The following six papers were presented at a meeting, held in September 1994, which reviewed some of the recent advances in the application of computational methods to mineralogy. Talks covered the developing and challenging field of ab initio quantum mechanical computations as well as new applications and insights afforded by the use and refinement of the more established methods of empirical simulation and modelling. The former attempt to solve Schrdinger's equation for the material in question, and in doing so determine the energy surface and electronic structure. The latter use parameterized interatomic potentials to describe the energy of interaction between pairs or groups of atoms, the parameters typically derived either by fitting to the results of quantum mechanical calculations of small clusters, or empirically determined from fitting to the known physical properties of crystals (e.g. to the elastic constants, structural parameters or dielectric constants). A certain rivalry and antipathy occasionally surfaces between computational theorists from either camp.

Ab initio total energy calculations based on the local density approximation (LDA) and using a conjugate-gradient solver for the Kohn-Sham equations have been performed for cordierite, brucite, (Mg(OH)2) and diaspore (AlOOH). The calculated fractional coordinates of all structures are in good agreement with experimental diffraction data. The angle of the non-linear hydrogen bond in diaspore is reproduced well. The Raman active OH stretching frequency in brucite has been calculated using the frozen phonon approach and the calculated stretching frequency is in very good agreement with the observed value. The energetically most favourable calculated orientation of the proton-proton vector of an H2O molecule incorporated in the structural channels of cordierite agrees with findings deduced from spectroscopic data, and the calculated energy of hydration is in reasonable agreement with calorimetric data. It is therefore concluded that ab initio total energy calculations can confidently be used to predict properties of hydrogen bonded structures, which is difficult with conventional parameterized static lattice energy minimization calculations. An extension to the model is necessary to improve the agreement of the predicted to the observed lattice parameters for small structures.

We review some of the most recent developments in classical and quantum mechanical molecular dynamics simulations, in particular as applied to Earth-forming phases at conditions prevalent in the Earth's deep interior. We pay special attention to the modelling of high pressures and temperatures, elucidating the problems associated with both the classical and quantum approaches in view of the empirical potentials required for the former, and the limitations of finite temperature calculations for the latter. We show the current status of such calculations for major phases such as MgSiO3 perovskite.

A new computer code (MARVIN) has been developed for the simulation of surfaces and interfaces. The models and methodologies employed within the program are briefly discussed. One application of the code, calculating crystal morphologies, is explored using zircon, quartz and α-Al2O3 as examples. The new code enables the use of covalent type force fields and the effect of surface relaxation on the growth morphology to be calculated for the first time. It is found that relaxation does affect the attachment energy but not by a large enough amount to significantly change the growth morphology for the three examples discussed here. Finally, the calculated surface relaxation for the basal plane of α-Al2O3 is found to be in complete agreement with Hartree-Fock ab initio calculations, verifying that the potentials, which are derived from bulk properties, transfer well to this surface.

The procedure for deriving interatomic potentials for molecular ionic materials, using empirical fitting procedures, is described. Potentials are obtained for carbonates, phosphates and perchlorates, and used to calculate crystal and lattice properties which are compared with available experimental data.

Kinetics of atomic ordering in a potassium feldspar is simulated using massively parallel computing. The simulation method is based on the Monte Carlo algorithm for the Al-Si redistribution (the Kawasaki dynamics) combined with the lattice relaxation. The Hamiltonian has the symbolic form

where u represents displacements of atoms from ideal positions, and p the Al and Si occupation numbers. The model is purely elastic; there is no direct interaction between Al and Si atoms. The simulated crystal is a thin film with (010) surfaces and consists of 64 × 64 unit cells; the unit cell defined for the whole film contains slightly more than 4 formula units. The (010) orientation is chosen in order to preserve in the film the main structural feature of feldspars: crankshaft-like sheets formed by four-tetrahedra rings. This makes it possible to observe the Pericline twins only. At the late stage of the kinetic run these twins are clearly seen. The direction for the domain walls is determined by the spontaneous strain and changes with the change of the model parameters; considerable local deviations from this direction are observed.

We describe a model for framework silicates in which the SiO4 (and AlO4) tetrahedra are treated as perfectly rigid and freely jointed. From this model we are able to identify low-energy modes of distortion of the structure, which we call Rigid unit modes. These modes can act as soft modes to allow easy distortions at phase transition. We discuss three forces that will operate at a phase transition in conjunction with the candidate soft modes to determine which of the rigid unit modes will actually precipitate a phase transition, and illustrate these ideas by detailed discussions of the phase transitions in quartz, leucite and cristobalite. The model can also be used to estimate the transition temperature, and the theory highlights an important role for the stiffness of the tetrahedra.

