High-pressure polymorphism and structural transitions of norsethite,BaMg(CO3)2

In situ high-pressure investigations on norsethite, BaMg(CO₃)₂, have been performed in sequence of diamond-anvil cell experiments by means of single-crystal X-ray and synchrotron diffraction and Raman spectroscopy. Isothermal hydrostatic compression at room temperature yields a high-pressure phase transition at P _c ≈ 2.32 ± 0.04 GPa, which is weakly first order in character and reveals significant elastic softening of the high-pressure form of norsethite. X-ray structure determination reveals C2/c symmetry (Z = 4; a = 8.6522(14) Å, b = 4.9774(13) Å, c = 11.1542(9) Å, β = 104.928(8)°, V = 464.20(12) Å³ at 3.00 GPa), and the structure refinement (R ₁ = 0.0763) confirms a distorted, but topologically similar crystal structure of the so-called γ-norsethite, with Ba in 12-fold and Mg in octahedral coordination. The CO₃ groups were found to get tilted off the ab-plane direction by ~16.5°. Positional shifts, in particular of the Ba atoms and the three crystallographically independent oxygen sites, give a higher flexibility for atomic displacements, from which both the relatively higher compressibility and the remarkable softening originate. The corresponding bulk moduli are K ₀ = 66.2 ± 2.3 GPa and dK/dP = 2.0 ± 1.8 for α-norsethite and K ₀ = 41.9 ± 0.4 GPa and dK/dP = 6.1 ± 0.3 for γ-norsethite, displaying a pronounced directional anisotropy (α: β _a ^?1  = 444(53) GPa, β _c ^?1  = 76(2) GPa; γ: β _a ^?1  = 5.1(1.3) × 10³ GPa, β _b ^?1  = 193(6) GPa β _c ^?1  = 53.4(0.4) GPa). High-pressure Raman spectra show a significant splitting of several modes, which were used to identify the transformation in high-pressure high-temperature experiments in the range up to 4 GPa and 542 K. Based on the experimental series of data points determined by XRD and Raman measurements, the phase boundary of the α-to-γ-transition was determined with a Clausius–Clapeyron slope of 9.8(7) × 10^?3 GPa K^?1. An in situ measurement of the X-ray intensities was taken at 1.5 GPa and 411 K in order to identify the nature of the structural variation on increased temperatures corresponding to the previously reported transformation from α- to β-norsethite at 343 K and 1 bar. The investigations revealed, in contrast to all X-ray diffraction data recorded at 298 K, the disappearance of the superstructure reflections and the observed reflection conditions confirm the anticipated \(R\bar{3}m\) space-group symmetry. The same superstructure reflections, which disappear as temperature increases, were found to gain in intensity due to the positional shift of the Ba atoms in the γ-phase.     

Perturbations of the Kepler Problem in Global Coordinates: A Program

The present paper is a brief report of how, along the lines of a previous paper, the implementation of the program KEPLER¹, for the numerical integration of the perturbations of the Kepler problem, has been carried out.     

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 and phase transitions in åkermanite and gehlenite

Thermal expansion has been measured by laboratory and synchrotron X-ray powder diffraction for end-member åkermanite (ak, Ca₂MgSi₂O₇) and gehlenite (ge, Ca₂Al₂SiO₇) in the range 20–1,500 K. In ak in the range 340–390 K, there is a negative linear thermal expansion in [001] direction. This is related to the phase transition from an incommensurate modulated structure (IC) to a normal one (N). The volumetric mean thermal expansion coefficients for ak and ge, obtained with a linear fit of the experimental data in the temperature range 298–1,400 K, are respectively 32.1×10^–6 and 28.3×10^–6 K^–1 . The variation of the c/a ratio with temperature, due to different thermal expansion along the crystallographic axes, can be related to the different behaviour of the tetrahedral layers in the N and IC phases. Analysis of the variation of the superstructure peaks intensity across the phase transition confirms the tricritical behaviour of the IC/N transition in ak.     

On the crystal chemistry and elastic behavior of a phlogopite 3<Emphasis Type="Italic">T</Emphasis>

