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     

Low-temperature heat capacities,entropies and enthalpies of Mg<Subscript>2</Subscript>SiO<Subscript>4</Subscript> polymorphs,and α−β−γ and post-spinel phase relations at high pressure

The low-temperature isobaric heat capacities (C _p) of β- and γ-Mg₂SiO₄ were measured at the range of 1.8–304.7 K with a thermal relaxation method using the Physical Property Measurement System. The obtained standard entropies (S°₂₉₈) of β- and γ-Mg₂SiO₄ are 86.4 ± 0.4 and 82.7 ± 0.5 J/mol K, respectively. Enthalpies of transitions among α-, β- and γ-Mg₂SiO₄ were measured by high-temperature drop-solution calorimetry with gas-bubbling technique. The enthalpies of the α−β and β−γ transitions at 298 K (ΔH°₂₉₈) in Mg₂SiO₄ are 27.2 ± 3.6 and 12.9 ± 3.3 kJ/mol, respectively. Calculated α−β and β−γ transition boundaries were generally consistent with those determined by high-pressure experiments within the errors. Combining the measured ΔH°₂₉₈ and ΔS°₂₉₈ with selected data of in situ X-ray diffraction experiments at high pressure, the ΔH°₂₉₈ and ΔS°₂₉₈ of the α−β and β−γ transitions were optimized. Calculation using the optimized data tightly constrained the α−β and β−γ transition boundaries in the P, T space. The slope of α−β transition boundary is 3.1 MPa/K at 13.4 GPa and 1,400 K, and that of β−γ boundary 5.2 MPa/K at 18.7 GPa and 1,600 K. The post-spinel transition boundary of γ-Mg₂SiO₄ to MgSiO₃ perovskite plus MgO was also calculated, using the optimized data on γ-Mg₂SiO₄ and available enthalpy and entropy data on MgSiO₃ perovskite and MgO. The calculated post-spinel boundary with a Clapeyron slope of −2.6 ± 0.2 MPa/K is located at pressure consistent with the 660 km discontinuity, considering the error of the thermodynamic data.     

An infrared spectroscopic and single-crystal X-ray study of malayaite, CaSnSiO5

Powder infrared spectroscopy and X-ray diffraction techniques on single crystals were used to study the thermal behaviour of malayaite, CaSnSiO₅. Infrared spectra show a discontinuity in the temperature evolution of phonon frequencies and absorbance near 500 K. However, crystal structure data collected at 300, 450, 550, 670, and 750 K show no evidence of a symmetry-breaking phase transition and no split positions. The most obvious change with heating is a tumbling motion of the SnO₆ octahedra and an increase of the anisotropic displacement factors of Ca. The thermal evolution of the mean-square vibrational amplitude of the Ca atom shows a pronounced change in slope near 500 K. The evidence suggests that the 500 K anomaly in malayaite is more similar in character to the 825 K (β-γ) transition as opposed to the 496 K (α-β) transition in synthetic titanite. Received: 26 March 1998 / Revised, accepted: 23 December 1998     

Temperature variation of elastic constants of quartz across the α - β transition

The α − β transition of quartz was successfully observed with using a single sample by means of the rectangular parallelepiped resonance (RPR) method. An oriented rectangular parallelepiped of α-quartz single crystal was prepared and the resonant frequencies of 30–11 vibrational modes were measured from room temperature to 700°C. The softening of quartz crystal was observed as the significant reduction of resonant frequencies near the α–β transition. The present study is the first application of the RPR method to the study of phase transition. The complete set of elastic constants of α- and β-quartz were determined as a function of temperature by the least-squares inversion of the measured frequency data obtained by a single run. This is a merit yielded by the RPR method. It is shown near the α − β transition in both α- and β-quartz that the elastic parameters decrease proportionally to |T−T ₀|⁻ⁿ , where T is temperature and T ₀ is the transition temperature, 573.0°C for α-quartz and 574.3°C for β-quartz. It was also seen that linear incompressibilities K ₁ = (C ₁₁ +C ₁₂ +C ₁₃)/3 and K ₃ = (C ₃₃ +2C ₁₃)/3 decrease rapidly toward the transition, whereas, shear moduli C ₄₄, C _S1 = (C ₁₁ +C ₃₃ -2C ₁₃)/4 and C _S3 = (C ₁₁ -C ₁₂)/2 = C ₆₆ decrease only slightly. The shear modulus C _S3 = C ₆₆ increased slightly in α-quartz. The elastic properties of isotropic aggregate of quartz were calculated, and it is shown that the longitudinal wave velocity significantly decreases at the α − β transition, whereas, the shear wave velocity decreases only slightly.     

