Materials Science Forum Vols. 461-464 (2004) pp. 147-152 online at http://www.scientific.net © (2004) Trans Tech Publications, Switzerland

Computer Simulation of Morphology Evolution of Oxide Scales during Oxidation S. Zhu1, Y. Xiong2, F. Zhang3, Y. Teng3, J. Zhang3, F. Wang3 and W. Wu3 1

State Key Laboratory for Corrosion and Protection, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China, [email protected] 2 State Key Laboratory for Corrosion and Protection, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China, [email protected] 3 State Key Laboratory for Corrosion and Protection, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China

Keywords: Morphology evolution, oxide scale, oxidation, computer simulation

Abstract. We proposed a phenomenological model for the morphology evolution of oxide scales thermally growing on metals and alloys during oxidation. This model is based on two well-known experimental facts: (1) the growth rates of the crystalline facets of oxide might differ from each other; (2) the nucleation density of oxide might vary from system to system of alloy/oxide. A twodimensional computer simulation was formulated. The simulations predicted the formation of equiaxial, needle-like, stump-like and flower-like morphology of oxide scales on alloys. The simulation results showed that equiaxial oxide scales formed when the nucleation rate was high and the growth rates of facets did not differ too much from each other, while needle-like scales formed when the growth rates of a pair of facets was much higher than those of other facets. It was also shown that the stump-like scales usually accompanied the flower-like ones when parts of facets grew at high rates. The numerical results were in good agreement with the morphologies of oxide scales on several sputtered CoCrAlY alloys. Introduction Thermal growth rates of oxide films on most metals and alloys at high temperature depend strongly upon the transportation rates of reactants via short-circuit diffusion paths, e.g. grain boundaries. In other words, the microstructures of oxide scales have great impact on the growth rates of scales. Therefore, it p is necessary to predict the microstructures of oxide scales in order to predict accurately the growth rates of such scales. Computer simulations are particularly useful and important for better understanding of modes and mechanisms of film growth. In the last decades, many models have been developed which are either completely stochastic or completely deterministic. Mean field rate equations (RE's) are a set of coupled ordinary differential equations (ODE's)[1,2]. This method has been successful in deducing microscopic parameters such as diffusion constants, adsorption and binding energies from comparison with experimental measurements. However, these equations contain no explicit spatial information, and thus do not readily yield information on surface morphology. Continuum models based on partial differential equations (PDE's) are appropriate mainly at large time and length scales.[3,4] By construction, features on the atomic scale are neglected, so they are poorly suited to describing growth on this scale. Atomistic models explicitly take into account the stochastic nature of each microscopic process that may occur during nucleation and growth of thin films. They are typically implemented in the form of molecular dynamics (MD)[5] or kinetic Monte Carlo (KMC)[6] simulations. MD simulations are very useful for identifying relevant microscopic processes, such as the detailed steps during nucleation. KMC simulations, on the other hand, have been used successfully to study qualitative, and in limited cases, quantitative, behavior of growth. But time and size limitations make them unfeasible for studying growth on technologically relevant time and length scales.[7] In this paper, a novel phenomenological model based on crystalline grain growth will be proposed for predicting the morphology evolution of oxide scales formed on metals and alloys at

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high temperature in oxidizing environments. Computer simulations of the formation of equiaxial, needle-like, stump-like and flower-like oxide scales will be performed. The simulated twodimensional morphologies will be compared with the Scanning Electronic Microscopic images of oxide films on several sputtered CoCrAlY alloys, which had the same chemical compositions and different microstructures. Modeling If the growth of oxide films on metals at high temperature is predominated by mass transportation through the growing film via diffusion of cations or anions, the growth rates of the films follow a power law, M s = kst ,

(1)

where M is a measurable value, e.g. the thickness of oxide film or mass gain of the specimen, t is the elapsed time, s and ks are constants dependent upon the oxidizing metals and the oxidation conditions. For a parabolic growth, s = 2 . The proposed model is based on two well-known experimental facts: (1) the growth rates of the crystalline facets of oxide might differ from each other; (2) the nucleation density of oxide might vary from system to system of alloy/oxide. Assume the oxide film is composed of crystalline grains. A grain is represented by a polyhedron. Each facet of the polyhedron may be assigned a distinct growth rate. The oxide scales grow at each step in the following manner: (1) Each facet of an oxide grain, if and only if any facets of other grains do not block it, grows at a rate of ∆h = α

k s ∆t , sr s −1

(2)

where ∆h is the increased thickness in the normal direction, r is the distance from the facet center to the oxide/alloy interface, α is a presumed factor for this facet; (2) The measurable, X, is calculated by X = ∑ Xi , i

(3)

where Xi is the measurable of the ith grain; (3) The number of new oxide nuclei is calculated by comparing the X in step (3) and the M determined by the power law Equ. (1); (4) New oxide nuclei, if any, are deployed at random sites of the oxidation front, i.e. the oxide/gas interface. Computer Simulation Method We formulated a two-dimensional simulation of the above model. A grain is represented by a dodecagon. The segments of the dodecagon represent facets of the crystalline grain. Parabolic growth is assumed, i.e. the mass gain of the oxide scale is proportional to the oxidation time. This relationship is described by: As = ni k s ∆t ,

(4)

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where A is the areas of the oxide scale, ni is the count of time step ∆t . At time ni ∆t , the increment of area of an outward growing oxide scale is

∆A =

k s ∆t . sA

(5)

Set the width and height of the oxide scale w and h , respectively. For outward growth, the average of increment of height of the scale is

∆h =

k s ∆t . sw s h

(6)

By comparing Equ. (2) and (6), and let s = 2 , we have

α≈

1 . w2

(7)

