Difference between revisions of "Temp"

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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.
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 for the various profile type 3 and 4 terms is given below.  Users are ''strongly'' encouraged to read this section of the GSAS manual at least once before (or after) blindly using this guide!
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.
 
== 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.
These peak profile functions are a [http://en.wikipedia.org/wiki/Voigt_profile pseudo-Voigt] type, combining Gaussian (G) and Lorentzian (L) components.
Line 11: Line 13:
These U, V, W, and P variables match the GU, GV, GW, and GP profile terms you see below.
These U, V, W, and P variables match the GU, GV, GW, and GP profile terms you see below.


11-BM users will '''not''' (''usually!'') need to change or refine these 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.
The Lorentzian shape is more complex (check the manual), but includes size and strain broadening terms.
 
== 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 ''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)


Sample effects in 11-BM data, such as size and strain broadening are (''usually!'') best fit 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).  
=== 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==


Constant Wavelength X-ray GSAS Profile Type 3
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 [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"
{| class="wikitable"
|-
|-
Line 24: Line 51:
|-
|-
| '''GP''' = Gaussian crystallite size broadening
| '''GP''' = Gaussian crystallite size broadening
| '''LX''' = Lorentzian crystallite size broadening  
| '''LX''' = Lorentzian isotropic crystallite size broadening  
| '''LY''' = Lorentzian strain broadening
| '''LY''' = Lorentzian isotropic strain broadening
|-
|-
| '''S/L''' = Finger-Cox Axial Divergence S term
| '''S/L''' = Axial Divergence S term
| '''H/L''' = Finger-Cox Axial Divergence H term
| '''H/L''' = Axial Divergence H term
| '''trns''' = sample transparency
| '''trns''' = Sample 'Transparency' (note 1)
|-
|-
| '''shft''' = sample displacement
| '''shft''' = Sample 'Displacement' (note 1)
| '''stec''' = anisotropic strain
| '''stec''' = Lorentzian anisotropic strain broadening (note 2)
| '''ptec''' = anisotropic crystallite size
| '''ptec''' = Lorentzian anisotropic crystallite size broadening
|-
|-
| '''sfec''' = sublattice anisotropic broadening (stacking faults)
| '''sfec''' = Lorentzian sublattice anisotropic broadening (note 3)  
| '''LXX''' = Lorentzian microstrain anisotropy
| '''LXX''' = Anisotropic Lorentzian microstrain (note 2)
| '''LYY''' = Lorentzian microstrain anisotropy
| '''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
 
==Constant Wavelength X-ray GSAS Profile Type 4==
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 50: Line 81:
|-
|-
| '''GP''' = Gaussian crystallite size broadening
| '''GP''' = Gaussian crystallite size broadening
| '''LX''' = Lorentzian crystallite size broadening  
| '''LX''' = Lorentzian isotropic crystallite size broadening  
| '''ptec''' = anisotropic crystallite size
| '''ptec''' = Lorentzian anisotropic crystallite size broadening
|-
|-
| '''trns''' = sample transparency
| '''trns''' = Sample 'Transparency' (note 1)
| '''shft''' = sample displacement
| '''shft''' = Sample 'Displacement' (note 1)
| '''sfec''' = sublattice anisotropic broadening (stacking faults)
| '''sfec''' = Lorentzian sublattice anisotropic broadening (note 2)
|-
|-
| '''S/L''' = Finger-Cox Axial Divergence S term
| '''S/L''' = Axial Divergence S term
| '''H/L''' = Finger-Cox Axial Divergence H term
| '''H/L''' = Axial Divergence H term
| '''eta''' = mixing factor, from pure Gaussian (0) to pure Lorentzian (1)
| '''eta''' = Gaussian-Lorentzian mixing factor (note 3)
|-
|-
| '''SXXX''' = Stephens anisotropic microstrain broadening
| '''SXXX''' = Anisotropic microstrain broadening (Lorentzian) (note 4)
| '''SYYY''' = Stephens anisotropic microstrain broadening
| '''SYYY''' = Anisotropic microstrain broadening (Lorentzian)
| '''SZZZ''' = Stephens anisotropic microstrain broadening  
| '''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 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.  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 [http://11bm.xor.aps.anl.gov/standards_data.html 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 [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:
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):
[[image:11BM_LaB6_Fit.png|250px|11BM_LaB6_Fit]]
==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://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] 
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

Latest revision as of 07:05, 2 May 2012

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 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. 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):

11BM_LaB6_Fit


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
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