Physics of Solids Under Strong Compression
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7 Apr 2021 Thermodynamic Response Functions . L03–1 Review Of
7 apr 2021 thermodynamic response functions . L03{1 Review of Thermodynamics. 3: Second-Order Quantities and Relationships Maxwell Relations • Idea: Each thermodynamic potential gives rise to several identities among its second derivatives, known as Maxwell relations, which express the integrability of the fundamental identity of thermodynamics for that potential, or equivalently the fact that the potential really is a thermodynamical state function. • Example: From the fundamental identity of thermodynamics written in terms of the Helmholtz free energy, dF = −S dT − p dV + :::, the fact that dF really is the differential of a state function implies that @ @F @ @F @S @p = ; or = : @V @T @T @V @V T;N @T V;N • Other Maxwell relations: From the same identity, if F = F (T; V; N) we get two more relations. Other potentials and/or pairs of variables can be used to obtain additional relations. For example, from the Gibbs free energy and the identity dG = −S dT + V dp + µ dN, we get three relations, including @ @G @ @G @S @V = ; or = − : @p @T @T @p @p T;N @T p;N • Applications: Some measurable quantities, response functions such as heat capacities and compressibilities, are second-order thermodynamical quantities (i.e., their definitions contain derivatives up to second order of thermodynamic potentials), and the Maxwell relations provide useful equations among them. Heat Capacities • Definitions: A heat capacity is a response function expressing how much a system's temperature changes when heat is transferred to it, or equivalently how much δQ is needed to obtain a given dT . The general definition is C = δQ=dT , where for any reversible transformation δQ = T dS, but the value of this quantity depends on the details of the transformation. -
High Temperature and High Pressure Equation of State of Gold
Journal of Physics: Conference Series OPEN ACCESS Related content - The equation of state of B2-type NaCl High temperature and high pressure equation of S Ono - Thermodynamics in high-temperature state of gold pressure scales on example of MgO Peter I Dorogokupets To cite this article: Masanori Matsui 2010 J. Phys.: Conf. Ser. 215 012197 - Equation of State of Tantalum up to 133 GPa Tang Ling-Yun, Liu Lei, Liu Jing et al. View the article online for updates and enhancements. Recent citations - Equation of State for Natural Almandine, Spessartine, Pyrope Garnet: Implications for Quartz-In-Garnet Elastic Geobarometry Suzanne R. Mulligan et al - High-Pressure Equation of State of 1,3,5- triamino-2,4,6-trinitrobenzene: Insights into the Monoclinic Phase Transition, Hydrogen Bonding, and Anharmonicity Brad A. Steele et al - High-enthalpy crystalline phases of cadmium telluride Adebayo O. Adeniyi et al This content was downloaded from IP address 170.106.202.8 on 25/09/2021 at 03:55 Joint AIRAPT-22 & HPCJ-50 IOP Publishing Journal of Physics: Conference Series 215 (2010) 012197 doi:10.1088/1742-6596/215/1/012197 High temperature and high pressure equation of state of gold Masanori Matsui School of Science, University of Hyogo, Kouto, Kamigori, Hyogo 678–1297, Japan E-mail: [email protected] Abstract. High-temperature and high-pressure equation of state (EOS) of Au has been developed using measured data from shock compression up to 240 GPa, volume thermal expansion between 100 and 1300 K and 0 GPa, and temperature dependence of bulk modulus at 0 GPa from ultrasonic measurements. -
Calculation of Thermal Pressure Coefficient of Lithium Fluid by Data
International Scholarly Research Network ISRN Physical Chemistry Volume 2012, Article ID 724230, 11 pages doi:10.5402/2012/724230 Research Article Calculation of Thermal Pressure Coefficient of Lithium Fluid by pVT Data Vahid Moeini Department of Chemistry, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran Correspondence should be addressed to Vahid Moeini, v [email protected] Received 20 September 2012; Accepted 9 October 2012 Academic Editors: F. M. Cabrerizo, H. Reis, and E. B. Starikov Copyright © 2012 Vahid Moeini. