Combined effect of rattling and compression on the microwave dielectric properties of B-site 1:3 ordered Li₆A₇Ti₁₁O₃₂ (A = Zn, Mg) spinels

Dense ceramics of two B-site 1:3 ordering spinels Li₆A₇Ti₁₁O₃₂ (A = Zn, Mg) with space group P4₃32 were prepared by solid-state reaction. Raman spectroscopy and XRD analysis revealed why the lattice parameters and volume of Li₆Mg₇Ti₁₁O₃₂ are abnormally greater than those of Li₆Zn₇Ti₁₁O₃₂. Li₆Zn₇Ti₁₁O₃₂ exhibits outstanding microwave dielectric properties (Q × f = 129,600 GHz (8.9 GHz), ε_r = 20.7, τ_f = −45 ppm/°C) and a low thermal expansion coefficient (α_L) of 5.5 ppm/°C. While Mg-analogue displayed a lower Q × f ∼108,600 GHz (9.1 GHz), a lower α_L ∼ 4.9 ppm/°C, a higher ε_r ∼ 21.9, and a slightly positive offset τ_f ∼ −21 ppm/°C relative to Li₆Zn₇Ti₁₁O₃₂. A significant positive deviation of 91.6% was observed between the corrected ε_r(corr) by the porosity and the calculated ε_r(C-M) by the Clausius-Mosotti (C-M) equation in the Li_1.33xA_2-2xTi_1+0.67xO₄ solid solution. The variation in ε_r and τ_f values of Li₆A₇Ti₁₁O₃₂ (x = 0.5625) compared to Li₂ATi₃O₈ (x = 0.75) might be attributed to the combined effect of rattling and compression cations at A-site and B-site. Moreover, the negative τ_f of Li₆A₇Ti₁₁O₃₂ (A = Zn, Mg) ceramics was balanced to near zero by adding CaTiO₃.