Showing papers on "Thermal equilibrium published in 1982"
TL;DR: After assuming that the transport of molecules between phases at thermal equilibrium results primarily from single molecular events, the expression for the rate of molecular transport between phases is developed by using a first order perturbation analysis of the Schrodinger equation and the Boltzmann definition of entropy.
Abstract: After assuming that the transport of molecules between phases at thermal equilibrium results primarily from single molecular events, the expression for the rate of molecular transport between phases is developed by using a first order perturbation analysis of the Schrodinger equation and the Boltzmann definition of entropy. This leads to an Einstein‐type relation with the constant of proportionality being the average rate of exchange between microscopic states of different molecular distributions. A hypothesis is introduced which leads to the conclusion that this exchange rate is unchanged as the system moves through the molecular distributions leading to equilibrium, and to it being equal to the molecular rate of exchange between phases in the final equilibrium state. This allows a complete expression for the rate of molecular transport between phases to be developed. The validity of the hypothesis can be examined by comparing the predictions that follow from the derived rate expressions with the available experimental data. This comparison is reported in subsequent parts of this work.
163 citations
TL;DR: In this article, a quasi-equilibrium transport model for disordered materials is proposed, in which the localized states are assumed to be distributed over some energy region in the gap, and the drift term is characterized by the equilibrium trap-controlled mobility.
Abstract: A concept of mobile and localized states is used for a description of carrier transport in disordered materials. The localized states are assumed to be distributed over some energy region in the gap. Two regimes of transport are possible: quasi-equilibrium and non-equilibrium. In the present work we concentrate on the quasi-equilibrium regime. Quasi-equilibrium transport takes place under conditions of thermal equilibrium between mobile and localized carrier fractions. The quasi-equilibrium transport equation obtained has the form of a conventional Fokker-Planck equation with drift and diffusion terms. The drift term is characterized by the equilibrium trap-controlled mobility. The diffusion term is determined by a coefficient which in its turn consists of two parts. The first describes conventional trap-controlled diffusion, while the second represents the so-called ‘field diffusion coefficient’ proportional to the second power of the electric field. The field diffusion is shown to have an anoma...
102 citations
TL;DR: In this paper, the concentrations of water clusters relative to the monomer concentration in expanding water vapor flows have been determined over a range of source pressures and temperatures by mass spectrometry.
Abstract: The concentrations of water clusters (2⩽n⩽40) relative to the monomer concentration in expanding water vapor flows have been determined over a range of source pressures and temperatures by mass spectrometry. The corresponding directed flow velocities and thermal velocity distributions of the monomers and clusters of each size have been determined by mass‐filtered time‐of‐flight (velocity) spectrometry. Relative concentration generally decreases exponentially with n. Translational thermal equilibrium ∼65 K prevails for the monomers and clusters of n≲5 under all source conditions. Translational temperatures of larger clusters generally increase with increasing n. The results suggest a kinetic process in which surviving smaller clusters are formed in three‐body collisions and larger ones in two‐body collisions.
80 citations
TL;DR: In this article, the vibration and rotational state distributions of a supersonic nitric oxide beam, scattered from a Pt(111) single crystal surface, were investigated and two-photon ionization technique was applied to monitor the internal energy content of the scattered molecules.
Abstract: The vibration and rotational state distributions of a supersonic nitric oxide beam, scattered from a Pt(111) single crystal surface, were investigated. A two-photon ionization technique was applied to monitor the internal energy content of the scattered molecules. Vibrational distributions were found to be colder than that corresponding to the crystal temperature between 450--1100 K. Rotational temperatures were also found to be colder than expected for thermal equilibrium with the platinum surface.
75 citations
TL;DR: In this paper, the authors investigated self-diffusion in a classical fluid composed of two species which are distinguished through the color of their particles, either black or white, but are identical as regards their mechanical properties.
