The influence of pressure on the structure and dynamics of hydrogen bonds in zoisite and clinozoisite

Density functional theory calculations have been used to study the pressure-induced changes of the hydrogen bond of Fe-free orthozoisite and clinozoisite and the concomitant shifts of the OH-stretching frequencies. Two independent parameter-free lattice dynamical calculations have been employed. One was based on a plane-wave basis set in conjunction with norm-conserving pseudopotentials and a density functional perturbation theory approach, while the other used a localised basis set and a finite displacement algorithm for the lattice dynamical calculations. Both models confirm the unusually large pressure-induced red-shift found experimentally (−33.89 cm⁻¹/GPa) in orthozoisite, while the pressure-induced shifts in clinozoisite are much smaller (−5 to −9 cm⁻¹/GPa). The atomistic model calculations show that in orthozoisite the nearly linear O–H⋯O arrangement is compressed by about 8% on a pressure increase to 10 GPa, while concomitantly the O–H distance is significantly elongated (by 2.5% at 10 GPa). In clinozoisite, the O–H⋯O arrangement is kinked at ambient conditions and remains kinked at high pressures, while the O-H distance is elongated by only 0.5% at 10 GPa. The current calculations confirm that correlations between the distances and dynamics of hydrogen bonds, which have been established at ambient conditions, cannot be used to infer hydrogen positions at high pressures.     

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.     

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     

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).     

P-V-T equation of state of lawsonite

A pressure-volume-temperature data set has been obtained for lawsonite [CaAl₂Si₂O₇(OH)₂.H₂O], using synchrotron X-ray diffraction and an externally heated diamond anvil cell. Unit-cell volumes were measured to 9.4 GPa and 767 K by angle dispersive X-ray diffraction using imaging plates. Phase changes were not observed within this pressure-temperature range, and lawsonite compressed almost isotropically at constant temperature. The P-V-T data have been analyzed using a Birch- Murnaghan equation of state and a linear equation of state expressed as β=–1/V₀ (∂V/∂P) _T . At room temperature, the derived equation of state parameters are: K ₀=124.1 (18) GPa K'₀ set to 4) and β^–1=142.0(24) GPa, respectively. Our results are intermediate between previously reported measurements. The high-temperature data show that the incompressibility of lawsonite decreases with increasing temperature to ∼500 K and then increases above. Hence, the second order temperature derivative of the bulk modulus is taken into account in the equation of state; a fit of the volume data yields K ₀=123.9(18) GPa, (∂K/∂T)_P=–0.111(3) GPa K^–1, (∂² K/∂T ²)_P=0.28(6) 10^–3 GPa K^–2, α₀=3.1(2) 10^–5 K^–1, assuming K'₀=4. Received: 2 June 1998 / Revised, accepted: 12 Ocotber 1998     

Pressure–volume–temperature equation of state of andradite and grossular, by high-pressure and -temperature powder diffraction

 The thermoelastic parameters of natural andradite and grossular have been investigated by high-pressure and -temperature synchrotron X-ray powder diffraction, at ESRF, on the ID30 beamline. The P–V–T data have been fitted by Birch-Murnaghan-like EOSs, using both the approximated and the general form. We have obtained for andradite K ₀=158.0(±1.5) GPa, (dK/dT )₀=−0.020(3) GPa K⁻¹ and α₀=31.6(2) 10⁻⁶ K⁻¹, and for grossular K ₀=168.2(±1.7) GPa, (dK/dT)₀=−0.016(3) GPa K⁻¹ and α₀=27.8(2) 10⁻⁶ K⁻¹. Comparisons between the present issues and thermoelastic properties of garnets earlier determined are carried out. Received: 7 July 2000 / Accepted: 20 October 2000     

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.     

