A-crystalline phase

The oriented overgrowth of a crystalline phase on the surface of a substrate that is also crystalline is called epitaxial growth [104]. Usually it is required that the lattices of the two crystalline phases match, and it can be a rather complicated process [105]. Some new applications enlist amorphous substrates or grow new phases on a surface with a rather poor lattice match. 

Fig. 3. Curve ihustrating the activation energy (barrier) to nucleate a crystalline phase. The critical number of atoms needed to surmount the activation barrier of energy AG is n and takes time equal to the iacubation time. One atom beyond n and the crystahite is ia the growth regime.

As mentioned earlier, if there is a large disparity in sttiicture at the film-substrate interface, such as a crystalline phase growing on an amorphous, glassy, substrate, the film may detach and grow a separate morphology. 

This approach is an alternative to quantitative metallography and in the hands of a master gives even more accurate results than the rival method. A more recent development (Chen and Spaepen 1991) is the analysis of the isothermal curve when a material which may be properly amorphous or else nanocrystalline (e.g., a bismuth film vapour-deposited at low temperature) is annealed. The form of the isotherm allows one to distinguish nucleation and growth of a crystalline phase, from the growth of a preexisting nanocrystalline structure. 

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. 

Note that the linear coefficient of expansion, at is obtedned finm the slope of the straight fine. The glass softening point is also easily observed as is the glass transitional temperature (which is the point where the amorphous assy phase begins its transition to a crystalline phase. These glass-points can also be used to cross-check values obtained by the DTA method. 

The occurrence of a restricted range within which most of the melting may be confined when conditions conducive to equilibration are adopted lends support to the concept of a crystalline phase, a subdivided one notwithstanding, having approximately uniform properties throughout. (It follows also that although the crystallites which melt under the conditions described may be small by ordinary standards, they are not so small as to cause their stabilities to be much dimin- —Specific volume-temperature... 

Two types of reactions producing a new phase can be distinguished (1) those producing a noncrystalline phase (gas bubbles liquid drops as, e.g., in the electrolytic deposition of mercury on substrates not forming amalgams), and (2) those producing a crystalline phase (cathodic metal deposition, anodic deposition of oxides or salts having low solubility). 

Taking into account all these effects, the intensity due to a crystalline phase is given by ... 

An expression including the diffuse background of a crystalline phase was calculated for a Bragg-Brentano geometry [55] ... 

Expression (25) describes the smooth background belonging to a crystalline phase due to the incoherent (or Compton) scattering and the TDS or disorder scattering. The last contribution in (25) is very approximate because it is known that the TDS has a very complicated shape with very large peaks centered in the same position as the Bragg ones [56]. 

To discuss the models in this section, we should mention two issues. First, the models assume the membrane is sufficiently soft that the tilt direction can vary with an energy cost that scales as (Vc(j)2. This is appropriate if the membrane is in a fluid phase like a smectic-C liquid crystal, with order in the tilt direction but not in the positions of the molecules. It is also appropriate if the membrane is in a tilted hexatic phase, with order in the orientations of the intermolecular bonds as well as the tilt. However, this assumption is not appropriate if the membrane is in a crystalline phase, because the tilt direction would be locked to the crystalline axes, and varying it would cost more energy than (V(f>)2. 

The argument of Oda et al. implies that helical ribbons are in a crystalline phase, and it suggests that tubules are also in a crystalline phase because they can grow out of helical ribbons. By contrast, in Section 6.4 we presented a theoretical argument that tubules and helical ribbons are not in a crystalline phase. As noted in that section, there is experimental evidence both for and against crystallinity. Thus, it is not yet clear how to reconcile the... 

