Ideal Grain Growth
Ideal grain growth is a special case of normal grain growth where boundary motion is driven only by the reduction of the total amount of grain boundary surface energy. 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
where d0 is the initial grain size, d is the final grain size and k is a temperature dependent constant given by an exponential law:
where k0 is a constant, T is the absolute temperature and Q is the activation energy for boundary mobility. 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.
Read more about this topic: Grain Growth
Famous quotes containing the words ideal, grain and/or growth:
“If we love-and-serve an ideal we reach backward in time to its inception and forward to its consummation. To grow is sometimes to hurt; but who would return to smallness?”
—Sarah Patton Boyle, U.S. civil rights activist and author. The Desegregated Heart, part 3, ch. 3 (1962)
“He never doubts his genius; it is only he and his God in all the world. He uses language sometimes as greatly as Shakespeare; and though there is not much straight grain in him, there is plenty of tough, crooked timber.”
—Henry David Thoreau (1817–1862)
“A person of mature years and ripe development, who is expecting nothing from literature but the corroboration and renewal of past ideas, may find satisfaction in a lucidity so complete as to occasion no imaginative excitement, but young and ambitious students are not content with it. They seek the excitement because they are capable of the growth that it accompanies.”
—Charles Horton Cooley (1864–1929)