Diffusion coefficients of impurities

Quite extraordinary diffusion coefficients of impurities from odier parts of die Periodic Table are found, and especially in die important case of lidiium or copper diffusion, where die eidiancement over self-diffusion is by six to eight orders of magnitude. This indicates diat diese atoms do not form part of die sp network in die sUmcture, but more closely resemble separate atoms in die sp iiiaUix. 

The value of the diffusion coefficients of impurities and dopants in semiconductors can be modified by the presence of compensating impurities or of crystal dislocations so that the interpretation of diffusion measurements requires some judgment, ft must also be mentioned that as the diffusing species can be ions, the diffusion coefficient can be modified by an electric field. 

After orienting the director of the liquid crystal relative to the gradient of the field (the gradient of the field may coincide with the direction of the average orienting field) the coefficients > and i j are calculated from the amplitude of the echo. This spin-echo method can also be applied to determine the diffusion coefficients of impurities in nematic liquid crystals (e.g., tetramethylsilane [103]). 

H. Kodera, 1963, Diffusion coefficients of impurities in silicon melt ... 

Diffusion coefficients in amorphous solids such as oxide glasses and glasslike amorphous metals can be measured using any of the methods applicable to crystals. In this way it is possible to obtain the diffusion coefficients of, say, alkah and alkaline earth metals in silicate glasses or the diffusion of metal impurities in amorphous alloys. Unlike diffusion in crystals, diffusion coefficients in amorphous solids tend to alter over time, due to relaxation of the amorphous state at the temperature of the diffusion experiment. 

Ti impurities substitute for Mg on doping MgO with a small amount of Ti02. Will the diffusion coefficient of Mg be expected to ... 

Ionization of solute molecules by photolysis or high-energy radiolysis produces electrons which may recombine with their geminate radical (ion), react with an impurity (usually an oxidant) or be trapped in a solvent vacancy. The properties of the solvated electron resemble those of anions (e.g. a diffusion coefficient of 4.9 x 10-9 m2 s-1 in water). It is... 

Purification of Solution. An approximate model for the purification of the solution can be developed by assuming that a stagnant melt initially contains an impurity at a uniform concentration, Cf°, and loss of dopant occurs by evaporation at the top surface. The rate of evaporation is assumed to be directly proportional to the difference in concentrations at the top surface and at equilibrium. If the proportionality constant is z, the diffusion coefficient of the impurity in the melt is D v and the depth of the melt is Z, then the following expression for the impurity concentration in the melt,... 

The diffusion coefficients of the process controlling superplasticity may be enhanced or retarded by the addition of impurities or solute atoms or by the addition of secondary phases, normally used as sintering aids, which distribute along the grain boundaries and triple-point junctions of the grains. 

In solution drag, the width of the grain bovmdaiy, w, is the zone over which impurities interact. The grain boimdary thickness is taken to be independent of grain size. The diffusion coefficients of the host, D , and the impvirity, D/, will depend on the structure in the grain boundary. Impurities can therefore have an effect on the grain boundary velocity, Vg, by either their effect on the Co term or an effect on the diffusion coefficients for host and impurity. 

Experimental and theoretical studies on H diffusion in silicon at lower temperatures, where trapping of hydrogen at defects and impurities and H2-molecule formation are significant, discovered much lower effective diffiisivities. Values for the H-diffiision coefficient in silicon expected from an extrapolation of the diffusion coefficient of (11.1) to lower temperatures are several orders of magnitude higher than experimentally obtained diffiisivities. This is illustrated in Fig. 11.2, which shows (11.1) and (11.2) extrapolated to low temperatures with experimentally determined values from Johnson et al. (1986). 

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