Microscopic dynamic and macroscopic thermodynamic character of the I\bar 1 - P\bar 1 phase transition in anorthite

The dynamic character of the phase transition in anorthite from Monte Somma has been studied by high-temperature hard mode infrared spectroscopy. The mean local order parameter, as revealed by the temperature evolution of the frequencies of absorption bands between 540 and 620 cm_-1, follows classical second-order Landau behaviour with a critical exponent β = 1.. There is no observable first-order step. Anomalous line broadening of the 582 cm_-1 band indicates that dynamic fluctuations with a relaxation time τ ≈ 10⁻¹⁰ s exist over a limited temperature interval of approximately 150 K about T_c, and decay rapidly as T becomes greater than T_c. Previous order-disorder models of the high-temperature phase are not supported by these results. The Ca-flip motions, which we link to the line broadening, stabilize the driving soft mode of the transition. These flip motion fluctuations do not give rise to departures from the classical Landau theory because of the essential co-elastic nature of the phase transition. In the light of these results the structural instability can be described as an essentially displacive transition.     

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     

A dynamical model for the P1 — I1 phase transition in anorthite,CaAl2Si2O8

Electron diffraction and electron microscopic evidence is presented for a dynamical and reversible phase transition in anorthite at T _c=516 K. Antiphase boundaries with a displacement vector, R=1/2[111] become unstable at T _c, while other antiphase boundary loops with the same displacement vector are formed. These interfaces are very mobile and vibrate with a frequency which increases strongly with temperature. At temperatures considerably above T _c, a shimmering effect is observed on imaging in dark field using diffuse c reflections. These observations are in agreement with the interpretation of the high temperature body-centered phase as a statistical dynamical average of very small c type antiphase domains of primitive anorthite. We propose that the c type antiphase domains in primitive anorthite originate from ordered and anti-ordered configurations around Ca²⁺ ions at (ooo) and (oio) [likewise (zoo) and (zio)] positions. The dynamical model for the transition involves a two-stage mechanism: a softmode mechanism causing the aluminosilicate framework to approach body-centered symmetry, followed by an orderdisorder of the Ca²⁺ ion configurations. Close to T _c, statistical fluctuations set in and breathing motion type lattice vibrations of the aluminosilicate framework cause the configurations around Ca (ooo) and Ca(oio) [likewise Ca(zoo) and Ca(zio)] in the configuration to dynamically interchange through an intermediate configuration. The dynamical nature of the phase transition in anorthite is comparable to the — phase transition in quartz.     

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     

Thermodynamics of plagioclases I: Theory of the I\bar 1 - P\bar 1 phase transition in anorthite and Ca-rich plagioclases

Landau theory of the \(P\bar 1 - I\bar 1\) phase transition in Ca-rich plagioclases reveals the sensitivity of the phase transition behaviour to a) Al, Si disorder, b) structural replacement of Ca by Na, and c) inhomogeneities of lattice strains. The following effects are predicted:

1. A tricritical phase transition exists in fully ordered anorthite. Al, Si disorder and Na, Ca exchange lead to second order phase transitions.
2. The transition temperatures depend sensitively on the degree of Al, Si disorder and the chemical composition of the Ca-rich plagioclases. Increasing Na-content decreases the transition temperatures.
3. The thermal evolution of c and d reflections depends on the homogeneity of the crystal and do not necessarily reflect the temperature evolution of the macroscopic lattice strain. A simple quadratic dependence of the X-ray scattering intensity on the order parameter exists only for fully ordered, homogeneous anorthite.

The role of inhomogeneous Al, Si distributions and lattice relaxations are discussed including possible structural modulations.     

