# two_power_law

This model calculates an empirical functional form for SAS data characterized by two power laws.

Parameter Description Units Default value
scale Source intensity None 1
background Source background cm-1 0.001
coefficent_1 coefficent A in low Q region None 1
crossover crossover location -1 0.04
power_1 power law exponent at low Q None 1
power_2 power law exponent at high Q None 4

The returned value is scaled to units of cm-1 sr-1, absolute scale.

Definition

The scattering intensity $$I(q)$$ is calculated as

$\begin{split}I(q) = \begin{cases} A q^{-m1} + \text{background} & q <= q_c \\ C q^{-m2} + \text{background} & q > q_c \end{cases}\end{split}$

where $$q_c$$ = the location of the crossover from one slope to the other, $$A$$ = the scaling coefficent that sets the overall intensity of the lower Q power law region, $$m1$$ = power law exponent at low Q, and $$m2$$ = power law exponent at high Q. The scaling of the second power law region (coefficent C) is then automatically scaled to match the first by following formula:

$C = \frac{A q_c^{m2}}{q_c^{m1}}$

Note

Be sure to enter the power law exponents as positive values!

For 2D data the scattering intensity is calculated in the same way as 1D, where the $$q$$ vector is defined as

$q = \sqrt{q_x^2 + q_y^2}$

References

None.

Author: NIST IGOR/DANSE on: pre 2010