Can anybody tell me how to calculate lattice misfit strain. There are n-numbers of literature and authors wrote about it and confused their own way. Let me say I have a film "a" which grows on substrate "b" and it is hetero epitaxial. I know the orientation relationship which follows like (010)a//(111)b and a//b. In this situation what should be the lattice misfit strain beween film and the substrate? Do I have to calculate the misfit in terms of d-spacing in this plane? or do I have to calculate the lattice vector in that direction.The structure is monoclinic(film-a) on cubic (substrate-b). Looking for some sensible answer.
hm not sure I understand completely. First of all, I guess that there was some typo in the direction: the diection is not part of the (111) planes in a cubic system. Did you mean (110)?
Second, what sort of cubic system is it: simple, bcc, or fcc? In order to have a chance have right angles (such that it fits with the right angles in the (010) plane of the monoclinic system) it should be a (100) plane in the fcc or simple cubic or bcc.
At any rate, I'd calculate the misfit strain such that the lattice vectors in the two parallel planes are the same.
At first, whatever the crystalline system is, atomic position for a and b should be nearly matched each other in various way, with off-axis angle.
please refer below
1. C. M. Carlson, P. A. Parilla, T. V. Rivkin, J. D. Perkins, and D. S. Ginley, Appl. Phys. Lett. 77, 3278 (2000)
2. L. Vegard, Z. Phys. 5, 17 (1921)
3. Landolt-Bőrnstein handbook
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