On the theory of Al,Si ordering in albite

Calculations of the equilibrium distribution of Al, Si in the albite framework based on quasi-chemical theories of order, disorder transformations (Yang 1945; Yang and Li 1947; Li 1949) were made for a two-dimensional framework model. The ordering is caused by the energy of Al, Si interchange between sites of different crystal-chemical types and the energy of nearest neighbour interaction. By taking into account the decrease in the energy of interchange between sites with increasing disordering and with increasing temperature, and by examining different relationships for site-to-site interchange energy and the nearest neighbour interaction, it is possible to understand the basic characteristics of the transformation from low (essentially ordered) to high (essentially disordered) albite as revealed by experiment. These characteristics are: (1) abrupt variation of the equilibrium degree of order within a narrow temperature range and possible first order phase transformation for the transition from low-albite to high-albite, (2) hysteresis of the synthetic high albite transformation path and of the low albite hydrothermal “annealing” path, (3) presence of a temperature range where high albite is stable and has a continually changing equilibrium degree of order.     

Computer modelling of Al/Si ordering in sillimanite

Computer simulation is used to investigate the effect of Al/Si disordering over the tetrahedral sites on the lattice energy and the lattice constants of the mineral sillimanite Al₂SiO₅. A methodology for an atomistic assessment of the energy of the reaction 2(Si-O-Al)→(Si-O-Si)+(Al-O-Al) and its various contributions is established. This ordering energy is 0.97 eV for nearest neighbour sites in the ab-plane and 0.56 eV for those separated in the c-direction. The large difference is due to a greater constraint on the atomic relaxation in the ab-plane and shows the structural dependence of the ordering energy. Its magnitude appears to be determined by a complicated balance between Coulomb and short-range repulsive energy involving strain over many bonds, both in the ordered and disordered structures. There is also a significant interaction between second neighbour sites whereas the contribution of more distant neighbours is negligible. The lattice energies of most of the 154 configurations studied show a linear behaviour as a function of short-range order, specified by the number of Al-Al pairs. The ordering temperature T_c, estimated on the basis of a statistical mechanical model of disordering, and the calculated ordering energies are in semi-quantitative agreement with experimental values.     

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     

Molecular dynamics study of the structures and bulk moduli of crystals in the system CaO-MgO-Al2O3-SiO2

Molecular dynamics (MD) simulations have been used to calculate the structures and bulk moduli of crystals in the system CaO-MgO-Al₂O₃-SiO₂ (CMAS) using an interatomic potential model (CMAS94), which is composed of pairwise additive Coulomb, van der Waals, and repulsive interactions. The crystals studied, total of 27, include oxides, Mg meta- and ortho-silicates, Al garnets, and various Ca or Al bearing silicates, with the coordination number of cations ranging 6 to 12 for Ca, 4 to 12 for Mg, 4 to 6 for Al, and 4 and 6 for Si. In spite of the simplicity of the CMAS94 potential and the diversity of the structural types treated, MD simulations are quite satisfactory in reproducing well the observed structural data, including the crystal symmetries, lattice parameters, and average and individual nearest neighbour Ca-O, Mg-O, Al-O, and Si-O distances. In addition MD simulated bulk moduli of crystals in the CMAS system compare well with the observed values.     

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.     

Determination of the origin and magnitude of Al/Si ordering enthalpy in framework aluminosilicates from ab initio calculations

Ab initio total energy calculations based on a new optimised oxygen pseudopotential has been used to determine the enthalpy of disorder for the exchange of Al and Si in tetrahedral coordination in simple derivative aluminosilicate structures based on the high temperature tridymite structure. The problem has been studied as a function of defect interaction, and defect concentration, and the results indicate that the energy for Al/Al neighbouring tetrahedra can be assigned primarily to two effects, the first, a coulombic effect, associated with the disturbed charge distribution, and the second associated with the strain related to misfit due to the very different dimensions of the Si and Al containing tetrahedra. In practice each of these effects contributes approximately 0.2 eV per Al−Al neighbour to the overal disorder enthalpy. These simple results were obtained after a careful study of possible chemical interaction between adjacent Al/Si containing tetrahedra which showed that chemical interaction was effectively absent. Since individual Al/Si tetrahedra proved to be discrete entities that are individually heavily screened by the shared oxygens it follows that coulombic and strain effects in disorder effectively account for the whole of the disorder enthalpy. The complete set of results have been used to establish new criteria for the structure and disorder enthalpies of the feldspar group of minerals and their long period derivatives. Received: October 7, 1996 / Revised, accepted: March 17, 1997     

Determination of the degree of Al,Si order Q od in kinetically disordered albite using hard mode infrared spectroscopy

Hard Mode Infrared Spectroscopy (HMIS) is used to correlate the line shifts Δω, the intensity changes ΔA and the variations of spectral line widths Γ of infrared absorption bands with the degree of Al, Si ordering, Q _od, in kinetically disordered Na-feldspar. A simple relationship Δω∝ΔA∝ΔΓ∝Q _od ² was found with the phonon band around 650 cm^?1 being particularly sensitive to small changes of the degree of Al, Si ordering. It is shown that the average degree of Al, Si order can be determined from HMIS with an accuracy of ca. 8 percent using 50 mg of Na-feldspar. The experimental results agree well with recent X-ray determinations using identical samples. The significance of HMIS for the study of kinetic processes in minerals is explained.     

