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.     

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.     

The effect of Al/Si disorder on the I \bar 1-P \bar 1Co-Elastic phase transition in Ca-rich plagioclase

The influence of Al/Si disorder in the anorthite tetrahedral framework upon the I \(\bar 1\) -P \(\bar 1\) displacive transition of that framework has been investigted at high-temperature by powder X-ray diffraction. The temperature-dependence of the order parameter in a heat-treated (disordered) anorthite and a Ca-rich plagioclase has been determined from spontaneous strain measurements. Both samples show appreciable disorder, with Q _od = 0.88 in both cases. In each, the critical exponent β appears to be intermediate between values for classical tricritical (1/4) and second-order (1/2) phase transitions. This critical behaviour is consistent with a Landau potential in which the coefficient of the quartic term is positive but smaller than the coefficient of the sixth order term, corresponding to a second-order phase transition close to a tricritical point. There does not appear to be any defect strain tail near T _c and inhomogeneities in Q _od appear to be on rather a short length scale in these samples. The role of changing Q _od appears to be more important than that of changing composition (albite component). The data are interpreted using a model of a homogeneous field due to changing Q _od which renormalizes the transition temperature, T _c ^* , and the fourth order coefficient, B _eff, in the Landau expansion. The results are consistent with classical Landau behaviour, and demonstrate the care which must be taken in interpreting apparently non-classical critical exponents for phase transitions close to a tricritical point.     

Application of infrared spectroscopy to studies of silicate glass structure: Examples from the melilite glasses and the systems Na2O-SiO2 and Na2O-Al2O3-SiO2

Infrared (IR) and Raman spectroscopic methods are important complementary techniques in structural studies of aluminosilicate glasses. Both techniques are sensitive to small-scale (<15 Å) structural features that amount to units of several SiO₄ tetrahedra. Application of IR spectroscopy has, however, been limited by the more complex nature of the IR spectrum compared with the Raman spectrum, particularly at higher frequencies (1200–800 cm^?1) where strong antisymmetric Si-O and Si-O-Si absorptions predominate in the former. At lower frequencies, IR spectra contain bands that have substantial contributions from ‘cage-like’ motions of cations in their oxygen co-ordination polyhedra. In aluminosilicates these bands can provide information on the structural environment of Al that is not obtainable directly from Raman studies. A middle frequency envelope centred near 700 cm^?1 is indicative of network-substituted AlO₄ polyhedra in glasses with Al/(Al+Si)>0·25 and a band at 520–620cm^?1 is shown to be associated with AlO₆ polyhedra in both crystals and glasses. The IR spectra of melilite and melilite-analogue glasses and crystals show various degrees of band localization that correlate with the extent of Al, Si tetrahedral site ordering. An important conclusion is that differences in Al, Si ordering may lead to very different vibrational spectra in crystals and glasses of otherwise gross chemical similarity.     

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.     

Vibrational spectroscopy of beryllium aluminosilicates: Heat capacity calculations from band assignments

Far-infrared, mid-IR, and Raman powder spectra were measured on six phases (bromellite, chrysoberyl, phenakite, bertrandite, beryl, and euclase) in the system BeO-Al₂O₃-SiO₂-H₂O. A single-crystal absorption spectrum of IR fundamentals in beryl is also presented, which more closely resembles the powder absorption spectrum than it does absorption spectra calculated from single-crystal reflection data. Assignments of the SiO₄ and BeO₄ internal vibrations are made in accordance with each mineral's symmetry and composition and by comparison to structural analogs. Heat capacities C _v calculated for these partial band assignments agree with C _v derived from experimental C _p for all six phases, provided that Kieffer's (1979c) model is slightly modified to correctly enumerate both Si-O and Be-O stretching modes in the high frequency region (>750 cm^?1). Si-O stretching bands were found to out-number Be-O stretching modes in the high-energy region of the vibrational spectra with two exceptions: (1) For those phases containing oxygen ions not coordinated to silicon, vibrations occurring at v>1,080 cm^?1 that are attributable to Be-O (H) stretching must be treated separately in the model in order to calculate C _v accurately. (2) Minerals consisting entirely of interlocking Si and Be tetrahedra (i.e., phases without Al or OH) can be modeled by one optic continuum representing all optical modes. These results, along with the occurrence of very low energy lattice vibrations for Be-silicates within Al, suggests that although Be-O bonds are generally weaker than neighboring Si-O bonds, Be mimics the network-forming characteristic of Si to a limited extent.     

