A computer simulation study of Al/Si ordering in gehlenite and the paradox of the low transition temperature

The ordering of Al and Si in gehlenite is considered using computer simulation. The enthalpy of ordering ΔH per 2Al+2Si atoms is found to be 0.52 eV. It is dominated by the nearest neighbour interaction, but the analysis is carried out to fifth neighbours. The nearest neighbour interaction differs significantly from that for other materials. The structure does not have a connected network of ordering sites, which mainly accounts for the unobservably low transition temperature for Al/Si ordering. Two alternatives are given for the likely ordering pattern.     

Atomic ordering around the oxygen vacancies in sillimanite

Computer simulation is used to investigate the short range ordering around an isolated oxygen vacancy in sillimanite. The static lattice energy with the use of empirical potentials is calculated, for different Al/Si distributions around a vacancy in a supercell of sillimanite. A parametrisation of the total energy is built up and used to deduce the best Al/Si ordering around the oxygen vacancy. It is found that a strong ordering about the vacancy occurs. In the ab-plane two sets of aluminium cluster are found besides the vacancy, surrounded above and below by silicon atoms, a configuration that promotes local charge balance. By placing two vacancies on sites directly adjacent to the same oxygen, the central oxygen site is bonded to four cations: this situation is found to be energetically unfavourable.     

NMR-spectroscopy of synthetic potassium-bearing cordierites

Potassic cordierites with the chemical composition K _x Mg₂Al_4+x Si₅–xO₁₈ (x = 0.00, 0.10, 0.20, and 0.25) were synthesized by annealing glasses at 1290° C for different lengths of time. The procedure resulted in cordierites with different states of Al,Si-order for the tetrahedral sites in the structure. The dependence between the potassium-content and the state of order on one side and between annealing time and the state of order on the other side was then studied using ²⁹Si MAS nuclear magnetic resonance (NMR) spectroscopy. The spectra show that the state of order is a continuous function of annealing time for all compositions considered, but the rate of ordering decreases with increasing K-content. Since the substitution K+Al Si leads to higher Al/Si-ratios; the lower rate of ordering is discussed as a consequence of changed statistics for Al, Si site exchanges. The Al atoms replacing silicon in the structure to balance the charge of potassium cations are not located close to the potassium ion but at a maximum distance from it. This is shown to be a consequence of an improvement in coordination of all oxygen atoms in the cordierite framework.     

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     

Atomic movements in plagioclase feldspars: Kinetic interpretation

The diffraction, n.q.r. and optical data on plagioclase feldspars are used to derive kinetic interpretations of structural changes induced by laboratory heat treatment and by geological processes. For anorthite, the Si, Al configuration is essentially ordered except for unusual transient processes. Cooperation between Ca atoms, and random nucleation, produces a domain texture in the primitive structure which is highly sensitive to temperature. The rapid inversion from the primitive to the body-centered structure is explained by increasingly rapid “rattling” of the Ca ions in the interstices of the semi-flexible alumino-silicate framework. The weakening of “b” reflections at higher temperatures is ascribed to incipient Si, Al disorder associated with irregular vibration of the alumino-silicate framework and the Ca atoms. Quenching phenomena are explained by variation of the domain boundary texture inherited from disorder at high temperature. For albite, the Si, Al configuration changes sluggishly from an ordered to a disordered pattern, and vice versa. Kinetic data are reinterpreted using a model in which the cell dimensions depend on local rather than distant order: the major change in distant order is deduced to occur at 450–600° C. Sodic plagioclase grown at high temperature shows distant disorder of the atoms, but cell dimensions suggest development of strong local order for calcic compositions. Low-entropy plagioclases of intermediate composition show complex intergrowths and domain structures because of kinetic barriers to atomic diffusion. X-ray diffraction data for slowly-cooled specimens are consistent with nucleation of albite- and anorthite-like regions from a high-temperature disordered phase. Electrostatic energy calculations show that Na and Ca atoms, although they face smaller energy barriers for diffusion, cannot form domains until the Si and Al atoms have moved jointly. The Si, Al ordering patterns of low albite and anorthite are topologically incompatible in a continuous framework if oxygen is not to be bonded to two Al. Therefore domains of low-albite and anorthite must be separated by disordered boundaries. For intermediate compositions, An₁₅-An₇₅, domains remain small. The anorthite-like domains probably form at higher temperatures than the albite-like domains. The latter tend to be about the same size for all bulk compositions. The atomic positions are influenced by neighboring atoms. Upon heating rapidly, Si and Al atoms remain in position and provide a memory for reformation of an identical structure upon cooling. The framework changes shape, and some Na, Ca atoms inter-diffuse to yield a quasi-homogeneous structure with a diffraction pattern which qualitatively approaches that of high albite. Upon prolonged heating at high temperature, Si, Al atoms inter-diffuse producing nonquenchable changes to the high-albite structure. At Na-rich bulk compositions, some domains of low albite grow into large lamellae while others remain small in contact with anorthite domains producing alternate lamellae of intermediate structure type; hence the peristerite intergrowth. A similar but opposite process could cause an intergrowth of lamellae of anorthite structure interposed with an intermediate type structure. A unique low plagioclase series is not expected. Plagioclases of intermediate composition trend towards slightly different endproducts depending on the details of the cooling history. Breaks and bends in plots of physical properties, and intergrowths for certain specimens, depend on special compositional, growth and annealing factors. The intergrowth responsible for iridescence of intermediate plagioclase is ascribed to Na, K segregation prior to development of the complex domain structure. Prolonged annealing at high temperature in a dry environment is suggested. It is futile to attempt to describe low entropy plagioclases in terms of classical thermodynamics: only a kinetic interpretation based on atomic and sub-microscopic textural factors can be viable.     

