Rigid unit modes at high pressure: an explorative study of a fibrous zeolite-like framework with EDI topology

We report a comparative study on the high pressure (HP) structural behaviour of a fibrous zeolite (with EDI topology) on the basis of rigid unit modes (RUM) modelling and previously published single-crystal X-ray diffraction. HP single-crystal diffraction data lead to a more precise determination of the elastic parameters (axial and volume compressibilities) useful to define the equation-of-state under isothermal conditions, and the structural refinements are useful to describe the main deformation mechanisms of the Si/Al framework and extra-framework content at high pressure. The RUM modelling is applied to simulate the compressive behaviour of the framework, under hydrostatic and non-hydrostatic conditions, using a minimum number of parameters, and to describe the deformation mechanism intuitively in terms of the rotations of the SiO₄ polyhedra. The local and global P-induced deformation mechanisms of the Si/Al framework observed in experiment (channel ellipticity, SBU rotation) are well reproduced by RUM modelling. The simulation of uniaxial compression (non-hydrostatic conditions) shows an interesting result on the structural behaviour. This comparative study tests the reliability of the RUM modelling in open-framework silicates with a complicated crystal structure.Electronic Supplementary Material: Supplementary material to this paper is available in electronic form at     

Comparative compressibility and equation of state of orthorhombic and tetragonal edingtonite

The high-pressure (HP) behaviour of a natural orthorhombic and tetragonal edingtonite from Ice River, Canada, has been investigated using in situ single-crystal X-ray diffraction. The two isothermal equations of state up to 6.74(5) GPa were determined. V₀, K_T0 and K refined with a third-order Birch–Murnaghan equation of state (BM-EoS) are: V₀ = 598.70(7) ų, K_T0 = 59(1) GPa and K=3.9(4) for orthorhombic edingtonite and V₀ = 600.9(2) ų, K_T0 = 59(1) GPa and K=4.2(5) for tetragonal edingtonite. The experiments were conducted with nominally hydrous pressure penetrating transmitting medium. No overhydration effect was observed within the pressure range investigated. At high-pressures the main deformation mechanism is represented by cooperative rotation of the secondary building unit (SBU).Si/Al distribution slightly influences the elastic behaviour of the tetrahedral framework: the SBU bulk moduli are 125(8) GPa and 111(4) GPa for orthorhombic and tetragonal edingtonite, respectively. Extra-framework contents of both zeolites show an interesting behaviour under HP conditions: the split Ba2 site at P >2.85 GPa is completely empty; only the position Ba1 is occupied. Electronic Supplementary Material. Supplementary material to this paper (Observed and calculated structure factors) is available in electronic form at Electronic Supplementary Material Supplementary material is available in the online version of this article at     

High-pressure X-ray study of LiCrSi2O6 clinopyroxene and the general compressibility trends for Li-clinopyroxenes

High-pressure single-crystal X-ray diffraction measurements of synthetic LiCrSi₂O₆ clinopyroxene (with space group P2₁/c) were performed in a diamond-anvil cell up to 7.970 GPa. No phase transition has been observed within the pressure range investigated, but the elastic behavior at lower pressures (up to ~2.5 GPa) is affected by an anomalous softening due to the proximity of the phase transition to the HT-C2/c phase at 330 K and at ambient pressure. A third-order Birch–Murnaghan equation of state fitted to the compression data above 2.5 GPa yields a bulk modulus K _T0 = 93(2) GPa and its first derivative K′ = 8.8(6). The structural data measured up to 7.970 GPa confirm that the space group P2₁/c is maintained throughout the whole pressure range investigated. The atomic parameters, obtained from the integrated diffraction intensities, suggest that the Li coordination polyhedron changes its coordination number from 5 to 6 at 6–7 GPa by means of the approach of the bridging O atom, related to the increased kinking of the B tetrahedral chain. Furthermore, at higher pressures, the structural evolution of LiCrSi₂O₆ provides evidence in the variation of kinking angles and bond lengths of a potential phase transition above 8 GPa to the HP-C2/c space group. A comparison of the Li-clinopyroxenes (M1 = Cr, Al, Sc, Ga, Mg + Fe) previously investigated and our sample shows that their elastic behavior and structural mechanisms of compression are analogous.     

