Cation ordering in amesite-2H2 from Antarctica has reduced the true symmetry from the ideal hexagonal space group P63 to triclinic P1. All crystals show 6-fold biaxial twin sectors on (001), and the twinned crystals produce an average diffraction symmetry that is hexagonal. Individual twin sectors cut from the larger aggregate have 2 V optic angles near 18°, slightly monoclinic unit-cell geometry, and triclinic diffraction symmetry. Structural refinement of an untwinned sector in subgroup symmetry shows nearly complete ordering of Si,Al in tetrahedral sites and of Mg, Al in octahedral sites.

In triclinic symmetry the two layers in the unit cell are no longer equivalent. Tetrahedra lying on the pseudo-63 screw axis are alternately Si-rich and Al-rich in adjacent layers. Of the three octahedral sites in each layer, one is smaller than the other two and is interpreted as Al-rich. The distribution of Al-rich and Mg-rich octahedra violates both the pseudo-3-fold rotation axis within each layer and the pseudo-63 screw axis that relates one layer to the next in the ideal space group. Local charge balance is achieved in adjacent layers by location of all tetrahedral and octahedral Al in lines parallel to X1 and spaced at intervals of b1/2. Similar charge balance patterns parallel to X2 and X3 are postulated to account for the sector twinning, which has been observed also in amesites from Chester, Massachusetts, USA, Saranovskoye, USSR, and Postmasburg, South Africa.

Long-range ordering of tetrahedral cations in micas is favored by phengitic compositions, by the 3T stacking sequence of layers, and by tetrahedral Si:Al ratios near 1:1. Phengites of the 1M, 2M1, and 2M2 polytypes are said to show partial ordering of tetrahedral cations, although the amounts of tetrahedral substitutions are small and the accuracies of determination are not as large as desired. The 3T structures of muscovite, paragonite, lepidolite, and protolithionite show tetrahedral ordering, as do the 2M1 brittle micas margarite and an intermediate between margarite and bityite. Muscovite-3T and margarite-2M1 are also slightly phengitic relative to their ideal compositions. Examples of octahedral cation ordering in micas are more abundant and are to be expected when cations of different size and charge are present. Octahedron M(1) with its OH,F groups in the trans orientation tends to be larger than the mean of the two cis octahedra as a result of the ordering of cations and vacancies. In some samples ordering has reduced the true symmetry to a subgroup of that of the ideal space group. If ordering in subgroup symmetry results in ordered patterns of different geometries but similar energies in very small domains, the average over all unit cells may simulate long-range disorder.

The crystal structure of a magnesian cronstedtite-2H2 from Pribram, Czechoslovakia, was refined in space group C1 to a residual of 5.4% with 1832 independent reflections. Tetrahedral ordering between Fe3+ and Si is judged to be complete on the basis of electron density maps, the first confirmation of such ordering in a layer silicate. Octahedral cations are disordered on the M sites. Mean T-O bond lengths do not confirm the tetrahedral ordering, perhaps due to tetrahedral distortion in order to relieve the extreme corrugation of the sheet that would arise from ordering of such different size cations.

In the initial stages of refinement the structure of the crystal under study could not be described adequately on the basis of a single 2H2 polytype. The structure contains two kinds of 2H2 domains that appear shifted by b/3 relative to one another due to a mistake in the interlayer stacking sequence. This mistake of zero shift (the normal 2H2 polytype consists of alternating —b/3 and +b/3 shifts) affects only the tetrahedral sheets. It creates adjacent enantiomorphic domains of 2H2 packets such that domains with small Si tetrahedra sit above larger Fe3+-rich tetrahedra and vice versa. This mechanism to relieve strain may indeed be the cause of the stacking mistakes. A third kind of domain contains regions in which the sense of tetrahedral rotation is reversed, giving rise to split basal oxygens on electron density maps. This multiple domain model best explains extra atomic positions observed on Fourier maps, lack of streaking of k ≠ 3n reflections, and possible nonintegral “satellitic” reflections observed on Weissenberg films.

