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Sample environment in experiments using X-ray synchrotron radiation
B. Buras
To cite this version:
B. Buras. Sample environment in experiments using X-ray synchrotron radiation. Re- vue de Physique Appliquée, Société française de physique / EDP, 1984, 19 (9), pp.697-703.
�10.1051/rphysap:01984001909069700�. �jpa-00245240�
Sample environment in experiments using X-ray synchrotron radiation
B.
Buras (* )
European Synchrotron Radiation Project, c/o CERN, CH-1211 Geneva 23, Switzerland
Résumé. 2014 Les anneaux de stockage à électrons (ou à
positrons)
modemes sontcapables
d’émettre des rayons X très intenses dans un spectre continuqui
s’étend jusqu’à 0,1 A. Cette lumière peut être produite dans les aimants de courbure ou dans des wigglers multipoles et wavelength shifters (écarteurs de longueur d’onde) installés dans les sections droites de l’anneau. Elle peut servir de façon immédiate aux expériences utilisant la lumière blancheet/ou après monochromatisation, aux expériences utilisant un faisceau de lumière monochromatique, dont la longueur d’onde peut être choisie à volonté dans le spectre continu émis. L’onduleur, un autre
dispositif
poursections droites,
produit
du rayonnement quasi monochromatique. Ces dispositifs installés dans les sections droites (wigglers, wavelength shifters et onduleurs) permettentd’adapter
le rayonnement synchrotron émis auxdemandes de l’utilisateur et peuvent donc être considérés comme premier élément
optique
de la ligne. Cet aspectest particulièrement important pour les expériences avec échantillons dans un environnement spécial parce que ceux-ci imposent des restrictions et sur les expériences de diffusion et sur les expériences
d’absorption.
Néanmoins,ces limitations peuvent être minimisées pour chaque cas
particulier
en trouvant la meilleure combinaison d’envi- ronnement d’échantillons spéciaux, de méthodeexpérimentale
employée, et du faisceau de rayonnement Xadapté
à
l’expérience
en ce qui concerne longueur d’onde, intensité, section efficace, divergence etpolarisation.
Ceci estdiscuté en quelque détail et illustré par des exemples.
Abstract 2014 Modern electron (positron) storage rings are able to emit very intense X-ray radiation with a conti-
nuous spectrum extending to 0.1
A,
frombending
magnets and insertion devices (wavelength shifters and multipole wigglers). It can be used directly for white beamexperiments
and/or for monochromatic beam experiments with wavelength chosen at will from the continuous spectrum. Another type of insertion device, called undulator producesquasi-monochromatic
radiation. The insertion devices enable the tailoring of the emitted S.R. to the requirementsof the users and can be treated as the first optical element of the beam line.
This feature is
especially
important forexperiments
with samples in special environment because the latter impo-ses limitations both on
scattering
andabsorption experiments.
However, these limitations can be minimized in each case by finding the best match between the design of the special environment, the experimental method used,and the X-ray beam tailored to the experiment with respect to wavelength. intensity, cross-section, divergence and
polarization.
This is discussed in some detail and illustratedby
examples.1. Introduction.
The
special
environment(e. g.
ahigh
pressurecell,
acryostat,
ahigh temperature furnace) imposes
ingeneral
limitations on theX-ray
studies. These limi- tations can be minimisedby finding
the bestpossible
match between the
design
of thespecial environment,
theexperimental
methodused,
and theX-ray
source.The main
goal
of this paper is to show that anX-ray synchrotron
radiation source is a very flexible sourcewhich can be tailored
individually
to therequirements
of the user and thus make it
relatively
easy to achieve (*) On leave from Copenhagen University and RisoeNational
Laboratory,
Denmark.REVUE DE PHYSIQUE APPLIQUÉE. - T. 19, N" 9, SEPTEMBRE 1984
a
good
match of the above mentionedrequirements.
