Third-order Birch-Murnaghan Equation Of State Research Articles

P-V-T equation of state of Ca3Cr2Si3O12 uvarovite garnet by using a diamond-anvil cell and in-situ synchrotron X-ray diffraction

The pressure-volume-temperature (P-V-T) equation of state (EoS) of synthetic uvarovite has been measured at high temperatures up to 900 K and high pressures up to 16.20 GPa, by using in situ angle-dispersive X-ray diffraction and diamond-anvil cell. Analysis of room-temperature P-V data to a third-order Birch-Murnaghari EoS yielded: V-0 = 1736.9 +/- 0.5 angstrom(3), K-0 = 162 +/- 2 GPa, and K-0(') = 4.5 +/- 0.3. With K-0(') fixed to 4.0, we obtained: V-0 = 1736.5 +/- 0.3 angstrom(3) and K-0 = 164 +/- 1 GPa. Fitting of our P-V-T data by means of the high-temperature third-order Birch-Murnaghan equations of state, given the thermoelastic parameters: V-0= 1736.8 +/- 0.8 angstrom(3), K-0 = 162 +/- 3 GPa, K-0(') = 4.3 +/- 0.4, (partial derivative K/partial derivative T)(P)=-0.021 +/- 0.004 GPa/K, and alpha(0) = (2.72 +/- 0.14)x10(-5) K-1.We compared our elastic parameters to the results from the previous studies for uvarovite. From the comparison of these fittings, we propose to constrain the bulk modulus and its pressure derivative to K-0 = 162 GPa and K-0(') = 4.0-4.5 for uvarovite. Present results were also compared with previous studies for other ugrandite garnets, grossular and andradite, which indicated that the compression mechanism of uvarovite might be similar with grossular and andradite. Furthermore, a systematic relationship, K-0(GPa) = 398.1(7)-0.136(8) V-0 (angstrom(3)) with a correlation coefficient R-2 of 0.9999, has been established based on these isostructural analogs. Combining these results with previous studies for pyralspite garnets-pyrope, almandine, and spessartine-the compositional dependence of the thermoelastic parameters (bulk modulus, thermal expansion, and the temperature derivative of the bulk modulus) were discussed.

Thermo-compression of pyrope-grossular garnet solid solutions: Non-linear compositional dependence

Unit-cell parameters of a series of synthetic garnets with the pyrope, grossular, and four intermediate compositions were measured up to about 900 K and to 10 GPa using synchrotron X-ray powder diffraction. Coefficients of thermal expansion of pyrope-grossular garnets are in the range 2.10–2.74 × 10−5 K−1 and uniformly increase with temperature. Values for the two end-members pyrope and grossular are identical within experimental error 2.74 ± 0.05 × 10−5 K−1 and 2.73 ± 0.01 × 10−5 K−1, respectively. Coefficients of thermal expansion for intermediate compositions are smaller than those of end-members and are not linearly dependent on composition. Bulk modulus of grossular is K = 164.3(1) GPa (with K ′ the pressure derivative of the bulk modulus fixed to 5.92) and bulk modulus of pyrope is K = 169.2(2) GPa (with K ′ fixed to 4.4) using a third-order Birch-Murnaghan equation of state, which are consistent with previously reported values. The bulk moduli of garnets of intermediate composition are between ~155 and ~160 GPa, smaller than those of the end-members no matter which K ′ is chosen. The compositional dependence of bulk modulus resembles the compositional dependence of thermal expansion. Intermediate garnets on this binary have large positive excess volume, which makes them more compressible. We find that excess volumes in the pyrope-grossular series remain relatively large even at high pressure (~6 GPa) and temperature (~800 K), supporting the observation of crystal exsolution on this garnet join. The curiously “W”-shaped compositional variation of thermal expansion and bulk modulus is anti-correlated with the compositional dependence of microstrain documented in our companion paper (Du et al. in preparation) on the excess volumes in this series of garnets. Minimum thermal expansions and bulk moduli go with maximum microstrains.

