High-pressure X-ray diffraction study of ε-FeOOH

An in situ synchrotron X-ray diffraction study was carried out on ε-FeOOH at room temperature up to a pressure of 8.6 GPa using the energy-dispersive method. The linear compressibility was determined to be β _a  = 1.69(3) × 10⁻³ GPa⁻¹, β _b  = 2.86(6) × 10⁻³ GPa⁻¹, and β _c  = 1.73(5) × 10⁻³ GPa⁻¹. The b-axis of the unit cell is more compressible than the a and c axes. The pressure–volume data were fitted to a third-order Birch–Murnaghan equation of state. The best fit was found using a room temperature isothermal bulk modulus of K ₀ = 126(3) GPa and its pressure derivative K′ = 10(1).     

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.     

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).     

Elastic behaviour and structural evolution of topaz at high pressure

The elastic behaviour and the high-pressure structural evolution of a natural topaz, Al_2.00Si_1.05O_4.00(OH_0.26F_1.75), have been investigated by means of in situ single-crystal X-ray diffraction up to 10.55(5) GPa. No phase transition has been observed within the pressure range investigated. Unit-cell volume data were fitted with a third-order Birch-Murnaghan Equation of State (III-BM-EoS). The III-BM-EoS parameters, simultaneously refined using the data weighted by the uncertainties in P and V, are: V ₀=345.57(7) ų, K _T0=164(2) GPa and K′=2.9(4). The axial-EoS parameters are: a ₀=4.6634(3) Å, K _T0(a)=152(2) GPa, K′(a)=2.8(4) for the a-axis; b ₀=8.8349(5) Å, K _T0(b)=224(3) GPa, K′(b)=2.6(6) for the b-axis; c ₀=8.3875(7) Å, K _T0(c)=137(2) GPa, K′(c)=2.9(4) for the c-axis. The magnitude and the orientation of the principal Lagrangian unit-strain ellipsoid were determined. At P−P ₀=10.55 GPa, the ratios ε₁:ε₂:ε₃ are 1.00:1.42:1.56 (with ε₁||b, ε₂||a, ε₃||c and |ε₃| > |ε₂| > |ε₁|). Four structural refinements, performed at 0.0001, 3.14(5), 5.79(5) and 8.39(5) GPa describe the structural evolution in terms of polyhedral distortions.     

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.     

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.     

Synchrotron X-ray analysis of norbergite, Mg2.98Fe0.01Ti0.02Si0.99O4(OH0.31F1.69) structure at high pressure up to 8.2?GPa

The natural norbergite, Mg_2.98Fe_0.01Ti_0.02Si_0.99O₄(OH_0.31F_1.69) is examined by synchrotron X-ray diffraction analysis at pressures up to 8.2 GPa. The measured linear compressibilities of the crystallographic axes are β _a  = 2.18(4) × 10⁻³, β _b  = 2.93(7) × 10⁻³, and β _c  = 2.77(7) × 10⁻³ (GPa⁻¹), respectively and the calculated isothermal bulk modulus of the norbergite is K _T = 113(2) GPa based on the Birch–Murnaghan equation of state assuming a pressure derivative of K′ = 4. The crystal structures of norbergite are refined at room temperature and pressures of 4.7, 6.3, and 8.2 GPa, yielding R values for the structure refinements of 4.6, 5.3, and 5.3%, respectively. The bulk moduli of the polyhedral sites are 293(15) GPa for the tetrahedron, 106(5) GPa for the M2 octahedron, 113(2) GPa for the M3 octahedron, and 113(3) GPa for the total void space. The bulk modulus exhibits a good linear correlation with the filling factor for polyhedral sites in structures of the humite minerals and forsterite, reflecting the Si⁴⁺ + 4O²⁻ ⇔ □ + 4(OH, F)⁻ substitution in the humite minerals. Moreover, two simply linear trends were observed in the relationship between bulk modulus and packing index for natural minerals and dense hydrous magnesium silicate minerals. This relationship would reflect that the differences in compression mechanism were involved with hydrogen bonding in these minerals. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

