Anomalous birefringence in andradite–grossular solid solutions: a quantum-mechanical approach

The static linear optical properties (refractive indices, birefringence and axial angle) of andradite–grossular (Ca₃Fe₂Si₃O₁₂–Ca₃Al₂Si₃O₁₂) solid solutions have been computed at the ab initio quantum-mechanical level through the Coupled Perturbed Kohn–Sham scheme, using an all-electron Gaussian-type basis set. Geometry relaxation after substitution of 1–8 Al for Fe atoms in the primitive cell of andradite yields 23 non-equivalent configurations ranging from cubic to triclinic symmetry. Refractive indices vary quite regularly between the andradite (1.860) and grossular (1.671) end-members; the birefringence δ and the axial angle 2V at intermediate compositions can be as large as 0.02° and 89°, respectively. Comparison with experiments suffers from inhomogeneities and impurities of natural samples; however, semi-quantitative agreement is observed.     

Low-temperature heat capacities of synthetic pyrope,grossular, and pyrope60grossular40

The heat capacities of synthetic pyrope (Mg₃Al₂Si₂O₁₂), grossular (Ca₃Al₂Si₃O₁₂) and a solid solution pyrope₆₀grossular₄₀ (Mg_1.8Ca_1.2Al₂Si₃O₁₂) have been measured by adiabatic calorimetry in the temperature range 10–350 K. The samples were crystallized from glasses in a conventional piston-cylinder apparatus.The molar thermophysical properties at 298.15 K (J mol^?1 K^?1) are:

     

3.

Vibrational spectroscopy of end-member silicate garnets     

A. M. Hofmeister  A. Chopelas 《Physics and Chemistry of Minerals》1991,17(6):503-526

Infrared reflectance (IR) and Raman spectra were collected on small (ca. 500 micron) single crystals of 5 natural garnets with nearly end-member compositions: pyrope (98% Mg₃Al₂Si₃O₁₂), almandine (83% Fe₃Al₂Si₃O₁₂), spessartine (98% Mn₃Al₂Si₃O₁₂), grossular (97% Ca₃Al₂Si₃O₁₂), and andradite (99% Ca₃Fe₂Si₃O₁₂). Frequencies and symmetry assignments were determined for all 17 IR modes and all 25 Raman modes. By using factor group analysis and by correlating the bands by their intensities, bands were assigned to either one of the SiO₄ internal motions, as a rotation, or to a type of translation. The assignments are supported by (1) the distinct trends of frequencies with cell size and cation masses for each of the different types of motion, (2) the similarity of garnet energies for each of the different types of motion to those of olivine with the same cation, and (3) the closeness of the T ₁ u IR frequencies to the T ₂ g Raman frequencies. Mode mixing appears to be weak. Correlations between frequencies and structural parameters suggests a direct dependence of force constants on lattice parameter. This relationship arises from bond lengths in the garnet structure being constrained by the size and compressibility of adjacent polyhedra through edge-sharing. Comparison of our endmember data with previous powder IR studies of intermediate garnets indicates that dodecahedral (X) and octahedral (Y) sites alone exhibit two-mode behavior for those solid solutions involving two ions with considerably different masses. However, for solid solutions involving cations of much different ionic radii, two-mode behavior is found for the translations of SiO₄ groups. This is the first report of two-mode behavior that is unrelated to mass, and instead is due to significantly different force constants in the pyralspites compared to the ugrandites.Anomalies in mixing volumes are linked to two-mode behavior of the SiO₄ translations, which leads to the suggestion that the mixing volume behavior is caused by the resistance of the Si-O bond to expansion and compression, as well as to changes in the dodecahedral site. Crystal-field effects may also play an important role within the ugrandite series. Deviation of molar volume dependence on composition from a linear to a asymmetric, non-linear (sometimes sigmoidal) dependence can be linked to solid solutions that possess slightly non-equivalent cation sites.     

4.

