Angus P. Wilkinson
School of Chemistry and Biochemistry
Georgia Institute of Technology
Atlanta, GA 30332-0400
Thanks are due to Alan Hewat and Ian Swainson for many of the slides

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Comparison of X-ray and neutron scattering
Applications of neutron diffraction
– “Light” elements
– Magnetism
– High Q data
– Penetration
What is a synchrotron and why use one?
Resonant scattering and the determination of complex cation distributions
Where X-rays meet neutrons – in the high energy regimen
Summary

X-rays Neutrons
Atomic scattering power varies smoothly with atomic number
Atomic scattering power varies erratically with atomic number
Atomic scattering power decreases as the scattering angle increases
Atomic scattering power is constant as the scattering angle changes
Largely insensitive to magnetic moments
Readily available as intense beams
Scattered by magnetic moments
Low intensity beams
Typically, strongly absorbed by all but low Z elements
Weakly absorbed by most materials

YBa
2
Cu
3
O
7 drawing from Capponi et al.
Europhys Lett 3 1301 (1987)
 Structure of the 90K high
T c superconductor
– Left -by X-rays
(Bell labs & others)
– Right -by Neutrons
(many neutron labs)
 The neutron picture gave a very different idea of the structure important in the search for similar materials.

 Hydrogen storage in metals
– Location of H among heavy atoms
– No single crystals
 Laves phases eg LnMg
2
H
7
(La,Ce)
– Binary alloys with large/small atoms
– Various arrangements of tetrahedral sites can be occupied by H-atoms
– Up to 7 Hydrogens per unit
Gingl, Yvon et al. (1997) J. Alloys Compounds 253, 313.
Kohlmann, Gingl, Hansen, Yvon (1999) Angew. Chemie 38, 2029. etc..

 Neutrons see hydrogen well – perhaps too well.
 Neutron incoherent scattering is an isotropic “random” scattering of neutrons. This is the basis of some techniques (quasi-elastic neutron scattering) but is a killer for neutron, at least powder, diffraction.
– Deuterate to avoid problems. This can be difficult and may change what you want to examine. For example, cement hydration in H
2 that in D
2
O
O is different from
% b c b i s c s i s s s a
H 99.985
-3.741
25.27
1.758
80.27
82.03
0.3326
D 0.015
6.671 4.04
5.592
2.051
7.643
0.000519
Unit of b is fm.
Unit of cross-section s is 4 p b 2 in barns (100 fm 2 ). s s
= s i
+ s c

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X-ray scattering amplitude is strongly dependent on sin q/l making it very difficult to get good quality x-ray data at high sin q/l
– This can give problems with determining “thermal parameters”
Neutrons give good signal at high sin q/l

 Time-of-flight neutron diffraction facilitates the collection of data to very high Q (small dspacing)
– No form factor fall off
– Highest flux at short wavelength
 Similar experiments can also be done with very high energy synchrotron radiation
Cu K a
Mo K a
Ni metal, synchrotron radiation, GE detector
From Peter Chupas

 MnO, NiO and FeO order antiferromagnetically
 After taking into account the arrangement of unpaired spins the unit cell is twice as big as the atomic arrangement would suggest
– So you get extra peaks in the neutron diffraction pattern

 Extra peaks are only present in the neutron diffraction pattern at temperatures where the unpaired spins are ordered (below Neel temperature).

 Neutrons can pass through a reasonable thickness of metal. This makes it easier to build sample environments
– No Be windows or other special approaches needed
– V and some alloys such as TiZr have essentially zero coherent scattering cross section and do not give any Bragg peaks

• Al vacuum body
• Water-cooled base
• W or Ta radiant elements
• Mo-foil heat shields
• 6 kW of power
• Turbo vac. 10 -7 Torr base pressure, 5e -6 at 2000K
• Gas inserts, static or purge
Courtesy of I. Swainson

• 1.5K to RT
• 200mK-1.5K He 3
• Up to 9T vertical field
Courtesy of I. Swainson

 Pressure is problematic for neutrons, due to low flux
 Usually need large sample volume and P = F / A acts against you Gas pressure cell made from aluminum.
Max P ~ 0.5 GPa
 But improvements in neutron optics, new sources (SNS etc) combined with advances in preparing large high strength single crystals (diamonds and Moissanite) for large volume gem anvil cells and the availability of devices such as the Paris-Edinburgh cell are expanding the accessible area of PT space

Neutron are not without absorption problems!
Tb
Dy
Ho
Er
Tm
Yb
Lu
Element Mean s a
Ce 0.63
Pr
Nd
11.5
50.5
Pm
Sm
Eu
Gd
168.4
5922
4530
49700
23.4
994
64.7
159
100
34.8
74
Hf 104.1
Isotope % s a
152
Gd 0.2 735
154
Gd 2.1 85
155
Gd 14.8 61100
156
Gd 20.6 1.5
157
Gd 15.7 259000
158
Gd 24.8 2.2
160
Gd 21.8 0.77
• Other (non-REE) absorbers include Cd and B
• 11 B, 7 Li however are relatively cheap to buy.
Courtesy of I. Swainson

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High intensity
Plane polarized
Intrinsically collimated
Wide energy range
Has well defined time structure

