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Combined refinement

With enabling BGMN for neutron diffraction, combined refinement of data from at least two experiments (one neutron, the other laboratory X-ray or synchrotron data) becomes of interest. Combined refinement was enabled with BGMN at main level 5.

combined refinement will be switched on by setting NDEVICES=... to the number of devices in the BGMN task description *.sav file. As a basic principle, combined refinement has multiple wavelength distributions, multiple device functions etc. In following, most of the entries in the *.sav file will be enriched by an additional (leftmost) index for the device number:

RU→RU[i],
EPS1→EPS1[i],
EPS2→EPS2[i],
EPS3→EPS3[i],
EPS4→EPS4[i],
LAMBDA→LAMBDA[i],
SYNCHROTRON→SYNCHROTRON[i],
NEUTRONS→NEUTRONS[i],
VERZERR→VERZERR[i],
POL→POL[i],
VAL[j]→VAL[i,j],
WMIN→WMIN[i],
WMAX→WMAX[i],
CUT[j]→CUT[i,j],
DIAGRAMM→DIAGRAMM[i],
OUTPUT→OUTPUT[i] etc.

Note: For the moment, the BGMNwin GUI does not understand the DIAGRAMM[i] entries. As a workaround, one may set an additional non-indexed DIAGRAMM entry, thus that diagram will be displayed during refinement.

No changes are to the LIST and STRUC[i] entries. The file as refered by the LIST entry will contain results for all devices. Structure description files *.str may contain several new items:

DeviceSelect(i,...) may be inserted at any position in the *.str file. In following, all subsequent entries in the *.str file will be valid only for the selected devices. Note: At least lattice parameters and space group must be unique for one structure. In following DeviceSelect will be ignored for lattice parameter and space group detection.
There is a new keyword for preferred orientation description by PO=SPHAR2 etc. In difference to GEWICHT=SPHAR2 etc, PO will set a pure preferred orientation model with mean value 1. You must give an additional scalar value for GEWICHT (or GEWICHT[1]) to scale the calculated to the measured pattern, for that reason. Both PO plus GEWICHT will be used in combination. This is useful in case of multidevice evaluation of a multiphase sample: The phase's scale factors will be of unique ratio for all the devices. But preferred orientation of a phase will change between devices, in general. In following, the PO feature has to be used. Note: PO=SPHAR... and GEWICHT=SPHAR... are mutual exclusive for a given device. In following, you may not use GEWICHT=SPHAR0 for defining a scalar value of GEWICHT. You must use PARAM=GEWICHT=0_0 instead.
Attention: In contrast to GEWICHT=SPHARx, there is no automatic switch-down for PO=SPHARx.
idev refers to the actual device number, ifxray is a logical switch which is true in case the actual device is an X-ray one, ifsynchrotron is a logical switch which is true in case the actual device is a synchrotron one and ifneutrons is a logical switch which is true in case the actual device is a neutrons one.

Example Lead Titanate

We are grateful to Dr. H. Boysen (LMU Munich) for kindly supporting the patterns. This example shows some pitfalls of multi device refinement. We will not discuss the geometric device functions here, there is still room for their improvement. In special, for the neutron device (SPODI at FRM II in Munich), a width formula for a single squared lorentzian was used. A minor content of β-PbO (Massicot) was present.

As a first step, the BGMN control file BleiTitanat.sav is set up:

NDEVICES=2
NEUTRONS[1]=0.1548
PI=2*acos(0)
HWB=sqrt(sqr(0.204)+sqr(0.21*sin(THETA*PI/180)*tan((90-zweiTheta)*PI/180)))
VERZERR[1]=HWB*PI/(720*sqrt(sqrt(2)-1))
VAL[1,1]=BleiTitanat_neutronen.dat
WMIN[1]=10
OUTPUT[1]=BleiTitanat_neutronen
DIAGRAMM[1]=BleiTitanat_neutronen
PARAM[1]=EPS1[1]=0_-0.005^0.005
PARAM[2]=EPS2[1]=0_-0.005^0.005
LAMBDA[2]=mo1
VERZERR[2]=device_xray
% Germanium-Monochromator A=5.658 (111)? d=3.267 A
POL=sqr(cos(12.46*PI/180))
VAL[2,1]=BleiTitanat_xray.dat
OUTPUT[2]=BleiTitanat_xray
DIAGRAMM[2]=BleiTitanat_xray
PARAM[3]=EPS1[2]=0_-0.005^0.005
PARAM[4]=EPS2[2]=0_-0.005^0.005
STRUC[1]=PbTiO3.str
STRUC[2]=PbO_beta_Massicot.str
gdev[1]=1
PARAM[5]=gdev[2]=1_0
denom=PbObetaMassicot+PbTiO3
GOAL[1]=PbTiO3/denom
GOAL[2]=PbObetaMassicot/denom
LIST=BleiTitanat
PROTOKOLL=Y

As you may see, we have introduced indexed EPS1/EPS2 for both the devices as parameter. A fifth parameter gdev[2] controls the principal ratio of intensities between both the devices. We use a named wavelength for the Mo K_α1 radiation, Pb has remarkable f'=-3.39 plus f"=10.11 for Mo K_α.

The next step will be setting up PbTiO₃ and PbO structure files for combined refinement.
File PbTiO3.str:

PHASE=PbTiO3_90693  SpacegroupNo=99 Setting=1 HermannMauguin=P4mm //
PARAM=A=0.3904_0.3884^0.3923 PARAM=C=0.4135_0.4114^0.4155 //
RP=4 PARAM=B1=0_0^0.01 PARAM=k1=0_0^1 
ANISOLIMIT=0 ANISO4LIMIT=0 k2=ANISO4^0.001 
// neutron data have no PO
DeviceSelect(2) PO=SPHAR6 DeviceSelect(1,2)
PARAM=GEWICHT=0_0 GEWICHT[1]=gdev[idev]*GEWICHT*ifthenelse(ifdef(d),exp(-my*d*3/4),1)
GOAL:PbTiO3=GEWICHT
GOAL=GrainSize(1,0,0) 
GOAL=sqrt(ANISO(k2,1,0,0))
GOAL=sqrt(ANISO(k2,0,0,1))
GOAL=sqrt(ANISO(k2,1,1,0))
GOAL=sqrt(ANISO(k2,sqrt(2),0,1))
GOAL=sqrt(ANISO(k2,1,1,1))
DeviceSelect(2) GOAL=my DeviceSelect(1,2)
E=PB Wyckoff=a z=0
DeviceSelect(1) PARAM=TDS=0.0053_0^0.02
DeviceSelect(2) PARAM=TDS=0.0053_0^0.02 DeviceSelect(1,2)
E=TI Wyckoff=b PARAM=z=0.5281_0.5^0.55 
DeviceSelect(1) PARAM=TDS=0.0029_0^0.005
DeviceSelect(2) PARAM=TDS=0.0029_0^0.01 DeviceSelect(1,2)
E=O Wyckoff=c PARAM=z=0.6130_0.58^0.64
DeviceSelect(1) PARAM=TDS=0.0142_0^0.03
DeviceSelect(2) PARAM=TDS=0.0142_0^0.03 DeviceSelect(1,2)
E=O Wyckoff=b PARAM=z=0.1339_0.1^0.16 
DeviceSelect(1) PARAM=TDS=0.0142_0^0.03
DeviceSelect(2) PARAM=TDS=0.0142_0^0.03

File PbO_beta_Massicot.str:

PHASE=PbO_beta_Massicot SpacegroupNo=57 HermannMauguin=P2/b2_1/c2_1/m
Group=Oxides Formula=Pb_O ICDD=381477 Reference=60135
PARAM=A=0.5893_0.5834^0.5952 PARAM=B=0.549_0.5435^0.5545
PARAM=C=0.4753_0.465^0.495
PARAM=B1=0_0^0.08 GOAL=GrainSize(1,0,0) RP=3
GEWICHT=SPHAR0 
GEWICHT[1]=gdev[idev]*GEWICHT*ifthenelse(ifdef(d),exp(-my*d*3/4),1)
GOAL:PbObetaMassicot=GEWICHT
E=PB  Wyckoff=d x=0.7703 y=0.4884 z=0 TDS=0.0107
E=O  Wyckoff=d x=0.1347 y=0.5917 z=0 TDS=0.0114