Trace element incorporation into pyrope–grossular solid solutions: an atomistic simulation study     

W. van Westrenen  N. L. Allan  J. D. Blundy  M. Yu Lavrentiev  B. R. Lucas  J. A. Purton 《Physics and Chemistry of Minerals》2003,30(4):217-229

 We have performed atomistic computer simulations on trace element incorporation into the divalent dodecahedral X-sites of pyrope (Py — Mg₃Al₂Si₃O₁₂) – grossular (Gr — Ca₃Al₂Si₃O₁₂) solid solutions. An ionic model and the Mott–Littleton two-region approach to defect energies were used to calculate the energetics of substitution by a range of divalent trace-elements and of charge-balanced substitution by trivalent ions in the static limit. Results are compared with experimental high-temperature, high-pressure garnet-melt trace element partitioning data obtained for the same garnet solid solution to refine our understanding of the factors controlling element partitioning into solid solutions. Defect energies (U _def,f), relaxation (lattice strain) energies (U _rel), and solution energies (U _sol) were derived using two different approaches. One approach assumes the presence of one type of hybrid X-site with properties intermediate between pure Mg and Ca sites, and the other assumes discrete Mg and Ca X-sites, and thus two distinct cation sublattices. The hybrid model is shown to be inadequate, since it averages out local distortions in the garnet structure. The discrete model results suggest trace elements are more soluble in Py₅₀Gy₅₀ than in either end-member compound. Physically this is due to small changes in size of the X-sites and the removal of unfavourable interactions between third nearest neighbours of the same size. Surprisingly, depending on the local order, large trace element cations may substitute for Mg²⁺ and small trace elements for Ca²⁺ in Py₅₀Gr₅₀. These solubilities provide an explanation for the anomalous trace-element partitioning behaviour along the pyrope–grossular join observed experimentally. Received: 27 January 2000 / Accepted: 14 February 2003     

5.

An experimental study of Ca-(Fe,Mg) interdiffusion in silicate garnets   总被引：1，自引：0，他引：1  

R. Freer  A. Edwards 《Contributions to Mineralogy and Petrology》1999,134(4):370-379

Ca-(Fe,Mg) interdiffusion experiments between natural single crystals of grossular (Ca_2.74Mg_0.15 Fe_0.23Al_1.76Cr_0.04Si_3.05O₁₂) and almandine (Ca_0.21Mg_0.40 Fe_2.23Mn_0.13Al_2.00Cr_0.08Si_2.99O₁₂ or Ca_0.43Mg_0.36Fe_2.11 Al_1.95Si_3.04O₁₂), were undertaken at 900–1100 °C and 30 kbar, and pressures of 15.0–32.5 kbar at 1000 °C. Samples were buffered by Fe/FeO in most cases. Diffusion profiles were determined by electron microprobe. Across the experimental couples the interdiffusion coefficients (D˜) were almost independent of composition. The diffusion rates in an unbuffered sample were significantly faster than in buffered samples. The temperature dependence of the D˜ (Ca-Fe,Mg) interdiffusion coefficients may be described by

	Cop	So298?So0	Ho298?Ho0/T
Pyrope	325.31	266.27	47852
Grossular	333.17	260.12	47660
Py60Gr40	328.32	268.32	47990

at 30 kbar and 900–1100 °C. This activation energy is marginally higher than previous experimental studies involving Ca-free garnets; the interdiffusion coefficients are higher than previous studies for Fe-Mg and Fe-Mn exchange in garnet. The pressure dependence of D˜ (Ca-Fe,Mg) at 1000 °C yielded an activation volume of 11.2 cm³ mol⁻¹, which is higher than previous results from studies involving garnet and olivine. Comparison with simulation studies suggests a vacancy mechanism for divalent ion migration in garnet, with extrinsic processes being dominant up to very high temperatures. Received: 15 December 1996 / Accepted: 3 November 1998     