P–V–T equation of state of spessartine–almandine solid solution measured using a diamond anvil cell and in situ synchrotron X-ray diffraction

The pressure–volume–temperature (P–V–T) equation of state (EoS) of two natural garnet samples along spessartine–almandine (Spe–Alm) join has been measured at high temperature up to 800 K and high pressures up to 15.46 and 16.17 GPa for Spe64Alm36 and Spe38Alm62, respectively, using in situ angle-dispersive X-ray diffraction and diamond anvil cell. Analysis of room-temperature P–V data to a third-order Birch–Murnaghan EoS yields: V 0 = 1,544.4 ± 0.4 A3, K 0 = 180 ± 3 GPa and $$ K_{0}^{{\prime }} $$ = 4.0 ± 0.4 for Spe38Alm62, and V 0 = 1,557.5 ± 0.3 A3, K 0 = 176 ± 2 GPa and $$ K_{0}^{{\prime }} $$ = 4.0 ± 0.3 for Spe64Alm36. Fitting of our P–V–T data by means of the high-temperature third-order Birch–Murnaghan EoS gives the thermoelastic parameters: V 0 = 1,544.6 ± 0.6 A3, K 0 = 180 ± 4 GPa, $$ K_{0}^{{\prime }} $$ = 4.0 ± 0.4, (∂K/∂T) P = −0.028 ± 0.005 GPa K−1 and α 0 = (3.16 ± 0.14) × 10−5 K−1 for Spe38Alm62, and V 0 = 1,557.7 ± 0.9 A3, K 0 = 176 ± 4 GPa, $$ K_{0}^{{\prime }} $$ = 4.0 ± 0.5, (∂K/∂T) P = −0.029 ± 0.005 GPa K−1 and α 0 = (3.04 ± 0.16) × 10−5 K−1 for Spe64Alm36. The results confirm that almandine content increases the bulk modulus of the spessartine–almandine join following a nearly ideal mixing model. The relation between bulk modulus and almandine mole fraction (X Alm) in this garnet join is derived to be K 0(GPa) = 171.6(±2.6) + 10.9(±1.8)X Alm. Present results are also compared with previously studies determined the thermoelastic properties of other garnets.

Pressure-volume equation of state for chromite and magnesiochromite: A single-crystal X-ray diffraction investigation

The pressure-volume equation of state for the two spinel end-member compositions chromite FeCr 2 O 4 and magnesiochromite MgCr 2 O 4 was determined for flux-grown synthetic single crystals at room temperature up to 8.2 and 9.2 GPa, respectively, by single-crystal X-ray diffraction using a diamond-anvil cell. The pressure-volume data show that the linear volume compressibility (here used only for purpose of comparison), calculated as β V = |[(Δ V / V 0 )/Δ P ]|, is 0.00468 and 0.00470 GPa −1 , for chromite and magnesiochromite, respectively, with a negligible difference below 0.5%. The experimental data were fitted to a third-order Birch-Murnaghan equation of state (BM3) allowing a simultaneous refining of the following coefficients: V 0 = 588.47(4) A 3 , K T0 = 184.8(1.7) GPa, and K′ = 6.1(5) for chromite and V 0 = 579.30(4) A 3 , K T0 = 182.5(1.4) GPa, and K′ = 5.8(4) for magnesiochromite. The difference in K T0 is reduced to 2 O 4 and MgCr 2 O 4 allowed us to fit the pressure-volume data of both to a single BM3 equation, resulting in a K T0 = 184.4(2.2) GPa and K′ = 5.7(6).

P–V–T equation of state of molybdenite (MoS2) by a diamond anvil cell and in situ synchrotron angle-dispersive X-ray diffraction

