Equation of state of adamite up to 11 GPa: a synchrotron X-ray diffraction study

The compression behavior of natural adamite [Zn₂AsO₄OH] has been investigated up to 11.07 GPa at room temperature utilizing in situ angle-dispersive X-ray diffraction and a diamond anvil cell. No phase transition has been observed within the pressure range investigated. A third-order Birch–Murnaghan equation of state fitted to all of the data points yielded V ₀ = 430.1(4) Å³, K ₀ = 80(3) GPa, K′ ₀ = 1.9(5). The K ₀ was obtained as 69(1) GPa when K′ ₀ was fixed at 4. Analysis of axial compressible moduli shows the intense compression anisotropy of adamite: K _a0 = 37(3) GPa, K _b0 = 153(6) GPa, K _c0 = 168(8) GPa; hence, a axis is the most compressible and the compressibility of b and c axis is comparable. Furthermore, the comparisons among the compressional properties of adamite, libethenite (Cu₂PO₄OH, also belongs to olivenite group), and andalusite (Al₂SiO₄O has the similar structure with adamite) at high pressure were made.     

Structural and vibrational behaviour of fluorapatite with pressure. Part I: in situ single-crystal X-ray diffraction investigation

Using single-crystal X-ray diffraction from a diamond anvil cell, the compressibility of a synthetic fluorapatite was determined up to about 7?GPa. The compression pattern was anisotropic, with greater change along a than c. Unit cell parameters varied linearly with β _a =3.32(8)?10^?3 and β _c =2.40(5)?10^?3 GPa^?1, giving a ratio β _a :β _c =1.38:1. Data fitted with a third-order Birch-Murnaghan EOS yielded a bulk modulus of K ₀=93(4)?GPa with K′=5.8(1.8). The evolution of the crystal structure of fluorapatite was analysed using data collected at room pressure, at 3.04 and 4.72?GPa. The bulk modulus of phosphate tetrahedron is about three times greater than the bulk modulus of calcium polyhedra. The values were 270(10), 100(4) and 86(3) GPa for P, Ca1 (nine-coordinated) and Ca2 (seven-coordinated) respectively. While the calcium polyhedra became more regular with pressure, the distortion of the phosphate tetrahedron remained unchanged. The size of the channel extending along the [001] direction represented the most compressible direction. The Ca2–Ca2 distance decreased from 3.982 to 3.897?Å on compression from 0.0001 to 4.72?GPa. The anisotropic compressional pattern may be understood in terms of the greater compressibility of the channel size over the polyhedral units. The reduction of the channel volume was measured by the evolution of the trigonal prism, having the Ca2–Ca2–Ca2 triangle as its base and the c lattice parameter as its height. This prism volume changed from 47.3?ų at room pressure to 44.78?ų at 4.72?GPa. Its relatively high bulk moduli, 86(3) GPa, indicated that the channel did not collapse with pressure and the apatite structure could remain stable at very high pressure.     

Hydrogen sites in the dense hydrous magnesian silicate phase E: a pulsed neutron powder diffraction study

Hydrogen site positions and occupancy in the crystal structure of dense hydrous magnesium silicate (DHMS) phase E were determined for the first time by pulsed neutron powder diffraction. A fully deuterated pure phase E powder sample, which had space group \(R\overline{3} m\) and lattice parameters of a = 2.97065(8) Å and c = 13.9033(4) Å, was synthesized at 15 GPa and 1100 °C. Through quantitative evaluation of refined structure parameters obtained with sufficient spatial resolution and very high signal-to-background ratio, we conclude that the O–D dipoles in the refined phase E structure are tilted by 24° from the direction normal to the layers of edge-shared MgO₆ octahedra (octahedral layers). The tilted dipole structure of phase E is in remarkable contrast to that of brucite, Mg(OH)₂, which has dipoles exactly normal to the octahedral layer. This contrast exists because the O–Si–O bonding unique in the phase E structure connects two adjacent octahedral layers and thereby reduces the interlayer O···O distance. This shrinkage of the interlayer distance induces the tilting of the O–D dipole and also generates unique O–D···O hydrogen bonding connecting all the layers in the phase E structure.     

