Statistical chemistry of calcic amphiboles

Principal components analysis is used to study the chemistry of 639 calcic amphiboles. Eigenvectors representing multiple partial correlation coefficients give various sets of substitutional relationships. The relative significance of each set can be noted by the percent variation of the data it represents. The highest percent variation (36%) is associated with the substitutions $$Si + Mg \rightleftharpoons Al^{IV} + Al^{VI} + Ti + Fe^{3 + } + Fe^{2 + } + Na + K$$ . Other expected substitutions among the ions such as Al^IV + Na ? Si, the positive correlation between Al^IV and Al^VI etc. are shown statistically. The substitution of Al in T ₁ and T ₂ positions imposes an ordering in the M ₁, M ₂ and M ₃ sites. Variability of OH in the amphiboles is found to be significant. There is no definite correlation between OH and Fe³⁺ but OH and Ti are positively correlated. Under certain conditions and provided the concentration of Al^IV does not change significantly, Fe and Mg may be assumed to mix ideally in the amphibole solid solution.     

DFT study of the cation arrangements in the octahedral and tetrahedral sheets of dioctahedral 2:1 phyllosilicates

Quantum mechanical calculations based on the density functional theory (DFT) are used to study the crystal structures of dioctahedral 2:1 phyllosilicates. The isomorphous cation substitution is investigated by exploring different substitutions of octahedral Al³⁺ by Mg²⁺ or Fe³⁺, tetrahedral substitution of Si⁴⁺ by Al³⁺, and different interlayer cations (IC) (Na⁺, K⁺, Ca²⁺, and Mg²⁺). Samples with different kinds of layer charges are studied: only tetrahedrally charged, only octahedrally charged, or mixed octahedral/tetrahedral charged. The effect of the relative arrangements of these substitutions on the lattice parameters and total energy is studied. The experimental observation of segregation tendency of Fe³⁺ and dispersion tendency of Mg²⁺ in the octahedral sheet is reproduced and explained with reference to the relative energies of the octahedral cation arrangements. These energies are higher than those due to the IC/tetrahedral and IC/octahedral relative arrangements. The tetrahedral and octahedral substitutions that generate charged layers also tend to be dispersed. The octahedral cation exchange potentials change with the IC-charge/ionic radius value.     

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.     

Sapphirine II

The crystal structure of aP2₁/a polymorph of sapphirine (a=11.286(3),b=14.438(2),c=9.957(2) Å, β=125.4(2) °) of composition [Mg_3.7Fe _0.1 ²⁺ Al_4.1- Fe _0.1 ³⁺ ]^IV[Si_1.8Al_4.2]^IVO₂₀ was refined using structure factors determined by both neutron and x-ray diffraction methods to conventionalR factors of 0.067 and 0.031. respectively, forF _obs>2σ. The results of the two refinements agree reasonably well, but a half-normal probability plot (Abrahams, 1974) comparing the two data sets indicates that the pooled standard deviations of the atomic coordinates have been underestimated by a factor of two. The structure of sapphirine, solved initially by Moore (1969), consists of cubic closest packed oxygens with octahedral and predominantly tetrahedral layers alternately stacked along [100]. The layer in which 70% of the octahedral sites are occupied has an Mg-Al distribution characterized by Mg-rich octahedra sharing edges mainly with Al-rich octahedra. Mean octahedral bond lengths correlate well with Al occupancy determined by neutron site refinement if the relative number of shared octahedral edges is taken into account (see Table 1). The predominantly tetrahedral layer has 10% of the octahedral sites occupied by Al and 30% of the tetrahedral sites occupied by Al-Si in the ratio 2.33∶1. There are single chains of Al-Si tetrahedra parallel toz with corner-sharing wing tetrahedra (T5 andT6) on either side in the (100) plane. The meanT-O distance is highly correlated with Al occupancy, X_Al, as determined from the neutron site refinement: $$\langle T - O\rangle = 1.656 + 0.105X_{Al} (r^2 = 0.995).$$ Details of the neutron refinement are summarized below.     

