Kinetic Monte Carlo modeling

Figure 2. Multiscale modeling hierarchy. AIMD ab initio molecular dynamics, MD molecular dynamics, KMC kinetic Monte Carlo modeling, and FEA finite element analysis.

For the surface defect mechanism, using a HF derived kinetic Monte Carlo model, Radeke and Carter98 showed that H2 desorption from Si(100)-2 x 1 via isolated dihydrides (Figure 11c) follows first-order kinetics. They further showed that the concentration of defects on the surface has a profound effect on the desorption rate constant. Recent studies proposed the importance of step sites rather than terraces99. 

A kinetic Monte Carlo model has been shown to be capable of simulating as-leached nano-porous structures that develop during leaching of NiAl alloys. 

Lou, Y.M., Christofides, P.D. Estimation and control of surface roughness in thin film growth using kinetic Monte-Carlo models. Chem. Eng. Sci. 2003, 58, 3115-29. 

The current part of the present chapter has had as its aim the use of the study of microstructural evolution as a case study in the techniques for bridging scales described earlier in the chapter. The examples that were recounted in our discussion of microstructure and its evolution drew from a variety of the resources discussed earlier in the chapter in the context of bridging scales . In particular, we have seen how kinetic Monte Carlo models adopt an information passage philosophy in which calculations of one type are used to inform those of another. Similarly, the description of solidification, including information on the local crystal orientations, using a linkage of cellular automata with continuum descriptions of heat flow illustrates how more than one computational scheme may be brought under the... 

Radeke MR, Carter EA (1997) Ab initio derived kinetic Monte Carlo model of H2 desorption from Si (100)-2xl. Phys Rev B Cond Mat 55 4649-4658... 

Vanderzande, DJ.M., Marin, G.B., 2011. Kinetic Monte Carlo modeling of the sulfinyl precursor route for poly (p-phenylene vinylene) synthesis. Macromolecules 44, 8716-8726. 

The master equation, however, can only be solved analytically for very simple systems such as the gas-phase reaction A—>B. The analysis of these systems typically requires numerical simulation of a lattice-based kinetic Monte Carlo model. The lattice gas model can then be used to formulate the respective transition probabilities in order to solve the master equationThe groups of both Zhdanov[ ° ° ] and Kreuzerl ° l have been instrumental in demonstrating the application of lattice gas models to solve adsorption and desorption processed from surfaces. Once a lattice model has been formulated there are three types of solution ... 

Kinetic Monte Carlo modeling of phase precipitation in alloys... 

Y. M. Lou and P. D. Christofides, Comput. Chem. Eng., 29, 225 (2004). Feedback Control of Surface Roughness of GaAs (001) Thin Films Using Kinetic Monte Carlo Models. 

E. Lee, F. B. Prinz, and W. Cai, Model. Simul. Mater. Sc., 20, 21 (2012). Ab Initio Kinetic Monte Carlo Model of Ionic Conduction in Bulk Yttria-Stabilized Zirconia. 

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