Lattice Monte Carlo Method Research Articles

Thermodynamic calculations using reverse Monte Carlo: A computational workflow for accelerated construction of phase diagrams for metal hydrides

Metal hydrides are promising candidates for hydrogen storage applications. From a materials discovery perspective, an accurate, efficient computational workflow is urgently required that can rapidly analyze/predict thermodynamic properties of these materials. In this paper, we develop a thermodynamic property estimation/phase diagram construction framework based on the lattice reverse Monte Carlo (RMC) method. We apply the technique to the nickel hydride (NiHx) system by calculating the pressure-composition-temperature (PCT) isotherm and constructing its phase diagram. Formation of nickel hydride entails significant volume expansion, strong interaction between hydrogen and the host atoms, lattice strain, and a phase transition. An attractive feature of our approach is that the entire phase diagram can be accurately constructed in few minutes by considering <10 configurations. In contrast, a popular technique based on grand canonical Monte Carlo would require sampling of several million configurations. The promising results obtained with our computational workflow suggest that the approach can be used in future for wider materials search and discovery.

Numerical study of the effective thermal conductivity of 2-phase magnesium alloys containing solid solution atoms using lattice Monte-Carlo

The assessment of thermal conductivity in alloy plays a crucial role in ensuring their stability and performance in thermal applications. This paper specifically focuses on simulating the thermal conductivity of complex microstructures, which involve solid solution atoms and second phases. The lattice Monte Carlo (LMC) method is employed to examine the effective thermal conductivity of the Mg-(Ce, La) model alloy. The results obtained from numerical simulation are compared to experimental data, demonstrating a good agreement between them. Additionally, the study establishes a correlation between the content of solid solution atoms and thermal resistance through rj,α = A/(1-2x). Furthermore, the impact of various factors, such as volume fraction (fβ), size (Z), and morphology (F‾) of the second phase on the effective thermal conductivity, is thoroughly investigated and summarized. Overall, this research contributes to a better understanding the thermal conductivity behavior in complex alloy microstructures.

Structural Quantification of the Surface-Confined Metal-Organic Precursors Simulated with the Lattice Monte Carlo Method.

The diversity of surface-confined metal-organic precursor structures, which recently have been observed experimentally, poses a question of how the individual properties of a molecular building block determine those of the resulting superstructure. To answer this question, we use the Monte Carlo simulation technique to model the self-assembly of metal-organic precursors that precede the covalent polymerization of halogenated PAH isomers. For this purpose, a few representative examples of low-dimensional constructs were studied, and their basic structural features were quantified using such descriptors as the orientational order parameter, radial distribution function, and one- and two-dimensional structure factors. The obtained results demonstrated that the morphology of the precursor (and thus the subsequent polymer) could be effectively tuned by a suitable choice of molecular parameters, including size, shape, and intramolecular distribution of halogen substituents. Moreover, our theoretical investigations showed the effect of the main structural features of the precursors on the related indirect characteristics of these constructs. The results reported herein can be helpful in the custom designing and characterization of low-dimensional polymers with adjustable properties.

Parton physics of the large- Nc mesons

We initiate the studies on the structural physics of the tower of stable large-$N_c$ mesons through a first computation of the collinear quark-structure of a large-$N_c$ pion using lattice Monte-Carlo methods. We adapt the large-$N_c$ continuum reduction for the determination of meson correlation functions involving the spatially-extended quasi-PDF operators as a perfect strategy to concentrate only on the short perturbative length scales. We find the internal structures of pion in the large-$N_c$ and $N_c=3$ theories to be quite similar. Interestingly, we find hints that even the observed differences could arise to a large extent via the different perturbative QCD evolution in the two theories from similar initial conditions at low factorization scales.