Sector trilling in cordierite and equilibrium overstepping in metamorphism

The origin of sector trilling in cordierite is due to the hexagonal-orthorhombic Al, Si ordering transformation which under non-equilibrium conditions proceeds via a short-range ordered modulated structure. The growth of these distortion waves associated with progressive ordering produces a strain field which is minimized by a cyclic distribution of symmetrically equivalent modulations.Sector and complexly trilled cordierites in metamorphic rocks grew as the hexagonal polymorph with a considerable degree of Al, Si disorder. The enthalpy and entropy of disorder are evaluated from recent experimental work. The implication is that, in metamorphic rocks, substantial overstepping of stable equilibrium phase boundaries is required to nucleate hexagonal cordierite. Moreover, its composition coexisting with other phases will also be significantly different from that of the stable ordered form.     

Octahedral cation ordering of illite and smectite. Theoretical exchange potential determination and Monte Carlo simulations

The distributions of Al ³⁺/Mg ²⁺ and Al ³⁺/ Fe ³⁺ were studied in the octahedral sheet of illites and smectites. Cation exchange interaction parameters J _i, as first, second, third and fourth neighbours were calculated by means of empirical interatomic potentials. Several compositions with different interlayer cations and tetrahedral charge were studied in both Al/Mg and Al/Fe systems. The values of J _i parameters were similar in all Al/Mg samples. From these J _i values, a strong trend to form AlMg pairs was observed in the Al/Mg system. In the Al/Fe system, the values of J _i are very small, indicating no preference for Al/Fe mixing. From these J _i parameters, Monte Carlo simulations of octahedral cation ordering were performed. In the Al/Mg system, an order/disorder phase transition was observed obtaining a fully ordered distribution without presence of an MgMg pair, according to experimental data. Similar phase transitions were observed for the octahedral compositions Al/Mg 1/1 and 3/1. In the Al/Fe system an order/disorder phase transition was also detected but at very low temperature for illite and smectite. Complete Al/Fe mixing is observed in the most stable ordered distribution. This is consistent with experimental results for synthetic Fe/Al smectites.     

Analysis of cation distribution in the octahedral sheet of dioctahedral 2:1 phyllosilicates by using inverse Monte Carlo methods

An inverse Monte Carlo (MC) method was developed to determine the distribution of octahedral cations (Al³⁺, Fe³⁺, and Mg²⁺) in bentonite illite–smectite (I–S) samples (dioctahedral 2:1 phyllosilicates) using FT–IR and ²⁷Al MAS NMR spectroscopies. FT–IR allows determination of the nature and proportion of different cation pairs bound to OH groups measuring the intensities of OH-bending bands. ²⁷Al MAS NMR data provide information about cation configuration because ²⁷Al MAS NMR intensity depends on Fe distribution. MC calculations based on FT–IR data alone show Fe segregation by short-range ordering (Fe clusters within 9 to 15?Å from a given Fe atom). Fe segregation increases with illite proportion. MC calculations based on IR and ²⁷Al NMR simultaneously yield similar configurations in which Fe clusters are smaller. The latter calculations fail to build appropriate cation distributions for those samples with higher number of illite layers and significant Fe content, which is indicative of long-range Fe ordering that cannot be detected by FT–IR and ²⁷Al MAS NMR. The proportion of Mg–Mg pairs is negligible in all samples, and calculations, in which the number of Mg atoms, as second neighbours, is minimised, create appropriate configurations.     

