Structured diffuse scattering, displacive flexibility and polymorphism in Ba-hexacelsian

 The results of a temperature-dependent electron diffraction study of the low frequency modes of distortion of Ba-hexacelsian and their relationship to the α-β polymorphic phase transition therein are presented. Cs- and Rb-doped Ba-hexacelsian specimens are also investigated. An extremely strong and characteristic diffuse intensity distribution in the form of polarized sheets of diffuse intensity perpendicular to the <1 1 0> directions is found for the high temperature polymorph and the doped specimens. The diffuse distribution appears to result from coupled tetrahedral rotation of <1 1 0> columns of corner-connected (Al,Si)O₄ tetrahedra about the [0 0 1] axis (uncorrelated from column to column as a result of the positioning of the rotation axes). Received: 25 January 1999 / Revised, accepted: 13 July 1999     

Periodic Hartree-Fock study of minerals: Tetracoordinated silica polymorphs

Periodic Hartree-Fock STO-3G calculations have been performed on several tetracoordinated silica polymorphs: low and high quartz, low and idealized high cristobalite and prototype tridymite. The optimized structural parameters are in overall good agreement with experimental data. In the particular case of -quartz, the SiO₄ tetrahedra are found to be irregular. The optimized values of the two different SiO bond lengths are respectively 1.608 Å and 1.613 Å. The potential energy versus tilt angle curves suggest a picture of the high temperature phases in terms of delocalized oxygen atoms which is consistent with a disordered structure. Finally, the bonding in silica polymorphs is discussed from electron density maps and Mulliken population analysis.     

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.     

Vibrational interactions of tetrahedra in silicate glasses and crystals

Normal coordinate calculations, producing synthetic infrared and Raman spectra, were carried out on melilites, pyroxenes, silica polymorphs and feldspars. Atomic motions are complex in the high-frequency Raman modes of melilites and aluminous pyroxenes. The symmetric T-Onb stretching vibrations of Si and Al tetrahedra with different numbers of bridging oxygens are separate from each other, but may combine individually with oscillation of bridging oxygens between Si and Al tetrahedra. The latter type of vibration tends to dominate as Al/Si increases. The frequencies of these vibrational components and the degree of such intermixing depend on T-O force constants, which vary greatly depending on local bonding configurations; individual bands in the high-frequency Raman cannot in general be assigned to single structural entities or fixed combinations thereof. Calculations confirm that in some Al-Si glasses such as jadeite and spodumene, i.e. those in which all Al can be tetrahedral without non-bridging oxygens, Al-O-Al linkages or linkage of more than two tetrahedra by a single oxygen, aluminum is predominantly in tetrahedral coordination. Other Al-Si glasses which are richer in aluminum or which have non-bridging oxygens may contain Al tetrahedral triclusters, non-tetrahedral Al, or both. On the basis of distinctive 450–750 cm^?1 infrared bands, both silica and feldspar glasses resemble tridymite and related stuffed derivatives, not other crystalline silica polymorphs or feldspars. Either these glasses have a structure like that of tridymite on a local scale, or the disorder of the glasses causes drastic modification to the vibrations in question.     

Mechanisms and geochemical significance of Si–Al substitution in zeolite solid solutions

Rock-forming zeolites often exhibit complex solid solutions reflecting isomorphous substitutions between Si and Al in tetrahedral framework sites, between charge-balancing extraframework cations, and between water molecules and vacancies. Although the number of moles of charge on extraframework cations in a zeolite must equal the moles of Al in order to maintain charge balance, the relationships between Si–Al and extraframework substitutions vary considerably across this mineral group. Review of available compositional data suggests that there are three main modes of Si–Al substitution in zeolites: 1) coupled CaAl–NaSi substitution; 2) coupled substitution of a single extraframework cation plus Al for Si; and 3) completely uncoupled substitution among extraframework cations and Si and Al on tetrahedral sites. Among zeolites that exhibit the latter two modes of solid solution, Si–Al substitution can be described by an SiO₂ (± H₂O) compositional exchange vector from a hypothetical, pure-silica endmember composition. Recent calorimetric, structural, and theoretical investigations suggest that Si–Al substitution follows a non-ideal, athermal solution model characterized by no excess enthalpies of mixing and negative excess entropies of mixing. Because Si–Al exchange in these minerals can be explicitly or implicitly described by exchange of an SiO₂ component, the Si/Al ratio in their framework can be predicted solely as a function of temperature, pressure, and the chemical potential of SiO₂. Application of this model leads to calculated Si/Al ratios in stilbite (coexisting with albite), analcime, and chabazite consistent with observed mineral compositions and parageneses in very low-grade metamorphic environments. Coexistence of silica polymorphs with zeolites containing SiO₂·nH₂O exchange vectors potentially provides a means of performing thermobarometric calculations in very low-grade metamorphic and diagenetic environments.     

