Crystal structures of Ca-rich clinopyroxenes on the CaMgSi2O6-Mg2Si2O6 join

Summary The structural changes occurring in the clinopyroxenes with composition Di100, Di90En10 and Di80En20, due to the Ca-Mg substitution in the M2 site, have been studied. Evidence is given that with increasing Mg content a small percentage of the atoms converts from the M2 position to a new M2 position which is solely occupied by Mg. The maximum conversion of M2 to M2 found in this study is 7%. The closest parallel to the M2 geometry is found in the ZnSiO₃ pyroxene (C2/c). The presence of this new site causes significant changes in the tetrahedral configuration, because the M2 atoms are not bonded to 03. The intermediate compositions, Di90En10 and Di80En20, may be thought of as the coexistence of two structural models: diopside and ZnSiO₃ pyroxene (C2/c).

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Kristallstrukturen Ca-reicher Klinopyroxene der CaMgSi₂O₆-Mg₂Si₂O₆-Reihe

Zusammenfassung Es wurden die strukturellen Änderungen von Klinopyroxenen der Zusammensetzungen Di100, Di90En10 und Di80En20, die durch den Mg-Ersatz für Ca verursacht werden, untersucht. Es zeigt sich, daß mit steigendem Mg-Gehalt ein kleiner Teil der Atome der M2-Position zu einer neuen M2-Position wechselt; diese wird ausschließlich durch Mg besetzt. Der größte in dieser Arbeit gefundene Übergang von M2 nach M2 beträgt ca. 7%. Die stärksten Parallelen zur Geometrie um M2 werden im Pyroxen ZnSiO₃ (C2/c) gefunden. Die Besetzung dieser neuen Position verursacht bedeutende Änderungen im Tetraederverband, da die M2-Atome nicht an O3 gebunden sind. Die Pyroxenstrukturen mit den intermediären Zusammensetzungen Di90En10 und Di80En20 können als Überlagerung zweier Modelle betrachtet werden: Diopsid und ZnSiO₃-Pyroxen (C2/c).

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Abbreviations En Enstatite - Di Diopside - Hd Hedenbergite - Fs Ferrosilite - ClEn Clinoenstatite - Di100 pure diopside - Di90 Di90En10 (mol.-%) - Di80 Di80En20 - brg bridging With 6 Figures     

Thermodynamic parameters of CaMgSi2O6-Mg2Si2O6 pyroxenes based on regular solution and cooperative disordering models

Thermodynamic parameters for the reaction: $$\begin{gathered} Mg_2 Si_2 O_6 = Mg_2 Si_2 O_6 \hfill \\ enstatite clinopyroxene \hfill \\ \end{gathered} $$ in the system CaO-MgO-SiO₂ have been deduced from phase equilibrium and enthalpy of solution data. From the regular solution theory, the seventeen currently available reversed experimental compositions of coexisting enstatite and clinopyroxene, presumed to be ordered diopside, lead, by a statistical regression, to the following best fit parameters: ΔH ^o=6.80 kJ ΔS ^o=2.75 J/K W _H ^Cpx =24.47 kJ (regular solution enthalpy parameter) W _V ^Cpx =0.105 J/bar (regular solution volume parameter). The derived parameters are not significantly affected by the (necessary) choice of W ^Opx in the range 20–50 kJ. The above values are in very good agreement with deductions from the solution calorimetry on synthetic CaMgSi₂O₆-Mg₂Si₂O₆ clinopyroxenes of Newton et al. (1979), which also places bounds on possible departures from the optimal values of these parameters. The calorimetric data may also be interpreted in terms of a Bragg-Williams cooperative-disordering model (Navrotsky and Loucks, 1977), in which diopside-structure clinopyroxene and a ‘relaxed’ low-Ca clinopyroxene (‘Fe-free pigeonite’) approach each other in composition, structural state, and stability with increasing temperature. The ΔH ^o parameter deduced from the regular solution theory is reinterpreted as the enthalpy change of enstatite to Mg₂Si₂O₆ pigeonite; the ΔH ^o of the transformation of enstatite to the diopside structure would, in this case, be considerably larger than 6.8 kJ. The curvature of the enthalpy of solution data, explained by the regular solution theory in terms of M2-site energetics (involving W _H ^cpx ), is reinterpreted as due to disordering and ‘relaxation’ in the Navrotsky-Loucks model. Although the regular solution theory with the best-fit parameters accounts for all of the reversed enstatite and diopside compositions to within 18 ° C, and is a convenient representation of the phase equilibria for purposes of geothermometry, the disordering model is, at the present level of knowledge, equally valid and allows for a region of stability of two coexisting clinopyroxenes.     

