Effect of phonon anomalies on the shear response of martensitic crystals.

The subject of martensitic phase transformation is one of considerable scientific as well as technological interest. Among the martensitic materials, the "shape-memory" alloys have received special attention. ' These alloys exhibit curious elastic behavior near the martensitic transformation temperature (M, ): They can be strained beyond the elastic limit in a reversible manner. In some cases, the return to the initial state occurs when the loading stress is released (pseudoelastic eA'ect) and in other cases the strain recovery is achieved by heating the sample (thermoelastic eft'ect). In many of these systems, partial softening of anomalous phonon modes has been reported as one approaches M, . However, the role of such premartensitic behavior in first-order displacive phase transitions remains controversial. To clarify this problem, we use a simple model to study the eAects of phonon anomalies and anharmonicity on the behavior of the parent phase under applied shear stress. We find that the anomalous phonon behavior is closely connected with the pseudoelastic and thermoelastic behavior of the parent crystals just above M, . ' Our results indicate that the anomalous elastic behavior observed in many martensitic systems is an intrinsic property of the parent crystal lattice near M„as opposed to usual materials in which the mechanical properties beyond the elastic limit are determined by dislocations and defects. We focused our attention on the Ni-Al alloys which are well-studied martensitic systems"' for which there exist recent detailed studies of anomalous phonon behavior in correlation with the martensitic transformation (see Fig. 1). As the temperature is lowered towards M„a dip appears in the dispersion curve near q = 016(1,1, 0)2 tr/.aAt the same time, quasielastic scattering can be detected which can be connected with electron-microscopy studies ' indicating the existence of a modulating strain in the host crystal. To model the elastic behavior of Ni-A1, we focus our attention on the shear-and-shuSe displacements of (110) planes in the lattice along the [110]direction: Such displacements are involved in the transformation from the B2 structure to close-packed (e.g. , 7R, 3R) structures. ' This degree of freedom also corresponds to atomic displacements for the anomalous [g(0] transverse-acoustic (TA) phonon branch. Thus, we view the crystal as a collection of rigid (110) planes interacting with each other through anharmonic interactions. The values of the interplanar force constants for small displacements are chosen to reproduce the dispersion of the TA phonon. Because of the sharp features introduced by the phonon anomalies, we found that it is necessary in some cases to include interactions up to eight neighboring planes to get a good fit to the experimental phonon curves. Since we expect large shear displacements to occur in a martensitic transformation, we have to include anharmonic eff'ects in our model. This is done by imposing the condition of translation periodicity on each of the interplanar springs. Thus, we represent the total energy of the crystal as a sum of the eA'ective interaction between