Low-temperature heat capacities of MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript> and spinels of the MgCr<Subscript>2</Subscript>O<Subscript>4</Subscript>–MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript> solid solution

We present results from low-temperature heat capacity measurements of spinels along the solid solution between MgAl₂O₄ and MgCr₂O₄. The data also include new low-temperature heat capacity measurements for MgAl₂O₄ spinel. Heat capacities were measured between 1.5 and 300 K, and thermochemical functions were derived from the results. No heat capacity anomaly was observed for MgAl₂O₄ spinel; however, we observe a low-temperature heat capacity anomaly for Cr-bearing spinels at temperatures below 15 K. From our data we calculate standard entropies (298.15 K) for Mg(Cr,Al)₂O₄ spinels. We suggest a standard entropy for MgAl₂O₄ of 80.9 ± 0.6 J mol⁻¹ K⁻¹. For the solid solution between MgAl₂O₄ and MgCr₂O₄, we observe a linear increase of the standard entropies from 80.9 J mol⁻¹ K⁻¹ for MgAl₂O₄ to 118.3 J mol⁻¹ K⁻¹ for MgCr₂O₄.     

Thermodynamic properties of nickel chromite (NiCr2O4) based on adiabatic calorimetry at low temperatures

 The hitherto unknown low-temperature heat capacity of nickel chromite (NiCr₂O₄) was measured between 8 and 381 K using adiabatic calorimetry, and some thermochemical functions [C_P(T), S(T), S°₂₉₈, H_(T)−H₍₀₎] were derived from the results. The standard entropy (S°₂₉₈=140.0 ± 0.3 J mol⁻¹ K⁻¹) for nickel chromite was calculated from the results. Our calorimetric measurements indicate three major anomalies in the heat-capacity curve at temperatures between 8 and 381 K. A short literature review indicates that two of these anomalies can be accounted for, whereas an anomaly peaking at 29 K has not been reported previously.     

Low-temperature heat capacity of magnesioferrite (MgFe2O4)

The low-temperature heat capacity of magnesioferrite (MgFe₂O₄) was measured between 1.5 K and 300 K, and thermochemical functions were derived from the results. No heat capacity anomaly was observed. From our data, we suggest a standard entropy (298.15 K) for magnesioferrite of 120.8±0.6 J mol⁻¹ K⁻¹, which is about 2.4 J mol⁻¹ K⁻¹ higher than previously reported calorimetric studies; but is in rough agreement with predictions from sets of internally consistent thermodynamic data.     

Thermodynamic data of the high-pressure phase Mg5Al5Si6O21(OH)7 (Mg-sursassite)

 Calorimetric and P–V–T data for the high-pressure phase Mg₅Al₅Si₆O₂₁(OH)₇ (Mg-sursassite) have been obtained. The enthalpy of drop solution of three different samples was measured by high-temperature oxide melt calorimetry in two laboratories (UC Davis, California, and Ruhr University Bochum, Germany) using lead borate (2PbO·B₂O₃) at T=700 ^∘C as solvent. The resulting values were used to calculate the enthalpy of formation from different thermodynamic datasets; they range from −221.1 to −259.4 kJ mol⁻¹ (formation from the oxides) respectively −13892.2 to −13927.9 kJ mol⁻¹ (formation from the elements). The heat capacity of Mg₅Al₅Si₆O₂₁(OH)₇ has been measured from T=50 ^∘C to T=500 ^∘C by differential scanning calorimetry in step-scanning mode. A Berman and Brown (1985)-type four-term equation represents the heat capacity over the entire temperature range to within the experimental uncertainty: C _P (Mg-sursassite) =(1571.104 −10560.89×T ^−0.5−26217890.0 ×T ⁻²+1798861000.0×T ⁻³) J K⁻¹ mol⁻¹ (T in K). The P V T behaviour of Mg-sursassite has been determined under high pressures and high temperatures up to 8 GPa and 800 ^∘C using a MAX 80 cubic anvil high-pressure apparatus. The samples were mixed with Vaseline to ensure hydrostatic pressure-transmitting conditions, NaCl served as an internal standard for pressure calibration. By fitting a Birch-Murnaghan EOS to the data, the bulk modulus was determined as 116.0±1.3 GPa, (K ^′=4), V _T,0 =446.49 ³ exp[∫(0.33±0.05) × 10⁻⁴ + (0.65±0.85)×10⁻⁸ T dT], (K _T/T) _P  = −0.011± 0.004 GPa K⁻¹. The thermodynamic data obtained for Mg-sursassite are consistent with phase equilibrium data reported recently (Fockenberg 1998); the best agreement was obtained with Δ_f H ⁰ ₂₉₈ (Mg-sursassite) = −13901.33 kJ mol⁻¹, and S ⁰ ₂₉₈ (Mg-sursassite) = 614.61 J K⁻¹ mol⁻¹. Received: 21 September 2000 / Accepted: 26 February 2001     

