The influence of ionic radii of cations and covalent forces on the unit cell dimensions of spinels

Fe-, Cr- and Al-spinels were synthesized and their unit cell sizes determined by means of X-rays. Differential thermal curves show that the magnetic inversion of Fe₂O₃ at 680° C accelerates the formation of the ferrites when the constituent oxides are heated together.A correlation can be made between ionic radii of cations and unit cell dimensions provided the effect of covalent forces in the lattice is taken into account. The values for ionic radii of cations as given byAhrens (1952) permit a better correlation than those ofGoldschmidt.A shrinkage of 0.01 Å in the unit cell size per 0.01 Å decrease in the ionic radius of the divalent cations was determined when spinels with the same cation arrangement in the same group were compared. A shrinkage of 0.027 Å in the unit cell size per 0.01 Å decrease in the ionic radius of the trivalent cations was determined in spinels having the same divalent cation and cation arrangement when the trivalent cations form the same type of bonds.The half-occupation of the 3d orbits in Mn²⁺ and Fe³⁺ causes abnormally high unit cell dimensions in spinels where these ions are incorporated in octahedral sites. This is attributed to the formation of electrovalent bonds by these ions. Variable forces of contraction in the lattice are revealed when the unit cell dimensions are correlated with the ionic radii of cations. The force of contraction can be satisfactorily explained as being due to covalent forces in the spinel structure. The magnitude of this force or the degree of covalence in the bonds increases in the following order of cations where these are situated in tetrahedral sites:The divalent transition element ions, Fe²⁺, Co²⁺ and Ni²⁺; the B-Sub-group element ions Cd²⁺ and Zn²⁺; Fe³⁺ in tetrahedral co-ordination.     

Prediction of Gibbs free energies of formation of minerals of the alunite supergroup

A method for the prediction of Gibbs free energies of formation for minerals belonging to the alunite family is proposed, based on an empirical parameter Δ_GO⁼ M^z+(c) characterizing the oxygen affinity of the cation M^z+. The Gibbs free energy of formation from constituent oxides is considered as the sum of the products of the molar fraction of an oxygen atom bound to any two cations, multiplied by the difference of oxygen affinity Δ_GO⁼ M^z+(c) between any two consecutive cations. The Δ_GO⁼ M^z+(c) value, using a weighing scheme involving the electronegativity of a cation in a specific site (12-fold coordination site, octahedral and tetrahedral) is assumed to be constant. It can be calculated by minimizing the difference between experimental Gibbs free energies (determined from solubility measurements) and calculated Gibbs free energies of formation from constituent oxides. Results indicate that this prediction method gives values within 0.5% of the experimentally measured values. The relationships between Δ_GO⁼ M^z+(alunite) corresponding to the electronegativity of a cation in either dodecahedral sites, octahedral sites or tetrahedral sites and known as Δ_GO⁼ M^z+(aq) were determined, thereby allowing the prediction of the electronegativity of rare earth metal ions and trivalent ions in dodecahedral sites and highly charged ions in tetrahedral sites. This allows the prediction of Gibbs free energies of formation of any minerals of the alunite supergroup (bearing various ions located in the dodecahedral and tetrahedral sites). Examples are given for hydronium jarosite and hindsalite, and the results appear excellent when compared to experimental values.     

The A and B mica layers and the crystal structure of sheet silicates

A discussion of the transition from the ideal hexagonal mica structure to the ideal ditrigonal one, leads to the conclusion that the single mica layer may have two different structures (labelled A and B). The recent literature data show that both the A and B structures have been detected in some triocahedral layer lattice silicates found in nature. An examination of the structural stability of the A and B structures suggests that the last one may not be realized by dioctahedral layer lattice silicates. The concept of two structurally different mica layers, which however have the same lattice constants, greatly improves the understanding of polymorphism and twin laws in layer lattice silicates.The structural features of the tetrahedral sheet, octahedral sheet and interlayer region are carefully examined. Thus we can reach the following conclusions: the tetrahedal sheet is not entirely free to reduce its lateral dimensions by the mechanism of tetrahedal rotation owing to the repulsion among O_bas atoms; the octahedral sheet in layer lattice silicates, may increase or reduce its lateral dimensions as compared to the lateral dimensions it has in the hydroxide minerals; the interlayer region is characterized by a regular octahedral coordination of the O_bas around the interlayer cation. On the ground of these conclusions, new structural models for some selected layer lattice silicates are proposed.Notations O_bas basal oxygen atoms of the (Al, Si)O₄ tetrahedra - O_ap apical oxygen atoms of the (Al, Si)O₄ tetrahedra - b _tetr b dimension which the tetrahedral sheet would assume if unconstrained - b _oct b dimension which the octahedral sheet has in the hydroxide minerals - b _obs observed value of b - c _oct ^* thickness of the octahedral sheet - d _o distance between an octahedral cation and an O_ap atom - d _int distance between an interlayer cation and an O_bas atom - average tetrahedral rotation from ideal hexagonal symmetry     

