Neutron Scattering Study of the Lattice-Dynamical Phase Transition inNb3Sn

Neutron scattering experiments have been carried out on a single crystal of ${\mathrm{Nb}}_3$Sn through the lattice-dynamical phase transition at $T_m=45\mathrm{}$ °K. A small tetragonal lattice distortion, $\frac{a}{c}=1.0062\mathrm{}$ at 4 °K, was previously established by x-ray studies, but sublattice displacements below $T_m$ have remained undertermined. The present study reveals that the tetragonal phase exhibits new Bragg reflections, which are forbidden by symmetry in the cubic phase. From the intensity distribution among these new reflections, the structure was determined uniquely as $D_{4h}^9$ with Nb displacements from the special positions of 0.016(3) Å at 4 °K. Only the Nb sublattices shift, and in a pattern identical with the eigenvectors of the ${\Gamma }_{12}\mathrm{}(+)q=0\mathrm{}$ optic-phonon mode in the cubic phase. Such a mode is linearly coupled with the soft [110] shear acoustic mode. This linear coupling requires, and our measurements confirm, that the intensities of new Bragg peaks are proportional to ${(\frac{a}{c}-1)}^2$. An optic-phonon instability is not required to explain these internal displacements.