Grain growth models

The grain growth models predict a kinetic equation of the form ... 

Dopant effects on densification and grain growth Models ... 

The merits and demerits of the many computer-simulation approaches to grain growth are critically analysed in a book chapter by Humphreys and Hatherly (1995), and the reader is referred to this to gain an appreciation of how alternative modelling strategies can be compared and evaluated. A still more recent and very clear critical comparison of the various modelling approaches is by Miodownik (2001). 

Grain growth involves no phase transformation, but a number of such transformations have been modelled and simulated in recent years. A recently published overview volume relates some experimental observations of phase... 

M. K. Venkitachalam, L.-Q. Chen, A. G. Khachaturyan, G. L. Messing. A multiple-component order parameter phase field model for anisotropic grain growth. Mater Sci Eng A 238 94, 1997. 

Ultimately, a knowledge of kinetics is valuable because it leads to prediction of the rates of materials processes of practical importance. Analyses of the kinetics of such processes are included here as an alternative to a purely theoretical approach. Some examples of these processes with well-developed kinetic models are the rates of diffusion of a chemical species through a material, conduction of heat during casting, grain growth, vapor deposition, sintering of powders, solidification, and diffusional creep. 

The ejection mechanisms considered by Watson and Salpeter are mainly photodesorption and ejection during molecule formation, the former being the most important process. Other mechanisms involving interaction with cosmic rays or with IR photons are of minor importance. Since ejection by UV photons is highly unlikely in very dense clouds, condensation of the interstellar gas and grain growth in the Watson-Salpeter-model would proceed without limit, which of course is in contradiction to observations. 

Crack growth models in monolithic solids have been well document-ed. 1-3,36-45 These have been derived from the crack tip fields by the application of suitable fracture criteria within a creep process zone in advance of the crack tip. Generally, it is assumed that secondary failure in the crack tip process zone is initiated by a creep plastic deformation mechanism and that advance of the primary crack is controlled by such secondary fracture initiation inside the creep plastic zone. An example of such a fracture mechanism is the well-known creep-induced grain boundary void initiation, growth and coalescence inside the creep zone observed both in metals1-3 and ceramics.4-10 Such creep plastic-zone-induced failure can be described by a criterion involving both a critical plastic strain as well as a critical microstructure-dependent distance. The criterion states that advance of the primary creep crack can occur when a critical strain, ec, is exceeded over a critical distance, lc in front of the crack tip. In other words... 

In real systems the final stage of sintering almost generally involves also grain growth, which complicates confrontation of the theoretical models with experimental data. 

An equation of the form provided in Equation (8) is often used to fit experimental coarsening data. The exponent, n, is used to infer the rate-controlling step for the growth process. This has proven useful for modeling grain growth in a number of metallic alloy... 

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