High pressure behaviour of lead feldspar (PbAl2Si2O8)

An in situ high pressure powder diffraction study, using high-brilliance synchrotron radiation, on lead feldspar (PbAl₂Si₂O₈) was performed. Two samples, with Q _od=0.68 and 0.76, were loaded in a diamond anvil cell and were compressed up to 11 GPa. Up to P=7.1 GPa the only phase present is lead feldspar. In the range 7.1–9.4 GPa sudden changes in the position of the reflections suggest the transformation of lead feldspar to a new phase (probably feldspar-like). The absence of split that would be compatible with triclinic symmetry rules out the monoclinic-triclinic transition, that was reported for the structurally similar strontium feldspar. At P>9.4 GPa some new extra reflections not indexable in the feldspar cell are present as well. During decompression the lead feldspar was the only phase present at P<6 GPa. Peak enlargement was observed with pressure, probably preliminary to amorphization. However almost complete amorphization was observed only after fortuitous shock compression at ∼18 GPa; the crystallinity was recovered at room pressure after decompression. The bulk modulus for lead feldspar was K=71.0(9) and 67.6(1.2) GPa for the two samples, in the range reported for feldspars. The cell parameters show a compression pattern which is similar to that observed in anorthite, with Δa/a ₀>Δc/c ₀>Δb/b ₀; comparison with the high temperature behaviour shows that for lead feldspar the strain tensor with pressure is more isotropic and the deformation along a is less prominent. A turnover in the behaviour of the β angle with pressure suggests a change in the compression behaviour at P∼2 GPa. Rietveld refinement of the Pb coordinates was performed in a series of spectra with pressure ranging from 0.6 to 6.5 GPa. The combined analysis of cell parameters and Pb coordinates with pressure showed that the compression of the structure is mainly achieved by an approach of Pb atoms along a *. Received: 21 July 1998 / Revised, accepted: 13 October 1998     

High-pressure properties of diaspore,AlO(OH)

The structural compression mechanism and compressibility of diaspore, AlO(OH), were investigated by in situ single-crystal synchrotron X-ray diffraction at pressures up to 7 GPa using the diamond-anvil cell technique. Complementary density functional theory based model calculations at pressures up to 40 GPa revealed additional information on the pressure-dependence of the hydrogen-bond geometry and the vibrational properties of diaspore. A fit of a second-order Birch–Murnaghan equation of state to the p–V data resulted in the bulk modulus B ₀ = 150(3) GPa and B ₀ = 150.9(4) GPa for the experimental and theoretical data, respectively, while a fit of a third-order Birch–Murnaghan equation of state resulted in B ₀ = 143.7(9) GPa with its pressure derivative B′ = 4.4(6) for the theoretical data. The compression is anisotropic, with the a-axis being most compressible. The compression of the crystal structure proceeds mainly by bond shortening, and particularly by compression of the hydrogen bond, which crosses the channels of the crystal structure in the (001) plane, in a direction nearly parallel to the a-axis, and hence is responsible for the pronounced compression of this axis. While the hydrogen bond strength increases with pressure, a symmetrisation is not reached in the investigated pressure range up to 40 GPa and does not seem likely to occur in diaspore even at higher pressures. The stretching frequencies of the O–H bond decrease approximately linearly with increasing pressure, and therefore also with increasing O–H bond length and decreasing hydrogen bond length. Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users.     

