Abstract—

The K₄Ag₁₈Te₁₁, Tl₄Ag₁₈Te₁₁, and BaHg₁₁ cubic structures have been crystallographically analyzed within the study of the “symmetry–stability of crystalline materials” problem. The high symmetry of these structures is initiated by the local symmetry of templates, which are cuboctahedra composed of twelve Ag polyhedra around a Te anion (for the former two compounds) and twelve Hg polyhedra around a central Hg atom (for the latter compound). Similar cuboctahedra, consisting of K, Tl, and Ba cations, are formed in the second coordination sphere. The role of symmetry in the reduction of atomic degrees of freedom, which provides the structure stability, has been estimated. The qualitative stability criteria are formulated.

中文翻译：

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立方（Fm $$ \ bar {3} $$ m）结构类型K 4 Ag 18 Te 11和相关结构中原子构型的晶体学分析

摘要-

K ₄ Ag ₁₈ Te ₁₁，Tl ₄ Ag ₁₈ Te ₁₁和BaHg ₁₁在研究“晶体材料的对称性-稳定性”问题的过程中，对晶体的立方结构进行了晶体学分析。这些结构的高度对称性是由模板的局部对称性引发的，模板是由围绕Te阴离子的十二个Ag多面体（对于前两种化合物）和围绕中心Hg原子的十二个Hg多面体（对于后一种化合物）组成的八面体。在第二配位区域中形成了由K，Tl和Ba阳离子组成的类似八面体。据估计，对称性在降低原子自由度中的作用可提供结构稳定性。制定了定性稳定性标准。