Isotopic diffusion profiles

Figure 3-4 Calculated oxygen isotope diffusion profile from both sides of a plane-sheet mineral, initial 5 0 in the mineral is l%o. The surface 8 0 is 10%o. The diffusivity D = 10 m /s. Compare this with Figure l-8b.

Oxygen exchange experiments were performed between single crystals of sanidine feldspar and oxygen gas enriched in 1°0, at 869 to 1053C, under a total pressure of latm. The O isotope diffusion profiles in a direction perpendicular to (001) were determined using an ion microprobe. The experimental data obeyed the Arrhenius relationship ... 

Fig. 4.31 (a) AES composition depth profile (b) SIMS isotope diffusion profile and (c) schematic layered oxide structure for a NisAl alloy oxidized in 02 and then 02 environment at 600 °C. Vertical dashed lines indicate oxide interfaces and vertical dotted lines indicate interfaces between isotope oxides. Reprinted with permission from Haasch RT, Venezia AM, Loxton, CM (1992) J Mater Res 7 1341-49. Copyright 1992, Materials Research Society... 

An alternative procedure which is sometimes used is to place a rod in which the concentration of the isotope is constant throughout c0, against a bar initially containing none of the isotope. The diffusion profile then shows a concentration at the interface which remains at one-half that in the original isotope-containing rod during the whole experiment. This is called the constant source procedure because the concentration of the isotope remains constant at the face of the rod which was originally isotope-free. The solution for the diffusion profile is with the boundary condition c = c0/2, x = 0, t > 0 is... 

Radioactive 180 was diffused into a poly crystalline pellet of ZnO at 900°C for 48 h. The diffusion profile had a marked tail showing that extensive grain boundary diffusion had occurred. The variation of the concentration of the radioactive isotope with depth for the tail of the penetration profile is given in the following table. Calculate the grain boundary diffusion coefficient, Dgb, of 180 if the bulk diffusion coefficient at 900°C is 5.53 x 10-21 m2 s-1 and the grain boundary width is taken as 1 nm. 

The isotopic fraction profiles may be described by a roughly constant diffusion coefficient across major concentration gradients. 

Based on these observations, the diffusivity extracted from isotopic fraction profiles is usually regarded to be similar to intrinsic diffusivity or self-diffusivity even in the presence of major element concentration gradients. That is, the multicomponent effect does not affect the length of isotopic fraction profiles (but it affects the isotopic fractions and the interface position). On the other hand, the diffusion of a trace or minor element is dominated by multicomponent effect in the presence of major element concentration gradients. 

Figure 3-24 Calculated diffusion-couple profiles for trace element diffusion and isotopic diffusion in the presence of major element concentration gradients using the approximate approach of activity-based effective binary treatment. The vertical dot-dashed line indicates the interface. The solid curve is the Nd trace element diffusion profile (concentration indicated on the left-hand y-axis), which is nonmonotonic with a pair of maximum and minimum, indicating uphill diffusion. The dashed curve is the Nd isotopic fraction profile. Note that the midisotopic fraction is not at the interface.

Equation 5.18 offers a convenient technique for measuring self-diffusion coefficients. A thin layer of radioactive isotope deposited on the surface of a flat specimen serves as an instantaneous planar source. After the specimen is diffusion annealed, the isotope concentration profile is determined. With these data, Eq. 5.18 can be written... 

Powerful methods for the determination of diffusion coefficients relate to the use of tracers, typically radioactive isotopes. A diffusion profile and/or time dependence of the isotope concentration near a gas/solid, liq-uid/solid, or solid/solid interface, can be analyzed using an appropriate solution of - Fick s laws for given boundary conditions [i-iii]. These methods require, however, complex analytic equipment. Also, the calculation of self-diffusion coefficients from the tracer diffusion coefficients makes it necessary to postulate the so-called correlation factors, accounting for nonrandom migration of isotope particles. The correlation factors are known for a limited number of lattices, whilst their calculation requires exact knowledge on the microscopic diffusion mechanisms. 

The rate of initial electron transfer from A,7V-dimethylaniline to [Fe(phen)3] + is diffusion-limited. This is followed by the rate-determining proton transfer from the radical cation to pyridine to give the deprotonated a-amino radical which is rapidly oxidized by a second equivalent of [Fe(phen)3] + to yield the product iminium ion. Kinetic isotope effects [kii/kjf) for the proton transfer were determined from the J3/tfo ratios of the products derived from p-substituted A-methyl-A-trideuteromethylanilines. The k /kx) value first increases and then decreases with increasing pAa of p-substituted A,A-dimethylaniline. Such a bell-shaped isotope effect profile is typical of proton-transfer reactions [82, 85]. The maximum kn/fco value is determined as 8.8 which is much larger than the corresponding value for the demethylation of the same substrate by cytochrome P-450 (2.6) [79]. 

A shortcoming of both NRA and SIMS is that the spatial resolution is not high in all three directions. While depth resolutions on the order of a few hundred nanometers or less are routine, the profiles are measured over surface areas of a few hundred square micrometers or even millimeters. Thus, the concentration profile can be an average from various localized reaction or fast diffusion (e.g. pipe diffusion). The consequences of dual-diffusion mechanisms on the geometry of isotopic profiles is discussed in more detail below. There is no available method to by pass these problems for isotopic diffusion, although for elemental diffusion, alytical Transmission Electron Microscopy (ATEM) offers an alternative (Meissner et al. 1997). 

Figure 19. (a) Representative example of a diffusion profile of oxygen isotopes measured in calcite reacted at 700°C and total pressme of 800 bars with a fluid containing Ico2 = 0.5 for 22 hours (Labotka et al.,... 

Isotope exchange diffusion profiles can also be measured ex situ by SIMS, and can, in principle, reveal surface kinetics in addition to bulk transport... 

Gal N/Gal N/Gal N isotope heterostructures were used to study nitrogen self-diffusion by secondary-ion mass spectrometry and thermally activated decomposition. After interdiffusion of Ga N and Ga N layers at between 770 and 970C the diffusion profiles were measured. The temperature dependence of the nitrogen self-diffusion coefficient in hexagonal GaN was described by ... 

The stable isotope, Si, was used to measure diffusion in amorphous material at 1110 to 14IOC. The diffusion profiles were determined by using secondary ion mass spectroscopy. The resultant diffusion coefficients were described by ... 

Diffusion of the stable Zr tracer isotope in 12mol% poly crystalline scandia-stabilized zirconia was studied in air at 1200 to 1600C. Secondary ion mass spectroscopy was used to record the tracer diffusion profiles. The diffusivities for bulk and grain boundary diffusion were given by,... 

The group of Carter and Steele [13] has developed the isotopic 02/ 02 exchange-diffusion profile (lEDP) technique, which allows estimating the surface exchange coefficient k and the diffusion coefficient D [14,15]. This technique is based on surfece thin film analysis by secondary ion mass spectrometry (SIMS) measuring a three-dimensional mapping of the distribution [16-18]. 

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