Elasticity of single-crystal MgAl2O4 spinel up to 1273 K by Brillouin spectroscopy

The adiabatic single-crystal elastic constants, C _ij , of stoichiometric magnesium aluminate spinel (MgAl₂O₄) have been measured up to 1273 K by highresolution Brillouin spectroscopy, using a 6-pass tandem Fabry-Pérot interferometer and an argon ion laser (514.5 nm). Two platelet samples were employed for probing the acoustic phonons along [100] and [110] directions by platelet and backscattering geometries. The measured temperature dependences of the elastic moduli show a distinct anomaly at 923 K in the shear modulus C _s = (C₁₁-C₁₂)/2 (along [110] direction) and the longitudinal modulus C₁₁ (along [100] direction). This anomaly is consistent with the order-disorder phase transition, resulting from the atomic exchange between Mg at the tetrahedral site and Al at the octahedral site, which has been well documented recently (Peterson et al. 1991; Millard et al. 1992) by neutron powder diffraction and ²⁷Al magic-angle spinning NMR. The values of the temperature derivatives of v _p , v _s , and K _s , in the temperature range 300–923 K, calculated by the Voigt-Reuss-Hill approximation are -0.40ms^?1 K^?1, -0.26ms^?1 K^?1, and -1.89 x 10^?2GPaK^?1.     

Shock effects in MgAl2O4-spinel

Shock recovery experiments on synthetic MgAl₂O₄-spinel samples in the pressure range 25.5 to 50.5 GPa have been performed in order to examine the effects of shock waves on this material. The shocked samples were subsequently studied in the transmission electron microscope. All samples showed shock-induced dislocations with the Burgers vector 1/2 〈110〉 and twin lamellae of the twin-law {111}. In addition, samples, which had experienced the higher pressures, showed lamellar areas of a crystalline phase that we have not yet been able fully to characterize. It is probably not ε-MgAl₂O₄.     

Compressibility of calcium ferrite-type MgAl2O4

 In situ X-ray diffraction experiments of calcium ferrite-type MgAl₂O₄ have been carried out using a diamond anvil cell combined with synchrotron radiation and an imaging plate X-ray detector under hydrostatic pressures up to 9 GPa. The observed unit-cell volumes at various pressures were fitted to the Birch-Murnaghan equation of state, yielding a bulk modulus of K _{T 0}= 241(3) GPa when K′ _{T 0}=4 is assumed. This relatively large bulk modulus of calcium ferrite-type MgAl₂O₄ is consistent with that expected from the systematic relation between bulk modulus and molar volume for the most compounds possessing fcc oxygen packing. Received March 5, 1996/Revised, accepted October 15, 1996     

High-Pressure crystal chemistry of spinel (MgAl2O4) and magnetite (Fe3O4): Comparisons with silicate spinels

High-pressure crystal structures and compressibilities have been determined by x-ray methods for MgAl₂O₄ spinel and its isomorph magnetite, Fe₃O₄. The measured bulk moduli, K, of spinel and magnetite (assuming K′=4) are 1.94±0.06 and 1.86±0.05 Mbar, respectively, in accord with previous ultrasonic determinations. The oxygen u parameter, the only variable atomic position coordinate in the spinel structure (Fd3m, Z=8), decreases with pressure in MgAl₂O₄, thus indicating that the magnesium tetrahedron is more compressible than the aluminum octahedron. In magnetite the u parameter is unchanged, and both tetrahedron and octahedron display the 1.9 Mbar bulk modulus characteristic of the entire crystal. This behavior contrasts with that of nickel silicate spinel (γ-Ni₂SiO₄), in which the u parameter increases with pressure because the silicon tetrahedron is relatively incompressible compared to the nickel octahedron.     