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. For thermodynamic performance to be optimized, particular attention must be paid to the fluid’s thermal pressure coefficients and thermodynamics properties. A new analytical expression based on the statistical mechanics is derived for thermal pressure coefficients of dense fluids using the intermolecular forces theory to be valid for liquid lithium as well. The results are used to predict the parameters of some binary mixtures at different compositions and temperatures metal-nonmetal lithium fluid which agreement with experimental data. In this paper, we have used newly presented parameters of analytical expressions based on the statistical mechanics and predicted the metal-nonmetal transition for liquid lithium. The repulsion term of the effective pair potential for lithium shows well depth at 1600 K, and the position of well depth maximum is in agreement with X-ray diffraction and small-angle X-ray scattering. 1. Introduction would be observed if each pair was isolated. -
A Bibliography of Experimental Saturation Properties of the Cryogenic Fluids1
National Bureau of Standards Library, K.W. Bldg APR 2 8 1965 ^ecknlcai rlote 92c. 309 A BIBLIOGRAPHY OF EXPERIMENTAL SATURATION PROPERTIES OF THE CRYOGENIC FLUIDS N. A. Olien and L. A. Hall U. S. DEPARTMENT OF COMMERCE NATIONAL BUREAU OF STANDARDS THE NATIONAL BUREAU OF STANDARDS The National Bureau of Standards is a principal focal point in the Federal Government for assuring maximum application of the physical and engineering sciences to the advancement of technology in industry and commerce. Its responsibilities include development and maintenance of the national stand- ards of measurement, and the provisions of means for making measurements consistent with those standards; determination of physical constants and properties of materials; development of methods for testing materials, mechanisms, and structures, and making such tests as may be necessary, particu- larly for government agencies; cooperation in the establishment of standard practices for incorpora- tion in codes and specifications; advisory service to government agencies on scientific and technical problems; invention and development of devices to serve special needs of the Government; assistance to industry, business, and consumers in the development and acceptance of commercial standards and simplified trade practice recommendations; administration of programs in cooperation with United States business groups and standards organizations for the development of international standards of practice; and maintenance of a clearinghouse for the collection and dissemination of scientific, tech- nical, and engineering information. The scope of the Bureau's activities is suggested in the following listing of its four Institutes and their organizational units. Institute for Basic Standards. Electricity. Metrology. Heat. Radiation Physics. Mechanics. Ap- plied Mathematics. -
Pressure—Volume—Temperature Equation of State
Pressure—Volume—Temperature Equation of State S.-H. Dan Shim (심상헌) Acknowledgement: NSF-CSEDI, NSF-FESD, NSF-EAR, NASA-NExSS, Keck Equations relating state variables (pressure, temperature, volume, or energy). • Backgrounds • Equations • Limitations • Applications Ideal Gas Law PV = nRT Ideal Gas Law • Volume increases with temperature • VolumePV decreases= nRTwith pressure • Pressure increases with temperature Stress (σ) and Strain (�) Bridgmanite in the Mantle Strain in the Mantle 20-30% P—V—T EOS Bridgmanite Energy A Few Terms to Remember • Isothermal • Isobaric • Isochoric • Isentropic • Adiabatic Energy Thermodynamic Parameters Isothermal bulk modulus Thermodynamic Parameters Isothermal bulk modulus Thermal expansion parameter Thermodynamic Parameters Isothermal bulk modulus Thermal expansion parameter Grüneisen parameter ∂P 1 ∂P γ = V = ∂U ρC ∂T ✓ ◆V V ✓ ◆V P—V—T of EOS Bridgmanite • KT • α • γ P—V—T EOS Shape of EOS Shape of EOS Ptotal Shape of EOS Pst Pth Thermal Pressure Ftot = Fst + Fb + Feec P(V, T)=Pst(V, T0)+ΔPth(V, T) Isothermal EOS dP dP K = = − d ln V d ln ρ P V = V0 exp − K 0 Assumes that K does not change with P, T Murnaghan EOS K = K0 + K00 P dP dP K = = − d ln V d ln ρ K00 ρ = ρ0 1 + P Ç K0 å However, K increases nonlinearly with pressure Birch-Murnaghan EOS 2 3 F = + bƒ + cƒ + dƒ + ... V 0 3/2 =(1 + 2ƒ ) V F : Energy (U or F) f : Eulerian finite strain Birch (1978) Second Order BM EOS 2 F = + bƒ + cƒ 3K V 7/3 V 5/3 5/2 0 0 0 P = 3K0ƒ (1 + 2ƒ ) = 2 V V ñ✓ ◆ − ✓ ◆ ô dP K V 7/3 V 5/3 0 0 0 5/2 K = V = 7 5 = K0(1 + 7ƒ )(1 + 2ƒ ) dV 2 V V − ñ ✓ ◆ − ✓ ◆ ô Birch (1978) Third Order BM EOS 2 3 F = + bƒ + cƒ + dƒ 7/3 5/3 2/3 3K0 V0 V0 V0 P = 1 ξ 1 2 V V V ñ✓ ◆ − ✓ ◆ ô® − ñ✓ ◆ − ô´ 3 ξ = (4 K00 ) 4 − Birch (1978) Truncation Problem 2 3 F = + bƒ + cƒ + dƒ + .. -
