Close-packed Oxygen Layers Research Articles

Stability, magnetic order, and electronic properties of ultrathin Fe3O4 nanosheets

We study the stability, magnetic order, charge segregation, and electronic properties of a novel three-layered Fe3O4 film by means of Hubbard-corrected density functional theory calculations. The stable film is predicted to consist of close-packed iron and oxygen layers, comprising a center layer with octahedrally coordinated Fe sandwiched between two layers with tetrahedrally coordinated Fe. The film exhibits an antiferromagnetic type I spin order. A charge analysis confirms that the stable structure has distinct charge segregation, with Fe2+ ions in the center layer and Fe3+ in the tetrahedral surface layers. Examination of the electronic band structures and densities of states shows that the bandgap is substantially reduced, from 2.4 eV for the bulk rocksalt to 0.3 eV for the film. The reduction in the bandgap is a consequence of the 2+ to 3+ change in oxidation state of Fe in the surface layers.

Vanadium Oxide Oligomers and Ordered Monolayers Supported on CeO2(111): Structure and Stability Studied by Density Functional Theory

Structures and stabilities of vanadium oxide oligomers as well as two candidate structures for a monolayer on the CeO2(111) surface have been studied by density functional theory, employing a genetic algorithm to determine the global energy minimum structures. These ceria-supported structures have predominantly 4-fold coordinated V5+ ions with V═O groups in common. The agglomeration of VO2 clusters deposited on the surface is a strongly exothermic process, particularly when ring structures with three or six VO2 units are formed that are commensurate with the close-packed surface-terminating oxygen layer. The VO2 and V2O5 monolayers feature larger coordination numbers (5, 6) of V and contain V atoms without V═O groups. Relative to oligomers, VO2 and V2O5 monolayer structures with and without oxygen defects are thermodynamically more stable. This, together with the fact that flat “monolayer” clusters are preferred to taller “bilayer” clusters, indicates the preference for a complete two-dimensional wetting ...

Surface Termination of Fe3O4(111) Films Studied by CO Adsorption Revisited.

Although the (111) surface of Fe3O4 (magnetite) has been investigated for more than 20 years, substantial controversy remains in the literature regarding the surface termination proposed based on structural and adsorption studies. The present article provides density functional theory results that allow to rationalize experimental results of infrared reflection-absorption spectroscopy and temperature-programmed desorption studies on CO adsorption, thus leading to a unified picture in which the Fe3O4(111) surface is terminated by a 1/4 monolayer of tetrahedrally coordinated Fe3+ ions on top of a close-packed oxygen layer as previously determined by low energy electron diffraction. However, surface defects play a crucial role in adsorption properties and may dominate chemical reactions on Fe3O4(111) when exposed to the ambient.

Structure and Electrochemistry of Lithium-Cobalt-Oxide Spinels and Their Role in 'layered-Spinel' Composite Cathodes

