Ca5Mg4+xV6O24 (− 0.05 ≤ x ≤ 0.15) ceramics were prepared via a conventional solid-state reaction route. XRD patterns and Raman spectra confirmed that a single garnet phase was formed in all samples. The full-width-at-half maximum of Raman peaks revealed that an appropriate excess of magnesium ions improves the ordering degree of cations and quality factor (Q × f) value. The dielectric constant (εr) was closely correlated with the relative density and ion polarizability. The connections among the Q × f value, lattice energy, and packing fraction were discussed. As for the variation of the temperature coefficient of resonant frequency (τf), it was explained by the bond energy of V–O. Ca5Mg4+xV6O24 (x = 0.05) ceramic sintered at 825 °C achieved optimal microwave dielectric properties: ɛr = 9.93, Q × f = 56192 GHz, and τf = − 48.3 ppm/°C.

中文翻译：

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非化学计量对Ca5Mg4+xV6O24 (− 0.05 ≤ x ≤ 0.15)陶瓷微观结构和微波介电性能的影响

Ca5Mg4+xV6O24 (− 0.05 ≤ x ≤ 0.15) 陶瓷是通过传统的固态反应路线制备的。XRD 图案和拉曼光谱证实在所有样品中都形成了单一的石榴石相。拉曼峰的半峰全宽表明，适当过量的镁离子可提高阳离子的有序度和品质因数 (Q × f) 值。介电常数 (εr) 与相对密度和离子极化率密切相关。讨论了 Q × f 值、晶格能和堆积率之间的联系。至于谐振频率温度系数（τf）的变化，可以用V-O的键能来解释。在 825 °C 下烧结的 Ca5Mg4+xV6O24 (x = 0.05) 陶瓷实现了最佳微波介电性能：ɛr = 9.93，Q × f = 56192 GHz，τf = − 48.3 ppm/°C。