The paper is
arranged
in thefollowing
way. Sec- tion 2 describesbriefly
the main features ofsynchro-
tron radiation
(S.R.)
and the devices used to define the incidentX-ray
beam. The limitationsimposed by
thespecial
environment are illustrated in section 3 with theexample
of a diamond anvilhigh
pressure cell. In section 4 the two diffraction methods -angle dispersive
and energy,dispersive
- arebriefly
recalled.In section
5,
theflexibility
of a S.R. source is discussedin some detail with the
example
of diffraction studies ofsamples
in a diamond anvilhigh
pressure cell.Similarly
theadvantage
of S.R. forabsorption
studieswith
samples
athigh
pressures arebriefly
mentionedin section 7. A
general
conclusion is made in section 8.48
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/rphysap:01984001909069700
698
2. Eléments of
synchrotron
radiation[ 1 ].
Electrons
(positrons) travelling
with avelocity
closeto that of
light along
a benttrajectory
emit electro-magnetic
radiation calledsynchrotron
radiation(S.R.).
In
practice
S.R. isproduced by high
energy electrons(positrons)
stored in a veryhigh
vacuum horizontal« torus » and forced onto a closed orbit
by dipole
magnets
(Fig. 1).
The « torus » iscomposed
of arcsof a
circle, placed
in themagnetic field,
andstraight
sections
joining
the arcs of the circle. These machinesare called storage
rings.
Fig.1. - Main components of an electron storage ring.
The radiation is emitted
tangential
to the arcs andis very well collimated in the vertical
plane (Fig. 2).
The
spectral
distribution of the radiation isdepicted
in
figure 3,
where thespectral
flux(called
in shortflux)
is defined asFig. 2. - Synchrotron radiation
emitted by
a relativistic electron travelling on a curved trajectory. B : magnetic field perpendicular to the electronorbit plane. 03C8 :
natural open-ing
angle in the vertical plane. P :polarization.
The slit S defines thelength
of the arc (angle cp) from which the radia- tion is taken.Fig. 3. - Spectral distributions of synchrotron radiation
emitted by electrons whose trajectory is determinated
by
(a) adipole
magnet, (b) a wavelength shifter and (c) a multipole wiggler. (Data for theproposed
ESRF.)integrated
in the verticalplane.
As can be seen fromfigure
3 thespectral
distribution is continuous. It is characterizedby
the so called characteristic wave-length Àc
which divides the spectrum into two parts ofequal
radiated power. It is related to the parameters of the storagering through
thefollowing equations :
where Â,
is inÀ,
thebending
radius p in meters, the electron energy in GeV and themagnetic
field intesla, For
example, E
= 5 GeV and B = 0.75 Tgives
p = 20 m
and Â,,,
= 0.89Á (1 ).
For an ideal electron
orbit,
the emitted radiation is very well collimated in the verticalplane
and theopening angle 03C8
isapproximately equal
toy -1,
whereFor the
example given above 4(
=10-4
radians = 0.1mrad - 20 seconds of an arc.
In real storage
rings,
the electron orbit is not ideal and theopening angle 03C8 might
be a bitlarger
butstill very small. The small
divergence
of the beam(1)
These are the parameters of the proposed EuropeanSynchrotron
RadiationFacility.
in the vertical
plane
results in ahigh spectral brightness (called
in shortbrightness)
defined as :The
high brightness
of S.R.plays
animportant
rolein
experiments
with smallsamples,
e.g. inhigh
pres-sure
cells,
inparticular
for « white » beamexperiments.
It is several orders of
magnitude larger
than that ofBremsstrahlung produced by
conventionalX-ray
tubes.
For
experiments
in which a monochromatic beam is focused at thesample (by
means of mirrorsand/or
bent
single crystals)
as, forexample,
in the case ofa
sample
in a diamond anvilcell,
the truefigure
ofmerit of the S.R. source is the brilliance defined as
As follows from
equation (1),
one candecrease Â,,, by increasing
themagnetic
fieldB,
and thus shift the whole spectrum toward shorterwavelengths.
This canbe done
locally
in astraight
section of the « torus ».Such a device is called a
single bump wiggler
or awavelength
shifter. Anexample
of a spectrum of radiation emitted from awavelength
shifter is shown infigure
3.At present also
periodic multipole
magnets arebeing developed forcing
the electrons to makewiggles
asshown in
figure
4. These magnets areplaced
instraight
sections of a storage
ring
andthey
are calledmultipole
Fig. 4. -
Trajectory
of electrons within a multipole wiggleror undulator.
wigglers
or undulatorsdepending
on their characteris- tic features.They
are best characterizedby
the socalled deflection
(or magnetic field)
parameterwhere
Bo
is thepeak magnetic
field intesla, à
is themagnet
spatial period
in millimeters and a is the maxi-mum deflection
angle.
