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Monte Carlo model

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Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005428
EISBN: 978-1-62708-196-2
... Abstract The misorientation of a boundary of a growing grain is defined not only by its crystallography but also by the crystallography of the grain into which it is growing. This article focuses on the Monte Carlo Potts model that is typically used to model grain growth, Zener-Smith pinning...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0004027
EISBN: 978-1-62708-185-6
... (observations shown in points). Source: Ref 11 Fig. 8 A series of snapshots during a two-dimensional grain-growth simulation using the Monte Carlo-Potts model. The system size is 400 by 400 with periodic boundary conditions and isotropic boundary energies and mobilities. Source: Ref 20 The...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005425
EISBN: 978-1-62708-196-2
... mechanism-based models, such as those designed to predict phase equilibria (e.g., Calphad), recrystallization and grain growth (Monte Carlo and cellular-automaton techniques), and precipitation and solidification problems (e.g., phase-field methods). The successful implementation of these newer techniques...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005459
EISBN: 978-1-62708-196-2
...,”  “Monte Carlo Models for Grain Growth and Recrystallization,” and “Network and Vertex Models for Grain Growth” in this Volume. Experimental observations of the various features and mechanisms of microstructure evolution during the TMP of superalloys (and similar materials) form the...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005434
EISBN: 978-1-62708-196-2
... article mainly focuses on phenomena and modeling approaches that are specific to VPP; however, most of the complementary information needed on general or specialized topics of interest (nucleation, microstructure evolution, Monte Carlo methods, etc.) is found in the cited references or in other articles...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005401
EISBN: 978-1-62708-196-2
... with a strong initial texture showing periods of rapid and slow growth. Source: Ref 22 Texture-controlled grain growth during beta annealing of titanium alloys has been simulated using both the Monte Carlo (Potts) and phase-field modeling approaches. In the work of Ivasishin et al. ( Ref 24...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005422
EISBN: 978-1-62708-196-2
... mobility of boundary junctions on grain growth. Various models have been used for the simulation of grain-boundary migration and related phenomena, in particular, grain growth and recrystallization, notably Monte Carlo ( Ref 1 , Ref 2 , Ref 3 , Ref 4 ), phase field ( Ref 5 , 6 ), and network models...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005414
EISBN: 978-1-62708-196-2
... traditionally been used to characterize microstructures. Mesoscale techniques are broadly classified into the following types: Monte Carlo simulations, cellular automata, and phase-field models ( Ref 53 ) (see the corresponding articles “Monte Carlo Models for Grain Growth and Recrystallization,” “Cellular...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005410
EISBN: 978-1-62708-196-2
... techniques. These can be atomic simulations, such as molecular dynamics ( Ref 65 , 66 ), for condensation of a gas into a liquid or crystallisation of a liquid, or kinetic Monte Carlo ( Ref 67 , Ref 68 , Ref 69 ) for solid-solid phase transformations, or phase-field simulations (see the Appendix at the...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005432
EISBN: 978-1-62708-196-2
... that distinguish CA simulations (and other representational simulations such as Monte Carlo simulations) from mean field analytical models and models employing a homogeneous effective medium. This article examines how CA can be applied to the simulation of static and dynamic recrystallization. It...
Series: ASM Handbook
Volume: 17
Publisher: ASM International
Published: 01 August 2018
DOI: 10.31399/asm.hb.v17.a0006463
EISBN: 978-1-62708-190-0
... it is needed, the history behind the development of POD, how POD assessments are performed, and how modeling and simulation can be integrated into the execution of a POD assessment. It describes the methods by which POD is determined. This includes detail on the experimental process to acquire the...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0009002
EISBN: 978-1-62708-185-6
... of microstructure evolution. cellular automata dynamic recovery grain growth hot working microstructure evolution microstructure evolution modeling Monte-Carlo techniques plastic flow recrystallization static recovery texture evolution models thermomechanical processing IN...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005430
EISBN: 978-1-62708-196-2
... energies ( Ref 21 , Ref 22 , 23 ). Diffusion coefficients can be extracted from kinetic Monte Carlo simulations using Kub-Green expressions ( Ref 24 , 25 ). Assuming a vacancy diffusion mechanism in a crystalline phase, the mobility matrix in the lattice-fixed frame, V M k i , which...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0004003
EISBN: 978-1-62708-185-6
... ). Furthermore, Monte Carlo models are being developed for beta grain growth in titanium ( Ref 48 ). These new tools are uncovering the complexities of grain growth within a textured material or a material with an evolving texture. Computer process modeling will continue to be at the forefront of advanced TMP...
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006638
EISBN: 978-1-62708-213-6
... alloy). The matrix correction calculations in DTSA-II are based upon the Pouchou and Pichoir φ(ρz) ionization depth distribution model ( Ref 10 ). Inspecting the results in Tables 2 – 10 reveals that all of the RDEV values for these 50 individual elemental analyses are less than ±4% relative, and the...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0003971
EISBN: 978-1-62708-185-6
... formulations seek to describe phenomena at the meso (grain) scale. Challenges with regard to the validation and industrial application of many mechanism-based models still remain, however, largely because of the dearth of reliable material-property data. Fig. 5 Monte Carlo (three-dimensional) model...
Book Chapter

By S. Lampman
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006645
EISBN: 978-1-62708-213-6
... calibrations, such as the Monte Carlo model, for archaeological materials. This model is currently being used to perform analyses of heterogeneous materials and investigations of complex photon interactions within a sample. Basically, it is a fundamental-parameter method, but it applies statistical models of...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.9781627081979
EISBN: 978-1-62708-197-9
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006637
EISBN: 978-1-62708-213-6
... effect subsequently disappears. Channeling was first predicted in 1912 ( Ref 11 ). In 1963, channeling was accidently observed through Monte Carlo simulations ( Ref 12 , 13 ), which immediately triggered intensive experimental and modeling studies ( Ref 14 , 15 ). In 1965, the systematic channeling...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005429
EISBN: 978-1-62708-196-2
... directly calculate the electronic state by quantum Monte Carlo methods. If properly coupled to next-generation supercomputers, this eventually could overtake all other developments ( Ref 11 ). The rest of this article is divided into three independent sections. The first reviews the general underlying...