The crystal chemistry and the elastic behavior under isothermal conditions up to 9 GPa of a natural, and extremely rare, 3T-phlogopite from Traversella (Valchiusella, Turin, Western Alps) [(K_0.99Na_0.05Ba_0.01)(Mg_2.60Al_0.20Fe _0.21 ²⁺ )[Si_2.71Al_1.29O₁₀](OH)₂, space group P3₁12, with a = 5.3167(4), c = 30.440(2) Å, and V = 745.16(9) ų] have been investigated by electron microprobe analysis in wavelength dispersion mode, single-crystal X-ray diffraction at 100 K, and in situ high-pressure synchrotron radiation powder diffraction (at room temperature) with a diamond anvil cell. The single-crystal refinement confirms the general structure features expected for trioctahedral micas, with the inter-layer site partially occupied by potassium and sodium, iron almost homogeneously distributed over the three independent octahedral sites, and the average bond distances of the two unique tetrahedra suggesting a disordered Si/Al-distribution (i.e., 〈T1-O〉 ~ 1.658 and 〈T2-O〉 ~ 1.656 Å). The location of the H-site confirms the orientation of the O–H vector nearly perpendicular to (0001). The refinement converged with R ₁(F) = 0.0382, 846 unique reflections with F _O > 4σ(F _O) and 61 refined parameters, and not significant residuals in the final difference-Fourier map of the electron density (+0.77/?0.37 e ^?/ų). The high-pressure experiments showed no phase transition within the pressure range investigated. The P–V data were fitted with a Murnaghan (M-EoS) and a third-order Birch-Murnaghan equation of state (BM-EoS), yielding: (1) M-EoS, V ₀ = 747.0(3) ų, K _T0 = 44.5(24) GPa, and K′ = 8.0(9); (2) BM-EoS, V ₀ = 747.0(3) ų, K _T0 = 42.8(29) GPa, and K′ = 9.9(17). A comparison between the elastic behavior in response to pressure observed in 1M- and 3T-phlogopite is made.     

The high-pressure stability of chlorite and other hydrates in subduction mélanges: experiments in the system Cr<Subscript>2</Subscript>O<Subscript>3</Subscript>–MgO–Al<Subscript>2</Subscript>O<Subscript>3</Subscript>–SiO<Subscript>2</Subscript>–H<Subscript>2</Subscript>O

The solubility of chromium in chlorite as a function of pressure, temperature, and bulk composition was investigated in the system Cr₂O₃–MgO–Al₂O₃–SiO₂–H₂O, and its effect on phase relations evaluated. Three different compositions with X _Cr = Cr/(Cr + Al) = 0.075, 0.25, and 0.5 respectively, were investigated at 1.5–6.5 GPa, 650–900 °C. Cr-chlorite only occurs in the bulk composition with X _Cr = 0.075; otherwise, spinel and garnet are the major aluminous phases. In the experiments, Cr-chlorite coexists with enstatite up to 3.5 GPa, 800–850 °C, and with forsterite, pyrope, and spinel at higher pressure. At P > 5 GPa other hydrates occur: a Cr-bearing phase-HAPY (Mg_2.2Al_1.5Cr_0.1Si_1.1O₆(OH)₂) is stable in assemblage with pyrope, forsterite, and spinel; Mg-sursassite coexists at 6.0 GPa, 650 °C with forsterite and spinel and a new Cr-bearing phase, named 11.5 Å phase (Mg:Al:Si = 6.3:1.2:2.4) after the first diffraction peak observed in high-resolution X-ray diffraction pattern. Cr affects the stability of chlorite by shifting its breakdown reactions toward higher temperature, but Cr solubility at high pressure is reduced compared with the solubility observed in low-pressure occurrences in hydrothermal environments. Chromium partitions generally according to \(X_{\text{Cr}}^{\text{spinel}}\) ? \(X_{\text{Cr}}^{\text{opx}}\) > \(X_{\text{Cr}}^{\text{chlorite}}\) ≥ \(X_{\text{Cr}}^{\text{HAPY}}\) > \(X_{\text{Cr}}^{\text{garnet}}\). At 5 GPa, 750 °C (bulk with X _Cr = 0.075) equilibrium values are \(X_{\text{Cr}}^{\text{spinel}}\) = 0.27, \(X_{\text{Cr}}^{\text{chlorite}}\) = 0.08, \(X_{\text{Cr}}^{\text{garnet}}\) = 0.05; at 5.4 GPa, 720 °C \(X_{\text{Cr}}^{\text{spinel}}\) = 0.33, \(X_{\text{Cr}}^{\text{HAPY}}\) = 0.06, and \(X_{\text{Cr}}^{\text{garnet}}\) = 0.04; and at 3.5 GPa, 850 °C \(X_{\text{Cr}}^{\text{opx}}\) = 0.12 and \(X_{\text{Cr}}^{\text{chlorite}}\) = 0.07. Results on Cr–Al partitioning between spinel and garnet suggest that at low temperature the spinel- to garnet-peridotite transition has a negative slope of 0.5 GPa/100 °C. The formation of phase-HAPY, in assemblage with garnet and spinel, at pressures above chlorite breakdown, provides a viable mechanism to promote H₂O transport in metasomatized ultramafic mélanges of subduction channels.