Partition functions and thermodynamic properties to high temperatures for H sub 3 and H sub 2 ions
Partition functions and thermodynamic properties to high temperatures for hydrogen triatomic and diatomic molecular ions
Mc Bride, B. J.↗
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Thermodynamic Activity Measurements with Knudsen Cell Mass Spectrometry
Coupling the Knudsen effusion method with mass spectrometry has proven to be one of the most useful experimental techniques for studying the equilibrium between condensed phases and complex vapors. The Knudsen effusion method involves placing a condensed sample in a Knudsen cell, a small "enclosure", that is uniformly heated and held until equilibrium is attained between the condensed and vapor phases. The vapor is continuously sampled by effusion through a small orifice in the cell. A molecular beam is formed from the effusing vapor and directed into a mass spectrometer for identification and pressure measurement of the species in the vapor phase. Knudsen cell mass spectrometry (KCMS) has been used for nearly fifty years now and continues to be a leading technique for obtaining thermodynamic data. Indeed, much of the well-established vapor specie data in the JANAF tables has been obtained from this technique. This is due to the extreme versatility of the technique. All classes of materials can be studied and all constituents of the vapor phase can be measured over a wide range of pressures (approximately 10(exp -4) to 10(exp -11) bar) and temperatures (500-2800 K). The ability to selectively measure different vapor species makes KCMS a very powerful tool for the measurement of component activities in metallic and ceramic solutions. Today several groups are applying KCMS to measure thermodynamic functions in multicomponent metallic and ceramic systems. Thermodynamic functions, especially component activities, are extremely important in the development of CALPHAD (Calculation of Phase Diagrams) type thermodynamic descriptions. These descriptions, in turn, are useful for modeling materials processing and predicting reactions such as oxide formation and fiber/matrix interactions. The leading experimental methods for measuring activities are the Galvanic cell or electro-motive force (EMF) technique and the KCMS technique. Each has specific advantages, depending on material and conditions. The EMF technique is suitable for lower temperature measurements, provided a suitable cell can be constructed. KCMS is useful for higher temperature measurements in a system with volatile components. In this paper, we briefly review the KCMS technique and identify the major experimental issues that must be addressed for precise measurements. These issues include temperature measurements, cell material and cell design and absolute pressure calibration. The resolution of these issues are discussed together with some recent examples of measured thermodynamic data.
Copland, Evan H.↗
A Three-Dimensional Thermodynamically Based Function for the Progressive Failure of Unidirectional Composites
A thermodynamically-based work potential theory for modeling progressive damage for laminated, unidirectional composites assuming plane stress (2D Schaperystheory) is extended to three dimensioanl (3D). An internal state variable, S, is defined to account for the dissipated energy due to damage evolution in the form of microstructure changes in the matrix. With the stationary of the total work potential with respect to the internal state variable, a thermodynamically-consistent set of evolution equationsis derived. The internal state variable is related to the transverse and shear modulithrough microdamage functions. In the first part of this work, coupon specimensare prepared to conduct experiments to characterize the relations between the internalstate variable and the transverse modulus as well as shear modulus. The informationis subsequent used for the prediction of three point bending test. In the second partof this work, objectivity is studied. Three separate methods utilizing different definitions of a reduced internal state variable or of the order of the polynomials are used to represent the matrix micro-damage functions are employed. The three methods are implemented in a user defined subroutine within a commercial finite element method software package. Results from numerical simulations of a center-notched composites panel are compared. The agreement in the maximum stress predictions among the three methods indicates that objectivity, with respect to the functional form of themicrodamage functions, is satisfied.
carbon fiber reinforced polymer composites↗
Circuit complexity and functionality: A statistical thermodynamics perspective
Circuit complexity, defined as the minimum circuit size required for implementing a particular Boolean computation, is a foundational concept in computer science. Determining circuit complexity is believed to be a hard computational problem. Recently, in the context of black holes, circuit complexity has been promoted to a physical property, wherein the growth of complexity is reflected in the time evolution of the Einstein-Rosen bridge (“wormhole”) connecting the two sides of an anti-de Sitter “eternal” black hole. Here, we are motivated by an independent set of considerations and explore links between complexity and thermodynamics for functionally equivalent circuits, making the physics-inspired approach relevant to real computational problems, for which functionality is the key element of interest. In particular, our thermodynamic framework provides an alternative perspective on the obfuscation of programs of arbitrary length—an important problem in cryptography—as thermalization through recursive mixing of neighboring sections of a circuit, which can be viewed as the mixing of two containers with “gases of gates.” This recursive process equilibrates the average complexity and leads to the saturation of the circuit entropy, while preserving functionality of the overall circuit. The thermodynamic arguments hinge on ergodicity in the space of circuits which we conjecture is limited to disconnected ergodic sectors due to fragmentation. The notion of fragmentation has important implications for the problem of circuit obfuscation as it implies that there are circuits of same size and functionality that cannot be connected via a polynomial number of local moves. Furthermore, we argue that fragmentation is unavoidable unless the complexity classes NP and coNP coincide, a statement that implies the collapse of the polynomial hierarchy of computational complexity theory to its first level.