Molecular dynamics simulation of the effect of the Al-O-Al linkage on the P&1macr;-I&1macr; phase transition of anorthite

Molecular dynamics (MD) simulations of the influence of the Al-O-Al linkage on the P&1macr;-I&1macr; phase transition of pure anorthite (An) were carried out using two different types of structures with fully ordered (FO) and partially disordered (PD) arrangements of Al/Si in tetrahedral sites. Discontinuous changes in unit cell volumes and structure factors at the transition temperature were observed in FO-An but not in PD-An. These results show that the orders of the transitions of FO-An and PD-An are first and non-first, respectively. In both structures, the motions of the Ca atoms and the framework are strongly correlated with each other during the transition and Ca atoms dominate the system. Since high-temperature X-ray studies have shown that the transition of natural anorthite is non-first order, it is suggested that the natural anorthite has a partially disordered arrangement of Al and Si atoms. Received: 22 October 1998 / Revised, accepted: 12 March 1999     

Structural states of Mg cordierite III: Infrared spectroscopy and the nature of the hexagonal-modulated transition

The time evolution of the Al, Si ordering and the ferroelastic distortion of the Mg-cordierite structure are quantified on a local length scale by Hard Mode Infrared Spectroscopy (HMIS). The line profiles of various absorption peaks were measured at room temperature and at 80 K. Their integrated intensities, frequencies and half width are correlated with the interacting order parameters Q _od (Al, Si ordering), Q (displacive orthorhombic distortion) and their equivalent short-range analogs. It is shown that the phase transition between hexagonal and modulated cordierite is stepwise, as predicted earlier. The local structural state of quenched, modulated cordierite is essentially equivalent to that of the orthorhombic phase. A general concept is outlined which allows, in general, the independent determination of various interacting order parameters using HMIS.     

Cation ordering in BaAl2Ge2O8-feldspar: implications for the phase transition in anorthite

BaAl₂Ge₂O₈-Feldspar undergoes an order-disorder phase transition I2/c↔C2/m at T _tr ≈1690 K. The thermodynamics of the Al,Ge cation ordering process is described in terms of the compressible Ising model in mean field approximation. The mean field potential predicts a first order character of the phase transition. This is compared to antiferromagnetic ordering in a two-dimensional square Ising model with NN-pair interactions and four-spin interactions on alternating squares. Calculated order parameters and short range ordering are in good agreement with the corresponding properties observed in BaAl₂Ge₂O₈-feldspar by means of X-ray diffraction, hard mode infrared spectroscopy and TEM. Using known calorimetric data a similar model is postulated for Al,Si ordering in anorthite, CaAl₂Si₂O₈, for which the derived potential describes a transition with slightly stronger first order character at T _tr ≈1928 K. Received: 30 January 1998 / Revised, accepted: 29 August 1998     

Structure,formation, and decomposition of APB's in calcic plagioclase

In calcic plagioclase (Ca, Na) [(Al, Si) AlSi₂O₈] Al-Si ordering produces superstructures with periodic and non periodic antiphase boundaries (APB's). Crystals growing at high temperature close to the melting point and cooling fairly rapidly order by nucleation of ordered domains which grow, resulting in an irregular pattern of curved APB's (b plagioclase). A modulated structure with periodic APB's forms by continuous ordering at large undercooling below the critical ordering temperature (e plagioclase). During annealing APB's are eliminated by pairwise recombination of adjacent APB's to reduce strain energy along the boundaries thereby transforming nonstable e plagioclase into stable b plagioclase without change in chemical composition. This process is often accompanied by a chemical phase separation with APB's providing favorable surfaces for diffusion. Transformations are documented by transmission electron microscopy (TEM) micrographs illustrating the variation in morphology of APB patterns in igneous and metamorphic plagioclase. They are in agreement with Korekawa et al.'s (1978) model of intermediate plagioclase which relies on periodic stacking of basic units rather than wavelike modulations. The paper includes observations of a new type of satellite in Stillwater bytownite (‘h’ satellites) which are due to fine lamellar exsolution.     