P–V Equations of State and the relative stabilities of serpentine varieties

Serpentines are hydrous phyllosilicates which form by hydration of Mg–Fe minerals. The reasons for the occurrence of the structural varieties lizardite and chrysotile, with respect to the variety antigorite, stable at high pressure, are not yet fully elucidated, and their relative stability fields are not quantitatively defined. In order to increase the database of thermodynamic properties of serpentines, the P–V Equations of State (EoS) of lizardite and chrysotile were determined at ambient temperature up to 10 GPa, by in situ synchrotron X-ray diffraction in a diamond-anvil cell. Neither amorphization nor hysteresis was observed during compression and decompression, and no phase transition was resolved in lizardite. In chrysotile, a reversible change in compression mechanism, possibly due to an unresolved phase transition, occurs above 5 GPa. Both varieties exhibit strong anisotropic compression, with the c axis three times more compressible than the others. Fits to ambient temperature Birch–Murnaghan EoS gave for lizardite V ₀=180.92(3) Å³, K ₀ = 71.0(19) GPa and K′ ₀=3.2(6), and for chrysotile up to 5 GPa, V ₀ = 730.57(31) Å³ and K ₀ = 62.8(24) GPa (K′ ₀ fixed to 4). Compared to the structural variety antigorite is stable at high pressure (HP) (Hilairet et al. 2006), the c axis is more compressible in these varieties, whereas the a and b axes are less compressible. These differences are attributed to the less anisotropic distribution of stiff covalent bonds in the corrugated structure of antigorite. The three varieties have almost identical bulk compressibility curves. Thus the compressibility has negligible influence on the relative stability fields of the serpentine varieties. They are dominated by first-order thermodynamic properties, which stabilizes antigorite at high temperature with respect to lizardite, and by out-of-equilibrium phenomena for metastable chrysotile (Evans 2004).     

Equations of state of magnesium silicates anhydrous B and superhydrous B

High-pressure single crystal X-ray diffraction experiments of phase anhydrous B and superhydrous B have been carried out to 7.3 and 7.7?GPa, respectively, at room temperature. Fitting a third-order Birch-Murnaghan equation of state to the P-V data yields values of V ₀?=?838.86?±?0.04?ų, K_T,0?=?151.5?±?0.9?GPa and K′?=?5.5?±?0.3 for Anhy-B and V ₀?=?624.71?± 0.03?ų, K_T,0?=?142.6?±?0.8?GPa and K′?=?5.8?±?0.2 for Shy-B. A similar analysis of the axial compressibilities in Anhy-B reveals that the c-axis is most compressible (K_c?=?137?±?3?GPa), the b-axis is least compressible (K_b?=?175?±?4?GPa), and the a-axis is intermediate (K_a?=?148?±?1?GPa). In Shy-B, the a-axis is most compressible (K_a?=?135?±?1?GPa), followed by the b- and c-axes which have similar compressibilities (K_b?=?146?±?3?GPa; K_c?=?148?±?3?GPa). The fact that the b-axis of Shy-B is approximately 16% more compressible than Anhy-B is primarily due to differences in the O-T layer in which the H atoms are located and the linkages with the adjacent O layers. The rigid edge-sharing chains of MgO₆ and SiO₆ octahedra in the O layer control compressibility along the a- and c-axes in both structures. The net result is a reduction in the overall anisotropic compression from ～22% in Anhy-B to ～9% in Shy-B.     