Some details of this structure files:

In the PbTiO3.str file, PO is enabled for X-ray data only. This is due to the lack of appropriate sample movement in the neutron device; the neutron sample was reported to have near to no PO. Both the devices share one common GEWICHT. So we may control the ratio of both the phase contents being identic for both the patterns.
We refine separate thermal displacement factors for the neutron and X-ray patterns, due to the different physical meaning of this parameter in both experiments.
The effective value of GEWICHT is that of GEWICHT[1] (BGMN first looks at that). So we may introduce the principal intensity ratio gdev[2] into this variable. For convenience, we have defined gdev[1]=1 in the *.sav file.
The usage of micro absorption must be changed. In the context of combined refinement, we cannot correct the helper GOAL values (it would be different for different devices). Instead of, we have to correct GEWICHT[1] by the inverse value.
We have introduced anisotropic micro strain into the PbTiO₃ structure file. This was suggested by H. Boysen [1], [2]. We tell BGMN to definitely use ANISO4 by setting ANISOLIMIT=0 plus ANISO4LIMIT=0.

Running BGMN on the BleiTitanat.sav control file will produce the following file BleiTitanat.lst:

Rietveld refinement to file(s) BleiTitanat_neutronen.dat BleiTitanat_xray.dat
BGMN version 5.0.19, 4500 measured points, 650 peaks, 91 parameters
Start: Tue May 18 17:34:28 2010; End: Tue May 18 17:35:05 2010
71 iteration steps

device 1: Rp=6.48%  Rpb=12.28%  R=8.94%  Rwp=8.55% Rexp=3.02%
          Durbin-Watson d=0.75
          1-rho=1.04%
device 2: Rp=2.43%  Rpb=14.69%  R=3.42%  Rwp=2.94% Rexp=2.54%
          Durbin-Watson d=1.34
          1-rho=0.663%

Global parameters and GOALs
****************************
PbTiO3/denom=0.9637+-0.0041
PbObetaMassicot/denom=0.0363+-0.0041
EPS1[1]=0.00111+-0.00018
EPS2[1]=-0.00095+-0.00017
EPS1[2]=-0.00422+-0.00029
EPS2[2]=0.00415+-0.00028
gdev[2]=0.2495+-0.0023

Local parameters and GOALs for phase PbTiO3_90693
******************************************************
SpacegroupNo=99
HermannMauguin=P4mm
device 1: XrayDensity=7.978
device 2: XrayDensity=7.978
Rphase=9.25%
UNIT=NM
A=0.389902+-0.000021
C=0.414957+-0.000023
B1=0.004079+-0.000062
k1=1.00000
GEWICHT=2.207+-0.011
GrainSize(1,0,0)=78.0+-1.2
sqrt(ANISO(k2,1,0,0))=0.000806+-0.000044
sqrt(ANISO(k2,0,0,1))=0.003062+-0.000049
sqrt(ANISO(k2,1,1,0))=0.000681+-0.000038
sqrt(ANISO(k2,sqrt(2),0,1))=0.000811+-0.000034
sqrt(ANISO(k2,1,1,1))=0.000754+-0.000035
my=0.069637+-0.000011
k2=ANISO4, MeanValue(k2)=0.000000292545
Atomic positions for phase PbTiO3_90693 in view of device 1
------------------------------------------------------------
  1     0.0000  0.0000  0.0000     E=(PB(1.0000))
TDS=0.00562+-0.00026

  1     0.5000  0.5000  0.5377     E=(TI(1.0000))
z=0.53771+-0.00064
TDS=0.00352+-0.00054

  2     0.5000  0.0000  0.6146     E=(O(1.0000))
z=0.61461+-0.00052
TDS=0.00585+-0.00024

  1     0.5000  0.5000  0.1097     E=(O(1.0000))
z=0.10971+-0.00060
TDS=0.00453+-0.00036

Atomic positions for phase PbTiO3_90693 in view of device 2
------------------------------------------------------------
  1     0.0000  0.0000  0.0000     E=(PB(1.0000))
TDS=0.00842+-0.00029

