Semi-grand Canonical Monte Carlo Research Articles

Phase diagram of brittle fracture in the semi-grand-canonical ensemble.

We present a simulation method to assess the quasistatic fracture resistance of materials. Set within a semi-grand-canonical Monte Carlo (SGCMC) simulation environment, an auxiliary field-the bond rupture potential-is introduced to generate a sufficiently large number of possible microstates in the semi-grand-canonical ensemble, and associated energy and bond fluctuations. The SGCMC approach permits identifying the full phase diagram of brittle fracture for harmonic and nonharmonic bond potentials, analogous to the gas-liquid phase diagram, with the equivalent of a liquidus line ending in a critical point. The phase diagram delineates a solid phase, a fractured phase, and a gas phase, and provides clear evidence of a first-order phase transition intrinsic to fracture. Moreover, energy and bond fluctuations generated with the SGCMC approach permit determination of the maximum energy dissipation associated with bond rupture, and hence of the fracture resistance of a widespread range of materials that can be described by bond potentials.

Effect of pH on the Supramolecular Structure of Helicobacter pylori Urease by Molecular Dynamics Simulations.

The effect of pH on the supramolecular structure of Helicobacter pylori urease was studied by means of molecular dynamics simulations at seven different pHs. Appropriate urease charge distributions were calculated using a semi-grand canonical Monte Carlo (SGCMC) procedure that assigns each residue’s charge state depending on the assigned individual p obtained by PROPKA. The effect of pH on protein stability has been analyzed through root-mean-square deviation (RMSD), radius of gyration (RG), solvent-accessible surface area (SASA), hydrogen bonds (HB) and salt bridges (SB). Urease catalyses the hydrolysis of urea in 12 active sites that are covered by mobile regions that act like flaps. The mobility of these flaps is increased at acidic pHs. However, extreme acidic conditions cause urease to have the least number of stabilizing interactions. This initiates the process of denaturalization, wherein the four subunits of the global structure (()) of urease start to separate.

Semi-grand canonical Monte Carlo simulation for derivation of thermodynamic properties of binary alloy

Semi-grand canonical Monte Carlo (SGCMC) simulations are performed to derive thermodynamic properties of binary alloy from atomistic-based simulations. Particularly, solidus and liquidus compositions are directly derived for Fe-Cr alloy described by two different EAM potentials. Although the SGCMC simulation can derive relationship between the free energy and composition at any temperature straightforwardly, partial phase diagram obtained from SGCMC simulations strongly depends on the choice of interatomic potential.

“Order-Order” Kinetics in Triple-Defect B2-Ordered Binary Intermetallics: Kinetic Monte Carlo Simulation

Triple-defect formation in B2-ordered binary A-B intermetallic compounds results fromthe asymmetry between the formation energies of A- and B-antisite defects. Chemical disorderingin such systems is strictly correlated with vacancy formation, which is the reason for usually veryhigh vacancy concentration. Consequently, Kinetic Monte Carlo (KMC) simulation of processes occurringin the triple-defect systems and controlled by atomic migration via vacancy mechanism mustinvolve complete vacancy thermodynamics – i.e. the simulated system must contain the equilibriumtemperature-dependent number of vacancies. The fully consistent approach based on two differentMonte Carlo techniques has been applied in the present study. The AB intermetallic was modelled withan Ising-type Hamiltonian and KMC simulated for “order-order” kinetics with temperature-dependentequilibrium number of vacancies previously determined by means of Semi Grand Canonical MonteCarlo (SGCMC) simulations. The procedure required in addition the determination of saddle -pointenergies assigned to particular atomic jumps to nn vacancies. Their values were estimated in relationto the nn pair-interaction energies with reference to Molecular Statics simulations performed for NiAlsystem with EAM energetics. The results elucidated the role of triple-defect formation as the atomisticscaleorigin of the experimentally observed surprisingly low rate of the “order-order” kinetics in bulkNiAl.

Semigrand Canonical and Kinetic Monte Carlo simulations of binary B2-ordered nano-films with triple defects

Equilibrium atomic configurations and the kinetics of “order–order” and surface segregation processes in B2-ordering stoichiometric A-50 at.%B binary thin films are investigated by means of Semigrand Canonical Monte Carlo (SGCMC) and Kinetic Monte Carlo (KMC) simulations. The (100)-oriented films are modeled with an Ising-type Hamiltonian with previously evaluated pair-interaction energy parameters yielding the effect of “triple-defect disordering”. The SGCMC simulations provide equilibrium vacancy concentration and atomic configuration in the films with B-atom termination of both free surfaces achieved at high temperatures by the generation of an antiphase boundary. Despite strong vacancy surface segregation, the thermodynamic activation energy for their formation inside the films is the same as in the bulk material. KMC simulations implemented with the SGCMC-determined equilibrium vacancy concentration reveal very slow relaxation of the films towards equilibrium configuration. The B-termination of the (100) free surfaces is produced by A-atom diffusion inwards into the films mediated by vacancies segregating on surfaces.

