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Create Ikeda Carpenter Parameters Fullprof¶
Introduction¶
This is how to take a Fullprof parameter file containing Ikeda-Carpenter-Pseudo-Voigt parameters and translate these into equivalent parameters for the Mantid implementation of this function.
Example Fullprof GEM ICPV instrument parameter file¶
Instrumental resolution function for GEM/ISIS L. Chapon 11/2003 ireso: 5
! To be used with function NPROF=13 in FullProf (Res=5)
! ---------------------------------------------------- Bank 1
! Type of profile function: Ikeda-Carpenter * pseudo-Voigt
NPROF 13
! Tof-min(us) step Tof-max(us)
TOFRG 1200.0000 1.0000 19000
! Dtt1 Dtt2 Zero
D2TOF 793.406 0.000 0.364
! TOF-TWOTH of the bank
TWOTH 9.39
! Sig-2 Sig-1 Sig-0
SIGMA 0.000 166.868 98.757
! Gam-2 Gam-1 Gam-0
GAMMA 0.000 0.277 0.000
! alph0 beta0 alph1 kappa
ALFBE 0.734079 32.017204 2.067249 48.734158
END
! ----------------------------------------------------- Bank 2
! Type of profile function: Ikeda-Carpenter * pseudo-Voigt
NPROF 13
! Tof-min(us) step Tof-max(us)
TOFRG 1500.0000 1.0000 19000.
! Dtt1 Dtt2 Zero
D2TOF 1476.065 0.011 1.881
! TOF-TWOTH of the bank
TWOTH 17.98
! Sig-2 Sig-1 Sig-0
SIGMA 0.000 263.595 0.000
! Gam-2 Gam-1 Gam-0
GAMMA 0.000 3.450 0.000
! alph0 beta0 alph1 kappa
ALFBE 0.734079 32.017204 2.067249 48.734158
END
! ----------------------------------------------------- Bank 3
! Type of profile function: Ikeda-Carpenter * pseudo-Voigt
NPROF 13
! Tof-min(us) step Tof-max(us)
TOFRG 2000.0000 1.0000 19000
! Dtt1 Dtt2 Zero
D2TOF 2798.554 -0.274 -1.621
! TOF-TWOTH of the bank
TWOTH 34.96
! Sig-2 Sig-1 Sig-0
SIGMA 0.000 287.456 0.000
! Gam-2 Gam-1 Gam-0
GAMMA 0.000 3.645 0.000
! alph0 beta0 alph1 kappa
ALFBE 0.734079 32.017204 2.067249 48.734158
END
! ----------------------------------------------------- Bank 3
! Type of profile function: Ikeda-Carpenter * pseudo-Voigt
NPROF 13
! Tof-min(us) step Tof-max(us)
TOFRG 2800.0000 1.0000 19000
! Dtt1 Dtt2 Zero
D2TOF 4869.121 -2.612 -4.127
! TOF-TWOTH of the bank
TWOTH 63.62
! Sig-2 Sig-1 Sig-0
SIGMA 0.000 176.833 0.000
! Gam-2 Gam-1 Gam-0
GAMMA 0.000 4.416 0.000
! alph0 beta0 alph1 kappa
ALFBE 0.734079 32.017204 2.067249 48.734158
END
! ----------------------------------------------------- Bank 3
! Type of profile function: Ikeda-Carpenter * pseudo-Voigt
NPROF 13
! Tof-min(us) step Tof-max(us)
TOFRG 3300.0000 1.0000 19000
! Dtt1 Dtt2 Zero
D2TOF 6671.694 -5.778 -5.029
! TOF-TWOTH of the bank
TWOTH 91.30
! Sig-2 Sig-1 Sig-0
SIGMA 0.000 63.410 0.000
! Gam-2 Gam-1 Gam-0
GAMMA 0.000 3.116 0.000
! alph0 beta0 alph1 kappa
ALFBE 0.734079 32.017204 2.067249 48.734158
END
! ----------------------------------------------------- Bank 3
! Type of profile function: Ikeda-Carpenter * pseudo-Voigt
NPROF 13
! Tof-min(us) step Tof-max(us)
TOFRG 4500.0000 1.0000 16700
! Dtt1 Dtt2 Zero
D2TOF 9077.306 -11.374 -6.370
! TOF-TWOTH of the bank
TWOTH 154.40
! Sig-2 Sig-1 Sig-0
SIGMA 0.000 29.321 0.000
! Gam-2 Gam-1 Gam-0
GAMMA 0.000 0.982 0.000
! alph0 beta0 alph1 kappa
ALFBE 0.734079 32.017204 2.067249 48.734158
END
Converting above Fullprof ICPV parameter into Mantid parameter file¶
The syntax for a Mantid parameter file is described here.
