Multiple phase transitions of leonite-type compounds: optical, calorimetric, and X-ray data

Summary Low-temperature phase transitions of leonite-type compounds, K₂Me²⁺(SO₄)₂ · 4H₂O (Me = Mg, Mn, Fe), are investigated by temperature dependent measurements of single-crystal X-ray reflection intensities and lattice parameters. The transition temperatures and the progress of the transitions are determined by birefringence data and differential scanning calorimetry. The cause for the phase transitions of leonite-type compounds is a dynamic disorder of sulphate groups at room temperature (C2/m), that freezes in to an ordered structure (I2/a) at −4(1) °C in leonite, K₂Mg(SO₄)₂ · 4H₂O. At −153(1) °C the crystal structure switches to another ordered phase (P2₁/a). The Mn analogue shows the same succession with transition temperatures at −68(1) °C and −104(1) °C. The disordered room temperature structure of the isotypic mineral mereiterite, K₂Fe(SO₄)₂ · 4H₂O, transforms directly to the ordered P2₁/a structure at 3(2) °C. Analysis of X-ray intensities and of excess birefringence reveals that the displacive I2/a ⇔ P2₁/a phase transition of leonite and Mn-leonite is first order. According to Landau theory the C2/m ⇔ I2/a (leonite, Mn-leonite) and C2/m ⇔ P2₁/a (mereiterite) order-disorder transitions are almost tricritical. Received March 7, 2001; revised version accepted June 27, 2001     

The cubic-tetragonal phase transition in the system majorite (Mg4Si4O12) – pyrope (Mg3Al2Si3O12), and garnet symmetry in the Earth's transition zone

 Garnets along the join Mg₄Si₄O₁₂ (majorite end member) – Mg₃Al₂Si₃O₁₂ (pyrope) synthesized at 2000 °C, 19 GPa are, after quench, tetragonal in the compositional range up to 20 mol% pyrope, but cubic at higher Al contents. Lattice constants a _tet and a _tet in the tetragonal compositional range converge with increasing pyrope contents towards the lattice constant of the cubic garnets. The elastic strain and the intensity of the (222) reflection as a function of composition indicate a second-order phase transition near 20 mol% pyrope. From the wedge-like shape of pseudomerohedral twins and their interaction near 90° twin-boundary corners, as well as from the absence of growth-induced dislocations, it is concluded that the Al-poor garnets are also cubic at synthesis conditions but invert by (Mg,Si) ordering on the octahedral sites into tetragonal phases of space group I4₁/a upon quench. This implies that the cubic-to-tetragonal phase transition in Mg₄Si₄O₁₂ garnet occurs below 2000 °C at 19 GPa and at even lower temperatures in more aluminous compositions. A composition-dependent Landau model is consistent with a direct transformation from Ia3d to I4₁/a. Comparison of the T-X stability field of majorite-pyrope garnets with the chemistry of majorite-rich garnets expected to occur in the Earth's transition zone shows that the latter will be cubic under all conditions. Softening of elastic constants, which commonly accompanies ferroelastic phase transitions, may affect the seismic velocities of garnets in the deeper transition zone where majorite contents are highest. Received July 5, 1996 / Revised, accepted September 24, 1996     

Phase transitions in leucite,KAISi2O6

An order parameter treatment of the phase transitions in leucite, KAlSi₂O₆, at approximately 950 and 920 K: (cubic) I4₁ acd(tetragonal) I4₁ a(tetragonal) is presented in terms of Landau theory and induced representation theory. The Al-Si order with decreasing temperature is taken as the primary order parameter to which other distortions (K⁺ ion displacements, strain components, etc.) couple linearly. The expected Al-Si ordering behavior and the associated K⁺ ion displacements for both transitions are derived and the resulting twin domain orientations are listed. The sequence of phase transitions results from a coupling of ₃ ⁺ and ₄ ⁺ representations. The Landau free energy for the five-dimensional reducible representation has been simplified to two components resulting in a linearquadratic coupling of the components. Possible phase diagrams are derived by free energy minimization. The cubic tetragonal transition is first-order, whereas the tetragonal-tetragonal transition may be second order. A tricritical point exists at which the first-order transition changes to second-order.     

