Qiu S L, Marcus P M
Department of Physics, Florida Atlantic University, Boca Raton, FL 33431-0991, USA.
J Phys Condens Matter. 2009 Oct 28;21(43):435403. doi: 10.1088/0953-8984/21/43/435403. Epub 2009 Oct 8.
Structures and properties of many of the phases of Ca under pressure are calculated from first principles by a systematic procedure that minimizes total energy E with respect to structure under the constraint of constant volume V. The minima of E are followed on successive sweeps of lattice parameters for 11 of 14 Bravais symmetries for one-atom-per-cell structures. The structures include the four orthorhombic phases. Also included are the hexagonal close-packed and cubic diamond phases with two atoms per primitive cell. No uniquely orthorhombic phases are found; all one-atom orthorhombic phases over a mega-bar pressure range are identical to higher-symmetry phases. The simple cubic phase is shown to be stable where it is the ground state. The number of distinct one-atom phases reduces to five plus the two two-atom phases. For each of these phases the Gibbs free energy at pressure p, G(p), is calculated for a non-vibrating lattice; the functions G(p) give the ground state at each p, the relative stabilities of all phases and the thermodynamic phase transition pressures for all phase transitions over a several-megabar range.
通过一种系统程序从第一性原理计算了处于压力下钙的许多相的结构和性质，该程序在恒定体积(V)的约束下，相对于结构使总能量(E)最小化。对于单原子晶胞结构的14种布拉维对称性中的11种，在晶格参数的连续扫描中追踪(E)的最小值。这些结构包括四个正交相。还包括每个原胞有两个原子的六方密堆积相和立方金刚石相。未发现唯一的正交相；在兆巴压力范围内，所有单原子正交相都与更高对称性的相相同。简单立方相在其为基态的地方被证明是稳定的。不同的单原子相的数量减少到五个加上两个双原子相。对于这些相中的每一个，计算了在压力(p)下非振动晶格的吉布斯自由能(G(p))；函数(G(p))给出了每个(p)下的基态、所有相的相对稳定性以及在几兆巴范围内所有相变的热力学相变压力。