The crystal structure of phengite-2M1 from Rio de Oro, Spanish Sahara, was refined in space group C2/c to a residual of 3.3% with 1267 independent X-ray diffraction reflections. The composition of the mica determined by electron microprobe analysis is (K0.948Na0.051Ba0.027)(Al1.510Mg0.273Fe0.144Cr0.095Ti0.010Mn0.003)2.035(Si3.253Al0.747)O10(OH)2. The cell dimensions are a = 5.2153(5), b = 9.043(2), c = 19.974(9) Å, β = 95.789(9)°, and V = 937.2(3) Å3. The substitution of Si for Al in the tetrahedral sheet and larger divalent cations for Al in the octahedra allows the amount of distortions that are generally required to alleviate tetrahedral-octahedral sheet lateral misfit in muscovite, such as tetrahedral rotation and octahedral flattening, to be reduced. The O…H vector is nearly horizontal and points slightly into the octahedral sheet where it may be involved in hydrogen bond contacts inside M(1). In contrast to previously reported refinements of all but one other phengite, no ordering of tetrahedral cations was found in the study specimen. This disorder is considered to be due to the low-pressure, high-temperature amphibolite facies environment of crystallization.

A monoclinic IIb-2 clinochlore from the Achmatov mine, Ural Mountains, U.S.S.R., was investigated by neutron diffraction. The formula, based on electron microprobe and wet chemical analyses, is (Mg4.54Al0.97Fe2+ 0.28 Fe3+ 0.18Mn0.01)(Si2.85Al1.15)O10(OH)8. A refinement based on 512 unique reflections converged in space group C2/m to a final R =.066. Cation disorder was found in the two octahedral positions of the 2:1 layer, whereas partial Mg and Al ordering occurs in the interlayer sheet. The two hydroxyl dipoles are roughly perpendicular to the interlayer sheet, forming weak to medium hydrogen bonds with O…O distances of 2.859 and 2.881 Å. The OH-dipole of the 2:1 layer is perpendicular to the (001) plane.

Double hydroxide solids precipitated homogeneously from three laboratory-synthesized aqueous solutions that simulated mildly contaminated surface or groundwater. Over a limited pH range, precipitates formed rapidly from dissolved ions, and more slowly by incorporating ions dissolving from other solids, including highly soluble aluminous solids. The precipitates were characterized by size and shape via transmission electron microscopy (TEM), by composition via inductively coupled plasma-mass spectrometry (ICP-MS) of mother solutions and analytical electron microscopy (AEM) of precipitates, and by structure via powder X-ray diffraction (XRD), TEM, and extended X-ray absorption fine structure (EXAFS) spectroscopy. They were identified as nanocrystalline cobalt hydrotalcite (CoHT) of the form [Co(II)1-xAl(III)x(OH)2]x+(An−x/n)·mH2O, with x = 0.17–0.25, A = CO32−, NO3−, or H3SiO4−n = anion charge and m undetermined. Complete solid solution may exist at the macroscopic level for the range of stoichiometrics reported, but clustering of Co atoms within hydroxide layers indicates a degree of immiscibility at the molecular scale. Composition evolved toward the Co-rich endmember with time for at least one precipitate. The small layer charge in the x = 0.17 precipitate caused anionic interlayers to be incomplete, producing interstratification of hydrotalcite and brucite-like layers. Solubility products estimated from solution measurements for the observed final CoHT stoichiometries suggest that CoHT is less soluble than the inactive forms of Co(OH)2 and CoCO3 near neutral pH. Low solubility and rapid formation suggest that CoHT solids may be important sinks for Co in contact with near neutral pH waters. Because hydrotalcite can incorporate a range of transition metals, precipitation of hydrotalcite may be similarly effective for removing other trace metals from natural waters.

The crystal structure of a natural, ordered IIb-4 triclinic clinochlore has been refined in space group C1̄ from 4282 unique X-ray intensity measurements of which 3833 are greater than 3 times the statistical counting error (3σ). Unit cell parameters are a = 5.3262(6) Å; b = 9.226(1) Å; c = 14.334(3) Å; α = 90.56(2)°; β = 97.47(2)°; and γ = 89.979(9)°, which represents the greatest deviation from mono-clinic symmetry yet recorded for a triclinic chlorite. The final weighted R is 0.059 for reflections with I > 3σ and 0.064 for all reflections. The chemical formula is (Mg0.966Fe0.034)MI(Mg0.962Fe0.038)M22(Si2.96Al1.04)O10 (OH)2(Mg0.996Fe0.004)M32(Al0.841FeIII0.102Cr0.004Ti0.004)M4(OH)6, which is consistent with electron microprobe (EMP), wet chemical analyses, Mössbauer spectroscopy and X-ray structure refinement. The high degree of ordering of the divalent versus trivalent octahedral cations in the interlayer is noteworthy, with FeIII and Al in M4 and virtually no Fe in M3. In the 2:1 layer, M1 and M2 each contain similar amounts of Fe. The 2 tetrahedral sites have nearly identical mean oxygen distances and volumes, and thus show no evidence of long-range cation ordering.