A
sharp
distinction does not exist between multi-pole wigglers
and undulators. For K > 1 the device is called amultipole wiggler.
With amagnetic
fieldthe same as in the
bending
magnets it does not shift the spectrum but increases the fluxby
a factorequal roughly
to the number ofpoles (Fig. 3). However, by changing
themagnetic
field of themultipole wig- gler
the spectrum can also be shifted.For K. less than 1 or of the order of 1 strong inter- ference effects occur which result in a spectrum of the emitted radiation
consisting
of one(for
K1)
or several
(for
K -1) quasi
monochromaticlines,
called harmonics.The
wavelength
of the ithharmonie
at obser-vation
angle 0 (radians)
relative to the axis isgiven by
On the axis
(0
=0)
we haveand
only
odd harmonics are present. However, a finitepinhole defining
theangle
0 orspread
in theangle
of electrons
passing through
the undulator will result in the presence of even harmonics also. A spectrum for a small finitepinhole
ispresented
infigure
5a for y = 10 000 and K = 0.5.Figure
5bFig. 5. - Spectrum produced by an undulator with K = 0.5 ; (a) observed through a small pinhole on axis, (b) angle
integrated,
i.e. without the pinhole.700
shows the
angle integrated
spectrum from the sameundulator,
i.e. without thepinhole.
The natural relative band width of the emitted radiation for an
ideally parallel
electron beam isgiven by
where N is the number of
spatial periods.
It
follows, however,
fromequation (4)
that due tothe
dependence
of thewavelength
on the observationangle
the width of the observed line is broadened relative to its natural valuegiven by equation (6).
A
broadening
may occur also due to thedivergence
of the electron beam. A detailed discussion of these
phenomena
isbeyond
the scope of this paper.The
photon brightness
emittedby
aparallel
beamof electrons at the ith harmonic in the forward direc- tion is
proportional
toN 2 y2
and the electron current.It is much
larger
than one can obtain frombending
magnets or
multipole wigglers.
3. Limitations
imposed by
thespécial
environment.We discuss
sample
environmentproblems using
theexample
ofsynchrotron X-ray
diffraction studies ofsamples
in a diamond anvilhigh
pressure cell.Figure
6shows the
principle
of such a cell. Thesample
isplaced
in a small hole o.1-0.3 mm in diameter made inFig. 6. - Principle diagram of a diamond anvil high pressure
cell.
an 0.01-0.1 mm thick metal foil
(gasket).
The pressure is exertedby
the two flat diamond facespressed against
each other.
The main limitations
imposed by
thehigh
pressure cell onX-ray
diffraction studies are thefollowing :
a)
theabsorption
of the incident and diffracted beamsby
thediamonds,
b)
the limitation in thescattering angle,
c)
the small cross-section and the small volume of thesample.
As will be shown in sections
5-6,
due to theflexibility
of a modern
synchrotron
radiation source, discussed in section2,
these limitations can be minimized.4. Diffraction
techniques [2].
As is well
known,
there are two diffractiontechniques
for
powdered samples, namely,
theangle-dispersive
and the
energy-dispersive
diffraction.In the
angle-dispersive
method a monochromatic beam ofwavelength Ao
is selected from the white SR beamby
means of acrystal
monochromator and theintensity
of the beam diffractedby
thepowdered sample
is measured as a function of thescattering angle
2 0. In theenergy-dispersive
method[2]
thescattering angle
200
is fixed and the white SR beam isimpinging
on thesample.
Thewavelength (photon energy) composition
of the diffracted beam isanalysed by
means of a solid state detector(SSD).
Because ofthe fixed
scattering angle
theenergy-dispersive
methodis
especially
suitable for diffraction studies ofsamples
in
special
environments and is at presentwidely
usedfor
high
pressure research.The
Bragg equations
for the two methods are :for
angle-dispersive diffraction,
andfor
energy-dispersive diffraction, (dH
denotes theinterplanar spacing, EH
thephoton
energy and H the set of reflection indicesHKL).
