Diffraction line profiles of spherical hollow nanocrystals

An analytical expression of diffraction line profiles of spherical hollow nanocrystals (NCs) is derived. The particular features of the profile lines, enhanced peak tail intensity, are analyzed and discussed as a function of the NC size parameters (outer and inner radius, shell thickness). The explicit formula for the integral breadth, the Fourier particle size , and the Scherrer constants are also obtained and discussed in detail. The diffraction line profiles of hollow CdS NCs of zincblende and wurtzite crystallographic structure are calculated and compared with Debye scattering profiles. The diffraction profiles of both approaches exhibit an enhanced peak tail intensity that can be considered as a fingerprint of the hollow NC structure.