Heat capacity of wadeite-type K2Si4O9 and the pressure-induced stable decomposition of K-feldspar

The heat capacity of synthetic, stoichiometric wadeite-type K₂Si₄O₉ has been measured by DSC in the 195≤T(K)≤598 range. Near the upper temperature limit of our data, the heat capacity observed by DSC agrees with that reported by Geisinger et al. (1987) based on a vibrational model of their infrared and Raman spectroscopic data. However, with decreasing temperature, the Cp observed by DSC is progressively higher than that predicted from the vibrational model, suggesting that the standard entropy of K₂Si₄O₉ is likely to be larger than 198.9 ± 4.0 J/K · mol computed from the spectroscopic data. A fit to the DSC data gave: Cp(T) = 499.13 (±1.87) − 4.35014 · 10³(±3.489 · 10¹) · T ^−0.5, with T in K and average absolute percent deviation of 0.37%. The room-temperature compressibilities of kalsilite and leucite, hitherto unknown, have been measured as well. The data, fitted to the Murnaghan equation of state, gave K _o = 58.6 GPa, K _o ^′ = 0.1 for kalsilite and K _o = 45 GPa, K _o ^′ = 5.7 for α-leucite. Apart from the above mentioned data on the properties of the individual phases, we have also obtained reaction-reversals on four equilibria in the system K₂O-Al₂O₃-SiO₂. The Bayesian method has been used simultaneously to process the properties of 13 phases and 15 reactions between them to derive an internally consistent thermodynamic dataset for the K₂O-Al₂O₃-SiO₂ ternary. The enthalpy of formation of K₂Si₄O₉ wadeite is in perfect agreement with its revised calorimetric value, the standard entropy is 232.1 ± 10.4 J/K · mol, ∼15% higher than that implied by vibrational modeling. The phase diagram, generated from our internally consistent thermodynamic dataset, shows that for all probable P-T trajectories in the subduction regime, the stable pressure-induced decomposition of K-feldspar will produce coesite + kalsilite rather than coesite + kyanite + K₂Si₄O₉ (cf. Urakawa et al. 1994). Received: 11 June 1997 / Accepted: 2 December 1997     

Thermodynamic functions of eskolaite Cr<Subscript>2</Subscript>O<Subscript>3</Subscript>(c) at 0–1800 K

The heat capacity of eskolaite Cr₂O₃(c) was determined by adiabatic vacuum calorimetry at 11.99–355.83 K and by differential calorimetry at 320–480 K. Experimental data of the authors and data compiled from the literature were applied to calculate the heat capacity, entropy, and the enthalpy change of Cr₂O₃ within the temperature range of 0–1800 K. These functions have the following values at 298.15 K: C _p ⁰ (298.15) = 121.5 ± 0.2 J K⁻¹mol⁻¹, S ⁰(298.15) = 80.95 ± 0.14 J K⁻¹mol⁻¹, and H ⁰(298.15)-H ⁰(0) = 15.30±0.02 kJ mol⁻¹. Data were obtained on the transitions from the antiferromagnetic to paramagnetic states at 228–457 K; it was determined that this transition has the following parameters: Neel temperature T _N = 307 K, Δ _tr S = 6.11 ± 0.12 J K⁻¹mol⁻¹ and δ _tr H = 1.87 ± 0.04 kJ mol⁻¹.     

