Calibration of Al/Si order variations in anorthite

New single crystal diffraction data for natural and heat-treated anorthite crystals (Angel et al. 1990) allow the determination of their states of Al/Si order in terms of a macroscopic order parameter,Q _OD , for the transition. Numerical values ofQ _OD obtained from estimates of site occupancies are shown to vary with the scalar spontaneous strain, _s , as _s Q _OD ² , and with the ratio of the sums of typeb (superlattice) reflections and typea (sublattice) reflections asI _b/I _a Q _OD ² . An empirical calibration for pure anorthite is obtained giving varies between 0.92 and 0.87 in samples equilibrated at T1300° C, but then falls off relatively rapidly with increasing temperature, reaching 0.7 near the melting point ( 1557° C). The observed temperature dependence does not conform to the predictions of the simplest single order parameter models; coupling ofQ _OD withQ of the transition is suspeeted.     

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.     

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.     

Field determination of sodium and potassium in feldspars by ion-selective electrodes

A field-lab technique has been developed to aid in the geochemical exploration for feldspars involving the determination of the K/Na ratio of feldspar samples with recently improved ion-selective electrodes. Feldspar is dissolved in a mixture of m-benzene disulfonic acid and hydrofluoric acid. The solution is neutralized with tetramethylammonium hydroxide in the presence of CDTA. K and Na determinations are then made with ion-selective electrodes in the neutral solution. The precision and accuracy of the technique have been tested and closely approach that of the flame photometer.     

Obliquity of potassium feldspars in the differentiation series of minettes

Summary The individual rock types of the differentiation series of minettes display different obliquity of potassium feldspars. In minettes,sensu stricto potassium feldspars with disordered monoclinic structure occur, in alkaline minettes both microcline and orthoclase are present, and in alkaline microgranites and microsyenites only microcline occurs. It may be assumed that the main factors controlling the ordering of K-feldspar structures in alkaline members of the minette series were the decrease of temperature below that of the orthoclase-microcline inversion and the presence of alkaline hydrothermal solution in the crystallizing magma.

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Die Triklinität der Kalifeldspäte in der Differentiationsreihe der Minetten

Zusammenfassung Die einzelnen Gesteinstypen der Minetten-Differentiationsreihe enthalten Kalifeldspäte mit unterschiedlich geordneten Strukturen. Minettensensu stricto enthalten Kalifeldspäte mit ungeordneter monokliner Struktur; Alkaliminetten sowohl Mikroklin als auch Orthoklas; Alkalimikrogranite und-syenite hingegen nur Mikroklin. Die Ordnung der Strukturen der Kalifeldspäte in den Alkaligesteinen wurde wahrscheinlich durch den Temperaturfall unter die Temperatur der Orthoklas-Mikroklin-Inversion und durch die Anwesenheit alkalischer hydrothermaler Restlösungen im kristallisierenden Magma bewirkt.

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With 1 Figure     

Thermodynamics of Al/Al avoidance in the ordering of Al/Si tetrahedral framework structures

The main driving force behind Al/Si ordering in tetrahedral framework aluminosilicates is nearest-neighbour Al/Al avoidance. Computer simulation is used to explore the direct consequences of such Al/Al avoidance. The main result is that the order-disorder transition temperature T _c falls dramatically as the concentration x of Al in the structure is reduced, and if the only interactions are those associated with nearest-neighbour Al/Al avoidance, T _c becomes zero for x less than some critical value x _c , where x _c =0.31 for the feldspar framework and x _c =0.34 for cordierite. Also a large degree of short range order is found above T _c . Both results differ radically from the standard Bragg-Williams model. Plots of entropy and enthalpy of ordering are given as functions of x and T, which may be used to interpret experimental data or for extrapolation into ranges of x and T inaccessible to experiment. Received: 14 May 1997 / Revised, accepted: 2 June 1997     

