Thermoelastic Properties of Materials with Negative Coefficients of Thermal Expansion

Abstract

Several families of ceramic materials composed of corner-linked coordination polyhedra are known to display the rare property of negative thermal expansion, i.e., reversible contraction upon heating. However, as shown herein, the ability of these thermomiotic (heat-shrinking) materials to successfully counteract positive thermal expansion depends on their elastic properties. This finding has motivated experimental and computational studies of thermal expansion, elasticity, and their interactions under thermal stress in thermomiotic materials. Finite element analysis showed that inclusion of compliant or low-thermal-expansion components, or those which undergo pressure-induced phase transitions, can reduce thermal stress due to thermal expansion mismatch. These strategies were applied in the synthesis of composites combining thermomiotic ZrW2O8 and Al2¬W3O12 and positive-thermal-expansion alumina-toughened zirconia, and in the synthesis of lamellar ZrW2O8/polymethylmethacrylate composites. The thermal expansivities of the composites were highly dependent on the stiffnesses of their components. The chemical flexibility of the A2M3O12 and AMgM3O12 material families, with thermal expansion ranging from negative to low-positive, was used to investigate relationships between elasticity and thermal expansion. Three series of solid solutions, In2−2x(HfMg)xMo3O12, Sc2−2xAl2xW3O12, and Cr2−2x(HfMg)xW3O12, were synthesized and characterized, and significant variations in the thermal expansion and stiffness with composition were observed. In general, materials with larger-magnitude thermal expansion were more compliant. ZrMgMo3O12 was found to have zero thermal expansion, and its structure was used to explain its thermal expansion and that of A2M3O12 materials. Thermal expansion in this group of materials was related to the ionic forces of the coordination polyhedra, with more distortable polyhedra leading to more negative thermal expansion. Density functional theory calculations of phonon band structure and experimental heat capacity measurements were performed on the simple thermomiotic material ScF3, showing the stability of its structure upon cooling to 0.38 K. The elastic tensors and Γ-point phonon frequencies of Al2Mo3O12, ZrMgMo3O12, and Sc2Mo3O12 were also calculated. These anisotropic materials showed correlations between axial thermal expansion and stiffness, with thermomiotic axes found to be stiffer. The calculated elastic tensors were then used to model thermal stress due to anisotropic thermal expansion in polycrystals, showing large extremal thermal stresses affected by coupling of thermal expansion and elastic anisotropy.