Heat capacity and phase equilibria of hollandite polymorph of KAlSi3O8

The low-temperature heat capacity (C _p ) of KAlSi₃O₈ with a hollandite structure was measured over the range of 5–303 K with a physical properties measurement system. The standard entropy of KAlSi₃O₈ hollandite is 166.2±0.2 J mol⁻¹ K⁻¹, including an 18.7 J mol⁻¹ K⁻¹ contribution from the configurational entropy due to disorder of Al and Si in the octahedral sites. The entropy of K₂Si₄O₉ with a wadeite structure (Si-wadeite) was also estimated to facilitate calculation of phase equilibria in the system K₂O–Al₂O₃–SiO₂. The calculated phase equilibria obtained using Perple_x are in general agreement with experimental studies. Calculated phase relations in the system K₂O–Al₂O₃–SiO₂ confirm a substantial stability field for kyanite–stishovite/coesite–Si-wadeite intervening between KAlSi₃O₈ hollandite and sanidine. The upper stability of kyanite is bounded by the reaction kyanite (Al₂SiO₅) = corundum (Al₂O₃) + stishovite (SiO₂), which is located at 13–14 GPa for 1,100–1,400 K. The entropy and enthalpy of formation for K-cymrite (KAlSi₃O₈·H₂O) were modified to better fit global best-fit compilations of thermodynamic data and experimental studies. Thermodynamic calculations were undertaken on the reaction of K-cymrite to KAlSi₃O₈ hollandite + H₂O, which is located at 8.3–10.0 GPa for the temperature range 800–1,600 K, well inside the stability field of stishovite. The reaction of muscovite to KAlSi₃O₈ hollandite + corundum + H₂O is placed at 10.0–10.6 GPa for the temperature range 900–1,500 K, in reasonable agreement with some but not all experiments on this reaction.     

Heat capacity and phase equilibria of wadeite-type K2Si4O9

The low-temperature heat capacity (C _p) of Si-wadeite (K₂Si₄O₉) synthesized with a piston cylinder device was measured over the range of 5–303 K using the heat capacity option of a physical properties measurement system. The entropy of Si-wadeite at standard temperature and pressure calculated from the measured heat capacity data is 253.8 ± 0.6 J mol⁻¹ K⁻¹, which is considerably larger than some of the previous estimated values. The calculated phase transition boundaries in the system K₂O–Al₂O₃–SiO₂ are generally consistent with previous experimental results. Together with our calculated phase boundaries, seven multi-anvil experiments at 1,400 K and 6.0–7.7 GPa suggest that no equilibrium stability field of kalsilite + coesite intervenes between the stability field of sanidine and that of coesite + kyanite + Si-wadeite, in contrast to previous predictions. First-order approximations were undertaken to calculate the phase diagram in the system K₂Si₄O₉ at lower pressure and temperature. Large discrepancies were shown between the calculated diagram compared with previously published versions, suggesting that further experimental or/and calorimetric work is needed to better constrain the low-pressure phase relations of the K₂Si₄O₉ polymorphs. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Heat capacity of γ-Fe2SiO4 between 5 and 303 K and derived thermodynamic properties

A multi-anvil device was used to synthesize 24 mg of pure γ-Fe₂SiO₄ crystals at 8.5 GPa and 1,273 K. The low-temperature heat capacity (C _p) of γ-Fe₂SiO₄ was measured between 5 and 303 K using the heat capacity option of a physical properties measurement system. The measured heat capacity data show a broad λ-transition at 11.8 K. The difference in the C _p between fayalite and γ-Fe₂SiO₄ is reduced as the temperature increases in the range of 50–300 K. The gap in C _p data between 300 and 350 K of γ-Fe₂SiO₄ is an impediment to calculation of a precise C _p equation above 298 K that can be used for phase equilibrium calculations at high temperatures and high pressures. The C _p and entropy of γ-Fe₂SiO₄ at standard temperature and pressure (S°₂₉₈) are 131.1 ± 0.6 and 140.2 ± 0.4 J mol⁻¹ K⁻¹, respectively. The Gibbs free energy at standard pressure and temperature (ΔG° _f,298) is calculated to be −1,369.3 ± 2.7 J mol⁻¹ based on the new entropy data. The phase boundary for the fayalite–γ-Fe₂SiO₄ transition at 298 K based on current thermodynamic data is located at 2.4 ± 0.6 GPa with a slope of 25.4 bars/K, consistent with extrapolated results of previous experimental studies.     