Ab initio calculated geometries and charge distributions for H4SiO4 and H6Si2O7 compared with experimental values for silicates and siloxanes

Ab initio STO-3G molecular orbital theory has been used to calculate energy-optimized Si-O bond lengths and angles for molecular orthosilicic and pyrosilicic acids. The resulting bond length for orthosilicic acid and the nonbridging bonds for pyrosilicic acid compare well with Si-OH bonds observed for a number of hydrated silicate minerals. Minimum energy Si-O bond lengths to the bridging oxygen of the pyrosilicic molecule show a close correspondence with bridging bond length data observed for the silica polymorphs and for gas phase and molecular crystal siloxanes when plotted against the SiOSi angle. In addition, the calculations show that the mean Si-O bond length of a silicate tetrahedron increases slightly as the SiOSi angle narrows. The close correspondence between the Si-O bond length and angle variations calculated for pyrosilicic acid and those observed for the silica polymorphs and siloxanes substantiates the suggestion that local bonding forces in solids are not very different from those in molecules and clusters consisting of the same atoms with the same coordination numbers. An extended basis calculation for H₄SiO₄ implies that there are about 0.6 electrons in the 3d-orbitals on Si. An analysis of bond overlap populations obtained from STO-3G* calculations for H₆Si₂O₇ indicates that Si-O bond length and SiOSi angle correlations may be ascribed to changes in the hybridization state of the bridging oxygen and (d – p) π-bonding involving all five of the 3d AO's of Si and the lone-pair AO's of the oxygen. Theoretical density difference maps calculated for H₆Si₂O₇ show a build-up of charge density between Si and O, with the peak-height charge densities of the nonbridging bonds exceeding those of the bridging bonds by about 0.05 e Å^?3. In addition, atomic charges (+1.3 and ?0.65) calculated for Si and O in a SiO₂ moiety of the low quartz structure conform reasonably well with the electroneutrality postulate and with experimental charges obtained from monopole and radial refinements of diffraction data recorded for low quartz and coesite.     

Electron microprobe measurement of pyroxenes coexisting with H2O-undersaturated liquid in the join CaMgSi2O6-Mg2Si2O6-H2O at 30 kilobars,with applications to geothermometry

Mixtures of synthetic crystalline enstatite and diopside were reacted with small water contents in sealed capsules in piston-cylinder apparatus at 30 kb between 1000° C and 1700° C. The compositions of coexisting enstatite and diopside solid solutions were measured with an ARL-EMX electron microprobe between 1000° C and 1500° C. Between 1100° C and 1500° C the pyroxenes coexisted with H₂O-undersaturated liquid which quenched to inhomogeneous pyroxene crystals. The presence of liquid facilitated growth of pyroxene crystals suitable for microprobe determinations. The solvus of Davis and Boyd (1966) is generally used in geothermometry; our enstatite solvus limb is a few mol-% richer in Mg₂Si₂O₆ in the temperature range 1000–1400° C; our diopside solvus limb is a few mol-% richer in Mg₂Si₂O₆ below 1100°C, in close agreement between 1100° C and 1200° C, but richer in CaMgSi₂O₆ between 1200° C and 1500° C. Estimated equilibration temperatures for a diopside with composition 78.7% Di is 1300° C according to our results compared with 1210° C for the Davis and Boyd solvus.     

