Determination of the degree of Al,Si order Q od in kinetically disordered albite using hard mode infrared spectroscopy

Hard Mode Infrared Spectroscopy (HMIS) is used to correlate the line shifts Δω, the intensity changes ΔA and the variations of spectral line widths Γ of infrared absorption bands with the degree of Al, Si ordering, Q _od, in kinetically disordered Na-feldspar. A simple relationship Δω∝ΔA∝ΔΓ∝Q _od ² was found with the phonon band around 650 cm^?1 being particularly sensitive to small changes of the degree of Al, Si ordering. It is shown that the average degree of Al, Si order can be determined from HMIS with an accuracy of ca. 8 percent using 50 mg of Na-feldspar. The experimental results agree well with recent X-ray determinations using identical samples. The significance of HMIS for the study of kinetic processes in minerals is explained.     

Structural states of Mg-cordierite I: Order parameters from synchrotron X-ray and NMR data

The hexagonal to orthorhombic phase transition in synthetic Mg-cordierite has been studied by (i) measuring the spontaneous strain associated with the transition using Synchrotron X-ray powder diffraction and (ii) measuring the degree of Al, Si order in terms of the number of Al-O-Al bonds per formula unit using solid state NMR spectroscopy. This defines the two order parametersQ andQ _od respectively, and their relationship as a function of annealing temperature and time is used to define the structural states of cordierite during the ordering sequence. The formation of modulated hexagonal cordierite within which a high degree of Al, Si order can be attained, results in a strongly non-linear relationship betweenQ andQ _od .The transition from modulated to orthorhombic cordierite is strongly first-order under all temperature conditions studied and involves a large step inQ, whileQ _od changes continuously throughout the ordering sequence with no marked discontinuity at the phase transition. The lattice distortion, traditionally defined in cordierite by the Δ index provides no full information on the degree of Al, Si order in anhydrous Mg-cordierite, and both order parameters must be used to define its structural state. Transmission electron microscopy has been used to study the mechanism of the transformation from hexagonal to modulated to orthorhombic cordierite.     

Structural states of natural potassium feldspar: An infrared spectroscopic study

Natural samples of K-feldspar representing various states of Al, Si order were characterised using X-ray methods, transmission electron microscopy, and Fourier transform infrared spectroscopy. Line profiles of infrared absorption bands were observed to show strong correlation with the degree of Al, Si order present. In particular, the absorption frequencies of the 540 cm^?1 and 640 cm^?1 bands were seen to vary by ca. 10 cm^?1 between sanidine and microcline, with modulated samples respresenting intermediate behaviour. Linewidths of these modes also decrease by ca. 50% in this series. The experimental results are discussed within the framework of Hard Mode Infrared Spectroscopy (HMIS), and it is shown that the absorption frequencies vary with the short range order parameter τ = (4t₁-1)² and the symmetry breaking order parameter describing Al, Si order, Q _od=(t₁ 0?t₁ m)/Q _od=(t₁ 0+t₁ m), where t₁ is the average Al occupancy on the T₁ sites and t₁ o and t₁ m are the individual site occupancies of the T₁ o and T₁ m sites, respectively. The structural state of orthoclase is characterised by strain-induced modulations with large spatial variations of the modulation wavelength. No such modulations were observed in the degree of local Al, Si order. Sanidine shows mode hardening in excess of the extrapolated effect of symmetry breaking Al, Si order, which is presumably related to nonsymmetry breaking ordering between T₁ and T₂ sites and/or as yet unobserved short range order of the symmetry breaking ordering scheme. The possibility of an additional phase transition in K-feldspar at temperatures above 1300 K is discussed.     

Order/disorder phase transition in cordierite and its possible relationship to the development of symplectite reaction textures in granulites

Based on a consistent set of empirical interatomic potentials, static structure energy calculations of various Al/Si configurations in the supercell of Mg-cordierite and Monte Carlo simulations the phase transition between the orthorhombic and hexagonal modifications of cordierite (Crd) is predicted at 1623 K. The temperature dependences of the enthalpy, entropy, and free energy of the Al/Si disorder were calculated using the method of thermodynamic integration. The simulations suggest that the commonly observed crystallization of cordierite in the disordered hexagonal form could be related to a tendency of Al to occupy T₁ site, which is driven by local charge balance. The increase in the Al fraction in the T₁ site over the ratio of 2/3(T1): 1/3(T2), that characterizes the ordered state, precludes formation of the domains of the orthorhombic phase. This intrinsic tendency to the crystallization of the metastable hexagonal phase could have significantly postponed the formation of the association of orthorhombic cordierite and orthopyroxene over the association of quartz and garnet in metapelites subjected to granulite facies metamorphism. The textures of local metasomatic replacement (the formation of Crd + Opx Or Spr + Crd symplectites between the grains of garnet and quartz) indicate the thermodynamic instability of the association of Qtz + Grt at the moment of the metasomatic reaction. This instability could have been caused by the difficulty of equilibrium nucleation of orthorhombic cordierite.     

