20.3%). In this case, the Fe anti-site atoms are preferred at the Al subllattices. The atomic size difference between Fe and Ni in Al sublattice (18.1%) is much larger than the difference between Fe and Ni in Ni sublattice (5.1%) indicates the larger slop in first section of fitted curve with Fe mole fraction up to 10%.

5.5 Atomic Volume Calculation for Al0.33 Ni(0.67-x) Fex System

The lattice parameter for compounds with constant 33 at. % Al obtained in present work is shown in Figure 5.3 where a1 is the lattice parameter of Al0.33 Ni0.67, a2 the lattice parameter of Al0.33 Ni0.50 Fe 0.17, a3 the lattice parameter of compound Al0.33 Fe0.67, a4 is the lattice parameter of a hypothetical compound Al0.33 Ni0.67 which both Al and Ni atoms reside on Ni sublattices. Table 5.4 lists the selected lattice parameters and corresponding compound composition as well as the site occupancy which will be used in the calculation.

106

a4 0.298

Lattice parameter (nm)

0.296 0.294 0.292

a3 0.290 a2

0.288 0.286

a1 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Fe, mole fraction Figure 5.3. Lattice Parameter of Al0.33 Ni(0.67-x) Fex

Table 5.3. Lattice Parameters Used in Calculation Coefficient Lattice parameter (nm) Composition 0.2887 (Al0.5) β ( Ni0.5) α a0 0.2850† (Al0.33 Ni0.17) β (Ni0.5) α a1 0.2886 (Al0.33 Fe0.17) β (Ni0.5) α a2 0.2897 (Al0.33 Fe0.17) β (Fe0.5) α a3 0.2994 (Al0.33) β (Fe0.67) β a4 †data extrapolated from [Noe94], α and β represent different sublattices

107 For compound Al0.5 Ni0.5: 0.5 mole of Al atoms occupy Al sublattices and 0.5 mole of Ni atoms occupy Ni sublattices, a0 is the lattice parameter of Ni0.5 Al0.5:

a03 1 1 VAl / Al + VNi / Ni = 2 2 2

(6)

For compound A0.33 Ni0.67: 0.33 mole of Al atoms occupy Al sublattices, 0.17 mole of Ni atoms occupy Al sublattices and 0.5 mole of Ni atoms occupy Ni sublattices.

a3 1 1 1 VAl / Al + VNi / Al + VNi / Ni = 1 2 3 6 2

(7)

For compound Al0.33 Ni0.50 Fe 0.17: 0.33 mole of Al atoms occupy Al sublattices, 0.17 mole of Fe occupy Al sublattices and 0.5 mole of Ni occupy Ni sublattices.

a3 1 1 1 VAl / Al + VFe / Al + VNi / Ni = 2 2 3 6 2

(8)

For compound Al0.33 Fe0.67: 0.33 mole of Al atoms occupy Al sublattices, 0.17 mole of Fe occupy Al sublattices and 0.5 mole of Fe occupy Ni sublattices.

a33 1 1 1 VAl / Al + VFe / Al + VFe / Ni = 2 3 6 2

(9)

108 For the hypothetical compound of Al0.33 Fe0.67 (Al in Al sublattices and Fe in Al sublattices): 0.33 mole of Al atoms occupy Al sublattices and 0.67 mole of Fe atoms occupy Al sublattices. 1 2 a3 VAl / Al + VFe / Al = 4 2 3 3

(10)

By solving the above 5 equations (6)-(10) with 5 knowns, we are able to obtain the following atomic volume in case of Al0.33 Ni(0.67-x) Fex system with constant 0.33 mole fraction Al.

VAl / Al = 0.0133 nm3 VNi / Al = 0.0107 nm3 VNi / Ni = 0.0106 nm3 VFe / Al = 0.0134 nm3 VFe / Ni = 0.0109 nm3

The atomic volume difference in Al and Ni sublattice can also be calculated:

∆V( Fe − Ni ) β =

VFe / Al − VNi / Al =19.9% VFe / Al

∆V( Fe − Ni )α =

VFe / Ni − VNi / Ni = 2.6% VFe / Ni

∆V( Fe − Al ) β =

VAl / Al − VFe / Al = 0.5% VAl / Al

∆V( Ni − Al ) β =

VAl / Al − VNi / Al = 19.5% VAl / Al

109 Similar to the case with 40% Al, we can also see the atomic size different between Fe and Al in Al sublattice (0.5%) is much smaller than the difference between Ni and Al in Al sublattices (19.5%). That is to say that the Fe anti-site atoms are preferred at the Al subllattices. The atomic size difference between Fe and Ni in Al sublattice (19.9%) is much larger than the difference between Fe and Ni in Ni sublattice (2.6%) indicates the larger slop in first section of fitted curve with Fe mole fraction up to 17%.

5.6 Excess Thermal Vancancy

The measured lattice parameters of Al0.50 Ni

(0.50-X) FeX

compounds and together with

Pike et al. [Pik02] in Figure 5.1 shows the lattice parameter is a function of reaction temperature as well as cooling rate. Similar phenomenon can also be observed for Al0.40 Ni

(0.60-X)

FeX in Figure 5.2. The lattice parameters in Al-Fe system (0.4≤ Al, mole

fraction ≤0.5) with different cooling rate and reaction temperature is also compared in Figure 5.4 where suggests different amount of thermal vacancies are generated in different heat treatment processes [Sch04]. The lattice parameter difference due to different cooling rate is getting higher in compounds with larger Fe content. This suggests possible thermal vacancies in Fe rich compounds at higher reaction temperature. However, the lattice parameter is independent of the heat treatment history for compounds with high Ni content because of stronger chemical bonding between Ni and Al atom. Kogachi et. al confirmed the constitutional vacancy doesn’t exist in NiAl by measureing density [Kog01] and thermal vacancy formation occurs on both Fe-site and Al-site for compounds AlxFe(1-x) (0.39
110 system [Su03] as shown in Table 5.4. The larger negative value of enthalpy of formation in Al-Ni system indicates higher stability of Al-Ni compounds and thus the stronger bonding between Al and Ni atoms than the one between Al and Fe atoms.

0.2910

Lattice parameter (nm)

0.2905 0.2900 0.2895 0.2890 0.2885

This work, furnace cooled from 1100°C Chang et al. [Cha93], quenched from 1000°C Chang et al. [Cha93], quenched from 500°C Bradley et al. [Cha93], slowly cooled from 750°C

0.2880 0.2875 0.2870 0.40

0.42

0.44

0.46

0.48

0.50

Al, mole fraction Figure 5.4. Lattice Parameter of Al-Fe System

Table 5.4. Enthalpy of Formation of Selected Compounds in Al-Fe and Al-Ni Compound ∆ Hf298K kJ/mole Experimental Al0.40Fe0.60 -25.9±1.2 Al0.50Fe0.50 -26.5±1.1 -61.8±1.1 Al0.50Ni0.50 -52 Al0.40Ni0.60

111 CHAPTER 6 ENTHALPY OF FORMATION IN Al-Ni-Ru SYSTEM The enthalpies of formation of ternary compounds in the Al-Ni-Ru system have been determined by high temperature reaction calorimetry. The composition dependence of the enthalpy of formation and lattice parameter of the compounds with B2 phase were determined in the region of 0.40≤Al≤0.5 mole fraction. Unusual behavior is observed for the composition dependence of the enthalpy of formation suggesting that formation o a miscibility gap is possible. The enthalpy values measured are compared to CALPHAD and extended Miedema modelpredictions. Using the extrapolated, un-optimized database and setting a miscibility gap, the calculated enthalpies of formation are in fair agreement with the experimental results.

6.1 Point Defect in B2 Phase Overview

The Al-Ni-Ru system is of practical interest since the RuAl intermetallic compound has shown potential for high temperature application [Fle93] and partial substitution for ruthenium by nickel could provide the ability to tailor the properties [Wol96] because of the extensive B2 phase field that some claim [Hor98] extends from NiAl to RuAl. The B2 structure can be visualized as an ordered bcc lattice. Unlike a bcc lattice one type of atom occupies the body-centered position and another type occupies the cube corners. This results in only one lattice point per unit cell and the lattice is therefore primitive cubic. When the composition deviates from stoichiometry constitutional defects must be introduced to preserve the crystal structure. The simple cubic lattice on which the Al atoms reside may be designated β and the corresponding transition metal lattice may

112 be designated α. In NiAl it is well established that on the Al rich side of stoichiometry vacancies are present on the α sublattice [Tay72]. On the Ni-rich side the excess Ni atoms occupy the β sublattice creating anti-structure defects. In the RuAl compound the constitutional defect structure appears different from NiAl but is not well understood [Gob03]. Due to the different constitutional defect structure between NiAl and RuAl, it is not straightforward to define the B2 phase field between NiAl and RuAl in the Al-Ni-Ru phase equilibria. The available phase equilibria data indicate that the B2 phase field between NiAl and RuAl exhibits either a miscibility gap [Cha86, Tsu80, Pet85, Try04] or complete miscibility [Hor98] in the B1 phase field of this system. It would be very helpful if enthalpy of formation data and lattice parameter data are available to help resolve the issue of the continuity of the B2 phase field and to provide data to optimize the Al-Ni-Ru system by the Calphad method. This paper reports on determinations of enthalpies of formation and precise lattice parameter measurements.

