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1. Experimental and theoretical P-V-T equation of state for Os 2 B 3

   https://doi.org/10.1080/08957959.2020.1858821  

   Burrage, Kaleb C. ; Lin, Chia-Min ; Chen, Wei-Chih ; Chen, Cheng-Chien ; Vohra, Yogesh K. ( December 2020 , High Pressure Research)

   null (Ed.)

   Thermoelastic behavior of transition metal boride Os2B3 was studied under quasi-hydrostatic and isothermal conditions in a Paris-Edinburgh cell to 5.4 GPa and 1273 K. In-situ Energy Dispersive X-ray diffraction was used to determine interplanar spacings of the hexagonal crystal structure and thus the volume and axial compression. P-V-T data were fitted to a 3rd Order Birch-Murnaghan equation of state with a temperature modification to determine thermal elastic constants. The bulk modulus was shown to be K0 = 402 ± 21 GPa when the first pressure derivative was held to K0’ = 4.0 from the room temperature P-V curve. Under a quadratic fit α=α_0+α_1 T-α_2 T^(-2), the thermal expansion coefficients were determined to be α_0=1.862×10^(-5) K-1, α_1=0.841×10^(-9) K-2, and α_2=-0.525 K. Density functional theory (DFT) with the quasi-harmonic approximation (QHA) were further employed to study Os2B3, including its P-V-T curves, phonon spectra, bulk modulus, specific heat, thermal expansion, and the Grüneisen parameter. A good agreement between the first-principle theory and experimental observations was achieved, highlighting the success of the Armiento-Mattsson 2005 generalized gradient approximation functional employed in this study and QHA for describing thermodynamic properties of Os2B3. 

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2. P-V-T equation of state of boron carbide

   Somayazulu, M. ; Ahart, M. ; Meng, Y. ; Ciezak, J. ; Velisavlevic, N. ; Hemley, R. J. ( October 2023 , Philosophical transactions A)

   We report the P-V-T equation of state measurements of B4C to 50GPa and approximately 2500K in laser-heated diamond anvil cells. We obtain an ambient temperature, third-order Birch–Murnaghan fit to the P-V data that yields a bulk modulus K0 of 221(2) GPa and derivative, (dK/dP)0 of 3.3(1). These were used in fits with both a Mie–Grüneisen– Debye model and a temperature-dependent, Birch– Murnaghan equation of state that includes thermal pressure estimated by thermal expansion (α) and a temperature-dependent bulk modulus (dK0/dT). The ambient pressure thermal expansion coefficient (α0+α1T), Grüneisen γ (V)=γ 0(V/V0)q and volumedependent Debye temperature, were used as input parameters for these fits and found to be sufficient to describe the data in the whole P-T range of this study. 

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3. Thermal equation of state of post-aragonite CaCO3-Pmmn

   https://doi.org/10.2138/am-2020-7279  

   Lv, Mingda ; Liu, Jiachao ; Greenberg, Eran ; Prakapenka, Vitali B. ; Dorfman, Susannah M. ( September 2020 , American Mineralogist)

   null (Ed.)

   Abstract Calcium carbonate (CaCO3) is one of the most abundant carbonates on Earth's surface and transports carbon to Earth's interior via subduction. Although some petrological observations support the preservation of CaCO3 in cold slabs to lower mantle depths, the geophysical properties and stability of CaCO3 at these depths are not known, due in part to complicated polymorphic phase transitions and lack of constraints on thermodynamic properties. Here we measured thermal equation of state of CaCO3-Pmmn, the stable polymorph of CaCO3 through much of the lower mantle, using synchrotron X-ray diffraction in a laser-heated diamond-anvil cell up to 75 GPa and 2200 K. The room-temperature compression data for CaCO3-Pmmn are fit with third-order Birch-Murnaghan equation of state, yielding KT0 = 146.7 (±1.9) GPa and K′0 = 3.4(±0.1) with V0 fixed to the value determined by ab initio calculation, 97.76 Å3. High-temperature compression data are consistent with zero-pressure thermal expansion αT = a0 + a1T with a0 = 4.3(±0.3)×10-5 K-1, a1 = 0.8(±0.2)×10-8 K-2, temperature derivative of the bulk modulus (∂KT/∂T)P = –0.021(±0.001) GPa/K; the Grüneisen parameter γ0 = 1.94(±0.02), and the volume independent constant q = 1.9(±0.3) at a fixed Debye temperature θ0 = 631 K predicted via ab initio calculation. Using these newly determined thermodynamic parameters, the density and bulk sound velocity of CaCO3-Pmmn and (Ca,Mg)-carbonate-bearing eclogite are quantitatively modeled from 30 to 80 GPa along a cold slab geotherm. With the assumption that carbonates are homogeneously mixed into the slab, the results indicate the presence of carbonates in the subducted slab is unlikely to be detected by seismic observations, and the buoyancy provided by carbonates has a negligible effect on slab dynamics. 

