Discontinuous cubic

Figure 3. Sketch of the principal phase behavior of amphiphilic compounds. Usual amphiphiles are represented by a vertical line in this scheme they exhibit only one type of mesophase. Extreme geometries of one of their molecular parts or the addition of solvents (linear alkanes or water) may lead to a deviation from the vertical orientation of that line, thus, amphiphilic compounds in such situations may form various types of liquid crystal phases T = temperature, SmB phase (rotator phase), Cubjn and Cub(,i = cubic discontinuous or cubic bicontinu-ous phases, respectively, Col, i = columnar hexagonal phase, Iso = isotropic phase.

In addition to the cubic and/or inverse cubic forms described above, further transitional forms exist between the lamellar phase and the hexagonal mesophase (cubic, type II) or inverse hexagonal mesophase (cubic, type III) [6]. In contrast to the discontinuous phases of types I and IV, cubic mesophases of type II and III belong to the bieontinuous phases (Fig. 4f). A range of lyotropic mesophases are possible, depending on the mesogen concentration, the lipophilic or hydrophilic characteristics of the solvent, and the molecule itself [6]. 

The linear log-log plots of reaction rate (in terms of oxygen consumption) versus time show for many alloys a discontinuity, or increase of reactivity. It appears that this transition is associated with the phase transformation in the protective film of Zr dioxide. The initial film formed on Zr is the cubic polymorph of Zr dioxide. After a period of oxidation this transforms to the tetragonal, and finally to the monoclinic (stable) form of Zr dioxide. When certain alloying constituents... 

The obvious case to be considered first is that of synthetic faujasites, which come in a range of compositions, and for which a considerable amount of spectral information is available. Evidence of Si, A1 ordering in zeolites X and Y is provided by the presence of discontinuities in the plot of the (cubic) lattice parameter versus the Si/Al ratio (60), which indicates stepwise rather than gradual change in Si, A1 distribution. This effect is even more pronounced in synthetic faujasitic gallosilicates (61). 

The phase transition in barium titanate is of first order, and as a result, there is a discontinuity in the polarization, lattice constant, and many other properties, as becomes clear in Figure 1.7. It is also clear in the figure that there are three phase transitions in barium titanate having the following sequence upon cooling rhombohedral, orthorhombic, tetragonal and cubic. 

Existing literature consistently reports a higher hydrogen solubility in -iron than in viron. Therefore, since the crystal structure of the clad vessel wall changes from face-centered cubic () to body-centered cubic ( ) at the 3S/CS interface, the predicted discontinuity could be expected. 

Since states on opposite faces of the zone are entirely equivalent, one may repeat the bands and the Fermi surface by constructing identical zones around every lattice wave number, as shown in Fig. 16-7. In this representation, called the periodic-zone scheme, the second-band Fermi surface is seen to consist (again, for the simple cubic structure) of three closed lens-shaped segments. The advantage of this representation is that all discontinuous jumps in wavenumber have been eliminated the wave numbers connected by diffractions have been plotted... 

This phase should not be confused with the "I" discontinuous cubic phase formed in some systems, which consists of a cubic packing of closed aggregates. 

For the cubic interpolating spline, there is the not-a-knot end-condition which forces the discontinuity of the third derivative at the second knot to be zero, thus making the first two spans part of the same polynomial. 

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