In my role as crystallographic editor for the American Mineralogist and The Canadian Mineralogist, I examine many papers that include crystal structure refinement data and discussions about this data. It is clear to me that understanding and working with the displacement parameters is a challenge to many researchers. The purpose of this chapter is to clearly define the meaning of these parameters and the mathematics needed to interpret them. Throughout this chapter, I will provide illustrative examples from the structure of quartz refined by Kihara (1990) at a variety of temperatures.

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It is well established that an atom in...

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