Elastic behavior of vanadinite,Pb<Subscript>10</Subscript>(VO<Subscript>4</Subscript>)<Subscript>6</Subscript>Cl<Subscript>2</Subscript>, a microporous non-zeolitic mineral

The high-pressure behavior of a vanadinite (Pb₁₀(VO₄)₆Cl₂, a = b = 10.3254(5), c = 7.3450(4) Å, space group P6₃/m), a natural microporous mineral, has been investigated using in-situ HP-synchrotron X-ray powder diffraction up to 7.67 GPa with a diamond anvil cell under hydrostatic conditions. No phase transition has been observed within the pressure range investigated. Axial and volume isothermal Equations of State (EoS) of vanadinite were determined. Fitting the P–V data with a third-order Birch-Murnaghan (BM) EoS, using the data weighted by the uncertainties in P and V, we obtained: V ₀ = 681(1) Å³, K ₀ = 41(5) GPa, and K′ = 12.5(2.5). The evolution of the lattice constants with P shows a strong anisotropic compression pattern. The axial bulk moduli were calculated with a third-order “linearized” BM-EoS. The EoS parameters are: a ₀ = 10.3302(2) Å, K ₀(a) = 35(2) GPa and K′(a) = 10(1) for the a-axis; c ₀ = 7.3520(3) Å, K ₀(c) = 98(4) GPa, and K′(c) = 9(2) for the c-axis (K ₀(a):K ₀(c) = 1:2.80). Axial and volume Eulerian-finite strain (fe) at different normalized stress (Fe) were calculated. The weighted linear regression through the data points yields the following intercept values: Fe _a (0) = 35(2) GPa for the a-axis, Fe _c (0) = 98(4) GPa for the c-axis and Fe _V (0) = 45(2) GPa for the unit-cell volume. The slope of the regression lines gives rise to K′ values of 10(1) for the a-axis, 9(2) for the c-axis and 11(1) for the unit cell-volume. A comparison between the HP-elastic response of vanadinite and the iso-structural apatite is carried out. The possible reasons of the elastic anisotropy are discussed.     

Pressure induced phase transition in Pb<Subscript>6</Subscript>Bi<Subscript>2</Subscript>S<Subscript>9</Subscript>

The crystal structure of Pb₆Bi₂S₉ is investigated at pressures between 0 and 5.6 GPa with X-ray diffraction on single-crystals. The pressure is applied using diamond anvil cells. Heyrovskyite (Bbmm, a = 13.719(4) Å, b = 31.393(9) Å, c = 4.1319(10) Å, Z = 4) is the stable phase of Pb₆Bi₂S₉ at ambient conditions and is built from distorted moduli of PbS-archetype structure with a low stereochemical activity of the Pb²⁺ and Bi³⁺ lone electron pairs. Heyrovskyite is stable until at least 3.9 GPa and a first-order phase transition occurs between 3.9 and 4.8 GPa. A single-crystal is retained after the reversible phase transition despite an anisotropic contraction of the unit cell and a volume decrease of 4.2%. The crystal structure of the high pressure phase, β-Pb₆Bi₂S₉, is solved in Pna2 ₁ (a = 25.302(7) Å, b = 30.819(9) Å, c = 4.0640(13) Å, Z = 8) from synchrotron data at 5.06 GPa. This structure consists of two types of moduli with SnS/TlI-archetype structure in which the Pb and Bi lone pairs are strongly expressed. The mechanism of the phase transition is described in detail and the results are compared to the closely related phase transition in Pb₃Bi₂S₆ (lillianite).     

Compressibility of strontium orthophosphate Sr<Subscript>3</Subscript>(PO<Subscript>4</Subscript>)<Subscript>2</Subscript> at high pressure

High pressure in situ synchrotron X-ray diffraction experiment of strontium orthophosphate Sr₃(PO₄)₂ has been carried out to 20.0 GPa at room temperature using multianvil apparatus. Fitting a third-order Birch–Murnaghan equation of state to the P–V data yields a volume of V ₀ = 498.0 ± 0.1 Å³, an isothermal bulk modulus of K _T  = 89.5 ± 1.7 GPa, and first pressure derivative of K _T ′ = 6.57 ± 0.34. If K _T ′ is fixed at 4, K _T is obtained as 104.4 ± 1.2 GPa. Analysis of axial compressible modulus shows that the a-axis (K _a  = 79.6 ± 3.2 GPa) is more compressible than the c-axis (K _c  = 116.4 ± 4.3 GPa). Based on the high pressure Raman spectroscopic results, the mode Grüneisen parameters are determined and the average mode Grüneisen parameter of PO₄ vibrations of Sr₃(PO₄)₂ is calculated to be 0.30(2).     

