Petrogenesis of andalusite–kyanite–sillimanite veins and host rocks, Sanandaj-Sirjan metamorphic belt, Hamadan, Iran

Quartz‐rich veins in metapelitic schists of the Sanandaj‐Sirjan belt, Hamadan region, Iran, commonly contain two Al₂SiO₅ polymorphs, and, more rarely, three coexisting Al₂SiO₅ polymorphs. In most andalusite and sillimanite schists, the types of polymorphs in veins correlate with Al₂SiO₅ polymorph(s) in the host rocks, although vein polymorphs are texturally and compositionally distinct from those in adjacent host rocks; e.g. vein andalusite is enriched in Fe₂O₃ relative to host rock andalusite. Low‐grade rocks contain andalusite + quartz veins, medium‐grade rocks contain andalusite + sillimanite + quartz ± plagioclase veins, and high‐grade rocks contain sillimanite + quartz + plagioclase veins/leucosomes. Although most andalusite and sillimanite‐bearing veins occur in host rocks that also contain Al₂SiO₅, kyanite‐quartz veins crosscut rocks that lack Al₂SiO₅ (e.g. staurolite schist, granite). A quartz vein containing andalusite + kyanite + sillimanite + staurolite + muscovite occurs in andalusite–sillimanite host rocks. Textural relationships in this vein indicate the crystallization sequence andalusite to kyanite to sillimanite. This crystallization sequence conflicts with the observation that kyanite‐quartz veins post‐date andalusite–sillimanite veins and at least one intrusive phase of a granite that produced a low‐pressure–high‐temperature contact aureole; these relationships imply a sequence of andalusite to sillimanite to kyanite. Varying crystallization sequences for rocks in a largely coherent metamorphic belt can be explained by P–T paths of different rocks passing near (slightly above, slightly below) the Al₂SiO₅ triple point, and by overprinting of multiple metamorphic events in a terrane that evolved from a continental arc to a collisional orogen.     

Deformation-induced polymorphic transformation: experimental deformation of kyanite, andalusite, and sillimanite

Torsion experiments were performed on the Al₂SiO₅ polymorphs in the sillimanite stability field to determine basic rheological characteristics and the effect of deformation on polymorphic transformation. The experiments resulted in extensive transformation of andalusite and kyanite to sillimanite. No transformation occurred during the hot-press (no deformation) stage of sample preparation, which was carried out at similar P–T conditions and duration as the torsion experiments. Experiments were conducted on fine-grained (< 15 µm) aggregates of natural andalusite, kyanite and sillimanite at 1250 °C, 300 MPa, and a constant shear strain rate of 2 × 10^− 4/s to a maximum shear strain of 400%. Electron back-scattered diffraction (EBSD) analysis of the experiments revealed development of lattice-preferred orientations, with alignment of sillimanite and andalusite [001] slightly oblique to the shear plane. The kyanite experiment could not be analyzed using EBSD because of near complete transformation to sillimanite. Very little strain ( 30%) is required to produce widespread transformation in kyanite and andalusite. Polymorphic transformation in andalusite and kyanite experiments occurred primarily along 500 µm wide shear bands oriented slightly oblique and antithetic to the shear plane and dominated by sub-µm (100–150 nm) fibrolitic sillimanite. Shear bands are observed across the entire strain field preserved in the torsion samples. Scanning transmission electron microscope imaging shows evidence for transformation away from shear bands; e.g. fibrolitic rims on relict andalusite or kyanite. Relict grains typically have an asymmetry that is consistent with shear direction. These experimental results show that sillimanite is by far the weakest of the polymorphs, but no distinction can yet be made on the relative strengths of kyanite and andalusite. These observations also suggest that attaining high bulk strain energy in strong materials such as the Al₂SiO₅ polymorphs is not necessary for triggering transformation. Strain energy is concentrated along grain boundaries, and transformation occurs by a dynamic recrystallization type process. These experiments also illustrate the importance of grain-size sensitive creep at high strains in a system with simultaneous reaction and deformation.     