The structure of SrTiOGeO4 and its solid solution with CaTiOGeO4

Solid solubility and structural phase transitions in (Ca _x Sr_1-x )TiOGeO₄have been studied by means of in situ high temperature X-ray powder diffraction. The displacive A2/a–P2₁/a phase transition analogous to titanite has been followed across the solid solution. Strain analysis indicates a transition temperature of T _c=594 ± 10 K for SrTiOGeO₄ and the additional occurrence of an isosymmetric anomaly at T _i =800 ± 25 K, in analogy to the isomorphous compound CaTiOGeO₄. Lattice parameters as a function of temperature and composition have been determined by X-ray powder diffraction between room temperature and a maximum temperature of 1123 K. The e ₁₁ and e ₁₃ components dominate the strain tensor. All compositions across the solid solution exhibit close to tricritical phase transitions P2₁/a–A2/a. The critical temperature remains almost unaffected by substitution of Sr for Ca, but the magnitude of the spontaneous strain drops significantly with even small amounts of Sr present.     

Elasticity and equation of state of Li<Subscript>2</Subscript>B<Subscript>4</Subscript>O<Subscript>7</Subscript>

A single crystal X-ray diffraction study on lithium tetraborate Li₂B₄O₇ (diomignite, space group I4₁ cd) has been performed under pressure up to 8.3 GPa. No phase transitions were found in the pressure range investigated, and hence the pressure evolution of the unit-cell volume of the I4₁ cd structure has been described using a third-order Birch–Murnaghan equation of state (BM-EoS) with the following parameters: V ₀  = 923.21(6) ų, K ₀  = 45.6(6) GPa, and K′ = 7.3(3). A linearized BM-EoS was fitted to the axial compressibilities resulting in the following parameters a ₀  = 9.4747(3) Å, K _0a  = 73.3(9) GPa, K′ _a  = 5.1(3) and c ₀  = 10.2838(4) Å, K _0c  = 24.6(3) GPa, K′ _c  = 7.5(2) for the a and c axes, respectively. The elastic anisotropy of Li₂B₄O₇ is very large with the zero-pressure compressibility ratio β _0c /β _0a  = 3.0(1). The large elastic anisotropy is consistent with the crystal structure: A three-dimensional arrangement of relatively rigid tetraborate groups [B₄O₇]²⁻ forms channels occupied by lithium along the polar c–axis, and hence compression along the c axis requires the shrinkage of the lithium channels, whereas compression in the a direction depends mainly on the contraction of the most rigid [B₄O₇]²⁻ units. Finally, the isothermal bulk modulus obtained in this work is in general agreement with that derived from ultrasonic (Adachi et al. in Proceedings-IEEE Ultrasonic Symposium, 228–232, 1985; Shorrocks et al. in Proceedings-IEEE Ultrasonic Symposium, 337–340, 1981) and Brillouin scattering measurements (Takagi et al. in Ferroelectrics, 137:337–342, 1992).     

Phase relations of REE-bearing minerals during the metamorphism of carbonaceous shales in the Tim-Yastrebovskaya structure,Voronezh Crystalline Massif,Russia

Paleoproterozoic carbonaceous shales in the Tim-Yastrebovskii ancient rift, which underwent zonal metamorphism at 350–550°C, contain REE mineralization of silicates (allanite, thorite, and Ce-P huttonite) fluorcarbonates (bastnaesite and synchysite), phosphates (monazite and xenotime), and REE-bearing apatite. The reason for the wide occurrence of bastnaesite and other REE minerals is relatively high REE concentrations in the sulfide-bearing carbonaceous shales, with these elements accumulated in the organic matter in the course of diagenesis. Reaction textures with REE-bearing chlorite, bastnaesite, and allanite suggest that REE-bearing chlorite and bastnaesite provided REE for the forming of higher temperature allanite and monazite. This is corroborated by the REE patterns of the monazite, allanite, and bastnaesite, which are almost identical and are characterized by the strong predominance of LREE. The replacements of REE minerals during metamorphism at 350–550°C took place via a number successive transitions: (1) Mnz → Aln, Chl _REE → Bst, Chl _REE → Aln, Bst → Aln and (2) Bst → Mnz and Ap _LREE → Mnz. These replacements can be accounted for by prograde metamorphic reactions.     

