Spatial correlation functions of paracrystals with radial symmetry.

We develop a phenomenological model to describe the structure of radially symmetric paracrystals whose long-range order are destroyed by propagation of particle fluctuations. General expressions are derived for the spatial correlation functions in one-, two-, and three-dimensional spaces. And the spatial correlation in paracrystals in reciprocal space is further discussed and clarified. The developed method can be used to quantitatively analyze the microstructure of paracrystalline materials in both real and reciprocal spaces via scattering experiments and computer simulations.