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Partial configurational thermodynamic functions of interstitial species in ternary solid solutions containing substitutional and interstitial solute atoms
Subroutines, FORTRAN 4 type, were developed for calculating isentropic natural gas mass flow rate through nozzle. Thermodynamic functions covering compressibility, entropy, enthalpy, and specific heat are included.
Handbook has been compiled by Cryogenic Data Center of National Bureau of Standards. It covers thermodynamic functions, physical properties, and heat transfer data for oxygen. Handbook addresses primarily low temperature regime, but also includes some data above room temperature.
A handbook is presented of the thermodynamic functions, transport properties, and physical properties of both liquid and gaseous oxygen. A bibliography of references is included.
A structural expansion for the static ground state energy of a simple metal is derived. An approach based on single particle band structure which treats the electron gas as a non-linear dielectric is presented, along with a more general many particle analysis using finite temperature perturbation theory. The two methods are compared, and it is shown in detail how band-structure effects, Fermi surface distortions, and chemical potential shifts affect the total energy. These are of special interest in corrections to the total energy beyond third order in the electron ion interaction, and hence to systems where differences in energies for various crystal structures are exceptionally small. Preliminary calculations using these methods for the zero temperature thermodynamic functions of atomic hydrogen are reported.
A structural expansion for the static ground-state energy of a simple metal is derived. Two methods are presented, one an approach based on single-particle band structure which treats the electron gas as a nonlinear dielectric, the other a more general many-particle analysis using finite-temperature perturbation theory. The two methods are compared, and it is shown in detail how band-structure effects, Fermi-surface distortions, and chemical-potential shifts affect the total energy. These are of special interest in corrections to the total energy beyond third order in the electron-ion interaction and hence to systems where differences in energies for various crystal structures are exceptionally small. Preliminary calculations using these methods for the zero-temperature thermodynamic functions of atomic hydrogen are reported.
A model of helium adsorption on an argon crystal is built up from the premise that local adsorption predominates in the first layer and nonlocal adsorption in the second. Application of the virial expansion theorem to the second layer gives a series in which the first term represents the motion of a single molecule in the external potential field and the second a two-body interaction under this field. The thermodynamic functions of the adsorbed phase are calculated ab initio, the gas-solid interaction potential being derived from lattice summation and the partition function from an appropriate choice of a site-spacing polynomial to describe the periodic potential. The mutual interaction of adsorbed molecules is calculated with a two-dimensional Lennard-Jones potential. The second virial coefficient is calculated and its dependence on temperature and choice of potential is studied. It is found that the second virial coefficient is very well approximated by a two-dimensional gas in free space. The adsorption isotherm, isosteric heat, and specific heat are obtained and compared with the results of Ross and Steele, giving excellent agreement.
Review of the literature on the nature and extent of hydrogen interactions with metals and the role of hydrogen in metal failure. The classification of hydrogen-containing systems is discussed, including such categories as covalent hydrides, volatile hydrides, polymeric hydrides, and transition metal hydride complexes. The use of electronegativity as a correlating parameter in determining hydride type is evaluated. A detailed study is made of the thermodynamics of metal-hydrogen systems, touching upon such aspects as hydrogen solubility, the positions occupied by hydrogen atoms within the solvent metal lattice, the derivation of thermodynamic functions of solid solutions from solubility data, and the construction of statistical models for hydrogen-metal solutions. A number of theories of hydrogen-metal bonding are reviewed, including the rigid-band model, the screened-proton model, and an approach employing the augmented plane wave method to solve the one-electron energy band problem. Finally, the mechanism of hydrogen embrittlement is investigated on the basis of literature data concerning stress effects and the kinetics of hydrogen transport to critical sites.
The thermodynamic functions, transport properties, and physical properties of both liquid and gaseous hydrogen are presented. The low temperature regime is emphasized. The tabulation of the properties of normal hydrogen in both Si and engineering units is given along with the tabulation of parahydrogen.
Calculations are presented for the thermodynamic functions and phase separation boundaries of solid metallic hydrogen helium alloys at temperatures between 0 K and 19,000 K and at pressures between 15 and 90 megabars. Expressions for the band structure energy of a randomly disordered alloy (including third order in the electron ion interaction) are derived and evaluated. Short and long range order are included by the quasi-chemical method, and lattice dynamics in the virtual crystal harmonic approximation. We conclude that at temperatures below 4,000 K there is complete phase separation of hydrogen helium alloys, and that a miscibility gap remains at the highest temperatures and pressures considered. The relevance of these results to models of the deep interior of Jupiter is briefly discussed.
Calculations are presented for the thermodynamic functions and phase-separation boundaries of solid metallic hydrogen-helium alloys at temperatures between zero and 19,000 K and at pressures between 15 and 90 Mbar. Expressions for the band-structure energy of a randomly disordered alloy (including third order in the electron-ion interaction) are derived and evaluated. Short- and long-range orders are included by the quasi-chemical method, and lattice dynamics in the virtual-crystal harmonic approximation. It is concluded that at temperatures below 4000 K, there is essentially complete phase separation of hydrogen-helium alloys and that a miscibility gap remains at the highest temperatures and pressures considered. The relevance of these results to models of the deep interior of Jupiter is briefly discussed.
Monte Carlo simulation, lattice dynamics in the harmonic approximation, and solution of the hypernetted chain equation were used to study the classical two-dimensional one component plasma. The system consists of a single species of charged particles immersed in a uniform neutralizing background. The particles interact via a l/r potential, where r is the two dimensional separation. Equations of state were calculated for both the liquid and solid phases. Results of calculation of the thermodynamic functions and one and two particle correlation functions are presented.
