The modification of chemical composition to improve desired material parameters is an effective method in materials science and engineering. In this work, Ca_1-xSr_xF₂ solid solution is chosen as the subject. Nd³⁺ and Y³⁺ ions are used as dopants. We have found that spectral properties of Nd³⁺:Ca_1-xSr_xF₂ and Nd³⁺,Y³⁺:Ca_1-xSr_xF₂ crystals vary nonlinearly with the ‘x’. The X-ray diffraction (XRD) patterns and the density functional theory (DFT) calculations on Ca_1-xSr_xF₂ solid solutions have ruled out the influence of matrix crystals on spectral properties. The rare-earth monomer centers of C_4v or C_3v symmetry, and the high order clusters are modeled. The calculated results show, that thermodynamic stabilities of the centers vary nonlinearly. Temperature-dependent dielectric losses and the results of projected density of states (pDOS) calculations also show nonlinear dependency. The nonlinearly evolved local structures from cubic to square antiprism sublattice cause the nonlinear variation of spectral properties. The methodology of rare-earth induced nonlinear structural evolutions is then proposed, which is useful for exploring new materials.

中文翻译：

---

萤石固溶体晶体中稀土诱导的非线性结构演化

改变化学成分以改善所需的材料参数是材料科学与工程中的一种有效方法。在这项工作中，选择Ca _1-x Sr _x F ₂固溶体作为研究对象。Nd ³⁺和Y ³⁺离子用作掺杂剂。我们发现 Nd ³⁺ :Ca _1-x Sr _x F ₂和 Nd ³⁺ ,Y ³⁺ :Ca _1-x Sr _x F ₂晶体的光谱性质随 ' x'。X 射线衍射 (XRD) 图案和对 Ca _1-x Sr _x F ₂固溶体的密度泛函理论 (DFT) 计算排除了基质晶体对光谱特性的影响。C _4v或C _3v的稀土单体中心对称性，并对高阶簇进行建模。计算结果表明，中心的热力学稳定性呈非线性变化。与温度相关的介电损耗和投影状态密度 (pDOS) 计算的结果也显示出非线性相关性。从立方体到方形反棱镜亚晶格的非线性演化局部结构导致光谱特性的非线性变化。然后提出了稀土诱导非线性结构演化的方法，这对探索新材料很有用。