IkedaCarpenterPV¶

Description¶

This peakshape function is designed to be used to fit time-of-flight peaks. In particular this function is the convolution of the Ikeda-Carpender function, which aims to model the neutron pulse shape from a moderator, and a pseudo-Voigt that model any broading to the peak due to sample properties etc.

The Ikeda-Carpender function is (Ref [1])

$\frac{\alpha}{2} \left\{ (1-R)*(\alpha t)^2e^{-\alpha t} + 2R\frac{\alpha^2\beta}{(\alpha-\beta)^3} \right\}$

where $\alpha$ and $\beta$ are the fast and slow neutron decay constants respectively, $R$ a maxing coefficient that relates to the moderator temperature and $t$ is time. $\alpha$ and $R$ are further modelled to depend on wavelength and using the notation in the Fullprof manual (Ref [2]) the refineable Ikeda-Carpender parameters are Alpha0, Alpha1, Beta0 and Kappa and these are defined as

$\alpha=1/(\mbox{Alpha0}+\lambda*\mbox{Alpha1})$

$\beta = 1/\mbox{Beta0}$

$R = \exp (-81.799/(\mbox{Kappa}*\lambda^2))$

, where $\lambda$ is the neutron wavelength. In general when fitting a single peak it is not recommended to refine both Alpha0 and Alpha1 at the same time since these two parameters will effectively be 100% correlated because the wavelength over a single peak is likely effectively constant. All parameters are constrained to be non-negative.

The pseudo-Voigt function is defined as a linear combination of a Lorentzian and Gaussian and is a computational efficient way of calculation a Voigt function. The Voigt parameters are related to the pseudo-Voigt parameters through a relation (see Fullprof manual eq. (3.16) which in revision July2001 is missing a power 1/5). It is the two Voigt parameters which you can refine with this peakshape function: SigmaSquared (for the Gaussian part) and Gamma (for the Lorentzian part). Notice the Voigt Gaussian FWHM=SigmaSquared*8*ln(2) and the Voigt Lorentzian FWHM=Gamma.

For information about how to create instrument specific values for the parameters of this fitting function see CreateIkedaCarpenterParameters.

The implementation of the IkedaCarpenterPV peakshape function here follows the analytical expression for this function as presented in the Fullprof manual, see Ref[2].

References:

S. Ikeda and J. M. Carpenter, Nuclear Inst. and Meth. in Phys. Res. A239, 536 (1985)
Fullprof manual, see http://www.ill.eu/sites/fullprof/

The figure below illustrate this peakshape function fitted to a TOF peak:

Properties (fitting parameters)¶

Name	Default	Description
I	0.0	The integrated intensity of the peak. I.e. approximately equal to HWHM times height of peak
Alpha0	1.6	Used to model fast decay constant
Alpha1	1.5	Used to model fast decay constant
Beta0	31.9	Inverse of slow decay constant
Kappa	46.0	Controls contribution of slow decay term
SigmaSquared	1.0	standard deviation squared (Voigt Guassian broadening)
Gamma	1.0	Voigt Lorentzian broadening
X0	0.0	Peak position

Categories: FitFunctions | Peak

Source¶

C++ source: IkedaCarpenterPV.cpp

C++ header: IkedaCarpenterPV.h