The α-β phase transition in cristobalite,SiO2

Cristobalite, a high temperature phase of silica, SiO₂, undergoes a (metastable) first-order phase transition from a cubic, , to a tetragonal, P4₃2₁2 (or P4₁2₁2), structure at around 220° C. The cubic C9-type structure for -cristobalite (Wyckoff 1925) is improbable because of two stereochemically unfavorable features: a 180° Si-O-Si angle and an Si-O bond length of 1.54 Å, whereas the corresponding values in tetragonal -cristobalite are 146° and 1.609 Å respectively. The structure of the -phase is still controversial. To resolve this problem, a symmetry analysis of the (or P4₁2₁2) transition in cristobalite has been carried out based on the Landau formalism and projection operator methods. The starting point is the ideal cubic ( ) C9-type structure with the unit cell dimension a (7.432 Å) slightly larger than the known a dimension (7.195 Å at 205° C) of -cristobalite, such that the Si-O-Si angle is still 180°, but the Si-O bond length is 1.609 Å. The six-component order parameter driving the phase transition transforms according to the X₄ representation. The transition mechanism essentially involves a simultaneous translation and rotation of the silicate tetrahedra coupled along 110. A Landau free-energy expression is given as well as a listing of the three types of domains expected in -cristobalite from the transition. These domains are: (i) transformation twins from a loss of 3-fold axes, (ii) enantiomorphous twins from a loss of the inversion center, and (iii) antiphase domains from a loss of translation vectors 1/2 110 (FP). These domains are macroscopic and static in -cristobalite, and microscopic and dynamic in -cristobalite. The order parameter , couples with the strain components as ², which initiates the structural fluctuations, thereby causing the domain configurations to dynamically interchange in the -phase. Hence, the - cristobalite transition is a fluctuation-induced first-order transition and the -phase is a dynamic average of -type domains.     

The α-β phase transition in AlPO4 cristobalite: Symmetry analysis,domain structure and transition dynamics

Despite their crystallographic differences, the mechanisms of the α-β phase transitions in the cristobalite phases of SiO₂ and AlPO₄ are very similar. The β→α transition in AlPO₄ cristobalite is from cubic ( $\left( {F\bar 43m} \right)$ ) to orthorhombic (C222₁), whereas that in SiO₂ cristobalite is from cubic ( $\left( {Fd\bar 3m} \right)$ ) to tetragonal (P4₃2₁2 or P4₁2₁2). These crystallographic differences stem from the fact that there are two distinct cation positions in AlPO₄ cristobalite as opposed to one in SiO₂ cristobalite and the ordered (Al,P) distribution is retained through the phase transition. As a result, there are significant differences in their crystal structures, domain configurations resulting from the phase transition and Landau free energy expressions. A symmetry analysis of the “improper ferroelastic” transition from $F\bar 43m \to C222_1$ in AlPO₄ cristobalite has been carried out based on the Landau formalism and the projection operator methods. The six-component order parameter, η driving the phase transition transforms as the X₅ representation of $F\bar 43m$ and corresponds to the simultaneous translation and rotation of the [AlO₄] and [PO₄] tetrahedra coupled along 110. The Landau free energy expression contains a third order invariant, the minimization of which requires a first-order transition, consistent with experimental results. The tetrahedral configurations of twelve α phase domains resulting from the β→α transition in AlPO₄ cristobalite are of two types: (1) transformation twins from a loss of the 3-fold axis, and (2) antiphase domains from the loss of the translation vectors 1/2[101] and 1/2[011] (F→C). In contrast to α-SiO₂ cristobalite, the α-AlPO₄ cristobalite (C222₁) does not have chiral elements (4₃, 4₁) and hence, enantiomorphous domains are absent. These transformation domains are essentially macroscopic and static in the α phase and microscopic and dynamic in the β phase. The order parameter, η couples with the strain components, which initiates the structural fluctuations causing the domain configurations to dynamically interchange in the β phase. An analysis of the MAS NMR data (²⁹Si, ¹⁷O, ²⁷Al) on the α α-β transitions in SiO₂ and AlPO₄ cristobalites (Spearing et al. 1992, Phillips et al. 1993) essentially confirms the dynamical model proposed earlier for SiO₂ cristobalite (Hatch and Ghose 1991) and yields a detailed picture of the transition dynamics. In both cases, small atomic clusters with the configuration of the low temperature α phase persist considerably above the transition temperature, T₀. The NMR data on the β phases above T₀ cannot be explained by a softening of the tetrahedral rotational and translational modes alone, but require the onset of an order-disorder mechanism resulting in a dynamic averaging due to rapidly changing domain configurations considerably below T₀.     