Introducing a spinel component into layered (LiMO2) or ‘layered-layered’ (Li2MnO3•LiMO2, typically M = Ni, Mn, Co) materials to form structurally integrated ‘layered-spinel’(LS) or ‘layered-layeredspinel’(LLS) materials has been demonstrated as a promising strategy to develop new cathode systems with enhanced electrochemical capacity and stability.[1-3] The rationale behind this approach is that 25% of the transition metal cations in the spinel component are located in the lithium-rich layers, thereby providing significant binding energy between the close-packed oxygen layers to maintain good stability at low lithium levels during the charging process. It is anticipated that these stabilizing M cations in the lithium layers, even in low concentrations, may contribute significantly to the performance of LS and LLS composite materials. However, relative to the extensive understanding of manganese-based spinel materials, little is known about the structural and electrochemical properties of lithium-cobalt-oxide (and nickel-substituted) spinel electrodes that can be synthesized in their discharged state, i.e., LiCo1-yNiyO2 (0≤y≤0.2), typically at about 400 °C;[4,5] These cobalt-based spinel electrodes, referred to as ‘lowtemperature’ LiCo1-yNiyO2 materials in the literature, have two notable advantages over lithiummanganese- oxide spinels: (1) lithium extraction from the lithiated spinel composition, LiCo1-yNiyO2, to the spinel composition, Li0.5Co1-yNiyO2 (or LiCo2-2yNi2yO4), occurs at a higher potential against lithium (~3.6V vs. 2.9V), and (2) a lower propensity for cobalt migration during the electrochemical reactions, particularly at high potentials, i.e., >4V, may be expected. This presentation will report on the structural and electrochemical properties of a series of Li2[Co1-x-yNixMny]2O4spinel materials, prepared by a ‘low-temperature’ solid-state synthesis route. The transition metal composition and synthesis conditions strongly affect the structure of these materials, and thereby their electrochemical properties. Efforts to integrate these spinel compositions into layered or ‘layered-layered’ electrode materials will be discussed. References C. S. Johnson, N. Li, J. T. Vaughey, S. A. Hackney, M. M. Thackeray, Electrochem. Commun., 7, 528 (2005).D. Kim, G. Sandi, J. R. Croy, K. G. Gallagher, S.-H. Kang, E. Lee, M. D. Slater, C. S. Johnson, M. Thackeray, J. Electrochem. Soc., 160, A31 (2013).B. R. Long, J. R. Croy, J. S. Park, J. Wen, D. J. Miller, M. M. Thackeray, J. Electrochem. Soc, 161, A2160 (2014)R. J. Gummow, M. M. Thackeray, W. I. F. David and S. Hull, Materials Research Bulletin, 27, 327 (1992).R. J. Gummow and M. M. Thackeray, Solid State Ionics, 53, 681 (1992). Acknowledgment Support from the Vehicle Technologies Program, Hybrid and Electric Systems, in particular, David Howell, Peter Faguy, and Tien Duong at the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, is gratefully acknowledged. The submitted document has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (“Argonne”). Argonne, a U.S. Department of Energy Office of Science laboratory, is operated under Contract No. DE-AC02-06CH11357. The U.S. Government retains for itself, and others acting on its behalf, a paid-up nonexclusive, irrevocable worldwide license in said article to reproduce, prepare derivative works, distribute copies to the public, and perform publicly and display publicly, by or on behalf of the Government.

Effect of mill type on the size reduction and phase transformation of gamma alumina

The influence of stress modes and comminution conditions on the effectiveness of particle size reduction of a common catalyst support; γ-Alumina is examined through a comparative assessment of three different mill types. Air jet milling is found to be the most effective in reducing particle size from a d90 of 37µm to 2.9µm compared to planetary ball milling (30.2µm) and single ball milling (10.5µm). XRD and TEM studies confirm that the planetary ball mill causes phase transformation to the less desired α-Alumina resulting in a notable decrease in surface area from 136.6m2/g to 82.5m2/g as measured by the BET method. This is consistent with the large shear stresses under high shear rates prevailing in the planetary ball mill when compared to the other mill types. These observations are consistent with a shear-induced phase transformation mechanism brought about by slip on alternate close packed oxygen layers from a cubic close packed to a hexagonal close packed structure.

Defects and inhomogeneities in Fe3O4(111) thin film growth on Pt(111)

Growth and surface termination of a Fe${}_{3}$O${}_{4}$(111) thin film on a Pt(111) surface were examined by a combination of low-energy electron microscopy, selected area low-energy electron diffraction (LEED), and x-ray-induced photoemission electron microscopy. The film exhibits the predominance of one out of two possible rotational domains, independent of film thickness. The morphology strongly depends on preparation conditions, e.g., at high oxidation temperature FeO/Pt(111) domains are formed that prevent the closure of the thin film. Dynamical LEED analysis and spot-profile analysis LEED (SPA-LEED) show that the surface exposes \textonequarter{} monolayer of Fe over a close-packed oxygen layer only when the sample is subsequently annealed in ultrahigh vacuum at 900 K. In contrast, the as-prepared films grown by oxidation at 1000 K and subsequent cooling down in oxygen, additionally exhibit small FeO${}_{x}$ agglomerates that rest upon the canonical surface termination. Their formation as a function of the various preparation conditions of the thin film is discussed.