High pressure study of ScAlO3 perovskite

The crystal structure of orthorhombic (Pbnm) ScAlO₃ perovskite has been refined to 5 GPa using single-crystal X-ray diffraction. The compression of the structure if anisotropic with β _a =1.39(3)×10⁻³ GPa⁻¹, β _b =1.14(3)×10⁻³ GPa⁻¹ and β _c =1.84(3)×10⁻³ GPa⁻¹. The isothermal bulk modulus of ScAlO₃, K _T , determined from fitting a Birch-Murnaghan equation of state (K ^′ _T =4) to the volume compression data is 218(1) GPa. The interoctahedral angles to not vary significantly with pressure, and the compression of the structure is entirely attributable to compression of the AlO₆ octahedra. The compressibilities of the constituent AlO₆ and ScO₁₂ are well matched: β_Al−O=1.6×10⁻³ GPa⁻¹ and β_Sc−O=1.5×10⁻³ GPa⁻¹. Therefore the distortion of the structure shows no significant change with increasing pressure. Received: 18 August 1997 / Revised, accepted: 11 November 1997     

Synchrotron X-ray powder diffraction study of natural P2 /n-omphacites at high-pressure conditions

 Synchrotron X-ray powder diffraction experiments at high pressure conditions (0.0001–13 GPa) were performed at ESRF (Grenoble-F), on the beamline ID9, to investigate the bulk elastic properties of natural P2/n-omphacites, with quasi-ideal composition. The monoclinic cell parameters a, b, c and β were determined as a function of pressure, and their compressibility coefficients are 0.00277(7), 0.00313(8), 0.00292(5) and 0.00116(4) GPa⁻¹, respectively. The third-order Birch-Murnaghan equation of state was used to interpolate the experimental P−V data, obtaining K ₀=116.6(±2.5) GPa and K′₀=6.03(±0.60). K ₀ was also determined by means of the axial and angular compressibilities [122.5(±1.7) GPa], and of the finite Lagrangian strain theory [121.5(±1.0) GPa]. The discrepancies on K ₀ are discussed in the light of a comparison between techniques to determine the bulk modulus of crystalline materials from static compression diffraction data. Received: 22 February 2000 / Accepted: 10 July 2000     

Effect of incorporation of iron and aluminum on the thermoelastic properties of magnesium silicate perovskite

In situ X-ray diffraction measurements of Fe- and Al-bearing MgSiO₃-rich perovskite (FeAl-Pv), which was synthesized from a natural orthopyroxene, were performed at pressures of 19–32 GPa and temperatures of 300–1,500 K using a combination of a Kawai-type apparatus with eight sintered-diamond anvils and synchrotron radiation. Two runs were performed using a high-pressure cell with two sample chambers, and both MgSiO₃ perovskite (Mg-Pv) and FeAl-Pv were synthesized simultaneously in the same cell. Thus we were able to measure specific volumes (V/V ₀) of Mg-Pv and FeAl-Pv at the same P−T conditions. At all the measurement conditions, values of the specific volume of FeAl-Pv are consistent with those of Mg-Pv within 2 Standard Deviation, strongly suggesting that effect of incorporation of iron and aluminum on the thermoelastic properties of magnesium silicate perovskite is undetectable in this composition, pressure, and temperature range. Two additional runs were performed using a high-pressure cell that has one sample chamber and unit-cell volumes of FeAl-Pv were measured at pressures and temperatures up to 32 GPa and 1,500 K, respectively. All the unit-cell volume data of FeAl-Pv perovskite were fitted to the high temperature Birch–Murnaghan equation of state and a complete set of thermoelastic parameters of this perovskite was determined with an assumption of K′ _300,0 = 4. The determined parameters are K _300,0 = 243(3) GPa, (∂K _T,0/∂T) _P = −0.030(8) GPa/K, a ₀ = 2.78(18) × 10⁻⁵ K⁻¹, and b ₀ = 0.88(28) × 10⁻⁸ K⁻², where a ₀ and b ₀ are the coefficients of the following expression describing the zero-pressure thermal expansion: α _T,0 = a ₀ + b ₀ T. The equation-of-state parameters of FeAl-Pv are in good agreement with those of MgSiO₃ perovskite at the conditions corresponding to the uppermost part of the lower mantle.     

