Effect of lattice-induced strain on microwave dielectric polarization and properties: A case study of Ga-based garnet

In microwave dielectric materials, the phenomenon that the measured permittivity ( ε _r) is inconsistent with the calculated permittivity ( ε _r(C-M) ) often occurs. In the present work, the intrinsic factors affecting the microwave dielectric properties of Ga-based garnet Ca ₃B _1.5Ga _3.5O ₁₂ (B = Nb, Ta) are studied by bond valence and the Phillips-Van Vechten-Levine (P-V-L) methods, and the relationship between lattice-induced strain effect and dielectric polarization is elucidated. Since the ionic polarizability of Nb ⁵⁺ is lower than that of Ta ⁵⁺, the ε _r(C-M) values of Ca ₃Nb _1.5Ga _3.5O ₁₂ (CNG) and Ca ₃Ta _1.5Ga _3.5O ₁₂ (CTG) are 11.06 and 12.17, respectively. However, this is the opposite trend of the measured values (15.00 and 12.62). The global instability index ( GII) is equal to 0.013 and 0.044 v.u., respectively. Both the indexes, bond strain index ( BSI) and GII, are related to the entire crystal structure. A stronger lattice-induced compressive strain and a higher degree of covalency lead to a lower measured ε _r, a higher Q×f, a higher temperature coefficient of permittivity τ _ε, and a larger negative τ _f.