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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

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ABSTRACT

Temperature and composition dependences of the I41/amd → phase transition in the MgxCu1 − xCr2O4 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 I41/amd space group except for the Mg end-member, which has cubic symmetry. In MgxCu1 − xCr2O4 the progressive substitution of the Jahn–Teller, d9 Cu2+ cation with spherical and closed-shell Mg2+ 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, et, and ∼ 1% volume strain, Vs, in the copper chromite end-member at room temperature. Observed strain relationships are consistent with pseudoproper ferroelastic behaviour ( ∝ Vs ∝ , where qJT is the order parameter). The I41/amd → 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.

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Variation of atomic displacement parameters as a function of composition: (a) isotropic ADPs of Cu/Mg (blue diamonds), Cr (green diamonds) and O (red diamonds); (b) anisotropic APDs U11 (circles) and U33 (triangles) for the Cu/Mg site.
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fig4: Variation of atomic displacement parameters as a function of composition: (a) isotropic ADPs of Cu/Mg (blue diamonds), Cr (green diamonds) and O (red diamonds); (b) anisotropic APDs U11 (circles) and U33 (triangles) for the Cu/Mg site.

Mentions: Homogeneity of the solid solution is quite good. EPMA spot analyses reveal a rather narrow composition range within each sample (Table 5 ▸), with Cu54 and Cu47 showing the highest e.s.d.s. When looking at the equivalent atomic displacement parameters (ADPs; Fig. 4 ▸a), crystals with intermediate compositions show slightly higher values than those of the two end-members due to some static disorder, with an overall behaviour that is common for solid solutions. Interestingly and as already reported previously (e.g. Kennedy & Zhou, 2008 ▸), in all Cu-bearing crystals, the Cu/Mg site is the one showing the highest displacement parameters. This is mainly due to an elongated displacement ellipsoid towards the c-axis (Fig. 4 ▸b). The Rmax/Rmin ratio of the principal axes of the thermal ellipsoid is 2.67 for the tetrahedral cation in Cu100 and decreases almost linearly with increasing Mg content, with Cu47 slightly deviating from this trend likely due to some compositional heterogeneity. However, the behaviour observed for the average structure by XRD does not necessarily allow to differentiate the distinct cation coordinations of Mg2+ and Cu2+ if they are different on the local length scale.


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
Variation of atomic displacement parameters as a function of composition: (a) isotropic ADPs of Cu/Mg (blue diamonds), Cr (green diamonds) and O (red diamonds); (b) anisotropic APDs U11 (circles) and U33 (triangles) for the Cu/Mg site.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5391857&req=5

fig4: Variation of atomic displacement parameters as a function of composition: (a) isotropic ADPs of Cu/Mg (blue diamonds), Cr (green diamonds) and O (red diamonds); (b) anisotropic APDs U11 (circles) and U33 (triangles) for the Cu/Mg site.
Mentions: Homogeneity of the solid solution is quite good. EPMA spot analyses reveal a rather narrow composition range within each sample (Table 5 ▸), with Cu54 and Cu47 showing the highest e.s.d.s. When looking at the equivalent atomic displacement parameters (ADPs; Fig. 4 ▸a), crystals with intermediate compositions show slightly higher values than those of the two end-members due to some static disorder, with an overall behaviour that is common for solid solutions. Interestingly and as already reported previously (e.g. Kennedy & Zhou, 2008 ▸), in all Cu-bearing crystals, the Cu/Mg site is the one showing the highest displacement parameters. This is mainly due to an elongated displacement ellipsoid towards the c-axis (Fig. 4 ▸b). The Rmax/Rmin ratio of the principal axes of the thermal ellipsoid is 2.67 for the tetrahedral cation in Cu100 and decreases almost linearly with increasing Mg content, with Cu47 slightly deviating from this trend likely due to some compositional heterogeneity. However, the behaviour observed for the average structure by XRD does not necessarily allow to differentiate the distinct cation coordinations of Mg2+ and Cu2+ if they are different on the local length scale.

View Article: PubMed Central - HTML - PubMed

ABSTRACT

Temperature and composition dependences of the I41/amd → phase transition in the MgxCu1 − xCr2O4 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 I41/amd space group except for the Mg end-member, which has cubic symmetry. In MgxCu1 − xCr2O4 the progressive substitution of the Jahn–Teller, d9 Cu2+ cation with spherical and closed-shell Mg2+ 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, et, and ∼ 1% volume strain, Vs, in the copper chromite end-member at room temperature. Observed strain relationships are consistent with pseudoproper ferroelastic behaviour ( ∝ Vs ∝ , where qJT is the order parameter). The I41/amd → 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.

No MeSH data available.


Related in: MedlinePlus