Tracer diffusion activation energy

The radioactive tracer diffusion coefficient of 22Na in glass is given in the following table. Estimate the activation energy for diffusion. 

The preceding data, though limited in nature, represent one of the first attempts to measure solid state diffusion rates of alkali elements into the near-surface region of feldspars and natural glasses at low temperature. As such, interesting comparisons can be made with diffusion coefficients and activation energies calculated from numerous high temperature isotope and tracer diffusion studies f 11-181. 

Activation energy for vacancy-mediated tracer diffusion... 

We should mention here that a better way to extract the activation energies for vacancy-mediated diffusion would be to plot the tracer diffusion coefficient of the embedded atoms vs. 1/kT, rather than their jump rate. As we discussed in Section 4, the mean square jump length depends on the proximity of steps, and so does the average jump frequency. This adds non-statistical noise to the two plots in Fig. 12. However, it can be shown easily that these effects on jump length and jump rate cancel in the resulting tracer diffusion coefficient, which thus becomes independent of the distance to steps. In this way, a more accurate value for the activation energy has been obtained for the case of In/Cu(0 0 1) of 717 30meV [23]. 

By definition, the rate at which the tracer atom is displaced by a surface vacancy is the product of the vacancy density at the site next to the tracer times the rate at which vacancies exchange with the tracer atom. For the case where the interaction between the tracer atom and the vacancy is negligible, the activation energy obtained from the temperature dependence of the total displacement rate equals the sum of the vacancy formation energy EF and the vacancy diffusion barrier ED. When the measurements are performed with finite temporal resolution and if there is an interaction present between the vacancy and the indium atom, this simple picture changes. 

Measurements have been made of tracer or intrinsic diffusion coefficients of water in a number of zeolites. Most refer to crystals nearly saturated with zeolitic water, while smoothed rather than adsorption areas were used in calculating the coefficients. From the temperature dependence of Da or Da, the activation energy, E, may be found using the Arrhenius equations Da = Do exp — E/RT or Da = Do exp — E/RT. Some results for tracer diffusion are summarized in Table VI. (iS). These shed considerable light upon certain aspects of intracrystalline diffusion for small polar molecules ... 

Magnesium oxide has been investigated by Robertson and by Henney and Jones. Surface diffusion was identified as the dominant mechanism of transport in both of these studies. The activation energies appeared excessive for this interpretation. In the reevaluation of these data it was shown that interpretation as volume diffusion produced = 0.02 exp (—70,000/i 7, which is in agreement with the tracer and mass spectrometer results compiled by Harrop in which the mean activation energy for Mg and O migration is 70,500 cal/mole. 

Similarly, the Henney and Jones activation energy for surface diffusion in UO2.005 of 110,000 cal is definitely excessive, whereas reinterpretation as volume diffusion produced = 0.22 exp (—71,000// r), which is in good agreement with tracer data. ... 

In an early experimental study of sintered monazite, Shestakov (1969) estimated an activation energy of 60 kcal/mol by volatilizing Pb in a stream of nitrogen at temperatures between 800 and 1100°C. Smith and Giletti (1997) measured the tracer diffusion of Pb in natural monazites using ion microprobe depth-profiling and observed Arrhenius parameters o E = 43 11 kcal/mol and Do = 6.6 x 10 mVsec in the temperature range of 1200 to 1000°C (Fig. 4). They found that transport parallel to the c-... 

The diffusion constant and activation energy can be measured directly by radioactive tracer techniques in which the initial distribution of radioactive ions is followed as a function of time and distance. Values of the diffusion constant and activation energies thus determined are then compared with values from ionic conductivities. 

Probably the most systematic and complete study on the influence of temperature on water transfer has been performed on mammalian red cells [10,20,28]. The dependence on temperature of both the tracer diffusional permeability coefficient (cotho) 3 nd the hydraulic conductivity (Lp) of water in human and dog red-cell membranes have been studied. The apparent activation energies calculated from these results for both processes are given in Table 2. The values for the apparent activation energies for water self-diffusion and for water transport in a lipid bilayer are also included in the table. For dog red cells, the value of 4.9 kcal/mol is not significantly different from that of 4.6-4.8 kcal/mol for the apparent activation energy of the water diffusion coefficient ( >,) in free solution. Furthermore, it can be shown that the product L — THOV )rt, where is the partial molar volume of water and the viscosity of water remains virtually independent of temperature for dog, hut not for the human red-cell membrane [20]. The similarity of the transmembrane diffusion with bulk water diffusion and the invariance of the... 

The diffusion coefficient of radioactive Cr tracers in the refractory oxide CraOs is given in the Table 7.7(d). Estimate the activation energy for difrusion. 

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