Magnetite activities across the MgAl2O4-Fe3O4 spinel join,with application to thermobarometric estimates of upper mantle oxygen fugacity

The activity of Fe₃O₄ component in MgAl₂O₄-Fe₃O₄ spinels has been measured at 900° and 1000° C and 1 atm total pressure using a zirconia oxygen electrolyte. As previously reported for the dilute Fe₃O₄ concentration region (Mattioli and Wood 1986a), magnetite activity at 1000° C is greater than at 900° C at constant Fe₃O₄ mole fraction, for compositions across the MgAl₂O₄-Fe₃O₄ join between 20 and 80 mol% Fe₃O₄ component. The 1-atm solvus crest lies between 900° and 1000° C and, at 900° C the limbs are at Fe₃O₄ mole fractions of 0.2 and 0.6 approximately.Application of the O'Neill and Navrotsky (1983, 1984) cation distribution model indicates that the unusual activity — composition behavior of Fe₃O₄ is caused by changes in the equilibrium state of disorder of mixed MgAl₂O₄-Fe₃O₄ spinels relative to the disordered Fe₃O₄ standard state. In addition, both stoichiometric volumes (Mattioli et al. 1987) and activities across the MgAl₂O₄-Fe₃O₄ join suggest that short range order is significant for this binary. Excess free energy terms must be added to ideal Fe₃O₄ activities formulated from equilibrium cation distributions in complex MgAl₂O₄-Fe₃O₄ spinels in order to increase Fe₃O₄ activities to values consistent with observation and to generate the apparent region of immiscibility at 900° C.We have applied our activity data to the estimation of upper mantle spinel-lherzolite oxygen fugacities. We calculated that minimum 's are about 2 log units below the synthetic QFM buffer at 15 kbar total pressure for Fe₃O₄ concentration of 2 mol%, in a Cr-free spinel phase. If a preliminary calibration of an additional 25 mol% Fe²⁺-substitution as FeCr₂O₄ or FeAl₂O₄ component is incorporated into Fe₃O₄ activity, then olivine-orthopyroxene-spinel assemblages of depleted-Type 1-spinel-lherzolite xenoliths indicate 's close to QFM at 15 kbar. This is in good agreement with previous thermobarometric estimates and in sharp contrast to 1 atm intrinsic measurements near IW.     

The stability and compressibility of MgAl2O4 high-pressure polymorphs

High-pressure and high-temperature experiments using a laser-heated diamond anvil cell (LHDAC) and synchrotron X-ray diffraction have revealed a phase transition in MgAl₂O₄. CaTi₂O₄-type MgAl₂O₄ was found to be stable at pressures between 45 and at least 117 GPa. The transition pressure of CaTi₂O₄-type phase in MgAl₂O₄ is much lower than that in the natural N-type mid-oceanic ridge basalt composition. The Birch–Murnaghan equation of state for CaTi₂O₄-type MgAl₂O₄ was determined from the experimental unit cell parameters with K ₀=219(±6) GPa, K ₀′=4(constrained value), and V ₀=238.9(±9) ų. The observed compressibility was in agreement with the theoretical compressibility calculated in a previous study. ε-MgAl₂O₄ was observed at pressures between 40 and 45 GPa, which has not been reported in natural rock compositions. The gradient (dP/dT slope) of the transition from the ε-type to CaTi₂O₄-type MgAl₂O₄ had a positive value. These results should resolve the dispute regarding the stable high-pressure phase of MgAl₂O₄, which has been reported in earlier studies using both the multi-anvil press and the diamond anvil cell.     

Raman spectroscopy and heat capacity measurement of calcium ferrite type MgAl2O4 and CaAl2O4