High-pressure phase transitions of CaRhO<Subscript>3</Subscript> perovskite

High-pressure phase transitions of CaRhO₃ perovskite were examined at pressures of 6–27 GPa and temperatures of 1,000–1,930°C, using a multi-anvil apparatus. The results indicate that CaRhO₃ perovskite successively transforms to two new high-pressure phases with increasing pressure. Rietveld analysis of powder X-ray diffraction data indicated that, in the two new phases, the phase stable at higher pressure possesses the CaIrO₃-type post-perovskite structure (space group Cmcm) with lattice parameters: a = 3.1013(1) Å, b = 9.8555(2) Å, c = 7.2643(1) Å, V _m  = 33.43(1) cm³/mol. The Rietveld analysis also indicated that CaRhO₃ perovskite has the GdFeO₃-type structure (space group Pnma) with lattice parameters: a = 5.5631(1) Å, b = 7.6308(1) Å, c = 5.3267(1) Å, V _m  = 34.04(1) cm³/mol. The third phase stable in the intermediate P, T conditions between perovskite and post-perovskite has monoclinic symmetry with the cell parameters: a = 12.490(3) Å, b = 3.1233(3) Å, c = 8.8630(7) Å, β = 103.96(1)°, V _m  = 33.66(1) cm³/mol (Z = 6). Molar volume changes from perovskite to the intermediate phase and from the intermediate phase to post-perovskite are –1.1 and –0.7%, respectively. The equilibrium phase relations determined indicate that the boundary slopes are large positive values: 29 ± 2 MPa/K for the perovskite—intermediate phase transition and 62 ± 6 MPa/K for the intermediate phase—post-perovskite transition. The structural features of the CaRhO₃ intermediate phase suggest that the phase has edge-sharing RhO₆ octahedra and may have an intermediate structure between perovskite and post-perovskite.     

Thermoelastic properties of chromium oxide Cr<Subscript>2</Subscript>O<Subscript>3</Subscript> (eskolaite) at high pressures and temperatures

A new synchrotron X-ray diffraction study of chromium oxide Cr₂O₃ (eskolaite) with the corundum-type structure has been carried out in a Kawai-type multi-anvil apparatus to pressure of 15 GPa and temperatures of 1873 K. Fitting the Birch–Murnaghan equation of state (EoS) with the present data up to 15 GPa yielded: bulk modulus (K _0,T0), 206 ± 4 GPa; its pressure derivative K′_0,T , 4.4 ± 0.8; (?K _0,T /?T) = ?0.037 ± 0.006 GPa K^?1; a = 2.98 ± 0.14 × 10^?5 K^?1 and b = 0.47 ± 0.28 × 10^?8 K^?2, where α _0,T  = a + bT is the volumetric thermal expansion coefficient. The thermal expansion of Cr₂O₃ was additionally measured at the high-temperature powder diffraction experiment at ambient pressure and α _0,T0 was determined to be 2.95 × 10^?5 K^?1. The results indicate that coefficient of the thermal expansion calculated from the EoS appeared to be high-precision because it is consistent with the data obtained at 1 atm. However, our results contradict α ₀ value suggested by Rigby et al. (Brit Ceram Trans J 45:137–148, 1946) widely used in many physical and geological databases. Fitting the Mie–Grüneisen–Debye EoS with the present ambient and high-pressure data yielded the following parameters: K _0,T0 = 205 ± 3 GPa, K′_0,T  = 4.0, Grüneisen parameter (γ ₀) = 1.42 ± 0.80, q = 1.82 ± 0.56. The thermoelastic parameters indicate that Cr₂O₃ undergoes near isotropic compression at room and high temperatures up to 15 GPa. Cr₂O₃ is shown to be stable in this pressure range and adopts the corundum-type structure. Using obtained thermoelastic parameters, we calculated the reaction boundary of knorringite formation from enstatite and eskolaite. The Clapeyron slope (with \({\text{d}}P/{\text{d}}T = - 0.014\) GPa/K) was found to be consistent with experimental data.     

