Wall and boundary free energies

The existence of wall or boundary free energies is discussed generally and analyzed explicitly for general lattice systems with scalar (real-valued) spin variables. For systems with ferromagnetic (positive) spin interaction potentials,K, in the bulk andW, for the walls, correlation inequalities and appropriate stability and tempering conditions are used to establish the existence and uniqueness of the limiting free energy per unit area,f _x(K,W), of an infinite planar wall.     

Wall and boundary free energies

The asymptotic free energy of a planar wall with potentialsW, cut in scalar spin systems, with ferromagnetic interactionsK, enclosed in general domains subject to reasonable shape conditions, is shown (under conditions used in Part I) to exist and to be equal to the unique limiting wall free energy,f _x(K,W), of simple rectangular or box domains. Similar results are found for sets of walls forming the complete boundaries of domains; for subfree walls bulk plus a uniquely-defined surface term. Some limited results for periodic boundary conditions are reported.     

Complex free energies and metastable lifetimes

For two simple models we consider the analytic continuation of the free energy across a first-order phase transition. For each system we also study an associated stochastic dynamics and decay rates for passage to the stable equilibrium. We then investigate the relation between the imaginary part of the free energy and the decay rate per unit volume.Supported in part by U.S.-Israel Binational Science Foundation and by National Science Foundation Grant MCS 77-20683.Alfred P. Sloan Research Fellow. On leave from Indiana University, Bloomington, Indiana.     

Equilibrium free energies from nonequilibrium metadynamics

In this Letter we propose a new formalism to map history-dependent metadynamics in a Markovian process. We apply this formalism to model Langevin dynamics and determine the equilibrium distribution of a collection of simulations. We demonstrate that the reconstructed free energy is an unbiased estimate of the underlying free energy and analytically derive an expression for the error. The present results can be applied to other history-dependent stochastic processes, such as Wang-Landau sampling.     

Interface free energies in p-spin glass models

The replica method is used to calculate the interface free energy associated with the change from periodic to antiperiodic boundary conditions in finite-dimensional p-spin glass models in the phase which at mean-field level has one-step replica symmetry breaking (1RSB). In any finite dimension the interface free energy is exponentially small for a large system. This result implies that, in finite dimensions, the 1RSB state does not exist, as it is destroyed by thermal excitation of arbitrarily large droplets. The implications of this for the theory of structural glasses are discussed.     

Core-electron binding energies in free and supported metal clusters

Core-electron binding energy shifts in free and supported clusters are discussed using the Born-Haber formalism. For grounded clusters this approach shows that the shift reflects the decrease in the average atomic cohesive energy of the cluster relative to that of the bulk metal. This shift is closely related to the surface-atom core level shift. For free clusters there is a second term reflecting the unit charge left on the cluster by the emission of the photoelectron. In small clusters this term results in the suppression of conduction electron screening. Clusters supported on amorphous carbon remain charged in the final-state, and are similar to free clusters, but have smaller shifts because the substrate reduces the energy of the final state by forming an image charge. The shift in monolayer islands on metallic substrates is determined largely by the adsorption enthalpy of the adatoms.     

Direct determination of free energies of colloidal dispersions

Helmholtz free energies of electrostatically-stabilized colloidal dispersions of monodispersed spherical particles have been obtained using computer experiments. Boltzmann sampling has been shown to be sufficient for determining free energy differences between two dispersions whose pair-potentials are close to each other. Non-Boltzmann sampling has been used when the pair-potentials differ substantially. These results have been compared with the results based on perturbation theory. The techniques used, thus, offer a direct method to test the latter.     

Optimized free energies from bidirectional single-molecule force spectroscopy

An optimized method for estimating path-ensemble averages using data from processes driven in opposite directions is presented. Based on this estimator, bidirectional expressions for reconstructing free energies and potentials of mean force from single-molecule force spectroscopy-valid for biasing potentials of arbitrary stiffness-are developed. Numerical simulations on a model potential indicate that these methods perform better than unidirectional strategies.     

Intrinsic rates and activation free energies from single-molecule pulling experiments

We present a unified framework for extracting kinetic information from single-molecule pulling experiments at constant force or constant pulling speed. Our procedure provides estimates of not only (i) the intrinsic rate coefficient and (ii) the location of the transition state but also (iii) the free energy of activation. By analyzing simulated data, we show that the resulting rates of force-induced rupture are significantly more reliable than those obtained by the widely used approach based on Bell's formula. We consider the uniqueness of the extracted kinetic information and suggest guidelines to avoid over-interpretation of experiments.     