High-pressure behavior of natural single-crystal epidote and clinozoisite up to 40 GPa

The comparative compressibility and high-pressure stability of a natural epidote (0.79 Fe-total per formula unit, Fe_tot pfu) and clinozoisite (0.40 Fe_tot pfu) were investigated by single-crystal X-ray diffraction and Raman spectroscopy. The lattice parameters of both phases exhibit continuous compression behavior up to 30 GPa without evidence of phase transformation. Pressure–volume data for both phases were fitted to a third-order Birch–Murnaghan equation of state with V ₀ = 461.1(1) ų, K ₀ = 115(2) GPa, and \(K_{0}^{'}\) = 3.7(2) for epidote and V ₀ = 457.8(1) ų, K ₀ = 142(3) GPa, and \(K_{0}^{'}\) = 5.2(4) for clinozoisite. In both epidote and clinozoisite, the b-axis is the stiffest direction, and the ratios of axial compressibility are 1.19:1.00:1.15 for epidote and 1.82:1.00:1.19 for clinozoisite. Whereas the compressibility of the a-axis is nearly the same for both phases, the b- and c-axes of the epidote are about 1.5 times more compressible than in clinozoisite, consistent with epidote having a lower bulk modulus. Raman spectra collected up to 40.4 GPa also show no indication of phase transformation and were used to obtain mode Grüneisen parameters (γ _i) for Si–O vibrations, which were found to be 0.5–0.8, typical for hydrous silicate minerals. The average pressure coefficient of Raman frequency shifts for M–O modes in epidote, 2.61(6) cm^?1/GPa, is larger than found for clinozoisite, 2.40(6) cm^?1/GPa, mainly due to the different compressibility of FeO₆ and AlO₆ octahedra in M3 sites. Epidote and clinozoisite contain about 2 wt% H₂O are thus potentially important carriers of water in subducted slabs.     

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.     

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).     

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.     

Elasticity of TiO2 rutile to 1800 K

The ambient pressure elastic properties of single-crystal TiO₂ rutile are reported from room temperature (RT) to 1800 K, extending by more than 1200 oK the maximum temperature for which rutile elasticity data are available. The magnitudes of the temperature derivatives decrease with increasing temperature for five of the six adiabatic elastic moduli (C _ij ). At RT, we find (units, GPa): C ₁₁=268(1); C ₃₃=484(2); C ₄₄=123.8(2); C ₆₆=190.2(5); C ₂₃=147(1); and C ₁₂=175(1). The temperature derivatives (units, GPa K⁻¹) at RT are: (∂C ₁₁/∂T) _P =−0.042(5); (∂C ₃₃/∂T) _P =−0.087(6); (∂C ₄₄/∂T) _P =−0.0187(2); (∂C ₆₆/∂T) _P =−0.067(2); (∂C ₂₃/∂T) _P =−0.025; and (∂C ₁₂/∂T) _P −0.048(5). The values for K _S (adiabatic bulk modulus) and μ (isotropic shear modulus) and their temperature derivatives are K _S =212(1) GPa; μ=113(1) GPa; (∂K _S /∂T) _P =−0.040(4) GPa K⁻¹; and (∂μ/∂T) _P =−0.018(1) GPa K⁻¹. We calculate several dimensionless parameters over a large temperature range using our new data. The unusually high values for the Anderson-Gròneisen parameters at room temperature decrease with increasing temperature. At high T, however, these parameters are still well above those for most other oxides. We also find that for TiO₂, anharmonicity, as evidenced by a non-zero value of [∂ln (K _T )/∂lnV] _T , is insignificant at high T, implying that for the TiO₂ analogue of stishovite, thermal pressure is independent of volume (or pressure). Systematic relations indicate that ∂² K _S /∂T∂P is as high as 7×10⁻⁴ K⁻¹ for rutile, whereas ∂²μ/∂T∂P is an order of magnitude less. Received: 19 September 1997 / Revised, accepted: 27 February 1998     

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     

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     

Structure and compressibility of synthetic ZnAl2O4 (gahnite) under high-pressure conditions, from synchrotron X-ray powder diffraction