The pressure–volume–temperature (P–V–T) equation of state (EoS) of a natural molybdenite (MoS2) has been measured at high temperature up to 700K and high pressures up to 18.26GPa, by using in situ angle-dispersive X-ray diffraction and diamond anvil cell. Analysis of room-temperature P–V data to a third-order Birch–Murnaghan EoS yields: V0=107.0±0.1Å3, K0=67±2GPa and K′0=5.0±0.3. With K′0 fixed to 4.0, we obtained: V0=106.7±0.1Å3 and K0=74.5±0.8GPa. Fitting of our P–V–T data by means of the high-temperature third order Birch–Murnaghan equations of state, gives the thermoelastic parameters: V0=107.0±0.1Å3, K0=69±2GPa, K′0=4.7±0.2, (∂K/∂T)P=−0.021±0.003GPaK−1, a=(2.2±0.7)×10−5K−1 and b=(2.9±0.8)×10−8K−2. The temperature derivative of the bulk modulus and thermal expansion coefficient of MoS2 are obtained for the first time. Present results are also compared with previously studies determined the elastic properties of MoS2 and WS2.

Equation of state and a high-pressure structural phase transition in the gillespite-structured phase Ba0.5Sr0.5CuSi4O10

The equation of state and the crystal structure of the gillespite-structured phase Ba 0.5 Sr 0.5 CuSi 4 O 10 have been determined at seventeen pressures, ambient to 6.5 GPa, using powder neutron diffraction. At ~4.45 GPa, a structural phase transition is observed from the low-pressure structure, in space group P 4/ ncc , to a high-pressure structure in space group P 42 1 2. No experimental evidence was found for the presence of weak superlattice reflections with wave vector (2π/3 a , 2π/3 a , 0) that have recently been observed in the high-pressure, single-crystal X-ray diffraction patterns of the isostructural compounds BaCuSi 4 O 10 and BaCrSi 4 O 10 , and it should be noted that the possibility remains that the crystal structure reported here may represent the average of a similar commensurately ordered phase. The isothermal bulk modulus of the low-pressure phase, determined using a third-order Birch-Murnaghan equation of state, is 81.6(8) GPa with an initial pressure derivative of −3.3(3). The bulk modulus of the high-pressure phase was found to be smaller, estimated as 59.4 GPa. The phase transition appears to be driven by the need to relax the strong over-bonding of the alkaline-earth site, but apparently not that associated with the square-planar copper sites, which remain significantly over-bonded in the high-pressure phase. The phase transition equates to the loss of the centres of symmetry in the low-pressure phase, and results in marked differences in the tilting of the symmetry-independent Si 2 O 7 polyhedral groups, and in the aplanarity of the associated bonded CuO 4 square-planar groups. From the limited data that exists on isostructural compounds of gillespite, the low-pressure structure appears to be unstable at volume reductions of 4–6 %, however the structure of the high-pressure phase seems to depend on whether or not the cation in the square-planar site is a Jahn-Teller ion.

The high-pressure behavior of bloedite: A synchrotron single-crystal X-ray diffraction study

High-pressure single-crystal synchrotron X-ray diffraction was carried out on a single crystal of bloedite [Na 2 Mg(SO 4 ) 2 4H 2 O] compressed in a diamond-anvil cell. The volume-pressure data, collected up to 11.2 GPa, were fitted by a second- and a third-order Birch-Murnaghan equation of state (EOS), yielding V 0 = 495.6(7) A 3 with K 0 = 39.9(6) GPa, and V 0 = 496.9(7) A 3 , with K 0 = 36(1) GPa and K ′ = 5.1 (4) GPa −1 , respectively. The axial moduli were calculated using a Birch-Murnaghan EOS truncated at the second order, fixing K ′ equal to 4, for a and b axes and a third-order Birch-Murnaghan EOS for c axis. The results were a 0 = 11.08(1) and K 0 = 56(3) GPa, b 0 = 8.20(2) and K 0 = 43(3) GPa, and c 0 = 5.528(5), K 0 = 40(2) GPa, K ′ = 1.7(3) GPa −1 . The values of the compressibility for a , b , and c axes are β a = 0.0060(3) GPa −1 , β b = 0.0078(5) GPa −1 , β c = 0.0083(4) GPa −1 with an anisotropic ratio of β a :β b :β c = 0.72:0.94:1. The evolution of crystal lattice and geometrical parameters indicates no phase transition up to 11 GPa. Sulfate polyhedra are incompressible, whereas the Mg polyhedral bulk modulus is 95 GPa. The sodium polyhedron is the softest part of the whole structure with a bulk modulus of 41 GPa. Pressure decreases significantly the distortion of Na coordination. Up to 10 GPa, the donor-acceptor oxygen distances decrease significantly and the difference between the two water molecules decreases with an increase in the strengths of hydrogen bonds. At the same time, the bond lengths from Na and Mg to O atoms of the water molecules decrease faster than other bonds to these cations suggesting that there is a coupling between the Na-Ow and Mg-Ow bond strengths and the “hydrogen transfer” to acceptor O atoms.