Crystal chemical variations in Ba-rich biotites from gabbroic rocks of lower crust (Ivrea Zone,NW Italy)

Biotites from mafic rocks occurring at different stratigraphic levels of the Ivrea-Verbano Mafic Complex are studied. The rocks are gabbros and diorites. All the biotites are intermediate between phlogopite and annite [0.282 (up to 7.14 and 9.32 wt%, respectively) with respect to those of the diorites (up to 1.26 and 6.26 wt%, respectively). Systematic compositional variations support the substitution model 2 ^IV Si+( ^IV R²⁺)2 ^IV Al+ ^VI Ti (R²⁺=Fe+Mg+Mn) in gabbros and ^IV Si+ ^VI Al ^IV Al+ ^VI Ti in diorites. A predominance of disordered stacking sequences, coexisting with 1M, 2M ₁ and 3T polytypes was observed in all biotites. It was possible to carry out structural refinements only on three biotites-2M ₁ from diorites (R-values between 2.68 and 3.77) and one biotite-1M from gabbros (R-value=3.09). It was shown that: (1) the reduced thickness of the tetrahedral sheet in Ba-rich biotites supports the coupled substitution ^IV Si+ ^XII K ^IV Al+ ^XII Ba; (2) the interlayer site geometry is affected by the whole layer chemistry and does not reflect only local chemical variations; (3) in two samples of the 2M ₁ polytype, the M(1) octahedral site is larger and more distorted than the M(2) sites because of the preferential ordering of Fe²⁺ in the M(1) site, whereas one sample shows complete cation disorder in the octahedral sites. Biotite-1M shows that Fe²⁺ can also be located in the M(2) site. Some of the differences between the biotites of gabbros and diorites (e.g. Ba concentration and exchange vectors) may be linked to the host rock composition and to its crystallization process. Biotite occurs in trace amounts in gabbros and its crystallization is related to the interstitial melt which contributed to the adcumulus growth of the main rock forming phases and became highly enriched in K, Ba and Ti. Diorites are the result of equilibrium crystallization of a residual melt rich in incompatible elements, where biotite is a major constituent.     

ELNES spectroscopy of mixed Si coordination minerals

 Si K- and L-edge ELNES spectroscopy and multiple-scattering (MS) calculations are used to examine mixed Si coordination compounds varying in Si^VI:Si^IV ratio. As in previous studies, the edges are influenced mainly by silicon coordination (tetrahedral vs. octahedral), as supported by the MS calculations. We demonstrate two methods semi-quantitatively to extract the value of Si^VI/(Si^VI+Si^IV): (1) A linear relationship between the L_2,3-L₁ splitting and Si^VI/(Si^VI+Si^IV) is observed, (2) a fitting method based on the coaddition of reference tetrahedral and octahedral Si spectra is applied to both Si K- and L-edge ELNES spectra. Received: February 10, 1997 / Revised, accepted: May 23, 1997     

Spectroscopic active IVFe3+–VIFe3+ clusters in spinel–magnesioferrite solid solution crystals: a potential monitor for ordering in oxide spinels