Abstract: We investigate self-diffusion in a classical fluid composed of two species which are distinguished through the color of their particles, either black or white, but are identical as regards their mechanical properties. Disregarding color the fluid is in thermal equilibrium. We show that if a single “test particle” in the one-component fluid moves asymptotically as Brownian motion, then the color density and current in certain classes of nonequilibrium states are related, on the appropriate macroscopic scale, through Fick's law, and the former is governed by the diffusion equation. If in addition several test particles move asymptotically as independent Brownian motions, then the colored fluid is, on a macroscopic scale, in local equilibrium with parameters governed by the solution of the diffusion equation.
69 citations
TL;DR: In this paper, the authors present a set of 39 determinations of heat flow and radiogenic heat production for several different geological environments in the State of New Hampshire (U.S.A.).
63 citations
TL;DR: In this article, a theory of multiple trapping with an arbitrary continuous energy distribution of trap density is used to interpret time-of-flight experiments, and it is shown that a so-called "normal" current shape occurs if the thermal equilibrium between mobile and localized carriers corresponds to a thermal equilibrium function, and a quasi-equilibrium carrier packet moves through a sample.
Abstract: A theory of multiple trapping with an arbitrary continuous energy distribution of trap density is used to interpret time-of-flight experiments. It is shown that a so-called ‘normal’ current shape occurs if an energy distribution of localized carriers corresponds to a thermal equilibrium function, and a quasi-equilibrium carrier packet moves through a sample. If the thermal equilibrium between mobile and localized carrier fractions has not time to be established earlier than that at which most of the carriers leave the sample, the current is caused by the drift of a non-equilibrium very-dispersive carrier packet. Propagation of such a packet results in so-called ‘anomalous’ behaviour of transient current characteristics. As a result of theoretical analysis of non-equilibrium and quasi-equilibrium transient current curves, a method for interpretation of experimental transient current data is suggested. This method may provide important information on the energy distribution of localized states.
48 citations
TL;DR: In this article, it was shown that the motion of a test particle in a hard sphere fluid in thermal equilibrium converges to the stochastic process governed by the linear Boltzmann equation.
Abstract: We prove that the motion of a test particle in a hard sphere fluid in thermal equilibrium converges, in the Boltzmann-Grad limit, to the stochastic process governed by the linear Boltzmann equation. The convergence is in the sense of weak convergence of the path measures. We use this result to study the steady state of a binary mixture of hard spheres of different colors (but equal masses and diameters) induced by color-changing boundary conditions. In the Boltzmann-Grad limit the steady state is determined by the stationary solution of the linear Boltzmann equation under appropriate boundary conditions.
44 citations
TL;DR: In this paper, the authors discussed linear and nonlinear susceptibilities of spin glasses in thermal equilibrium and qualitatively discussed the apparent discrepancy between theoretical results, implying lack of Edwards-Anderson order and hence a divergence of the susceptibility at zero temperature, and experiments showing a susceptibility saturating at finite values.
Abstract: Linear and nonlinear susceptibilities of spin glasses in thermal equilibrium are qualitatively discussed in terms of magnetic short-range order. The apparent discrepancy between theoretical results, implying lack of Edwards-Anderson order and hence a divergence of the susceptibility at zero temperature, and experiments showing a susceptibility saturating at finite values, is considered. It is suggested that the susceptibility must indeed have a static maximum if the system exhibits a (“frustrated”) ferromagnetic phase with a reentrant phase boundary. At the reentrancy point, some exponents of the ferromagnet take twice their normal value, and hence a crossover near this point occurs similar to multicritical points. These observations are used to interpret a number of recent experiments, and it is shown that neither of them proves the existence of a static spin glass phase. As a quantitative example of gradual onset of order without a phase transition in three-dimensional systems, numerical results for susceptibility and specific heat of the fully frustrated Ising fcc antiferromagnet at its critical field are given.
44 citations
TL;DR: The thermodynamics of an ideal relativistic quantum gas in expansion is studied in this paper, where it is shown that only for conformally invariant fields in conformally static spacetime can thermal equilibrium be strictly maintained.