Triclinicity and barium content of potassium feldspars from muscovite pegmatites

Potassium feldspars in pegmatites of the Mama district are microclines and orthoclases. In granitoid pegmatites and undifferentiated vein pegmatites, unaffected by postmagmatic processes, the feldspars are represented by orthoclase with the X-ray triclinism (△p) as 0.0-0.4. Wherever postmagmatic solutions were active, in granitoid pegmatitic fields or zonal bodies of vein pegmatites, the feldspars are represented by microcline with △p as 0.5-1.0. At that, the ultimate microcline is recorded only in micaceous zones. There is a connection between △p and Ba content of the feldspars High concentrations of Ba interfere with order in the feldspar crystal structures. There is a definite inverse relationship between △p and Ba in feldspars containing 0.9-2.6% Ba. In feldspars which are low in Ba, △p may vary at one and the same concentration of Ba. Such state of the crystal structure of feldspars is metastable. The magnitude of △p depends upon conditions of the original crystallization and on factors conducive to orderliness in the crystal structure, as well as the interferences, specifically the effect of the admixture elements. — Authors.     

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.     

Equilibrium thermodynamics of Al/Si ordering in anorthite

Variations in the equilibrium degree of Al/Si order in anorthite have been investigated experimentally over the temperature range 800-1535° C. Spontaneous strain measurements give the temperature dependence of the macroscopic order parameter, Q, defined with respect to the \(C\bar 1 \rightleftharpoons I\bar 1\) phase transition, while high temperature solution calorimetric data allow the relationship between Q and excess enthalpy, H, to be determined. The thermodynamic behaviour can be described by a Landau expansion in one order parameter if the transition is first order in character, with an equilibrium transition temperature, T _tr, of ～2595 K and a jump in Q from 0 to ～0.65 at T_tr. The coefficients in this Landau expansion have been allowed to vary with composition, using Q=1 at 0 K for pure anorthite as a reference point for the order parameter. Published data for H and Q at different compositions allow the calibration of the additional parameters such that the free energy due to the \(C\bar 1 \rightleftharpoons I\bar 1\) transition in anorthite-rich plagioclase feldspars may be expressed (in cal. mole^-1) as: \(\begin{gathered}G = \tfrac{1}{2} \cdot 9(T - 2283 + 2525X_{Ab} )Q^2 \\ {\text{ + }}\tfrac{1}{4}( - 26642 + 121100X_{Ab} )Q^4 \\ {\text{ + }}\tfrac{1}{6}(47395 - 98663X_{Ab} )Q^6 \\ \end{gathered}\) where X _Ab is the mole fraction of albite component. The nature of the transition changes from first order in pure anorthite through tricritical at ～An₇₈ to second order, with increasing albite content. The magnitude of the free energy of \()\) ordering reduces markedly as X _Ab increases. At ～700° C incommensurate ordering in crystals with compositions ～An₅₀–An₇₀ needs to have an associated free energy reduction of only a few hundred calories to provide a more stable structure. These results, together with a simple mixing model for the disordered ( \()\) ) solid solution, an assumed tricritical model for the incommensurate ordering and published data for ordering in albite have been used to calculate a set of possible free energy relations for the plagioclase system. The incommensurate structure should appear on the equilibrium phase diagram, but its apparent stability with respect to the assemblage albite plus anorthite at low temperatures depends on the values assigned to the mixing parameters of the $$$$ solid solution.     

Estimation of the Al,Si distribution of feldspars from the lattice translations Tr[110] and Tr[110]

A method is proposed to estimate the Al,Si distribution of alkali feldspars from two lattice translations, called Tr[110] and Tr[1¯10], which are the repeat distances in the [110] and [1¯10] directions. The Al content t₁0 of the T₁0 tetrahedral site is estimated from Tr[1¯10], whereas Tr[110] measures t₁m, the Al content of the T₁m site. In order to simplify the estimation procedure, the line separation =2 (131)-2 (1¯31) is given as a function of t₁0 and t₁0-t₁m.     