6.2 Experiment

The enthalpies of formation were determined using a high temperature reaction calorimeter with a typical accuracy of ±1kJ/mole [Kle98]. The measurements were made with the calorimeter set at 1373±2K, and using a protective argon atmosphere. The calorimeter was calibrated using pure copper. Samples were produced by mixing elemental powders in a mortar in the required molar ratio, and pressing them into a small pellet. Typical sample weight was about 100 mg. The nickel and iron powders used were reduced in hydrogen prior to preparation of the samples to remove oxygen and carbon

113 which would be a source of errors. The enthalpy of formation is measured in two steps. ∆HReaction is obtained first by dropping the pellet into the calorimeter from room temperature. A minimum of six separate samples were measured. The pellets were subsequently removed and again dropped from room temperature into the calorimeter to obtain the heat content of the compound, ∆HHeat Content. The difference between the two measurements yields the heat of formation at 298K. The results are averages of the six individual measurements. With the standard deviations from the reaction and heat content experiments designated as δ1 and δ2 and from the calibration as δ 3 the overall uncertainty in the measurements, δ, was determined from δ = (δ 12 + δ 22 + δ 32)1/2. Material from the reacted compound was used to obtain an x-ray diffraction pattern to confirm that the reacted sample was the desired compound.

6.3 Lattice Parameter Calculation

X-ray diffraction was performed using Cu Kα radiation. Scans were taken over a 2θ range of 5° to 120°. A NIST alumina reference material was used as a standard to correct d-spacing. The lattice parameter was calculated using 7–9 peaks. The NelsonRiley method was used for calculating systematic errors [Cul01].

6.4 Prediction of Enthalpies of Formation

For comparison with our experimental results we have used Miedema's semiempirical model extended for ternary alloys [Bak98] to calculate the standard enthalpy of formation, ∆Hf

298K

:

114

∆H f

298K

inter

= CA ƒBA∆H

inter

(A in B) + CA ƒCA ∆H

inter

(A in C) + CB ƒBC ∆H

(B in C)

CA and CB are the molar ratios of A and B elements respectively in the corresponding compounds, ƒBA is the degree of surface contact of an A atom with B neighbors while the inter

ƒCA is the degree of surface contact of an A atom with C neighbors. ∆H

is interfacial

enthalpy.

6.5 Results

The enthalpies of formation of the Al-Ni-Ru compounds and measured lattice parameters are listed in Table 6.1, together with values calculated in this work based on Miedema’s model. It can be observed that as the Al content increases, the enthalpy tends to be more exothermic. The Miedema model predicts less exothermic values than the measured values for all compositions. Figure 6.1 shows the enthalpy results for compounds in the proposed B2 phase region between NiAl and RuAl.

115 Table 6.1. Summary of High Temperature Reaction Calorimetry Results and Miedema's Semi-empirical Model Results in the Al-Ni-Ru System. Calorimeter temperature set at 1373K

Compound

∆ H formation, kJ/mole Experimental

Structure Analysis by XRD

∆ H formation, kJ/mole Lattice Calculated by Parameter (nm) Miedema’s model

Al0.50Ni0.50

-61.8±1.1

B2

-50

0.2887

Al0.50Ni0.10Ru0.40

-62.0±1.3

B2

-43

0.2972

Al0.50Ni0.20Ru0.30

-63.1±0.8

B2

-38

0.2956

Al0.50Ni0.30Ru0.20

-61.5±1.1

B2

-37

0.2931

Al0.50Ni0.35Ru0.15

-58.2±2.0

B2

-39

0.2914

Al0.50Ni0.40Ru0.10

-55.9±2.1

B2

-41

0.2902

Al0.50Ni0.45Ru0.05

-58.7±2.4

B2

-50

0.2891

Al0.50Ru0.50

-54.5±1.2

B2

-44

0.2988*

Al0.45Ni0.10Ru0.45

-56.1±0.8

B2

-43

0.2971

Al0.45Ni0.20Ru0.35

-56.9±1.9

B2

-39

0.2956

Al0.45Ni0.30Ru0.25

-58.1±1.5

B2

-38

0.2942

Al0.45Ni0.35Ru0.20

-57.6±0.6

B2

-38

0.2931

Al0.45Ni0.45Ru0.10

-55.5±1.2

B2

-42

0.2904

Al0.40Ni0.40Ru0.20†

-51.6±1.0

B2

-38

0.2936

Al0.40Ni0.50Ru0.10†

-49.5±1.4

B2

-38

0.2872

Al0.82Ni0.12Ru0.06 ‡

-31.5±1.5

-

-19

-

† Reacted sample was not predominantly B2 phase * Data from reference [Gob03]

116

Ni 1.0

0.0 : B2 Phase Unit: kJ/mole

0.8

At om ic fra cti on Al

0.2

(-52)

0.6

0.4

(-49.5)

(-61.8)

(-55.5)

0.6 (-58.7) (-55.9) (-58.2)

(-57.6)

(-61.5)

0.8

0.4

(-51.6) (-58.1)

0.2

(-63.1) (-56.9) (-62.0)

1.0

Al 0.0

0.2

0.4

(-56.1)

0.0 (-54.5) 0.6

0.8

1.0

Atomic fraction Ru

Figure 6.1. Enthalpies of Formation in B2 Phase Field of Al-Ni-Ru System

Ru

117 Figure 6.2 and Figure 6.3 show the enthalpies of formation of compounds along constant 50 at. % Al indicated as Al0.50 Ni(0.50-X) RuX and 45 at. % Al indicated as Al0.45 Ni(0.55-X) RuX respectively.

-50

Al0.45Ni(0.55-X)RuX

-52

Enthalpy of formaiton (kJ/mole)

-54 -56 -58 -60 -62 -64 -66 -68 -70 0.0

0.1

0.2

0.3

0.4

0.5

Ru, mole fraction

Figure 6.2. Enthalpies of Formation of Al0.45 Ni (0.55-X) RuX

118

-50

Al0.5Ni(0.5-X)RuX

Enthalpy of formation (kJ/mole)

-52 -54 -56 -58 -60 -62 -64 -66 -68 -70 0.0

0.1

0.2

0.3

0.4

0.5

Ru, mole fraction

Figure 6.3. Enthalpies of Formation of Al0.50 Ni(0.50-X) RuX

There is a decrease in the enthalpy of formation of the B2 compound around 0.1 mole fraction of Ru indicating a reduction in stability which will likely result in a miscibility gap. The effect diminishes on reducing the Al concentration below stoichiometry. The relation observed in the enthalpy results of constant Al content in Al-Ni-Ru system is quite different from the linear relations previously reported in the Al-Ni-Fe system [Su03].

119 6.6 Three Dimensional Curve Fitting for Enthalpies of Formation Result

Since the enthalpy of formation is composition dependent, the enthalpies of formation results determined in this study (in the range 0.4 ≤Al mole fraction ≤ 0.5), were fitted as a three dimensional surface with the following polynomial equation:

z = a + b * y + c * y 2 + d * y 3 + e * y 4 + f * x + g * xy + h * xy 2 + i * xy 3 + j * xy 4 where z is the enthalpy of formation, x is Ru mole fraction and y is Ni mole fraction.

a ~ j are coefficients of the fitted polynomial equation. The obtained coefficients are shown in Table 6.2. Sample standard deviation of absolute error is 0.78. The result based on the fitting equation together with the experiment result and absolute error between fitting and experiment are listed in Table 6.3 where the maximum absolute error is 1.7 kJ/mole for Al0.50Ru0.50 and in most cases the fitting error is within the experimental error range. Since the available experimental data are only within the range where Al mole fraction is between 0.4-0.5, the equation is therefore only valid in the same range. Table 6.2. Coefficients of Fitted Equation of Enthalpy of Formation Coefficients in Fitted Equation a = -60 b = -991 c = 6267 d = -13179 e = 9180 f = 11 g = 1782 h = -8030 i = 8000 j = 3713

Table 6.3. Comparison of Enthalpies of Formation Between Experimental Result and Fitted Result

120

Compound

∆ H formation, kJ/mole

∆ H formation, kJ/mole

Absolute Error kJ/mole (difference between experiment and fitted value) 0.4

Experimental

Calculated by fitted curve

Al0.50Ni0.50

-61.8±1.1

-62.2

Al0.50Ni0.10Ru0.40

-62.0±1.3

-61.8

0.2

Al0.50Ni0.20Ru0.30

-63.1±0.8

-63.4

0.3

Al0.50Ni0.30Ru0.20

-61.5±1.1

-60.9

0.6

Al0.50Ni0.35Ru0.15

-58.2±2.0

-58.9

0.7

Al0.50Ni0.40Ru0.10

-55.9±2.1

-57.4

1.5†

Al0.50Ni0.45Ru0.05

-58.7±2.4

-57.8

0.9

Al0.50Ru0.50

-54.5±1.2

-54.6

0.1

Al0.45Ni0.10Ru0.45

-56.1±0.8

-55.9

0.2

Al0.45Ni0.20Ru0.35

-56.9±1.9

-57.6

0.7

Al0.45Ni0.30Ru0.25

-58.1±1.5

-57.4

0.7

Al0.45Ni0.35Ru0.20

-57.6±0.6

-56.4

1.2

Al0.45Ni0.45Ru0.10

-55.5±1.2

-54.4

1.1

Al0.40Ni0.40Ru0.20

-51.6±1.0

-52.8

1.2

Al0.40Ni0.50Ru0.10

-49.5±1.4

-49.5

0

† denoted as the maximum error between experiment and calculation result The purpose of the surface fitting is to provide a tool for interpolation of data.