Calorimetric study of perovskite solid solutions in the CaSiO3–CaGeO3 system

 Enthalpies of drop solution (ΔH _drop-sol) of CaGeO₃, Ca(Si_0.1Ge_0.9)O₃, Ca(Si_0.2Ge_0.8)O₃, Ca(Si_0.3Ge_0.7)O₃ perovskite solid solutions and CaSiO₃ wollastonite were measured by high-temperature calorimetry using molten 2PbO · B₂O₃ solvent at 974 K. The obtained values were extrapolated linearly to the CaSiO₃ end member to give ΔH _drop-sol of CaSiO₃ perovskite of 0.2 ± 4.4 kJ mol⁻¹. The difference in ΔH _drop-sol between CaSiO₃, wollastonite, and perovskite gives a transformation enthalpy (wo → pv) of 104.4 ± 4.4 kJ mol⁻¹. The formation enthalpy of CaSiO₃ perovskite was determined as 14.8 ± 4.4 kJ mol⁻¹ from lime + quartz or −22.2 ± 4.5 kJ mol⁻¹ from lime + stishovite. A comparison of lattice energies among A²⁺B⁴⁺O₃ perovskites suggests that amorphization during decompression may be due to the destabilizing effect on CaSiO₃ perovskite from a large nonelectrostatic energy (repulsion energy) at atmospheric pressure. By using the formation enthalpy for CaSiO₃ perovskite, phase boundaries between β-Ca₂SiO₄ + CaSi₂O₅ and CaSiO₃ perovskite were calculated thermodynamically utilizing two different reference points [where ΔG(P,T )=0] as the measured phase boundary. The calculations suggest that the phase equilibrium boundary occurs between 11.5 and 12.5 GPa around 1500 K. Its slope is still not well constrained. Received: 20 September 2000 / Accepted: 17 January 2001     

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     

On the entropy of glaucophane Na2Mg3Al2Si8O22(OH)2

The heat capacity of glaucophane from the Sesia-Lanza region of Italy having the approximate composition (Na_1.93Ca_0.05Fe_0.02) (Mg_2.60Fe_0.41) (Al_1.83Fe_0.15Cr_0.01) (Si_7.92Al_0.08)O₂₂(OH)₂ was measured by adiabatic calorimetry between 4.6 and 359.4 K. After correcting the C _p ⁰ data to values for ideal glaucophane, Na₂Mg₃Al₂Si₈O₂₂(OH)₂ the third-law entropy S ₂₉₈ ⁰ -S ₀ ⁰ was calculated to be 541.2±3.0 J·mol^-1·K^-1. Our value for S ₂₉₈ ⁰ -S ₀ ⁰ is 12.0 J·mol^-1·K^-1 (2.2%) smaller than the value of Likhoydov et al. (1982), 553.2±3.0, is within 6.2 J·mol^-1·K^-1 of the value estimated by Holland (1988), and agrees remarkably well with the value calculated by Gillet et al. (1989) from spectroscopic data, 539 J·mol^-1·K^-1.     

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     

Electronic absorption and luminescence spectroscopic studies of kyanite single crystals: differentiation between excitation of FeTi charge transfer and Cr3+ dd transitions