35 citations
TL;DR: In this article, the authors extended the Zelovich-von Neumann-Doring (ZND) model of a one-dimensional, steady state detonation wave in a gaseous explosive to include the thermal relaxation processes which precede and follow the exothermic chemical reconstitution reactions.
TL;DR: In this article, a theoretical and experimental study of the thermally unstable behavior of graphite-to-graphite and graphite to metal contacts is presented, and it is shown that for any given size of contact there is a maximum current which may be passed safely.
TL;DR: In this paper, the free energy contribution of the acoustic degrees of freedom of high-temperature gases was investigated under nonequilibrium conditions, particularly if the acoustic fluctuations exhibit intensity levels corresponding to turbulence.
Abstract: sound oscillations has to be considered in the evaluation of the thermodynamic functions of high-temperature gases only at high densities. Gases with a considerable acoustic noise background are encountered in various high-temperature engineering systems, such as gas turbines, jet engines, rocket exhausts, etc. The theory presented permits calculation of the free energy AF of the acoustic degrees of freedom in such systems, provided that the acoustic noise is in thermal equilibrium. Considerably larger free-energy contributions are to be expected under nonequilibrium conditions, particularly if the acoustic fluctuations exhibit intensity levels corresponding to turbulence.
TL;DR: In this article, a method for the calculation of temperature in the shoe-film-rotor assembly of a thrust bearing is presented, which allows reverse flow to occur and simplifies the calculations of hot oil carry-over.
TL;DR: In this article, the charge, mass, and electron density fluctuation spectra of strongly correlated, fully ionized two-component plasmas within the framework of the Mori-Zwanzig memory function formalism are analyzed.
Abstract: Charge, mass, and electron density fluctuation spectra of strongly correlated, fully ionized two‐component plasmas within the framework of the Mori–Zwanzig memory function formalism are analyzed. All dynamical correlation functions are expressed in terms of the memory functions of the ion and electron velocity autocorrelation functions by a generalized effective field approximation which preserves the exact initial values (i.e., static correlations). The theory reduces correctly to the mean field (or collisionless Vlasov) results in the weak coupling limit, and yields charge density fluctuation spectra in good agreement with available computer simulation data, as well as reasonable estimates of the transport coefficients. The collisional damping and frequency shift of the plasma oscillation mode are sizeable, even in the long wavelength limit. The theory also predicts the propagation of well‐defined sound waves in dense plasmas in thermal equilibrium.
TL;DR: In this article, the role of vacancies and self-interstitials in self-and impurity diffusion in silicon above about 700°C is discussed and the existence and the nature of a recombination barrier slowing down the recombination process are discussed in this context.
Abstract: The paper highlights recent progress in understanding the role of vacancies and self-interstitials in self- and impurity diffusion in silicon above about 700°C. How surface oxidation of silicon leads to a perturbation of the pointdefect population is described. An analysis of the resulting oxidationenhanced or -retarded diffusion of group III and group V dopants shows that under thermal equilibrium as well as under oxidation conditions both vacancies and self-interstitials are present. For sufficiently long times vacancies and self-interstitials attain dynamical equilibrium which involves their recombination and spontaneous thermal creation in the bulk of silicon crystals. The existence and the nature of a recombination barrier slowing down the recombination process are discussed in this context. Recent experimental and theoretical results on the diffusion of gold in silicon enable us to determine the selfinterstitial component of silicon self-diffusion and to obtain an estimate of the respective vacancy contribution. The two components turn out to be of the same order of magnitude from 700°C up to the melting point.
TL;DR: In this paper, the escape of nucleons which do not take part in the thermal equilibrium is considered by including drain terms in these equations, and the energy spectra of the escaped nucleons and of the nucleons evaporated after the break up of the fluid are compared.
Abstract: The collision process is described by hydrodynamical equations. The escape of nucleons which do not take part in the thermal equilibrium are considered by including drain terms in these equations. The energy spectra of the escaped nucleons and of nucleons evaporated after the break up of the fluid are compared.