Electronic absorption and luminescence spectroscopic studies of kyanite single crystals: differentiation between excitation of FeTi charge transfer and Cr3+ dd transitions

A selected set of five different kyanite samples was analysed by electron microprobe and found to contain chromium between <0.001 and 0.055 per formula unit (pfu). Polarized electronic absorption spectroscopy on oriented single crystals, R₁, R₂-sharp line luminescence and spectra of excitation of λ₃- and λ₄-components of R₁-line of Cr³⁺-emission had the following results: (1) The Fe²⁺–Ti⁴⁺ charge transfer in c-parallel chains of edge connected M(1) and M(2) octahedra shows up in the electronic absorption spectra as an almost exclusively c(||Z′)-polarized, very strong and broad band at 16000 cm⁻¹ if <, in this case the only band in the spectrum, and at an invariably lower energy of 15400 cm⁻¹ in crystals with  ≥ . The energy difference is explained by an expansion of the O_f–O_k, and O_b–O_m edges, by which the M(1) and M(2) octahedra are interconnected (Burnham 1963), when Cr³⁺ substitutes for Al compared to the chromium-free case. (2) The Cr³⁺ is proven in two greatly differing crystal fields a and b, giving rise to two sets of bands, derived from the well known dd transitions of Cr^{3+ 4}A_2g→⁴T_2g(F)(I), →⁴T_1g(F)(II), and →⁴T_1g(P)(III). Band energies in the two sets a and b, as obtained by absorption, A, and excitation, E, agree well: I: 17300(a, A), 17200(a, E), 16000(b, A), 16200(b, E); II: 24800(a, A), 24400(a, E); 22300(b, A), 22200(b, E); III: 28800(b,A) cm⁻¹. Evaluation of crystal field parameters from the bands in the electronic spectra yield Dq(a)=1730 cm⁻¹, Dq(b)=1600 cm⁻¹, B(a)=790 cm⁻¹, B(b)=620 cm⁻¹ (errors ca. ±10 cm⁻¹), again in agreement with values extracted from the λ³, λ⁴ excitation spectra. The CF-values of set a are close to those typical of Cr³⁺ substituting for Al in octahedra of other silicate minerals without constitutional OH⁻ as for sapphirine, mantle garnets or beryl, and are, therefore, interpreted as caused by Cr³⁺ substituting for Al in some or all of the M(1) to M(4) octaheda of the kyanite structure, which are crystallographically different but close in their mean Al–O distances, ranging from 1.896 to 1.919 A (Burnham 1963), and slight degrees of distortion. Hence, band set a originates from substitutive Cr³⁺ in the kyanite structural matrix. The CF-data of Cr³⁺ type b, expecially B, resemble those of Cr³⁺ in oxides, especially of corundum type solid solutions or eskolaite. This may be interpreted by the assumption that a fraction of the total chromium contents might be allocated in a precursor of a corundum type exsolution. Received: 3 January 1997 / Revised, accepted: 2 May 1997     

Displacive phase transitions in C-centred clinopyroxenes: spodumene, LiScSi2O6 and ZnSiO3

The clinopyroxenes spodumene (LiAlSi₂O₆), LiScSi₂O₆ and ZnSiO₃, all with space group C2/c at ambient conditions, were studied under high pressures by single-crystal X-ray diffraction in a diamond-anvil cell. Changes in the evolution of the unit-cell parameters, optical properties and the appearance of h + k odd reflections characteristic of a primitive lattice, indicate that all three pyroxenes undergo phase transitions. The transitions are mostly displacive in character, and are non-quenchable. Transition pressures are 3.19 GPa in spodumene, ∼0.6 GPa in LiScSi₂O₆ and 1.92 GPa in ZnSiO₃. The space group of all three high-pressure phases was determined to be P2₁/c by structure refinement to single-crystal X-ray intensity data collected in the DAC. In the ZnSiO₃ clinopyroxene the intermediate P2₁/c phase further transforms to a second C2/c phase (HP-C2/c) at 4.9 GPa (confirmed by structure refinement). The volume change at this transition is about 2.6%, three times larger than in the first phase transition, and typical of the P2₁/c→ HP-C2/c phase transitions found previously in MgSiO₃, FeSiO₃, etc. These results therefore provide the first direct evidence that the HP-C2/c and the HT-C2/c structures of pyroxenes are distinct polymorphs with the same space group. The phase transition from C2/c to P2₁/c symmetry in spodumene and LiScSi₂O₆ therefore occurs because the polymorphs stable at ambient conditions are isotypic to the high-temperature C2/c phases of clinopyroxenes such as pigeonite and clinoenstatite. Received: 22 December 1999 / Accepted: 7 June 2000     

