Grain growth in zone-refined iron

Hu, Hsun

doi:10.1179/cmq.1974.13.1.275

Cited by 84 publications

(30 citation statements)

References 21 publications

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“…Similar results were obtained with the size distribution in 2-D sections of zonerefined iron. [6] It is seen in Figure 6(b) that the face number distribution is unlikely to be log-normal, either.…”

Section: Distribution Of Grain Volume and Surface Areamentioning

confidence: 89%

“…Hillert [20] applied the theory of Ostwald ripening to grain growth and obtained the size distribution function [6] where u ϭ R/R cr and R cr is related to ϽRϾ as ϽRϾ ϭ 8R cr /9. The term A is a constant and ␤ ϭ 3 for grain growth in three dimensions.…”

Section: Distribution Of Grain Volume and Surface Areamentioning

confidence: 99%

“…[4,5] The alloy systems to which these techniques are applicable are limited, and the experimental procedures are often very tedium. Thus, efforts are being made to correlate the distributions in 2-D sections to those in 3-D. [2,6] For the same reason, computer simulation has become a very popular means of studying the evolution of microstructure in polycrystalline solids. [7][8][9][10] In this article, serial sectioning is employed to characterize the grain structure in cold-rolled and recrystallized ␣-iron.…”

Section: Introductionmentioning

confidence: 99%

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Characterization of three-dimensional grain structure in polycrystalline iron by serial sectioning

Zhang

Enomoto

Suzuki

et al. 2004

Metall Mater Trans A

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The face number, the volume, and the surface area (boundary area) of grains are measured in recrystallized ␣-iron by serial sectioning coupled with quantitative microstructural analysis on twodimensional (2-D) sections. The sampling volume contained approximately 1000 grains whose mean grain size was ϳ15 m. The grain volume distribution decreased monotonously with increasing grain volume, whereas the surface area had a peak around one-half of the average. The distribution of the sphere equivalent radii significantly deviated from the log-normal distribution and distributions predicted from mean field theories. The peak and the mean of the face number distribution were f ϭ 11 and 12.1, respectively. The linear relationship between the face number of a central grain and the mean face number of surrounding grains, known as the Aboav-Weaire law, was observed in three dimensions. The mean radius of f-faced grains was not proportional to the face number (perimeter law in 3-D), but appeared to be related by a curve convex upward.

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Section: Distribution Of Grain Volume and Surface Areamentioning

confidence: 89%

Section: Distribution Of Grain Volume and Surface Areamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Characterization of three-dimensional grain structure in polycrystalline iron by serial sectioning

Zhang

Enomoto

Suzuki

et al. 2004

Metall Mater Trans A

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“…Both experiments and simulations have shown that grain growth follows power-law kinetics and their grain size distribution (GSD) can be described by a log-normal distribution [4][5][6][7]. In the early 1950s, Lifshitz and Slyozov [8] proposed a theoretical framework to model grain growth.…”

Section: Introductionmentioning

confidence: 99%

Grain growth as a stochastic and curvature-driven process

Zheng

Mai

et al. 2006

Philosophical Magazine Letters

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Grain growth subjected to the interplay of stochastic and curvature-driven mechanisms in a single-phase system has been investigated. Numerical results have shown that when the grains are smaller than several tens of nanometres the dominating mechanism is stochastic diffusion control of boundaries. As the grains grow the influence of the deterministic curvature-driven mechanism increases and finally controls the process. In terms of finite-difference solutions to the Fokker-Planck continuity equation, the predicted grain size approaches a log-normal distribution, which agrees well with experimental observations.

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“…Equation (1) can be written formally where m is the mobility. The conceptual division of the velocity into a mobility (of the boundary) and a driving force acting on the boundary according t o (2), which is almost always made in the analysis of experimental data [9], implies that m and p are independent variables of the existing system. Since, however, both quantities depend on the structural characteristics of the system (lattice CY -grain boundary -lattice P ) this independence is to be expected theoretically only in very special cases.…”

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confidence: 99%

Single-Process Theories of Grain Boundary Migration in the Light of Recent Experimental Results

Haessner

1975

J. Phys. Colloques

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Abstract. -Theoretical treatment of the mechanisms associated with thermally activated grain boundary migration requires a knowledge of the atomistic and electronic structure of the grain boundary. Although in recent years a whole range of new data has been acquired concerning the atomistic structure of grain boundaries (see for example the relevant papers presented at this colloquium) they can do no more than qualitatively extend the existing, in some cases really old, heuristic concepts of grain boundary migration mechanisms. The effect of the electronic structure on grain boundary migration has not been considered at all till now. The idea that this aspect also is of importance is rather new.In view of this, and considering that there are already a number of recent review articles on the subject of grain boundary migration [1][2][3][4], the present paper is restricted essentially to the discussion of several unanswered questions which are of general importance for a deeper theoretical understanding of grain boundary migration in very pure metals. The discussion is also restricted to large angle grain boundaries. Orientation effects will not be included because they are discussed in another of the papers to be presented.1. Current theories. -The theories are divided into single process and group process according to the assumed method of materia] transport which effects the displacement of the grain boundary [1]. In single process theories it is assumed that the elementary process depends on the uncorrelated release or deposition of individual atoms from the lattice and on to the lattice of the neighbouring grain. The rate of grain boundary migration has been calculated many times on this basis of this theory [1, 5]. The individual treatments differ only in the way in which the overall process is split into individual stages. In the group process theories it is assumed that a group of atoms change from one lattice to the other in a thermally activated event.Here again various explicit formulations exist for the rate of grain boundary migration [1].In the past, interest has centred primarily on single process theories because it was considered that they would yield better agreement with experimental data for grain boundary migration in very pure metals than group process theories [1,2, 6]. In spite of the success of the single process theories, several fundamental questions have still not been answered completely or have been provoked again by more recent experimental observations. Single process theories yield an expression for the rate of migration of a boundary of the form in which b is the atomic diameter, v the effective attack frequency, p the driving force (energy per atom), AS and AH the activation entropy and enthalpy and

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Grain growth in zone-refined iron

Cited by 84 publications

References 21 publications

Characterization of three-dimensional grain structure in polycrystalline iron by serial sectioning

Characterization of three-dimensional grain structure in polycrystalline iron by serial sectioning

Grain growth as a stochastic and curvature-driven process

Single-Process Theories of Grain Boundary Migration in the Light of Recent Experimental Results

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