Compressibility and crystal structure of sillimanite, Al2SiO5, at high pressure

The unit-cell dimensions and crystal structure of sillimanite at various pressures up to 5.29 GPa have been refined from single-crystal X-ray diffraction data. As pressure increases, a and b decrease linearly, whereas c decreases nonlinearly with a slightly positive curvature. The axial compression ratios at room pressure are β_a:β_b:β_c=1.22:1.63:1.00. Sillimanite exhibits the least compressibility along c, but the least thermal expansivity along a (Skinner et al. 1961; Winter and Ghose 1979). The bulk modulus of sillimanite is 171(1) GPa with K′=4 (3), larger than that of andalusite (151 GPa), but smaller than that of kyanite (193 GPa). The bulk moduli of the [Al1O₆], [Al2O₄], and [SiO₄] polyhedra are 162(8), 269(33), and 367(89) GPa, respectively. Comparison of high-pressure data for Al₂SiO₅ polymorphs reveals that the [SiO₄] tetrahedra are the most rigid units in all these polymorphic structures, whereas the [AlO₆] octahedra are most compressible. Furthermore, [AlO₆] octahedral compressibilities decrease from kyanite to sillimanite, to andalusite, the same order as their bulk moduli, suggesting that [AlO₆] octahedra control the compression of the Al₂SiO₅ polymorphs. The compression of the [Al1O₆] octahedron in sillimanite is anisotropic with the longest Al1-OD bond shortening by ～1.9% between room pressure and 5.29 GPa and the shortest Al1-OB bond by only 0.3%. The compression anisotropy of sillimanite is primarily a consequence of its topological anisotropy, coupled with the compression anisotropy of the Al-O bonds within the [Al1O₆] octahedron.     

Resolving the Routine Presence of Kyanite,Andalusite and Sillimanite across a Region using Foliation Intersection/Inflection Axes Preserved in Porphyroblasts,Petrographic Observations and Thermobarometry

Constraints from P-T pseudosections (MnNCKFMASH system), foliation intersection/inflection axes preserved in porphyroblasts (FIAs), mineral assemblages and textural relationships for rocks containing all three Al2SiO5 polymorphs indicate a kyanite→ andalusite→ sillimanite sequential formation at different times rather than stable coexistence at the Al2SiO5 triple point. All three Al2SiO5 polymorphs grew in the Chl, Bt, Ms, Grt, St, Pl and Crd bearing Ordovician Clayhole Schist in Balcooma, northeastern Australia separately along a looped P-T-t-D path that swaps from clockwise to anticlockwise in the tectono-metamorphic history of the region. Kyanite grew during crustal thickening in an Early Silurian Orogenic event followed by decompression/heating, andalusite and fibrolitic sillimanite growth during Early Devonian exhumation.     

Composition and conditions of formation of andalusite-kyanite-sillimanite pegmatoid segregations in metamorphic rocks of the Tsel block (Mongolian Altay)

Pegmatoid segregations containing three polymorphous Al₂SiO₅ modifications have been revealed in metamorphic rocks of the Tsel block localized in the Hercynian belt on the southern flank of Mongolian Altay. Petrographic study showed a successive substitution of polymorphs in the sequence: andalusite–kyanite–fibrolite–sillimanite. Estimated parameters of the host-rock metamorphism indicate that the mineral assemblage of pegmatoid veins formed at two successive stages of metamorphism: andalusite-sillimanite and kyanite-sillimanite. It is suggested that the transformation of Al₂SiO₅ from one to another polymorphous modification occurs by the ion exchange mechanism with the participation of muscovite.     