Atomically resolved interface structure of a vanadium sesquioxide(0 0 0 1) film grown on Cu 3Au(0 0 1)

Heterointerfaces between oxides and metals are of wide-ranging importance. High resolution transmission electron microscopy (HRTEM) with spherical aberration (Cs) image correction has been used to unravel the metal–oxide interface on an atomic scale. The method is exemplified at the interface of a thin two-dimensional monocrystalline film of V 2O 3(0 0 0 1) grown on a Cu 3Au(0 0 1) sample. At the interface an extra vanadium monolayer is introduced between the part of the Cu 3Au substrate and the oxide layer. The location of the extra vanadium is not related with the V 2O 3 crystallography but instead connected to the Cu 3Au(0 0 1) metal side. The oxide layer ends at the interface with the quasi-hexagonal close packed oxygen layer of bulk truncated V 2O 3(0 0 0 1). The stacking sequence of oxygen columns follows visibly the vanadium oxide part and is directionally decoupled from the Cu 3Au(0 0 1)–V region. The HRTEM images show not only the position of the metal atoms but clearly also the oxygen sites which makes this method well suited for the investigation of metal oxide interfaces.

Molecular scale investigations of the reactivity of magnetite with formic acid, pyridine, and carbon tetrachloride

The (111) surface of magnetite, a dominant growth and fracture surface of this mineral, has been studied using Scanning Tunneling Microscopy (STM) at atomic resolution. In line with previous work, this surface shows three possible terminations which can be related to different level slices through the bulk structure. The reactivities of these different surface terminations have been explored by exposing them, under highly controlled conditions, to formic acid, pyridine, and carbon tetrachloride and undertaking further imaging at atomic resolution. These investigations have, themselves, helped to discriminate between competing models of surface structure. The so-called A′ surface termination we now regard as exposing 1/4 monolayer of tetrahedrally coordinated Fe ions over a close packed oxygen layer, and the A surface termination as being these same Fe ions but each capped by a single oxygen. The so-called B surface termination, previously thought to expose 1/2 monolayer of equal numbers of octahedral and tetrahedral Fe ions over a close packed oxygen layer, we now regard as this same arrangement but again with each Fe capped with an oxygen. For all three molecules, the A′ surface is most reactive but the reactions observed are markedly different. Formic acid undergoes dissociation at the magnetite surface, apparently chemisorbing at the A′ surface via a bidentate non-bridging complex. On the same A′ surface, pyridine is chemisorbed through a monodentate linkage via the ‘basal’ nitrogen of the molecule. For both formate and pyridine, a weaker interaction (a ‘physisorption’) was observed with the A and B surfaces, interpreted as involving attachment of the intact molecule. The exceptions to this were where the interaction involved chemisorption at defects on A and B type surfaces. The behavior of carbon tetrachloride on the magnetite surface is very different to the other molecules studied. Only the A′ surface is significantly reactive, and the molecule undergoes a series of temperature-dependant dissociation and surface chemical reactions. These involve sorption of intact CCl 4 molecules at the lowest temperatures, dissociation into CCl 2 and Cl species at around room temperature, and removal from the magnetite of surface oxygens to form OCCl 2 and then Fe to form FeCl 2 at successively higher temperatures. At around room temperature, both strongly bonded Cl atoms and weakly bonded CCl 2 molecules appear to co-exist on the same (A′ type) surface, a situation not previously observed in iron oxide systems.

Structure of synthetic 6-line ferrihydrite by electron nanodiffraction

Single-crystal electron diffraction patterns of nanocrystals in two samples of synthetic six-line ferrihydrite (6LFh) were obtained using electron nanodiffraction to produce diffraction patterns from areas between ~0.7 and 5 nm across. One of the samples was synthesized at 75 °C by a conventional method; the other was synthesized by a recently developed room-temperature technique. Structures of individual nanocrystals were investigated by comparing experimental and simulated electron-diffraction patterns. The most common structure in each sample is based on double-hexagonal (ABAC) stacking of close-packed oxygen layers, and is similar to the “defect-free ferrihydrite” structure proposed by Drits and co-workers. Nanocrystals with maghemite- or magnetite-like structures and structures similar to those in two-line ferrihydrite (2LFh) occur less commonly in both samples. The sample synthesized at room temperature has a small amount of hematite, which was not found in nanodiffraction patterns from the 75 °C sample. The most common structure in 6LFh is distinct from those previously determined by nanodiffraction of 2LFh, indicating that 6LFh is not simply a more crystalline form of 2LFh.