Vibrational spectroscopy of end-member silicate garnets

Infrared reflectance (IR) and Raman spectra were collected on small (ca. 500 micron) single crystals of 5 natural garnets with nearly end-member compositions: pyrope (98% Mg₃Al₂Si₃O₁₂), almandine (83% Fe₃Al₂Si₃O₁₂), spessartine (98% Mn₃Al₂Si₃O₁₂), grossular (97% Ca₃Al₂Si₃O₁₂), and andradite (99% Ca₃Fe₂Si₃O₁₂). Frequencies and symmetry assignments were determined for all 17 IR modes and all 25 Raman modes. By using factor group analysis and by correlating the bands by their intensities, bands were assigned to either one of the SiO₄ internal motions, as a rotation, or to a type of translation. The assignments are supported by (1) the distinct trends of frequencies with cell size and cation masses for each of the different types of motion, (2) the similarity of garnet energies for each of the different types of motion to those of olivine with the same cation, and (3) the closeness of the T ₁ u IR frequencies to the T ₂ g Raman frequencies. Mode mixing appears to be weak. Correlations between frequencies and structural parameters suggests a direct dependence of force constants on lattice parameter. This relationship arises from bond lengths in the garnet structure being constrained by the size and compressibility of adjacent polyhedra through edge-sharing. Comparison of our endmember data with previous powder IR studies of intermediate garnets indicates that dodecahedral (X) and octahedral (Y) sites alone exhibit two-mode behavior for those solid solutions involving two ions with considerably different masses. However, for solid solutions involving cations of much different ionic radii, two-mode behavior is found for the translations of SiO₄ groups. This is the first report of two-mode behavior that is unrelated to mass, and instead is due to significantly different force constants in the pyralspites compared to the ugrandites.Anomalies in mixing volumes are linked to two-mode behavior of the SiO₄ translations, which leads to the suggestion that the mixing volume behavior is caused by the resistance of the Si-O bond to expansion and compression, as well as to changes in the dodecahedral site. Crystal-field effects may also play an important role within the ugrandite series. Deviation of molar volume dependence on composition from a linear to a asymmetric, non-linear (sometimes sigmoidal) dependence can be linked to solid solutions that possess slightly non-equivalent cation sites.     

Trace element incorporation into pyrope–grossular solid solutions: an atomistic simulation study

 We have performed atomistic computer simulations on trace element incorporation into the divalent dodecahedral X-sites of pyrope (Py — Mg₃Al₂Si₃O₁₂) – grossular (Gr — Ca₃Al₂Si₃O₁₂) solid solutions. An ionic model and the Mott–Littleton two-region approach to defect energies were used to calculate the energetics of substitution by a range of divalent trace-elements and of charge-balanced substitution by trivalent ions in the static limit. Results are compared with experimental high-temperature, high-pressure garnet-melt trace element partitioning data obtained for the same garnet solid solution to refine our understanding of the factors controlling element partitioning into solid solutions. Defect energies (U _def,f), relaxation (lattice strain) energies (U _rel), and solution energies (U _sol) were derived using two different approaches. One approach assumes the presence of one type of hybrid X-site with properties intermediate between pure Mg and Ca sites, and the other assumes discrete Mg and Ca X-sites, and thus two distinct cation sublattices. The hybrid model is shown to be inadequate, since it averages out local distortions in the garnet structure. The discrete model results suggest trace elements are more soluble in Py₅₀Gy₅₀ than in either end-member compound. Physically this is due to small changes in size of the X-sites and the removal of unfavourable interactions between third nearest neighbours of the same size. Surprisingly, depending on the local order, large trace element cations may substitute for Mg²⁺ and small trace elements for Ca²⁺ in Py₅₀Gr₅₀. These solubilities provide an explanation for the anomalous trace-element partitioning behaviour along the pyrope–grossular join observed experimentally. Received: 27 January 2000 / Accepted: 14 February 2003     

An experimental study of Ca-(Fe,Mg) interdiffusion in silicate garnets

Ca-(Fe,Mg) interdiffusion experiments between natural single crystals of grossular (Ca_2.74Mg_0.15 Fe_0.23Al_1.76Cr_0.04Si_3.05O₁₂) and almandine (Ca_0.21Mg_0.40 Fe_2.23Mn_0.13Al_2.00Cr_0.08Si_2.99O₁₂ or Ca_0.43Mg_0.36Fe_2.11 Al_1.95Si_3.04O₁₂), were undertaken at 900–1100 °C and 30 kbar, and pressures of 15.0–32.5 kbar at 1000 °C. Samples were buffered by Fe/FeO in most cases. Diffusion profiles were determined by electron microprobe. Across the experimental couples the interdiffusion coefficients (D˜) were almost independent of composition. The diffusion rates in an unbuffered sample were significantly faster than in buffered samples. The temperature dependence of the D˜ (Ca-Fe,Mg) interdiffusion coefficients may be described by

XAFS characterization of the structural site of Yb in synthetic pyrope and grossular garnets