Optical absorption spectra (OAS) of synthetic single crystals of the solid solution spinel sensu stricto (s.s.)–magnesioferrite, Mg(Fe³⁺Al_1???y)₂O₄ (0?y?≤ 0.3), have been measured between 12 500 and 28 500?cm^?1. Chemical composition and Fe³⁺ site distribution have been measured by electron microprobe and Mössbauer spectroscopy, respectively. Ferric iron is ordered to the tetrahedral site for samples with small magnesioferrite component, and this ordering is shown to increase with magnesioferrite component. The optical absorption spectra show a strong increase in band intensities with Fe³⁺→Al substitution. Prominent and relatively sharp absorption bands are observed at 25 300 and 21 300?cm^?1, while less intense bands occur at 22 350, 18 900, 17 900 and 15 100?cm^?1. On the basis of band energies, band intensities and the compositional effect on band intensity, as well as structural considerations, we assign the observed bands to electronic transitions in ^IVFe³⁺–^VIFe³⁺clusters. A linear relationship (R ²= 0.99) between the α_net value of the absorption band at 21 300?cm^?1 and [^IVFe³⁺]?·?[^VIFe³⁺] concentration product has been defined: α_net=2.2?+?15.8 [^IVFe³⁺]?·?[^VIFe³⁺]. Some of the samples have been heat-treated between 700 and 1000?°C to investigate the relation between Fe³⁺ ordering and absorption spectra. Increase of cation disorder with temperature is observed, which corresponds to a 4% reduction in the number of active clusters. Due to the high spatial resolution (??～?10?μm), the OAS technique may be used as a microprobe for determination of Fe³⁺ concentration or site partitioning. Potential applications of the technique include analysis of small crystals and of samples showing zonation with respect to total Fe³⁺ and/or ordering.     

Structure analysis on synthetic emerald crystals

Single crystals of emerald synthesized by means of the flux method were adopted for crystallographic analyses. Emerald crystals with a wide range of Cr³⁺-doping content up to 3.16 wt% Cr₂O₃ were examined by X-ray single crystal diffraction refinement method. The crystal structures of the emerald crystals were refined to R ₁ (all data) of 0.019–0.024 and wR ₂ (all data) of 0.061–0.073. When Cr³⁺ substitutes for Al³⁺, the main adjustment takes place in the Al-octahedron and Be-tetrahedron. The effect of substitution of Cr³⁺ for Al³⁺ in the beryl structure results in progressively lengthening of the Al–O distance, while the length of the other bonds remains nearly unchanged. The substitution of Cr³⁺ for Al³⁺ may have caused the expansion of a axis, while keeping the c axis unchanged in the emerald lattice. As a consequence, the Al–O–Si and Al–O–Be bonding angles are found to decrease, while the angle of Si–O–Be increases as the Al–O distance increases during the Cr replacement.     

Nonstoichiometry in sillimanite: Mullite compositions with sillimanite-type superstructures

Complete solid solution between sillimanite and mullite is shown to occur when Fe³⁺, in the virtual absence of Ti, replaces Al^VI. All members of the series adopt the sillimanite (Al, Si)^IV ordering scheme in preference to the modulated structure typical of synthetic and titaniferous natural mullites.     

Magnetic behavior of trioctahedral micas with different octahedral Fe ordering

This contribution is finalized at the discussion of the magnetic structure of two samples, belonging to phlogopite–annite [sample TK, chemical composition ^IV(Si_2.76Al_1.24) ^VI(Al_0.64Mg_0.72 $ {\text{Fe}}_{1.45}^{2 + } $ Mn_0.03Ti_0.15) (K_0.96Na_0.05) O_10.67 (OH)_1.31 Cl_0.02] and polylithionite–siderophyllite joints [sample PPB, chemical composition ^IV(Si_3.14Al_0.86)^VI(Al_0.75Mg_0.01 $ {\text{Fe}}_{1.03}^{2 + } $ $ {\text{Fe}}_{1.03}^{3 + } $ Mn_0.01Ti_0.01Li_1.09) (K_0.99Na_0.01) O_10.00 (OH)_0.65F_1.35]. Samples differ for Fe ordering in octahedral sites, Fe²⁺/(Fe²⁺?+?Fe³⁺) ratio, octahedral composition, defining a different environment around Fe cations, and layer symmetry. Spin-glass behavior was detected for both samples, as evidenced by the dependency of the temperature giving the peak in the susceptibility curve from the frequency of the applied alternating current magnetic field. The crystal chemical features are associated to the different temperature at which the maximum in magnetic susceptibility is observed: 6?K in TK, where Fe is disordered in all octahedral sites, and 8?K in PPB sample, showing a smaller and more regular coordination polyhedron for Fe, which is ordered in the trans-site and in one of the two cis-sites.     