Defect structures on epitaxialFe3O4(111)films

Epitaxial ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}(111)$ films were grown onto a Pt(111) substrate by repeated cycles of iron deposition and subsequent oxidation in ${10}^{\ensuremath{-}6}$ mbar oxygen. A previous low energy electron diffraction (LEED) intensity analysis revealed the regular ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}(111)$ surface to expose $\frac{1}{4}$ monolayer Fe atoms over a close-packed oxygen layer underneath. With scanning tunneling microscopy (STM) a hexagonal lattice of protrusions with a 6 \AA{} periodicity is observed. The protrusions are assigned to the topmost layer Fe atoms, which agrees with the dominating $\mathrm{Fe}3d$ electron density of states near the Fermi level related to these surface atoms, as revealed by ab initio spin-density-functional theory calculations. The most abundant type of point defects observed by STM are attributed to iron vacancies in the topmost layer, which was confirmed by LEED intensity calculations where different types of vacancy defects have been simulated. For oxidation temperatures around 870 K the regular ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}(111)$ surface coexists with several different surface structures covering about 5% of the films, which expose $\frac{3}{4}$ ML iron atoms or close-packed iron and oxygen layers, resulting in surface domains that are FeO(111) and ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}(111)$ in nature. These domains are arranged periodically on the surface and form ordered biphase superstructures. At 1000 K oxidation temperature they vanish and only the regular ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}(111)$ surface remains.

Fe 3O 4(111) surface structure determined by LEED crystallography

The surface structure formed on epitaxial Fe 3O 4(111) magnetite films grown onto Pt(111) was re-examined by a full dynamical low energy electron diffraction (LEED) intensity analysis. Prior to the LEED measurements the films were investigated with scanning tunneling microscopy regarding their surface defect concentrations and the possible coexistence of different surface terminations. After a final oxidation at 1000 K in 10 −6 mbar oxygen partial pressure one defined surface structure is formed, and for films with low surface defect concentrations the best fit structure reveals a Pendry R-factor of 0.20 based on a data set with a total energy range of 1300 eV. It corresponds to an unreconstructed bulk termination of Fe 3O 4(111), which exposes 1/4 monolayer of iron atoms over a hexagonal close-packed oxygen layer underneath. The outermost iron plane is relaxed inward towards the underlying oxygen plane by 41±7% of the corresponding bulk spacing, followed by strong relaxations of the next three interlayer spacings. The same surface termination with slightly different relaxations was obtained in an earlier analysis, which corresponded to a local R-factor minimum in parameter space [W. Weiss et al., Phys. Rev. Lett. 71 (1993) 1848]. The energetics of the Fe 3O 4(111) surface structure is discussed considering the mixed iono-covalent bond character in this oxide.

Topotactic Routes to Layered Calcium Cobalt Oxides

Four CaxCoO2(0.26≤x≤0.50) oxides have been synthesized by the low-temperature ion exchange of layered NaxCoO2oxides. The CaxCoO2structures all consist of [CoO2]nsheets of edge-sharing octahedra with Ca2+ions between layers in trigonal prismatic coordination. Different packing sequences of the close-packed oxygen layers can be obtained. Ca0.50CoO2(a=4.881(2) Å,b=2.826(1) Å,c=5.654(3) Å,β=105.86(5)°) and Ca0.26CoO2(a=4.961(7) Å,b=2.805(3) Å,c=5.671(6) Å,β=106.7(1)°) assume the monoclinicP′3 structure, while Ca0.35CoO2(a=2.812(3) Å,c=10.872(2) Å) and Ca0.27CoO2(a=2.812(1) Å,c=10.874(5) Å) take the hexagonalP2 structure. The structural relationships between the CaxCoO2products and their NaxCoO2precursors are discussed, and the relationship between composition and [CoO2]nlayer-spacing in variousAxCoO2systems is illustrated.

