Concentration-Dependent Carbon Diffusivity in Austenite
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TION
AN extensive literature extending from 1948 to 1997 exists on the concentration dependence of carbon diffusion in austenite. A review of this literature has been conducted to determine the most appropriate model for numerical simulations of carbon diffusion under the particular conditions of low-temperature carburization.[1–3] In the following, we assess these models in the chronological order in which they have been published.[4] To make the expressions as consistent as possible, all these models are presented in the form: ~C ¼ DC fðYC Þ; D
½1
where the concentration-dependent diffusion coefficient ~C of carbon is expressed as a product of the diffusion D coefficient DC of carbon at infinite carbon dilution and a function f of the carbon site fraction YC ¼
XC ; 1 XC
½2
where XC is the atomic fraction of carbon. This format allows ready use of the CALPHAD database to evaluate f(YC). We note that anomalous nitrogen depth profiles have been observed in stainless steels nitrided at relatively low temperatures and explained by a trapping model.[5–7] While a similar argument might be advanced for the anomalous carbon depth profiles found for austenitic stainless steel carburized at low temperatures,[1–4,8] it is more straightforward to explain these data by a concentration-dependent carbon diffusivity. We further XIAOTING GU, formerly Doctoral Student, with the Department of Materials Science and Engineering, Case Western Reserve University, Cleveland, OH 44106, is now Research Scientist with Atotech USA Inc., Cleveland, OH. Contact e-mail: [email protected]; [email protected] The late GARY M. MICHAL, Professor, formerly with the Department of Materials Science and Engineering, Case Western Reserve University, is now deceased. FRANK ERNST and ARTHUR H. HEUER, Professors, and HAROLD KAHN, Research Associate Professor, are with the Department of Materials Science and Engineering, Case Western Reserve University. Manuscript submitted September 1, 2013. Article published online May 23, 2014 3790—VOLUME 45A, AUGUST 2014
note that carbon diffusion under paraequilibrium conditions is of great current interest in the so-called third generation of advanced high strength steel (AHSS) using the Quench and Partition (Q and P) process.[9–12] This study was actually motivated by work from our group[1–4,8] on gas-phase low-temperature ‘‘paraequilibrium’’ carburization of AISI 316L stainless steel (Table I). Figure 1 shows a carbon concentration-depth profile after a 38-hour carburization experiment; the data cannot be readily fit using the standard complementary erf-function solution for constant diffusivity, because the diffusivity is a strong function of carbon concentration. We note that similar anomalous carbon depth profiles arise from low temperature plasma carburization of austenitic stainless steels.[13] In the next section, we discuss each model in detail; Table II summarizes the appropriate form of the models that have been put forward to explain the concentration dependence of carbon diffusivity in austenite. II.
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