Structural evolution of hemimorphite at high pressure up to 4.2 GPa

The high-pressure structural evolution of hemimorphite, Zn₄Si₂O₇(OH)₂·H₂O, a = 8.3881(13), b = 10.7179(11), c = 5.1311(9) Å, V = 461.30(12) Å³, space group Imm2, Z = 2, was studied by single-crystal X-ray diffraction with a diamond anvil cell under hydrostatic conditions up to 4.2 GPa. In the pressure range of 0.0001–2.44 GPa, the unit-cell parameters change almost linearly. The phase transition (probably of the second order) with symmetry reduction from Imm2 (hemimorphite-I) to Pnn2 (hemimorphite-II) was found near 2.5 GPa. The structure compressibility increases somewhat above the phase transition. Namely, the initial unit-cell volume decreases by 3.6% at 2.44 GPa and by 7.2% at 4.20 GPa. The hemimorphite framework can be described as built up of secondary building units (SBU) Zn₄Si₂O₇(OH)₂. These blocks are combined to form the rods arranged along the c-axis; these rods are multiplied by basic and I-translations of orthorhombic unit cell. The symmetry reduction is caused by the rotation of the rods along their axis. In hemimorphite-I, the compression affects mainly the SBU dimensions, whereas a rectangular section of the channels having mm2 symmetry remains practically unchanged. An appreciable decrease in this section in hemimorphite-II is determined by its oblique distortion with the loss of m planes. It results from opposite rotation of adjacent SBU, which also leads into the loss of I-translation. In hemimorphite-I, the coordination of H₂O molecules is fourfold planar; the hydrogen-bonded hydroxyls and H₂O molecules form infinite ribbons along the c-axis. In hemimorphite-II, an additional short H₂O–O contact appears as a result of asymmetric deformation of the channels. The appearance of this new contact provides the possibility for re-orientation of hydrogen bonds. The planar coordination of H₂O molecules changes to tetrahedral and the ribbons are transformed to islands (OH)₂–H₂O.     

In situ neutron diffraction study of deuterated portlandite Ca(OD)2 at high pressure and temperature

The structure of deuterated portlandite, Ca(OD)₂, has been investigated using time-of-flight neutron diffraction at pressures up to ∼4.5 GPa and temperatures up to ∼823 K. Rietveld analysis of the data reveals that with increasing pressure, unit-cell parameter c decreases at a rate about 4.5 times larger than that for a, which is largely due to rapid contraction of the interlayer spacing in this pressure range. Fitting of the determined cell volumes to the third-order Birch–Murnaghan equation of state yields a bulk modulus (K ₀) of 32.2 ± 1.0 GPa and its first derivative (K ₀′) of 4.4 ± 0.6. Moreover, on compression, hydrogen-mediated interatomic interactions within the interlayer become strengthened, as reflected by decreases in interlayer D···O and D···D distances with increasing pressure. Correspondingly, D–D, the distance between the three equivalent sites over which D is disordered, increases, suggesting a pressure-induced hydrogen disorder. This behavior is similar to that reported in brucite at elevated pressure. On heating at ∼2.1 GPa, cell parameter c increases more rapidly than a, as expected. However, because of the pressure effect, the thermal expansion coefficients, particularly along c, are much smaller than those at ambient pressure. With increasing temperature, the three partially occupied D sites become further apart, and the D-mediated interactions, mainly the interlayer D···D repulsion, become weakened.     

High-pressure elastic behavior of Ca4La6(SiO4)6(OH)2 a synthetic rare-earth silicate apatite: a powder X-ray diffraction study up to 9.33 GPa

The compression behavior of a synthetic Ca₄La₆(SiO₄)₆(OH)₂ has been investigated to about 9.33 GPa at 300 K using in situ angle-dispersive X-ray diffraction and a diamond anvil cell. No phase transition has been observed within the pressure range investigated. The values of zero-pressure volume V ₀, K ₀, and $K_{0}^{'}$ refined with a third-order Birch–Murnaghan equation of state are V ₀ = 579.2 ± 0.1 Å³, K ₀ = 89 ± 2 GPa, and $K_{0}^{'} = 10.9 \pm 0.8$ . If $K_{0}^{'}$ is fixed at 4, K ₀ is obtained as 110 ± 2 GPa. Analysis of axial compressible modulus shows that the a-axis (K _a0 = 79 ± 2 GPa) is more compressible than the c-axis (K _c0 = 121 ± 7 GPa). A comparison between the high-pressure elastic response of Ca₄La₆(SiO₄)₆(OH)₂ and the iso-structural calcium apatites is made. The possible reasons of the different elastic behavior between Ca₄La₆(SiO₄)₆(OH)₂ and calcium apatites are discussed.     