X-ray diffraction study of magnesite at high pressure and high temperature

 P–V–T measurements on magnesite MgCO₃ have been carried out at high pressure and high temperature up to 8.6 GPa and 1285 K, using a DIA-type, cubic-anvil apparatus (SAM-85) in conjunction with in situ synchrotron X-ray powder diffraction. Precise volumes are obtained by the use of data collected above 873 K on heating and in the entire cooling cycle to minimize non-hydrostatic stress. From these data, the equation-of-state parameters are derived from various approaches based on the Birch-Murnaghan equation of state and on the relevant thermodynamic relations. With K′₀ fixed at 4, we obtain K₀=103(1) GPa, α(K⁻¹)=3.15(17)×10⁻⁵ +2.32(28)×10⁻⁸ T, (∂K_T/∂T)_P=−0.021(2) GPaK⁻¹, (dα/∂P)_T=−1.81×10⁻⁶ GPa⁻¹K⁻¹ and (∂K_T/∂T)_V= −0.007(1) GPaK⁻¹; whereas the third-order Birch-Murnaghan equation of state with K′₀ as an adjustable parameter yields the following values: K₀=108(3) GPa, K′₀=2.33(94), α(K⁻¹)=3.08(16)×10⁻⁵+2.05(27) ×10⁻⁸ T, (∂K_T/∂T)_P=−0.017(1) GPaK⁻¹, (dα/∂P)_T= −1.41×10⁻⁶ GPa⁻¹K⁻¹ and (∂K_T/∂T)_V=−0.008(1) GPaK⁻¹. Within the investigated P–T range, thermal pressure for magnesite increases linearly with temperature and is pressure (or volume) dependent. The present measurements of room-temperature bulk modulus, of its pressure derivative, and of the extrapolated zero-pressure volumes at high temperatures, are in agreement with previous single-crystal study and ultrasonic measurements, whereas (∂K_T/∂T)_P, (∂α/∂P)_T and (∂K_T/∂T)_V are determined for the first time in this compound. Using this new equation of state, thermodynamic calculations for the reactions (1) magnesite=periclase+CO₂ and (2) magnesite+enstatite=forsterite+CO₂ are consistent with existing experimental phase equilibrium data. Received September 28, 1995/Revised, accepted May 22, 1996     

The effect of oxygen vacancies and aluminium substitution on the high-pressure properties of brownmillerite-structured Ca2Fe2?xAlxO5

The structural evolution with pressure and the equations of state of three members of the brownmillerite solid solution, Ca₂(Fe_2−x Al _x )O₅, have been determined by single-crystal X-ray diffraction up to a maximum pressure of 9.73 GPa. The compositions of the samples were x = 0.00 and x = 0.37 (with Pnma symmetry) and x = 0.55 (with I2mb symmetry). No phase transitions were observed in the experiments. The equation of state parameters determined from the pressure-volume data are K _0T = 128.0 (7) GPa, K′₀ = 5.8 (3) for the sample with x = 0.00, K _0T = 131 (2) GPa, K′₀ = 5.5 (4) for x = 0.37, and K _0T = 137.5 (6) GPa, K′₀ = 4 for x = 0.55. The bulk modulus therefore increases with Al content, being 11% higher in the x = 0.55 sample than in the Al-free sample. The unit-cell compression is anisotropic, with the c-axis being stiffer than a or b, and the anisotropy increases with increasing Al content of the structure. The structural response to pressure of all samples is similar. The (Al,Fe)O₄ tetrahedra and the (Al,Fe)O₆ octahedra undergo approximately isotropic compression. There is an increase in the twists of the chains of corner-sharing (Al,Fe)O₄ tetrahedra, and an increase in the tilts of the (Al,Fe)O₆ octahedra, because these framework polyhedra are stiffer than the Ca–O bonds to the extra-framework Ca site. The alignment of the two shortest Ca–O bonds sub-parallel to [001] accounts for the relative stiffness of the c-axis and thus the elastic anisotropy. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

