Calculation of effective penetration depth in X-ray diffraction for pharmaceutical solids

The use of the glancing incidence X-ray diffraction configuration to depth profile surface phase transformations is of interest to pharmaceutical scientists. The Parratt equation has been used to depth profile phase changes in pharmaceutical compacts. However, it was derived to calculate 1/e penetration at glancing incident angles slightly below the critical angle of condensed matter and is, therefore, applicable to surface studies of materials such as single crystalline nanorods and metal thin films. When the depth of interest is 50-200 microm into the surface, which is typical for pharmaceutical solids, the 1/e penetration depth, or skin depth, can be directly calculated from an exponential absorption law without utilizing the Parratt equation. In this work, we developed a more relevant method to define X-ray penetration depth based on the signal detection limits of the X-ray diffractometer. Our definition of effective penetration depth was empirically verified using bilayer compacts of varying known thicknesses of mannitol and lactose.