• Talbot, Peter

Abstract

We have calculated the extent of the E<sub>2g</sub> phonon anomaly for Mg<sub>1−x</sub>M<sub>x</sub>B<sub>2</sub> where M = Sc, Ti, Cd and Ba for 0 < x < 1 using <i>ab initio</i> DFT models with the LDA and GGA functionals. Using superlattice models along the <i>c</i> axis to represent metal substitution in MgB<sub>2</sub>, we show that phonon dispersion (PD) plots vary significantly with x, in particular, the nature and extent of the phonon anomaly around the origin, <b>G</b>, of the reciprocal lattice. Measurement of this phonon anomaly along the <b>G-K</b> and <b>G-M</b> directions provides an estimate of the thermal energy, T<sub>δ</sub>, of the anomaly, which approximates experimentally determined T<sub>c</sub> within standard error for Sc and Ti substitution. We demonstrate that substitutions of Cd and Ba in MgB<sub>2</sub> show a higher calculated T<sub>δ</sub> than MgB<sub>2</sub> by more than 20 K. Syntheses of these Cd and Ba compositions are not extant and may not be possible given the limited solubility of metals in MgB<sub>2</sub>. Nevertheless, <i>ab initio</i> DFT models of phonon behaviour in AlB<sub>2</sub>–type structures provide an effective tool for prediction of physical properties and for design of new materials.

Topics

• dispersion
• density functional theory
• superconductivity
• superconductivity