Sapphirine I

Microprobe analyses of 26 natural sapphirines from 17 localities indicate that the predominant chemical substitutions in this mineral occur along the solid solution join^VI(Mg,Fe)²⁺+^IVSi⁴⁺=^VI(Al, Fe)³⁺+^IVAl³⁺. Chromium and manganese are minor substituents. Evidence for the substitution SiAl+1/2Mg+1/2 vacancy is absent within the limits of analytical error.A partitioning scheme based on electrostatic charge balance considerations has been devised permitting calculation of Fe²⁺ and Fe³⁺ from total iron content. Results are in good agreement with previous Mössbauer studies which indicate Fe³⁺ is sometimes in octahedral and/or tetrahedral coordination.Distribution coefficients for Fe²⁺-Mg exchange equilibria between sapphirine-spinel and sapphirine-orthopyroxene are similar for most mineral pairs and suggest that most of the assemblages equilibrated at about the same temperature or that the exchange reactions are insensitive to temperature.Compositions of synthetic sapphirines as a function of temperature and pressure are qualitatively predictable from crystal chemical considerations. Changes in sapphirine composition along the MgSi= AlAl solid solution join toward more aluminous compositions stabilize the sapphirine structure at high temperatures and low pressures. The limited extent of MgSi=AlAl solid solution observed in natural sapphirines appears to be related to the requirements of geometrical fit among octahedra and tetrahedra in the almost idealized cubic closest-packed anion framework.     

An experimental investigation into the metastable formation of phosphoran olivine and pyroxene

The formation of phosphoran olivine by crystallization from a melt was investigated experimentally using a one atmosphere furnace, using San Carlos olivine [(Mg,Fe)₂SiO₄] mixed with either iron phosphide (FeP) or magnesium pyrophosphate (Mg₂P₂O₇). Both dynamic crystallization and isothermal experiments produced phosphoran olivine as zoned single crystals and as overgrowths surrounding normal, phosphorus-free olivine grains. The crystallization pathways that form phosphoran olivine were traced and confirm that it is a metastable phase that can crystallize from a phosphorus-rich melt over timescales of hours to days. Removal of the P and equilibration of the olivine however requires weeks to months in the presence of silicate melt. Phosphoran olivine with up to 27 wt% P₂O₅ was generated and up to 69% of the Si tetrahedral sites were replaced by P. The substitution of Si by P into olivine was confirmed as 4^VIM⁺² + 2^IVSi⁺⁴ ↔ 3^VIM⁺² + 2^IVP⁺⁵ + ^VI[]. Phosphoran olivine compositions that vary from (Mg,Fe)₂SiO₄ to (Mg,Fe)_1.65[]_0.35Si_0.3P_0.7O₄ have been produced in these experiments.Phosphoran pyroxene was also generated in a few experiments and forms when phosphoran olivine reacts with either tridymite or melt. It has compositions compatible with protopyroxene, orthopyroxene, pigeonite and sub-calcic augite, and can contain up to 31.5 wt% P₂O₅. Like phosphoran olivine, it is also a metastable phase. Phosphorus replaces Si in pyroxene by the following substitution methods: 8^IVSi⁺⁴ ↔ 3^IVSi⁺⁴ + 4^IVP⁺⁵ + ^IV[] with Al entering the structure by the exchange 2^IVSi⁺⁴ ↔ ^IVAl⁺³ + ^IVP⁺⁵. Phosphoran pyroxene compositions vary from (Mg,Fe)₈Si₈O₂₄ to (Mg,Fe)₈Si₃P₄[]O₂₄.     

