High-temperature phase transition and local structure of a hydrous anorthoclase

The in situ Raman spectra of a hydrous anorthoclase at temperatures of 20–800 °C have been measured using a LABRAM-HR spectrometer and Linkam TS 1500 heating stage. The frequencies of modes at 54, 99, 130 and 162 cm^?1 related to M–O vibrations decrease sharply and then increase drastically or keep steady at temperatures above 200 °C. A knee point can be clearly seen at about 200 °C for those modes. The frequency of the mode at 282 cm^?1 shows little temperature dependence. However, for the two strongest modes at 471 and 512 cm^?1, the frequencies decrease linearly with increasing temperature. From evolution of the frequencies of modes at 54, 99, 130 and 162 cm^?1 with temperature, the following conclusions can be drawn: (1) The distance of the local M–O bond shortens rather than lengthens at temperatures above 200 °C; (2) The abrupt changes of the local structure of M site induce a collapse of the framework structure and displacive phase transition at 200 °C; and (3) The H atoms incorporated in anorthoclase are located at the M site. These results are indicative for the structure and properties of anorthoclase at deep earth conditions.     

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.     

High-pressure displacive phase transition of a natural Mg-rich pigeonite

A high-pressure single-crystal X-ray diffraction study has been carried out on a P2₁/c natural Mg-rich pigeonite sample with composition ca. Wo₆En₇₆Fs₁₈ using a diamond anvil-cell. The unit-cell parameters were determined at 14 different pressures to 7.14 GPa. The sudden disappearance of the b-type reflections (h + k = odd) and a strong discontinuity (about 2.8%) in the unit-cell volume indicated a first-order P2₁/c–C2/c phase transition between 4.66 and 4.88 GPa. The P(V) data of the P2₁/c phase were fitted to 4.66 GPa by a third-order Birch–Murnaghan equation of state (BM3 EoS), whereas the limited number of experimental data collected within the C2/c phase between 4.88 and 7.14 GPa were fitted using the same equation of state but with K′ constrained to the value obtained for the P2₁/c fitting. The equation of state coefficients are V ₀ = 424.66(6) ų, K _T0 = 104(2) GPa and K′ = 8(1) for the P2₁/c phase, and V ₀ = 423.6(1) ų, K _T0 = 112.4(8) GPa, and K′ fixed to 8(1) for the C2/c phase. The axial moduli for a, b, and c for the P2₁/c phase were obtained using also a BM3-EoS, while for the C2/c phase only a linear calculation could be performed, and therefore the same approach was applied for comparison also to the P2₁/c phase. In general the C2/c phase exhibits axial compressibilities (β _c > β _a >> β _b) lower than those of the P2₁/c phase (β _b > β _c ≈ β _a; similar to those found in previous studies in clinopyroxenes and orthopyroxenes). The lower compressibility of the C2/c phase compared with that of the P2₁/c could be ascribed to the greater stiffness along the b direction. A previously published relationship between P _c and M2 average cation radius (i.r.) has been updated using all the literature data on P2₁/c clinopyroxene containing large cations at M2 site and our new data. The following weighted regression was obtained: P _c (GPa) = 26(4) ? 28(5) ×  i.r (Å), R ² = 0.97. This improved equation can be used to predict the critical pressure of natural P2₁/c clinopyroxene samples just knowing the composition at M2 site.     

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     

Ferroelastic phase transition in cryolite,Na3AlF6, a mixed fluoride perovskite: High temperature single crystal X-ray diffraction study and symmetry analysis of the transition mechanism

Cryolite, Na₃AlF₆[ = 2Na⁺(Na_0.5 ⁺Al_0.5 ³⁺)F₃] is a mixed fluoride perovskite, in which the corner-sharing octahedral framework is formed by alternating [NaF₆] and [AlF₆] octahedra and the cavities are occupied by Na⁺ ions. At 295 K, it is monoclinic (α phase), space group P2 ₁/n with a = 5.4139 (7), b = 5.6012 (5) and c = 7.7769 (8) Å and β = 90.183 (3)°, Z = 2. A high temperature single crystal X-ray diffraction study in the range 295–900 K indicates a fluctuation-induced first-order phase transition from monoclinic to orthorhombic symmetry at T ₀ ～ 885 K, in contrast to a previous report that it becomes cubic at ～823 K. The space group of the high temperature β phase is Immm with a = 5.632 (4), b = 5.627 (3) and c = 7.958 (4) Å, Z = 2 at 890 K. Above T ₀, the coordination number of the Na⁺ ion in the cavity increases from eight to twelve and the zigzag Na1 — Al octahedral chains parallel to c become straight with the Na1-F-Al angle = 180 °. The phase transition is driven by two coupled primary order parameters. The first corresponds to the rotation of the nearly rigid [AlF₆] group and transforms according to the Γ ₄ ⁺ irreducible representation of Immm. Coupled to the [AlF₆] rotation is a second primary order parameter corresponding to the displacement of the Na2⁺ ion in the cavity from its equilibrium position. This order parameter transforms according to the X ₃ ⁺ irreducible representation of Immm. Following Immm → P2 ₁ /n phase transition, four equivalent domains of P2 ₁/n are determined relative to Immm, which are in an antiphase and/or twin relationship. The abrupt shortening of the octahedral Al-F and Na-F bonds and a sudden change in orientations of the atomic thermal vibration ellipsoids above T ₀ indicate a crossover from displacive to an order-disorder mechanism near the transition temperature. The β phase is interpreted as a dynamic average of four micro-twin and -antiphase domains of the a phase. This view is consistent with the entropy of phase transition, ΔS_trans (11.43 JK^?1 mol^?1) calculated from heat capacity measurements (Anovitz et al. 1987), which corresponds closely to R ln4 (11.53 JK^?1 mol^?1), where 4 is the number of domains formed during the phase transition. The dynamic nature of the β phase is independently confirmed from a considerable narrowing of the ²⁷Al nuclear magnetic resonance (NMR) line-shape above T ₀ (Stebbins et al. 1992).     

