# Guinier plot

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

Smaller particles require measurement of lower q for Guinier analysis, as Guinier scaling is only maintained up to a certain maximum q:

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