Changes in / [dc76240:4cdc4b1] in sasmodels


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  • sasmodels/models/guinier.py

    r2d81cfe rc9fc873  
    77.. math:: 
    88 
    9     I(q) = \text{scale} \cdot \exp{\left[ \frac{-Q^2R_g^2}{3} \right]} 
     9    I(q) = \text{scale} \cdot \exp{\left[ \frac{-Q^2 R_g^2 }{3} \right]} 
    1010            + \text{background} 
    1111 
     
    1919 
    2020.. math:: q = \sqrt{q_x^2 + q_y^2} 
     21 
     22In scattering, the radius of gyration $R_g$ quantifies the objects's 
     23distribution of SLD (not mass density, as in mechanics) from the objects's 
     24SLD centre of mass. It is defined by 
     25 
     26.. math:: R_g^2 = \frac{\sum_i\rho_i\left(r_i-r_0\right)^2}{\sum_i\rho_i} 
     27 
     28where $r_0$ denotes the object's SLD centre of mass and $\rho_i$ is the SLD at 
     29a point $i$. 
     30 
     31Notice that $R_g^2$ may be negative (since SLD can be negative), which happens 
     32when a form factor $P(Q)$ is increasing with $Q$ rather than decreasing. This 
     33can occur for core/shell particles, hollow particles, or for composite 
     34particles with domains of different SLDs in a solvent with an SLD close to the 
     35average match point. (Alternatively, this might be regarded as there being an 
     36internal inter-domain "structure factor" within a single particle which gives 
     37rise to a peak in the scattering). 
     38 
     39To specify a negative value of $R_g^2$ in SasView, simply give $R_g$ a negative 
     40value ($R_g^2$ will be evaluated as $R_g |R_g|$). Note that the physical radius  
     41of gyration, of the exterior of the particle, will still be large and positive.  
     42It is only the apparent size from the small $Q$ data that will give a small or  
     43negative value of $R_g^2$. 
    2144 
    2245References 
     
    4265 
    4366#             ["name", "units", default, [lower, upper], "type","description"], 
    44 parameters = [["rg", "Ang", 60.0, [0, inf], "", "Radius of Gyration"]] 
     67parameters = [["rg", "Ang", 60.0, [-inf, inf], "", "Radius of Gyration"]] 
    4568 
    4669Iq = """ 
    47     double exponent = rg*rg*q*q/3.0; 
     70    double exponent = fabs(rg)*rg*q*q/3.0; 
    4871    double value = exp(-exponent); 
    4972    return value; 
     
    6689 
    6790# parameters for demo 
    68 demo = dict(scale=1.0, rg=60.0) 
     91demo = dict(scale=1.0,  background=0.001, rg=60.0 ) 
    6992 
    7093# parameters for unit tests 
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