Cordierite under hydrostatic compression: Anomalous elastic behavior as a precursor for a pressure-induced phase transition

The high-pressure behavior of cordierite was investigated by means of in situ experiments using piston-cylinder press and diamond-anvil cell. Static compression in diamond-anvil cells was conducted with various penetrating and non-penetrating pressure media (H 2 O up to 2 GPa, argon and 4:1-methanol-ethanol up to 7 GPa). The measurement of lattice parameters revealed neither a significant influence on the elasticity nor any indication for effects in analogy to over-hydration within the experimental pressure ranges. Volumetric compression experiments at constant rates up to 1.2 GPa in a piston-cylinder apparatus insinuate subtle irregularities in the low-pressure range at around ~0.35 and ~0.85 GPa. The Δ V / V contribution related to the anomalous compression behavior in that pressure range is of the order of 5 × 10 −4 . The results obtained from single-crystal X-ray diffraction between 10 −4 and 7 GPa revealed an unexpected and anomalous linear volume decrease, corresponding to K T,298 = 131±1 GPa for the bulk modulus and K ′ = −0.4±0.3 for its pressure derivative for a third-order Birch-Murnaghan equation of state. The compressional behavior of the main axis directions is anisotropic with β a −1 ≈ β b −1 > β c −1 for an initial pressure regime up to ~3 GPa. At pressures above ~4 GPa, the compression of the a - and b -axis starts to differ significantly, with the b -axis showing elastic softening as indicated by negative values for ∂(β b −1 )/∂ P . The diversification between the a - and b -axis is also expressed by the pressure-depending increase of the distortion parameter Δ. The pronounced elastic softening in both the b -axis and c -axis directions ∂(β b −1 )/∂ P = −4.3±0.9, ∂(β c −1 )/∂ P = −1.2±0.8) are responsible for the apparent linear bulk compression, which indicates the structural instability and precedes a so far not reported ferroelastic phase transition to a triclinic polymorph, following a primitive lattice above the critical transition at ~6.9 GPa.

Phase transitions and equation of state of forsterite to 90 GPa from single-crystal X-ray diffraction and molecular modeling

Forsterite, Mg2SiO4, the magnesian end-member of the olivine system, is the archetypal example of an orthosilicate structure. We have conducted synchrotron-based single-crystal X-ray diffraction experiments to 90 GPa on synthetic end-member forsterite to study its equation of state and phase transitions. Upon room-temperature compression, the forsterite structure is observed to 48 GPa. By fitting a third-order Birch-Murnaghan equation of state to our compression data, we obtain the zero-pressure isothermal bulk modulus, K 0T = 130.0(9) GPa and its pressure derivative, K ′0T = 4.12(7) for a fixed room-pressure volume, V = 290.1(1) A3, in good agreement with earlier work. At 50 GPa, a phase transition to a new structure (forsterite II) occurs, followed by a second transition to forsterite III at 58 GPa. Forsterite III undergoes no additional phase transitions until at least 90 GPa. There is an ~4.8% volume reduction between forsterite and forsterite II, and a further ~4.2% volume reduction between forsterite II and III. On decompression forsterite III remains until as low as 12 GPa, but becomes amorphous at ambient conditions. Using our X-ray diffraction data together with an evolutionary crystal structure prediction algorithm and metadynamics simulations, we find that forsterite II has triclinic space group P 1 and forsterite III has orthorhombic space group Cmc 21. Both high-pressure phases are metastable. Metadynamics simulations show a stepwise phase transition sequence from 4-coordinated Si in forsterite to mixed tetrahedral and octahedral Si (as in forsterite II), and then fully sixfold-coordinated Si (as in forsterite III), occurring by displacement in \[001\](100). The forsterite III structure is a member of the family of post-spinel structures adopted by compositions such as CaFe2O4 and CaTi2O4.

