Can volume conserving tetragonal shear change FCC to BCC structure ?
Given that the packing densities are dissimilar (0.74 for fcc compared to 0.68 for bcc) and the "atomic radius" remains essentially unchanged for a given element irrespective of which lattice structure it forms, I would argue that volume-preserving tetragonal shear cannot accomplish such a transformation.
No, the FCC to BCC transformation can not achieved by volume-conserving tetragonal shear. The answer given by Dr. Philip Eisenlohr is pretty much correct. I would like to add a few more aspects to it. Typically, the lattice parameters for BCC and FCC crystal structures consisting of the same atom/atoms are 4r/3^0.5 and 4r/2^0.5 with r as the radius of the atom. The difference in the lattice parameter suffices the difference in the volume.
Furthermore, we metallurgy people are familiar with austenite to martensite transformation in steels during quenching that, is from FCC to BCT crystal structure. If you look into the strain tensor associated with this transformation, it has shear as well as hydrostatic components. The hydrostatic components would lead to a change in the volume.
Hope this helps.....
Happy learning...
Regards
Dr. Subha Sanket Panda
Indian Institute of Technology Kanpur
No,volume conserving with change from FCC to BCC is not possible because of packing densities difference as mentioned by Philip Eisenlohr..
@1. During the phase transformation, there is a change in volume and a shift along the C axis. This explains the change in the shape of the workpiece when the steel is rolled
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