Molar Volume Correlation between Nonstoichiometric M1 − xRxF2 + x (0 ≤ x ≤ 0.5) and Ordered MmRnF2m + 3n (m/n = 8/6, 9/5) Phases in Systems MF2–RF3 (M = Ca, Sr, Ba, Pb; and R = Rare-Earth Elements)

Abstract

A correlation between the molar volumes of nonstoichiometric M_{1 − x}R_xF_{2 + x} (0 ≤ x ≤ 0.5) phases with a fluorite-type (CaF₂) structure and ordered M_mR_nF_{2m + 3n} (m/n = 8/6, 9/5) phases with a fluoritederivative structure has been found in systems MF₂–RF₃ (M = Ca, Sr, Ba, Pb; R = rare-earth elements Y, La-Lu). This correlation validates the cluster concept of the atomic structure of M_{1 − x}R_xF_{2 + x} nonstoichiometric crystals, the concept postulating that the structure is built of matrix fragments {M₁₄F₆₄} and octahedral-cubic clusters {M₈B₆F_68–69}, where the cations 6B are rare-earth cations (6R) or a mixture of cations (5R + M).