A Kinetic Lattice Monte Carlo Method to Study Drug Release from Swelling Porous Delivery Systems

A Kinetic Lattice Monte Carlo Method to Study Drug Release from Swelling Porous Delivery Systems

Halogenated Anthracenes as Building Blocks for the On-Surface Synthesis of Covalent Polymers: Structure Prediction with the Lattice Monte Carlo Method

Functionalized polycyclic aromatic hydrocarbons (PAHs) have been recently recognized as promising building blocks for surface-assisted polymerization reactions producing low-dimensional covalent structures with tailorable properties. In this work, we used the lattice Monte Carlo (MC) simulation method to predict the structure of the labile metal–(halogenated)anthracene connections preceding the formation of covalent polymers in the Ullmann-type coupling reaction occurring on catalytically active metallic surfaces. To that purpose, a coarse-grained model of mono-, di-, and trisubstituted anthracene monomers and two-coordinate metal atoms was proposed, in which these components were adsorbed on a triangular lattice. The formation of metal–organic nodes cementing the resulting superstructures was assumed to be dependent on the directionality of the short-range interactions assigned differently to PAH molecules. Our extensive MC simulations performed for the complete set of 50 positional isomers predicted various organometallic intermediates with morphologies ranging from cyclic oligomers, chains, ladders, ribbons to aperiodic networks and others. These results were compared with the analogous findings obtained for the smaller naphthalene unit. The outcome of the theoretical studies reported herein can be helpful in designing low-dimensional covalent polymers with tunable architecture and functions.

Lattice parameter of Am, Np bearing MOX fuel: an empirical potential study

An empirical potential study was performed for the americium (Am), neptunium (Np) containing uranium (U) and Plutonium (Pu) mixed oxides (MOX). The configurational space of a complex U1-y-y′-y″PuyAmy′Npy″O2 system was predicted by the rigid lattice Monte Carlo method. Based on the computing time and efficiency performance, the method was found to rapidly converge towards the optimal configuration. From that configuration, the relaxed lattice parameter of Am, Np bearing MOX fuel was investigated and compared with available literature data. As a result, a linear behaviour of the lattice parameter as a function of Am, Np content was observed.

Impurity lattice Monte Carlo for hypernuclei

We consider the problem of including varLambda hyperons into the ab initio framework of nuclear lattice effective field theory. In order to avoid large sign oscillations in Monte Carlo simulations, we make use of the fact that the number of hyperons is typically small compared to the number of nucleons in the hypernuclei of interest. This allows us to use the impurity lattice Monte Carlo method, where the minority species of fermions in the full nuclear Hamiltonian is integrated out and treated as a worldline in Euclidean projection time. The majority fermions (nucleons) are treated as explicit degrees of freedom, with their mutual interactions described by auxiliary fields. This is the first application of the impurity lattice Monte Carlo method to systems where the majority particles are interacting. Here, we show how the impurity Monte Carlo method can be applied to compute the binding energies of the light hypernuclei. In this exploratory work we use spin-independent nucleon–nucleon and hyperon–nucleon interactions to test the computational power of the method. We find that the computational effort scales approximately linearly in the number of nucleons. The results are very promising for future studies of larger hypernuclear systems using chiral effective field theory and realistic hyperon–nucleon interactions, as well as applications to other quantum many-body systems.

Controlling of the 2D Self-Assembly Process by the Variation of Molecular Geometry

In this paper, we check how the molecular architecture influences the self-assembly process of tetrapod molecules. These particles were built of the linear core and four attached arms. For this purpose, we employ molecular dynamics simulation together with the lattice Monte Carlo method to investigate the formation of supramolecular networks. To characterize them, we evaluated structure parameters such as distribution of the core–core angle, average degree of association, and theoretical diffractograms. Moreover, we conclude that for the latter parameter, the influence of the rotation of differently oriented domains may lead to wrong interpretation of results.

Lattice Monte Carlo for quantum Hall states on a torus

Monte Carlo is one of the most useful methods to study the quantum Hall problems. In this paper, we introduce a fast lattice Monte Carlo method based on a mathematically exact reformulation of the torus quantum Hall problems from continuum to lattice. We first apply this new technique to study the Berry phase of transporting composite fermions along different closed paths enclosing or not enclosing the Fermi surface center in the half filled Landau level problem. The Monte Carlo result agrees with the phase structure we found on small systems and confirms it on much larger sizes. Several other quantities including the Coulomb energy in different Landau levels, structure factor, particle-hole symmetry are computed and discussed for various model states. In the end, based on certain knowledge of structure factor, we introduce a algorithm by which the lattice Monte Carlo efficiency is further boosted by several orders.

Lattice models and Monte Carlo methods for simulating DNA origami self-assembly.

