Difference between revisions of "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:
 
A Guinier analysis attempts to extract the size-scale for a structure by fitting the [[scattering]] to an equation of the form:
 
:<math>I(q) = I_0 \exp \left( - \frac{R_g^2}{3} q^{2} \right) </math>
 
:<math>I(q) = I_0 \exp \left( - \frac{R_g^2}{3} q^{2} \right) </math>
 +
or equivalently,
 
:<math>\ln(I(q)) = \ln(I_0) - (R_g^2/3)q^{2} </math>
 
:<math>\ln(I(q)) = \ln(I_0) - (R_g^2/3)q^{2} </math>
 
Thus a plot of ln(''I'') vs. ''[[q]]''<sup>2</sup> 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]]).
 
Thus a plot of ln(''I'') vs. ''[[q]]''<sup>2</sup> 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]]).
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==Rule of thumb==
 
==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'':
 
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, <math>\scriptstyle q_{\mathrm{max}} < 1.3 / R_g </math>
+
* For spherical particles, <math>\scriptstyle q_{\mathrm{max}} < 1.3 R_g </math>
* For elongated particles, <math>\scriptstyle q_{\mathrm{max}} < 0.8 / R_g </math>
+
* For elongated particles, <math>\scriptstyle q_{\mathrm{max}} < 0.8 R_g </math>
  
 
==See Also==
 
==See Also==

Revision as of 11:10, 13 August 2020

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

or equivalently,

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,
  • For elongated particles,

See Also