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.     

The tetrahedral framework in glasses and melts — inferences from molecular orbital calculations and implications for structure,thermodynamics, and physical properties

Results of ab initio molecular orbital (MO) calculations provide a basis for the interpretation of structural and thermodynamic properties of crystals, glasses, and melts containing tetrahedrally coordinated Si, Al, and B. Calculated and experimental tetrahedral atom-oxygen (TO) bond lengths are in good agreement and the observed average SiO and AlO bond lengths remain relatively constant in crystalline, glassy, and molten materials. The TOT framework geometry, which determines the major structural features, is governed largely by the local constraints of the strong TO bonds and its major features are modeled well by ab initio calculations on small clusters. Observed bond lengths for non-framework cations are not always in agreement with calculated values, and reasons for this are discussed in the text. The flexibility of SiOSi, SiOAl, and AlOAl angles is in accord with easy glass formation in silicates and aluminosilicates. The stronger constraints on tetrahedral BOB and BOSi angles, as evidenced by much deeper and steeper calculated potential energy versus angle curves, suggest much greater difficulty in substituting tetrahedral B than Al for Si. This is supported by the pattern of immiscibility in borosilicate glasses, although the occurrence of boron in trigonal coordination is an added complication. The limitations on glass formation in oxysulfide and oxynitride systems may be related to the angular requirements of SiSSi and Si(NH)Si groups. Although the SiO and AlO bonds are the strongest ones in silicates and aluminosilicates, they are perturbed by other cations. Increasing perturbation and weakening of the framework occurs with increasing ability of the other atom to compete with Si or Al for bonding to oxygen, that is, with increasing cation field strength. The perturbation of TOT groups, as evidenced by TO bond lengthening predicted by MO calculations and observed in ordered crystalline aluminosilicates, increases in the series Ca, Mg and K, Na, Li. This perturbation correlates strongly with thermochemical mixing properties of glasses in the systems SiO₂-M ₁ ^n/n+ AlO₂ and SiO₂-M ⁿ⁺O _n/2 (M=Li, Na, K, Rb, Cs, and Mg, Ca, Sr, Ba, Pb), with tendencies toward immiscibility in these systems, and with systematics in vibrational spectra. Trends in physical properties, including viscosity at atmospheric and high pressure, can also be correlated.     

Structural states of Mg-cordierite II: Landau theory

Mg-cordierite undergoes a ferroelestic phase transitionP6/mmc-Cccm. The order parameterQ is proportional to the spontaneous strain as reflected by changes of the lattice parametersa andb during the phase transition. The order parameter,Q _od, which describes the Al, Si ordering, isnot directly involved in the phase transition and only “triggers” the structural collapse. Landau theory predicts that cordierite can exist in stable or metastable states with hexagonal, orthorhombic or monoclinic symmetry. Hexagonal cordierite can develop modulated structures which have been found by Putnis et al. (1987). The phase transition is predicted to be accompanied by singularities of the elastic constantsC ₁₁,C ₂₂ andC ₁₂ leading to an elastic softening of the crystal structure.     

Kinetic rate laws derived from order parameter theory IV: Kinetics of Al,Si disordering in Na-feldspars