High-temperature and high-pressure equation of state for the hexagonal phase in the system NaAlSiO4 – MgAl2O4

Thermal equation of state of an Al-rich phase with Na_1.13Mg_1.51Al_4.47Si_1.62O₁₂ composition has been derived from in situ X-ray diffraction experiments using synchrotron radiation and a multianvil apparatus at pressures up to 24 GPa and temperatures up to 1,900 K. The Al-rich phase exhibited a hexagonal symmetry throughout the present pressure–temperature conditions and the refined unit-cell parameters at ambient condition were: a=8.729(1) Å, c=2.7695(5) Å, V ₀=182.77(6) Å³ (Z=1; formula weight=420.78 g/mol), yielding the zero-pressure density ρ₀=3.823(1) g/cm³ . A least-square fitting of the pressure-volume-temperature data based on Anderson’s pressure scale of gold (Anderson et al. in J Appl Phys 65:1534–543, 1989) to high-temperature Birch-Murnaghan equation of state yielded the isothermal bulk modulus K ₀=176(2) GPa, its pressure derivative K ₀ ^′ =4.9(3), temperature derivative (?K _T /?T) _P =?0.030(3) GPa K^?1 and thermal expansivity α(T)=3.36(6)×10^?5+7.2(1.9)×10^?9 T, while those values of K ₀=181.7(4) GPa, (?K _T /?T) _P =?0.020(2) GPa K^?1 and α(T)=3.28(7)×10^?5+3.0(9)×10^?9 T were obtained when K ₀ ^′ was assumed to be 4.0. The estimated bulk density of subducting MORB becomes denser with increasing depth as compared with earlier estimates (Ono et al. in Phys Chem Miner 29:527–531 2002; Vanpeteghem et al. in Phys Earth Planet Inter 138:223–230 2003; Guignot and Andrault in Phys Earth Planet Inter 143–44:107–128 2004), although the difference is insignificant (<0.6%) when the proportions of the hexagonal phase in the MORB compositions (～20%) are taken into account.     

The order–disorder potential of the crystal structure of monohydrocalcite,CaCO3·H2O

Mineralogy and Petrology - Monohydrocalcite, CaCO3·H2O, forms a P31 structure composed of composite rods in which a spiral arrangement of Ca ions is accompanied by spiral arrangements of CO3...     

Incommensurate–normal phase transition in natural melilite: an in situ high-temperature X-ray single-crystal study

The structure of a natural melilite with chemical composition (Ca_1.87Sr_0.02Na_0.10K_0.02)_2.01(Mg_0.96Al_0.07)_1.03(Si_1.98Al_0.02)_2.00O₇ has been investigated by X-ray single-crystal diffraction methods within the temperature range 298–773 K. The values of the coefficient of the modulation wave vector were determined at 298 K, 323 K, 348 K, and 358 K. These values show a continuous linear decrease from 0.2833(6) at 298 K to 0.2763(9) at 358 K. The incommensurate phase undergoes a phase transition to the normal phase at 359 K. The refinements of the structure, carried out at 298 K, 348 K, 359 K, 373 K, 413 K, 463 K, 513 K, 573 K, 673 K, and 773 K, showed that the normal phase (high-temperature phase) does not significantly differ from the basic structure (the average structure of the incommensurate structure). This study confirms that in natural melilites with chemical composition close to that of åkermanite the wavelength of the incommensurate modulation increases when the temperature rises. The different behaviour of the q-vector as a function of temperature in natural and synthetic åkermanite is discussed.     

