Calculation of phononic images of ionic superlattice crystals

Abstract<br /> A theoretical study has been presented for the calculation of phonon focusing for the ballistic phonons in multi layer superlattice. The calculated image has been discussed on the base of the slowness and group velocity surfaces. The phonon group velocity is calculated from the dispersion relation. The shell model and Sangster and Atwood potential which prove its success with alkali hailed crystals had been used to calculate the dispersion relation for the crystals in this study. The zone folding has been observed, which occurs as a result of the periodic structure of the superlattice crystal. in the present study it appear in one choices of the unit cell. An efficient algorithm has been used for the calculation of the slowness and group velocity surfaces, which is the fast and more precise in accumulated necessary points to draw the surfaces and phonon images. This algorithm depends on an iterative calculations for finding the position of the given point of the wave vector on the slowness surface. To calculate the phonon images in the dispersion region for the superlattice crystal, an algorithm for the branch separation has been modified depending on the continuity properties of the eigen values and eigen vectors. To present the images of the phonon focusing inside the crystal without any losses of any information and give a full description of gray level of the image, code has been constructed based on the histogram equalization algorithm has been written for process and enhancement the images.