Influence of Germanium Substitution on the Crystal Chemistry and Dielectric Properties of Mg₂SnO₄

The effects of Ge⁴⁺ substitution on the microwave dielectric properties of inverse spinel Mg₂SnO₄ ceramics were systematically investigated. A series of Mg₂(Sn_1-xGe_x)O₄ (x = 0.00-0.05) ceramics were synthesized via solid-state reaction and sintered at 1450-1600 °C. X-ray diffraction confirmed single-phase inverse spinel structures (Fd-3 m) for compositions up to x = 0.03, while minor MgSnO₃ secondary phases appeared at x = 0.05. Rietveld refinement revealed a linear decrease in lattice parameter from 8.6579 Å (x = 0) to 8.6325 Å (x = 0.05), consistent with Vegard's law for the substitution of smaller Ge⁴⁺ (0.53 Å, Shannon ionic radius, octahedral coordination) for Sn⁴⁺ (0.69 Å, Shannon ionic radius, octahedral coordination) in octahedral sites. Optimal dielectric properties were achieved at x = 0.03 sintered at 1550 °C; the dielectric constant (ε_r) increased from 7.6 to 8.0, while the quality factor (Qf) improved by 19% from 56,200 to 67,000 GHz, which is attributed to reduced phonon scattering from Ge-induced lattice contraction. The temperature coefficient of resonant frequency (τ_f) remained stable (-64 to -68 ppm/°C) across all compositions. Property degradation at x = 0.05 correlated with the onset of Ge⁴⁺ solubility limit and MgSnO₃ formation. These results demonstrate that controlled Ge⁴⁺ substitution effectively enhances the microwave dielectric performance of Mg₂SnO₄ ceramics for communication applications.