Kinetic rate laws derived from order parameter theory III: Al,Si ordering in sanidine

The time dependence of the ordering and disordering of Al and Si in sanidine is described within the framework of the kinetic rate laws developed in papers I and II of this series. It was found that the relevant order parameter Q _t is homogeneous and non-conserved. The rate law is:

Enthalpy effects associated with Al/Si ordering in anhydrous Mg-cordierite

Measurements of the heats of solution (ΔH_soln) in molten Pb₂B₂O₅ at 708°C of anhydrous magnesian cordierites, prepared with a range of structural states, show that the enthalpy effect associated with Al/Si ordering is substantial (? 9.76 ± 1.56 kcal mole^?1). Differences in the state of order between synthetic cordierites used in phase equilibrium studies and cordierites in the natural environment could lead to significant errors in the estimation of palaeo-pressures and temperatures. A continuous change of ΔH_soln with annealing time supports the suggestion of putnis (1980) that the hexagonal → orthorhombic transformation in cordierite, which can occur via a modulated structure, is truly continuous under metastable conditions. In addition, a linear relation between ΔH_soln and the logarithm of annealing time has been found, which provides some insight into the nature of the ordering mechanisms at an atomic level. Al and Si exchanges occur continuously between neighbouring tetrahedral sites with a net drift towards increasing order. No kinetic or thermochemical distinction can be made between the development of long range and short range order.The enthalpy of vitrification (~ 12 kcal mole^?1) for a metastable stuffed β-quartz polymorph of cordierite composition is similar to that for pure quartz (on a per two oxygen basis), while the heat of vitrification for even the most disordered cordierite seen in this study is more than a factor of three greater (~40 kcal mole^?1). This is consistent with the view that cordierite glass resembles the quartz structure more closely than the crystalline cordierite structure, and that crystallisation of the glass below ~900°C is controlled by a tetrahedral framework.     

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.     

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.     

Mg-cordierite: Si/Al ordering,optical properties,and distortion

Flux-grown crystals of Mg-cordierite, Mg_1.93 Al_3.95 Si_5.07 O₁₈ synthesized by Lee and Pentecost (1976) appear biaxial (2V _x=10°–25°) under the polarizing microscope whereas their distortion index =0°. Between crossed polars, (001) sections display lamellar and cyclic twinning on {110} and, less frequently, {310}. As duration of annealing at 1,300° C, increased, 2V _x increased. Simultaneously, undulatory extinction and intragrain variations in 2V _x increased slightly up to 4 h annealing, then steadily decreased. For this Mg-cordierite, which lacks significant channel H₂O or CO₂, 2V _x and reach maxima of 88° (=589 nm) and 0.25° after 42 h of annealing but other sectors still display lesser values for 2V _x. Presumably, to the extent 2V _x is less than 88°, these sectors represent intergrown submicros copically twinned orthorhombic domains and thus possess shortrange but not long-range order. Annealing at 1,300° C likely increased long-range order by promoting growth of larger domains at the expense of smaller ones. Ultimately, two differently oriented domains, growing toward each other by annexation (and re-orientation) of smaller domains, meet in a twin boundary that, with time, tends to become straight.The cause of intermediate values for , whether compositional or from submicroscopic {110} or {310} twinning, may be revealed by single crystal X-ray photographs. Streaking of diffraction spots along a^* or b^* (but not c^*) will indicate such twinning as the sole or major cause.     