A selected set of five different kyanite samples was analysed by electron microprobe and found to contain chromium between <0.001 and 0.055 per formula unit (pfu). Polarized electronic absorption spectroscopy on oriented single crystals, R₁, R₂-sharp line luminescence and spectra of excitation of λ₃- and λ₄-components of R₁-line of Cr³⁺-emission had the following results: (1) The Fe²⁺–Ti⁴⁺ charge transfer in c-parallel chains of edge connected M(1) and M(2) octahedra shows up in the electronic absorption spectra as an almost exclusively c(||Z′)-polarized, very strong and broad band at 16000 cm⁻¹ if <, in this case the only band in the spectrum, and at an invariably lower energy of 15400 cm⁻¹ in crystals with  ≥ . The energy difference is explained by an expansion of the O_f–O_k, and O_b–O_m edges, by which the M(1) and M(2) octahedra are interconnected (Burnham 1963), when Cr³⁺ substitutes for Al compared to the chromium-free case. (2) The Cr³⁺ is proven in two greatly differing crystal fields a and b, giving rise to two sets of bands, derived from the well known dd transitions of Cr^{3+ 4}A_2g→⁴T_2g(F)(I), →⁴T_1g(F)(II), and →⁴T_1g(P)(III). Band energies in the two sets a and b, as obtained by absorption, A, and excitation, E, agree well: I: 17300(a, A), 17200(a, E), 16000(b, A), 16200(b, E); II: 24800(a, A), 24400(a, E); 22300(b, A), 22200(b, E); III: 28800(b,A) cm⁻¹. Evaluation of crystal field parameters from the bands in the electronic spectra yield Dq(a)=1730 cm⁻¹, Dq(b)=1600 cm⁻¹, B(a)=790 cm⁻¹, B(b)=620 cm⁻¹ (errors ca. ±10 cm⁻¹), again in agreement with values extracted from the λ³, λ⁴ excitation spectra. The CF-values of set a are close to those typical of Cr³⁺ substituting for Al in octahedra of other silicate minerals without constitutional OH⁻ as for sapphirine, mantle garnets or beryl, and are, therefore, interpreted as caused by Cr³⁺ substituting for Al in some or all of the M(1) to M(4) octaheda of the kyanite structure, which are crystallographically different but close in their mean Al–O distances, ranging from 1.896 to 1.919 A (Burnham 1963), and slight degrees of distortion. Hence, band set a originates from substitutive Cr³⁺ in the kyanite structural matrix. The CF-data of Cr³⁺ type b, expecially B, resemble those of Cr³⁺ in oxides, especially of corundum type solid solutions or eskolaite. This may be interpreted by the assumption that a fraction of the total chromium contents might be allocated in a precursor of a corundum type exsolution. Received: 3 January 1997 / Revised, accepted: 2 May 1997     

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     

Thermodynamic properties of CoCr2O4: specific heat and magnetic entropy

We present the temperature dependence of the specific heat of CoCr₂O₄ between 2.08 K and 306 K in zero magnetic field. The lattice component can be described by the Komada–Westrum model with a characteristic temperature Θ_KW = 541 K. The entropy of the magnetic component amounts to 33.51 J mol^?1 K^?1 at T = 298.15 K, in good agreement with the magnetic entropy of Co²⁺ and Cr³⁺ ions with completely quenched orbital moments. We compare our results with data available in literature.     

A high-temperature and high-pressure Raman spectroscopic study of CaGeO3 garnet

 High-pressure and high-temperature Raman spectra of CaGeO₃ tetragonal garnet have been collected to 11.5 GPa and 1225 K, respectively, in order to investigate possible intrinsic anharmonic behaviour in this phase. The Raman peak positions were observed to vary linearly with pressure and temperature within the ranges studied, with the higher-energy peaks showing larger P- and T-induced shifts than the low energy modes. The observed T-induced shifts are similar to those reported for grossular and andradite, while the observed P-induced shifts are generally larger than those of aluminosilicate and MgSiO₃ majorite garnets (Gillet et al. 1992; Rauch et al. 1996) due to the larger bulk modulus of CaGeO₃ garnet. The observed mode shifts of CaGeO₃ garnet were used to determine the isothermal and isobaric mode Grüneisen parameters for this phase. These parameters are similar in value to those reported previously for grossular and andradite (Gillet et al. 1992). The calculated intrinsic anharmonic parameters, a _i , for CaGeO₃ garnet were determined to be nonzero, indicating significant anharmonic behaviour for this phase. These values, which range from −3.8 × 10⁻⁵ K⁻¹ to −1.3 × 10⁻⁵ K⁻¹, are also similar to those reported for andradite and grossular, but smaller than those determined for pyrope (Gillet et al. 1992). Hence, we expect MgSiO₃ majorite to show greater anharmonicity than the germanate analogue studied by us. The anharmonic parameters determined for CaGeO₃ tetragonal garnet may now be introduced into quasiharmonic vibrational heat capacity models to account for the observed anharmonic behaviour. Received: 21 April 1999 / Revised, accepted: 11 September 1999     