Single-crystal elastic constants of fluorite (CaF2) to 9.3 GPa

 The second-order elastic constants of CaF₂ (fluorite) have been determined by Brillouin scattering to 9.3 GPa at 300 K. Acoustic velocities have been measured in the (111) plane and inverted to simultaneously obtain the elastic constants and the orientation of the crystal. A notable feature of the present inversion is that only the density at ambient condition was used in the inversion. We obtain high-pressure densities directly from Brillouin data by conversion to isothermal conditions and iterative integration of the compression curve. The pressure derivative of the isentropic bulk modulus and of the shear modulus determined in this study are 4.78 ± 0.13 and 1.08 ± 0.07, which differ from previous low-pressure ultrasonic elasticity measurements. The pressure derivative of the isothermal bulk modulus is 4.83 ± 0.13, 8% lower than the value from static compression, and its uncertainty is lower by a factor of 3. The elastic constants of fluorite increase almost linearly with pressure over the whole investigated pressure range. However, at P ≥ 9 GPa, C ₁₁ and C ₁₂ show a subtle structure in their pressure dependence while C ₄₄ does not. The behavior of the elastic constants of fluorite in the 9–9.3 GPa pressure range is probably affected by the onset of a high-pressure structural transition to a lower symmetry phase (α-PbCl₂ type). A single-crystal Raman scattering experiment performed in parallel to the Brillouin measurements shows the appearance of new features at 8.7 GPa. The new features are continuously observed to 49.2 GPa, confirming that the orthorhombic high-pressure phase is stable along the whole investigated pressure range, in agreement with a previous X-ray diffraction study of CaF₂ to 45 GPa. The high-pressure elasticity data in combination with room-pressure values from previous studies allowed us to determine an independent room-temperature compression curve of fluorite. The new compression curve yields a maximum discrepancy of 0.05 GPa at 9.5 GPa with respect to that derived from static compression by Angel (1993). This comparison suggests that the accuracy of the fluorite pressure scale is better than 1% over the 0–9 GPa pressure range. Received: 10 July 2001 / Accepted: 7 March 2002     

The equation of state of Al,H-bearing SiO2 stishovite to 58 GPa

We have determined the P-V equation of state of Al-rich H-bearing SiO₂ stishovite by X-ray powder diffraction at pressures up to 58 GPa using synchrotron radiation. The sample contained 1.8 wt% Al₂O₃ and up to 500 ppm H₂O, and had a composition that would coexist with Mg-silicate perovskite in a subducted slab. By fitting a third-order Birch-Murnaghan equation of state to our compression data, we obtained a bulk modulus K _T0=298(7) GPa with K′=4.3(5). With K′ fixed to a value of 4, the bulk modulus K _T0=304(3) GPa. Our results indicate that Al³⁺ and H⁺ have a small effect on the elastic properties of stishovite. Compared with data obtained up to 43.8 GPa, peak intensities changed and we observed a decreased quality of fit to a tetragonal unit cell at pressures of 49 GPa and higher. These changes may be an indication that the rutile↔CaCl₂ transition occurs between these pressures. After laser annealing of the sample at 58.3(10) GPa and subsequent decompression to room conditions, the cell volume is the same as before compression, giving strong evidence that the composition of the recovered sample is also unchanged. This suggests that Al and H are retained in the sample under extreme P-T conditions and that stishovite can be an agent for transporting water to the deepest lower mantle.     

Modelling of structural and elastic changes of forsterite (Mg2SiO4) under stress

The method of crystal static deformation, including inner strain effects, was applied to calculate the structure configuration and the elastic constants of forsterite under anisotropic and isotropic pressure. A Born type interatomic potential is used, with optimized atomic charges and repulsive radii; SiO₄ tetrahedra are approximated as rigid units. Computations were carried out in the range 1–8 GPa, with steps of 1 GPa, for the three uniaxial stresses τ₁, τ₂, τ₃ and for pressure p. By interpolation of results, interatomic distances and elastic tensor components are shown to depend quadratically on stress. A non-linear behaviour generally appears above 4 GPa; the importance of inner strain and non-linear effects is analyzed. Mg-O bond lengths and O-O edges of coordination polyhedra respond differently to anisotropic and to isotropic stresses, according to the topological features of the structure. Elastic and structural results for hydrostatic pressure are compared to experimental literature data, discussing the range of validity of the rigid body approximation for SiO₄ groups.     

Elasticity of CaIrO<Subscript>3</Subscript> with perovskite and post-perovskite structure

Compression behaviors of CaIrO₃ with perovskite (Pv) and post-perovskite (pPv) structures have been investigated up to 31.0(1.0) and 35.3(1) GPa at room temperature, respectively, in a diamond-anvil cell with hydrostatic pressure media. CaIrO₃ Pv and pPv phases were compressed with the axial compressibility of β _a > β _c > β _b and β _b > β _a > β _c, respectively and no phase transition was observed in both phases up to the highest pressure in the present study. The order of axial compressibility for pPv phase is consistent with the crystallographic consideration for layer structured materials and previous experimental results. On the other hand, Pv phase shows anomalous compression behavior in b axis, which exhibit constant or slightly expanded above 13 GPa, although the applied pressure remained hydrostatic. Volume difference between Pv and pPv phases was gradually decreased with increasing pressure and this is consistent with the results of theoretical study based on the ab initio calculation. Present results, combined with theoretical study, suggest that these complicate compression behaviors in CaIrO₃ under high pressure might be caused by the partially filled electron of Ir⁴⁺. Special attention must be paid in case of using CaIrO₃ as analog materials to MgSiO₃, although CaIrO₃ exhibits interesting physical properties under high pressure.     