Science & Technology - Other Topics↗
Tables of critical-flow functions and thermodynamic properties for methane and computational procedures for both methane and natural gas
Procedures for calculating the mass flow rate of methane and natural gas through nozzles are given, along with the FORTRAN 4 subroutines used to make these calculations. Three sets of independent variables are permitted in these routines. In addition to the plenum pressure and temperature, the third independent variable is either nozzle exit pressure, Mach number, or temperature. A critical-flow factor that becomes a convenient means for determining the mass flow rate of methane through critical-flow nozzles is tabulated. Other tables are included for nozzle throat velocity and critical pressure, density, and temperature ratios, along with some thermodynamic properties of methane, including compressibility factor, enthalpy, entropy, specific heat, specific-heat ratio, and speed of sound. These tabulations cover a temperature range from 120 to 600 K and pressures to 3 million N/sq m.
Johnson, R. C.↗
Neural network representations of multiphase Equations of State
Abstract Equations of State model relations between thermodynamic variables and are ubiquitous in scientific modelling, appearing in modern day applications ranging from Astrophysics to Climate Science. The three desired properties of a general Equation of State model are adherence to the Laws of Thermodynamics, incorporation of phase transitions, and multiscale accuracy. Analytic models that adhere to all three are hard to develop and cumbersome to work with, often resulting in sacrificing one of these elements for the sake of efficiency. In this work, two deep-learning methods are proposed that provably satisfy the first and second conditions on a large-enough region of thermodynamic variable space. The first is based on learning the generating function (thermodynamic potential) while the second is based on structure-preserving, symplectic neural networks, respectively allowing modifications near or on phase transition regions. They can be used either “from scratch” to learn a full Equation of State, or in conjunction with a pre-existing consistent model, functioning as a modification that better adheres to experimental data. We formulate the theory and provide several computational examples to justify both approaches, highlighting their advantages and shortcomings.
Science & Technology - Other Topics↗
Fortran IV program for calculation of thermodynamic data
Fortran IV program for calculating thermodynamic functions, fitting them to empirical equations, and calculating heats of formation and equilibrium constants
THERMODYNAMICS↗
Specific Hardening Function Definition and Characterization of a Multimechanism Generalized Potential-based Viscoelastoplasticity Model
Given the previous complete-potential structure framework together with the notion of strain- and stress-partitioning in terms of separate contributions of several submechanisms (viscoelastic and viscoplastic) to the thermodynamic functions (stored energy and dissipation) a detailed viscoelastoplastic multimechanism characterization of a specific hardening functional form of the model is presented and discussed. TIMETAL 21S is the material of choice as a comprehensive test matrix, including creep, relaxation, constant strain-rate tension tests, etc. are available at various temperatures. Discussion of these correlations tests, together with comparisons to several other experimental results, are given to assess the performance and predictive capabilities of the present model particularly with regard to the notion of hardening saturation as well as the interaction of multiplicity of dissipative (reversible/irreversible) mechanisms.
Arnold, S. M.↗
High-temperature mass spectrometry - Vaporization of group 4-B metal carbides
The high temperature vaporization of the metal-carbon systems TiC, ZrC, HfC, and ThC was studied by the Knudsen effusion - mass spectrometric method. For each system the metal dicarbide and tetracarbide molecular species were identified in the gas phase. Relative ion currents of the carbides and metals were measured as a function of temperature. Second- and third-law methods were used to determine enthalpies. Maximum values were established for the dissociation energies of the metal monocarbide molecules TiC, ZrC, HfC, and ThC. Thermodynamic functions used in the calculations are discussed in terms of assumed molecular structures and electronic contributions to the partition functions. The trends shown by the dissociation energies of the carbides of Group 4B are compared with those of neighboring groups and discussed in relation to the corresponding oxides and chemical bonding. The high temperature molecular beam inlet system and double focusing mass spectrometer are described.
Stearns, C. A.↗
Thermodynamic Data to 20,000 K For Monatomic Gases
This report contains standard-state thermodynamic functions for 50 gaseous atomic elements plus deuterium and electron gas, 51 singly ionized positive ions, and 36 singly ionized negative ions. The data were generated by the NASA Lewis computer program PAC97, a modified version of PAC91 reported in McBride and Gordon. This report is being published primarily to document part of the data currently being used in several NASA Lewis computer programs. The data are presented in tabular and graphical format and are also represented in the form of least-squares coefficients. The tables give the following data as functions of temperature : heat capacity, enthalpy, entropy Gibbs energy, enthalpy of formation, and equilibrium constant. A brief discussion and a comparison of calculated results are given for several models for calculating ideal thermodynamic data for monatomic gases.
Gordon, Sanford↗
ThermoBuild: Online Method Made Available for Accessing NASA Glenn Thermodynamic Data
The new Web site program "ThermoBuild" allows users to easily access and use the NASA Glenn Thermodynamic Database of over 2000 solid, liquid, and gaseous species. A convenient periodic table allows users to "build" the molecules of interest and designate the temperature range over which thermodynamic functions are to be displayed. ThermoBuild also allows users to build custom databases for use with NASA's Chemical Equilibrium with Applications (CEA) program or other programs that require the NASA format for thermodynamic properties. The NASA Glenn Research Center has long been a leader in the compilation and dissemination of up-to-date thermodynamic data, primarily for use with the NASA CEA program, but increasingly for use with other computer programs.