The Fullprof Ikeda Carparter parameters of the above Fullprof file is the four numbers stored to the right of ALFBE.
These are the same for all the banks and in Mantid these are therefore assigned to the top level component of the GEM instrument (see GEM_Definition.xml),
which is called GEM, and Mantid representation of Alpha0, Beta0, Alpha1 and Kappa are:
<component-link name="GEM" >
<parameter name="IkedaCarpenterPV:Alpha0" type="fitting">
<formula eq="0.734079" result-unit="TOF"/>
<fixed />
</parameter>
<parameter name="IkedaCarpenterPV:Beta0" type="fitting">
<formula eq="32.017204" result-unit="TOF"/>
<fixed />
</parameter>
<parameter name="IkedaCarpenterPV:Alpha1" type="fitting">
<formula eq="2.067249" result-unit="TOF"/>
<fixed />
</parameter>
<parameter name="IkedaCarpenterPV:Kappa" type="fitting">
<formula eq="48.734158"/>
<fixed />
</parameter>
</component-link>
Notice <fixed /> has been added to each of these 4 parameters. This means that by default the Mantid fitting will treat these parameters as fixed.
Also notice, the result-unit="TOF" tag for 3 of the parameters. The result-unit is the unit of the parameter, see IDF.
The advantage of specifying units of the parameters is that Mantid will then automatically be able to convert the specified
parameter values to be correct independently of whether the workspace is for instance in units of dSpacing or TOF.
For the IkedaCarpenterPV peak-shape function setting these units has one additional complication.
From the formulas on page IkedaCarpenterPV it is seen that this peak shape function explicitly depends on both the time-of-flight (\(t\)) and wavelength (\(\lambda\)).
The units for Alpha0, beta0, Alpha1 and Kappa are: \(TOF\), \(TOF\), \(\frac{TOF}{Wavelength}\) and \(\frac{1}{Wavelength^2}\) respectively, see IkedaCarpenterPV.
However, the IkedaCarpenterPV algorithm calculates the value of (\(\lambda\)) separately and to the same unit regardless of what the workspace unit is.
Therefore for IkedaCarpenterPV to ensure Alpha1 and Kappa works regardless of the workspace unit the result-unit is assigned
for these to TOF and dimensionless respectively (i.e. ignoring the wavelength bit of the unit).
SIGMA in the Fullprof file is the sigma pseudo-voigt parameter. For the 1st bank it is SIGMA 0.000 166.868 98.757,
and it can be found to translates into the equation: \(variance=SigmaSquared = Sig \mbox{-}2 * d^4 + Sig \mbox{-}1 * d^2 + Sig \mbox{-}0\),
where variance is in units of \(TOF^2\), and \(d\) is the dSpacing at the centre of the peak.
This translates into the Mantid parameter:
<parameter name="IkedaCarpenterPV:SigmaSquared" type="fitting">
<formula eq="0.0*centre^4+166.868*centre^2+98.757" unit="dSpacing" result-unit="TOF^2"/>
</parameter>
Note for illustration purpose only 0.0*centre^4 has been added to the parameter formula equation above.
Note in addition to using the result-unit attribute this formula also assigns unit="dSpacing", which is the unit of centre variable in the formula.
GAMMA in the Fullprof file is the gamma pseudo-voigt parameter.
