金属钌同素异构体问题的第一性原理计算研究

First-Principle Investigation on Problem of Ruthenium Allotropic Phase Stability

针对Ru同素异构问题,先假定Ru可能结构为fcc,hcp,bcc,bct,而后用密度泛函方法计算这些结构的基态能量、晶格常数、弹性系数矩阵等参数。各结构内聚能为hcpfcc〉bcc〉bct,比值为：1.000∶0.995∶0.967∶0.873。计算得各结构弹性系数矩阵,用Voigt理论计算得0 K的体弹性模量、杨氏模量、剪切模量、泊松比等参量,结合塑脆判据发现bcc和bct是塑形晶体,hcp和fcc为脆性晶体,对hcp结构的结论与实验一致。基于晶体力学稳定性判据首次发现0 K下只有bcc结构是不稳定的,其他结构稳定。从热力学角度研究结构的稳定性,用德拜准简谐理论及公式,结合力学性能计算数据,计算了常压下各结构的Ru的自由能曲线,分析得到常压下0~2343 K内Ru稳定性是：hcp〉fcc〉bcc〉bct,2343 K至熔点2523 K内Ru稳定性是：hcp〉bcc〉fcc〉bct。比较已有数据和计算结果,可确定常压下在Ru熔点以下只有hcp结构Ru存在,解决了Ru的同素异构问题。

In order to solve the problem of ruthenium allotropic phase stability, firstly, the possible phase structures of ruthenium were assumed to be fcc, hcp, bcc and bct, and then lattice parameter, ground state energy and elastic coefficient matrix were calculated by density function theory for those phase structures. The calculation results of cohesive energy showed the order of hcp 〈 fcc 〈 bce 〈 bct, and agreed well with other calculation results. The calculation results of lattice constant were the same with experimental results. The calculation results of density was in the order of hcp 〉 fcc 〉 bcc 〉 bct, and the ratio was 1. 000： 0. 995： 0. 967： 0. 873. The important mechanical parameters under 0 K including elastic constants, bulk modulus, shear modulus and Poisson＇s ratio were all based on calculation results of elastic constants matrix by Voigt method. It was first found that only the bcc phase was unstable from phase stability criterion and calculation results at 0 K. Based on Debye-harmonic theory and many formulas, the thermodynamic stable order was hcp〉 fcc 〉 bcc 〉 bct from 0 to 2343 K, and that from 2343 K to melting point of ruthenium was hcp 〉 bcc 〉 fcc 〉 bct. The hcp structure was the most stable ruthenium structure under normal pressure, and this conclusion agreed with the present thermodynam- ic calculation results, and the problem of ruthenium allotropic phase stability was solved.