Cooperative Jahn–Teller effect and the role of strain in the tetragonal-to-cubic phase transition in Mg x Cu 1 − x Cr 2 O 4
Résumé
Temperature and composition dependences of the I 4 1 / amd → Fd\bar 3m phase transition in the Mg x Cu 1 − x Cr 2 O 4 spinel solid solution, due to the melting of the cooperative Jahn–Teller distortion, have been studied by means of single-crystal X-ray diffraction. Crystals with x = 0, 0.10, 0.18, 0.43, 0.46, 0.53, 1 were grown by flux decomposition methods. All crystals have been refined in the tetragonal I 4 1 / amd space group except for the Mg end-member, which has cubic symmetry. In Mg x Cu 1 − x Cr 2 O 4 the progressive substitution of the Jahn–Teller, d 9 Cu 2+ cation with spherical and closed-shell Mg 2+ has a substantial effect on the crystal structure, such that there is a gradual reduction of the splitting of a and c unit-cell parameters and flattening of the tetrahedra. Single-crystal diffraction data collected in situ up to T = 1173 K show that the tetragonal-to-cubic transition temperature decreases with increasing Mg content. The strength of the Cu—Cu interaction is, in effect, modulated by varying the Cu/Mg ratio. Structure refinements of diffraction data collected at different temperatures reveal that heating results in a gradual reduction in the tetrahedron compression, which remains significant until near the transition temperature, however, at which point the distortion of the tetrahedra rapidly vanishes. The spontaneous strain arising in the tetragonal phase is large, amounting to 10% shear strain, e t , and ∼ 1% volume strain, V s , in the copper chromite end-member at room temperature. Observed strain relationships are consistent with pseudoproper ferroelastic behaviour (e_{\rm t}^2 ∝ V s ∝ q_{\rm JT}^2, where q JT is the order parameter). The I 4 1 / amd → Fd\bar 3m phase transition is first order in character for Cu-rich samples and then evolves towards second-order character. Although a third order term is permitted by symmetry in the Landau expansion, this behaviour appears to be more accurately represented by a 246 expansion with a change from negative to positive values of the fourth-order coefficient with progressive dilution of the Jahn–Teller cation.