Compressibility of a natural P4/nnc vesuvianite

In situ synchrotron-radiation powder X-ray diffraction was applied to a natural vesuvianite with P 4/ nnc structure, (Ca 19.0 Na 0.259 K 0.012 ) ∑=19.271 (Al 9.089 Fe 3+ 1.376 Ti 0.341 Mg 2.156 Fe 2+ 0.216 Mn 0.008 ) ∑=13.186 P 0.098 (Si 17.977 Al 0.023 ) ∑=18 O 70.208 (OH) 7.792 by means of the diamond anvil cell technique up to 27.9 GPa at room temperature. The isothermal pressure–volume relationship of vesuvianite was well fitted by the third-order Birch-Murnaghan equation of state with V 0 = 2865.9(4) A 3 , K 0 = 143(3) GPa and K 0 ′ = 5.2(4). The compressibility of the structure is anisotropic with β c = 2.76*10 −3 GPa −1 > β a = β b = 2.14*10 −3 GPa −1 . Thermoelastic properties of vesuvianite were compared and analyzed with its structural analogues (grossular, hydrogrossular and epidote).

P–V–T equation of state of Na-majorite to 21 GPa and 1673 K

The P–V–T equation of state (EoS) for Na-majorite at pressures to 21GPa and temperatures to 1673K was obtained from in situ X-ray diffraction experiments using a Kawai-type multi-anvil apparatus. Analyses of the room-temperature P–V data to a third-order Birch–Murnaghan EoS yielded ambient unit cell volume, V0=1476 (1) (Å3); isothermal bulk modulus, K0,300=181 (9) GPa; and its pressure derivative, K0,300′=4.4 (1.2). When fitting a high-temperature Birch–Murnaghan EoS using entire P–V–T data at a fixed V0=1475.88Å3, K0,300=184 (4) GPa, K0,300′=3.8 (6), (∂K0,T/∂ T)P=−0.023 (5) (GPaK−1), and a=3.17 (16)×10−5K−1, b=0.16 (26)×10−8K−2, where α=a+bT is the volumetric thermal expansion coefficient. Fitting the Mie–Grüneisen–Debye EoS with the present data to Debye temperature fixed at θ0=890K yielded Grüneisen parameter, γ0=1.35 at q=1.0 (fixed). The new data on Na-majorite were compared with the previous data on majorite type garnets. The compression mechanism of majoritic garnets was described in detail. The entire dataset enabled to examine the thermoelastic properties of important mantle garnets and these data will have further applications for modeling P–T conditions in the transition zone of the Earth’s mantle using ultradeep mineral assemblages.

Compressibility and structural stability of two variably hydrated olivine samples (Fo97Fa3) to 34 GPa by X-ray diffraction and Raman spectroscopy

The content and transport of fluid phases such as water into the deep Earth is of great importance not only to correlate seismological models of the planet’s interior with mineralogical models, but also for the understanding of the evolution of the solid Earth as well as the Earth’s atmosphere. This study reports on the influence of water on the structural and physical properties of olivine, which is known to be the main constituent of the upper mantle. Two hydrous olivines of composition Fo 97 Fa 3 with water content of 4883 parts per million by weight (ppmw) (SZ0407A) and 8000 ppmw (SZ0407B) were synthesized at 1250 °C and 12 GPa. Single-crystal X-ray diffraction was used to determine unit-cell parameters of SZ0407A and SZ0407B at pressures up to 7.1 GPa at room temperature. Synchrotron powder X-ray diffraction and Raman scattering experiments were performed on sample SZ0407A in a diamond-anvil cell to 34 GPa at room temperature. For both samples, the compressibility is the largest along the b -axis and smallest along the a -axis. Using the compression ( V / V o ) vs. pressure data for sample SZ0407A to 29 GPa, in conjunction with the third-order Birch-Murnaghan equation of state, we calculate the isothermal bulk modulus and its pressure derivative as K o = 119.2(12) GPa and K ′ o = 6.6(4). Single-crystal compression data for sample SZ0407A to 7 GPa give K o = 121.5(6) GPa and K ′ o = 5.7(2); and for sample SZ0407B K o = 122.2(12) GPa and K ′ o = 6.2(4). High-pressure Raman spectra for SZ0407A up to 34 GPa show a continuous shift of all the observed bands to higher frequency with increasing pressure; there is no indication of any first-order phase transition. However, the Raman spectra indicate subtle discontinuous changes around 22 GPa, unobserved in previously reported studies on anhydrous olivines.