Amphibolites in the Mesozoic part of the parautochthonous Lower Schieferhülle (LSH), the allochthonous Upper Schieferhülle (USH) and the overlying Austroalpine basement (AA) in and around the western Tauern Window (Eastern Alps) suffered a progressive Alpine deformation. Lineations and foliations L1-S1, L2-S2 defined by preferentially oriented (Na-Ca) amphiboles as well as F3 folds and further foliations Smyl and S4 in the metabasites are structures of successive deformational stages with a constant W-E main extension axis of strain. The (Na-Ca) amphiboles in assemblages with epidote, chlorite, albite/oligoclase and quartz are zoned with similar continuous zonation trends from early actinolite in the cores to magnesio-hornblende and tschermakitic hornblende, and from magnesio-hornblende to late actinolite in the rims in the three lithostratigraphic units. Geothermobarometry involving tremolite-edenite and (pargasite-hastingsite)-tremolite end-member equilibria in amphiboles allowed us to reconstruct prograde-retrograde P-T paths for the Alpine greenschist-amphibolite facies event. The paths passed P/Tmax at 6–7 kbar/600°C. Similar shapes of the paths in AA, USH and Mesozoic LSH indicate a common metamorphic history and a stacking of these units prior to or during the pre-Pmax evolution. Moderate P-T ratios are characteristic for the temperature-dominated compression paths and indicate continental collisional rather than subduction zone metamorphism. The middle to late Alpine greenschist-amphibolite facies event appears as an independent metamorphism along a complete P-T loop which may have followed an earlier and poorly documented high-pressure/low-temperature event.

Some twenty kimberlite pipes outcrop along the eastern and western borders of the Kundelungu plateau, Shaba Province, Zaire. They are arranged roughly along two north-south trending alignments. The pipes probably intruded the Bangweulu Block, which stabilized around 1800 Ma. The exceptionally fresh kimberlites contain mantle-derived nodules (peridotites and eclogites), as well as megacrysts which may reach up to several cm in diameter. The most important megacrysts are garnets, ilmenites, clinopyroxenes, orthopyroxenes and olivines. Micas and diamonds are rarely observed. The clinopyroxenes can be subdivided in two groups: (1) a Ca-rich, low-T type, similar to the Cr-rich diopsides found in ‘depleted’ (granular) peridotites; and (2) subcalcic clinopyroxene comparable to the megacrysts and to the clinopyroxenes of ‘fertile’ (sheared) peridotites. The orthopyroxenes are less frequent and are Ca-poor enstatites (0.07–0.42 wt.% CaO) and Ti-bronzites (CaO <1.3 wt.%). All the analysed garnets are Ca-rich (>4.5 wt.% CaO) and all fall in the lherzolite field defined by Sobolev et al., 1973. The low-Ca garnets which appear in many diamond-bearing kimberlites have never been observed in Zaire, neither in the diamond-poor Kundelungu pipes nor in the diamond-rich Mbuji-Mayi pipes. The ilmenites define a trend close to the ‘magmatic Mg-enrichment trend';. The olivine macrocrysts have Fo contents comparable to those of peridotites (Fo90–93). The ultramafic nodules comprise lherzolites, harzburgites, pyroxenites, wehrlites and dunites. The granular textures and P-T equilibrium conditions (770–1380°C and 28–61 kbar) deduced from their mineral compositions, show clearly that they were derived from a mantle zone on the continental geotherm (90–190 km depth). The eclogite nodules, which are less frequent, contain only two mineral phases (pyrope-almandine-grossular and omphacite), and the texture and the mineral compositions are similar to those of Roberts Victor eclogites. Our findings support the conclusion of Nixon and Condliffe (1989) that low-T peridotites, eclogites and pyroxenites derived from ‘depleted’ lithosphere, while Cr-poor garnet, subcalcic diopside and bronzite megacrysts cristallized from fertile asthenosphere.

Mackinawite, tetragonal FeS, has been synthesised by reacting iron with Na2S solutions. A Rietveld structure refinement of X-ray powder diffraction data, recorded using X-rays monochromated from synchrotron radiation with a wavelength of 0.6023 Å, has been performed. The structure has been refined in the tetragonal space group, P4/nmm, and has the following cell parameters: a = 3.6735(4), c = 5.0328(7) Å, V = 67.914(24) Å3. Our refinement shows that the FeS4 tetrahedron in mackinawite is almost perfectly regular, with a much smaller distortion than has been previously reported. An improved X-ray diffraction data set is provided.

The system Pd-Fe-Ni-S was studied at 900 and 725°C by means of dry condensed charges. At both temperatures it is dominated by the phase relationships involving sulphide melt. Pd-Fe-Ni alloys with broad miscibility primarily coexist with the melt; they are relatively enriched in Pd, whereas the associated melt is enriched in Ni. With decreasing temperature the melt recedes from Fe-rich regions. The incompatibility of PdS (extensive solid solution with Ni) and mss at 900°C is replaced by their co-crystallization (± disulphide(s) of Ni,Fe or ± sulphide melt) at 725°C The Ni/Fe ratio in the melt changes regularly against that in mss with increasing S fugacity and Pd contents in these two phases. (Ni,Fe)3±xS2 and Pd4S play important roles at 725°C. The data offer an array of distribution coefficients and solubility values suitable for geological interpretations.

