Structural Interpretation in Composite Systems Using Powder X-ray Diffraction: Applications of Error Propagation to the Pair Distribution Function

Abstract

To develop a method for drawing statistical inferences from differences between multiple experimental pair distribution function (PDF) transforms of powder X-ray diffraction (PXRD) data. The appropriate treatment of initial PXRD error estimates using traditional error propagation algorithms was tested using Monte Carlo simulations on amorphous ketoconazole. An amorphous felodipine:polyvinyl pyrrolidone:vinyl acetate (PVPva) physical mixture was prepared to define an error threshold. Co-solidified products of felodipine:PVPva and terfenadine:PVPva were prepared using a melt-quench method and subsequently analyzed using PXRD and PDF. Differential scanning calorimetry (DSC) was used as an additional characterization method. The appropriate manipulation of initial PXRD error estimates through the PDF transform were confirmed using the Monte Carlo simulations for amorphous ketoconazole. The felodipine:PVPva physical mixture PDF analysis determined ±3σ to be an appropriate error threshold. Using the PDF and error propagation principles, the felodipine:PVPva co-solidified product was determined to be completely miscible, and the terfenadine:PVPva co-solidified product, although having appearances of an amorphous molecular solid dispersion by DSC, was determined to be phase-separated. Statistically based inferences were successfully drawn from PDF transforms of PXRD patterns obtained from composite systems. The principles applied herein may be universally adapted to many different systems and provide a fundamentally sound basis for drawing structural conclusions from PDF studies.