Investigations of MX-1 tridymite by 29Si MAS NMR — Modulated structures and structural phase transitions

MX-1 tridymite is one of the room-temperature polymorphs of SiO₂ tridymite and has an underlying monoclinic structure (Cc) with incommensurate modulations along a ^* and c ^* (Hoffmann et al. 1983; Löns and Hoffmann 1987). With increasing temperature up to 500° C, MX-1 is reported to experience at least five structural phase transitions. However, its structures and the relationships to other tridymite polymorphs are unclear. We present here a ²⁹Si MAS NMR study of the room-temperature incommensurate structure of MX-1 and its structural phase transitions up to 540° C. Our results suggest that at room temperature, all the Si sites in MX-1 tridymite are in positions with similiar ∠Si-O-Si of ～150° and are consistent with the presence of two incommensurate modulations proposed by Hoffmann et al. (1983). Simulations of the spectra yield modulation amplitudes of 1.33 and 0.87 ppm, corresponding to 0.009 and 0.006 Å for Si-Si. The maximum atomic displacements along a and b due to the modulations appear to be ～0.01–0.02 Å. The structural phase transitions of MX-1 are significantly different from those of MC tridymite below 220° C. Our high temperature results confirm that MX-1 tridymite transforms to the H5 phase at about 65° C. The most important transition occurs near 110° C, where the H5 phase transforms to a phase yielding a single, narrow NMR peak, indicating the disappearance of the superstructure and possibly the onset of the dynamic averaging. The NMR lineshapes of H5 are consistent with the metrically orthorhombic unit cell and commensurate superstructure of 2a, 2b and 10c proposed by Graetsch and Flörke (1991). The phase present above 110° C is probably similar to the OC phase, but has a mean ∠Si-O-Si of ～152.0° at 113° C, 152.9° at 185° C and 154.1° at 500° C. The transitions at ～160 and 220° C for MX-1 are subtle and probably due to impurity MC. Analysis of the modulations in the OS phase of MC tridymite indicates that their amplitudes are of the order of 0.02 Å, significantly less than the value 0.3 Å proposed by Nukui et al. (1979).     

Crystal structures of Zn2SiO4 III and IV synthesized at 6.5–8 GPa and 1,273 K

We report the crystal structures determined under ambient condition for two Zn₂SiO₄ polymorphs synthesized at 6.5 GPa and 1,273 K (phase III) and 8 GPa and 1,273 K (phase IV) and also compare their ²⁹Si MAS NMR spectroscopic characteristics with those of other Zn₂SiO₄ polymorphs (phases I, II and V). Electron microprobe analysis revealed that both of phases III and IV are stoichiometric like the lower-pressure polymorphs (phases I and II), contrary to previous report. The crystal structures were solved using an ab initio structure determination technique from synchrotron powder X-ray diffraction data utilizing local structural information from ²⁹Si MAS NMR as constraints and were further refined with the Rietveld technique. Phase III is orthorhombic (Pnma) with a = 10.2897(5), b = 6.6711(3), c = 5.0691(2) Å. It is isostructural with the high-temperature (Zn_1.1Li_0.6Si_0.3)SiO₄ phase and may be regarded as a ‘tetrahedral olivine’ type that resembles the ‘octahedral olivine’ structure in the (approximately hexagonally close packed) oxygen arrangement and tetrahedral Si positions, but has Zn in tetrahedral, rather than octahedral coordination. Phase IV is orthorhombic (Pbca) with a = 10.9179(4), b = 9.6728(4), c = 6.1184(2) Å. It also consists of tetrahedrally coordinated Zn and Si and features unique edge-shared Zn₂O₆ dimers. The volumes per formula under ambient condition for phases III and IV are both somewhat larger than that of the lower-pressure polymorph, phase II, suggesting that the two phases may have undergone structural changes during temperature quench and/or pressure release.     

