Order-parameter coupling and strain relaxation behavior of Ti50Pd50−xCrx martensites

Abstract

A group theoretical model is proposed for linear/quadratic coupling between order parameters which arise from electronic and soft-mode instabilities in doped shape memory alloys, together with coupling to symmetry breaking shear strains. This model is tested by using resonant ultrasound spectroscopy (RUS) to follow the elastic and anelastic anomalies which accompany transitions from B2 to B19, 9R, and incommensurate structures in ${\mathrm{Ti}}_{50}{\mathrm{Pd}}_{50\ensuremath{-}x}{\mathrm{Cr}}_{x}$ alloy samples ($0\ensuremath{\le}x\ensuremath{\le}12$). The pure soft-mode transition gives rise to an incommensurate structure but without any associated changes in the shear modulus, implying that coupling with shear strains is weak. By way of contrast, the observed pattern of softening ahead of and stiffening below the martensitic transition is typical of pseudoproper ferroelastic behavior and confirms that there is strong bilinear coupling of the tetragonal shear strain to the order parameter associated with irrep ${\mathrm{\ensuremath{\Gamma}}}_{3}^{+}$ of the parent space group. The second order parameter has the symmetry properties of ${\mathrm{M}}_{5}^{\ensuremath{-}}$ in TiPd or of a point along the \ensuremath{\Sigma} line of the Brillouin zone for the 9R and incommensurate structures with high Cr contents. Comparison of shear modulus data for Cr-rich samples obtained by RUS at ${10}^{5}\ensuremath{-}{10}^{6}\phantom{\rule{0.16em}{0ex}}\mathrm{Hz}$ with previously reported Young's modulus data obtained for different samples by dynamical mechanical analysis at \ensuremath{\sim}0.1--10 Hz has not revealed the dispersion with frequency that would be expected for a glass transition governed by Vogel-Fulcher dynamics. The two techniques differ in the magnitude of effective applied stress, however, and differences in chemical homogeneity between samples or decomposition during high-temperature measurements might also be a factor.