New high-pressure phases in BaCO<Subscript>3</Subscript>

Barium carbonate (BaCO₃) was examined in a diamond anvil cell up to a pressure of 73 GPa using an in situ angle-dispersive X-ray diffraction technique. Three new phases of BaCO₃ were observed at pressures >10 GPa. From 10 to 24 GPa, BaCO₃-IV had a post-aragonite structure with space group Pmmn. There are two molecules in a single unit cell (Z = 2) of the orthorhombic phase, which is same as the high-pressure phases of CaCO₃ and SrCO₃. The isothermal bulk modulus of BaCO₃-IV is K ₀ = 84(4) GPa, with V ₀ = 129.0(7) Å³ when K ₀′ = 4. The c axis of the unit cell parameter is less compressible than the a and b axes. The relative change in volume that accompanies the transformation between BaCO₃-III and BaCO₃-IV is ～6%. BaCO₃-V, which has an orthorhombic symmetry, was synthesized at 50 GPa. As the pressure increases, BaCO₃-V is transformed into tetragonal BaCO₃-VI. This transformation is likely to be second order, because the diffraction pattern of BaCO₃-V is similar to that of BaCO₃-VI, and some single peaks in BaCO₃-VI become doublets in BaCO₃-V. After decompression, the new high-pressure phases transform into BaCO₃-II. Our findings resolve a dispute regarding the stable high-pressure phases of BaCO₃.     

Hydrogen bond effects on compressional behavior of isotypic minerals: high-pressure polymorphism of cristobalite-like Be(OH)<Subscript>2</Subscript>

Three isotypic crystals, SiO₂ (α-cristobalite), ε-Zn(OH)₂ (wülfingite), and Be(OH)₂ (β-behoite), with topologically identical frameworks of corner-connected tetrahedra, undergo displacive compression-driven phase transitions at similar pressures (1.5–2.0 GPa), but each transition is characterized by a different mechanism resulting in different structural modifications. In this study, we report the crystal structure of the high-pressure γ-phase of beryllium hydroxide and compare it with the high-pressure structures of the other two minerals. In Be(OH)₂, the transition from the ambient β-behoite phase with the orthorhombic space group P2₁2₁2₁ and ambient unit cell parameters a = 4.5403(4) Å, b = 4.6253(5) Å, c = 7.0599(7) Å, to the high-pressure orthorhombic γ-polymorph with space group Fdd2 and unit cell parameters (at 5.3(1) GPa) a = 5.738(2) Å, b = 6.260(3) Å, c = 7.200(4) Å takes place between 1.7 and 3.6 GPa. This transition is essentially second order, is accompanied by a negligible volume discontinuity, and exhibits both displacive and reversible character. The mechanism of the phase transition results in a change to the hydrogen bond connectivities and rotation of the BeO₄ tetrahedra.     

New insights on pressure,temperature, and chemical stability of CsAlSi<Subscript>5</Subscript>O<Subscript>12</Subscript>, a potential host for nuclear waste

A Cs-bearing polyphase aggregate with composition (in wt%): 76(1)_CsAlSi5O12 + 7(1)_CsAlSi2O6 + 17(1)_amorphous, was obtained from a clinoptilolite-rich epiclastic rock after a beneficiation process of the starting material (aimed to increase the fraction of zeolite to 90 wt%), cation exchange and then thermal treatment. CsAlSi₅O₁₂ is an open-framework compound with CAS topology; CsAlSi₂O₆ is a pollucite-like material with ANA topology. The thermal stability of this polyphase material was investigated by in situ high-T X-ray powder diffraction, the combined P–T effects by a series of runs with a single-stage piston cylinder apparatus, and its chemical stability following the “availability test” (“AVA test”) protocol. A series of additional investigations were performed by WDS–electron microprobe analysis in order to describe the P–T-induced modification of the material texture, and to chemically characterize the starting material and the run products. The “AVA tests” of the polyphase aggregate show an extremely modest release of Cs⁺: 0.05 mg/g. In response to applied temperature and at room P, CsAlSi₅O₁₂ experiences an unquenchable and displacive Ama2-to-Amam phase transition at about 770 K, and the Amam polymorph is stable in its crystalline form up to 1600 K; a crystalline-to-amorphous phase transition occurs between 1600 and 1650 K. In response to the applied P = 0.5 GPa, the crystalline-to-amorphous transition of CsAlSi₅O₁₂ occurs between 1670 and 1770 K. This leads to a positive Clapeyron slope (i.e., dP/dT > 0) of the crystalline-to-amorphous transition. When the polyphase aggregate is subjected at P = 0.5 GPa and T > 1770 K, CsAlSi₅O₁₂ melts and only CsAlSi₂O₆ (pollucite-like; dominant) and Cs-rich glass (subordinate) are observed in the quenched sample. Based on its thermo-elastic behavior, P–T phase stability fields, and Cs⁺ retention capacity, CsAlSi₅O₁₂ is a possible candidate for use in the immobilization of radioactive isotopes of Cs, or as potential solid hosts for ¹³⁷Cs γ-radiation source in sterilization applications. More in general, even the CsAlSi₅O₁₂-rich aggregate obtained by a clinoptilolite-rich epiclastic rock appears to be suitable for this type of utilizations.     