In the calculation, we set α = β / w 2 , where β = 0.01 ~ 1.0 since lateral growth of the dodecagons is allowed in the simulation. Now let us consider how to express the nucleation number ( γ ) at time ni ∆t . The number of new oxide nuclei is defined as

γi ≈

ni k s ∆t − ∑ Bi a

,

(8)

where Bi is the area of the ith dodecagon, a is the area of a nucleus. In the calculation, we set ∆q = k p ∆t . Results and Discussions

Fig. 1 shows the influence of choice of ∆q = k p ∆t on the morphology evolution of equiaxed growth. The larger the ∆q is, the higher the nucleation rate is, according to Equ. 8, because nucleation only occurs at a discrete step ∆q . One can see in Fig. 1 that the finer grains correspond to larger ∆q . A grain keeps growing until all of its facets are blocked by other grains. If the nucleation density is higher, the free space for the lateral growth of grains will be smaller. And the total growth rate of the scale will slow down once the lateral growth terminates, because the total rate is the summation of growth rates of all the grains. Thus, new nuclei have to form on top of the scale in order to describe the overall growth rate according to Equ. 4.

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(a)

(b)

Fig. 1. Simulated equiaxed morphology.

(c) w = 3,

β i = 0.1, i = 1, K12 , (a)

∆q = 1 × 10 −2 , (b) ∆q = 5 × 10 −3 , (c). ∆q = 3 × 10 −3 . Fig. 2 shows a growth mode opposite to the mode shown in Fig. 1. This needle-like morphology occurred when a pair of facets grew much faster than all the other facets. The initial nucleation density was set to be high by setting a relatively larger ∆q . The consequential nucleation rate drops down quickly, however, because the very fast growth of parts of grains whose fast growth facets happen to be nearly normal to the surface is able to conserve Equ. 4. The formation of flower-like and stump-like morphology occurred when parts of the facets grew at larger rates than the others, as shown in Fig. 3. Actually, this mode of growth was very complex, the flower-like grains were accompanied by stump-like large and small grains.

Fig.

(a)

(b)

(c)

(d)

2. Simulated evolvement of needle-like ∆q = 1 × 10 −2 , β i = 1.6, i = 1; β i = 0.1, i ≠ 1 .

morphology.

w = 3,

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Fig. 3. Simulated mixed flower-like and stump-like morphology. ∆q = 1 × 10 −2 , w = 3 , β i = 0.4, i = 1,2,7,8; β i = 0.1, i ≠ 1,2,7,8 .

Comparing Fig. 1 and 2 with Fig. 4a and 4b , one can conclude that the simulated equiaxed scale shown in Fig. 1 and needle-like scale shown in Fig. 2 were in good agreement with the oxide scales shown in Fig. 4(a) and 4(b), respectively. Fig. 4a shows fine-grained α-Al2O3 scales. α-Al2O3 has close-packed hexagonal crystalline structure with space group R3 c (ITC number 167). αAl2O3 scales usually grow very much slower than other oxide scales, e.g. Cr2O3, because of its very low density of defects. θ-Al2O3 has monoclinic crystalline structure with space group C 2 / m (ITC number 12). θ-Al2O3 scales are non-protective to high temperature oxidation of alloys due to their porous morphology as shown in Fig. 2 and Fig. 4b. The flower- and stump-like α-Al2O3 shown in Fig. 4c formed on very small parts of a specimen prepared by normal-incidental sputtering deposition. The morphology of the main part of this specimen is that shown in Fig. 4a. The crystalline structures of the flower- and stump-like oxide grains were unknown, but EDAX showed they were alumina.

(a)

(b)

(c)

Fig. 4. Surface morphologies of oxide scales on magnetron sputtered CoCrAlY after 10 min oxidation in air at 1000 oC. (a) α-Al2O3 scale on CoCrAl by normal-incident deposition (α-Co solid solution, fcc, strong (110) texture). (b) θ-Al2O3 scale on CoCrAl by oblique-incident deposition (ε-Co solid solution, hcp, weak (100) texture). (c) Al2O3 scale on microstructure defects of CoCrAl by normal-incident deposition.

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Conclusions We proposed a phenomenological model for the morphology evolution of oxide scales thermally growing on metals and alloys during oxidation. The computer simulations of 2-dimensional growth predicted the evolution of equiaxial, needle-like, stump-like and flower-like morphology of oxide scales. The simulation results showed that equiaxial oxide scales formed when the nucleation rate was high and the growth rates of facets did not differ too much from each other, while needle-like scales formed when the growth rates of a pair of facets were much higher than those of other facets. It was also shown that the stump-like scales usually accompanied the flower-like ones when parts of facets grow at high rates. The numerical results were in good agreement with the morphologies of oxide scales on several sputtered CoCrAlY alloys. Acknowledgements This project is supported by the Hundred-Talent Project of the Chinese Academy of Sciences and by the High Technology Projects of China. References [1] G. Zinsmeister: Vacuum Vol. 16 (1966), p. 529 [2] S. Zhu, S. Yang, Y. Xiong, M. Li, S. Geng, C. Hu, F. Wang and W. Wu: Acta Metal. Sinica Vol 14 (2001), p. 544 [3] J. Villain: J. Phys. Vol. I1 (1991), p. 19 [4] J. Krug: Adv. Phys. Vol. 139 (1997), p. 46 [5] L. Zhou, S. Zhu: Scripta Mater. Vol. 47 (2002), p. 677 [6] K. A. Fichthorn and W. H. Weinberg: J. Chem. Phys. Vol. 95 (1991), p. 1090 [7] D. Frenkel, B. Smit: Understanding Molecular Simulations: From Algorithms to Applications (Academic Press, Boston 1996)