Compression behavior of manganite

A high-pressure X-ray diffraction study of manganite (γ-MnOOH) was performed using 10.1 GPa at room temperature. The aim of this study was to determine the compression behavior of an oxyhydroxide with an InOOH-related structure. The pressure-volume data were fitted by a third-order Birch-Murnaghan equation of state with the following parameters: V0 = 270.47(9) Å3, K0 = 91(3) GPa, and K0' = 7(1). Analysis of axial compressibility showed that the a-and b-axes were more compressible than the c-axis.

Compression and structure of brucite to 31 GPa from synchrotron X-ray diffraction and infrared spectroscopy studies

Synchrotron X-ray powder diffraction and infrared (IR) spectroscopy studies on natural brucite were conducted up to 31 GPa using diamond-anvil cell (DAC) techniques at beamlines X17C and U2A of National Synchrotron Light Source (NSLS). The lattice parameters and unit-cell volumes were refined in P 3 m 1 space group throughout the experimental pressure range. The anisotropy of lattice compression decreases with pressure due to a more compressible c axis and the compression becomes nearly isotropic in the pressure range of 10–25 GPa. The unit-cell volumes are fitted to the third-order Birch-Murnaghan equation of state, yielding K 0 = 39.4(1.3) GPa, K 0 ′ = 8.4(0.4) for the bulk modulus and its pressure-derivative, respectively. No phase transition or amorphization was resolved from the X-ray diffraction data up to 29 GPa, however, starting from ~4 GPa, a new infrared vibration band (~3638 cm −1 ) 60 cm −1 below the OH stretching A 2u band of brucite was found to coexist with the A 2u band and its intensity continuously increases with pressure. The new OH stretching band has a more pronounced redshift as a function of pressure (−4.7 cm −1 /GPa) than the A 2u band (−0.7 cm −1 /GPa). Comparison with first-principles calculations suggests that a structural change involving the disordered H sublattice is capable of reconciling the observations from X-ray diffraction and infrared spectroscopy studies.

On the crystal structure and compressional behavior of talc: a mineral of interest in petrology and material science

The crystal structure of a natural triclinic talc (1Tc polytype) [with composition: (Mg2.93Fe0.06)Σ2.99(Al0.02Si3.97)Σ3.99O10(OH)2.10] has been investigated by single-crystal X-ray diffraction at 223 and 170 K and by single-crystal neutron diffraction at 20 K. Both the anisotropic X-ray refinements (i.e. at 223 and 170 K) show that the two independent tetrahedra are only slightly distorted. For the two independent Mg-octahedra, the bond distances between cation-hydroxyl groups are significantly shorter than the others. The ditrigonal rotation angle of the six-membered ring of tetrahedra is modest (α ~ 4°). The neutron structure refinement shows that the hydrogen-bonding scheme in talc consists of one donor site and three acceptors (i.e. trifurcated configuration), all the bonds having O···O ≤ 3.38 Å, H···O ~ 2.8 Å, and O–H···O ~ 111–116°. The three acceptors belong to the six-membered ring of tetrahedra juxtaposed to the octahedral sheet. The vibrational regime of the proton site appears being only slightly anisotropic. The elastic behavior of talc was investigated by means of in situ synchrotron single-crystal diffraction up to 16 GPa (at room temperature) using a diamond anvil cell. No evidence of phase transition has been observed within the pressure range investigated. P–V data fit, with an isothermal third-order Birch-Murnaghan equation of state, results as follows: V 0 = 454.7(10) Å3, K T0 = 56(3) GPa, and K′ = 5.4(7). The “Eulerian finite strain” versus “normalized stress” plot yields: Fe(0) = 56(2) GPa and K′ = 5.3(5). The compressional behavior of talc is strongly anisotropic, as reflected by the axial compressibilities (i.e. β(a):β(b):β(c) = 1.03:1:3.15) as well as by the magnitude and orientation of the unit-strain ellipsoid (with ε 1:ε 2:ε 3 = 1:1.37:3.21). A comparison between the elastic parameters of talc obtained in this study with those previously reported is carried out.