Crystal field transitions in Co2[Al4Si5]O18 cordierite and CoAl2O4 spinel determined by neutron spectroscopy

Inelastic magnetic neutron scattering has been used to determine the energy of the ⁴ A ₂→⁴ T ₂ transition in CoAl₂O₄ spinel and the δ₁ transition in Co₂[Al₄Si₅]O₁₈ cordierite. The observed crystal field splitting in Co-spinel is 485 meV (3900 cm⁻¹), which corresponds to a crystal field stabilization energy of 56.2 kJmol⁻¹. The transition energy of the δ₁ transition in Co-cordierite has been determined to be 21 meV (170 cm⁻¹). The present data demonstrate that magnetic neutron scattering can be used to measure crystal field transitions at energies of interest in the study of 3d-containing silicates. It may be used to measure transition energies when the use of optical spectroscopy is inappropriate. Received: 30 January 1997 / Accepted: 5 July 1997     

Time-resolved luminescence of Fe3+ and Mn2+ ions in hydrous volcanic glasses

 Time-resolved luminescence spectra of natural and synthetic hydrous volcanic glasses with different colors and different Fe, Mn, and H₂O content were measured, and the implications for the glass structure are discussed. Three luminescence ranges are observed at about 380–460, 500–560, and 700–760 nm. The very short-living (lifetimes less than 40 ns) blue band (380–460 nm) is most probably due to the ⁴T₂(⁴D) →⁶A₁(⁶S) and ⁴A₁(⁴G) →⁶A₁(⁶S) ligand field transitions of Fe³⁺. The green luminescence (500–560 nm) arises from the Mn²⁺ transition ⁴T₁(⁴G) →⁶A₁(⁶S). It shows weak vibronic structure, short lifetimes less than 250 μs, and indicates that Mn²⁺ is tetrahedrally coordinated, occupying sites with similar distortions and ion–oxygen interactions in all samples studied. The red luminescence (700–760 nm) arising from the ⁴T₁(⁴G) →⁶A₁(⁶S) transition of Fe³⁺ has much longer lifetimes of the order of several ms, and indicates that ferric iron is also mainly tetrahedrally coordinated. Increasing the total water content of the glasses leads to quenching of the red luminescence and decrease of the distortions of the Fe³⁺ polyhedra. Received: 30 July 2001 / Accepted: 15 November 2001     

Paleostress-tensor analysis of late deformation events in the Odenwald Crystalline Complex and comparison with other units of the Mid-German Crystalline Rise, Germany

Summary Geometric data of fault planes and fault plane lineations, together with the observed sense of shear on the slip planes, were used to calculate paleostress tensors and fields responsible for the post metamorphic peak D3 and D4 deformation events in the four Odenwald units sensu Krohe (1991). The paleostress fields were calculated using the method of Will and Powell (1991). As inferred from the paleostress analysis, the D3 strike-slip deformation west of the Otzberg fault zone was caused by a, ± N-S directed, compressional regional stress field, with shallowly plunging σ₁ axes and σ₃ directions that plunge at shallow to moderate angles to the E or W; the calculated mean orientations are: σ₁ 06 → 350, σ₂ 77 → 234 and σ₃ 12 → 085. The B?llsteiner Odenwald east of the Otzberg fault zone was not affected by this stress field. This implies that the Bergstr?sser and B?llsteiner Odenwald were spatially separated and formed independent crustal blocks during D3. The D4 faulting event is recognised in all areas investigated, even though most prominently in units III and IV, and juxtaposed the Bergstr?sser and B?llsteiner Odenwald. This faulting episode was caused by a paleostress field with a steeply westerly plunging σ₁ axis and a shallowly southsoutheasterly plunging σ₃ axis. The orientations of the principal stresses are: σ₁ 52 → 270, σ₂ 38 → 085 and σ₃ 06 → 174. With continued deformation from D3 to D4, there was a progressive change in the orientation of the stress field indicating a change from a N-S compressional to extensional stress field, accompanied by the progressive development of strike-slip faults and late normal faults. Paleostress field orientations in the Pfalz Forest, SW of the Odenwald, determined by Fl?ttmann and Oncken (1992) are very similar to those obtained for the Odenwald region and indicate a regionally consistent stress pattern in the southwestern part of the Mid-German Crystalline Rise (MGCR) during strike-slip and normal faulting deformations.