Performance of limestones laden with mixed salt solutions of Na2SO4–NaNO3 and Na2SO4–K2SO4

The behaviour of two types of limestones having a different porosity, Maastricht and Euville limestone, laden with aqueous solutions of equimolar mixtures of sodium sulphate/sodium nitrate or sodium sulphate/potassium sulphate was investigated. At 50 % RH, the efflorescences on Maastricht samples during the first 30 h of drying consisted of similar amounts of thenardite and darapskite in case of an equimolar mixture of sodium sulphate/sodium nitrate while those on Euville samples under the same conditions contained mainly darapskite. After drying at 20 °C and 85 % RH, thenardite, formed through the precipitation and dehydration of mirabilite, was mostly detected in the efflorescences on both Maastricht and Euville samples. Re-wetting by increasing the RH from 50 to 85 % resulted in substantial damage on Maastricht stone laden with an equimolar mixture of sodium sulphate/sodium nitrate as a consequence of high supersaturation of mirabilite. In case of a contamination with equimolar amounts of sodium sulphate and potassium sulphate, the efflorescence on both limestones during drying at 50 % RH contained predominantly aphthitalite. The observed crystallisation behaviour is compared to the theoretical behaviour. The results indicate a strong influence of stone properties on the crystallisation behaviour of salt mixtures.     

Solid-liquid Equilibria for the Quaternary NaCl–Na2SO4–Na2B4O7–H2O System at 348 K

正1 Introduction China has very abundant liquid mineral resources.Especially,the brine resources in the west of Sichuan Basin are pushed into the first place in China,whose K and B contents are unusually high.These rare liquid mineral resources have very good exploitation prospect(Lin,2001;2006).Generally speaking,phase equilibrium     

High-temperature behaviour of melilite: in situ X-ray diffraction study of gehlenite–åkermanite–Na melilite solid solution

High-temperature X-ray diffraction experiments have been performed on melilite solid solutions, on single crystal and powder samples. In åkermanite–gehlenite series, the volumetric thermal expansion increases from gehlenite, 26.5(2) E-06 K-1, to åkermanite, 31.2(1) E-06 K-1. The variation is related to the cation content in the tetrahedral T1 site of the structure, and the linear expansion along the a axis has the greatest variation as a function of composition. The expansion perpendicular to the tetrahedral layers does not present any significant variation as a function of composition. In the åkermanite–Na melilite series, the presence of Na in the [8]-coordinated site strongly increases the linear expansion along the c axis, while the volumetric expansion decreases from åkermanite to Na melilite, whose value can be extrapolated to 27.4 E-06 K-1     

Ternary Ca–Fe–Mg carbonates: subsolidus phase relations at 3.5 GPa and a thermodynamic solid solution model including order/disorder

Subduction carries atmospheric and crustal carbon hosted in the altered oceanic crystalline basement and in pelagic sediments back into the mantle. Reactions involving complex carbonate solid solutions(s) lead to the transfer of carbon into the mantle, where it may be stored as graphite/diamond, in fluids or melts, or in carbonates. To constrain the thermodynamics and thus reactions of the ternary Ca–Mg–Fe carbonate solid solution, piston cylinder experiments have been performed in the system CaCO₃–MgCO₃–FeCO₃ at a pressure of 3.5 GPa and temperatures of 900–1,100°C. At 900°C, the system has two miscibility gaps: the solvus dolomite–calcite, which closes at X _MgCO3 ~0.7, and the solvus dolomite–magnesite, which ranges from the Mg to the Fe side of the ternary. With increasing temperature, the two miscibility gaps become narrower until complete solid solutions between CaCO₃–Ca_0.5Mg_0.5CO₃ is reached at 1,100°C and between CaCO₃–FeCO₃ at 1,000°C. The solvi are characterized by strong compositional asymmetry and by an order–disorder mechanism. To deal with these features, a solid solution model based on the van Laar macroscopic formalism has been calculated for ternary carbonates. This thermodynamic solid solution model is able to reproduce the experimentally constrained phase relations in the system CaCO₃–MgCO₃–FeCO₃ in a broad P–T range. To test our model, calculated phase equilibria were compared with experiments performed in carbonated mafic protolithes, demonstrating the reliability of our solid solution model at pressures up to 6 GPa in complex systems.     

