Comparison of the surface structure of the tetrahedral sheets of muscovite and phlogopite by AFM

 The surface structure of the tetrahedral sheet of dioctahedral mica muscovite was compared to that of the tetrahedral sheet of trioctahedral mica phlogopite using atomic force microscopy (AFM). AFM revealed distinct structural differences between the tetrahedral sheet surfaces of the two micas. The hexagonal ring in the AFM image of muscovite elongates in the [3 1 0] direction, and the groove runs perpendicular to the [3 1 0] direction. On the phlogopite surface, the hexagonal ring contracts slightly in the a axis direction, but the groove is not apparent. These results were consistent with the bulk structure data of the two micas determined by X-ray diffraction (XRD). The degree of surface relaxation was much larger in muscovite than in phlogopite. In muscovite, the interlayer K reduces the amount of tetrahedral rotation that actually occurs, since the interlayer K is too large for its hexagonal hole after full tetrahedral rotation. Thus, it is naturally expected that muscovite will show more tetrahedral rotation after removal of the interlayer K. It is also expected that muscovite will show more tilting of SiO₄ tetrahedra after cleaving, since an attractive force between the hydrogen in the OH group and the lower basal oxygen should be in operation, due to the decreased distance between them following interlayer K removal. Received: 14 March 2000 / Accepted: 29 July 2000     

原子力显微镜在粘土矿物学研究中的应用

研究粘土矿物表面组成与表面结构的手段和方法多种多样,但由于粘土矿物特殊的晶体结构,这些手段和方法都有一定的局限性和不足。原子力显微镜是近年来发展起来的一种能达到原子分辨能力的表面结构分析仪器,能够分辨粘土矿物硅氧四面体片上的六方环结构及八面体片的羟基团,是研究粘土矿物表面反应、表面改性及表面溶蚀作用的重要手段。     

Crystal data on 1M and 2M2 lepidolites

A coarse-grained, colourless lepidolite from a pegmatite of the Elba Island (Italy) has been examined. X-ray powder-diffraction and single-crystal patterns reveal the presence of the 1M and 2M₂ polymorphs, for wich cell parameters are given. On the basis of the optical and X-ray data the same composition for both the polymorphs is inferred. From the chemical analysis data of the whole micaceous material the following formula has been computed: (Ca_0,01Na_0,06K_0,92Rb_0,06) (Al_1,27Mg_0,01Li_1,75) (Si_3,36Al_0,64)O₁₀ (F_1,53OH_0,47). The crystal structure of this mica has been studied by means of one-dimensional Fourier projections on c^* and several interesting structural parameters were derived. Among them the mean tetrahedral rotation results to be about 11° for both the polymorphs: a value (quite similar to those of the other trioctahedral micas with K⁺ as interlayer cation) wich does not confirm Radoslovich's hypothesis that lepidolites should have a symmetry of the tetrahedral layers very close to the perfect hexagonality. Finally a new hypothesis on the structure of the 2M₂ polymorph consistent with such a proved ditrigonal symmetry of the basal oxygens arrangement in the lepidolites is pointed out.Notations O_bas basal oxygen atoms of the (Al, Si)O₄ tetrahedra. - O_ap apical oxygen atoms of the (Al, Si)O₄ tetrahedra. - b _tetr b dimension which the tetrahedral sheet would assume if unconstrained. - b _obs observed value of b. - c _oct ^* thickness of the octahedral sheet. - c _tetr ^* thickness of the tetrahedral sheet. - average tetrahedral rotation from ideal hexagonal symmetry. - separation of two O_bas sheets in contact with the interlayer cation. - O_ap-Si-O_bas angle. This research was supported by Consiglio Nazionale delle Ricerche, Roma.     