The incorporation and site preference of minor amounts (about 1 wt%) of Yb³⁺ in synthetic pyrope (Mg₃Al₂Si₃O₁₂) and grossular (Ca₃Al₂Si₃O₁₂) garnet were studied by X-ray Absorption Fine-Structure (XAFS) Spectroscopy. The measurements, performed in the temperature range 77–343 K at both Yb L_I- and L_III-edges, demonstrate that Yb³⁺ enters the garnet structure and is located in the dodecahedral site in both samples. The coordination environment of Yb³⁺ in the two samples was compared to that of the X-site cation in end-member synthetic pyrope and grossular and in Yb₃Al₅O₁₂ as determined by single-crystal X-ray diffraction. The local geometry around Yb³⁺ is different from that of Mg and Ca in the bulk of the garnet, and also from that of Yb³⁺ in Yb₃Al₅O₁₂. Τhe XAFS results indicate that, (1) structural relaxation occurs around Yb³⁺ in the garnet structure; (2) the host garnet matrix exerts a major structural control on the incorporation of Yb³⁺, and (3) minor amounts of Yb³⁺ in garnet are located in structural sites and not in ill-defined defects. Received: 15 January 1998/ Revised, accepted: 21 July 1998     

The high-temperature P2/c<Subscript>1</Subscript>–C2/c phase transition in Fe-free Ca-rich P2<Subscript>1</Subscript>/c clinopyroxenes

An in situ, high-temperature, powder diffraction investigation was performed for iron-free clinopyroxenes with compositions Ca_0.40Mg_1.60Si₂O₆, Ca_0.52Mg_1.46Al_0.05Si_1.98O₆, Ca_0.59Mg_1.41Si₂O₆ and Ca_0.70Mg_1.30Si₂O₆, up to 850 °C using synchrotron radiation (ESRF, Grenoble). In samples with compositions Ca_0.52Mg_1.46Al_0.05Si_1.98O₆ and Ca_0.59Mg_1.41Si₂O₆, evidence of for the P2₁/c-C2/c displacive phase transition was seen in changes in lattice parameters at T 550 and 300 °C respectively. Landau modelling of the phase transition behaviour for the sample with composition Ca_0.52Mg_1.46Al_0.05Si_1.98O₆ shows a tricritical behaviour [T _c =547(16)]. Comparison with the transition behaviour in other samples with lower Ca contents along the join diopside–enstatite indicates that a decrease in T _{c ,} and a switch from first-order to tricritical behavior occurs with increasing Ca content. The change in the transition behaviour was related to an interaction with the antiphase domains at the nanoscale.     

Ca–Mn exchange between grossular and MnCl2 solutions at 2 kbar and 600°°C: reaction mechanism and evidence for non-ideal mixing in spessartine-grossular garnets

 The hydrothermal reaction between grossular and 1 molar manganese chloride solution was studied at 2 kbar and 600 °C at various bulk Ca/(Ca+Mn) compositions: Ca₃Al₂Si₃O₁₂+3Mn²⁺(aq) ⇔ Mn₃Al₂Si₃O₁₂+3Ca²⁺(aq) The reaction products are garnets of the spessartine-grossular solid-solution series which discontinuously armour the dissolving grossular grains. The first garnet to crystallize is spessartine rich (X ^gt _Mn≥0.95), reflecting the high Mn content of the solution, but as the reaction proceeds more calcium-rich garnets progressively overgrow the initial products. The armouring product layer is detached from the dissolving grossular, which allows the progressive overgrowth to occur on both its external and internal surfaces and results in the development of a two directional Ca/(Ca+Mn) zoning pattern in the product grains. The compositional changes in the run products are consistent with attainment of heterogeneous equilibrium between the external rims of the spessartine-grossular garnets and the bulk solutions in runs of duration ≥24 hours. Plots of ln K_D versus X ^gt _Ca maxima show linear variations that are not consistent with the ideal mixing that has been proposed for spessartine-grossular garnets at temperatures of 900 to 1200 °C. The data rather fit a regular solution model with the parameters ΔG° (600 °C, 2 kbar)=−8.0±0.8 kJ/mol and w ^gt _CaMn=2.6±2.0 kJ/mol. Existing solubility measurements and thermodynamic data from other Ca and Mn silicates support the calculated data. Grossular activities calculated using the w ^gt _CaMn parameter indicate that even in manganese-rich metapelites pressure estimates calculated using the garnet-plagioclase-Al₂SiO₅-quartz barometer will not be increased by more than 0.2 kbar. Received: 18 January 1995/Accepted: 4 June 1996     