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Zusammenfassung Paleostress-Tensor Analyse sp?ter Deformationsereignisse im Odenwald-Kristallin und ein Vergleich mit anderen Einheiten der Mitteldeutschen Kristallinzone, Deutschland Für die vier Odenwald-Einheiten im Sinne von Krohe (1991) wurden Pal?ostressfelder für die Blattverschiebungs- und Abschiebungsereignisse D3 und D4 mit der Methode von Will und Powell (1991) berechnet. Die Analyse ergibt, da? das regionale Spannungsfeld, das westlich der Otzberg-Zone im Bergstr?sser Odenwald zum D3-Ereignis führte, ein ± N-S gerichtetes kompressives Stresssfeld war. Die σ₁-Achse f?llt flach nach N bzw. S ein, die σ₃-Achse mit kleinen bis moderaten Winkeln nach E bzw. W; die berechneten Orientierungen der Hauptspannungsrichtungen sind: σ₁ 08 → 350, σ₂ 77 → 234 and σ₃ 12 → 085. Der B?llsteiner Odenwald, ?stlich der Otzberg-Zone, wurde von diesem Spannungsfeld nicht erfa?t. Dies impliziert, da? Bergstr?sser und B?llsteiner Odenwald w?hrend des D3-Ereignisses voneinander getrennt waren und separate Krusteneinheiten darstellten. Auswirkungen der D4-Deformation k?nnen im gesamten Untersuchungsgebiet erkannt werden, am st?rksten jedoch in den Einheiten III und IV. Dieses Ereignis wurde von einem Pal?ostressfeld mit einer steil nach W einfallenden σ₁- und einer flach nach SSE einfallenden σ₃-Achse verursacht und führte zum Zusammenschlu? von Bergstr?sser und B?llsteiner Odenwald. Die berechneten Orientierungen der Hauptspannungsrichtungen sind: σ₁ 52 → 270, σ₂ 38 → 085 und σ₃ 06 → 174. Die Rotation der Hauptspannungsrichtungen war mit einer ?nderung von einem kompressionalen N-S gerichteten (D3) hin zu einem extensionalen (D4) Stressfeld verbunden. Die erzielten Ergebnisse sind sehr ?hnlich mit Resultaten, die Fl?ttmann und Oncken (1992) im Pf?lzer Wald ermittelten. Dies weist auf ein regional übereinstimmendes Spannungsfeld im SW-Teil der Mitteldeutschen Kristallinzone hin.

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Received July 8, 1999; revised version accepted March 28, 2000     

The stability and equation of state for the cotunnite phase of TiO2 up to 70 GPa

The stability and equation of state for the cotunnite phase in TiO₂ were investigated up to a pressure of about 70 GPa by high-pressure in situ X-ray diffraction measurements using a laser-heated diamond anvil cell. The transition sequence under high pressure was rutile → α-PbO₂ phase → baddeleyite phase → OI phase → cotunnite phase with increasing pressure. The cotunnite phase was the most stable phase at pressures from 40 GPa to at least 70 GPa. The equation of state parameters for the cotunnite phase were established on the platinum scale using the volume data at pressures of 37–68 GPa after laser annealing, in which the St value, an indicator of the magnitude of the uniaxial stress component in the samples, indicates that these measurements were performed under quasi-hydrostatic conditions. The third-order Birch-Murnaghan equation of state at K ₀′ = 4.25 yields V ₀ = 15.14(5) cm³/mol and K ₀ = 294(9), and the second-order Birch-Murnaghan equation of state yields V ₀ = 15.11(5) cm³/mol and K ₀ = 306(9). Therefore, we conclude that the bulk modulus for the cotunnite phase is not comparable to that of diamond.     

