Monte Carlo simulation of PGNAA system for determining element content in the rock sample

The element content in rock sample can be determined by prompt gamma ray activation analysis technology. The neutron distributions under the conditions with different moderating materials, moderator size and distance from neutron source to lead-out hole were simulated using Monte Carlo method, and then the optimal structure parameters to get the highest thermal neutron flux was obtained. The PGNAA system with optimal parameters based on ²⁵²Cf neutron source was founded. In addition, the rock and element standard samples were irradiated by thermal neutron in this system. Moreover, the element content was calculated by processing gamma ray spectroscopy recorded, and it is in agreement with result of XRF method.     

Kinetic Monte Carlo simulation of electrodeposition of polycrystalline Cu

A two-dimensional cross-sectional poly-lattice kinetic Monte Carlo (2DCSP-KMC) model has been developed for simulation of the electrodeposition of polycrystalline copper on a copper and gold substrate. The mis-orientation and higher energetic state of grain boundaries are taken into account by introducing a ‘strange’ coordination number and a correction coefficient while determining the diffusion rate. The evolution of the microstructure, the average grain size, the variance of grain size and the distribution of grain-boundary mis-orientation of the deposit are also considered in simulations. The model has proven capable of capturing some key aspects of nucleation and growth mechanism including the nucleation type (e.g. homogeneous or heterogeneous), texture development, the growth of grains and higher energetic state of grain boundaries. The simulated microstructure qualitatively agrees with our experimental observation on the copper deposition on gold.     

A Monte Carlo simulation of Fe2+ aqueous solvation

A Monte Carlo simulation of Fe²⁺ aqueous solvation, at 298 K, including 100 water molecules, has been done using periodic boundary conditions under the minimum image conversion. The energy has been calculated in the pair-potential approach, employing the MCY potential for the H₂OH₂O interaction and an ab initio analytical potential generated by us for the Fe²⁺H₂O interaction. The examination of interaction energies and of the radial distribution functions clearly show that the first hydration shell is formed by eight water molecules. By classifying the generated configurations into different significant structures of the solvent, it has been found that the eight water molecules of the first hydration shell are situated in a lightly distorted D_4d structure which maximizes the water—solute stabilization and minimizes the water—water repulsion. Finally, the validity of our theoretical predictions is discussed.     

Monte Carlo simulation of bremsstrahlung emission by electrons

The basic components of Monte Carlo simulation of bremsstrahlung emission by electrons are presented. Various theoretical cross-sections that have been used in Monte Carlo codes are described and the emphasis is on the more accurate partial-wave cross-sections for which numerical databases are available. Sampling algorithms for a combination of numerical scaled energy-loss cross-sections and various analytical approximations to the intrinsic angular distribution are presented. Analogue simulation of the energy spectra and angular distribution of X rays from targets irradiated by electron beams is very inefficient and a simple variance-reduction technique, which is easy to implement and has proven to be particularly effective in speeding up these simulations, is described. Results from simulations of X-ray spectra with the general-purpose Monte Carlo code penelope are compared with experimental data for different materials and incident electrons with energies in the 20 keV to 1 GeV energy range.     

Monte Carlo simulation of order-disorder transformation in nano particles of Cu3Au alloy

The ground state energy of nano particles of the Cu₃Au alloy is calculated by utilizing the modified embedded atom method(MEAM), and a computer simulation is made of the order-disorder transition therein by Monte Carlo method with the many-body potential obtained by MEAM. The calculations have been made for three kinds of model crystals of nano particles with 2 nm and 3 nm in diameter, containing 321 and 1061 atoms, respectively, and of a bulk with a size of 5 × 5 × 5 unit cells, on which the periodic boundary condition is imposed. As a result, it is found that the difference in ground state energy between perfectly ordered and disordered states becomes less in nano particles than in the bulk, and that the critical temperature T _c decreases markedly with decreasing particle size. According to our previous experiments, there seems to be a certain critical size for the atomic ordering in the nano particles, and T _c is depressed remarkably in the nano particles. These experimental results appear to be accounted for by the present calculated ones qualitatively.     

