From the Structure Factor to Measured Intensities

From the Structure Factor to Measured Intensities

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From the Structure Factor to Measured Intensities

The previous section explained how to calculate the amplitude or intensity from the structure factor equation. However this calculation was really just a prediction of the intensity value from the point of view of an ideal crystal itself; the actual experimentally measured intensity will be yet different again since a number of additional experimental effects need to be taken into account, the main ones being:

multiplicity, j
the polarisation factor, P
the Lorentz factor, L
X-ray absorption, A
temperature

The first four are often referred to as "corrections" though "allowances" would be a better term: one is making allowances for the way in which the experiment actually measures the diffracted intensity. It is true that the fifth factor, temperature, also refers ultimately to the experimental conditions but the effect of temperature is so intimately tied into the structure that we think of it rather in those terms. We can write down a very simple equation to accommodate the first four factors:

I_hkl = c jPLA F_hkl²

in which c can be considered to contain all the remaining factors (e.g. amount of X-ray exposure; sensitivity of the detector etc.).

We will now consider these factors in turn, illustrating by means of the previous example on NaCl:

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Author(s): Paul Barnes
Martin Vickers