Structure and compressibility of synthetic ZnAl2O4 (gahnite) under high-pressure conditions, from synchrotron X-ray powder diffraction

 The structural behavior of synthetic gahnite (ZnAl₂O₄) has been investigated by X-ray powder diffraction at high pressure (0–43 GPa) and room temperature, on the ID9 beamline at ESRF. The equation of state of gahnite has been derived using the models of Birch–Murnaghan, Vinet and Poirier–Tarantola, and the results have been mutually compared (the elastic bulk modulus and its derivatives versus P determined by the third-order Birch–Murnaghan equation of state are K ₀=201.7(±0.9) GPa, K ^′ ₀=7.62(±0.09) and K ^″ ₀=−0.1022 GPa⁻¹ (implied value). The compressibilities of the tetrahedral and octahedral bond lengths [0.00188(8) and 0.00142(5) GPa⁻¹ at P=0, respectively], and the␣polyhedral volume compressibilities of the four-␣and␣sixfold coordination sites [0.0057(2) and 0.0041(2) GPa⁻¹ at P=0, respectively] are discussed. Received: 15 January 2001 / Accepted: 23 April 2001     

MgSiO3 ilmenite: Heat capacity,thermal expansivity,and enthalpy of transformation

A new determination, using high temperature drop-solution calorimetry, of the enthalpy of transformation of MgSiO₃ pyroxene to ilmenite gives H ₂₉₈ = 59.03 ±4.26 kJ/mol. The heat capacity of the ilmenite and orthopyroxene phases has been measured by differential scanning calorimetry at 170–700 K; C_p of MgSiO₃ ilmenite is 4–10 percent less than that of MgSiO₃ pyroxene throughout the range studied. The heat capacity differences are consistent with lattice vibrational models proposed by McMillan and Ross (1987) and suggest an entropy change of -18 ± 3 J-K^-1 ·mol^-1, approximately independent of temperature, for the pyroxene-ilmenite transition. The unit cell parameters of MgSiO₃ ilmenite were measured at 298–876 K and yield an average volume thermal expansion coefficient of 2.44 × 10^-5 K^-1. The thermochemical data are used to calculate phase relations involving pyroxene, -Mg₂SiO₄ plus stishovite, Mg₂SiO₄ spinel plus stishovite, and ilmenite in good agreement with the results of high pressure studies.     

Elasticity of the pyrope (Mg3Al2Si3O12)-majorite (MgSiO3) garnets solid solution

Dense isotropic polycrystalline specimens of majorite-rich garnets (Py₁₀₀, Py₆₂Mj₃₈, Py₅₀Mj₅₀, Py₂₁Mj₇₉ and Mj₁₀₀) along the pyrope (Mg₃Al₂Si₃O₁₂ = Py₁₀₀)-majorite (MgSiO₃ = Mj₁₀₀) join were fabricated in a 2000-ton uniaxial split-sphere anvil apparatus (USSA-2000) at pressures from 10 to 18.5 GPa and temperatures from 1200 to 1850 °C, within their stability fields in runs of 2–4-h duration, using hot-pressing techniques developed by Gwanmesia et al. (1993). These specimens are single-phased, fine-grained (≤5 mm), free of microcracks, and have bulk densities greater than 99% of the corresponding single-crystal X-ray density. Elastic compressional (P) and shear (S) wave velocities were determined at room pressure and temperature for these polycrystalline garnet specimens by phase comparison ultrasonic interferometry. For Mj₁₀₀, the P and S wave velocities are within 1% of the Hashin-Shtrikman averages calculated from the single crystal elastic moduli measured by Brillouin spectroscopy. Both the elastic bulk modulus (K) and the shear modulus (G) decrease continuously with increasing majorite content from pyrope garnet (Py₁₀₀) to pure majorite garnet (Mj₁₀₀). The compositional dependence of K and G are given by K = 172.3 (40) − 0.085X, and G = 91.6 (10) − 0.038X, where X = mol% majorite), respectively, indicating that substitution of Si for Mg and Al decreases both K and G by about 5% along the solid solution series. Received: 25 March 1999 / Accepted: 12 July 1999