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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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Perspective views of the crystal structures of CuCr2O4 (left) and MgCr2O4 (right) along the a-axis of the I41/amd cell. CuO4 tetrahedra are drawn in green, MgO4 tetrahedra in grey. In CuCr2O4, the contraction along the c direction due to JT flattening of tetrahedral sites is given by a change of tetrahedral angles. Relevant geometrical parameters are reported.
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fig1: Perspective views of the crystal structures of CuCr2O4 (left) and MgCr2O4 (right) along the a-axis of the I41/amd cell. CuO4 tetrahedra are drawn in green, MgO4 tetrahedra in grey. In CuCr2O4, the contraction along the c direction due to JT flattening of tetrahedral sites is given by a change of tetrahedral angles. Relevant geometrical parameters are reported.

Mentions: The most common distortion of the spinel structure is by far the tetragonal distortion, whereby one of the cubic axes would become compressed or elongated with respect to the other two. If no additional symmetry breaking occurs, the tetragonal distortion alone decreases the symmetry from to I41/amd (No. 141). The c/a ratio is normally used as a parameter of tetragonal distortion. A phase transition from the cubic to the tetragonal structure may be induced by a sufficient concentration of non-spherical, Jahn–Teller (JT) ions, such as Cu2+ or Mn3+, causing a cooperative distortion. Although less common, tetrahedral Cu2+ on the A site can display JT activity. The degeneracy of the partially occupied t2 levels is broken by compressing the tetrahedron and thereby lowering the symmetry, as in copper chromite, CuCr2O4, which is a tetragonally distorted spinel with unit-cell parameters ratio c/a < 1 (Fig. 1 ▸, left panel). Cu2+ cations can be stabilized in flattened tetrahedral environments because of the preference of Cr3+ ions to occupy the octahedral sites. The cooperative nature of the crystal distortion can be rationalized in terms of elastic interactions among locally distorted tetrahedra, as a consequence of coupling of electronic states to bulk deformation via elastic strain. On heating, CuCr2O4 undergoes a first-order structural transition from the tetragonal distorted spinel structure to the archetypal cubic spinel structure at 853 K (Yé et al., 1994 ▸; Kennedy & Zhou, 2008 ▸). The structural distortion in CuCr2O4 is large and the transition temperature high, in particular if considering that CuO4 tetrahedra are not directly linked but separated from each other by non-JT ions. Nonetheless, enhancement of the ground-state JT splitting and of lattice distortion have been explained by considering the electronic and elastic coupling of Cu2+ and Cr3+ (Atanasov et al., 1993 ▸; Reinen et al., 1988 ▸). The relevance of strain associated with the Jahn–Teller distortion is curiously showed in NiCr2O4 by the observation that the crystals literally jump off a flat surface when they pass through the transition point (Crottaz et al., 1997 ▸), due to the large and abrupt change in shear strain.


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
Perspective views of the crystal structures of CuCr2O4 (left) and MgCr2O4 (right) along the a-axis of the I41/amd cell. CuO4 tetrahedra are drawn in green, MgO4 tetrahedra in grey. In CuCr2O4, the contraction along the c direction due to JT flattening of tetrahedral sites is given by a change of tetrahedral angles. Relevant geometrical parameters are reported.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig1: Perspective views of the crystal structures of CuCr2O4 (left) and MgCr2O4 (right) along the a-axis of the I41/amd cell. CuO4 tetrahedra are drawn in green, MgO4 tetrahedra in grey. In CuCr2O4, the contraction along the c direction due to JT flattening of tetrahedral sites is given by a change of tetrahedral angles. Relevant geometrical parameters are reported.
Mentions: The most common distortion of the spinel structure is by far the tetragonal distortion, whereby one of the cubic axes would become compressed or elongated with respect to the other two. If no additional symmetry breaking occurs, the tetragonal distortion alone decreases the symmetry from to I41/amd (No. 141). The c/a ratio is normally used as a parameter of tetragonal distortion. A phase transition from the cubic to the tetragonal structure may be induced by a sufficient concentration of non-spherical, Jahn–Teller (JT) ions, such as Cu2+ or Mn3+, causing a cooperative distortion. Although less common, tetrahedral Cu2+ on the A site can display JT activity. The degeneracy of the partially occupied t2 levels is broken by compressing the tetrahedron and thereby lowering the symmetry, as in copper chromite, CuCr2O4, which is a tetragonally distorted spinel with unit-cell parameters ratio c/a < 1 (Fig. 1 ▸, left panel). Cu2+ cations can be stabilized in flattened tetrahedral environments because of the preference of Cr3+ ions to occupy the octahedral sites. The cooperative nature of the crystal distortion can be rationalized in terms of elastic interactions among locally distorted tetrahedra, as a consequence of coupling of electronic states to bulk deformation via elastic strain. On heating, CuCr2O4 undergoes a first-order structural transition from the tetragonal distorted spinel structure to the archetypal cubic spinel structure at 853 K (Yé et al., 1994 ▸; Kennedy & Zhou, 2008 ▸). The structural distortion in CuCr2O4 is large and the transition temperature high, in particular if considering that CuO4 tetrahedra are not directly linked but separated from each other by non-JT ions. Nonetheless, enhancement of the ground-state JT splitting and of lattice distortion have been explained by considering the electronic and elastic coupling of Cu2+ and Cr3+ (Atanasov et al., 1993 ▸; Reinen et al., 1988 ▸). The relevance of strain associated with the Jahn–Teller distortion is curiously showed in NiCr2O4 by the observation that the crystals literally jump off a flat surface when they pass through the transition point (Crottaz et al., 1997 ▸), due to the large and abrupt change in shear strain.

View Article: PubMed Central - HTML - PubMed

ABSTRACT

Temperature and composition dependences of the I41/amd &rarr; phase transition in the MgxCu1&thinsp;&minus;&thinsp;xCr2O4 spinel solid solution, due to the melting of the cooperative Jahn&ndash;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&thinsp;&minus;&thinsp;xCr2O4 the progressive substitution of the Jahn&ndash;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&#8197;K show that the tetragonal-to-cubic transition temperature decreases with increasing Mg content. The strength of the Cu&mdash;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 &sim;&#8197;1% volume strain, Vs, in the copper chromite end-member at room temperature. Observed strain relationships are consistent with pseudoproper ferroelastic behaviour ( &prop; Vs &prop; , where qJT is the order parameter). The I41/amd &rarr; 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&ndash;Teller cation.

No MeSH data available.


Related in: MedlinePlus