A high-pressure neutron diffraction study of the ferroelastic phase transition in RbCaF3

The fluoroperovskite phase RbCaF₃ has been investigated using high-pressure neutron powder diffraction in the pressure range ~0–7.9 GPa at room temperature. It has been found to undergo a first-order high-pressure structural phase transition at ~2.8 GPa from the cubic aristotype phase to a hettotype phase in the tetragonal space group I4/mcm. This transition, which also occurs at ~200 K at ambient pressure, is characterised by a linear phase boundary and a Clapeyron slope of 2.96 × 10^?5 GPa K^?1, which is in excellent agreement with earlier, low-pressure EPR investigations. The bulk modulus of the high-pressure phase (49.1 GPa) is very close to that determined for the low-pressure phase (50.0 GPa), and both are comparable with those determined for the aristotype phases of CsCdF₃, TlCdF₃, RbCdF₃, and KCaF₃. The evolution of the order parameter with pressure is consistent with recent modifications to Landau theory and, in conjunction with polynomial approximations to the pressure dependence of the lattice parameters, permits the pressure variation of the bond lengths and angles to be predicted. On entering the high-pressure phase, the Rb–F bond lengths decrease from their extrapolated values based on a third-order Birch–Murnaghan fit to the aristotype equation of state. By contrast, the Ca–F bond lengths behave atypically by exhibiting an increase from their extrapolated magnitudes, resulting in the volume and the effective bulk modulus of the CaF₆ octahedron being larger than the cubic phase. The bulk moduli for the two component polyhedra in the tetragonal phase are comparable with those determined for the constituent binary fluorides, RbF and CaF₂.     

Neutron powder diffraction study of the orientational order–disorder phase transition in calcite, CaCO3

Neutron powder diffraction studies of calcite on heating towards the orientational order–disorder phase transition show that the phase transition is not a simple analogue of an Ising-like transition, but more similar to a rotational analogue of Lindemann melting. The transition is precipitated by the librational amplitude of the carbonate molecular ions exceeding a critical value rather than a result of a statistical entropy of ‘wrong’ orientations. Using tested interatomic potentials the single-particle orientational potential and nearest-neighbour orientational interactions have been calculated.     

The high-pressure phase transformations of PbO2: An in-situ X-ray diffraction study

Using a diamond-anvil high-pressure cell, an in situ X-ray diffraction study of PbO₂ to about 240 kbar at room temperature has revealed the following phase transformations: rutile → αPbO₂ → tetragonal fluorite → cubic fluorite with increasing pressure. The volume change for the transition rutile → αPbO₂ is about ?2% and for the transition αPbO₂ → tetragonal fluorite is about ?6%, nearly constant within the pressure range of investigation. The volume difference between the tetragonal and the cubic fluorite-type phases is negligibly small. Both the tetragonal and the cubic fluorite-type phases cannot be preserved after removal of the pressure, even after heating by the laser. Both phases have been found to revert to αPbO₂ at one atmospheric pressure. Optically, the colour of αPbO₂ changes from an opaque black to transparent red with increasing pressure. The tetragonal fluorite-type phase, which exists in the pressure range between about 90 and 180 kbar at toom temperature, is slightly transparent with very dark red or brown colour, and the cubic fluorite-type phase is dark red and transparent.     

