MONTE CARLO STABILITY ANALYSIS OF STRAINED LAYER SUPERLATTICE INTERFACES

1985 ◽  
Vol 56 ◽  
Author(s):  
BRIAN W. DODSON
Keyword(s):  
Monte Carlo ◽  
Stability Analysis ◽  
Lattice Mismatch ◽  
Three Dimensional ◽  
Model Systems ◽  
Model Potentials ◽  
Strained Layer ◽  
Limits Of Stability ◽  
Lennard Jones ◽  
Strained Layer Superlattice

AbstractWe have developed a procedure, based on conventional Monte Carlo methods, to investigate the limits of stability of a strained layer superlattice (SLS) system as a function of lattice mismatch and layer thickness. The method is demonstrated by the analysis of two-dimensional Lennard-Jones SLS systems, for which the regime of absolute SLS stability is mapped out. Extension of the technique to three-dimensional silicon-like model systems is discussed, and appropriate model potentials for stability analysis of the Si/SiGe system are introduced.

Stability and Growth of Lennard-Jones Strained Layer Superlattice Interfaces

1984 ◽  
Vol 37 ◽  
Author(s):  
Brian W. Dodson
Keyword(s):  
Monte Carlo ◽  
Model System ◽  
Interatomic Potentials ◽  
Growth Processes ◽  
Strained Layer ◽  
Monte Carlo Techniques ◽  
Lennard Jones ◽  
Strained Layer Superlattice ◽  
The Stability

AbstractIn the context of a model system whose atoms interact via Lennard-Jones (LJ) interatomic potentials, we have studied the stability of an initially perfect strained layer superlattice interface (SLS) and the process of growth of a mismatched layer on a substrate using Monte Carlo techniques. An initially perfect SLS interface is found to be metastable up to 12% mismatch, a much higher value than is found on real SLS systems. In contrast, we find that, within the limitations of the calculations, a perfect SLS interface cannot be grown in an LJ system. The implications of these results for understanding SLS growth processes is discussed.

The limits of strain and lattice parameter measurements by CBED

1989 ◽  
Vol 47 ◽  
pp. 518-519
Author(s):  
Hamish L. Fraser
Keyword(s):  
Electron Beam ◽  
Mirror Symmetry ◽  
Local Symmetry ◽  
Lattice Parameter ◽  
Growth Direction ◽  
Surface Relaxation ◽  
Strained Layer ◽  
Axis Parallel ◽  
Local Lattice ◽  
Strained Layer Superlattice

The topic of strain and lattice parameter measurements using CBED is discussed by reference to several examples. In this paper, only one of these examples is referenced because of the limitation of length. In this technique, scattering in the higher order Laue zones is used to determine local lattice parameters. Work (e.g. 1) has concentrated on a model strained-layer superlattice, namely Si/Gex-Si1-x. In bulk samples, the strain is expected to be tetragonal in nature with the unique axis parallel to [100], the growth direction. When CBED patterns are recorded from the alloy epi-layers, the symmetries exhibited by the patterns are not tetragonal, but are in fact distorted from this to lower symmetries. The spatial variation of the distortion close to a strained-layer interface has been assessed. This is most readily noted by consideration of Fig. 1(a-c), which show enlargements of CBED patterns for various locations and compositions of Ge. Thus, Fig. 1(a) was obtained with the electron beam positioned in the center of a 5Ge epilayer and the distortion is consistent with an orthorhombic distortion. When the beam is situated at about 150 nm from the interface, the same part of the CBED pattern is shown in Fig. 1(b); clearly, the symmetry exhibited by the mirror planes in Fig. 1 is broken. Finally, when the electron beam is positioned in the center of a 10Ge epilayer, the CBED pattern yields the result shown in Fig. 1(c). In this case, the break in the mirror symmetry is independent of distance form the heterointerface, as might be expected from the increase in the mismatch between 5 and 10%Ge, i.e. 0.2 to 0.4%, respectively. From computer simulation, Fig.2, the apparent monocline distortion corresponding to the 5Ge epilayer is quantified as a100 = 0.5443 nm, a010 = 0.5429 nm and a001 = 0.5440 nm (all ± 0.0001 nm), and α = β = 90°, γ = 89.96 ± 0.02°. These local symmetry changes are most likely due to surface relaxation phenomena.

