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classical nucleation theory

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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
... Abstract This article describes the results obtained by Volmer, Weber, Farkas, Becker, and Doring, which constitute the classical nucleation theory. These results are the predictions of the precipitate size distribution, steady-state nucleation rate, and incubation time. The article reviews...
Image
Published: 01 December 2009
) and lines to predictions of the classical nucleation theory. Full lines correspond to the equilibrium cluster size distribution ( Eq 7 ) for n ≤ n * and dotted lines to the steady-state distributions ( Eqs 8 and 85 ). More
Series: ASM Handbook
Volume: 9
Publisher: ASM International
Published: 01 December 2004
DOI: 10.31399/asm.hb.v09.a0003732
EISBN: 978-1-62708-177-1
... is the mechanism of classical nucleation and growth ( Fig. 1a ) of precipitates from a metastable solid solution. Instead, spinodal reactions involve spontaneous unmixing or diffusional clustering of atoms, where a two-phase structure forms by spontaneous growth from small composition fluctuations ( Fig. 1b...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005435
EISBN: 978-1-62708-196-2
... controlled by weak defect or homogeneous nucleation at high driving forces can require significant nonclassical corrections. For bulk polycrystals, where transformation is dominated by strong defects at relatively low driving forces, classical heterogeneous nucleation theory ( Ref 45 ) can be applied...
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
... transformations based on classical nucleation theory and diffusional growth, and grain growth, among others, in the 1940s to1960s. Beginning in the 1980s, the incorporation of the fundamental concepts of thermodynamics and thermal physics (due to, for example, Gibbs, Ising, and others) led to a great expansion...
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 explicit nucleation algorithm does not specify how to compute Δ F * in Eq 25 , the activation energy of nucleation. This gives the flexibility to choose any nucleation theory for the model. In the classical nucleation theory for homogeneous nucleation, for example: (Eq 27) Δ F * = α σ d...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005409
EISBN: 978-1-62708-196-2
...-growth phenomena in the single-phase alpha or beta fields, inasmuch as such processes are strongly influenced by the dependence of nucleation and growth events on the local orientation of individual grains as well as the misorientation across grain boundaries. As such, microstructure and texture...
Book Chapter

Series: ASM Handbook
Volume: 3
Publisher: ASM International
Published: 27 April 2016
DOI: 10.31399/asm.hb.v03.a0006229
EISBN: 978-1-62708-163-4
... processes. (a) Classical nucleation and growth. (b) Spinodal decomposition. Source: Ref 8 as published in Ref 9 The underlying theory of spinodal decomposition involves the concept of the gradient energy. The concept of gradient energy (which is the energy associated with a diffuse interface...
Series: ASM Handbook
Volume: 1A
Publisher: ASM International
Published: 31 August 2017
DOI: 10.31399/asm.hb.v01a.a0006304
EISBN: 978-1-62708-179-5
...) Spheroidal graphite iron, 30 mm diam bar. Courtesy of R. Boeri and G. Rivera Nucleation in cast alloys is heterogeneous, that is, on nuclei having a different chemical composition than the solidifying iron-carbon alloy. Predictions with the classic theory of heterogeneous nucleation, which...
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
... , the inner integral expresses the radius of the grains that nucleated at time τ and grew until time t . The growth velocity in Eq 1 and 2 is calculated as a function of undercooling, using generally the form v ( Δ T ) = A Δ T 2 (where A is a constant), which comes from classical...
Series: ASM Handbook Archive
Volume: 10
Publisher: ASM International
Published: 01 January 1986
DOI: 10.31399/asm.hb.v10.a0001763
EISBN: 978-1-62708-178-8
... undergoing phase separation depends on the assumed mechanism, that is, nucleation and growth versus spinodal decomposition. Because nucleation involves the formation of nuclei and growth at random locations within the material, Eq 4 can be used. The formal analogy between the theory of SAS...
Book Chapter

By W.L. Johnson
Series: ASM Handbook
Volume: 2
Publisher: ASM International
Published: 01 January 1990
DOI: 10.31399/asm.hb.v02.a0001095
EISBN: 978-1-62708-162-7
..., and copious nucleation and growth of crystals is observed. The rise in the nucleation rate is finally halted when the configurational freezing temperature is approached. Using classical nucleation theory, Turnbull developed a model for the rate of crystal nucleation ( N ˙ ) (measured as the number...
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
...) constants; and ε c and ε 0.5 denote the critical strain for the onset of DDRX (≈ 5ε p /6) and the strain for 50% recrystallization, respectively. Equation 10 is a classical Avrami-type relation ( Ref 1 , Ref 20 ) for the nucleation-and-growth type processes that characterize DDRX. The Avrami exponent...
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
... mobility. Heterogeneous Nucleation Homogeneous nucleation is the most difficult kinetic path to crystal formation because of the relatively large activation barrier for nucleus development (Δ G cr ). To overcome this barrier, classical theory predicts that large undercooling values are required...
Series: ASM Handbook
Volume: 6A
Publisher: ASM International
Published: 31 October 2011
DOI: 10.31399/asm.hb.v06a.a0005599
EISBN: 978-1-62708-174-0
... Kinetics The classical theory for particle coarsening was developed independently by Lifshitz and Slyozov ( Ref 18 ) and by Wagner ( Ref 19 ). According to their analysis, the kinetics is controlled by volume diffusion through the matrix. Provided that no solute is lost to the surrounding matrix...
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
...) represent the corresponding concentration profiles of the three regions. The solute boundary layer, δ, is indicated in (c). Source: Ref 17 Cooperative Eutectic Growth Models In the classic JH theory ( Ref 5 ) for solidification of binary eutectic alloys, it was considered that the solute...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005520
EISBN: 978-1-62708-197-9
.... However, the supersaturations predicted by classical homogeneous or heterogeneous nucleation theory are huge. Jones et al. ( Ref 40 ) reviewed the theory of nucleation of gas bubbles in a supersaturated solution, classifying the nucleation mechanisms into four types: I, classical homogeneous nucleation...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005458
EISBN: 978-1-62708-196-2
... Abstract Any model that describes the early stage of cavitation must therefore address experimental observations of continuous nucleation, cracklike interface cavities, cavity growth from nanometer-scale sizes, and debonding at particle interfaces and formation of large-faceted cavities...
Series: ASM Handbook
Volume: 9
Publisher: ASM International
Published: 01 December 2004
DOI: 10.31399/asm.hb.v09.a0003734
EISBN: 978-1-62708-177-1
... Peritectic Structures The classical description of peritectic reactions postulates heterogeneous nucleation of β at the α/liquid interface at the peritectic equilibrium temperature T p ( Ref 26 ). Undercoolings of up to 4% of T p are required for the systems investigated ( Ref 35 ). If nucleation...
Series: ASM Handbook
Volume: 9
Publisher: ASM International
Published: 01 December 2004
DOI: 10.31399/asm.hb.v09.a0003723
EISBN: 978-1-62708-177-1
... are useful in determining the conditions for proper heat treatment (solid-state transformation) of metals and alloys. The influence of the mechanisms of phase nucleation and growth on the morphology, size, and distribution of grains and second phases is also described. bainite eutectic alloy system...