PRELIMINARY DATA PROCESSING AND PHASE ANALYSIS

In the first three chapters of this book, we considered the fundamentals of crystallographic symmetry, the phenomenon of diffraction from a crystal lattice, and the basics of a powder diffraction experiment. Familiarity with these broad subjects is essential in understanding how waves are scattered by crystalline matter, how structural information is encoded into a three-dimensional distribution of discrete intensity maxima, and how it is convoluted with numerous instrumental and specimen-dependent functions when projected along one direction and measured as the scattered intensity V versus the Bragg angle 20. We already learned that this knowledge can be applied to the structural characterization of materials as it gives us the ability to decode a one-dimensional snapshot of a reciprocal lattice and therefore, to reconstruct a three-dimensional distribution of atoms in an infinite crystal lattice by means of a forward Fourier transformation. 

Our experience with applications of the powder method in diffraction analysis was for the most part, conceptual, and in the remainder of this book, we will discuss key issues that arise during the processing and interpretation of powder diffraction data. Despite the apparent simplicity of onedimensional diffraction patterns, which are observed as series of constructive interference peaks (both resolved and partially or completely overlapped), created by elastically scattered waves and placed on top of a nonlinear background noise, the complexity of their interpretation originates from the complexity of events involved in converting the underlying structure into the experimentally observed data. Thus, nearly every component of data processing in powder diffraction is computationally intense. 

The presence of symmetry (Chapter 1) coupled with well-defined analytical relationships determining both the directions and intensities of scattered beams (Chapter 2), in addition to known properties of both the specimen and instrument employed to obtain a powder diffraction pattern (Chapter 3), makes it possible to develop both the general methodology and algorithm(s) suitable for automation. Given the amount of numerical data collected in a typical powder diffraction experiment, their interpretation and processing usually involves a broad use of computers. 

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