A New Empirical Formula for the Calculation of an Elementary Cell Parameter of Synthetic Oxides–Garnets

✍ Scribed by Yu.P. Vorobiov; O.V. Carban

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 277 KB
• Volume: 134
• Category: Article
• ISSN: 0022-4596
• DOI: 10.1006/jssc.1997.7570

✦ Synopsis

An empirical formula is proposed which allows one to calculate the lattice constant of cubic synthetic oxides-garnets taking into account the chemical composition, the distribution of cation in the crystallographically nonequivalent positions, and wellknown Shannon-Prewitt cation radii. The formula is developed assuming cation size effects on the elementary cell parameter for the cation radii r VIII from 0.097 to 0.114 for the cations on dodecahedral, 0.054 < r VI < 0.079 for the cations on octahedral, and 0.028 < r IV < 0.049 for the cations on tetrahedral lattice sites. Selected crystal lattice parameters for 350 compositions, excluding garnets-silicates, have been used for derivation of the formula by means of the least-squares method for multimeasured functions (n-measured space with coordinates r VIII , r VI , r IV , a). The average deviation of the calculated values a cal from the experimental values is less than 0.001 nm.