Global Parameters in Rietveld Refinement · Na2Ca3Al2F14 (921) reflection. From left to right: the...
Transcript of Global Parameters in Rietveld Refinement · Na2Ca3Al2F14 (921) reflection. From left to right: the...
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What determines the intensities? (1) Structure Factors
• Atomic positions • Atomic scattering factors • Occupancies • Displacement coefficients • Lattice parameters • Symmetry
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What determines the intensities? (2) Global Parameters
• Concentration • Incident intensity • Background • Diffuse scattering • Extinction • Absorption
• Preferred orientation • Multiplicity • Lp factor • Profile function • Diffractometer
parameters • …
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Background
• Crucial to get right – affects integrated intensities (and thus the structure) – especially the displacement coefficients
• Interacts with the profile function • Peak tails • Use a few parameters as possible • Crystalline sample – slowly varying • Background parameters may be highly-correlated
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Physics of Background
P. Riello, G. Fagherazzi, D. Clemente, and P. Canton, “X-ray Rietveld Analysis with a Physically Based Background”, J. Appl. Cryst., 28(2), 115-120 (1995).
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Background Contributions • Air scattering • Incoherent scattering • Diffuse scattering
– Thermal disorder – First-kind lattice disorder
• Amorphous scattering • Thermal diffuse scattering • Short-range order • Small-angle scattering • Scattering off diffractometer parts, specimen holders +
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2[1 exp( )]bk inc inc dis coh airi i i i iY K I K ks I Y= + − − +
1/ sin(2 )airiY θ∝
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10 15 20 25 30 35 40 45Two-Theta (deg)
0
250
500
750
1000
1250
Inte
nsity
(Cou
nts)
[kadu1406.raw] SRM 660a La B6 (30,10,0.1,2.5,1) JAK[kadu1405.raw] 20307-1-4 w/ Si (30,10,0.1,2.5,1) JAK[kadu1411.raw] Office Snax sugar (30,10,0.1,2.5,1) JAK
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Background Functions
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Shifted Chebyshev Polynomials of the First Kind
11
( )N
b j jj
I B T x−=
=∑T0(x) = 1, T1(x) = x, T2(x) = 2x2-1, Tn+1(x) = 2xTn(x) - Tn-1(x)
min
max min
2(2 2 ) 12 2
x θ θθ θ
−= −
−
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Cosine Fourier Series
12
cos[ ( 1)]N
b jj
I B B x j=
= + −∑
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Polynomial
11
0
2 1m
b mm
I BBKPOS
θ=
= −
∑
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Diffuse Scattering The Debye Equation
2
4 sinsin
( ) ( ) 2 ( ) ( ) 4 sin
ij
n i jijn i j
r
I f f f r
π θλ
θ θ θ θ π θλ
= +
∑ ∑∑
P. Debye, Annalen der Physik, 351, 809 (1915)
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Diffuse Scattering in GSAS (#1)
2sin( ) 1exp2DS
RQI A UQRQ
= −
Q = 2π/d
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GSAS Diffuse Scattering Function #1 Terms
2θ, deg
0 20 40 60 80 100 120 140 160
Back
grou
nd In
tens
ity
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
0.020
R = 1.6, U = 0.05R = 2.4, U = 0.05R = 1.6, U = 0.2
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Differences in Diffuse Scattering Terms
2θ, deg
0 20 40 60 80 100 120 140 160
Back
grou
nd In
tens
ity
0
1e-5
2e-5
3e-5
4e-5
5e-5
1.6/0.05-2.4/0.051.6/0.2-2.4/0.2
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χ2 = 1.112
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Profile Coefficients
• Crucial to getting the right answers • Structure/intensities/overlap/tails • Valuable information in profile coefficients
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Convolution
The Fundamental Parameters approach!
( )( ) ( ) ( ) ( ) ( )f g t f g t d f t g dτ τ τ τ τ τ∞ ∞
−∞ −∞∗ = ⋅ − = − ⋅∫ ∫
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http://en.wikipedia.org/wiki/Convolution
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Convolution
• Convolution of one function (input) with a second function (impulse response) gives the output of a system
• A weighted moving average • In optics, “blur” is described by convolution
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ESRF BM16 (now ID31) Second Monochromator Crystal Rocking Curve
Left; perfect Si(111) Darwin profile. Right: perfect Si(111) reflection convoluted with first crystal strain function. Center: experimental data and fit by convolution of left and right curves. O. Masson, E. Dooryhee, and A. N. Fitch, “Instrument line-profile synthesis in high-resolution synchrotron powder diffraction”, J. Appl. Cryst., 36, 286-294 (2003).
