Diffrazione ad “alti” angoli su un 2 Diffrazione ad “alti” angoli su un 2 assi:assi:
i problemi, le misure & l’analisi datii problemi, le misure & l’analisi datiEleonora GUARINI Eleonora GUARINI
Dipartimento di Fisica, Università di FirenzeDipartimento di Fisica, Università di [email protected]@fi.infn.it
Giornate Didattiche 2010 Giornate Didattiche 2010
Hotel Steinpent, S. Giovanni in Valle Aurina 27 – 30 Giugno 2010
Società Italiana di Spettroscopia Neutronica
OutlineOutline
What we measure Versus what we look for
The ideal neutron scattering experiment
A first step towards the real case: neutrons in a material
The real experiment: effects influencing the neutron measurements
Basic treatment of neutron diffraction data
Tailoring and Performing an experiment on a 2-axis diffractometer
The sought-for quantityThe sought-for quantity
The central quantity in the study of the microscopic structure of an isotropically scattering sample (a liquid, a powder…) is
N
,
ii eeN
,QSdQS1
001
RQRQ
STATIC STRUCTURE FACTOR
The accessible quantity The accessible quantity On a two-axis diffractormeter (fixed incident energy, angular dispersive) we measure:
2I
Origin of the accessible Origin of the accessible quantity Iquantity IThe double-differential cross section for nuclear neutron scattering
(b’s are the scattering lengths) is
,
tiiti eebbN
edtk
k
dd
d RQRQ 0
0
12 1
2
1
the probe the probe fingerprintfingerprint
While, from the theory of space- and time-dependent correlation functions, it is found:
N
,
tiiti eeN
edt,QS1
01
2
1
RQRQ
Let’s make the resemblance between double-differential cross section and S(Q,) more evident as:
,
tiiti eebbN
edt,QS~
,QS~
k
k
dd
d
RQRQ 0
0
12
1
2
1
Were the scattering lengths (i.e. the fingerprint of the probe we are using) absent, this would be exactly the dynamic structure factor
with
ωΩ
σ)η( ΔΩΦ2
2
1 dd
dNk,I
beam detector sample
Origins II… (in the ideal Origins II… (in the ideal casecase))
2k0
k1
2Q
k0
k1 2
120
2
10
10
10
2
,,
kkEEE
kkfQ
m
kkQ
Restrictions:no magnetic effects, no polarizations.
Assumption:fixed incident energy E0
Energy analysis of emerging neutrons
(,)
In the ideal case ALL relevant quantities are exactly definedA “size-less” perfectly straight beam (of flux ) is supposed to impinge on a “size-less” sample composed of N atoms, all equally exposed to the beam (a paradox, nearly!).
Even in such ideal conditions, the “measured” signal
would NOT coincide with the double-differential cross section. The latter, in turn, DOES NOT give immediately the dynamic structure
factor
Counts per unit time and unit
frequency interval
Origins III… Origins III…
Our 2-axis diffractometer is UNABLE, however, to perform an energy analysis
of the emerging neutrons…What we actually collect at the detector is:
!!QSBA,QS~
k
kkdN
dd
dkdN,IdI
tcos
tcostcos
0
11
2
2
1
22
)η( ΔΩΦ
ωΩ
σ)η( ΔΩΦ22
0
00
This quantity differs EVEN from the differential cross-section, which is defined as:
related to related to the probe the probe fingerprintfingerprint
ωΩ
σ2
2
2
0
dd
dd
d
d
tcos
because of the detector’s efficiency dependence on the energy of the scattered neutrons.
BUT,BUT,if inelasticity effects are if inelasticity effects are
SMALL…. SMALL…. i.e., … if E0 >> E , then:
elQkkQ
sin212 cos211 000
0
20
0
20
21 1 kkk
elQtetancosQtetancos
~0
2
00101 constant Efixedatkkkk
and also:
2coh
2inc0
2
cost
0
cost
0
2
1
2
andwithΩ
σ)η( ΔΩΦ
ωΩ
σ)η( ΔΩΦ
)η( ΔΩΦωΩ
σ)η( ΔΩΦ2
0
0
bBbA!!QSBAd
dkN
dd
ddkN
,QS~
dkNdd
dkdNI
Qtcos
per un monoatomico e monoisotopico
Dreaming a little Dreaming a little more...more...
