Gregory Grochola

On fitting a gold embedded atom method potential using the force matching method

We fit a new gold embedded atom method (EAM) potential using an improved force matching methodology which included fitting to high-temperature solid lattice constants and liquid densities. The new potential shows a good overall improvement in agreement to the experimental lattice constants, elastic constants, stacking fault energy, radial distribution function, and fcc/hcp/bcc lattice energy differences over previous potentials by Foiles, Baskes, and Daw (FBD) [Phys. Rev. B 33, 7983 (1986)] Johnson [Phys. Rev. B 37, 3924 (1988)], and the glue model potential by Ercolessi et al. [Philos. Mag. A 50, 213 (1988)]. Surface energy was improved slightly as compared to potentials by FBD and Johnson but as a result vacancy formation energy is slightly inferior as compared to the same potentials. The results obtained here for gold suggest for other metal species that further overall improvements in potentials may still be possible within the EAM framework with an improved fitting methodology. On the other hand, we also explore the limitations of the EAM framework by attempting a brute force fit to all properties exactly which was found to be unsuccessful. The main conflict in such a brute force fit was between the surface energy and the liquid lattice constant where both could not be fitted identically. By intentionally using a very large number of spline sections for the pair potential, electron-density function, and embedding energy function, we eliminated a lack of functional freedom as a possible cause of this conflict and hence can conclude that it must result from a fundamental limitation in the EAM framework.

Constrained fluid λ-integration: Constructing a reversible thermodynamic path between the solid and liquid state

A novel lambda-integration path is proposed for calculating the Gibbs free energy difference between any arbitrary solid and liquid state needed for the location of melting lines. This technique involves reversibly forcing a liquid state to a solid state across the phase transition along a nonphysical path, thermodynamically coupling the two states directly. The process eliminates the need for coupling to idealized reference states as is presently performed and hence simplifies the location of phase transitions for computer simulation systems. More specifically the path involves a three stage process, whereby, initially a liquid state is transformed to a weakly attractive fluid using linear lambda-integration scaling of the intermolecular potential. In the second stage, the resulting fluid is then constrained to the required solid configurational phase space via the insertion of a periodic lattice of 3D Gaussian wells. The final stage involves reversing to full strength the main intermolecular potential while gradually turning off the constraining 3D Gaussian lattice finally resulting in a stable (or metastable) solid state. Each stage was found to be completely reversible and the resulting change in free energy was thermodynamically integrable. The methodology is demonstrated and validated by calculating solid-liquid coexistence points using the new technique and comparing to those in present literature for the truncated and shifted Lennard-Jones system. The results are found to be in good agreement. The new method is not limited to melting phase transitions and is readily applicable to any simulation methodology, simulation cell size and/or intermolecular potential including ab initio methods.

“Exact” surface free energies of iron surfaces using a modified embedded atom method potential and λ integration

Previously a new universal λ-integration path and associated methodology was developed for the calculation of “exact” surface and interfacial free energies of solids. Such a method is in principle applicable to any intermolecular potential function, including those based on ab initio methods, but in previous work the method was only tested using a relatively simple embedded atom method iron potential. In this present work we apply the new methodology to the more sophisticated and more accurate modified embedded atom method (MEAM) iron potential, where application of other free- energy methods would be extremely difficult due to the complex many-body nature of the potential. We demonstrate that the new technique simplifies the process of obtaining “exact” surface free energies by calculating the complete set of these properties for the low index surface faces of bcc and fcc solid iron structures. By combining these data with further calculations of liquid surface tensions we obtain the first complete set o...

On simulation methods to compute surface and interfacial free energies of disordered solids

We study λ-integration paths, specifically designed for calculating “exact” surface and interfacial free energies of solids at elevated temperatures using molecular dynamics or Monte Carlo simulation methods. We compare various paths with the standard technique of thermodynamic integration by application to the surface free energy for the (100) and (110) faces of alpha iron using embedded atom method (EAM) potentials. We demonstrate which paths are completely reversible at high temperatures and show consistency of results for these paths. The λ-integration paths can be applied with confidence to find equilibrium surface free energies, within the limits of the surface area, intermolecular potentials and other approximations implicit to the simulation methods used.

On the relative stabilities of gold nanoparticles

We calculate and compare the relative free energies of ideal/pristine gold nanoparticles for morphologies produced previously in vapor synthesis computer simulations. The results in conjunction with previous work provide a unique and direct quantitative comparison between ideal thermodynamics and kinetics in the synthesis of gold nanoparticles for an identical system. The ideal/pristine free energies suggest that the I(h) morphology was the most stable structure up to the 147(I(h)) followed by the TO(h) for all the remaining nanoparticle sizes. A grouping of m-D(h) structures was identified in the size range N=146-318 with stabilities which were very close to the most stable I(h) and TO(h) structures. The free energy analysis was somewhat at odds with population statistics obtained from our kinetic growth simulations where the I(h) dominated and where very little presumably stable TO(h) nanoparticles were produced, implying that kinetic mechanisms are more influential than thermodynamic considerations. On the other hand other possible reasons for such discrepancies are discussed; one of these includes an interesting observation where the I(h) morphology was found to have a unique ability to incorporate exposed surface disorder such as adatoms into stable hexagonal surface structures through internal and surface structural rearrangements, leading to a possible enhancement in stabilities of I(h)-type morphologies.