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Na2Ca3Al2F14 (921) reflection. From left to right: the incident beam source profile, the transfer function of the monochromator, the pure sample profile, the reflection profile of the analyzer, and the axial divergence asymmetry function. Masson, Dooryhee, and Fitch, in A. Le Bail, “The Profile of a Bragg Reflection for Extracting Intensities”, in R. E. Dinnebier and S. J. L. Billinge, Powder Diffraction: Theory and Practice, RSC Publishing (2008).
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Bragg-Brentano Diffractometer
A. Kern, “Profile Analysis”, in A. Clearfield, J. Reibenspies, and N. Bhuvanesh, Principles and Applications of Powder Diffraction, Wiley (2008).
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Profile Contributions
Epsilon, degree
-0.10 -0.05 0.00 0.05 0.10
Inte
nsity
(arb
itrar
y un
its)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
source flat surface axial divergence transparency receiving slit
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Profile Contributions Effect Equation Range
X-ray Source exp(-k12ε2)
k1 = 1.67(FWHM) -∞ to +∞
Flat Surface |ε|-1/2 -(γ2cotθ)/114.6 to 0 γ = divergence
Axial Divergence |2εcotθ|-1/2 -(δ2cotθ)/(4×57.3) to 0 δ = axial divergence
Transparency exp(k4ε) k4 = (4µR/114.6)sin2θ
-∞ to 0
Receiving Slit -(FWHM)/2 to + (FWHM)/2
H. P. Klug and L. E. Alexander, X-ray Diffraction Procedures, Wiley (1974).
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Plus the Cu Kα Profile
J. Hartwig, G. Hölzer, J. Wolf, and E. Förster, “Remeasurement of the Profile of the Characteristic Cu Kα Emission Line with High Precision and Accuracy”, J. Appl. Cryst., 26, 539-548 (1993).
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More on Emission Profiles
G. Hölzer, M. Fritsch, M. Deutsch, J. Härtwig, and E. Förster, “Kα1,2 and Kβ1,3 emission lines of 3d transition metals”, Phys. Rev. A, 56, 4554-4568 (1997).
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Hugo Rietveld’s low-resolution neutron diffraction peaks were Gaussian (determined mainly by the neutron spectral distribution, the monochromator
response function, and the divergences of the Soller collimators).
He used the “Caglioti” function to describe the widths.
H. M. Rietveld, “A Profile Refinement Method for Nuclear and Magnetic Strutcures”, J. Appl. Cryst., 2, 65-71 (1969).
G. Caglioti, A. Paoletti, and F. P. Ricci, “Choice of Collimators for a Crystal Spectrometer for Neutron Diffraction:,
Nucl. Inst., 3, 223-228 (1958).
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FWHM2 = Utan2θ + Vtanθ + W
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FWHM2 = Atan2θ + Btanθ + C + Dcot2θ
R. W. Cheary and J. P. Cline, “An Analysis of the Effect of Different Instrumental Conditions on the Shapes of X-ray Powder Line Profiles”, Adv. X-ray Anal., 38, 75-82 (1995).
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Specimen Contributions
Size and (micro)Strain
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Size Broadening
P. Scardi, “Microstructural Properties: Lattice Defects and Domain Size Effects”, in R. E. Dinnebier and S.J. L. Billinge, Powder Diffraction: Theory and Practice, RSC Publishing (2008)
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Integral Breadth
( )
2
2
2 2
2
0
sin ( )( ) 1( )
sin ( )(0) ( )( )s
Nas dsI s ds as Nas
NasI Na DLimas
ππ
βπ
π
∞∞
−∞−∞
→
= = = =∫∫
Convert to 2θ space from reciprocal space:
(2 )cosK
Dβλ
β θθ
=
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Scherrer Constants for Various Crystallite Shapes
Shape K (FWHM) K (integral breadth) Sphere 0.89 1.07 Cube 0.83-0.91 1.00-1.16
Tetrahedron 0.73-1.03 0.94-1.39 Octahedron 0.82-0.94 1.04-1.14
J. I. Langford and A. J. C. Wilson, “Scherrer after sixty years: A survey and some new results in the determination of crystallite size”, J. Appl. Cryst., 11, 102-113 (1978)
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Shape?