Raman spectra of high-pressure polymorphs of SiO2 at various temperatures

Raman spectra of the two high-pressure polymorphs of SiO₂ (coesite and stishovite) were investigated in the temperature range 105–875 K at atmospheric pressure. Coesite remained intact after the highest temperature run, but stishovite became amorphous at temperatures above about 842～872 K. Most Raman modes exhibit a negative frequency shift with temperature for these polymorphs, but positive trends were also observed for some modes. Except for some weak modes, nonlinear temperature variation were established for these polymorphs within the experimental uncertainty and temperature range spanned. The slopes of the variation (δv_i/δT)_P for these polymorphs were compared with the published values. When compared with quartz and stishovite, the four-membered rings of SiO₄-tetrahedra in coesite exhibit very little change with both temperature and pressure. It is also suggested that temperature and pressure should have opposite effects on the Raman shift of each vibrational mode.     

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.     

The low temperature field of liquid immiscibility in the system K2O-Al2O3-FeO-SiO2 with special reference to the join fayalite-leucite-silica

The extent of the low temperature field of liquid immiscibility in the system K₂O-FeO-Al₂O₃-SiO₂ in the vicinity of the plane fayalite-leucite-silica has been experimentally determined. The combination of direct oxygen buffering with the use of a zirconia probe to monitor oxygen activity has allowed minimisation of K₂O-loss in the experiments while oxygen activity appropriate to the iron-wüstite buffer has been maintained. The four-phase assemblage, fayalite+tridymite+FeO-rich liquid+SiO₂-rich liquid, isobaric univariant in the quaternary system, occurs over a very small temperature range at about 1,163° C on the iron-wüstite buffer. Both liquids appear to be in a coprecipitation relationship with tridymite and fayalite although the relationships between the two liquids are more complicated. The distribution of elements between the two coexisting liquids shows an interesting concordance when plotted in a new way. The results make sense in terms of current knowledge about silicate liquid structure, including the (familiar) observation that K/Al in the SiO₂-rich liquid is always greater than in the coexisting FeO-rich liquid.     

Thermally induced phase transitions in tridymite: an infrared spectroscopy study

The temperature dependence of the infrared active modes of meteoritic and synthetic tridymite have been investigated between 23 K and 1073 K in IR absorption and IR emission experiments. At room temperature both tridymite samples consist of a mixture of low temperature forms, in different proportions, due to the grinding. The sequence of phase transitions in Steinbach tridymite deduced from the IR data agrees well with recent X-ray and calorimetry studies using identical samples (Cellai et al. 1994). The previously suspected structural phase transition P6₃22P6₃/mmc is confirmed by the disappearance of the 470 cm^-1 mode and a temperature anomaly of the spectral shift of the 790 cm^-1 mode. Changes in the infrared spectra of synthetic tridymite give a different sequence of phase transitions from those of the meteoritic sample, consistent with the structural phase transitions observed in a ²⁹Si MAS NMR investigation using the same sample (Xiao et al. 1993).     

PT-diagram of the system SiO2-H2O

The high-temperature and medium-pressure part of the PT-diagram of the system SiO₂-H₂O has been investigated experimentally. The equilibrium diagram is discussed in the light of Schreinemakers general theory of PT-diagrams. The triple invariant point cristobalite + tridymite + quartz lies at 1190°C and 1430 atm. Neither cristobalite nor tridymite are stable at high pressure. Quartz may precipitate from the melt at a very high temperature (1360°C and higher), if the pressure is great enough, and if the water content is low. Using new experimental and published data a PT-diagram of the system SiO₂-H₂O in the large PT-region is given.     

The structures of albite and jadeite composition glasses quenched from high pressure

The structures of jadeite and albite composition glasses quenched from 10 and 15 kbar, respectively, have been studied using radial distribution analysis. It is found that aluminum does not undergo a coordination increase at these pressures, in agreement with recent Raman and NMR studies of these glass compositions. Radial distribution functions (RDF's) indicate that the structural response of albite and Jadeite composition melts to pressure up to 10–15 kbar has to do primarily with a distortion of the tetrahedral sites, a slight collapse of the tetrahedral rings forming the framework, and a small loss of short range order resulting in a more densely packed framework structure. The RDF's do not provide any clues concerning T-O-T angular changes at these pressures. It is suggested that the observed structural changes should be closely related to those that take place in melts of rhyolitic composition. Such changes in rhyolitic melts would result in a density increase and viscosity decrease with increasing pressure similar to that observed for melts of albite and jadeite composition.     

