.. _func-BackToBackExponential: ===================== BackToBackExponential ===================== .. index:: BackToBackExponential Description ----------- A back-to-back exponential peakshape function is defined as: .. math:: I\frac{AB}{2(A+B)}\left[ \exp \left( \frac{A[AS^2+2(x-X0)]}{2}\right) \mbox{erfc}\left( \frac{AS^2+(x-X0)}{S\sqrt{2}} \right) + \exp \left( \frac{B[BS^2-2(x-X0)]}{2} \right) \mbox{erfc} \left( \frac{[BS^2-(x-X0)]}{S\sqrt{2}} \right) \right]. This peakshape function represent the convolution of back-to-back exponentials and a Gaussian function and is designed to be used for the data analysis of time-of-flight (TOF) neutron powder diffraction data, see Ref. 1. The parameters :math:`A` and :math:`B` represent the absolute value of the exponential rise and decay constants (modelling the neutron pulse coming from the moderator) and :math:`S` represent the standard deviation of the Gaussian. The parameter :math:`X0` is the location of the peak; more specifically it represent the point where the exponentially modelled neutron pulse goes from being exponentially rising to exponentially decaying. In general :math:`X0` does not conicide with the maximum of the peak (it is typically at slightly lower TOF than the maximum, by an amount that depends on :math:`A`, :math:`B` and :math:`S`). :math:`I` is the integrated intensity. For information about how to convert Fullprof back-to-back exponential parameters into those used for this function see :ref:`CreateBackToBackParameters `. References 1. R.B. Von Dreele, J.D. Jorgensen & C.G. Windsor, `J. Appl. Cryst., 15, 581-589, 1982 `_ The figure below illustrate this peakshape function fitted to a TOF peak: .. figure:: /images/BackToBackExponentialWithConstBackground.png :alt: BackToBackExponentialWithConstBackground.png .. attributes:: .. properties:: .. note:: the initial default guesses for in particular A and B are only based on fitting a couple of peaks in a dataset collected on the ISIS's HRPD instrument. .. categories:: .. sourcelink::