Disordered systems and small particles

Disordered magnetic systems fall into three main types  

Analytical techniques to extract the form of the hyperfine field distribution from the shape of the broadened lines of the magnetically split spectra of disordered materials were first proposed by Window (1971) and by Hesse Rubartsch (1974). In the analysis of Window (1971), the hyperfine field distribution, i.e. probability of hyperfine field p(By ) versus hyperfine field expressed as a series expansion of trigonometric terms, 

While the methods discussed above may provide a good fit to the observed spectra, they typically need to be provided with mean values for the isomer shift and quadrupole splitting and with relative intensities for the outer, middle and inner pairs of lines in the magnetically split sextet spectrum. A different value for these relative intensities will often lead to an equally good fit to the Mossbauer spectrum, with a different, compensating distribution of the hyperfine field. Thus these analyses do not provide a sensitive and reliable method of determining the relative intensities of the 

The effect of a single charge and spin dipole moment at a point whose 

An ingenious method of studying distributions of quadrupole splitting and isomer shift in the ferromagnetically ordered phase of ferromagnetic amorphous materials, without interference from the distribution of hyperfine fields, has been repo rted by Kopcewicz, Wagner Gonser (1984). In this method a radio-frequency field is applied to the sample to reverse the 

---

Small-angle neutron scattering (SANS) can be applied to food systems to obtain information on intra- and inter-particle structure, on a length scale of typically 10-1000 A. The systems studied are usually disordered, and so only a limited number of parameters can be determined. Some model systems (e.g., certain microemulsions) are characterized by only a limited number of parameters, and so SANS can describe them fully without complementary techniques. Food systems, however, are often disordered, polydisperse and complex. For these systems, SANS is rarely used alone. Instead, it is used to study systems that have already been well characterized by other methods, viz., light scattering, electron microscopy, NMR, fluorescence, etc. SANS data can then be used to test alternative models, or to derive quantitative parameters for an existing qualitative model. 

All natural systems composed of small particles have therefore a tendency to change from states in which the arrangement of the particles, or of the motions of the particles, are ordered to the state in which there is the greatest molecular disorder or chaos. Stable equilibrium is not attained until the chaos is complete, and until the state of the system has a greater probability than any other possible state. By a possible state... 

As we have seen in Figure 5 the local densities of state in ordered 1 1 alloys AB are different on the two different sites (one site for constituent A, the other for B). It is easy to understand that in a disordered alloy of the same overall composition, there will be many different sites for each of the constituents, depending on, e.g., the composition of the surrounding layer of atoms. Indeed, the NMR lines in alloys are always broader than those in pure metals. A further complication is added when we make small particles of disordered alloys. The catalytic activity of Pti- Pd protected by films of poly(A-vinyl-2-pyrrolidone) (PVP) varies strongly with composition [75]. One would like to study both metals by NMR, but unfortunately lo pd NMR is very difficult and has not been attempted on small particles. Some information on small palladium particles is available from susceptibility measurements on catalysts [76] and on cluster molecules [77]. In both cases it was concluded that the susceptibility of the surface atoms is less than that of the bulk, just as is found for platinum particles from their NMR data. It is then reasonable to assume that in these systems the Pd susceptibility heals back when going from the surface to the interior, and that also for Pti Pdx particles an expression like Eq. (17) is valid. 

The studies of optimum conditions for SEIRA measurements [356, 357, 368, 376, 378, 393,410b] showed that the optimum thickness of a metal islandlike film is in the 4-25-mn range, depending on the system and the metal film morphology. For thicker films, the enhancement is reduced and eventually disappears because of absorption from the metal itself. The greatest enhancements were observed in metal nonpercolating deposits with sharply defined islets [357, 388] and for particles with a small cnrvature (e.g., needle-shaped) [357]. Ordered arrays of metal particles prodnce enhancement comparable to that on disordered vapor-deposited island films [350], It is important for analytical purposes that the SEIRA band intensities are finear functions of the film thickness for the first two to three adsorbed monolayers only [357]. 

The XRD patterns of Ti containing samples consist of a main peak at 20 < 3° corresponding to the 100 diffraction, sometimes accompanied by much weaker 110, 200 and 210 reflections in the 20 range of 4 to T. HMS based catalysts exhibit only the 100 diffraction peak because of excessive broadening of the hkO reflections due to too small scattering domain sizes [69,71,139,142] or more likely to the presence of a poorly ordered pore system [55]. Indeed, TEM studies indicated that the pore structure of Ti-HMS is much less ordered than that of Ti-MCM-41 [147]. In addition, SEM [143] and TEM [147] show that Ti-HMS is comprised of spherical particles with 0.2-0.3 pm in diameter. N2 adsorption isotherms obtained by Pinnavaia et al. [71,139,142] showed that in addition to the framework-confined mesoporosity due to the presence of parallel channels, HMS materials display a well developed textural mesoporosity. However, other workers found that the N2 adsorption-desorption isotherm of Ti-HMS is reversible [143,147]. The pore distribution was broader for HMS as compared to MCM-41 materials. The Ti-MSU-1 material also exhibited only the 100 diffraction peak due to the occurrence of disordered, hexagonal-like packing channels [72]. These samples displayed reversible N2 adsorption-desorption isotherms with no hysteresis. 

The mixing of all systems of matter involves a relative displacement of the particles, whether they are molecules, globules, or small crystals, until a state of maximum disorder is created and a completely random arrangement is achieved. 

---