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Recently, a high-pressure x-ray diffraction study was performed on liquid germanium (l-Ge͒, in order to clarify the change in the local structure of a liquid under pressure. Inspired by this work, we perform tightbinding ͑TB͒ molecular dynamics simulations for l-Ge at seven different pressures. To this end, we construct a new TB scheme by modifying a previously reported nonorthogonal TB scheme. By explicitly taking into account the nonorthogonality of the atomic wave functions, we obtain a TB scheme which is accurate at both low and high pressures. The pair distribution function g(r), static structure factor S(Q), and bond-angle distribution function g (3) (r c ,) are calculated, along with other quantities. The calculated g(r) and S(Q) are in excellent agreement with the above-mentioned experiments, which confirms the validity of our TB scheme. From a detailed analysis of atomic configurations, we elucidate the change in the local structure of l-Ge under pressure. We find that bonding in l-Ge is interpreted as a mixture of covalent and metallic bonding, and that as pressure increases, the ratio of covalent bonds decreases, although they still exist at pressures as high as 24.0 GPa. We further find that, by dividing g (3) (r c ,) into covalent and isotropic parts, the covalent contribution to the local structure of l-Ge changes from a ''disordered'' ␤-Sn structure in the low-pressure region to a ''pure'' ␤-Sn structure in the high-pressure region.

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We theoretically investigate the piezoelectric properties of Mg–Nb codoped wurtzite AlN by first-principles calculations and find the following two points. First, doping induces a remarkable softening of elastic constants, especially the diagonal component along the c-axis. This results in the increased piezoelectric strain constant d33, which is about 4.3 times larger than that of wurtzite AlN. Second, the c-axis lattice length increases up to the dopant concentration of around 60 at. %, and then decreases. These features are in excellent agreement with the experimental results previously reported.

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