For the purpose of our
discussion,
theintegrated
intensities
[3]
can beexpressed conveniently
in thefollowing
way :angle-dispersive
diffraction :energy-dispersive
diffraction :with :
where
1(À)
is the number ofphotons/s . cm2
and per unit interval ofwavelength
incident on thesample, T(À)
the transmissionfactor, 039403B80
the overall diver- gence of the beam in the energydispersive method,
Ca constant
depending
on thegeometry
of theexperi-
ment,
sample
volume and unit cellvolume, j
is themultiplicity
factor andFH
the structure factor. R (a)and R(e) determine the relative
wavelength
bandwidths related to reflections in both
methods,
res-pectively.
In order tosimplify
our discussion we assume that R (a) =R(e).
For the same reason weneglect
thepolarization
factors and detector efficiencies.We are, of course, interested
only
in thejH | 1 F H 12
values,
but we measure, as can be seen from equa- tions(8),
these values « modulated »by
factorsin the
angle-dispersive
andenergy-dispersive methods, respectively.
In the next section we discuss thedepen-
dence of these modulation factors on
wavelength
and
angle.
5.
Flexibility
of the S.R. source.We discuss first the
dependence
of1(À) 03BB4 T(À)
onwavelength,
and in order tosimplify
the discussion further we do not take into account theabsorption
inthe
sample.
Figure
7shows,
as anexample, i(Â)
and1(À) À.4
atFig. 7. - i(Â),
i(À.) À,4
T(À) and i(Â) À.4 T(À.) as functions ofwavelength of synchrotron radiation with a characteristic
wavelength of 0.55 A (see text).
the
position
of thesample
located in the electron orbitplane
40 m from thebending
magnet sourcepoint
of D4RIS
(5 GeV, 1 mA, R
= 12.12 m,A,
= 0.54À).
The
figure
also showsT(03BB)
for an empty cell com-posed
of twodiamonds,
each 2.5 mm thick. Wenotice that
i(03BB) 03BB4
favourslong wavelengths
andT(03BB)
the short ones, as
expected
As a result1(À) 03BB4 T(03BB)
reaches a maximum at about 0.8
A
and falls off veryrapidly
on both sides.The character of the
1(À)
À4T(À)
curv c does notchange
if one uses amultipole wiggler
source insteadof a
bending
magnet source of the same critical wave-length, although
all values ofi(À) À4 T(À)
increaseby
a constant factor
equal roughly
to the number ofpoles, resulting
in a decrease inmeasuring
time. Asingle- bump wavelength-shifter,
however, shifts the curvetoward shorter
wavelength,
as can be seen from theexample
infigure
8.Accepting
a decrease atlong
wave-lengths
one obtains again
at shortwavelengths.
Thus1(À) À 4 T(À.)
can be tailoredaccording
to therequire-
ments of the
experiments.
Fig. 8. - i(Â) l4 T(Â) as a function of wavelength for syn- chrotron radiation of two critical wavelengths, 0.27 A and 1.08 A.
We discuss now the influence of the modulation factor on the
X-ray
pattern,beginning
with the ençrgy-dispersive
methodFigure
9shows,
as anexample,
M(e) as a function of theinterplanar spacing d.
fortwo
scattering angles,
100 and 200. We notice that the modulation factorchanges rapidly
with theinterplanar spacings
Thus the accuracy of measure- ments due to the statistics is very different for diffe- rentparts
of thepattern.
In the
angle-dispersive
method onemight
tend touse a
wavelength corresponding
to the maximum of the1(%.)
Î..4T(/u)
curve. However, as can be seen from702
Fig. 9. - The modulation factor M(e) for the
energy-dis- persive
method as a function of the interplanarspacing
fortwo scattering angles, 10° and 20°.
figure
10 the limitation in thescattering angle
putsa lower limit on the range of measured
interplanar spacings.
If it is notpossible
to increase 26max by
a proper
design
of the pressurecell,
then one is forcedto use a shorter
wavelength
with a smalleri(À.o) À. 4 T(/))
value
leading
to an increase of themeasuring
time.As can be seen from
figure
10 the modulation factor M(a)changes
alsorapidly
in theangle-dispersive
method.