Thermal equation of state of CaIrO<Subscript>3</Subscript> post-perovskite

The pressure–volume–temperature (P–V–T) relation of CaIrO₃ post-perovskite (ppv) was measured at pressures and temperatures up to 8.6 GPa and 1,273 K, respectively, with energy-dispersive synchrotron X-ray diffraction using a DIA-type, cubic-anvil apparatus (SAM85). Unit-cell dimensions were derived from the Le Bail full profile refinement technique, and the results were fitted using the third-order Birth-Murnaghan equation of state. The derived bulk modulus \( K_{T0} \) at ambient pressure and temperature is 168.3 ± 7.1 GPa with a pressure derivative \( K_{T0}^{\prime } \) = 5.4 ± 0.7. All of the high temperature data, combined with previous experimental data, are fitted using the high-temperature Birch-Murnaghan equation of state, the thermal pressure approach, and the Mie-Grüneisen-Debye formalism. The refined thermoelastic parameters for CaIrO₃ ppv are: temperature derivative of bulk modulus \( (\partial K_{T} /\partial T)_{P} \) = ?0.038 ± 0.011 GPa K^?1, \( \alpha K_{T} \) = 0.0039 ± 0.0001 GPa K^?1, \( \left( {\partial K_{T} /\partial T} \right)_{V} \) = ?0.012 ± 0.002 GPa K^?1, and \( \left( {\partial^{2} P/\partial T^{2} } \right)_{V} \) = 1.9 ± 0.3 × 10^?6 GPa² K^?2. Using the Mie-Grüneisen-Debye formalism, we obtain Grüneisen parameter \( \gamma_{0} \) = 0.92 ± 0.01 and its volume dependence q = 3.4 ± 0.6. The systematic variation of bulk moduli for several oxide post-perovskites can be described approximately by the relationship K _T0  = 5406.0/V(molar) + 5.9 GPa.     

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

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

Synthesis,TEM characterization and thermal behaviour of LiNiSi<Subscript>2</Subscript>O<Subscript>6</Subscript> pyroxene

A pyroxene with composition LiNiSi₂O₆ was synthesized at T = 1,473 K and P = 2.0 GPa; the cell parameters at T = 298 K are a = 9.4169(6) Å, b = 8.4465(7) Å, c = 5.2464(3) Å, β = 110.534(6)°, V = 390.78(3) Å³. TEM examination of the LiNiSi₂O₆ pyroxene showed the presence of h + k odd reflections indicative of a primitive lattice, and of antiphase domains obtained by dark field imaging of the h + k odd reflections. A HT in situ investigation was performed by examining TEM selected area diffraction patterns collected at high temperature and synchrotron radiation powder diffraction. In HTTEM the LiNiSi₂O₆ was examined together with LiCrSi₂O₆ pyroxene. In LiCrSi₂O₆ the h + k odd critical reflections disappear at about 340 K; they are sharp up to the transition temperature and do not change their shape until they disappear. In LiNiSi₂O₆ the h + k odd reflections are present up to sample deterioration at 650 K. A high temperature synchrotron radiation powder diffraction investigation was performed on LiNiSi₂O₆ between 298 and 773 K. The analysis of critical reflections and of changes in cell parameters shows that the space group is P-centred up to the highest temperature. The comparative analysis of the thermal and spontaneous strain contributions in P2₁/c and C2/c pyroxenes indicates that the high temperature strain in P-LiNiSi₂O₆ is very similar to that due to thermal strain only in C2/c spodumene and that a spontaneous strain contribution related to pre-transition features is not apparent in LiNiSi₂O₆. A different high-temperature behaviour in LiNiSi₂O₆ with respect to other pyroxenes is suggested, possibly in relation with the presence of Jahn–Teller distortion of the M1 polyhedron centred by low-spin Ni³⁺.     

