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:
“Every epoch which seeks renewal first projects its ideal into a human form. In order to comprehend its own essence tangibly, the spirit of the time chooses a human being as its prototype and raising this single individual, often one upon whom it has chanced to come, far beyond his measure, the spirit enthuses itself for its own enthusiasm.”
—Stefan Zweig (18811942)
“Raise children for your old age as you would store up grain against famine.”
—Chinese proverb.
“When I have plucked the rose,
I cannot give it vital growth again,
It needs must wither. Ill smell it on the tree.”
—William Shakespeare (15641616)