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Create Ikeda Carpenter Parameters GSAS¶
Introduction¶
Here we show 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.
Annotating GSAS GEM instrument parameter file¶
This GSAS file is one generated for the GEM instrument at ISIS. The syntax is described in some detail from page 221 in the GSAS Technical Manual in section entitled “Instrument Parameter File”.
COMM Y2O3 + Si cycle 13/2
INS BANK 6
INS HTYPE PNTR
INS 1 ICONS 746.96 -0.24 3.04
INS 1BNKPAR 2.3696 9.39 0.00 .00000 .3000 1 1
INS 1I ITYP 0 1.000 25.000 2
INS 1PRCF 2 15 0.00100
INS 1PRCF 1 0.000000E+00 0.200000E+00 0.317927E+02 0.544205E+02
INS 1PRCF 2 0.000000E+00 0.176802E+03 0.000000E+00 0.000000E+00
INS 1PRCF 3 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00
INS 1PRCF 4 0.000000E+00 0.000000E+00 0.000000E+00
INS 2 ICONS 1482.98 0.98 12.65
INS 2BNKPAR 1.7714 17.98 0.00 .00000 .3000 1 1
INS 2I ITYP 0 1.000 21.000 2
INS 2PRCF 2 15 0.00100
INS 2PRCF 1 0.000000E+00 0.200000E+00 0.317927E+02 0.544205E+02
INS 2PRCF 2 0.000000E+00 0.295572E+03 -0.134662E+01 0.000000E+00
INS 2PRCF 3 0.361229E+01 0.000000E+00 0.000000E+00 0.000000E+00
INS 2PRCF 4 0.000000E+00 0.000000E+00 0.000000E+00
INS 3 ICONS 2813.67 1.41 6.22
INS 3BNKPAR 1.4450 34.96 0.00 .00000 .3000 1 1
INS 3I ITYP 0 1.000 20.000 2
INS 3PRCF 2 15 0.00100
INS 3PRCF 1 0.000000E+00 0.200000E+00 0.317927E+02 0.544205E+02
INS 3PRCF 2 0.000000E+00 0.280289E+03 0.272947E+01 0.000000E+00
INS 3PRCF 3 0.444792E+01 0.000000E+00 0.000000E+00 0.000000E+00
INS 3PRCF 4 0.000000E+00 0.000000E+00 0.000000E+00
INS 4 ICONS 4844.99 -1.73 -1.50
INS 4BNKPAR 1.2212 63.62 0.00 .00000 .3000 1 1
INS 4I ITYP 0 1.000 20.000 2
INS 4PRCF 2 15 0.00100
INS 4PRCF 1 0.000000E+00 0.200000E+00 0.317927E+02 0.544205E+02
INS 4PRCF 2 0.000000E+00 0.202940E+03 0.446899E+01 0.000000E+00
INS 4PRCF 3 0.416948E+01 0.000000E+00 0.000000E+00 0.000000E+00
INS 4PRCF 4 0.000000E+00 0.000000E+00 0.000000E+00
INS 5 ICONS 6662.11 -4.58 -2.30
INS 5BNKPAR 1.3793 91.37 0.00 .00000 .3000 1 1
INS 5I ITYP 0 1.000 18.000 2
INS 5PRCF 2 15 0.00100
INS 5PRCF 1 0.000000E+00 0.200000E+00 0.317927E+02 0.544205E+02
INS 5PRCF 2 0.000000E+00 0.111084E+03 -0.175113E+01 0.000000E+00
INS 5PRCF 3 0.284103E+01 0.000000E+00 0.000000E+00 0.000000E+00
INS 5PRCF 4 0.000000E+00 0.000000E+00 0.000000E+00
INS 6 ICONS 9084.64 -8.58 -2.85
INS 6BNKPAR 1.3554 154.46 0.00 .00000 .3000 1 1
The annotation of this file is as follows:
COMM Y2O3 + Si cycle 13/2
Is a comment.
INS BANK 6
Tells that this file contains parameters for 6 different banks, where a bank can be mean any collection of detector on an instrument.
INS HTYPE PNTR
Specify histogram type used in obtaining the fitting paramters.
Here PNTR, which is P for powder data, N for neutron data, T for time-of-flight data, and the last letter is a status flag,
R stands for ‘read powder data’. Initially we may have a test in Mantid that checks if it is this type and if not tells the user that this is not supported.
INS 1 ICONS 746.96 -0.24 3.04
INS 1BNKPAR 2.3696 9.39 0.00 .00000 .3000 1 1
INS 1I ITYP 0 1.000 25.000 2
These three lines are not relevant to Mantid.
INS 1PRCF 2 15 0.00100
This tells you which profile function, NTYP, this file contains parameters for.
Here NTYP=2, which is the GSAS Ikeda-Carpenter-pseudo-voigt function described from page 144 in the GSAS Technical Manual.
The following number, 15, is the number of parameters of this function and the last number, 0.00100, is not relevant to Mantid.
INS 1PRCF 1 0.000000E+00 0.200000E+00 0.317927E+02 0.544205E+02
INS 1PRCF 2 0.000000E+00 0.176802E+03 0.000000E+00 0.000000E+00
INS 1PRCF 3 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00
INS 1PRCF 4 0.000000E+00 0.000000E+00 0.000000E+00
These lines are the actual the 15 GSAS parameters for this profile function. From page 147 in the GSAS manual these 15 parameters are, in the order listed, the values of:
"alp-0", "alp-1", "beta", "switch",
"sig-0", "sig-1", "sig-2", "gam-0",
"gam-1", "gam-2", "stec", "ptec",
"difc", "difa" & "zero".
The rest of the file is a repeat for the remaining 5 banks.
Converting GSAS parameters into Mantid parameters¶
From comparing the formula for the fitting function IkedaCarpenterPV with formulas in the GSAS Technical Manual the conversion equations are estimated to be:
Where \(d\) is the dSpacing at the centre of the peak.
Note for now I have ignored GSAS parameters stec and ptec.
In code it should be checked that these are zero and if not a warning returned to the user.
I believe the remaining three parameter difc, difa and zero can be ignored for the exercise here.
The syntax for a Mantid parameter file is described here, in particular look for the section on fitting parameter on that page.
So the translation of the example above for bank 1 into IkedaCarpenterPV parameters gives:
<parameter name="IkedaCarpenterPV:Alpha0" type="fitting">
<formula eq="0.0" result-unit="TOF"/>
<fixed />
</parameter>
<parameter name="IkedaCarpenterPV:Alpha1" type="fitting">
<formula eq="0.200000" result-unit="TOF"/>
<fixed />
</parameter>
<parameter name="IkedaCarpenterPV:Beta0" type="fitting">
<formula eq="31.7927" result-unit="TOF"/>
<fixed />
</parameter>
<parameter name="IkedaCarpenterPV:Kappa" type="fitting">
<formula eq="54.4205"/>
<fixed />
</parameter>
<parameter name="IkedaCarpenterPV:SigmaSquared" type="fitting">
<formula eq="0.0 + 176.802*centre^2 + 0.0*centre^4" unit="dSpacing" result-unit="TOF^2"/>
</parameter>
<parameter name="IkedaCarpenterPV:Gamma" type="fitting">
<formula eq="0.0 + 0.0*centre + 0.0*centre^2" unit="dSpacing" result-unit="TOF"/>
</parameter>