Hausmannite (Mn3O4), a manganese oxide with a tetragonally distorted spinel structure, is considered to be ferrimagnetic with a very low Curie temperature of 42.5 K. However, strongly magnetic hausmannite has been discovered in some of the hydrothermally altered high-grade manganese ores of the giant Kalahari manganese deposit in South Africa. EDS-electron microprobe analyses indicate magnetic hausmannite to contain on average between 3 and 11.3 wt.% Fe2O3. In contrast non-magnetic hausmannite contains on average about 1–3 wt.% Fe2O3. X-ray powder diffraction analyses reveal small changes in cell dimensions of the magnetic hausmannite related to the high iron content. Mössbauer spectroscopy suggests that all iron is in the trivalent state. Optical microscopy and scanning electron microscopy (electron back-scatter imaging) proved the magnetic hausmannite to be homogeneous in composition, containing only a few minute inclusions of hematite. Magnetic blocking temperatures of the iron-rich hausmannite, approximating the Curie temperature, are of the order of 750 K. It is suggested that the ferrimagnetic state of hausmannite is stabilized and enhanced by replacement of Mn3+ by Fe3+.

Titanites rich in antimony (up to 12.59 wt.% Sb2O5; equal to 0.165 Sb5+ per Si4+ = 1.000) arc described for the first time. They coexist with various greenschist-facies minerals in three different petrographical environments in the manganese concentrations at St. Marcel-Praborna in the Aosta Valley, Italy. These titanites are chemically zoned, the Sb-richest parts generally occurring alongside grain boundaries, microfractures, pores or inclusions. Moderately-good positive correlations exist between the Sb, Al and Fe contents, with negative correlations of each of these elements with Ti. Cr has perturbed the Al and Fe contents since a better negative correlation with Ti is obtained with [Al + Cr + Mn + Fe]. The Sr, Ba, Mn and F contents are rather small and vary irregularly. Several crystal-chemical hypotheses are presented concerning the method of structural formula calculation and the valencies and site distributions of Sb and the companion additional minor elements. The favoured interpretation is to place: Sr2+, Ba2+, Mn2+, Fe2+ and possibly also Sb3+ in the viiCa2+ site; Sb5+, Cr3+, Al3+, Sb3+, Fe3+ and possibly also Mn3+ in the viTi4+ site; and Al3+ in the ivSi4+ site; this indicates the existence of a natural silicate containing not only both trivalent and pentavalent Sb, but also both valencies in the same site. The principal ionic substitution is believed to be: 2 viTi4+ = vi[Al3+ + Cr3+ + Mn3+ + Fe3+] + viSb5+ accompanied by a substantial minor proportion of: 2 viTi4+ = viSb3+ + viSb5, or possibly = 2 viSb4+ The data indicate a very late stage penetration of pre-existing titanites by mobilized Sb, Al, Cr, Mn, Fe, F and presumably also (OH) at this locality, whereas Sr and Ba were mobile at an earlier stage. Manganese, which existed in the sedimentary protoliths, did not enter the titanite structure in very significant quantities.

Monazite is a light rare-earth element (LREE)-bearing accessory phase common in felsic granitic rocks, and strongly influences LREE concentrations in granites and the chemistry of melts and residues formed during partial melting. Cheralite-rich (high-Th) monazite-(Ce) has been recorded as rims on partially dissolved cores in a suite of granulite-facies migmatites generated by disequilibrium melting. High-Th monazite has previously been recorded only in granitic-pegmatite occurrences. Subidiomorphic monazite-(Ce) from leucosome, melanosome and mesosome consists of complexly zoned cores (up to 300 µm in diameter) containing 5.17–9.87 wt.% ThO2, overgrown by essentially unzoned rims (containing up to 21.4 wt.% ThO2). Uranium contents are average for Th-rich monazite-(Ce) (0.22–3.17 wt.% UO2). Th enrichment (relative to LREE) in monazite-(Ce) rims is ascribed to the presence of fluorine-bearing melts (formed during the incongruent breakdown of biotite to produce a water-undersaturated melt), allowing the formation of REE-fluoride complexes in the melt, coupled with the increased charge balanced substitutions Th4+ + Si4+ ⇌ REE3+ + P5+ and Th4+ + Ca2+ ⇌ 2REE3+ into monazite-(Ce). Fractionation of Th and U (reflected by an increased in Th/U in rims relative to cores) may have occurred due to the removal by a CO2-rich fluid phase in the melt. These interpretations are consistent with elevated CO2 and F contents of granitic liquids produced during the water-undersaturated breakdown of biotite under granulite-facies conditions. Evidence for restricted monazite-(Ce)-melt equilibration and rapid melt removal is provided by the ubiquitous presence of partially embayed cores and unzoned rims.