The crystal chemistry and mössbauer study of schorlomite

Six schorlomite samples with TiO₂ contents varying between 9.70 and 15.34 weight percent were studied by means of Mössbauer spectroscopy and chemical analysis. The measured Mössbauer spectra have complex shapes. The spectra of these samples were fitted with six doublets, which can be assigned to ^VIIIFe²⁺, ^VIFe²⁺, ^VIFe³⁺, ^IVFe³⁺ and two electron delocalizations, ^IVFe³⁺ ? ^VIIIFe²⁺ and ^IVFe³⁺ ? ^VIFe²⁺, respectively. The assignment of iron absorption doublets and their Mössbauer parameters are discussed in terms of the single crystal structure data of one of the samples studied in this work. Cation distributions are also given. The occupancies of cations at the tetrahedral (Z) site are Fe³⁺>Al³⁺, Ti⁴⁺, and the relative enrichments at Z site are always Fe³⁺>Ti⁴⁺. Most of the six samples contain Ti³⁺. Ti³⁺/ΣTi ratios range from 1.43 percent to 6.40 percent. Fe²⁺/ΣFe ratios vary from 8.84 percent to 11.31 percent. Four types of substitution must be considered for Ti entering the garnet structure.     

IIb trioctahedral chlorite from the Barberton greenstone belt: crystal structure and rock composition constraints with implications to geothermometry

IIb trioctahedral chlorite in the Barberton greenstone belt (BGB) metavolcanic rocks was formed during pervasive greenschist metamorphism. The chem‐ical composition of the chlorite is highly variable, with the Fe/(Fe+Mg) ratio ranging from 0.12 to 0.8 among 53 samples. The chemical variation of the chlorite results from the chemical diversity of the host rock, especially the MgO content of the rock, but major details of the variation pattern of the chlorite are due to the crystal structure of the chlorite. All major cation abundances in the chlorite are strongly correlated with each other. Sil‐icon increases with Mg and decreases with Fe, while Al^IV and Al^VI decrease with Mg and increase with Fe²⁺. A complex exchange vector explains over 90% of the chlorite compositional variation: Mg₄SiFe²⁺ ₋₃Al^VI ₋₁ Al^IV ₋₁, which has 3 parts Fe-Mg substitution coupled with one part tschermakite substitution. This ratio is required to maintain the charge and site balances and the dimensional fit between the tetrahedral and octahedral sheets. The subtle change in Al substitution in chlorite implies that Al^VI is preferentially ordered in the M(4) site, and about 84% of the Al^VI present is in the M(4) sites when they are nearly filled with Al^VI. Based on 47 analyzed chlorite-bearing rock samples, chlorite (Chl) composition is strongly correlated with the MgO content of the host rock. Calculated correlation coefficients are +0.91 for SiO_2Chl-MgO_Rock, −0.87 for Al₂O_3Chl-MgO_Rock, +0.89 for MgO_Chl-MgO_Rock, and −0.85 for FeO_Chl-MgO_Rock. Only weak correlations have been found between chlorite oxides and other oxides of rock (between same oxides in chlorite and rock: SiO₂−0.67, Al₂O₃ + 0.59, FeO −0.41). However, MgO_Chl is saturated at about 36 wt% in rocks that have MgO above 22 wt%.The MgO_Chl is about 5 wt% when the host rock approaches 0 wt% of MgO. This implies that Mg substituting into the chlorite is approximately limited to 1.5–9.2 Mg atoms per formula unit and 1.0–3.2 Al^IV. Chlorite geothermometers can not be applied to all BGB samples. However, the empirical chlorite geothermometer based on Al^IV of chlorite may be applicable to chlorites formed under metamorphic conditions because it can predict the chemical composition of the chlorite from basaltic and dacitic samples in this study. An estimated temperature of about 320°C for the greenschist metamorphism of the greenstone belt through this geothermometer is consistent with that obtained by other geothermometers. Received: 22 January 1996 / Accepted: 15 August 1996     

Characterization of NH4-phlogopite (NH4) (Mg3) [AlSi3O10] (OH)2 and ND4-phlogopite (ND4) (Mg3) [AlSi3O10] (OD)2 using IR spectroscopy and Rietveld refinement of XRD spectra