121 6.7 Lattice Parameter Result

Figure 6.4 and Figure 6.5 show the lattice parameters of Al0.50 Ni(0.50-X) RuX and Al0.45 Ni (0.55-X) RuX, respectively. No indication of phase separation was observed on any of the XRD patterns. The higher Ru content leads to larger lattice parameter as expected because the atomic radius of Ru is larger than Ni (atomic radius of Ru is 0.134 nm and Ni atom is 0.124 nm). The positive deviation observed for compounds with Ru mole fraction larger than 0.15 in Figure 6.4 and all compounds in Figure 6.5 suggest the lattice parameter is affected not only by the atomic sizes but also another effect which leads compounds to be less stable and thus higher lattice parameters are observed than expected based on Vegard’s rule. This effect also indicates unusual alloying behavior and provides indirect support for the miscibility gap.

122

Lattice parameter of Al0.50Ni(0.50-X)RuX

Lattice parameter (nm)

0.298

0.296

0.294

0.292

This study from reference [Nob92]

0.290

0.288 0.0

0.1

0.2

0.3

0.4

Ru, mole fraction

Figure 6.4. Lattice Parameters of Al0.50 Ni (0.50-X) RuX

0.5

123

0.298

Lattice parameter of Al0.45Ni(0.55-X)RuX

Lattiec parameter (nm)

0.296

0.294

0.292

This study from reference [Nob92]

0.290

0.288

0.286 0.0

0.1

0.2

0.3

0.4

Ru, mole fraction Figure 6.5. Lattice Parameters of Al0.45 Ni (0.55-X) RuX

0.5

124 6.8 Al-Ni-Ru Phase Equilibrium

The liquids surface for the Al-Ni-Ru ternary system is shown in Figure 6.10 [Hor97, Hoh00]. Since no monovariant trough is shown across the B2 phase there is no three phase equilibrium between liquid and two separate B2 phase compositions. This implies that at least close to the liquidus the B2 phase exhibits complete solid solution. Experimental data on the existence or not of the miscibility gap is ambiguous. In this work the heats of formation suggest that there is a miscibility gap, while no evidence was found from X-ray diffraction, Figure 6.6 and Figure 6.7. However, one might expect differences in lattice parameters of the two B2 compositions which would give rise to angular separation of about 0.26°. Such a difference would be difficult to observe. However if the miscibility close before melting, Figure 6.8, this would provide a consistent interpretation of the results. Harte et al [Har97] interpreted alloys between the NiAl and RuAl as being cored, rather than comprising two distinct phases. Dendrite coring is assumed because two phase of differing composition occurs in alloys throughout the constant 50 atomic % Al region, rather than little variation at specific location. If the cores for all composition are all Ru rich compared to dendritic region, Figure 6.8 is correct, If Ni rich cores on the Ni rich side and Ru rich cores on the Ru rich side, Figure 6.9 is suggested.

B2 (310)

B2 (300)

B2 (220)

B2 (211)

B2 (210)

B2 (200)

B2 (111)

B2 (110)

B2 (100)

125

Al0.50Ni0.10Ru0.40

Intensity

Al0.50Ni0.20Ru0.30 Al0.50Ni0.30Ru0.20 Al0.50Ni0.35Ru0.15 Al0.50Ni0.40Ru0.10 Al0.50Ni0.45Ru0.05

30

40

50

60

70

80

90

100

2θ Figure 6.6. XRD Patterns of Al0.50 Ni(0.50-x) Rux

110

120

B2 (310)

B2 (300)

B2 (220)

B2 (211)

B2 (210)

B2 (200)

B2 (111)

B2 (110)

B2 (100)

126

Intensity

Al0.45Ni0.10Ru0.45 Al0.45Ni0.20Ru0.30 Al0.45Ni0.30Ru0.25 Al0.45Ni0.35Ru0.20 Al0.45Ni0.45Ru0.10

30

40

50

60

70

80

90

100

2θ Figure 6.7. XRD Patterns of Al0.45 Ni(0.55-x) Rux

110

120

127

2000 1900

Temperature °C

1800 1700 1600 1500 1400 1300 1200

0.0

AlNi

0.5

Ru, mole fraction

AlRu

Figure 6.8. Schematic of Proposed Vertical Section of Al-Ni-Ru System at Constant 50 Atomic % Al

2000 1900

Temperature °C

1800 1700 1600 1500 1400 1300 1200

NiAl

Ru, mole fraction

RuAl

Figure 6.9. Schematic of Proposed Vertical Section of Al-Ni-Ru System at Constant 50 Atomic % Al

128 6.9 Thermodynamic Modeling

A CALPHAD based thermodynamic model for the ternary Al-Ni-Ru system has been developed by interpolating data from the assessed binaries: Al-Ni by Dup in [Dup03], AlRu by Prins [Pri03] and Ni-Ru by Hallstrom [Hal03]. There were slight differences in some parameters and descriptions.

These differences were fixed manually and the

ternary database accurately reproduces the binary phase diagrams. None of the four ternary phases reported by Mi et. al. [Mi03] have been included. Except for the bcc-B2 phase, third element solubility in the binary phases have not yet been considered. The current effort focused on the bcc-B2 phase. Since the solubility ranges of the binary B2 phases are dependent on the defect structures, these should be considered when modeling the system. Al-Ni and Al-Ru are based on different defect structures, and this caused some initial problems in the extrapolation. Furthermore, discrepancies in the literature on the B2 in the ternary (continuous phase or miscibility gap) hindered the ternary optimization of this phase. Initial reports favored a miscibility gap, then Horner

et. al [Hor97, Hor98] proposed a continuous B2 phase between the Al-Ni and Al-Ru binaries. Figure 6.10 shows the experimental result of liquidus surface [Hor97, Hoh00] and T is the ternary Al14Ni2Ru phase. Recently, Tryon et. al. [Try04] reported results based on the presence of a miscibility gap.

Using the extrapolated, un-optimized

database and setting a miscibility gap, the calculated enthalpies of formation are in only fair agreement with the experimental results Figure 6.11. In part this results from the use of an enthalpy of formation of NiAl which is too exothermic by -4 kJ/mole [Hu05]. Incorporation of the revised value of -62 kJ/mole would improve the agreement with experiment but requires the complete reassessment of the Ni-Al binary system.

129

Figure 6.10. Experimental Liquidus Surface Projection for Al-Ni-Ru

130 Recently, new experimental [Try04, Mi03, Yok02] and theoretical calculations [Boz02, Gar03] regarding the Al-Ni-Ru system have been published. Four ternary phases have been proposed in the Al-rich corner, at least two of the phases are approximated as quasi-crystals. However, these publications, especially the results on the bcc-B2 phase, are not consistent with previous work, and some of the results are in disagreement with phase equilibria in the binary systems. A critical assessment of the available data will be needed before additional modeling is attempted. CALPHAD model of the binary database is used for predicting enthalpy of formation. The enthalpy of formation for the bcc-B2 phase has been calculated using the miscibility gap approach. It was not possible to calculate the enthalpy of formation for a continuous B2 phase with the current extrapolation, since there are no parameters to ensure that vacancies don’t become too stable. B2-NiAl shows solubility for ~10 at. % Ru, and B2RuAl shows less than 5 at. % solubility for Ni if the miscibility gap is not introduced. The calculated enthalpies of formation are shown in Figure 6.11.