The nonlinear anomalous lattice elasticity associated with the high-pressure phase transition in spodumene: a high-precision static compression study

The high-pressure behavior of the lattice elasticity of spodumene, LiAlSi₂O₆, was studied by static compression in a diamond-anvil cell up to 9.3 GPa. Investigations by means of single-crystal XRD and Raman spectroscopy within the hydrostatic limits of the pressure medium focus on the pressure ranges around ~3.2 and ~7.7 GPa, which have been reported previously to comprise two independent structural phase transitions. While our measurements confirm the well-established first-order C2/c–P2₁/c transformation at 3.19 GPa (with 1.2% volume discontinuity and a hysteresis between 0.02 and 0.06 GPa), both unit-cell dimensions and the spectral changes observed in high-pressure Raman spectra give no evidence for structural changes related to a second phase transition. Monoclinic lattice parameters and unit-cell volumes at in total 59 different pressure points have been used to re-calculate the lattice-related properties of spontaneous strain, volume strain, and the bulk moduli as a function of pressure across the transition. A modified Landau free energy expansion in terms of a one component order parameter has been developed and tested against these experimentally determined data. The Landau solution provides a much better reproduction of the observed anomalies than any equation-of-state fit to data sets truncated below and above P _tr, thus giving Landau parameters of K ₀ = 138.3(2) GPa, K′ = 7.46(5), λ _V  = 33.6(2) GPa, a = 0.486(3), b = −29.4(6) GPa and c = 551(11) GPa.     

On the elastic behaviour of zeolite mordenite: a synchrotron powder diffraction study

The high-pressure elastic behaviour of a synthetic zeolite mordenite, Na₆Al_6.02Si_42.02O₉₆·19H₂O [a=18.131(2), b=20.507(2), c=7.5221(5) Å, space group Cmc2₁], has been investigated by means of in situ synchrotron X-ray powder diffraction up to 5.68 GPa. No phase transition has been observed within the pressure range investigated. Axial and volume bulk moduli have been calculated using a truncated second-order Birch–Murnaghan equation-of-state (II-BM-EoS). The refined elastic parameters are: V ₀=2801(11) ų, K _T0= 41(2) GPa for the unit-cell volume; a ₀=18.138(32) Å, K _T0(a)=70(8) GPa for the a-axis; b ₀=20.517(35) Å, K _T0(b)=29(2) GPa for the b-axis and c ₀=7.531(5) Å, K _T0(c)=38(1) GPa for the c-axis [K _T0(a): K _T0(b): K _T0(c)=2.41:1.00:1.31]. Axial and volume Eulerian finite strain versus “normalized stress” plots (fe–Fe plot) show an almost linear trend and the weighted linear regression through the data points yields the following intercept values: Fe(0)=39(4) GPa for V; Fe _a (0)=65(18) GPa for a; Fe _b (0)=28(3) GPa for b; Fe _c (0)=38(2) GPa for c. The magnitudes of the principal Lagrangian unit-strain coefficients, between 0.47 GPa (the lowest HP-data point) and each measured P>0.47 GPa, were calculated. The unit-strain ellipsoid is oriented with ε₁ || b, ε₂ || c, ε₃ || a and |ε₁|> |ε₂|> |ε₃|. Between 0.47 and 5.68 GPa the relationship between the unit-strain coefficient is ε₁: ε₂: ε₃=2.16:1.81:1.00. The reasons of the elastic anisotropy are discussed.An erratum to this article can be found at     

Thermoelasticity and high-<Emphasis Type="Italic">T</Emphasis> behaviour of anthophyllite