(Ca,Mg)2Si2O6 clinopyroxenes: A solution model based on nonconvergent site-disorder

Experiments at high pressure and temperature indicate that excess Ca may be dissolved in diopside. If the (Ca, Mg)₂Si₂O₆ clinopyroxene solution extends to more Ca-rich compositions than CaMgSi₂O₆, macroscopic regular solution models cannot strictly be applied to this system. A nonconvergent site-disorder model, such as that proposed by Thompson (1969, 1970), may be more appropriate. We have modified Thompson's model to include asymmetric excess parameters and have used a linear least-squares technique to fit the available experimental data for Ca-Mg orthopyroxene-clinopyroxene equilibria and Fe-free pigeonite stability to this model. The model expressions for equilibrium conditions \(\mu _{{\text{Mg}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{opx}}} = \mu _{{\text{Mg}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{cpx}}} \) (reaction A) and \(\mu _{{\text{Ca}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{opx}}} = \mu _{{\text{Ca}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{cpx}}} \) (reaction B) are given by: 1 $$\begin{gathered} \Delta \mu _{\text{A}}^{\text{O}} = {\text{RT 1n}}\left[ {\frac{{(X_{{\text{Mg}}}^{{\text{opx}}} )^2 }}{{X_{{\text{Mg}}}^{{\text{M1}}} \cdot X_{{\text{Mg}}}^{{\text{M2}}} }}} \right] - \frac{1}{2}\{ W_{21} [2(X_{{\text{Ca}}}^{{\text{M2}}} )^3 - (X_{{\text{Ca}}}^{{\text{M2}}} ] \hfill \\ {\text{ + 2W}}_{{\text{22}}} [X_{{\text{Ca}}}^{{\text{M2}}} )^2 - (X_{{\text{Ca}}}^{{\text{M2}}} )^3 + \Delta {\text{G}}_{\text{*}}^{\text{0}} (X_{{\text{Ca}}}^{{\text{M1}}} \cdot X_{{\text{Ca}}}^{{\text{M2}}} )\} \hfill \\ {\text{ + W}}^{{\text{opx}}} (X_{{\text{Wo}}}^{{\text{opx}}} )^2 \hfill \\ \Delta \mu _{\text{B}}^{\text{O}} = {\text{RT 1n}}\left[ {\frac{{(X_{{\text{Ca}}}^{{\text{opx}}} )^2 }}{{X_{{\text{Ca}}}^{{\text{M1}}} \cdot X_{{\text{Ca}}}^{{\text{M2}}} }}} \right] - \frac{1}{2}\{ 2W_{21} [2(X_{{\text{Mg}}}^{{\text{M2}}} )^2 - (X_{{\text{Mg}}}^{{\text{M2}}} )^3 ] \hfill \\ {\text{ + W}}_{{\text{22}}} [2(X_{{\text{Mg}}}^{{\text{M2}}} )^3 - (X_{{\text{Mg}}}^{{\text{M2}}} )^2 + \Delta {\text{G}}_{\text{*}}^{\text{0}} (X_{{\text{Mg}}}^{{\text{M1}}} \cdot X_{{\text{Mg}}}^{{\text{M2}}} )\} \hfill \\ {\text{ + W}}^{{\text{opx}}} (X_{{\text{En}}}^{{\text{opx}}} )^2 \hfill \\ \hfill \\ \end{gathered} $$ where 1 $$\begin{gathered} \Delta \mu _{\text{A}}^{\text{O}} = 2.953 + 0.0602{\text{P}} - 0.00179{\text{T}} \hfill \\ \Delta \mu _{\text{B}}^{\text{O}} = 24.64 + 0.958{\text{P}} - (0.0286){\text{T}} \hfill \\ {\text{W}}_{{\text{21}}} = 47.12 + 0.273{\text{P}} \hfill \\ {\text{W}}_{{\text{22}}} = 66.11 + ( - 0.249){\text{P}} \hfill \\ {\text{W}}^{{\text{opx}}} = 40 \hfill \\ \Delta {\text{G}}_*^0 = 155{\text{ (all values are in kJ/gfw)}}{\text{.}} \hfill \\ \end{gathered} $$ . Site occupancies in clinopyroxene were determined from the internal equilibrium condition 1 $$\begin{gathered} \Delta G_{\text{E}}^{\text{O}} = - {\text{RT 1n}}\left[ {\frac{{X_{{\text{Ca}}}^{{\text{M1}}} \cdot X_{{\text{Mg}}}^{{\text{M2}}} }}{{X_{{\text{Ca}}}^{{\text{M2}}} \cdot X_{{\text{Mg}}}^{{\text{M1}}} }}} \right] + \tfrac{1}{2}[(2{\text{W}}_{{\text{21}}} - {\text{W}}_{{\text{22}}} )(2{\text{X}}_{{\text{Ca}}}^{{\text{M2}}} - 1) \hfill \\ {\text{ + }}\Delta G_*^0 (X_{{\text{Ca}}}^{{\text{M1}}} - X_{{\text{Ca}}}^{{\text{M2}}} ) + \tfrac{3}{2}(2{\text{W}}_{{\text{21}}} - {\text{W}}_{{\text{22}}} ) \hfill \\ {\text{ (1}} - 2X_{{\text{Ca}}}^{{\text{M1}}} )(X_{{\text{Ca}}}^{{\text{M1}}} + \tfrac{1}{2})] \hfill \\ \end{gathered} $$ where δG _E ⁰ =153+0.023T+1.2P. The predicted concentrations of Ca on the clinopyroxene Ml site are low enough to be compatible with crystallographic studies. Temperatures calculated from the model for coexisting ortho- and clinopyroxene pairs fit the experimental data to within 10° in most cases; the worst discrepancy is 30°. Phase relations for clinopyroxene, orthopyroxene and pigeonite are successfully described by this model at temperatures up to 1,600° C and pressures from 0.001 to 40 kbar. Predicted enthalpies of solution agree well with the calorimetric measurements of Newton et al. (1979). The nonconvergent site disorder model affords good approximations to both the free energy and enthalpy of clinopyroxenes, and, therefore, the configurational entropy as well. This approach may provide an example for Febearing pyroxenes in which cation site exchange has an even more profound effect on the thermodynamic properties.     