In situ RHEED and XPS studies of epitaxial thin α-Fe2O3(0001) films on sapphire

In situ RHEED and XPS measurements of epitaxial α-Fe2O3(0001) films are reported as a function of the number of deposited monolayers. The films were prepared on α-Al2O3(0001) substrates by MBE. The RHEED patterns suggest that layer-by-layer growth of α-Fe2O3(0001) occurs for the first few monolayers. Subsequently, the growth mode changes to three-dimensional growth. The in-plane lattice constant of the first monolayer of α-Fe2O3(0001) is expanded relative to that of the bulk, although in the case of lattice matching between α-Al2O3 and α-Fe2O3 a contraction would be expected. This can be explained by assuming a basic hexagonal structure for the first monolayer with a random distribution of ferric ions over the octahedral sites between the close-packed oxygen layers. Beyond the first monolayer, the ordered corundum structure is formed. The lineshapes of the XPS Fe 2p core level spectra are also found to be thickness-dependent. The deviation of the Madelung potential at the surface shifts the positions of the Fe 2p peaks to lower binding energies. For the first few monolayers, the satellite intensity is reduced because the interplanar contraction leads to a shorter Fe-O distance.

γ-Al2O3 formation from pulsed-laser irradiated sapphire

High-resolution transmission electron microscopy was used to examine the effect of laser irradiation of sapphire (single crystalline α-Al2O3). It was observed that laser-melted material resolidified as γ-Al2O3 epitactically grown on the (0001) plane of α-Al2O3 having an orientation relationship (0001)α//(111)γ and [011̄0]α//[11̄0]γ. The interface between unmelted α-Al2O3 and resolidified γ-Al2O3 is atomically flat with steps of one to a few close-packed oxygen layers. The high thermal gradient in the α-Al2O3 did not produce any interfacial dislocations. However, pronounced lattice distortions existed in the resolidified γ-Al2O3. It is argued that the very rapid cooling rate present during solidification prevents the ordering of Al atoms that is required for the formation of the stable α-Al2O3 phase.

Direct Observations of β″″-Structures in a K2O-Fe2O3-CdO System by High-Resolution Electron Microscopy

The direct confirmation of the existence of Cd-stabilized β″″-ferrite prepared as a stable phase in a K2O-Fe2O3-CdO system was done by high-resolution electron microscopy. It was confirmed that the Cd-stabilized β″″-ferrite had a rhombohedral symmetry with lattice constants a = 0.600 and c = 5.026 nm. The structure is composed of an alternate stacking of ion-conductive layers and spinel-like blocks which have six cubic close-packed oxygen layers expressed as · · · A1(BCABCA)B1(CABCAB)C1(ABCABC)A1 · · ·. In addition, twins which had reversed stacking sequences were observed in the spinel-like blocks.

Magnetite Fe 3O 4(111): surface structure by LEED crystallography and energetics

The atomic structure of the Fe 3O 4(111) surface was determined by means of dynamical low-energy electron diffraction (LEED) after being prepared in two different ways. In a first experiment up to 10 monolayers of well-ordered iron oxide films were grown epitaxially onto Pt(111) substrates. A 1 monolayer thick film forms a hexagonal lattice with a lateral repeat distance of 3.2 Å, 15% larger than the lateral periodicity of Pt(111). Above 1 monolayer coverage the LEED pattern reveals a lateral repeat distance of 3.0 Å, indicating a contraction of the oxide lattice with respect to the first monolayer. This new LEED pattern shows half-order spots and is compatible with (2 × 2) reconstructed FeO(111) and bulk terminated Fe 3O 4(111) surfaces. By applying automated tensor LEED to many possible surface structures of these two iron oxides, 8 monolayer thick films were identified to be magnetite, Fe 3O 4. Auger electron spectroscopy (AES) measurements on these films also reveal a stoichiometry close to that of Fe 3O 4. In a second experiment the (111) surface of an α-Fe 2O 3 single crystal was prepared by Ar + ion bombardment and subsequent annealing. Brief annealing to 900, 1000 and 1200 K in 10 −10 and 10 −6 mbar oxygen creates three different LEED patterns indicating structural transformations occurring in the surface region of this crystal. Prolonged annealing to temperatures between 900 and 1200 K stabilizes the same LEED pattern and gives identical intensity-voltage curves as obtained on the 8 monolayer thick films. Therefore the crystal surface region has been reduced to Fe 3O 4 and has the same surface structure as the epitaxially grown films. X-ray photoelectron spectroscopy (XPS) measurements on this surface also reveal a stoichiometry dose to that of Fe 3O 4. The best fit structure for both preparations corresponds to an unreconstructed, but strongly relaxed, polar (111) surface termination of magnetite that exposes 1 4 monolayer of Fe ions over a distorted hexagonal close-packed oxygen layer and minimizes the number of dangling bonds. The surface relaxations are probably driven by electrostatic forces. Our results indicate that minimization of both the number of dangling bonds and the electrostatic surface energy are important in determining the termination and relaxations of this polar metal oxide surface. The electrostatic surface energetics is qualitatively discussed within general, simple concepts applicable to all ionic crystals.