Adaptive finite element analysis of mode I fracture in cement‐based materials

Microscopic studies using advanced experimental techniques have provided better insight into the fracture mechanisms in cement‐based materials. A clear understanding of fracture mechanisms is critical for the development of rigorous computational models for analysing fracture. Fracture analysis is usually carried out by finite element method. Accuracy of FE analysis depends upon the choice of mesh and for the predictions to be reliable, discretization errors are to be minimized. In cohesive crack approach, the non‐linearity is limited to the boundary conditions along the geometric discontinuity while the bulk of the material retains its elastic nature. The paper presents a mesh‐adaptive strategy based on ZZ error estimator to model discrete crack propagation in cement‐based materials. Examples of simulations have demonstrated the potential of the mesh‐adaptive technique in modelling the evolution of the localized strain profiles as well as failure of concrete test specimen. Copyright © 2001 John Wiley & Sons, Ltd.     

Structural evolution of a 2M 1 phengite mica up to 11 GPa: an in situ single-crystal X-ray diffraction study

The structural evolution at high pressure of a natural 2M ₁-phengite [(K_0.98Na_0.02)_Σ=1.00(Al_1.55Mg_0.24Fe_0.21Ti_0.02)_Σ=2.01(Si_3.38Al_0.62)O₁₀(OH)₂; a = 5.228(2), b = 9.057(3), c = 19.971(6)Å, β = 95.76(2)°; space group: C2/c] from the metamorphic complex of Cima Pal (Sesia Zone, Western Alps, Italy) was studied by single-crystal X-ray diffraction with a diamond anvil cell under hydrostatic conditions up to ~11 GPa. A series of 12 structure refinements were performed at selected pressures within the P range investigated. The compressional behaviour of the same phengite sample was previously studied up to ~25 GPa by synchrotron X-ray powder diffraction, showing an irreversible transformation with a drastic decrease of the crystallinity at P > 15–17 GPa. The elastic behaviour between 0.0001 and 17 GPa was modelled by a third-order Birch–Murnaghan Equation of State (BM-EoS), yielding to K _T0 = 57.3(10) GPa and K′ = ?K _T0/?P = 6.97(24). The single-crystal structure refinements showed that the significant elastic anisotropy of the 2M ₁-phengite (with β(a):β(b):β(c) = 1:1.17:4.60) is mainly controlled by the anisotropic compression of the K-polyhedra. The evolution of the volume of the inter-layer K-polyhedron as a function of P shows a negative slope, Fitting the P–V(K-polyhedron) data with a truncated second-order BM-EoS we obtain a bulk modulus value of K _T0(K-polyhedron) = 26(1) GPa. Tetrahedra and octahedra are significantly stiffer than the K-polyhedron. Tetrahedra behave as quasi-rigid units within the P range investigated. In contrast, a monotonic decrease is observed for the octahedron volume, with K _T0 = 120(10) GPa derived by a BM-EoS. The anisotropic response to pressure of the K-polyhedron affects the P-induced deformation mechanism on the tetrahedral sheet, consisting in a cooperative rotation of the tetrahedra and producing a significant ditrigonalization of the six-membered rings. The volume of the K-polyhedron and the value of the ditrigonal rotation parameter (α) show a high negative correlation (about 93%), though a slight discontinuity is observed at P >8 GPa. α increases linearly with P up to 7–8 GPa (with ?α/?P ≈ 0.7°/GPa), whereas at higher Ps a “saturation plateau” is visible. A comparison between the main deformation mechanisms as a function of pressure observed in 2M ₁- and 3T-phengite is discussed.     

