Howard Reiss

Statistical Mechanics of Rigid Spheres

An equilibrium theory of rigid sphere fluids is developed based on the properties of a new distribution function G(r) which measures the density of rigid sphere molecules in contact with a rigid sphere solute of arbitrary size. A number of exact relations which describe rather fully the functional form of G(r) are derived. These are based on both geometrical considerations and the virial theorem. A knowledge of G(a) where a is the diameter of a rigid sphere enables one to arrive at the equation of state. The resulting analytical expression which is exact up to the third virial coefficient gives the fourth virial coefficient within 3% and the fifth, insofar as it is known, within 5%. Furthermore over the entire range of fluid density, the equation of state derived from theory agrees with that computed using machine methods. Theory also gives an expression for the surface tension of a hard sphere fluid in contact with a perfectly repelling wall. The dependence of surface tension on curvature is also given. ...

Aspects of the Statistical Thermodynamics of Real Fluids

By extending the ideas previously applied to the statistical mechanical theory of hard sphere fluids of Reiss, Frisch, and Lebowitz, an approximate expression has been determined for the work of creating a spherical cavity in a real fluid. In turn the knowledge of this entity permits an evaluation of properties such as the surface tension and the normal heats of vaporization of fluids and the Henrys law constants of fluid mixtures. The agreement between the calculated and experimental properties is satisfactory.

Chemical Effects Due to the Ionization of Impurities in Semiconductors

This paper contains a theoretical account of the possible effects which the ionization of donor and acceptor impurities can induce in the thermodynamic phase relations involving their solutions with semiconductors. These effects reflect the energy band structure of the semiconductor. Furthermore, the phenomenon has an interest of its own, for within a certain range of experimental conditions the effects can be attributed to a chemical‐like, mass action behavior of the electrons which play the roles of negative ions.Section V is a brief discussion of a fine point concerning the Fermi level. It is shown that although the Fermi level is certainly the electronic electrochemical potential, it is not the Gibbs free energy per electron unless the density of electron energy levels is linear in the volume of the system.This paper contains a theoretical account of the possible effects which the ionization of donor and acceptor impurities can induce in the thermodynamic phase relations involving their solutions with semiconductors. These effects reflect the energy band structure of the semiconductor. Furthermore, the phenomenon has an interest of its own, for within a certain range of experimental conditions the effects can be attributed to a chemical‐like, mass action behavior of the electrons which play the roles of negative ions.Section V is a brief discussion of a fine point concerning the Fermi level. It is shown that although the Fermi level is certainly the electronic electrochemical potential, it is not the Gibbs free energy per electron unless the density of electron energy levels is linear in the volume of the system.

Theory of the Heats of Mixing of Certain Fused Salts

A theory is presented for the heats of mixing of fused salts. This theory is based on an assumption made in earlier work that the short‐range potential between ions of like sign can be ignored. The development is essentially a conformal solution treatment modified to apply to the special potentials involved in fused salts. The predicted form for the heat of mixing agrees with that discovered by Kleppa and Hersh in connection with measurements on mixtures of alkali nitrates.

Oxygen precipitation and stacking‐fault formation in dislocation‐free silicon

The kinetics of the growth of Frank interstitial stacking‐fault loops formed as a result of oxygen precipitation at high temperatures in bulk dislocation‐free silicon have been measured over a temperature range 1000–1200 °C. From TEM observations at early and later stages of stacking‐fault formation, it is concluded that the fault can be nucleated at a precipitate particle (assumed to be SiO2) by either interstitial collapse or by a dislocation reaction involving a perfect dislocation dissociating to form a Shockley and Frank partial. Once nucleated, the fault grows by (1) oxygen diffusing to the central precipitate and (2) interstitials, formed to accommodate the large volume change accompanying precipitation, migrating to the stacking fault causing it to grow. A detailed model of the growth of a precipitate and its related fault involving several steps in series has been worked out in the Appendix. The assumptions underlying this derivation have been treated in the Appendix and the preceding paper. The ...

Scaled Particle Theory of Fluids

A statistical thermodynamic theory has been developed employing distance scaling as a coupling procedure. This is an extension to real fluids of the technique applied by Reiss, Frisch, and Lebowitz to rigid‐sphere systems. One considers molecules interacting with pair potential u(r), except for one particle which interacts with potential u(r/λ). This single particle, essentially a scaled version of a normal molecule, is termed a λ‐cule. It is convenient to restrict discussion to potentials with rigid cores at r=a and cutoffs at γa. Attention is focused on a function, θ(λ, ρ, T), which reduces to G of footnote reference 1 in the case of rigid spheres. The pressure, chemical potential, and work of expanding a λ‐cule are simply related to θ. One can write θ exactly for λ<1/2γ and simple connection conditions hold at λ=1/2γ. An integral condition and λ=∞ condition on θ also exist. While θ is not completely specified, the foregoing conditions determine much of its behavior.

Precipitation of lithium in germanium

Abstract The precipitation of lithium in germanium has been studied by resistivity methods. The kinetics of precipitation follow an exponential (time) 3 2 law with constants predicted by theory. This indicates that the precipitate particles are approximately spherical. Considerable evidence is found that nucleation centers are vacant germanium lattice sites.

Refined Theory of Ion Pairing. I. Equilibrium Aspects

This paper contains a detailed theory of ion pairing based on the viewpoint that the distribution of pairs is more fundamental than the density of ions in an ionic atmosphere. This distribution is then evaluated by considering the kinetic mechanism by means of which pairs exchange partners. The functions so derived, besides being applicable to nonequilibrium situations, are free of many of the inconsistencies which attend the simple theory of pairing based on mass action considerations. The present paper restricts attention to the properties at equilibrium.

Theory of the Ionization of Hydrogen and Lithium in Silicon and Germanium

This paper contains an effective mass‐quantum mechanical investigation of the ionizability of interstitial hydrogen and lithium in germanium and silicon. It is concluded that hydrogen should not ionize while lithium should. This seems in accord with experimental findings.

On the composition of nuclei in binary systems

It is shown that some past thermodynamic treatments of the so‐call ’’classical’’ nucleus for nucleation in a liquid–liquid miscibility gap have neglected certain important terms. These occur in the chemical potential and are associated with the dependence of interfacial tension on composition. A careful thermodynamic development is presented which yields the more complete result. In 1959 Cahn and Hilliard (CH) presented a thermodynamic theory for the nucleus based on the use of ’’gradient’’ terms in the interfacial transition zone in place of the conventional interfacial tension. The properties of their nucleus differed appreciably from those of what they termed the ’’classical’’ nucleus in connection with which more conventional interfacial concepts are used. For example, at the spinodal, the CH nucleus has no free energy of formation and is of infinite size with a composition infinitesimally different from that of the parent solution while the ’’classical’’ nucleus requires finite free energy, has finit...