P. Scardi, “Microstructural Properties: Lattice Defects and Domain Size Effects”, in R. E. Dinnebier and S.J. L. Billinge, Powder Diffraction: Theory and Practice, RSC Publishing (2008)
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P. Scardi and M. Leoni, “Diffraction line profiles from polydisperse
crystalline systems”, Acta Cryst. Sect. A, 57,
604-613 (2001).
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0 2 4 6 8 10 12 140
5
10
15
20
25
30
35
40 TEM WPPM
fre
quen
cy
grain diameter D (nm)
Size Distribution in Ceria Powder
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Strain Broadening
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Macrostrain
2 sin0 2 sin 2 cos0 2 sin 2 cos
2 2 tan 2 tan
ddd d d
d dd
d
λ θθ θ θθ θ θ
θ θ ε θ
== += ∆ + ∆
∆∆ = − = −
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Microstrain
1/ 22(2 ) tanβ θ ε θ∝
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Microstrain
P. Scardi, “Microstructural Properties: Lattice Defects and Domain Size Effects”, in R. E. Dinnebier and S.J. L. Billinge, Powder Diffraction: Theory and Practice, RSC Publishing (2008)
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Anisotropic Strain P.W. Stephens, “Phenomenological model of anisotropic peak broadening
in powder diffraction”, J. Appl. Cryst., 32, 281-289 (1999)
2 2 22
2 2 21 2 3 4 5 62
2
,
2
2 4 4 4 2 2400 040 004 220
2 2 2 2 3202 022 310 103
1
1
( )
( )
4( ) 3(
) 2(
hkl
hkl
hkl iji j i j
H K Lhkl HKL
HKL
hkl
M Ah Bk Cl Dkl Ehl Fhkd
M h k l kl hl hkd
M MM C
M S h k l
H K LM S h S k S l S h kS h l S k l S h k S
α α α α α α
σα α
σ
σ
= = + + + + +
= = + + + + +
∂ ∂=
∂ ∂
=
+ + =
= + + +
+ + + +
∑
∑
3
3 3 3 3031 130 301 013
2 2 2211 121 112
)
3( )
hlS k l S hk S h l S kl
S h kl S hk l S hkl+ + + +
+ + +
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Functional Forms of Size and Strain Broadening
2 theta, degrees0 20 40 60 80 100 120 140
Rel
ativ
e Pe
ak W
idth
0
2
4
6
8
size strain size + strain
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Real peaks have both Gaussian and Lorentzian (Cauchy) components
epsilon, deg
-0.2 -0.1 0.0 0.1 0.2
Inte
nsity
0
5
10
15
20
25
30
Gaussian Lorentzian
Same FWHM and area!
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Profile Equations
2, 2
2 ln 2 4ln 2expi kk k
IH H
ε −
=
1
2, 2
2 4( 2 1)1i kk k
IH H
επ
− −
= +
Gaussian Lorentzian
S. A. Howard and K. D. Preston, “Profile Fitting of Powder Diffraction Patterns”, in D. L. Bish and J. E. Post, Modern Powder Diffraction (1989), p. 217-275.
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SRM 660a LaB6
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So use combination of Gaussian and Lorentzian
Voigt (convolution) pseudo-Voigt (sum)
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GSAS Profile Function #2 (3-5) pseudo-Voigt
2 22tan tan
cosPU V Wσ θ θθ
= + + +
( )cos cos tancos
X ptec Y stecϕγ ϕ θθ
+= + +
2 cos sin 2tan 2
if asymzero shift trnsθ θ θθ
∆ = + + +
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Size Broadening
18000( )iso
inst
KLX X
λπ
=−
18000( )inst
KLX ptec X
λπ
=+ −
18000( )inst
KLX X
λπ⊥ = −
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Strain Broadening - Isotropic
( )100%18000 instS Y Yπ
= −
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Strain Broadening - Anisotropic
( )100%18000 instS Y stec Yπ
= + −
( )100%18000 instS Y Yπ
⊥ = −
2
( ) 100%18000
H K LS
HKL
dS hkl h k lπ= ∑
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Constant Microstrain Surface
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Asymmetry (Rietveld)
H. M. Rietveld, “A Profile Refinement Method for Nuclear and Magnetic Structures”, J. Appl. Cryst., 2, 65-71 (1969). C. J. Howard, J. Appl. Cryst., 15, 615-620 (1982).
