Crystal structure and phonon softening in Ca$_3$Ir$_4$Sn${13}$
Résumé
We investigated the crystal structure and lattice excitations of the ternary intermetallic stannide Ca$_3$Ir$_4$Sn${13}$ using neutron and x-ray scattering techniques. For $T$ > $T*$ approximate to 38 K, the x-ray diffraction data can be satisfactorily refined using the space group Pm3n. Below T*, the crystal structure is modulated with a propagation vector of (q) over right arrow = (1/2,1/2,0). This may arise from a merohedral twinning in which three tetragonal domains overlap to mimic a higher symmetry, or from a doubling of the cubic unit cell. Neutron diffraction and neutron spectroscopy results show that the structural transition at $T*$ is of a second-order, and that it is well described by mean-field theory. Inelastic neutron scattering data point towards a displacive structural transition at T* arising from the softening of a low-energy phonon mode with an energy gap of Delta(120 K) = 1.05 meV. Using density functional theory, the soft phonon mode is identified as a "breathing" mode of the Sn$_{12}$ icosahedra and is consistent with the thermal ellipsoids of the Sn2 atoms found by single-crystal diffraction data.