Grain growth

This occurs when recovery and recrystallisation are complete and further reduction in the internal energy can only be achieved by reducing the total area of grain boundary.

The practical performances of polycrystalline materials are strongly affected by the formed microstructure inside, which is mostly dominated by grain growth behaviors.

Since boundaries are regions of high energy they make excellent sites for the nucleation of precipitates and other second-phases e.g. Mg–Si–Cu phases in some aluminium alloys or martensite platlets[check spelling] in steel.

Grain growth has long been studied primarily by the examination of sectioned, polished and etched samples under the optical microscope.

Although such methods enabled the collection of a great deal of empirical evidence, particularly with regard to factors such as temperature or composition, the lack of crystallographic information limited the development of an understanding of the fundamental physics.

[4][5] According to the general GB migration model, the classical linear relation can only be used in a specical case.

Development of theoretical models describing grain growth is an active field of research.

Many models have been proposed for grain growth, but no theory has yet been put forth that has been independently validated to apply across the full range of conditions and many questions remain open.

[8] Other models have indicated that triple junctions play an important role in determining the grain growth behavior in many systems.

Additional contributions to the driving force by e.g. elastic strains or temperature gradients are neglected.

If it holds that the rate of growth is proportional to the driving force and that the driving force is proportional to the total amount of grain boundary energy, then it can be shown that the time t required to reach a given grain size is approximated by the equation

Theoretically, the activation energy for boundary mobility should equal that for self-diffusion but this is often found not to be the case.

In general these equations are found to hold for ultra-high purity materials but rapidly fail when even tiny concentrations of solute are introduced.

Inspired by the work of Lifshitz and Slyozov on Ostwald ripening, Hillert has suggested that in a normal grain growth process the size distribution function must converge to a self-similar solution, i.e. it becomes invariant when the grain size is scaled with a characteristic length of the system

It was shown that the origin of the deviation from Hillert's distribution is indeed the geometry of grains specially when they are shrinking.

[15] In common with recovery and recrystallisation, growth phenomena can be separated into continuous and discontinuous mechanisms.

[16] If there are additional factors preventing boundary movement, such as Zener pinning by particles, then the grain size may be restricted to a much lower value than might otherwise be expected.

To mitigate this problem in a common sintering procedure, a variety of dopants are often used to inhibit grain growth.

Computer Simulation of Grain Growth in 3D using phase field model . Click to see the animation.
Click to see the animation. Geometry of a single growing grain is changing during grain growth. This is extracted from a large scale phase-field simulation. Here surfaces are "grain boundaries", edges are "triple junctions" and corners are vertexes or higher-order junctions. For more information please see. [ 10 ]
Distinction between continuous (normal) grain growth, where all grains grow at roughly the same rate, and discontinuous (abnormal) grain growth , where one grain grows at a much greater rate than its neighbours.