Hydrostatic compression of galenobismutite (PbBi<Subscript>2</Subscript>S<Subscript>4</Subscript>): elastic properties and high-pressure crystal chemistry

A single-crystal sample of galenobismutite was subjected to hydrostatic pressures in the range of 0.0001 and 9 GPa at room temperature using the diamond-anvil cell technique. A series of X-ray diffraction intensities were collected at ten distinct pressures using a CCD equipped 4-circle diffractometer. The crystal structure was refined to R1(|F₀| > 4σ) values of approximately 0.05 at all pressures. By fitting a third-order Birch-Murnaghan equation of state to the unit-cell volumes V ₀ = 700.6(2) ų, K ₀ = 43.9(7) GPa and dK/dP = 6.9(3) could be determined for the lattice compression. Both types of cations in galenobismutite have stereochemically active lone electron pairs, which distort the cation polyhedra at room pressure. The cation eccentricities decrease at higher pressure but are still pronounced at 9 GPa. Galenobismutite is isotypic with CaFe₂O₄ (CF) but moves away from the idealised CF-type structure during compression. Instead of the two octahedral cation sites and one bi-capped trigonal-prismatic site, PbBi₂S₄ attains a new high-pressure structure characterised by one octahedral site and two mono-capped trigonal-prismatic sites. Analyses of the crystal structure at high pressure confirm the preference of Bi for the octahedral site and the smaller one of the two trigonal-prismatic sites.     

Equation of state of synthetic qandilite Mg<Subscript>2</Subscript>TiO<Subscript>4</Subscript> at ambient temperature

Using a diamond-anvil cell and synchrotron X-ray diffraction, the compressional behavior of a synthetic qandilite Mg_2.00(1)Ti_1.00(1)O₄ has been investigated up to about 14.9 GPa at 300 K. The pressure–volume data fitted to the third-order Birch–Murnaghan equation of state yield an isothermal bulk modulus (K _T0) of 175(5) GPa, with its first derivative \(K_{T0}^{{\prime }}\) attaining 3.5(7). If \(K_{T0}^{{\prime }}\) is fixed as 4, the K _T0 value is 172(1) GPa. This value is substantially larger than the value of the adiabatic bulk modulus (K _S0) previously determined by an ultrasonic pulse echo method (152(7) GPa; Liebermann et al. in Geophys J Int 50:553–586, 1977), but in general agreement with the K _T0 empirically estimated on the basis of crystal chemical systematics (169 GPa; Hazen and Yang in Am Miner 84:1956–1960, 1999). Compared to the K _T0 values of the ulvöspinel (Fe₂TiO₄; ~148(4) GPa with \(K_{T0}^{{\prime }} = 4\)) and the ringwoodite solid solutions along the Mg₂SiO₄–Fe₂SiO₄ join, our finding suggests that the substitution of Mg²⁺ for Fe²⁺ on the T sites of the 4–2 spinels can have more significant effect on the K _T0 than that on the M sites.     

Crystal chemistry of selenates with mineral-like structures. III. Heteropolyhedral chains in the crystal structure of [Mg(H<Subscript>2</Subscript>O)<Subscript>4</Subscript>(SeO<Subscript>4</Subscript>)]<Subscript>2</Subscript>(H<Subscript>2</Subscript>O)

The crystal structure of a new compound [Mg(H₂O)₄(SeO₄)]₂(H₂O) (monoclinic, P2 ₁/a, a = 7.2549(12), b = 20.059(5), c = 10.3934(17) Å, β = 101.989(13), V = 1479.5(5) ų) has been solved by direct methods and refined to R ₁ = 0.059 for 2577 observed reflections with |F _hkl | ≥ 4σ|F _hkl |. The structure consists of [Mg(H₂O)₄(SeO₄)]⁰ chains formed by alternating corner-sharing Mg octahedrons and (SeO₄)^2? tetrahedrons. O atoms of Mg octahedrons that are shared with selenate tetrahedrons are in a trans orientation. The heteropoly-hedral octahedral-tetrahedral chains are parallel to the c axis and undulate within the (010) plane. The adjacent chains are linked by hydrogen bonds involving H₂O molecules not bound with M²⁺ cations.     