Low-temperature thermodynamic properties of disordered zeolites of the natrolite group

 The heat capacity of paranatrolite and tetranatrolite with a disordered distribution of Al and Si atoms has been measured in the temperature range of 6–309 K using the adiabatic calorimetry technique. The composition of the samples is represented with the formula (Na_1.90K_0.22Ca_0.06)[Al_2.24Si_2.76O₁₀]·nH₂O, where n=3.10 for paranatrolite and n=2.31 for tetranatrolite. For both zeolites, thermodynamic functions (vibrational entropy, enthalpy, and free energy function) have been calculated. At T=298.15 K, the values of the heat capacity and entropy are 425.1 ± 0.8 and 419.1 ±0.8 J K⁻¹ mol⁻¹ for paranatrolite and 381.0 ± 0.7 and 383.2 ± 0.7 J K⁻¹ mol⁻¹ for tetranatrolite. Thermodynamic functions for tetranatrolite and paranatrolite with compositions corrected for the amount of extraframework cations and water molecules have also been calculated. The calculation for tetranatrolite with two water molecules and two extraframework cations per formula yields: C _p (298.15)=359.1 J K⁻¹ mol⁻¹, S(298.15) −S(0)=362.8 J K⁻¹ mol⁻¹. Comparing these values with the literature data for the (Al,Si)-ordered natrolite, we can conclude that the order in tetrahedral atoms does not affect the heat capacity. The analysis of derivatives dC/dT for natrolite, paranatrolite, and tetranatrolite has indicated that the water- cations subsystem within the highly hydrated zeolite may become unstable at temperatures above 200 K. Received: 30 July 2001 / Accepted: 15 November 2001     

Chromium-aluminum mixing in garnet: A thermochemical study

The enthalpies of mixing of synthetic grossular (Ca₃Al₂Si₃O₁₂)-uvarovite (Ca₃Cr₂Si₃O₁₂) solid solutions have been determined by oxide melt calorimetry at 970 K. The results indicate that the solid solution exhibits a very small negative deviation from Raoult's law. In terms of the regular solution model a chromium-aluminum interaction parameter $\text{W}{}_{\mathrm{H}}{}^{\mathrm{Cr-Al}}$ of between 0 and ?1000 cal/gm atom is consistent with the data.     

XAFS characterization of the structural site of Yb in synthetic pyrope and grossular garnets. II: XANES full multiple scattering calculations at the Yb LI- and LIII-edges

We present an X-ray absorption near-edge structure study performed at the Yb L_I- and L_III-edges on synthetic pyrope (Mg₃Al₂Si₃O₁₂) and grossular (Ca₃Al₂Si₃O₁₂) garnets containing about 1% wt of Yb. For the first time Yb L-edge XANES spectra are analyzed by full multiple scattering theory using clusters of different sizes and different final-state potentials. A comparison between experimental spectra and model calculations indicates that Yb³⁺ enters the dodecahedral X-site in both pyrope and grossular, in agreement with the results of an EXAFS study. Based on the present results, the charge balancing substitution mechanism required by the replacement of divalent Mg and Ca cations with trivalent Yb³⁺ is discussed in terms of vacancies in dodecahedral sites surrounding the central Yb³⁺ absorber. Received: 7 December 1998 / Revised, accepted: 7 May 1999     

Partition coefficients for REE between garnets and liquids: implications of non-Henry's Law behaviour for models of basalt origin and evolution