Kinetic control of staurolite–Al2SiO5 mineral assemblages: Implications for Barrovian and Buchan metamorphism

The distribution and textural features of staurolite–Al₂SiO₅ mineral assemblages do not agree with predictions of current equilibrium phase diagrams. In contrast to abundant examples of Barrovian staurolite–kyanite–sillimanite sequences and Buchan‐type staurolite–andalusite–sillimanite sequences, there are few examples of staurolite–sillimanite sequences with neither kyanite nor andalusite anywhere in the sequence, despite the wide (~2.5 kbar) pressure interval in which they are predicted. Textural features of staurolite–kyanite or staurolite–andalusite mineral assemblages commonly imply no reaction relationship between the two minerals, at odds with the predicted first development (in a prograde sense) of kyanite or andalusite at the expense of staurolite in current phase diagrams. In a number of prograde sequences, the incoming of staurolite and either kyanite, in Barrovian sequences, or andalusite, in Buchan‐type sequences, is coincident or nearly so, rather than kyanite or andalusite developing upgrade of a significant staurolite zone as predicted. The width of zones of coexisting staurolite and either kyanite, in Barrovian sequences, or andalusite, in Buchan‐type sequences, is much wider than predicted in equilibrium phase diagrams, and staurolite commonly persists upgrade until its demise in the sillimanite zone. We argue that disequilibrium processes provide the best explanation for these mismatches. We suggest that kyanite (or andalusite) may develop independently and approximately contemporaneously with staurolite by metastable chlorite‐consuming reactions that occur at lower P–T conditions than the thermodynamically predicted staurolite‐to‐kyanite/andalusite reaction, a process that involves only modest overstepping (<15°C) of the stable chlorite‐to‐staurolite reaction and which is favoured, in the case of kyanite, by advantageous nucleation kinetics. If so, the pressure difference between Barrovian kyanite‐bearing sequences and Buchan andalusite‐bearing sequences could be ~1 kbar or less, in better agreement with the natural record. The unusual width of coexistence of staurolite and Al₂SiO₅ minerals, in particular kyanite and andalusite, can be accounted for by a combination of lack of thermodynamic driving force for conversion of staurolite to kyanite or andalusite, sluggish dissolution of staurolite, and possibly the absence of a fluid phase to catalyse reaction. This study represents an example of how kinetic controls on metamorphic mineral assemblage development have to be considered in regional as well as contact metamorphism.     

The selective replacement of the aluminium silicates by white mica: A comment

Characteristic patterns in the preferential replacement of Al₂SiO₅ polymorphs by white mica have been interpreted by Kwak (1971) as indicating that, for alkali equilibria, the fields in order of decreasing stability are: kyanite + soln < andalusite + soln < sillimanite + soln Alternatively, preferential replacement patterns may be interpreted as reflecting the repetition of certain types of Pressure-Temperature-time paths in various metamorphic episodes.I am grateful to J. S. Fox for commenting on this comment.     

Interpreting prograde-growth histories of Al2SiO5 triple-point rocks using oxygen-isotope thermometry: an example from the Truchas Mountains, USA

Oxygen‐isotope compositions of kyanite, andalusite, prismatic sillimanite and fibrolite from the Proterozoic terrane in the Truchas Mountains, New Mexico differ from one another, suggesting that these minerals did not grow in equilibrium at the Al₂SiO₅ (AS) polymorph‐invariant point as previously suggested. Instead, oxygen‐isotope temperature estimates indicate that growth of kyanite, andalusite and prismatic sillimanite occurred at c. 575, 615 and 640 °C respectively. Temperature estimates reported in this paper are interpreted as those of growth for the different AS polymorphs, which are not necessarily the same as peak metamorphic temperatures for this terrane. Two distinct temperature estimates of c. 580 °C and c. 700 °C are calculated for most fibrolite samples, with two samples yielding clear evidence of quartz‐fibrolite oxygen‐isotope disequilibrium. These data indicate that locally, and potentially regionally, oxygen‐isotope disequilibrium between quartz and fibrolite may have resulted from rapid fibrolite nucleation. Pressures of mineral growth that were extrapolated from oxygen‐isotope thermometry results and calculated using petrological constraints suggest that kyanite and one generation of fibrolite grew during M1 at 5 kbar, and that andalusite, prismatic sillimanite and a second generation of fibrolite grew during M2 at 3.5 kbar. M1 and M2 therefore represent two distinct metamorphic events that occurred at different crustal levels. The ability of the AS polymorphs to retain δ¹⁸O values of crystallization make these minerals ideal to model prograde‐growth histories of mineral assemblages in metamorphic terranes and to understand more clearly the pressure–temperature histories of multiple metamorphic events.     