The thermoelastic behaviour of anthophyllite has been determined for a natural crystal with crystal-chemical formula ^ANa_0.01 ^B(Mg_1.30Mn_0.57Ca_0.09Na_0.04) ^C(Mg_4.95Fe_0.02Al_0.03) ^T(Si_8.00)O₂₂ ^W(OH)₂ using single-crystal X-ray diffraction to 973 K. The best model for fitting the thermal expansion data is that of Berman (J Petrol 29:445–522, 1988) in which the coefficient of volume thermal expansion varies linearly with T as α _V,T  = a ₁ + 2a ₂ (T − T ₀): α₂₉₈ = a ₁ = 3.40(6) × 10⁻⁵ K⁻¹, a ₂ = 5.1(1.0) × 10⁻⁹ K⁻². The corresponding axial thermal expansion coefficients for this linear model are: α _a ,₂₉₈ = 1.21(2) × 10⁻⁵ K⁻¹, a _2,a  = 5.2(4) × 10⁻⁹ K⁻²; α _b ,₂₉₈ = 9.2(1) × 10⁻⁶ K⁻¹, a _2,b  = 7(2) × 10⁻¹⁰ K⁻². α _c ,₂₉₈ = 1.26(3) × 10⁻⁵ K⁻¹, a _2,c  = 1.3(6) × 10⁻⁹ K⁻². The thermoelastic behaviour of anthophyllite differs from that of most monoclinic (C2/m) amphiboles: (a) the ε ₁ − ε ₂ plane of the unit-strain ellipsoid, which is normal to b in anthophyllite but usually at a high angle to c in monoclinic amphiboles; (b) the strain components are ε ₁ ≫ ε ₂ > ε ₃ in anthophyllite, but ε ₁ ~ ε ₂ ≫ ε ₃ in monoclinic amphiboles. The strain behaviour of anthophyllite is similar to that of synthetic C2/m ^ANa ^B(LiMg) ^CMg₅ ^TSi₈ O₂₂ ^W(OH)₂, suggesting that high contents of small cations at the B-site may be primarily responsible for the much higher thermal expansion ⊥(100). Refined values for site-scattering at M4 decrease from 31.64 epfu at 298 K to 30.81 epfu at 973 K, which couples with similar increases of those of M1 and M2 sites. These changes in site scattering are interpreted in terms of Mn ↔ Mg exchange involving M1,2 ↔ M4, which was first detected at 673 K.     

High-pressure behaviour of Ca-rich C 2 /c clinopyroxenes along the join diopside-enstatite (CaMgSi2O6-Mg2Si2O6)

 An in situ high-pressure (HP) X-ray diffraction investigation of synthetic diopside and of the Ca_0.8Mg_1.2Si₂O₆ clinopyroxene (Di₈₀En₂₀) was performed up to respectively P=40.8 and 15.1 GPa, using high brilliance synchrotron radiation. The compression of the cell parameters is markedly anisotropic, with β_b ⋙ β_c > β_a > β_asinβ for any pressure range and for both diopside and Di₈₀En₂₀. The compressibility along the crystallographic axes decreases significantly with pressure and is higher in Di₈₀En₂₀ than in diopside. The β cell parameter decreases as well with pressure, at a higher rate in Di₈₀En₂₀. The cell volume decreases at almost the same rate for the two compositions, since in diopside a higher compression along a* occurs. A change in the mechanism of deformation at P higher than about 5–10 GPa is suggested for both compositions from the analysis of the strain induced by compression. In diopside at lower pressures, the deformation mainly occurs, at a similar rate, along the b axis and at a direction 145° from the c axis on the (0 1 0) plane. At higher pressures, instead, the deformation occurs mostly along the b axis. In Di₈₀En₂₀ the orientation of the strain axes is the same as in diopside. The substitution of Ca with Mg in the M2 site induces at a given pressure a higher deformation on (0 1 0) with respect to diopside, but a similar change in the compressional behaviour is found. Changes in the M2 polyhedron with pressure can explain the above compressional behaviour. A third-order Birch-Murnaghan equation of state was fit to the retrieved volumes, with K=105.1(9) GPa, K′=6.8(1) for diopside and K=107.3(1.4) GPa, K′=5.7(3) for Di₈₀En₂₀; the same equation can be applied for any pressure range. The elasticity of diopside is therefore not significantly affected by Mg substitution into the M2 site, in contrast to the significant stiffening occurring for Ca substitution into Mg-rich orthopyroxenes. Received: 3 January 2000 / Accepted: 21 May 2000     

