Molecular dynamics simulations of the phase transition between low-temperature and high-temperature clinoenstatites

 Phase transition between low-temperature clinoenstatite (LT-CEn) and high-temperature clinoenstatite (HT-CEn) was studied by using molecular dynamics (MD) simulations, based on empirical potential parameters. Starting from LT-CEn, the MD calculations were carried out at atmospheric pressure and at elevated pressures (1–6 GPa). At elevated temperatures the transformation from the starting LT-CEn to HT-CEn occurred at any pressure. It was confirmed that the HT-CEn has the same space group C2/c as diopside but the M2 site is six-coordinated, unlike diopside. A significant difference in the MD-simulated cell volumes between LT-CEn and HT-CEn was also observed, showing a first-order transition. In addition, there were some temperature ranges where LT-CEN and HT-CEn would be coexistent and very small thermal hystereses between increasing and decreasing temperatures during the transition. These behaviors are consistent with the characteristic of a thermoelastic-martensitic transformation. The phase boundary between LT-CEn and HT-CEn was determined for the first time. Its positive dT/dP slope strongly shows that the high-pressure clinoenstatite is a significantly distinct phase from HT-CEn although the both phases have the same space group, C2/c. Received: 8 November 2000 / Accepted: 28 April 2001     

Molecular dynamics interpretation of structural changes in quartz

 Constant temperature and constant pressure molecular dynamics (MD) simulations were applied to quartz to calculate the structural details which are indeterminable in usual X-ray structure studies. The dynamics of the structural changes was analyzed by means of time-dependent atomic displacement parameters. The Si-O bonds expand with increasing temperatures through the α- and β-phases, and atoms vibrate around the α₁- (or α₂-) sites at lower temperatures in the α-phase, and over the energy barriers between the α₁- and the α₂-sites at higher temperatures in the α- and the β-phases. The ratios of time lengths spent by atoms in the α₁- and α₂-sites determine the apparent atomic positions as obtained in usual structure studies of α-quartz. More frequent transfer of atoms over the α₁- and the α₂-sites contributes positively to the thermal expansions, whereas larger amplitudes of vibrations, which carry atoms more distantly and more frequently from the β-sites, contribute negatively. The well-known steep thermal expansion in the α-phase is attributed to the additive contribution from the expansions of the Si-O bond lengths, the widening of Si-O-Si angles, and the increase of the atomic transfer-frequency between the α₁- and the α₂-sites. The nearly zero or negative expansion in the β-phase is caused by balancing the negative to the positive effects. The MD crystal transforms to the β-phase via a transitional state, where the α- and β-structures appear alternately with time, or coexist. The slight and continuous expansions observed right after the steep rise(s) of the volume or cell dimensions up to the nearly horizontal curve(s) are attributed to the continuous changes within the transitional state. Received: 17 July 2000 / Accepted: 13 January 2001     

Non-convergent ordering and displacive phase transition in pigeonite: in situ HT XRD study

A natural Ca-rich pigeonite (En₄₇Fs₄₃Wo₁₀), free of augite exsolution products, was studied by in situ high-temperature single-crystal X-ray diffraction. The sample, monoclinic P2 ₁ /c (a=9.719(7) Å, b=8.947(9) Å, c=5.251(3) Å, β=108.49(5), V=433.0(6) ų), was annealed up to 1000 °C to induce a phase transition from P2 ₁ /c to C2/c symmetry. Complete single-crystal X-ray diffraction data collections were carried out in situ at 650, 750, 850 and 950 °C after the crystal had reached equilibrium for the Fe–Mg intracrystalline exchange reaction at each temperature. The variation, with increasing temperature, of lattice parameters, of intensity of hkl reflections with h + k=2n + 1 (which vanish at high temperature) and of some geometrical parameters from structure refinement, showed that the displacive phase transition P2 ₁ /c?C2/c was continuous in character. This contrasts with the first-order character for the HT phase transition in pigeonite containing significantly less calcium.     

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     

Spontaneous strain at the structural phase transition in NaNO3

The temperature dependence of the hexagonal c unit cell parameter of high-purity NaNO₃ shows an anomaly at 553 K corresponding to the orientational ordering transition. The a unit cell parameter is barely influenced by the transition. The single component spontaneous strain for this zone boundary instability is large (55×10^–3 at 295 K), and couples quadratically with the order parameter. The critical exponent is found to have the value 0.22 ± 0.01, which differs from that expected in the classical case. Below ca 450 K, crossover to tricritical behaviour is observed (=1/4). The temperature evolution of the macroscopic order parameter as revealed by the temperature dependence of the spontaneous strain follows a tricritical behaviour between 70 K and 450 K. At temperatures below 70 K order parameter saturation is observed. Combined with recent data from specific heat measurements, the critical exponents suggest that the three-dimensional, three-states Potts model may describe the transition.Precursor spontaneous strain above T _c is consistent with local ordering and may result from fluctuations associated with an antiordered NO₃ group pair configuration.     