Structural states of Mg-cordierite II: Landau theory

Mg-cordierite undergoes a ferroelestic phase transitionP6/mmc-Cccm. The order parameterQ is proportional to the spontaneous strain as reflected by changes of the lattice parametersa andb during the phase transition. The order parameter,Q _od, which describes the Al, Si ordering, isnot directly involved in the phase transition and only “triggers” the structural collapse. Landau theory predicts that cordierite can exist in stable or metastable states with hexagonal, orthorhombic or monoclinic symmetry. Hexagonal cordierite can develop modulated structures which have been found by Putnis et al. (1987). The phase transition is predicted to be accompanied by singularities of the elastic constantsC ₁₁,C ₂₂ andC ₁₂ leading to an elastic softening of the crystal structure.     

Al,Si ordering in cordierite using “magic angle spinning” NMR

A method of determining the number of Al-O-Al bonds per unit cell from ²⁹Si nuclear magnetic resonance (NMR) data of synthetic cordierites with increasing Si, Al order is described. The number of Al-O-Al bonds is found to vary linearly with the logarithm of the annealing time. This may be correlated with previously published heat of solution data on similar samples (Carpenter et al. 1983) to determine the enthalpy change Δh, associated with a single Al?Si interchange in cordierite. Δh is found to be 8.1 kcal/mole. The NMR data show that the short range Al, Si order cannot be described in terms of twin domains of ordered orthorhombic cordierite. An ordering model derived from group theoretical constraints on possible Al, Si distributions within the hexagonal symmetry of the cordierite is found to provide a better fit to the NMR data.     

Sector trilling in cordierite and equilibrium overstepping in metamorphism

The origin of sector trilling in cordierite is due to the hexagonal-orthorhombic Al, Si ordering transformation which under non-equilibrium conditions proceeds via a short-range ordered modulated structure. The growth of these distortion waves associated with progressive ordering produces a strain field which is minimized by a cyclic distribution of symmetrically equivalent modulations.Sector and complexly trilled cordierites in metamorphic rocks grew as the hexagonal polymorph with a considerable degree of Al, Si disorder. The enthalpy and entropy of disorder are evaluated from recent experimental work. The implication is that, in metamorphic rocks, substantial overstepping of stable equilibrium phase boundaries is required to nucleate hexagonal cordierite. Moreover, its composition coexisting with other phases will also be significantly different from that of the stable ordered form.     

Application of infrared spectroscopy to studies of silicate glass structure: Examples from the melilite glasses and the systems Na2O-SiO2 and Na2O-Al2O3-SiO2

Infrared (IR) and Raman spectroscopic methods are important complementary techniques in structural studies of aluminosilicate glasses. Both techniques are sensitive to small-scale (<15 Å) structural features that amount to units of several SiO₄ tetrahedra. Application of IR spectroscopy has, however, been limited by the more complex nature of the IR spectrum compared with the Raman spectrum, particularly at higher frequencies (1200–800 cm^?1) where strong antisymmetric Si-O and Si-O-Si absorptions predominate in the former. At lower frequencies, IR spectra contain bands that have substantial contributions from ‘cage-like’ motions of cations in their oxygen co-ordination polyhedra. In aluminosilicates these bands can provide information on the structural environment of Al that is not obtainable directly from Raman studies. A middle frequency envelope centred near 700 cm^?1 is indicative of network-substituted AlO₄ polyhedra in glasses with Al/(Al+Si)>0·25 and a band at 520–620cm^?1 is shown to be associated with AlO₆ polyhedra in both crystals and glasses. The IR spectra of melilite and melilite-analogue glasses and crystals show various degrees of band localization that correlate with the extent of Al, Si tetrahedral site ordering. An important conclusion is that differences in Al, Si ordering may lead to very different vibrational spectra in crystals and glasses of otherwise gross chemical similarity.     