Quasi-harmonic computer simulations of the structural behaviour and EOS of pyrope at high pressure and high temperature

Numerical simulations, using empirical interatomic potentials within the framework of lattice dynamics and quasi-harmonic approximation, have been carried out to model the behaviour of the structure and of some thermoelastic properties of pyrope at high pressure and high temperature conditions (0–50 GPa, 300–1500 K). Comparison with observed data, available as a function either of P or of T, suggests that the pressure effects are satisfactorily modelled, whilst the effect of T on the simulations is underestimated. The cell edge, bond lengths and polyhedral volumes have been studied as a function of P along five isotherms, spaced by 300 K steps. These isotherms tend to converge at high pressure, which demonstrates that the pressure effects become dominant compared to those of thermal origin in affecting the structural properties far from ambient conditions. The cell parameter, bond distances, and other structural and thermoelastic quantities determined through simulations have been parametrised as a function of P and T by polynomial expansions. Bulk modulus and thermal expansion have been discussed in the light of the high-temperature-Birch-Murnaghan and of the Vinet P – V – T equations of state. The predictions of the bulk modulus versus P and T from the present calculations and from the Vinet-EOS agree up to 10 GPa, but they differ at higher pressure. Received: 23 October, 1998 / Revised, accepted: 23 April, 1999     

Anomalous elasticity of talc at high pressures: Implications for subduction systems

Talc is a layered hydrous silicate mineral that plays a vital role in transporting water into Earth’s interior and is crucial for explaining geophysical observations in subduction zone settings. In this study, we explored the structure, equation of state, and elasticity of both triclinic and monoclinic talc under high pressures up to 18 GPa using first principles simulations based on density functional theory corrected for dispersive forces. Our results indicate that principal components of the full elastic constant tensor C₁₁ and C₂₂, shear components C₆₆, and several off-diagonal components show anomalous pressure dependence. This non-monotonic pressure dependence of elastic constant components is likely related to the structural changes and is often manifested in a polytypic transition from a low-pressure polytype talc-I to a high-pressure polytype talc-II. The polytypic transition of talc occurs at pressures within its thermodynamic stability. However, the bulk and shear elastic moduli show no anomalous softening. Our study also shows that talc has low velocity, extremely high anisotropy, and anomalously high V_P/V_S ratio, thus making it a potential candidate mineral phase that could readily explain unusually high V_P/V_S ratio and large shear wave splitting delays as observed from seismological studies in many subduction systems.     

Stability at high pressure, elastic behavior and pressure-induced structural evolution of “Al5BO9”, a mullite-type ceramic material

Elastic behavior and pressure-induced structural evolution of synthetic boron-mullite “Al₅BO₉” (a = 5.678(2) Å, b = 15.015(4) Å and c = 7.700(3) Å, space group Cmc2₁, Z = 4) were investigated up to 7.4 GPa by in situ single-crystal X-ray diffraction with a diamond anvil cell under hydrostatic conditions. No phase transition or anomalous compressional behavior occurred within the investigated P range. Fitting the P–V data with a truncated second-order (in energy) Birch-Murnaghan Equation-of-State (BM-EoS), using the data weighted by the uncertainties in P and V, we obtained: V ₀ = 656.4(3) Å³ and K _T0 = 165(7) GPa (β _V0 = 0.0061(3) GPa^?1). The evolution of the Eulerian finite strain versus normalized stress (f _E–F _E plot) leads to an almost horizontal trend, showing that a truncated second-order BM-EoS is appropriate to describe the elastic behavior of “Al₅BO₉” within the investigated P range. The weighted linear regression through the data points gives: F _E(0) = 159(11) GPa. Axial compressibility coefficients yielded: β _a  = 1.4(2) × 10^?3 GPa^?1, β _b  = 3.4(4) × 10^?3 GPa^?1, and β _c  = 1.7(3) × 10^?3 GPa^?1 (β _a :β _b :β _c  = 1:2.43:1.21). The highest compressibilities observed in this study within (100) can be ascribed to the presence of voids represented by five-membered rings of polyhedra: Al1–Al3–Al4–Al1–Al3, which allow accommodating the effect of pressure by polyhedral tilting. Polyhedral tilting around the voids also explains the higher compressibility along [010] than along [001]. The stiffer crystallographic direction observed here might be controlled by the infinite chains of edge-sharing octahedra running along [100], which act as “pillars”, making the structure less compressible along the a-axis than along the b- and c-axis. Along [100], compression can only be accommodated by deformation of the edge-sharing octahedra (and/or by compression of the Al–O bond lengths), as no polyhedral tilting can occur. In addition, a comparative elastic analysis among the mullite-type materials is carried out.     

