J. Faber, Faber Consulting, Thornton, [email protected]
610.357.7065
NEW NEUTRON DIFFRACTION DATA CAPABILITY IN THE ICDD PDF-4+ 2014
RELATIONAL DATABASE
INTRODUCTION
WHY NEUTRONS? ~30 facilities, world-wide, most with user access agreements for industry
and academic users Neutron powder diffraction is a useful tool because elemental scattering
contrast is quite different when compared to X-rays.
-30
0
30
60
90
120
-0.5
0
0.5
1
1.5
2
0 20 40 60 80 100
# E
lect
ron
s
Neu
tron
Sca
tter
ing
Le
ng
th (
10
-12
cm)
Atomic Number
Neutrons vs. X-rays - Coherent Scattering
Neutrons
INTRODUCTION (continued)
Neutrons have atomic scattering lengths – scalars Good for occupation determinations High-angle reflections don’t diminish as quickly
Absorption cross sections are low Volume penetrating power Minimal preferred orientation
Singlet radiation (no alpha1-alpha2)
ICDD CALCULATESNEUTRON DATA
The PDF-4+ 2014 has ~241,000 entries with atomic coordinates that can be used to calculate complete powder diffraction patterns. For intensities, we must accurately account for the
wavelength of the incident beam, the energy dependence of the sample absorption cross section, the precise details of the cylindrical sample geometry (Debye-
Scherrer with sample diameter and packing fraction). For peak profiles
The CW neutron diffraction resolution is broader than for x-rays, and tends to be dominated by the source rather than the sample contributions.
Fixed resolution for PDF Card; user preferences for fully digitized pattern (on-the-fly calculations): user selectable resolution.
MATHEMATICAL BASIS FORFLUX ON SAMPLE
For simulated powder patterns we take the X-ray expressions from (Hubbard, et. al. (1976)). Using the internal standard method, corundum, Al2O3 is selected as the reference material for the I/Ic method. I/Ic is defined as a ratio of the strongest line of corundum for a 1:1 mixture by weight of the two phases.
More recently, POWD12 (Clark, et. al., (1973)) used the integrated intensity measure of all the peaks in the unknown compared to corundum. This is called the Reference Intensity Ratio. In addition to the 500 or so reference powder patterns from which the method has been built, the ICDD PDF-4+ now contains over 241,000 patterns with I/Ic calculated from structural data for X-rays and neutrons.
FOR X-RAYS ANDBRAGG-BRENTANO GEOMETRY
In Eq.1, the first bracket contains the source dependent terms,the second is the Thompson one-electron scattering,
the third is the sample dependent terms and the incident wavelength,and the last is the Lorentz-Polarization factor.
FOR NEUTRONS AND CYLINDRICAL GEOMETRY
The power per unit length is (Bacon, 1975):
In Eq. 2, the first term contains incident geometry and incident wavelength,the second contains the actual sample volume corrected for packing density,the third contains the multiplicity, j, and the Lorentz factor.
Ahkl is the absorption factor (energy dependent). The apparent density compared to the theoretical density,becomes the packing fraction for the powder in a cylindrical container.
We choose λ=1.5406 Å as the reference state so that I/I c =1.0for corundum at that wavelength.
CALCULATION OF THE LINEAR ABSORPTION COEFFICIENT
The cross sections are from Spears (1992) and are referenced to v=2.200 Km/s neutrons, with λ=1.79895 Å. Cross sections are in barns. The remainder of the quantities listed below have units as specified.
where MW is the molecular weight of the particular atomic species, and m is the mass fraction of species i.
NEUTRON ABSORPTION
Neutron Constant Wavelength (CW)Resolution Function
MACHINE WAVELENGTH U V WD1A 1.909 Å 354.11 -760.32 651.60
PDF-4+ Pref. 0.1964 -0.4217 .3614BT1 1.53966 Å 236.37 -283.25 167.50
PDF-4+ Pref 0.1311 -0.1571 0.0929HB2A(113) 2.4111 Å 398.46 -343.2 162.99
PDF-4+ Pref 0.2210 -0.1903 0.0904HB2A(115) 1.5378 Å 376.83 -510.25 273.15
PDF-4+ Pref 0.2029 -0.2830 0.1515“average” U,V,W
338.70 -474.23 313.72
PDF-4+ Pref 0.18785 -0.2630 0.1740“weighted” U,V,W
177.42 -240.24 162.82
PDF-4+ Pref 0.09840 -0.13324 0.09030
U,V,W are parameters in the “caglioti” function:
2
2 2
var tan tan
FWHM iancewhere U V W
σσ= =
= Θ+ Θ+
Note: PDF-4+ entries deal with angles in degrees;Whereas GSAS deals with angles in centidegrees
Neutron Constant Wavelength (CW)Resolution Function
The weighted FWHM values are lower-limit estimates for neutron resolution; as with x-rays this just means that Bragg peak resolution is slightly better than most instruments.