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     

New thermoelastic parameters of natural <Emphasis Type="Italic">C</Emphasis>2/<Emphasis Type="Italic">c</Emphasis> omphacite

The compressibility at room temperature and the thermal expansion at room pressure of two disordered crystals (space group C2/c) obtained by annealing a natural omphacite sample (space group P2/n) of composition close to Jd₅₆Di₄₄ and Jd₅₅Di₄₅, respectively, have been studied by single-crystal X-ray diffraction. Using a Birch–Murnaghan equation of state truncated at the third order [BM3-EoS], we have obtained the following coefficients: V ₀ = 421.04(7) Å³, K _T0 = 119(2) GPa, K′ = 5.7(6). A parameterized form of the BM3 EoS was used to determine the axial moduli of a, b and c. The anisotropy scheme is β _c  ≤ β _a  ≤ β _b , with an anisotropy ratio 1.05:1.00:1.07. A fitting of the lattice variation as a function of temperature, allowing for linear dependency of the thermal expansion coefficient on the temperature, yielded α_V(1bar,303K) = 2.64(2) × 10⁻⁵ K⁻¹ and an axial thermal expansion anisotropy of α _b  ≫ α _a  > α _c . Comparison of our results with available data on compressibility and thermal expansion shows that while a reasonable ideal behaviour can be proposed for the compressibility of clinopyroxenes in the jadeite–diopside binary join [K _T0 as a function of Jd molar %: K _T0 = 106(1) GPa + 0.28(2) × Jd_(mol%)], the available data have not sufficient quality to extract the behaviour of thermal expansion for the same binary join in terms of composition.     

An elevated temperature X-ray study of synthetic disordered Na-K alkali feldspars

The temperature dependence of cell parameters for three disordered, synthetic alkali feldspars (Or₁₉, Or₃₈, and Or₁₀₀) has been determined up to 1,000 °C. The samples show no change in composition or degree of Si-Al disorder during the experiments. The triclinic-monoclinic inversion in the sample of composition Or₁₉ occurs at 560 °±10 °C and is accompanied by changes in the rates of expansion of a, b and c; the rate for a increases and those for b and c decrease above the inversion. The b and c parameters in Or₁₀₀ show small decreases with increasing temperature and this may be due to thermal motion effects causing a contraction of cell directions that are fully expanded at room temperature. Calculation of the thermal expansion ellipsoids for the monoclinic phases shows that the major expansion coefficients (₁) for all three samples are more than an order of magnitude greater than the intermediate (₂) and minor (₃) coefficients. Thus the thermal expansion of these phases is dominated by that of ₁ which makes an angle of 22 ± 4 ° with+a; this orientation is parallel to that of the short M-OA2 bonds. The thermal expansion mechanism for monoclinic, disordered alkali feldspars may involve tilting within the framework releasing compression along this direction and allowing the M-OA2 bonds to show high expansion rates. The stretching of the crankshaft units, which are parallel to a, may only play a subordinate role in controlling the expansion of the feldspar framework.     

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     

Occurrence of highly abundant bacterial hopanoids in Dajiuhu peatland, central China

Based on gas chromatography and gas chromatography-mass spectrometry analyses, an amazing amount of hopanoids was detected in the peat deposits in the Dajiuhu National Wetland Park in central China. The hopanoids identified included hopanes (C₂₇-C₃₁ αβ, C₂₇-C₃₂ ββ, C₂₉ βα), hopenes (hop-22(29)-ene, 22,29,30-trinorhop-17(21)-ene, hop-17(21)-ene, hop-13(18)-ene, etc.), hopanoic acids (C₃₁-C₃₄ ββ, C₃₂-C₃₃ βα, C₃₂ αβ), hopanols (C₃₂ ββ and αβ) and hopanone (22,29,30-trinorhop-21-one). C₃₁ αβ-22R hopane was found to be the dominant hopanoid, more abundant than individual nalkanes derived from higher plants. These hopanoids, exclusive of some hopenes, are proposed to be primarily from bacteria. The dominant C₃₁ αβ-22R hopane in young sediments, without any thermal maturation, might be formed through microbial epimerization under acidic conditions in the peatland as suggested before, or directly from aerobic bacteria. This finding highlights the importance of microbes in the formation of peatland as well as in the reconstruction of paleoenvironments.     

