Micrometre-sized MgB2 crystals of varying quality, synthesized at low temperature and autogenous pressure, are compared using a combination of Raman and infra-red (IR) spectroscopy. These data, which include new peak positions in both spectroscopies for high quality MgB2, are interpreted using DFT calculations on phonon behaviour for symmetry-related structures. Raman and IR activity additional to that predicted by point group analyses of the P6/mmm symmetry are detected. These additional peaks, as well as the overall shapes of calculated phonon dispersion (PD) models are explained by assuming a double super-lattice, consistent with a lower symmetry structure for MgB2. A 2× super-lattice in the c-direction allows a simple correlation of the pair breaking energy and the superconducting gap by activation of corresponding acoustic frequencies. A consistent physical interpretation of these spectra is obtained when the position of a phonon anomaly defines a super-lattice modulation in the a-b plane.

We show that the well-known Kohn anomaly predicts Tc for ordered AlB2-type structures. We use ab initio density functional theory to calculate phonon dispersions for Mg1-xAlxB2 compositions and identify a phonon anomaly with magnitude that predicts experimental values of Tc for all x. Key features of these anomalies correlate with the electronic structure of Mg1-xAlxB2. This approach predicts Tc for other known AlB2-type structures as well as new compositions. We predict that Mg0.5Ba0.5B2 will show Tc = 63.6 ± 6.6 K. Other forms of the Mg1-xBaxB2 series will also be superconductors when successfully synthesised. Our calculations predict that the end-member composition, BaB2, is likely to show a Tc significantly higher than currently achieved by other diborides although an applied pressure ∼16 GPa may be required to stabilise the structure.

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