Mechanisms of exsolution in sodic pyroxenes

The free energy curves for simple binary solid solutions with limited miscibility or atomic ordering have been combined to predict the phase relations and exsolution mechanisms for a system in which both ordering and exsolution are possible. The nature of the ordering process affects which exsolution mechanisms may be used. If the ordering is second (or higher) order in character then continuous mechanisms predominate and a ‘conditional spinodal’ (Alien and Cahn, 1976) can be described which operates between ordered and disordered end members. For a first order case, the ordered phase can only precipitate a disordered phase by nucleation and growth. Microstructures in omphacites observed by transmission electron microscopy include exsolution lamellae and antiphase domains and the relations between them in selected specimens have been used to interpret the exsolution mechanisms which operated under geological conditions. It appears that most omphacites undergo cation ordering, and then remain homogeneous or exsolve a disordered pyroxene by spinodal decomposition. The predominance of continuous mechanisms has been used to indicate that the C2/c→P2/n transformation may be second (or higher) order in character. A possible phase diagram for jadeite-augite is presented. It is based on the idea that there should be limited miscibility between the disordered end members at low temperatures and that the cation ordering at intermediate compositions (omphacite) is superimposed on a solvus. It is adequate to explain many of the observed microstructures and fits with petrographic evidence of broad two phase fields between impure jadeite and omphacite and between omphacite and sodic augite. The effect of adding acmite is analogous to increasing temperature so that the phase relations for jadeite-acmite-augite can also be predicted.     

Structural characterisation of the high-pressure phase CaAl4Si2O11

Single crystals of CaAl₄Si₂O₁₁ were synthesised at 1,500?°C and 14 GPa in a multi-anvil press, and the structure of the phase determined by single-crystal X-ray diffraction at room conditions. The structure-type is that of the “hexagonal barium ferrites”. The space group of the average structure is P6 ₃ /mmc and the cell parameters are a?=?5.4223(4) Å, c?=?12.7041(6) Å, V?=?323.28(5) ų, with Z?=?2, and its density is 3.905?g?cm^?3, which is reasonable for a high-pressure alumino-silicate phase. The 22 oxygen and two calcium atoms within the unit-cell form an approximate hexagonal-close-packed array. Ten of the twelve octahedral interstices within this array that have only oxygen atoms for apices are filled with Si and/or Al. M1 octahedra share edges to form a spinel-like sheet of octahedra. The average bond length ?=?1.833 Å suggests mixed occupancy by Si and Al. The M1 octahedral sheets are linked by shared corners to pairs of face-sharing M2 octahedra containing Al, with ?= 1.918 Å. The remaining two cations of the unit-cell contents statistically occupy four tetrahedrally-coordinated interstices, which occur as face-sharing pairs. The average bond length for these sites (1.742 Å) suggests that they are occupied by Al, although Si occupancy cannot be excluded by the data. It is proposed that only one interstice of each pair is locally occupied, with the possibility of some short-range ordering of such occupancies. Complete long-range order leading to the acentric space group P6 ₃ mc is excluded by the data, as is the possibility of the average structure being comprised of merohedral (0?0?0?1) twins of P6 ₃ mc symmetry.     

官地银金矿中锰的化学物相分析

根据官地银金矿中锰矿物的共生组合情况，引用Al（NO3）3溶液作碳酸锰矿物的选择性溶剂，H2SO4-KF-HF混合溶液作水锰矿、褐锰矿的选择性溶剂，于滤渣中测定软锰矿（包括少量硅酸锰矿物）。实验表明，所引方法适用于官地银金矿区锰矿物的相态分离，所得结果与外检结果一致，满足了矿床划带的实际需要。     

A computational study of Al/Si ordering in cordierite

The ordering of Al and Si in Mg cordierite Mg₂Al₄Si₅O₁₈ is considered using computer simulation. First the enthalpy of interaction J _ij between sites is derived by computer modelling 101 different Al/Si configurations and analysing their energies. They are compared with similar results for three other minerals and with ab initio calculations to assess the whole approach. Secondly the ordering process is studied using Monte Carlo simulation applied to the J _ij . The ordering phase transition temperature T _c is found as 1800°C in reasonable agreement with the experimental estimate of 1450° C. These are much lower than the estimate T _c(ABW)≈7600°C obtained from Bragg-Williams theory. Strong short-range order sets in below T _c(ABW), and the reasons for much lower temperature T _c of long-range ordering are discussed. Strong short-range also sets in very rapidly in a simulated anneal, in agreement with experiment. Thirdly an attempt is made to compare our calculated enthalpies directly with the results of NMR and calorimetry experiments, not completely successfully. A free energy ΔG≈4.6 eV for the activation barrier for ordering is suggested.     