Enthalpy effects associated with Al/Si ordering in anhydrous Mg-cordierite

Measurements of the heats of solution (ΔH_soln) in molten Pb₂B₂O₅ at 708°C of anhydrous magnesian cordierites, prepared with a range of structural states, show that the enthalpy effect associated with Al/Si ordering is substantial (? 9.76 ± 1.56 kcal mole^?1). Differences in the state of order between synthetic cordierites used in phase equilibrium studies and cordierites in the natural environment could lead to significant errors in the estimation of palaeo-pressures and temperatures. A continuous change of ΔH_soln with annealing time supports the suggestion of putnis (1980) that the hexagonal → orthorhombic transformation in cordierite, which can occur via a modulated structure, is truly continuous under metastable conditions. In addition, a linear relation between ΔH_soln and the logarithm of annealing time has been found, which provides some insight into the nature of the ordering mechanisms at an atomic level. Al and Si exchanges occur continuously between neighbouring tetrahedral sites with a net drift towards increasing order. No kinetic or thermochemical distinction can be made between the development of long range and short range order.The enthalpy of vitrification (~ 12 kcal mole^?1) for a metastable stuffed β-quartz polymorph of cordierite composition is similar to that for pure quartz (on a per two oxygen basis), while the heat of vitrification for even the most disordered cordierite seen in this study is more than a factor of three greater (~40 kcal mole^?1). This is consistent with the view that cordierite glass resembles the quartz structure more closely than the crystalline cordierite structure, and that crystallisation of the glass below ~900°C is controlled by a tetrahedral framework.     

The reaction forsterite+cordierite=aluminous orthopyroxene+spinel in the system MgO-Al2O3-SiO2

Reversal experiments at 1,150–1,300°C on the reaction forsterite+cordierite=aluminous orthopyroxene+spinel in the system MgO-Al₂O₃-SiO₂ show the equilibrium to have a negativedT/dP. The slope andT-P location of this equilibrium have been modelled using available heat capacity data and various structural models which explore the configurational entropy contributions to the totalΔS. The experimental data are consistent with the aluminous orthopyroxene model of Ganguly and Ghose (1979) where limited Al disorder occurs between theM1 andM2 sites, Al-Si mixing occurs on the tetrahedralB site with the ‘aluminum avoidance’ principle maintained, and Mg-Al disorder occurs in spinel with an interchange enthalpy of 9–12 kcal mol^?1. Additionally, Al-Si disordering which occurs in the indialite structure of cordierite is inconsistent with the experimental data and all pyroxene and spinel mixing models; consequently, Si and Al in anhydrous cordierites to 1,300°C in the system MgO-Al₂O₃-SiO₂ must be largely ordered.     

A calorimetric investigation of the stability of anhydrous magnesium cordierite with application to granulite facies metamorphism

The heats of solution of synthetic anhydrous Mg-cordierite and of its high-pressure breakdown assemblage sapphirine + quartz (+ enstatite?) have been measured in a lead borate melt at 694°C. The ΔH of this reaction at this temperature and one atmosphere is 6.1±1 kilocalorie per mole of cordierite. A P-T stability diagram of cordierite relative to other synthetic phases in the system MgO-Al₂O₃-SiO₂ was constructed which satisfies the heat of reaction data and all other reliable observations pertaining to the stability of anhydrous cordierite. The stability field of cordierite is limited by boundaries of very small dP/dT slopes. The maximum pressure of cordierite stability is about 8 kilobars. Above an invariant point near 950°C the sapphirine-bearing assemblage is the stable breakdown product of cordierite. Below 950°C the stable breakdown assemblage is enstatite + sillimanite + quartz. New heat of solution data for orthorhombic enstatite are presented which allow a calculation of the lower-temperature breakdown boundary. This calculation is in good agreement with the boundary deduced above. The calculated breakdown pressure of cordierite at 700°C is 5.6±1.5 kilobars. This is much lower than estimates of earlier workers and shows that cordierite stability is greatly restricted under very dry conditions. Heat of solution data of natural low-iron cordierite and sapphirine samples are presented. These indicate that synthetic cordierite is energetically close to natural cordierite and is therefore an adequate stability model to apply to natural occurrences but that the synthetic sapphirine prepared by the breakdown of cordierite is quite different from natural sapphirine. An estimate of the breakdown relations of cordierite relative to natural sapphirine is presented, which looks quite like the diagram of the synthetic system except that the invariant point is shifted to considerably lower temperatures. A consequence of the present work is that if conditions of metamorphism were very dry, pressures of only six to eight kilobars would have been necessary to produce the dense anhydrous assemblages equivalent to natural cordierite which are found in some ancient granulites. The subcrustal pressures considered necessary by some workers should not be regarded as established by presently available evidence.     

