On the Relation between X-Ray Diffraction Angle and Atomic Spacing in Metallic Glasses

The Bragg equation, which is usually employed to calculate the lattice constants of crystals, cannot be directly applied to amorphous alloys because they do not sustain long-range periodicity. A correction factor has to be involved, and the Debye equation predicts this to have a value of 1.23. Here, the amorphous structure of metallic glasses is investigated with XRD (Cu Kα) and the diffraction angle where the broad amorphous peak emerges is shown to be dependent on composition. By fitting the data of the dependence of the average atomic spacing on l/(2sinq), a factor of 1.22 was attained for metallic glasses with predominantly metallic bonding character, and even lower values if considerable covalent-like bonding is present. The lower factor can be explained by denser atomic packing in real amorphous metallic systems compared to that predicted by the random packing model.