Experimental study of the pyroxene-garnet phase transition in the Na2MgSi5O12 system at pressures of 13–20 GPa: First synthesis of sodium majorite

Doklady Earth Sciences -     

In situ Raman observation of the crystallization in NaNO3–Na2SO4–H2O solution droplets

Several double salts have been detected in building materials and most of these salts are incongruently soluble compounds. In contrast to single salts, however, no systematic investigations of the crystallization behavior and deleterious effects of incongruently soluble double salts exist. To assess the damage potential of these salts, a systematic investigation of their highly complex behavior is desirable. This paper deals with the crystallization behavior of various solids in the ternary mixed NaNO₃–Na₂SO₄ system including the formation of the double salt darapskite, Na₃NO₃SO₄·H₂O. The crystallization sequence during droplet evaporation experiments at room conditions was determined using Raman and polarization microscopy. The basic idea of this research is to use deviations of the crystallization sequence of a salt or a mixed salt solution from the equilibrium pathway as an indicator to detect the degree of supersaturation. The observed crystallization pathway includes the formation of the metastable phases Na₂SO₄(III), Na₂SO₄(V) and darapskite. The experimental observations are discussed on the basis of the NaNO₃–Na₂SO₄–H₂O phase diagram and the results provide evidence for crystal growth from highly supersaturated solutions in both systems. If the crystals growing under these conditions are confined, these supersaturations result in substantial crystallization pressures.     

Shear modulus, heat capacity, viscosity and structural relaxation time of Na2O–Al2O3–SiO2 and Na2O–Fe2O3–Al2O3–SiO2 melts

The configurational heat capacity, shear modulus and shear viscosity of a series of Na₂O–Fe₂O₃–Al₂O₃–SiO₂ melts have been determined as a function of composition. A change in composition dependence of each of the physical properties is observed as Na₂O/(Na₂O + Al₂O₃) is decreased, and the peralkaline melts become peraluminous and a new charge-balanced Al-structure appears in the melts. Of special interest are the frequency dependent (1 mHz–1 Hz) measurements of the shear modulus. These forced oscillation measurements determine the lifetimes of Si–O bonds and Na–O bonds in the melt. The lifetime of the Al–O bonds could not, however, be resolved from the mechanical spectrum. Therefore, it appears that the lifetime of Al–O bonds in these melts is similar to that of Si–O bonds with the Al–O relaxation peak being subsumed by the Si–O relaxation peak. The appearance of a new Al-structure in the peraluminous melts also cannot be resolved from the mechanical spectra, although a change in elastic shear modulus is determined as a function of composition. The structural shear-relaxation time of some of these melts is not that which is predicted by the Maxwell equation, but up to 1.5 orders of magnitude faster. Although the configurational heat capacity, density and shear modulus of the melts show a change in trend as a function of composition at the boundary between peralkaline and peraluminous, the deviation in relaxation time from the Maxwell equation occurs in the peralkaline regime. The measured relaxation times for both the very peralkaline melts and the peraluminous melts are identical with the calculated Maxwell relaxation time. As the Maxwell equation was created to describe the timescale of flow of a mono-structure material, a deviation from the prediction would indicate that the structure of the melt is too complex to be described by this simple flow equation. One possibility is that Al-rich channels form and then disappear with decreasing Si/Al, and that the flow is dominated by the lifetime of Si–O bonds in the Al-poor peralkaline melts, and by the lifetime of Al–O bonds in the relatively Si-poor peralkaline and peraluminous melts with a complex flow mechanism occurring in the mid-compositions. This anomalous deviation from the calculated relaxation time appears to be independent of the change in structure expected to occur at the peralkaline/peraluminous boundary due to the lack of charge-balancing cations for the Al-tetrahedra.     

