Quasi-one-dimensional model of pretransitional soft mode behavior
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INTRODUCTION
THEORIES of displacive phase transformations, developed during the last fifty years, have appeared independently in 'physical' and 'metallurgical' camps, and include electronic, thermodynamic, and critical dynamics of many body systems in the former, and crystallographic and metallurgical aspects of the structural change in the latter. The developments include geometric models, ~-5 soliton models,6'7'8 phenomenological theories, 9'~°'n and a modem soft mode lattice-variant-shear-theory (LVST) 12-16which reconciles both camps by combining lattice dynamical fluctuations and soft modes in many body systems with crystallographic and metallurgical aspects of the structural change. In this theory the martensitic transformation is shown to be onedimensional in origin because this is energetically and mechanistically the most effective way to transform the lattice in bulk crystals; this behavior is generally independent of the dimensionality of other physical properties and shows why cooperative phenomena in widely different materials give rise to similar displacive and critical transformation behavior. The idea of the soft mode came originally from suggestions by Anderson ~7and Cochran ~8that the phase transition in certain ferroelectrics might result from an instability of one of the normal vibrational modes of the lattice. Since then it has been applied to a wide range of materials. In Cochran's theory, demonstrated for ionic crystals, there are two contributions to the phonon frequency which are of opposite sign and tend to cancel each other. One is the short range repulsive force between ions and the other a contribution from the long range Coulomb forces. Their temperature dependence leads to a cancellation of the effective force constant and to the formation of a soft transverse optical phonon whose frequency ~0, ~ 0 as T ~ To. While this model could account for soft optical modes and the spontaneous polarization in polar transitions, it does S. MENDELSON is Adjunct Professor, The City University of New York, New York, NY 10031. This paper is based on a presentation made in the symposium "Pretransformation Behavior Related to Displacive Transformations in Alloys," presented at the 1986 annual AIME meeting in New Orleans, March 2-6, 1986, under the auspices of the ASM-MSD Structures Committee. METALLURGICALTRANSACTIONS A
not explain soft acoustic modes in nonpolar transitions which drive martensitic transformations. It also fails to account for other soft mode behavior; in particular it does not account for the narrow component centered at zero frequency transfer (the central peak) and exhibiting critical divergence, found in a wide range of materials; ~9the modem LVST predicts both responses. The soft mode criterion 14 has been well established in the 'physical' camp for ferroelectrics, ferromagnetics, A15 superconductors, and other compounds, 2°-23 but until recently the 'metallurgical' camp has largely ignored it. The normal inertia that a successful phenomenological theory generates is one fact
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