Ab initio quantum-mechanical modeling of pyrophyllite [Al2Si4O10(OH)2] and talc [Mg3Si4O10(OH)2] surfaces

Bulk and slab geometry optimizations and calculations of the electrostatic potential at the surface of both pyrophyllite [Al₂Si₄O₁₀(OH)₂] and talc [Mg₃Si₄O₁₀(OH)₂] were performed at Hartree–Fock and DFT level. In both pyrophyllite and talc cases, a modest (001) surface relaxation was observed, and the surface preserves the structural features of the crystal: in the case of pyrophyllite the tetrahedral and octahedral sheets are strongly distorted with respect to the ideal hexagonal symmetry (and basal oxygen are located at different heights along the direction normal to the basal plane), whereas the structure of talc deviates slightly from the ideal hexagonal symmetry (almost co-planar basal oxygen). The calculated distortions are fully consistent with those experimentally observed. Although the potentials at the surface of pyrophyllite and talc are of the same order of magnitude, large topological differences were observed, which could possibly be ascribed to the differences between the surface structures of the two minerals. Negative values of the potential are located above the basal oxygen and at the center of the tetrahedral ring; above silicon the potential is always positive. The value of the potential minimum above the center of the tetrahedral ring of pyrophyllite is ?0.05 V (at 2 Å from the surface), whereas in the case of talc the minimum is ?0.01 V, at 2.7 Å. In the case of pyrophyllite the minimum of potential above the higher basal oxygen is located at 1.1 Å and it has a value of ?1.25 V, whereas above the lower oxygen the value of the potential at the minimum is ?0.2 V, at 1.25 Å; the talc exhibits a minimum of ?0.75 V at 1.2 Å, above the basal oxygen.     

On local structural changes in lizardite-1T: {Si4+/Al3+}, {Si4+/Fe3+}, [Mg2+/Al3+], [Mg2+/Fe3+] substitutions

Geometrical changes induced by cation substitutions {Si⁴⁺/Al³⁺}[Mg²⁺/Al³⁺], {2Si⁴⁺/2Al³⁺} [2Mg²⁺/2Al³⁺], {Si⁴⁺/Fe³⁺} [Mg²⁺/Al³⁺] or [Mg²⁺/Fe³⁺], where {} and [] indicate tetrahedral and octahedral sheet in lizardite 1T, are studied by ab-initio quantum chemistry calculations. The majority of the models are based on the chemical compositions reported for various lizardite polytypes with the amount of Al in the tetrahedral sheets reported to vary from 3.5% to 8% in the 1T and 2H ₁, up to ~30% in the 2H ₂ polytype. Si⁴⁺ by Fe³⁺ substitution in the tetrahedral sheet with an Al³⁺ (Fe³⁺) in the role of a charge compensating cation in the octahedral sheet is also examined. The cation substitutions result in the geometrical changes in the tetrahedral sheets, while the octahedral sheets remain almost untouched. Substituted tetrahedra are tilted and their basal oxygens pushed down from the plane of basal oxygens. Ditrigonal deformation of tetrahedral sheets depends on the substituting cation and the degree of substitution.     

Pressure dependence of structural parameters of paragonite

The compressibility and structure of a 2M₁ paragonite with composition [Na_0.88K_0.10Ca_0.01Ba_0.01] [Al_1.97Ti_0.007Fe_0.01Mn_0.002Mg_0.006]Si_3.01Al_0.99O₁₀OH₂ were determined at pressures between 1 bar and 41 kbar, by single crystal X-ray diffraction using a Merrill-Bassett diamond anvil cell. Compressibility turned out to be largely anisotropic, linear compressibility coefficients parallel to the unit cell edges being β_a=3.5(1)·10^?4, β_b=3.6(1)·10^?4, β_c=8.3(3)·10^?4 kbar^?1 (β_a:β_b·β_c=1:1028:2.371). The isothermal bulk modulus, calculated as the reciprocal of the mean compressibility of the cell volume, was 650(20) kbar. The main features of the deformation mechanism resulting from structural refinements at pressures of 0.5, 25.4, 40.5 kbar were: –?variation in sheet thickness, showing that compression of the c parameter was mainly due to the interlayer thickness reduction from 3.07 Å at 0.5 kbar to 2.81 Å at 40.5 kbar; –?the compressibility of octahedra was greater than that of tetrahedra, the dimensional misfit between tetrahedral and octahedral sheets increased with P, so that tetrahedral rotation angel α increased from 15° at 0.5 kbar to 21.6° at 40.5 kbar; –?the basal surface corrugation (Δz) of the tetrahedral layer, due to the different dimensions of M1 and M2 octahedra and to the octahedral distortion, decreased with P (Δz=0.19 and 0.12 Å at 0.5 and 40.5 kbar respectively). Comparison of the new data on paragonite with those of a K-muscovite and a Na-rich muscovite (Comodi and Zanazzi 1995) revealed a clear trend toward decreasing of compressibility when Na substitutes for K atoms in the interlayer sites.     

