Domain width

The exchange energy coefficient M characterizes the energy associated with the (anti)paraHel coupling of the ionic moments. It is direcdy proportional to the Curie temperature T (70). Experimental values have been derived from domain-width observations (69). Also the temperature dependence has been determined. It appears thatM is rather stable up to about 300°C. Because the Curie temperatures and the unit cell dimensions are rather similar, about the same values forM may be expected for BaM and SrM. 

Conditions which promote multi-domainic goethites are high ionic strength (either [KOH] or salt) and also low synthesis temperature (<40°C). In alkaline solutions, multi-domainic character decreases and domain width increases as Al substitution increases to Al/(Fe-i-Al) of 0.15, whereas at Al/( Al-nFe) >0.15 single domain crystals result (Schulze Schwertmaim, 1984 Mann et al., 1985). Multidomainic goethites can recrystallize to single domain crystals as a result of hydrothermal treatment at 125-180 °C (Fig. 4.9) (Schwertmann et al., 1985). 

Fig. 27. Temperature dependence of the width of domain stripes as measured by Shono et al. (2000) for the Gao.957Mno.043 As film with the easy axis along the growth direction (full squares). Computed domain width is shown by the solid line. The dashed line is computed assuming that the parameter Ac (eq. (20)) is by a factor of...

Nanometer scale domain configurations in fe bulk crystals pave the way for a new class of photonic devices. As an example, preliminary calculations show that a uv laser (A = 300 nm) based on second harmonic generation in LiTaC>3 crystal requires a periodic nanodomain superlattice with domain widths of around 700 nm. In addition, the current domain gratings in ferroelectric crystals are suitable only for quasi-phase-matched nonlinear interactions in the forward direction, where the pump and generated beams propagate in the same direction. Sub-micron ferroelectric domain gratings are the basis for a new family of devices based on backward nonlinear quasi-phase-matched optical interactions in which the generated beam travels in a reverse or another non-collinear direction to the incident beam. Non-collinear... 

Figure 18.5 PFM measurement of the PTO sample after heating it for 10 min at 200°C. The measurement was taken under vacuum conditions. In the topographical image surface steps due to the 90° domainwalls can be found. Note the linescan, determining the domain width through the topographical measurement leads to a smaller value (51 nm) than determining it from the PFM images (56 nm). This discrepancy is explained by the inspection depth of the PFM mode (Figure 18.6).

In addition to the direct effect of stress described above, a reduction in 90° domain width can enhance permittivity because the domain wall area per unit volume of ceramic increases. The argument outlined below follows that developed by Arlt et al. [19]. 

Eq. (5.45) agrees quite well with experimental data for grain sizes between 1 and 10 pm. Above 10 pm more complex domain walls form and the domain width is limited to about 0.8 pm. Below 1 pm the stresses are large enough to reduce the tetragonality and this simple model is no longer valid. 

Figure 9.14 Transmission electron micrograph of a section of bicontinuous phase formed by 53 wt% polystyrene and 47 wt% polymethylmethacrylate blended with a Brabender mixer at a rate of 20 rpm, which is roughly equivalent to 90 sec, at 200°C. At this shear rate, the two components have about the same viscosity, around 1000 Pa s. The characteristic domain width is around 1 /xm. (From Miles and Zurek 1988, reprinted with permission from the Society of Plastics Engineers.)...

In Figure 5c, we observe the same time-domain cosine wave as in Figure 5a, but for only a finite period, T sec. The result is that the frequency spectrum is now broadened from an infinitely sharp spike to a signal whose frequency width is of the order of (1/T) Hz. This result is an example of a classical "uncertainty principle" the product of the time-domain width (T) and the frequency-domain width (1/T) is constant. In other words, the only way to determine the frequency of a time-domain signal with perfect accuracy (i.e., infinite frequency "resolution") is to observe it for an infinite length of time. 

Kulkarni et al. [83] studied the failure processes occurring at the micro-scale in heterogeneous adhesives using a multi-scale cohesive scheme. They also considered failure effect on the macroscopic cohesive response. Investigating the representative volume element (RVE) size has demonstrated that for the macroscopic response to represent the loading histories, the microscopic domain width needs to be 2 or 3 times the layer thickness. Additionally, they analyzed the effect of particle size, volume fraction and particle-matrix interfacial parameters on the failure response as well as effective... 

Figure 8.8 illustrates the texture of cogelled xerogel catalysts. In the micropore domain (width < 2 nm), the catalysts exhibit a very narrow pore size distribution centered around a mean value of about 0.8 nm that corresponds to the steep volume increase followed by a plateau. In the range of meso- (2 nm < width < 50 nm) and macropores (width > 50 nm), all samples exhibit a broad continuous distribution starting at about 2 nm and extending up to several hundred nanometers. 

Fig. 5.33 Plot of melting temperatures for HBVC diblocks ( ) and VCHBVC triblocks (o) against reciprocal of domain width, w. (From Weimann, etal. (191))...

Fig. 4 The upper panel describes schematically the chain configuration of an AB-type diblock copolymer, in which Da and Db denote the domain widths of block A and block B, respectively, with D being the periodicity distance, and the lower panel describes schematictilly the concentration profiles, in which (pA and (ps denote the local concentration profiles for block A and block B,...

---