HgO at high pressures: the transition to the NaCl structure (HgO-III) and the equation of state of tetragonal HgO-II

The high-pressure behavior of HgO-montroydite was investigated up to 36.5 GPa using angle-dispersive X-ray diffraction. The tetragonal phase of this material (HgO-II), a distortion of the NaCl structure, transforms into the cubic NaCl structure (HgO-III) above ~31.5 GPa. The transformation of mercury oxide from the orthorhombic Pnma (HgO-I) structure to a tetragonal I4/mmm structure (HgO-II) is confirmed to occur at 13.5 ± 1.5 GPa. Neither of the high-pressure phases, HgO-II nor HgO-III, is quenchable in pressure. The derived isothermal bulk modulus of HgO-II and its pressure derivative strongly depend on the assumed zero-pressure volume of this phase, but our elasticity results on HgO-II nevertheless lie significantly closer to theoretical calculations than prior experimental results, and the measured pressure of the phase transformation to the NaCl structure is also in agreement with recent theoretical results. The general accord with theory supports the existence of significant relativistic effects on the high-pressure phase transitions of HgO.     

P-V-T equation of state of magnesiowüstite (Mg0.6Fe0.4)O

The lattice parameter of magnesiowüstite (Mg_0.6Fe_0.4)O has been measured up to a pressure of 30 GPa and a temperature of 800 K, using an external heated diamond anvil cell and diffraction using X-rays from a synchrotron source. The experiments were conducted under quasi-hydrostatic condition, using neon as a pressure transmitting medium. The experimental P-V-T data were fitted to a thermal-pressure model with the isothermal bulk modulus at room temperature K _T0 = 157 GPa, (?K _TO /?P) _T =4, (?K _T /?T) _P =-2.7(3) × 10^-2 GPa/K, (?K _T /?T) _v =-0.2(2) × 10^-2 GPa/K and the Anderson-Grüneisen parameter δ _T =4.3(5) above the Debye temperature. The data were also fitted to the Mie-Grüneisen thermal equation of state. The least-squares fit yields the Debye temperature θ _DO = 500(20) K, the Grüneisen parameter γ ₀=1.50(5), and the volume dependence q=1.1(5). Both thermal-pressure models give consistent P-V-T relations for magnesiowüstite to 140 GPa and 4000 K. The P-V-T relations for magnesiowüstite were also calculate by using a modified high-temperature Birch-Murnaghan equation of state with a δ _t of 4.3. The results are consistent with those calculated by using the thermal-pressure model and the Mie-Grüneisen relation to 140 GPa and 3000 K.     

A simple approach for the determination of bulk modulus and equation of state under the effect of high temperature for minerals

A simple theoretical method for the determination of bulk modulus and equation of state is investigated and applied for six minerals of geophysical importance. The results obtained at different temperatures are found to present a good agreement with the experimental data. The simplicity of the method is discussed in the light of other methods in high temperature research on minerals. Received: 7 January 1996 / Revised, accepted: 11 June 1997     

P-V-T equation of state of lawsonite

A pressure-volume-temperature data set has been obtained for lawsonite [CaAl₂Si₂O₇(OH)₂.H₂O], using synchrotron X-ray diffraction and an externally heated diamond anvil cell. Unit-cell volumes were measured to 9.4 GPa and 767 K by angle dispersive X-ray diffraction using imaging plates. Phase changes were not observed within this pressure-temperature range, and lawsonite compressed almost isotropically at constant temperature. The P-V-T data have been analyzed using a Birch- Murnaghan equation of state and a linear equation of state expressed as β=–1/V₀ (∂V/∂P) _T . At room temperature, the derived equation of state parameters are: K ₀=124.1 (18) GPa K'₀ set to 4) and β^–1=142.0(24) GPa, respectively. Our results are intermediate between previously reported measurements. The high-temperature data show that the incompressibility of lawsonite decreases with increasing temperature to ∼500 K and then increases above. Hence, the second order temperature derivative of the bulk modulus is taken into account in the equation of state; a fit of the volume data yields K ₀=123.9(18) GPa, (∂K/∂T)_P=–0.111(3) GPa K^–1, (∂² K/∂T ²)_P=0.28(6) 10^–3 GPa K^–2, α₀=3.1(2) 10^–5 K^–1, assuming K'₀=4. Received: 2 June 1998 / Revised, accepted: 12 Ocotber 1998     