Raman spectroscopy of calcium ferrite type MgAl₂O₄ and CaAl₂O₄ and heat capacity measurement of CaAl₂O₄ calcium ferrite were performed. The heat-capacity of CaAl₂O₄ calcium ferrite measured by a differential scanning calorimeter (DSC) was represented as C_P(T)=190.6–1.116 × 10⁷T^–2 + 1.491 × 10⁹T^–3 above 250 K (T in K). The obtained Raman spectra were applied to lattice dynamics calculation of heat capacity using the Kieffer model. The calculated heat capacity for CaAl₂O₄ calcium ferrite showed good agreement with that by the DSC measurement. A Kieffer model calculation for MgAl₂O₄ calcium ferrite similar to that for CaAl₂O₄ calcium ferrite was made to estimate the heat capacity of the former. The heat capacity of MgAl₂O₄ calcium ferrite was represented as C_P(T)=223.4–1352T ^–0.5 – 4.181 × 10⁶T ^–2 + 4.300 × 10⁸T ^–3 above 250 K. The calculation also gave approximated vibrational entropies at 298 K of calcium ferrite type MgAl₂O₄ and CaAl₂O₄ as 97.6 and 114.9 J mol^–1 K^–1, respectively.     

High-temperature thermal expansion of lime, periclase, corundum and spinel

The high-temperature cell parameters of lime (CaO), periclase (MgO), corundum (Al₂O₃), and spinel (MgAl₂O₄) have been determined from 300 up to 3000 K through X-ray diffraction experiments with synchrotron radiation. The good agreement found with dilatometric results suggests that vacancy-type defects do not make a large contribution to thermal expansion for these oxides, even near the melting point, justifying the use of X-ray diffraction for determining volume properties up to very high temperatures. Thermal expansion coefficients were determined from the measured cell volumes with equations of the form α=α₀ + α₁ T + α₂/T ². Along with available isobaric heat capacity and compressibility data, these derived coefficients clearly show that anharmonic effects contribute little to the isochoric heat capacities (C _v ) of CaO, MgO, and Al₂O₃, which do not depart appreciably from the 3nR Dulong and Petit limit. Received: 31 March 1999 / Revised, accepted: 23 June 1999     

Vibrational structure of luminiscence spectrum of Cr3+ in MgAl2O4

The optical absorption and luminescence spectra of MgAl₂O₄:Cr³⁺ natural spinel (from Ural) have been measured at 77 K and 293 K. The luminescent emission from ⁴ T _2g , ² E _g covers wide region of 600–750 nm. The emission spectrum at 77 K shows a very rich vibrational structure which can be mainly explained through the vibrational modes of the oxygen octahedron.     

Magnetic properties of the Fe2SiO4-Fe3O4 spinel solid solutions

 Magnetic measurement of Fe_{3− x} Si _x O₄ spinel solid solutions indicates that their Curie temperatures decrease gradually, but not linearly, from 851 to 12 K with increasing content of nonmagnetic ions Si⁴⁺. Magnetic hysteresis becomes more noticeable in solid solutions having a larger content of Fe₂SiO₄. Saturation magnetizations of Fe_{3− x} Si _x O₄ samples increase up to x=0.357 and they are easily saturated in the field of H=0.1 T. However, magnetization of the sample of x=0.794 does not approach saturation even at high field of H=7.0 T and has a large coercive force. The Si⁴⁺ disordered distribution is confirmed to be ^tetr[Fe³⁺ _{1− x + x t} Si⁴⁺ _{x (1− t )}] ^octa[Fe²⁺ _{1+ x} Fe³⁺ _{1− x − x t} Si⁴⁺ _{x t} ] O₄ by the spin moment, which is consistent with site occupancy obtained from X-ray crystal structure refinement. Their molecular magnetizations would be expressed as M _B={4(1+x)+10xt}μ_B as functions of composition parameter x and Si⁴⁺ ordering parameter t of the solid solution. The sample of x=0.794 is antiferromagnetic below the Néel temperature, mainly due to the octahedral cation interaction M _O–M _O, while both M _T–M _O and M _O–M _O interactions induce a ferrimagnetic property. Concerning magnetic spin configuration, in the case of x>0.42, the lowest dɛ level becomes a singlet, resulting in no orbital angular momentum. Received: 20 April 2000 / Accepted: 11 September 2000     