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     

First-principles-based calculations of the CaCO<Subscript>3</Subscript>–MgCO<Subscript>3</Subscript> and CdCO<Subscript>3</Subscript>–MgCO<Subscript>3</Subscript> subsolidus phase diagrams

 Planewave pseudopotential calculations of supercell total energies were used as bases for first-principles calculations of the CaCO₃–MgCO₃ and CdCO₃–MgCO₃ phase diagrams. Calculated phase diagrams are in qualitative to semiquantitative agreement with experiment. Two unobserved phases, Cd₃Mg (CO₃)₄ and CdMg₃(CO₃)₄, are predicted. No new phases are predicted in the CaCO₃–MgCO₃ system, but a low-lying metastable Ca₃Mg(CO₃)₄ state, analogous to the Cd₃Mg(CO₃)₄ phase is predicted. All of the predicted lowest-lying metastable states, except for huntite CaMg₃(CO₃)₄, have dolomite-related structures, i.e. they are layer structures in which A _m B _n cation layers lie perpendicular to the rhombohedral [111] vector. Received: 6 May 2002 / Accepted: 23 October 2002 Acknowledgements This work was partially supported by NSF contract DMR-0080766 and NIST.     

Molecular dynamics study of the α–β transition in quartz: elastic properties, finite size effects, and hysteresis in the local structure

The α–β transition in quartz is investigated by molecular dynamics simulations in the constant stress ensemble. Based on a frequently used two-body interaction potential for silica, it is found that anomalies in the elastic constants are at least in semiquantitative agreement with experiment despite the fact that no anomaly in the c/a ratio is observed in the simulations. A finite-size scaling analysis shows that first-order Landau theory is applicable to the employed model potential surface. This statement also applies to the susceptibility below the transition temperature T _tr, which has not yet been measured experimentally. Examination of the local order near T _tr reveals that the deformation of SiO₄ tetrahedral units is equally large in the β phase as in the α phase. However, large hysteresis effects can be observed in the local structure for distances r > 4 Å. The results are in agreement with the picture of a first-order displacive phase transformation which is driven by the motion of deformed tetrahedral SiO₄ units. Yet, the fast oscillations of oxygen atoms are around (time-dependent) positions that do not correspond to the ideal oxygen positions in β-quartz. The averaged configurations resemble the ideal structure only if averaged over at least a few nanoseconds.     

Phase transition of synthetic zinc ferrite spinel (ZnFe2O4) at high pressure, from synchrotron X-ray powder diffraction

 Synthetic Zn-ferrite (ideally ZnFe₂O₄; mineral name: franklinite) was studied up to 37 GPa, by X-ray powder diffraction at ESRF (Grenoble, France), on the ID9 beamline; high pressure was achieved by means of a DAC. The P-V equation of state of franklinite was investigated using the Birch-Murnaghan function, and the elastic properties thus inferred [K₀ = 166.4(±3.0) GPa K₀ ^′ = 9.3(±0.6) K₀ ^″ = −0.22 GPa⁻¹] are compared with earlier determinations for MgAl-spinel and magnetite. The structural behaviour of Zn-ferrite as a function of pressure was studied by Rietveld refinements, and interpreted in the light of a phase transition from spinel to either CaTi₂O₄- or MnFe₂O₄-like structure; this transformation occurs above 24 GPa. Received: 15 March 1999 / Accepted: 22 April 2000     

H T -XRD study of synthetic ferrian magnesian spodumene: the effect of site dimension on the P 21/ c → C 2/ c phase transition

