Department of Physics, Florida Atlantic University, Boca Raton, FL 33431-0991, USA.
J Phys Condens Matter. 2012 Jun 6;24(22):225501. doi: 10.1088/0953-8984/24/22/225501. Epub 2012 May 3.
The phase transition between the cubic diamond (cd) and beta-tin (β-Sn) phases of Si under pressure and the region of interaction of the two phases are studied by first-principles total energy calculations. For a non-vibrating crystal we determine the pressure of the thermodynamic phase transition p(t) = 96 kbar, the Gibbs free energy barrier at p(t) of ΔG = 19.6 mRyd/atom that stabilizes the phases against a phase transition and the finite pressure range in which both phases are stable. We show that the phases in that pressure range are completely described by three equilibrium lines of states along which the structure, the total energy E, the hydrostatic pressure p that would stabilize the structure and the values of G all vary. Two equilibrium lines describe the two phases (denoted the ph-eq line, ph is cd or β-Sn phase); a third line is a line of saddle points of G with respect to structure (denoted the sp-eq line) that forms a barrier of larger G against instability of the metastable ranges of the phase lines. An important conclusion is that the sp-eq line merges with the two ph-eq lines: one end of the sp-eq line merges with the cd-eq line at high pressure, the other end merges with the β-Sn-eq line at low pressure. The mergers end the barrier protecting the metastable ranges of the two ph-eq lines, hence the lines go unstable beyond the mergers. The mergers thus simplify the phase diagram by providing a natural termination to the stable parts of all metastable ranges of the ph-eq lines. Although 96 kbar is lower than the experimental transition pressure, we note that phonon pressure raises the observed transition pressure.
采用第一性原理总能量计算方法研究了 Si 在压力下从立方金刚石（cd）相到β-锡（β-Sn）相的相变以及两相的相互作用区域。对于非振动晶体，我们确定了热力学相变的压力 p(t) = 96 kbar，在 p(t) 处稳定相的吉布斯自由能势垒为 ΔG = 19.6 mRyd/atom，以及在该压力范围内两个相都稳定的有限压力范围。我们表明，在该压力范围内的相完全可以通过三条平衡状态线来描述，沿着这些线，结构、总能量 E、将稳定结构的静水压力 p 以及 G 的值都发生变化。两条平衡线描述了两个相（分别表示为 cd 或β-Sn 相的 ph-eq 线）；第三条线是 G 相对于结构的鞍点线（表示为 sp-eq 线），它形成了一个较大的 G 势垒，以抵抗相线的亚稳范围的不稳定性。一个重要的结论是，sp-eq 线与两条 ph-eq 线合并：sp-eq 线的一端在高压下与 cd-eq 线合并，另一端在低压下与β-Sn-eq 线合并。这些合并结束了保护亚稳范围的势垒，因此，两条线在合并后变得不稳定。这些合并通过为 ph-eq 线的所有亚稳范围的稳定部分提供自然终止，从而简化了相图。尽管 96 kbar 低于实验相变压力，但我们注意到声子压力会提高观察到的相变压力。
