A pattern recognition optimization scheme coupled with a quasiharmonic lattice dynamics method is used to determine the minimum energy structures and magnetic orientations of solid oxygen. It is shown that the magnetic interaction is responsible for the stability of α-O2 with respect to β-O2 at zero temperature and pressure. The calculated α-O2 lattice parameters, magnetic orientations, and sublimation energy are in good agreement with experiment. Phonon dispersion curves are calculated at k ≠ 0 and the acoustic sound velocities are determined. The rms translational and orientational fluctuations from equilibrium are also calculated. The β-O2 phase is described by constraining the magnetic moments so that the magnetic Hamiltonian preserves the hexagonal symmetry of the crystal. The calculated lattice parameters are in good agreement with experiment and a three sublattice, quasihelical magnetic orientation is predicted from structural and energetic considerations.

Properties of argon adlayers deposited on a graphite substrate are calculated using a high resolution Monte Carlo calculation. Nine different surface densities are examined ranging from very partial to slightly beyond a complete monolayer. At low densities the calculated specific heats show two peaks. One is very sharp and one is broad. The sharp peak is shown to signal on orientational transition of the adlayer, and the broad one signals melting. The melting curve is calculated and compared with experiments, as are the lattice parameters at various temperatures. It is shown that second layer promotion plays an important role in the behavior of adlayers at some densities and temperatures. The orientational angle of the adlayer, with respect to the sublattice, is determined at various temperatures, and it is argued that the rotational transition is due to the relaxation of stress on the adlayer. It is found that the rotational transition disappears when the surface density increases beyond about 84% of that of a complete monolayer. This is in accord with experimental evidence. In order to identify and characterize the features of adlayers, various order parameters and probability distributions are calculated.

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This calculation examines the properties of partial monolayers of argon deposited on graphite, over an interval 20< or =T< or =90 K. In particular, we focus upon the phase transitions. Two peaks in the specific heat are found. The first peak is very sharp and narrow. It has been identified as a rotation of the adlayer from an angle off the substrate symmetry axis, to that axis. The calculated orientational behavior is compared with predictions of the two dimensional Ising model. The broad peak around 49.5 K is identified as a melting transition which is characterized by a loss of local sixfold symmetry.

A quenched disordered hcp phase of solid nitrogen has been studied as a function of pressure (up to 20 kbar), in the temperature region where a dynamical crossover is observed between nearly free rotations and activated tumbling motion. At low pressure the crystal structure below the crossover temperature remains hcp with the molecular orientations frustrated due to the incompatibility the strong quadrupolar interactions with a hexagonal lattice. At higher pressure (p greater than or equal to 10 kbar) this frustrated structure is unstable and transforms into an orthorhombic structure. We conclude that pressure suppresses the frustrated state observed at zero pressure. This glassy system, with increasing pressure, relaxes into a metastable 2-sublattice structure with a herringbone (out of plane) order.

The thermodynamic stability of the low temperature α, γ, and ε phases of nitrogen is examined using an energy minimization technique. Three of the most successful potential forms available are studied and the results are not satisfactory. A recent potential form is modified by optimizing its parameters to seek agreement with experiment. This search yields phase transitions between the α, γ, and ε phases that are in good agreement with experiment, as are other important thermodynamic properties. The reason for this success is explained.

The microscopic character of melting for quasi–two dimensional N2adlayers on graphite is examined for surface densities 0.2 ≤ ρ ≤ 1, where the upper limit corresponds to a complete monolayer. A Monte Carlo method, with the multiple histogram procedure, is employed to determine various thermodynamic quantities. Using the calculated specific heats and selected order parameters, determined at various surface densities, the mechanism for melting is shown to be vacancy mediated. The somewhat unusual behavior of the melting temperature versus density is shown to be entirely due to the vacancy concentration and their topology. Because this is determined by the free energy, our analysis should be general. Preliminary results for Xe on graphite supports this claim.