Al,Si ordering in cordierite using “magic angle spinning” NMR

A method of determining the number of Al-O-Al bonds per unit cell from ²⁹Si nuclear magnetic resonance (NMR) data of synthetic cordierites with increasing Si, Al order is described. The number of Al-O-Al bonds is found to vary linearly with the logarithm of the annealing time. This may be correlated with previously published heat of solution data on similar samples (Carpenter et al. 1983) to determine the enthalpy change Δh, associated with a single Al?Si interchange in cordierite. Δh is found to be 8.1 kcal/mole. The NMR data show that the short range Al, Si order cannot be described in terms of twin domains of ordered orthorhombic cordierite. An ordering model derived from group theoretical constraints on possible Al, Si distributions within the hexagonal symmetry of the cordierite is found to provide a better fit to the NMR data.     

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.     

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.     

Al,Si ordering on cordierite using “magic angle spinning” NMR

Silicon-29 “magic angle spinning” nuclear magnetic resonance (NMR) spectroscopy has been used to study the changes in local Si environment during Al, Si ordering in synthetic cordierite, Mg₂Al₄Si₅O₁₈. In the most disordered form, crystallized from a glass, eight distinct tetrahedral sites for silicon can be identified and assigned, while there are only two distinguishable Si sites in the well-annealed ordered form. This allows the changes in the Si site environments to be determined as a function of annealing time for the transformation from the disordered to the ordered form. The first crystallized state has a considerable degree of partitioning between T₁ and T₂ sites with the following site occupancies: T₁ ? Al:Si=0.80:0.20, T₂?Al:Si=0.27:0.73 The changes in Si environment are approximately linear with log time. The measured values of ²⁹Si isotropic chemical shift do not fit well to previously determined correlations of shift with various structural parameters.     

X-Ray radial distribution function analysis of acid volcanic glasses from the Eastern Rhodopes,Bulgaria

Five natural acid volcanic glasses (perlites) from the Eastern Rhodope mountains, Bulgaria, have been studied by X-ray diffraction. The quantity of the microlites varies from 1–3.5 weight percent. It is higher in the glasses from the rhyolite-perlite transition zone. Total pair correlation functions have been calculated for three of the glasses with less than 2 weight percent microlites. All total pair correlation functions are quite similar and have six well defined peaks up to 8 Å. Beyond 8 Å they are practically featureless. The general form of the curves and peak positions suggests that the short-range order in all the three glasses is compatible with a 6-membered tetrahedral ring polymerization scheme with some contribution of fourmembered rings. The T-01 (T=Si, Al) distance shows linear correlation with the weight percent ratio Al₂O₃/SiO₂. The averaged first nearest neighbour distances T-01, O-01 and T-T1 are 1.615±0.005 Å, 2.66±0.02 Å and 3.16±0.02 Å, respectively. The mean T-O-T bond angle is 157±4°. Energy minimization and topology considerations of the possible distribution of different tetrahedral rings are discussed.     

Defects and short-range order in nepheline group minerals: a silicon-29 nuclear magnetic resonance study

²⁹Si magic-angle spinning nuclear magnetic resonance (NMR) spectra are presented for seven crystalline phases of the nepheline group: natural nephelines from a plutonic environment (Bancroft, Ontario) and a volcanic deposit (Mt. Somma, Italy), kalsilite, synthetic pure Na nepheline, carnegieite, and two samples of orthorhombic KAlSiO₄. In all phases, nearly all of the Si sites have four Al neighbors, indicating nearly complete Al-Si ordering. Excess Si over the 1:1 stoichiometric Si/Al ratio appears to substitute randomly for Al on an ordered lattice, adding Si sites with 3 and 0 Al neighbors in a 3:1 ratio. Various types of structural disorder, including Al-Si disorder, that are reported from some x-ray diffraction studies are probably long range in nature and are due to the presence of ordered domains. In naturally occurring nepheline, the relative abundance of T sites with three-fold local symmetry is maintained at the ideal stoichiometric value of 1/4, even when the K/(K+Na) ratio is substantially lower. This is in agreement with conclusions reached about the average structure from x-ray data. The distinction between the two sites, at least in terms of the local structure that is reflected in ²⁹Si NMR chemical shifts, is lost in a pure Na nepheline sample.     

