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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。
For the allotopic Ru problem, we assume that Ru may have the structure fcc, hcp, bcc, bct, and then calculate the ground state energies, lattice constants and elastic coefficient matrix of these structures by density functional method. The cohesive energy of each structure is hcp fcc> bcc> bct, and the ratio is 1.000: 0.995: 0.967: 0.873. Calculated the elastic modulus matrix of each structure, and calculated body elastic modulus, Young’s modulus, shear modulus, Poisson’s ratio and other parameters of 0 K by Voigt theory, and found that bcc and bct are plastic crystals , hcp and fcc as brittle crystals, the conclusions of the hcp structure consistent with the experiment. For the first time, based on the criterion of crystal mechanics stability, only bcc structure is unstable at 0 K, and other structures are stable. From the thermodynamic point of view, the stability of the structure was studied. The free energy curve of Ru under normal pressure was calculated by the Debye quasi-harmonic theory and the formula and the mechanical performance data. The Ru The stability is: hcp> fcc> bcc> bct, Ru stability from 2343 K to melting point 2523 K is: hcp> bcc> fcc> bct. Comparing the available data with the calculated results, it can be confirmed that only hcp structure Ru exists under the Ru melting point under atmospheric pressure, which solves the problem of allotopic Ru.