Ab initio calculation of interatomic force constants in H6Si2O7 and the bulk modulus of α quartz and α cristobalite

Ab initio force constants calculated for Si-O stretch and Si...Si non-bonded interactions in H₆Si₂O₇ are found comparable with experimental values derived from the lattice dynamics of α quartz. The bulk moduli of α quartz and α cristobalite are calculated using the molecular Si...Si force constant and assuming rigid regular SiO₄ tetrahedra. In the case (α quartz) where data are available the calculation agrees well with experiment.     

Magnetic order in grunerite,Fe7Si8O22(OH)2A quasi-one dimensional antiferromagnet with a spin canting transition

Magnetization and neutron diffraction measurements have been made on grunerite, Fe₇Si₈O₂₂(OH)₂, a monoclinic double-chain silicate with Fe²⁺ octahedral bands. The mineral orders antiferromagnetically at 47K into a collinear structure with a second transition at 8K to a canted arrangement. The magnetic susceptibility follows a Curie-Weiss Law above 120K, with a paramagnetic Curie temeprature ?_p=67K. Magnetization measurements below 47K indicate a spin-flop or metamagnetic transition in an applied field of about 12KOe. Powder neutron diffraction measurements between 8–45K reveal that all the Fe²⁺ spins within an octahedral band are ferromagnetically coupled parallel to the b axis, with each band antiferromagnetically coupled to neighboring bands. Below 8K Fe²⁺ spins at the M1 and M4 sites are canted away from the b axis, whereas those at the M2 and M3 sites are not significantly affected. The ordered Fe²⁺ moment on the M4 site is substantially lower than those on the other sites, most likely indicating strong covalency effects, i.e. considerable spin transfer to neighboring oxygen atoms.     

Constraints on the origin of Archean trondhjemites based on phase relationships of Nûk gneiss with H2O at 15 kbar