Kinetic Monte Carlo study of submonolayer heteroepitaxial growth comparing Cu/Ni and Pt/Ni on Ni(100)

The surface patterns formed during submonolayer Cu/Ni and Pt/Ni heteroepitaxy upon a Ni(100) substrate have been investigated by kinetic Monte Carlo (KMC) simulations. The two-dimensional (2D) KMC simulations are based upon rate constants for a complete nearest-neighbor set of 729 uncorrelated Cu or Pt atoms and/or Ni site-to-site hopping mobilities. The rate constant activation energies are determined by classical-potential total-energy calculations using an embedded-atom method potential function from the literature. We find that diffusion of Cu atoms occurs at a faster rate and Pt atoms at a slower rate than that of Ni atoms on the flat Ni(100) surface, and the initial nucleation and growth patterns of 2D islands and the kinetic versus thermodynamic control of the growth vary as a consequence. In the temperature and deposition time regime in which we work, the Cu/Ni systems show less than random mixing, while the Pt/Ni systems show more than random mixing. The Cu/Ni system has bonding energies that result in a tendency to segregate toward subdomains of pure Ni and Cu, though kinetic effects in the epitaxy trap the development of the system at small subdomain sizes. The Pt/Ni system has bonding energies giving a tendency to intermix completely, while epitaxial kinetic effects modestly interfere with the complete mixing. The kinetically determined island morphologies under various Cu/Ni and Pt/Ni compositions and deposition rates differ substantially over time periods that are long on the deposition time scale, and therefore the island patterns can become frozen in place.     

Melting of palladium clusters – density of states determination by Monte Carlo simulation

The density of states (DOS) has been calculated for the metal clusters Pd₁₃, Pd₅₅ and Pd₁₄₇ using the recently proposed reference system equilibration (RSE) method. The interaction within the clusters was described by a many-body alloy potential. Using this DOS, the caloric curve of Pd₁₃ has been calculated and excellent agreement with canonical Monte Carlo simulations is obtained. For Pd₅₅ and Pd₁₄₇, the solid and one molten isomers have been isolated in order to calculate the DOS for the isomers separately. The melting of the clusters occurs when the DOS for the solid and the molten isomers are equal. Comparison with previous microcanonical Monte Carlo simulations shows that the number of statistically equivalent molten isomers are 1.1×10¹⁸ for Pd₅₅ and 4.1×10⁴¹ for Pd₁₄₇.     

A new technique for metropolis Monte Carlo simulation to capture aggregate structures of fine particles: Cluster-moving Monte Carlo algorithm

We present a new Monte Carlo simulation procedure which is capable of capturing aggregate structures in a suspension where fine particles are dispersed. The algorithm we call the “cluster-moving” Monte Carlo algorithm involves moving aggregates (clusters) as unitary particles at every certain Monte Carlo step. We discuss here the theoretical background of the cluster-moving Monte Carlo algorithm and the availability of the algorithm for simulations of systems where fine particles aggregate. The results of simulations for two model systems, magnetic fluids and colloidal dispersions, have shown that the new algorithm produces much more rapid convergence than the conventional one for unstable dispersion systems and reproduces physically reasonable aggregate structures of fine particles.     

Monte Carlo simulation of DNA electrophoresis

This paper describes an attempt to study the electrophoresis mobility of a DNA molecule in a gel by means of a Monte Carlo simulation. We find that the electrophoresis mobility mu can be well described by the empirical equation mu v kappa 1/N + kappa 2E2 with N being the number of monomers of the model chain and E being the applied field. For small E the data can merge into the linear response result mu = kappa 1/N. The paper also discusses necessary extensions of the present approach.     

