Scherrer Equation — XRD Peak Broadening & Nanocrystallite Sizing

Shrink a nanocrystal down to a few dozen unit cells and its X-ray diffraction peak stops looking like a sharp line and starts looking like a hill — a direct, measurable consequence of the crystal simply not having enough planes left to interfere destructively away from the Bragg angle. This simulator renders the nanocrystal as a real 3D lattice of atoms, computes its diffraction peak from the exact finite-size interference (Laue) function, folds in a diffractometer's own instrumental broadening, and then runs the same Warren quadratic correction and Scherrer equation a metrology lab uses to read a crystallite size back out of that peak — so you can watch the measured size track (or miss) the true size as every knob moves.