Meaning
Diffraction methodology separates the broadening effects of finite crystallite size from those caused by internal microstrain within the lattice. Plotting the integral breadth against the scattering angle reveals a linear relationship where the intercept points to the crystal size and the slope indicates the strain levels. This technique governs the assessment of structural health in materials that have undergone mechanical or thermal stress.
Data Fitting
Multiple peaks from a single diffraction scan are measured to ensure that the trend lines cover a representative range of the reciprocal space. Consistent peak shapes are required to prevent errors in the calculation of the integral width. The resulting values differentiate between particles that are small and particles that are highly defective.
Grain Study
Calculation of crystallite size through this method provides an average figure that describes the primary grain dimensions across thousands of grains. Higher microstrain slopes in the Williamson-Hall analysis suggest significant atomic disorder from processing errors or cycle wear. Applying this mathematical treatment allows for a more detailed structural check than Scherrer analysis alone.
Quality Control
Manufacturers use these results to confirm that annealing temperatures were high enough to relieve internal pressures after sintering. Samples from degraded cells show how the microstrain increases as ions are repeatedly removed and replaced. Reliable slope determination confirms the consistency of mass produced powder batches.