Ba₃MgNb₂O₉ is a double perovskite niobate with a trigonal structure with space group D_3d³. Such a niobium‐based compound has a great potential for applications as microwave dielectrics in the telecommunication industry. In this work, we report the lattice dynamics calculation results using a Short‐Range Force Field Model and Density Functional Theory to represent the optical phonon modes at Γ‐point of the Brillouin zone. The classical method uses the nearest neighbor interactions through the interatomic force constants to describe the local order for Raman and infrared spectra. At the same time, density functional theory methods took into account two functionals (PBE and B3LYP) in order to provide the optical modes through second derivatives of the total energy. In both methods, theoretical optical modes are in good agreement with reported experimental data. The combination of both classical and quantum theoretical methods provided basis for a systematic discussion on the origin of the optical modes including the prediction of the dielectric tensor. We believe that this work presents useful information about the structural and vibrational characterization of Ba₃MgNb₂O₉ perovskite and possible targeting for its application as microwave dielectrics for the communication technology.

中文翻译：

---

1：2有序三角形Ba3MgNb2O9钙钛矿中的光学声子模式：经典方法和量子方法的协同作用

Ba ₃ MgNb ₂ O ₉是具有空间群D _{3 d} ³的三角形结构的双钙钛矿铌酸盐。这种铌基化合物在电信行业中作为微波电介质具有巨大的潜力。在这项工作中，我们使用短程力场模型和密度泛函理论报告晶格动力学计算结果，以表示布里渊区Γ点处的光学声子模。经典方法通过原子间力常数使用最邻近的相互作用来描述拉曼光谱和红外光谱的局部顺序。同时，密度泛函理论方法考虑了两个泛函和B3LYP），以便通过总能量的二阶导数提供光学模式。在这两种方法中，理论光学模式与报告的实验数据都非常吻合。古典和量子理论方法的结合为系统地讨论光学模式的起源（包括介电张量的预测）提供了基础。我们认为，这项工作提供了有关Ba ₃ MgNb ₂ O ₉钙钛矿的结构和振动特性的有用信息，以及可能将其用作通信技术的微波电介质的目标。