A model for the origin of the cell-doubling phase transitions in clinopyroxene and body-centred anorthite

Comparisons of the structures of the high-pressure and high-temperature phases of both anorthite and clinopyroxene show that they are quite distinct although they share a common space group and site symmetries for all atoms. The low-pressure, low-temperature phases in both systems are formed by zone-boundary transitions from the high-pressure or high-temperature structures, and have structures that are made up of the alternation of portions of the high-pressure and high-temperature structures. This behaviour is analyzed in terms of the order parameter behaviour of the high-symmetry structures, and it is shown that the stability of the low-symmetry phases arises naturally from inhomogeneity in this order parameter.     

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.     

A dynamical model for the I\bar 1 - P\bar 1 phase transition in anorthite,CaAl2Si2O8

The non-ferroic triclinic to triclinic \(I\bar 1 - P\bar 1\) phase transition in anorthite is described in terms of the spontaneous onset of an order parameter η. A triclinic to triclinic phase transition can be driven by order parameters (representations) arising from the Γ, Z, X, U, V, R, Y, and T points of symmetry of the Brillouin zone. Each point leads to a set of two inequivalent representations and thus there is a total of sixteen inequivalent order parameters. However, only the R ₁ ⁺ representation is consistent with the change from the body-centered to primitive cell (increase of primitive cell size of two) and also with the origin of the two space groups (inversion center) being at the same position. The R ₁ ⁺ order parameter of the high symmetry triclinic phase \(P\bar 1_0\) (or equivalently \(I\bar 1\) ) causes a reciprocal lattice change and, in terms of the lower symmetry reciprocal lattice, the order parameter corresponds to the b^* point. This is consistent with experimentally observed x-ray diffuse scattering. Using induced representation theory, microscopic distortions compatible with the R ₁ ⁺ order parameter are obtained. Assuming a distortion in an arbitrary direction at the general 2(i) Wyckoff position (x₀,y₀,z₀) of \(P\bar 1_0\) (the higher symmetry phase) induced representation theory demands an opposite displacement at the position (x₀, y₀, z₀), an opposite displacement at (x₀+1,y₀+1,z₀+1), and the same displacement at ( \(\bar x\) ₀+1, \(\bar y\) ₀+1, \(\bar z\) ₀+1) of \(P\bar 1_0\) . This is also consistent with experiment. The presence of the weak c-type reflections above the transition is attributed to the fluctuating lower symmetry antiphase domains related by the translation (1/2, 1/2, 1/2).     

Effect of anorthite on granite phase relations: Experimental data and models

New experimental data on the effect of anorthite (An) on liquidus phase equilibria in the system Qz–Ab–Or are presented. The data were obtained for 5 wt% An added to variable Qz/Ab/Or compositions at 300 MPa and under H₂O-saturated conditions. Crystal–liquid equilibria were determined for 13 synthetic glass compositions made from gels in experiments performed between 660 and 750 °C in cold-seal pressure vessels. Forward and reversal experiments were systematically conducted on each composition to demonstrate equilibrium. A total of 51 charges was examined. Three crystalline phases, quartz, alkali feldspar and plagioclase appear on the H₂O-saturated liquidus surface. The determined minimum liquidus 5 wt% An “piercing” point (39% Qz, 33% Ab, 28% Or) is shifted away from the Ab apex toward the Qz–Or sideline when compared with the An-free 300 MPa H₂O-saturated minimum. This shift is of the same type as that observed at 100 MPa in the same system and at 200 MPa in a rhyolitic system. The new experimental results are used to test both empirical and thermodynamic models for silicic magmas. Empirical models reproduce reasonably well the new experimental data, although more sophisticated calculations schemes appear to be required to improve their accuracy. The new experimental results in the haplogranodiorite system are not well reproduced with the model of Holland and Powell (2001), mainly because plagioclase stability appears greatly enhanced in the model. Rhyolite-MELTS satisfactorily reproduces the Qz-, Pl- and Af-liquid phase equilibria, but model H₂O solubilities are significantly lower and crystallization temperatures higher than in experiments.     