An electron diffraction study of the polymorphs of siO2-tridymite

The results of a detailed TEM study of the low frequency modes of distortion of high temperature SiO₂-tridymite and their relationship to the extensive structural polymorphism of tridymite are presented. It is found that low energy modes of distortion of the ideal tridymite tetrahedral framework structure give rise to a strong and extremely characteristic diffuse intensity distribution (which can be broken into two component types) for the two highest temperature polymorphs of tridymite. Experimental results strongly suggest that this observed diffuse distribution is not a result of irreversible beam damage but is rather an intrinsic property of the ideal tridymite tetrahedral framework structure. The diffuse intensity distribution is closely related to the lower temperature polymorphs of tridymite — in particular, the primary modulation wave-vectors of these low temperature polymorphs always fall on the higher temperature diffuse distribution. The first type of diffuse distribution appears to result from coupled tetrahedral edge rotation of 〈110〉 columns of corner-connected SiO₄ tetrahedra (uncorrelated from column to column as a result of the tetrahedral connectivity of the ideal tridymite framework structure). The real space structural origin of the second curved type of diffuse distribution, however, remains unclear.     

Structure of mineral glasses—I. The feldspar glasses NaAlSi3O8, KAlSi3O8, CaAl2Si2O8

The short range distribution of interatomic distances in three feldspar glasses has been determined by X-ray radial distribution analysis. The resulting radial distribution functions (RDF's) are interpreted by comparison with RDF's calculated for various quasi-crystalline models of the glass structure.The experimental RDF's of the alkali feldspar glasses were found to be inconsistent with the four-membered rings of tetrahedra associated with crystalline feldspars; the structures of these glasses are probably based on interconnected six-membered rings of the type found in tridymite, nepheline, or kalsilite. In contrast, the RDF of calcic feldspar glass is consistent with a four-membered ring structure of the type found in crystalline anorthite. T-O bond lengths (T = Si,Al) increase from 1.60 Å in SiO₂ glass [J. H. Konnert and J. Karle (1973) Acta Cryst.A29, 702–710] to 1.63 Å in the alkali feldspar glasses to 1.66 Å in the calcic feldspar glass due to the substitution of Al for Si in the tetrahedra] sites. The T-O-T bond angles inferred from the RDF peak positions are 151° in SiO₂ glass (see reference above), 146° in the alkali feldspar glasses, and 143° in the calcic feldspar glass. Detail in the RDF at distances greater than 5 Å suggests that the alkali feldspar glasses have a higher degree of long range order than the calcic feldspar glasses.Assuming that the structural details of our feldspar glasses are similar to those of the melts, the observed structural differences between the alkali feldspar and calcic feldspar glasses helps explain the differences in crystallization kinetics of anhydrous feldspar composition melts. Structural interpretations of some thermodynamic and rheologic phenomena associated with feldspar melts are also presented based on these results.     

