Temperature effect on the breadth of powder pattern reflections

A general method is developed for calculating the temperature diffuse intensity for cubic powder patterns. The method is applied to the pattern of an f.c.c. crystal containing 10¹² atoms. The effect of temperature vibration is a spreading out at the base of the peak. In terms of the integral breadth, there is an increase which may be of the order of several percent. But the main part of the peak is essentially unaltered, and the increase does not relate to what is generally measured as a breadth. The usual observation is better represented by the breadth at half maximum intensity, and for this quantity there is an increase of less than 0.07% for 2M = 1.0 and less than 0.17% for 2M = 2.0. It is concluded that a real temperature broadening of powder pattern peaks will always be too small to be of importance, or to be experimentally observable.