 Ferrian magnesian spodumene was synthesized in the MLFSH system at P=0.4 GPa, T=700 °C, fO₂=NNO+2.3. The space group at room T is P2₁/c [a=9.638(3) ?, b=8.709(2) ?, c=5.258(2) ?, β=109.83(3)^∘, V=415.2 ?³]. The structure is topologically equivalent to that of ferrian spodumene, LiFeSi₂O₆, and has two symmetrically independent tetrahedral chains, A and B, and two independent octahedral sites, M1 and M2. The crystal-chemical composition was determined combining EMP, SIMS and single-crystal XRD analysis, yielding ^M2(Li_0.85Mg_0.09Fe²⁺ _0.06) ^M1(Fe³⁺ _0.85Mg_0.15)Si₂O₆. Li is ordered at the M2 site and Fe³⁺ is ordered at the M1 site, whereas Mg (and Fe²⁺) distribute over both octahedral sites. Structure refinements done at different temperatures (25, 70, 95, 125, 150 and 200 °C) allowed characterization of a reversible displacive P2₁/c→C2/c transition at 106 °C. Previous HT-XRD studies of Li-clinopyroxenes had shown that the transition temperature is inversely related to the size of the M1 cation. For the crystal of this work, the aggregate ionic radius at M1 is longer than that of ferrian spodumene, for which the transition temperature is −44 °C. The higher transition temperature observed can only be explained on the basis of the shorter aggregate radius at the M2 site (due to the presence of Mg substituting after Li), in keeping with the results obtained for ferromagnesian P2₁/c pyroxenes. The effects of all the chemical substitutions must be considered when modelling transition temperatures and thermodynamic behaviour in clinopyroxenes. Received: 7 May 2002 / Accepted: 23 October 2002     

Molecular dynamics study of structural changes in berlinite

Fractional coordinates and anisotropic temperature factors of atoms in berlinite, AlPO₄ with the quartz topology, were successfully simulated in a molecular dynamics simulation (MDS) at high temperatures. Time-dependent and time-averaged atomic order parameters were analyzed in detail with the aid of spectral densities calculated from trajectory data. These parameters show characteristic behavior of the order-disorder regime for a structure change, where atoms spend most of the time oscillating around the ₁-sites (or ₂-sites) in the low temperature α-phase, but oscillate over both sites in the higher temperature α-phase and the β-phase. In the spectral density functions calculated for atom order parameters, a nearly zero-frequency excitation, which is accompanied by the emergence of large-scale ₁ and ₂ clusters, appears at the Γ point of the Brillouin zone below the transition point T _o, and increases in intensity up to T _o. A low-lying optic branch along Γ-M, which is strongly temperature dependent in the small q-region, is another characteristic of the spectral density functions for the β phase. The spectrum at Γ continuously reduces its frequency from 0.6 THz at temperatures far above T _o to nearly 0 THz at temperatures approaching T _o from above. The dynamical behavior in β berlinite rapidly but continuously changes from that in less oscillatory clusters in the vicinity of T _o to that in the typical β phase at temperatures departing from T _o. Received: 10 August 1998 / Revised, accepted: 18 February 1999     

Microsommite: crystal chemistry, phase transitions, Ising model and Monte Carlo simulations

Microsommite, ideal formula [Na₄K₂(SO₄)] [Ca₂Cl₂][Si₆Al₆O₂₄], is a rare feldspathoid that occurs in volcanic products of Vesuvius. It belongs to the cancrinite–davyne group of minerals, presenting an ABAB… stacking sequence of layers that contain six-membered rings of tetrahedra, with Si and Al cations regularly alternating in the tetrahedral sites. The structure was refined in space group P6₃ to R=0.053 by means of single-crystal X-ray diffraction data. The cell parameters are a=22.161?Å=√3a _dav, c=5.358?Å=c _dav; Z=3. The superstructure arises due to the long-range ordering of extra-framework ions within the channels of the structure. This ordering progressively decreases with rising temperature until it is completely lost and microsommite transforms into davyne. The order–disorder transformation has been monitored in several crystals by means of X-ray superstructure reflections and the critical parameters T _c?≈?750?°C and β?≈?0.12 were obtained. The kinetics of the ordering process were followed at different temperatures and the activation energy was determined to be about 125?kJ?mol^?1. The continuous order–disorder phase transition in microsommite has been discussed on the basis of a two-dimensional Ising model in a triangular lattice with nn (nearest neighbours) and nnn (next-nearest neighbours) interactions. Such a model was simulated using a Monte Carlo technique. The theoretical model well matches the experimental data; two phase transitions were indicated by the simulated runs: at low temperature only one of the three sublattices begins to disorder, whereas the second transition involves all three sublattices.     