The optimal design of DNA origami systems that assemble rapidly and robustly is hampered by the lack of a model for self-assembly that is sufficiently detailed yet computationally tractable. Here, we propose a model for DNA origami that strikes a balance between these two criteria by representing these systems on a lattice at the level of binding domains. The free energy of hybridization between individual binding domains is estimated with a nearest-neighbour model. Double helical segments are treated as being rigid, but we allow flexibility at points where the backbone of one of the strands is interrupted, which provides a reasonably realistic representation of partially and fully assembled states. Particular attention is paid to the constraints imposed by the double helical twist, as they determine where strand crossovers between adjacent helices can occur. To improve the efficiency of sampling configuration space, we develop Monte Carlo methods for sampling scaffold conformations in near-assembled states, and we carry out simulations in the grand canonical ensemble, enabling us to avoid considering states with unbound staples. We demonstrate that our model can quickly sample assembled configurations of a small origami design previously studied with the oxDNA model, as well as a design with staples that span longer segments of the scaffold. The sampling ability of our method should allow for good statistics to be obtained when studying the assembly pathways and is suited to investigating, in particular, the effects of design and assembly conditions on these pathways and their resulting final assembled structures.

Three-Dimensional ES Barrier Promotes the Steps Formation

Physical vapor deposition (PVD) has been an important method to synthesize metallic nanorods during the past two decades. Based on the main physical process of crystal growth, this letter made a growth model of metallic nanorods with kinetic lattice Monte Carlo (KLMC) method and studied the effects of three-dimensional (3D) Ehrlich–Schwoebel (ES) barrier during the metallic nanorods growth. According to the simulation results, a large 3D ES barrier affects the surface morphology apparently. With analyze the simulation results, 3D ES barrier promotes the step formation and increases the step height greatly, and it is the main factor of metallic nanorods formation.

New approach to effective diffusion coefficient evaluation in the nanostructured two-phase media

Most widely used basic and combined models for evaluation of the effective diffusion parameters of inhomogeneous two-phase zone are reviewed. A new combined model of effective medium is analyzed for the description of diffusion processes in the two-phase zones. In this model the effective diffusivity depends on the growth kinetic coefficients of each phase, the volume fractions of phases and on the additional parameter that generally characterizes the structure type of the two-phase zone. Our combined model describes two-phase zone evolution in the binary systems based on consideration of the diffusion fluxes through both phases. The Lattice Monte Carlo method was used to test the validity of different phenomenological models for evaluation of the effective diffusivity in nanostructured two-phase zones with different structural morphology.

A Lattice Kinetic Monte Carlo Solver for First-Principles Microkinetic Trend Studies.

Mean-field microkinetic models in combination with Brønsted-Evans-Polanyi like scaling relations have proven highly successful in identifying catalyst materials with good or promising reactivity and selectivity. Analysis of the microkinetic model by means of lattice kinetic Monte Carlo promises a faithful description of a range of atomistic features involving short-range ordering of species in the vicinity of an active site. In this paper, we use the "fruit fly" example reaction of CO oxidation on fcc(111) transition and coinage metals to motivate and develop a lattice kinetic Monte Carlo solver suitable for the numerically challenging case of vastly disparate rate constants. As a result, we show that for the case of infinitely fast diffusion and absence of adsorbate-adsorbate interaction it is, in fact, possible to match the prediction of the mean-field-theory method and the lattice kinetic Monte Carlo method. As a corollary, we conclude that lattice kinetic Monte Carlo simulations of surface chemical reactions are most likely to provide additional insight over mean-field simulations if diffusion limitations or adsorbate-adsorbate interactions have a significant influence on the mixing of the adsorbates.

Interstitial micelles in binary blends of ABA triblock copolymers and homopolymers.

We investigate triblock-homopolymer blends of types A1BA2/A and A1BA2/B, using a lattice Monte Carlo method. While the simulated triblock chains are compositionally symmetric in terms of the A-to-B volume ratio, the A1 block is significantly shorter than the A2 block. For the pure A1BA2 melt and the A1BA2 solutions in selective solvent the phase behavior is relatively well known, including existence and stability of the interstitial micelles which were discovered in previous Monte Carlo simulations. In this paper we study the stability of the interstitial micelles as a function of triblock volume fraction in selective homopolymers of either type A or type B, using two significantly different homopolymer chain lengths. We found that adding selective homopolymer of type A shifts the stability of the interstitial micelles into significantly higher temperatures. We also obtained, via self-assembly, intriguing new nanostructures which can be identified as ordered truncated octahedra. Finally, we established that the phase behavior of the triblock-homopolymer blends depends relatively weakly on the chain length of the added homopolymer.