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4. High pressure raman spectroscopy and X-ray diffraction of K2Ca(CO3)2 bütschliite: multiple pressure-induced phase transitions in a double carbonate

   https://doi.org/10.1007/s00269-023-01262-5  

   Zeff, G. ; Kalkan, B. ; Armstrong, K. ; Kunz, M. ; Williams, Q. ( January 2024 , Physics and Chemistry of Minerals)

   The crystal structure and bonding environment of K₂Ca(CO₃)₂bütschliite were probed under isothermal compression via Raman spectroscopy to 95 GPa and single crystal and powder X-ray diffraction to 12 and 68 GPa, respectively. A second order Birch-Murnaghan equation of state fit to the X-ray data yields a bulk modulus,$${K}_{0}=46.9$$$K_0=46.9$GPa with an imposed value of$${K}_{0}^{\prime}= 4$$$K_0^{\prime }=4$for the ambient pressure phase. Compression of bütschliite is highly anisotropic, with contraction along thec-axis accounting for most of the volume change. Bütschliite undergoes a phase transition to a monoclinicC2/mstructure at around 6 GPa, mirroring polymorphism within isostructural borates. A fit to the compression data of the monoclinic phase yields$${V}_{0}=322.2$$$V_0=322.2$ Å³$$,$$$,$$${K}_{0}=24.8$$$K_0=24.8$GPa and$${K}_{0}^{\prime}=4.0$$$K_0^{\prime }=4.0$using a third order fit; the ability to access different compression mechanisms gives rise to a more compressible material than the low-pressure phase. In particular, compression of theC2/mphase involves interlayer displacement and twisting of the [CO₃] units, and an increase in coordination number of the K⁺ion. Three more phase transitions, at ~ 28, 34, and 37 GPa occur based on the Raman spectra and powder diffraction data: these give rise to new [CO₃] bonding environments within the structure.

    

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5. Thermoelastic Properties of Eclogitic Garnets and Omphacites: Implications for Deep Subduction of Oceanic Crust and Density Anomalies in the Upper Mantle

   https://doi.org/10.1029/2018GL081170  

   Xu, Jingui ; Zhang, Dongzhou ; Fan, Dawei ; Dera, Przemyslaw K. ; Shi, Feng ; Zhou, Wenge ( January 2019 , Geophysical Research Letters)

   Synchrotron‐based high‐pressure/high‐temperature single‐crystal X‐ray diffraction experiments to ~24 GPa and 700 K were conducted on eclogitic garnets (low‐Fe: Prp₂₈Alm₃₈Grs₃₃Sps₁and high‐Fe: Prp₁₄Alm₆₂Grs₁₉Adr₃Sps₂) and omphacites (low‐Fe: Quad₅₇Jd₄₂Ae₁and high‐Fe: Quad₅₃Jd₂₇Ae₂₀), using an externally heated diamond anvil cell. Fitting the pressure‐volume‐temperature data to a third‐order Birch‐Murnaghan equation of state yields the thermoelastic parameters including bulk modulus (K_T0), its pressure derivative (K′_T0), temperature derivative ((∂K_T/∂T)_P), and thermal expansion coefficient (α_T). The densities of the high‐Fe and low‐Fe eclogites were then modeled along typical geotherms of the normal mantle and the subducted oceanic crust to the transition zone depth (550 km). The metastable low‐Fe eclogite could be a reason for the stagnant slabs within the upper range of the transition zone. Eclogite would be responsible for density anomalies within 100–200 km in the upper mantle of Asia.

    

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