The idealized diffraction experimentidealized diffraction experiment would require the combination of:
- a “perfect” instrument- an “ideal” sample
- a direct I(2) S(Q) relation
the perfect the perfect diffractometerdiffractometer
the ideal samplethe ideal sample
No background
Uniform and collimated beam
Perfect k0 definition
High angular resolution
Detector efficiency 100%
Some features ofSome features of
Bare and highly scattering
No absorption
“point-like” (no size, no MS)
Fully Coherent
Simple
“Extremely interesting”
TO OPTIMIZE YOUR EXPERIMENT AND SAMPLE PREPARATION YOU NEED TO KNOW WHAT ARE the PROBLEMS IN NEUTRON SCATTERING AND DIFFRACTION…
xIxI T exp0
Towards the real Towards the real case .I.case .I.Beam attenuationBeam attenuation
When a neutron beam goes through a material, the beam intensity is attenuated because of the 2 possible processes able to remove neutrons from the beam, i.e. absorptionabsorption and scatteringscattering.
Consider the simplest case where a uniform, collimated, and monochromatic beam crosses a homogeneous slab sampleslab sample perpendicular to the beam axis:
0 L
dx
x
I0
What is What is TT ? ?T is necessarily proportional to:
-the ability of an atom to scatter and absorb (total cross section)-the number atoms (i.e. present removing units)
asTTT n withThus,
Towards the real case .II.Towards the real case .II.Transmission & Attenuation Transmission & Attenuation coefficientscoefficients
LnI
LxIT 0T
0
exp
Fraction of
transmitted neutrons
The transmission of a slab sample is
Of course, R = 1 -T is the fraction of removed (scattered or absorbed) neutrons.
Can we further generalize the “transmission” concept in order to take into account:-any sample and beam shape- that some neutrons are NOT scattered in the beam (i.e. forward) direction and that scattered neutrons too can be absorbed or scattered again (the overall attenuation should depend also on the specific, -dependent, path after scattering)
?A first improvement is the Paalman&Pings coefficient,first introduced for X-rays diffraction (elastic scattering):
y
0x
2P 2
12 scatTincT ,PPexpdV
VA ill
ill
so that 222 11 IAI exp
0° 120°2
A(2)
0.68
0.70
Liquid in a cylindrical container
Towards the real case .III.Towards the real case .III.Multiple scattering Multiple scattering
If a neutron is scattered once, it can be scattered If a neutron is scattered once, it can be scattered twice... (thrice, etc.)!twice... (thrice, etc.)!
Multiple scattering affects the sought-for signal (i.e. the single-scattering intensity I(1), related to the double-differential cross section) in a two-fold way:
It removes singly scattered neutrons from the original direction. Therefore it ATTENUATES the single scattering single scattering intensityintensity detectable at a given angle
It contributes to the intensity detected at ‘another’another’ angle. Therefore it INTENSIFIES the signal, mixing up with the true true single scatteringsingle scattering component at a given angle.
Multiple scattering causes both the loss of Multiple scattering causes both the loss of “good” neutrons“good” neutrons
and the detection of “bad” ones! and the detection of “bad” ones! Generally, one can write:
exp)2(exp)(exp)(exp1expwith IIIII mm
The multiple scattering intensity can be evaluated, starting from the double contribution, by Monte Carlo integration. Different degrees of approximation are possible.
2
k1 + k1k0 + k0
2e
The real-life situationThe real-life situation R
eal in
str
um
en
tR
eal in
str
um
en
tR
eal sam
ple
Real sam
ple
Effect Uncertainty on Main consequence Background noise (hopefully constant in time!) Zero-signal level
Beam divergence Focussing devices 2, E0, paths in the sample
Monochromator characteristics: crystal quality
E0
Finite detector size 2, paths in the sample
Affect Q and E resolution
Detector efficiency Signal attenuation and distorsion
Container scattering and absorption Bare sample signal “Background”, attenuation
Sample absorption Signal attenuation
Sample scattering Multiple scattering
Finite sample size 2, paths in the sample
Q resolution,
absorption multiple scattering
Incoherent too and “complex” ……. ……..
,MS
Instrumental Instrumental effects .I.effects .I.
Background noiseBackground noiseIt partly depends on the sample+container, and requires specific measurements. In principle, one should perform: Beam stop
Void sample position
1) An empty beam run (no sample+container) in order to collect IEB(,) which approximates the thorough instrumental noise.2) A run with a “full” absorber (typically Cadmium) in place of the sample+container system. The collected ICd(,) is due to those background neutrons which are unaffected by the presence of sample + container.
Sample-like Cd specimen
That part of background which is modified by the sample+container can be estimated as:
- =Attenuated background
I b(s+c) ICd + Tsc (I EB – I Cd) (changing with the sample density)
Instrumental Instrumental effects .II.effects .II.
