gems, advanced testing, analytical testing, chemistry, crystallography, unit cell dimensions

Analytical calculation of unit cell dimension in silicates. Least-squares analysis of the Gladstone–Dale constants (GDCs) on the basis of data from 574 silicates confirms Jaffe’s (1988) conclusion that the GDC for an oxide in a silicate structure depends on the cation’s coordination number. The effect is most prominent for Al and Ca; the GDC for IVAl₂O₃ is 0.221, and for VIAl₂O₃ it is 0.188. The GDC for VICaO is 0.221, and for VIIICaO it is 0.205. The new GDCs yield better agreement between observed and calculated mean indices of refraction than previous compilations (all but one sample agree to within 4σ) and bring the garnets into conformity with the other silicate groups. The Gladstone–Dale relation appears to be a special case of Anderson’s (1975) general refractivity equation, applicable to structures with intermediate ionic–covalent bonding.