Theory of diffusion-limited precipitation

Ham, Frank S.

doi:10.1016/0022-3697(58)90053-2

Cited by 830 publications

(258 citation statements)

References 21 publications

Supporting

Mentioning

241

Contrasting

Unclassified

Order By: Relevance

“…The growth kinetics at temperatures above 750 C is well understood within a diffusion-driven growth model 7 in moderately doped material where the doping content is low compared to the O concentration. However, the normal diffusivity 8 becomes enhanced at temperatures below 750 C, [9][10][11][12] which influences both the nucleation and the growth kinetics in this temperature regime.…”

mentioning

confidence: 99%

Diffusion-driven precipitate growth and ripening of oxygen precipitates in boron doped silicon by dynamical x-ray diffraction

Will

Gröschel

Bergmann

et al. 2014

Journal of Applied Physics

View full text Add to dashboard Cite

X-ray Pendellösung fringes from three silicon single crystals measured at 900 °C are analyzed with respect to density and size of oxygen precipitates within a diffusion-driven growth model and compared with TEM investigations. It appears that boron doped (p+) material shows a higher precipitate density and a higher strain than moderately (p-) boron crystals. In-situ diffraction reveals a diffusion-driven precipitate growth followed by a second growth regime in both materials. An interpretation of the second growth regime in terms of Ostwald ripening yields surface energy values (around 70 erg/cm2) similar to published data. Further, an increased nucleation rate by a factor of ∼13 is found in the p+ sample as compared to a p- sample at a nucleation temperature of 450 °C.

show abstract

mentioning

confidence: 99%

Diffusion-driven precipitate growth and ripening of oxygen precipitates in boron doped silicon by dynamical x-ray diffraction

Will

Gröschel

Bergmann

et al. 2014

Journal of Applied Physics

View full text Add to dashboard Cite

show abstract

“…In contradiction Ham's early works [20,21] corresponds to a positive influence. In this paper, Ham's original treatment is extended and verified by a detailed 3D numerical solution to model precipitation of arbitrarily-shaped particles.…”

Section: Introductionmentioning

confidence: 78%

“…The diffusion solutions required for invariant field solutions have been provided for cases of spheroids, including special cases of elliptical platelets and infinitely long cylinders, by Ham in [20,21], corresponding to the shape invariant time-dependent solutions [14,15]. Ferrante and Doherty [22] utilized a simplification of Ham's solution for the growth and coarsening of very thin plate-shaped precipitates in Al-Ag alloys, with width to thickness aspect ratio of more than 100.…”

Section: Introductionmentioning

confidence: 99%

Precipitation of Non-Spherical Particles in Aluminum Alloys Part I: Generalization of the Kampmann–Wagner Numerical Model

Holmedal

Osmundsen

2015

Metall Mater Trans A

View full text Add to dashboard Cite

Particles precipitated during aging treatments often have non-spherical shapes, e.g. needles or plates, while in the classical Kampmann-Wagner Numerical (KWN) precipitation model it is assumed that the particles are of spherical shape. This model is here generalized resulting in two correction factors accounting for the effects induced by the particles' non-spherical shape on their growth kinetics. The first one is for the correction of the growth rate. It is derived from the approximate solution of the diffusion problem on spheroidal coordinate and verified by the three-dimensional numerical solutions for cuboid particles. The second factor is for the energetic correction due to the particle surface curvature. It is derived from chemical potential equality (or Gibbs energy minimization principle) at equilibrium for non-spherical particles and provides a correction factor for the Gibbs-Thomson effect. In the accompanying paper the two correction factors are implemented into a multi-component KWN modelling framework and the resulting improvements on the model's predictive power are demonstrated.

show abstract

“…Its emergence in the increase form of precipitates has little effect on ~x. Therefore, one can assume that this is a "diffusion-limited" precipitation process [9] in which case the precipitates are homogeneously distributed throughout the lattice, as indicated in Fig. 9.…”

Section: Resultsmentioning

confidence: 99%

“…The bulk concentration decreases with time as [9] 0) where c is the average concentration at time t, Co the initial concentration, and T is a "relaxation time", determined by the diffusion coefficient. Ham [9] found that for short times n=1.5 and for long times n=l.O. Converting the concentration c to ~x values, Eq.…”

Section: Resultsmentioning

confidence: 99%

Search for NDE Methods to Characterize Thermal History and Mechanical Properties of Al-Li Alloys

Bracci

Garikepati

Jiles

et al. 1988

Review of Progress in Quantitative Nondestructive Evaluation

View full text Add to dashboard Cite

Theory of diffusion-limited precipitation

Cited by 830 publications

References 21 publications

Diffusion-driven precipitate growth and ripening of oxygen precipitates in boron doped silicon by dynamical x-ray diffraction

Diffusion-driven precipitate growth and ripening of oxygen precipitates in boron doped silicon by dynamical x-ray diffraction

Precipitation of Non-Spherical Particles in Aluminum Alloys Part I: Generalization of the Kampmann–Wagner Numerical Model

Search for NDE Methods to Characterize Thermal History and Mechanical Properties of Al-Li Alloys

Contact Info

Product

Resources

About