Spontaneous strain below the I\bar 1 - P\bar 1 transition in anorthite at pressure

The phase transition between the and phases of anorthite has been studied at elevated pressure by single-crystal X-ray diffraction in a diamond-anvil cell. The phase transition is shown to be first-order in character for both end-member anorthite (CaAl₂Si₂O₈) and for an anorthite with a small amount of albite component (NaAlSi₃O₈) in solid solution. Reversals of the transition across the phase boundary at three other compositions show that the transition pressure (P _Tr) increases with increasing albite content. This behaviour is compared with that observed at elevated temperatures, and is analysed in terms of Landau theory.     

西藏普兰地幔橄榄岩中尖晶石内的钙长石包裹体及其成因

西藏普兰超镁铁岩体之东南缘与玄武岩接触界线附近的地幔橄榄岩中除有粒状半自形的钙长石产出外,还在尖晶石中发现有呈蠕虫状、浑圆状的钙长石包裹体存在.研究发现两种产状的钙长石An值都大于95且均无环带构造,说明钙长石从高Ca/Al比值的熔体中结晶时具有结晶时间短、结晶速度快的特点,可能形成于地壳较浅部位.从化学成分来看,包裹体形态的钙长石具有较高的Cr2O3含量,其寄主矿物尖晶石的Cr#值低且TiO2含量比深海橄榄岩中的尖晶石低得多,推断钙长石包裹体与寄主矿物尖晶石是在液相条件下几乎同时结晶的产物.综合研究表明钙长石包裹体的成因可能是玄武岩熔体在地壳较浅部位侵入方辉橄榄岩时,高温的玄武质熔体提供热源,使得方辉橄榄岩中尖晶石内的Cpx+ Opx细粒矿物包裹体在高温环境下发生熔融,发生Opx+ Cpx+ Sp→Ol+ Pl的反应,由于这种情况下尖晶石有剩余,故新生成的橄榄石和钙长石矿物仍然包裹于尖晶石内,从而形成尖晶石内部呈蠕虫状的钙长石包裹体.     

High-pressure phase transition in MnTiO3 from the ilmenite to the LiNbO3 structure

Crystals of a high-pressure phase of MnTiO₃ have been synthesized at pressures of 60 kbar using the SAM-85 cubic-anvil high pressure apparatus. Although all crystals examined were twinned on (10 \(\bar 1\) \(\bar 2\) ), a set of diffraction intensities that are essentially unaffected by the twinning were obtained. Three possible structure models were considered: (1) the corundum (completely disordered Mn and Ti), (2) the partially-disordered ilmenite, and (3) the LiNbO₃ structures. The R factors of the corundum and the disordered ilmenite models were much larger than that of LiNbO₃. Using structure factors unaffected by twinning, the final LiNbO₃-type refinement gave R _w=0.037 and R=0.034. The averaged bond lengths for Mn-O and Ti-O were consistent with ones calculated using Shannon and Prewitt's (1969) radii. The study concludes that MnTiO₃ II actually has an ordered LiNbO₃-type structure rather than the disordered one as reported previously. From the analysis of the two MnTiO₃ structures, the transition can be related to a cation reordering process, in which half of the cations participate, accompanied by the rotation of oxygens to accommodate the cations.     

High-pressure isosymmetrical phase transition in calaverite

Using density functional theory, we perform ab initio calculations of the behaviour of calaverite, AuTe₂, at high pressures. Calaverite has a distorted CdI₂ structure, that presents a pronounced two-dimensional character and a rather anisotropic response to pressure. Increasing the pressure, we predict an isosymmetrical phase transition between 55 and 60 GPa, that is accompanied by an important distortion of the structure, observed in all its geometrical parameters, especially the c lattice parameter. Relaxing the pressure, the reverse phase transition is observed between 30 and 25 GPa.     