 A synthesis technique is described which results in >99% pure NH₄-phlogopite (NH₄) (Mg₃) [AlSi₃O₁₀] (OH)₂ and its deuterium analogue ND₄-phlogopite (ND₄) (Mg₃) [AlSi₃O₁₀] (OD)₂. Both phases are characterised using both IR spectroscopy at 298 and 77 K as well as Rietveld refinement of their X-ray powder diffraction pattern. Both NH₄ ⁺ and ND₄ ⁺ are found to occupy the interlayer site in the phlogopite structure. Absorption bands in the IR caused by either NH₄ ⁺ or ND₄ ⁺ can be explained to a good approximation using T_d symmetry as a basis. Rietveld refinement indicates that either phlogopite synthesis contains several mica polytypes. The principle polytype is the one-layer monoclinic polytype (1M), which possesses the space group symmetry C2/m. The next most common polytype is the two-layer polytype (2M ₁ ) with space group symmetry C2/c. Minor amounts of the trigonal polytype 3T with the space group symmetry P3₁12 were found only in the synthesis run for the ND₄-phlogopite. Electron microprobe analyses indicate that NH₄-phlogopite deviates from the ideal phlogopite composition with respect to variable Si/Al and Mg/Al on both the tetrahedral and octahedral sites, respectively, due to the Tschermaks substitution ^VIMg²⁺+^IVSi⁴⁺↔^VIAl³⁺+^IVAl³⁺ and with respect to vacancies on the interlayer site due to the exchange vector ^XII(NH₄)⁺+^IVAl³⁺↔^XII□+^IVSi⁴⁺. Received: 30 August 1999 / Accepted: 2 October 2000     

Computational study of tetrahedral Al–Si ordering in muscovite

 The nature of Al–Si ordering across the tetrahedral sites in muscovite, K₂Al₄(Si₆Al₂O₂₀)(OH)₄, was investigated using various computational techniques. Values of the atomic exchange interaction parameters J _l were obtained. From these parameters, a two-dimensional Al–Si ordering scheme was deduced. The transition temperature T _c for this two-dimensional ordering is 1900 K. There are several possible ordering schemes in three dimensions, based on different stacking sequences of ordered sheets of tetrahedral sites. Monte Carlo simulations of both two-dimensional and three-dimensional ordering were performed, but in the three-dimensional simulation only the two-dimensional ordering is seen, implying that three-dimensional ordering is too slow to be attained during the timescale of the simulation. The effect of the three-dimensional interactions is to raise the two-dimensional ordering temperature to 2140 K. From the three-dimensional Monte Carlo simulation, the frequency of occurrence of 4Si0Al, 3Si1Al, 2Si2Al and 1Si3Al clusters was determined, which match those inferred by ²⁹Si MAS–NMR measurements reasonably well. In fact, the match suggests that the cation ordering seen in experiments corresponds to a configuration with considerable short-range order but no long-range order, similar to a state that is at a temperature just above an ordering phase transition. Received: 28 August 2000 / Accepted: 12 March 2001     

Germanium crystal chemistry in hematite and goethite from the Apex Mine,Utah, and some new data on germanium in aqueous solution and in stottite

At the Apex Mine in southwest Utah, fine-grained hematite contains as much as 1.0 wt. percent Ge, and fine-grained goethite contains as much as 0.7 wt. percent Ge. The mode of Ge incorporation in these minerals was investigated by high-resolution K-edge fluorescence spectroscopy using synchrotron radiation. Analysis of extended fine structure (EXAFS) K-edge data for Ge and Fe shows that Ge substitutes for Fe in the octahedral metal sites of the studied hematite and goethite, with average Ge-ligand bond lengths of 1.88 Å. The solid solution in hematite probably occurs through the coupled substitution 2Fe(III) = Ge(IV) + Fe(II), similar to the coupled substitution 2Fe(III) = Ti(IV) + Fe(II) that occurs in the solid solution series hematite-ilmenite. The solid solution in goethite probably occurs by the loss of an H atom from an OH group, through the coupled substitution Fe(III) + H(I) = Ge(IV). In related experiments, EXAFS data indicate that in a neutral aqueous solution containing 790 ppm Ge, the Ge occurs predominately as Ge(OH)₄, with tetrahedral Ge-OH bond lengths of 1.74 Å. In stottite, FeGe(OH)₆, Fe(II) and Ge(IV) occur in octahedral sites with average Fe-OH and Ge-OH bond lengths of about 2.20 Å and 1.88 Å.     

