Symmetry and strain analysis of combined electronic and structural instabilities in tungsten trioxide, W O 3

Lattice parameter data from the literature have been used to provide a complete description of spontaneous strain variations across each of the six known phase transitions of W O 3 in the temperature interval 5-1273 K. Analysis of strain/order parameter coupling reveals the character of each phase transition, a unified description of strain across the full temperature range, the relationship between strain and electronic effects, and new insights into the strain gradients likely to be present in each of the different domain walls that develop in four different ferroelastic phases. Tetragonal and orthorhombic shear strains have values of 4%-6% and 2%-3%, respectively, and are dominated by coupling with the order parameter for antiferroelectric-type displacements. Conversely, shear strains, e 4, e 5, and e 6, of up to 2% are controlled by octahedral tilting. Changes in electronic structure and properties have been related back to the susceptibility of W 6 + to develop cooperative second-order-Jahn-Teller distortions. Proximity to tilt instabilities along with group-subgroup relationships in the P 4 / n m m parent structure results in two overlapping sequences of structural phase transitions, which differ in the form of their electronic structure. The possibility of a ground state structure in space group P 2 1 / c can be rationalized in terms of the efficiency by which different combinations of shearing and tilting of the W O 6 octahedra can reduce the unit cell volume and would imply that W O 3 has a re-entrant phase transition. Gradients in up to three order parameters coupled with gradients in strain of up to 12% across ferroelastic domain walls indicate that the different ferroelastic phases of W O 3 should have domain walls with varied and potentially exotic electronic properties for device applications such as in nanoelectronics and neuromorphic computing.