A formal physical cluster theory for an imperfect gas, valid for an arbitrary definition of a ``physical cluster,'' is described The role of the definition of the physical cluster is stressed For a particular definition of the physical cluster, which may be appropriate in nucleation theory, the Helmholtz free energy of 13‐, 43‐, 60‐, 70‐, 80‐, 87‐, and 100‐atom argon clusters is calculated in the classical limit for temperatures ranging from absolute zero to 100°K using Monte Carlo techniques It is found that a cluster's free energy is almost independent of its definition provided that the definition is reasonable and the temperature is sufficiently low The results are compared with the predictions using the harmonic approximation

Theory and Monte Carlo simulation of physical clusters in the imperfect vapor

The general expressions, valid for any potential, for the calculation of elastic constants through computer simulation are given. At zero temperature, the elastic constants are found to be the sum of a generalization of the Born term and a term accounting for internal relaxations that arise when a system with more than one atom in the primitive unit cell is strained. The fluctuation formulae used in finite temperature simulations are found to be straightforward generalizations of those used for pair potentials. The connection between the finite‐temperature and zero‐temperature methods is also made.

Generalized expressions for the calculation of elastic constants by computer simulation

In order to understand the static and dynamic bases of macroscopic fracture mechanics, we study flawed microscopic crystals obeying Newton's equations of motion. The particles in these crystals interact with truncated Hooke's-law forces. The static results for energy, entropy, stress concentration, and crack structure are all consistent with expectations from macroscopic elasticity theory. Dynamic theory is less well developed. Our dynamic results illustrate the importance of surface energy and nonlinear terms in the interparticle forces in influencing crack morphology and propagation velocity. The propagating cracks, except in crystals preloaded nearly to the theoretical tensile strength, travel at speeds somewhat less than the long-wavelength Rayleigh surface-wave speed.

http://williamhoover.info/Scans1970s/1976-1.pdf

Microscopic fracture studies in the two-dimensional triangular lattice

A method for calculating thermodynamic properties of clusters from knowledge of a sample of minima on the potential energy surface using a harmonic superposition approximation is extended to incorporate anharmonicity using Morse correction terms to the density of states. Anharmonicity parameters are found for different regions of the potential energy surface by fitting to simulation results using the short‐time averaged temperature as an order parameter. The resulting analytical expression for the density of states can be used to calculate many thermodynamic properties in a variety of ensembles, which accurately reproduce simulation results. This method is illustrated for 13‐atom and 55‐atom Lennard‐Jones clusters.

/pdf/calculation-of-thermodynamic-properties-of-small-lennard-4qwcaj7gp3.pdf

Calculation of thermodynamic properties of small Lennard‐Jones clusters incorporating anharmonicity

Many crystals, such as those of metals, can transform from one symmetry into another having lower free energy via a diffusionless transformation. Here we create binary colloidal crystals consisting of polymer microspheres, pulled together by DNA bridges, that induce specific, reversible attractions between two species of microspheres. Depending on the relative strength of the different interactions, the suspensions spontaneously form either compositionally ordered crystals with CsCl and CuAu-I symmetries, or disordered, solid solution crystals when slowly cooled. Our observations indicate that the CuAu-I crystals form from CsCl parent crystals by a diffusionless transformation, analogous to the Martensitic transformation of iron. Detailed simulations confirm that CuAu-I is not kinetically accessible by direct nucleation from the fluid, but does have a lower free energy than CsCl. The ease with which such structural transformations occur suggests new ways of creating unique metamaterials having structures that may be otherwise kinetically inaccessible.

/pdf/driving-diffusionless-transformations-in-colloidal-crystals-2f0ohj93bl.pdf

Driving diffusionless transformations in colloidal crystals using DNA handshaking

The approach of small‐crystal thermodynamic properties to the large‐crystal limit of thermodynamics is studied numerically. We calculate the number dependence of the vibrational entropy for two‐ and three‐dimensional crystallites by direct integration of the canonical partition function. A simple functional representation of the data shows that small‐crystal entropies lie within 10k of the predictions of macroscopic thermodynamics.

Alan C. Hindmarsh

Papers

Number Dependence of Small‐Crystal Thermodynamic Properties. I