High-pressure decomposition of MCr2O4 spinels (M=Mg, Mn, Zn) by ab initio methods

The high-pressure equation of state of the normal spinels MgCr₂O₄ (picrochromite), MnCr₂O₄ and ZnCr₂O₄, and their reaction of decomposition into Cr₂O₃ (eskolaite) and MO (rocksalt-type) component oxides, were investigated by periodic unrestricted Hartree-Fock calculations. All-electron basis sets, and an a posteriori correction for the electron correlation energy, based on Density-Functional-Theory, were employed. Interpolation of results by the P-V Murnaghan equation of state yielded the equilibrium volume and energy, and the bulk modulus and its pressure derivative, for each of the seven phases (three spinels, three rocksalt oxides and eskolaite) considered. The simulated behaviour of interatomic distances vs pressure shows similar compressibilities of M-O bonds in both octahedral and tetrahedral coordinations. Binding energies and formation enthalpies of spinels from oxides are also computed and compared to available experimental data. The predicted decomposition pressures of Mg, Mn and Zn chromium spinels are 19, 23 and 34 GPa, respectively. The greater stability of ZnCr₂O₄ is related to Zn²⁺ being better suited to tetrahedral coordination than the other M²⁺ cations. Such results are strongly supported by the excellent agreement previously obtained between simulated (11 GPa) and experimental (13 GPa) pressures of the decomposition of MgAl₂O₄ spinel into corundum and periclase. Received: 9 February 1998 / Accepted: 12 October 1998     

The factors influencing cation site-preferences in spinels a new mendelyevian approach

Pseudopotential orbital radii r _s , r _p are used to construct an index, r _σ=r _s +r _p , which characterizes the average potential experienced by atomic valence electrons. A plot of r _A ^σ verses r _B ^σ for 172 chalogenide spinels (AB₂X₄, X=O, S, Se, Te) leads to two well defined areas, which separate normal and inverse spinels, with only four errors (a predictive success rate of 98%). The gross sorting is achieved without recourse either to the number of d-electrons or an orbital radius r _d , from which it is inferred that it is the energies and extents of the cation s and p-orbitals which primarily determine coordination number in these systems. This approach to the problem of cation distribution in spinels is contrasted with the less generally applicable, traditional, crystal field ideas. The relevance of both r _σ and crystal field stabilization energies to the thermodynamics of spinel reactions is also discussed.     

Speciation and thermodynamic properties for cobalt chloride complexes in hydrothermal fluids at 35-440 °C and 600 bar: An in-situ XAS study

