Structure–property correlation over five phases and four transitions in Pb5Al3F19

Abstract

The calorimetric and dielectric properties of Pb5Al3F19 in the five phases stable under ambient pressure are correlated with structure for fuller characterization of each phase. The first-order transition between ferroelectric phase V and antiferroelectric phase IV at T V,IV = 260 (5) K exhibits a thermal hysteresis of 135 (5) K on heating, with a maximum atomic displacement Δ(xyz)max = 1.21 (6) Å; the transition from phase IV to ferroelastic phase III at 315 (5) K is also first order but with a thermal hysteresis of 10 (5) K and Δ(xyz)max = 0.92 (7)  Å; that from phase III to paraelastic phase II at 360 (5) K is second order without hysteresis and has Δ(xyz)max = 0.69 (4) Å; and the transition from phase II to paraelectric phase I at 670 (5) K is second or higher order, with Δ(xyz)max = 0.7 (4) Å. The measured entropy change ΔS at T V,IV agrees well with ΔS as derived from the increased configurational energy by Stirling's approximation. For all other phase transitions, 0.5 ≥ ΔS > 0 J mol−1 K−1 is consistent with an entropy change caused primarily by the changes in the vibrational energy. The structure of phase III is determined both by group theoretical/normal mode analysis and by consideration of the structures of phases II, IV and V reported previously; refinement is by simultaneous Rietveld analysis of the X-ray and neutron diffraction powder profiles. The structure of prototypic phase I is predicted on the basis of the atomic arrangement in phases II, III, IV and V. The introduction of 3d electrons into the Pb5Al3F19 lattice disturbs the structural equilibrium, the addition of 0.04% Cr3+ causing significant changes in atomic positions and increasing T IV,III by ∼15 K. Substitution of Al3+ by 20% or more Cr3+ eliminates the potential minima that otherwise stabilize phases IV, III and II.