A Monte Carlo simulation, lattice dynamics in the harmonic approximation, and solution of the hypernetted chain equation are used to study the classical two-dimensional one-component plasma. A fluid phase is found for a specified dimensionless quantity, and a solid phase for higher values of this quantity. It is reported that the solid phase shows directional long range order, noting that in the solid phase positional long range order is lost as the thermodynamic limit is approached. Finally, the results of calculations of the thermodynamic functions and one- and two-particle correlation functions are presented.
A method of structural expansions for use in determining the equation of state of metallic hydrogen (and indeed other metals) up to the 4th order in the perturbation theory was developed. The electrical and thermal transport properties of the planetary interior of Jupiter were calculated. The nature of the interaction between molecules at short range and the importance of multicenter terms in arriving at an adequate description of the thermodynamic functions of condensed molecular hydrogen were also investigated.
This report is a compilation of thermodynamic functions of 50 elements in their standard reference state. The functions are C(sub p)(sup 0), (H(sup 0)(T) - H(sup 0)(0)), S(sup 0)(T), and -(G(sup 0)(T) - H(sup 0)(O)) for the elements Ag, Al, Ar, B, Ba, Be, Br2, C, Ca, Cd, Cl2, Co, Cr, Cs, Cu, F2, Fe, Ge, H2, He, Hg, I2, K, Kr, Li, Mg, Mn, Mo, N2, Na, Nb, Ne, Ni, O2, P, Pb, Rb, S, Si, Sn, Sr, Ta, Th, Ti, U, V, W, Xe, Zn, and Zr. Deuterium D2 and electron gas e(sup -) are also included. The data are tabulated as functions of temperature as well as given in the form of least-squares coefficients for two functional forms for C(sub p)(sup 0) with integration constants for enthalpy and entropy. One functional form for C(sub p)(sup 0) is a fourth-order polynomial and the other has two additional terms, one with T(exp -1) and the other with T(exp -2). The gases Ar, D2, e(sup -), H2, He, Kr, N2, Ne, O2, and Xe are tabulated for temperatures from 100 to 20,000 K. The remaining gases Cl2 and F2 are tabulated from 100 to 6000 K and 1000 to 6000 K. The second functional form for C(sub p)(sup 0) has an additional interval from 6000 to 20,000 K for the gases tabulated to 20,000 K. The fits are constrained so that the match at the common temperature endpoints. The temperature ranges for the condensed species vary with range of the data, phase changes, and shapes of the C(sub p)(sup 0) curves.
A rapidly convergent successive approximation process is described that simultaneously determines both composition and temperature resulting from a chemical reaction. This method is suitable for use with any set of reactants over the complete range of mixture ratios as long as the products of reaction are ideal gases. An approximate treatment of limited amounts of liquids and solids is also included. This method is particularly suited to problems having a large number of products of reaction and to problems that require determination of such properties as specific heat or velocity of sound of a dissociating mixture. The method presented is applicable to a wide variety of problems that include (1) combustion at constant pressure or volume; and (2) isentropic expansion to an assigned pressure, temperature, or Mach number. Tables of thermodynamic functions needed with this method are included for 42 substances for convenience in numerical computations.
This report is a compilation of thermodynamic functions of 50 elements in their reference state. The functions are: C(sup 0, sub p), {H(T)-H(sup 0)(0)}, S(sup 0)(T), and - {G(sup 0)(T) - H(sup 0)(0)} for the elements Ag, Al, Ar, B, Ba, Be, Br2, C, Ca, Cd, Cl2, Co, Cr, Cs, Cu, F2, Fe, Ge, H2, He, Hg, I2, K, Kr, Li, Mg, Mn, Mo, N2, Na, Nb, Ne, Ni, O2, P, Pb, Rb, S, Si, Sn, Sr, Th, Th, Ti, U, V, W, Xe, Zn, and Zr. Deuterium D, and electron gas e(sup -) are also included. The data are tabulated as functions of temperature as well as given in the form of least-squares coefficients for two functional forms for C(sup 0, sub p) with integration constants for enthalpy and entropy. One functional form for C(sup 0, sub p) is a fourth-order polynomial and the other has two additional terms, one with T(sup -1) and the other with T(sup -2). The gases Ar, D2, e(sup -), H2, He, Kr, N2, Ne, O2, and Xe are tabulated for temperatures from 100 to 20 000 K. The remaining gases Cl2 and F2 are tabulated from 100 to 6000 K. The polynomial functional form for C(sup 0, sub p) for all these gases is split into two temperature intervals of 200 to 1000 K and 1000 to 6000 K. The second functional form for (sup 0, sub p) has an additional interval from 6000 to 20 000 K for the gases tabulated to 20 000 K. The fits are constrained so that the properties match at the common temperature endpoints. The temperature ranges for the condensed species vary with range of the data, phase changes, and shapes of the C(sup 0, sub p) curves.
A solution methodology has been developed to efficiently model multi-specie, chemically frozen, thermally perfect gas mixtures. The method relies on the ability to generate a single (composite) set of thermodynamic and transport coefficients prior to beginning a CFD solution. While not fundamentally a new concept, many applied CFD users are not aware of this capability nor have a mechanism to easily and confidently generate new coefficients. A database of individual specie property coefficients has been created for 48 species. The seven coefficient form of the thermodynamic functions is currently used rather then the ten coefficient form due to the similarity of the calculated properties, low temperature behavior and reduced CPU requirements. Sutherland laminar viscosity and thermal conductivity coefficients were computed in a consistent manner from available reference curves. A computer program has been written to provide CFD users with a convenient method to generate composite specie coefficients for any mixture. Mach 7 forebody/inlet calculations demonstrated nearly equivalent results and significant CPU time savings compared to a multi-specie solution approach. Results from high-speed combustor analysis also illustrate the ability to model inert test gas contaminants without additional computational expense.