Polymorphism in the negative thermal expansion material magnesium hafnium tungstate

Magnesium hafnium tungstate [MgHf(WO₄)₃] was synthesized by high-energy ball milling followed by calcination. The material was characterized by variable- temperature neutron and x-ray diffraction. It crystallized in space group P2₁/a below 400 K and transformed to an orthorhombic structure at higher temperatures. The orthorhombic polymorph adopted space group Pnma, instead of the Pnca structure commonly observed for other A₂(MO₄)₃ materials (A = trivalent metal, M = Mo, W). In contrast, the monoclinic polymorphs appeared to be isostructural. Negative thermal expansion was observed in the orthorhombic phase with α_a = −5.2 × 10⁻⁶ K⁻¹, α_b = 4.4 × 10⁻⁶ K⁻¹, α_c = −2.9 × 10⁻⁶ K⁻¹, α_V = −3.7 × 10⁻⁶ K−¹, and α_l = −1.2 × 10⁻⁶ K⁻¹. The monoclinic to orthorhombic phase transition was accompanied by a smooth change in unit-cell volume, indicative of a second-order phase transition.