Electronic structure and electric field gradient calculations of Al2SiO5 polymorphs

 The electronic structure of the three polymorphs of Al₂SiO₅, andalusite, sillimanite, and kyanite, is studied by linearized-augmented-plane-wave (LAPW) calculations using the WIEN code. Total energy calculations verify, in agreement with recent pseudopotential calculations, that andalusite is the most stable phase, followed by sillimanite and kyanite.We determine the electronic charge density distribution and find strong polarizations on all oxygen ions. We identify different polarizations due to Al or Si neighbors which depend on their respective distances to the oxygen atom. The chemical bonding is not purely ionic in nature but has important covalent contributions. Electric field gradients (EFGs) at all sites are calculated and agree well (within 10%) with available experimental data on Al. We identify the origin of the EFGs and demonstrate its relation to the nearest-neighbor coordination and the resulting anisotropy of the electronic charge distribution. Received: 22 March 2000 / Accepted: 3 August 2000     

Dislocation strain energy in the Al2SiO5 polymorphs

Molar elastic strain energy arising from dislocations in andalusite and sillimanite were calculated using equations derived from a non-core, linear elasticity model. For perfect (unit) c screw dislocations in these polymorphs, minimum dislocation densities of about 10¹⁰/cm² are necessary to significantly perturb the andalusite=sillimanite equilibrium boundary in P-T space. Compared to unit c dislocations, smaller energy perturbations arise from dissociated c screw dislocations, which are commonly observed in kyanite and sillimanite. A low computed value of stacking fault energy (～30 ergs/cm²) in these polymorphs is compatible with the large separations of dissociated dislocations in these phases. Dislocation densities in naturally occurring Al₂SiO₅ polymorphs are typically <10⁸/cm². Assuming that these densities are representative of those existing during metamorphism, as is supported by the lack of microtextures indicative of strong recovery, it is concluded that molar strain energies corresponding to observed dislocation densities (<10⁸/cm²) result in insignificant perturbation of P-T phase equilibrium boundaries of the Al₂SiO₅ polymorphs.     

The selective replacement of the aluminum silicates by white mica

From considerations of relativeG-T surfaces inferred from publishedP-T data and the occurrence of replacement textures of Al₂SiO₅ polymorphs in rocks, the relative positions of curves representing the following equation in _K+ —T — pH ispace on substituting Al₂SiO₅ different polymorphs are derived.3 Al₂SiO₅ + 3 SiO₂ (quartz) + 2 K⁺ + 3 H₂O 2 KAl₂[AlSi₃O₁₀](OH)₂ (muscovite)+ 2 H⁺. The curves are different because of the differentG-T values for the polymorphs which, in the field, is borne out by the observation that in a rock containing two or three Al₂SiO₅ polymorphs, in nearly all instances only one polymorph is replaced by white mica. Instances of textural relations showing the interpreted selective replacement of one Al₂SiO₅ polymorph by a white mica in the presence of one (or two) other Al₂SiO₅ polymorph(s) are cited both from the literature and various field examples. The selective replacement of kyanite if sillimanite and/or andalusite is/are present, and of andalusite if only sillimanite is present are interpreted to show that generally during the muscovitization reaction, the field of sillimanite in the above reaction (left hand side) at a particular pH (H⁺ concentration) and is larger in _K+ —T space than that of andalusite which in turn is larger than that of kyanite. Theoretically it is shown that variations to this can exist but the field evidence suggests these only occur under rare geological conditions. Although this is not totally conclusive, the selectiveness of the replacement is interpreted to show that the fluid was buffered with respect to K⁺ and H⁺ on or near the curve of the polymorph showing the lowest stability field until that polymorph is totally consumed, after which the fluid composition moves to the next lowest curve for the remaining polymorph(s) present in the rock. The alteration of more than one polymorph by an apparently simultaneous process of alteration is rare and usually occurs at a low grade of metamorphism. This is interpreted to show that the buffering reaction could not keep pace with the influx of fluid and change the composition of this fluid (in most cases).     