Partition coefficients for the rare earth elements (REE) Ce, Sm and Tm between coexisting garnets and hydrous liquids have been determined at high pressure and temperatures (30 kbar and 1300 and 1500°C). Two synthetic systems were studied, Mg₃Al₂Si₃O₁₂-H₂O and Ca₃Al₂Si₃O₁₂-H₂O, in addition to a natural pyrope-bearing system.Deviations from Henry's Law behaviour occur at geologically relevant REE concentrations. At concentrations < 3 ppm Ce, < 12 ppm Sm, < 80 ppm Tm in pyrope and < 100 ppm Ce, < 250 ppm Sm, < 1000 ppm Tm in grossular (at 30 kbar and 1300°C), D^{garnet liquid}_REE increases as the REE concentration in the garnet decreases. At higher concentrations, D_REE is constant. D^{grossular liquid}_REE also constant when the garnet contains less than about 2 ppm Sm or Tm. The REE concentration at which D_REE becomes constant increases with increasing temperature, decreasing REE ionic radius and increasing Ca content of the garnet.Partitioning behaviour of Ce, Sm and Tm between a natural pyrope-rich garnet and hydrous liquid is analogous to that in the synthetic systems and substantiates the substitution model proposed by Harrison and Wood (1980).Values of D_REE^{garnet/liquid} for which Henry's Law is obeyed are systematically higher for grossular than for pyrope (D^{pyrope/liquid} = 0.067(Ce), 0.108(Sm), 0.155(Tm) and D^{grossular/Liquid} = 0.65(Ce), 0.75(Sm), 4.55(Tm).The implications of non-Henry's Law partitioning of REE for models of basalt petrogenesis involving garnet are far-ranging. Deviations from Henry's Law permit refinements to be made to calculated REE abundances once basic model parameters have been defined.     

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     

High-T phase transition of synthetic ANaB(LiMg)CMg5Si8O22(OH)2 amphibole: an X-ray synchrotron powder diffraction and FTIR spectroscopic study

The synthetic amphibole Na_0.95(Li_0.95Mg_1.05)Mg₅Si₈O₂₂(OH)₂ was studied in situ at high-T, using IR OH-stretching spectroscopy and synchrotron X-ray powder diffraction. At room-T the sample has P2₁ /m symmetry, as shown by the FTIR spectrum. It shows in the OH region two well-defined and intense absorptions at 3,748 and 3,712 cm⁻¹, respectively, and two minor bands at 3,667 and 3,687 cm⁻¹. The main bands are assigned to the two independent O–H groups in the primitive structure. The two minor bands evidencing the presence of small amount of vacant A-site (^A□_0.05). With increasing T, these bands shift continuously and merge into a unique absorption at high temperature. A change as a function of increasing T is revealed by the evolution of the refined unit-cell parameters, whose trend shows a transition to C2/m at about 320–330°C. The spontaneous scalar strain, fitted with a tricritical 2–6 Landau potential, gives a T _c of 325(10)°C (β parameter = 0.27). Comparison with the second-order P2₁ /m ⇔ C2/m phase transition at 255°C for synthetic amphibole ^ANa_0.8^B(Na_0.8Mg_1.2)^CMg₅Si₈O₂₂(OH)₂ indicates that the substitution of Na with Li at the B-sites strongly affects the thermodynamic character and the T _c of the phase transition. The comparison of LNMSH amphiboles with cummingtonitic ones shows that the high-T thermodynamic behaviour is affected by A-site occupancy.     

The stability of hercynite at high pressures and temperatures

The stability of hercynite (FeAl₂O₄) has been investigated experimentally between 7 and 24 GPa and 900 and 1,700°C. Hercynite breaks down to its constituent oxides at 7–8.5 GPa and temperatures >1,000°C. The incorporation of a small magnetite component in the hercynite necessitated a small correction to fix the location of the endmember reaction: FeAl₂O₄  = Al₂O₃ + FeO in P–T space. After making this correction, the position of the phase boundary was used to evaluate thermodynamic data for hercynite. Our results support a relatively large S ₂₉₈^° for hercynite, on the order of 115 J mol⁻¹ K⁻¹. Experiments up to 24 GPa and 1,400°C failed to detect any high-pressure polymorph of FeAl₂O₄; only corundum + wüstite were detected. This behaviour contrasts with that observed for the analogous MgAl₂O₄ system where the constituent oxides recombine at high pressure to produce “post-spinel” phases with CaFe₂O₄-type and CaTi₂O₄-type structures.     

An experimental investigation of the partitioning of REE between garnet and liquid with reference to the role of defect equilibria