131

-50

Enthalpy of formation (kJ/mole)

-52

Experimental Calculated

-54 -56 -58 -60 -62 -64 -66 -68 -70 0.0

0.1

0.2

0.3

0.4

0.5

Ru, mole fraction

Figure 6.11. Comparison of Calculated and Experimental Enthalpies of Formation for Compounds with Constant 50 at. % Al

132 CHAPTER 7 CONCLUSION The enthalpies of formation of ternary compounds in the Al-Ni-Y, Al-Ni-Fe and AlNi-Ru system have been determined by high temperature reaction calorimetry. For Al-NiY system, the heats of formation exhibit maximum negative values in the section containing 50 atomic % Al. Miedema model predictions are generally less exothermic than the measured values. Ternary compounds appear mostly at a few fixed Y/(Ni+Al) ratios such as 1:5, 1:3 and 1:2. Based on this alloying behavior it is predicted that ternary compounds with compositions AlNiY3 and AlNiY2 will exist in this system and that the binary phases corresponding to these ratios will exhibit some solubility for the third element. For Al-Ni-Fe compounds, the Miedema model predictions show the correct trend but in most cases are significantly less exothermic than the measured values and Thermocalc prediction are generally about 5 kJ/mole more exothermic than the experimental results determined in this work. Lattice parameter measurement shows the strong tendency for Fe atom to occupy Al sublattice due to very small atomic size difference between Fe and Al. The atomic size is also composition dependent which could be correlated to the composition dependent enthalpy coefficients in the Wagner-Schottky formulation. For Al-Ni-Ru compounds, the enthalpies of formation predicted by Miedema model are less exothermic than experiment value. The enthalpy of formation and lattice parameter measurement for Al-Ni-Ru suggest the existence of a miscibility gap across the B2 phase field between AlNi and AlRu.

133 Al-Ni-Fe system contains B2 phase field across region with 50% Al but a miscibility gap exists in the B2 phase field with 50% Al in the Al-NiRu system. Different site occupancy of Fe and Ru to NiAl can be expected if we compare the lattice parameter vs composition diagrams. Turning points can be observed in Al0.40 Ni(0.6-x) Fex and Al0.33 Ni(0.33-x) Fex systems and gradual lattice parameter change is shown as Ru content increases in Al-Ni-Ru system. This suggests Fe preferentially occupies Al sublattice while the Ru atom has relatively equal distribution to both Al and Ni sublattice. Miedema’s enthalpy of formation prediction is always less exothermic then experimental value because the ternary atomic interaction is not taken into account in this extended Miedema’s model which has been extended from binary compound application to ternary compound application.

134

APPENDIX A MATERIAL SOURCE

135

Name Aluminum

Condition

Source

Aluminum powder ~325mesh 99.97%

Alfa Aesar

Nickel

Nickel powder ~120 mesh, puratronic, 99.996%,

Alfa Aesar

Yttrium

Yttrium Ingot 99.9%

Alfa Aesar

Iron

Iron Powder ~10µ, 99.9+%

Aldrich

Ruthenium Ruthenium Sponge ~20 mesh, 99.95 %,

Alfa Aesar

Copper

14AWG Copper wire

ARCOR

Argon

Compressed, Prepurified

Mettler Supply Inc.

Helium

Compressed, High purity

Mettler Supply Inc.

Alumina

NIST 1976 XRD Flat-Plat Intensity Standard

NIST

136

APPENDIX B SPACE GROUP NUMBER AND SPACE GROUP SYMBOL

137 1 P1

2 P -1

3 P2

4 P 21

5 C2

6 Pm

7 Pc

8 Cm

9 Cc

10 P 2/m

11 P 21/m

12 C 2/m

13 P 2/c

14 P 21/c

15 C 2/c

16 P 2 2 2

17 P 2 2 21

18 P 21 21 2

19 P 21 21 21

20 C 2 2 21

21 C 2 2 2

22 F 2 2 2

23 I 2 2 2

24 I 21 21 21

25 P m m 2

26 P m c 21

27 P c c 2

28 P m a 2

29 P c a 21

30 P n c 2

31 P m n 21

32 P b a 2

33 P n a 21

34 P n n 2

35 C m m 2

36 C m c 21

37 C c c 2

38 A m m 2

39 A b m 2

40 A m a 2

41 A b a 2

42 F m m 2

43 F d d 2

44 I m m 2

45 I b a 2

46 I m a 2

47 P m m m

48 P n n n

49 P c c m

50 P b a n

51 P m m a

52 P n n a

53 P m n a

54 P c c a

55 P b a m

56 P c c n

57 P b c m

58 P n n m

59 P m m n

60 P b c n

61 P b c a

62 P n m a

63 C m c m

64 C m c a

65 C m m m

66 C c c m

67 C m m a

68 C c c a

69 F m m m

70 F d d d

71 I m m m

72 I b a m

73 I b c a

74 I m m a

75 P 4

76 P 41

77 P 42

78 P 43

79 I 4

80 I 41

81 P -4

82 I -4

83 P 4/m

84 P 42/m

85 P 4/n

86 P 42/n

87 I 4/m

88 I 41/a

89 P 4 2 2

90 P 4 21 2

91 P 41 2 2

92 P 41 21 2

93 P 42 2 2

94 P 42 21 2

95 P 43 2 2

96 P 43 21 2

97 I 4 2 2

98 I 41 2 2

99 P 4 m m

100 P 4 b m

101 P 42 c m

102 P 42 n m

103 P 4 c c

104 P 4 n c

105 P 42 m c

106 P 42 b c

107 I 4 m m

108 I 4 c m

109 I 41 m d

110 I 41 c d

111 P -4 2 m

112 P -4 2 c

113 P -4 21 m

114 P -4 21 c

115 P -4 m 2

138 116 P -4 c 2

117 P -4 b 2

118 P -4 n 2

121 I -4 2 m

122 I -4 2 d

123 P 4/m m m 124 P 4/m c c

126 P 4/n n c

127 P 4/m b m 128 P 4/m n c

131 P 42/m m c 132 P 42/m c m 133 P 42/n b c

119 I -4 m 2

120 I -4 c 2 125 P 4/n b m

129 P 4/n m m 130 P 4/n c c 134 P 42/n n m 135 P 42/m b c

136 P 42/m n m 137 P 42/n m c 138 P 42/n c m 139 I 4/m m m 140 I 4/m c m 141 I 41/a m d

142 I 41/a c d

143 P 3

144 P 31

145 P 32

146 R 3

147 P -3

148 R -3

149 P 3 1 2

150 P 3 2 1

151 P 31 1 2

152 P 31 2 1

153 P 32 1 2

154 P 32 2 1

155 R 3 2

156 P 3 m 1

157 P 3 1 m

158 P 3 c 1

159 P 3 1 c

160 R 3 m

161 R 3 c

162 P -3 1 m

163 P -3 1 c

164 P -3 m 1

165 P -3 c 1

166 R -3 m

167 R -3 c

168 P 6

169 P 61

170 P 65

171 P 62

172 P 64

173 P 63

174 P -6

175 P 6/m

176 P 63/m

177 P 6 2 2

178 P 61 2 2

179 P 65 2 2

180 P 62 2 2

181 P 64 2 2

182 P 63 2 2

183 P 6 m m

184 P 6 c c

185 P 63 c m

186 P 63 m c

187 P -6 m 2

188 P -6 c 2

189 P -6 2 m

190 P -6 2 c

191 P 6/m m m 192 P 6/m c c

193 P 63/m c m 194 P 63/m m c 195 P 2 3

196 F 2 3

197 I 2 3

198 P 21 3

199 I 21 3

200 P m -3

201 P n -3

202 F m -3

203 F d -3

204 I m -3

205 P a -3

206 I a -3

207 P 4 3 2

208 P 42 3 2

209 F 4 3 2

210 F 41 3 2

211 I 4 3 2

212 P 43 3 2

213 P 41 3 2

214 I 41 3 2

215 P -4 3 m

216 F -4 3 m

217 I -4 3 m

218 P -4 3 n

219 F -4 3 c

220 I -4 3 d

221 P m -3 m

222 P n -3 n

223 P m -3 n

224 P n -3 m

225 F m -3 m

226 F m -3 c

227 F d -3 m

228 F d -3 c

229 I m -3 m

230 I a -3 d

139

APPENDIX C COMPARISON BETWEEN EXPERIMENTAL PEAK INTENSITY AND CALCULATED PEAK INTENSITY FOR COMPOUNDS IN Al-Ni-Fe SYSTEM

140 Calculated Peak Information of (Al 0.33 Fe 0.10 Ni 0.07) β (Ni 0.50) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

1.01E+00 1.12E+01 2.41E-01 1.68E+00 2.73E-01 3.28E+00 1.14E+00 1.59E-01 2.17E+00 1.43E-01 9.60E-01 2.74E-01

9 100 2.1 15 2.4 29.2 10.1 1.4 19.3 1.3 8.6 2.4

10 10 10 10 10 10 10 10 10 10 10 10

Calculated Peak Information of (Al 0.33 Fe 0.17) β (Fe 0.50) α Peak No.