High-pressure Raman spectroscopic study of Co- and Ni-olivines

 The Raman spectra of synthetic α-Co₂SiO₄ and α-Ni₂SiO₄ olivines have been studied at room temperature and various pressures. All the Raman frequencies of the two olivines increase with increasing pressure, and most of the frequency–pressure plots obtained under both quasi- and nonhydrostatic conditions are nonlinear. It has been found that the average pressure derivative of Raman frequencies of the lattice modes in both Co- and Ni-olivines is smaller than that of the internal modes of SiO₄, indicating that the distortion of SiO₄ tetrahedra under static compression may be more severe than that of MO₆ octahedra. In addition, four new Raman bands were observed in Ni-olivine under nonhydrostatic compression and above 30 GPa. This result suggests that a new phase of Ni-olivine should be formed at 30 GPa or amorphization may occur at still higher pressure. Received: 11 July 2000 / Accepted: 19 December 2000     

Raman Spectroscopy of Garnet—group Minerals

The Raman spectra of the natural end members of the garnet-group minerals,which include pyrope, almandine and spessarite of Fe-Al garnet series and grossularite ,andradite and uvarovite of Ca-Fe garnet series, have been strdied.Measured Raman spectra of these minerals are reasonably and qualitatively assigned to the internal modes, translational and rotatory modes of SiO4 tetrahedra, as well as the translational motion of bivalent cations in the X site.The stretch and rotatory A1g modes for the Fe-Al garnet series show obvious Raman shifts as compared with those for the Ca-Fe garnet series ,owing to the cations residing in the Xsite connected with SiO4 tetrahedra by sharing the two edges.The Raman shifts of all members within either of the series are attributed mainly to the properties of cations in the X site for the Fe-Al garnet series andin the Y site for the Ca-Fe garnet series.     

Andalusite in granulites of the bohemian massif

Summary In granulites of South-Bohemia not only the usually occurring Al₂SiO₅ polymorphs, kyanite and sillimanite, were found but also andalusite. Its presence indicates that the metamorphic development of these granulites is characterized by a high PT-gradient. The granulitic rocks of the Bohemian Massif can be regarded as a facies series ranging from the granulite facies through the amphibolite facies to the hornblende-hornfels facies. The lower limit of the PT-conditions of this series should be placed below the position of the triple point of Al₂SiO₅.

---

Andalusit in Granuliten der Böhmischen Masse

Zusammenfassung In den Mineralparagenesen der südböhmischen Granulite wurde neben den üblicherweise auftretenden Al₂SiO₅-Modifikationen, Disthen und Sillimanit, auch Andalusit gefunden. Seine Anwesenheit weist darauf hin, daß die metamorphe Entwicklung der erwähnten Granulite durch einen ausgeprägten PT-Gradienten gekennzeichnet wurde. Die Granulitgesteine der Böhmischen Masse kann man als eine Faziesserie ansehen, die von der Granulitfazies über die Amphibolitfazies bis in die Hornblende-Hornfelsfazies reicht. Die untere Grenze der PT-Bedingungen dieser Serie ist unter die Lage des Tripelpunktes von Al₂SiO₅ zu setzen.

---

---

With 5 Figures     

The Effects of Fe3? and Mn3? on Aluminum Silicate Phase Relations in North-Central New Mexico, U.S.A.