Transformation Trillings in Cordierite

Cordierite sector trillings, which are found well developedin some A1-rich volcanic rocks and pelitic buchites, are thoughtto have formed initially as hexagonal high cordierite crystals.Subsequent ordering of the (Al, Si) configuration in the crystalstructure would have produced the present orthorhombic modificationand simultaneously the sector trilling, preserving in the processthe hexagonal habit of form. The predominance of the regularsixfold sector pattern in the composition plane configurationof the resulting trilling is best explained by assuming thatits formation is kinetically more advantageous than that ofother configurations because it mimics the hexagonal trend setby the initial crystal. The three orthorhombic orientations in the cordierite trillingshave parallel c-axes and each can be transformed into eitherof the other two by operation of a threefold axis (rotationthrough 120°) parallel to the common c-axis and coincidentwith the main axis of the original hexagonal form. The compositionplanes in the sector trilling pattern are shown to be essentiallyirregular in the present orthorhombic form; they do not belongto {110} or {130}. The traditional explanation that the trillings are multipletwins with repeated twin and composition planes of {110} or{130} is rejected since elementary geometrical considerationsshow that this model is only feasible if (110) (110) of orthorhombiccordierite equals 120°. X-ray work shows conclusively thatthis is not the case. In fact (110) (110) = 120° woulddefine a hexagonal symmetry.     

NMR-spectroscopy of synthetic potassium-bearing cordierites

Potassic cordierites with the chemical composition K _x Mg₂Al_4+x Si₅–xO₁₈ (x = 0.00, 0.10, 0.20, and 0.25) were synthesized by annealing glasses at 1290° C for different lengths of time. The procedure resulted in cordierites with different states of Al,Si-order for the tetrahedral sites in the structure. The dependence between the potassium-content and the state of order on one side and between annealing time and the state of order on the other side was then studied using ²⁹Si MAS nuclear magnetic resonance (NMR) spectroscopy. The spectra show that the state of order is a continuous function of annealing time for all compositions considered, but the rate of ordering decreases with increasing K-content. Since the substitution K+Al Si leads to higher Al/Si-ratios; the lower rate of ordering is discussed as a consequence of changed statistics for Al, Si site exchanges. The Al atoms replacing silicon in the structure to balance the charge of potassium cations are not located close to the potassium ion but at a maximum distance from it. This is shown to be a consequence of an improvement in coordination of all oxygen atoms in the cordierite framework.     

Al,Si ordering on cordierite using “magic angle spinning” NMR

Silicon-29 “magic angle spinning” nuclear magnetic resonance (NMR) spectroscopy has been used to study the changes in local Si environment during Al, Si ordering in synthetic cordierite, Mg₂Al₄Si₅O₁₈. In the most disordered form, crystallized from a glass, eight distinct tetrahedral sites for silicon can be identified and assigned, while there are only two distinguishable Si sites in the well-annealed ordered form. This allows the changes in the Si site environments to be determined as a function of annealing time for the transformation from the disordered to the ordered form. The first crystallized state has a considerable degree of partitioning between T₁ and T₂ sites with the following site occupancies: T₁ ? Al:Si=0.80:0.20, T₂?Al:Si=0.27:0.73 The changes in Si environment are approximately linear with log time. The measured values of ²⁹Si isotropic chemical shift do not fit well to previously determined correlations of shift with various structural parameters.     

Computer modelling of Al/Si ordering in sillimanite

Computer simulation is used to investigate the effect of Al/Si disordering over the tetrahedral sites on the lattice energy and the lattice constants of the mineral sillimanite Al₂SiO₅. A methodology for an atomistic assessment of the energy of the reaction 2(Si-O-Al)→(Si-O-Si)+(Al-O-Al) and its various contributions is established. This ordering energy is 0.97 eV for nearest neighbour sites in the ab-plane and 0.56 eV for those separated in the c-direction. The large difference is due to a greater constraint on the atomic relaxation in the ab-plane and shows the structural dependence of the ordering energy. Its magnitude appears to be determined by a complicated balance between Coulomb and short-range repulsive energy involving strain over many bonds, both in the ordered and disordered structures. There is also a significant interaction between second neighbour sites whereas the contribution of more distant neighbours is negligible. The lattice energies of most of the 154 configurations studied show a linear behaviour as a function of short-range order, specified by the number of Al-Al pairs. The ordering temperature T_c, estimated on the basis of a statistical mechanical model of disordering, and the calculated ordering energies are in semi-quantitative agreement with experimental values.     