Hydrostatic compression and crystal structure of pyrope to 33 GPa

The equation of state and crystal structure of pyrope were determined by single crystal X-ray diffraction under hydrostatic conditions to 33 GPa, a pressure that corresponds to a depth of about 900 km in the lower mantle. The bulk modulus K _T0 and its pressure derivative K ^' _T0 were determined simultaneously from an unweighted fit of the volume data at different pressures to a third order Birch-Murnaghan equation of state. They are 171(2) GPa and 4.4(2), respectively. Over the whole pressure range, MgO₈ polyhedra showed the largest compression of 18.10(8)%, followed by AlO₆ and SiO₄ polyhedra, with compression of 11.7(1)% and 4.6(1)%, respectively. The polyhedral bulk moduli for MgO₈, AlO₆ and SiO₄ are 107(1), 211(11) and 580(24) GPa, respectively, with K ^' _T0 fixed to 4. Significant compression of up to 1.8(1)% in the very rigid Si−O bonding in pyrope could be detected to 33 GPa. Changes in the degree of polyhedral distortion for all three types of polyhedra could also be observed. These changes could be found for the first time for AlO₆ and SiO₄ in pyrope. It seems that the compression of pyrope crystal structure is governed by the kinking of the Al−O−Si angle between the octahedra and tetrahedra. No phase transition could be detected to 33 GPa. Received: 24 March 1997 / Revised, accepted: 29 July 1997     

Pressure-induced migration of zeolitic water in laumontite

A polycrystalline sample of natural laumontite (Pleasant Valley, Connecticut) was studied up to 6.8 (1) GPa at room temperature using monochromatic synchrotron X-ray powder diffraction and a diamond-anvil cell. A methanol: ethanol: water mixture was used as a penetrating pressure-transmitting fluid. A dry sample measured before adding the pressure fluid inside the diamond-anvil cell contained ~12 H₂O per formula unit, consistent with the water content of partially dehydrated laumontite. Upon increasing the pressure to 0.2 (1) GPa, fully hydrated laumontite with 18 H₂O per unit cell formed and the unit-cell volume expanded by 2.6%. Further pressure increase up to 2.4 (1) GPa resulted in a gradual contraction of the unit-cell volume and individual cell lengths. During this process, a successive order–disorder transition of hydrogen-bonded water molecules from their symmetry sites was observed, concomittent with an inflectional behavior of the monoclinic beta angle and the channel ellipticity. Above 3 GPa, a tripling of the b axis was detected. Thereafter, up to 6.8 (1) GPa, the compression behavior was reversed for the c axis length and the monoclinic beta angle which showed a gradual increase and decrease, respectively, without any apparent volume discontinuity. We suspect that different ordering of the water molecules or Ca cations inside the channels along the b axis may be responsible for the observed supercell transition above 3 GPa.     

The solubility of water in NaAlSi3O8 melts: a re-examination of Ab−H2O phase relationships and critical behaviour at high pressures

The solubility of water in melts in the NaAlSi₃O₈–H₂O system at high P and T was deduced from the appearance of quenched products and from water concentrations in the quenched glasses measured by ion probe, calibrated by hydrogen manometry. Starting materials were gels with sufficient water added to ensure saturation of the melts under the run conditions. Experiments were carried out for 10–30 h in an internally heated argon pressure vessel (eight at 1400° C and 0.2–0.73 GPa and three at 0.5 GPa and 900–1200° C) and for 1 h in a piston-cylinder apparatus (three at 1200° C, 1–1.3 GPa). No bubbles were observed in the glasses quenched at P<0.5 GPa or from T<1300° C at 0.5 GPa. Bubble concentration in glasses quenched from 1400° C was low at 0.5, moderate at 0.55 GPa and very high at 0.73 GPa and still higher in glasses quenched in the piston cylinder. Water concentration was measured in all glasses, except for the one at 0.55 GPa, for which it was only estimated, and for those at 0.73 GPa because bubble concentration was too high. Inferred water solubilities in the melt increase strongly with increasing P at 1400° C (from 6.0 wt% at 0.2 GPa to 15 at 0.55 GPa) and also with increasing T at 0.5 GPa (from 9.0 wt% at 900° C to 12.9 at 1400° C). The T variation of water solubility is fundamental for understanding the behaviour of melts on quenching. If the solubility decreases with T at constant P (retrograde solubility), bubbles cannot form by exsolution on isobaric quenching, whereas if the solubility is prograde they may do so if the cooling rate is not too fast. It is inferred from observed bubble concentrations and from our and previous solubility data that water solubility is retrograde at low P and prograde at and above 0.45 GPa; it probably changes with T from retrograde below to prograde above 900° C at 0.5 GPa. Moreover, the solubility is very large at higher pressures (possibly>30 wt% at 1.3 GPa and 1200° C) and critical behaviour is approached at 1.3 GPa and 1200° C. The critical curve rises to slightly higher P at lower T and intersects the three-phase or melting curve at a critical end point near 670° C and 1.5 GPa, above which albite coexists only with a supercritical fluid.     

