Carbon Diffusion in Austenite: Computer Simulation and Theoretical Analysis

1. Introduction Carbon interstitial diffusion in austenite (γ-Fe) has been studied experimentally and analytically for many years. Two experimental studies have been made of carbon diffusion in austenite at low carbon contents. One is a measurement of the carbon chemical or intrinsic diffusion coefficient at 1075 K, 1124 K and 1273 K, and as a function of carbon content [1]; the other is a measurement of the tracer carbon diffusion coefficient at the single temperature 1273 K as a function of carbon content [2]. These data demonstrate that both the carbon tracer and chemical diffusion coefficients increase with carbon content. The data have been analyzed on many occasions with two different diffusion models. The first is the well-known interacting lattice gas model in which nearest neighbour pair interactions are supposed between the carbon atoms and an inter–site transition rate based on those interactions is formulated; see, for example, [3]. Repulsive interactions between the carbon atoms are required in order to make quantitative contact with the diffusion data. A difficulty with the lattice gas model is one of uniquely describing 'rotational jumps' (a second atom making a rotational jump from one nearest neighbour site to another of a given atom) in the f.c.c. lattice when simple inter–site transition probabilities are used. In the second model [4] (which is appropriate only at very low carbon content) it is supposed that the interstitials can diffuse only as isolated atoms or as bound nearest neighbour pairs. Because this model is based on a specification of fundamental jump frequencies it is a more general starting point for a diffusion kinetics analysis than the first, which started with effective interactions from which jump frequencies can be derived. In this second model, four atom – vacant site exchange frequencies are explicitly specified. These are: an atom – vacant site exchange frequency for jumps of isolated interstitial atoms, a rotational atom – vacant site frequency of one atom about the other when the pair of interstitial atoms are first nearest neighbours, a dissociative exchange frequency of a first nearest neighbour pair and the frequency of the reverse jump (associative) to form a pair. All other interstitial jumps are assumed in this model to occur with the same frequency as for jumps of isolated interstitial atoms. The increase in diffusion with carbon content could be ascribed to a higher mobility of pairs than isolated carbon atoms. The most important …