The transition between fcc and hcp solid phases of N2 is examined by calculating their Helmholtz free energies using the Monte Carlo method. This shows that the transition occurs at about 41 K, with an entropy change very close to the experimental value. No plastic phase intermediate between the α and β structures is indicated. However, within a few degrees of the transition, orientational exchange of the molecules from one body diagonal to another commence. Another precursor to the transition are considerably increased orientational fluctuations.

A methodology of the free energy computer simulations in the application to realistic models of molecular crystals has been presented. It is based on the symmetry properties of solid phases and a definition of the reversible path between then. Examples of calculations for nitrogen and carbon dioxide solid states have been used to illustrate advantages of the approach.

Monte Carlo simulations that utilize an (N, P, T) ensemble with periodic deformable boundary conditions cannot describe phase transitions properly when a large potential barrier is involved. An alternative method is to calculate the Gibbs free energy difference between phases; the transition occurs when the difference is equal to zero. The Gibbs free-energy difference can be calculated using a generalized free-energy method. This method is used to determine theβ-δ phase transition of solid nitrogen at room temperature. The Gibbs freeenergy difference between theβ and theδ phase was obtained at 4.0 GPa. The difference at other pressures could be determined with the equation of state. The transition pressure was found at about 6.2 GPa, 1.3 GPa above the experimental pressure.

The α–β phase transition in solid N2 has been investigated using the constant pressure Monte Carlo method. This is accomplished by examining both phases in the temperature range 25≤T≤50 K, where they are everywhere at least metastable. It is found that the cubic α phase undergoes an orientational order–disorder transition into a disordered cubic phase as the temperature is increased to T=41 K, and remains in this state until melting. Similarly the orientationally disordered hexagonal phase persists from melting down to 33 K, where it undergoes a transition into a hexagonal structure with short-range orientational order.

Techniques are developed to calculate the pressures and temperatures at which solid–solid phase transitions occur. In particular, attention is focused upon those transitions in which standard methods are inadequate. These include transitions between phases for which large hysteresis exists and/or at high temperatures, where entropy contributions to the free energy may be important. These techniques are applied to solid N2O and CO2. Specific results and comparison with experiments are given.

The main thrust of this work was directed to the task of determining the thermodynamic behavior of condensed solids and fluids containing simple molecules. Properties calculated include specific heats, equations of state, compressibilities, sound velocities, virial coefficients, viscosities, and thermal expansion. In addition, details of the structural, orientational, and magnetic phase transitions were determined. Dynamical quantities calculated include the lattice, libron, and vibron mode frequencies at various pressures and temperatures. Also, we developed new techniques required to meet our objectives. One was a method for accurately calculating the Gibbs free energy of various phases. Another is the multiple-histogram Monte Carlo which can dramatically reduce computing time and can provide a continuous map of thermodynamic averages over a range of some thermodynamical variable.

Free-energy techniques are generalized to calculate phase transitions in solids at high pressures, using the constant-pressure Monte Carlo method with periodic, deformable boundary conditions. The procedures are then applied to CO2, and a room-temperature phase transition is found at P(t)=4.43+/-0.01 GPa, into an orthorhombic Cmca structure. The volume and entropy change on transition is found to be DELTAV=0.35 cm3/mole and DELTAS=0.07+/-0.14 cal/mol K.

Previously developed methods that determine properties of a system over a range of thermodynamic points, using information accumulated at a single point, are summarized, as is an extension called the multiple histogram method. These strategies are applied to Monte Carlo calculations of melting for N 2 adlayers on graphite. The results are used to show the utility of the multiple histogram method and the inadequacy of the single point method for this application to a physical system.

Techniques are developed for calculating phase transitions in solids where entropy contributions to the Gibbs free energy may be important and/or where large potential barriers between competing phases exist. These methods are applied to solid N2O, CO2, and N2. Results are described.