Electric conductivity of Fe2SiO4–Fe3O4 spinel solid solutions

 The spinel solid solution was found to exist in the whole range between Fe₃O₄ and γ-Fe₂SiO₄ at over 10 GPa. The resistivity of Fe_{3− x} Si _x O₄ (0.0<x<0.288) was measured in the temperature range of 80∼300 K by the AC impedance method. Electron hopping between Fe³⁺ and Fe²⁺ in the octahedral site of iron-rich phases gives a large electric conductivity at room temperature. The activation energy of the electron hopping becomes larger with increasing γ-Fe₂SiO₄ component. A nonlinear change in electric conductivity is not simply caused by the statistical probability of Fe³⁺–Fe²⁺ electron hopping with increasing the total Si content. This is probably because a large number of Si⁴⁺ ions occupies the octahedral site and the adjacent Fe²⁺ keeping the local electric neutrality around Si⁴⁺ makes a cluster, which generates a local deformation by Si substitution. The temperature dependence of the conductivity of solid solutions indicates the Verwey transition temperature, which decreases from 124(±2) K at x=0 (Fe₃O₄) to 102(±5) K at x=0.288, and the electric conductivity gap at the transition temperature decreases with Si⁴⁺ substitution. Received: 15 March 2000 / Accepted: 4 September 2000     

Cation ordering in NiAl2O4 spinel by a 111 systematic row CBED technique

A focussed probe wide angle systematic row CBED technique has been used to determine the degree of cation inversion, i.e. the magnitude of the cation ordering parameter x, in (Ni_{1− x} Al _x ) [Ni _{x /2}Al_{1− x /2}]₂O₄ spinel to an estimated accuracy of ±0.1. For comparison purposes, the same technique has also been applied to an MgCr₂O₄ spinel (where very little cation inversion is expected). The simplicity of this CBED technique in conjunction with the fact that the experimental data can be obtained from small illuminated areas several tens to 100 nm in diameter, suggests that it may be a very useful technique for estimating the extent of cation inversion in multi-phase mineralogical specimens containing spinels. Received: 19 October 1998 / Revised, accepted: 14 June 1999     

Crystal field transitions in Co2[Al4Si5]O18 cordierite and CoAl2O4 spinel determined by neutron spectroscopy

Inelastic magnetic neutron scattering has been used to determine the energy of the ⁴ A ₂→⁴ T ₂ transition in CoAl₂O₄ spinel and the δ₁ transition in Co₂[Al₄Si₅]O₁₈ cordierite. The observed crystal field splitting in Co-spinel is 485 meV (3900 cm⁻¹), which corresponds to a crystal field stabilization energy of 56.2 kJmol⁻¹. The transition energy of the δ₁ transition in Co-cordierite has been determined to be 21 meV (170 cm⁻¹). The present data demonstrate that magnetic neutron scattering can be used to measure crystal field transitions at energies of interest in the study of 3d-containing silicates. It may be used to measure transition energies when the use of optical spectroscopy is inappropriate. Received: 30 January 1997 / Accepted: 5 July 1997     

High-pressure synthesis and properties of magnesiocarpholite,MgAl2[Si2O6] (OH)4

Magnesiocarpholite has been synthesized on its own composition between 15 and 25 kb water pressure and 415°–600° C. Best conditions are 25 kb-550° C, starting from a mixture of oxides and synthetic cordierite. Within the MgO-Al₂O₃-SiO₂-H₂O system, possible substitutions appear to be very limited in magnesiocarpholite. Cell-parameters are a=13.706(3), b= 20.075(3), c=5.107(l) Å, space group Ccca. The larger cell, as compared with the most magnesian natural carpholites, is tentatively ascribed to structural disorder. Preliminary stability data confirm the low-temperature character of this mineral which is shown to be a high-pressure equivalent of sudoite+quartz.     