Phase transition and mixing behaviour of the cummingtonite–grunerite solid solution

 Natural amphiboles with composition close to the binary join cummingtonite–grunerite and crystals of the same samples annealed at 700 °C for 55.5 h, in order to obtain different degrees of non-convergent cation order, have been characterised by means of X-ray single-crystal diffraction and IR spectroscopy. Long-range order parameters describing the non-convergent order of Mg/Fe among the different octahedral sites have been calculated from the site occupancies of the investigated samples. Values of the O6-O5-O6 angles and of the 〈M4-O〉 mean bond distances depend on the C2/m → P2₁/m phase transition for a given degree of order. In the IR spectra, only two phonon lines dominated by the bending of the tetrahedral chains are sensitive to the displacive phase transition and to the different degree of cation order; all the other wavenumber shifts are correlated with compositional changes only. The local strains arising from the cation substitution, ordering and phase transition have been quantified by means of the autocorrelation function. Very small local heterogeneities are associated with the Mg/Fe substitution and disordering in samples at intermediate composition. The displacive phase transition seems to occur in order to reduce local distortions and the P2₁/m samples are as homogeneous as orthorhombic anthophyllites. The orthorhombic structure, however, appears less flexible than the monoclinic in accommodating cations larger than Mg at the octahedral sites. Received: 9 February 2000 / Accepted: 30 September 2000     

High-pressure phase transformations in the MgFe2O4 and Fe2O3–MgSiO3 systems

 The crystal structure of MgFe₂O₄ was investigated by in situ X-ray diffraction at high pressure, using YAG laser annealing in a diamond anvil cell. Magnesioferrite undergoes a phase transformation at about 25 GPa, which leads to a CaMn₂O₄-type polymorph about 8% denser, as determined using Rietveld analysis. The consequences of the occurrence of this dense MgFe₂O₄ form on the high-pressure phase transformations in the (MgSi)_0.75(Fe^III)_0.5O₃ system were investigated. After laser annealing at about 20 GPa, we observe decomposition to two phases: stishovite and a spinel-derived structure with orthorhombic symmetry and probably intermediate composition between MgFe₂O₄ and Mg₂SiO₄. At pressures above 35 GPa, we observe recombination of these products to a single phase with Pbnm perovskite structure. We thus conclude for the formation of Mg₃Fe₂Si₃O₁₂ perovskite. Received: 27 March 2000 / Accepted: 1 October 2000     

Thermal expansion and structural transformations of stuffed derivatives of quartz along the LiAlSiO4–SiO2 join: a variable-temperature powder synchrotron XRD study

 The structural behavior of stuffed derivatives of quartz within the Li_{1− x} Al_{1− x} Si_{1+ x} O₄ system (0 ≤ x ≤ 1) has been studied in the temperature range 20 to 873 K using high-resolution powder synchrotron X-ray diffraction (XRD). Rietveld analysis reveals three distinct regimes whose boundaries are defined by an Al/Si order-disorder transition at x=∼0.3 and a β–α displacive transformation at x=∼0.65. Compounds that are topologically identical to β-quartz (0 ≤ x < ∼0.65) expand within the (0 0 1) plane and contract along c with increasing temperature; however, this thermal anisotropy is significantly higher for structures within the regime 0 ≤ x < ∼0.3 than for those with compositions ∼0.3 ≤ x < ∼0.65. We attribute this disparity to a tetrahedral tilting mechanism that occurs only in the ordered structures (0 ≤ x < ∼0.3). The phases with ∼0.65 ≤ x ≤ 1 adopt the α-quartz structure at room temperature, and they display positive thermal expansion along both a and c from 20 K to their α–β transition temperatures. This behavior arises mainly from a rotation of rigid Si(Al)-tetrahedra about the <100> axes. Landau analysis provides quantitative evidence that the charge-coupled substitution of Li+Al for Si in quartz dampens the α–β transition. With increasing Li+Al content, the low-temperature modifications exhibit a marked decrease in spontaneous strain; this behavior reflects a weakening of the first-order character of the transition. In addition, we observe a linear decrease in the α–β critical temperature from 846 K to near 0 K as the Li+Al content increases from x=0 to x=∼0.5. Received: 26 June 2000 / Accepted: 1 December 2000     

The crystal and magnetic structure of Li-aegirine LiFe3+Si2O6: a temperature-dependent study