Phase transitions in leucite: X-ray diffraction studies

Lattice parameters, and intensities of selected X-ray reflexions, have been measured as a function of temperature for natural leucite, to characterise the phase transformation behaviour. At low temperatures leucite has a large ferroelastic distortion, but the temperature evolution of lattice parameters cannot be explained in terms of a purely ferroelastic phase transition; in particular, the considerable change in volume with temperature implies an additional transition mechanism, which we correlate with off-centring of K-ions in the low-temperature phase, and a collapse of the 111 structural channels. The transition behavior can therefore be rationalised in terms of two competing mechanisms: (I) Ferroelastic (consistent with the change m3m 4/mmm); (II) Volume-changing (consistent with m3m 4/m). Coupling of the two order parameters Q_I, and Q_II gives rise to the intermediate 4/mmm tetragonal phase.Our results confirm the existence of an I4 ₁/aI4 ₁/acd transition, but the non-disappearance of the 200 reflexion at high temperatures implies that the expected transition from I4₁/acd to Ia3d (cubic) symmetry does not occur. We attribute this to a residual strain field conjugated to the order parameter, due to defects (with possible Al/Si order). Nevertheless, within our experimental resolution, the lattice becomes metrically cubic at 665° C.     

Calculation of CO2 activities using scapolite equilibria: constraints on the presence and composition of a fluid phase during high grade metamorphism

Thermodynamic and phase equilibrium data for scapolite have been used to calculate CO₂ activities (aCO₂) and to evaluate the presence or absence of a fluid phase in high-grade scapolite bearing meta-anorthosite, granulites, calc-silicates, and mafix xenoliths. The assemblage scapolite-plagioclase-garnet±quartz may be used to calculate or limit aCO₂ by the reaction Meionite+Quartz = Grossular+Anorthite+CO₂. Granulites from four high-grade terranes (Grenville Province, Canada; Sargut Belt, India; Furua Complex, Tanzania; Bergen Arcs, Norway) yield aCO₂=0.4-1, with most >0.7. For scapolite-bearing granulites from the Furua Complex, in which aCO₂≥0.9, calculated H₂O activities (aH₂O) based on phlogopite dehydration equilibria are uniformly low (0.1–0.2). The aCO₂ calculated for meta-anorthosite from the Grenville Province, Ontario, ranges from 0.2 to 0.8. For Grenville meta-anorthosite also containing epidote, the aH₂O calculated from clinozoisite dehydration ranges from 0.2 to 0.6. Calc-silicates from the Grenville, Sargur, and Furua terranes mostly yield aCO₂< 0.5. The presence of calcite and/or wollastonite provides additional evidence for the low aCO₂ in calc-silicates. Samples from six xenolith localities (Lashaine, Tanzania; Eifel, W. Germany; Lesotho; Delegate, Gloucester, and Hill 32, Australia) yield a wide range of aCO₂ (0.1 to >1). The calculated fluid activities are consistent with metamorphism (1) in the presence of a mixed CO₂−H₂O fluid phase in which CO₂ is the dominant fluid species but other C−O−H−S species are minor, (2) in the absence of a bulk fluid phase (“fluid-absent metamorphism”), or (3) in the presence of a fluid-bearing melt phase. The results for many granulites and Grenville meta-anorthosite are consistent with the presence of a CO₂-rich, mixed CO₂−H₂O fluid phase. In contrast the relatively restricted and low values of aCO₂ for calc-silicates require an H₂O-rich fluid or absence of a fluid phase during metamorphism. The range of values for xenoliths are most consistent with absence of a fluid phase. The primary implication of these results is that a CO₂-rich fluid accounts for the reduced aH2_O in scapolite-bearing granulites. However, scapolite may be stable with a wide range of fluid compositions or in the absence of a fluid phase, and the presence of scapolite is not a priori evidence of a CO₂-rich fluid phase. In addition, close association of scapolite-free mafic granulites with scapolite-bearing granulites having identical mineral compositions in the Furua Complex, and the absence of scapolite from most granulite terranes implies that a CO₂-rich fluid phase is not pervasive on an outcrop scale or common to all granulite terranes. Contribution No. 474 from the Mineralogical Laboratory, University of Michigan     