Aqueous Co(II) chloride complexes play a crucial role in cobalt transport and deposition in ore-forming hydrothermal systems, ore processing plants, and in the corrosion of special Co-bearing alloys. Reactive transport modelling of cobalt in hydrothermal fluids relies on the availability of thermodynamic properties for Co complexes over a wide range of temperature, pressure and salinity. Synchrotron X-ray absorption spectroscopy was used to determine the speciation of cobalt(II) in 0-6 m chloride solutions at temperatures between 35 and 440 °C at a constant pressure of 600 bar. Qualitative analysis of XANES spectra shows that octahedral species predominate in solution at 35 °C, while tetrahedral species become increasingly important with increasing temperature. Ab initio XANES calculations and EXAFS analyses suggest that in high temperature solutions the main species at high salinity (Cl:Co >> 2) is CoCl₄²⁻, while a lower order tetrahedral complex, most likely CoCl₂(H₂O)_2(aq), predominates at low salinity (Cl:Co ratios ∼2). EXAFS analyses further revealed the bonding distances for the octahedral Co(H₂O)₆²⁺ (^octCo-O = 2.075(19) Å), tetrahedral CoCl₄²⁻ (^tetCo-Cl = 2.252(19) Å) and tetrahedral CoCl₂(H₂O)_2(aq) (^tetCo-O = 2.038(54) Å and ^tetCo-Cl = 2.210(56) Å). An analysis of the Co(II) speciation in sodium bromide solutions shows a similar trend, with tetrahedral bromide complexes becoming predominant at higher temperature/salinity than in the chloride system. EXAFS analysis confirms that the limiting complex at high bromide concentration at high temperature is CoBr₄²⁻. Finally, XANES spectra were used to derive the thermodynamic properties for the CoCl₄²⁻ and CoCl₂(H₂O)_2(aq) complexes, enabling thermodynamic modelling of cobalt transport in hydrothermal fluids. Solubility calculations show that tetrahedral CoCl₄²⁻ is responsible for transport of cobalt in hydrothermal solutions with moderate chloride concentration (∼2 m NaCl) at temperatures of 250 °C and higher, and both cooling and dilution processes can cause deposition of cobalt from hydrothermal fluids.     

The molar volume of FeO–MgO–Fe2O3–Cr2O3–Al2O3–TiO2 spinels

We define and calibrate a new model of molar volume as a function of pressure, temperature, ordering state, and composition for spinels in the supersystem (Mg, Fe²⁺)(Al, Cr, Fe³⁺)₂O₄ ? (Mg, Fe²⁺)₂TiO₄. We use 832 X-ray and neutron diffraction measurements performed on spinels at ambient and in situ high-P, T conditions to calibrate end-member equations of state and an excess volume model for this system. The effect on molar volume of cation ordering over the octahedral and tetrahedral sites is captured with linear dependence on Mg²⁺, Al³⁺, and Fe³⁺ site occupancy terms. We allow standard-state volumes and coefficients of thermal expansion of the end members to vary within their uncertainties during extraction of the mixing properties, in order to achieve the best fit. Published equations of state of the various spinel end members are analyzed to obtain optimal values of the bulk modulus and its pressure derivative, for each explicit end member. For any spinel composition in the supersystem, the model molar volume is obtained by adding excess volume and cation order-dependent terms to a linear combination of the five end-member volumes, estimated at pressure and temperature using the high-T Vinet equation of state. The preferred model has a total of 9 excess volume and order-dependent parameters and fits nearly all experiments to within 0.02 J/bar/mol, or better than 0.5 % in volume. The model is compared to the current MELTS spinel model with a demonstration of the impact of the model difference on the estimated spinel-garnet lherzolite transition pressure.     

DFT study of the cation arrangements in the octahedral and tetrahedral sheets of dioctahedral 2:1 phyllosilicates

Quantum mechanical calculations based on the density functional theory (DFT) are used to study the crystal structures of dioctahedral 2:1 phyllosilicates. The isomorphous cation substitution is investigated by exploring different substitutions of octahedral Al³⁺ by Mg²⁺ or Fe³⁺, tetrahedral substitution of Si⁴⁺ by Al³⁺, and different interlayer cations (IC) (Na⁺, K⁺, Ca²⁺, and Mg²⁺). Samples with different kinds of layer charges are studied: only tetrahedrally charged, only octahedrally charged, or mixed octahedral/tetrahedral charged. The effect of the relative arrangements of these substitutions on the lattice parameters and total energy is studied. The experimental observation of segregation tendency of Fe³⁺ and dispersion tendency of Mg²⁺ in the octahedral sheet is reproduced and explained with reference to the relative energies of the octahedral cation arrangements. These energies are higher than those due to the IC/tetrahedral and IC/octahedral relative arrangements. The tetrahedral and octahedral substitutions that generate charged layers also tend to be dispersed. The octahedral cation exchange potentials change with the IC-charge/ionic radius value.     

