Interfacial Energy and Equilibrium Shape of B1 type Compound in Austenite

Introduction

The energy of partially coherent austenite/B1 type compound interface has been recognized as having both chemical and structural components. The structural energy arises from the presence of misfit dislocations at the interface, while the chemical energy is due to the composition difference across the interface. The present work calculates orientation dependence of the total interfacial energy and predicts equilibrium shape of B1 type compound in austenite.

Calculation of chemical interfacial energy

The chemical component of austenite (g)/ B1 type compound interfacial energy is calculated previously^[1] by nearest neighbor broken bond method. From the calculation, it is seen that in contrast to ordinary f.c.c./f.c.c. interfacial energy, an interface parallel to (111) has the largest energy among all planes. This is because the energy related with metal and non-metallic atom bond dominates the interfacial energy compared with that of metal-metal bond at the interface.

Calculation of structural interfacial energy

The relatively large misfit (~15% or more) at /B1 type compound interface nevertheless products significant structural interfacial energy. The misfit dislocation model^[2] is employed to study the structural energy, including using Bollmann's O-lattice theory to determine the dislocation structure of interphase boundaries between two fcc crystals of identical orientation, and calculating the structural energy of these interfaces from Hirth and Lothe's elastic dislocation energy equations, which describe the structural energy as the summation of self energy and interaction energy of dislocations. In this context, (110) plane has the largest structural energy due to high dislocation density as well as high out-of-plane component of Burgers vector.

Results and Discussion

The calculation was made for carbides and nitrides of Ti, V, Zr and Nb, respectively. Generally, /nitride interfacial energy is larger than /carbide and compounds of heavy atoms have larger interfacial energy with than that of light atoms. For all the compounds, the result indicates both chemical (calculate at 0K) and structural component contribute significantly to the total interfacial energy, although the latter is larger. Especially, anisotropy of chemical energy is much stronger than that of structural energy, which dominates the wulff construction and corresponding equilibrium shape of compounds in . As an example, the equilibrium shape of TiC cube-on-cube oriented with is shown in Fig. 1, which is somewhat like a cube (from chemical energy) with eight corners cut down to small facets(from structural energy).

Fig.1 (a) (110) section of the polar plot for /TiC interfacial energy with the Wulff construction, and (b) the corresponding three-dimension shape.

Reference

1. Z.-G. Yang and M. Enomoto: CAMP-ISIJ, Vol. 11(1998), 584
2. G. Spanos: Ph.D. Thesis, Carnegie-Mellon University, Pittsburgh, PA (1989)

Zhi-Gang Yang, Dept. of Materials Science, Ibaraki University, Nakanarusawa, Hitachi, Ibaraki,316 Japan

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