The thermoelastic behavior of clintonite up to 10?GPa and 1,000°C

The thermoelastic behavior of a natural clintonite-1M [with composition: Ca_1.01(Mg_2.29Al_0.59Fe_0.12)_Σ3.00(Si_1.20Al_2.80)_Σ4.00O₁₀(OH)₂] has been investigated up to 10 GPa (at room temperature) and up to 960°C (at room pressure) by means of in situ synchrotron single-crystal and powder diffraction, respectively. No evidence of phase transition has been observed within the pressure and temperature range investigated. P–V data fitted with an isothermal third-order Birch–Murnaghan equation of state (BM-EoS) give V ₀ = 457.1(2) ?³, K _T0 = 76(3)GPa, and K′ = 10.6(15). The evolution of the “Eulerian finite strain” versus “normalized stress” shows a linear positive trend. The linear regression yields Fe(0) = 76(3) GPa as intercept value, and the slope of the regression line leads to a K′ value of 10.6(8). The evolution of the lattice parameters with pressure is significantly anisotropic [β(a) = 1/3K _T0(a) = 0.0023(1) GPa⁻¹; β(b) = 1/3K _T0(b) = 0.0018(1) GPa⁻¹; β(c) = 1/K _T0(c) = 0.0072(3) GPa⁻¹]. The β-angle increases in response to the applied P, with: β_P = β₀ + 0.033(4)P (P in GPa). The structure refinements of clintonite up to 10.1 GPa show that, under hydrostatic pressure, the structure rearranges by compressing mainly isotropically the inter-layer Ca-polyhedron. The bulk modulus of the Ca-polyhedron, described using a second-order BM-EoS, is K _T0(Ca-polyhedron) = 41(2) GPa. The compression of the bond distances between calcium and the basal oxygens of the tetrahedral sheet leads, in turn, to an increase in the ditrigonal distortion of the tetrahedral ring, with ∂α/∂P ≈ 0.1°/GPa within the P-range investigated. The Mg-rich octahedra appear to compress in response to the applied pressure, whereas the tetrahedron appears to behave as a rigid unit. The evolution of axial and volume thermal expansion coefficient α with temperature was described by the polynomial α(T) = α₀ + α₁ T ^−1/2. The refined parameters for clintonite are as follows: α₀ = 2.78(4) 10⁻⁵°C⁻¹ and α₁ = −4.4(6) 10⁻⁵°C^1/2 for the unit-cell volume; α₀(a) = 1.01(2) 10⁻⁵°C⁻¹ and α₁(a) = −1.8(3) 10⁻⁵°C^1/2 for the a-axis; α₀(b) = 1.07(1) 10⁻⁵°C⁻¹ and α₁(b) = −2.3(2) 10⁻⁵°C^1/2 for the b-axis; and α₀(c) = 0.64(2) 10⁻⁵°C⁻¹ and α₁(c) = −7.3(30) 10⁻⁶°C^1/2for the c-axis. The β-angle appears to be almost constant within the given T-range. No structure collapsing in response to the T-induced dehydroxylation was found up to 960°C. The HP- and HT-data of this study show that in clintonite, the most and the less expandable directions do not correspond to the most and the less compressible directions, respectively. A comparison between the thermoelastic parameters of clintonite and those of true micas was carried out.     