The kinetic rate laws of Al-Si disordering under dry conditions (T = 1353K, 1253 K, 1223 K, 1183 K) and in the presence of water (p = 1 kbar, T = 1023 K, 1073 K, 1103 K) were studied both experimentally and theoretically. A gradual change of the degree of order was found under dry conditions. For intermediate degrees of order broad distributions of the order parameter Q _od occur. The variations of Q _od are correlated with structural modulations as observed in the transmission electron microscope. The time evolution of the mean value of Q _od can be well described by the rate law: $$\frac{{dQ_{od} }}{{dt}} = - \frac{\gamma }{{RT}}\exp \sum\limits_{i = 1}^n {X_i^2 } \left[ {\frac{{ - (G_a^0 + \varepsilon (\Delta Q_{od} )^2 )}}{{RT}}} \right]\frac{{dG}}{{dQ_{od} }}$$ with the excess Gibbs energy G and G _a ⁰ = 433.8 kJ/mol, ?= -27.4 kJ/mol, γ = 1.687 · 10¹⁴ h ^?1. Under wet conditions, two processes were found which occur simultaneously. Firstly, some material renucleated with the equilibrium degree of order. Secondly, the bulk of the material transformed following the same rate law as under dry conditions but with the reduced activation energy G _a ⁰ = 332.0 kJ/mol and ? = -43.0 kJ/ mol, γ = 1.047 · 10¹³ h^?1. The applicability of the kinetic theory is discussed and some ideas for the analysis of geological observations are evolved.     

Empirical study of the infrared lattice vibrations (1100–350 cm−1) of phlogopite

A detailed evaluation of the assignments given to the infrared (IR) vibrations in the lattice stretching region is presented here based on observations of the effects of various chemical substitutions in synthetic analogues of phlogopite, KMg₃(AlSi₃)O₁₀(OH)₂. As in previous studies, this study has confirmed that the 995, 960, and 460 cm^?1 vibrations are influenced by Si, the 822 and 760 cm^?1 vibrations by Al, the 915 and 725 cm^?1 vibrations by Al and Si, and the 592 cm^?1 vibration by OH. Contrary to previous studies, it is shown here that the 690, 495, and 375 cm^?1 vibrations are strongly linked with Mg and not just Si. The 655 cm^?1 band in phlogopite is attributed to an in-plane Al-O vibration rather than an Al-O-Si vibration. As a check on the band assignments made here, IR spectra were obtained for synthetic clintonite, CaMg₂Al(Al₃Si)O₁₀(OH)₂, as well as its chemical analogues and compared with the IR spectrum of phlogopite. The band intensities for the Si-O, Al-O, and Si-O-Mg vibrations changed in accord with the composition of clintonite. The most intense band in clintonite at 660 cm^?1 appears to be associated only with Al and is assigned here to a tetrahedral Al-O-Al vibration which must be present, if not dominant, in this mineral. The near coincidence of an in-plane Al-O vibration at 655 cm^?1 (phlogopite) and an in-plane Al-O-Al vibration at 660 cm^?1 (clintonite) makes the identification of tetrahedral Al-Si order-disorder in trioctahedral layered silicates by IR spectroscopy very difficult. The ratio of the 822/995 cm^?1 bands may, however, prove to be very useful for discerning the amount of tetrahedrally coordinated Al in these types of minerals.     

57Fe mössbauer study of clinopyroxenes in the join CaFe3+ AlSiO6 - CaTiAl2O6

Synthetic clinopyroxenes of compositions between CaFe³⁺AlSiO₆ and CaFe _0.85 ³⁺ Ti_0.15Al_1.15Si_0.85O₆ have been studied by ⁵⁷Fe Mössbauer spectroscopy. The spectra consist of two doublets assigned to Fe³⁺ in M1 and T sites. From the area ratios of the doublets the site occupancies of Fe³⁺ and Al were determined. Si decreases from 1.00 to 0.85 and Al+Fe³⁺ increases from 1.00 to 1.15 per formula unit with increasing CaTiAl₂O₆ component of the clinopyroxene. The atomic ratio of Fe³⁺(T)/Fe³⁺(total) is 0.11–0.16; 4.5–7.5 percent of the T sites are occupied by Fe³⁺. Thus the presence of Si-O-Fe³⁺, Al-O-Fe³⁺, and Fe³⁺-O-Fe³⁺ bonds is expected in addition to Si-O-Si, Si-O-Al and Al-O-Al bonds. However, the possibility of the former bonds being present would be small, because the amount of Fe³⁺(T) is far less than that of Si and Al. The isomer shift of Fe³⁺(T) is one of the largest in the values found previously for Fe³⁺(T) in silicates. It increases with increasing CaTiAl₂O₆ component and seems to be correlated to the ionic character of the cation — anion bonds calculated from electronegativity. The quadrupole splittings of Fe³⁺(M1) and Fe³⁺(T) decrease with the substitution of Fe³⁺?Ti⁴⁺ in the M1 and of Si?Al in the T sites.     

