✦ LIBER ✦

Grain size distribution in two dimensions in the long time limit

✍ Scribed by C.S. Pande; K.P. Cooper; G.B. McFadden

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 279 KB
Volume: 56
Category: Article
ISSN: 1359-6454
DOI: 10.1016/j.actamat.2008.07.008

No coin nor oath required. For personal study only.

✦ Synopsis

It is shown that the inclusion of a ''noise" term in the growth rate of individual grains leads to a stochastic model that provides a more realistic description of grain growth phenomenon. The resulting Fokker-Planck equation for the grain size distribution is solved numerically due to the difficulties in obtaining an analytical solution. The analysis is limited to two dimensions and assumes quasi-stationary distributions in the long time limit. The resulting grain size distribution is shown to be in agreement with that obtained from computer simulations, indicating the validity of the stochastic approach.

📜 SIMILAR VOLUMES

Self-similar grain size distribution in

✍ C.S. Pande; K.P. Cooper 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 375 KB

Consideration of the physics and topology of two-dimensional grain growth suggests that a stochastic treatment is required to determine grain size distribution [Pande CS. Acta Metall 1987;35:2671]. In this paper, a size-based continuum stochastic formulation is presented based on topological conside

The role of grain size distributions in

The role of grain size distributions in diffusional creep

✍ J.H. Schneibel; R.L. Coble; R.M. Cannon 📂 Article 📅 1981 🏛 Elsevier Science ⚖ 701 KB

Modelling of the grain size probability

Modelling of the grain size probability distribution in polycrystalline nanomaterials

✍ T.B. Tengen; R. Iwankiewicz 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 356 KB

Theoretical analyses have always resulted in nanomaterials' grain size probability distribution being of varied form: approximately either lognormal, Rayleigh, normal, Weibull, etc. The isotropic Hillert's model of grain growth which is more suitable for soap froth has been frequently used to establ

The effect of initial grain size distrib

The effect of initial grain size distribution on abnormal grain growth in single-phase materials

✍ W.E. Benson; J.A. Wert 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 475 KB

AbstractÐA model that describes the temporal evolution of an initial grain size distribution (GSD) has been used to analyze the eect of initial GSD on grain growth. Based upon the work of Hillert, and Hunderi and Ryum, this model uses a ®nite dierence technique to numerically solve the continuity eq

Effect of the grain size on the tunnel d

Effect of the grain size on the tunnel distribution in (NH4)2ZnCl4

✍ Z.S. Liu; M. Punkkinen; A.H. Vuorimäki; E.E. Ylinen 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 143 KB

The classical limit of the relativistic

The classical limit of the relativistic Vlasov–Maxwell system in two space dimensions

✍ Hayoung Lee 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 274 KB

## Abstract The motion of a collisionless plasma is modelled by the Vlasov–Maxwell system. In this paper, solutions of the relativistic Vlasov–Maxwell system are considered in two space dimensions. The speed of light, __c__, appears as a parameter in the system. With representations of the electric