Temperature evolution between 50 K and 320 K of the thermal expansion tensor of gypsum derived from neutron powder diffraction data

The unit cell parameters, extracted from Rietveld analysis of neutron powder diffraction data collected between 4.2 K and 320 K, have been used to calculate the temperature evolution of the thermal expansion tensor for gypsum for 50 ≤ T ≤ 320 K. At 300 K the magnitudes of the principal axes are α ₁₁  = 1.2(6) × 10⁻⁶ K⁻¹, α ₂₂  = 36.82(1) × 10⁻⁶ K⁻¹ and α ₃₃  = 25.1(5) × 10⁻⁶ K⁻¹. The maximum axis, α ₂₂ , is parallel to b, and using Institution of Radio Engineers (IRE) convention for the tensor orthonormal basis, the axes α ₁₁ and α ₃₃ have directions equal to (−0.979, 0, 0.201) and (0.201, 0, 0.979) respectively. The orientation and temperature dependent behaviour of the thermal expansion tensor is related to the crystal structure in the I2/a setting. Received 12 February 1998 / Revised, accepted 19 October 1998     

Behavior of epidote at high pressure and high temperature: a powder diffraction study up to 10 GPa and 1,200 K

The thermo-elastic behavior of a natural epidote [Ca_1.925 Fe_0.745Al_2.265Ti_0.004Si_3.037O₁₂(OH)] has been investigated up to 1,200 K (at 0.0001 GPa) and 10 GPa (at 298 K) by means of in situ synchrotron powder diffraction. No phase transition has been observed within the temperature and pressure range investigated. P–V data fitted with a third-order Birch–Murnaghan equation of state (BM-EoS) give V ₀ = 458.8(1)ų, K _T0 = 111(3) GPa, and K′ = 7.6(7). The confidence ellipse from the variance–covariance matrix of K _T0 and K′ from the least-square procedure is strongly elongated with negative slope. The evolution of the “Eulerian finite strain” vs “normalized stress” yields Fe(0) = 114(1) GPa as intercept values, and the slope of the regression line gives K′ = 7.0(4). The evolution of the lattice parameters with pressure is slightly anisotropic. The elastic parameters calculated with a linearized BM-EoS are: a ₀ = 8.8877(7) Å, K _T0(a) = 117(2) GPa, and K′(a) = 3.7(4) for the a-axis; b ₀ = 5.6271(7) Å, K _T0(b) = 126(3) GPa, and K′(b) = 12(1) for the b-axis; and c ₀ = 10.1527(7) Å, K _T0(c) = 90(1) GPa, and K’(c) = 8.1(4) for the c-axis [K _T0(a):K _T0(b):K _T0(c) = 1.30:1.40:1]. The β angle decreases with pressure, β_P(°) = β_P0 −0.0286(9)P +0.00134(9)P ² (P in GPa). The evolution of axial and volume thermal expansion coefficient, α, with T was described by the polynomial function: α(T) = α₀ + α₁ T ^−1/2. The refined parameters for epidote are: α₀ = 5.1(2) × 10⁻⁵ K⁻¹ and α₁ = −5.1(6) × 10⁻⁴ K^1/2 for the unit-cell volume, α₀(a) = 1.21(7) × 10⁻⁵ K⁻¹ and α₁(a) = −1.2(2) × 10⁻⁴ K^1/2 for the a-axis, α₀(b) = 1.88(7) × 10⁻⁵ K⁻¹ and α₁(b) = −1.7(2) × 10⁻⁴ K^1/2 for the b-axis, and α₀(c) = 2.14(9) × 10⁻⁵ K⁻¹ and α₁(c) = −2.0(2) × 10⁻⁴ K^1/2 for the c-axis. The thermo-elastic anisotropy can be described, at a first approximation, by α₀(a): α₀(b): α₀(c) = 1 : 1.55 : 1.77. The β angle increases continuously with T, with β_T(°) = β_T0 + 2.5(1) × 10⁻⁴ T + 1.3(7) × 10⁻⁸ T ². A comparison between the thermo-elastic parameters of epidote and clinozoisite is carried out.     

Thermal expansion of gehlenite, Ca2Al[AlSiO7], and the related aluminates LnCaAl[Al2O7] with Ln = Tb, Sm

