Local lattice dynamics in the Mg _0.5Al _0.5B ₂ superconductor

We have studied temperature evolution of the local as well as the average crystal structure of MgB ₂ and Mg _0.5Al _0.5B ₂ using real-space atomic pair distribution function (PDF) measured by high resolution neutron powder diffraction in a wide temperature range of T=10-600 K. The mean square relative displacements (MSRD) of atomic B-B, B-Mg (B-Al) pairs are compared with mean-square displacements (MSD) to calculate atomic correlations. In spite of the enhanced atomic disorder in Mg _0.5Al _0.5B ₂, where the boron-boron, and boron-magnesium pair motions are found to be small, we find that the same atomic correlations in MgB ₂ assume even slightly lower values and remain nearly constant in a wide temperature range of 0-600 K. This anomalous behavior and its physical interpretation provoke new questions on our understanding to the local lattice dynamics in this material.