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L. W. Finger, D. E. Cox, and A. P. Jephcoat, “A Correction for Powder Diffraction Peak Asymmetry due to Axial Divergence”,
J. Appl. Cryst., 27, 892-900 (1994).
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GSAS Profile Functions #3-5
S/L = sample “half height”/diffractometer radius H/L = slit “half height”/diffractometer radius
6/240 = 0.025
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Cubic ZnS, 14.7(1) Å 13 parameters, χ2 = 1.550
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18 parameters, χ2 = 1.345
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Control of Peak Positions
• Lattice parameters • Specimen displacement • Specimen transparency • (Zero)
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Specimen Displacement
36000Rshfts π−
=
2 cosshftθ θ∆ =
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Specimen Displacement
Displacement, µm shift a, Å -670 36.79(3) 3.90997(2) -390 21.25(5) 3.91010(2) -100 5.56(4) 3.91016(2) 38 -2.06(3) 3.91025(1) 200 -10.78(4) 3.91007(2) 520 -28.57(4) 3.91025(2) 820 -44.75(5) 3.91025(2)
Average 3.9102(1)
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Specimen Transparency
2 sin 2trnsθ θ∆ =
9000eff Rtrns
µπ−
=
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70
Specimen Transparency When the specimen is long enough to
intercept the whole beam, and
an additional component of the profile g is generated:
-∞ < ε ≤ 0 (°)
t ≥32.
'sin
µρρ
θ
gR
=
exp
.sin
4114 6
2π ε
θ
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71
Transparency
• Significant for thick organic specimens • Additional low-angle asymmetry • Peak shift to low angles
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Extra Low-Angle Asymmetry Peak Shift to Low-Angles
5 10 15 20 25 30Two-Theta (deg)
0
50
100
150
SQR
(Cou
nts)
[wong664.raw] DAL0 (30,10,0.2,1.5,1,qzbc,96chan) JAK[wong642.raw] DAL0 (30,10,0.6,2.5,3) JAK
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10% RuO2/SiO2 Catalyst
25 30 35 40 45 50 55Two-Theta (deg)
0
2500
5000
7500
Inte
nsity
(Cou
nts)
[kuma001.raw] RuO2:SiO2 (0.1:0.9) 09/05/11) (30,10,0.6,2.5,3) JAK[kuma002.raw] RuO2:SiO2 (0.1:0.9) 09/05/11 (30,10,0.6,2.5,3,qzbc) JAK
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Penetration Depth, µm
2θ, ° 28 130 Pure RuO2 22 70
10% RuO2/90% SiO2 100 340
74
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Instrument Profiles
“Typical values of Rietveld instrument profile coefficients”, J. A. Kaduk and J. Reid, Powder
Diffraction, 26(1), 88-93 (2011).
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Table II. GSAS Function #2 Instrument Profile Parameters for a Variety of LaboratoryDiffractometers.
Diffractometer Date U V W X Y asymX’Pert ProPIXcel/0.04rad Soller
08/2010 0.8048 0 0.5103 2.537 1.946 4.343
D2/Lynxeye 05/2010 1.371 0 2.393 2.183 1.199 2.774D2/Lynxeye 10/2009 2.8329 0 2.695 1.853 2.488 2.194X’Pert ProPIXcel/mono
01/2008 0.7565 0 3.646 2.428 1.902 1.063
X’Pert ProPIXcel/no mon
01/2008 2.6369 0 0 2.778 0 2.486
D8/VANTEC 04/2004 0.2879 0 1.124 2.477 2.103 2.052PAD V 06/2007 1.0270 0 6.640 1.237 2.693 2.109D/MAX-B 06/2002 0.567 0 18.680 2.301 1.960 6.048Miniflex 09/2001 5.568 0 20.47 3.614 0 5.487PW17xx 08/1998 0 0 5.217 0 9.77 7.603
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Table III. GSAS Function #3 Instrument Profile Parameters for a Variety of LaboratoryDiffractometers.