The thermal expansion of gehlenite, Ca₂Al[AlSiO₇], (up to T=830 K), TbCaAl[Al₂O₇] (up to T=1100 K) and SmCaAl[Al₂O₇] (up to T=1024 K) has been determined. All compounds are of the melilite structure type with space group Thermal expansion data were obtained from in situ X-ray powder diffraction experiments in-house and at HASYLAB at the Deutsches Elektronen Synchrotron (DESY) in Hamburg (Germany). The thermal expansion coefficients for gehlenite were found to be: α₁=7.2(4)×10⁻⁶×K⁻¹+3.6(7)×10⁻⁹ΔT×K⁻² and α₃=15.0(1)×10⁻⁶×K⁻¹. For TbCaAl[Al₂O₇] the respective values are: α₁=7.0(2)×10⁻⁶×K⁻¹+2.0(2)×10⁻⁹ΔT×K⁻² and α₃=8.5(2)×10⁻⁶×K⁻¹+2.0(3)×10⁻⁹ΔT×K⁻², and the thermal expansion coefficients for SmCaAl[Al₂O₇] are: α₁=6.9(2)×10⁻⁶×K⁻¹+1.7(2)×10⁻⁹ΔT×K⁻² and α₃=9.344(5)×10⁻⁶×K⁻¹. The expansion mechanisms of the three compounds are explained in terms of structural trends obtained from Rietveld refinements of the crystal structures of the compounds against the powder diffraction patterns. No structural phase transitions have been observed. While gehlenite behaves like a ‘proper’ layer structure, the aluminates show increased framework structure behavior. This is most probably explained by stronger coulombic interactions between the tetrahedral conformation and the layer-bridging cations due to the coupled substitution (Ca²⁺+Si⁴⁺)–(Ln ³⁺+Al³⁺) in the melilite-type structure. This article has been mistakenly published twice. The first and original version of it is available at .     

Thermophysical properties of the α–β–γ polymorphs of Mg<Subscript>2</Subscript>SiO<Subscript>4</Subscript>: a computational study

Thermophysical properties of the various polymorphs (i.e. α-, β- and γ) of Mg₂SiO₄ were computed with the CRYSTAL06 code within the framework of CO-LCAO-GTF approach by using the hybrid B3LYP density functional method. Potential wells were calculated through a symmetry preserving, variable cell-shape structure relaxation procedure. Vibrational frequencies were computed at the long-wavelength limit corresponding to the center of the Brillouin zone (k → 0). Thermodynamic properties were estimated through a semiclassical approach that combines B3LYP vibrational frequencies for optic modes and the Kieffer’s model for the dispersion relation of acoustic modes. All computed values except volume (i.e. electronic energy, zero point energy, optical vibrational modes, thermal corrections to internal energy, standard state enthalpy and Gibbs free energy of reaction, bulk modulus and its P and T derivatives, entropy, C _V, C _P) are consistent with available experimental data and/or reasonable estimates. Volumes are slightly overestimated relative to those determined directly by X-ray diffraction. A set of optimized volumetric properties that are consistent with the other semiclassical properties of the phases α, β and γ have been derived by optimization procedure such that the calculated boundaries for the α/β and β/γ equilibria have the best overall agreement with the experimental data for these transitions. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.

Defect structure of the low temperature α-cristobalite phase and the cristobalite ⇆ tridymite transformation in (Si-Ge)O2

Using minimum exposure techniques, it is feasible to perform high resolution electron microscopy on the α-cristobalite phase of (Si_0.9 Ge_0.1)O₂, which is extremely radiation sensitive. Such images reveal atomic scale information of twins and tridymite-like stacking faults on (1 1 1)_β planes, as well as of domain boundaries resulting from the β→α transition. Polytype structures are formed in certain cases. Morphological features suggest that the phase transformation cristobalite → tridymite proceeds by means of a zonal dislocation mediated synchro-shear process on (1 1 1)_β planes; the geometry of this process is analyzed. Received: 13 June 1999 / Accepted: 30 October 1999     

Structural thermal behavior of paragonite and its dehydroxylate: a high-temperature single-crystal study

