Difference between revisions of "GSAS Profile Terms"

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== Peaks Profile terms for Rietveld Analysis==
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.
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 re-
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 [http://www.aps.anl.gov/Xray_Science_Division/Powder_Diffraction_Crystallography/ Powder Diffraction Crystallography Video lectures] are also a great resource for both beginners and experts.
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.


Please consult other references (such as the [https://subversion.xor.aps.anl.gov/trac/EXPGUI GSAS manual]) or [http://www.aps.anl.gov/Xray_Science_Division/Powder_Diffraction_Crystallography/ Powder Diffraction Crystallography Video Features]
== Pseudo-Voigt Profile Functions ==


These peak profile functions are a [http://en.wikipedia.org/wiki/Voigt_profile 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 &asymp; U*tan<sup>2</sup>&theta; + V*tan&theta; + W + P/cos<sup>2</sup>&theta;


These U, V, W, and P variables match the GU, GV, GW, and GP profile terms you see below.


for details on Rietveld profile functions.
The Lorentzian shape is more complex (check the manual), but includes size and strain broadening terms.  


== 11-BM Profile Fitting ==
== Asymmetry, Zero-Shift and Related Terms ==
=== Asymmetry ===
[http://youtu.be/SIz6Ng6UzAw 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 intrinsic instrument asymmetry for low angle (< 5 deg theta for 30 Kev 11-BM data), and is related to the goniometer radius, or distance from the sample to the detector (about ~1000 mm for 11-BM).


Representative LaB6 data for 11-BM (high resolution powder XRD) can be [http://11bm.xor.aps.anl.gov/standards_data.html downloaded from the 11-BM webpage] here (pick your format):
Most 11-BM users will not need to refine these terms from the default (1.2E-03) values included in 11-BM GSAS instrument parameter files. If your fit shows an asymmetric misfit to strong low angle peaks, my might try to refine, but never refine both simultaneously.


Full details for the dataset collected in Feb. 2010 are as follows:
=== Transparency ===
precise wavelength = 0.412235 A
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 dataDo '''*not*''' use for 11-BM data which is collected in a transmission geometry (Debye-Scherrer)
data was collected on a spinning 0.8 mm diameter capillary of LaB6 660a
The NIST [https://wiki-ext.aps.anl.gov/ug11bm/index.php/NIST_SRM_Certificates LaB6 660a SRM certificate] lattice value = 4.15691(1) A.  
  The estimated muR ([https://wiki-ext.aps.anl.gov/ug11bm/index.php/X-ray_absorption_%26_fluorescence 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:
=== 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)


space group: Pm-3m
=== ZERO ===
a = 4.156917(1)
Instead of '''trns''' or '''shft''', 11-BM users should refine the 2&theta zero shift term "ZERO". This term is found in EXPGUI under the Histogram tabIt describes any shift (error) in the absolute 2theta "0" position for the data and is measured in units of centi-degrees (100*2&theta;).
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
GSAS users refining 11-BM data should refine this term near the end of a refinement to ensure the most accurate lattice parameters. Typical values for 11-BM might be in the range +/- 0.1 (i.e. 0.001 degrees).
wRp = 6.45%,  Rp = 4.86%,  CHI**2 = 3.349 (for 14 variables)                


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


[[image:11BM_LaB6_Fit.png|250px|11BM_LaB6_Fit]]
The background function type 1 (Chebyshev polynomial) is recommended.  Use the minimum number of terms needed to fit the pattern background.  Start with 3 or 4 terms, and increase as needed.  Sometimes 10-20 tems are needed for complex backgrounds.


Just remember that the background also represents scattering from something (sample holders, air, sample?).  Try to think about what may contributes to the background for your sample.  This might contain valuable information.




==Conversion of pseudo-Voigt function terms==
==Suggested Profile Types & Terms for Fitting 11-BM Data==


11-BM provides uses with instrument profiles terms for GSAS.  Its easy to convert these values to Fullprof terms using the formulas below.
11-BM users are encouraged to use the GSAS constant wavelength (CW) profile type 3 or type 4Profile #4 is best for cases in which anisotropic terms are required.  