On heating from a crystalline phase, DOBAMBC melts to form a SmC phase, which exists as the thermodynamic minimum structure between 76 and 95°C. At 95°C a thermotropic transition to the SmA phase occurs. Finally, the system clears to the isotropic liquid phase at 117°C. On cooling, the SmC phase supercools into the temperature range where the crystalline solid is more stable (a common occurrence). In fact, at 63°C a new smectic phase (the SmF) appears. This phase is metastable with respect to the crystalline solid such phases are termed monotropic, while thermodynamically stable phases are termed enantiotropic. The kinetic stability of monotropic LC phases is dependent upon purity of the sample and other conditions such as the cooling rate. However, the appearance of monotropic phases is typically reproducible and is often reported in the phase sequence on cooling. It is assumed that phases appearing on heating a sample are enantiotropic. 

Examples of the fourth type of changes were described by To and Flink [ 1.931 and Van Scoik and Carstensen [ 1,94 According to To and Flink the change from an amorphous to a crystalline phase is induced either by to high storage temperatures T(T> Tc) or by water... 

Our analysis is, however, not complete in any respect. For instance, as the large difference in Fermi momenta renders the BCS-type condensation in the classical 2SC phase difficult, it seems to be worthwhile to consider other possibilities. Among others we thereby think of a crystalline phase, deformed Fermi surfaces [32, 35], spin-1 pairing [20] or the gapless 2SC [33, 34] or CFL phase [60], We conclude that whether quark matter exists in hybrid or... 

Clathrate formation is very attractive for exploitation in solid-state chemistry. It allows one to modify in a simple way the environment of the guest molecule, to place this molecule in a crystalline phase with a structure different from its own (one structure may be chiral, and the other not), and even to achieve a stable crystalline structure at a temperature above the melting point of the pure guest. Some of the variety available for a single compound, acetic acid, is... 

At a given (low) temperature and pressure a crystalline phase of some substance is thermodynamically stable vis a vis the corresponding amorphous solid. Furthermore, because of its inherent metastability, the properties of the amorphous solid depend, to some extent, on the method by which it is prepared. Just as in the cases of other substances, H20(as) is prepared by deposition of vapor on a cold substrate. In general, the temperature of the substrate must be far below the ordinary freezing point and below any possible amorphous crystal transition point. In addition, conditions for deposition must be such that the heat of condensation is removed rapidly enough that local crystallization of the deposited material is prevented. Under practical conditions this means that, since the thermal conductivity of an amorphous solid is small at low temperature, the rate of deposition must be small. 

As also mentioned in Sect. 2.1.2, Varin et al. [27] showed that a long-term air exposure of nanocrystalUne MgH for a few months led to a massive formation of crystalline Mg(OH)j not only on the surface but also in the bulk by conversion of the entire MgH particles into Mg(OH)2. Apparently, the initial amorphous hydroxide layer Mg(OH) grows and transforms into a crystalline-phase Mg(OH)2 (the reaction of (2.3)). 

For a crystalline phase, we have already seen that internal energy corresponds to lattice energy at the zero point. At higher T, the internal energy of the phase increases as a result of the increase in vibrational motion of all the atoms in the lattice. 

A typical vibrational spectrum of a crystalline phase appears as a section of the dispersion diagram along the ordinate axis. Figure 3.7 shows a generaUzed... 

Figure 3J Schematic representation of a vibrational spectrum of a crystalline phase. Dotted curves acoustic branches and optical continuum. Solid line total spectrum, and 0) 2 Einstein oscillators. Reprinted with permission from Kieffer (1979c), Review of Geophysics and Space Physics, 17, 35-39, copyright 1979 by the American Geophysical Union.

Note 1 The assumption is made that the sample can be subdivided into a crystalline phase and an amorphous phase (the so-called two-phase model). 

Example The following compound exhibits a crystalline phase (Cr), smectic SmC, cubic (Cub), smectic SmA mesophases, and an isotropic (I) phase, with transitions at the specified temperatures ... 

Defects play a critical role in diffusion in a crystalline phase because diffusivity is roughly proportional to the concentration of vacancy defects. It is important to understand how defect concentration varies with other parameters. 

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