The partitioning of samarium and thulium between garnets and melts in the systems Mg₃Al₂-Si₃O₁₂-H₂O and Ca₃Al₂Si₃O₁₂-H₂O has been studied as a function of REE concentration in the garnets at 30 kbar pressure. Synthesis experiments of variable time under constant P, T conditions indicate that garnet initially crystallizes rapidly to produce apparent values of D _Sm (D _Sm=concentration of Sm in garnet/concentration of Sm in liquid) which are too large in the case of pyrope and too small in the case of grossular. As the experiment proceeds, Sm diffuses out of or into the garnet and the equilibrium value of D _Sm is approached. Approximate values of diffusion coefficients for Sm in pyrope garnet obtained by this method are 6 × 10^–13 cm² s^–1 at 1,300 ° C and 2 × 10^–12 cm² s^–1 at 1,500 ° C, and for grossular, 8.3 × 10^–12 cm² s^–1 at 1,200 ° C and 4.6 × 10^–11 cm² s^–1 at 1,300 ° C. The equilibrium values of D _Sm have been reversed by experiments with Sm-free pyrope and Sm-bearing glass, and with Sm-bearing grossular and Sm-free glass.Between 12 ppm and 1,000 ppm Sm in pyrope at 1,300 ° C and between 80 ppm and >2 wt.% Tm in pyrope at 1,500 ° C, partition coefficients are constant and independent of REE concentration. Above 100 ppm of Sm in garnet at 1,500 ° C, partition coefficients are independent of Sm concentration. At lower concentrations, however, D _Sm is dependent upon the Sm content of the garnet. The two regions may be interpreted in terms of charge-balanced substitution of Sm₃Al₅O₁₂ in the garnet at high Sm concentrations and defect equilibria involving cation vacancies at low concentrations. At very low REE concentrations (< 1 ppm Tm in grossular at 1,300 ° C) D_REE garnet/liquid again becomes constant with an apparent Henry's Law value greater than that at high concentrations. This may be interpreted in terms of a large abundance of cation vacancies relative to the number of REE ions.The importance of defects in the low concentration region has been confirmed by adding other REE (at 80 ppm level) to the system Mg₃Al₂Si₃O₁₂-H₂O at low Sm concentrations. These change D _Sm in the defect region, demonstrating their role in the production of vacancies.Experiments on a natural pyropic garnet indicate that defect equilibria are of importance to REE partitioning within the concentration ranges found in nature.     

Study on Al2O3 content and phase stability of aluminous-CaSiO3 perovskite at high pressure and temperature

 In order to clarify Al₂O₃ content and phase stability of aluminous CaSiO₃-perovskite, high-pressure and high-temperature transformations of Ca₃Al₂Si₃O₁₂ garnet (grossular) were studied using a MA8-type high-pressure apparatus combined with synchrotron radiation. Recovered samples were examined by analytical transmission electron microscopy. At pressures of 23–25 GPa and temperatures of 1000–1600 K, grossular garnet decomposed into a mixture of aluminum-bearing Ca-perovskite and corundum, although a metastable perovskite with grossular composition was formed when the heating duration was not long enough at 1000 K. On release of pressure, this aluminum-bearing CaSiO₃-perovskite transformed to the “LiNbO₃-type phase” and/or amorphous phase depending on its Al₂O₃ content. The structure of this LiNbO₃-type phase is very similar to that of LiNbO₃ but is not identical. CaSiO₃-perovskite with 8 to 25 mol% Al₂O₃ was quenched to alternating lamellae of amorphous layer and LiNbO₃-type phase. On the other hand, a quenched product from CaSiO₃-perovskite with less than 6 mol% consisted only of amorphous phase. Most of the inconsistencies amongst previous studies could be explained by the formation of perovskite with grossular composition, amorphous phase, and the LiNbO₃-type phase. Received: 11 April 2001 / Accepted: 5 July 2002     