Diffusion in single crystal of melilite: interdiffusion of Al + Al vs. Mg + Si

Interdiffusion coefficients of Al + Al vs. Mg + Si in the gehlenite–åkermanite system of melilite were determined by coupled annealing of synthesized end-member single crystals. The observed diffusion coefficients for a couple-annealed sample vary for about 2 orders of magnitude, showing strong dependence on the gehlenite–åkermanite composition: diffusion coefficient observed at 1350 °C, for example, is 3 × 10^?13 cm² s^?1 at 5 mol% åkermanite composition (Ak₅), increases to 2 × 10^?11 cm² s^?1 at Ak₈₀, and then decreases to 1 × 10^?12 cm² s^?1 at Ak₉₅. The diffusion coefficient–temperature relation indicates high activation energy of diffusion of about 420 kJ mol^?1 for gehlenite-rich melilite. The observed diffusion coefficient–composition relation may be explained by a combination of (1) the diffusion coefficient–melting temperature relation (Flynn's rule) and (2) the feasibility of local charge compensation, which can possibly be maintained more easily in the intermediate chemical composition. The high activation energy value for gehlenitic melilite appears to correspond to the complex diffusion mechanism. The observed highly variable diffusion coefficients suggest that gehlenite–åkermanite zoning in the melilite crystals in Ca, Al-rich inclusions in the carbonaceous meteorites may provide a sensitive indicator for the thermal history of the inclusions.     

Al/Si interdiffusion in albite: effect of pressure and the role of hydrogen

The effect of pressure on the rate of Al/Si disorder in albite has been determined at temperatures from 800° C to 1050° C and at pressures up to 24 kbar, using dried samples in welded Pt containers, in piston-cylinder devices and internally-heated gas apparatus. In the piston-cylinder device with NaCl medium, the effect of pressure is profound. A pure low albite from Clear Creek, California reaches the equilibrium state of disorder at 850° C and 22 kbar in 10 h, whereas at 6 kbar it has not equilibrated in three weeks, and at one bar it probably cannot be disordered at 850° C in the laboratory. The enhancement of Al/Si interdiffusion takes place under dry conditions: any H₂O penetrating the samples would have produced melting, and none was observed. Hydrogen, however, is produced by dissociation of moisture in the pressure medium and can penetrate the Pt sample capsules. If the samples are deprived of hydrogen by replacing NaCl with glass or by embedding the samples in a hydrogen getter such as Fe₂O₃ or ZnO, the order-disorder reaction is greatly inhibited.A mechanism is suggested in which OH^– groups are formed by hydrogen hopping in albite. The smaller charge on the tetrahedral complex induces transient coordination of Al greater than four at elevated pressures, facilitating Al/Si interchange during the bond-breaking process. This results in an exponential pressure dependence of diffusion. It is also suggested that the presence of hydrogen at high pressures can greatly effect the mechanical properties and reactivity of deep crustal and mantle rocks. In nature, as well as in the laboratory, equilibration at elevated pressures may be as much dependent on the availability of hydrogen as on time or temperature.     

X-射线衍射研究钾长石结构中的Al/Si分布状态

长石族矿物产于各种成因类型岩石中,在地壳中广泛分布,为一极其重要的造岩矿物。而钾长石的结构状态(或叫多形变体)能提供有关矿物形成条件的各种信息(温度、压力、结晶速度等),从而引起人们的兴趣。钾长石结构状态主要地由Al、Si在四个非等效位置,     

Iī-I2/c phase transition in alkaline-earth feldspars along the CaAl2Si2O8-SrAl2Si2O8 join: Thermodynamic behaviour

Feldspars crystallized in the range SrF₈₀An₂₀-SrF₆₀An₄₀ of the join CaAl₂Si₂O₈-SrAl-₂Si₂O₈ from gels at T = 1350–1500° C for short time show cell parameters significantly different from those obtained from longer heating. This difference has been interpreted as due to higher metastable Al/Si disorder in short heated samples and to more ordered configurations with longer heat treatments. HT powder spectra show that the T _c of the Iī-I2/c phase transition of feldspars changes with composition and with the degree of order at constant composition; the evolution of the spontaneous strain (～cosα^*) versus T for the samples examined shows a variation in the order of the transition from continuous (II order) in more ordered and Sr-rich samples to a discontinuous behaviour (presumably I order) for more disordered and Sr-poor samples. A biquadratic coupling between displacive and OD parameters is therefore suggested.     

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

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