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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.

No MeSH data available.


Variation of (a) tetrahedral O—(Cu,Mg)—O angles and (b) O⋯O edges as a function of Mg content. Error bars are within the symbols.
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fig3: Variation of (a) tetrahedral O—(Cu,Mg)—O angles and (b) O⋯O edges as a function of Mg content. Error bars are within the symbols.

Mentions: The influence of the Jahn–Teller effect can be better estimated by looking at the geometry of the tetrahedra. These are flattened and, with respect to the ideal tetrahedron, display four smaller and two angles larger than 109.47° (see Fig. 1 ▸ for visual reference). The distortion of the tetrahedra is large, with ΔO—Cu—O = 12.94° in the Cu end-member. The distortion of the tetrahedra in the tetragonal phase is also evident in the behaviour of the O⋯O edges. In Fig. 3 ▸, O—(Cu,Mg)—O angles and O⋯O edges are plotted as a function of composition. With increasing Mg content, the flattening of the tetrahedra is reduced: the two sets of O—(Cu,Mg)—O tetrahedral angles converge towards 109.47°, as required by the site symmetry of the cubic phase. A similar behaviour is shown by the tetrahedral edges. Variation of the (Cu,Mg)—O bond length (Table 5 ▸) is related to the difference in ion size between Cu2+ and Mg2+.


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 (a) tetrahedral O—(Cu,Mg)—O angles and (b) O⋯O edges as a function of Mg content. Error bars are within the symbols.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig3: Variation of (a) tetrahedral O—(Cu,Mg)—O angles and (b) O⋯O edges as a function of Mg content. Error bars are within the symbols.
Mentions: The influence of the Jahn–Teller effect can be better estimated by looking at the geometry of the tetrahedra. These are flattened and, with respect to the ideal tetrahedron, display four smaller and two angles larger than 109.47° (see Fig. 1 ▸ for visual reference). The distortion of the tetrahedra is large, with ΔO—Cu—O = 12.94° in the Cu end-member. The distortion of the tetrahedra in the tetragonal phase is also evident in the behaviour of the O⋯O edges. In Fig. 3 ▸, O—(Cu,Mg)—O angles and O⋯O edges are plotted as a function of composition. With increasing Mg content, the flattening of the tetrahedra is reduced: the two sets of O—(Cu,Mg)—O tetrahedral angles converge towards 109.47°, as required by the site symmetry of the cubic phase. A similar behaviour is shown by the tetrahedral edges. Variation of the (Cu,Mg)—O bond length (Table 5 ▸) is related to the difference in ion size between Cu2+ and Mg2+.

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.