hkl

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

6.52E-01 9.67E+00 1.45E-01 1.43E+00 1.58E-01 2.78E+00 9.64E-01 9.12E-02 1.84E+00 8.40E-02 8.22E-01 1.66E-01

6.7 100 1.5 14.8 1.6 28.7 10 0.9 19.1 0.9 8.5 1.7

67 67 67 67 67 67 67 67 67 67 67 67

141

Calculated Peak Information of (Al 0.33 Fe 0.17) β (Ni 0.07Fe 0.43) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

7.05E-01 9.85E+00 1.59E-01 1.46E+00 1.74E-01 2.84E+00 9.85E-01 1.01E-01 1.88E+00 9.26E-02 8.38E-01 1.82E-01

7.2 100 1.6 14.9 1.8 28.8 10 1 19.1 0.9 8.5 1.8

60 60 60 60 60 60 60 60 60 60 60 60

142 Calculated Peak Information of (Al 0.33 Fe 0.17) β (Ni 0.10Fe 0.40) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

Intensity (%)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

7.28E-01 9.93E+00 1.65E-01 1.48E+00 1.82E-01 2.86E+00 9.94E-01 1.05E-01 1.90E+00 9.64E-02 8.46E-01 1.89E-01

7.3 100 1.7 14.9 1.8 28.8 10 1.1 19.1 1 8.5 1.9

57 57 57 57 57 57 57 57 57 57 57 57

7.3 100.0 1.7 14.9 1.8 28.8 10.0 1.1 19.1 1.0 8.5 1.9

Experimental Peak Information of Al0.33Ni0.10Fe0.57 Experiment Peak No. hkl 2-Theta 001 1 2 3 4 5 6 7 8

101 111 200 021 112 202 122 130

I/Imax

Fe (at. %)

35.14 40.87 44.18

6.6 4.9 100

64.38 81.41 94.37 97.69 114.57

22.6 71.2 9.3 26.6 39.6

57 57 57 57 57 57 57 57 57 57 57 57

143 Calculated Peak Information of (Al 0.33 Fe 0.17) β (Ni 0.17Fe 0.33) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

7.84E-01 1.01E+01 1.80E-01 1.51E+00 2.00E-01 2.92E+00 1.01E+00 1.16E-01 1.94E+00 1.06E-01 8.62E-01 2.06E-01

7.7 100 1.8 14.9 2 28.9 10 1.1 19.1 1 8.5 2

50 50 50 50 50 50 50 50 50 50 50 50

Experimental Peak Information of Al0.33Ni0.17Fe0.50 Experiment Peak No. hkl 2-Theta 1 2 3 4 5 6 7 8

001 101 111 200

9 021 10 11

112 202 122 130

16.90 25.49 30.77 37.70 44.18 52.47 57.45 61.21 68.00 77.04 81.41 -

I/Imax

Fe (at. %)

25.5 56.7 7.5 14.6 100 22.5 41.7 12.4 52.6 25.9 15.4 -

50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50

144 Calculated Peak Information of (Al 0.33 Fe 0.17) β (Ni 0.20Fe 0.30) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

8.09E-01 1.02E+01 1.86E-01 1.52E+00 2.08E-01 2.95E+00 1.02E+00 1.20E-01 1.95E+00 1.10E-01 8.69E-01 2.13E-01

7.9 100 1.8 14.9 2 28.9 10 1.2 19.2 1.1 8.5 2.1

47 47 47 47 47 47 47 47 47 47 47 47

Calculated Peak Information of (Al 0.33 Fe 0.17) β (Ni 0.27Fe 0.23) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

8.67E-01 1.04E+01 2.02E-01 1.55E+00 2.27E-01 3.01E+00 1.04E+00 1.32E-01 1.99E+00 1.19E-01 8.86E-01 2.31E-01

8.4 100 1.9 14.9 2.2 29 10.1 1.3 19.2 1.2 8.5 2.2

40 40 40 40 40 40 40 40 40 40 40 40

145 Calculated Peak Information of (Al 0.33 Fe 0.17) β (Ni 0.30Fe 0.20) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

8.93E-01 1.05E+01 2.09E-01 1.56E+00 2.35E-01 3.04E+00 1.05E+00 1.37E-01 2.01E+00 1.24E-01 8.94E-01 2.39E-01

8.5 100 2 14.9 2.2 29 10.1 1.3 19.2 1.2 8.5 2.3

37 37 37 37 37 37 37 37 37 37 37 37

Calculated Peak Information of (Al 0.33 Fe 0.17) β (Ni 0.37Fe 0.13) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

9.55E-01 1.07E+01 2.26E-01 1.59E+00 2.55E-01 3.10E+00 1.08E+00 1.49E-01 2.05E+00 1.34E-01 9.11E-01 2.58E-01

9 100 2.1 15 2.4 29.1 10.1 1.4 19.2 1.3 8.5 2.4

30 30 30 30 30 30 30 30 30 30 30 30

146 Calculated Peak Information of (Al 0.33 Fe 0.17) β (Ni 0.40Fe 0.10) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

9.82E-01 1.07E+01 2.33E-01 1.61E+00 2.64E-01 3.12E+00 1.08E+00 1.54E-01 2.07E+00 1.39E-01 9.18E-01 2.66E-01

9.1 100 2.2 15 2.5 29.1 10.1 1.4 19.2 1.3 8.5 2.5

27 27 27 27 27 27 27 27 27 27 27 27

Calculated Peak Information of (Al 0.33 Fe 0.17) β (Ni 0.45Fe 0.05) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

1.03E+00 1.09E+01 2.46E-01 1.63E+00 2.80E-01 3.17E+00 1.10E+00 1.63E-01 2.10E+00 1.47E-01 9.30E-01 2.80E-01

9.4 100 2.3 15 2.6 29.1 10.1 1.5 19.3 1.3 8.6 2.6

22 22 22 22 22 22 22 22 22 22 22 22

147 Experimental Peak Information of Al0.33Ni 0.45Fe0.22 Experiment Peak No. hkl 2-Theta 1 2 001 3 4 5 6 7

8

101 111 200 021 112 202 122 130

16.75 25.49 34.99 37.70 44.48 52.47 57.45 81.71 -

I/Imax

Fe (at. %)

12.1 12.1 29.1 7.82 100 13.4 8.6 11.3 -

22 22 22 22 22 22 22 22 22 22 22 22 22 22

Calculated Peak Information of (Al 0.33 Fe 0.17) β (Ni 0.47Fe 0.03) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

1.05E+00 1.09E+01 2.51E-01 1.64E+00 2.86E-01 3.19E+00 1.11E+00 1.66E-01 2.11E+00 1.50E-01 9.35E-01 2.86E-01

9.6 100 2.3 15 2.6 29.2 10.1 1.5 19.3 1.4 8.6 2.6

20 20 20 20 20 20 20 20 20 20 20 20

148 Calculated Peak Information of (Al 0.33 Fe 0.17) β (Ni 0.50) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

1.07E+00 1.10E+01 2.58E-01 1.65E+00 2.95E-01 3.21E+00 1.12E+00 1.72E-01 2.12E+00 1.55E-01 9.43E-01 2.95E-01

9.8 100 2.3 15 2.7 29.2 10.1 1.6 19.3 1.4 8.6 2.7

17 17 17 17 17 17 17 17 17 17 17 17

Experimental Peak Information of Al0.33Ni 0.50Fe0.17 Experiment Peak No. hkl 2-Theta 1 001 2 3 4 5 6 7 8

101 111 200 021 112 202 122 130

25.53 35.11 37.70 44.39 52.46 57.48 66.45 68.12 -

I/Imax

Fe (at. %)

19.3 7.7 6.7 39.3 100 4.7 5.0 4.4 -

17 17 17 17 17 17 17 17 17 17 17 17 17 17

149 Calculated Peak Information of (Al 0.33 Ni 0.17) β (Ni 0.50) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

9.19E-01 1.15E+01 2.16E-01 1.73E+00 2.44E-01 3.37E+00 1.17E+00 1.42E-01 2.23E+00 1.28E-01 9.86E-01 2.47E-01

8 100 1.9 15.1 2.1 29.3 10.2 1.2 19.4 1.1 8.6 2.1

0 0 0 0 0 0 0 0 0 0 0 0

Calculated Peak Information of (Al 0.40 Fe 0.10) β (Fe 0.50) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

9.58E-01 8.80E+00 2.13E-01 1.31E+00 2.32E-01 2.55E+00 8.84E-01 1.34E-01 1.69E+00 1.23E-01 7.52E-01 2.44E-01

10.9 100 2.4 14.9 2.6 28.9 10 1.5 19.2 1.4 8.5 2.8

60 60 60 60 60 60 60 60 60 60 60 60

150 Calculated Peak Information of (Al 0.40 Fe 0.10) β (Ni 0.10Fe 0.40) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