Compression of witherite to 8 GPa and the crystal structure of BaCO3II

Natural witherite (Ba_0.99Sr_0.01CO₃) has been studied by single-crystal X-ray diffraction in the diamond anvil cell at eight pressures up to 8 GPa. At ambient pressure, cell dimensions are a?=?5.3164(12) Å, b?=?8.8921(19) Å, c?=?6.4279(16) Å, and the structure was refined in space group Pmcn to R(F)?=?0.020 from 2972 intensity data. The unit cell and atom position parameters for the orthorhombic cell were refined at pressures of 1.2, 2.0, 2.9, 3.9, 4.6, 5.5, 6.2, and 7.0 GPa. The volume-pressure data are used to calculate equation of state parameters K _T0?=?50.4(12) GPa and K′?=?1.9(4). At approximately 7.2 GPa, a first-order transformation to space group P3¯1c was observed. Cell dimensions of the high-pressure phase at 7.2 GPa are a?=?5.258(6) Å, c?=?5.64(1) Å. The high pressure structure was determined and refined to R(F)?=?0.06 using 83 intensity data, of which 15 were unique. This high-pressure phase appears to be more compressible than the orthorhombic phase with an estimated initial bulk modulus (K _7.2GPa) of 10 GPa.     

Compressibility and crystal structure of sillimanite, Al2SiO5, at high pressure

The unit-cell dimensions and crystal structure of sillimanite at various pressures up to 5.29 GPa have been refined from single-crystal X-ray diffraction data. As pressure increases, a and b decrease linearly, whereas c decreases nonlinearly with a slightly positive curvature. The axial compression ratios at room pressure are β_a:β_b:β_c=1.22:1.63:1.00. Sillimanite exhibits the least compressibility along c, but the least thermal expansivity along a (Skinner et al. 1961; Winter and Ghose 1979). The bulk modulus of sillimanite is 171(1) GPa with K′=4 (3), larger than that of andalusite (151 GPa), but smaller than that of kyanite (193 GPa). The bulk moduli of the [Al1O₆], [Al2O₄], and [SiO₄] polyhedra are 162(8), 269(33), and 367(89) GPa, respectively. Comparison of high-pressure data for Al₂SiO₅ polymorphs reveals that the [SiO₄] tetrahedra are the most rigid units in all these polymorphic structures, whereas the [AlO₆] octahedra are most compressible. Furthermore, [AlO₆] octahedral compressibilities decrease from kyanite to sillimanite, to andalusite, the same order as their bulk moduli, suggesting that [AlO₆] octahedra control the compression of the Al₂SiO₅ polymorphs. The compression of the [Al1O₆] octahedron in sillimanite is anisotropic with the longest Al1-OD bond shortening by ～1.9% between room pressure and 5.29 GPa and the shortest Al1-OB bond by only 0.3%. The compression anisotropy of sillimanite is primarily a consequence of its topological anisotropy, coupled with the compression anisotropy of the Al-O bonds within the [Al1O₆] octahedron.     

High pressure behaviour of lead feldspar (PbAl2Si2O8)

An in situ high pressure powder diffraction study, using high-brilliance synchrotron radiation, on lead feldspar (PbAl₂Si₂O₈) was performed. Two samples, with Q _od=0.68 and 0.76, were loaded in a diamond anvil cell and were compressed up to 11 GPa. Up to P=7.1 GPa the only phase present is lead feldspar. In the range 7.1–9.4 GPa sudden changes in the position of the reflections suggest the transformation of lead feldspar to a new phase (probably feldspar-like). The absence of split that would be compatible with triclinic symmetry rules out the monoclinic-triclinic transition, that was reported for the structurally similar strontium feldspar. At P>9.4 GPa some new extra reflections not indexable in the feldspar cell are present as well. During decompression the lead feldspar was the only phase present at P<6 GPa. Peak enlargement was observed with pressure, probably preliminary to amorphization. However almost complete amorphization was observed only after fortuitous shock compression at ∼18 GPa; the crystallinity was recovered at room pressure after decompression. The bulk modulus for lead feldspar was K=71.0(9) and 67.6(1.2) GPa for the two samples, in the range reported for feldspars. The cell parameters show a compression pattern which is similar to that observed in anorthite, with Δa/a ₀>Δc/c ₀>Δb/b ₀; comparison with the high temperature behaviour shows that for lead feldspar the strain tensor with pressure is more isotropic and the deformation along a is less prominent. A turnover in the behaviour of the β angle with pressure suggests a change in the compression behaviour at P∼2 GPa. Rietveld refinement of the Pb coordinates was performed in a series of spectra with pressure ranging from 0.6 to 6.5 GPa. The combined analysis of cell parameters and Pb coordinates with pressure showed that the compression of the structure is mainly achieved by an approach of Pb atoms along a *. Received: 21 July 1998 / Revised, accepted: 13 October 1998     