The hildebrand equation of state for minerals relevant to geophysics

The Hildebrand thermal equation of state (EOS) is revived and applied to minerals appropriate to the earth's interior. The chief virtue of this EOS is that it escapes the necessity of evaluating a Grüneisen parameter at high compression and high temperature. The classical Grüneisen parameter is replaced by the product of two experimentally measured parameters: α, the coefficient of thermal expansivity, and K _T , the isothermal bulk modulus. In order for the Hildebrand EOS to be useful in geophysical conditions it is necessary to show that α K _T is, to a large extent, independent of volume. This can be done directly by experiment, following Yagi, or indirectly using thermodynamic formulae where other measurements are used in place of α K _T . Four such tests are proposed, two of them following tests proposed by Swenson. The result indicates that most, if not all, of the close-packed minerals relevant to geophysics follow the rule that the value of α K _T is to a satisfactory extent independent of compression.     

P-V equation of state of portlandite, Ca(OH)2, from powder neutron diffraction data

 A high pressure neutron powder diffraction study of portlandite [Ca(OH)₂] has been performed at ISIS facility (U.K.); nine spectra have been collected increasing the pressure by steps, up to 10.9 GPa, by means of a Paris-Edinburgh cell installed on the POLARIS diffractometer. The tensorial formalism of the lagrangian finite strain theory and the Birch-Murnaghan equation of state have been used to determine, independently, two values of the bulk modulus of portlandite, obtaining K ₀=38.3(±1.1) GPa [linear incompressibilities: K _0a=188.4(±9.9), K _0c=64.5(±2.5) GPa] and K ₀=34.2(±1.4) GPa, respectively. The present results comply with values from previous measurements by X-ray diffraction [K ₀=37.8(±1.8) GPa] and Brillouin spectroscopy [K ₀=31.7(±2.5) GPa]. Reasonably, Ca(OH)₂ has revealed to be bulkly softer than Mg(OH)₂ [K ₀=41(±2), K _0a=313, K _0c=57 GPa]. The Ca(OH)₂ linear incompressibility values reflect the nature of forces acting to stabilize the (001) layer structure and, further, prove that the replacement Ca/Mg mainly affects the elastic properties in the (001) plane, rather than along the [001] direction. Data from a full refinement of the structure at room pressure are reported. Received January 12, 1996/Revised, accepted June 15, 1996     

Correction of Holloway's (1977) adaptation of the modified Redlich-Kwong equation of state for calculation of the fugacities of molecular species in supercritical fluids of geologic interest

Consideration of constraints imposed on fugacity coefficients by the Gibbs-Duhem equation and those inherent in the Redlich-Kwong equation of state (Redlich and Kwong, 1949) and its modification by de Santis et al. (1974) indicates that Holloway's (1977) adaptation of the Redlich-Kwong equation for calculating fugacity coefficients of molecular species in gas mixtures is in error. Revised calculations using the correct equation lead to much smaller departures from ideality than those generated by Holloway.     

NaCl溶液对土体冻结特征影响的试验研究

冻结特征曲线(SFCC)是指冻土中温度和未冻水含量之间的关系,采用核磁共振系统和低温恒温冷浴获得了采用不同浓度Na Cl溶液饱和的黏土的冻结特征曲线。根据试验结果分析不同浓度的孔隙溶液对冻结特征的影响规律,结果表明:随着溶液浓度的增大,冻结特征曲线向上移动,也就是说在相同未冻水含量下,浓度越大,冻结温度越低。这主要是因为盐溶液引起了渗透势能,使得孔隙水中总势能降低,从而降低了孔隙水的冰点。在冻土中,孔隙水的冻结温度与能量状态有关,其中孔隙水的势能包括基质势能和渗透势能,而基质势能部分又分为毛细部分和吸附部分,渗透势能与孔隙溶液的浓度有关。当土体中未冻水含量较低时,主要是吸附效应在起作用。此时未冻水是以吸附膜的形式吸附在土颗粒的周围,将非饱和土的概念引入到冻土中,采用分子间作用力和吸附水膜厚度之间的关系,以描述处于吸附状态的冻结特征曲线。结合渗透势能来模拟不同浓度下的冻结特征曲线,与试验数据拟合结果较好。     