The P–V–T equation of state of CaPtO3 post-perovskite

Orthorhombic post-perovskite CaPtO3 is isostructural with post-perovskite MgSiO3, a deep-Earth phase stable only above 100 GPa. Energy-dispersive X-ray diffraction data (to 9.4 GPa and 1,024 K) for CaPtO3 have been combined with published isothermal and isobaric measurements to determine its P–V–T equation of state (EoS). A third-order Birch–Murnaghan EoS was used, with the volumetric thermal expansion coefficient (at atmospheric pressure) represented by α(T) = α0 + α1(T). The fitted parameters had values: isothermal incompressibility, \( K_{{T_{0} }} \) = 168.4(3) GPa; \( K_{{T_{0} }}^{\prime } \) = 4.48(3) (both at 298 K); \( \partial K_{{T_{0} }} /\partial T \) = −0.032(3) GPa K−1; α0 = 2.32(2) × 10−5 K−1; α1 = 5.7(4) × 10−9 K−2. The volumetric isothermal Anderson–Gruneisen parameter, δT, is 7.6(7) at 298 K. \( \partial K_{{T_{0} }} /\partial T \) for CaPtO3 is similar to that recently reported for CaIrO3, differing significantly from values found at high pressure for MgSiO3 post-perovskite (−0.0085(11) to −0.024 GPa K−1). We also report axialP–V–T EoS of similar form, the first for any post-perovskite. Fitted to the cubes of the axes, these gave \( \partial K_{{aT_{0} }} /\partial T \) = −0.038(4) GPa K−1; \( \partial K_{{bT_{0} }} /\partial T \) = −0.021(2) GPa K−1; \( \partial K_{{cT_{0} }} /\partial T \) = −0.026(5) GPa K−1, with δT = 8.9(9), 7.4(7) and 4.6(9) for a, b and c, respectively. Although \( K_{{T_{0} }} \) is lowest for the b-axis, its incompressibility is the least temperature dependent.

High-pressure structural studies of eskolaite by means of single-crystal X-ray diffraction

The structural behavior of Cr2O3 was investigated up to ~70 GPa using single-crystal X-ray diffraction under a quasi-hydrostatic pressure (neon pressure medium) at room temperature. The crystal structure remains rhombohedral with the space group R3̄c (No. 167) and upon compression the oxygen atoms approach an ideal hexagonal close-packing arrangement. An isothermal bulk modulus of Cr2O3 and its pressure derivative were found to be 245(4) GPa and 3.6(2), respectively, based on a third-order Birch-Murnaghan equation of state and V0 = 288.73 Å3. An analysis of the crystal strains suggest that the non-hydrostatic stresses can be considered as negligible even at the highest pressure reached.

Isothermal compression of face-centered cubic iron

Isothermal compression curves of face-centered cubic iron (γ-Fe) were determined at high temperatures (1273 and 1073 K) up to 27 GPa by in situ X-ray diffraction experiments using synchrotron radiation and the Kawai-type multi-anvil apparatus. Fits of the third-order Birch-Murnaghan equation of state to pressure-volume data yielded V 0 = 48.997 ± 0.040 Å 3 , K T0 = 108.3 ± 2.4 GPa, and K′ T = 5.8 ± 0.2 for 1273 K, and V 0 = 48.600 ± 0.098 Å 3 , K T0 = 88.9 ± 5.1 GPa, and K′ T = 8.9 ± 0.7 for 1073 K, where V 0 , K T0 , and K′ T are unit-cell volume, bulk modulus and its pressure derivative, respectively, at ambient pressure. The relatively large values of K′ T are attributable to successive electronic spin state transitions from mixed-spin at lower pressures to low-spin at higher pressures. When discussing the constituents of Earth’s (or other planets’) solid inner core in terms of density and equations of state, one must carefully consider the influence of the electronic spin state.