Aluminum silicate triple-point occurrences are common in metamorphicrocks of northern New Mexico. The three polymorphs show extensivesolid solution, with Fe and Mn substituting for Al. Mineraltextures, the spatial distribution of phases, and the systematicpartitioning of Fe and Mn indicate that the kyanite-andalusite-sillimaniteassemblages crystallized in equilibrium. The compositions ofminerals in the three-phase assemblage vary across the studyarea, recording regional variations in the pressures and temperaturesof metamorphism. The highest-pressure rocks, exposed at RioMora, contain kyanite at higher elevations and sillimanite atlower elevations. A sub-horizontal isograd separates the twominerals. Kyanite and sillimanite have nearly identical Fe contentwhich varies systematically with X_Fe2O3 in hematite or ilmenite.Andalusite occurs only along a single manganiferous layer, incrystals rich in MnAlSiO₅ and saturated in FeAlSiO₅. Triple-pointassemblages can be found wherever the folded manganiferous layercrosses the unfolded kyanite-sillimanite isograd. The TruchasRange, preserving slightly lower pressures of metamorphism,shows kyanite-andalusite-sillimanite in rocks with titaniferoushematite. Andalusite is enriched in Fe relative to kyanite andsillimanite, but no polymorphs contain Mn. Rocks with lowerX_Fe2O3 in hematite have kyanite and sillimanite without andalusite,whereas rocks with pure hematite contain only andalusite. Theshallowest erosional levels are preserved in the western PicurisRange where the three polymorphs occur as pure minerals in ilmenite-bearingrocks. Hematitic samples contain only andalusite which showsextensive solid solution of both Fe and Mn. The assemblage kyanite-andalusite-sillimanite is not invariant.Iron and manganese both add degrees of freedom. These transitionmetals have stabilized the three-phase assemblage, in apparentchemical equilibrium, across a P-T interval of 500-540 ?C, 3?8-4?6kb in rocks from New Mexico. The saturation level of FeAlSiO5in andalusite does not vary with Mn content but does vary withpressure and temperature. Calculations indicate that a 2-3 kbdecrease in pressure or a 25-50 ?C increase in temperature resultsin a 1 mole per cent increase in X_FeAlSiO5 in iron-saturatedandalusite.     

Correlation of spectroscopic properties and substitutional sites of Cr3+ in aluminosilicates: II. Andalusite and sillimanite

This paper is an extension of the earlier one dealing with kyanite in which the best fitting value of the oxygen ligand distance for Cr³⁺ is adopted to study the spectroscopic properties of Cr³⁺ ions doped at the two possible Al sites in the other two polymorphs of the aluminosilicate group (Al₂O₃ · SiO₂), namely, andalusite and sillimanite. The superposition model and the crystal field analysis package recently developed for 3d ions doped at arbitrary low symmetry sites in crystals are used to predict energy levels and statevectors within the whole 3d ³ configuration. Then the values of the ground state zerofield splitting for Cr³⁺ ions at each Al sites in the two crystals are obtained. The splittings of the lower excited states ² E and ⁴ T ₂ as well as the admixture of ⁴ T ₂ into ² E have also been predicted. Comparison of our results with the available experimental data enable us to correlate the optical and EPR Spectroscopic properties with the substitutional Cr³⁺ sites. The conclusion is that in andalusite and sillimanite only the Al sites with nearly-octahedral six-fold coordination seem to be occupied by Cr³⁺ ions.     

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.     

Sillimanite group minerals: a new promising raw material for the Russian aluminum industry