Rotation and dilation deformation mechanisms for auxetic behaviour in the α-cristobalite tetrahedral framework structure

 Analytical expressions are derived for the Poisson's ratios associated with a three-dimensional network of regular, corner-sharing tetrahedra in which: (1) the tetrahedra are assumed to be rigid and free to rotate relative to each other; (2) the tetrahedra are assumed to maintain shape and orientation but are free to change size (dilate); (3) tetrahedral rotation and dilation are assumed to act concurrently. The structure has a primitive unit cell containing four tetrahedra and is analogous to the molecular structure of α-cristobalite. Strain-dependent variations in Poisson's ratio are also predicted by the models. For deformation due to tetrahedral rotation the network is found to exhibit negative Poisson's ratios in each of the three principal directions, with the magnitude of the Poisson's ratio being dependent on the angle of rotation of the tetrahedra. The behaviour of the Poisson's ratio is isotropic in the transverse plane, but anisotropic elsewhere. In the dilation model negative Poisson's ratios equal to −1 are observed for uniaxial loading in any of the principal directions, with the value being constant irrespective of tetrahedral size. The model for concurrent tetrahedral rotation and dilation allows positive as well as negative Poisson's ratios, with the values determined by the framework geometry and relative strengths of the two mechanisms. The concurrent model also offers a design route to materials and structures having ultrahigh Young's moduli. Received: 15 February 2000 / Accepted: 1 October 2000     

Raman spectra from the Al2SiO5 polymorphs at high pressures and room temperature

Raman spectra of the three Al₂SiO₅ polymorphs; andalusite, sillimanite and kyanite were recorded as a function of pressure at room temperature. All the Raman active bands which could be observed from the high-pressure cell showed a linear pressure dependence for each of the three Al₂SiO₅ polymorphs and no phase changes were observed over the pressure ranges used in this study. In andalusite and to a lesser extent in sillimanite, vibrations which could be correlated with internal motions of the SiO₄ tetrahedra were generally well separated from the lattice modes and showed a greater pressure dependence than that observed for other modes. The distinct pressure dependence of the internal SiO₄ modes is less evident in kyanite, probably due to the lack of continuous tetrahedral chains and the fact that the rigid SiO₄ tetrahedra now form an integral part of the structural network. At ambient pressure, kyanite also exhibits two fluorescence bands at 705 and 706.2 nm which are due to small amounts of Cr³⁺ in the kyanite crystals. These fluorescence bands showed a non-linear frequency shift as pressure was increased.     

Rietveld analysis of a new high-pressure strontium silicate SrSi2O5

High-pressure synthesis of a new SrSi₂O₅ phase was performed at 16 GPa and 900°C by using a Kawai-type multianvil apparatus. The powder X-ray diffraction pattern of the compound was analyzed by Rietveld refinement based on the structure of a high-pressure polymorph of BaGe₂O₅, BaGe₂O₅ III. The structure is orthorhombic with space group Cmca and cell parameters of a = 5.2389(1) Å, b = 9.2803(2) Å, c = 13.4406(1) Å, V=653.46(2) Å ³ (Z=8, _calc=4.549 g/cm³). The structure consists of layers containing SiO₆ octahedra and SiO₄ tetrahedra. In a unit layer, oxygen and strontium atoms are arranged in an approximation to hexagonal close-packing. The strontium atom is accommodated in a 12-coordinated site. Each SiO₆ octahedron shares four corners with SiO₄ tetrahedra and the other two corners with another SiO₆ octahedra. The SiO₆ octahedra are linked to each other to form SiO₆ chains along the a-axis. This is the first known example of a silicate with a BaGe₂O₅ III-type structure.     

Ab initio calculated electron densities for tetrahedral sheet [H2Si2O5]∞ in phyllosilicates

Periodic ab initio Hartree-Fock LCAO calculations have been carried out on the two dimensional sheet of SiO₄ tetrahedra, representing one of the basic constituting units of layer silicates, using Huzinaga's DZP basis sets. The influence of the basis set on the chemical bonding picture is characterized by Mulliken atomic charges and by electron density maps. Silicon atomic charges +1.6 ¦e¦ are more realistic than those +2.4 ¦e¦ reported for smaller basis sets. The silicon d orbital population is found to be 0.6 in close agreement with molecular data. Electron density maps indicate the absence of charge density in the center of the ditrigonal cavity. The charge buildup of nonbonding basal oxygen orbitals is directed mainly downwards perpendicular to the sheet plane.     