  1     0.5000  0.5000  0.5377     E=(TI(1.0000))
z=0.53771+-0.00064
TDS=0.0053+-0.0010

  2     0.5000  0.0000  0.6146     E=(O(1.0000))
z=0.61461+-0.00052
TDS=0.0043+-0.0032

  1     0.5000  0.5000  0.1097     E=(O(1.0000))
z=0.10971+-0.00060
TDS=0.0085+-0.0049


Local parameters and GOALs for phase PbO_beta_Massicot
******************************************************
SpacegroupNo=57
HermannMauguin=P2/b2_1/c2_1/m
device 1: XrayDensity=9.435
device 2: XrayDensity=9.435
Rphase=9.01%
UNIT=NM
A=0.583400
B=0.5540+-0.0014
C=0.4861+-0.0011
B1=0.0500+-0.0074
GrainSize(1,0,0)=8.5+-1.2
GEWICHT=SPHAR0=0.0830+-0.0097
Atomic positions for phase PbO_beta_Massicot in view of device 1
------------------------------------------------------------
  4     0.7703  0.4884  0.2500     E=(PB(1.0000))
  4     0.1347  0.5917  0.2500     E=(O(1.0000))
Atomic positions for phase PbO_beta_Massicot in view of device 2
------------------------------------------------------------
  4     0.7703  0.4884  0.2500     E=(PB(1.0000))
  4     0.1347  0.5917  0.2500     E=(O(1.0000))

The atomic position results in view of both the devices are identic in this case. Different thermal displacement factors TDS between X-ray and neutron data are a known issue: X-ray and neutron TDS origin from the movement of electronic shell and atomic nucleus, respectively. We get a strong anisotropic micro strain for PbTiO₃: Maximum at (001), somewhat enlarged for (100) compared to (110).

Literature:
[1] H. Boysen, Ferroelastic phase transitions and domain structures in powders, Z. Kristallogr. 220 (2005) 726-734
[2] H. Boysen, Coherence effects in the scattering from domain structures, J. Phys. Condens. Matter 19 (2007) 275206

Named wavelengths

You may, for convenience, set a synchrotron wavelength by giving it's wavelength in the *.sav file, e.g.

SYNCHROTRON=0.0657096

The pitfall of such a notation: all anomalous dispersion will be set to zero. But there are cases you are in need for anomalous dispersion. An example is a pair of patterns measured on a sychrotron, one just below an absorption edge of a certain element and the other just above. In such case, you must provide named wavelengths. All the common X-ray tube anodes are already present as named wavelengths. So you may use the files cu.* as a guide, for example.

As a first, we must select a name, let it be syn0657096. Then provide a wavelength file. Its content is the wavelength distribution. Each line must contain three values:

intensity position width

position and width are in the reciprocal nanometer scale. width may be zero describing a sharp delta function. The first line of the wavelength file is a header line. The only mandatory entry is ILAM, the number of lorentzians used to describe the wavelength distribution. In our case, we create a file syn0657096.lam containing

ILAM=1
1 1/0.0657096 0

and place it in the bgmnwin directory, where all the other *.lam files reside. For enabling anomalous dispersion, you must provide a file syn0657096.ano. It may contain several lines, each with three fields:

element f' f"

Here is a on-line calculator for plotting f' plus f".

You may also provide a file syn0657096.mdr. The extension mdr stands for my div rho, where my is the linear dispersion coefficient of the solid element and rho is its density, which then in turn gives the mass absorption coefficient. If a *.mdr file is present, BGMN will provide linear absorption coefficients for the phases, from which you may calculate micro absorption corrections.

Having provided all that files, you now may place an entry

SYNCHROTRON=syn0657096

into your *.sav file and BGMN will use anomalous scattering for your synchrotron wavelength. You still should use SYNCHROTRON=, not LAMBDA=, which will slightly change the behaviour of BGMN (synchrotron lines are sharper and have no tube tails at all).

Site map

Combined refinement

Example Lead Titanate

Named wavelengths