Directions 1 : [1 -1 0] // [1 1 -2 0] and Direction 2: [0 0 1]//[1 -1 0 0] .
Cr is a substrate; Cr2O3 is a grown film.
Film grown on Cr{1 1 0}
I provide you a suggestion which is atomic overlapping between the orientation relationships of the Cr and Cr2O3. For example, you can take advantage of the software (like as crystalkey) to draw the atomic planes ,i.e. (1-10)Cr and (11-20)Cr2O3 and then make both planes to form atomic overlapping figure. According to the orientation relationship between Cr and Cr2O3, you can try to find the Near Coincidence Site Lattices(NCSL) and attempt to calculate the misfit in their parallel directions. You can find the smallest strain with respect to the unstrained lattice spacing you want to find. By the way, I think that the calculated result of the misfit must consist with your results regarding to TEM (diffraction pattern) ,XRD or EBSD.
Narendra Bandaru; i reply here also to your private message. It is my feeling that you (as many others posing basic questions of crystallography through ResearchGate) had very little or even no courses of basic crystallography. In fact the calculation of interplanar spacings, d(hkl), is a very basic exercise. In similar sistuations it becomes very difficult, not to say impossible, to help you. Anyway, to obtain the data you are looking for, you need the cell parameters of the two compounds forming the interface. Then using the formula relating d(hkl) to (a, b, c, alpha, beta, gamma) and (hkl) (BASIC CRYSTALLOGRAPHY!) you can calculate d(hkl). Since you need values only for few simple directions, the calculations can even be done manually in a short time. Finally, this is for tutors and teachers: students/researchers cannot deal with crystalline materials without a minimum of general preparation on crystallography.
Giovanni Ferraris sir,
I know how to calculate d values for different systems by using basic formulas.
And i know how to calculate misfit values for cubic on cubic.
But i am facing a problem for finding cubic on hexagonal system for different directions.
can you see once pic what i send to you.
Thank you sir.
I suppose that with the term “misfit” it is intended the (percent) difference between the periodicities of two compounds along a common direction. Let suppose that compound 1 (C1) and compound 2 (C2) have in common the directions [100] (periodicity P1) and [110] (periodicity P2): P1 – P2 is the misfit, according the definition given above. Please remember that if the crystallographic reference system is not orthogonal, P[uvw] does not correspond to a d(hkl). If you do not know the directions that are shared by the two compounds (i.e., you do not know the orientations of the two layers), you can calculate a list of P[uvw] for both compounds and see which ones are close each other. Usually oriented growth is ruled by directions with small values of u, v and w (typically between -2 and 2): therefore the calculations can be limited to few P[uvw]. The following article could be useful http://users.wfu.edu/ucerkb/Nan242/L12-Epitaxy.pdf
Probably your problem is comparing a cubic with a hexagonal compound to find misfit. This is true if you compare only the lattice parameters; if instead you, more properly, compare the periodicities along directions (as I have written before) the problem should be simple.
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