“…The explicit formulas expressing dependences of the half-time t 1∕2 of YAG synthesis on the average diffusion rate were obtained. In the case of the synthesis by sol-gel reaction method, the half-time could be expressed as t 1∕2 = 5.169 − 2.065e5 ⋅ D(t) + 7.53e9 ⋅ D(t) 2 , when the diffusion rate D t, x, C 3 (t, x) is calculated by (7) and when the diffusion rate D t, x, C 3 (t, x) was calculated by (8) the half-time could be expressed as 4 . In the case of the synthesis by solid-state reaction method, the dependencies are t 1∕2 = 6.69 − 7288e4 ⋅ D(t) + 7.297e6 ⋅ D(t) 2 − 2.918e9 ⋅ D(t) 3 for (7) and t 1∕2 = 10.32 − 3.312e4 ⋅ D(t) + 7.636e7 ⋅ D(t) 2 − 8.4e10 ⋅ D(t) 3 + 3.506e13 ⋅ D(t) 4 for (8).…”