Self-diffusion and ‘order–order’ kinetics in B2-ordering AB binary systems with a tendency for triple-defect formation: Monte Carlo simulation

Self-diffusion of component atoms and ‘order–order’ relaxations in a B2-ordering binary system AB showing a tendency for triple-defect formation were consistently simulated by means of two Monte Carlo techniques. In view of a strict correlation between antisite-defect and vacancy concentrations the Kinetic Monte Carlo (KMC) simulations were implemented with a temperature-dependent vacancy concentration determined by means of Semi-Grand Canonical Monte Carlo (SGCMC) simulations. The Ising model of the system was completed with local-configuration-dependent saddle-point energy parameters related to vacancy mediated atomic jumps. The simulations elucidated the atomistic origin of the experimentally observed low rate of ‘order–order’ relaxations in NiAl, as well as reproduced the experimental relation between the activation energies for ‘order–order’ kinetics and Ni self-diffusion in NiAl. Higher value of the deduced activation energy for atomic migration with respect to the effective energy barriers related to individual atomic jumps indicated their high correlation.

Semi-grand canonical Monte Carlo simulation of ternary bcc lattice-gas decomposition: Vacancy formation correlated with B2 atomic ordering in A–B intermetallics

Lattice-gas decomposition model for equilibrium vacancy concentration in B2-ordered triple defect A–B binary intermetallic systems previously formulated and solved within the Bragg–Williams approximation was now simulated by means of Semi-Grand Canonical Monte Carlo (SGCMC) technique. Simulations of a ternary Ising lattice gas A–B–V with pair-interaction energies promoting the generation of A-antisites and A-vacancies revealed a miscibility gap and a coexistence of vacancy-poor and vacancy-rich phases within a wide range of temperature. The B2-ordered vacancy-poor phases were identified with intermetallic compounds containing equilibrium number of vacancies, which, at sufficiently low temperature, resulted proportional to the number of antisite defects. The latter effect additionally accompanied by the presence of constitutional vacancies in B-rich systems was interpreted as a signature of triple defect formation. The reliability of the model was checked by its implementation with Ni–Al EAM potential and by comparing the calculated vacancy concentrations in NiAl with the available experimental data. The modelled temperature dependence of the equilibrium vacancy concentration and configuration in triple defect B2-ordering binary intermetallics will be applied in Kinetic Monte Carlo (KMC) simulations of “order–order” kinetics in these systems.

Lattice-Gas-Decomposition Model for Vacancy Formation Correlated with B2 Atomic Ordering in Intermetallics

AbstractThermal vacancy formation correlated with atomic ordering was modelled in B2-ordering A-B binary intermetallics. Ising Hamiltonian was implemented with a specific thermodynamic formalism for thermal vacancy formation based on the phase equilibria in a lattice gas composed of atoms and vacancies. Extensive calculations within the Bragg-Williams approximation [1] were followed by Semi-Grand Canonical Monte Carlo (SGCMC) simulations. It has been demonstrated that for the atomic pair-interaction energies favouring vacancy formation on A-atom sublattice, equilibrium concentrations of vacancies and antisite defects result mutually proportional in well defined temperature ranges. The effect observed both in stoichiometric and non-stoichiometric (both A-rich and B-rich) binary alloys was interpreted as a tendency for triple defect formation. In B-rich alloys vacancy concentration did not extrapolate to zero at 0 K, which indicated the formation of constitutional vacancies. Energetic conditions for the occurrence of the effects were analysed in detail. The modelled temperature dependence of vacancy concentration in the B2-ordering A-B binaries with triple defects will be included in the Kinetic Monte Carlo (KMC) simulations of chemical ordering kinetics in these systems with reference to the experimental results obtained for NiAl [2].

Simulation of mechanical properties of oriented glassy polystyrene

Mechanical properties of processed polymers depend sensitively on their microstructure. In order to understand how different processing conditions affect the mechanical properties of polymers, one needs a means to describe the process-induced microstructure. Because the characteristic relaxation times of processed polymer chains often span several orders of magnitude, it is commonly the case that partial relaxation of the chains is frozen into the final product. We report results of molecular simulations by the Semi-Grand Canonical Monte Carlo (SGMC) method to study the orientation-dependent elasticity of glassy polystyrene as a function of both the system-average degree of orientation and the degree of relaxation of chain ends at a constant average orientation, in accord with the tube model of Doi and Edwards. Our simulations reproduce quantitatively the experimentally observed trends in the tensile modulus E11 as a function both of the system-average orientation and of the inhomogeneity of the orientation along the chain due to rapid relaxation of chain ends. The results show that the partial relaxation of the polymer chains is sufficient to explain the observed variation of mechanical properties for samples that differ in processing history, yet have the same observed birefringence.