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.     

Polarized EXAFS of biotite and chlorite

Polarized Fe K-edge EXAFS spectra of biotite and chlorite monocrystals have been recorded using the Synchrotron radiation at LURE, Orsay. The anisotropic contribution of the nearest cation shell is clearly brought to evidence. In the limit case in which the electric field vector would be disposed normal to the layer plane, the contribution of cations belonging to octahedral sheets would not be sampled. At this orientation, the Fe-(Si, Al) contribution is selected and it is then possible by extrapolation of spectra taken at lower angles to extract phase and amplitude functions associated with this atomic pair. Two applications of this experiment are presented, (i) In chlorite, the amplitude of the Fe-(Si, Al) contribution is directly proportional to the distribution of Fe atoms between the TOT layer and the interlayer. It is found that about 25 percent of the iron is located in the interlayer. (ii) In the biotite structure, the contribution of the (Si, Al) shell is almost constant for a wide range of Fe-containing phyllosilicates and can be subtracted from their EXAFS spectrum. Such an operation will permit a more accurate analysis of the reality of solid solutions.     

Structural states of natural potassium feldspar: An infrared spectroscopic study

Natural samples of K-feldspar representing various states of Al, Si order were characterised using X-ray methods, transmission electron microscopy, and Fourier transform infrared spectroscopy. Line profiles of infrared absorption bands were observed to show strong correlation with the degree of Al, Si order present. In particular, the absorption frequencies of the 540 cm^?1 and 640 cm^?1 bands were seen to vary by ca. 10 cm^?1 between sanidine and microcline, with modulated samples respresenting intermediate behaviour. Linewidths of these modes also decrease by ca. 50% in this series. The experimental results are discussed within the framework of Hard Mode Infrared Spectroscopy (HMIS), and it is shown that the absorption frequencies vary with the short range order parameter τ = (4t₁-1)² and the symmetry breaking order parameter describing Al, Si order, Q _od=(t₁ 0?t₁ m)/Q _od=(t₁ 0+t₁ m), where t₁ is the average Al occupancy on the T₁ sites and t₁ o and t₁ m are the individual site occupancies of the T₁ o and T₁ m sites, respectively. The structural state of orthoclase is characterised by strain-induced modulations with large spatial variations of the modulation wavelength. No such modulations were observed in the degree of local Al, Si order. Sanidine shows mode hardening in excess of the extrapolated effect of symmetry breaking Al, Si order, which is presumably related to nonsymmetry breaking ordering between T₁ and T₂ sites and/or as yet unobserved short range order of the symmetry breaking ordering scheme. The possibility of an additional phase transition in K-feldspar at temperatures above 1300 K is discussed.     

偏岭石结构研究

用广角度X射线散射 (WAXS)和由它得到的径向分布函数 (RDF)研究了偏岭石的结构。偏岭石是一种以非晶组份为主的部分有序的中间序性物质。构成偏岭石的结构单元是四面体 [MO₄ ](M =Si,Al)和八面体 [AlO₆](O =O,OH)。偏岭石结构中近邻四面体与四面体共顶连接构成M-O层,八面体与八面体共棱或共面连接构成Al-O层;而四面体与八面体通过不规则的共顶连接构成近程层状结构。它的近程结构将不随序性或结晶性变化。它的微结构及其随热处理温度的变化主要决定于结构基元之间的关系和序性。偏岭石是结构不同于变高岭石的一种粘土.     

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。     

Experimental determination of the solubility of the assemblage paragonite,albite, and quartz in supercritical H2O

The concentrations of Na, Al, and Si in an aqueous fluid in equilibrium with natural albite, paragonite, and quartz have been measured between 350°C and 500°C and 1 to 2.5 kbar. Si is the dominant solute in solution and is near values reported for quartz solubility in pure H₂O. At 1 kbar the concentrations of Na and Al remain fairly constant from 350°C to 425°C but then decrease at 450°C. At 2 kbar, Na increases slightly with increasing temperature while Al remains nearly constant. Concentrations of Si, Na, and Al all increase with increasing pressure at constant temperature.The molality of Al is close to that of Na and is nearly a log unit greater than calculated molalities assuming Al(OH)⁰₃ is the dominant Al species. This indicates a Na-Al complex is the dominant Al species in solution as shown by Anderson and Burnham (1983) at higher temperature and pressure. The complex can be written as NaAl(OH)⁰₄ ± nSiO₂ where n is the number of Si atoms in the complex. The value of n is not well constrained but appears to be less than or equal to 3.The results indicate Al can be readily transported in pure H₂O solutions at temperatures and pressures as low as 350°C and 1 kbar.