Some geobarometers involving cordierite in the FeO-Al2O3-SiO2(±H2O) system: refinements,thermodynamic calibration,and applicability in granulite facies rocks

Five geobarometers involving cordierite have been formulated for quantitative pressure sensing in high grade metapelites. The relevant reactions in the FeO-Al₂O₃-SiO₂ (±H₂O) system are based on the assemblages (A) cordierite-garnet-sillimanite-quartz, (B) cordierite-spinel-quartz, (C) cordierite-garnet-spinel-sillimanite, (D) cordierite-garnet-orthopyroxene-quartz and (E) cordierite-orthopyroxene-sillimanite-quartz. Application of the barometric formulations to a large number of granulite grade rocks indicates that the cordierite-garnet-sillimanite-quartz equilibrium is widely applicable and registers pressures which are in good agreement with the “consensus” pressure estimates. The dispersion in the computed P values, expressed as one standard deviation, is within ±1.2 kbar. The geobarometers (B) and (C) also yield pressures which are reasonable and compare well with those computed from equilibrium (A). The estimated pressures from (D) and (E), both involving orthopyroxene, are at variance with these estimates. It has been argued that the discrepancy in pressures obtained from these geobarometers stems from an inadequate knowledge of activity-composition relations and/or errors in input thermodynamic data of aluminous orthopyroxene. The convergence of pressure values estimated from the barometric formulations, especially (A), (B) and (C), implies that the present formulations are more dependable than the existing formulations and are also capable of setting limits on P values in response to varying $$\begin{gathered} {\text{1/2Fe}}_{\text{2}} {\text{Al}}_{\text{4}} {\text{Si}}_{\text{5}} {\text{O}}_{{\text{18}}} \hfill \\ {\text{ = 1/3Fe}}_{\text{3}} {\text{Al}}_{\text{2}} {\text{Si}}_{\text{3}} {\text{O}}_{{\text{12}}} {\text{ + 2/3Al}}_{\text{2}} {\text{SiO}}_{\text{5}} {\text{ + 5/6SiO}}_{\text{2}} {\text{. (A)}} \hfill \\ {\text{1/2Fe}}_{\text{2}} {\text{Al}}_{\text{4}} {\text{Si}}_{\text{5}} {\text{O}}_{{\text{18}}} {\text{ = FeAl}}_{\text{2}} {\text{O}}_{\text{4}} {\text{ + 5/2SiO}}_{\text{2}} {\text{. (B)}} \hfill \\ {\text{Fe}}_{\text{2}} {\text{Al}}_{\text{4}} {\text{Si}}_{\text{5}} {\text{O}}_{{\text{18}}} {\text{ + FeAl}}_{\text{2}} {\text{O}}_{\text{4}} \hfill \\ = {\text{Fe}}_{\text{3}} {\text{Al}}_{\text{2}} {\text{Si}}_{\text{3}} {\text{O}}_{{\text{12}}} {\text{ + 2Al}}_{\text{2}} {\text{SiO}}_{\text{5}} {\text{. (C)}} \hfill \\ {\text{1/2Fe}}_{\text{2}} {\text{Al}}_{\text{4}} {\text{Si}}_{\text{5}} {\text{O}}_{{\text{18}}} {\text{ + Fe}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} \hfill \\ = {\text{Fe}}_{\text{3}} {\text{Al}}_{\text{2}} {\text{Si}}_{\text{3}} {\text{O}}_{{\text{12}}} {\text{ + 3/2SiO}}_{\text{2}} .{\text{ (D)}} \hfill \\ {\text{1/2Fe}}_{\text{2}} {\text{Al}}{}_{\text{4}}{\text{Si}}_{\text{5}} {\text{O}}_{{\text{18}}} \hfill \\ = 1/2{\text{Fe}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} {\text{ + Al}}_{\text{2}} {\text{SiO}}_{\text{5}} {\text{ + 1/2SiO}}_{\text{2}} .{\text{ (E)}} \hfill \\ \end{gathered}$$ . The present communication addresses the calibration, applicability and reliability of these barometers with reference to granulite facies metapelites.     

