Computer Simulation of the Diffusional Growth of Ternary Oxide Scales on Binary Alloys

Abstract

A computer solution is made of the equations for growth by ambipolar diffusion of metal of the ternary monoxide scales on Co-Fe and Co-Ni alloys. Computations demonstrate that the parabolic scaling rates and the compositional profiles in these scales calculated using independently obtained diffusional and thermodynamic properties of the solid phases in the alloy-oxide systems are in agreement with the experimental determinations. Results are analyzed for oxidation of Co-Fe containing up to 10 a/o Fe to (CoFe)O at 1473 K in oxygen at 10 ~ Po~ ~ 105 Pa and the oxidation of Co-Ni alloys containing up to 7 a/o Ni to (CoNi)O at 1373, 1473, and 1573 K in oxygen at 105 Pa. A ternary diffusion model was introduced by Wagner (1) to describe the growth of a solid solution scale on a binary alloy by parabolic kinetics and the cation distribution profiles in this scale. This model was expanded subsequently by Coates and Dalvi (2) and Whittle (3) to account for oxygen penetration into the alloy.Several investigators (4-17) have studied the suitability of Wagner's equations for describing scale growth on binary alloys by measuring cation distributions in the scales and comparing these results with theoretical profiles. In order to minimize computing time for evaluation of the nonlinear differential equations, alternate approximate expressions (14, 15) have been developed for calculating the reaction rate and cation profile in a scale. Although agreement has been obtained between the measured and calculated variables, the tests of the equations are incomplete either because of a failure to observe boundary conditions or because it is necessary to use results from the oxidation experiment in the computations. An extensive simulation was carried out recently by Bastow et aI. (16) to clarify the effect of each kinetic and thermodynamic parameter on the diffusion-controlled growth of these types of scales. More recently, Young et al. (17) have shown that a complete computer simulation of Wagner's equations capable of determining oxidation rates of the binary alloy using independently obtained diffusional and thermodynamic data provides a more rigorous description of binary alloy oxidation than suggested by the analyses in the earlier investigations.The purpose of this contribution is to determine the magnitude of the parabolic reaction kinetics, the oxygen activity and metal concentration profiles in the scales formed on Co-Fe and Co-Ni alloys using the ternary diffusion model in conjunction with independently determined diffusional and thermodynamic properties of the solid phases and, subsequently, to compare the predicted oxidation behavior with that determined experimentally. These two above alloys containing up to 10 atomic percent (a/o) Fe and 7.2 a/o Ni, respectively, exhibit parabolic growth of a solid solution scale without internal oxidation at elevated temperatures (18,19). Further, there is sufficient information on the diffusional and thermodynamic properties of the oxide and alloy phases for computer simulation of the ...

Oxidation of iron at 600 °C – experiments and simulations

“…Analytical equations describing the evolution of an external oxide scale on a binary alloy were first derived by Wagner [12]. Simulations of external oxide scale growth using independently assessed data have been performed by Narita et al [13] and Hallstr€ om et al [14]. Calphad-type databases were used by Hallstr€ om et al who simulated growth of Cr 2 O 3 on pure Cr with the Dictra software [15] using a moving phase boundary approach.…”

Numerical Model for Oxide Scale Growth with Explicit Treatment of Vacancy Fluxes

“…For boundary conditions, we chose fixed equilibrium vacancy concentrations at the interfaces. Notice that at the surface, the concentrations of the equilibrium vacancies in the oxide can be directly related to a fixed oxygen partial pressure [26]. Last, we have applied the two severe cases for behaviour of cationic incoming vacancies at the interface : in the first case vacancies are all eliminated at the interface, in the second case, all incoming vacancies are injected in the metal (RHS of Eq.…”

Strategies for High-Temperature Corrosion Simulations of Fe-Based Alloys Using the Calphad Approach: Part I

“…Modelling of oxide scale growth traces its roots to the analytical work by Wagner. [9] An early example of a computer simulation using independently assessed diffusion coefficients is the work by Narita et al [10] A number of research have used Calphad approach to investigate oxidation in different types of materials. For example Krupp et al [11] used Chemapp software [12] to model diffusion-based oxidation in Ni-based superalloys and Cr-containing steels.…”