Analysis of the lattice kinetic Monte Carlo method in systems with external fields.

The lattice kinetic Monte Carlo (LKMC) method is studied in the context of Brownian particles subjected to drift forces, here principally represented by external fluid flow. LKMC rate expressions for particle hopping are derived that satisfy detailed balance at equilibrium while also providing correct dynamical trajectories in advective-diffusive situations. Error analyses are performed for systems in which collections of particles undergo Brownian motion while also being advected by plug and parabolic flows. We demonstrate how the flow intensity, and its associated drift force, as well as its gradient, each impact the accuracy of the method in relation to reference analytical solutions and Brownian dynamics simulations. Finally, we show how a non-uniform grid that everywhere retains full microscopic detail may be employed to increase the computational efficiency of lattice kinetic Monte Carlo simulations of particles subjected to drift forces arising from the presence of external fields.

Towards entropy-driven interstitial micelles at elevated temperatures from selective A1BA2 triblock solutions.

We simulate selective A1BA2-A and A1BA2-B triblock solutions (that is, mixtures of the A1BA2 triblock with a solvent of either type A or type B) using a lattice Monte Carlo method. Although the simulated triblock chains are compositionally symmetric in terms of the A to B volume ratio, the A1 block is significantly shorter than the A2 block. For the pure A1BA2 melt the phase behavior is relatively well known, including the existence and stability of the recently discovered interstitial micelles which were found at the very strong segregation limit. In this paper, we investigate the stability of the interstitial micelles as a function of triblock volume fraction in a selective solvent of either type A or type B. The main finding of this paper is that adding a selective solvent of type A shifts the stability of the interstitial micelles into significantly higher temperatures which may provide a pathway towards experimental studies of interstitial micelles in real triblock solutions. We also find that adding selective solvents to the A1BA2 melt gives rise to a variety of nonlamellar nanostructures for temperatures and compositions at which the interstitial micelles are stable.

Hard-wall and non-uniform lattice Monte Carlo approaches to one-dimensional Fermi gases in a harmonic trap

We present in detail two variants of the lattice Monte Carlo method aimed at tackling systems in external trapping potentials: a uniform-lattice approach with hard-wall boundary conditions, and a non-uniform Gauss–Hermite lattice approach. Using those two methods, we compute the ground-state energy and spatial density profile for systems of N=4–8 harmonically trapped fermions in one dimension. From the favorable comparison of both energies and density profiles (particularly in regions of low density), we conclude that the trapping potential is properly resolved by the hard-wall basis. Our work paves the way to higher dimensions and finite temperature analyses, as calculations with the hard-wall basis can be accelerated via fast Fourier transforms; the cost of unaccelerated methods is otherwise prohibitive due to the unfavorable scaling with system size. To illustrate this point, we show a brief performance comparison of accelerated versus unaccelerated methods across spatial dimensions.

Ground state of the two-dimensional attractive Fermi gas: Essential properties from few to many body

We calculate the ground-state properties of unpolarized two-dimensional attractive fermions in the range from few to many particles. Using first-principles lattice Monte Carlo methods, we determine the ground-state energy, Tan's contact, momentum distribution, and single-particle correlation function. We investigate those properties for systems of $N=4,8,...,40$ particles and for a wide range of attractive couplings. As the attractive coupling is increased, the thermodynamic limit is reached at progressively lower $N$ due to the dominance of the two-body sector. At large momenta $k$, the momentum distribution displays the expected $k^{-4}$ behavior, but its onset shifts from $k \simeq 1.8 k^{}_F$ at weak coupling towards higher $k$ at strong coupling.

Harmonically trapped fermions in two dimensions: Ground-state energy and contact of SU(2) and SU(4) systems via a nonuniform lattice Monte Carlo method

We study harmonically trapped, unpolarized fermion systems with attractive interactions in two spatial dimensions with spin degeneracies Nf = 2 and 4 and N/Nf = 1, 3, 5, and 7 particles per flavor. We carry out our calculations using our recently proposed quantum Monte Carlo method on a nonuniform lattice. We report on the ground-state energy and contact for a range of couplings, as determined by the binding energy of the two-body system, and show explicitly how the physics of the Nf-body sector dominates as the coupling is increased.