The solution behavior of H2O in peralkaline aluminosilicate melts at high pressure with implications for properties of hydrous melts

Solubility and solution mechanisms of H₂O in depolymerized melts in the system Na₂O-Al₂O₃-SiO₂ were deduced from spectroscopic data of glasses quenched from melts at 1100 °C at 0.8-2.0 GPa. Data were obtained along a join with fixed nominal NBO/T = 0.5 of the anhydrous materials [Na₂Si₄O₉-Na₂(NaAl)₄O₉] with Al/(Al+Si) = 0.00-0.25. The H₂O solubility was fitted to the expression, X_H2O=0.20+0.0020f_H2O-0.7X_Al+0.9(X_Al)², where X_H2O is the mole fraction of H₂O (calculated with O = 1), f_H2O the fugacity of H₂O, and X_Al = Al/(Al+Si). Partial molar volume of H₂O in the melts, , calculated from the H₂O-solulbility data assuming ideal mixing of melt-H₂O solutions, is 12.5 cm³/mol for Al-free melts and decreases linearly to 8.9 cm³/mol for melts with Al/(Al+Si) ∼ 0.25. However, if recent suggestion that is composition-independent is applied to constrain activity-composition relations of the hydrous melts, the activity coefficient of H₂O, , increases with Al/(Al+Si).Solution mechanisms of H₂O were obtained by combining Raman and ²⁹Si NMR spectroscopic data. Degree of melt depolymerization, NBO/T, increases with H₂O content. The rate of NBO/T-change with H₂O is negatively correlated with H₂O and positively correlated with Al/(Al+Si). The main depolymerization reaction involves breakage of oxygen bridges in Q⁴-species to form Q² species. Steric hindrance appears to restrict bonding of H⁺ with nonbridging oxygen in Q³ species. The presence of Al³⁺ does not affect the water solution mechanisms significantly.     

Cordierite-garnet-H2O equilibrium: A geological thermometer,barometer and water fugacity indicator

The high-grade assemblage Cd-Ga-Si-Qz can be thermodynamically modelled from available calorimetric data on the metastable reaction: (I) $$3 MgCd \rightleftarrows 2 Py + 4 Si + 5 Qz$$ naturalK _D ^Fe-Mg between garnet and cordierite and experimental results on cordierite hydration. In the system SiO₂-Al₂O₃-MgO-H₂O, reaction (I) becomes (II) $$3 MgCd \cdot nH_2 O \rightleftarrows 2 Py + 4 Si + 5 Qz + 3 nH_2 O$$ . However, hydrous cordierite is neither a hydrate nor a solid solution between water and anhydrous cordierite and when nH₂O (number of moles of H₂O in Cd) is plotted against \(P_{H_2 O} \) , the resulting isotherms are similar to adsorption isotherms characteristic of zeolitic minerals. Reaction (II) can thus be considered as a combination of reaction (I) with a physical equilibrium of the type nH₂O (in Cd)?nH₂O (in vapor phase). Starting from a point on equilibrium (I), introduction of H₂O into anhydrous Mg-cordierite lowers the chemical potential of MgCd and hence stabilizes this mineral to higher pressure relative to the right-hand assemblage in reaction (I). The pressure increment of stabilization,ΔP, above the pressure limit of anhydrous cordierite stability at constantT, has been calculated using the standard thermodynamics of adsorption isotherms. Cordierite is regarded as a mixture of Mg₂Al₄Si₅O₁₈ and H₂O. The activity of H₂O in the cordierite is evaluated relative to an hypothetical standard state extrapolated from infinite H₂O dilution, by using measured hydration data. The activity of Mg₂Al₄Si₅O₁₈ in the cordierite is then obtained by integration of the Gibbs-Duhem equation, and the pressure stabilization increment,ΔP, computed by means of the relation: $$\Delta V_s \Delta P \cong - RT\ln a_{MgCd}^{MgCd \cdot nH2O} \left( {\Delta V indepentdent of P and T} \right)$$ . Thus, one may contour theP-T plane in isopleths of nH₂O=constant within the area of Mg-cordierite stability allowed by the hydration data for \(P_{H_2 O} = P_{total} \) . The present model indicates greater stabilization of cordierite by H₂O than the model of Newton and Wood (1979) and the calculated curve for metastable breakdown of hydrous MgCd is consistent with experimental data on cordierite breakdown at \(P_{H_2 O} = P_{total} \) . Mg/(Mg+Fe) isopleths have been derived for cordierites of varying nH₂O in the SiO₂-Al₂O₃-MgO-FeO-H₂O system using the additional assumptions that (Fe, Mg) cordierite and (Fe, Mg) garnet behave as ideal solutions, and that typical values of the distribution coefficient of Fe and Mg between coexisting garnet and cordierite observed in natural parageneses can be applied to the calculations. The calculated stable breakdown curve of Fe-cordierite under conditions of \(P_{H_2 O} = P_{total} \) to almandine, sillimanite, quartz and vapor has a positive slope (dP/dT) apparently in contrast to the experimental negative slope. This may be explained by hydration kinetics, which could have allowed systematic breakdown of cordierites of metastable hydration states in the experiments. The bivariant Cd-Ga fields calibrated from the present model are, potentially, good petrogenetic indicators, as, given the iron-magnesium ratio of garnet and cordierite and the hydration number of cordierite, the temperature, pressure and water fugacity are uniquely determined. As this geothermobarometer is in part based on the water content of cordierite, it can be used only if there is some assurance that the actual hydration is inherited from high-grade metamorphic conditions. Such conditions could be realised if the slope of unloading-cooling retrograde metamorphism is more or less parallel to a cordierite isohydron.     

