Lattice cubic phases

Figure B3.6.4. Illustration of tliree structured phases in a mixture of amphiphile and water, (a) Lamellar phase the hydrophilic heads shield the hydrophobic tails from the water by fonning a bilayer. The amphiphilic heads of different bilayers face each other and are separated by a thin water layer, (b) Hexagonal phase tlie amphiphiles assemble into a rod-like structure where the tails are shielded in the interior from the water and the heads are on the outside. The rods arrange on a hexagonal lattice, (c) Cubic phase amphiphilic micelles with a hydrophobic centre order on a BCC lattice.

The initial configuration is set up by building the field 0(r) for a unit cell first on a small cubic lattice, A = 3 or 5, analogously to a two-component, AB, molecular crystal. The value of the field 0(r) = at the point r = (f, 7, k)h on the lattice is set to 1 if, in the molecular crystal, an atom A is in this place if there is an atom B, 0, is set to —1 if there is an empty place, j is set to 0. Fig. 2 shows the initial configuration used to build the field 0(r) for the simple cubic-phase unit cell. Filled black circles represent atoms of type A and hollow circles represent atoms of type B. In this case all sites are occupied by atoms A or B. 

To avoid this phase change, zirconia is stabilized in the cubic phase by the addition of a small amount of a divalent or trivalent oxide of cubic symmetry, such as MgO, CaO, or Y2O3. The additive oxide cation enters the crystal lattice and increases the ionic character of the metal-oxygen bonds. The cubic phase is not thermodynamically stable below approximately 1400°C for MgO additions, 1140°C for CaO additions, and below 750°C for Y2O3 additions. However, the diffusion rates for the cations are so low at Xhtstsubsolidus temperatures that the cubic phase can easily be quenched and retained as a metastable phase. Zirconia is commercially applied by thermal spray. It is also readily produced by CVD, mostly on an experimental basis. Its characteristics and properties are summarized in Table 11.8. 

Boron phases with formulas MB50, and MB,00 (M = Y, Sm, Gd, Tb, Dy, Ho, Er, Yb, Tm, Lu, Th and Pu) are the same cubic phase from x-ray powder data , with the Fm3c Sjpace group. Single crystals of yttrium and thorium borides lead to the formula The MB lattice constant data are given in Table 1. 

Studies on crystalline CggO [39] using calorimetry and high-resolution X-ray powder diffraction show a face centered cubic lattice (a = 14.185 A) with an orientational disorder at room temperature. An orientational ordering transition occurs at 278 K, upon which a simple cubic phase develops. At 19 K this phase, which is similar to the orientational ordered phase of Cgg itself, shows additional randomness due to a distribution of orientation of the oxygens in CggO. 

Fig. 4.44 Phase diagram for aqueous solutions of Pluronic P104 (PEOi7PP05,PFX)27) (Noolandi et al. 1996). Notation iso, isotropic (polymer poor) solution cubic, cubic phase hex[, hexagonal phase lam, lamellar phase, hex2, inverse hexagonal phase, cubicj, inverse cubic phase, iso2, isotropic (polymer rich) solution. The solid and dashed lines are calculated from the continuum and lattice versions of self-consistent field theory respectively.

An example of such order is shown by the hexagonal symmetry of SBS as revealed by LAXD, electron microscopy and mechanical measurements. In composite materials the choice of phase is at the disposal of the material designer and the phase lattice and phase geometry may be chosen to optimise desired properties of the material. The reinforcing phase is usually regarded elastically as an inclusion in a matrix of the material to be reinforced. In most cases the inclusions do not occupy exactly periodic positions in the host phase so that quasi-hexagonal or quasi-cubic structure is obtained rather than, as in the copolymers, a nearly perfect ordered structure. 

Self assembly of spheroidic aggregates leads in most cases to micellar cubic phases (Cub ) [30-35], where closed spheroidic aggregates are organized on a cubic 3D lattice (Fig. 2d,e).2... 

For polycatenar hydrogen bonded complexes with fluorinated chains at both ends (e.g., 138,139, see Fig. 36) formation of columnar phases was observed [246]. However, compound 137, having a branched Rp-chain at one end and three RH-chains at the other has a sequence of three distinct phases in the unusual sequence Cub-Col-SmA-Iso. For the SmA phase of compound 137 a structure with intercalated aromatic cores and RF-chains and separated layers of the hydrocarbon chains was proposed. At lower temperature, when incompatibility rises and the aromatics and Rp-chains disintegrate, all three components form their own layers. However, this produces interface curvature and a columnar phase with square lattice is formed. On further cooling a transition to a cubic phase with Im3m lattice takes place which is most likely of the bicontinuous type [262]. This leads to the unusual phase sequence Cubv-Col-SmA where the positions of the Cubv and Col phases are exchanged with respect to the usually observed phase sequences. The Col-Cub transition at lower temperature could be the result of the decreased conformational disorder of the terminal chains which reduces the steric frustration and hence reduces the interface curvature. 

Figure 6.12 Calculated diffraction patterns for Pb(Zro.52Tio.48)03 thin films with a. ..c/a/c/a... domain-structured tetragonal phase and a pseudo-cubic phase. The lattice parameters for the two phases were measured by XRD-RSMs.

Nitrides. At 500—1500°C hexagonal V3N is in thermodynamic equilibrium with a-VN solid solution 357 ageing of V-N alloys containing 8 and 10 atom % N at 500°C results in the formation of an intermediate cubic phase which has a lattice parameter 3.105 A some 2 % larger than that of the corresponding a-solid solution. 

Endothermic occlusion takes place by diffusion of hydrogen into a metal lattice which is very little changed by the process. In exothermic occlusion by palladium, however, the face-centred cubic lattice (a phase) of palladium, with lattice constant 3.88 A, will accomodate, below 100°C, no more than about 5 at. % hydrogen, and then undergoes a transition to an expanded phase ( 3 phase), with lattice constant 4.02 A and H/Pd = 0.5—0.6. The H—Pd system thus splits into a and 3 phases in the manner familiar for two partially miscible liquids. The consolute temperature (rarely observable for solid phases) is about 310°C at H/Pd = 0.22. The phase diagram is, however, not well established because formation of the... 

In accordance with obtained results one can to suppose that simple cubic phase of C32 is insulator with forbidden gap width about 1.5 eV and crystal lattice period a = 6.749 A. 

Watanabe (649) has observed antiferromagnetic Mn3+-Mn3+ interactions in cubic phases of the system Lai-ySr MnO, which would appear to support Jonker s (308) suggestion that the sign of the Mn3+-Mn3+ interaction changes as the lattice parameter gets smaller than a critical value of a 3.87 A. However, it is to be noted that the Watanabe compounds that were Mn3+ rich, antiferro-... 

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