# two_power_law

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

Parameter |
Description |
Units |
Default value |
---|---|---|---|

scale |
Scale factor or Volume fraction |
None |
1 |

background |
Source background |
cm |
0.001 |

coefficent_1 |
coefficent A in low Q region |
None |
1 |

crossover |
crossover location |
Å |
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

where \(q_c\) = the location of the crossover from one slope to the other, \(A\) = the scaling coefficient 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 (coefficient C) is then automatically scaled to match the first by following formula:

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

**Source**

**References**

None.

**Authorship and Verification**

**Author:**NIST IGOR/DANSE**Date:**pre 2010**Last Modified by:**Wojciech Wpotrzebowski**Date:**February 18, 2016**Last Reviewed by:**Paul Butler**Date:**March 21, 2016