为了更好地理解L12、D022和D023结构HfAl3的相对稳定性和键合特征，采用第一性原理计算了L12、D022和D023结构HfAl3的形成焓、电子结构和热力学性质。结果表明：平衡晶格参数与形成焓的计算结果与实验结果一致，不同结构的HfAl3稳定性大小为D023>D022>L12；态密度、电荷与键布局分析结果表明D023为最稳定结构；声子计算得到的热力学性质与温度的关系表明，D023结构的、熵和自由能随温度变化比L12和D022结构要快得多；L12、D022和 D023结构HfAl3的德拜温度分别为399、407和416 K；HfAl3的体积热膨胀系数在低温时成倍增加，而在高温时线性增加。
To better understand the relative stability and bonding characteristics of the L12, D022 and D023 structures for HfAl3, the formation enthalpies, electronic structures and thermodynamics properties were investigated by first-principles calculations. The agreement of calculated equilibrium lattice parameters and formation enthalpies with experimental results indicates the reliability of this work. The order of structural stability is D023>D022>L12. The results of densities of states, atomic Mulliken charge and bond population support the best structural stability for D023 structure. Variations of thermodynamic properties with temperature were predicted via phonon frequencies calculation. The enthalpy, entropy, free energy of D023 structure change more quickly than those of the other two structures. The Debye temperatures of L12, D022 and D023 structures are 399, 407 and 416 K, respectively. The volume thermal expansions for HfAl3 increase exponentially at the low temperature, whereas the thermal expansion coefficients increase linearly at the high temperature.
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