^{Addendum G}

Crystal phases are not related. Crystallography is mistaken by assuming existence of a structural or symmetry relationship between polymorphs. A result is speculations about changes in the initial phase (like deformation, displacements, distortion, etc.) reforming it into the resultant phase. It is true that some similarity and even orientation relationship are frequently found, but they misled the scientists. They are due to the polymorphs being built from the same atoms and molecules (Sec.1.4.3).

      The mechanism of all crystal phase transitions is nucleation and growth (pivotal theme of the book), and this fact is incompatible with modification of initial phase into the resultant. The former serves simply a medium where crystal growth of the latter takes place. Only epitaxial effect upon nucleation in a solid medium may occur. Each polymorph forms independently according to minimum free energy under its particular p,t. The "relationship", however, would take preference over minimum energy principle. The nucleation-and-growth mechanism of crystal phase transitions is merely a part of general principle that any crystal structure resulted from nucleation and growth. Nature produced a better process of solid-state phase transitions than most brilliant human beings, even Nobel Prize winners, were able to invent: it is simple, universal and energy-efficient.

      The nucleation-and-growth mechanism of phase transitions involves nucleation lags (hysteresis) and rearrangement at interfaces separating two coexisting phases. Any claim that a phase transition is lacking those features is erroneous; they would be revealed upon careful re-examination. Any theory, or interpretation, of phase transitions assuming an instant, homogeneous in the bulk, nucleation-free process (continuous, cooperative, second-order, critical, displacive, distortive, etc.) is at variance with the reality. Soft-mode and incommensurate theories (or interpretations) of phase transitions fall in that category. Besides, as opposed to any imperfect crystals, polycrystals, quasicrystals, amorphous matter, liquid crystals, ODC and liquids, the resultant "incommensurate" state can’t materialize due to disregarding the optimum intermolecular / interatomic distances. Mechanism of crystal phase transitions involving modulation by vibration modes is a theoretical fiction. The idea of "incommensurately modulated structure", when introduced, was bound exclusively to crystal phase transitions and meant distortion of original crystal by an optical mode of wavelength irrational towards the crystal parameters. Keeping this in mind, statements found in the literature like "Crystals grown from ethanol revealed an incommensurately modulated structure" make no sense.   

      Then, what to do, for example, with those weak diffuse x-ray reflections indicating an approximate superstructural periodicity? The cause should be found in the conditions of crystal growth in each particular case. Thus, a phenomenon comes to mind of a "rhythmical" crystal growth from liquid phase, caused by accumulation of latent heat, demonstrated by late A. V.   Shubnikov.  I observed analogous effect upon phase transition in thin elongated plates of hexachloroethane: strips across the plate, caused by (approximately) periodical release of accumulating internal strains during propagation of the interface along the plate, were observed under microscope. Another example is a long period produced by folding of long-chain molecules.  There can be other reasons for existence of super- or irregular periodicity. If one finds an "aperiodic" structure, as in case of irregular layer stacking in layered crystals, the "modulation" occurred not by action of a vibration mode, but during crystallization - keeping in mind that phase transitions in solids are crystallization as well.