Guinier plot

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

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

or equivalently,

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

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

See Also

• P. Thiyagarajan, T. S. Burkoth, V. Urban, S. Seifert, T. L. S. Benzinger, D. M. Morgan, D. Gordon, S. C. Meredith and D. G. Lynn pH dependent self assembly of beta-amyloid(10-35) and beta-amyloid(10-35)-PEG3000 J. Appl. Cryst. 2000, 33, 535-539. doi: 10.1107/S0021889899014387
• A. V. Smirnov, I. N. Deryabin and B. A. Fedorov Small-angle scattering: the Guinier technique underestimates the size of hard globular particles due to the structure-factor effect J. Appl. Cryst. 2015, 48. doi: 10.1107/S160057671501078X
• C. D. Putnam Guinier peak analysis for visual and automated inspection of small-angle X-ray scattering data J. Appl. Cryst. 2016, 49. doi: 10.1107/S1600576716010906