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. Gaussian sample size broadening is *rarely* observed; this requires a very tight mono-disperse size distribution rarely encountered in powder samples (solid metal samples may be an exception).

Please consult other references (such as the GSAS manual) or Powder Diffraction Crystallography Video lectures for details on Rietveld profile functions.

11-BM Profile Fitting

Lanthanum Hexaboride (LaB6) is used an X-ray powder diffraction profile standard because of its sharp peak shape. An example dataset and fit for LaB6 data collected at 11-BM is given below.

Representative LaB6 data for 11-BM (high resolution powder XRD) can be downloaded from the 11-BM webpage here (pick your format):

Full details for the dataset collected in Feb. 2010 are as follows:

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

For the 11-BM dataset collected on LaB6 in Feb. 2010, the following parameters provide a good Rietveld fit using GSAS/EXPGUI:

space group: 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
background = 4-term Shifted Chebyschev (type #1)

Gives the following Rietveld fit statistics

wRp = 6.45%,  Rp = 4.86%,  CHI**2 = 3.349 (for 14 variables)                 

Image of fit plot is shown below (click to enlarge):

Conversion of pseudo-Voigt function terms

11-BM provides users with instrument profiles terms for GSAS. Convert these values to Fullprof profile terms using the formulas below.

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

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

GSAS Refinement Hints

Profile type #4 anisotropy Sxxx terms

Q: What is the "best" order for incorporating GSAS profile 4 anisotropy Sxxx terms into a refinement?

A: from Robert Von Dreele (July 28, 2011)
 "Usually, I do the S4xx ones first & then the others. The thing is fairly stable after that.
Do do all of them at once in any case  in the end. The S4xx must be > 0 but the rest can be any sign.
If you want a quick way of seeing the shape, run mustrplot (spelling?) in GSAS; 
you'll need gnuplot to see the plot. For monoclinics, it might look like two beans back-to-back."
-Bob