1.05E+00 9.05E+00 2.37E-01 1.35E+00 2.61E-01 2.63E+00 9.12E-01 1.51E-01 1.74E+00 1.38E-01 7.74E-01 2.72E-01

11.6 100 2.6 14.9 2.9 29 10.1 1.7 19.2 1.5 8.6 3

50 50 50 50 50 50 50 50 50 50 50 50

Experimental Peak Information of Al0.40Ni 0.10Fe0.50 Experiment Peak No. hkl 2-Theta 1 2 3 4 5

001 101 111 200 021 112 202 122 130

30.77 44.18 57.45 64.23 81.41 -

I/Imax

Fe (at. %)

8.4 100 29.9 5.4 8.8 -

50 50 50 50 50 50 50 50 50

151 Calculated Peak Information of (Al 0.40 Fe 0.10) β (Ni 0.20Fe 0.30) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

1.15E+00 9.31E+00 2.63E-01 1.39E+00 2.91E-01 2.71E+00 9.41E-01 1.69E-01 1.79E+00 1.54E-01 7.97E-01 3.00E-01

12.3 100 2.8 15 3.1 29.1 10.1 1.8 19.3 1.7 8.6 3.2

40 40 40 40 40 40 40 40 40 40 40 40

Experimental Peak Information of Al0.40Ni 0.20Fe0.40 Experiment Peak No. hkl 2-Theta 1 2 3 4 5

001 101 111 200 021 112 202 122 130

30.95 44.28 64.40 81.66 98.09 -

I/Imax

Fe (at. %)

10.7 100 4.9 10.7 3.8 -

40 40 40 40 40 40 40 40 40

152 Calculated Peak Information of (Al 0.40 Fe 0.10) β (Ni 0.30Fe 0.20) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

1.25E+00 9.56E+00 2.89E-01 1.43E+00 3.24E-01 2.79E+00 9.70E-01 1.88E-01 1.85E+00 1.71E-01 8.20E-01 3.31E-01

13 100 3 15 3.4 29.2 10.1 2 19.3 1.8 8.6 3.5

30 30 30 30 30 30 30 30 30 30 30 30

Experimental Peak Information of Al0.40Ni 0.30Fe0.30 Experiment Peak No. hkl 2-Theta 1 2 3 4 5 6 7

001 101 111 200 021 112 202 122 130

30.95 44.40 55.23 64.64 81.66 98.21 115.95

I/Imax

Fe (at. %)

7.5 100 3.6 4.2 9.0 2.7 3.0

30 30 30 30 30 30 30 30 30

153 Calculated Peak Information of (Al 0.40 Fe 0.10) β (Ni 0.40Fe 0.10) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

1.35E+00 9.82E+00 3.18E-01 1.48E+00 3.58E-01 2.88E+00 9.99E-01 2.08E-01 1.90E+00 1.88E-01 8.44E-01 3.63E-01

13.7 100 3.2 15 3.6 29.3 10.2 2.1 19.4 1.9 8.6 3.7

20 20 20 20 20 20 20 20 20 20 20 20

Experimental Peak Information of Al0.40Ni 0.40Fe0.20 Experiment Peak No. hkl 2-Theta 1 2 3 4 5 6 7

001 101 111 200 021 112 202 122 130

31.07 44.40 55.23 64.52 81.78 98.45 116.66 -

I/Imax

Fe (at. %)

8.9 100 2.2 3.8 7.5 2.5 2.2 -

20 20 20 20 20 20 20 20 20

154 Calculated Peak Information of (Al 0.40 Fe 0.10) β (Ni 0.50) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

1.46E+00 1.01E+01 3.47E-01 1.52E+00 3.94E-01 2.96E+00 1.03E+00 2.29E-01 1.96E+00 2.07E-01 8.67E-01 3.96E-01

14.5 100 3.4 15.1 3.9 29.4 10.2 2.3 19.4 2 8.6 3.9

10 10 10 10 10 10 10 10 10 10 10 10

Experimental Peak Information of Al0.40Ni 0.50Fe0.10 Experiment Peak No. hkl 2-Theta 1 2 3 4 5

001 101 111 200 021 112 202 122 130

31.19 44.52 55.47 66.54 81.90 -

I/Imax 6.7 100 3.0 6.0 6.0 -

Fe (at. %) 10 10 10 10 10 10 10 10 10 10

155 Calculated Peak Information of (Al 0.40 Ni 0.10) β (Ni 0.50) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

1.35E+00 1.04E+01 3.18E-01 1.56E+00 3.58E-01 3.05E+00 1.06E+00 2.08E-01 2.02E+00 1.88E-01 8.92E-01 3.63E-01

13 100 3.1 15.1 3.5 29.5 10.2 2 19.5 1.8 8.6 3.5

0 0 0 0 0 0 0 0 0 0 0 0

Calculated Peak Information of (Al 0.50) β (Fe 0.50) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

1.50E+00 7.64E+00 3.32E-01 1.14E+00 3.62E-01 2.23E+00 7.76E-01 2.09E-01 1.48E+00 1.93E-01 6.57E-01 3.81E-01

19.6 100 4.4 15 4.7 29.2 10.2 2.7 19.4 2.5 8.6 5

50 50 50 50 50 50 50 50 50 50 50 50

156 Calculated Peak Information of (Al 0.50) β (Ni 0.10Fe 0.40) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

1.61E+00 7.87E+00 3.63E-01 1.18E+00 3.98E-01 2.31E+00 8.02E-01 2.31E-01 1.53E+00 2.11E-01 6.78E-01 4.16E-01

20.5 100 4.6 15 5.1 29.3 10.2 2.9 19.4 2.7 8.6 5.3

40 40 40 40 40 40 40 40 40 40 40 40

Calculated Peak Information of (Al 0.50) β (Ni 0.20Fe 0.30) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

1.73E+00 8.10E+00 3.94E-01 1.22E+00 4.36E-01 2.39E+00 8.29E-01 2.53E-01 1.58E+00 2.31E-01 6.99E-01 4.51E-01

21.3 100 4.9 15.1 5.4 29.4 10.2 3.1 19.5 2.8 8.6 5.6

30 30 30 30 30 30 30 30 30 30 30 30

157 Calculated Peak Information of (Al 0.50) β (Ni 0.30Fe 0.20) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

1.85E+00 8.34E+00 4.27E-01 1.26E+00 4.75E-01 2.46E+00 8.56E-01 2.76E-01 1.63E+00 2.51E-01 7.21E-01 4.88E-01

22.2 100 5.1 15.1 5.7 29.5 10.3 3.3 19.5 3 8.6 5.9

20 20 20 20 20 20 20 20 20 20 20 20

Calculated Peak Information of (Al 0.50) β (Ni 0.40Fe 0.10) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

1.98E+00 8.59E+00 4.61E-01 1.30E+00 5.17E-01 2.54E+00 8.84E-01 3.00E-01 1.68E+00 2.72E-01 7.43E-01 5.27E-01

23 100 5.4 15.1 6 29.6 10.3 3.5 19.6 3.2 8.6 6.1

10 10 10 10 10 10 10 10 10 10 10 10

158 Calculated Peak Information of (Al 0.50) β (Ni 0.50) α Peak No. hkl 1 2 3 4 5 6 8 9 10 11 12 13

001 101 111 200 021 112 202 122 130 131 222 203

D-spacing

2-Theta

Intensity

I/Imax

Fe (at. %)

2.8500 2.0153 1.6455 1.4250 1.2746 1.1635 1.0076 0.9500 0.9013 0.8593 0.8227 0.7905

31.36 44.94 55.82 65.44 74.36 82.91 99.71 108.35 117.44 127.37 138.85 154.04

2.11E+00 8.83E+00 4.96E-01 1.34E+00 5.59E-01 2.63E+00 9.12E-01 3.25E-01 1.73E+00 2.94E-01 7.65E-01 5.67E-01

23.9 100 5.6 15.2 6.3 29.7 10.3 3.7 19.6 3.3 8.7 6.4

0 0 0 0 0 0 0 0 0 0 0 0

159

APPENDIX D CROSS PLATFORM MIEDEMA’S SEMI-EMPIRICAL CALCULATION PROGRAM IN HTML AND JAVASCRIPT LANGUAGE

160

 

Miedema's semi-empirical calculation for enthalpy of alloys

 

 

---

 

Binary system: 

 

164

 