A note on non-equilibrium work fluctuations and equilibrium free energies

We consider in this paper, a few important issues in non-equilibrium work fluctuations and their relations to equilibrium free energies. First we show that the Jarzynski identity can be viewed as a cumulant expansion of work. For a switching process which is nearly quasistatic the work distribution is sharply peaked and Gaussian. We show analytically that dissipation given by average work minus reversible work W_R, decreases when the process becomes more and more quasistatic. Eventually, in the quasistatic reversible limit, the dissipation vanishes. However the estimate of p, the probability of violation of the second law given by the integral of the tail of the work distribution from −∞ to W_R, increases and takes a value of 0.5 in the quasistatic limit. We show this analytically employing Gaussian integrals given by error functions and the Callen-Welton theorem that relates fluctuations to dissipation in process that is nearly quasistatic. Then we carry out Monte Carlo simulation of non-equilibrium processes in a liquid crystal system in the presence of an electric field and present results on reversible work, dissipation, probability of violation of the second law and distribution of work.     

Antiphase boundary formation energies in L10 and L11 superstructures

We described an approach suitable for obtaining an analytical expression for the energy of an antiphase boundary in an ordered alloy in the hard sphere model using pair interatomic interaction potentials. Depending on the orientation of the antiphase boundary, the crystal is subdivided into two-dimensional monatomic packings parallel to the defect, and its energy is determined by the sum of the energies of the two-dimensional packings. The results of the calculations for antiphase boundaries of different orientations are given in the form of matrix expressions for each of the considered superstructures.Altai Polytechnical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 68–72, March, 1993.     

Solid/liquid interfacial free energies in binary systems

The interfacial segregation and the free energy of segregation for solid/liquid interfaces between binary solutions are computed for the (111) boundary of face-centered-cubic crystals. A lattice-liquid interfacial model and pair-bonded regular solution model are employed in the treatment with an accommodation for liquid interfacial entropy. It is concluded that the zone of compositional transition across the interface is generally a few atomic layers in width and is moderately narrower for ideal solutions. The free energy of the segregated interface depends primarily upon the solid composition and the heats of fusion of the component atoms, the composition difference of the solutions, and the difference of the heats of mixing of the solutions. Master plots are presented for predicting the segregation and interfacial free energies in general binary systems.     

Equilibrium free energies from nonequilibrium measurements using maximum-likelihood methods

We present a maximum likelihood argument for the Bennett acceptance ratio method, and derive a simple formula for the variance of free energy estimates generated using this method. This derivation of the acceptance ratio method, using a form of logistic regression, a common statistical technique, allows us to shed additional light on the underlying physical and statistical properties of the method. For example, we demonstrate that the acceptance ratio method yields the lowest variance for any estimator of the free energy which is unbiased in the limit of large numbers of measurements.     

Interfacial free energies and solute diffusivities from data on Ostwald ripening

Using recent theoretical modifications of the kinetic constants characterizing Ostwald ripening, it is demonstrated that accurate values of the interfacial free energy, , and solute diffusivities, D, can be obtained from experimental data when the kinetics of particle growth are measured in conjunction with independent measurements of either the decrease of the matrix supersaturation or the increase in volume fraction with aging time. The accuracy of is limited only by the assumption that the matrix phase is an ideal solid solution, and is effectively independent of the influence of equilibrium volume fraction, _e, on the kinetics of coarsening. Analyses of the available data on the coarsening of -type (Ni₃X) precipitates in binary Ni–Al, Ni–Si and Ni–Ti alloys yield values of =6.9±0.3, 10.2±3.0 and 13.0 mJ/m², respectively, assuming ideal solution thermodynamics; a more realistic thermodynamic model for the Ni–Al solid solution raises the value of in Ni–Al alloys to 8.1±0.2 mJ/m². Proportional increases probably obtain in the other two alloys. The accuracy with which D can be evaluated from comparable data depends theoretically on _e. However, analyses of the same data yield values of D in very good agreement with the results of conventional diffusion experiments. This is consistent with the absence of an effect of _e on the kinetics of Ostwald ripening in these alloys over the ranges of _e investigated.     

Inequalities for magnetic-flux free energies and confinement in lattice gauge theories

Rigorous inequalities among magnetic-flux free energies of tori with varying diameters are derived in lattice gauge theories. From the inequalities, it follows that if the magnetic-flux free energy vanishes in the limit of large uniform dilatation of a torus, the free energy must always decrease exponentially with the area of the cross section of the torus. The latter property is known to be sufficient for permanent confinement of static quarks. As a consequence of this property, a lower bound V(R) ? const · R for the static quark-antiquark potential is obtained in three-dimensional U(N) lattice gauge theory for sufficiently large R.     

Relative grain boundary free energy and surface free energy of some metals and alloys

By the method of thermal etching measurements were carried out of the ratio of grain boundary free energy _GB to the surface free energy _s in silver, copper, nickel, gamma-iron and cobalt of 99·999 pct. purity each, three copper-aluminium alloys and eight nickel-cobalt alloys, the total concentration of impurities in each alloy not exceeding 0·01 pct, as a function of the temperature and sometimes of the annealing medium.     

Upper bounds on free energies in terms of hard-sphere results

The Gibbs-Bogoliubov inequality is used to develop a first-order perturbation theory that provides an upper bound on the free energy. Charged systems as well as a system of Lennard-Jones particles are discussed, and detailed numerical estimates of the bounds are presented.