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regular solution model

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Published: 01 December 2008
Fig. 2 Calculated phase diagrams for a liquid (L) and solid (S) phase using the regular solution model with various regular solution parameters Ω L and Ω S . (a) Ω L = Ω S = 0 (ideal solution). (b) Ω L = 10 kJ/mol; Ω S = 20 kJ/mol. (c) Ω L = Ω S = 20 kJ/mol. The transformation entropies More
Series: ASM Handbook
Volume: 1A
Publisher: ASM International
Published: 31 August 2017
DOI: 10.31399/asm.hb.v01a.a0006307
EISBN: 978-1-62708-179-5
... without going into dislocation theory. The article discusses modeling of hardness in cast iron based on a regular solution equation in which the properties of each phase depend on chemical composition and coarseness. It describes the evaluation of material parameters from the tensile stress-strain curve...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005206
EISBN: 978-1-62708-187-0
...) T c φ = Ω φ 2 R Fig. 2 Calculated phase diagrams for a liquid (L) and solid (S) phase using the regular solution model with various regular solution parameters Ω L and Ω S . (a) Ω L = Ω S = 0 (ideal solution). (b) Ω L = 10 kJ/mol; Ω S = 20 kJ/mol. (c) Ω L = Ω S = 20...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005211
EISBN: 978-1-62708-187-0
...) ( Δ T ν ) =  Constant Various theories have been proposed to explain these relationships, and several rigorous mathematical and phenomenological models have been developed to explain the various features of the regular lamellar and rodlike eutectic structures ( Ref 9 , 13 , 14...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005517
EISBN: 978-1-62708-197-9
..., and this assumption can often be quite reasonable and used for process models that include the gas phase. However, in condensed phases, there is always some interaction between components. Nonideal Solutions: Regular and Subregular Solution Models The regular solution model is the simplest of the nonideal...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005207
EISBN: 978-1-62708-187-0
...                     = R T [ C B ln C B + ( 1 − C B ) ln ( 1 − C B ) ] With more concentrated alloys, a regular solution model is often applied in which the heat of mixing is given by the symmetrical term Ω C B (1 − C B ), where Ω reflects the net interatomic...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005408
EISBN: 978-1-62708-196-2
... in microchemistry, that is, the variation in solute level and precipitation, during thermomechanical processing. The resulting anisotropic properties — here, earing — are simulated with a polycrystalplasticity model. The possibility of a coupled microstructure and texture simulation is then illustrated by way...
Series: ASM Handbook
Volume: 3
Publisher: ASM International
Published: 27 April 2016
DOI: 10.31399/asm.hb.v03.a0006223
EISBN: 978-1-62708-163-4
... the important phase transformations in metallurgy mainly occur at a fixed pressure of 1 atm, the focus is on changes in composition and temperature. In order to introduce some of the basic concepts of the thermodynamics of alloys, a simple physical model for binary solid solutions is presented. Gibbs Free...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005407
EISBN: 978-1-62708-196-2
.... It has a memory-reduction feature for use when the training set is large. The time required for training can be dramatically reduced using this method. However, it is sometimes difficult to find the best model using this algorithm. Bayesian regularization is a modification of the Levenberg-Marquardt...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005521
EISBN: 978-1-62708-197-9
... growth kinetics, the characteristic dendrite arm spacing, the shape of the grain envelope, as well as the solute flow inside and outside the grain envelope—information that are inputs to more approximate modeling approaches. The main drawback is the excessively high computational resources required...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005415
EISBN: 978-1-62708-196-2
.... The gradient term is a major feature in phase-field models where the field representation of microstructure results in a unified description of multiple phases and a smooth transition from one phase to another. (This is compared to conventional moving-boundary diffusion models in which the diffusion solution...
Series: ASM Handbook
Volume: 24A
Publisher: ASM International
Published: 30 June 2023
DOI: 10.31399/asm.hb.v24A.a0006994
EISBN: 978-1-62708-439-0
... Abstract Process optimization is the discipline of adjusting a process to optimize a specified set of parameters without violating engineering constraints. This article reviews data-driven optimization methods based on genetic algorithms and stochastic models and demonstrates their use...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005439
EISBN: 978-1-62708-196-2
... Abstract This article presents various equations that are essential for the modeling of both single-phase and multiphase profiles. It includes the fundamental laws of diffusion, along with its equations and solutions. The article provides information on the series of applications...
Series: ASM Handbook
Volume: 6A
Publisher: ASM International
Published: 31 October 2011
DOI: 10.31399/asm.hb.v06a.a0005636
EISBN: 978-1-62708-174-0
... metal arc welding (GMAW), laser welding, electron beam welding, and laser-arc hybrid welding. Furthermore, the models are based on the solution of governing conservation equations for mass, momentum, energy, and chemical species. The calculated results from the heat and mass transfer models, especially...
Series: ASM Handbook
Volume: 4F
Publisher: ASM International
Published: 01 February 2024
DOI: 10.31399/asm.hb.v4F.a0007008
EISBN: 978-1-62708-450-5
... model on a commercial software such as Ansys Fluent or an open-source software such as OpenFOAM. In this phase, the system geometries are provided along with boundary and initial conditions. Depending on the problem situation, it could be a steady-state solution (on a continuous process, i.e., steel...
Series: ASM Handbook
Volume: 1A
Publisher: ASM International
Published: 31 August 2017
DOI: 10.31399/asm.hb.v01a.a0006314
EISBN: 978-1-62708-179-5
... include the dendrite growth models and the cooperative eutectic growth models. The article provides some solutions using numerical models to simulate the kinetics of microstructure formation in cast iron. It concludes with a discussion on cellular automaton (CA) technique that can handle complex topology...
Series: ASM Handbook
Volume: 4C
Publisher: ASM International
Published: 09 June 2014
DOI: 10.31399/asm.hb.v04c.a0005876
EISBN: 978-1-62708-167-2
...), and partially on thermal fields. For obvious reasons, the early models, mostly applied to induction heating and/or melting processes, involved closed-form analytical solutions. Analytical solutions of MEs are possible only for very simple geometries and in the hypothesis of linear, homogeneous...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005501
EISBN: 978-1-62708-197-9
... a large number of prototype binary phase diagrams with different topological features using ideal and regular solution models. Since then, many researchers began to incorporate phase equilibrium data to evaluate the thermodynamic properties of alloys. It was not until the late 1980s that a number of phase...
Series: ASM Handbook
Volume: 14B
Publisher: ASM International
Published: 01 January 2006
DOI: 10.31399/asm.hb.v14b.a0005133
EISBN: 978-1-62708-186-3
... creep in terms of a constitutive model, and then using the constitutive model in a process model or finite element analysis to predict the final part shape. age-forming finite element analysis low-temperature creep mechanical test stress AGE FORMING is a shaping process for heat treatable...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005518
EISBN: 978-1-62708-197-9
... of the heat and/or solute diffusion equations, taking into account the local conditions at the solid/liquid interface, and the influence of anisotropic solid/liquid interfacial energies and mobilities. Direct models of the microstructure have been used to calculate solidification patterns, giving rise...