A combined powder X-ray diffraction (XRD) and X-ray absorption (XAS) study of Fe(III) cation ordering within pyroaurite is described. It is concluded that there is no correlation between Fe(III) cation positions over distances of a few tens of angstroms, but that there is a very high level of local ordering, involving the absence of Fe(III)-Fe(III) neighbors. These observations are rationalized in terms of a significant frequency of lattice defects in the form of cation vacancies or Mg for Fe(III) substitutions. These results are expected to be generalizable to other M(II)/M(III) layered double hydroxides (LDHs), but are in contrast to the long-range cation ordering observed in Li/Al LDHs. This raises the interesting possibility of differing properties and stabilities based on the degree of cation ordering.

The order-disorder behavior of the isomorphous cation substitution of the octahedral sheet of phyllosilicates was investigated by Monte Carlo simulations based only on atomistic models in some three-species systems Al/Fe/Mg including a wide range of different octahedral compositions that can be relevant to clay compositions found in nature, especially for smectites and illites. In many cases, phase transitions do not occur, in that long-range order is not attained, but most systems exhibit short-range order at low temperature. The ordering of the octahedral cations is highly dependent on the cation composition. Variations in the tetrahedral charge (smectite vs. illite) produce slight differences in the cation distribution and the short-range and long-range order of octahedral cations do not change drastically. The average size of Fe clusters and the long-range order of Fe are not larger in illites than in smectites as previous reports concluded, but the proportion of Fe3+ cations non-clustered is higher in smectites than in illites. This behavior supports the experimental behavior of the Fe effect on the Al-NMR signal, which is lower in illites than in smectites.

Layered double hydroxides (LDH) are extremely important materials for industrial processes and in the environment, and their physical-chemical behavior depends in large part on their hydration state, but the characterization of these hydration effects on their properties are incomplete. The present study was designed to explore the interpolytype transitions induced by variation in the ambient humidity among LDHs. The cooperative behavior of intercalated water molecules resulted in a sudden, single-step, reversible dehydration of the [Zn-Cr-SO4] LDH. The [Zn-Al-SO4] LDH provided an interesting contrast with (1) the coexistence of the end members of the hydration cycle over the 40-20% relative humidity range during the dehydration cycle, and (2) a random interstratified intermediate in the hydration cycle. These observations showed that the [Zn-Al-SO4] LDH offered sites having a range of hydration enthalpies, whereby, at critical levels of hydration (20–40%), the non-uniform swelling of the structure resulted in an interstratified phase. The variation in domain size during reversible hydration was also responsible for the differences observed in the hydration vs. the dehydration pathways. This behavior was attributed to the distortion in the array of hydroxyl ions which departs from hexagonal symmetry on account of cation ordering as shown by structure refinement by the Rietveld method. This distortion was much less in the [Zn-Cr-SO4] LDH, whereby the nearly hexagonal array of hydroxyl ions offered sites of uniform hydration enthalpy for the intercalated water molecules. In this case, all the water molecules experienced the same force of attraction and dehydrated reversibly in a single step. The changes in basal spacing were also accompanied by interpolytype transitions, involving the rigid translations of the metal hydroxide layers relative to one another.

Different types of dioctahedral smectites (nontronite, beidellite, montmorillonite) were investigated by X-ray fluorescence analysis (XRF) and Fourier transmission infrared spectroscopy (FTIR). Starting with the chemical composition of the octahedral sheet, the occupancies within the octahedral sheet were adjusted by computer simulations to fit the occupancies derived from FTIR. For both cis-and trans-vacant smectites the AlAl and FeFe pairs are mainly randomly distributed but seem to be aligned along OH-bonded directions. Relative to the chemical composition, AlFe pairs are enriched in cis-vacant smectites and depleted in nontronites. This behaviour can be explained by the necessity to dehydrate and hydrolyse cations when they become incorporated into the structure during crystal growth. The first and second hydrolysis steps are necessary for incorporating cations in trans-vacant smectites, whereas only the first hydrolysis step is necessary for cis-vacant smectites. The corresponding difference in energy may explain why mostly cis-vacant smectites occur in low-temperature environments.