On the weak reflections violating body-centered symmetry in scapolites

Summary X-ray diffraction studies reveal that most scapolites belong to space groupP4 ₂ /n. The mean intensity of weak reflections violating body-centered symmetry, reaches a maximum around 37 per cent meionite and extrapolates to zero at the pure end-members. All intermediate scapolites of the marialitemeionite series are pseudobody-centered, and as the composition approaches that of the end-members the structure becomes truly body-centered (I4/m).The weakh+k+l odd reflections are directly related to (1) orderdisorder of Al and Si in the tetrahedral framework and (2) structural distortion from body-centered symmetry.Scapolites may be regarded as a continuous, homogeneous solid solution. The cell dimensions are only approximately linearly related to composition and there is a maximum deviation from linearity, for those scapolites (25% Me 45% Me) whose symmetry departs the most from body-centered symmetry. These phenomena are interpreted in terms of the structural characteristic of the scapolites.

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Über schwache Reflexe, welche der Raumzentrierung der Skapolithe widersprechen

Zusammenfassung Röntgenbeugungs-Untersuchungen zeigen, daß die meisten Skapolithe der RaumgruppeP4 ₂ /n angehören. Die durchschnittliche Intensität der schwachen Reflexe, welche der Raumzentrierung widersprechen, erreicht bei 37% Meionit-Momponente ein Maximum — für die reinen Endglieder nähert sie sich dem Wert Null. Alle intermediären Skapolithe der Marialith-Meionit-Reihe sind pseudo-raumzentriert und mit Annäherung der Zusammensetzung an jene der Endglieder wird die Struktur echt raumzentriert (I4/m)Die schwachenh+k+l ungerade Reflexe stehen (1) mit Ordnung-Unordnung von Al und Si im Tetradergerüst und (2) mit strukturellen Abweichungen von der Raumzentrierung in Beziehung.Die Skapolithe können als kontinuierliche homogene Mischkristallreihe betrachtet werden. Die Zelldimensionen ändern sich nur ungefähr linear mit der Zusammensetzung; die stärkste Abweichung von der Linearität tritt bei jenen Skapolithen (25% Me bis 45% Me) auf, deren Symmetrie am stärksten von der Raumzentrierung abweicht. Diese Phänomene werden aus den strukturellen Eigenheiten der Skapolithe interpretiert.

     

Pressure-induced phase transition in synthetic trioctahedral Rb-mica

 The crystal structure of a synthetic Rb analog of tetra-ferri-annite (Rb–TFA) 1M with the composition Rb_0.99Fe²⁺ _3.03(Fe³⁺ _1.04 Si_2.96)O_10.0(OH)_2.0 was determined by the single-crystal X-ray diffraction method. The structure is homooctahedral (space group C2/m) with M1 and M2 occupied by divalent iron. Its unit cell is larger than that of the common potassium trioctahedral mica, and similar lateral dimensions of the tetrahedral and octahedral sheets allow a small tetrahedral rotation angle α=2.23(6)°. Structure refinements at 0.0001, 1.76, 2.81, 4.75, and 7.2 GPa indicate that in some respects the Rb–TFA behaves like all other micas when pressure increases: the octahedra are more compressible than the tetrahedra and the interlayer is four times more compressible than the 2:1 layer. However, there is a peculiar behavior of the tetrahedral rotation angle α: at lower pressures (0.0001, 1.76, 2.81 GPa), it has positive values that increase with pressure [from 2.23(6)° to 6.3(4)°] as in other micas, but negative values −7.5(5)° and −8.5(9)° appear at higher pressures, 4.75 and 7.2 GPa, respectively. This structural evidence, together with electrostatic energy calculations, shows that Rb–TFA has a Franzini A-type 2:1 layer up to at least 2.81 GPa that at higher pressure yields to a Franzini B-type layer, as shown by the refinements at 4.75 and 7.2 GPa. The inversion of the α angle is interpreted as a consequence of an isosymmetric displacive phase transition from A-type to B-type structure between 2.81 and 4.75 GPa. The compressibility of the Rb–TFA was also investigated by single-crystal X-ray diffraction up to a maximum pressure of 10 GPa. The lattice parameters reveal a sharp discontinuity between 3.36 and 3.84 GPa, which was associated with the phase transition from Franzini-A to Franzini-B structure. Received: 21 October 2002 / Accepted: 25 February 2003     

