Monte Carlo simulation case study

Ruling out a time-dependent criterion (such as the proton has to remain bound to the acceptor atom for a given time period f) enables the application of the ATU in studies that do not propagate the system in time as it is the case in Monte-Carlo simulations and geometry optimisations. 

In this review we put less emphasis on the physics and chemistry of surface processes, for which we refer the reader to recent reviews of adsorption-desorption kinetics which are contained in two books [2,3] with chapters by the present authors where further references to earher work can be found. These articles also discuss relevant experimental techniques employed in the study of surface kinetics and appropriate methods of data analysis. Here we give details of how to set up models under basically two different kinetic conditions, namely (/) when the adsorbate remains in quasi-equihbrium during the relevant processes, in which case nonequilibrium thermodynamics provides the needed framework, and (n) when surface nonequilibrium effects become important and nonequilibrium statistical mechanics becomes the appropriate vehicle. For both approaches we will restrict ourselves to systems for which appropriate lattice gas models can be set up. Further associated theoretical reviews are by Lombardo and Bell [4] with emphasis on Monte Carlo simulations, by Brivio and Grimley [5] on dynamics, and by Persson [6] on the lattice gas model. 

In all these examples, the importance of good simulation and modeling cannot be stressed enough. A variety of methods have been used in this field to simulate the data in the cases studies described above. Blander et al. [4], for example, used a semi-empirical molecular orbital method, MNDO, to calculate the geometries of the free haloaluminate ions and used these as a basis for the modeling of the data by the RPSU model [12]. Badyal et al. [6] used reverse Monte Carlo simulations, whereas Bowron et al. [11] simulated the neutron data from [MMIM]C1 with the Empirical Potential Structure Refinement (EPSR) model [13]. 

The lattice gas has been used as a model for a variety of physical and chemical systems. Its application to simple mixtures is routinely treated in textbooks on statistical mechanics, so it is natural to use it as a starting point for the modeling of liquid-liquid interfaces. In the simplest case the system contains two kinds of solvent particles that occupy positions on a lattice, and with an appropriate choice of the interaction parameters it separates into two phases. This simple version is mainly of didactical value [1], since molecular dynamics allows the study of much more realistic models of the interface between two pure liquids [2,3]. However, even with the fastest computers available today, molecular dynamics is limited to comparatively small ensembles, too small to contain more than a few ions, so that the space-charge regions cannot be included. In contrast, Monte Carlo simulations for the lattice gas can be performed with 10 to 10 particles, so that modeling of the space charge poses no problem. In addition, analytical methods such as the quasichemical approximation allow the treatment of infinite ensembles. 

Atomic jumps in random walk diffusion of closely bound atomic clusters on the W (110) surface cannot be seen. A diatomic cluster always lines up in either one of the two (111) surface channel directions. But even in such cases, theoretical models of the atomic jumps can be proposed and can be compared with experimental results. For diffusion of diatomic clusters on the W (110) surface, a two-jump mechanism has been proposed by Bassett151 and by Cowan.152 Experimental studies are reported by Bassett and by Tsong Casanova.153 Bassett measured the probability of cluster orientation changes as a function of the mean square displacement, and compared the data with those derived with a Monte Carlo simulation based on the two-jump mechanism. The two results agree well only for very small displacements. Tsong Casanova, on the other hand, measured two-dimensional displacement distributions. They also introduced a correlation factor for these two atomic jumps, which resulted in an excellent agreement between their experimental and simulated results. We now discuss briefly this latter study. 

At the next to our previous steps we want to study the additional aspect caused by A-diffusion [22], In Fig. 9.5 the coverages of A and B and the reaction rate Rco2 are shown as a function of the mole fraction of A (or CO) in the gas phase for the different diffusion rates D = 0,1,10, and 100. One can see that the phase transition at y is not influenced by the A-diffusion because at this value of Yco there are only few A particles on the lattice. The value of t/2 increases with increasing D. The character of the phase transitions is not changed by the influence of the diffusion. This is also in agreement with the Monte Carlo simulations where t/2 approaches in the case of very fast diffusion the value of 2/3 [3],... 

Calculations of the incident electron penetration depth into the dielectric layer is a well understood phenomenon [58,59] in recent years many Monte Carlo simulation tools were developed to study it. In our case it allowed an easy calculation of the photoresist layer thickness for different exposure parameters of the eb. For example if the eb exposure is done with Vo = 15 kV accelerating voltage and the dielectric layer is selected to be polymethylmethacrylate (pmma), we estimate the penetration depth by Kanaya and Okayama s [58] expression ... 

Liguras, D.K., et al., Monte Carlo Simulation of Complex Reactive Mixtures An FCC Case Study, in AIChE Symposium Series Advanced FCC Technology. G. Young and R.M. Benslay, eds., 1992. 

All of the considerations discussed lead naturally to the question of what price the analyst pays for this less-than-ideal spike/sample ratio. In most cases, error in the measurement of Rm makes the largest contribution to analytical uncertainty the isotopic compositions of sample and spike are usually well known in comparison to Rm. The matter of error propagation in isotope dilution analyses has been extensively treated by Adriaens et al., [13], and Patterson et al. used Monte Carlo simulation to study the problem [14]. Using propagation of error laws, Heumann derived the following relationship with which to calculate tfopt, the optimum spike-to-sample ratio (neglecting cost and availability) [8] ... 

Scanning tunneling microscopy of solid films of Cm and C > clearly demonstrate the occurrence of photochemical polymerization of these fullerenes in the solid state. X-ray diffraction studies show that such a polymerization is accompanied by contraction of the unit-cell volume in the case of Cm and expansion in the case of C70. This is also evidenced from the STM images. These observations help to understand the differences in the amotphization behavior of Cm and C70 under pressure. Amorphization of Cm under pressure is irreversible because it is accompanied by polymerization associated with a contraction of the unit cel volume. Monte Carlo simulations show how pressure-induced polymerization is favored in Cm because of proper orientation as well as the required proximity of the molecules. Amorphization of C70, on the other hand, is reversible because Cn is less compressible and polymerization is not favored under pressure. 

Case Study The Role of Monte Carlo Simulation 286... 

CASE STUDY THE ROLE OE MONTE CARLO SIMULATION... 

---