Cation distribution and structure modelling of spinel solid solutions

 This paper presents an improved generalisation of cation distribution determination based on an accurate fit of all crystal-chemical parameters. Cations are assigned to the tetrahedral and octahedral sites of the structure according to their scattering power and a set of bond distances optimised for spinel structure. A database of 295 spinels was prepared from the literature and unpublished data. Selected compositions include the following cations: Mg²⁺, Al³⁺, Si⁴⁺, Ti⁴⁺, V³⁺, Cr³⁺, Mn²⁺, Mn³⁺, Fe²⁺, Fe³⁺, Co²⁺, Ni²⁺, Zn²⁺ and vacancies. Bond distance optimisation reveals a definite lengthening in tetrahedral distance when large amounts of Fe³⁺ or Ni²⁺ are present in the octahedral site. This means that these cations modify the octahedral angle and hence the shared octahedral edge, causing an increase in the tetrahedral distance with respect to the size of the cations entering it. Some applications to published data are discussed, showing the capacity and limitations of the method for calculating cation distribution, and for identifying inconsistencies and inaccuracies in experimental data. Received: 19 February 2001 / Accepted: 1 June 2001     

Atomic and ionic radii: a comparison with radii derived from electron density distributions

 The bonded radii of anions obtained in topological analyses of theoretical and experimental electron density distributions differ from atomic, ionic and crystal radii in that oxide-, fluoride-, nitride- and sulfide-anion radii are not constant for a given coordination number. They vary in a regular way with bond length and the electronegativity of the cation to which they are bonded, exhibiting radii close to atomic radii when bonded to a highly electronegative cation and radii close to ionic radii when bonded to a highly electropositive cation. The electron density distributions show that anions are not spherical but exhibit several different radii in different bonded directions. The bonded radii of cations correlate with ionic and atomic radii. But unlike ionic radii, the bonded radius of a cation shows a relatively small increase in value with an increase in coordination number. In contrast to atomic and ionic radii, the bonded radius of an ion in a crystal or molecule can be used as a reliable and well-defined estimate of its radius in the direction of its bonds. Received April 16, 1996 / Revised, accepted August 6, 1996     

Sapphirine II

The crystal structure of aP2₁/a polymorph of sapphirine (a=11.286(3),b=14.438(2),c=9.957(2) Å, β=125.4(2) °) of composition [Mg_3.7Fe _0.1 ²⁺ Al_4.1- Fe _0.1 ³⁺ ]^IV[Si_1.8Al_4.2]^IVO₂₀ was refined using structure factors determined by both neutron and x-ray diffraction methods to conventionalR factors of 0.067 and 0.031. respectively, forF _obs>2σ. The results of the two refinements agree reasonably well, but a half-normal probability plot (Abrahams, 1974) comparing the two data sets indicates that the pooled standard deviations of the atomic coordinates have been underestimated by a factor of two. The structure of sapphirine, solved initially by Moore (1969), consists of cubic closest packed oxygens with octahedral and predominantly tetrahedral layers alternately stacked along [100]. The layer in which 70% of the octahedral sites are occupied has an Mg-Al distribution characterized by Mg-rich octahedra sharing edges mainly with Al-rich octahedra. Mean octahedral bond lengths correlate well with Al occupancy determined by neutron site refinement if the relative number of shared octahedral edges is taken into account (see Table 1). The predominantly tetrahedral layer has 10% of the octahedral sites occupied by Al and 30% of the tetrahedral sites occupied by Al-Si in the ratio 2.33∶1. There are single chains of Al-Si tetrahedra parallel toz with corner-sharing wing tetrahedra (T5 andT6) on either side in the (100) plane. The meanT-O distance is highly correlated with Al occupancy, X_Al, as determined from the neutron site refinement: $$\langle T - O\rangle = 1.656 + 0.105X_{Al} (r^2 = 0.995).$$ Details of the neutron refinement are summarized below.     