A room-temperature phase transition in maximum microcline

A type of hysteresis, similar to that observed in the heat capacity measurements (Openshaw et al., 1979), has been found in the room temperature unit cell parameters of a microcline sample 71104 and likewise indicates the existence of two forms of this microcline. The A-form (obtained on cooling the sample to approximately 80 K) has significantly different values of b, β and V to the B-form which is the more stable form above 300±10 K. The transition from the A- to the B-form occurs over a period of months and has an associated ΔV of ?0.0011 nm³. The cell parameters of the B-form have been measured up to 1278 K and show significant changes: a and V increase, b constracts, and c is unchanged on increasing temperature. The calculated thermal expansion ellipsoid is nearly uniaxial and similar in shape to that for sanidine. Below room temperature the isobaric thermal expansion coefficent α_p, for a natural microcline is nearly four times as large as that for sanidine. Above room temperature α_p for 71104 microcline decreases markedly with increasing temperature. This implies a rapid change in the thermal expansion behavior of microcline which has been correlated with the proposed phase transition.     

Polymorphic phase transition in Superhydrous Phase B

We synthesized superhydrous phase B (shy-B) at 22 GPa and two different temperatures: 1200°C (LT) and 1400°C (HT) using a multi-anvil apparatus. The samples were investigated by transmission electron microscopy (TEM), single crystal X-ray diffraction, Raman and IR spectroscopy. The IR spectra were collected on polycrystalline thin-films and single crystals using synchrotron radiation, as well as a conventional IR source at ambient conditions and in situ at various pressures (up to 15 GPa) and temperatures (down to −180°C). Our studies show that shy-B exists in two polymorphic forms. As expected from crystal chemistry, the LT polymorph crystallizes in a lower symmetry space group (Pnn2), whereas the HT polymorph assumes a higher symmetry space group (Pnnm). TEM shows that both modifications consist of nearly perfect crystals with almost no lattice defects or inclusions of additional phases. IR spectra taken on polycrystalline thin films exhibit just one symmetric OH band and 29 lattice modes for the HT polymorph in contrast to two intense but asymmetric OH stretching bands and at least 48 lattice modes for the LT sample. The IR spectra differ not only in the number of bands, but also in the response of the bands to changes in pressure. The pressure derivatives for the IR bands are higher for the HT polymorph indicating that the high symmetry form is more compressible than the low symmetry form. Polarized, low-temperature single-crystal IR spectra indicate that in the LT-polymorph extensive ordering occurs not only at the Mg sites but also at the hydrogen sites.     

High-temperature 29Si MAS NMR spectroscopy of anorthite (CaAl2Si2O8) and its P\bar 1-I\bar 1structural phase transition

We present ²⁹Si MAS NMR data for a well-ordered natural anorthite, obtained in situ at temperatures of from 25 to 500° C, which follow the changes in the aluminosilicate framework through the P $\bar 1$ -I $\bar 1$ structural phase transition. Pairs of peaks due to sites offset by approximately 1/2 [111] converge through the P $\bar 1$ phase and only four peaks are present above about 241° C. The variation of the peak positions with temperature and correlations based on structural data for the P $\bar 1$ and I $\bar 1$ phases allow assignment of all the MAS-NMR peaks to crystallographic sites. A Landau-type analysis gives an expression that relates the separation of pairs of con verging peaks to the local order parameter for the P $\bar 1$ -I $\bar 1$ transition, from which we determine its temperature dependence. Data for the best-constrained set of peak positions give for the order parameter critical exponent β = 0.27±0.04, consistent with previous results indicating that the P $\bar 1$ -I $\bar 1$ transition in pure anorthite is tricritical. No significant change in the ²⁹Si spin-lattice relaxation rate occurs across the P $\bar 1$ -I $\bar 1$ transition.