Computer modelling of a pressure induced phase change in clinoenstatite pyroxenes

 Using lattice dynamic modelling of pure MgSiO₃ clinopyroxenes, we have be able to simulate the properties of both the low-clino (P2₁/c) and a high-density-clino (C2/c) phases and our results are comparable with the high pressure (HP) X-ray study of these phases (Angel et al. 1992). The transition between the two phases is predicted to occur at 6GPa. The volume variation with pressure for both phases is described by a third-order Birch-Murnaghan equation of state with the parameters V _{0  low}=31.122 cm³·mol⁻¹, K _{T0  low}= 107.42 GPa, K′ _{T0  low}=5.96, V _{0  high}=30.142 cm³·mol^–1, K _{T0  high}102.54 GPa and K′ _{T0  high}=8.21. The change in entropy between the two modelled phases at 6GPa is ΔS _{6 Gpa}=−1.335 J·mol⁻¹·K⁻¹ and the equivalent change in volume is ΔV _{6 GPa}=−0.92 cm³·mol⁻¹, from which the gradient of the phase boundary δP/δT is 0.0014 GPa·K⁻¹. The variation of the bulk modulus with pressure was also determined from the modelled elastic constants and compares very well with the EOS data. The reported Lehmann discontinuity, ∼220 km depth and pressure of 7.11Gpa, has an increase in the seismic compressional wave velocity, v _p , of 7.14% using the data given for PREM (Anderson 1989). At a pressure of 7GPa any phase transition of MgSiO₃ pyroxene would be between ortho (Pbca) and high-clino. We find the value of v _p at 7GPa, for modelled orthoenstatite (Pbca), is 8.41 km·sec⁻¹ and that for the modelled high-clino phase at 7GPa is 8.93 km·sec⁻¹, giving a dv _p /v _p of 6.18%. Received: July 26, 1996 / Revised, accepted: September 27, 1996     

(Na,Ca)(Ti3+,Mg)Si2O6-clinopyroxenes at high pressure: influence of cation substitution on elastic behavior and phase transition

A compressional study of (Na,Ca)(Ti³⁺,Mg)Si₂O₆-clinopyroxenes was carried out at high pressures between 10⁻⁴ and 10.2 GPa using in situ single-crystal X-ray diffraction, Raman spectroscopy and optical absorption spectroscopy. Compressional discontinuities accompanied by structural changes, in particular, the appearance of two distinct Ti³⁺–Ti³⁺ distances within the octahedral chains at 4.37 GPa, provide evidence for the occurrence of a phase transition in NaTi³⁺Si₂O₆. Equation-of-state parameters are K ₀ = 115.9(7) GPa with K′ = −0.9(3) and K ₀ = 102.7(8) GPa with K′ = 4.08(5) for the low- and high-pressure range, respectively. The transition involves a C2/c–P [`1] \overline{1} symmetry change, which can be confirmed by the occurrence of new modes in Raman spectra. Since no significant discontinuity in the evolution of the unit-cell volume with pressure has been observed, the transition appears to be second-order in character. The influence of the coupled substitution Na⁺Ti³⁺↔Ca²⁺Mg²⁺ on the static compression behavior and the structural stability has been investigated using a sample of the intermediate composition (Na_0.54Ca_0.46)(Mg_0.46Ti_0.54)Si₂O₆. No evidence for a deviation from continuous compression behavior has been found, neither in lattice parameter nor in structural data and the fit of a third-order Birch–Murnaghan equation-of-state to the pressure–volume data yields a bulk modulus of K ₀ = 109.1(5) GPa and K′ = 5.02(13). Raman and polarized absorption spectra have been compared to NaTiSi₂O₆ and reveal major similarities. The main driving force for the phase transition in NaTi³⁺Si₂O₆ is the localization of the Ti³⁺ d-electron and the accompanying distortion, which is suppressed in the (Na,Ca)(Ti³⁺,Mg)Si₂O₆-clinopyroxene.     

