Thank You very much Mr. Daniel for your suggestion, and the information you provided is very helpful.

when two materials overlaid, their lattices are parallel but parameters slight different , their HRTEM image also shows Moiré pattern, the wide of the fringer related to  their lattice difference. one my paper is about this phenomenon and calculate relationship between fringer wide and lattice parameter.

Dear professor Zhengfei Hu, I am very interested to read your paper about the moire patterns in HRTEM images, mentioned in your posti from above. How could I get a copy of your article ?

As described in well-known book from Williams and Carter, translational Moiré fringes are parallel contrast lines formed in high resolution TEM (HRTEM) imaging by the interference of diffracting crystal lattice planes that are overlapping, and which might have different spacing and/or orientation. In materials science, one of the known examples exhibiting Moiré contrast are nanoparticles of MX-type overlapping with face-centered cubic matrix. Both crystal structures are f.c.c. and are oriented cube-on-cube. However, they have significant lattice misfit of about 22%. In literature mostly one can find observations of Moiré contrast using HRTEM, i.e. phase contrast imaging where wave function amplitudes are added resulting in an interference image. However, if we use probe corrected HAADF-STEM imaging, we can get more direct interpretation of the crystal structure in terms of atom types and positions.

Example of such probe corrected HAADF-STEM observation of Moiré contrast exhibited by overlapping NbC and Fe-Ni-Cr matrix complemented also by rigorous Moiré contrast simulation (using μSTEM program) was published recently in:

DOI: 10.1016/j.msea.2018.02.004

https://www.researchgate.net/publication/323120822_Atomic_resolution_characterization_of_strengthening_nanoparticles_in_a_new_high-temperature-capable_43Fe-25Ni-225Cr_austenitic_stainless_steel