Equations of state, phase relations, and oxygen fugacity of the Ru-RuO2 buffer at high pressures and temperatures

2020 ◽  
Vol 105 (3) ◽  
pp. 333-343
Author(s):  
Katherine Armstrong ◽  
Nicki C. Siersch ◽  
Tiziana Boffa-Ballaran ◽  
Daniel J. Frost ◽  
Tony Yu ◽  
...  
Keyword(s):  
High Pressure ◽  
Free Energy ◽  
Gibbs Free Energy ◽  
Oxygen Fugacity ◽  
Equations Of State ◽  
Experimental Studies ◽  
Phase Relations ◽  
Cubic Phase ◽  
High Pressure And Temperature ◽  
Energy Expression

Abstract Experimental studies and measurements of inclusions in diamonds show that ferric iron components are increasingly stabilized with depth in the mantle. To determine the thermodynamic stability of such components, their concentration needs to be measured at known oxygen fugacities. The metal-oxide pair Ru and RuO2 are ideal as an internal oxygen fugacity buffer in high-pressure experiments. Both phases remain solid to high temperatures and react minimally with silicates, only exchanging oxygen. To calculate oxygen fugacities at high pressure and temperature, however, requires information on the phase relations and equation of state properties of the solid phases. We have made in situ synchrotron X-ray diffraction measurements in a multi-anvil press on mixtures of Ru and RuO2 to 19.4 GPa and 1473 K with which we have determined phase relations of the RuO2 phases and derived thermal equations of state (EoS) parameters for both Ru and RuO2. Rutile-structured RuO2 was found to undergo two phase transformations, first at ~7 GPa to an orthorhombic structure and then above 12 GPa to a cubic structure. The phase boundary of the cubic phase was constrained for the first time at high pressure and temperature. We have derived a continuous Gibbs free energy expression for the tetragonal and orthorhombic phases of RuO2 by fitting the second-order phase transition boundary and P-V-T data for both phases, using a model based on Landau theory. The transition between the orthorhombic and cubic phases was then used along with EoS terms derived for both phases to determine a Gibbs free energy expression for the cubic phase. We have used these data to calculate the oxygen fugacity of the Ru + O2 = RuO2 equilibrium, which we have parameterized as a single polynomial across the stability fields of all three phases of RuO2. The expression is log10fO2(Ru – RuO2) = (7.782 – 0.00996P + 0.001932P2 – 3.76 × 10–5P3) + (–13 763 + 592P – 3.955P2)/T + (–1.05 × 106 – 4622P)/T2, which should be valid from room pressure up to 25 GPa and 773–2500 K, with an estimated uncertainty of 0.2 log units. Our calculated fO2 is shown to be up to 1 log unit lower than estimates that use previous expressions or ignore EoS terms.

Phase relations and equations of state ofZrO2under high temperature and high pressure

2001 ◽  
Vol 63 (17) ◽  
Author(s):  
O. Ohtaka ◽  
H. Fukui ◽  
T. Kunisada ◽  
T. Fujisawa ◽  
K. Funakoshi ◽  
...  
Keyword(s):  
High Pressure ◽  
High Temperature ◽  
Equations Of State ◽  
Phase Relations

Gibbs Free Energy Expression for the System Polystyrene in Methylcyclohexane and Its Application to Microencapsulation

Langmuir ◽  
2003 ◽  
Vol 19 (13) ◽  
pp. 5240-5245 ◽  
Author(s):  
Takayuki Narita ◽  
Takao Yamamoto ◽  
Eri Hosoya ◽  
Toshiaki Dobashi
Keyword(s):  
Free Energy ◽  
Gibbs Free Energy ◽  
Energy Expression

scholarly journals GIBBS FREE ENERGY OF NATURAL GAS COMPONENTS FORMATION IN SEDIMENTARY STRATA

2019 ◽  
Vol 2 (179) ◽  
pp. 37-46
Author(s):  
Yuri KHOKHA ◽  
Oleksandr LYUBCHAK ◽  
Myroslava YAKOVENKO
Keyword(s):  
Heat Flux ◽  
Free Energy ◽  
Natural Gas ◽  
Gibbs Free Energy ◽  
Equations Of State ◽  
Carbon Number ◽  
Hydrocarbon Chain ◽  
Heat Fluxes ◽  
Energy Calculation ◽  
Free Energies

The main methods of calculating the composition of geochemical systems in the thermodynamic equilibrium state were considered in the article. It was shown that the basis for such calculations was the determination of the Gibbs Free Energy of each system components at given temperatures and pressures. The methods of Gibbs Free Energy calculation at standard pressure and under conditions that are realized within the sedimentary strata were analyzed. The equations of state for natural gas individual components were selected and their Gibbs Free Energies for heat fluxes ranging from 40 to 100 mW/m2 and depths of 0–20 km were calculated. The results showed that the pressure significantly affects the value of Gibbs Free Energies formation of natural gas components within the sedimentary strata. Changes of the Gibbs Free Energies of natural gas components formation, as a function of depth, subordinated to the same laws for each compound. This regularity was better expressed in more heated areas. It was shown that with depth increasing the Gibbs Free Energy of natural gas components formation first rapidly decreases and reaches its minimum ranging from 2 to 6 km. Moreover, as the value of the heat flux increases, the maximum value of the Gibbs Free Energy of formation of natural gas components, expressed in kilometers, decreases. With further immersion/deepening to depths greater than 6 km, the Gibbs Free Energy of the formation of natural gas components gradually increases, and in areas with greater heat flux, a sharp increase was characteristic, and with less, it was slow and weakly expressed. There is a stability area for hydrocarbon and non-hydrocarbon components of natural gas ranging from 2 to 6 km. With the increase of Carbon number in the hydrocarbon chain, the value of Gibbs Free Energy of the natural gas hydrocarbon components formation decreases, which indicates the presence of a stability zone for heavy natural gas components (it should be expected that oil also) within the depths of 2–6 km.