Structural changes of synthetic opal by heat treatment

The structural changes of synthetic opal by heat treatment up to 1,400 °C were investigated using scanning electron microscopy, X-ray diffraction, and Fourier transform infrared and Raman spectroscopies. The results indicate that the dehydration and condensation of silanol in opal are very important factors in the structural evolution of heat-treated synthetic opal. Synthetic opal releases water molecules and silanols by heat treatment up to 400 °C, where the dehydration of silanol may lead to the condensation of a new Si–O–Si network comprising a four-membered ring structure of SiO₄ tetrahedra, even at 400 °C. Above 600 °C, water molecules are lost and the opal surface and internal silanol molecules are completely dehydrated by heat effect, and the medium-temperature range structure of opal may begin to thermally reconstruct to six-membered rings of SiO₄ tetrahedra. Above 1,000 °C, the opal structure almost approaches that of silica glass with an average structure of six-membered rings. Above 1,200 °C, the opal changes to low-cristobalite; however, minor evidence of low-tridymite stacking was evident after heat treatment at 1,400 °C.     

Model systems for anatexis of pelitic rocks

A consistent arrangement of solidus curves for reactions involving white mica, alkali feldspar, Al₂SiO₅, quartz and H₂O, as expressed by the components KAlO₂-NaAlO₂-Al₂O₃-SiO₂-H₂O, provides a generally accurate and useful model for the origin of migmatites and peraluminous granites through partial melting of pelitic rocks. The complexities of the univariant (Na-K) reactions may be easily seen on the projection from SiO₂ and H₂O onto the Ab-Or-Al₂O₃ plane. Alternative topologies for the appearance of muscovite, paragonite and Al₂SiO₅ on the quartz and H₂O-saturated liquidus may be eliminated by a consideration of possible compositions of liquid and solid phases and Schreinemakers' analysis around (Na-K) invariant points. Paragonite is not likely to be an important phase on the liquidus for most melting paths. Melting paths for natural assemblages may be easily constructed appropriate to P-T-aH₂O paths in the model system. Such paths are consistent with observed textures in natural assemblages. Although general models can be developed for decreased aH₂O, it is difficult to separate such effects from those involving participation of a calcic component without careful examination of natural assemblages and experimental calibration of appropriate reactions.     

The A and B mica layers and the crystal structure of sheet silicates

A discussion of the transition from the ideal hexagonal mica structure to the ideal ditrigonal one, leads to the conclusion that the single mica layer may have two different structures (labelled A and B). The recent literature data show that both the A and B structures have been detected in some triocahedral layer lattice silicates found in nature. An examination of the structural stability of the A and B structures suggests that the last one may not be realized by dioctahedral layer lattice silicates. The concept of two structurally different mica layers, which however have the same lattice constants, greatly improves the understanding of polymorphism and twin laws in layer lattice silicates.The structural features of the tetrahedral sheet, octahedral sheet and interlayer region are carefully examined. Thus we can reach the following conclusions: the tetrahedal sheet is not entirely free to reduce its lateral dimensions by the mechanism of tetrahedal rotation owing to the repulsion among O_bas atoms; the octahedral sheet in layer lattice silicates, may increase or reduce its lateral dimensions as compared to the lateral dimensions it has in the hydroxide minerals; the interlayer region is characterized by a regular octahedral coordination of the O_bas around the interlayer cation. On the ground of these conclusions, new structural models for some selected layer lattice silicates are proposed.Notations O_bas basal oxygen atoms of the (Al, Si)O₄ tetrahedra - O_ap apical oxygen atoms of the (Al, Si)O₄ tetrahedra - b _tetr b dimension which the tetrahedral sheet would assume if unconstrained - b _oct b dimension which the octahedral sheet has in the hydroxide minerals - b _obs observed value of b - c _oct ^* thickness of the octahedral sheet - d _o distance between an octahedral cation and an O_ap atom - d _int distance between an interlayer cation and an O_bas atom - average tetrahedral rotation from ideal hexagonal symmetry     

Effects of substrate structure and composition on the structure, dynamics, and energetics of water at mineral surfaces: A molecular dynamics modeling study

