The methods for X-ray crystal orientation are rapidly evolving towards versatility, fewer goniometry measurements, automation, high accuracy and precision. One method that attracts a lot of attention is energy-dispersive X-ray diffraction (EDXRD) which is based on detecting reflections from crystallographic planes in a crystal at fixed angles of a parallel polychromatic X-ray incident beam. In theory, an EDXRD peak can move in a diffraction pattern as a function of a crystallographic plane d-spacing and its orientation relative to a fixed direction in space can change also. This is equivalent to the possibility of measuring the orientation of single crystals. The article provides a modeling for the EDXRD method whose main feature is the nonmoving crystal in the sense of traditional goniometry where the angle measurements of diffracting planes are a must. The article defines the equation of orientation for the method and shows the derivation in great detail. It is shown that the exact solutions of the equations can be obtained using the generalized reduced gradient method, a mathematical subroutine that is implemented in Excel software. The significance and scientific impact of the work are discussed along with the validated tested results.

中文翻译：

---

高对称晶体取向的能量色散 X 射线衍射建模

X 射线晶体取向方法正在迅速向多功能性、更少的测角测量、自动化、高精度和高精度发展。一种备受关注的方法是能量色散 X 射线衍射 (EDXRD)，该方法基于检测平行多色 X 射线入射光束在固定角度下晶体中晶面的反射。理论上，EDXRD 峰可以根据晶面在衍射图中移动d-间距及其相对于空间中固定方向的方向也可以改变。这相当于测量单晶取向的可能性。本文提供了 EDXRD 方法的建模，其主要特征是传统测角学意义上的非移动晶体，其中必须测量衍射平面的角度。该文章定义了该方法的取向方程并详细展示了推导过程。结果表明，可以使用广义降梯度法（一种在以下代码中实现的数学子程序）获得方程的精确解：Excel软件。讨论了这项工作的意义和科学影响以及经过验证的测试结果。