TL;DR: In this article, a general Heisenberg system in an external field is solved by a second order cumulant-cluster approximation, and the uncompatibility between the solutions of the polarization self-consistency and minimum free energy equations is discussed.
Abstract: A general Heisenberg system in an external field is solved by a second order cumulant cluster approximation. The uncompatibility between the solutions of the polarization self consistency and minimum free energy equations is discussed. A correlated mean-field is then introduced which allows the removal of such difficulty at low temperature.
TL;DR: Several reaction mechanisms have been shown to contribute to the emission of energetic light particles, ranging from the sequential statistical decay of excited projectile residues, direct breakup and knock-out reactions, to multistep emission processes that can be rather well described in terms of the concept of local thermal equilibrium as discussed by the authors.
TL;DR: In this article, stable state temperature profiles in a magnetically confined tokamak type plasma are derived by balancing Ohmic power input, thermal diffusion, and radiation, and critical values of parameters that cause the onset of a new branch or instability are determined.
Abstract: Steady‐state temperature profiles in a magnetically confined tokamak type plasma are derived by balancing Ohmic power input, thermal diffusion, and radiation. A comprehensive study is presented of the impact that different electron conductivities, K ⊥ boundary conditions, and radiation may have on thermal stability. In particular, their influence on the bifurcation in the position of the minor radius as a function of the temperature at the center T m is considered. Points of bifurcation correspond to marginally stable equilibria. However, it is also possible to have both branches without marginally stable equilibrium. Critical values of parameters that cause the onset of a new branch or instability are determined. Growth rates are not calculated, but domains of stabilty of all possible equilibria are determined. It is shown that Ohmically heated plasma in the classical scaling is thermally unstable to convective boundary conditions or if the plasma is cold at the edge. It is shown that a finite temperature at the edge will generate a stable, lower branch, but the upper branch will be unstable as long as p<0.5, where K ⊥(T)∼T p .
TL;DR: In this article, the basic equations for the kick-out mechanism of diffusion are solved numerically for the diffusion of gold in silicon at 1100°C for both in-diffusion and annealing, and analytical expressions for the solutions are given.
Abstract: The basic equations for the kick-out mechanism of diffusion are a set of non-linear differential equations. These equations are solved numerically for the diffusion of gold in silicon at 1100°C for both in-diffusion and annealing, and analytical expressions for the solutions are given. It is found that the numerical solution for the interstitial gold atoms reaches the thermal equilibrium value most rapidly. The time at which the interstitial gold atoms reach their thermal equilibrium, and the time at which the interchange reactions between substitutional and interstitial gold atoms reach a local equilibrium are obtained from the analytical expressions of the numerical solutions.
TL;DR: In this article, the authors generalized the results of broadening of the line absorption profile to a relativistic gas in thermal equilibrium by taking into account the relativism variance of the volume absorption coefficients of the gas, as derived by L.H. Thomas.
Abstract: The classical results of Doppler broadening of the line absorption profile are generalized to a relativistic gas in thermal equilibrium by taking into account the relativistic variance of the volume absorption coefficients of the gas, as derived by L.H. Thomas. This variance produces a small correction, even in the non-relativistic approximation.
TL;DR: In this paper, the effect of a radially bounding wall on a magnetically confined single-species plasma near thermal equilibrium is considered, and the boundary conditions at the wall follow from simple physical considerations.
Abstract: The effect of a radially bounding wall on a magnetically confined single‐species plasma near thermal equilibrium is considered. Solutions to the like‐particle collisional transport equation are obtained; the boundary conditions at the wall follow from simple physical considerations. Integral constraints on the plasma evolution imply that only a fraction of the plasma can ever be lost to the wall. Analytic estimates and numerical solutions give the scaled wall flux in terms of the unperturbed equilibrium density at the radius of the wall.