Stability and equation of state of post-aragonite BaCO3

At ambient conditions, witherite is the stable form of BaCO₃ and has the aragonite structure with space group Pmcn. Above ~10 GPa, BaCO₃ adopts a post-aragonite structure with space group Pmmn. High-pressure and high-temperature synchrotron X-ray diffraction experiments were used to study the stability and equation of state of post-aragonite BaCO₃, which remained stable to the highest experimental P–T conditions of 150 GPa and 2,000 K. We obtained a bulk modulus K ₀ = 88(2) GPa with $K'$  = 4.8(3) and V ₀ = 128.1(5) ų using a third-order Birch-Murnaghan fit to the 300 K experimental data. We also carried out density functional theory (DFT) calculations of enthalpy (H) of two structures of BaCO₃ relative to the enthalpy of the post-aragonite phase. In agreement with previous studies and the current experiments, the calculations show aragonite to post-aragonite phase transitions at ~8 GPa. We also tested a potential high-pressure post–post-aragonite structure (space group C222 ₁ ) featuring four-fold coordination of oxygen around carbon. In agreement with previous DFT studies, ΔH between the C222 ₁ structure and post-aragonite (Pmmn) decreases with pressure, but the Pmmn structure remains energetically favorable to pressures greater than 200 GPa. We conclude that post–post-aragonite phase transformations of carbonates do not follow systematic trends observed for post-aragonite transitions governed solely by the ionic radii of their metal cations.     

Dynamic Dark Energy Equation of State (EoS) and Hubble Constant Analysis Using Type Ia Supernovae from Union 2.1 Dataset

This paper constraints dynamic dark energy equation of state (EoS) parameters using the type Ia supernovae from Union 2.1 dataset. The paper also discusses the dependency of dynamic dark energy EoS parameters on the chosen or assumed value of the Hubble Constant. To understand the correlation between the Hubble Constant values and measured dynamic dark energy EoS parameters, we used recent surveys being done through various techniques such as cosmic microwave background studies, gravitational waves, baryonic acoustic oscillations and standard candles to set values for different Hubble Constant values as fixed parameters with CPL and WCDM models. Then we applied trust region reflective (TRF) and dog leg (dogbox) algorithms to fit dark energy density parameter and dynamic dark energy EoS parameters. We found a significant negative correlation between the fixed Hubble Constant parameter and measured EoS parameter, $${{w}_{0}}$$. Then we used two best fit Hubble Constant values (70 and 69.18474) km s–1 Mpc–1 based on Chi-square test to test more dark energy EoS parameters like: JBP, BA, PADE-I, PADE-II, and LH4 models and compared the results with $$\Lambda $$-CDM with constant $${{w}_{{{\text{de}}}}} = - 1$$, WCDM and CPL models. We conclude that flat $$\Lambda $$‑CDM and WCDM models clearly provide best results while using the BIC criteria as it severely penalizes the use of extra parameters. However, the dependency of EoS parameters on Hubble Constant value and the increasing tension in the measurement of Hubble Constant values using different techniques warrants further investigation into looking for optimal dynamic dark energy EoS models to optimally model the relation between the expansion rate and evolution of dark energy in our universe.     

