Isomorphous phase

This transition produces an isomorphous phase and the resulting y-alumina has the same morphology and texture as its boehmite precursor. With increasing temperature and time the mean pore diameter increases gradually and other phases appear (S-, 6-alumina). Due to the broad XRD lines, the distinction between y- and S-alumina cannot be made 6-alumina occurs at about 900°C while the conversion to the chemically very stable a-alumina phase takes place at T> 1000°C. Some typical results for alumina membranes synthesized without binders are given in Table 2.4. When PVA was used as a binder, thermogravimetric analysis showed that, provided the appropriate binder type was used, the binder could be effectively removed at T > 400°C. The ash residue is of the order of 0.01 wt.%. Mean pore size and... 

Figure 2.17 Isotherms through the ternary isomorphous phase diagram. Reprinted, by permission, from F.N. Rhines, Phase Diagrams in Metallurgy. Copyright 1956 by McGraw-Hill Book Co.

The electric conductivity was also measured for complexes of taper-shaped mesogens with oligo(ethylene oxide) central groups. The DC conductivity is in a range of 10 9 to 10 6 S cm-1 and shows a step-like increase at the crystal-columnar phase transition [86]. It was also shown that taper-shaped molecules adjacent to different endo-receptors such as crown ethers or oligo(ethylene oxide) chains were miscible with a poly(methacrylate) matrix and formed isomorphic phases [87]. Applications as columnar reaction media for polymerizations were foreseen. Comprehensive summaries of Percec s taper-shaped molecules can be found in the literature [88, 89]. 

Rare earth orthovanadates (RVO4) t) ically include two isomorphic phase structures with rare earth orthophosphates, monoclinic (m-) monazite type, and tetragonal (f-) zircon t) e. The selectivity also relies on the... 

Independently, a highly interesting problem recently revived is that of the alignment of molecules in liquid crystals due to externally applied static and alternating electric fidds. The problem was first approached by Jezewski and Kast, and was developed by Carr, Helfrich, Wysocki et al. and many others, studying various aspects, such as dielectric loss in electric fields and anomalous alignment in the smectic phase and domains, the effect of an electric field on the temperature of mesomorphic-isomorphic phase tranritions of liquid crystals, electric... 

Fig. 2 shows the diffuse reflectance spectrum of the RhMoe phase, which is compared to C0M06 and CrMo6 isomorphous phases. 

Another example of this kind of transition is shown in table 11.1, taken from the work of Smith and Kmetko [601]. It is a quasiperiodic table of all the transition elements and lanthanides in the periodic table, arranged in order of mean localised radius in the vertical direction, and adjusted horizontally so that filled and empty d and / subshells coincide. What Smith and Kmetko discovered is that a broad diagonal sweep across this table separates metals with localised electron properties (magnets) from those with itinerant electron properties (conductors). This boundary (shown as a shaded curve in the figure) is the locus of the Mott transition. Metals lying along this curve are sensitive to pressure effects (Ce has an isomorphic phase transition from the a to the 7 phase at about 1 kbar, U becomes... 

A well-known example of critical phenomena encountered in solid state physics is the pressure-sensitive isomorphic phase transition in the amorphous solid SmS [621]. A similar effect is the a-y transition on solid Ce. In both cases, the structure of the solid does not change, but there is... 

An interpretable electron density map has since been obtained using a combination of optimised anomalous and isomorphous phase information modified by solvent flattening techniques (Rule, Harding and Sawyer, unpublished). 

Cey xThx- This system crystallizes in the fee structure and undergoes an isomorphic phase transition around Tg = 150 K (Shapiro et al. 1977). The transition involves a reduction in unit cell volume of 16% and is of first order for x < 0.26 and of second order otherwise. For T > one observes Cmie-type susceptibility. At the magnitude of x drops by 60% and x then remains essentially independent of temperature (Lawrence et al. 1975). 

Jensen et al. have very successfully used difference Fourier maps using phases calculated from the atomic co-ordinates, in the refinement of the structure of the small protein, rubredoxin. Shifts derived from the first difference Fourier synthesis at 1.5 A resolution reduced the R factor (the agreement factor) from 0.372 to 0.321. Eventually difference syntheses revealed the positions of 127 water molecules oxygen atoms representing water were included if peaks were present in the 2 A isomorphous phased Fourier as well as the difference Fourier map. Occupancy factors were made proportional to peak height. This led to an appreciable decrease in R. After calculation of four difference Fourier syntheses, the method of least squares was used to refine the positional and thermal parameters despite the fact that their number was exceeded by the number of structure factors by... 

I. L. Aptekar and E. G. Por atovsky, A contribrrtion to theory of cerium isomorphic phase transformation artd (tltical trarrsition, Dokl. Akad. Nauk. SSSR 173,851-853 (1967). 

Route I leads to acrylic acid via intermediate formation of propene and acrolein. This route is preferred formixedoxides, where (M cM3,Moi 3 -3>)50i4, withx = V and = Nb (Ml analogu) and Sb4Moio03i (M2 isomorph) phases are simultaneously present. Our results also suggest that propane is activated and oxidized to acrylic acid on (M cM3,Moi c->-)50i4 (as observed for air-calcined catalysts) and... 

Fig. 2.5 Compositions of U.S. technical alloys mapped onto a pseudobinary 3-isomorphous phase diagram (Nis84],...

MgC, an isomorphous phase of the M23C5 thermal phase, is accelerated by segregation of Ni and Si under irradiation. 

The deviations from Vegard s law, as shown in the figure, are due to the change of the samarium valence, Welber, Jayaraman [5]. A similar curve of the lattice constants for samples obtained by a dynamical high pressure method is given by Batsanov et al. [1]. No variation of a (=6.20 A) is observed on films between x = 0 and 0.15 because of the inaccuracy of the measurements by Dumas, Schlenker [3]. The shift of the line in the X-ray spectrum of Smi xNdxSe mixed crystals remains close to zero (i.e., no isomorphous phase transition occurs), for a figure, see the paper, Sumbaev [6]. 

Given the similarity of atomic radii between the 4d and 5d transition metals, one would expect those pairs in the same column to be isomoiphous. This is the case for Hf-Zr, Mo-W, Ru-Os, and Au-Ag. Si-Ge is also isomorphous as are several compoimd systems such as HgTe-CdTe, Al203-Cr203 that exhibit pseudobinary isomorphous phase diagrams. 

Numerous structure refinements have been performed on isomorphous phases by X-ray powder diffraction (Bartram, 1965 Thornber et al., 1968 Thornber and Bevan, 1970 Rossell, 1976), by neutron powder diffraction (von Dreele et al., 1975), and by single crystal X-ray diffraction (Latavalya, 1976). The UY6O12 structure is a fluorite superstructure resulting from the ordering of cations and formal anion vacancies. These vacancies occur in pairs across the body diagonal of MOs cubes so that the special metals in the hexagonal unit cell become... 

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