Diffusion domain

Lovera, O. M., Richter, F. M. Harrison, T. M. (1989). The 40Ar/39Ar thermochronometry for slowly cooled samples having a distribution of diffusion domain sizes. J. Geophys. Res., 94, 17917-35. 

Figure 11,22 (A) Saddle-shaped age spectra of calcic plagioclases from amphibolites, Broken Hill, Australia. (B) Arrhenius plots of reactor-produced isotopes for two of the hve samples, defining existence of three diffusion domains corresponding to albite-rich lamellae (domain 1) and anorthite-rich lamellae of different widths (domains 2 and 3). Reproduced with modifications from T. M. Harrison and I. McDougall (1981), with kind permission from Elsevier Science Publishers B.V, Amsterdam, The Netherlands.

Harrison T.M., Lovera O.M., and Heizler M.T. (1991) °Ar/ Ar results for alkali feldspars containing diffusion domains with differing activation energy. Geochim. Cosmochim. Acta 55, 1435-1448. 

Diffusion domains determined by Ar released during step heating. 

Fig. 5.17 Simulated concentration profiles at a diffusion domain containing a spherical particle. Category 1 = 1CT3. Category 2 1% = 0.1. Category 3 1% = 1. Category 4 = 100. For all categories, the distance between particles is two times the radius. Reproduced from [57] with permission...

Regarding the discrepancies between disc and spherical electrodes, these are more evident as the frequency decreases (i.e., longer potential pulses) and so the differences in the diffusion domains are more apparent. 

Farley, 2000 Reiners and Farley, 1999, 2001), but this relationship breaks down in samples subjected to intensive ductile or brittle deformation (e.g., Amaud and Eide, 2000 Kramar et al, 2001 Mulch et al, 2002). In general, it seems prudent to assume that a is related to the physical grain size when applying Equations (17) and (19) unless samples show textural evidence for the extensive development of subgrain boundaries that may act as fast diffusion pathways, or— in the case of K-feldspar— show direct evidence of the existence of multiple diffusion domains during incremental heating experiments. 

Spin diffusion Domain sizing e.g. polymers, connectivity Caravatti et al. (1983), (1982)... 

All microparticles on the array surface will contribute to the observed current-voltage I-E response. To describe the random distribution, the following parameters are defined [35]. The microscopic coverage 0 refers to the fractional coverage of an individual diffusion domain (see next section) ... 

The Diffusion Domain Approach The so-called diffusion domain approach was first proposed by Amatore et al. [36], and has proved highly useful in several theoretically based reports on this subject to model the diffusion current at those randomly distributed spherical micro- (or nano-) particle arrays [35, 37-39]. 

The electrode surface can be understood as an ensemble of independent cylindrical diffusion domains of radius Tq with the respective solid microparticle at the center (Figures 6.13 and 6.14). 

These zones are approximated as being cylindrical, with the particle situated at the symmetry axis. If a random spatial distribution of microparticles is assumed, the respective diffusion domains (cylinders) are of different sizes, with a probability distribution function as follows [41] ... 

Figure 6.14 Coordinate system used to model the diffusion domain for a cylindrically approximated diffusion domain. The plane to be simulated is shaded [40].

Davies and Compton simulated a regular array of microelectrodes, varying the diffusion domain approach, as illustrated in Figure 6.20. 

Figure6.21 Simulated linearsweepvoltammograms for diffusion domains (see text). The system parameters are V = 0.1 Vs ...

Figure 6.22 Simulated linear sweep voltammograms for a microdisk of radius R, = 1 pm in a diffusion domain of radius (a) Ro = 200pm (effectively a single unshielded microdisk) and (b) Ro = 3Opm, D= 10 cm s ko= 1 cm s and [A] j, = 1 mM. In both parts the scan rate is varied from 0.005 to 2Vs as indicated [35],...

The electrode surface was assumed to contain N electroactive metal or metal oxide centers, respectively, which can be not only uniformly but also (mimicking more realistic experimental conditions) randomly distributed an example is the results of atomic force microscopy (AFM) studies on microparticle electrodes [53]. Here, the diffusion domain approach (as described in Section 6.3.2.2.1) has been employed that is, the electrode surface is assumed to be an arrangement of independent diffusion domains of radius Fq. If all particles are of the same radius, rj, but are distributed in a random manner, then a distribution of diffusion domains with different domain radii, ro, follows. The local position-dependent coverage is given by T. The electroactive microparticle flat disks of the radius rj are located in the center of the respective diffusion domain cylinder. The simulated (linear sweep voltammetric) reaction follows a one-electron transfer, and species B is stripped from the electrode surface into the solution, forming A, or ... 

This is not dependent on the size of domains - that is, the size distribution of the diffusion domains. However, by assuming an electrochemically reversible stripping, Ep is given by (adapted from Refs [51, 52] to this simulation model) ... 

The scan rate dependence on peak potential makes it dear that, at high microscopic coverage, a near-linear dependence of p on ln(v) applies, with the slope approaching RT/2F. At low 6, however, a hemispherical diffusion becomes predominant. With higher scan rates, the diffusion layer will become thinner and the diffusion regime more planar. Adjacent diffusion domains will then overlap with each other. 

For particles whose diameter is larger than 10 xm, the diffusion domain is the diffraction one. This phenomenon is characterised by UV-visible spectra with absorbance values slightly dependent on wavelength (diffraction and Mie/diffraction domain), which are almost independent from the wavelength. The ratio between absorbance values at 200 and 800 nm is about 2. 

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