Theory of Oxygen Tracer Diffusion Along Grain Boundaries and in the Bulk in Two-Stage Oxidation Experiments. Part III: Monte-Carlo Simulations

1997 ◽  
Vol 7 (9) ◽  
pp. 1797-1811 ◽  
Author(s):  
Yuri Mishin ◽  
J�rg Schimmelpfennig ◽  
G�nter Borchardt
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Grain Boundaries ◽  
Tracer Diffusion ◽  
Two Stage ◽  
Oxygen Tracer

ATOMIC RESOLUTION STUDIES OF SOLUTE-ATOM SEGREGATION AT GRAIN BOUNDARIES : EXPERIMENTS AND MONTE CARLO SIMULATIONS

1990 ◽  
Vol 51 (C1) ◽  
pp. C1-47-C1-57 ◽  
Author(s):  
D. N. SEIDMAN ◽  
J. G. HU ◽  
S.-M. KUO ◽  
B. W. KRAKAUER ◽  
Y. OH ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Grain Boundaries ◽  
Solute Atom ◽  
Atomic Resolution

Polynomial Approximation for Two Stage Stochastic Programming with Separable Objective

2012 ◽  
pp. 322-333
Author(s):  
Lijian Chen ◽  
Dustin J. Banet
Keyword(s):  
Monte Carlo ◽  
Stochastic Programming ◽  
Monte Carlo Simulations ◽  
Programming Model ◽  
Optimal Solution ◽  
Two Stage ◽  
Convex Objective Function ◽  
Stochastic Programming Model ◽  
Gradient Type ◽  
Norm Approximation

In this paper, the authors solve the two stage stochastic programming with separable objective by obtaining convex polynomial approximations to the convex objective function with an arbitrary accuracy. Our proposed method will be valid for realistic applications, for example, the convex objective can be either non-differentiable or only accessible by Monte Carlo simulations. The resulting polynomial is constructed by Bernstein polynomial and norm approximation models. At a given accuracy, the necessary degree of the polynomial and the replications are properly determined. Afterward, the authors applied the first gradient type algorithms on the new stochastic programming model with the polynomial objective, resulting in the optimal solution being attained.

Atomistic Monte Carlo Simulations of Homogeneous and Heterogeneous Precipitation on Grain Boundaries of NbC in Steels

2005 ◽  
Vol 237-240 ◽  
pp. 721-726 ◽  
Author(s):  
Céline Hin ◽  
Frédéric Soisson ◽  
Philippe Maugis
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Grain Boundaries ◽  
Vacancy Concentration ◽  
Recrystallization Process ◽  
Thermal Treatments ◽  
Heterogeneous Precipitation ◽  
Defect Source ◽  
Equilibrium Segregation ◽  
Diffusion Properties

The precipitation of niobium carbides in industrial steels is commonly used to control the recrystallization process or the amount of interstitial atoms in solid solution. It is then important to understand the precipitation kinetics and especially the competition between homogeneous and heterogeneous precipitation, since both of them have been observed experimentally, depending on the alloy composition, microstructure and thermal treatments. We propose Monte Carlo simulations of NbC precipitation in α-iron, based on a simple atomic description of the main parameters which control the kinetic pathway : - realistic diffusion properties, with a rapid diffusion of C atoms by interstitial jumps and a slower diffusion of Fe and Nb atoms by vacancy jumps - a simple model of grain boundaries which reproduces the equilibrium segregation properties of Nb and C - a point defect source which drives the vacancy concentration towards its equilibrium value. Depending on the precipitation conditions, MC simulations predict different kinetic behaviours, including homogeneous and heterogeneous NbC precipitation, early segregation of C atoms and its importance as a first stage for NbC precipitation, wetting phenomena on grain boundaries and transient precipitation of metastable carbides.

Insight into the adsorption mechanism of benzene in HY zeolites: the effect of loading

RSC Advances ◽  
2016 ◽  
Vol 6 (41) ◽  
pp. 34175-34187 ◽  
Author(s):  
Huimin Zheng ◽  
Liang Zhao ◽  
Qing Yang ◽  
Shanqing Dang ◽  
Yuxian Wang ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Inflection Point ◽  
Adsorption Mechanism ◽  
Two Stage ◽  
Hy Zeolites ◽  
Insight Into

An interesting two-stage adsorption mechanism, defined as “ideal adsorption” and “insertion adsorption”, was first proposed for the benzene/HY system by Metropolic Monte Carlo simulations at loadings below and above an “inflection point”.

scholarly journals Tracer Diffusion by Six-Jump-Cycles in Nonstoichiometric B2 Intermetallic Compounds

2005 ◽  
Vol 247-248 ◽  
pp. 9-20 ◽  
Author(s):  
K.L. Gosain ◽  
D.K. Chaturvedi ◽  
Irina V. Belova ◽  
Graeme E. Murch
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Intermetallic Compounds ◽  
Diffusion Coefficients ◽  
Tracer Diffusion ◽  
Jump Frequency ◽  
Single Vacancy ◽  
Frequency Model ◽  
Jump Frequencies ◽  
Tracer Diffusion Coefficients

Tracer diffusion in non-stoichiometric B2 intermetallic compounds having antistructural disorder is investigated using the six-jump-cycle (6JC) as a fundamental diffusion unit. For non-stoichiometric compositions, the antistructural atoms are assumed to be isolated and located at one of the six [110]-type and [100]-type sites (as only these sites are involved in the 6JC or 2JC). The jump frequencies for the 6JC involving a perfectly ordered configuration are calculated in terms of a four-frequency-model, using the meanfirst- passage concept of Arita et al. The jump frequency of an antistructural atom at [110] or [100]-type sites is taken to be the harmonic mean of frequencies of two successive nearestneighbour jumps of the same kind of atoms. The expressions for the tracer diffusion coefficients are derived for both atomic components at deviations from stoichiometry, assuming that the 6JC mechanism is valid. The results are compared with Monte Carlo simulations based on single vacancy jumps and found to be in fair agreement for compositions close to stoichiometry.

Monte Carlo Simulation of Oxygen Tracer Diffusion in a Growing Oxide Film

1997 ◽  
Vol 143-147 ◽  
pp. 1225-1230
Author(s):  
Yuri M. Mishin ◽  
J. Schimmelpfennig ◽  
M. Göbel ◽  
Günter Borchardt
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Oxide Film ◽  
Tracer Diffusion ◽  
Oxygen Tracer
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