For more info see: [http://link.aip.org/link/doi/10.1154/1.3548128 "Typical values of Rietveld instrument profile coefficients" Kaduk J, Reid J. Powder Diffraction (2011) vol. 26 pp. 88]   
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 [http://www.aps.anl.gov/Xray_Science_Division/Powder_Diffraction_Crystallography/GSASparameters.html tutorial video]
 
 
==Constant Wavelength X-ray GSAS Profile Type 3==
{| class="wikitable"
|-
| <font color="#C11B17">'''GU''' = Gaussian U term</font>
| <font color="#C11B17">'''GV''' = Gaussian V term</font>
| <font color="#C11B17">'''GW''' = Gaussian W term</font>
|-
| <font color="#C36900">'''GP''' = Gaussian crystallite size broadening</font>
| <font color="#2C820E">'''LX''' = Lorentzian isotropic crystallite size broadening </font>
| <font color="#2C820E">'''LY''' = Lorentzian isotropic strain broadening</font>
|-
| <font color="#C36900">'''S/L''' = Axial Divergence S term</font>
| <font color="#C36900">'''H/L''' = Axial Divergence H term
| <font color="#C11B17">'''trns''' = Sample 'Transparency' </font> ''(note 1)''
|-
| <font color="#C11B17">'''shft''' = Sample 'Displacement'</font> ''(note 1)''
| <font color="#C36900">'''stec''' = Lorentzian anisotropic strain broadening</font> ''(note 2)''
| <font color="#2C820E">'''ptec''' = Lorentzian anisotropic crystallite size broadening</font>
|-
| <font color="#C36900">'''sfec''' = Lorentzian sublattice anisotropic broadening</font> ''(note 3)''
| <font color="#C36900">'''LXX''' = Anisotropic Lorentzian microstrain</font> ''(note 2)''
| <font color="#C36900">'''LYY''' = Anisotropic Lorentzian microstrain</font> ''(note 2)''
|-
|}
Color denotes indicates terms 11-BM users should 
<font color="#2C820E">'''Refine''' (green) </font>,
<font color="#C36900">'''Sometimes''' Refine (yellow) </font>, and
<font color="#C11B17">''' Not''' Refine (red) </font>
 
*''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==
{| class="wikitable"
|-
| <font color="#C11B17">'''GU''' = Gaussian U term</font>
| <font color="#C11B17">'''GV''' = Gaussian V term</font>
| <font color="#C11B17">'''GW''' = Gaussian W term</font>
|-
| <font color="#C36900">'''GP''' = Gaussian crystallite size broadening</font>
| <font color="#2C820E">' '''LX''' = Lorentzian isotropic crystallite size broadening</font>
| <font color="#2C820E">''''ptec''' = Lorentzian anisotropic crystallite size broadening</font>
|-
| <font color="#C11B17">'''trns''' = Sample 'Transparency'</font> ''(note 1)''
| <font color="#C11B17">'''shft''' = Sample 'Displacement'</font> ''(note 1)''
| <font color="#C36900">'''sfec''' = Lorentzian sublattice anisotropic broadening</font> ''(note 2)''
|-
| <font color="#C36900">'''S/L''' = Axial Divergence S term</font>
| <font color="#C36900">'''H/L''' = Axial Divergence H term</font>
| <font color="#C36900">'''eta''' = Gaussian-Lorentzian mixing factor</font> ''(note 3)''
|-
| <font color="#2C820E">''''SXXX''' = Anisotropic microstrain broadening (Lorentzian)</font> ''(note 4)''
| <font color="#2C820E">''''SYYY''' = Anisotropic microstrain broadening (Lorentzian)</font>
| <font color="#2C820E">''''SZZZ''' = Anisotropic microstrain broadening (Lorentzian)</font>
|}
Color denotes indicates terms 11-BM users should 
<font color="#2C820E">'''Refine''' (green) </font>,
<font color="#C36900">'''Sometimes''' Refine (yellow) </font>, and
<font color="#C11B17">''' Not''' Refine (red) </font>
 