High-pressure behaviour of Ca-rich C 2 /c clinopyroxenes along the join diopside-enstatite (CaMgSi2O6-Mg2Si2O6)

 An in situ high-pressure (HP) X-ray diffraction investigation of synthetic diopside and of the Ca_0.8Mg_1.2Si₂O₆ clinopyroxene (Di₈₀En₂₀) was performed up to respectively P=40.8 and 15.1 GPa, using high brilliance synchrotron radiation. The compression of the cell parameters is markedly anisotropic, with β_b ⋙ β_c > β_a > β_asinβ for any pressure range and for both diopside and Di₈₀En₂₀. The compressibility along the crystallographic axes decreases significantly with pressure and is higher in Di₈₀En₂₀ than in diopside. The β cell parameter decreases as well with pressure, at a higher rate in Di₈₀En₂₀. The cell volume decreases at almost the same rate for the two compositions, since in diopside a higher compression along a* occurs. A change in the mechanism of deformation at P higher than about 5–10 GPa is suggested for both compositions from the analysis of the strain induced by compression. In diopside at lower pressures, the deformation mainly occurs, at a similar rate, along the b axis and at a direction 145° from the c axis on the (0 1 0) plane. At higher pressures, instead, the deformation occurs mostly along the b axis. In Di₈₀En₂₀ the orientation of the strain axes is the same as in diopside. The substitution of Ca with Mg in the M2 site induces at a given pressure a higher deformation on (0 1 0) with respect to diopside, but a similar change in the compressional behaviour is found. Changes in the M2 polyhedron with pressure can explain the above compressional behaviour. A third-order Birch-Murnaghan equation of state was fit to the retrieved volumes, with K=105.1(9) GPa, K′=6.8(1) for diopside and K=107.3(1.4) GPa, K′=5.7(3) for Di₈₀En₂₀; the same equation can be applied for any pressure range. The elasticity of diopside is therefore not significantly affected by Mg substitution into the M2 site, in contrast to the significant stiffening occurring for Ca substitution into Mg-rich orthopyroxenes. Received: 3 January 2000 / Accepted: 21 May 2000     

P-V equation of state of portlandite, Ca(OH)2, from powder neutron diffraction data

 A high pressure neutron powder diffraction study of portlandite [Ca(OH)₂] has been performed at ISIS facility (U.K.); nine spectra have been collected increasing the pressure by steps, up to 10.9 GPa, by means of a Paris-Edinburgh cell installed on the POLARIS diffractometer. The tensorial formalism of the lagrangian finite strain theory and the Birch-Murnaghan equation of state have been used to determine, independently, two values of the bulk modulus of portlandite, obtaining K ₀=38.3(±1.1) GPa [linear incompressibilities: K _0a=188.4(±9.9), K _0c=64.5(±2.5) GPa] and K ₀=34.2(±1.4) GPa, respectively. The present results comply with values from previous measurements by X-ray diffraction [K ₀=37.8(±1.8) GPa] and Brillouin spectroscopy [K ₀=31.7(±2.5) GPa]. Reasonably, Ca(OH)₂ has revealed to be bulkly softer than Mg(OH)₂ [K ₀=41(±2), K _0a=313, K _0c=57 GPa]. The Ca(OH)₂ linear incompressibility values reflect the nature of forces acting to stabilize the (001) layer structure and, further, prove that the replacement Ca/Mg mainly affects the elastic properties in the (001) plane, rather than along the [001] direction. Data from a full refinement of the structure at room pressure are reported. Received January 12, 1996/Revised, accepted June 15, 1996