Structure determination of β- and γ-BaAlF5 by X-ray and neutron powder diffraction: A model for the α → β γ transitions

{beta}-BaAlF{sub 5} is monoclinic (space group P2{sub 1}/n): a = 5.1517(1) {angstrom}, b = 19.5666(4) {angstrom}, c = 7.5567(2) {angstrom}, {beta} = 92.426(1){degree}, Z = 8. {gamma}-BaAlF{sub 5} is monoclinic (space group P2{sub 1}): a = 5.2584(1) {angstrom}, b = 9.7298(2) {angstrom}, c = 7.3701(2) {angstrom}, {beta} = 90.875(1){degree}, Z = 4. Both structures are determined ab initio from X-ray powder data; final results are given from neutron powder data refinements (R{sub I} = 0.038, R{sub P} = 0.072, and R{sub WP} = 0.087 and R{sub I} = 0.048, R{sub P} = 0.083, and R{sub WP} = 0.101 for the {beta} and {gamma} phases, respectively). Like {alpha}-BaAlF{sub 5}, the {beta} and {gamma} phases are built up from isolated infinite (AlF{sub 5}){sup 2n{minus}}{sub n} chains with AlF{sub 6} octahedra sharing corners in a cis-position. Close structural relationships are shown to exist between the Ba-Al cationic subnetwork of: {alpha}-BaAlF{sub 5} and the CrB-type structure; {beta}-BaAlF{sub 5} and the SrAg-type; {gamma}-BaAlF{sub 5} and the FeB-type.