I/Ic for Quantitative Phase ID
3 2 2'2( )( )( )
8 sin 2 sinWs c
hklo
l jN FP V e AI r
λ ρπ ρ θ θ
−=
“Neutron Diffraction”, G. E. Bacon, 3rd
edition,Clarendon Press Oxford, 1975, p. 112.
4λ
Neutron Power/Unit Length:
X-Ray Power/Unit Length:
“The Reference intensity Ratio for Computer Simulated Powder Patterns”C. R. Hubbard, E. H. Evansand D. K. Smith, Acta Cryst. 9,169-174 (1976).
[ ]
[ ]
234 2
2 4 2 2
430
2 4)
2
2
1 cos 2)( )( )( )32 2 sin cos
( )( )32 )
2
, c is corundum
( Toi
absT rel
c
c c c
M FP ePR m c V
P eKR m c
MLp FI IK VI where subscriptI
λ θπ µ θ θ
λπ
γµ
µγρµ γ ρ
+=
=
= =
=
A Simple Case of Scattering Contrast V2O5
X-ray Case: V is the “heavy atom” scatterer;Much less information about the oxygen sublattices
Neutron Case: Oxygen is the “heavy atom” scatterer;Much less information about the vanadium sublattices
X-rays and NeutronsComplementary Tools
Scattering contrast Neutron scattering lengths (occupation factors,
etc.) Neutron Debye-Scherrer cylindrical geometry –
less preferred orientation We have created Hanawalt/Fink/Long8 searches
for neutron data We have created Normalized R-Index for total
pattern matching All of Sieve+ power for neutrons
Normalized R-Index forTotal Pattern Matching
where n refers to the number of data points, are the individual digitized values from the reference pattern (obtained using on-the-fly techniques from the PDF-4+) and are digitized values from the experimental pattern of interest.
Normalized R-Index (continued)
Modified from that shown by Faber and Blanton (2008): normalization factors for both the experimental pattern (count) and the calculated pattern (calc).
Normalization takes into account differences in temperature factors used in the calculated patterns when compared to the experimental pattern.
Normalized R-Index (continued)
The range of R(index) values is: 0< R(index)< 2. The lower the index value, the better the match.
Applications of the Similarity Index in the PDF-4+ can be applied to both the Search Results (DDView+) and Search-Indexing (SIeve+) search results.
Normalized R-Index, D1A Garnet Experimental Data
Ambient, Y, Al, Fe Search135 hit results
Background Removal
Normalized R-Index = 0.24(lowest 2 entries)
Best Match: Y3Fe2.03Al2.97O12PDF #: 04-005-8693
LLB, France2.4266 Å Data courtesy of Robert PapoularNikos Kourkoumelis (U. Ioannina, Greece)
TWO EXAMPLES OF PHASE ID USINGNEUTRON SCATTERING DATA
LLB, Saclay, France2.4266 Å Data courtesy of Robert PapoularNikos Kourkoumelis (U. Ioannina, Greece)
Ca5(PO4)3(OH) 04-017-1626CaO 04-017-9575
CaOCaO
Data courtesy Andrew Payzant Oak Ridge National Laboratory
Neutron diffractometer HB-2A at HFIR
Just (H and Mo and Mn and O)Generates 659 entries
Neutron diffractometer HB-2A at HFIR.Oak Ridge National Laboratory(Data courtesy of Andrew Payzant)
Highest GOM, Similarity Index, Use neutron default parameters, 31 candidate matches
Neutron diffractometer HB-2A at HFIR
3 Phase Match
Enlargement
Mn2O3MoO3
Mn(MoO4)
Three phase solution
Mn(MoO4) ………….MoO3…….Mn2O3
NEUTRON TOF RELATIONSHIPS
2( sec ) d + DIFA d + ZEROt micro onds DIFC= • •
[ ] [ ]{ }1 12( ) (1 ) ( ) ( ) Im exp( ) ( ) Im exp( ) ( )u v NH t N e erfc y e erfc z p E p q E qηηπ
∆ = − + − +
and 2 2
i ip t q tαγ βγα β= − ∆ + = − ∆ +
( ) ( )2 2
2 2
2 22 , 2 , , z=
2 2 2 2t tu t v t yα β ασ βσασ βσ
σ σ+ ∆ + ∆
= + ∆ = − ∆ =
4 2 2 2 2 2 4 21 0 1 0 1 2 0 1 2/ , / , , d d d d d dα α β β β σ σ σ σ γ γ γ γ= = + = + + = + +
Where∆t=t-tpeak, E1 is defined as an exponential integral,
,
,
.The details of these parameters and equations are spelled out in the GSAS Technical Manual, pp. 143-148.