NaCl溶液对土体持水特性影响的试验研究

分别采用不同浓度的NaCl溶液对低塑性黏土进行饱和,然后进行压力板和蒸汽平衡法试验,获得整个吸力范围内的土-水特征曲线（SWCC）。分析不同浓度的孔隙溶液对SWCC的影响规律,结果表明：盐分对基质吸力的影响较小,对总吸力影响较大,这主要是因为盐溶液引起的渗透吸力所致。在蒸汽平衡法试验中,随着含水率的降低,孔隙浓度增大,渗透吸力增大。然而,基质吸力随着含水率的减小迅速增大,使得渗透吸力所占的比例逐渐减小。在非饱和土中,总吸力包括基质吸力和渗透吸力;基质吸力包括毛细部分和吸附部分,当土体中含水率较低时,主要是吸附效应在起作用;渗透吸力与溶液浓度有关。根据试验结果深入分析了吸附水膜和土颗粒之间的相互作用,得出由于溶质的存在对分子间吸附力的影响规律。根据表面化学原理,建立了分子间作用力和吸附水膜厚度之间的关系,以描述处于吸附状态的土-水特征曲线。     

An equation of state for carbon dioxide valid from zero to extreme pressures

A new form of equation of state is described with application to carbon dioxide from 215 K to T>2000 K and from zero pressure to more than 10⁵ bar (10 GPa). The equation was calibrated using properties predicted by existing formulations at low to moderate PT conditions, original experimental PVT data at higher pressures, corresponding states comparisons at higher temperatures and using shock compression data at still higher PTs. Extensive comparisons illustrating the correlation of our new EOS with available phase equilibria and volumetric data are provided. Fugacities of carbon dioxide at high pressures and temperatures predicted using our EOS are in agreement with mineral equilibria calculated from internally consistent thermodynamic data for minerals.     

状态方程法在渗流-应力耦合场求解中的应用

提出了一种计算土体渗流-应力耦合场的状态方程法。按平面应变问题,将描述渗流-应力耦合的平面固结方程进行空间离散,并用状态方程表示了有限元控制方程。利用牛顿-柯特斯公式,导出了当前时间步节点位移向量与前一时间步位移向量之间关系的递推公式。算例表明：状态方程法解决土体渗流-应力耦合问题与传统差分法相比的优势在于用较少的机时即可得到较为精确的解。     

撞击坑数值模拟中状态方程替代原则及误差分析

撞击坑是太阳系内大多数类地行星表面的一种重要地质过程,文中介绍了撞击坑形成的机制和撞击坑研究中的数值模拟方法。首先介绍模拟撞击成坑过程的基本理论与策略,着重指出状态方程在数值模拟中具有重要作用。然而,相对于客观世界物质复杂多样,在撞击坑数值模拟中仅有少数物质的状态方程,因此在研究中不可避免地使用其他物质的状态方程进行替换。详细阐述了状态方程替换的概念和原则,即它们的雨贡纽曲线必须相似。其次进一步从理论上分析这种替代过程对物理属性以及溅射速度的影响。最后,开展两个小型撞击坑的数值模拟,靶区分别使用花岗岩和石英岩,模拟结果显示了两次模拟中的峰值压力、温度以及密度的相似性和差异性。这种分析能够有助于行星科学领域的研究,尤其是在目前从月球、火星以及其他星体正在获取越来越多数据的阶段。     

Effects of carbaryl (SEVIN) on the state I zoeae of the red-jointed fiddler crab,Uca minax (LeConte)

Shortly after spawning, zoeae of the red-jointed fiddler crab,Uca minax, were exposed to 1.0, 0.5 and 0.1 mg l^?1 of the insecticide carbaryl. Exposed zoeae were observed for fatalities, changes in phototaxis, and altered swimming behavior. Fifty per cent mortalities in these concentrations occurred after 12.5, 14.5 and 25 h, respectively. Zoeae displayed a rapid loss of positive phototaxis, which occurred after 2, 4 and 16 h, respectively. Abnormal swimming behavior was observed in all exposed groups, with total cessation of swimming activity occurring in 6 hours in groups I and II and 16 hours in group III.     