Thermodynamics of plagioclase III: Spontaneous strain at the I\overline 1 - P\overline 1 phase transition in Ca-rich plagioclase

The lattice parameters of anorthites An₉₈Ab₂ and An₁₀₀ have been measured from 22 to 1100 K. The spontaneous strain arising from the \(I\overline 1 - P\overline 1\) displacive transition in An₉₈ follows second order Landau behaviour. The spontaneous strain (? _s) couples quadratically to the order parameter (Q ⁰) with ? _s∝Q ⁰²∝(T _c ^* ?T) and T _c ^* =530 K in An₉₈. This is in contrast to the tricritical behaviour observed in pure anorthite. These observations are consistent with a Landau model for the free energy of Ca-rich plagioclases in which Al/Si order and Na content renormalize the fourth order coefficient.     

Growth and ordering processes in synthetic hydrothermal anorthite

Anorthite crystals were synthetized from gel under hydrothermal conditions (P=1000 bar, T=700° C) with run durations from 2 h to 110 days. The products were observed at room temperature by optical microscopy, X-ray powder diffraction and transmission electron microscopy (TEM). It has been shown that crystallization progresses as a function of time as follows: from t=2 h to t=7 days, the proportion of amorphous material decreases from 80 to 0 percent; the average crystal size grows from 1 to 20 μm; the number of crystals per unit volume decreases from 2.10¹¹ to 5.10⁸cm⁻³, indicating substantial recrystallization. The average A1, Si state of order increases with time and reaches a steady state after seven days. The crystals exhibit a core few micrometers in diameter and a rim whose width increases with time from 1 to 10 μm. The core, highly disordered in Al, Si, displays weak b reflexions and small antiphase domains (APDs), the rim, more ordered in Al, Si, differs from the core by sharp b reflexions and larger APDs extending radially. Both macroscopic results and microscopic observations show that crystals grow by two successive processes: at first, nucleation and growth from gel giving rise to the core, then recrystallization giving rise to the rim.     

Constraints on the structure and dynamics of the β-cristobalite polymorphs of SiO2 and AlPO4 from 31P, 27Al and 29Si NMR spectroscopy to 770 K

Nuclear magnetic resonance spectroscopic data are presented for the cristobalite polymorphs of AlPO₄ and SiO₂ from RT to 770 K, through their respective α-β transitions. The nuclear magnetic resonance (NMR) data include chemical shifts for ³¹P, ²⁷Al, and ²⁹Si, ²⁷Al quadrupole coupling parameters, and ³¹P and ²⁷Al spin-lattice relaxation rates. Also presented are electron diffraction patterns of β-cristobalite AlPO₄ that show diffuse scattering similar to that reported previously for SiO₂. For the α-phases of both AlPO₄ and SiO₂, the chemical shifts decrease approximately linearly with increasing temperature from RT to T_c and discontinuously by -2 to -3 ppm from α to β. This result is consistent with a small, continuous increase in the mean T-O-T angle (〈θ〉) of the α-phases with increasing T and an increase of 〈θ〉 by about 4° across the α-β transition for both cristobalite and its AlPO₄ analogue. Based on the ²⁹Si chemical shifts, the mean Si-O-Si angle for β-cristobalite is 152.7±1° near T_c. For AlPO₄-cristobalite, the ²⁷Al nuclear quadrupole coupling constant (C_Q) decreases approximately linearly from 1.2 MHz at RT to 0.94 MHz near T_c (493±10 K). At the α-β transition the ²⁷Al C_Q approaches zero, in agreement with the cubic average structure observed by diffraction. The satellite transitions retain a small frequency distribution above the α-β transition from electric field gradients attributed to defects. The short-range cubic symmetry of the Al-site and non-linear Al-O-P angle support a dynamically disordered model of the β-cristobalite structure. Complete averaging of the ²⁷Al quadrupole coupling in the β-phase indicates that the lifetime of any short-range ordered domains must be shorter than about 1 μs.     

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.     