The crystal and magnetic structure of Li-aegirine LiFe3+Si2O6: a temperature-dependent study

Single crystals of Li-aegirine LiFe³⁺Si₂O₆ were synthesized at 1573?K and 3?GPa, and a polycrystalline sample suitable for neutron diffraction was produced by ceramic sintering at 1223?K. LiFe³⁺Si₂O₆ is monoclinic, space group C2/c, a=9.6641(2)?Å, b= 8.6612(3)?Å, c=5.2924(2)?Å, β=110.12(1)^° at 300?K as refined from powder neutron data. At 229?K Li-aegirine undergoes a phase transition from C2/c to P2₁ /c. This is indicated by strong discontinuities in the temperature variation of the lattice parameters, especially for the monoclinic angle β and by the appearance of Bragg reflections (hkl) with h+k≠2n. In the low-temperature form two non-equivalent Si-sites with 〈SiA–O〉=1.622?Å and 〈SiB–O〉=1.624?Å at 100?K are present. The bridging angles of the SiO₄ tetrahedra O3–O3–O3 are 192.55(8)° and 160.02(9)° at 100?K in the two independent tetrahedral chains in space group P2₁ /c, whereas it is 180.83(9)° at 300?K in the high-temperature C2/c phase, i.e. the chains are nearly fully expanded. Upon the phase transition the Li-coordination changes from six to five. At 100?K four Li–O bond lengths lie within 2.072(4)–2.172(3)?Å, the fifth Li–O bond length is 2.356(4)?Å, whereas the Li–O3?A bond lengths amount to 2.796(4)?Å. From ⁵⁷Fe Mössbauer spectroscopic measurements between 80 and 500?K the structural phase transition is characterized by a small discontinuity of the quadrupole splitting. Temperature-dependent neutron powder diffraction experiments show first occurrence of magnetic reflections at 16.5?K in good agreement with the point of inflection in the temperature-dependent magnetization of LiFe³⁺Si₂O₆. Distinct preordering phenomena can be observed up to 35?K. At the magnetic phase transition the unit cell parameters exhibit a pronounced magneto-striction of the lattice. Below T _N Li-aegirine shows a collinear antiferromagnetic structure. From our neutron powder diffraction experiments we extract a collinear antiferromagnetic spin arrangement within the a–c plane.     

Crystal structure, Raman and FTIR spectroscopy, and equations of state of OH-bearing MgSiO3 akimotoite

MgSiO₃ akimotoite is stable relative to majorite-garnet under low-temperature geotherms within steeply or rapidly subducting slabs. Two compositions of Mg–akimotoite were synthesized under similar conditions: Z674 (containing about 550 ppm wt H₂O) was synthesized at 22 GPa and 1,500 °C and SH1101 (nominally anhydrous) was synthesized at 22 GPa and 1,250 °C. Crystal structures of both samples differ significantly from previous studies to give slightly smaller Si sites and larger Mg sites. The bulk thermal expansion coefficients of Z674 are (153–839 K) of a ₁ = 20(3) × 10^?9 K^?2 and a ₀ = 17(2) × 10^?6 K^?1, with an average of α ₀ = 27.1(6) × 10^?6 K^?1. Compressibility at ambient temperature of Z674 was measured up to 34.6 GPa at Sector 13 (GSECARS) at Advanced Photon Source Argonne National Laboratory. The second-order Birch–Murnaghan equation of state (BM2 EoS) fitting yields: V ₀ = 263.7(2) Å³, K _T0 = 217(3) GPa (K′ fixed at 4). The anisotropies of axial thermal expansivities and compressibilities are similar: α _a  = 8.2(3) and α _c  = 10.68(9) (10^?6 K^?1); β _a  = 11.4(3) and β _c  = 15.9(3) (10^?4 GPa). Hydration increases both the bulk thermal expansivity and compressibility, but decreases the anisotropy of structural expansion and compression. Complementary Raman and Fourier transform infrared (FTIR) spectroscopy shows multiple structural hydration sites. Low-temperature and high-pressure FTIR spectroscopy (15–300 K and 0–28 GPa) confirms that the multiple sites are structurally unique, with zero-pressure intrinsic anharmonic mode parameters between ?1.02 × 10^?5 and +1.7 × 10^?5 K^?1, indicating both weak hydrogen bonds (O–H···O) and strong OH bonding due to long O···O distances.     

