B-phase

More recent studies have involved the formation, composition, and microstructure of B-phase in much more detail [54] - especially in the Y- and Er-sialon systems. The composition is variable, both in cation and O N ratios, depending to some extent on the starting composition, with the simplest whole number M Si Al ratio being 4 3 2, and a nitrogen content of approximately 10-15 eq%. It is apparent that the B-phase forms most readily from glasses close to this composition when heat-treated at low temperatures (1000-1100 °C). Although additional structural studies have been conducted on this phase, and appear to imply that B-phase has a chain [55] rather than 

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Figure A2.5.14. Quasi-lattice representation of an equimolar binary mixture of A and B (a) randomly mixed at high temperature, and (b) phase separated at low temperature.

Figure C2.1.10. (a) Gibbs energy of mixing as a function of the volume fraction of polymer A for a symmetric binary polymer mixture = Ag = N. The curves are obtained from equation (C2.1.9 ). (b) Phase diagram of a symmetric polymer mixture = Ag = A. The full curve is the binodal and delimits the homogeneous region from that of the two-phase stmcture. The broken curve is the spinodal.

The transition from smectic A to smectic B phase is characterized by tire development of a sixfold modulation of density witliin tire smectic layers ( hexatic ordering), which can be seen from x-ray diffraction experiments where a sixfold symmetry of diffuse scattering appears. This sixfold symmetry reflects tire bond orientational order. An appropriate order parameter to describe tlie SmA-SmB phase transition is tlien [18,19 and 20]... 

Leadbetter A J, Frost J C and Mazid M A 1979 Interlayer oorrelations in smeotio B phases J. Physique Lett 40 325-9... 

Pindak R, Monoton D E, Davey S C and Goodby J W X-ray observation of a staoked hexatio liquid-orystal B phase Phys.Rev.Leff 46 1135-8... 

Fluang C C, Viner J M, Pindak R and Goodby J W 1981 Heat-oapaoity study of the transition from a staoked-hexatio-B phase to a smeotio-A phase 1981 Phys.Rev.Lett 46 1289-92... 

The positional order of the molecules within the smectic layers disappears when the smectic B phase is heated to the smectic A phase. Likewise, the one-dimensional positional order of the smectic M phase is lost in the transition to the nematic phase. AH of the transitions given in this example are reversible upon heating and cooling they are therefore enantiotropic. When a given Hquid crystal phase can only be obtained by changing the temperature in one direction (ie, the mesophase occurs below the soHd to isotropic Hquid transition due to supercooling), then it is monotropic. An example of this is the smectic A phase of cholesteryl nonanoate [1182-66-7] (4), which occurs only if the chiral nematic phase is cooled (21). The transitions are aH reversible as long as crystals of the soHd phase do not form. 

Fig. 8. Process-2one shielding mechanisms (a) Microcrack cloud (b) phase transformation (c) yielding of ductile reinforcements.

B. Phase Diagrams of 2D systems with repulsive interactions 85... 

Thermotropic liquid-crystalline properties of different metal alkanesulfonates are studied by microscopy and X-ray diffraction [59]. Sodium soaps show smectic polymorphism of smectic A and smectic B phases. Ammonium soaps only show smectic A phases but polymorphism in the crystalline state. Calcium soaps show columnar mesophases. In Figs. 32 and 33 some textures and x-ray diffraction patterns are depicted. 

FIG. 32 Textures of Sodium Pentadecane 1-Sulfonate, (a), Crystalline phase at 80°C (b), smectic B phase at 113°C (c), smectic A phase at 250°C. Sample window 1.4 mm2, crossed Nicols. 

The structure of CaB contains bonding bands typical of the boron sublattice and capable of accommodating 20 electrons per CaB formula, and separated from antibonding bands by a relatively narrow gap (from 1.5 to 4.4 eV) . The B atoms of the B(, octahedron yield only 18 electrons thus a transfer of two electrons from the metal to the boron sublattice is necessary to stabilize the crystalline framework. The semiconducting properties of M B phases (M = Ca, Sr ", Ba, Eu, Yb ) and the metallic ones of M B or M B5 phases (Y, La, Ce, Pr, Nd ", Gd , Tb , Dy and Th ) are directly explained by this model . The validity of these models may be questionable because of the existence and stability of Na,Ba, Bft solid solutions and of KB, since they prove that the CaB -type structure is still stable when the electron contribution of the inserted atom is less than two . A detailed description of physical properties of hexaborides involves not only the bonding and antibonding B bands, but also bonds originating in the atomic orbitals of the inserted metal . ... 

The distribution of the intermolecular vector is also of value in distinguishing between smectic A and smectic B phases with the latter having long range bond orientational order [23, 24]. At the local level we can define a bond orientational order parameter, PeCn) for molecule i at position q by [25]... 

Fig. 8. The distance dependence of the bond orientational correlation function gs (r ) found for the mesogen GB(4.4, 20.0, 1, 1) in the smectic A (.) and the smectic B (—) phases...

The dimer model proposed by Wilson [83] was found not to exhibit a nematic phase but smectic A and B phases and so, although semi-realistic features are included, the model is not able to reproduce the behaviour of real dimers such as the a,co-bis(4 -cyanobiphenyl-4-yloxy) [87], which exhibit nematic phases, although liquid crystal dimers exhibiting smectic phases are also known [88]. In these simulations, the GB-GB interaction appears to be too strong and so the system forms a smectic phase in which the GB and LJ units... 

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