The apparent difference in microwave dielectric properties of Ca3MZnGe3O12 (M = Zr, Sn) garnets originating from compression and rattling effects

Ca 3 MZnGe 3 O 12 ( M  = Zr, Sn) ceramics crystallized in a cubic garnet structure (A 3 B 2 C 3 O 12 ) with a space group of Ia- 3 d , and promising microwave dielectric properties with low coefficients of thermal expansion ( α L ) were obtained, namely, ε r  = 10.5 and 9.3, Q  ×  f  = 79,700, and 96,040 GHz, τ f  = − 36.1 and − 61.5 ppm/°C, and α L  = 4.3 and 4.7 ppm/°C for Ca 3 ZrZnGe 3 O 12 and Ca 3 SnZnGe 3 O 12 , respectively. Bond valence calculation reveals that Ca 3 SnZnGe 3 O 12 exhibits a slight “compressed” effect at A-site and B-site with a slightly negative deviation (Δ ε r  ~ − 1.01%) of the porosity corrected ε r (corr) from theoretical ε r (C–M) calculated by the C–M equation, while Ca 3 ZrZnGe 3 O 12 shows a “rattling” effect at the A-site and C-site with a large positive Δ ε r  ~ 15.8%, leading to a high ε r , a more close to zero τ f and a lower Q  ×  f value as compared to those of Ca 3 SnZnGe 3 O 12 . The relationship between structure and their intrinsic microwave dielectric properties was investigated by complex chemical bond theory and far-infrared reflectivity spectra.