第一性原理结合晶格动力学研究Ti，Zr和Hf中温度驱动的$α$到$β$相变
Temperature driven $α$ to $β$ phase-transformation in Ti, Zr and Hf from first principles theory combined with lattice dynamics
摘要：
晶格动力学方法用于预测晶体中的相变通常处理谐波声子谱，因此不适用于其中一个竞争晶体结构在谐波近似下不稳定的重要情况，例如Ti，Zr和Hf中的hcp到bcc马氏体相变中涉及的bcc结构。在这里，我们提出了一个表达式的自由能，不遭受这样的缺点，我们表明自洽的{ \it从头计算}晶格动力学计算（SCAILD），的临界温度的hcp bcc相转变的Ti，Zr和Hf，可以有效地计算从两个阶段之间的自由能差。这开辟了定量研究的可能性，从第一原理理论，温度诱导的相变。
英文摘要：
Lattice dynamical methods used to predict phase transformations in crystals typically deal with harmonic phonon spectra and are therefore not applicable in important situations where one of the competing crystal structures is unstable in the harmonic approximation, such as the bcc structure involved in the hcp to bcc martensitic phase transformation in Ti, Zr and Hf. Here we present an expression for the free energy that does not suffer from such shortcomings, and we show by self consistent {\it ab initio} lattice dynamical calculations (SCAILD), that the critical temperature for the hcp to bcc phase transformation in Ti, Zr and Hf, can be effectively calculated from the free energy difference between the two phases. This opens up the possibility to study quantitatively, from first principles theory, temperature induced phase transitions.
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