Numerical study of transverse lattice waves connected with martensitic transformation
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THE diffusionless structural transformation in materials like SrTiO 3 or quartz has been understood satisfactorily in terms of the soft phonon model? The soft phonon model in its original form is found inadequate to understand the nucleation process of the martensite. 2 It is accepted, however, that the transverse lattice wave is somehow involved in the nucleation process of the martensite since the famous proposal by Zener? The transverse lattice waves which propagate perpendicular to the close-packed atomic plane in the fcc lattice of (110) plane in the bcc lattice has the largest amplitude a m o n g the various modes of the lattice vibrations. This large amplitude transverse lattice wave is responsible for the diffuse streaks observed in m a n y metals, alloys, covalent crystals and alkali halide crystals? -6 These crystals which show diffuse streaks do not always transform martensitically. In the same vein, the presence of the transverse lattice wave with large amplitude does not always lead to the nucleation of the martensite. The question is what is the condition which makes the connection between the presence of the transverse lattice wave and the nucleation of the martensite. 2. A N H A R M O N I C M O D E L 2.1 Anharmonicity and Nucleation The importance of the a n h a r m o n i c i t y - - t h e higher order elastic constants--in the nucleation process of the TETSURO SUZUKI, formerly with Physics Department Yokohama City University, Yokohoma 236, Japan, is now with Institute of Applied Physics, University of Tsukuba, Sakura, Ibaraki 305, Japan. This paper is based on a presentation made at a symposium on "Pretransformation Phenomena, Fluctuations and Related Effects" held at the annual meeting of The Metallurgical Society of AIME, New Orleans, Louisiana, February 18-22, 1979, under the sponsorship of the Structures Activity, Materials Science Dwision, ASM. METALLURGICAL TRANSACTIONS A
martensite has been suggested. 7.8 Although the perturbation method has been established as a powerful method to treat such anharmonic properties as the thermal expansion and the temperature dependence of elastic constants, it is not adequate to attack the problem of nucleation, because the deformation strain involved is extremely large. Hence, the numerical approach is adopted to study the role of the anharmonicity in determining the behavior of the transverse lattice waves by use of a one-dimensional model of the crystal. 9,~~All the parameters in the model and also their temperature dependence are assumed as inputs to the model, which must be chosen so that they are consistent with the observed data of elastic constants and dispersion relationships of the transverse lattice waves.
2.2 Construction of Model The fcc lattice consists of the stacking of the closepacked atomic planes. Similarly, the bcc lattice consists of the stacking of the (110)-type atomic planes. The martensitic transformation is described as the transformation in the stacking of these atomic planes, as shown in Fig. 1. In order to complete the martensi
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