Semi-Grand Canonical Monte Carlo (SGMC) Simulations to Interpret Experimental Data on Processed Polymer Melts and Glasses

We describe the application of the semi-grand canonical Monte Carlo (SGMC) method to analyze and interpret experimental data for nonequilibrium polymer melts and glasses. Experiments that provide information about atomic-level ordering, e.g., birefringence, are amenable to this approach. Closure of the inverse problem of determining the structural detail from limited data is achieved by selecting the lowest-free-energy ensemble of configurations that reproduces the experimental data. The free energy is calculated using the thermodynamic potential of the appropriate semi-grand canonical (SGC) ensemble [NPTΔμ(I)], as defined by the experimental data. To illustrate the method, we examine uniaxially oriented polyethylene melts of average chain length up to C400. The simulation results are analyzed for features not explicitly measured by birefringence, such as the density, torsion angle distribution, molecular scale orientation, and free energy, to understand more fully the underlying features of these nonequilibrium states. The stress-optical rule for polyethylene is evaluated in this way.

Static and dynamic critical behavior of a symmetrical binary fluid: A computer simulation

A symmetrical binary, A+B Lennard-Jones mixture is studied by a combination of semi-grand-canonical Monte Carlo (SGMC) and molecular dynamics (MD) methods near a liquid-liquid critical temperature T(c). Choosing equal chemical potentials for the two species, the SGMC switches identities (A-->B-->A) to generate well-equilibrated configurations of the system on the coexistence curve for T<T(c) and at the critical concentration, x(c)=12, for T>T(c). A finite-size scaling analysis of the concentration susceptibility above T(c) and of the order parameter below T(c) is performed, varying the number of particles from N=400 to 12 800. The data are fully compatible with the expected critical exponents of the three-dimensional Ising universality class. The equilibrium configurations from the SGMC runs are used as initial states for microcanonical MD runs, from which transport coefficients are extracted. Self-diffusion coefficients are obtained from the Einstein relation, while the interdiffusion coefficient and the shear viscosity are estimated from Green-Kubo expressions. As expected, the self-diffusion constant does not display a detectable critical anomaly. With appropriate finite-size scaling analysis, we show that the simulation data for the shear viscosity and the mutual diffusion constant are quite consistent both with the theoretically predicted behavior, including the critical exponents and amplitudes, and with the most accurate experimental evidence.

A comprehensive study of the phase diagram of symmetrical hard-core Yukawa mixtures

The phase diagrams of hard-core Yukawa mixtures (HCYM), constituted of equal sized hard spheres interacting through an attractive Yukawa tail, are determined by means of Gibbs Ensemble Monte Carlo (GEMC) simulations, Semi-grand Canonical Monte Carlo (SGCMC) simulations, and through the modified hypernetted-chain (MHNC) theory. Freezing lines are obtained according to an approach recently proposed by Giaquinta and co-workers [Physica A 187, 145 (1992); Phys Rev. A 45, 6966 (1992)] in which an analysis of multiparticle contributions to the excess entropy, Δs, is performed, with the determination of the Δs=0 locus. Liquid–vapor coexistence, determined through GEMC simulations, turns out to be favored when the strength ratio ν of unlike to like particle interaction, is close to 1. For lower ν’s, liquid–vapor coexistence is favored at low densities, and liquid–liquid coexistence, determined through SGCMC simulations, at high densities. The liquid–vapor binodal shifts downward in temperature and flattens when ν decreases, with a decrease of the critical temperature. At ν=0.9 a triple point can be identified from the intersection of the freezing line with the binodal line; at ν=0.7, instead, the binodal ends on the line of liquid–liquid (consolute) critical points, the intersection of the two lines thus identifying the “crossover” density and temperature between the two equilibrium regimes which correspond to the critical end point of the mixture. We find that, for not too high densities, consolute equilibrium can be also explored through GEMC simulations; the results for liquid–liquid coexistence obtained through this method and SGCMC simulations compare quite satisfactorily with each other. The trend of the liquid–vapor binodal to disappear for relatively weak unlike interactions is discussed in connection with the disappearance of liquid–vapor equilibrium which occurs in one component hard-core Yukawa fluids characterized by very short ranged attractive forces. The latter behavior has been conjectured to be relevant for the onset of crystallization in protein solutions; the implications of the present results, which are obtained in the context of a two component, albeit rough, modelization of a realistic solution, are discussed. In agreement with similar results obtained by Giaquinta et al., we finally find that the Δs=0 locus not only brings the signature of the freezing transition, but also of structural rearrangements preluding to other phase equilibria; in fact, the Δs=0 line turns out to be coincident to a high accuracy with the line of consolute critical points and with the gas branches of the liquid–vapor binodals.