Thermal dependence of the Pb5Al3F19 lattice parameters in phases I–IV

Abstract

Abstract Pb5Al3F19 undergoes three first-order phase transitions; on cooling from phase I (4/m) to phase II (2/m) at 365 K, from phase II to phase III (4/m) at 305 K, and from phase III to phase IV (4mm) at 120 K. The lengths of the a- and c-axes undergo continuous change at the highest temperature phase transition as the β-angle increases from 90[unk] below 365 K; no difference is detectable between the lengths of the a- and b-axes in monoclinic phase II, within an accuracy of 0.007 Å. The β-angle temperature dependence follows a power law with exponent that does not differ significantly from 1/2. At the 305 K first-order phase transition, the β-angle abruptly changes from its maximum value of 90.41° in phase II to 90[unk] in tetragonal phase III; the a- and c-axes, however, maintain their continuous change in length through this transition. The 120 K first-order phase transition is characterized by an abrupt 0.77% decrease in the length of the normalized a-axis, and an equally abrupt 1.89% increase in the c-axis length, on cooling from phase III to phase IV. The a- and c-axes in all four phases are characterized by linear thermal coefficients, with magnitudes presented below. The normalized a-axis lengths in phases I, II and III extrapolated to 0 K differ by less than 0.021 Å from 14.174 Å, the corresponding c-axis lengths at 0 K differ by less than 0.004 Å from 7.194 Å. The normalized unit cell volume thermal dependence of phases I, II and III is linear and continuous between 400 and 120 K but undergoes a discontinuity of 0.40% at the transition from phase III to phase IV.