Linear birefringence and X-Ray diffraction studies of the structural phase transition in titanite,CaTiSiO5

The antiferroelectric phase transition in titanite characterised by a collinear displacement of Ti-atoms from their central octahedral position is investigated using linear optical birefringence and X-ray diffraction techniques. Both methods indicate a continuous transition near 496 K and extra contributions to δΔn and X-ray intensity signals at higher temperatures. The critical exponent of the macroscopic order parameter is found to be β = 0.14 ± 0.02 and the transformation is interpreted in terms of a two-dimensional quasi-spin model. Topological features of the structure agree well with the spatial distribution of the diffuse scattering of the superstructure reflection 40 \(\bar 3\) .     

In situ X-ray diffraction study of an aluminous phase in MORB under lower mantle conditions

In situ X-ray diffraction study was conducted to identify the crystal structure of the “Al-phase”, which was previously reported to form in basaltic compositions at pressures and temperatures of the uppermost part of the lower mantle. Le Bail whole-pattern fitting method was adopted to investigate the structure of the Al-phase under high pressure and temperature as well as ambient conditions. Observed patterns were satisfactorily fitted using the “hexagonal phase” with space group P6₃/m (plus minor amount of garnet) under both of these conditions. On the other hand, the calcium ferrite structure model proposed in some earlier studies based on quench experiments yielded profile-fitting results at significantly lower confidence levels, particularly at simultaneous high pressure and high temperature conditions, suggesting that this phase may not form in oceanic crust materials subducted in the uppermost lower mantle. The difference in densities of hexagonal and calcium ferrite phases, however, is only ~1% under pressures and temperatures of the uppermost part of the lower mantle conditions, which yields a negligible effect on the bulk density of the subducted oceanic crust.     

High temperature single crystal X-ray diffraction studies of the ortho-proto phase transition in enstatite,Mg2Si2O6 at 1360 K

A high temperature single-crystal X-ray diffraction study of enstatite, Mg₂Si₂O₆ was undertaken at 296, 900, 1200, 1360 and 1400 K. During the X-ray data collection at 1360 K (T₀), orthoenstatite (Pbca) transformed to protoenstatite (Pbcn). The unit cell parameters measured at T₀ are a=18.456(4), b=8.960(2) and c=5.270(1) Å for ortho and a=9.306(1), b=8.886(1) and c=5.360(1) Å for proto. The discontinuous increase in c and decrease in b due to the ortho to proto transformation are associated with the drastic unkinking of the silicate chains, whereas the abrupt increase in a results from the large expansion of the M2 — O distances along a coupled with the increase in the out-of-plane tilting of the silicate tetrahedra. Stacking faults form in ortho prior to the phase transition, as well as in proto between 1360 and 1400 K. With increasing temperature, the silicate B chain in ortho straightens faster than the A chain as the configurations of the SiA and SiB tetrahedra tend to become similar. At T₀, the A and B chains with the O3-O3-O3 angles (O3 being the bridging oxygen atom) of 163.0° and 149.5° in ortho, respectively, attain an identical angle of 168.4° in proto. The configuration of the silicate chain in proto resembles that of the A chain in ortho. Rigid-body thermal vibration analysis suggests that between 1200 and 1400 K the largest, the second largest and the smallest thermal librational motions of the [SiO₄] tetrahedra in both ortho and proto are approximately around a, c and b, respectively. Below 1200 K, the largest thermal librational amplitudes of the SiA and SiB tetrahedra in ortho are quite different, but become nearly equivalent at T₀. In contrast to the results reported for all iron-bearing orthopyroxenes at high temperature, switching of the O3B atoms coordinated with the M2 cation occurs during the ortho to proto transformation, but not in ortho below T₀. The ortho-proto transition does not affect the configuration of the M1 octahedron significantly, but results in a decrease of the mean M2 — O bond distance by 0.043 Å and a highly distorted M2 octahedron in proto.     

Neutron diffraction study of the tricritical orientational order/disorder phase transition in calcite at 1260 K

Neutron powder diffraction measurements of the temperature dependence of superlattice reflections in calcite have shown that there is a continuous phase transition at 1260 K. The change in space group symmetry and the halving of the unit cell size on heating indicate that this transition is an orientational order/disorder transition. The intensities of the superlattice reflections show that the temperature dependence of the order parameter, Q, is of the form (T _c –T), where is 0.25, indicating that the transition is tricritical. The transition is accompanied by a large contraction along the c axis on cooling, defining a spontaneous strain e₃ which is related to the order parameter (and hence temperature) via e₃ Q ². No evidence for critical lowering of the value of was found. These measurements confirm that, apart from the detailed critical behaviour, the phase transition in calcite is similar to that observed in NaNO₃.     

