I remember that 20+ years ago we used a program called Powder Cell to calculate diffraction patterns from models of materials (for example, to compare it with experimental data from powder diffraction). I just fired this program up under wine and it still works:
What are modern alternatives?
Note: this program takes description of a unit cell (atoms and unit cell parameters) and produces indexed pattern. This is different than using the Debye scattering formula to calculate diffraction pattern of any set of atoms, but without Miller indices.