# Guinier plot

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A Guinier analysis attempts to extract the size-scale for a structure by fitting the scattering to an equation of the form:

${\displaystyle I(q)=I_{0}\exp \left(-{\frac {R_{g}^{2}}{3}}q^{2}\right)}$,

or equivalently,

${\displaystyle \ln(I(q))=\ln(I_{0})-(R_{g}^{2}/3)q^{2}}$

Thus a plot of ln(I) vs. q2 can be used to highly the scaling of the scattering. A straight-line in such a plot is indicative of Guinier scaling. Such an analysis is typically only done with the low-q portion of the data. Linear (Guinier) scaling suggests that the system is essentially monodisperse; it can thus be used as a means of quality control before further data analysis (e.g. Form factor).

## Rule of thumb

The larger one's particles are, the smaller the minimum q must be. One also only expects the Guinier scaling to be maintained up to a certain maximum q:

• For spherical particles, ${\displaystyle \scriptstyle q_{\mathrm {max} }<1.3/R_{g}}$
• For elongated particles, ${\displaystyle \scriptstyle q_{\mathrm {max} }<0.8/R_{g}}$