A thermodynamic analysis of the system LiAlSiO4-NaAlSiO4-Al2O3-SiO2-H2O based on new heat capacity, thermal expansion, and compressibility data for selected phases

Heat capacity, thermal expansion, and compressibility data have been obtained for a number of selected phases of the system NaAlSiO₄-LiAlSiO₄-Al₂O₃-SiO₂-H₂O. All C _p measurements have been executed by DSC in the temperature range 133–823 K. The data for T ≥ 223 K have been fitted to the function C _p (T) = a + cT ⁻² + dT ^−0.5 + fT ⁻³, the fit parameters being The thermal expansion data (up to 525 °C) have been fitted to the function V ⁰(T) = V ⁰(T) [1 + v ₁ (T−T ⁰) + v ₂ (T−T ⁰)²], with T ⁰ = 298.15 K. The room-temperature compressibility data (up to 6 GPa) have been smoothed by the Murnaghan equation of state. The resulting parameters are These data, along with other phase property and reaction reversal data from the literature, have been simultaneously processed by the Bayes method to derive an internally consistent thermodynamic dataset (see Tables 6 and 7) for the NaAlSiO₄-LiAlSiO₄-Al₂O₃-SiO₂-H₂O quinary. Phase diagrams generated from this dataset are compatible with cookeite-, ephesite-, and paragonite-bearing assemblages observed in metabauxites and common metasediments. Phase diagrams obtained from the same database are also in agreement with the cookeite-free, petalite-, spodumene-, eucryptite-, and bikitaite-bearing assemblages known to develop in the subsolidus phase of recrystallization of␣lithium-bearing pegmatites. It is gratifying to note that the cookeite phase relations predicted earlier by Vidal and Goffé (1991) in the context of the system Li₂O-Al₂O₃-SiO₂-H₂O agree with our results in a general way. Received: 19 May 1998 / Accepted: 25 June 1998     

Vibrational spectroscopy of aluminate spinels at 1 atm and of MgAl2O4 to over 200 kbar

Single-crystal Raman and infrared reflectivity data including high pressure results to over 200 kbar on a natural, probably fully ordered MgAl₂O₄ spinel reveal that many of the reported frequencies from spectra of synthetic spinels are affected by disorder at the cation sites. The spectra are interpreted in terms of factor group analysis and show that the high energy modes are due to the octahedral internal modes, in contrast to the behavior of silicate spinels, but in agreement with previous data based on isotopic and chemical cation substitutions and with new Raman data on gahnite (～ ZnAl₂O₄) and new IR reflectivity data on both gahnite and hercynite (～Fe_0.58Mg_0.42Al₂O₄). Therefore, aluminate spinels are inappropriate as elastic or thermodynamic analogs for silicate spinels. Fluorescence sideband spectra yield complementary information on the vibrational modes and provide valuable information on the acoustic modes at high pressure. The transverse acoustic modes are nearly pressure independent, which is similar to the behavior of the shear modes previously measured by ultrasonic techniques. The pressure derivative of all acoustic modes become negative above 110 kbar, indicating a lattice instability, in agreement with previous predictions. This lattice instability lies at approximately the same pressure as the disproportionation of spinel to MgO and Al₂O₃ reported in high temperature, high pressure work.     

Temperature-dependent magnetic susceptibility behaviour of spinelloid and spinel solid solutions in the systems Fe2SiO4–Fe3O4 and (Fe,Mg)2SiO4–Fe3O4

The magnetic behaviour and Curie temperatures (T _C ) of spinelloids and spinels in the Fe₃O₄–Fe₂SiO₄ and Fe₃O₄–(Mg,Fe)₂SiO₄ systems have been determined from magnetic susceptibility (k) measurements in the temperature range –192 to 700 °C. Spinelloid II is ferrimagnetic at room temperature and the k measurements display a characteristic asymmetric hump before reaching a T _C at 190 °C. Spinelloid V from the Mg-free system is paramagnetic at room temperature and hysteresis loops at various low temperatures indicate a ferri- to superparamagnetic transition before reaching the T _{C .} The T _C shows a non-linear variation with composition between –50 and –183 °C with decreasing magnetite component (X _Fe3O₄). The substitution of Mg in spinelloid V further decreases T _C . Spinelloid III is paramagnetic over nearly the total temperature range. Ferrimagnetic models for spinelloid II and spinelloid V are proposed. The T _C of Fe₃O₄–Fe₂SiO₄ spinel solid solutions gradually decrease with increasing Si content. Spinel is ferrimagnetic at least to a composition of X _Fe3O₄=0.20, constraining a ferrimagnetic to antiferromagnetic transition to occur at a composition of X _Fe3O₄<0.20. A contribution of the studied ferrimagnetic phases for crustal anomalies on the Earth can be excluded because they lose their magnetization at relatively low temperatures. However, their relevance for magnetic anomalies on other planets (Mars?), where these high-pressure Fe-rich minerals could survive their exhumation or were formed by impacts, has to be considered.     