Controlled time–temperature oxidation reaction in a synthetic Mg-hercynite

The oxidation of a synthetic hercynite with composition Fe²⁺ _0.699Mg_0.301Al_1.941Fe³⁺ _0.059O₄ was investigated by X-ray single-crystal diffraction. Heating runs at 500°C up to 212 h did not produce detectable oxidation, but only a small variation in oxygen coordinate u, consistent with very limited reordering of Mg and Al in tetrahedral (T) and octahedral (M) sites, respectively. Oxidation began after the first run at 600°C, producing progressive decreases in u, cell parameter a and the mean atomic number in T site. After 1,842 h at 600°C, the transformation was close to equilibrium, with about 70% of ferrous iron transformed into ferric. This produced about 0.17 vacancies per formula unit, and caused a great increase in the displacement parameters of oxygen and M sites. Vacancies were strongly ordered in M sites, and the oxygen displacement parameter becames anisotropic, unlike stoichiometric spinels—because some of the oxygen coordination polyhedra have a vacancy instead of a cation in one vertex. The behaviour of displacement parameters in this case supports the calculated point defect distribution.     

Interpretation of K X-ray emission spectra and chemical bonding in oxides of Mg,Al and Si using quantitative molecular orbital theory

Quantitative molecular orbital calculations are reported for Mg, Al and Si in tetrahedral and octahedral coordination with oxygen. These calculations are employed to assign and interpret the ME_α, ME_β and OK_α X-ray emission spectra of the corresponding oxides. The interpretation of the MK_β spectrum reproduces the observed trends in main peak and satellite energies with variation of metal, ligand and geometry. The splitting of the main K_β peak, observed in many oxides, is found to be a result of interaction between adjacent metal atoms. The calculations also reproduce the observed trends in OK_α spectra. The electronic structures of the various oxides are discussed briefly.     

How stacking disorder can conceal the actual structure of micas: the case of phengites

The present study deals with how stochastic stackings of tetrahedral/octahedral phengitic sheets bearing diverse cation distributions affect diffraction signals and the structural inferences therefrom derived. The interest for such minerals is dictated by that the stability of phengite polytypes, their cation distributions and P/T conditions of crystallization are related to each other. We focus our attention on layers’ probabilistic sequences that preserve the topology of the polytypes 2M ₁(SG: C2/c) and 3T(SG: P3₁12). Neutron diffraction intensities are modelled by a Monte Carlo approach and then used as artificial experimental data for conventional structure refinements that yield the occupancy factors in the fourfold (Si, Al) and sixfold (Al, Mg) coordination sites of 2M ₁ and 3T. The cation ordering from structure refinement tallies with the one of the “average structure” of a stochastic stacking, but it can significantly differ from those of the individual tetrahedral/octahedral sheets. For instance, sheets having ordered cation arrangements can lead to a stochastic structure which is supposed to bear a fully disordered cation partitioning according to structure refinement. This affects the configuration entropy contributions: the values obtained by conventional refinements can deviate from the correct ones up to 30 %. The analysis of the equivalent reflection intensities brings to light the anomalies hinting at the occurrence of such stacking disorder (using modelled reflections, the mean ratio between standard deviation and average intensity of symmetry equivalent reflections is ideally 0 for perfect crystal structures, but it can amount up to 6 in stochastically disordered phengites). However, taking into account the instrumental uncertainties and the deviations from ideality of actual crystals, such phenomena are very difficult to be detected experimentally.     

Structural and IR relations among brucite-like divalent metal hydroxides

The a and c unit cell parameters of M(OH)₂, brucite-like structures with M=Mg, Ni, Co, Fe, Mn, Cd, and Ca, are considered in relation to M-O distances taken as the sum of the ionic radii, M^VI and O^IV. The a parameters are related to (M-O) by flattening of the octahedral coordination groups, with a flattening angle α=97.4±0.4°. The c parameters are divided into the octahedral layer thickness, h(oct), and the interlayer spacing h(inter). The latter is related to the (O-H) distances, which decrease as (M-O) increases. Infrared v(O-H) stretching frequencies vary with (M-O) in the same manner as h(inter) varies with (M-O). The values of v(O-H) decrease as h(inter) decreases and the atomic weight of the cations increases. The results are consistent with previous data for cation-substituted talcs. It is suggested that the M²⁺ ions associated with the O^2? ions modify the reduced mass of the O-H vibrations so that v(O-H) decreases with increasing mass of M.     