Analysis of the incommensurately modulated OS phase of SiO2 tridymite

The structure, symmetry and origin of the incommensurately modulated OS phase of tridymite (SiO₂) and its lock-in to the OP three-fold superlattice structure are discussed in a computational study. The structure of the OS phase (which has not been determined experimentally) is deduced as the only geometrically possible structure derived from the parent OC phase by rotation and translation of the SiO₄ tetrahedra without significant distortion of these units. It can be visualised conveniently in terms of the McConnell formalism of two component difference structures C₁ and C₂ whose space group symmetries are derived. The results are in accordance with the known lock-in structure at wave vector Q= a ^*. In the latter, the ±C₁ regions expand and the structure can square up in a very general way to take advantage of the lost symmetries (lost compared with the OC phase). Received: 4 August 1997 / Revised, accepted 24 November 1997     

Rigid unit modes in the high-temperature phase of SiO2 tridymite: calculations and electron diffraction

Calculations of the rigid unit mode (RUM) spectrum of the high-temperature phase of SiO₂ tridymite are used to explain the patterns of diffuse scattering seen in transmission electron microscopy experiments. These results show that RUM's can occur with wave vectors on curved surfaces in reciprocal space rather than being confined to symmetry points, lines or planes. The fact that the calculations reproduce the detail seen in the diffuse scattering provides a striking nontrivial confirmation of the validity of the rigid unit mode model.     

Molecular dynamics study of the crystal structure and phase relation of the GeO2 polymorphs

A two-body interatomic potential model for GeO₂ polymorphs has been determined to simulate the structure change of them by semi-empirical procedure, total lattice energy minimization of GeO₂ polymorphs. Based on this potential, two polymorphs of GeO₂; α-quartz-type and rutile-type, have been reproduced using the molecular dynamics (MD) simulation techniques. Crystal structures, bulk moduli, volume thermal expansion coefficients and enthalpies of these polymorphs of GeO₂ were simulated. In spite of the simple form of the potential, these simulated structural values, bulk moduli and thermal expansivities are in excellent agreement with the reliable experimental data in respect to both polymorphs. Using this potential, MD simulation was further used to study the structural changes of GeO₂ under high pressure. We have investigated the pressure-induced amorphization. As reported in previous experimental studies, quartz-type GeO₂ undergoes pressure-induced crystalline-to-amorphous transformation at room temperature, the same as other quartz compounds; SiO₂, AlPO₄. Under hydrostatic compression, in this study, α-quartz-type GeO₂ transformed to a denser amorphous state at 7.4 GPa with change of the packing of oxygen ions and increase of germanium coordination. At higher pressure still, rutile-type GeO₂ transformed to a new phase of CaCl₂-type structure as a post-rutile candidate. Received: 29 July 1996 / Revised, accepted: 30 April 1997     

On the Sequence of Phase Transitions in Tridymite

We consider the phase transitions in tridymite from the perspective of the rigid unit mode model. The rigid unit modes are the low-frequency phonons of a crystal structure that consists of an infinite framework of tetrahedra linked at corners, that can propagate without the tetrahedra distorting. Because they give distortions of the structure with a low energy cost they are the natural soft modes for displacive phase transitions. We consider the normal phase transition sequence in tridymite on cooling, HP LHP ..., as a successive condensation of rigid unit modes acting as soft modes. Some of the low-temperature phases (e.g. MX-1) arise as rigid unit mode distortions of the high-temperature structure and do not follow the sequence of phases found at higher temperatures. We are able to account for all the commensurate phases and some of the modulated phase within the framework of the rigid unit mode model. Received: 20 April 1998 / Accepted: 3 September 1998     

Molecular dynamics study of the α–β transition in quartz: elastic properties, finite size effects, and hysteresis in the local structure

The α–β transition in quartz is investigated by molecular dynamics simulations in the constant stress ensemble. Based on a frequently used two-body interaction potential for silica, it is found that anomalies in the elastic constants are at least in semiquantitative agreement with experiment despite the fact that no anomaly in the c/a ratio is observed in the simulations. A finite-size scaling analysis shows that first-order Landau theory is applicable to the employed model potential surface. This statement also applies to the susceptibility below the transition temperature T _tr, which has not yet been measured experimentally. Examination of the local order near T _tr reveals that the deformation of SiO₄ tetrahedral units is equally large in the β phase as in the α phase. However, large hysteresis effects can be observed in the local structure for distances r > 4 Å. The results are in agreement with the picture of a first-order displacive phase transformation which is driven by the motion of deformed tetrahedral SiO₄ units. Yet, the fast oscillations of oxygen atoms are around (time-dependent) positions that do not correspond to the ideal oxygen positions in β-quartz. The averaged configurations resemble the ideal structure only if averaged over at least a few nanoseconds.     

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.