点缺陷浓度对非化学计量比L12型结构的A13Sc弹性性能的影响

采用密度泛函理论与Wagner-Schottky热力学模型计算了金属间化合物L1₂-A1₃Sc中点缺陷浓度与温度、成分间的关系. 结果表明: 在考察的温度区间(T=300-1200 K), 理想化学计量比L1₂-A1₃Sc中的点缺陷主要为Al空位和Sc空位, 且缺陷浓度较低(在1200 K时仅约为10^-6). 当L1₂-A1₃Sc偏离化学计量比成分时, 富Al成分端的点缺陷主要为Al反位与Sc空位, 且两种缺陷的浓度相当; 富Sc成分端的点缺陷则主要为Sc反位. 利用超胞模型进一步计算了含点缺陷L1₂-A1₃Sc晶体的弹性常数, 并计算预测了点缺陷形式和浓度对其弹性性能的影响. 结果表明: 在理想化学计量比成分附近, 点缺陷的引入均会降低非化学计量比L1₂-Al₃Sc晶体的杨氏、剪切和体积弹性模量, 增加非化学计量比L1₂-Al₃Sc弹性性能的各向异性, 但是对其脆-韧性的影响不大.

Effects of point defect concentrations on elastic properties of off-stoichiometric L12-type A13Sc

Elastic properties and phase stabilities of L1₂-A1₃Sc precipitate phase in Al-Sc alloys have been topics of experimental and theoretical research over the past years. However, these properties of off-stoichiometric L1₂-A1₃Sc have not been investigated. Firstly, in combination with Wagner-Schottky model, the first-principles total energy calculations based on density functional theory are performed to study point defect concentrations of intermetallic L1₂-A1₃Sc each as a function of temperature and alloy composition. We calculate the point defect formation enthalpies and plot the point defect density curves of stoichiometric and off-stoichiometric L1₂-A1₃Sc at 1000 K. The results show that within the whole temperature range (300-1200 K), Al and Sc vacancies dominate on stoichiometric L1₂-A1₃Sc but with low concentrations (~10^-6 even at 1200 K); on the Al-rich side of off-stoichiometric L1₂-A1₃Sc, the Al anti-site and the Sc vacancy concentrations dominate, and their concentrations are comparable, however, on Sc-rich side of off-stoichiometric L1₂-A1₃Sc, the Sc anti-site defect dominates. Furthermore, the lattice constants and the elastic constants of stoichiometric and off-stoichiometric L1₂-A1₃Sc are calculated, and it is worth noting that 2×2×2 supercell models with a point defect are used for off-stoichiometric L1₂-A1₃Sc in the calculation. Then employing calculated elastic constants, the values of Young’s modulus, shear modulus, bulk modulus, anisotropic index, G/B ratio, Cauchy pressure, and Poisson ratio of stoichiometric and off-stoichiometric L1₂-A1₃Sc are computed. And lastly, combining these data with point defect concentrations of off-stoichiometric L1₂-A1₃Sc at 1000 K, the comprehensive effects of four point defects on elastic properties of L1₂-A1₃Sc are evaluated. The four point defects coexist in L1₂-A1₃Sc as we know from the calculations of equilibrium point defect density. The conclusions are as follows. 1) The point defects can cause off-stoichiometric L1₂-A1₃Sc lattice distortion. On the Sc-rich side, lattice constant appears to be an increasing tendency, from 4.105 Å to the biggest value of ~4.13 Å (~0.5% growth), while on the Al-rich side, it shows an opposite trend, from 4.105 Å to the smallest value of ~4.10 Å (~0.24% fall). Although there is the lattice distortion in off-stoichiometric L1₂-A1₃Sc, off-stoichiometric L1₂-A1₃Sc can still keep stable crystal structure for the value of x_Al in a range of 0.72-0.78. 2) The point defects also affect elastic constants of off-stoichiometric L1₂-A1₃Sc. Specifically, on the Sc-rich side, elastic constant c₁₁ decreases with the increase of deviation degree of stoichiometric ratio, and the maximal reduction is ~9% at x_Al = 0.72, while elastic constants c₁₂ and c₄₄ show the opposite variation trends, and the maximal increase is ~8% at x_Al = 0.72. On the Al-rich side, there are little changes for elastic constants c₁₁, c₁₂ and c₄₄. 3) The point defects obviously increase the elastic anisotropy of off-stoichiometric L1₂-A1₃Sc, and especially on the Sc-rich side, the notable increase is found, which jumps from 1.6×10^-6 to 0.04. 4) The values of Young’s modulus, shear modulus, and bulk modulus of off-stoichiometric L1₂-A1₃Sc decrease due to point defects, with the maximal reduction being 3%-4%. These elastic modules fall first rapidly and then slowly on the Sc-rich side, while they present approximately a linear downward trend on the Al-rich side. In addition, weak influences are exerted on brittleness and toughness of off-stoichiometric L1₂-A1₃Sc by the point defects, compared with the other elastic effects mentioned above.In summary, in the scope of x_Al = 0.72-0.78, the point defects can not only reduce Young’s modulus, shear modulus, and bulk modulus of off-stoichiometric L1₂-A1₃Sc, but also increase the anisotropies of the elastic properties of off-stoichiometric L1₂-A1₃Sc. However, the point defects have weak influences on the brittleness and toughness of off-stoichiometric L1₂-A1₃Sc.