 The structural behavior of synthetic gahnite (ZnAl₂O₄) has been investigated by X-ray powder diffraction at high pressure (0–43 GPa) and room temperature, on the ID9 beamline at ESRF. The equation of state of gahnite has been derived using the models of Birch–Murnaghan, Vinet and Poirier–Tarantola, and the results have been mutually compared (the elastic bulk modulus and its derivatives versus P determined by the third-order Birch–Murnaghan equation of state are K ₀=201.7(±0.9) GPa, K ^′ ₀=7.62(±0.09) and K ^″ ₀=−0.1022 GPa⁻¹ (implied value). The compressibilities of the tetrahedral and octahedral bond lengths [0.00188(8) and 0.00142(5) GPa⁻¹ at P=0, respectively], and the␣polyhedral volume compressibilities of the four-␣and␣sixfold coordination sites [0.0057(2) and 0.0041(2) GPa⁻¹ at P=0, respectively] are discussed. Received: 15 January 2001 / Accepted: 23 April 2001     

Single-crystal electronic absorption spectroscopy of synthetic chromium-, cobalt-, and vanadium-bearing pyropes at different temperatures and pressures

 Single crystals of synthetic vanadium-, chromium- and cobalt-bearing garnets, Pyr:V0.06, Pyr:V0.13, Pyr:Cr0.04, Pyr:Co0.10, and Gt:Co3.00, and a natural vanadium-bearing grossular, Gross:V0.07 (Cr³⁺ < 0.005), were studied by electronic absorption spectroscopy in the wavenumber range 35 000–5000 cm⁻¹ under ambient conditions and at temperatures up to 600 K and pressures up to 8 GPa. The T and P behavior of the absorption band energies and intensities shows the following for the different transition metal-bearing garnets: Cr: The thermal expansion of chromium octahedra are similar to and the Racah parameter the same in synthetic Cr-doped pyrope, α_poly≅ 1.3 × 10⁻⁵ K⁻¹, and in natural pyrope, α_poly≅ 1.5 × 10⁻⁵ K⁻¹, and B=655 cm⁻¹, respectively. Ca^2+[8]-free garnets have a slightly stronger crystal field at the Y^[6] site and, therefore, the energies of the two spin-allowed Cr³⁺ dd bands are ca. 300 cm⁻¹ higher in Mg-pyrope than in natural Ca-bearing pyrope. Co: Increasing temperature causes only a small thermal expansion of the cobalt dodecahedra. Increasing pressure gives rise to appreciable compression, which is similar to that of the Fe²⁺-dodecahedra in almandine, where k=125 ± 25 GPa. T and P dependence of the Co band intensities may be caused by strong spin-orbit coupling. V: Occurs in at least two valence states and structural sites: (1) V³⁺ in octahedral sites gives rise to two spin-allowed bands, at 17 220 cm⁻¹ and 24 600 cm⁻¹, whose temperature dependence is typical for spin-allowed dd transitions in centrosymmetric sites. (2) V⁴⁺, which causes a set of dd absorption bands similar to those observed in the spectrum of V⁴⁺-doped Zr[SiO₄]. The P behavior of the V absorption bands indicates an interaction between V³⁺ and V⁴⁺ species. Received: 27 June 2001 / Accepted: 19 December 2001     

Experimental investigation of zoisite–clinozoisite phase equilibria in the system CaO–Fe2O3–Al2O3–SiO2–H2O

