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GSAS offers 5 different Constant Wavelength (CW) X-ray profile functions. They are described in detail within the GSAS technical manual (see page 156). 11-BM users are encouraged to use either profile type 3 or type 4.
A quick reference guide to terms in the CW profile type 3 and 4 functions is given below after a brief introduction. Users are strongly encouraged to read this section of the GSAS manual at least once before (or after) blindly using this guide! The Powder Diffraction Crystallography Video lectures are also a great resource for both beginners and experts.
Pseudo-Voigt Profile Functions
These peak profile functions are a pseudo-Voigt type, combining Gaussian (G) and Lorentzian (L) components.
The general Gaussian shape (as a function of angle θ) is described by the Cagliotti function
Gaussian Profile ≈ U*tan2θ + V*tanθ + W + P/cos2θ
These U, V, W, and P variables match the GU, GV, GW, and GP profile terms you see below.
The Lorentzian shape is more complex (check the manual), but includes size and strain broadening terms.
Asymmetry, Zero-Shift and Related Terms
Asymmetry
Axial Divergence (i.e. low angle peak asymmetry) is modeled in GSAS profile types 3 & 4 with the Finger-Cox-Jephcoat model (see GSAS manual). The profile terms S/L & H/L describe the instrumental asymmetry. Most users of 11-BM will not need to refine these terms.
Transparency
This is the trns profile term describing the x-ray penetration depth into a flat plate sample . It should *only* be used for fitting flat-plate reflection geometry (Bragg-Brentano) powder diffraction data. Do *not* use for 11-BM data which is collected in a transmission geometry (Debye-Scherrer)
Displacement
This is the shft profile term describing vertical displacement of the flat plate sample . It should *only* be used for fitting flat-plate reflection geometry (Bragg-Brentano) powder diffraction data. Do *not* use for 11-BM data which is collected in a transmission geometry (Debye-Scherrer)
ZERO
Instead of trns or shft, 11-BM users may wish to refine the 2&theta zero shift "ZERO". This term is found in EXPGUI under the Histogram tab. It describes any shift in the absolute 2theta "0" position and is measured in units of centi-degrees (100*2θ).
Typical values for 11-BM might be in the range +/- 0.1 (i.e. 0.001 degrees). If used, it should be turned on near the end of the refinement.
Suggested Profile Types & Terms for Fitting 11-BM Data
11-BM users are encouraged to use the GSAS constant wavelength (CW) profile type 3 or type 4. Profile #4 is best for cases in which anisotropic terms are required.
11-BM users will not (usually!) need to change or refine the default 'G' terms given in the instrumental parameter file. For the high-resolution synchrotron powder data collected at 11-BM, the instrumental resolution is well described by Gaussian terms.
On the other hand, sample effects in 11-BM data, such as size and strain broadening are (usually!) best fit and refined using Lorentzian terms. Gaussian crystallite size broadening (GP) is *rarely* observed; this requires a very tight mono-disperse size distribution rarely encountered in powder samples (solid metal samples may be an exception).
Many 11-BM diffraction patterns can be well fit by refining only the LX (size), LY (strain) and anisotropic Lorentzian size & microstrain terms. Profile type 4 is recommended if the later are required.
For more info see a EXPGUI-GSAS Parameter tutorial video
Constant Wavelength X-ray GSAS Profile Type 3
| GU = Gaussian U term | GV = Gaussian V term | GW = Gaussian W term |
| GP = Gaussian crystallite size broadening | LX = Lorentzian isotropic crystallite size broadening | LY = Lorentzian isotropic strain broadening |
| S/L = Axial Divergence S term | H/L = Axial Divergence H term | trns = Sample 'Transparency' (note 1) |
| shft = Sample 'Displacement' (note 1) | stec = Lorentzian anisotropic strain broadening (note 2) | ptec = Lorentzian anisotropic crystallite size broadening |
| sfec = Lorentzian sublattice anisotropic broadening (note 3) | LXX = Anisotropic Lorentzian microstrain (note 2) | LYY = Anisotropic Lorentzian microstrain (note 2) |
- note 1: Do *not* use for 11-BM data, see above
- note 2: Better to use Profile Type #4 Anisotropic microstrain terms
- note 3: See GSAS Manual before using
Constant Wavelength X-ray GSAS Profile Type 4
| GU = Gaussian U term | GV = Gaussian V term | GW = Gaussian W term |
| GP = Gaussian crystallite size broadening | LX = Lorentzian isotropic crystallite size broadening | ptec = Lorentzian anisotropic crystallite size broadening |
| trns = Sample 'Transparency' (note 1) | shft = Sample 'Displacement' (note 1) | sfec = Lorentzian sublattice anisotropic broadening (note 2) |
| S/L = Axial Divergence S term | H/L = Axial Divergence H term | eta = Gaussian-Lorentzian mixing factor (note 3) |
| SXXX = Anisotropic microstrain broadening (Lorentzian) (note 4) | SYYY = Anisotropic microstrain broadening (Lorentzian) | SZZZ = Anisotropic microstrain broadening (Lorentzian) |
- note 1: Do *not* use for 11-BM data, see above
- note 2: See GSAS Manual before using
- note 3: Changes pseudo-Voigt mix from pure Gaussian (eta=0) to pure Lorentzian (eta=1). Typical 11-BM data is fit well using (or at least starting with) eta = 1
- note 4: Number of SXXX, SYYY etc terms changes with phase crystal symmetry (ie. a monoclinic phase will have more of these terms than a cubic symmetry phase)
Physical Meaning of Profile Terms
Some of the CW profile terms can be interpreted to give physically meaningful strain and particle size information. See the page 162 of GSAS technical manual for details
Particle size broadening
Using the isotropic LX profile term
then particle size = (18000*K*λ)/(π*LX)
where K = Scherrer constant (typically ~ 1), π = 3.1416
and size units are in Angstroms (Å), same units as wavelength (λ), typically ~ 0.41 Å for 11-BM data
Strain broadening
Strain is more difficult to quantify.
For profile type 3, using the isotropic LY term, then
isotropic strain (%) = 100% * LY * (π/18000)
For profile type 4, consult the GSAS manual. The anisotropic strain are best visualized using gnuplot. See the Rietveld Mailing List note from Robert Von Dreele below
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 in GSAS; you'll need gnuplot to see the plot. For monoclinics, it might look like two beans back-to-back." -Bob
Example 11-BM Profile Fit and Terms
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):
Convert GSAS profile terms to Fullprof 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 are equivalent in GSAS & Fullprof
GSAS S/L = Fullprof S_L GSAS H/L = Fullprof D_L
