Addendum F
Introduction
It is generally accepted that understanding the physics of shape memory effect in alloys is vital to widen its practical application. To date, valuable empirical information has been accumulated, but the basic phenomenon leading to the effect, called "martensitic transformation", was misinterpreted. Even though the shape memory effect, as such, was not a subject of the now available 1st edition of the present book, the book contains all basic data and new important specifics for its correct interpretation. This Addendum is a guide to the book regarding the shape memory effect. The particular sections and pages of the book will be referred to.
The current views
There is no specific " martensitic" mechanism of solid-solid phase transitions (Sec. 1.5.1, p.14). Not a single property was proven to make it unique. Except for general consensus that it is "nucleation and growth" and "first order", all initial assumptions of the concept, such as a "habit plane" moving with speed of sound, or specific "martensitic" temperatures, fail when encountered with reality. The concept was fading until its more recent renaissance related to the phenomenon of shape memory alloys; its failings are now disregarded or forgotten, or both.
Here are two examples of how "martensitic transformations" are presented nowadays. Ahlers [1]: "A cooperative movement in which the atom arrangements can change their volume and shape, but neighbors remain neighbors"; "kinetics and morphology is dominated by the strain energy"; "diffusionless"; "distortion of the original matrix". Otsuka and Kakeshita [2]: "The martensitic (also called displacive or diffusionless) transformation is a classical cooperative phenomenon in solids similar to ferromagnetism" [probably, "to ferromagnetic phase transition" - Yu. M.].
Neither of the above descriptions is correct. They would be appropriate for a homogeneous process, but not fit well to the rearrangements at interfaces, even presented as propagation of the "habit plane" as a whole. Solid-state phase transitions (PTs) - "martensitic", "displacive", or otherwise - are not a "cooperative", much less "classical cooperative", phenomenon. The term "cooperative" is defined as "all together" and was used by theorists in its correct capacity for description of non-existent homogeneous "second-order" PTs. The only alternative to that homogeneous process is "molecule-by-molecule" rearrangement (Sec.1.2, p.3); propagation of the "habit plane" as a whole is outside of the allowed possibilities. PTs are not a "distortion of the original matrix". "Martensitic" PTs are not "diffusionless", for "diffusional" PTs do not exist*). Their kinetics depends on temperature and presence of crystal defects. Strain energy is not their moving force and affects kinetics only as a secondary effect. The comparison with ferromagnetic PTs is in a sharp contrast with the theory presenting the latter as a second-order, but is partially correct in a sense that, contrary to the theory, ferromagnetic PTs occur by nucleation and growth (Chapter 4).
Finally, they are not "displacive". Introduction of "martensitic" and "displacive" mechanisms of PTs in the first half of 20th century had nothing to do with each other. The former was described as first-order, nucleation-and-growth, driven with speed of sound by strains resulted from a mismatch at the interfaces. The latter, on the other hand, believed to be second-order, a cooperative, homogeneous distortion/deformation of the original structure by displacement of its atoms/molecules to the new positions without bond-breaking. There is no scientific reason to blend them (see Addenda C and E).
What are "martensitic transformations"?
As indicated in [2], they are divided in two categories: thermoelastic and non-thermoelastic. Only the former can produce a shape memory effect. This is well correlated with statement of this book that all solid-solid PTs are nucleation and growth, but divided in two categories: epitaxial, when nucleation of the new phase is oriented by the original structure, and non-epitaxial, when the nuclei can form in different unspecified orientations. The "thermoelastic martensitic transformations" are, in fact, epitaxial nucleation-and-growth phase transitions. They are characteristic of layered structures or those with a pronounced cleavage. Their major features, studied on a number of organic crystals, were published in 1975 (Ref. 7, p. XV) and summarized again in this book (Sec. 2.8, p. 121-144). They are:
Þ strict structural orientation relationship prior to and after PTs,
Þ small temperature hysteresis due to low nucleation barriers,
Þ formation of the new structure with different stacking of almost (but not exactly) the same molecular layers,
Þ molecule-by-molecule rebuilding of every layer rather than displacement of the whole layers to the new type of layer stacking..
The source of shape
A growing single crystal tends to acquire an external shape reflecting its internal structure. This is true even when crystals of new phase grow within single-crystal medium of the original phase during PTs (see picture on the book cover and Figs. 2.2 to 2.10). As opposed to the "displacive", "soft mode", "martensitic", "topological", "second order", etc., theories, these pictures reflect general nature of solid-solid PTs. Their molecular mechanism, illustrated on p. 68 and on this web site, is similar to that of melt crystallization: molecule-by-molecule changing their phase affiliation at a contact interface to fill "kinks" on the crystal face of the new growing crystal. There are no cooperative deformations, distortions or displacements, no propagation as a whole of "habit" planes. Strains always emerge, but they are secondary effect frequently obscuring the underlying molecular mechanism.