High Resolution Transmission Electron Microscopy of Metallic Film/Laser-Irradiated Alumina Couples.

AbstractA near-surface thin layer is melted when single crystal alumina (sapphire) is pulsed laserirradiated in an Ar-4%H2 atmosphere. γ-alumina grows epitaxially from the (0001) face of axalumina (sapphire) during the rapid solidification of this layer that occurs once the laser pulse is over. Cross sectional high resolution transmission electron microscopy (HRTEM) reveals that the interface between unmelted sapphire and γ-alumina is atomistically flat with steps of one to a few close-packed oxygen layers; however, pronounced lattice distortions exist in the resolidified γ-alumina. HRTEM also is used to study the metal-ceramic interface of a copper film deposited on a laser-irradiated alumina substrate. The observed changes of the interfacial structure relative to that of unexposed substrates are correlated with the strong enhancement of film-substrate bonding promoted by laser irradiation. HRTEM shows that a thin amorphous film is produced after irradiation of 99.6% polycrystalline alumina. Formation of a diffuse interface and atomic rearrangements that can take place in metastable phases contribute to enhance the bonding strength of copper to laser-irradiated alumina.

Surface structure determination of an oxide film grown on a foreign substrate: Fe3O4 multilayer on Pt(111) identified by low energy electron diffraction.

For the first time a detailed surface structure determination is reported for an oxide film grown on a foreign metal substrate. Well-ordered iron oxide films were grown onto Pt(111) substrates and were identified by a dynamical low energy electron diffraction analysis to be magnetite, Fe[sub 3]O[sub 4]. They form an unreconstructed polar (111) surface termination that exposes 1/4 monolayer of Fe ions over a distorted hexagonal close-packed oxygen layer and minimizes the number of dangling bonds. The surface also exhibits large relaxations that may be driven by electrostatic forces.

The nature of the dispersoids in INCONEL alloy M A6000

Analytical transmission electron microscopy has been used to examine the oxide dispersion in the mechanically alloyed, nickel-based, dispersion strengthened superalloy INCONEL alloy MA6000. Four mixed AI-Y oxides were identified in consolidated powder: Y3Al5O12, yttrium aluminium garnet (YAG); YAIO3, yttrium aluminium perovskite (YAP); Y4Al2O9, yttrium aluminium monoclinic (YAM), and a previously unidentified YAlOI3 polymorph. This new phase, designated yttrium aluminium hexagonal (YAH), has lattice parameters ofa = 2.206 ±0.035 nm andc = 3.219 ± 0.096 nm, a space group of P63mc and consists of 18 closepacked oxygen layers with the yttrium and aluminium cations in the resulting interstices. It is proposed that the high local stresses, strains and temperatures which occur during the mechanical alloying process facilitate the formation of the highly complex YAH phase. All four oxide types also contain significant amounts of zirconium (up to 13 cation at%) which randomly substitutes for both the yttrium and aluminium ions. This substitution was sufficient to have caused the removal of 75% of the zirconium from solution in the matrix.

Brillouin-scattering measurements of single-crystal forsterite to 40 kbar at room temperature

The first Brillouin-scattering measurements of single-crystal Mg2SiO4 have been made at 1 atm and pressures up to 40 kbar in a diamond-anvil cell at room temperature. The elastic moduli C11,C22,C33,C44,C55, and C66, and their pressure derivatives were obtained. These results were compared with those obtained by ultrasonic measurements up to 10 kbar. The observation of low dCij/dP slopes for the transverse moduli. C44, C55, and C66, and the evidence for negative second derivatives as well, support Poirier’s proposed mechanism for the olivine→spinel transition due to gliding of close-packed oxygen layers. Moreover, the numerical relationships among photoelastic constants were determined by studying the intensity ratio of LA to TA modes.