田黄的X射线衍射研究

用X射线衍射分析的方法测定了12个田黄样品,其中,青田石1个,寿山石9个,昌化田黄石2个。确定青田石由叶蜡石(58%)、绢云母(36.1%)和高岭石(5.9%)组成;昌化田黄石由迪开石组成;寿山石分别由迪开石、高岭石、叶蜡石及绢云母组成。     

X-ray diffraction study of the orientational order/disorder transition in NaNO3: Evidence for order parameter coupling

The orientational ordering transition R \(R\bar 3m - R\bar 3c\) in NaNO₃ near 552 K has been investigated using x-ray diffraction techniques. NaNO₃ is a model system for CaCO₃ and other minerals with orientational disorder of triangular molecules in a simple NaCl-type matrix. The temperature evolution of the integrated intensities of the superlattice reflection \(\bar 1\) 23 and the fundamental reflection 110 are discussed in terms of Landau theory of two coupled order parameters. It is shown that the known phenomenological critical exponent (Poon and Salje 1988) and the anomalous thermal expansion at T > T _tr (Reeder et al. 1988) can be understood as the result of a Z point instability which mainly describes the NO ₃ ^- disorder, and a second order parameter linked with the spontaneous strain of this phase transition.     

High-pressure single-crystal X-ray diffraction study of jadeite and kosmochlor

The crystal structures of natural jadeite, NaAlSi₂O₆, and synthetic kosmochlor, NaCrSi₂O₆, were studied at room temperature, under hydrostatic conditions, up to pressures of 30.4 (1) and 40.2 (1) GPa, respectively, using single-crystal synchrotron X-ray diffraction. Pressure–volume data have been fit to a third-order Birch–Murnaghan equation of state yielding V ₀ = 402.5 (4) Å³, K ₀ = 136 (3) GPa, and K ₀ ^′  = 3.3 (2) for jadeite and V ₀ = 420.0 (3) Å³, K ₀ = 123 (2) GPa and K ₀ ^′  = 3.61 (9) for kosmochlor. Both phases exhibit anisotropic compression with unit-strain axial ratios of 1.00:1.95:2.09 for jadeite at 30.4 (1) GPa and 1:00:2.15:2.43 for kosmochlor at 40.2 (1) GPa. Analysis of procrystal electron density distribution shows that the coordination of Na changes from 6 to 8 between 9.28 (Origlieri et al. in Am Mineral 88:1025–1032, 2003) and 18.5 (1) GPa in kosmochlor, which is also marked by a decrease in unit-strain anisotropy. Na in jadeite remains six-coordinated at 21.5 (1) GPa. Structure refinements indicate a change in the compression mechanism of kosmochlor at about 31 GPa in both the kinking of SiO₄ tetrahedral chains and rate of tetrahedral compression. Below 31 GPa, the O3–O3–O3 chain extension angle and Si tetrahedral volume in kosmochlor decrease linearly with pressure, whereas above 31 GPa the kinking ceases and the rate of Si tetrahedral compression increases by greater than a factor of two. No evidence of phase transitions was observed over the studied pressure ranges.     

X-ray diffraction study of arsenopyrite at high pressure

The high-pressure X-ray diffraction study of a natural arsenopyrite was investigated up to 28.2 GPa using in situ angle-dispersive X-ray diffraction and a diamond anvil cell at National Synchrotron Light Source, Brookhaven National Laboratory. The 16:3:1 methanol–ethanol–water mixture was used as a pressure-transmitting medium. Pressures were measured using the ruby-fluorescence method. No phase change has been observed up to 28.2 GPa. The isothermal equation of state (EOS) was determined. The values of K ₀, and K′ ₀ refined with a third-order Birch–Murnaghan EOS are K ₀ = 123(9) GPa, and K′ ₀ = 5.2(8). Furthermore, we confirm that the linear compressibilities (β) along a, b and c directions of arsenopyrite is elastically isotropic (β _a  = 6.82 × 10⁻⁴, β _b  = 6.17 × 10⁻⁴ and β _c  = 6.57 × 10⁻⁴ GPa⁻¹).     

Phase transition in CaGeO3 perovskite: Evidence from X-ray powder diffraction,thermal expansion and heat capacity

High-temperature x-ray powder diffraction study by the full pattern Rietveld method of orthorhombic CaGeO₃ (Pbnm at ambient condition) perovskite confirms the previously observed phase transition at Tc=520 K. The measured volumetric thermal expansion coefficients are 3.1 x 10^-5 (K^-1) below Tc and 3.5x 10^-5 (K^-1) above Tc. The space group at T>Tc has been tentatively identified as Cmcm. Such a transition involves the disappearance of one of the two octahedral rotations in the (001) plane, and the doubling of the unit cell volume, with c axis unchanged. Although this transition should be of first order from symmetry considerations, the distortion of the Pbnm phase decreases continuously as the temperate approaches Tc and there is no observable volume discontinuity at Tc. The measured heat capacity places an upper limit on the enthalpy of transition of 50 J/mol, which is quite reasonable in terms of the crystallographic nature of this phase transition.A National Science Foundation Science and Technology Center