Agreement?

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Agreement?

The formula previously given, relating the measured intensity to the structure factor, I_hkl = c j_hkl P_hkl L_hkl A F_hkl², can now be used with respect to all parameters except A (absorption), which is not important for the purpose of this exercise (assuming our data are measured in Bragg-Brentano geometry). The various values that have been calculated in this section for the case of 111 diffraction are:

Multiplying these (and ignoring absorption) gives:

where c is the constant mentioned previously.

The units are not important since the usual approach in Crystallography is to compare two values by measuring them under, as far as possible, identical conditions. In other words, our interest is usually in relative intensities rather than absolute ones. When forming ratios, the constant c will cancel, as will the absorption factor, but only for Bragg-Brentano data.

A similar calculation for the 200 reflection gives:

from which the ratio I₁₁₁/I₂₀₀ can be calculated as 0.0958. If these "correction" factors had not been used, the simple ratio of F₁₁₁²/F₂₀₀² would have been 0.052.

So basically the three factors have "corrected" the predicted ratio from an initial value of around 5% to a final value of 9.6%. A value measured in our laboratory using a capillary sample in transmission geometry (so as to avoid preferred orientation) was 9.5%, which is in amazingly good agreement with the calculated value! You might wonder why. The answer is that there are two competing effects that effectively cancel each other out with the sample as measured: absorption and temperature factors. The effect of temperature on the structure factor will be discussed next.

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