[Paper Review] Structural relaxation around substitutional Cr3+ in MgAl2O4

Amélie Juhin, Georges Calas+3 more|arXiv (Cornell University)|Apr 6, 2007

Advanced Condensed Matter Physics35 references56 citations

TL;DR

This study investigates Cr³⁺ substitution in MgAl₂O₄ spinel using Cr K-edge EXAFS and XANES spectroscopies combined with DFT-LSDA calculations. It reveals that Cr³⁺ induces full relaxation of its first-shell O neighbors and partial relaxation of the second-shell Al atoms, violating Vegard's law due to strain-induced bond buckling in Mg-centered tetrahedra, while maintaining local D₃d symmetry.

ABSTRACT

The structural environment of substitutional Cr3+ ion in MgAl2O4 spinel has been investigated by Cr K-edge Extended X-ray Absorption Fine Structure (EXAFS) and X-ray Absorption Near Edge Structure (XANES) spectroscopies. First-principles computations of the structural relaxation and of the XANES spectrum have been performed, with a good agreement to the experiment. The Cr-O distance is close to that in MgCr2O4, indicating a full relaxation of the first neighbors, and the second shell of Al atoms relaxes partially. These observations demonstrate that Vegard's law is not obeyed in the MgAl2O4-MgCr2O4 solid solution. Despite some angular site distortion, the local D3d symmetry of the B-site of the spinel structure is retained during the substitution of Cr for Al. Here, we show that the relaxation is accomodated by strain-induced bond buckling, with angular tilts of the Mg-centred tetrahedra around the Cr-centred octahedron. By contrast, there is no significant alteration of the angles between the edge-sharing octahedra, which build chains aligned along the three four-fold axes of the cubic structure.

Motivation & Objective

• To determine the local structural environment of substitutional Cr³⁺ in MgAl₂O₄ spinel.
• To investigate whether Vegard's law holds in the MgAl₂O₄–MgCr₂O₄ solid solution at the atomic scale.
• To understand the role of radial and angular relaxation in accommodating Cr³⁺ substitution in the spinel structure.
• To link structural relaxation to macroscopic properties such as color and mechanical stability in Cr-doped spinel.
• To validate experimental XAS data with first-principles DFT-LSDA calculations for accurate structural modeling.

Proposed method

• Employed Cr K-edge X-ray Absorption Spectroscopy (XAS) in fluorescence mode at the ESRF BM30b beamline.
• Conducted EXAFS and XANES data analysis using ATHENA and IFEFFIT, with multiple-shell fitting in q-space.
• Used uvarovite garnet (Ca₃Cr₂Si₃O₁₂) as a reference to determine the amplitude reduction factor S₀² = 0.81.
• Performed first-principles DFT-LSDA calculations on a 2×2×2 supercell of MgAl₂O₄ with isolated Cr³⁺ substitution.
• Applied plane-wave basis sets and norm-conserving pseudopotentials in the Kleinman-Bylander form.
• Simulated structural relaxation and XANES spectra, comparing them directly with experimental data.

Experimental results

Research questions

• RQ1 How does the local structure around Cr³⁺ in MgAl₂O₄ deviate from idealized cubic symmetry upon substitution for Al³⁺?
• RQ2 To what extent does the Cr³⁺-induced lattice relaxation violate Vegard’s law in the MgAl₂O₄–MgCr₂O₄ solid solution?
• RQ3 What is the role of angular distortions and bond buckling in accommodating the ionic radius mismatch between Cr³⁺ and Al³⁺?
• RQ4 How do radial and angular relaxations differ between Cr³⁺ in spinel and in corundum (α-Al₂O₃)?
• RQ5 Does the local D₃d symmetry of the B-site octahedra persist despite Cr³⁺ substitution and structural relaxation?

Key findings

• The Cr–O distance in MgAl₂O₄ is nearly identical to that in MgCr₂O₄, indicating full radial relaxation of the first-shell oxygen atoms.
• The second-shell Al atoms exhibit partial relaxation, with significant angular tilts of Mg-centered tetrahedra around the Cr-centered octahedron.
• Despite local distortions, the local D₃d symmetry of the B-site is preserved, indicating a high degree of structural integrity.
• The angles between edge-sharing Cr- and Al-bearing octahedra remain largely unchanged, indicating minimal alteration of the chain structure along the fourfold axes.
• Strain-induced bond buckling is the dominant mechanism for accommodating Cr³⁺ substitution, with no significant angular relaxation in the octahedral chains.
• Vegard’s law is not obeyed in the MgAl₂O₄–MgCr₂O₄ system, as confirmed by the discrepancy between average diffraction data and local XAS/DFT results.