High Pressure and Temperature Dependence of Thermodynamic Properties of Model Food Solutions Obtained from in Situ Ultrasonic Measurements
HIGH PRESSURE AND TEMPERATURE DEPENDENCE OF THERMODYNAMIC PROPERTIES OF MODEL FOOD SOLUTIONS OBTAINED FROM IN SITU ULTRASONIC MEASUREMENTS By ROGER DARROS BARBOSA A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2003 Copyright 2003 by Roger Darros Barbosa To Neila who made me feel reborn, and To my dearly loved children Marina, Carolina and especially Artur, the youngest, with whom enjoyable times were shared through this journey ACKNOWLEDGMENTS I would like to express my sincere gratitude to Dr. Murat Ö. Balaban and Dr. Arthur A. Teixeira for their valuable advice, help, encouragement, support and guidance throughout my graduate studies at the University of Florida. Special thanks go to Dr. Murat Ö. Balaban for giving me the opportunity to work in his lab and study the interesting subject of this research. I would also like to thank my committee members Dr. Gary Ihas, Dr. D. Julian McClements and Dr. Robert J. Braddock for their help, suggestions, and words of encouragement along this research. A special thank goes to Dr. D. Julian McClements for his valuable assistance and for receiving me in his lab at the University of Massachusetts. I am grateful to the Foundation for Support of Research of the State of São Paulo (FAPESP 97/07546-4) for financially supporting most part of this project. I also gratefully acknowledge the Institute of Food and Agricultural Sciences (IFAS) Research Dean, the chair of the Food Science and Human Nutrition Department, the chair of Department of Agricultural and Biological Engineering at the University of Florida, and the United States Department of Agriculture (through a research grant), for financially supporting parts of this research. -
CHAPTER 17 Internal Pressure and Internal Energy of Saturated and Compressed Phases Ainstitute of Physics of the Dagestan Scient
CHAPTER 17 Internal Pressure and Internal Energy of Saturated and Compressed Phases ILMUTDIN M. ABDULAGATOV,a,b JOSEPH W. MAGEE,c NIKOLAI G. POLIKHRONIDI,a RABIYAT G. BATYROVAa aInstitute of Physics of the Dagestan Scientific Center of the Russian Academy of Sciences, Makhachkala, Dagestan, Russia. E-mail: [email protected] bDagestan State University, Makhachkala, Dagestan, Russia cNational Institute of Standards and Technology, Boulder, Colorado 80305 USA. E- mail: [email protected] Abstract Following a critical review of the field, a comprehensive analysis is provided of the internal pressure of fluids and fluid mixtures and its determination in a wide range of temperatures and pressures. Further, the physical meaning is discussed of the internal pressure along with its microscopic interpretation by means of calorimetric experiments. A new relation is explored between the internal pressure and the isochoric heat capacity jump along the coexistence curve near the critical point. Various methods (direct and indirect) of internal pressure determination are discussed. Relationships are studied between the internal pressure and key thermodynamic properties, namely expansion coefficient, isothermal compressibility, speed of sound, enthalpy increments, and viscosity. Loci of isothermal, isobaric, and isochoric internal pressure maxima and minima were examined in addition to the locus of zero internal pressure. Details were discussed of the new method of direct internal pressure determination by a calorimetric experiment that involves simultaneous measurement of the thermal pressure coefficient (∂P / ∂T )V , i.e. internal pressure Pint = (∂U / ∂V )T and heat capacity cV = (∂U / ∂T )V . The dependence of internal pressure on external pressure, temperature and density for pure fluids, and on concentration for binary mixtures is considered on the basis of reference (NIST REFPROP) and crossover EOS. -
Route to High-Energy Density Polymeric Nitrogen T-N Via Heâˆ'n Compounds
