Journal ArticleDOI
Microstructure and normal grain growth in metals and ceramics. Part I. Theory
S. K. Kurtz,F. M. A. Carpay +1 more
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In this paper, a detailed statistical theory of normal grain growth has been constructed by extending the theory of Feltham and combining it with the work of Rhines and Craig, and complete solutions are found for the grain growth kinetics of each class, as well as the transfer rates between classes.Abstract:
By extending the theory of Feltham and combining it with the work of Rhines and Craig, a detailed statistical theory of normal grain growth has been constructed. The theory exhibits all four attributes of normal grain growth: uniformity, scaling, stability, and lognormality. A prime new feature of the theory is the division of the grains into topological classes (14 planar, 34 spatial), each with a lognormal distribution of grain sizes. Growth is found to be controlled by the rate of loss of grains from the lowest topological class. Complete solutions are found for the grain growth kinetics of each class, as well as the transfer rates between classes. The latter result is used to explain how the median diameter of those classes in which grains are shrinking still manages to increase in the manner required to keep their number a constant fraction of the total population. A parabolic growth law is found for the median grain size of the whole population as well as the median grain size in each topological class. The growth constant for each class is found to increase approximately as the cube of the planar topological parameter or the square of the spatial topological parameter. The Rhines‐Craig structural gradient is shown to be independent of time and hence a basic constant of normal grain growth. Stability is due to a maximum in the grain boundary velocity with increasing grain size. The ratio of the maximum to median grain diameter is found to be e(=2.718). A comparison of the present theory is made with that of Hillert. Possible origins of the lognormality are discussed.read more
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Journal ArticleDOI
Powder Processing Science and Technology for Increased Reliability
TL;DR: In this paper, issues concerning powder consolidation methods compatible with the colloidal approach and issues associated with other powder processing steps, viz., densification and microstructural control, are presented with regard to research directions leading to more reliable ceramics.
Journal ArticleDOI
Overview no. 65
TL;DR: In this article, the development of theories for normal grain growth in pure single phase systems is reviewed and a major theme which emerges is the interplay between the topological requirements for space filling and the kinetics of change in mean grain size with time.
Journal ArticleDOI
Soap, cells and statistics – random patterns in two dimensions
Denis Weaire,Nicolas Rivier +1 more
TL;DR: A survey of random two-dimensional patterns, paying particular attention to soap cell networks, metallurgical grain structures and the Giant's Causeway.
Journal ArticleDOI
Computer simulation of grain growth—II. Grain size distribution, topology, and local dynamics
TL;DR: In this article, the authors analyzed the microstructures produced by the grain growth simulation technique described in the previous paper and found that the grain size distribution function is time invariant when the grain sizes, R, is scaled by the mean grain size, R, and is shown to fit the experimental data better than either the log-normal function or the grain distribution function suggested by Hillert.
Journal ArticleDOI
Computer simulation of normal grain growth in three dimensions
TL;DR: In this paper, the microstructure of polycrystalline materials is digitized by dividing the polycrystaline material into small volume elements and storing the spatial location and crystallographic orientation of each element.
References
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Journal ArticleDOI
The Lognormal Distribution.
J. Aitchison,J. A. C. Brown +1 more
TL;DR: Lloyds Bank has its main root in a substantial private bank founded in Birmingham nearly two centuries ago; one hundred years ago this Bank still had only the one office in Birmingham, with a related private banking house in Lombard Street, and by amalgamation it has absorbed scores of other eighteenth and nineteenth century banks, both private and joint stock, and at least two of the former reach back into Restoration London, perhaps Cromwellian London.
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The lognormal distribution
TL;DR: Lloyds Bank has its main root in a substantial private bank founded in Birmingham nearly two centuries ago; one hundred years ago this Bank still had only the one office in Birmingham, with a related private banking house in Lombard Street, and by amalgamation it has absorbed scores of other eighteenth and nineteenth century banks, both private and joint stock, and at least two of the former reach back into Restoration London, perhaps Cromwellian London.
Journal ArticleDOI
On the theory of normal and abnormal grain growth
TL;DR: In this article, a growth equation for individual grains in single-phase materials is suggested, which is used to calculate a rate equation for normal grain growth and the size distribution in the material.
Journal ArticleDOI
Dislocation Models of Crystal Grain Boundaries
W. T. Read,William Shockley +1 more
TL;DR: In this article, the authors investigated the energies and motions of grain boundaries between two crystallites using the dislocation model of grain boundary and provided a quantitative expression for energy per unit area for small angles.