分别建立了有序结构r'相亚点阵中原子置换行为引起的体应变最小和不同密排方向上原子尺寸失配度最小的目标函数, 并给出了两个亚点阵(顶角与面心)之间元素含量平衡分配及其范围的约束条件。以单晶合金CMSX--2和SRR99为对象, 使用Powell和Simplex复合优化算法, 分别计算了r'相单位晶胞两个亚点阵中的元素浓度(原子位置浓度)和亚点阵分数(单位晶胞内顶角和面心原子各占百分数); 此外, 建立了已知亚点阵元素浓度计算r'相点阵常数的算式, 并将其分别用于Ni3Al和上述两种合金r'相的点阵常数计算.将上述计算结果与用原子探针场离子显微分析导出的元素出现概率法所得亚点阵元素浓度进行了比较, 并将计算与报道所得r'相点阵常数进行了比较,吻合性良好。从而, 给出了一种只需知道有序结构相成分, 即可测算其单位晶胞中亚点阵元素浓度及点阵常数的新方法。
Objective functions on minimizing the atomic volume elastic strain and the atomic size misfit in close--packed directions due to the atomic substitution in sublattices of r’ phase are established, respectively. Constrain conditions on equilibrium partition of alloying elements and on their concentration range in sublattices of r’ phase are correspondingly built up. Using superalloys CMSX--2 and SRR99 as objects investigated and adopting a compound optimization calculation method with the Powell and the Simplex algorithms, the elemental concentration and the site fraction of the two sublattices can be calculated. In addition, a calculation formula on lattice parameter of r’phase closely associated with the elemental concentration and with the site occupancy of the sublattices is derived. All the calculated results by use of the present methods show quite good accordance with the reported values. The method proposed can predict the elemental concentration in sublattices and the lattice parameter of r’phase when the chemical composition of the r’ phase investigated is known.
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