As mentioned above, PTs are a crystal growth of two kinds. In case of non-epitaxial PTs, crystal growth of the new phase is limited by the external frame of the original crystal; it stops after the new structure fills out the old frame (see photo, Fig. 2.6g, p. 44). This case corresponds to the alloys with PTs not producing a shape memory effect.
The outcome in epitaxial PTs is different. In this case the crystal layers grow quickly in lateral directions through the whole original single crystal and come to its surface. After many successive layers that surface becomes a crystal face of the new structure. In other words, the previous shape is replaced by the new one. The new structure can be similar to the original one, differing basically by the manner of layer stacking; it was resulted from molecule-by-molecule crystal growth rather than mutual displacements of the whole layers. The details are in Sec. 2.8, p. 121 to 144. A shape change resulted from epitaxial PT is shown in Figs. 2.37c and 2.44, even though their original purpose was not to illustrate shape memory effect.
The source of memory
The memory is hidden in the location, structure, and the number of the crystal defects serving as the heterogeneous nucleation sites of the new phase. The results of experimental study of nucleation in solid-solid PTs were published in 1976 (Ref. 8, p. XV) and summarized again in this book (Sec. 2.5, p. 77-89). Basic features of the nucleation are:
Þ It is heterogeneous: without at least one proper crystal defect serving as a nucleation site the PT cannot occur at any temperature.
Þ Nucleation lags are solely responsible for PT hysteresis which is inevitable and higher in more perfect and smaller crystals.
Þ Temperature of a PT is "pre-coded" in the individual structure of the particular defect; it is not the same in different nucleation sites (Fig. 2.24).
Þ In case of epitaxial nucleation, the hysteresis level is drastically lower.
Þ Orientation of a nucleus (and orientation and shape of the new crystal) is "pre-coded" in the structure of the defect / nucleation site (p. 83 and Fig. 2.25, p. 84).
Þ Epitaxial nucleation in a layered structure gives rise to strict structural orientation relationship with the same direction of layers before and after PT (Fig. 2.37, p. 128).
Þ Nucleation sites exhibit different degrees of stability upon cyclic PTs: some survive only a single PT, others - several cycles, and some can practically become permanent nucleation sites (p. 84).
Þ Only one type of defects serves as the nucleation sites: microcavities of a certain optimal size (Sec. 2.5.4, p. 87-89). In case of layered structures, they are interlayer wedge-like microcracks predominantly located at the faces composed of the layers ends (p. 190 and Fig. 3.10a).
Shape + Memory
Let us consider a PT in a single crystal of rectangular lattice and pronounced cleavage (Fig.2.45a, p 144). Usually there is abundance of wedge-like microcracks on its side faces. This is why the PT will probably turn out multi-nucleus, resulting in the formation of a stack of laminar domains (Fig. 2.45b). If the resultant phase has a lower symmetry, the stack of alternating domains will exhibit zigzag side surfaces (which one should expect to see if Fig.2.45b is enlarged). The number of different domain orientations (called "variants" in the literature) is determined by the number of equally probable symmetry-equivalent ways of epitaxial nucleation (three in Fig.2.45c).
In principle, a desirable shape memory effect, apart from a number of practical parameters, should consist of two elements: (a) significant shape change upon PT and (b) single stable nucleation site serving as such in both directions upon cyclic PTs. One can imagine a 'single crystalàsingle crystal' PT resulted from a single nucleus (crystal defect) that, luckily, turned out to be stable in both directions of the PT, or also a lucky situation of two stable nucleation sites, one acting upon heating, the other upon cooling. In more realistic cases of multiple nucleation the number of nucleation sites can be reduced by eliminating less stable sites by cyclic back-and-forth PTs (p. 84). Ultimately, elimination of all "unwanted" sites can sometimes be achieved, making possible a "two way" shape memory effect (reiteration of the same shapes in cyclic PTs).
Application of stress
The last point to mention here is application of stress to force a stack of alternating domains to acquire the same orientation. This effect, not touched in the book, is easy to understand. Stress makes domains of a certain crystallographic orientation energetically preferable, causing their growth at the expense of others. Macroscopically, the preferable domains become thicker by movement of the twin boundaries separating them from the "unfavorable" neighbors. Microscopically, rearrangement of every successive layer at the twin boundary occurs by filling "kinks", molecule by molecule". (Running little steps along the twin boundary in a similar process called "mechanical twinning" have been observed). On the same reason, application of a sufficient stress can produce change of shape by causing PT in the original crystal at the temperature where the latter was stable. This will also occur by nucleation and growth, but will give rise to a single crystal orientation independent of the number of activated nuclei.
References
1. M. Ahlers, The martensitic transformation, www.materials-sam.org.ar, (2005).
2. Kazuhiro Otsuka and Tomoyuki Kakeshita, Science and technology of shape-memory alloys: new developments. MRS Bulletin, February 2002.
*) We leave notion "phase transition" to a process with chemically identical phases.