unified_power_Rg¶
Unified Power Rg
Parameter 
Description 
Units 
Default value 

scale 
Scale factor or Volume fraction 
None 
1 
background 
Source background 
cm^{1} 
0.001 
level 
Level number 
None 
1 
rg[level] 
Radius of gyration 
Å 
15.8 
power[level] 
Power 
None 
4 
B[level] 
cm^{1} 
4.5e06 

G[level] 
cm^{1} 
400 
The returned value is scaled to units of cm^{1} sr^{1}, absolute scale.
Definition
This model employs the empirical multiple level unified Exponential/Powerlaw fit method developed by Beaucage. Four functions are included so that 1, 2, 3, or 4 levels can be used. In addition a 0 level has been added which simply calculates
The Beaucage method is able to reasonably approximate the scattering from many different types of particles, including fractal clusters, random coils (Debye equation), ellipsoidal particles, etc.
The model works best for mass fractal systems characterized by Porod exponents between 5/3 and 3. It should not be used for surface fractal systems. Hammouda (2010) has pointed out a deficiency in the way this model handles the transitioning between the Guinier and Porod regimes and which can create artefacts that appear as kinks in the fitted model function.
Also see the guinier_porod model.
The empirical fit function is:
where
For each level, the four parameters \(G_i\), \(R_{gi}\), \(B_i\) and \(P_i\) must be chosen. Beaucage has an additional factor \(k\) in the definition of \(q_i^*\) which is ignored here.
For example, to approximate the scattering from random coils (Debye equation), set \(R_{gi}\) as the Guinier radius, \(P_i = 2\), and \(B_i = 2 G_i / R_{gi}\)
See the references for further information on choosing the parameters.
For 2D data: The 2D scattering intensity is calculated in the same way as 1D, where the \(q\) vector is defined as
Source
References
G Beaucage, J. Appl. Cryst., 28 (1995) 717728
G Beaucage, J. Appl. Cryst., 29 (1996) 134146
B Hammouda, Analysis of the Beaucage model, J. Appl. Cryst., (2010), 43, 14741478
Authorship and Verification
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