The crystal structure of alumoklyuchevskite,K<Subscript>3</Subscript>Cu<Subscript>3</Subscript>AlO<Subscript>2</Subscript>(SO<Subscript>4</Subscript>)<Subscript>4</Subscript>

The crystal structure of the unstable mineral alumoklyuchevskite K₃Cu₃AlO₂(SO₄)₄ [monoclinic, I2, a = 18.772(7), b = 4.967(2), c = 18.468(7) Å, β = 101.66(1)°, V = 1686(1) Å] was refined to R ₁ = 0.131 for 2450 unique reflections with F ≥ 4σF _hkl. The structure is based on oxocentered tetrahedrons (OAlCu ₃ ⁷⁺ ) linked into chains via edges. Each chain is surrounded by SO₄ tetrahedrons forming a structural complex. Each complex is elongated along the b axis. This type of crystal structure was also found in other fumarole minerals of the Great Tolbachik Fissure Eruption (GTFE, Kamchatka Peninsula, Russia, 1975–1976), klyuchevskite, K₃Cu₃Fe³⁺O₂(SO₄)₄; and piypite, K₂Cu₂O(SO₄)₂.     

The compressibility of Fe- and Al-bearing phase D to 30 GPa

High-pressure in situ X-ray diffraction experiment of Fe- and Al-bearing phase D (Mg_0.89Fe_0.14Al_0.25Si_1.56H_2.93O₆) has been carried out to 30.5 GPa at room temperature using multianvil apparatus. Fitting a third-order Birch–Murnaghan equation of state to the P–V data yields values of V ₀ = 86.10 ± 0.05 ų; K ₀ = 136.5 ± 3.3 GPa and K′ = 6.32 ± 0.30. If K′ is fixed at 4.0 K ₀ = 157.0 ± 0.7 GPa, which is 6% smaller than Fe–Al free phase D reported previously. Analysis of axial compressibilities reveals that the c-axis is almost twice as compressible (K _c  = 93.6 ± 1.1 GPa) as the a-axis (K _a  = 173.8 ± 2.2 GPa). Above 25 GPa the c/a ratio becomes pressure independent. No compressibility anomalies related to the structural transitions of H-atoms were observed in the pressure range to 30 GPa. The density reduction of hydrated subducting slab would be significant if the modal amount of phase D exceeds 10%.     

Crystal chemistry of natural and synthetic lead oxyhalides. Part I. Crystal structure of Pb<Subscript>13</Subscript>O<Subscript>10</Subscript>Cl<Subscript>6</Subscript>

Crystals of lead oxychloride Pb₁₃O₁₀Cl₆ have been synthesized on the basis of high-temperature solid-state reactions. The Pb₁₃O₁₀Cl₆ structure was studied using X-ray single-crystal diffraction analysis. The compound is monoclinic, and the space group is C2/c; the unit-cell dimensions are a = 16.1699(14), b = 7.0086(6), c = 23.578(2) Å, β = 97.75°, and V = 2647.6(4) ų. The structure has been solved by direct methods and refined to R ₁ = 0.0505 for 2671 observed unique reflections. The structure is a 3D framework consisting of OPb₄ tetrahedrons. Chlorine atoms are located in the framework channels. The structure contains seven symmetrically independent Pb atoms, which are coordinated by 2 to 4 O^2? and 2 to 4 Cl^? anions. The synthesized compound is compared with other natural and synthetic lead oxyhalides.     

Thermal equation of state of natural tourmaline at high pressure and temperature

Synchrotron-based in situ angle-dispersive X-ray diffraction experiments were conducted on a natural uvite-dominated tourmaline sample by using an external-heating diamond anvil cell at simultaneously high pressures and temperatures up to 18 GPa and 723 K, respectively. The angle-dispersive X-ray diffraction data reveal no indication of a structural phase transition over the P–T range of the current experiment in this study. The pressure–volume–temperature data were fitted by the high-temperature Birch–Murnaghan equation of state. Isothermal bulk modulus of K ₀ = 96.6 (9) GPa, pressure derivative of the bulk modulus of \(K_{0}^{\prime } = 12.5 \;(4)\), thermal expansion coefficient of α ₀ = 4.39 (27) × 10^?5 K^?1 and temperature derivative of the bulk modulus (?K/?T) _P  = ?0.009 (6) GPa K^?1 were obtained. The axial thermoelastic properties were also obtained with K _a0 = 139 (2) GPa, \(K_{a0}^{\prime }\) = 11.5 (7) and α _a0 = 1.00 (11) × 10^?5 K^?1 for the a-axis, and K _c0 = 59 (1) GPa, \(K_{c0}^{\prime }\) = 11.4 (5) and α _c0 = 2.41 (24) × 10^?5 K^?1 for the c-axis. Both of axial compression and thermal expansion exhibit large anisotropic behavior. Thermoelastic parameters of tourmaline in this study were also compared with that of the other two ring silicates of beryl and cordierite.     

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

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