The quantity T that occurs in eq. (1.4.6) has been commonly referred to either as the Debye-Waller factor or the temperature factor because Debye (1913) and Waller (1923) first understood and formulated the effect that thermal vibrations would have on the intensity of X-ray scattering. It has, however, long been recognized, as discussed in Section 1.4 above, that static displacements would have a similar effect. We therefore avoid the term ``temperature factor", and recommend that others do so also, in part because of this ambiguity about the origin of the atomic displacements that cause the diminution in scattering. Another reason for avoiding the phrase ``temperature factor" is the confusion caused by the fact that it has not infrequently in the past been used for terms in the exponent in expressions like that on the right side of eqs. (1.4.12) and (1.4.13), rather than for the entire exponential multiplicative factor.
A detailed treatment of the physical background of possible atomic displacements is quite beyond the scope of this report. However, we shall try to summarize and describe briefly the most important components of the displacement. The best known is the displacement arising from atomic vibrations. When these result from the motion of molecules or molecular fragments (e.g., Willis & Pryor, 1975), they are usually characterized by relatively large amplitudes. In crystals containing relatively strongly bonded atoms (e.g., molecular and ionic crystals), much smaller displacement amplitudes result from the ever-present internal vibrations, such as bond stretching and bending (e.g., Wilson, Decius, & Cross, 1954). All of these motions are temperature-dependent, unless the temperature is very low. Other effective displacements from the mean position may arise as a result of a variety of possible types of disorder. These include small deviations from ideal periodicity, present in all real crystals; orientational disorder, present in many molecular crystals; density and displacement modulations; and short- and long-range displacive correlations. Many types of disorder give rise to diffuse scattering, which can often be analyzed (e.g., Jagodzinski & Frey, 1993). There are, in addition, numerous other possible contributions to apparent displacements, one of the most important of which is use of an inadequate model, e.g., inadequate absorption correction, or use of a Gaussian probability density function when it is inappropriate.
In view of the large number of possible causes of an apparent atomic displacement, we recommend expanding the definition of ``Debye-Waller factor" to include displacements arising from any source. We will use the term ``Debye-Waller factor" when we mean the entire factor that multiplies the scattering factor of an atom at rest, and recommend that this term be used when words are wanted to refer to the quantity , or T, that occurs in equations such as (1.4.6), (1.4.8), and (1.4.10) through (1.4.13).
There was considerable discussion in our Subcommittee concerning the proper words to use when referring to the terms in the exponent that are variables during a typical least-squares refinement to fit a structural model to intensity data. These terms are formulated and symbolized in various ways, discussed in detail in Section 2.1 below. We recommend unanimously the term ``displacement parameters" (often ``anisotropic displacement parameters", or ADPs) to describe these quantities. Two of us initially favored ``displacement coefficients", believing that once refinement is completed, this term is more appropriate, but were persuaded that current usage strongly favors the recommended term, ``displacement parameters".
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