Single crystals of Li-aegirine LiFe³⁺Si₂O₆ were synthesized at 1573?K and 3?GPa, and a polycrystalline sample suitable for neutron diffraction was produced by ceramic sintering at 1223?K. LiFe³⁺Si₂O₆ is monoclinic, space group C2/c, a=9.6641(2)?Å, b= 8.6612(3)?Å, c=5.2924(2)?Å, β=110.12(1)^° at 300?K as refined from powder neutron data. At 229?K Li-aegirine undergoes a phase transition from C2/c to P2₁ /c. This is indicated by strong discontinuities in the temperature variation of the lattice parameters, especially for the monoclinic angle β and by the appearance of Bragg reflections (hkl) with h+k≠2n. In the low-temperature form two non-equivalent Si-sites with 〈SiA–O〉=1.622?Å and 〈SiB–O〉=1.624?Å at 100?K are present. The bridging angles of the SiO₄ tetrahedra O3–O3–O3 are 192.55(8)° and 160.02(9)° at 100?K in the two independent tetrahedral chains in space group P2₁ /c, whereas it is 180.83(9)° at 300?K in the high-temperature C2/c phase, i.e. the chains are nearly fully expanded. Upon the phase transition the Li-coordination changes from six to five. At 100?K four Li–O bond lengths lie within 2.072(4)–2.172(3)?Å, the fifth Li–O bond length is 2.356(4)?Å, whereas the Li–O3?A bond lengths amount to 2.796(4)?Å. From ⁵⁷Fe Mössbauer spectroscopic measurements between 80 and 500?K the structural phase transition is characterized by a small discontinuity of the quadrupole splitting. Temperature-dependent neutron powder diffraction experiments show first occurrence of magnetic reflections at 16.5?K in good agreement with the point of inflection in the temperature-dependent magnetization of LiFe³⁺Si₂O₆. Distinct preordering phenomena can be observed up to 35?K. At the magnetic phase transition the unit cell parameters exhibit a pronounced magneto-striction of the lattice. Below T _N Li-aegirine shows a collinear antiferromagnetic structure. From our neutron powder diffraction experiments we extract a collinear antiferromagnetic spin arrangement within the a–c plane.     

High-pressure behavior of MnGeO3 and CdGeO3 perovskites and the post-perovskite phase transition

The stability and high-pressure behavior of perovskite structure in MnGeO₃ and CdGeO₃ were examined on the basis of in situ synchrotron X-ray diffraction measurements at high pressure and temperature in a laser-heated diamond-anvil cell. Results demonstrate that the structural distortion of orthorhombic MnGeO₃ perovskite is enhanced with increasing pressure and it undergoes phase transition to a CaIrO₃-type post-perovskite structure above 60 GPa at 1,800 K. A molar volume of the post-perovskite phase is smaller by 1.6% than that of perovskite at equivalent pressure. In contrast, the structure of CdGeO₃ perovskite becomes less distorted from the ideal cubic perovskite structure with increasing pressure, and it is stable even at 110 GPa and 2,000 K. These results suggest that the phase transition to post-perovskite is induced by a large distortion of perovskite structure with increasing pressure.     

Clinopyroxene-perovskite phase transition of FeGeO3 under high pressure and room temperature

In order to confirm the possible existence of FeGeO₃ perovskite, we have performed in situ X-ray diffraction measurements of FeGeO₃ clinopyroxene at pressures up to 40 GPa at room temperature. The transition of FeGeO₃ clinopyroxene into orthorhombic perovskite is observed at about 33GPa. The cell parameters of FeGeO₃ perovskite are a=4.93(2) Å, b=5.06(6) Å, c=6.66(3) Å and V=166(3) ų at 40 GPa. On release of pressure, the perovskite phase transformed into lithium niobate structure. The previously reported decomposition process of clino-pyroxene into Fe₂GeO₄ (spinel)+GeO₂ (rutile) or FeO (wüstite) +GeO₂ (rutile) was not observed. This shows that the transition of pyroxene to perovskite is kinetically accessible compared to the decomposition processes under low-temperature pressurization.     

Rigid Unit Modes in disordered nepheline: a study of a displacive incommensurate phase transition

 Calculations of the Rigid Unit Modes (RUMs) allowed in the nepheline structure are used to explain the diffuse scattering previously seen in electron diffraction experiments. The RUM calculations also show that the modulation wavelength for incommensurate nephelines is essentially determined by the framework topology. X-ray diffraction is used to measure the intensity of the diffuse scattering as a function of temperature. The diffuse intensity increases sharply at 308 K. This effect is interpreted as being due to the softening of a phonon mode, indicating a phase transition. Measurements of this phase transition below the transition temperature are made using hard mode infrared spectroscopy. Received: 17 February 1999 / Revised, accepted. 15 October 1999