New lambda integration method to compute surface free energies of disordered surfaces

Previously we studied a range of λ-integration paths, specifically designed for calculating surface and interfacial free energies of solids with disordered surfaces or interfaces, using molecular dynamics or Monte Carlo simulation methods. Some of these were successfully applied to the stable low index (100) and (110) Fe bcc surfaces, up to temperatures high enough (1200 K) to induce the onset of surface disorder via the formation of adatoms. Here we apply these same methods to the high energy (111) bcc Fe face, where the “ideal” surface structure was found to be metastable at low temperatures. The results showed that application of paths used in our previous study lead to irreversibility. Hence we further refine the paths with the development of a much more powerful and general path, which we termed the “blanket lambda” path. We show the newest path to be reversible and to provide “exact” surface free energy reference points for the stable and metastable surface structures of the (111) bcc Fe face. We al...

Further application of the constrained fluid λ-integration method

Previously we proposed a three stage, and recently a single stage nonphysical lambda-integration path for thermodynamically coupling bulk solid and liquid states directly. In this work we further apply these paths, specifically the newer single stage path, to the calculation of the complete truncated and shifted Lennard-Jones (R(cutoff)=2.5sigma) and aluminum glue potential melting lines, and the zero pressure melting point for a commonly used gold glue potential. The results showed accurate agreement with presently available literature. We found the single stage constrained fluid lambda-integration methodology to be robust in terms of reversibility over this extended range of temperatures, pressures, and intermolecular potentials.

Application of the constrained fluid λ-integration path to the calculation of high temperature Au(110) surface free energies

Recently a method termed constrained fluid lambda-integration was proposed for calculating the free energy difference between bulk solid and liquid reference states via the construction of a reversible thermodynamic integration path; coupling the two states in question. The present work shows how the application of the constrained fluid lambda-integration concept to solid/liquid slab simulation cells makes possible a generally applicable computer simulation methodology for calculating the free energy of any surface and/or surface defect structure, including surfaces requiring variations in surface atom or density number, such as the (1 x 5) Au(100) or (1 x 2) missing row Au(110) reconstructed surfaces or excess adatom/vacancy/step populated surfaces. We evaluate the methodology by calculating the free energy of various disordered high temperature Au(110) embedded atom method surfaces constrained to differing excess surface atom numbers [including those corresponding to the (1 x 2) missing row reconstructed surface] and obtained the interesting result that at 1000 K (as distinct from lower temperatures) the free energy difference between these surfaces is reduced to zero; a result which is consistent with an expected order-disorder phase transition for the Au(110) surface at such high temperatures.

On the computational calculation of surface free energies for the disordered semihexagonal reconstructed Au(100) surface

Previously we developed a general method for calculating the free energy of any surface constrained to a distinct surface excess number/density. In this paper we show how to combine a range of such surfaces, whose free energies have been calculated, to produce an ad hoc semigrand canonical ensemble of surfaces from which ensemble surface properties can be calculated, including the ensemble surface free energy. We construct such an ensemble for the disordered Au(100) semihexagonal reconstructed surface using a Glue model potential at 1000 K and calculate the ensemble surface free energy to be 0.088 18 eVA(2). The ensemble average surface lateral density was found to be 1.375 (with respect to the bulk), which is in agreement with previous grand canonical Monte Carlo studies.

Influence of substrate morphology on the growth of gold nanoparticles

We have simulated the vacuum deposition and subsequent growth of gold nanoparticles on various substrates in order to explore the effects that substrate morphology has on the resultant morphology of gold nanoparticles. The substrates and conditions explored included, the three low index faces, namely, (111), (100), and (110) for both fcc and bcc crystalline substrate structures, including various substrate lattice constants and temperatures. Firstly, we cataloged the major nanoparticle morphologies produced overall. While some substrates were found to produce a mixture of the main nanoparticle morphologies we were successful in identifying certain substrates and temperature conditions for which only I(h), D(h), or certain fcc crystalline nanoparticles can be grown almost exclusively. The substrate characteristics, temperature conditions, and governing growth dynamics are analyzed. We shed light on the balance between substrate influences and vacuum growth tendencies. From observations we can speculate that a substrate alters both the free energy stability of gold nanoparticles and/or the free energy barriers to transformation between certain morphologies. As such we find that substrates are an effective tool in templating the selective growth of desired nanoparticles or surface nanostructures.