Structural change associated with the incommensurate-normal phase transition in akermanite, Ca2MgSi2O7, at high pressure

The structural changes associated with the incommensurate (IC)-normal (N) phase transition in akermanite have been studied with high-pressure single-crystal X-ray diffraction up to 3.79?GPa. The IC phase, stable at room pressure, transforms to the N phase at ～1.33?GPa. The structural transformation is marked by a small but discernable change in the slopes of all unit-cell parameters as a function of pressure. It is reversible with an apparent hysteresis and is classified as a tricritical phase transition. The linear compressibility of the a and c axes are 0.00280(10) and 0.00418(6)?GPa^?1 for the IC phase, and 0.00299(11) and 0.00367(8)?GPa^?1 for the N phase, respectively. Weighted volume and pressure data, fitted to a second-order Birch-Murnaghan equation of state (K′≡4.0), yield V₀=307.4(1)?ų and K₀=100(3)?GPa for the IC phase and V₀=307.6(2)?ų and K₀=90(2)?GPa for the N phase. No significant discontinuities in Si–O, Mg–O and Ca–O distances were observed across the transition, except for the Ca–O1 distance, which is more compressible in the IC phase than in the N phase. From room pressure to 3.79?GP the volume of the [SiO₄] tetrahedron is unchanged (2.16?ų), whereas the volumes of the [MgO₄] and [CaO₈] polyhedra decrease from 3.61 to 3.55(1)?ų and 32.8 to 30.9(2)?ų, respectively. Intensities of satellite reflections are found to vary linearly with the isotropic displacement parametr of Ca and the librational amplitude of the [SiO₄] tetrahedron. At room pressure, there is a mismatch between the size of the Ca cations and the configuration of tetrahedral sheets, which appears to be responsible for the formation of the modulated structure; as pressure increases, the misfit is diminished through the relative rotation and distortion of [MgO₄] and [SiO₄] tetrahedra and the differential compression of individual Ca–O distances, concurrent with a displacement of Ca along the (110) mirror plane toward the O1 atom. We regard the high-pressure normal structure as a result of the elimination of microdomains in the modulated structure.     

Compressional behavior of omphacite to 47 GPa

Omphacite is an important mineral component of eclogite. Single-crystal synchrotron X-ray diffraction data on natural (Ca, Na) (Mg, Fe, Al)Si₂O₆ omphacite have been collected at the Advanced Photon Source beamlines 13-BM-C and 13-ID-D up to 47 GPa at ambient temperature. Unit cell parameter and crystal structure refinements were carried out to constrain the isothermal equation of state and compression mechanism. The third-order Birch–Murnaghan equation of state (BM3) fit of all data gives V ₀ = 423.9(3) Å³, K _T0 = 116(2) GPa and K _T0′ = 4.3(2). These elastic parameters are consistent with the general trend of the diopside–jadeite join. The eight-coordinated polyhedra (M2 and M21) are the most compressible and contribute to majority of the unit cell compression, while the SiO₄ tetrahedra (Si1 and Si2) behave as rigid structural units and are the most incompressible. Axial compressibilities are determined by fitting linearized BM3 equation of state to pressure dependences of unit cell parameters. Throughout the investigated pressure range, the b-axis is more compressible than the c-axis. The axial compressibility of the a-axis is the largest among the three axes at 0 GPa, yet it quickly drops to the smallest at pressures above 5 GPa, which is explained by the rotation of the stiffest major compression axis toward the a-axis with the increase in pressure.     

