Deformation cooperative

The yield behavior is also a kinetic phenomenon and has been treated as the nonlinear cooperative deformation (21). Consider a... 

The foregoing experimental observations strongly suggested the connection between creep deformation at or near the crack tip and crack growth. For steady-state crack growth, the cooperative deformation at various positions ahead of the crack tip is required. The material at these positions experiences different levels of plastic strain and is subject to different flow stresses. The observed K dependence, therefore, represents the integrated effect and would have to be determined... 

Qin, Z. and Buehler, M.J. (2010) Cooperative deformation of hydrogen bonds in beta-strands and beta-sheet nanocrystals. Physical Review E, 82, 061906. 

Gupta HS, Seto J, Wagermaier W et al (2006) Cooperative deformation of mineral and collagen in bone at the nanoscale. Proc Natl Acad Sci USA 103 17741-17746... 

Glassy state In amorphous plastics, below the Tg, cooperative molecular chain motions are frozen , so that only limited local motions are possible. Material behaves mainly elastically since stress causes only limited bond angle deformations and stretching. Thus, it is hard, rigid, and often brittle. 

To motivate our next step recall that the LOFF spectrum can be view as a dipole [oc Pi (a )] perturbation of the spherically symmetrical BCS spectrum, where Pi(x) are the Legendre polynomials, and x is the cosine of the angle between the particle momentum and the total momentum of the Cooper pair. The l = 1 term in the expansion about the spherically symmetric form of Fermi surface corresponds to a translation of the whole system, therefore it preserves the spherical shapes of the Fermi surfaces. We now relax the assumption that the Fermi surfaces are spherical and describe their deformations by expanding the spectrum in spherical harmonics [17, 18]... 

In practice, the deformation parameters e/ (l > 2) are determined from the minimization of the free-energy of the system in full analogy to the total momentum Q of a Cooper pair. And they can be determined in a volume conserv-... 

For large enough asymmetries the homogeneous state becomes unstable towards formation of either the LOFF phase - a superconducting state with nonzero center-of-mass momentum of the Cooper pairs, or the DFS phase - a superconducting state which requires a quadrapole deformation of Fermi surfaces. A combined treatment of these phases in non-relativistic systems shows that while the LOFF phase corresponds to a local minimum, the DFS phase has energy lower that the LOFF phase. These phases break either the rotational, the translational or both symmetries. 

The phase transition consists of a cooperative mechanism with charge-ordering, anion order-disorder, Peierls-like lattice distortion, which induces a doubled lattice periodicity giving rise to 2 p nesting, and molecular deformation (Fig. 11c). The high temperature metallic phase is composed of flat EDO molecules with +0.5 charge, while the low temperature insulating phase is composed of both flat monocations... 

Condis crystals and glasses of macromolecules are a newly recognized type of mesophase. The mobility in this mesophase may lead to chain extension, and as a corollary, it may be possible that mechanical deformation can cause the stabilization of the condis state. Several examples of stable condis crystals are documented, but there seem to be also examples of metastable condis crystals which are produced as intermediates to crystallization. The size of the condis crystal transitions vary depending on the number of conformational isomers involved in the cooperative transitions. 

These last few years superconductivity in metals and alloys has mainly been explained with the help of the so-called Cooper electron pairs. At the low temperatures at which super-conductivity occurs, the metal ions do not vibrate any more. In that case the movement of an electron through the lattice is enough to deform that lattice. The metal ions in the vicinity of the electron move towards that electron and thus provide a net positive charge, causing a second electron to be attracted, (fig. 11.4.13b). In the figure b and c, the metal ions have been reduced in size because the figure is more clear then. 

These results show the dependence of the plastic deformation of PMMA on the thermal history of the sample. The relation with the cooperativity of the ft transition motions is addressed later in Sect. 3.1.1.6. 

As regards the micromechanisms of deformation, it appears to be clear that SDZs are controlled by the cooperativity of fi transition motions. Occurring at 50 °C for PMMA, they are shifted at temperatures above 100 °C for CMIMx, in which such a cooperativity disappears. However, for MGI-rich copolymers they are present at 10 °C, owing to the MGI-MGI cooperativity. 

---