In situ high-temperature powder X-ray diffraction study on the spinel solid solutions (Mg1?xMnx)Cr2O4

Using a conventional high-T furnace, the solid solutions between magnesiochromite and manganochromite, (Mg_1−x Mn _x )Cr₂O₄ with x = 0.00, 0.19, 0.44, 0.61, 0.77 and 1.00, were synthesized at 1,473 K for 48 h in open air. The ambient powder X-ray diffraction data suggest that the V–x relationship of the spinels does not show significant deviation from the Vegard’s law. In situ high-T powder X-ray diffraction measurements were taken up to 1,273 K at ambient pressure. For the investigated temperature range, the unit-cell parameters of the spinels increase smoothly with temperature increment, indicating no sign of cation redistribution between the tetrahedral and octahedral sites. The V–T data were fitted with a polynomial expression for the volumetric thermal expansion coefficient (a_T = a₀ + a₁ T + a₂ T ^{- 2} \alpha_{T} = a_{0} + a_{1} T + a_{2} T^{ - 2} ), which yielded insignificant a ₂ values. The effect of the composition on a ₀ is adequately described by the equation a ₀ = [17.7(8) − 2.4(1) × x] 10⁻⁶ K⁻¹, whereas that on a ₁ by the equation a ₁ = [8.6(9) + 2.1(11) × x] 10⁻⁹ K⁻².     

Experimental study on the phase equilibria in the join CaMgSi2O6-CaCrCrSiO6 with special reference to the blue diopside

The behaviour of tetrahedrally coordinated and octahedrally coordinated Cr³⁺ ions in diopside is discussed from the study on the join CaMg-Si₂O₆-CaCrCrSiO₆. The molecule CaCrCrSiO₆ decomposes into uvarovite+eskolaite and its maximum solubility in diopside is 6.7 wt percent at 940 ° C. Crystalline phases are diopside ss (ss is abbreviation of solid solution), uvarovite ss, wollastonite ss, spinel and eskolaite. The diopside ss is blue in colour. Its optical spectra were measured in the wavelenght range of 325–2600 nm, and assigned after tetrahedral configuration Td and octahedral configuration Oh. It is estimated that octahedral Cr³⁺ ions are in high spin state, while tetrahedral Cr³⁺ ions may be probably in low spin state. The _t and B are 10,300–10,370 cm^–1 and 429–432 cm^–1. The CFSE for tetrahedral low spin Cr³⁺ ions is nearly the same as that for octahedral high spin Cr³⁺ ions. The ionic radii of tetrahedral low spin Cr³⁺ ions calculated are 0.47–0.53 Å, shrinked from the radius of octahedral high spin Cr³⁺ ion (0.615 Å) as much as 14–24 percent. Petrologic implications of the result are also discussed.The first half of the D. Sc. dissertation of K. Ikeda presented to Hokkaido University in June, 1976     

On local structural changes in lizardite-1T: {Si4+/Al3+}, {Si4+/Fe3+}, [Mg2+/Al3+], [Mg2+/Fe3+] substitutions

Geometrical changes induced by cation substitutions {Si⁴⁺/Al³⁺}[Mg²⁺/Al³⁺], {2Si⁴⁺/2Al³⁺} [2Mg²⁺/2Al³⁺], {Si⁴⁺/Fe³⁺} [Mg²⁺/Al³⁺] or [Mg²⁺/Fe³⁺], where {} and [] indicate tetrahedral and octahedral sheet in lizardite 1T, are studied by ab-initio quantum chemistry calculations. The majority of the models are based on the chemical compositions reported for various lizardite polytypes with the amount of Al in the tetrahedral sheets reported to vary from 3.5% to 8% in the 1T and 2H ₁, up to ~30% in the 2H ₂ polytype. Si⁴⁺ by Fe³⁺ substitution in the tetrahedral sheet with an Al³⁺ (Fe³⁺) in the role of a charge compensating cation in the octahedral sheet is also examined. The cation substitutions result in the geometrical changes in the tetrahedral sheets, while the octahedral sheets remain almost untouched. Substituted tetrahedra are tilted and their basal oxygens pushed down from the plane of basal oxygens. Ditrigonal deformation of tetrahedral sheets depends on the substituting cation and the degree of substitution.     