Structural control of polyhedral compression in synthetic braunite, Mn2+Mn3+ 6O8SiO4

The compression of synthetic braunite, Mn²⁺Mn³⁺ ₆O₈SiO₄, was studied by high-pressure single-crystal X-ray diffraction carried out in a diamond-anvil cell. The equation of state at room temperature (third-order Birch-Murnaghan equation of state: V ₀=1661.15(8) ų, K _0,298=180.7±0.9 GPa, K′=6.5±0.3) was determined from unit-cell volume data to 9.18 GPa. Crystal structures were determined at 6 different pressures to 7.69 GPa. Compression of the structure (space group I4₁/acd) was found to be slightly anisotropic (a ₀=9.4262(4) Å, K _a =499±4 GPa, K _a ′=19.7±0.9; c ₀=18.6964(6) Å, K _c =657±6 GPa, K _c ′=15.7±1.4) which can be attributed to the fact that the Mn³⁺-O bonds, which are the most compressible bonds, are aligned closer to the (001) plane than to the c axis. The large bulk modulus is the result of the structural topology in which 2/3 and 1/2 of the edges of the Mn²⁺O₈ and Mn³⁺O₆ polyhedra share edges with other polyhedra. The Mn²⁺O₈ polyhedra were found to compress isotropically, whereas anisotropic compressional behaviour was observed for all three Mn³⁺O₆ octahedra. Although the polyhedral geometry of all three crystallographically independent Mn³⁺ sites shows the same type of uniaxially elongated distortion, the compression of the individual octahedral configurations was found to be strongly dependent upon both the geometry of the polyhedron itself and the types of, and the connectivity to, the neighbouring polyhedra. The differences in the configuration of the different oxygen atoms, and therefore the structural topology, is one of the major factors determining the type and degree of the pressure-induced distortion, while the Jahn-Teller effect plays a subordinate role.     

High-pressure behaviour and equation of state of calcite, CaCO3

The high-pressure response of the cell parameters of calcite, CaCO₃, has been investigated by single crystal X-ray diffraction. The unit cell parameters have been refined from 0 to 1.435?GPa, and the linear and volume compressibilities have been measured as β _a =2.62(2)?×?10^?3?GPa^?1,β _c =7.94(7)?×?10^?3?GPa^?1, β _v =13.12?×?10^?3?GPa^?1. The bulk modulus has been obtained from a fit to the Birch-Murnaghan equation of state, giving K ₀=73.46?±?0.27?GPa and V ₀=367.789 ±?0.004?ų with K′=4. Combined with earlier data for magnesite, ankerite and dolomite, these data suggest that K ₀ V ₀ is a constant for the Ca-Mg rhombohedral carbonates.     

Elastic behavior and pressure-induced structure evolution of topaz up to 45 GPa

The behavior of a natural topaz, Al_2.00Si_1.05O_4.00(OH_0.26F_1.75), has been investigated by means of in situ single-crystal synchrotron X-ray diffraction up to 45 GPa. No phase transition or change in the compressional regime has been observed within the pressure-range investigated. The compressional behavior was described 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 as follows: K _V = 158(4) GPa and K _V ′ = 3.3(3). The confidence ellipse at 68.3 % (Δχ² = 2.30, 1σ) was calculated starting from the variance–covariance matrix of K _V and K′ obtained from the III-BM-EoS least-square procedure. The ellipse is elongated with a negative slope, indicating a negative correlation of the parameters K _V and K _V ′, with K _V = 158 ± 6 GPa and K _V ′ = 3.3 ± 4. A linearized III-BM-EoS was used to obtain the axial-EoS parameters (at room-P), yielding: K(a) = 146(5) GPa [β _a = 1/(3K(a)) = 0.00228(6) GPa^?1] and K′(a) = 4.6(3) for the a-axis; K(b) = 220(4) GPa [β _b = 0.00152(4) GPa^?1] and K′(b) = 2.6(3) for the b-axis; K(c) = 132(4) GPa [β _c = 0.00252(7) GPa^?1] and K′(c) = 3.3(3) for the c-axis. The elastic anisotropy of topaz at room-P can be expressed as: K(a):K(b):K(c) = 1.10:1.67:1.00 (β _a:β _b:β _c = 1.50:1.00:1.66). A series of structure refinements have been performed based on the intensity data collected at high pressure, showing that the P-induced structure evolution at the atomic scale is mainly represented by polyhedral compression along with inter-polyhedral tilting. A comparative analysis of the elastic behavior and P/T-stability of topaz polymorphs and “phase egg” (i.e., AlSiO₃OH) is carried out.     