Compositional zoning in garnet and kinetics of metamorphic crystallization

The kinetics of zoned garnet porphyroblast growth is exemplified in a sample of garnet-staurolite-biotite schist from the northern Ladoga region. The diffusion-controlled porphyroblast growth was accompanied by a decrease in the kinetic coefficient during phase reactions. Even at insignificant (1–2°C) thermal overstepping, the leading role of diffusion as a factor that controls kinetics of porphyroblast growth in medium-grade metapelites is consistent with the parameters of metamorphic crystallization: T = 500–650°C, t = 1 Ma; D _A1 ^app = 10^?14 cm²/s, L = 0.2–0.6 cm, r = 1–3 mm, ΔC _Al = 1.5 × 10^?4–1.5 × 10^?3 mol/cm³.     

Tracing quartz through the environment

Quartz, SiO₂, a pure mineral with tight crystal structure, is widespread in rocks and soil. Cosmic rays produce¹⁰Be (t _1/2=1·5×10⁶, yr) and²⁶Al (t _1/2=7·05×10⁵ yr) in quartz exposed at or near the earth’s surface. The use of accelerator mass spectrometry permits measurement of these nuclides in samples exposed at sea level for typical periods.In situ production makes interpretation relatively straightforward. Potential applications include age determination, measurement of erosion and deposition rates, and use as a tracer for continental weathering processes.     

A single-crystal neutron and X-ray diffraction study of pezzottaite, Cs(Be2Li)Al2Si6O18

The chemical composition and the crystal structure of pezzottaite [ideal composition Cs(Be₂Li)Al₂Si₆O₁₈; space group: ${\it{R}} \overline{\text{3}} $ c, a?=?15.9615(6) ?, c?=?27.8568(9) ?] from the type locality in Ambatovita (central Madagascar) were investigated by electron microprobe analysis in wavelength dispersive mode, thermo-gravimetric analysis, Fourier-transform infrared spectroscopy, single-crystal X-ray (at 298?K) and neutron (at 2.3?K) diffraction. The average chemical formula of the sample of pezzottaite resulted ^Cs1,Cs2(Cs_0.565Rb_0.027K_0.017)_Σ0.600 ^Na1,Na2(Na_0.101Ca_0.024)_Σ0.125Be_2.078Li_0.922 ^Al1,Al2(Mg_0.002Mn_0.002Fe_0.003Al_1.978)_Σ1.985 ^Si1,Si2,Si3(Al_0.056Si_5.944)_Σ6O₁₈·0.27H₂O. The (unpolarized) IR spectrum over the region 3,800–600?cm^?1 was collected and a comparison with the absorption bands found in beryl carried out. In particular, two-weak absorption bands ascribable to the fundamental H₂O stretching vibrations (i.e. 3,591 and 3,545?cm^?1) were observed, despite the mineral being nominally anhydrous. The X-ray and neutron structure refinements showed: (a) a non-significant presence of aluminium, beryllium or lithium at the Si1, Si2 and Si3 sites, (b) the absence (at a significant level) of lithium at the octahedral Al1, Al2 and Al3 sites and (c) a partial lithium/beryllium disordering between tetrahedral Be and Li sites.     

Thermodynamics of plagioclase II: Temperature evolution of the spontaneous strain at the I\bar 1 \leftrightarrow P\bar 1 phase transition in anorthite

The temperature dependence of the lattice parameters of pure anorthite with high Al/Si order reveals the predicted tricritical behaviour of the \(I\bar 1 \leftrightarrow P\bar 1\) phase transition at T _c ^* =510 K. The spontaneous strain couples to the order parameter Q° as x _i∝S _xQ ⁱ Q°² with S _xQ ¹ =4.166×10^?3, S _xQ ² =0.771×10^?3, S _xQ ³ =?7.223×10^?3 for the diagonal elements. The temperature dependence of Q° is $$Q^{\text{o}} = \left( {1 - \frac{T}{{510}}} \right)^\beta ,{\text{ }}\beta = \tfrac{{\text{1}}}{{\text{4}}}$$ A strong dependence of T _c ^* , S _xQ ⁱ and β is predicted for Al/Si disordered anorthite.