Cation distribution and structure modelling of spinel solid solutions

 This paper presents an improved generalisation of cation distribution determination based on an accurate fit of all crystal-chemical parameters. Cations are assigned to the tetrahedral and octahedral sites of the structure according to their scattering power and a set of bond distances optimised for spinel structure. A database of 295 spinels was prepared from the literature and unpublished data. Selected compositions include the following cations: Mg²⁺, Al³⁺, Si⁴⁺, Ti⁴⁺, V³⁺, Cr³⁺, Mn²⁺, Mn³⁺, Fe²⁺, Fe³⁺, Co²⁺, Ni²⁺, Zn²⁺ and vacancies. Bond distance optimisation reveals a definite lengthening in tetrahedral distance when large amounts of Fe³⁺ or Ni²⁺ are present in the octahedral site. This means that these cations modify the octahedral angle and hence the shared octahedral edge, causing an increase in the tetrahedral distance with respect to the size of the cations entering it. Some applications to published data are discussed, showing the capacity and limitations of the method for calculating cation distribution, and for identifying inconsistencies and inaccuracies in experimental data. Received: 19 February 2001 / Accepted: 1 June 2001     

Computational study of tetrahedral Al–Si and octahedral Al–Mg ordering in phengite

 As part of a wider study of the nature and origins of cation order–disorder in micas, a variety of computational techniques have been used to investigate the nature of tetrahedral and octahedral ordering in phengite, K₂ ^[6](Al₃Mg)^[4](Si₇Al)O₂₀(OH)₄. Values of the atomic exchange interaction parameters J _n used to model the energies of order–disorder were calculated. Both tetrahedral Al–Si and octahedral Al–Mg ordering were studied and hence three types of interaction parameter were necessary: for T–T, O–O and T–O interactions (where T denotes tetrahedral sites and O denotes octahedral sites). Values for the T–T and O–O interactions were taken from results on other systems, whilst we calculated new values for the T–O interactions. We have demonstrated that modelling the octahedral and tetrahedral sheets alone and independently produces different results from modelling a whole T–O–T layer, hence justifying the inclusion of the T–O interactions. Simulations of a whole T–O–T layer of phengite indicated the presence of short-range order, but no long-range order was observed. Received: 8 August 2002 / Accepted: 14 February 2003 Acknowledgements The authors are grateful to EPSRC (EJP) and the Royal Society (CIS) for financial support. Monte Carlo simulations were performed on the Mineral Physics Group's Beowulf cluster and the University of Cambridge's High Performance Computing Facility.     

Influence of structural factors on 29Si and 27Al NMR chemical shifts of phyllosilicates 2:1

The ²⁹Si and ²⁷Al nuclear magnetic resonance (NMR) analysis of synthetic trioctahedral phyllosilicates 2:1, with tetrahedral ratios Al _T/(Si + Al _T) ranging from 0 to 0.5, has shown that the ditrigonal distortion of tetrahedral rings (angle ) is the main factor controlling chemical shift values of tetrahedral components in both signals. The increase of ditrigonal rotation angle shifts these components towards more positive values. For each sample, the composition of tetrahedral and octahedral sheets determine the value of , and from this parameter, the mean tetrahedral Tot angle and the chemical shift values of components are deduced. For a given environment, variations on ditrigonal angle are responsibles for the observed evolution of chemical shift values with bulk composition. The comparative analysis of micas and saponite samples has demonstrated that the location of compensating charge (interlayer and octahedral sheet) does not affect chemical shift values.