A powder neutron diffraction study of the crystal structure of the fluoroperovskite NaMgF<Subscript>3</Subscript> (neighborite) from 300 to 3.6 K

The cell dimensions and crystal structures of the fluoroperovskite NaMgF₃ (neighborite), synthesized by solid state methods, have been determined by powder neutron diffraction and Rietveld refinement over the temperature range 300–3.6 K using Pt metal as an internal standard for calibration of the neutron wavelength. These data show that Pbnm NaMgF₃ does not undergo any phase transitions to structures of lower symmetry with decreasing temperature. The cell dimensions and atomic coordinates together with polyhedron volumes and distortion indices are given for Pbnm NaMgF₃ at 25 K intervals from 300 to 3.6 K. Decreases in the a and c cell dimensions reach a saturation point at 50 K, whereas the b dimension becomes saturated at 150 K. The distortion of the structure of Pbnm NaMgF₃ from the aristotype cubic structure is described in terms of the tilting of the MgF₆ octahedra according to the tilt scheme a ⁻ a ⁻ c ⁺ . With decreasing temperature the antiphase tilt (a ⁻) increases from 14.24° to 15.39°, whereas the in-phase tilt (c ⁺ ) remains effectively constant at ∼10.7°. Changes in the tilt angles are insufficient to cause changes in the coordination sphere of Na that might induce a low temperature phase transition. The structure of Pbnm NaMgF₃ is also described in terms of normal mode analysis and displacements of the condensed normal modes are compared with those of Pbnm KCaF₃.     

X-ray powder diffraction study on the modulated high temperature forms of SiO2 tridymite between 110 and 220 °C

 The crystal structure of intermediate incommensurate tridymite was refined at 150 °C from powder data. Upon cooling from above 220 °C, the basic structure with space group symmetry C222₁ is gradually distorted from orthorhombic to monoclinic symmetry. With decreasing temperature, the monoclinic angle γ smoothly opens up to 90.3°, while a displacive modulation with temperature-dependent wavelength develops. The 3 + 1 dimensional superspace group of the incommensurate phase is C112₁(αβ0). The modulation mainly consists of two sinusoidal transverse displacement waves for the silicon atoms coupled to rotations of the rigid SiO_4/2 tetrahedra. The wave vector is r=0.1192(1)a* − 0.0043(1)b* at 150 °C. Below 150 °C tridymite discontinuously transforms to another orthorhombic phase and the modulation partially locks in at the wave vector r ₁=1/3a*. Simultaneously, an additional incommensurate modulation with r ₂= 0.0395(1)b* − 0.3882(1)c* is formed. The two-dimensional modulation does not vary significantly with the temperature. Received: 13 September 2000 / Accepted: 29 January 2001     

Thermal behaviour and kinetics of dehydration of gypsum in air from in situ real-time laboratory parallel-beam X-ray powder diffraction

Thermal behaviour and kinetics of dehydration of gypsum in air have been investigated using in situ real-time laboratory parallel-beam X-ray powder diffraction data evaluated by the Rietveld method. Thermal expansion has been analysed from 298 to 373 K. The high-temperature limits for the cell edges and for the cell volume, calculated using the Einstein equation, are 4.29 × 10⁻⁶, 4.94 × 10⁻⁵, 2.97 × 10⁻⁵, and 8.21 × 10⁻⁵. Thermal expansion of gypsum is strongly anisotropic being larger along the b axis mainly due to the weakening of hydrogen bond. Dehydration of gypsum has been investigated in isothermal conditions within the 348–403 K range with a temperature increase of 5 K. Dehydration proceeds through the CaSO₄·2H₂O → CaSO₄·0.5H₂O → γ-CaSO₄ steps. Experimental data have been fitted with the Avrami equation to calculate the empirical activation energy of the process. No change in transformation mechanism has been observed within the analysed temperature range and the corresponding E _a is 109(12) kJ/mol.     