The Hydrolysis of Al(III) in NaCl solutions: A Model for M(II), M(III), and M(IV) Ions

Understanding the identity and stability of the hydrolysis products of metals is required in order to predict their behavior in natural aquatic systems. Despite this need, the hydrolysis constants of many metals are only known over a limited range of temperature and ionic strengths. In this paper, we show that the hydrolysis constants of 31 metals [i.e. Mn(II), Cr(III), U(IV), Pu(IV)] are nearly linearly related to the values for Al(III) over a wide range of temperatures and ionic strengths. These linear correlations allow one to make reasonable estimates for the hydrolysis constants of +2, +3, and +4 metals from 0 to 300°C in dilute solutions and 0 to 100°C to 5 m in NaCl solutions. These correlations in pure water are related to the differences between the free energies of the free ion and complexes being almost equal $$ \Updelta {\text{G}}^\circ \left( {{\text{Al}}^{3 + } } \right) - \Updelta {\text{G}}^\circ \left( {{\text{Al}}\left( {\text{OH}} \right)_{j}^{{\left( {3 - j} \right)}} } \right) \cong \Updelta {\text{G}}^\circ \left( {{\text{M}}^{n + } } \right) - \Updelta {\text{G}}^\circ \left( {{\text{M}}\left( {\text{OH}} \right)_{j}^{{\left( {n - j} \right)}} } \right) $$ The correlation at higher temperatures is a result of a similar relationship between the enthalpies of the free ions and complexes $$ \Updelta {\text{H}}^\circ \left( {{\text{Al}}^{3 + } } \right) - \Updelta {\text{H}}^\circ \left( {{\text{Al}}\left( {\text{OH}} \right)_{j}^{3 - j} } \right) \cong \Updelta {\text{H}}^\circ \left( {{\text{M}}^{n + } } \right) - \Updelta {\text{H}}^\circ \left( {{\text{M}}\left( {\text{OH}} \right)_{j}^{n - j} } \right) $$ The correlations at higher ionic strengths are the result of the ratio of the activity coefficients for Al(III) being almost equal to that of the metal. $$ \gamma \left( {{\text{M}}^{n + } } \right)/\gamma \left( {{\text{M}}\left( {\text{OH}} \right)_{j}^{n - j} } \right) \cong \gamma \left( {{\text{Al}}^{3 + } } \right)/\gamma \left( {{\text{Al}}\left( {\text{OH}} \right)_{j}^{3 - j} } \right) $$ The results of this study should be useful in examining the speciation of metals as a function of pH in natural waters (e.g. hydrothermal fresh waters and NaCl brines).     

An equation of state for biologically active lake sediments and its implications for interpretations of sediment data

The aim of this work is to link physical sediment parameters to biological parameters by an equation of state, which describes how the given variables interact in biologically active deposits from accumulation areas, i.e. lake areas where fine material is being continuously deposited. In the model the following parameters are utilized: sediment depth, rate of deposition, degree of compaction, bulk density, water content, net biotransport, upward biotransport, downward biotransport, and substrate decomposition. The equation of state has been empirically tested with data from Lake Ekoln and Lake Vänern, Sweden. The model enables determinations of age frequency distributions for arbitrary sediment layers, and it has been shown that, for example, the sediment layer 12-13 cm in Lake Ekoln has a median age of 15.3 years and that the deposits from the median year only constitutes about 15% of the total amount of material in this particular sediment layer. The spread due to bioturbation is considerable and the range at this sediment layer is 22 years. A mechanism to explain secondary lamination is introduced and discussed in the light of the results from the model.     

Perturbation theory based equation of state for polar molecular fluids: I. Pure fluids

Based on the thermodynamic perturbation theory an equation of state (EOS) for molecular fluids has been formulated which can be used for many fluid species in geological systems. The EOS takes into account four substance specific parameters. These are the molecular dipole moment, the molar polarizability and the two parameters of the Lennard-Jones potential. For many fluids these parameters can be evaluated directly or indirectly from experimental measurements. In the absence of direct experimental determinations, as a first approximation, for a pure fluid the parameters of the Lennard-Jones potential can be evaluated using the critical temperature and the critical density if for polar molecules in addition the dipole moment is known with reasonable accuracy. The EOS with its model potential has the appropriate asymptotic behaviour at high pressures and temperatures and can be used to calculate both vapor-liquid equilibria and thermodynamic properties of single phase fluids up to at least 10 GPa and 2000 K. Currently, parameters for 98 inorganic and organic compounds are available. In this article the EOS for pure fluids is presented. In a further communication the EOS is extended to fluid mixtures (Churakov and Gottschalk, 2003).     