Diffractometer U V W X Y S/L H/LX’Pert ProPIXcel/0.04 radSoller
1.423 0 0.5061 2.842 1.509 0.03547 0.00522
D2/Lynxeye 1.376 0 2.640 2.410 0.850 0.02951 0.0005X’Pert ProPIXcel/mono
1.153 -0.928 4.161 2.472 1.814 0.01577 0.0005
X’Pert ProPIXcel/no mon
2.314 0 0 3.040 0 0.02788 0.0005
D8/VÅNTEC 0.3365 0 1.032 2.526 2.051 0.02695 0.0005PAD V 1.103 0 6.412 1.173 2.842 0.03018 0.0005D/MAX-B 3.219 -7.822 24.370 2.460 1.609 0.03858 0.0005
In all of these profile functions, P = 0.
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Table IV. GSAS Profile #2 Functions for Several Synchrotron Diffractometers
Instr. Date U V W X Y asym APS
5-BM-C 10/2002 0.1 0 0 0.2505 0.9462 0
APS 5-BM-C 08/2006 17.1 -8.8 1.3 0 0 0
APS 1-ID 02/2002 0.1 0 0 0.2505 0.9462 0.0646
APS 10-ID-B 01/2000 0.3540 0 0.2908 0.3565 0.5177 0.4744
APS 32-ID 12/2004 0.3120 0 0.0104 0.1186 0.4062 0.0419
LNLS D10B 0.8777 -0.1600 0.1063 0.7604 1.1904 0.5157
NSLS X3B1 03/2004 6.427 -1.067 0 0.6102 0.6796 0.6733
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Table V. GSAS Profile #3 Instrument Parameters for Several Synchrotron Diffractometers
Inst. Date U V W P X Y S/L H/L
APS 5-BM-C 10/2002 1.212 0 0 0 1.980 0 0.00135 0.00718
APS 1-ID 02/2002 0.1 0 0 0 0.1845 11.190 0.0005 0.00458
APS 10-ID 10/2003 1.212 0 0 0 0.198 0 0.00135 0.00718
APS 11-BMB 02/2009 1.163 -0.126 0.063 0 0.173 0 0.00110 0.00110
APS 32-ID 12/2004 1.212 0 0 0 0.198 0 0.00135 0.00718
AS PD 0.0522 0.5640 0.0621 0 0.293 0.171 0.0000 0.0000
NSLS X7B 0 -125.9 73.3 0 2.03 0 0.0001 0.1000
NSLS X16C 0 0 0 1 3 30 0.014 0.014
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GU(GSAS) = 1803.4U(FullProf) (9)GV(GSAS) = 1803.4V(FullProf) (10)GW(GSAS) = 1803.4W(Fullprof) (11)GP(GSAS) = 1803.4IG(FullProf) (12)LX(GSAS) = 100Y(FullProf) (13)LY(GSAS) = 100X(Fullprof) (14)S/L(GSAS) = S_L(Fullprof) (15)H/L(GSAS) = D_L(Fullprof) (16)
fil l i i l i i h d d fil
GSAS/FullProf Conversions
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GSAS Instrument Profile Parameters Bruker D2 Phaser, SRM 660a LaB6
Profile 2 3 4 Avg Div/Soller 0.6/2.5 0.2/1.5 0.6/2.5 0.2/1.5 0.6/2.5 0.2/1.5
File 1450 1473 1450 1473 1450 1473 U 2.336 2.976 1.613 2.522 1.718 3.259 2.04(66) V 0 0 0 0 0 0 0 W 3.777 2.718 4.749 3.911 4.751 3.648 3.93(76) P - - 0 0 0 0 0 X 2.718 2.214 2.854 2.609 2.847 2.706 2.66(24) Y 1.868 1.219 0 0.310 - - 0.85(85)
trns 2.408 2.501 1.847 1.104 1.831 2.148 1.97(12) asym 3.759 2.356 - - - - - S/L - - 0.03334 0.01100 0.03325 0.02241 H/L - - 0.0005 0.0005 0.0005 0.0005 eta - - - - 0.900 0.408
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Lorentz-Polarization Factor IPOLA Lp Functional Form Description
0
Normal (POLA = 0.5)
1
incident beam monochromator
2
Lp up to the user
3
?
2
2
(1 )cos 22 sin cos
POLA POLAV
θθ θ
+ −
2
2
1 cos 2sin cos
POLAV
θθ θ
+
1V
2
2
(1 )cos 2 sin 22 sin cos
POLA POLAV
θ θθ θ
+ −
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83
Texture (Preferred Orientation)
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85
Stereographic Projection
http://www.3dsoftware.com/Cartography/USGS/MapProjections/Azimuthal/Stereographic
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March-Dollase Function
W. A. Dollase, “Correction of Intensities for Preferred Orientation in Powder Diffractometry:
Application of the March Model”, J. Appl. Cryst., 19(4), 267-272 (1986).