High-pressure behavior of zoisite

A high-pressure single-crystal X-ray diffraction (XRD) study has been carried out on two natural zoisite samples Ca 2 Al 3-x FexSi 3 O 12 OH, one Fe-free (x = 0) and one Fe-rich (x = 0.12). The unit-cell parameters were determined for the Fe-free sample at 18 different pressures up to 7.76 GPa and for the Fe-rich sample at 13 different pressures up to 7.63 GPa. The P(V) data for both of the samples were fitted by a third-order Birch-Murnaghan equation of state (BM3 EoS). The equation of state coefficients are: V 0 = 903.39(5) Å 3 , K T0 = 122.1(7) GPa, and K 0 ′ = 6.8(2) for the Fe-free sample and V 0 = 906.95(5) Å 3 , K T0 = 119.1(7) GPa, and K 0 ′ = 7.3(2) for the Fe-rich sample. This shows that the addition of Fe in to the crystal structure of zoisite leads to a slight softening of the structure. Both compositions exhibit axial compressibilities β c > β a >> β b , with the compressibilities of the a and b axes of the two samples being indistinguishable. The softening of the bulk modulus of zoisite with Fe content follows from softening of the c-axis of the structure. A high-pressure structural study of the Fe-free sample showed that the main compression mechanisms in the structure are the compression of soft inter-octahedral distance along [001] and soft intra-octahedral distances along [010] directions, while along [100] the main compression occurs because of the compression of stiff intra-octahedral distances. The substitution of Fe on to the M3 octahedral site of the structure leads to an increase of the intra-octahedral distance of the M3 that triggers the rotation of M12 and therefore leads to the softening of the M12 inter-octahedral distances that accounts for the softening of the c-axis of the structure.

Reversible high-pressure phase transition in LaN

In situ high-pressure X-ray powder diffraction experiments on LaN up to 60.1 GPa at ambient temperature in a diamond-anvil cell revealed a reversible, first-order structural phase transition starting at ∼22.8 GPa and completed at ∼26.5 GPa from the ambient cubic phase (Fm3¯m, no. 225) to a tetragonal high-pressure phase (P4/nmm, no. 19, a = 4.1060(6), c = 3.0446(6) Å, Z = 2, wRp = 0.011), which has not been claimed in theoretical predictions. HP-LaN is isotypic with a high-pressure polymorph of BaO, which crystallizes in a tetragonally distorted CsCl-type structure. The phase transition is accompanied by a volume collapse of about 11% which corresponds well with the reported data on HP-BaO. A linear extrapolation of the c/a ratio of the tetragonally distorted CsCl-type sub-cell reaches a value c/a = 1 of cubic CsCl-type HP-LaN at 91(12) GPa. In addition, the compressibility of LaN was investigated and resulted in a bulk modulus for the ambient pressure phase of B0 = 135(3) GPa and B′ = 5.0(5) after fitting a third-order Birch-Murnaghan equation of state to the experimental p–V data. The corresponding extrapolated bulk modulus of HP-LaN is found to be B0 = 278(6) GPa and its pressure derivative B′ = 1.2(2). Both as-calculated bulk moduli are compared to the respective values obtained from an Eulerian strain versus normalized stress plot to be 143(2) GPa for ambient LaN and 293(7) GPa for HP-LaN. Compared to other binary nitrides such as δ-ZrN or δ-HfN having bulk moduli of 285 GPa and 306 GPa, respectively, the extrapolated bulk moduli of HP-LaN are in the same order of magnitude, ranking HP-LaN as a highly incompressible material.