Monte Carlo simulation of polymer welding

Monte Carlo Modelling of random polymer chains, course grained onto a cubic F lattice, provides the ability to monitor the long range relaxation processes and the dynamic parameters of chains up to 400 units long. The model, described and verified by Haire et al. (Haire KR, Carver TJ, Windle AH. A Monte Carlo model for dense polymer systems and its interlocking with molecular dynamics simulation. Computational and Theoretical Polymer Science 2000; in press), is here applied to the study of molecular parameters in the vicinity of different types of surface and also to the process of polymer welding, whereby adhesion between two adjacent surfaces is achieved by the interpenetration of chains which are across the surface.The model demonstrates that a surface distorts the conformation of chains adjacent to it to give an oblate molecular envelope, that the concentration of vacant sites and chain ends increases near to the surface and that the density of points representing the centres of mass of the chains increases in the sub-surface regions. These results confirm earlier predictions and provide additional confidence in the model.Modelling of the welding process leads to the parameter intrinsic weld time, t_w, which is the time from initial perfect contact of the surfaces to the achievement of a weld within which the chain conformation is indistinguishable from the bulk. After the initial period in which the mating surfaces roughen, the welding proceeds according to the t^1/4 law predicted by reptation theory. The time to a given level of interdiffusion across the boundary is proportional to the chain length l, a comparatively weak dependence, while t_w is proportional to l³, a strong dependence. This is the same dependence on length as for the relaxation time of the chain end-to-end vectors. In fact, the agreement between the relaxation time, measured on the model of the bulk, and t_w is surprisingly close, at least for the monodisperse polymers investigated here.     

Monte Carlo simulation of polymer adsorption

We developed and employed the incremental gauge cell method to calculate the chemical potential (and thus free energies) of long, flexible homopolymer chains of Lennard-Jones beads with harmonic bonds. The free energy of these chains was calculated with respect to three external conditions: in the zero-density bulk limit, confined in a spherical pore with hard walls, and confined in a spherical pore with attractive pores, the latter case being an analog of adsorption. Using the incremental gauge cell method, we calculated the incremental chemical potential of free polymer chains before and after the globual-random coil transitions. We also found that chains confined in attractive pores exhibit behaviors typical of low temperature physisorption isotherms, such as layering followed by capillary condensation.     

Monte Carlo simulation of osmotic equilibria

We present a Metropolis Monte Carlo simulation algorithm for the Tpπ-ensemble, where T is the temperature, p is the overall external pressure, and π is the osmotic pressure across the membrane. The algorithm, which can be applied to small molecules or sorption of small molecules in polymer networks, is tested for the case of Lennard-Jones interactions.     

Order-parameter-based Monte Carlo simulation of crystallization

A Monte Carlo simulation method is presented for simulation of phase transitions, with emphasis on the study of crystallization. The method relies on a random walk in order parameter Phi(q(N)) space to calculate a free energy profile between the two coexisting phases. The energy and volume data generated over the course of the simulation are subsequently reweighed to identify the precise conditions for phase coexistence. The usefulness of the method is demonstrated in the context of crystallization of a purely repulsive Lennard-Jones system. A systematic analysis of precritical and critical nuclei as a function of supercooling reveals a gradual change from a bcc to a fcc structure inside the crystalline nucleus as it grows at large degrees of supercooling. The method is generally applicable and is expected to find applications in systems for which two or more coexisting phases can be distinguished through one or more order parameters.     

Monte Carlo simulation of hard spheroids

We present Monte Carlo simulations of the equation of state and radial distribution function for a model fluid composed of hard spheroids.     

Monte Carlo simulation of block copolymers

Monte Carlo simulations deal with crudely simplified but well-defined models and have the advantage that they treat the statistical thermodynamics of the considered model exactly (apart from statistical errors and problems due to finite size effects). Therefore, these simulations are well suited to test various approximate theories of block copolymer ordering, e.g. the self-consistent field theory. Recent examples of this approach include the study of block copolymer ordering at melt surfaces and confinement effects in thin films, adsorption of block copolymers at interfaces of unmixed homopolymer blends, the phase behavior of ternary mixtures of two homopolymers and their block copolymer, and micelle formation in selective solvents.     

Collective-variable Monte Carlo simulation of DNA

Monte Carlo simulations have been carried out on DNA oligomers using an internal coordinate model associated with a pseudorotational representation of sugar repuckering. It is shown that when this model is combined with the scaled collective variable approach of Noguti and Go, much more efficient simulations are obtained than with simple single variable steps. Application of this method to a DNA oligomer containing a recognition site for the TATA-box binding protein leads to striking similarities with results recently obtained from a 1-ns molecular dynamics simulation using explicit solvent and counterions. In particular, large amplitude bending fluctuations are observed directed toward the major groove. Conformational analysis of the Monte Carlo simulation shows clear base sequence effects on conformational fluctuations and also that the DNA energy hypersurface, like that of proteins, is complex with many local, conformational substates. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 2001–2011, 1997     

Confinement effect in diffusion-controlled stepwise polymerization by Monte Carlo simulation

Diffusion-controlled stepwise polymerization of a linear polymer confined in nanoscopic slits is simulated through a Monte Carlo approach. A noticeable influence of the confinement on the kinetics is found. The confinement modifies both the spatial pair distribution function and the diffusive properties of the polymers. As a consequence, the confined system can show either faster or slower reaction kinetics with respect to the bulk system, depending on the strength of intermolecular interactions. The predicted polydispersity of the polymer is in agreement with recent theories of diffusion-controlled stepwise polymerization, and can be slightly affected by the confinement.     