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March-Dollase Function 3/ 22
2 2
1
sin1 cospM
jph j
jp
AO Ratio A
M Ratio=
= +
∑
hp = reciprocal lattice vector Mp = multiplicity of hp Aj = angle between specified unique axis and hp Ratio = the refinable parameter “aspect ratio” Cylindrical specimen symmetry assumed
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BFDH Morphology - Folic Acid Dihydrate
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March-Dollase Function (B-B)
Plates Ratio < 1 Oblate spheroid
Needles Ratio > 1 Prolate spheroid
Check consistency with anisotropic broadening!
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Spherical Harmonics Function
R. B. Von Dreele, “Quantitative texture analysis by Rietveld refinement”,
J. Appl. Cryst., 30, 517-525 (1997).
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Spherical Harmonics Function
( ) ( ) ( )2
4, 12 1
LN L Lmn m n
p L L LL m L n L
O h y C k h k yLπ
= =− =−
= ++∑ ∑ ∑
Terms depend on crystal and sample symmetry cylindrical 2/m (shear) mmm (rolling) no symmetry
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Spherical Harmonics
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Texture Index
2
2
112 1
LN L LmnL
L m L n LJ C
L= =− =−
= ++∑ ∑ ∑
J = 1 for random J = ∞ for single crystal
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[ssjr010.raw] Sample #3, 1 (30,10,0.6,2.5,3,qzbc,static) JAK[ssjr018.raw] Sample #3, parallel (30,10,0.6,2.5,3,qzbc,static) JAK[ssjr019.raw] Sample #3, vertical (30,10,0.6,2.5,qzbc,static) JAK
Polymer Dip Tubes
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96
Texture in HDPE Pipe
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A Rietveld Example Nature’s Bounty B-Complex
James A. Kaduk Poly Crystallography Inc.
Naperville IL 60540 [email protected]
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“Default” Search/Match
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04-013-3344> Brushite - HCa(PO 4)(H2O)2
02-063-2297> C 6H8O6 - L-Ascorbic acid
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[kadu1599.raw] Nature's Bounty B-Complex (30,10,0.6,2.5,3,96) JAK
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Zoom and Repeat
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02-063-2297> C 6H8O6 - L-Ascorbic acid
01-075-1520> Monetite - CaHPO 4
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[kadu1599.raw] Nature's Bounty B-Complex (30,10,0.6,2.5,3,96) JAK
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3-Phase Rietveld Refinement
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Pick Peaks Off Difference Plot d, Å I d, Å I
6.0665 280 4.1566 1194 5.9849 491 4.1166 1450 5.8320 365 3.8871 727 4.7189 491 3.7890 1170 4.3332 580 3.4636 617
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Search the PDF-4 Organics with SIeve
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Phases 4, 5 and 6
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[kadu1599.raw] Nature's Bounty B-Complex (30,10,0.6,2.5,3,96) JAK02-062-0118> C 6H14O6 - D-Mannitol
02-070-4954> C 6H6N2O - Nicotinamide02-072-5617> C 12H17N4OS·NO 3 - Thiamine nitrate
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6-Phase Rietveld Refinement
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Add Cellulose Iα from 00-056-1719
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From the label Phase wt% Vitamin C, ascorbic acid 17.7 Niacin, niacinamide 3.7 D-Ca pantothenate 1.5 Vitamin B-1, thiamin 0.7 Vitamin B-2, riboflavin 0.7 Vitamin B-6, pyroxidine HCl 0.7 Folic acid 0.06 Vitamin B-12, cyanocobalmin 0.04 Biotin 0.04
plus cellulose
dicalcium phosphate stearic acid
and < 2% palm leaf glaze
silica Mg stearate
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From the Rietveld Refinement Phase Observed, wt% Expected, wt% Brushite, CaH(PO4)(H2O)2 6.7(1) Monetite, CaHPO4 2.5(2) β-D-mannitol 0.7(1) Ascorbic acid 17.7 17.7 Nicotinamide 0.6(1) 3.7 Thiamine nitrate 0.9(1) 0.7 Cellulose Iα (+ silica?) 17.4(7) Sum 46.5 > 1 unidentified