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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):