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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
... of an aluminum solid solution at 500 °C. At this temperature, the solubility limit is x Zr e = 0.0548 % . Symbols correspond to atomic simulations (kinetic Monte Carlo) ( Ref 18 ) and lines to predictions of the classical nucleation theory. Full lines correspond to the equilibrium cluster size...
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
... 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 / ( Δ f V ) d − 1...
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
... gb and the growth of the α wgb . Classical nucleation theory and Fick's law are used to quantify the rate of nucleation and the planar growth of α gb , respectively. The appearance of α wgb sideplates is described empirically based on a critical thickness of the α gb , and their growth is modeled...
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
... 10. Avrami M.J. , Kinetics of Phase Change I: General Theory , J. Chem. Phys. , Vol 7 , 1939 , p 1103 – 1102 ; Vol 8 , 1940 , p 212 – 224 ; Vol 9 , 1941 , p 177 – 184 11. Cahn J.W. , The Kinetics of Grain Boundary Nucleated Reactions , Acta Metall. , Vol 4 , 1956...
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
... in the theory of martensitic nucleation. Olson and Roitburd ( Ref 35 ) reviewed the full range of possible theoretical mechanisms of martensitic nucleation set forth in the pioneering work of Morris Cohen. A central issue has been whether nucleation operates in the “classical” limit, where a critical nucleus...
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
.... At greater undercoolings, the crystallization rate rises very rapidly with falling temperature, 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...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005511
EISBN: 978-1-62708-197-9
... for the prediction of liquation cracking of aluminum welds, with the classic nucleation/growth theory for the simulation of precipitation kinetics of nickel alloys, with the phase-field model for the study of microstructural evolution of a diffusion couple, and with the microscopic and cellular automaton model...
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
... sequences for the formation of a two-phase mixture by diffusion 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...
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 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 eutectic growth theory ( Ref 33...
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
... yields a measure of the radius of gyration of the scattering entity. The theory for interpreting the scattering from multicomponent materials undergoing phase separation depends on the assumed mechanism, that is, nucleation and growth versus spinodal decomposition. Because nucleation involves...
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 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, denoted as n 6 above, typically has a value of approximately 2...
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
... nature of the particles suggests that TiB 2 may not be the actual grain initiation site. 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...
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
...” recrystallization, for which new nucleation is not required. This may partially or completely replace classical recrystallization in postdynamic recrystallization. When recrystallization is complete, the grain-boundary energy provides the driving pressure for normal grain coarsening (growth), which can...
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
...) growing on a cuboidal TiC. Reprinted with permission from Elsevier. Source: Ref 28 Fig. 6 Graphite nucleated on a MnS sulfide, which in turn nucleated on an aluminum, magnesium, silicon, calcium oxide. Source: Ref 8 Fig. 7 Karsay’s gas bubble theory. A, gas bubble; B, graphite; C...
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
.... The first application of the CA technique to cast iron was developed by Charbon and Rappaz ( Ref 59 ). They used the classic model of Wetterfall et al. ( Ref 7 ) for diffusion-controlled graphite growth through the austenite shell to describe spheroidal graphite (SG) iron solidification. The nucleation...
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
..., and eventually, a significant supersaturation can occur. When there is sufficient supersaturation, a pore should nucleate. 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...
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
... of a monotectoid reaction. Fig. 6 (a) Pearlite nucleation. (b) Colony growth. (c) Deep-etched steel sample showing pearlite colony growth off of proeutectoid cementite plate. Source: (a) and (b) from Ref 4 , p 331, (c) from Ref 6 Fig. 7 Growth of intergranular pearlite nodules (numbered...
Series: ASM Handbook
Volume: 4E
Publisher: ASM International
Published: 01 June 2016
DOI: 10.31399/asm.hb.v04e.a0006277
EISBN: 978-1-62708-169-6
.... , Perspectives on Titanium Science and Technology , Acta Mater ., Vol 61 , 2013 , p 844 – 879 10.1016/j.actamat.2012.10.043 2. Nag S. , “Influence of Beta Instabilities on the Early Stage of Nucleation and Growth of Alpha in Beta Titanium Alloys,” Ph.D. dissertation, The Ohio State...