Single-crystal x-ray diffraction of brucite to 14 GPa

Single-crystal brucite, Mg(OH)₂, was studied to 14 GPa in a quasi-hydrostatic pressure medium using a diamond anvil cell and energy-dispersive synchrotron x-ray diffraction. The parameters of a third-order Birch-Murnaghan equation of state fit to the data are: K _OT=42(2) GPa, and (?K _OT/?P)_T= 5.7(5). The bulk modulus is significantly lower than that obtained in recent shock compression and powder x-ray diffraction experiments under non-hydrostatic conditions. No evidence was found for a transition involving the Mg -O sub-structure over the pressure range of these experiments. This implies that the structural change previously identified at high pressure by Raman spectroscopy probably involves rearrangement of hydrogen atoms, leaving the Mg — O substructure largely unaffected.     

Stability at high-pressure,elastic behaviour and pressure-induced structural evolution of CsAlSi<Subscript>5</Subscript>O<Subscript>12</Subscript>, a potential host for nuclear waste

The elastic and structural behaviour of the synthetic zeolite CsAlSi₅O₁₂ (a = 16.753(4), b = 13.797(3) and c = 5.0235(17) Å, space group Ama2, Z = 2) were investigated up to 8.5 GPa by in situ single-crystal X-ray diffraction with a diamond anvil cell under hydrostatic conditions. No phase-transition occurs within the P-range investigated. Fitting the volume data with a third-order Birch–Murnaghan equation-of-state gives: V ₀ = 1,155(4) ų, K _T0 = 20(1) GPa and K′ = 6.5(7). The “axial moduli” were calculated with a third-order “linearized” BM-EoS, substituting the cube of the individual lattice parameter (a ³, b ³, c ³) for the volume. The refined axial-EoS parameters are: a ₀ = 16.701(44) Å, K _T0a = 14(2) GPa (β_a = 0.024(3) GPa^?1), K′ _a = 6.2(8) for the a-axis; b ₀ = 13.778(20) Å, K _T0b = 21(3) GPa (β_b = 0.016(2) GPa^?1), K′ _b = 10(2) for the b-axis; c ₀ = 5.018(7) Å, K _T0c = 33(3) GPa (β_c = 0.010(1) GPa^?1), K′ _c = 3.2(8) for the c-axis (K _T0a:K _T0b:K _T0c = 1:1.50:2.36). The HP-crystal structure evolution was studied on the basis of several structural refinements at different pressures: 0.0001 GPa (with crystal in DAC without any pressure medium), 1.58(3), 1.75(4), 1.94(6), 3.25(4), 4.69(5), 7.36(6), 8.45(5) and 0.0001 GPa (after decompression). The main deformation mechanisms at high-pressure are basically driven by tetrahedral tilting, the tetrahedra behaving as rigid-units. A change in the compressional mechanisms was observed at P ≤ 2 GPa. The P-induced structural rearrangement up to 8.5 GPa is completely reversible. The high thermo-elastic stability of CsAlSi₅O_12, the immobility of Cs at HT/HP-conditions, the preservation of crystallinity at least up to 8.5 GPa and 1,000°C in elastic regime and the extremely low leaching rate of Cs from CsAlSi₅O₁₂ allow to consider this open-framework silicate as functional material potentially usable for fixation and deposition of Cs radioisotopes.