一种利用实验测量和数值计算确定3m点群晶体弹性系数的方法

An Alternative Method in Measurement of Elastic Constants of a Crystal with 3 m Symmetry

将实验测量与数值计算相结合确定低对称性晶体弹性系数的方法可以弥补常规方法测量时造成的弹性系数非对角元误差大的不足。本文将该方法由正交系晶体推广到了三方系 3m点群晶体 ,在数值计算中选取了目前公认的无约束最优化方法中最稳定的两种算法—单纯形法和BFGS法 ,并增加了弹性系数的约束条件 ,提高了方法的适应性和正确性。在此基础上 ,本文利用 3m点群晶体LiNbO3 和LiTaO3 的弹性劲度系数 [cij]和顺服系数 [sij]的实验数据对该方法进行了讨论及验证。结果表明这种方法对 3m点群晶体弹性系数非对角元的计算是可行的。另外 ,本文还对数值计算时 ,初值的选取和检验结果合理性等关键性问题进行了详细的讨论。

Combining numerical calculation and experimental measurement, an approach to measure the complete anisotropic elastic constants [ c_ ij ]([ s_ ij ]) can avoid the troublesome, error-prone determination of off-diagonal constants by the usual measurements along nonprincipal directions. In our present work, the approach is extended from mm 2 symmetry to 3 m symmetry. In order to improve the adaptability and the correctness of numerical calculation, two more stable unconstrained optimization algorithms-simplex and BFGS and the restrict conditions of elastic constants are applied. The elastic constants of LiNbO_3 and LiTaO_3 are used to test the approach, and the results are satisfied. Some important problems during numerical calculating such as the choice of initial values and reasonability of final values are also discussed.