J. Faber, Faber Consulting, Thornton, PAjgfaber@verizon.net

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)