GSAS Profile Terms

Peaks Profile terms for Rietveld Analysis

Most Rietveld refinement programs use a pseudo-Voigt term combining Gaussian and Lorentzian peak shapes (plus other correction terms). In general, the X-ray source can be described by a Gaussian function, while sample effects are described by Lorentzian terms.

For the synchrotron powder XRD data from 11-BM, the instrumental resolution is well described by Gaussian terms. Sample effects, such as size and microstrain broadening (i.e. local variations in the lattice parameters) are usually fit best by Lorentzian terms.

<math> m &= \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}</math>

Peter,

I'm following up on an email Brian Toby forwarded me before the break.

As he may have replied already, representative LaB6 data for 11-BM (high resolution powder XRD) can be downloaded from our webpage here (pick your format):

   http://11bm.xor.aps.anl.gov/standards_data.html

and beamline/instrument details here:

   http://11bm.xor.aps.anl.gov/description.html

more details about this specific LaB6 dataset follow:

precise wavelength = 0.412235
data was collected on a spinning 0.8 mm diameter capillary of LaB6 660a  [NIST SRM certificate lattice value = 4.15691(1)  A] .  Estimated muR is ~ 1.0 
collection Temp: 295 K
2theta range: 0.5 deg - 50.0 deg
step size: 0.001 deg

My GSAS/EXPGUI refinement gives a good fit (image attached) with the following parameters:

SG: Pm-3m
a =  4.156917(1)
zero shift:  -0.00029 deg 2theta
La   @ 0, 0, 0 (Ui/Ue*100 =  0.62)
B  @  0.1984(1), 1/2, 1/2  (Ui/Ue*100 =  0.29)

GSAS Profile type 4:  (non-listed terms = 0.0)
Coeff.   :   GU         GV         GW             LX        S/L          H/L
Value    :  2.552E+00 -5.439E-01  5.990E-02   2.790E-01  1.2E-03  1.2E-03

4-term Shifted Chebyschev (type #1) background

wRp =  0.0645,    Rp = 0.0486
CHI**2 =  3.349     for   14 variables                     

Let me know if you need any additional information.

Conversion of pseudo-Voigt function terms

GSAS <-> Fullprof Gaussian Parameters GSAS Term <=> Fullprof Term : (description) GU = 1803.4 * U : (instrumental term, ~ tan^2 of theta) GV = 1803.4 * V : (instrumental term, ~ tan of theta) GW = 1803.4 * W : (instrumental term, ~ constant with theta) GP = 1803.4 * IG : (size broadening)

note: 1083.4 => centidegrees squared divided by 8*ln(2)

Lorentzian Parameters GSAS Term <=> Fullprof Term : (description) LX = 100 * Y : (size broadening) LY = 100 * X : (microstrain)

note: 100 => degrees to centidegrees

Finger-Cox-Jephcoat asymmetry parameters GSAS S/L = Fullprof S_L GSAS H/L = Fullprof D_L

Note: terms are equivalent

S / L = the sample “half height”/diffractometer radius H / L = the slit half height/diffractometer radius

"Typical values of Rietveld instrument profile coefficients" Kaduk J, Reid J. Powder Diffraction (2011) vol. 26 pp. 88

size and microstrain broadening (i.e. local variations in the lattice parameters) are Lorentzian for 11-BM data

Only rarely is Gaussian size broadening observed; this re- quires a very tight monodisperse distribution, which is rarely encountered in powder specimens but is sometimes seen in polycrystalline solid specimens such as pieces of metal.