SELECTED TOFPEAK SIMULATIONS
Snap-shot of the TOFtchProfileTest program using the POWGEN instrument parameter file. The d-spacing, d=4.1571A.
SELECTED TOFPEAK SIMULATIONS
LaB6(100)
NORMALIZATION – I/MICROSECOND
Ignoring for the moment the peak shifts due to the asymmetric profiles,And using a manual extraction for the 8 largest d reflections (ignoring intensities). We get the following tabulation:
These can then be imported into PDF-4+ 2014 for analysis by Sieve+ using a Long8 search:
SIeve+SEARCH/MATCH RESULTS
SELECTED PEAK, ISIS HRPD
Finding peak positions fromsimple peak findingwill NOT be effective
Recommendations
Encourage ICDD customers to supplement in-house x-rays, with data at national neutron and synchrotron facilities (tax-payer funded)
Encourage experimental data submission to ICDD (neutron and synchrotron)
Use these facilities to optimize scattering contrast Consider isotope substitution
Consider X/N analyses with Rietveld packages, e.g., GSAS, GSAS-II, JANA, FULLPROF, magnetic scattering
Move toward neutron tof – high resolution instruments rival in-house x-ray resolution and
TOF data in PDF-4+2016 with search/match from Sieve+tanQ cons t
Q∆ ≈
ACKNOWLEDGEMENTS
Acknowledgement: JF for support from the ICDD
Collaboration with:
J. Blanton, K. Zhong, S. Kabekkodu, O. Gourdon*,T. Blanton, T. Fawcett, C. Crowder
International Centre for Diffraction Data (ICDD), Newtown Square, PA
* Present address: Los Alamos National Lab, Los Alamos, NM
REFERENCES
Bacon, G. E. (1975). Neutron Diffraction, 3rd edition (Clarendon Press Oxford), p. 112 and p. 147.
Clark. C., Smith, D. K., and Johnson, G. G. (1973). “ A Fortran Program for Calculating X-ray Powder Diffraction Patterns, Version 5, Department of Geological sciences, Pennsylvania State University, University Park, PA. POWD12++ is Version 12 and has been subsequently developed at the ICDD.
Faber, J, Fawcett, T, (2002). “The Powder Diffraction File: Present and Future,” Acta Cryst. B58, 325-332.
Faber, J. (2004). “ICDD's New PDF-4 Organic Database: Search Indexes, Full Pattern Analysis and Data Mining,” Crystallography Reviews 10, 97-107.
REFERENCES (CONTINUED)
Faber, J. and Blanton J. (2008). “Full Pattern Comparison of Experimental and Calculated Powder Patterns using the Integral Index Method in PDF-4+,” Powder Diffraction 23, 141-145. See also Hofmann, D and Kuleshova, L. (2005). “New Similarity Index for Crystal Structure Determination from X-Ray Powder Diagrams”, J. Appl. Cryst. 38, 861-866.
Fischer P., Halg W., Roggwiller P., Czerlinsky E.R. (1975). “Distributions of Cations in Y-Fe-Al Garnets,” Solid State Commun. 16, 987.
Hubbard, C. R., Evans, E. H., and Smith, D. K. (1976). “The Reference Intensity Ratio, I/Ic for Computer Simulated Powder Patterns,” J. Appl. Cryst. 9, 169-174. The literature citations in this reference are particularly extensive.
Larson, A. C and Von Dreele, R. B. (2000). “General Structure Analysis System (GSAS),” Los Alamos National Laboratory Report LAUR 86-748. See also: Toby, B. H. (2001), “EXPGUI, a graphical user interface for GSAS”, J. Appl. Cryst. 34, 210-213. Note that Toby has published a number of useful web-based applications that allow calculation of absorption corrections.
Spears, V. F. (1992). “Neutron Scattering Lengths and Cross Sections,” Neutron News 3, 29-37.
REFERENCES (CONTINUED)