Domain radius

As the growth rate is inversely proportional to the domain radius,smaller domains are able to grow faster than larger ones, thus giving rise to a narrowing of the size distribution with time. 

Under the fbd conditions the domain radius r is larger by an order of magnitude than the radius of the tip apex curvature R. For the tip brought in contact with a surface the distance S equals approximately to the lattice constant (0.5 nm). Therefore sn r is satisfied and Equation (10.9) becomes ... 

Figure 10.11 shows the theoretical dependence of the domain radius on the applied voltage, which was compared to an experimental data obtained in lithium niobate. This calculation was performed in the range of voltages between 0 and 1.4 kV, using Ps = 75/xC/cm2, ec = 30, ea = 84. The surface energy density aw was obtained by a fitting procedure where it was a free parameter as expected, the obtained value aw = 4 mJ/m2 was relatively small. 

Figure 10.11 Theoretical dependence of the domain radius on the applied voltage obtained by taking of the surface energy density as a free parameter and adjustment to the experimental results.

Compared to domain-wall thicknesses, the determination of domain sizes tends to be very complicated [13, 14, 51, 93, 99-101], This is because domains are caused by the strongly geometry- and size-dependent magnetostatic selfinteraction. An exception is the critical single-domain radius... 

Figure 6.26 Plot showing the variation in peak potential with increasing domain radius ro- In all cases, rj = 1 x 10 cm, v = 0.1Vs , D=1 X lO cm ...

FWHMcorr is corrected for the instrumental resolution and K varies with Ad/d and the FWHM. Setting the Scherrer constant K to unity one then plots FWHMcorr cost against sin0 as abscissa. One can then extract the scattering domain radius A from the intercept with the ordinate and Ad/d from the slope (see Figure 4). 

Fortunately, a set of equations are available for the statistical treatment of nearest-neighbour distance in a random distribution of particles [18, 23]. For a particular value of rg, knowledge of N and A allows us to determine the distribution of diffusion domain sizes (in terms of domain radius, relectrode surface. The probability, P(rd), of finding domains of radius is given by the equation (a Poisson distribution) ... 

The expectation value (mean) domain radius, (r[Pg.212]

Fig. 2.7 a TFCD energy relative to the flat-layer state versus domain radius, a, for a flat substrate, with LC thickness h increasing from uppermost to lowermost curves h = 2, 2.5, 3, 3.5, 4, 5 pm. b TFCD energy relative to the flat-layer state versus domain radius for defects on top of the pillar at varying pillar diameters,... 

The growth kinetics of binary immiscible fluid and phase separation has been smdied by using variety theoretical and computational tools. The time-dependent growth of average domain radius R t), which follows algebraic growth laws of the form... 

Calculation of volume fractions required values of domain radius or thickness, these were determined from SANS data at intermediate Q, i.e. where A(Q) = 1,... 

This program is patterned after UiyiDE DIRECT, with the difference that the/ axis is limited by the diffusion domain radius Rj, at some given multiple of the disk radius, as discussed in Chap. 12, Sect. 12.5. Effectively, at this radius, there is a cylindrical wall around the electrode, across which there is no flux, so we have a zero gradient boundary condition there. 

At IV s , the forward sweep of the voltammogram lasts about 0.15s. In this time, a mean diffusional distance is sj2Dt from the Einstein equation, which is about 17 /xm. For a coverage of 1%, the diffusion domain radius is 10 fe. Hence, the overlap of the diffusion layers is only partial in the case of fe = 1 jjtm, and so the voltammetry exhibits Case 3 diffusional behaviour, whereas for fe = 10 nm the overlap is complete and Case 4 behaviour is observed. 

Fig. 3.6 Schematic diagrams showing a (i) the overhead view of a section of the basal plane HOPG surface and (if) the r proximation of each island/band combination as a partially covered circular disc of the same area b the resulting drfiusion domain from the approximation in (a) (ii) and the cylindrical coordinate system employed. Reproduced from Ref. [23] with permission from The Royal Society of Chemistry. Note that the island radius is termed Ri, and the domain radius is Ro...

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