An empirical Redlich-Kwong-type equation of state for water to 1,000 °C and 200 Kbar

An empirically derived Redlich-Kwong type of equation of state (ERK) is proposed for H₂O, expressing a, the term related to the attraction between the molecules, as a pressure-independent function of temperature, and b, the covolume, as a temperature-independent function of pressure. The coefficients of a(T) and b(P) were derived by least squares non-linear regression, using P-V-T data given by Burnham et al. (1969b) and Rice and Walsh (1957) in conjunction with more precise recent data obtained by Tanishita et al. (1976), Hilbert (1979) and Schmidt (1979): $$a(T) = 1.616 x 10^8 - 4.989 x 10^4 T - 7.358 x 10^9 T^{ - 1} $$ and $$ = \frac{{1 + 3.4505x 10^{--- 4} P + 3.8980x 10^{--- 9} P^2 - 2.7756x 10^{--- 15} P^3 }}{{6.3944x 10^{--- 2} + 2.3776x 10^{--- 5} + 4.5717x 10^{--- 10} P^2 }}$$ , where T is expressed in Kelvin and P in bars. The ERK works very well at upper mantle conditions, at least up to 200 kbar and 1,000 °C. At subcritical conditions and those somewhat above the critical point, it still reproduces the molar Gibbs energy, \(\tilde G_{{\text{H}}_{\text{2}} {\text{O}}} \) , with a maximum deviation of 400 joules. Thus, for the purpose of calculation of geologically interesting heterogeneous equilibria, it predicts the thermodynamic properties of H₂O well enough. The values of molar volume, \(\tilde V_{{\text{H}}_{\text{2}} {\text{O}}} \) , and \(\tilde G_{{\text{H}}_{\text{2}} {\text{O}}} \) are tabulated in the appendix over a considerable P-T range. A FORTRAN program generating these functions as well as a FORTRAN subroutine for calculating the fugacity values, \(f_{{\text{H}}_{\text{2}} {\text{O}}} \) for incorporation into existing programs, are available upon request.     

Comparative compressibility and equation of state of orthorhombic and tetragonal edingtonite

The high-pressure (HP) behaviour of a natural orthorhombic and tetragonal edingtonite from Ice River, Canada, has been investigated using in situ single-crystal X-ray diffraction. The two isothermal equations of state up to 6.74(5) GPa were determined. V₀, K_T0 and K refined with a third-order Birch–Murnaghan equation of state (BM-EoS) are: V₀ = 598.70(7) ų, K_T0 = 59(1) GPa and K=3.9(4) for orthorhombic edingtonite and V₀ = 600.9(2) ų, K_T0 = 59(1) GPa and K=4.2(5) for tetragonal edingtonite. The experiments were conducted with nominally hydrous pressure penetrating transmitting medium. No overhydration effect was observed within the pressure range investigated. At high-pressures the main deformation mechanism is represented by cooperative rotation of the secondary building unit (SBU).Si/Al distribution slightly influences the elastic behaviour of the tetrahedral framework: the SBU bulk moduli are 125(8) GPa and 111(4) GPa for orthorhombic and tetragonal edingtonite, respectively. Extra-framework contents of both zeolites show an interesting behaviour under HP conditions: the split Ba2 site at P >2.85 GPa is completely empty; only the position Ba1 is occupied. Electronic Supplementary Material. Supplementary material to this paper (Observed and calculated structure factors) is available in electronic form at Electronic Supplementary Material Supplementary material is available in the online version of this article at