Molecular dynamics computer simulations of the molecular structure, diffusive dynamics and hydration energetics of water adsorbed on (0 0 1) surfaces of brucite Mg(OH)₂, gibbsite Al(OH)₃, hydrotalcite Mg₂Al(OH)₆Cl · 2H₂O, muscovite KAl₂(Si₃Al)O₁₀(OH)₂, and talc Mg₃Si₄O₁₀(OH)₂ provide new insight into the relationships between the substrate structure and composition and the molecular-scale structure and properties of the interfacial water. For the three hydroxide phases studied here, the differences in the structural charge on the octahedral sheet, cation occupancies and distributions, and the orientations of OH groups all affect the surface water structure. The density profiles of water molecules perpendicular to the surface are very similar, due to the prevalent importance of H-bonding between the surface and the water and to their similar layered crystal structures. However, the predominant orientations of the surface water molecules and the detailed two-dimensional near-surface structure are quite different. The atomic density profiles and other structural characteristics of water at the two sheet silicate surfaces are very different, because the talc (0 0 1) surface is hydrophobic whereas the muscovite (0 0 1) surface is hydrophilic. At the hydrophilic and electrostatically neutral brucite and gibbsite (0 0 1) surfaces, both donating and accepting H-bonds from the H₂O molecules are important for the development of a continuous hydrogen bonding network across the interfacial region. For the hydrophilic but charged hydrotalcite and muscovite (0 0 1) surfaces, only accepting or donating H-bonds from the water molecules contribute to the formation of the H-bonding network at the negatively and positively charged interfaces, respectively. For the hydrophobic talc (0 0 1) surface, H-bonds between water molecules and the surface sites are very weak, and the H-bonds among H₂O molecules dominate the interfacial H-bonding network. For all the systems studied, the orientation of the interfacial water molecules in the first few layers is influenced by both the substrate surface charge and the ability by the surfaces to facilitate H-bond formation. The first layer of water molecules at all surfaces is well ordered in the xy plane (parallel to the surface) and the atomic density distributions reflect the substrate crystal structure. The enhanced ordering of water molecules at the interfaces indicates reduced orientational and translational entropy. In thin films, water molecules are more mobile parallel to the surface than perpendicular to it due to spatial constraints. At neutral, hydrophilic substrates, single-monolayer surface coverage stabilizes the adsorbed water molecules and results in a minimum of the surface hydration energy. In contrast, at the charged and hydrophilic muscovite surface, the hydration energy increases monotonically with increasing water coverage over the range of coverages studied. At the neutral and hydrophobic talc surface, the adsorption of H₂O is unfavorable at all surface coverages, and the hydration energy decreases monotonically with increasing coverage.     

Structural control on bulk melt properties: Single and double quantum Si NMR spectroscopy on alkali-silicate glasses

The structure of 21 binary potassium, rubidium and cesium silicate glasses (in the range 15-50 mol% alkali oxide) was analyzed by ²⁹Si single quantum and double quantum MAS NMR spectroscopy. Their glass transition temperatures (T_g) were measured by calorimetry. The chemical shifts and the relative abundance of Qⁿ species correlate with the cationic field strength (Z/r) of the network modifier. A correlation is observed between T_g and the inverse of the entropy of mixing of the different Qⁿ species, which is explained in the framework of the Adam-Gibbs relaxation theory. At high alkali content, up to 44% of the SiO₄ tetrahedra are part of three-membered rings. At a given alkali content, the abundance of these rings increases with increasing cation size. The abundance of three-membered rings in K-silicate melts correlates with a temperature and a non-linear composition dependence of the heat capacity. It is also a possible cause for the anomalous volumetric behavior of potassium silicate glasses.     