We report the T-X(H₂O) phase relations for the trondhjemitic Nûk gneiss which comprises the principal component of the second phase of Archean (3.0–2.8 by) igneous activity in the Godthåb region of southwestern Greenland. A pressure of 15 kbar was chosen to place constraints on possible protoliths for trondhjemitic melts at lower crustal depths. Under H₂O-saturated conditions, a melting interval of 135° C separates the solidus at 610° C from the liquidus at 745° C. H₂O-saturation at 15 kbar occurs at approximately 15.5 wt % H₂O. The H₂O-undersaturated liquidus extends along a curved path from 745° C at 15.5 wt % H₂O to 1100° C at 2% H₂O. Lower H₂O contents were not investigated. At low H₂O contents (<6%) sodic plagioclase (Pl, An₃₂) is the liquidus phase followed at lower but still near-liquidus temperatures by quartz (Qz) and then garnet (Ga). At 6% H₂O, Ga replaces Pl on the liquidus and is joined at slightly lower temperatures by Pl and hornblende (Hb). The field for liquidus Ga extends to only 7.5% H₂O where it is replaced by Hb which is the liquidus phase up to 13% H₂O. At all higher H₂O contents, epidote (Ep) is the first phase to crystallize, followed by biotite (Bi) at slightly lower temperatures. Following the standard inverse approach, the near-liquidus phase assemblages are interpreted as potential residues from which trondhjemitic melts could be extracted. At high melt H₂O contents (>7%), mafic residues consisting of some combination of Hb, Ga, Ep, and Bi are possible and could correspond to amphibolitic source rocks. At lower melt H₂O contents (< 5%), possible residues consist of Na-Pl+Qz±Ga and could correspond to an earlier generation of tonalitic-trondhjemitic rocks. However, such residues would not impart the highly fractionated REE patterns characteristic of Archean trondhjemites. If a first generation of tonalitic-trondhjemitic melts was generated by higher pressure partial fusion of eclogite and emplaced at 55 km depth, it would crystallize to an assemblage consisting almost entirely of Na-Pl+Qz with highly fractionated REE patterns. These rocks in turn could be partially melted to yield a second generation of trondhjemites which would inherit the highly fractionated REE patterns because neigher Pl nor Qz is capable of significantly fractionating HREE from LREE.     

Determination of the origin and evolution of building stones as a function of their chemical composition using the inertia criterion based on an HJ-biplot

The aim of the present work is to determine the origin and background of 72 samples of four varieties of granite s.l. from quarries and different parts of the Cathedral Group Buildings of Avila (Spain) subject to different microenvironmental conditions. To do so, the results of the chemical analyses of major and trace elements of all samples were analysed statistically using the inertia method based on an HJ-biplot. Clusters of samples related to their origin, quarry or building were obtained. The statistical method employed is a useful tool for determining the origin of the stone located on different parts of the historical monument. This is of great interest when the stone needs to be replaced for maintenance and restoration purposes.     

High-grade metamorphism, dehydration and crustal melting: a reinvestigation based on new experiments in the silica-saturated portion of the system KAlO2–MgO–SiO2–H2O–CO2 at P≤ 1.5 GPa

The system KAlO₂–MgO–SiO₂–H₂O–CO₂ has long been used as a model for the processes of granulite-facies metamorphism and the development of orthopyroxene-bearing mineral assemblages through the breakdown of biotite-bearing assemblages. There has been considerable controversy regarding the role of carbon dioxide in metamorphism and partial melting. We performed new experiments in this system (at pressures of 342 to 1500 MPa with T between 710 and 1045 °C and X ^Fl _H2O between 0.05 and 1.00), accurately locating most of the dehydration and melting equilibria in P-T-X ^Fl _H2O space. The most important primary result is that the univariant reaction Phl + Qtz + Fl = En + Sa + melt must be almost coincident with the fluid-absent reaction (Phl + Qtz = En + Sa + melt) in the CO₂-free subsystem. In conjunction with the results of previous measurements of CO₂ solubility in silicate melts and phase equilibrium experiments, our theoretical analysis and experiments suggest that CO₂ cannot act as a flux for partial melting. Crustal melting in the presence of H₂O–CO₂ mixed fluids will always occur at temperatures higher than with pure H₂O fluid present. Magmas produced by such melting will be granitic (s.l.) in composition, with relatively high SiO₂ and low MgO contents, irrespective of the H₂O–CO₂ ratio in any coexisting fluid phase. We find no evidence that lamprophyric magmas could be generated by partial fusion of quartz-saturated crustal rocks. The granitic melts formed will not contain appreciable dissolved CO₂. The channelled passage of hot CO₂-rich fluids can cause local dehydration of the rocks through which they pass. In rock-dominated (as opposed to fluid-dominated) systems, minor partial melting can also occur in veins initially filled with CO₂-rich fluid, as dehydration and local disequilibrium drive the fluid towards H₂O-rich compositions. However, CO₂ is unlikely to be a significant agent in promoting regional granulite-grade metamorphism, melting, magma generation, metasomatism or long-range silicate mass transfer in Earth's crust. The most viable model for the development of granulite-facies rocks involves the processes of fluid-absent partial melting and withdrawal of the melt phase to higher crustal levels. Received: 28 November 1996 / Accepted: 25 June 1997