 The lattice constants of paragonite-2M₁, NaAl₂(AlSi₃)O₁₀(OH)₂, were determined to 800 °C by the single-crystal diffraction method. Mean thermal expansion coefficients, in the range 25–600 °C, were: α_a = 1.51(8) × 10⁻⁵, α_b = 1.94(6) × 10⁻⁵, α_c = 2.15(7) ×  10⁻⁵ °C⁻¹, and α_V = 5.9(2) × 10⁻⁵ °C⁻¹. At T higher than 600 °C, cell parameters showed a change in expansion rate due to a dehydroxylation process. The structural refinements of natural paragonite, carried out at 25, 210, 450 and 600 °C, before dehydroxylation, showed that the larger thermal expansion along the c parameter was mainly due to interlayer thickness dilatation. In the 25–600 °C range, Si,Al tetrahedra remained quite unchanged, whereas the other polyhedra expanded linearly with expansion rate proportional to their volume. The polyhedron around the interlayer cation Na became more regular with temperature. Tetrahedral rotation angle α changed from 16.2 to 12.9°. The structure of the new phase, nominally NaAl₂ (AlSi₃)O₁₁, obtained as a consequence of dehydroxylation, had a cell volume 4.2% larger than that of paragonite. It was refined at room temperature and its expansion coefficients determined in the range 25–800 °C. The most significant structural difference from paragonite was the presence of Al in fivefold coordination, according to a distorted trigonal bipyramid. Results confirm the structural effects of the dehydration mechanism of micas and dioctahedral 2:1 layer silicates. By combining thermal expansion and compressibility data, the following approximate equation of state in the PTV space was obtained for paragonite: V/V ₀ = 1 + 5.9(2) × 10⁻⁵ T(°C) − 0.00153(4) P(kbar). Received: 12 July 1999 / Revised, accepted: 7 December 1999     

Thermal expansion and decomposition of jarosite: a high-temperature neutron diffraction study

The structure of deuterated jarosite, KFe₃(SO₄)₂(OD)₆, was investigated using time-of-flight neutron diffraction up to its dehydroxylation temperature. Rietveld analysis reveals that with increasing temperature, its c dimension expands at a rate ~10 times greater than that for a. This anisotropy of thermal expansion is due to rapid increase in the thickness of the (001) sheet of [Fe(O,OH)₆] octahedra and [SO₄] tetrahedra with increasing temperature. Fitting of the measured cell volumes yields a coefficient of thermal expansion, α = α₀ + α₁ T, where α₀ = 1.01 × 10⁻⁴ K⁻¹ and α₁ = −1.15 × 10⁻⁷ K⁻². On heating, the hydrogen bonds, O1···D–O3, through which the (001) octahedral–tetrahedral sheets are held together, become weakened, as reflected by an increase in the D···O1 distance and a concomitant decrease in the O3–D distance with increasing temperature. On further heating to 575 K, jarosite starts to decompose into nanocrystalline yavapaiite and hematite (as well as water vapor), a direct result of the breaking of the hydrogen bonds that hold the jarosite structure together.     

Thermal expansion of gehlenite, Ca2Al[AlSiO7], and the related aluminates LnCaAl[Al2O7] with Ln=Tb, Sm

The thermal expansion of gehlenite, Ca₂Al[AlSiO₇], (up to T=830 K), TbCaAl[Al₂O₇] (up to T=1,100 K) and SmCaAl[Al₂O₇] (up to T=1,024 K) has been determined. All compounds are of the melilite structure type with space group Thermal expansion data was obtained from in situ X-ray powder diffraction experiments in-house and at HASYLAB at the Deutsches Elektronen Synchrotron (DESY) in Hamburg (Germany). The thermal expansion coefficients for gehlenite were found to be: α₁=7.2(4)×10⁻⁶ K⁻¹+3.6(7)×10⁻⁹ΔT K⁻² and α₃=15.0(1)×10⁻⁶ K⁻¹. For TbCaAl[Al₂O₇] the respective values are: α₁=7.0(2)×10⁻⁶ K⁻¹+2.0(2)×10⁻⁹ΔT K⁻² and α₃=8.5(2)×10⁻⁶ K⁻¹+2.0(3)×10⁻⁹ΔT K⁻², and the thermal expansion coefficients for SmCaAl[Al₂O₇] are: α₁=6.9(2)× 10⁻⁶ K⁻¹+1.7(2)×10⁻⁹ΔT K⁻² and α₃=9.344(5)×10⁻⁶ K⁻¹. The expansion-mechanisms of the three compounds are explained in terms of structural trends obtained from Rietveld refinements of the crystal structures of the compounds against the powder diffraction patterns. No structural phase transitions have been observed. While gehlenite behaves like a ’proper’ layer structure, the aluminates show increased framework structure behaviour. This is most probably explained by stronger coulombic interactions between the tetrahedral conformation and the layer-bridging cations due to the coupled substitution (Ca²⁺+Si⁴⁺)-(Ln ³⁺+Al³⁺) in the melilite-type structure. Electronic Supplementary Material Supplementary material is available for this article at