Clusters in carbon martensite: Thermodynamics and kinetics
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INTRODUCTION
NUMEROUS experimental investigations have shown that mechanical, electric, and other properties of alloys depend not only on the structure of the crystal lattice but also to a considerable extent on the relative position of the atoms in the lattice. The study of configuration states of solid solutions and the kinetics of ordering, clustering, and spinodal decomposition is of great interest. Numerous systematic investigations of short-range order in carbon martensite by ME and NMR have revealed distinct deviations of carbon distribution in the solution from a statistical distribution.[1] This is interpreted as being generated by two-particle clusters with distances C-C(1/2)^111&, C-C^110&, and C-C^100&. Some satellite Mo¨ssbauer lines by Genin[1] are interpreted as generated by a three-particle cluster with distances ab(1/2)^111&, b-c(1/2)^111&, and a-c^110&. In previous work,[2] based on experimentally verified values of the concentration expansion tensor, two-particle C-C potentials have been calculated. From these calculations, it appears that the existence of very strongly bonded additional twoparticle cluster of C-C^002& type are possible. Furthermore, in such a system, favorable conditions exist for atoms to form larger clusters, consisting of four or even five particles. We have also shown[2] that under special conditions, the carbon superlattice in a carbon martensite can also be L. DA BROWSKI, Associate Professor, is with the Institute of Atomic Energy, ‘05-400 Otwock-Swierk, Poland. Manuscript submitted June 23, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS A
formed. These results have qualitative rather than quantitative character because the effects associated with longrange ordering are not taken into account. Although the short-range order plays a major role,[3] the full image of ordering can be obtained only when parameters of both long- and short-range order are simultaneously included in the calculations. The present article extends the concepts proposed in Reference 2. One of its aims is to obtain qualitative solutions. In the calculations, besides the long-range order interactions, the energy of the internal strains is also taken into account. In Section III, the system is analyzed in thermodynamical equilibrium conditions. The values of the equilibrium parameter of long-range ordering h are determined for two cases: when internal strains exist and when they are absent. The stability of the system is analyzed in the subsequent states of the local energy minimum. In the case of the substitional alloys, there is a good agreement between the experimental values of ordering parameters with those derived from the analysis based on the thermodynamic equilibrium models. We have already showed this agreement in the example of stoichiometric CuZn alloy.[5] However, there are some indications that the carbon martensite represents an example of strongly nonequilibrium alloy. The X-ray measurements showed that in freshly quenched martensite, the c/a ratio at room temperature decreases at a hig
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