Thermodynamic properties of almandine-grossular garnet solid solutions

The mixing properties of Fe₃Al₂Si₃O₁₂-Ca₃Al₂Si₃O₁₂ garnet solid solutions have been studied in the temperature range 850–1100° C. The experimental method involves measuring the composition of garnet in equilibrium with an assemblage in which the activity of the Ca₃Al₂Si₃O₁₂ component is fixed. Experiments on the assemblage garnet solid solution, anorthite, Al₂SiO₅ polymorph and quartz at known pressure and temperature fix the activity of the Ca₃Al₂Si₃O₁₂ component through the equilibrium: 1 $$\begin{gathered} {\text{3CaAl}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{8}} \rightleftarrows {\text{Ca}}_{\text{3}} {\text{Al}}_{\text{2}} {\text{Si}}_{\text{3}} {\text{O}}_{{\text{12}}} \hfill \\ {\text{Anorthite garnet}} \hfill \\ {\text{ + 2Al}}_{\text{2}} {\text{SiO}}_{\text{5}} {\text{ + SiO}}_{\text{2}} \hfill \\ {\text{ sillimanite/kyanite quartz}}{\text{.}} \hfill \\ \end{gathered}$$ This equilibrium, with either sillimanite or kyanite as the aluminosilicate mineral, was used to control \({\text{a}}_{{\text{Ca}}_{\text{3}} {\text{Al}}_{\text{2}} {\text{Si}}_{\text{3}} {\text{O}}_{{\text{12}}} }^{{\text{gt}}} \) . The compositions of the garnet solutions produced were determined by measurement of their unit cell edges. At 1 bar Fe₃Al₂Si₃O₁₂-Ca₃Al₂Si₃O₁₂ garnets exhibit negative deviations from ideality at the Fe-rich end of the series and positive deviations at the calcium end. With increasing pressure the activity coefficients for the Ca₃Al₂Si₃O₁₂ component increase because the partial molar volume of this component is greater than the molar volume of pure grossular. Previous studies indicate that the activity coefficients for the Ca₃Al₂Si₃O₁₂ component also increase with increasing (Mg/Mg+Fe) ratio of the garnet. The region of negative deviation from ideality implies a tendency towards formation of a stable Fe-Ca garnet component. Evidence in support of this conclusion has been found in a natural Fe-rich garnet which was found to contain two different garnet phases of distinctly different compositions.     

Estimating Influence of Crystallizing Latent Heat on Cooling-Crystallizing Process of a Granitic Melt and Its Geological Implications

Based on the theory of thermal conductivity, in this paper we derived a formula to estimate the prolongation period （AtL） of cooling-crystallization process of a granitic melt caused by latent heat of crystallization as follows：△tL=QL×△tcol/（TM-TC）×CP where TM is initial temperature of the granite melt, Tc crystallization temperature of the granite melt, Cp specific heat, △tcol cooling period of a granite melt from its initial temperature （TM） to its crystallization temperature （Tc）, QL latent heat of the granite melt.
The cooling period of the melt for the Fanshan granodiorite from its initial temperature （900℃） to crystallization temperature （600℃） could be estimated -210,000 years if latent heat was not considered. Calculation for the Fanshan melt using the above formula yields a AtL value of -190,000 years, which implies that the actual cooling period within the temperature range of 900°-600℃ should be 400,000 years. This demonstrates that the latent heat produced from crystallization of the granitic melt is a key factor influencing the cooling-crystallization process of a granitic melt, prolongating the period of crystallization and resulting in the large emplacement-crystallization time difference （ECTD） in granite batholith.     

Uvarovite: Stability of uvarovite-grossularite solid solution at low pressure

Uvarovite (Ca₃Cr₂Si₃O₁₂) forms a complete solid solution series with grossularite (Ca₃Al₂Si₃O₁₂) below 855 ± 5 ° C at a total pressure of 1 atm. Pure uvarovite decomposes to pwo (CaSiO₃) + esk (Cr₂O₃) at 1385 ± 10 ° C. The incorporation of about 5 wt-% of Ca₃Al₂ Si₃O₁₂ component in the uvarovite structure raises the thermal stability of the garnet_ss to 1410 ± 5 ° C, and uvarovite₉₅ grossularite₀₅ melts incongruently to pwo (CaSiO₃) + coresk_ss ((Al, Cr)₂O₃) + L. Pure grossularite decomposes to wo (CaSi0₃) + geh (Ca₂Al₂SiO₇) + and (CaAl₂Si₂O₈) at 855 ± 5 ° C, grossularite thermal stability is increased by incorporation of Ca₃Cr₂Si₃O₁₂ component by 530 ° C. At 1280±5 ° C coresk_ss + L react to gar_ss + geh + an defining an invariant tequilibrium of the CaO-Cr₂O₃-Al₂O₃-SiO₂ quaternary system. Liquid reacts to gar_ss + pwo + geh + an at 1263 ±5 ° C terminating univariant and divariant liquid relations occurring along the join Ca₃Cr₂Si₃O₁₂-Ca₃Al₂Si₃O₁₂. The unit-cell parameter for uvarovite is 11.996(2) Å, the refractive index 1.865(3). The substitution of Cr by Al decreases a and n almost linearly toward the grossularite end member which displays a unit-cell parameter of 11.848(2) Å and a refractive index of 1.732 (1).