Structural states of Mg-cordierite I: Order parameters from synchrotron X-ray and NMR data

The hexagonal to orthorhombic phase transition in synthetic Mg-cordierite has been studied by (i) measuring the spontaneous strain associated with the transition using Synchrotron X-ray powder diffraction and (ii) measuring the degree of Al, Si order in terms of the number of Al-O-Al bonds per formula unit using solid state NMR spectroscopy. This defines the two order parametersQ andQ _od respectively, and their relationship as a function of annealing temperature and time is used to define the structural states of cordierite during the ordering sequence. The formation of modulated hexagonal cordierite within which a high degree of Al, Si order can be attained, results in a strongly non-linear relationship betweenQ andQ _od .The transition from modulated to orthorhombic cordierite is strongly first-order under all temperature conditions studied and involves a large step inQ, whileQ _od changes continuously throughout the ordering sequence with no marked discontinuity at the phase transition. The lattice distortion, traditionally defined in cordierite by the Δ index provides no full information on the degree of Al, Si order in anhydrous Mg-cordierite, and both order parameters must be used to define its structural state. Transmission electron microscopy has been used to study the mechanism of the transformation from hexagonal to modulated to orthorhombic cordierite.     

Probing the local environment of substitutional Al$$^{}$$ in goethite using X-ray absorption spectroscopy and first-principles calculations

We present experimental and calculated Al K-edge X-ray absorption near-edge structure (XANES) spectra of aluminous goethite with 10–33 mol% of AlOOH and diaspore. Significant changes are observed experimentally in the near- and pre-edge regions with increasing Al concentration in goethite. First-principles calculations based on density functional theory (DFT) reproduce successfully the experimental trends. This permits to identify the electronic and structural parameters controlling the spectral features and to improve our knowledge of the local environment of \(\hbox {Al}^{3+}\) in the goethite–diaspore partial solid solution. In the near-edge region, the larger peak spacing in diaspore compared to Al-bearing goethite is related to the nature (Fe or Al) of the first cation neighbours around the absorbing Al atom (Al*). The intensity ratio of the two near-edge peaks, which decreases with Al concentration, is correlated with the average distance of the first cations around Al* and the distortion of the \(\hbox {AlO}_6\) octahedron. Finally, the decrease in intensity of the pre-edge features with increasing Al concentration is due to the smaller number of Fe atoms in the local environment of Al since Al atoms tend to cluster. In addition, it is found that the pre-edge features of the Al K-edge XANES spectra enable to probe indirectly empty 3d states of Fe. Energetic, structural and spectroscopic results suggest that for Al concentrations around 10 mol%, Al atoms can be considered as isolated, whereas above 25 mol%, Al clusters are more likely to occur.     

Ca- and Mg-perovskite phases in the Earth’s mantle as a probable reservoir of Al: Computer-simulation evidence

Semi-empirical and quantum chemical studies of Al atom energy in CaSiO₃ and MgSiO₃ with the perovskite-type structure at pressures and temperatures of the Earth’s mantle are reported. The phase diagram for CaSiO₃ is reproduced and refined. Probable mechanisms of Al incorporation in the structures studied are considered. According to the results of the calculations, Al is preferably incorporated into MgSiO₃, rather than into CaSiO₃. Evaluation of the isomorphic capacity of perovskite phases in relation to Al shows that the Al content in MgSiO₃ may reach 2.4 mol % at 120 GPa and 2400 K. CaSiO₃ cannot be a source of Al atoms in the Earth’s mantle.     

桐庐杂岩体中共存的两种碱性长石研究

桐庐同熔型火山－侵入杂岩中出现两种碱性长石，一种为无色透明，另一种为微红色，本文利用X射线衍射仪，电子探针，透射电镜对其结构态，成分及出溶微结构进行了对比研究。结果表明，两者成分差别不大，而结构差别较大，无色透明的为透长石，出溶叶片发育；微红色的为正长石或低透长石，出溶结构不发育。而且随着冷却速率的变慢，无色透明碱性长石的Al/Si有序度增大，微红色碱性长石的有序度降低，分析后认为这种共存现象是岩浆混和造成的，从而为桐庐杂岩体的岩浆混合成因提供了有力的证据。