Lattice dynamics of the high-temperature shape-memory alloy Nb-Ru

Nb-Ru is a high-temperature shape-memory alloy that undergoes a martensitic transformation from a parent cubic β-phase into a tetragonal β^′ phase at T_M∼900 °C. Measurements of the phonon dispersion curves on a single crystal show that the [110]-TA₂ phonon branch, corresponding in the q=0 limit to the elastic constant C^′=1∕2(C₁₁−C₁₂) has an anomalous temperature dependence. Nearly the entire branch softens with decreasing temperature as T_M is approached. The temperature dependence of the low-q phonon energies suggests that the elastic constants would approach 0 as T approaches T_M, indicating a second-order transition. No additional lattice modulation is observed in the cubic phase.