Bk2BkExpConvPV

Description

A back-to-back exponential convoluted pseudo-voigt function is defined as:

F(X)=IΩ(x)

where Ω is defined to be

Ω(x)=(1η)N{euerfc(y)+everfc(z)}2Nηπ{(epE1(p))+(eqE1(q))},

given that

u=12α(ασ2+2(xX0)),
y=12σ2(ασ2+xX0),
v=12β(βσ22(xX0)),
z=12σ2(βσ2x+X0),
p=α(xX0)+αH2i,
q=β(xX0)+βH2i,
N=αβ2(α+β).

η is approximated by

η=1.36603γH0.47719(γH)2+0.11116(γH)3,

where,

H=γ5+0.07842γ4HG+4.47163γ3HG2+2.42843γ2HG3+2.69269γHG4+HG5,
HG=8σ2log(2).

erfc is the complementary error function and E1 is the exponential integral with complex argument given by

erfc(x)=1erf(x)=12π0xeu2du=2πxeu2du,
E1(z)=zettdt.

The parameters A and B represent the absolute value of the exponential rise and decay constants (modelling the neutron pulse coming from the moderator) and S represent the standard deviation of the gaussian. The parameter 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. I is the integrated intensity.

For information about how to convert Fullprof back-to-back exponential parameters into those used for this function see CreateBackToBackParameters.

Properties (fitting parameters)

Name

Default

Description

X0

-0.0

Location of the peak

Intensity

0.0

Integrated intensity

Alpha

0.04

Exponential rise

Beta

0.02

Exponential decay

Sigma2

1.0

Sigma squared

Gamma

0.0

Categories: FitFunctions | Peak

Source

C++ header: Bk2BkExpConvPV.h

C++ source: Bk2BkExpConvPV.cpp