TL;DR: In this paper, experimental determinations of light scattering spectra and the plasma densities and temperatures deduced from these observations are compared with theory for a thermal equilibrium plasma in the range 1<α<2, (α =(kλD)-1) with plasma properties determined independently by standard spectroscopic techniques.
Abstract: Experimental determinations of light scattering spectra and the plasma densities and temperatures deduced from these observations are compared with theory for a thermal equilibrium plasma in the range 1<α<2, (α =(kλD)-1) with plasma properties determined independently by standard spectroscopic techniques. Good agreement, with experimental errors of about 10% is obtained for both parameters.
TL;DR: In this paper, an experimental demonstration is provided of a mechanism of ion heating whereby cold ions are energized by a voltage drop of a few volts near the walls of the plasma device, returned from the walls to the plasma volume in the form of fast neutral atoms and subsequently re-ionized by charge exchange.
Abstract: Ion temperatures of 0.2-0.8 eV are measured in discharge devices, rather than the approximately 0.03 eV expected from thermal equilibrium with the gas background. An experimental demonstration is provided of a mechanism of ion heating whereby cold ions are energized by a voltage drop of a few volts near the walls of the plasma device, returned from the walls to the plasma volume in the form of fast neutral atoms and subsequently re-ionized by charge exchange.
07 Jun 1982
TL;DR: In this article, the relativistic quantum electron gas embedded in a strong magnetic field is studied by calculating its covariant Wigner function in thermal equilibrium, and the polarization tensor is calculated with the use of a covariant quantum BGK equation.
Abstract: The relativistic quantum electron gas embedded in a strong magnetic field is studied by calculating its covariant Wigner function in thermal equilibrium. Previous results obtained earlier by Canuto and Chiu are then recovered in a unified way. The polarization tensor is calculated with the use of a covariant quantum BGK equation. Also the lifetime of the neutron in such a medium is calculated for the sake of illustration of the usefulness of the covariant Wigner function.
TL;DR: In this paper, the transverse:field Ising model is solved within the scheme of the generalized mean-field method earlier proposed by the authors, and the uncompatibility between the self.consistency condition and the thermal equilibrium is corrected through the introduction of a correlated mean·field, realized by a virtual field parameter.
Abstract: The transverse:field Ising model is solved within the scheme of the generalized mean·field method earlier proposed by the authors. The uncompatibility between the self.consistency condition and the thermal equilibrium is corrected through the introduction of a correlated mean·field, realized by a virtual· field parameter. Numerical results are discussed in detail, from which the specific heat and the transverse·field/critical·temperature phase boundary diagram are derived
TL;DR: In this article, the effects of inhomogeneous ripple on thermal equilibrium and stability properties are discussed, and it is qualitatively shown that this could have serious effects on thermal equilibria.
Abstract: Alpha particle losses during slowing-down in a rippled magnetic field are studied under some simplifying assumptions. In particular, it is assumed that the ripple is homogeneous over the plasma cross section. It is found that the fractions of particles and of energy that are lost are large, of the order of 40-60% and 15-30% respectively. The effects of inhomogeneous ripple are discussed, and it is qualitatively shown that this could have serious effects on thermal equilibrium and stability properties.
TL;DR: In this paper, collision-induced infrared spectroscopy has been used to measure the initial rate of the chemical exchange of equimolar D2 and T2 in liquid and solid forms from 9 to 23K over 23 to 45 h.
Abstract: Collision-induced infrared spectroscopy has been used to measure the initial rate of the chemical exchange of equimolar D2 and T2 in liquid and solid forms from 9 to 23K over 23 to 45 h. If first-order kinetics are assumed, the time constant is 100-140 h for thermal equilibrium and 160-180 h for a hot-atom equilibrium. The latter is favoured, but cannot be confirmed. Approximately three DT molecules are formed per ion pair (using the gas-phase value of 36.6 eV/ion pair). A likely mechanism is reaction of the T2+ to the T3+ ion, followed by exchange. The slowness of the exchange suggests that molecular DT can be isolated and handled for fusion applications.