How does one find misfit values between two different orientations for HCP (substrate) and cubic (film).
Looking for clear explanation.
For two crystals (1 and 2) at a given orientation relationship, the misfit between two vectors from crystal 1 and 2 can be defined as deta x = x1 - x2. In simple but not strict manner, x1 and x2 connect the nearest atoms from crystal 1 and 2 respectively. For defining the more useful quantity, i.e. misfit strain, which is defined as |deta x|/|x1| with crystal 1 as reference cystal, x1 and x2 should be close to the origin so that they do not cross a dislocation.
Are you talking about a single-crystalline substrate, and if you mention two different orientations...do you mean a certain orientation of the hexagonal and the cubic phase?
Do you need help for a theoretical understanding, or recommendations for experimental techniques which enable the determination of lattice misfit?
Still another comment: lattice misfit describes the mismatch of two frameworks of mathematical points. Actually, they are only rarely identical to atomic positions (onöy for very simple structures). From my point of view, only on the atomic level a mismatch discussion makes sense. Thus, the lattice mismatch might be big but on the atomic level the fit along the interface might be remarkably good.
Depending on the orientation relationship between the two phases (can be found using TEM based techniques), you can find the deformation gradient, from which you can get strain or misfit strain. If you are dealing with bulk materials then the strain will be stress-free-transformation-strains. In case of the film on substrate , the strains in the two directions will be fairly large compared to the third direction - in essence a sort of a biaxial strain condition. The direction with less strain will have a free surface (e.g. film) , or no boundary constraint, which will reduce the strain perpendicular to that surface. Ofcourse, the above explanation assumes that you have a single crystal film deposited on the surface of a substrate. In case you have a polycrystalline film , you may have to consider the entire deformation gradient.
- Badges
- Science topic
- Similar topics
- Chemistry
- Nanotechnology
- Nanostructures
- Thin Films