Disorder and successive structure transitions in the tridymite forms of SiO2

Disorder models of oxygen positions in P6₃/ mmc, C222₁ and P2₁2₁2₁ tridymites were given in applying geometrical and lattice dynamical calculations. Sixmembered rings of rigid SiO₄ units are all collapsed in these forms; with silicon atoms fixed, SiO₄ units can take six different orientations in forming tridymite frameworks in both the P6₃/mmc and C222₁ forms, and three orientations in the P2₁2₁2₁ form. Atomic distances and angles obtained from the distance least-squares method are about equal for the three forms: 〈Si-O〉 (mean Si-O) = 1.611 Å, 〈O-O〉 = 2.629 Å, and 〈Si-O-Si〉 = 147°. Domain formation models are given for the three forms. The tridymite framework structures may possibly undergo lattice vibrations with low frequencies in two kinds of pair-wise rotational modes of SiO₄ units joined by the apical oxygen atoms, at the Γ-point: one is around 〈100〉 (or 〈210〉 for the hexagonal case), and the other is around 〈010〉. As temperature approaches the hexagonal-orthorhombic transition from below, the rotational mode around 〈100〉 remarkably softens at the Γ-point. The behavior of the atoms at the hexagonal-orthorhombic transition is explained in terms of a coupled softening of the two rotational modes of neighboring local domains in different orientations.     

Empirical calibration of six geobarometers for the mineral assemblage quartz+muscovite+biotite+plagioclase+garnet

Six equilibria among quartz, plagioclase, biotite, muscovite, and garnet were empirically calibrated using mineral composition data from 43 samples having the assemblage quartz+muscovite+biotite+garnet+plagioclase+Al₂SiO₅ (sillimanite or kyanite). Pressures and temperatures in the data set used for calibration were determined through the simultaneous application of garnet-biotite geothermometry and garnet-quartz-plagioclase-Al₂SiO₅ geobarometry. Thermodynamic expressions for four of the six equilibria incorporate interaction parameters that model non-ideality in the mixing of cations in the octahedral sites of both muscovite and biotite. With pressure chosen as the dependent variable, multiple regression was used to solve for unknowns in the equilibrium thermodynamic expressions. The regressions yielded multiple correlation coefficients ranging from 0.983 to 0.999, with corresponding standard deviations of 338 and 92 bars in the residuals. The standard deviations in the residuals may be explained largely or entirely by the propagation of errors associated with electron microprobe analysis. These equilibria enable the determination of pressures from equilibrium assemblages of quartz+garnet+plagioclase+muscovite+biotite, and give results closely comparable to the experimentally calibrated garnet-quartz-plagioclase-Al₂SiO₅ geobarometer. Geobarometric applications should be restricted to rocks in which equilibrium constants and compositional variables fall within the same ranges as those used for calibration.     

An X-ray diffraction study of shock-wave-densified SiO<Subscript>2</Subscript> glasses

 The densification and structural changes in SiO₂ glass compressed up to 43.4 GPa by shock experiments are investigated quantitatively by the X-ray diffraction technique. Direct structural data (average Si–O and Si–Si distances and Si–O–Si angles, coordination number of the Si atom) of these shock-densified SiO₂ glasses have been obtained by analyzing the radial distribution function curves, RDF(r), calculated with X-ray diffraction data. The coordination number of all densified glasses is about 4 and shows almost no pressure variation. The SiO₂ glass has shown density increase of 11% at a shock compression of 26.3 GPa. This density evolution could not be explained by the coordination change. The reduction of the average Si–O–Si angle (144° at 0 GPa to 136° at 26.3 GPa) obtained from RDF(r) data may account for this density increase. This Si–O–Si angle change may be caused by shrinkage of the network structure and the increase of small rings of SiO₄ tetrahedra. For higher shock pressure, a decrease in the Si–O–Si angle to 140° was observed. This is consistent with the decrease in density at 32.0 and 43.2 GPa. This decrease in the Si–O–Si angle and density could be attributed to an annealing effect due to high after-shock residual temperature. This pressure dependence of average Si–O–Si angles in shock-densified SiO₂ glass agrees with the results of our previous Raman spectroscopic study. On the other hand, the pressure variation for the first sharp diffraction peak (FSDP) was analyzed to estimate the evolution of intermediate range structures. It is suggested that the mean d value (d _m ) obtained from the position of FSDP strongly depends on the shock and residual temperature, as well as shock pressure. Received: 29 June 2001 / Accepted: 14 November 2001