 The high level of intrinsic collimation and high intensity of the source facilitates the construction of powder diffractometers with unrivaled resolution
– More information in the powder pattern
 Can achieve good time resolution, although not combined with ultrahigh resolution
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Can do experiments at short wavelengths
– Facilitates collection of high Q (small d-spacing) data, and reduces or eliminates problems due to absorption
Can do resonant scattering
– Chose a wavelength close to an absorption edge and tune the scattering power of the elements in you samples

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Crystal analyzer gives very good resolution, low count rate and is insensitive to sample displacement, useable with flat plate or capillary
Soller slits give modest resolution, good count rate and insensitivity to sample displacement
Simple receiving slits give good count rate, easily adjustable resolution, can be used with flat plate or capillary

11BM high resolution diffractometer
12 channel analyzer system

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Many real materials do not have just one species on a given crystallographic site
– YBa
2
Cu
3
O
7-x
» Can have both oxygen and oxygen vacancies on a given site
– Zeolites, M x
[Si
1-x
Al x
O
2
]
» Extraframework cations M occupy sites that may also have vacancies and water present
» Al may not be randomly distributed over all available sites
– NiFe
2
O
4
» What is the distribution of nickel and ion over the tetrahedral and octahedral sites in the spinel?
It can be difficult to pin down the distribution of species over the available sites

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Bragg scattering provides a measure of the scattering density at a particular crystallographic site
F hkl
=  i n i f i exp[

8 p
2
U i
(sin
2 q
/ l
2
)] exp[ 2 p i ( hx i
+ ky i
+ lz i
)]
With one diffraction data set it can be very difficult
/impossible to estimate, x i n i and U species on nominally the same site i for multiple
– typically we assume that the x i and U species at nominally the same site i
» This may be a gross approximation!
are the same for all
– to estimate individual n i the species must differ in scattering power, even then more than two species can not be handled
» Determining Mn/Fe distribution in MnFe
2
O
4 using neutrons is easy

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In some cases lab x-ray data does not generate enough contrast to solve a problem
– Ni/Fe distribution and other “neighboring element problems”
Neutrons may generate the needed contrast
– But not for Ni/Fe!
More than one data set with different scattering contrast levels may be needed
– Differing scattering contrast data set per species on the site?
» constraints on composition and site occupancy reduce this requirement
– Can get these additional data sets by isotopic substitution and neutron scattering or by resonant x-ray scattering

 Isotopic substitution is very expensive
 Different isotopically substituted samples may not be the same!
 Resonant x-ray scattering makes use of the same sample for all measurements
 Reliable resonant scattering factors can be awkward to get
 Absorption and restricted d-spacing range can be a problem with resonant scattering measurements

 The elastic scattering is given by, f ( E , Q )
= f o
( Q )
+ f ' ( E )
+ if " ( E )
 For a spherical atom, f o
Q
=
p
 

0 r 2

r
Qr dr
Qr

 f” “mirrors” the absorption coefficient f " ( E )
=
2 p mc

0 e
2 h
E
 a
 f’ is intimately related to the absorption coefficient f ' ( E )
=
2 p



0
Ef
( E
0
2
" ( E )

E
2
) dE

8
4
42
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Cd location in the type I clathrate Cs
8
Cd
4
Sn
42
– Is the Cd randomly distributed over all the available framework sites?
– Distribution of Cd effects Seebeck coefficient and thermoelectric performance
– Cd absorbs neutrons
Cd and Sn have similar atomic number
– essentially indistinguishable by X-ray scattering unless Xrays have energy close to absorption edge
– collect data at 80 keV, Cd K-edge and Sn K-edge
» more good data improves reliability of the results
» Scattering factors estimated from absorption measurements
Chem. Mater. 14 , 1300-1305 ( 2002 ).

8
4
42
 Anomalous scattering terms calculated from
Kramers-Kronig transformation of absorption data
4.5
4
3.5
3 f"
2.5
2
1.5
-8.5
-9
1 -9.5
0.5
-10
29180 29190 29200 29210 29220 29230 29240
Energy / ev
-6
-6.5
-7
-7.5
f'
-8

8
4
42
 Selecting an X-ray energy close to an absorption edge distinguishes Cd from Sn
Diffraction data recorded at up sin q
/ l ~0.7Å -1

8
4
42
 Cd is located only on 6c sites
– From analysis of data collected at 80 keV and both the Cd and Sn K-edges
Type I framework. 6c site (red), 16i site (grey) and 24k site (green)

 High energy X-rays offer many of the advantages associated with neutrons – along with a lot more flux!
– Can use massive sample environment due to penetrating nature of X-rays
– Can map out phase and stress distributions inside parts due to penetrating power
– Systematic errors due to absorption and extinction are eliminated
– Can make measurements to very high Q
» provides a lot of structural detail

 Synchrotron based instruments offer very high resolution, excellent peak to background ratio, high data rates, low absorption and the ability to tune an elements scattering power
 Synchrotron instruments are expensive and the data is often harder to analyze than that obtained using neutrons
 Neutrons excellent for low Z element problems
 Neutrons usually the tools of choice for magnetism