The tetrahedral framework in glasses and melts — inferences from molecular orbital calculations and implications for structure,thermodynamics, and physical properties

Results of ab initio molecular orbital (MO) calculations provide a basis for the interpretation of structural and thermodynamic properties of crystals, glasses, and melts containing tetrahedrally coordinated Si, Al, and B. Calculated and experimental tetrahedral atom-oxygen (TO) bond lengths are in good agreement and the observed average SiO and AlO bond lengths remain relatively constant in crystalline, glassy, and molten materials. The TOT framework geometry, which determines the major structural features, is governed largely by the local constraints of the strong TO bonds and its major features are modeled well by ab initio calculations on small clusters. Observed bond lengths for non-framework cations are not always in agreement with calculated values, and reasons for this are discussed in the text. The flexibility of SiOSi, SiOAl, and AlOAl angles is in accord with easy glass formation in silicates and aluminosilicates. The stronger constraints on tetrahedral BOB and BOSi angles, as evidenced by much deeper and steeper calculated potential energy versus angle curves, suggest much greater difficulty in substituting tetrahedral B than Al for Si. This is supported by the pattern of immiscibility in borosilicate glasses, although the occurrence of boron in trigonal coordination is an added complication. The limitations on glass formation in oxysulfide and oxynitride systems may be related to the angular requirements of SiSSi and Si(NH)Si groups. Although the SiO and AlO bonds are the strongest ones in silicates and aluminosilicates, they are perturbed by other cations. Increasing perturbation and weakening of the framework occurs with increasing ability of the other atom to compete with Si or Al for bonding to oxygen, that is, with increasing cation field strength. The perturbation of TOT groups, as evidenced by TO bond lengthening predicted by MO calculations and observed in ordered crystalline aluminosilicates, increases in the series Ca, Mg and K, Na, Li. This perturbation correlates strongly with thermochemical mixing properties of glasses in the systems SiO₂-M ₁ ^n/n+ AlO₂ and SiO₂-M ⁿ⁺O _n/2 (M=Li, Na, K, Rb, Cs, and Mg, Ca, Sr, Ba, Pb), with tendencies toward immiscibility in these systems, and with systematics in vibrational spectra. Trends in physical properties, including viscosity at atmospheric and high pressure, can also be correlated.     

The ordering behaviour of reedmergnerite,NaBSi3O8

Reedmergnerite (NaBSi₃O₈) has been synthesised hydrothermally from gels containing 10 wt.% excess SiO₂. The degree of B, Si order increases with time at constant temperature and pressure. Complete order is achieved in 250 h at 400° C, P _fluid=1 kbar and in 700 h at 300° C, 1 kbar. Lower pressures and/ or low water contents greatly reduce the rate of ordering. The ordering behaviour of reedmergnerite is insensitive to the composition of the co-existing fluid and this contrasts with the behaviour of albite. It is suggested that ordering takes place by a process of solution and re-precipitation.