Intermediate compositions along the bornite–digenite join exsolve during quenching from above-solvus temperatures. This involves vacancy clustering and cation ordering processes, and is facilitated by fast cation diffusion rates in the presence of a large (10–25%) metal vacancy population. Samples of six different compositions across the bornite–Cu9S5 join, synthesised from component elements in sealed quartz capsules, were water-quenched from 600°C and analysed using high-resolution neutron powder diffraction (HRPD). Time-of-flight spectra measured at room temperature showed all intermediate compositions had exsolved into mixtures of bornite and low digenite with a 5.0a superstructure. No evidence for the presence of any other phase was found. Variations in the lattice parameters of the exsolved bornite phase were observed for different bulk compositions across the join, and ascribed to variations in the degree of order. Bornite exsolved from digenite-rich compositions may not be fully ordered due to the much lower solvus temperatures at the Cu-rich end of the solid solution. As only slight differences were observed between the diffraction patterns of a visibly exsolved and a rapidly quenched sample of the same bulk composition, the formation of optically-visible exsolution lamellae on {100} is ascribed to a process of coalescence of sub-microscopic domains initially formed during the quenching process. The rapid kinetics of exsolution at geologically low temperatures, explains the lack of authenticated natural occurrences of intermediate compositions in the solid solution in nature, and the limited degree of stoichiometric variation observed in end-members.

The crystal structure of quintinite-2H-3c, [Mg4Al2(OH)12](CO3)(H2O)3, from the Kovdor alkaline massif, Kola peninsula, Russia, was solved by direct methods and refined to an agreement index (R1) of 0.055 for 484 unique reflections with |Fo| ≥ 4σF. The mineral is rhombohedral, R32, a = 5.2745(7), c = 45.36(1) Å. The diffraction pattern of the crystal has strong and sharp Bragg reflections having h–k = 3n and l = 3n and lines of weak superstructure reflections extended parallel to c* and centred at h–k ≠ 3n. The structure contains six layers within the unit cell with the layer stacking sequence of …AC=CA=AC=CA=AC=CA… The Mg and Al atoms are ordered in metal hydroxide layers to form a honeycomb superstructure. The full superstructure is formed by the combination of two-layer stacking sequence and Mg-Al ordering. This is the first time that a long-range superstructure in carbonate-bearing layered double hydroxide (LDH) has been observed. Taking into account Mg-Al ordering, the unique layer sequence can be written as …=Ab1C=Cb1A=Ab2C=Cb2A=Ab3C=Cb3A=… The use of an additional suffix is proposed in order to distinguish between LDH polytypes having the same general stacking sequence but with different c parameters compared with the ‘standard’ polytype. According to this notation, the quintinite studied here can be described as quintinite-2H-3c or quintinite-2H-3c[6R], indicating the real symmetry.

The systematics of cation ordering in binary spinel solid solutions have been investigated using an interatomic potential model combined with Monte Carlo simulations. The formalism to describe a system containing three cation species ordering over two non-equivalent sub-lattices is developed and the method applied to the MgAl2O4-FeAl2O4 binary solid solution. Our results compare favourably with experimental measurements of site-occupancy data, although the experiments display a slightly larger degree of non-ideality than the simulations. A possible kinetic origin of the non-ideal behaviour was examined by performing simulations in which only exchange of Mg and Fe2+ between tetrahedral and octahedral sites was permitted below the Al-blocking temperature of 1160 K. This approach improves the agreement with the experimental site occupancies, and suggests that the blocking temperature for moving Mg and Fe2+ between tetrahedral and octahedral sites is significantly lower than for moving Al

The original structure determination of asisite, nominally Pb7SiO8Cl2, has been re-evaluated in the light of electron-diffraction data (TEM) on the original sample material. Electron diffraction patterns indicate a super-structure based upon a metrically tetragonal 26-cation-site super-sheet motif (14x14x23 Å). Given the strong ordering of elements substituting for Pb in closely-related litharge-based oxychlorides (parkinsonite, symesite, kombatite, schwartzembergite), the asisite superstructure is inferred to be due to strong ordering of Si within the PbO sheet. The original chemical analyses of asisite given by Rouse et al. (1988) are shown to be consistent with such a super-structure, which has a 12Pb:1Si cation ratio. A new formula for asisite is proposed that is based upon this superstructure: Pb12(SiO4)O8Cl4 (Z = 8). The structure of asisite determined by Rouse et al. (1988) is that of the average Pb/Si-disordered tetragonal sub-cell (I4/mmm: 4x4x23 Å) and belies the highly ordered real state. The structure of the tetragonal sub-cell has been re-determined here: R = 5.6% for 178 unique Fo > 4σFo and an anisotropic model. A significantly reduced 72% occupancy of the Pb(2) site was found that implies the nominal formula Pb7SiO8Cl2, thus confirming the findings of Rouse et al. (1988). Comparisons with kombatite and symesite support the assignment of Si to Pb(2) and imply that Si in asisite is also likely to be in tetrahedral coordination, with the apical oxygen cross-linking PbO sheets. However, because most of the key information relating to the location of Si is provided by the super-lattice reflections, the inability of X-ray diffraction to register these reflections introduces a significant ambiguity into the interpretation of Pb/Si ordering behaviour in this mineral.