The system Ca₂Al₃Si₃O₁₁(O/OH)-Ca₂Al₂FeSi₃O₁₁(O/OH), with emphasis on the Al-rich portion, was investigated by synthesis experiments at 0.5 and 2.0 GPa, 500-800 °C, using the technique of producing overgrowths on natural seed crystals. Electron microprobe analyses of overgrowths up to >100 µm wide have located the phase transition from clinozoisite to zoisite as a function of P-T-X_ps and a miscibility gap in the clinozoisite solid solution. The experiments confirm a narrow, steep zoisite-clinozoisite two-phase loop in T-X_ps section. Maximum and minimum iron contents in coexisting zoisite and clinozoisite are given by X_ps^zo (max) = 1.9*10 ^{- 4} T+ 3.1*10 ^{- 2} P - 5.36*10 ^{- 2}{\rm X}_{{\rm ps}}^{{\rm zo}} {\rm (max) = 1}{\rm .9*10}^{ - 4} T{\rm + 3}{\rm .1*10}^{ - 2} P - {\rm 5}{\rm .36*10}^{ - 2} and X_ps^czo (min) = (4.6 * 10 ^{- 4} - 4 * 10 ^{- 5} P)T + 3.82 * 10 ^{- 2} P - 8.76 * 10 ^{- 2}{\rm X}_{{\rm ps}}^{{\rm czo}} {\rm (min)} = {\rm (4}{\rm .6} * {\rm 10}^{ - {\rm 4}} - 4 * {\rm 10}^{ - {\rm 5}} P{\rm )}T + {\rm 3}{\rm .82} * {\rm 10}^{ - {\rm 2}} P - {\rm 8}{\rm .76} * {\rm 10}^{ - {\rm 2}} (P in GPa, T in °C). The iron-free end member reaction clinozoisite = zoisite has equilibrium temperatures of 185ᇆ °C at 0.5 GPa and 0ᇆ °C at 2.0 GPa, with (H_r⁰=2.8ǃ.3 kJ/mol and (S_r⁰=4.5ǃ.4 J/mol2K. At 0.5 GPa, two clinozoisite modifications exist, which have compositions of clinozoisite I ~0.15 to 0.25 X_ps and clinozoisite II >0.55 X_ps. The upper thermal stability of clinozoisite I at 0.5 GPa lies slightly above 600 °C, whereas Fe-rich clinozoisite II is stable at 650 °C. The schematic phase relations between epidote minerals, grossular-andradite solid solutions and other phases in the system CaO-Al₂O₃-Fe₂O₃-SiO₂-H₂O are shown.     

(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.     

Pressure-induced structural transition in Ln2Zr2O7 (Ln = Ce, Nd, Gd) pyrochlores

The structural behavior under pressure of three lanthanide pyrochlore zirconates Ln₂Zr₂O₇ (Ln³⁺ = Ce, Nd and Gd) has been investigated by X-ray diffraction up to 50 GPa. For all three compounds, a symmetry reduction from cubic to monoclinic is observed under increasing pressure dependant on a pressure value that increases with the ionic radius of the lanthanide ions, r _Ln. The cubic and monoclinic phases coexist over a wide pressure range which increases with r _Ln. The zero-pressure bulk modulus of the cubic phase, B ₀, and its pressure derivative, B ₀′, have been determined by fitting the experimental compressibility curves to the Birch–Murnaghan equation of state.     

The high-pressure stability of zoisite and phase relationships of zoisite-bearing assemblages

The fluid-absent reaction 12 zoisite = 3 lawsonite + 7 grossular + 8 kyanite + 1 coesite was experimentally reversed in the model system CaO-Al₂O₃-SiO₂-H₂O (CASH) using a multi-anvil apparatus. The upper pressure stability limit for zoisite was found to extend to 5.0 GPa at 700 °C and to 6.6 GPa at 950 °C. Additional experiments both in the H₂O-SiO₂-saturated and in the H₂O-Al₂O₃-saturated portions of CASH provide further constraints on high pressure phase relationships of lawsonite, zoisite, grossular, kyanite, coesite, and an aqueous fluid. Consistency of the present experiments with the H₂O-saturated breakdown of lawsonite is demonstrated by thermodynamic analysis using linear programming techniques. Two sets of data consistent with databases of Berman (1988) and Holland and Powell (1990) were retrieved combining experimental phase relationships, calorimetric constraints, and recently measured elastic properties of solid phases. The best fits result in G _{f ,1,298} ^∘,zoisite=−6,499,400 J and S _1,298 ^∘,zoisite=302 J/K, and G _{f ,1,298} ^{∘,lawsonite}=−4,514,600 J and S _1,298 ^{∘,lawsonite}=220 J/K for the dataset of Holland and Powell, and G _{f ,1,298} ^∘,zoisite=−6,492,120 J and S _1,298 ^∘,zoisite=304 J/K, and G _{f ,1,298} ^{∘,lawsonite}=−4,513,000 J and S _1,298 ^{∘,lawsonite}= 218 J/K for the dataset of Berman. Examples of the usage of zoisite as a geohygrometer and as a geobarometer in rocks metamorphosed at eclogite facies conditions are worked, profiting from the thermodynamic properties retrieved here. Received: 23 December 1996 / Accepted: 29 August 1997