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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 tetrahedral O—(Cu,Mg)—O angles as a function of temperature. Blue: CuCr2O0; red: Mg0.10Cu0.90Cr2O4; orange: Mg0.18Cu0.82Cr2O4; green: Mg0.46Cu0.54Cr2O4. Error bars are within the symbols.
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fig6: Variation of tetrahedral O—(Cu,Mg)—O angles as a function of temperature. Blue: CuCr2O0; red: Mg0.10Cu0.90Cr2O4; orange: Mg0.18Cu0.82Cr2O4; green: Mg0.46Cu0.54Cr2O4. Error bars are within the symbols.

Mentions: The temperature dependence of the angles within the (Cu,Mg)O4 tetrahedron is illustrated in Fig. 6 ▸ for all the analysed Cu-rich samples. Heating results in a gradual reduction of the compression of the tetrahedron but, clearly, the compression remains significant until near the transition temperature. The variation with temperature of the O—(Cu,Mg)—O angles for the samples of intermediate composition mimics the change in the lattice parameters, the discontinuity of distortion at the transition decreases when Mg is added.


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 tetrahedral O—(Cu,Mg)—O angles as a function of temperature. Blue: CuCr2O0; red: Mg0.10Cu0.90Cr2O4; orange: Mg0.18Cu0.82Cr2O4; green: Mg0.46Cu0.54Cr2O4. Error bars are within the symbols.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig6: Variation of tetrahedral O—(Cu,Mg)—O angles as a function of temperature. Blue: CuCr2O0; red: Mg0.10Cu0.90Cr2O4; orange: Mg0.18Cu0.82Cr2O4; green: Mg0.46Cu0.54Cr2O4. Error bars are within the symbols.
Mentions: The temperature dependence of the angles within the (Cu,Mg)O4 tetrahedron is illustrated in Fig. 6 ▸ for all the analysed Cu-rich samples. Heating results in a gradual reduction of the compression of the tetrahedron but, clearly, the compression remains significant until near the transition temperature. The variation with temperature of the O—(Cu,Mg)—O angles for the samples of intermediate composition mimics the change in the lattice parameters, the discontinuity of distortion at the transition decreases when Mg is added.

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.