The raw-material base of the Russian aluminum industry is considered. The raw materials include common (bauxites, nepheline syenites) and uncommon (nepheline ores, synnyrites, anorthosites, power-and-heating plant ashes, kaolines) types of ores. With regard to many criteria (reserves and quality of ores, technology of their processing, etc.), the problem of alumina deficit can be solved by mining sillimanite group minerals Al₂SiO₅ (wt.%: Al₂O₃ = 62.9, SiO₂ = 37.1), namely, andalusite, sillimanite, and kyanite. Their proved reserves converted to the final product (aluminum) exceed 400 mln tons. This will be enough for more than a hundred years provided that aluminum is produced in the present-day output (4 mln tons in 2008). Almost all deposits can be explored by strip mining, with application of the gravitation, flotation, and electromagnetic separation methods for ore dressing. The alumina content in concentrates reaches 60–62 wt.%. Only high-grade bauxites and the above concentration methods can ensure such a high yield of Al₂O₃. Sillimanite group minerals can be processed together with nepheline ores by sintering or be used for the direct electrothermal production of silumin and aluminum, excluding the alumina production stage. The latter method is the most promising in Russia.     

ELF isosurface maps for the Al2SiO5 polymorphs

This study examines the electron localization function (ELF) isosurfaces of the Al₂SiO₅ polymorphs kyanite, sillimanite, and andalusite to see how differences in coordination and geometry of the cations and anions affect the ELF isosurfaces. Examination of the ELF isosurfaces indicates that their shapes are dependent on the coordination and geometry of the oxygen atoms and are not sensitive to coordination of the surrounding cations. Of the 18 crystallographically distinct oxygen atoms in the Al₂SiO₅ polymorphs, 13 are bonded to two aluminum atoms and one silicon atom (Al₂–O–Si) and are associated with two different ELF isosurface shapes. The shape of the ELF isosurface is dependent on the distance at which the oxygen atom lies from a plane defined by the three surrounding cations: at a distance greater than 0.2 Å the ELF can be defined as horseshoe-shaped and at a distance less then 0.2 Å it can be described as concave hemispherical. This feature is also seen in the ELF isosurfaces for the oxygens bonded to three aluminum atoms (Al₃–O) where the isosurfaces can be defined as trigonally toroidal and uniaxially trigonally toroidal. The changes in the ELF isosurfaces for the three coordinated oxygens are also indicative of changes in hybridization. The ELF isosurface for the two-fold coordinated oxygen (Al–O–Si) has a large mushroom-shaped isosurface along the Al–O bond and a concave hemispherical isosurface along the Si–O. The four-fold coordinated oxygen (Al₄–O) contains two concave hemispherical isosurfaces along the shorter Al–O bonds and a banana-shaped isosurface, which encompasses the longer Al–O bonds. In addition, this study shows the homeomorphic relationship between the ELF isosurfaces and electron density difference maps with respect to number and arrangement of domains.     

The accuracy of standard enthalpies and entropies for phases of petrological interest derived from density-functional calculations

The internal energies and entropies of 21 well-known minerals were calculated using the density functional theory (DFT), viz. kyanite, sillimanite, andalusite, albite, microcline, forsterite, fayalite, diopside, jadeite, hedenbergite, pyrope, grossular, talc, pyrophyllite, phlogopite, annite, muscovite, brucite, portlandite, tremolite, and CaTiO₃–perovskite. These thermodynamic quantities were then transformed into standard enthalpies of formation from the elements and standard entropies enabling a direct comparison with tabulated values. The deviations from reference enthalpy and entropy values are in the order of several kJ/mol and several J/mol/K, respectively, from which the former is more relevant. In the case of phase transitions, the DFT-computed thermodynamic data of involved phases turned out to be accurate and using them in phase diagram calculations yields reasonable results. This is shown for the Al₂SiO₅ polymorphs. The DFT-based phase boundaries are comparable to those derived from internally consistent thermodynamic data sets. They even suggest an improvement, because they agree with petrological observations concerning the coexistence of kyanite?+?quartz?+?corundum in high-grade metamorphic rocks, which are not reproduced correctly using internally consistent data sets. The DFT-derived thermodynamic data are also accurate enough for computing the P–T positions of reactions that are characterized by relatively large reaction enthalpies (>?100 kJ/mol), i.e., dehydration reactions. For reactions with small reaction enthalpies (a few kJ/mol), the DFT errors are too large. They, however, are still far better than enthalpy and entropy values obtained from estimation methods.