MONTE CARLO STUDY OF EPITAXIAL OVERLAYER WITH SUBSTANTIAL LATTICE MISMATCH

1987 ◽  
Vol 48 (C5) ◽  
pp. C5-199-C5-202
Author(s):  
T. MIYASAKI ◽  
K. AIZAWA ◽  
H. AOKI ◽  
C. ITOH ◽  
M. OKAZAKI
Keyword(s):  
Monte Carlo ◽  
Lattice Mismatch ◽  
Monte Carlo Study

Casimir forces and vacuum energy

2017 ◽  
Author(s):  
Serge Reynaud ◽  
Astrid Lambrecht
Keyword(s):  
Casimir Force ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Thermal Fluctuations ◽  
Model Systems ◽  
Vacuum Field ◽  
Force Measurements ◽  
Casimir Forces ◽  
Current State ◽  
Field Fluctuations

The Casimir force is an effect of quantum vacuum field fluctuations, with applications in many domains of physics. The ideal expression obtained by Casimir, valid for perfect plane mirrors at zero temperature, has to be modified to take into account the effects of the optical properties of mirrors, thermal fluctuations, and geometry. After a general introduction to the Casimir force and a description of the current state of the art for Casimir force measurements and their comparison with theory, this chapter presents pedagogical treatments of the main features of the theory of Casimir forces for one-dimensional model systems and for mirrors in three-dimensional space.

scholarly journals Evaluating variability in coseismic slips of paleoearthquakes from an incomplete slip history: an example from displaced terrace flights across the Kamishiro fault, central Japan

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Naoya Takahashi ◽  
Shinji Toda
Keyword(s):  
Monte Carlo ◽  
Three Dimensional ◽  
Seismic Hazard Assessment ◽  
Probabilistic Seismic Hazard Assessment ◽  
Reverse Fault ◽  
Central Japan ◽  
Systematic Analysis ◽  
Fluvial Terraces ◽  
Rupture Length ◽  
Slip History

AbstractExamining the regularity in slip over seismic cycles leads to an understanding of earthquake recurrence and provides the basis for probabilistic seismic hazard assessment. Systematic analysis of three-dimensional paleoseismic trenches and analysis of offset markers along faults reveal slip history. Flights of displaced terraces have also been used to study slips of paleoearthquakes when the number of earthquakes contributing to the observed displacement of a terrace is known. This study presents a Monte Carlo-based approach to estimating slip variability using displaced terraces when a detailed paleoseismic record is not available. First, we mapped fluvial terraces across the Kamishiro fault, which is an intra-plate reverse fault in central Japan, and systematically measured the cumulative dip slip of the mapped terraces. By combining these measurements with the age of the paleoearthquakes, we estimated the amount of dip slip for the penultimate event (PE) and antepenultimate event (APE) to be 1.6 and 3.4 m, respectively. The APE slip was nearly three times larger than the most recent event of 2014 (Mw 6.2): 1.2 m. This suggests that the rupture length of the APE was much longer than that of the 2014 event and the entire Kamishiro fault ruptured with adjacent faults during the APE. Thereafter, we performed the Monte Carlo simulations to explore the possible range of the coefficient of variation for slip per event (COVs). The simulation considered all the possible rupture histories in terms of the number of events and their slip amounts. The resulting COVs typically ranged between 0.3 and 0.54, indicating a large variation in the slip per event of the Kamishiro fault during the last few thousand years. To test the accuracy of our approach, we performed the same simulation to a fault whose slip per event was well constrained. The result showed that the error in the COVs estimate was less than 0.15 in 86% of realizations, which was comparable to the uncertainty in COVs derived from a paleoseismic trenching. Based on the accuracy test, we conclude that the Monte Carlo-based approach should help assess the regularity of earthquakes using an incomplete paleoseismic record.

scholarly journals Identification of Efficient Sampling Techniques for Probabilistic Voltage Stability Analysis of Renewable-Rich Power Systems

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2328
Author(s):  
Mohammed Alzubaidi ◽  
Kazi N. Hasan ◽  
Lasantha Meegahapola ◽  
Mir Toufikur Rahman
Keyword(s):  
Monte Carlo ◽  
Stability Analysis ◽  
Power Systems ◽  
Large Scale ◽  
Voltage Stability ◽  
Sampling Technique ◽  
Coefficient Of Determination ◽  
Sampling Techniques ◽  
Quasi Monte Carlo ◽  
Efficient Sampling

This paper presents a comparative analysis of six sampling techniques to identify an efficient and accurate sampling technique to be applied to probabilistic voltage stability assessment in large-scale power systems. In this study, six different sampling techniques are investigated and compared to each other in terms of their accuracy and efficiency, including Monte Carlo (MC), three versions of Quasi-Monte Carlo (QMC), i.e., Sobol, Halton, and Latin Hypercube, Markov Chain MC (MCMC), and importance sampling (IS) technique, to evaluate their suitability for application with probabilistic voltage stability analysis in large-scale uncertain power systems. The coefficient of determination (R2) and root mean square error (RMSE) are calculated to measure the accuracy and the efficiency of the sampling techniques compared to each other. All the six sampling techniques provide more than 99% accuracy by producing a large number of wind speed random samples (8760 samples). In terms of efficiency, on the other hand, the three versions of QMC are the most efficient sampling techniques, providing more than 96% accuracy with only a small number of generated samples (150 samples) compared to other techniques.

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