McBride, Bonnie↗
Infrared spectra of molecules and materials of astrophysical interest
The Raman spectra of gaseous, liquid and solid, and infrared spectra of gaseous and solid isopropylamine-d sub 0 and -d sub 2 was investigated between 4000 and 50 cm superscript -1. Differences between the spectrum of the solid phase and that of the fluid phases were interpreted in terms of an equilibrium between low energy s-trans and high energy gauche conformers, and a complete vibrational assignment was proposed for the s-trans conformer. The far infrared spectra of the gaseous compounds contained bands due to the asymmetric amino and coupled methyl torsions; the assignment of these bands was aided by observation of a number of two quantum transitions for each vibrational mode. The asymmetric potential functions were calculated, which resulted in values for the enthalpy differences between conformers in the gaseous phase of 446 and 523 callmole for the sub 0 -d and -d sub 2 compounds, respectively. The methyl torsional potential function of isopropylamine-d sub 0 was calculated which led to a value for the barrier height to internal rotation of the methyl rotors of 4.23 + or - 0.06 kcal/mole. Values for the ideal gas thermodynamic functions were calculated over a range of temperatures.
Durig, J. R.↗
BMINN: Learning chemical potentials and parameters from voltage data for multi-phase battery modeling
Free-energy landscapes and chemical potentials govern the dynamics of phase transitions, transport, and stability in functional materials, yet they remain experimentally inaccessible under realistic operating conditions. Here we introduce a Bayesian model-integrated neural network (BMINN) that embeds physics-based formulations of non-autonomous partial differential-algebraic equations into probabilistic learning. This approach reconstructs hidden thermodynamics directly from macroscopic current-voltage data, providing quantitative access to metastable states, staging transitions, and energy barriers without synchrotron probes. Demonstrated on lithium-graphite electrodes, BMINN recovers full Gibbs free-energy landscapes with fidelity validated against operando X-ray diffraction. The framework generalizes across dynamical regimes, enabling accurate voltage prediction, internal state estimation, and inference of governing parameters. Beyond batteries, BMINN exemplifies a broadly applicable strategy for learning missing physics in multiphase, non-equilibrium systems, offering a new pathway to uncover hidden thermodynamic functions across condensed matter and materials physics.
25 ENERGY STORAGE↗
Second and third virial coefficients for hydrogen
Second and third virial coefficients for parahydrogen have been derived from closely spaced PVT data from 24 to 100 "K. They are in good agreement at 100 OK with published data for normal hydrogen. Analytical representations of the combined data from about 20 to 423 "K are presented which may be useful in computation of thermodynamic functions of the gas. These formulas are related to those resulting from the use of the Lennard-Jones potential.
HYDROGEN↗
New Dimension in Ab Initio Electronic Structure Theory: Temperature, Pressure, and Chemical Potential
Ab initio electronic structure theory has transformed gas-phase molecular science with its predictive ability. In the attempt to bring such predictive ability to macroscopic systems and condensed matter, the theory must integrate quantum mechanics with statistical thermodynamics, so that thermodynamic functions such as free energy, internal energy, entropy, and chemical potentials are computed as functions of temperature in a systematically converging series of approximations. Here, a general, versatile strategy of elevating ab initio electronic structure theory to nonzero temperatures is introduced and discussed.
74 ATOMIC AND MOLECULAR PHYSICS↗
Thermodynamic properties of “near-perfect” gas
When applied thermodynamics requires simple representations of thermodynamic quantities, one often finds quantities such as pressure and the thermal energy density expressed as a monomial linear product of density and temperature power laws. This is a simple generalization of the product of density and temperature used for the perfect gas that admits a broader range of thermodynamic behavior into analytic fluid calculations or provides an analytic form that is readily fit to tabulated equation-of-state data for an arbitrary material. This paper reviews the thermodynamic properties of this generalized perfect-gas model, treating it as a class of “near-perfect-gas” models that are defined and unified here, for the first time, through a shared Helmholtz free energy. This generalization from perfect to near-perfect-gas models preserves some perfect-gas properties (e.g., constant adiabatic exponents) but not others (e.g., constant specific heats) and is constrained by thermodynamic consistency. It is important to be aware of the properties of this class of near-perfect-gas models when using them as surrogates for real nonperfect materials that may have properties that cannot be captured by near-perfect-gas models.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Certain problems in the thermodynamics of the critical point <nekotoryye voprosy termodinamiki kriticheskoy tochki<
Taylor series expansion in powers of deviation from critical point for integral thermodynamic functions
INTEGRAL FUNCTION↗
Maxwell relations in the statistical atom model.
Independent differential relationship, virial theorem and linear dependence set among thermodynamic functions in statistical atom model for arbitrary temperature
Gilvarry, J. J.↗