Hydrostatic compression of galenobismutite (PbBi<Subscript>2</Subscript>S<Subscript>4</Subscript>): elastic properties and high-pressure crystal chemistry

A single-crystal sample of galenobismutite was subjected to hydrostatic pressures in the range of 0.0001 and 9 GPa at room temperature using the diamond-anvil cell technique. A series of X-ray diffraction intensities were collected at ten distinct pressures using a CCD equipped 4-circle diffractometer. The crystal structure was refined to R1(|F₀| > 4σ) values of approximately 0.05 at all pressures. By fitting a third-order Birch-Murnaghan equation of state to the unit-cell volumes V ₀ = 700.6(2) ų, K ₀ = 43.9(7) GPa and dK/dP = 6.9(3) could be determined for the lattice compression. Both types of cations in galenobismutite have stereochemically active lone electron pairs, which distort the cation polyhedra at room pressure. The cation eccentricities decrease at higher pressure but are still pronounced at 9 GPa. Galenobismutite is isotypic with CaFe₂O₄ (CF) but moves away from the idealised CF-type structure during compression. Instead of the two octahedral cation sites and one bi-capped trigonal-prismatic site, PbBi₂S₄ attains a new high-pressure structure characterised by one octahedral site and two mono-capped trigonal-prismatic sites. Analyses of the crystal structure at high pressure confirm the preference of Bi for the octahedral site and the smaller one of the two trigonal-prismatic sites.     

Synthetic and natural chromium-bearing spinels: an optical spectroscopy study

Four samples of synthetic chromium-bearing spinels of (Mg, Fe²⁺)(Cr, Fe³⁺)₂O₄ composition and four samples of natural spinels of predominantly (Mg, Fe²⁺)(Al, Cr)₂O₄ composition were studied at ambient conditions by means of optical absorption spectroscopy. Synthetic end-member MgCr₂O₄ spinel was also studied at pressures up to ca. 10 GPa. In both synthetic and natural samples, chromium is present predominantly as octahedral Cr³⁺ seen in the spectra as two broad intense absorption bands in the visible range caused by the electronic spin-allowed ⁴ A _2g  → ⁴ T _2g and ⁴ A _2g  → ⁴ T _1g transitions (U- and Y-band, respectively). A distinct doublet structure of the Y-band in both synthetic and natural spinels is related to trigonal distortion of the octahedral site in the spinel structure. A small, if any, splitting of the U-band can only be resolved at curve-fitting analysis. In all synthetic high-chromium spinels, a couple of relatively narrow and weak bands of the spin-allowed transitions ⁴ A _2g  → ² E _g and ⁴ A _2g  → ² T _1g of Cr³⁺, intensified by exchange-coupled interaction between Cr³⁺ and Fe³⁺ at neighboring octahedral sites of the structure, appear at ~14,400 and ~15,100 cm^?1. A vague broad band in the range from ca. 15,000 to 12,000 cm^?1 in synthetic spinels is tentatively attributed to ^IVCr²⁺ + ^VICr³⁺ → ^IVCr³⁺ + ^VICr²⁺ intervalence charge-transfer transition. Iron, mainly as octahedral Fe³⁺, causes intense high-energy absorption edge in near UV-range (ligand–metal charge-transfer O^2? → Fe³⁺, Fe²⁺ transitions). As tetrahedral Fe²⁺, it appears as a strong infrared absorption band at around 4,850 cm^?1 caused by electronic spin-allowed ⁵ E → ⁵ T ₂ transitions of ^IVFe²⁺. From the composition shift of the U-band in natural and synthetic MgCr₂O₄ spinels, the coefficient of local structural relaxation around Cr³⁺ in spinel MgAl₂O₄–MgCr₂O₄ system was evaluated as ~0.56(4), one of the lowest among (Al, Cr)O₆ polyhedra known so far. The octahedral modulus of Cr³⁺ in MgCr₂O₄, derived from pressure-induced shift of the U-band of Cr³⁺, is ~313 (50) GPa, which is nearly the same as in natural low-chromium Mg, Al-spinel reported by Langer et al. (1997). Calculated from the results of the curve-fitting analysis, the Racah parameter B of Cr³⁺ in natural and synthetic MgCr₂O₄ spinels indicates that Cr–O-bonding in octahedral sites of MgCr₂O₄ has more covalent character than in the diluted natural samples. Within the uncertainty of determination in synthetic MgAl₂O₄ spinel, B does not much depend on pressure.