Crystallization behavior of Na2SO4–MgSO4 salt mixtures in sandstone and comparison to single salt behavior

We report on the crystallization behavior and the salt weathering potential of Na₂SO₄, MgSO₄ and an equimolar mixture of these salts in natural rock and porous stone. Geochemical modeling of the phase diagram of the ternary Na₂SO₄–MgSO₄–H₂O system was used to determine the equilibrium pathways during wetting (or deliquescence) of incongruently soluble minerals and evaporation of mixed electrolyte solutions. Model calculations include stable and metastable solubilities of the various hydrated states of the single salts and the double salts Na₂Mg(SO₄)₂·4H₂O (bloedite), Na₂Mg(SO₄)₂·5H₂O (konyaite), Na₁₂Mg₇(SO₄)₁₃·15H₂O (loeweite) and Na₆Mg(SO₄)₄ (vanthoffite). In situ Raman spectroscopy was used to study the phase transformations during wetting of pure MgSO₄·H₂O (kieserite) and of the incongruently soluble salts bloedite and konyaite. Dissolution of kieserite leads to high supersaturation resulting in crystallization of higher hydrated phases, i.e. MgSO₄·7H₂O (epsomite) and MgSO₄·6H₂O (hexahydrite). This confirms the high damage potential of magnesium sulfate in salt damage of building materials. The dissolution of the incongruently soluble double salts leads to supersaturation with respect to Na₂SO₄·10H₂O (mirabilite). However, the supersaturation was insufficient for mirabilite nucleation. The damage potential of the two single salts and an equimolar salt mixture was tested in wetting–drying experiments with porous sandstone. While the high damage potential of the single salts is confirmed, it appears that the supersaturation achieved during wetting of the double salts at room temperature is not sufficient to generate high crystallization pressures. In contrast, very high damage potentials of the double salts were found in experiments at low temperature under high salt load.1     

HTP21/c–C2/c phase transition and kinetics of Fe2+–Mg order–disorder of an Fe-poor pigeonite: implications for the cooling history of ureilites

A natural Ca-poor pigeonite (Wo₆En₇₆Fs₁₈) from the ureilite meteorite sample PCA82506-3, free of exsolved augite, was studied by in situ high-temperature single-crystal X-ray diffraction. The sample, monoclinic P2₁/c, was annealed up to 1,093°C to induce a phase transition from P2₁/c to C2/c symmetry. The variation with increasing temperature of the lattice parameters and of the intensity of the b-type reflections (h + k = 2n + 1, present only in the P2₁/c phase) showed a displacive phase transition P2₁/c to C2/c at a transition temperature T _Tr = 944°C, first order in character. The Fe–Mg exchange kinetics was studied by ex situ single-crystal X-ray diffraction in a range of temperatures between the closure temperature of the Fe–Mg exchange reaction and the transition temperature. Isothermal disordering annealing experiments, using the IW buffer, were performed on three crystals at 790, 840 and 865°C. Linear regression of ln k _D versus 1/T yielded the following equation: ln k_\textD = - 3717( ±416)/T(K) + 1.290( ±0.378);    (R² = 0.988) \ln \,k_{\text{D}} = - 3717( \pm 416)/T(K) + 1.290( \pm 0.378);\quad (R^{2} = 0.988) . The closure temperature (T _c) calculated using this equation was ∼740(±30)°C. Analysis of the kinetic data carried out taking into account the e.s.d.'s of the atomic fractions used to define the Fe–Mg degree of order, performed according to Mueller’s model, allowed us to retrieve the disordering rate constants C ₀ K _dis⁺ for all three temperatures yielding the following Arrhenius relation: ln( C₀ K_\textdis ⁺ ) = ln K₀ - Q/(RT) = 20.99( ±3.74) - 26406( ±4165)/T(K);    (R² = 0.988) \ln \left( {C_{0} K_{\text{dis}}^{ + } } \right) = \ln \,K_{0} - Q/(RT) = 20.99( \pm 3.74) - 26406( \pm 4165)/T(K);\quad (R^{2} = 0.988) . An activation energy of 52.5(±4) kcal/mol for the Fe–Mg exchange process was obtained. The above relation was used to calculate the following Arrhenius relation modified as a function of X _Fe (in the range of X _Fe = 0.20–0.50): ln( C₀ K_\textdis ⁺ ) = (21.185 - 1.47X_\textFe ) - \frac(27267 - 4170X_\textFe )T(K) \ln \left( {C_{0} K_{\text{dis}}^{ + } } \right) = (21.185 - 1.47X_{\text{Fe}} ) - {\frac{{(27267 - 4170X_{\text{Fe}} )}}{T(K)}} . The cooling time constant, η = 6 × 10⁻¹ K⁻¹ year⁻¹ calculated on the PCA82506-3 sample, provided a cooling rate of the order of 1°C/min consistent with the extremely fast late cooling history of the ureilite parent body after impact excavation.     