scholarly journals High-pressure polymorphism in pyridine

IUCrJ ◽  
2020 ◽  
Vol 7 (1) ◽  
pp. 58-70 ◽  
Author(s):  
Nico Giordano ◽  
Christine M. Beavers ◽  
Branton J. Campbell ◽  
Václav Eigner ◽  
Eugene Gregoryanz ◽  
...  
Keyword(s):  
High Pressure ◽  
Phase Ii ◽  
Density Functional ◽  
Equations Of State ◽  
Density Functional Theory Calculations ◽  
Phase Iii ◽  
Mode Analysis ◽  
Cubic Phase ◽  
X Ray ◽  
Lattice Mode

Single crystals of the high-pressure phases II and III of pyridine have been obtained by in situ crystallization at 1.09 and 1.69 GPa, revealing the crystal structure of phase III for the first time using X-ray diffraction. Phase II crystallizes in P212121 with Z′ = 1 and phase III in P41212 with Z′ = ½. Neutron powder diffraction experiments using pyridine-d5 establish approximate equations of state of both phases. The space group and unit-cell dimensions of phase III are similar to the structures of other simple compounds with C 2v molecular symmetry, and the phase becomes stable at high pressure because it is topologically close-packed, resulting in a lower molar volume than the topologically body-centred cubic phase II. Phases II and III have been observed previously by Raman spectroscopy, but have been mis-identified or inconsistently named. Raman spectra collected on the same samples as used in the X-ray experiments establish the vibrational characteristics of both phases unambiguously. The pyridine molecules interact in both phases through CH...π and CH...N interactions. The nature of individual contacts is preserved through the phase transition between phases III and II, which occurs on decompression. A combination of rigid-body symmetry mode analysis and density functional theory calculations enables the soft vibrational lattice mode which governs the transformation to be identified.

Phase relations of Fe–Ni alloys at high pressure and temperature

2006 ◽  
Vol 155 (1-2) ◽  
pp. 146-151 ◽  
Author(s):  
Wendy L. Mao ◽  
Andrew J. Campbell ◽  
Dion L. Heinz ◽  
Guoyin Shen
Keyword(s):  
High Pressure ◽  
Phase Relations ◽  
High Pressure And Temperature ◽  
Ni Alloys

A Thermodynamical Model for Analysis of Isothermal Phase Transformations under High Pressure

2007 ◽  
Vol 553 ◽  
pp. 57-62
Author(s):  
Veneta Grigorova ◽  
Dimitar Roussev
Keyword(s):  
Phase Transition ◽  
High Pressure ◽  
Free Energy ◽  
Phase Transformations ◽  
Gibbs Free Energy ◽  
Structure Type ◽  
Transformation Process ◽  
Partial Derivatives ◽  
Degree Of Stability ◽  
Thermodynamical Model

In the present study we elaborated a thermodynamical model for analysis of isothermal phase transformations under high pressure. Our study was provoked by the necessity to characterise the behaviour of MTe2 chemical compounds (M = Pd, Pt) while subjected isothermally to high pressure. As known [1] MTe2 powders are representatives of the CdI2 structure type. This structure type is a bi-dimensional one and as such is atypical for the big family of lamellar MQ2-type dichalcogenides (M = Pd, Pt; Q = S, Se, Te). Specific of lamellar structure is the strong ionicity of the bonds. One of the most interesting points stands on the possibility for realising interactions between the layers of different types of ions. That could be done under high pressure by any of the following transformation processes: (i) phase transition to the typical pyrite structure; (ii) phase rearrangement changing the parameters of the crystal cell but keeping the 2D-type structure. In this framework our aim was to elaborate a thermodynamical model for analysis of such isothermal phase transformations under high pressure. Our analysis model is designed to answer the following questions: (i) if the treated compound undergoes a classical phase transition or a phase rearrangement; (ii) which is the order of the phase transition or the phase rearrangement, respectively; and (iii) what is the degree-of-stability of the treated compound under high pressure. To detect if the transformation process is a phase transition or a rearrangement, we compute both volumetric and longitudinal Gibbs free energies and their partial derivatives. We recognise the transformation to be: (i) a phase transition when it affects the volumetric Gibbs free energy and its partial derivatives; (ii) a phase rearrangement if it affects the longitudinal Gibbs free energy and its partial derivatives. The order of the transformation process (phase transition or rearrangement, respectively) is determined by the order of the partial derivative of the Gibbs free energy (volumetric or longitudinal, respectively), which is discontinuous in the transformation point. Hence, we compute the two first partial derivatives (i.e., the first one and the second one) of the Gibbs free energy (both volumetric and longitudinal). For characterising the degree of stability of the treated compound under high pressure we calculate its entropy generation (volumetric and longitudinal, respectively) during the treatment process. The established model was further applied to PdTe2 and to PtTe2 while subjected isothermally to high pressure.

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