  Solute Ag Al As Au B Ba Be Bi C Ca Cd Ce4+ Ce3+ Co Cr Cs Cu Dy

165 Er Eu2+ Eu3+ Fe Ga Gd Ge H Hf Hg Ho In Ir K La Li Lu Mg Mn Mo N Na Nb

166 Nd Ni Os P Pb Pd Pm Pr Pt Pu Rb Re Rh Ru Sb Sc Si Sm Sn Sr Ta Tb Tc

167 Th Ti Tl Tm U V W Y Yb2+ Yb3+ Zn Zr mole Solvent Ag Al As Au B Ba Be

168 Bi C Ca Cd Ce4+ Ce3+ Co Cr Cs Cu Dy Er Eu2+ Eu3+ Fe Ga Gd Ge H Hf Hg Ho In

169 Ir K La Li Lu Mg Mn Mo N Na Nb Nd Ni Os P Pb Pd Pm Pr Pt Pu Rb Re

170 Rh Ru Sb Sc Si Sm Sn Sr Ta Tb Tc Th Ti Tl Tm U V W Y Yb2+ Yb3+ Zn Zr

171 mole      

 Interfacial energy:

binary alloy delta H =  kJ/mole

 

---

Ternary system: 

 

 

Element A Ag Al As

172 Au B Ba Be Bi C Ca Cd Ce4+ Ce3+ Co Cr Cs Cu Dy Er Eu2+ Eu3+ Fe Ga Gd Ge H

173 Hf Hg Ho In Ir K La Li Lu Mg Mn Mo N Na Nb Nd Ni Os P Pb Pd Pm Pr

174 Pt Pu Rb Re Rh Ru Sb Sc Si Sm Sn Sr Ta Tb Tc Th Ti Tl Tm U V W Y

175 Yb2+ Yb3+ Zn Zr mole Element B Ag Al As Au B Ba Be Bi C Ca Cd Ce4+ Ce3+ Co Cr

176 Cs Cu Dy Er Eu2+ Eu3+ Fe Ga Gd Ge H Hf Hg Ho In Ir K La Li Lu Mg Mn Mo

177 N Na Nb Nd Ni Os P Pb Pd Pm Pr Pt Pu Rb Re Rh Ru Sb Sc Si Sm Sn Sr

178 Ta Tb Tc Th Ti Tl Tm U V W Y Yb2+ Yb3+ Zn Zr mole    

Element C Ag Al As

179 Au B Ba Be Bi C Ca Cd Ce4+ Ce3+ Co Cr Cs Cu Dy Er Eu2+ Eu3+ Fe Ga Gd Ge H

180 Hf Hg Ho In Ir K La Li Lu Mg Mn Mo N Na Nb Nd Ni Os P Pb Pd Pm Pr

181 Pt Pu Rb Re Rh Ru Sb Sc Si Sm Sn Sr Ta Tb Tc Th Ti Tl Tm U V W Y

182 Yb2+ Yb3+ Zn Zr mole

  Interfacial energy:  A (solute) in B (solvent) :

 A (solute) in C (solvent) :

 &; B (solute) in C (solvent) :  

         

ternary alloy delta H =  kJ/mole       

  

---

Empirical approximation of ternary alloy enthalpy from three binary alloy enthalpies

183

 

formation enthalpy of A-B =    kJ/mole         Amount :   A= mole

  B-C =   B= mole    

  A-C =    kJ/mole  C= mole

 

formation enthalpy of A-B-C =   kJ/mole  (Toop's method 1965)

     kJ/mole  (Kohler's method 1960)

184

     kJ/mole  (bonnier's method)

 

 

 

 

---

Black Color  -----  Solvent element

Blue Color -------- Solute element

Interfacial energy can be obtained by this Table which X-Axis is Solvent and Y-axis is Solute; 

185

 

186

APPENDIX E CROSS PLATFORM MOLAR RATIO TO WEIGHT RATIO CONVERTOR IN HTML AND JANASCRIPT LANGUAGE

187

Mole Ratio to Weight Ratio convertor for sample preparation

---

 

190 style="LINE-HEIGHT: 100%; MARGIN-BOTTOM: 3px; MARGIN-TOP: 3px">Step 1: Choose elements

Step 2: Input mole ratio

Step 3: Input desired total sample weight

Step 4: Click "Calculate"

 

The numbers shown in the "Element weight" row are the weight required for

each element to meet the desired total sample weight.

191

 

 

   Element A Ac Ag Al Am Ar As At Au B Ba Be Bh Bi Bk

192 Br C Ca Cd Ce Cf Cl Cm Co Cr Cs Cu Db Dy Er Es Eu F Fe Fm Fr Ga Gd

193 Ge H He Hf < Hg Ho Hs I In Ir K Kr La Li Lr Lu Md Mg Mn Mo Mt N Na

194 Nb Nd Ne Ni No Np O Os P Pa Pb Pd Pm Po Pr Pt Pu Ra Rb Re Rf Rh Rn

195 Ru S Sb Sc Se Sg Si Sm Sn Sr Ta Tb Tc Te Th Ti Tl Tm U Uub Uun Uuu V

196 W Xe Y Yb Zn Zr     Element B Ac Ag Al Am Ar As At Au B Ba Be Bh Bi Bk Br

197 C Ca Cd Ce Cf Cl Cm Co Cr Cs Cu Db Dy Er Es Eu F Fe Fm Fr Ga Gd Ge

198 H He Hf < Hg Ho Hs I In Ir K Kr La Li Lr Lu Md Mg Mn Mo Mt N Na Nb

199 Nd Ne Ni No Np O Os P Pa Pb Pd Pm Po Pr Pt Pu Ra Rb Re Rf Rh Rn Ru

200 S Sb Sc Se Sg Si Sm Sn Sr Ta Tb Tc Te Th Ti Tl Tm U Uub Uun Uuu V W

201 Xe Y Yb Zn Zr     Element C Ac Ag Al Am Ar As At Au B Ba Be Bh Bi Bk Br

202 C Ca Cd Ce Cf Cl Cm Co Cr Cs Cu Db Dy Er Es Eu F Fe Fm Fr Ga Gd Ge

203 H He Hf < Hg Ho Hs I In Ir K Kr La Li Lr Lu Md Mg Mn Mo Mt N Na Nb

204 Nd Ne Ni No Np O Os P Pa Pb Pd Pm Po Pr Pt Pu Ra Rb Re Rf Rh Rn Ru

205 S Sb Sc Se Sg Si Sm Sn Sr Ta Tb Tc Te Th Ti Tl Tm U Uub Uun Uuu V W

206 Xe Y Yb Zn Zr     Element D Ac Ag Al Am Ar As At Au B Ba Be Bh Bi Bk Br

207 C Ca Cd Ce Cf Cl Cm Co Cr Cs Cu Db Dy Er Es Eu F Fe Fm Fr Ga Gd Ge

208 H He Hf < Hg Ho Hs I In Ir K Kr La Li Lr Lu Md Mg Mn Mo Mt N Na Nb

209 Nd Ne Ni No Np O Os P Pa Pb Pd Pm Po Pr Pt Pu Ra Rb Re Rf Rh Rn Ru

210 S Sb Sc Se Sg Si Sm Sn Sr Ta Tb Tc Te Th Ti Tl Tm U Uub Uun Uuu V W

211 Xe Y Yb Zn Zr

Mole ratio     =        mole      mole         mole       mole

 

Desired total sample weight =     (arbitrary unit)

212 style="LINE-HEIGHT: 100%; MARGIN-BOTTOM: 2px; MARGIN-TOP: 2px"> 

weight of Paper =

 

 

Molecular weight =          

 

Weight ratio        =          
213 size=6>     :           :           :      

 

Element weight    =                                                  

---

214 style="LINE-HEIGHT: 100%; MARGIN-BOTTOM: 2px; MARGIN-TOP: 2px">Cumulated weight for sample preparation

 

paper + A             ;          =         

paper +A+ B             ;   =   

paper + A+ B + C         =   

paper + A+ B + C + D 

215 =   

---

2001/10/23

Any suggestion, comments, bug reports, please send to [email protected]

216

APPENDIX F CROSS PLATFORM WEIGHT RATIO TO MOLAR RATIO CONVERTOR IN HTML AND JANASCRIPT LANGUAGE

217

219 size=5>Weight Ratio to Mole Ratio convertor for sample preparation

---

 

Step 1: Choose elements

Step 2: Input weight ratio

Step 3: Click "Calculate"

 

 

 