ARTICLE DOI: 10.1038/s41467-018-03200-4 OPEN Route to high-energy density polymeric nitrogen t- N via He−N compounds Yinwei Li1, Xiaolei Feng2,3, Hanyu Liu4, Jian Hao1, Simon A.T. Redfern 3,5, Weiwei Lei6, Dan Liu6 & Yanming Ma2,7 Polymeric nitrogen, stabilized by compressing pure molecular nitrogen, has yet to be recovered to ambient conditions, precluding its application as a high-energy density material. 1234567890():,; Here we suggest a route for synthesis of a tetragonal polymeric nitrogen, denoted t-N, via He-N compounds at high pressures. Using first-principles calculations with structure searching, we predict a class of nitrides with stoichiometry HeN4 that are energetically stable (relative to a mixture of solid He and N2) above 8.5 GPa. At high pressure, HeN4 comprises a polymeric channel-like nitrogen framework filled with linearly arranged helium atoms. The nitrogen framework persists to ambient pressure on decompression after removal of helium, forming pure polymeric nitrogen, t-N. t-N is dynamically and mechanically stable at ambient pressure with an estimated energy density of ~11.31 kJ/g, marking it out as a remarkable high- energy density material. This expands the known polymeric forms of nitrogen and indicates a route to its synthesis. 1 School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, China. 2 State Key Laboratory of Superhard Materials, College of Physics, Jilin University, Changchun 130012, China. 3 Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, UK. 4 Geophysical Laboratory, Carnegie Institution of Washington, Washington, DC 20015, USA. 5 Center for High Pressure Science and Technology Advanced Research (HPSTAR), Shanghai 201203, China. -
Relationships Between Volume Thermal Expansion and Thermal Pressure Based on the Stacey Reciprocal K-Primed EOS
Indian Journal of Pure & Applied Physics Vol. 49, February 2011, pp. 99-103 Relationships between volume thermal expansion and thermal pressure based on the Stacey reciprocal K-primed EOS S S Kushwah* & Y S Tomar Department of Physics, Rishi Galav College, Morena 476 001, MP, India *E-mail: [email protected] Received 25 February 2010; revised 22 December 2010; accepted 10 January 2011 It has been found that the Stacey reciprocal K-primed EOS is consistent with the experimental data for bulk modulus and thermal pressure as it yields correct values for volume expansion at high temperatures. The comparison of calculated values with the experimental data has been presented in case of NaCl, KCl, MgO, CaO, Al 2O3 and Mg 2SiO 4. It is also emphasized that the two equations mimicking the Stacey EOS recently used by Shrivastava [ Physica B , 404 (2009) 251] are in fact originally due to Kushwah et al . [ Physica B , 388 (2007) 20]. The results obtained for the thermal pressure using the Kushwah EOS are in good agreement for all the solids under study. Keywords : Equation of state; Bulk modulus; Thermal pressure; Thermal expansion 1 Introduction In writing Eqs (2 and 3), it has been assumed that Thermal pressure is a physical quantity of central the thermal pressure is a function of temperature importance 1 for investigating the thermoelastic only 1. At atmospheric pressure, i.e. at P(V,T) = 0, we properties of materials at high temperatures 2-7. The have: volume expansion of solids due to the rise in 8,9 temperature is directly related to thermal pressure . -
Polymeric Nitrogen by Plasma Enhanced Chemical Vapor Deposition
New Jersey Institute of Technology Digital Commons @ NJIT Dissertations Electronic Theses and Dissertations Fall 1-31-2015 Polymeric nitrogen by plasma enhanced chemical vapor deposition El Mostafa Benchafia New Jersey Institute of Technology Follow this and additional works at: https://digitalcommons.njit.edu/dissertations Part of the Materials Science and Engineering Commons Recommended Citation Benchafia, El Mostafa, "Polymeric nitrogen by plasma enhanced chemical vapor deposition" (2015). Dissertations. 98. https://digitalcommons.njit.edu/dissertations/98 This Dissertation is brought to you for free and open access by the Electronic Theses and Dissertations at Digital Commons @ NJIT. It has been accepted for inclusion in Dissertations by an authorized administrator of Digital Commons @ NJIT. For more information, please contact [email protected]. Copyright Warning & Restrictions The copyright law of the United States (Title 17, United States Code) governs the making of photocopies or other reproductions of copyrighted material. Under certain conditions specified in the law, libraries and archives are authorized to furnish a photocopy or other reproduction. One of these specified conditions is that the photocopy or reproduction is not to be “used for any purpose other than private study, scholarship, or research.” If a, user makes a request for, or later uses, a photocopy or reproduction for purposes in excess of “fair use” that user may be liable for copyright infringement, This institution reserves the right to refuse to accept -