The influence of the Jahn–Teller effect at Fe<Superscript>2+</Superscript> on the structure of chromite at high pressure

The crystal structure of chromite FeCr₂O₄ was investigated to 13.7 GPa and ambient temperature with single-crystal X-ray diffraction techniques. The unit-cell parameter decreases continuously from 8.3832 (5) to 8.2398 (11) Å up to 11.8 GPa. A fit to the Birch–Murnaghan equation of state (EoS) based on the P–V data gives: K ₀ = 209 (13) GPa, K′ = 4.0 (fixed), and V ₀ = 588 (1) ų. The FeO₄ tetrahedra and CrO₆ octahedra are compressed isotropically with pressure with their Fe–O and Cr–O bond distances decreasing from 1.996 (6) to 1.949 (7) Å and from 1.997 (3) to 1.969 (7) Å, respectively. The tetrahedral site occupied by the Fe²⁺ cation is more compressible than the octahedral site occupied by the Cr³⁺ cation. The resulting EoS parameters for the tetrahedral and the octahedral sites are K ₀ = 147 (9) GPa, K′ = 4.0 (fixed), V ₀ = 4.07 (1) ų and K ₀ = 275 (24) GPa, K′ = 4.0 (fixed), V ₀ = 10.42 (2) ų, respectively. A discontinuous volume change is observed between 11.8 and 12.6 GPa. This change indicates a phase transition from a cubic (space group Fd-[`3]{\overline{3}} m) to a tetragonal structure (space group I4₁ /amd). At the phase transition boundary, the two Cr–O bonds parallel to the c-axis shorten from 1.969 (7) to 1.922 (17) Å and the other four Cr–O bonds parallel to the ab plane elongate from 1.969 (7) to 1.987 (9) Å. This anisotropic deformation of the octahedra leads to tetragonal compression of the unit cell along the c-axis. The angular distortion in the octahedron decreases continuously up to 13.7 GPa, whereas the distortion in the tetrahedron rises dramatically after the phase transition. At the pressure of the phase transition, the tetrahedral bond angles along the c-axis direction of the unit cell begin decreasing from 109.5° to 106.6 (7)°, which generates a “stretched” tetrahedral geometry. It is proposed that the Jahn–Teller effect at the tetrahedrally coordinated Fe²⁺ cation becomes active with compression and gives rise to the tetrahedral angular distortion, which in turn induces the cubic-to-tetragonal transition. A qualitative molecular orbital model is proposed to explain the origin and nature of the Jahn–Teller effect observed in this structure and its role in the pressure-induced phase transition.     

Melting of iron–silicon alloy up to the core–mantle boundary pressure: implications to the thermal structure of the Earth’s core

The melting temperature of Fe–18 wt% Si alloy was determined up to 119 GPa based on a change of laser heating efficiency and the texture of the recovered samples in the laser-heated diamond anvil cell experiments. We have also investigated the subsolidus phase relations of Fe–18 wt% Si alloy by the in-situ X-ray diffraction method and confirmed that the bcc phase is stable at least up to 57 GPa and high temperature. The melting curve of the alloy was fitted by the Simon’s equation, P(GPa)/a = (T _m(K)/T ₀) ^c , with parameters, T ₀ = 1,473 K, a = 3.5 ± 1.1 GPa, and c = 4.5 ± 0.4. The melting temperature of bcc Fe–18 wt% Si alloy is comparable with that of pure iron in the pressure range of this work. The melting temperature of Fe–18 wt% Si alloy is estimated to be 3,300–3,500 K at 135 GPa, and 4,000–4,200 K at around 330 GPa, which may provide the lower bound of the temperatures at the core–mantle boundary and the inner core–outer core boundary if the light element in the core is silicon.