Isotropic Low Thermal Expansion over a Wide Temperature Range in Ti_{1- x}Zr _xF_{3+ x} (0.1 ≤ x ≤ 0.5) Solid Solutions

TiF₃ exhibits a rhombohedral to ReO₃-type cubic phase transformation at ∼340 K. Here we report that, by introducing ZrF₄ into TiF₃, the cubic phase is stabilized at least down to 123 K in the Ti_{1- x}Zr _xF_{3+ x} compounds. All compounds exhibit low thermal expansion (LTE) between 123 and 623 K, and a nearly zero thermal expansion (ZTE) was obtained in Ti_0.7Zr_0.3F_3.3 (α_L = 0.91 ppm/K). The analysis of pair distribution function reveals that the cation-centered octahedra are partially changed to pentagonal bipyramids in Ti_{1- x}Zr _xF_{3+ x} due to the excess fluorines relative to the case of TiF₃. Therefore, the cooperative rotation of the polyhedra tends to be restricted, and the cubic phase is thus stabilized. The restrained polyhedral rotations compete against the lattice softening caused by the introduction of Zr⁴⁺, giving rise to the LTE. Our present strategy is applicable to other rhombohedral metal trifluorides for the design of new isotropic ZTE materials.