skip to main content

Title: Thermal Pressure in the Thermal Equation of State for Solid and a Proposed Substitute

The thermal equation of state (TEOS) for solids is a mathematic model among pressure, temperature and density, and is essential for geophysical, geochemical, and other high pressure–temperature (high P–T) researches. However, in the last few decades, there has been a growing concern about the accuracy of the pressure scales of the calibrants, and efforts have been made to improve it by either introducing a reference standard or building new thermal pressure models. The existing thermal equation of state,P(V,T) = P(V,T0) + Pth(V,T), consists of an isothermal compression and an isochoric heating, while the thermal pressure is the pressure change in the isochoric heating. In this paper, we demonstrate that, for solids in a soft pressure medium in a diamond anvil cell, the thermal pressure can neither be determined from a single heating process, nor from the thermal pressure of its calibrant. To avoid the thermal pressure, we propose to replace the thermal pressure with a well-known thermal expansion model, and integrate it with the isothermal compression model to yields a Birch–Murnaghan-expansion TEOS model, called VPT TEOS. The predicted pressure of MgO and Au at ambient pressure from Birch–Murnaghan-expansion VPT TEOS model matches the experimental pressure of zero (0) GPa very well, while the more » pressure prediction from the approximated Anderson PVT TEOS exhibit a big deviation and a wrong trend.

« less
Publication Date:
Journal Name:
International Journal of Thermophysics
Springer Science + Business Media
Sponsoring Org:
National Science Foundation
More Like this
  1. 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.
  2. 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.more »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.« less
  3. Experimental techniques, such as cryo-electron microscopy, require biological samples to be recovered at cryogenic temperatures ( T ≈ 100 K) with water being in an amorphous ice state. However, (bulk) water can exist in two amorphous ices at P < 1 GPa, low-density amorphous (LDA) ice at low pressures and high-density amorphous ice (HDA) at high pressures; HDA is ≈20–25% denser than LDA. While fast/plunge cooling at 1 bar brings the sample into LDA, high-pressure cooling (HPC), at sufficiently high pressure, produces HDA. HDA can also be produced by isothermal compression of LDA at cryogenic temperatures. Here, we perform classical molecular dynamics simulations to study the effects of LDA, HDA, and the LDA–HDA transformation on the structure and hydration of a small peptide, polyalanine. We follow thermodynamic paths corresponding to (i) fast/plunge cooling at 1 bar, (ii) HPC at P = 400 MPa, and (iii) compression/decompression cycles at T = 80 K. While process (i) produced LDA in the system, path (iii) produces HDA. Interestingly, the amorphous ice produced in process (ii) is an intermediate amorphous ice (IA) with properties that fall in-between those of LDA and HDA. Remarkably, the structural changes in polyalanine are negligible at all conditions studiedmore »(0–2000 MPa, 80–300 K) even when water changes among the low and high-density liquid states as well as the amorphous solids LDA, IA, and HDA. The similarities and differences in the hydration of polyalanine vitrified in LDA, IA, and HDA are described. Since the studied thermodynamic paths are suitable for the cryopreservation of biomolecules, we also study the structure and hydration of polyalanine along isobaric and isochoric heating paths, which can be followed experimentally for the recovery of cryopreserved samples. Upon heating, the structure of polyalanine remains practically unchanged. We conclude with a brief discussion of the practical advantages of (a) using HDA and IA as a cryoprotectant environment (as opposed to LDA), and (b) the use of isochoric heating as a recovery process (as opposed to isobaric heating).« less
  4. High pressure study on ultra-hard transition-metal boride Os2B3 was carried out in a diamond anvil cell under isothermal and non-hydrostatic compression with platinum as an X-ray pressure standard. The ambient-pressure hexagonal phase of Os2B3 is found to be stable with a volume compression V/V0 = 0.670 ± 0.009 at the maximum pressure of 358 ± 7 GPa. Anisotropic compression behavior is observed in Os2B3 to the highest pressure, with the c-axis being the least compressible. The measured equation of state using the 3rd-order Birch-Murnaghan fit reveals a bulk modulus K0= 397 GPa and its first pressure derivative K0'= 4.0. The experimental lattice parameters and bulk modulus at ambient conditions also agree well with our density-functional-theory (DFT) calculations within an error margin of ~1%. DFT results indicate that Os2B3 becomes more ductile under compression, with a strong anisotropy in the axial bulk modulus persisting to the highest pressure. DFT further enables the studies of charge distribution and electronic structure at high pressure. The pressure-enhanced electron density and repulsion along the Os and B bonds result in a high incompressibility along the crystal c-axis. Our work helps to elucidate the fundamental properties of Os2B3 under ultrahigh pressure for potential applications in extrememore »environments.« less
  5. Abstract

    This work demonstrates the processing, modeling, and characterization of nanocrystalline refractory metal tantalum (Ta) as a new structural material for microelectromechanical system (MEMS) thermal actuators (TAs). Nanocrystalline Ta films have a coefficient of thermal expansion (CTE) and Young’s modulus comparable to bulk Ta but an approximately ten times greater yield strength. The mechanical properties and grain size remain stable after annealing at temperatures as high as 1000 °C. Ta has a high melting temperature (Tm = 3017 °C) and a low resistivity (ρ = 20 µΩ cm). Compared to TAs made from the dominant MEMS material, polycrystalline silicon (polysilicon,Tm = 1414 °C,ρ = 2000 µΩ cm), Ta TAs theoretically require less than half the power input for the same force and displacement, and their temperature change is half that of polysilicon. Ta TAs operate at a voltage 16 times lower than that of other TAs, making them compatible with complementary metal oxide semiconductors (CMOS). We selectα-phase Ta and etch 2.5-μm-thick sputter-deposited films with a 1 μm width while maintaining a vertical sidewall profile to ensure in-plane movement of TA legs. This is 25 times thicker than the thickest reactive-ion-etchedα-Ta reported in the technical literature. Residual stress sensitivities to sputter parameters and to hydrogen incorporation are investigated and controlled. Subsequently, a V-shaped TA is fabricated andmore »tested in air. Both conventional actuation by Joule heating and passive self-actuation are as predicted by models.

    « less