220 Element A Ac Ag Al Am Ar As At Au B Ba Be Bh Bi Bk Br C Ca Cd Ce Cf Cl Cm

221 Co Cr Cs Cu Db Dy Er Es Eu F Fe Fm Fr Ga Gd Ge H He Hf < Hg Ho Hs I

222 In Ir K Kr La Li Lr Lu Md Mg Mn Mo Mt N Na Nb Nd Ne Ni No Np O Os

223 P Pa Pb Pd Pm Po Pr Pt Pu Ra Rb Re Rf Rh Rn Ru S Sb Sc Se Sg Si Sm

224 Sn Sr Ta Tb Tc Te Th Ti Tl Tm U Uub Uun Uuu V W Xe Y Yb Zn Zr    

225 Element B Ac Ag Al Am Ar As At Au B Ba Be Bh Bi Bk Br C Ca Cd Ce Cf Cl Cm

226 Co Cr Cs Cu Db Dy Er Es Eu F Fe Fm Fr Ga Gd Ge H He Hf < Hg Ho Hs I

227 In Ir K Kr La Li Lr Lu Md Mg Mn Mo Mt N Na Nb Nd Ne Ni No Np O Os

228 P Pa Pb Pd Pm Po Pr Pt Pu Ra Rb Re Rf Rh Rn Ru S Sb Sc Se Sg Si Sm

229 Sn Sr Ta Tb Tc Te Th Ti Tl Tm U Uub Uun Uuu V W Xe Y Yb Zn Zr    

230 Element C Ac Ag Al Am Ar As At Au B Ba Be Bh Bi Bk Br C Ca Cd Ce Cf Cl Cm

231 Co Cr Cs Cu Db Dy Er Es Eu F Fe Fm Fr Ga Gd Ge H He Hf < Hg Ho Hs I

232 In Ir K Kr La Li Lr Lu Md Mg Mn Mo Mt N Na Nb Nd Ne Ni No Np O Os

233 P Pa Pb Pd Pm Po Pr Pt Pu Ra Rb Re Rf Rh Rn Ru S Sb Sc Se Sg Si Sm

234 Sn Sr Ta Tb Tc Te Th Ti Tl Tm U Uub Uun Uuu V W Xe Y Yb Zn Zr    

235 Element D Ac Ag Al Am Ar As At Au B Ba Be Bh Bi Bk Br C Ca Cd Ce Cf Cl Cm

236 Co Cr Cs Cu Db Dy Er Es Eu F Fe Fm Fr Ga Gd Ge H He Hf < Hg Ho Hs I

237 In Ir K Kr La Li Lr Lu Md Mg Mn Mo Mt N Na Nb Nd Ne Ni No Np O Os

238 P Pa Pb Pd Pm Po Pr Pt Pu Ra Rb Re Rf Rh Rn Ru S Sb Sc Se Sg Si Sm

239 Sn Sr Ta Tb Tc Te Th Ti Tl Tm U Uub Uun Uuu V W Xe Y Yb Zn Zr

240 style="LINE-HEIGHT: 100%; MARGIN-BOTTOM: 3px; MARGIN-TOP: 3px">Weight ratio     =            :             :              :       

 

 

 

241 style="LINE-HEIGHT: 100%; MARGIN-BOTTOM: 2px; MARGIN-TOP: 2px">Molecular weight =          

 

Mole ratio           =           %     :     %      :       %   :       %          &nbs p;      (total 100%)

 

---

242

2002/10/28

Any suggestion, comments, bug reports, please send to [email protected]

243

APPENDIX G CROSS PLATFORM ENTHALPY OF FORMATION CALCULATOR FOR DIRECT SYNTHESIS CALORIMETER IN HTML AND JAVASCRIPT LANGUAGE

244

Enthalpy of Formation Calculator for Direct Synthesis Calorimeter

---

 

Step 1: Input Molecular weight and Correction factor

Step 2: Input Sample weight and Heat effect (counts)

249 style="LINE-HEIGHT: 100%; MARGIN-BOTTOM: 3px; MARGIN-TOP: 3px">Step 3: Click Check Box to select samples to be considered in the average enthalpy

Step 4: Click "Calculate"

 

molecular weight=  (counts/Joule)

 

    sample weight(g)&; mmol(milli mole  heat effect (counts)  heat effect (Joule)  delta-H  (kJ/mole)  check box

1)  

250     & nbsp;   

2)       &   

3)   & nbsp; & nbsp; & nbsp; & nbsp;

4) & nbsp; & nbsp; & nbsp;

251 & nbsp; & nbsp;

5) & nbsp; & nbsp; & nbsp; & nbsp; & nbsp;

6) & nbsp; & nbsp; & nbsp; & nbsp; & nbsp;

7) & nbsp; & nbsp; & nbsp;  

252  

8)   & nbsp; & nbsp; & nbsp; & nbsp;

 

& nbsp; enthalpy of formation =  ?/font>      (kJ/mole)

---

2002/10/29

Any suggestion, comments, bug reports, please send to [email protected]

253

APPENDIX H CROSS PLATFORM ENTHAPY MEASUREMENT ERROR CALCULATOR FOR DIRECT SYNTHESIS CALORIMETER IN HTML AND JAVASCRIPT LANGUAGE

254

255

Error Calculation

---

 

 delta H of copper at several temperature

 

1300K& nbsp; 27.756 kJ/mol

1357K (Solid)    29.610 kJ/mol

1357K (Liquid)  42.664 kJ/mol

256 style="LINE-HEIGHT: 100%; MARGIN-BOTTOM: 3px; MARGIN-TOP: 3px">1400K  44.082 kJ/mol  

1500K& nbsp; 47.346 kJ/mol 

 

calorimeter temperature   = (degree C)    calibration error =  %

reaction experiment error = (kJ/mole)& nbsp; heat content error = (kJ/mole)

 

Note: 

257 style="LINE-HEIGHT: 100%; MARGIN-BOTTOM: 3px; MARGIN-TOP: 3px">1) The calculation can be applied for calorimeter temperature higher than 1357K

2) delta H (kJ/mol)=0.0327 * temperature (K) - 1.7372 (between 1357K liguid phase and 1500K), R=1 

 

& nbsp;

 

Total error =    (kJ/mole)

---

2002/10/29

Any suggestion, comments, bug reports, please send to [email protected]

258

APPENDIX I HIGH-TEMPERATURE DATA FOR CONDENSED PHASE Cu

259 High-Temperature Data for Condensed Phase Cu

T(K) 298.15 400 500 600 700 800 900 1000 1100 1200 1300 1356.55(s) 1356.55(l) 1400 1500 1600 1700 1800 1900 2000 2200 2400 2500 2600 2700 2800 2836 2900

Cp Cal/mole/K 5.840 6.036 6.192 6.328 6.451 6.570 6.703 6.850 7.046 7.296 7.687 7.970 7.80 7.80 7.80 7.80 7.80 7.80 (7.80) (7.80) (7.80) (7.80) (7.80) (7.80) (7.80) (7.80) (7.80) (7.80)

Tm= 1356.55(±0.2)

Condensed Phase ST-Sst HT-Hst Cal/mole Cal/mole/K 0 0.000 605 1.745 1217 3.109 1834 4.251 2482 5.236 3133 6.105 3797 6.886 4475 7.600 5169 8.262 5886 8.886 6634 9.484 7077 9.817 10197 12.117 10536 12.363 11316 12.902 12096 13.405 12876 13.878 13656 14.324 (14436) (14.745) (15216) (15.145) (16776) (15.889) (18336) (16.568) (19116) (16.886) (19896) (17.192) (20676) (17.486) (21456) (17.770) (21737) (17.869) (22236) (18.044)

∆Hm=3120(±200)

-(GT-Hst)/T Cal/mol/K 7.923 8.155 8.598 9.102 9.613 10.111 10.509 11.049 11.486 11.904 12.304 12.524 12.524 12.761 13.281 13.768 14.227 14.660 (15.071) (15.461) (16.187) (16.851) (17.163) (17.463) (17.752) (18.030) (18.127) (18.299)

∆Sm=2.300(±0.15)

260 High-Temperature Data for Gas Phase Cu T(K) 298.15 400 500 600 700 800 900 1000 1100 1200 1300 1356.55(s) 1356.55(l) 1400 1500 1600 1700 1800 1900 2000 2200 2400 2500 2600 2700 2800 2836 2900

Cp Cal/mole/K 4.968 4.968 4.968 4.968 4.968 4.968 4.968 4.968 4.969 4.970 4.972 4.975 4.975 4.977 4.985 4.997 5.016 5.041 5.074 5.116 5.229 5.379 5.468 5.564 5.668 5.777 5.818 5.892

Gas Phase, Cu(g) ST-Sst HT-Hst Cal/mole Cal/mole/K 0 0.000 506 1.460 1003 2.569 1500 3.474 1996 4.240 2493 4.904 2990 5.489 3487 6.012 3983 6.486 4480 6.918 4977 7.316 4977 7.524 5259 7.524 5475 7.684 5973 8.010 6472 8.350 6973 8.654 7475 8.941 7981 9.214 8490 9.476 9524 9.968 10584 10.429 11127 10.651 11678 10.867 12240 11.079 12812 11.287 13021 11.361 13396 11.492

-(GT-Hst)/T Cal/mol/K 39.742 39.938 40.306 40.718 41.131 41.530 41.909 42.268 42.607 42.927 43.229 43.390 43.390 43.516 43.770 44.047 44.294 44.530 44.756 44.973 45.381 45.762 45.943 46.117 46.288 46.454 46.512 46.615

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