Theory of the bcc-to-9Rstructural phase transformation of Li

Abstract

We present a Landau theory of the martensitic structural phase transformation undergone by bcc Li into the 9R phase. We propose that the transition occurs via incomplete softening of the ((1/3 1) /3 0) ${\Sigma }_4$ phonon. Even though this branch does not soften to zero frequency (or even close to zero frequency), because the system is strongly anharmonic, a first-order transition can occur. Coupled to this distortion are the two homogeneous strains possessing the soft Zener elastic constant 1/2($c_{11}$-$c_{12}$). These strains shear and stretch the (110) planes. As a result of our studies, we propose that Li may transform into any member of a family of displacement patterns, the 9R stacking sequence corresponding to one solution within this family. In addition, our theory describes the stacking faults that are known to occur in terms of (i) domain-wall structures, which model twin faults, and (ii) a multiple domain-wall solution of the double sine-Gordon equation (an equation that describes the phase-modulation equilibrium condition around defects), which models deformation faults. We also discuss the possible extension of this theory to other β-cubic structures that undergo martensitic phase transformations, viz., the other alkali metals, and the TiNi(Fe) alloy system.