Y型分子筛中苯分子定域和流动性的蒙特卡罗模拟研究

用巨正则蒙特卡罗模拟方法研究了NaY分子筛中苯的扩散性质。结果表明,在苯分子的扩散过程中,钠Y分子筛中存在两个不同的吸附位点。并且,通过高吸附值下这两个吸附位点附近苯分子粒子分布云图的分析,可以发现这两个吸附位点附近的苯分子具有不同的迁移特性,位点C附近的苯分子基本上是定域的,但位点W附近的苯分子则分散在一个相对较广的区域内,可以在超笼内从一个位点迁移到另一个位点。     

The flame photometric determination of Fe,Ni, Co,Cu, Mn,Cr, and Al in waters

Summary A method for the flame photometric determination of Fe, Ni, Co, Cu, Mn, Al, and Cr in various waters is described. Samples can be analysed directly after removal of interfering anions or after separation (and concentration) of the elements to be determined from any interfering cations. Fe, Ni, Co, and Cu are extracted as carbamates, Al as cupferronate, and Cr as the ion-association complex HCrO₃Cl. The extractant used for all is hexone.The elimination of the interference of Mg with Fe is discussed. The variation of the relative error of the emission measurement with the concentration of the elements was investigated.

---

Zusammenfassung Eine Methode zur flammenphotometrischen Bestimmung von Fe, Ni, Co, Cu, Mn, Al und Cr in Wässern wurde beschrieben. Nach Entfernung der störenden Anionen oder nach Abtrennung (und Anreicherung) der zu bestimmenden Elemente von etwa störenden Kationen können die Proben direkt analysiert werden. Fe, Ni, Co und Cu werden als Carbamate extrahiert, Al als Cupferronat und Cr in Form des Ionen-Assotiationskomplexes HCrO₃Cl. Als Extraktionsmittel dient in allen Fällen Hexon.Die Beseitigung des störenden Einflusses von Magnesium bei der Eisenbestimmung wurde diskutiert. Die Variation des relativen Fehlers der Emissionsmessung mit der Konzentration der Elemente wurde untersucht.

---

Résumé On décrit une méthode pour le dosage par photométrie de flamme du Fe, Ni, Co, Cu, Mn, Al et Cr dans des eaux variées. On peut faire l'analyse directe après élimination des anions qui interfèrent ou après séparation (et concentration) des éléments à doser d'avec les cations gênants. On extrait Fe, Ni, Co et Cu sous forme de carbamates, Al en cupferronate, et Cr à l'état de complexe par association ionique, HCrO₃Cl. Dans tous les cas, on utilise l'hexone comme agent d'extraction.On discute l'élimination de l'interférence du Mg par le Fe. On a suivi la variation de l'erreur relative dans la mesure de l'émission en fonction de la concentration des éléments.

---

---

Paper presented at the Symposium on Analytical Chemistry, Graz, 29th September–1st October 1965.     

Monte Carlo simulation of catalytic CO oxidation

A simple Monte Carlo model of the CO oxidation on a single-crystal catalyst surface is presented. The simulation model considers the following elementary reaction steps:

1. (1) chemisorption of a CO molecule, its surface migration and possible desorption

2. (2) physisorption of an O₂ molecule to a precursor state and its subsequent dissociative chemisorption

3. (3) activated reaction of adsorbed O and CO (the Langmuir - Hinshelwood reaction mechanism), formation of CO₂ and its rapid desorption.

The changes in the activation energy of reaction and in the adsorption energy of CO resulting from the interactions between adsorbed species are also considered. The model makes possible to monitor temperature programmed reaction spectra or reaction spectra obtained during changes of the ratio of the partial pressures of CO and O₂. The results of simulations for a Pd(111) single-crystal plane are compared with experiment.