R. D. Etters

Phase transitions in small clusters of atoms

The Monte Carlo method is used to calculate the average thermodynamic properties of small (N?13) clusters of atoms. All cluster sizes studied exhibit fairly sharp solid–liquid, as well as liquid–gas, transitions. In addition, some of the larger clusters also undergo structural transitions between different isomeric forms. The solid–liquid transition temperature is determined by four independent tests. The melting points predicted by these tests do not differ by more than 5%.

On the character of the melting transition in small atomic aggregates

The melting transition in small clusters of N atoms is investigated, using a biased random walk, Monte Carlo procedure. A high density of data points, with small statistical uncertainities (about 0.3%) is generated near the melting transitions Tm(N). The results show an abrupt change in physical properties near melting, but there is no evidence that the transition is either first or second order in character. Rather, the transition is more gradual. The Tm(N) for N=13, 11, 8, and 6 are 28.75, 20.0, 10.2, and 9.6K, respectively. N=6 and 8 evaporate at TB?31 K. The low temperature structures are dynamically determined to be octahedron, pentagonal bipyramid plus one, pentagonal bipyramid plus four, and icosahedron, for N=6, 8, 11, and 13, respectively.

Calculated thermodynamic properties and phase transitions of solid N2 at temperatures 0≤T≤300 K and pressures 0≤P≤100 GPa

Thermodynamic properties of solid nitrogen are calculated over a variety of isotherms and isobars using a constant pressure Monte Carlo method with deformable, periodic boundary conditions. Vibron frequencies are calculated using a simple perturbation theory. In addition, pressure–volume relations, thermal expansion coefficients, structures, and phase transition pressures and temperatures are determined. In particular, the nature of the orientational disorder in the plastic crystal phases is examined by calculating a variety of orientational order parameters.

Thermodynamic properties and phase transitions in CO2 molecular clusters

The thermodynamic properties of (CO2) N molecular aggregates of size 2 ⩽ N ⩽ 13 have been investigated. These crystallites exhibit well defined orientational order–disorder rotational transitions accompanied by a structural transition into a plastic crystallite phase. In addition, they exhibit melting and disassociation transitions. It is shown that the interpretation of experimental data, based upon dimer properties, depends crucially on these results. Equilibrium structures and orientations are also given.

Thermodynamic properties and equation of state of dense fluid nitrogen

Results of constant‐pressure Monte Carlo calculations on dense fluid nitrogen over a pressure range of 2 to 300 kbar and a temperature range of 300–3000 K are presented. From analytic fits to the calculated volumes, enthalpies and vibrational frequency shifts, a comprehensive set of thermodynamic quantities is derived, including: thermal expansivity, compressibility, specific heat, Gruneisen parameter, and speed of sound. Comparison of the theoretical results to experiment at room temperature shows very good agreement (within 0.3% in volume and 1% in speed of sound, for instance). Good agreement is also obtained with earlier simulation data. In agreement with experimental studies of fluid metals, we find that the speed of sound varies linearly with density; along isotherms as well as along the Hugoniot. We find that ργG, the density times the Gruneisen parameter, which is assumed to be a constant in an often‐used phenomenological equation of state, varies considerably with density and temperature. Compari...

Static and dynamic properties of solid CO2 at various temperatures and pressures

A constant pressure Monte Carlo formalism, lattice dynamics, and classical perturbation theory are used to calculate the thermal expansion, pressure–volume relation at room temperature, the temperature dependence of the zone center libron frequencies, and the pressure dependence of the three vibron modes of vibration, in solid CO2 at pressures 0≤p≤16 GPa and temperatures 0≤T≤300 K. The agreement with experiment is good. At room temperature the observed Pa3 phase is predicted for P≤11 GPa, above which a transition occurs into an orthorhombic Cmca structure, with a volume change upon transition of ΔV=0.4 cm3 /mol. Calculated physical quantities in this phase are consistent with experiment.

The ground state properties of spin‐aligned atomic hydrogen, deuterium, and tritium

The bulk, ground state properties of atomic hydrogen, deuterium, and tritium systems are calculated assuming that all pair interactions occur via the 3Σ+u atomic triplet potential. The conditions required to obtain this system, including inhibition of recombination through the energetically favorable singlet interaction, are discussed. The internal energy, pressure, and compressibility are calculated over the volume range 40 cm3/mole ? V ⩽200 cm3/mole applying the Monte Carlo technique with a quantum mechanical variational wavefunction. The system studied consisted of 32 atoms in a box with periodic boundary conditions. Results show that atomic triplet hydrogen and deuterium remain gasous at 0 K; i.e., the internal energy is positive at all molar volumes considered. Under the same conditions, tritium forms a liquid with a binding energy of E0 ? −0.75 K per atom, at a volume of V ? 130 cm3/mole. The pair distribution function for these systems is also calculated. A brief discussion of the predicted superfl...

Predictions for partial and monolayer coverages of O2 on graphite

Monolayer properties of O2 on graphite are calculated using a pattern recognition, optimization scheme. Equilibrium monolayers are predicted at two different densities with properties in agreement with recent x‐ray diffraction, specific heat, and neutron scattering data. Properties of the extremely low density regime are calculated using a model based upon a distribution of two‐dimensional O2 clusters. The results are consistent with experimental evidence.

A dilute hard-sphere bose-gas model calculation of low-density atomic hydrogen gas properties

The isolated pair wave equation is solved for two isolated hydrogen atoms interacting via the 3Σu+ potential, from which a scattering length a = 0.72 » is determined and used as an effective hard-core diameter in a dilute hard-sphere Bose-gas model calculation. In the low-density limit, these results for the ground state energy compare closely with earlier Monte Carlo data. Using established criteria for the values of density and temperature over which the hard-sphere model is valid, we have calculated the energy, first- and secondsound velocities, depletion factor, and superfluid transition temperature, and expressions are given for the specific heat and normal fluid fraction. The scattering length of atomic hydrogen interacting via the singlet potential is found to be 0.12 » and similar calculations for helium give a scattering length much too large to justify application of the hard-sphere model.

Predicted properties of CO monolayers on graphite

Abstract The structure and orientations of CO monolayers deposited on graphite are calculated using a pattern recognition optimization of the energy. The results were found to depend importantly on assumptions made concerning the applicability of various substrate mediated interactions that have been proposed, and on the nature of CO-CO interaction itself. Despite these uncertainties, the calculations clearly show that the low density structures are herringbone with the molecules tilting slightly out of the substrate plane. Although the registered herringbone is energetically more favorable at ϱ/ϱ0 = 1, where ϱ0 is the density at registry, than the unregistered herringbone, its thermodynamic stability depends on the magnitude of the substrate mediated interactions incorporated into the calculations. With increasing density a minimum in the energy occurs at ϱ/ϱ 0 ⋍ 1.12 . The equilibrium structure for all densities ϱ/ϱ0 ≳ 1.12 is a four sublattice pinwheel arrangement that is thermodynamically stable. Thus, these results are generally in agreement with experiment. Contrary to experiment, however, is the prediction of orientational ordering with respect to the two dissimilar ends of the molecules, and reasons for this difference are presented. Properties of small clusters of N molecules deposited on graphite, 1 ≤ N ≤ 6, are also calculated. They register on the substrate which supports evidence that registered islands of CO form in the region 0≤ϱ/ϱ0≤1.