The fluorescence sideband method for obtaining acoustic velocities at high compressions: application to MgO and MgAl2O4

Sound velocities to 37 GPa have been obtained for MgO based on new sideband measurements and sound velocities have been calculated for MgAl₂O₄ to 11 GPa based on previous sideband measurements. The basic principles of the sideband fluorescence method are presented and it is shown that the vibrational mode energies in the sidebands are independent of the impurity cation and represent modes of the undisturbed lattice. Furthermore, it is shown that the acoustic modes represent spherically averaged velocities by comparison of these results to the directional information provided by ultrasonic data. The resulting pressure derivatives of the elastic moduli for both materials are in excellent agreement with those derived from lower-pressure ultrasonic data. The velocities over the pressure range of this study may be described by the following relations: for MgO, v_s=6.05 (1)+0.0381 (13) · P-3.6(4) × 10^?4 · P² and v_P=9.70(2)+0.0704(20) · P-5.6(6)×10^?4 · P² and for MgAl₂O₄, v_s=5.49(5)+0.001(11) · P and v_P = 9.785 (11)+0.047 (5) · P-0.0010(5) · P² where the pressure P is in GPa. Velocity is linear with density over the pressure range of this study.     

Negative thermal expansion in beta-quartz

Computer modelling and theoretical analysis are used to explain the nearly zero and slightly negative coefficients of thermal expansion in β-quartz well above the α-β phase transition temperature. Quartz was selected for study as an archetypal material with a framework structure of stiff units, namely SiO₄ tetrahedra, linked through shared oxygen atoms as very flexible hinges. The contributions of the soft mode, the Vallade mode, the TA_z phonon branch and the phonon spectrum as a whole are discussed in detail. The results fully support and illustrate a recent theory of the negative contribution to thermal expansion in framework structures. It is a geometrical effect due to the rotation of the tetrahedral units, folding together as they vibrate. The very rapid increase in the lattice parameters for about 20 K above the transition temperature is well accounted for within quasiharmonic theory, and is therefore not evidence for critical fluctuations or fluctuating patches of α ₊, α ₋ structure. Received August 14 1997 / Revised, accepted January 26 1998     

Temperature dependence of the cation distribution in nickel aluminate (NiAl2O4) spinel: a powder XRD study

NiAl₂O₄ is a largely inverse spinel, which in detail shows increasing randomisation with temperature of Ni and Al between the octahedral and tetrahedral cation sites of the spinel structure. We have used powder XRD to determine this cation distribution in various samples of NiAl₂O₄ quenched after annealing between 700 and 1400° C. The inversion parameter (x) can be measured with a precision of ± 0.004 (one standard deviation), and a comparison of different methods of synthesis, X-ray diffraction and refinement techniques, suggests a probable accuracy of better than 0.01. The results are supported by some preliminary single crystal refinements on flux-grown samples.Below 800° C the rate of cation ordering becomes very slow, and, despite reaching an apparently steady state, it is doubtful if our samples attained complete internal equilibrium. Above 1250° C the cation redistribution becomes so fast that the quenching method becomes unreliable. Between 800 and 1250° C inclusive, the degree of inversion changes smoothly from 0.87 at 800° C to 0.79 at 1250° C, and is accompanied by linear changes in u, the oxygen parameter, from 0.2555 to 0.2563 (±0.0002), and a₀, the lattice parameter, from 8.0462 to 8.0522 Å (±0.0002 Å).