It follows from the above discussion that
by shifting
the emitted spectrum and
increasing
theintensity
incident on the
sample
one is able to match the S.R.Fig. 10. - The modulation factor M(a) for the angle-dis- persive method as a function of the interplanar
spacing
forthree different wavelengths,
;’0
= 0.2Á,
0.4 À and 0.8 Á.to the
requirements
of theexperiments
in each indivi-dual case. For
angle-dispersive
diffraction one canalso use
properly designed
undulators with their veryhigh
brilliance.6. The small cross-section and small volume of the
sample.
In order to avoid diffraction lines from the
gasket, obscuring
theX-ray
pattern, and in order tokeep
thebackground
as low aspossible,
it ismandatory
thatthe
X-ray
beam hits thesample only.
In recent expe- riments with pressures up to several hundred of kbar the beam cross-section istypically
0.1 x 0.1mm’.
In the
megabar region
these dimensions must beeven smaller. This
points
to both(i)
thenecessity
to use a very
good
collimated incidentbeam,
and(ii)
ahigh precision
of the movements of thehigh
pressure cell in the vertical and horizontal
planes.
The collimation of the incident beam is determined
by (i)
the sourcedimensions, (ii)
thesample
dimen-sions,
and(iii)
the distance between the source and thesample.
For dimensions of the source of about 1 mm in eachplane, typical
for most of thepresent machines,
a 0.1 x 0.1mm’
slit in front of thehigh
pressure cell and a 30 m
source-sample distance,
thecollimation in the horizontal and vertical
plane
amounts to about 0.03 mrad or 7 seconds of arc. This
Fig. 11. - Absorption of SmS at différent pressures as
function of incident photon energy [3].
is
satisfactory
for mostexperiments
which indicates that - at least at present -high
pressure energy-dispersive
diffractionexperiments
do not need smallersource sizes. It indicates also that as far as collimation is concerned the horizontal and vertical
scattering planes
areequivalent. They differ, however,
with respect topolarization and,
as it is wellknown,
avertical
scattering plane
ispreferable
in this respect.For
angle-dispersive
diffraction onemight
focus thebeam on the
sample
and then a small source size isimportant.
The volume of the
sample,
asalready mentioned,
isvery small
(10- 3-105 mm3),
whichespecially
inpowder
diffraction results in a very small
intensity
of thediffracted beams and thus increases the
measuring
times. This
points
to both thenecessity
ofusing
moreintense
X-ray
sources and less timeconsuming measuring techniques.
Asynchrotron
radiation sourceand the
energy-dispersive
method haveproved
to bea
good
solution to thisproblem [2].
It follows from the discussion above that small
samples require
a source ofhigh brightness
forenergy-dispersive
diffraction and a source ofhigh
brilliance for
angle-dispersive
diffraction.7.
Absorption
studies athigh
pressures.The
high brightness
ofsynchrotron
radiation sourcesalso allows
absorption
measurements ofsamples
inspecial
environments.Figure
11shows,
as anexample,
results of
absorption
measurements of SmS at diffe- rent pressures as function of incidentphoton
energy[4].
One notices the shift of theabsorption edge
withpressure
indicating
valencechange
of Samarium from 2+ to 3+.8. Conclusion.
As could be seen from the above discussion a modern storage
ring
is an excellent source ofX-ray
radiationfor studies of
sampler
inspecial
environments. This is due to the fact that thebrightness
and brilliance of such a S.R. source are much greater than those of X- ray tubes and that it can be tailored to therequire-
ments of the
experiment.
References
[1] Handbook on Synchrotron Radiation, edited by
E. E. Koch (North-Holland Publishing Com-
pany, Amsterdam) 1983. See also European Syn-
chrotron Radiation Facility, Suppl. II : The Ma- chine, eds. D. J. Thompson and N. M. Poole
(European Science Foundation,
Strasbourg,
Fran- ce) May 1979.[2] See, for example, BURAS, B., FOURME, R. and KOCH, M. H. J., ibid p. 1017-1090 and references therein.
[3] BURAS, B., Nucl.
Phys.
Methods 208 (1983) 563-568.[4] FRANK, K. H., KAINDE, G., FELDHAUS, J., WORTMAN, G., KRONE, W., MATERLIK, G., BACH, H. in Valence Instabilities edited by P. Wrachter and H. Boppart (North-Holland Publishing Com-
pany, Amsterdam) 1982, p. 189-194.