Diffusion of Lattice Defects in a Temperature Gradient

Abstract

1389this operator the absolute value of the total nuclear angular momentum, 121; |, is conserved. Therefore, instead of the orientation N m f /Nm-i~n-/n+ of the individual nuclei (see the preceding note), one obtains an orientation in which each of the nuclear states with well-defined value of (21;) 2 is oriented, with conservation, however, of their statistical weights found in thermal equilibrium. There are, of course, processes that may cause a change A|2I t -| =±1, but these are due to corrections to the previously mentioned interaction, and therefore are much less probable. One possibility is a nuclear spin exchange back and forth with the neighboring alkali nuclei not belonging to the F center. Another effect, which might be more important, is produced by a deformation of the F center of static nature or due to thermal or zero point vibrations, which cause slight differences of the coupling constants, a(l+5») of the electron with the nuclei. The relaxation time corresponding to a transition from the original partial orientation to the orientation of the individual nuclei is proportional to 1/(5 2 )A V , and can be of the order of seconds instead of microseconds. Inversely, if the electron resonance radiation causing saturation is suddenly decreased in intensity, first an isotropic distribution of nuclear spin states of predominantly the largest |SI»|-value is obtained, which then changes gradually into the equilibrium distribution. If the second relaxation time is microscopically long, one could observe this phenomenon in different ways, for example by first saturating the electron system and then observing resonance absorption under small amplitude. Then (2/ max +l) lines would appear with approximately equal intensity (provided txoH/kT is not too small), and this pattern would gradually change into the conventional Gaussian line corresponding to random nuclear orientation. Perhaps the 19 equidistant and equi-intense lines observed by Schneider 2 in the hfs of F centers in LiF could be explained in terms of this or a similar process. A promising possibility for observing the nuclear orientation is offered by the spin exchange with neighboring alkali nuclei, which has been mentioned already. By this process the nuclear orientation diffuses into the space between the F centers, where a direct observation by nuclear resonance is not limited by the perturbation from the electron. i Kip, Kittel, Levy, and Portis, Phys. Rev. 91, 1066 (1953). 2 E. E. Schneider (private communication).S HOCKLEY 1 has recently pointed out that in a crystal in which there is a temperature gradient there is also a gradient in the concentration of lattice defects, and that observable macroscopic deformation may result from the flow of defects due to this concentration gradient. Le Claire 2 and Brinkman 3 have called attention to another driving force acting on the defects, that due to the interaction between the flow of heat toward low temperatures and the flow of vacancies, but comment by Shockley 4 shows that they have used an incor...

Thermal Diffusion in Crystalline Solids

“…Apart from the isolated observation (100) that carbon diffused to the hot end of y-Fe, no further observations on thermal diffusion in solids were published until 1954 when Soret measurements (36) for three binary alloys were published. In the same year the possible usefulness of thermal diffusion measurements in determining atomic mechanisms of diffusion in solids was debated (25,89,102,164) following a suggestion by Shockley (163). It w7as by then know7n that migration of atoms is intimately connected with the properties of point defects, and, in order to understand Shockley's proposal and subsequent developments, a few7 pertinent facts must be reviewed.…”