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The Concept of Peak Shape

Powder diffraction peaks should ideally be sharp. But however sharp a peak may be it will still have a distinctive shape. If the peak is very sharp then it simply means that we must scan with small steps (typically 6 to 10 steps as discussed earlier) through the region of 2θ within which the peak resides in order to have sufficient sampling to define its shape. The next figure shows the 211 and 886 peaks of yttrium oxide using a laboratory powder diffractometer to scan slowly through the two peaks, counting for 10 seconds every 0.01° 2θ for the 211 and 20 seconds every 0.01° 2θ for the 886. The experimental procedures for examining peak shapes are obviously a little different: here we have spent 45 minutes collecting just two peaks, whereas this would normally be sufficient to collect nearly the whole pattern. In point of fact you will notice the high angle peak is not as clear and smooth as the low angle peak. This is because it is much less intense (a peak height 37 times smaller) yet has only been scanned for twice as long. In order for the profile data to be statistically equivalent we would have to have collected for far longer, resulting in a collection time of many hours for this peak alone.

Low Angle Peak (hkl = 2 1 1) High Angle Peak (hkl = 8 8 6)

In this section, the following discussion relates to angle-dispersive powder diffraction. One immediately recognises that, regardless of height, the peak shape changes somewhat with 2θ angle but nevertheless some of its intrinsic features remain. Being able to describe and use features of the peak shape (or "line profile" as it is also called) is the subject of this section. First we must define some basic parameters used to describe the shape of a diffraction peak (below):

The relevant parameters are:

The sheer amount of scientific energy that has been invested over the years into studying the various features of peak shape is enormous, and one might wonder why this is so. There are perhaps two relatively separate communities that have good reason to nail down the peak shape(s) within a given powder diffraction pattern: One community effectively sees the peak shape as a problem that has to be overcome in order to resolve closely separated peaks in a pattern and thereby maximise the available information for the purpose of refining the crystalline structure of the powder (the so called "Rietveld" method that is covered elsewhere in this course); this particular community has little interest in the reasons behind why a peak has a given shape except that it needs to be handled. The second community is interested more in the extraction of whatever information concerning structural/micro-crystalline defects is locked up inside the peak shape. Both interests are covered in the remaining sections.
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© Copyright 1997-2006.  Birkbeck College, University of London.
Author(s): Paul Barnes
Simon Jacques
Martin Vickers