Principle
Crystalline materials are never perfect on a microscale. Some sites of atoms in the crystal lattice can be occupied by point defects, such as "alien" particles or vacancies. Vacancies can actually be thought of as chemical species themselves (or part of a compound species/component) that may then be treated using heterogeneous phase equilibria. The number of vacancies may also be influenced by the number of chemical impurities in the crystal lattice, if such impurities require the formation of vacancies to exist in the lattice.
A vacancy can move through the crystal structure when the neighbouring particle "jumps" in the vacancy, so that the vacancy moves in effect one site in the crystal lattice. Chemical bonds need to be broken and new bonds have to be formed during the process, therefore a certain activation energy is needed. Moving a vacancy through a crystal becomes therefore easier when the temperature is higher.
The most stable state will be when all vacancies are evenly spread through the crystal. This principle follows from Fick's law:
In which Jx stands for the flux ("flow") of vacancies in direction x; Dx is a constant for the material in that direction and is the difference in concentration of vacancies in that direction. The law is valid for all principal directions in (x, y, z)-space, so the x in the formula can be exchanged for y or z. The result will be that they will become evenly distributed over the crystal, which will result in the highest mixing entropy.
When a mechanical stress is applied to the crystal, new vacancies will be created at the sides perpendicular to the direction of the lowest principal stress. The vacancies will start moving in the direction of crystal planes perpendicular to the maximal stress. Current theory holds that the elastic strain in the neighborhood of a defect is smaller toward the axis of greatest differential compression, creating a defect chemical potential gradient (depending upon lattice strain) within the crystal that leads to net accumulation of defects at the faces of maximum compression by diffusion. A flow of vacancies is the same as a flow of particles in the opposite direction. This means a crystalline material can deform under a differential stress, by the flow of vacancies.
Highly mobile chemical components substituting for other species in the lattice can also cause a net differential mass transfer (i.e. segregation) of chemical species inside the crystal itself, often promoting shortening of the rheologically more difficult substance and enhancing deformation.
Read more about this topic: Diffusion Creep
Famous quotes containing the word principle:
“Thus it seemed that this one hillside illustrated the principle of all the operations of Nature. The Maker of this earth but patented a leaf. What Champollion will decipher this hieroglyphic for us, that we may turn over a new leaf at last?”
—Henry David Thoreau (1817–1862)
“For me chemistry represented an indefinite cloud of future potentialities which enveloped my life to come in black volutes torn by fiery flashes, like those which had hidden Mount Sinai. Like Moses, from that cloud I expected my law, the principle of order in me, around me, and in the world.... I would watch the buds swell in spring, the mica glint in the granite, my own hands, and I would say to myself: “I will understand this, too, I will understand everything.””
—Primo Levi (1919–1987)
“Look through the whole history of countries professing the Romish religion, and you will uniformly find the leaven of this besetting and accursed principle of action—that the end will sanction any means.”
—Samuel Taylor Coleridge (1772–1834)