Impossible angles in the Porod relationship, an open question

The unbiquitous porod relationship, as published in many places, is often written as:
lim I = K/s^4.

Here, s is the scattering vector, described by s=2/lambda sin(theta) with lambda the radiation wavelength, and theta as half the scattering angle.

Strangely, though, the limit in the porod relationship is often written as the limit when s becomes infinity. Looking at the description of s, however, one sees immediately that this is not possible, whilst the maximum value of s (with a constant wavelength) is 2/lambda for a scattering angle of 90 degrees.

So how am I to read that porod relationship then? as a limit where s goes to 2/lambda, or where s goes to an unreachable infinity?

Theoretically, the scattering vector $q$ or $s$ can indeed go to infinity, but only if the radiation wavelength approaches zero. Nevertheless, it remains interesting why the limit is not to 2/lambda, but instead is written as it goes to infinity.

1 Comment

  1. hi, brian,it is interesting to talk to you here.nice blog, nice content although i can not understand everything about your PhD project. good luck!

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