“…The minimum amount of Lu 3+ (∼17 at%) calculated from the ionic size of Tb 3+ (0.1040 nm for CN = 8), however, is significantly larger than the ∼10 at% found in practice (figure 3(b)). This indicates that stable garnet solid solutions exist if the average ionic size of (Ln 1 ,Ln 2 ) 3+ pair lies in between those of Gd 3+ (0.1053 nm for CN = 8) and Tb 3+ , in agreement with the fact that TbAG [28–30] and even (Gd 0.9 Lu 0.1 )AG [31, 32] can be further doped with larger Eu 3+ (0.1066 nm, CN = 8) and Ce 3+ (0.1143 nm, CN = 8) for luminescence. Taking the average ionic size of (Gd 0.9 Lu 0.1 ) 3+ (~0.1045 nm) as a standard, Li et al [33] analyzed the minimum amounts of various small Ln 3+ that are needed for GAG stabilization, and the x value was predicted to be ∼0.5 for Tb 3+ , 0.3 for Dy 3+ (0.1027 nm), 0.22 for Y 3+ (0.1019 nm), 0.2 for Ho 3+ (0.1015 nm), 0.15 for Er 3+ (0.1004 nm), 0.13 for Tm 3+ (0.0994 nm), and 0.11 for Yb 3+ (0.0985 nm).…”