Guinier plot

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

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle I(q) = I_0 \exp \left( - \frac{R_g^2}{3} q^{2} \right) }

or equivalently,

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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.

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

• For spherical particles, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \scriptstyle q_{\mathrm{max}} < 1.3 R_g }
• For elongated particles, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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