Pressure-Induced Stability and Polymeric Nitrogen in Alkaline Earth
RSC Advances View Article Online PAPER View Journal | View Issue Pressure-induced stability and polymeric nitrogen in alkaline earth metal N-rich nitrides (XN ,X¼ Ca, Cite this: RSC Adv.,2021,11, 17222 6 Sr and Ba): a first-principles study† Zhipeng Liu, Shuli Wei, * Yanhui Guo, Haiyang Sun, Hao Sun, Qiang Chang and Yuping Sun * Multi-nitrogen or polynitrogen compounds can be used as potential high energy-density materials, so they have attracted great attention. Nitrogen can exist in alkaline earth metal nitrogen-rich (N-rich) compounds in the form of single or double bonds. In recent years, to explore N-rich compounds which are stable and easy to synthesize has become a new research direction. The N-rich compounds XN6 (X ¼ Ca, Sr and Ba) have been reported under normal pressure. In order to find other stable crystal structures, we have performed XN6 (X ¼ Ca, Sr and Ba) exploration under high pressure. We found that SrN6 has a new P1 phase at a pressure of 22 GPa and an infinite nitrogen chain structure, and BaN6 has a new C2/m phase Creative Commons Attribution-NonCommercial 3.0 Unported Licence. at 110 GPa, with an N6 ring network structure. Further, we observed that the infinite nitrogen chain and 2 the N6 ring network structure contain typical covalent bonds formed by the hybridization of the sp and 3 sp orbitals of N, respectively. It is found that both SrN6 and BaN6 are semiconductor materials and the N-2p orbital plays an important role in the stability of the crystal structure for P1-SrN6 and C2/m-BaN6. -
Speed of Sound Measurements and Fundamental Equations of State for Octamethyltrisiloxane and Decamethyltetrasiloxane
Speed of Sound Measurements and Fundamental Equations of State for Octamethyltrisiloxane and Decamethyltetrasiloxane Monika Thol1*, Frithjof H. Dubberke2, Elmar Baumhögger2, Jadran Vrabec2, Roland Span1 1Thermodynamics, Ruhr-Universität Bochum, Universitätsstraße 150, 44801 Bochum, Germany 2Thermodynamics and Energy Technology, Universität Paderborn, Warburger Straße 100, 33098 Paderborn, Germany E-mail addresses: [email protected], Fax: +49 234 32 14163 (corresponding author) [email protected] [email protected] [email protected] [email protected] ABSTRACT Equations of state in terms of the Helmholtz energy are presented for octamethyltrisiloxane and decamethyltetrasiloxane. The restricted databases in the literature are augmented by speed of sound measurements, which are carried out by a pulse-echo method. The equations of state are valid in the fluid region up to approximately 600 K and 130 MPa and can be used to calculate all thermodynamic properties by combining the Helmholtz energy and its derivatives with respect to the natural variables. The accuracy of the equation is validated by comparison to experimental data and correct extrapolation behavior is ensured. Keywords: Bethe-Zel'dovich-Thompson fluids, decamethyltetrasiloxane, equation of state, Helmholtz energy, octamethyltrisiloxane, speed of sound, thermodynamic properties 1 INTRODUCTION The accurate description of thermodynamic properties of fluids is an important discipline in energy, process, and chemical engineering. For many applications in research and industry, these properties are mandatory for process simulation and the energetically but also economically efficient construction of plants. Nowadays, such information is provided by fundamental equations of state, whose parameters are adjusted to experimental data. Therefore, it is evident that the quality of the corresponding mathematical models is primarily dependent on the availability and the accuracy of experimental data.