Bain deformation

The standard (postulated) mechanism for the transition is the Bain deformation, which involves a 20% contraction in one direction and a 12% expansion in two perpendicular directions. This was described by Bowles and... 

Bain Deformation. The conversion of one crystal lattice into another by a simple expansion or contraction along the orthogonal axes. A martensitic... 

Ward, A. D., Berry, M. G., Mellor, C. D., Bain, C. D., Optical sculpture controlled deformation of emulsion droplets with ultralow interfacial tensions using optical tweezers. Chem. Commun. 2006, 4515-4517. 

Bain-Ackerman and Lavallee " have measured the rate parameters for the entry of five bivalent metal ions into A-methyltetraphenylporphyrin in dmf solution. All reactions follow a second-order rate law and with the exception of Mn(II), the order of the porphyrin metalation rate constants (Cu(II) > Zn(II) > Co(II) > Ni(II)) coincides with that of solvent exchange at the metal ions. The values of k for this deformed porphyrin (Table 6.4) are all larger than for the corresponding metal ion reacting with planar porphyrins. The authors favor a mechanism which involves solvent dissociation from the metal ion as an important rate-determining factor but they also point out that porphyrin deformation... 

Similarly, other deformations of a lattice can give other elastic constants, or combinations of them. The deformation in Fig. 1, leading to Eq. (3), is the most common version of a Bain path. In the volume-conserving approximation, the volume of the system is kept constant, while da is varied. A more accurate calculation allows also the volume to vary, so that the energy is minimised for each da. 

We consider two simple transformation paths connecting cubic structures. They are the bcc-fcc transformation path via tetragonal deformation corresponding to extension along the [001] axis (the usual Bain s path) and the trigonal deformation path that corresponds to uniaxial deformation along the [111] axis (Figs. 1 and 2). 

Modern crystallographic theories suppose that, in addition to the Bain strain (the 3x3 matrix B) and rotation (R) alluded to earlier, a simple shear (S) occurs simultaneously (actually, no temporal sequence is implied by these operations). These three operations taken together are equivalent to the IPS shape deformation (P), or in matrix form... 

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