In situ high-temperature powder X-ray diffraction study on the spinel solid solutions (Mg1?xMnx)Cr2O4

Using a conventional high-T furnace, the solid solutions between magnesiochromite and manganochromite, (Mg_1−x Mn _x )Cr₂O₄ with x = 0.00, 0.19, 0.44, 0.61, 0.77 and 1.00, were synthesized at 1,473 K for 48 h in open air. The ambient powder X-ray diffraction data suggest that the V–x relationship of the spinels does not show significant deviation from the Vegard’s law. In situ high-T powder X-ray diffraction measurements were taken up to 1,273 K at ambient pressure. For the investigated temperature range, the unit-cell parameters of the spinels increase smoothly with temperature increment, indicating no sign of cation redistribution between the tetrahedral and octahedral sites. The V–T data were fitted with a polynomial expression for the volumetric thermal expansion coefficient (a_T = a₀ + a₁ T + a₂ T ^{- 2} \alpha_{T} = a_{0} + a_{1} T + a_{2} T^{ - 2} ), which yielded insignificant a ₂ values. The effect of the composition on a ₀ is adequately described by the equation a ₀ = [17.7(8) − 2.4(1) × x] 10⁻⁶ K⁻¹, whereas that on a ₁ by the equation a ₁ = [8.6(9) + 2.1(11) × x] 10⁻⁹ K⁻².     

Modelling phase–assemblage diagrams for magnesian metapelites in the system K2O–FeO–MgO–Al2O3–SiO2–H2O: geodynamic consequences for the Monte Rosa nappe, Western Alps

Magnesian metamorphic rocks with metapelitic mineral assemblage and composition are of great interest in metamorphic petrology for their ability to constrain P–T conditions in terranes where metamorphism is not easily visible. Phase–assemblage diagrams for natural and model magnesian metapelites in the system KFMASH are presented to document how phase relationships respond to water activity, bulk composition, pressure and temperature. The phase assemblages displayed on these phase diagrams are consistent with natural mineral assemblages occurring in magnesian metapelites. It is shown that the equilibrium assemblages at high pressure conditions are very sensitive to a(H₂O). Specifically, the appearance of the characteristic HP assemblage chloritoid–talc–phengite–quartz (with excess H₂O) in the magnesian metapelites of the Monte Rosa nappe (Western Alps) is due to the reduction of a(H₂O). Furthermore, the mineral assemblages are determined by the whole-rock FeO/(FeO+MgO) ratio and effective Al content X _A as well as P and T. The predicted mineral associations for the low- and high-X _A model bulk compositions of magnesian metapelites at high pressure are not dependent on the X _A variations as they show a similar sequence of mineral assemblages. Above 20 kbar, the prograde sequence of assemblages associated with phengite (with excess SiO₂ and H₂O) for low- and high-X _A bulk compositions of magnesian metapelites is: carpholite–chlorite → chlorite–chloritoid → chloritoid–talc → chloritoid–talc–kyanite → talc–garnet–kyanite → garnet–kyanite ± biotite. At low to medium P–T conditions, a low-X _A stabilises the phengite-bearing assemblages associated with chlorite, chlorite + K-feldspar and chlorite + biotite while a high-X _A results in the chlorite–phengite bearing assemblages associated with pyrophyllite, andalusite, kyanite and carpholite. A high-X _A magnesian metapelite with nearly iron-free content stabilises the talc–kyanite–phengite assemblage at moderate to high P–T conditions. Taking into account the effective bulk composition and a(H₂O) involved in the metamorphic history, the phase–assemblage diagrams presented here may be applied to all magnesian metapelites that have compositions within the system KFMASH and therefore may contribute to gaining insights into the metamorphic evolution of terranes. As an example, the magnesian metapelites of the Monte Rosa nappe have been investigated, and an exhumation path with P–T conditions for the western roof of the Monte Rosa nappe has been derived for the first time. The exhumation shows first a near-isothermal decompression from the Alpine eclogite peak conditions around 24 kbar and 505°C down to approximately 8 kbar and 475°C followed by a second decompression with concomitant cooling.M. Frey: deceased     

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.