The crystal chemistry of a natural, gem-quality, blue-grey Zn-rich spinel crystal from Jemaa, Kaduna State, Nigeria, was studied using electron microprobe, single-crystal X-ray diffraction, optical absorption and Raman spectroscopies. The composition of the crystal approaches the gahnite endmember (ZnAl2O4), ∼94 mol.%, with the remainder being dominated by a hercynite component (FeAl2O4). The unit-cell dimension is 8.0850(3) Å and the tetrahedral and octahedral bond distances are determined as T–O 1.9485(6) Å and M–O 1.9137(3) Å. Crystal chemical analysis resulted in the empirical structural formula T(Zn0.94Fe2+0.03Al0.03)M (Al1.96Fe2+0.03Fe3+0.01)O4, which shows Zn and Al almost fully ordered in the tetrahedrally and octahedrally coordinated T and M sites, respectively. Raman spectra obtained using the excitation of the blue 473.1 nm line of a Nd:YAG laser display three of the five Raman-active modes predicted for the general oxide spinel group of minerals. These are the Eg mode at 420.6 cm–1 and the T2g modes at 510 cm–1 and 661 cm–1, due to vibrations in the AlO6 octahedra. Optical absorption spectra recorded in the UV/VIS-NIR-MIR range 2000 29000 cm–1 show a dominant absorption band at ∼5000 cm–1 which is caused by spin-allowed electronic d–d transitions in Fe2+ located at the T sites. The blue-grey hue exhibited by the sample is mainly due to spin-forbidden electronic transitions in TFe2+ and to MFe2+ ↔MFe3+ intervalence charge transfer, and the poor saturation of the colour is due to the small concentration of Fe2+ and Fe3+.

The [4]Al/Si and [6]Al/Mg order-disorder behaviour of minerals in the tremolite-tschermakite solid solution (namely, end-member tschermakite and the 50:50 composition, magnesiohornblende) has been investigated by Monte Carlo simulation, using a model Hamiltonian in which atomic interaction parameters Ji were derived from empirical lattice energy calculations, and chemical potential terms μj (to express the preferences of cations for particular crystallographic sites) were derived from ab initio methods. The simulations performed were increasingly complex. Firstly, ordering in one tetrahedral double chain with Al:Si = 1:3 (tschermakite) was simulated. Although the low-temperature cation distribution in this system was ordered, there was no phase transition (due to the quasi-one-dimensional nature of the system). Next, interactions between tetrahedral Al:Si = 1:3 double chains were included, and a phase transition was observed, with the cation distribution in one double chain lining up with respect to that in the next. Finally, interactions between tetrahedral and octahedral sites were incorporated, to model the whole unit cell, and compositions corresponding to tschermakite and magnesiohornblende were investigated. The whole-cell simulation results compare favourably with experimental conclusions for magnesiohornblende, in that Al at T1 is preferred over Al at T2, and Al at M2 is favoured over that at M1 and M3, but the significant amount of Al at M1 is at odds with experimental observation.

The structural and thermodynamic properties of minerals are strongly affected by cation site-ordering processes. We describe methods to determine the main interatomic interactions that drive the ordering process, which are based on parameterizing model Hamiltonians using empirical interatomic potentials and/or ab initio quantum mechanics methods. The methods are illustrated by a number of case study examples, including Al/Si ordering in aluminosilicates, Mg/Ca ordering in garnets, simultaneous Al/Si and Mg/Al ordering in pyroxenes, micas and amphiboles, and Mg/Al non-convergent ordering in spinel using only quantum mechanical methods.

This paper reviews recent applications of Monte Carlo methods for the study of cation ordering in minerals. We describe the program Ossia99, designed for the simulation of complex ordering processes and for use on parallel computers. A number of applications for the study of long-range and short-range order are described, including the use of the Monte Carlo methods to compute quantities measured in an NMR experiment. The method of thermodynamic integration for the determination of the free energy is described in some detail, and several applications of the method to determine the thermodynamics of disordered systems are outlined.