"Displacive" phase transitions (PTs) have been misinterpreted: there are no displacements. The idea of "displacive" PTs was put forward by Buerger in 1950^th as a cooperative deformation / distortion of the original structure by displacements of atoms / molecules in the crystal lattice without breaking their bonding. The alternative was "reconstructive" PTs when such structural modification could not be imagined without breaking bonds; how the latter can occur remained unknown. The classification was not based on experimental investigation of the process. Rather, it was assumed from comparisons of the initial and final structures. The comparisons resulted more frequently in "hybrid" cases with some bonds being broken; these cases were assorted "displacive" anyway. The underlying specific structural orientation relationship (OR) was not verified.

Presently the notion "displacive" PTs is loosely used by scientific literature in cases where the structures of polymorphs seem to be "sufficiently similar". Theorists sometimes claim "displacive" PTs to be second order (simultaneous participation of all particles in the bulk). Experiments usually find them first order (actually, a rearrangement at interfaces). Some consider them to occur by "soft-mode" mechanism (which requires instant cooperative movement of atoms / molecules to their final positions - in contradiction with actual observations). Some combine all the contradictory notions by identifying "martensitic" PTs (first order) not only as "displacive", but even resulted from soft-modes (see Addendum E). In many instances, especially when dealing with ferroelectrics, "displacive" PTs are placed against "order/disorder", rather than "reconstructive" PTs. This classification is plagued by observations of "crossovers" of the two; at that, "order / disorder" PTs are believed to be a cooperative process, which is not.

There are PTs, however, and plenty of them, that even most inventive theorists were unable to "squeeze" into "displacive" category. The molecular mechanism of these "reconstructive" PTs cried for explanation. If not by displacement, then how? The answer was: still by displacement / deformation / distortion of the original structure. In the abstract world of theoretical thinking, not attentive to the available contradicting facts, the "natural" idea of atomic/molecular displacements in the original structure was advanced further by "topological" theories in which "reconstructive" PTs proceed through several intermediate, more or less "displacive", imaginary stages. Even though this must lead to a certain fixed OR, the idea of its verification rarely comes about. What is more, it is becoming difficult to ignore the fact that both "displacive" and "reconstructive" PTs involve nucleation; hence the need to reconcile flame (nucleation) and water ("continuum" modeling).

The above cumbersome state of affairs has radical solution presented initially in my experimental articles in scientific journals, and then in this book. It turns out, a transition to another polymorph is like building a new house from the bricks obtained by disassembling the nearby abandoned brick house; the new house may, or may not, resemble the old one: the only feature they share is the construction material. All PTs in crystals (believed to be "displacive", "martensitic", "reconstructive", “order / disorder”, or otherwise) proceed exclusively by nucleation and (temperature-dependent) crystal growth, constituting two inseparable stages of the general molecular mechanism of the PTs. However attractive the idea of a modification of the original structure can be, PTs are simply a crystal growth from a solid medium, very much like that from liquids. The new crystal phase is built by molecule-by-molecule taken from the original phase, filling molecular "kinks" at contact interfaces. The function of the old phase is to supply "bricks" (atoms, molecules); its actual crystal structure, however similar the polymorphs may sometimes be or seem, isn't anymore relevant than the structure of liquid phase upon crystal growth from solution or melt. The original structure is responsible only for nucleation in its crystal defects - microcavities - where different nucleation temperatures and orientations of the new crystals are "encoded". In certain cases, e.g. in layered structures, the nucleation is epitaxial, leading to a certain OR, in other cases is not (for example, OR in p-dichlorobenzene is different in every sample). The event of a phase transition is determined by two factors: free energies of the polymorphs and nucleation lags (manifesting themselves as hysteresis).

CONCLUSION: The idea of crystal phase transitions by displacements / distortion / deformation may seem self-evident, but it is not materialized. The phase transitions are always crystal growth.