For the 1st bank it is GAMMA 0.000 0.277 0.000, and it can be found to translate into the equation:
\(GAMMA=Gamma = Gam \mbox{-}2 * d^2 + Gam \mbox{-}1 * d + Gam \mbox{-}0\), where Gamma is in units of TOF and \(d\) is the dSpacing at the centre of the peak.
This translates into the Mantid parameter:
<parameter name="IkedaCarpenterPV:Gamma" type="fitting">
<formula eq="0.0*centre^2+0.277*centre+0.0" unit="dSpacing" result-unit="TOF"/>
</parameter>
A copy of the full translation of the above Fullprof instrument file into a Mantid parameter file is shown below
(this parameter file can be applied to a GEM workspace with LoadParameterFile v1 or by copying in into MantidInstall/instrument/GEM_Parameters.xml):
<?xml version="1.0" encoding="UTF-8" ?>
<parameter-file instrument="GEM" date = "2003-11-30 23:59:59">
<component-link name="GEM" >
<parameter name="IkedaCarpenterPV:Alpha0" type="fitting">
<formula eq="0.734079" result-unit="TOF"/>
<fixed />
</parameter>
<parameter name="IkedaCarpenterPV:Beta0" type="fitting">
<formula eq="32.017204" result-unit="TOF"/>
<fixed />
</parameter>
<parameter name="IkedaCarpenterPV:Alpha1" type="fitting">
<formula eq="2.067249" result-unit="TOF"/>
<fixed />
</parameter>
<parameter name="IkedaCarpenterPV:Kappa" type="fitting">
<formula eq="48.734158"/>
<fixed />
</parameter>
</component-link>
<component-link name="bank1" >
<parameter name="IkedaCarpenterPV:SigmaSquared" type="fitting">
<formula eq="166.868*centre^2+98.757" unit="dSpacing" result-unit="TOF^2"/>
</parameter>
<parameter name="IkedaCarpenterPV:Gamma" type="fitting">
<formula eq="0.277*centre" unit="dSpacing" result-unit="TOF"/>
</parameter>
</component-link>
<component-link name="bank2" >
<parameter name="IkedaCarpenterPV:SigmaSquared" type="fitting">
<formula eq="263.595*centre^2" unit="dSpacing" result-unit="TOF^2"/>
</parameter>
<parameter name="IkedaCarpenterPV:Gamma" type="fitting">
<formula eq="3.45*centre" unit="dSpacing" result-unit="TOF"/>
</parameter>
</component-link>
<component-link name="bank3" >
<parameter name="IkedaCarpenterPV:SigmaSquared" type="fitting">
<formula eq="287.456*centre^2" unit="dSpacing" result-unit="TOF^2"/>
</parameter>
<parameter name="IkedaCarpenterPV:Gamma" type="fitting">
<formula eq="3.645*centre" unit="dSpacing" result-unit="TOF"/>
</parameter>
</component-link>
<component-link name="bank4" >
<parameter name="IkedaCarpenterPV:SigmaSquared" type="fitting">
<formula eq="176.833*centre^2" unit="dSpacing" result-unit="TOF^2"/>
</parameter>
<parameter name="IkedaCarpenterPV:Gamma" type="fitting" result-unit="TOF">
<formula eq="4.416*centre" unit="dSpacing"/>
</parameter>
</component-link>
<component-link name="bank5" >
<parameter name="IkedaCarpenterPV:SigmaSquared" type="fitting">
<formula eq="63.41*centre^2" unit="dSpacing" result-unit="TOF^2"/>
</parameter>
<parameter name="IkedaCarpenterPV:Gamma" type="fitting">
<formula eq="3.116*centre" unit="dSpacing" result-unit="TOF"/>
</parameter>
</component-link>
<component-link name="bank6" >
<parameter name="IkedaCarpenterPV:SigmaSquared" type="fitting">
<formula eq="29.321*centre^2" unit="dSpacing" result-unit="TOF^2"/>
</parameter>
<parameter name="IkedaCarpenterPV:Gamma" type="fitting">
<formula eq="0.982*centre" unit="dSpacing" result-unit="TOF"/>
</parameter>
</component-link>
</parameter-file>