*''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 Stephen's microstrain terms SXXX, SYYY etc 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*&lambda;)/(&pi;*LX)
 
where K = Scherrer constant (typically ~ 1), &pi; = 3.1416
 
and size units are in Angstroms (&#8491;), same units as wavelength (&lambda;), typically ~ 0.41 &#8491; 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 * (&pi;/18000)
 
For profile type 4, consult the GSAS manual.  The anisotropic strain are best visualized using gnuplot.  See the Robert Von Dreele's Rietveld Mailing List post from July 28th, 2011 below:
 
Q: What is the "best" order for incorporating GSAS profile 4 anisotropy Sxxx terms into a refinement?
A: Robert Von Dreele writes: "Usually, I do the S4xx ones first & then the others.
The thing is fairly stable after that. 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 ==
[http://en.wikipedia.org/wiki/Lanthanum_hexaboride Lanthanum Hexaboride (LaB6)] is used an X-ray powder diffraction profile standard because of its sharp peak shape. 
 
Representative LaB6 data for 11-BM (high resolution powder XRD) can be downloaded from the 11-BM wiki:
 
https://wiki-ext.aps.anl.gov/ug11bm/index.php/Standards_Data
 
On the same Wiki page find more details about Instrument Parameter and Input Files, plus example fits to LaB6 data measured at 11-BM
 
 
==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: [http://dx.doi.org/10.1154/1.3548128 "Typical values of Rietveld instrument profile coefficients" Kaduk J, Reid J. Powder Diffraction (2011) vol. 26 pp. 88]   


Gaussian Parameters
Gaussian Parameters
Line 72: Line 189:
  note: 100 => degrees to centidegrees
  note: 100 => degrees to centidegrees


Finger-Cox-Jephcoat asymmetry parameters
Finger-Cox-Jephcoat asymmetry parameters are equivalent in GSAS & Fullprof
  GSAS S/L = Fullprof S_L
  GSAS S/L = Fullprof S_L
  GSAS H/L = Fullprof D_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

Latest revision as of 13:31, 20 March 2014

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 intrinsic instrument asymmetry for low angle (< 5 deg theta for 30 Kev 11-BM data), and is related to the goniometer radius, or distance from the sample to the detector (about ~1000 mm for 11-BM).

Most 11-BM users will not need to refine these terms from the default (1.2E-03) values included in 11-BM GSAS instrument parameter files. If your fit shows an asymmetric misfit to strong low angle peaks, my might try to refine, but never refine both simultaneously.

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 should refine the 2&theta zero shift term "ZERO". This term is found in EXPGUI under the Histogram tab. It describes any shift (error) in the absolute 2theta "0" position for the data and is measured in units of centi-degrees (100*2θ).

GSAS users refining 11-BM data should refine this term near the end of a refinement to ensure the most accurate lattice parameters. Typical values for 11-BM might be in the range +/- 0.1 (i.e. 0.001 degrees).

Background Function

The background function type 1 (Chebyshev polynomial) is recommended. Use the minimum number of terms needed to fit the pattern background. Start with 3 or 4 terms, and increase as needed. Sometimes 10-20 tems are needed for complex backgrounds.

Just remember that the background also represents scattering from something (sample holders, air, sample?). Try to think about what may contributes to the background for your sample. This might contain valuable information.


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)

Color denotes indicates terms 11-BM users should Refine (green) , Sometimes Refine (yellow) , and Not Refine (red)

  • 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)

Color denotes indicates terms 11-BM users should Refine (green) , Sometimes Refine (yellow) , and Not Refine (red)

  • 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 Stephen's microstrain terms SXXX, SYYY etc 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 Robert Von Dreele's Rietveld Mailing List post from July 28th, 2011 below:

Q: What is the "best" order for incorporating GSAS profile 4 anisotropy Sxxx terms into a refinement?
A: Robert Von Dreele writes: "Usually, I do the S4xx ones first & then the others.
The thing is fairly stable after that. 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.

Representative LaB6 data for 11-BM (high resolution powder XRD) can be downloaded from the 11-BM wiki:

https://wiki-ext.aps.anl.gov/ug11bm/index.php/Standards_Data

On the same Wiki page find more details about Instrument Parameter and Input Files, plus example fits to LaB6 data measured at 11-BM


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