Melt–Fluid and Fluid–Fluid Immiscibility in a Na2SO4–SiO2–H2O System and Implications for the Formation of Rare Earth Deposits

Liquid–liquid immiscibility has crucial influences on geological processes, such as magma degassing and formation of ore deposits. Sulfate, as an important component, associates with many kinds of deposits. Two types of immiscibility, including (i) fluid–melt immiscibility between an aqueous solution and a sulfate melt, and (ii) fluid–fluid immiscibility between two aqueous fluids with different sulfate concentrations, have been identified for sulfate–water systems. In this study, we investigated the immiscibility behaviors of a sulfate- and quartz-saturated Na2SO4–SiO2–H2O system at elevated temperature, to explore the phase relationships involving both types of immiscibility. The fluid–melt immiscibility appeared first when the Na2SO4–SiO2–H2O sample was heated to ~270°C, and then fluid–fluid immiscibility emerged while the sample was further heated to ~450°C. At this stage, the coexistence of one water-saturated sulfate melt and two aqueous fluids with distinct sulfate concentrations was observed. The three immiscible phases remain stable over a wide pressure–temperature range, and the appearance temperature of the fluid–fluid immiscibility increases with the increased pressure. Considering that sulfate components occur extensively in carbonatite-related deposits, the fluid–fluid immiscibility can result in significant sulfate fractionation and provides implications for understanding the formation of carbonatite-related rare earth deposits.     

Infrared and Raman spectroscopy studies of the α–β phase transition in cristobalite

Infrared and Raman spectra of cristobalite are presented as a function of temperature through the phase transition. The modes are assigned and the assignments compared to those of earlier workers. The compatibility of modes at the G-point of the a-phase with the X and G-points of the ß-phase is given. In the transition region of ca. 500–550 K, smooth changes in intensity, frequency and linewidths are seen in many modes, indicative of coexistence of a- and ß-forms.     

The high-pressure C2/c–P21/c phase transition along the LiAlSi2O6–LiGaSi2O6 solid solution

Two synthetic single-crystals with composition Li(Al_0.53Ga_0.47)Si₂O₆ and LiGaSi₂O₆ and space group C2/c at room conditions have been studied under pressure by means of X-ray diffraction using a diamond anvil cell. The unit-cell parameters were determined at 12 and 10 different pressures up to P = 8.849 and P = 7.320 GPa for Li(Al_0.53Ga_0.47)Si₂O₆ and LiGaSi₂O₆, respectively. The sample with mixed composition shows a C2/c to P2₁/c phase transformation between 1.814 and 2.156 GPa, first-order in character. The transition is characterised by a large and discontinuous decrease in the unit-cell volume and by the appearance of the b-type reflections (h + k = odd) typical of the primitive symmetry. The Ga end-member shows the same C2/c to P2₁/c transformation at a pressure between 0.0001 and 0.39 GPa. The low-pressure value at which the transition occurred did not allow collecting any data in the C2/c pressure stability field except that on room pressure. Our results compared with those relative to spodumene (LiAlSi₂O₆, Arlt and Angel 2000a) indicate that the substitution of Al for Ga at the M1 site of Li-clinopyroxenes strongly affects the transition pressure causing a decrease from 3.17 GPa (spodumene) to less than 0.39 GPa (LiGaSi₂O₆) and decreases the volume discontinuity at the transition. As already found for other compounds, the C2/c low-pressure phases are more rigid than the P2₁ /c high-pressure ones. Moreover, the increase of the M1 cation radius causes a decrease in the bulk modulus K _T0. The axial compressibility among the Li-bearing clinopyroxenes indicates that the c axis is the most rigid for the C2/c phases while it becomes the most compressible for the P2₁ /c phases.