Detector efficiencyDetector efficiencyIt is measured by the absorbing power of the detection system, i.e. by
the coefficient R seen before, with T = abs. Efficiency depends on:a) the specific absorbing material (abs) b) geometryc) energy of the neutrons (scattered by the sample and) reaching the detector, because of the absorption dependence on energy.
For a slab detector with gas density nD and thickness L:
Lknk D 1abs1 exp1
For a cylindrical detector perpendicular to the beam, with radius r and density nD:
r
y
0
dy
x
L(y)
r
rkn
yrkndyr
k
D
r
D
1abs
0
221abs
1
2exp1
2exp1
1
Sample-related Sample-related effects .I.effects .I.AttenuationAttenuation
Due to absorption and multiple scattering in the sample we have 2222 111
ss,sexp
ss IAII
As,s() is a “generalized transmission”(volume average of transmission over the possible paths contributing to the intensity at 2)
It depends on (because of sample geometry)
It depends on (because of the absorption
dependence on E1)BUT INELASTIC EFFECTS ARE TYPICALLY NEGLECTED IN THE
EVALUATION OF THE ATTENUATIONThe expression of As,s (2) can however be derived by taking geometrical and size effects into account...
Attenuation & size-effectsAttenuation & size-effects
Let’s write our best expression for Is(1) exp(2):
D,P,
dd
dd
D,PL
cos
PdSdVnI
scatTtrue
incT
S
d
V
ills
exps
dill
s
1
2
12
01
exp2
exp2
0
with = 0 - 1 AND L = L(P,D) = (P,D) true = true(P,D)
If we neglect the (weak) dependence of 2true on P and D, as well as the energy dependence of T over the scattered flight path, we can still factor out a sort of “Paalman&PingsPaalman&Pings" coefficient including size-effects:
2
0022
11
exp
220
D,PL
cosdSdV
D,PPD,PL
cosdSdV
,dd
ddNI
dill
s
dill
s
S
d
V
ills
scatTincT
S
d
V
ills
exps
Sd /LD
2
222 11s,ss
exps AII
θtrue
L
D
θ
LD
P
dSd
0
1
Correction for Correction for AttenuationAttenuation
A priori experimental “correction”A priori experimental “correction” (minimization):Level 0: use of low absorption samples if possible (isotopic substitution)
Level 1: use of thin and symmetry-adapted samples, compatibly with intensity needsLevel 2: ‘maximize’ the incident energy, compatibly with the property under study(your wavelength should fit your “d-spacings”!!)
A posteriori correctionA posteriori correction:
Expt.orCalc.
For each 2 of the experiment, calculate As,s()!
The only practicable way is by Monte Carlo integration. Still, it is a time-consuming procedure.(Otherwise, simulate directly the single-scattering intensity… but youneed a good model for the unknown double differential cross section…)
To simplify things, it is often assumed that:
As,s(2) As,s( = 0, = 0)= Ts
Complication: Complication: the the containercontainerIn neutron experiments on liquids the container plays an important
role. It contributes to the measured intensity (additional ‘background’). The scattering from the container is (as for the sample) attenuated:
1.
It contributes to the attenuation of the signal from the sample.
2.
In turn, the sample attenuates the scattering from the container. An empty can run is NOT the true container contribution in a s+c measurement.
3.
c,c c,sc c,c
s,sc
expcs
expcs
exps
cc,cexp
c
csc,cssc,sexp
cs
ITII
IAI
IAIAI
111
11
111
222
22222
Correction for Correction for attenuationattenuation
in the presence of a in the presence of a containercontainer
A priori experimental “correction”A priori experimental “correction” (minimization):
A posteriori correctionA posteriori correction:
Level 0: use of low absorbing and low scattering materials
Level 1:
Level 2: ‘maximize’ the incident energy, compatibly with resolution requirements
use of thin containers, compatibly with sample conditions (e.g. pressure) or environment (cryostat/furnace).
For each 2 of your experiment, calculate Ac,c(2), Ac,sc(2) and As,sc(2) !!!
Example:
dill
c
dill
c
SV
dill
c
SV
dill
c
sccdSdV
adSdV
A
exp
,,
D,PPD,PPa sscat
sT
sinc
sT
cscat
cT
cinc
cT 0000
Monte Carlo integration(P,D) couples are randomly sampled over the 5-dimensional space (Vc
ill + Sd)
(in the elastic approximation)
PAUSA?????
Sample-related Sample-related effects .II.effects .II.
Multiple scatteringMultiple scatteringDue to multiple scattering in the sample we have
222
222232
11
exps
exps
expms
expms
exps
exps
exps
III
IIII
But we can’t measure Is(m)exp and we don’t know the scattering law.
L
θθ1
θ2
LD
D
P1
dSd
P2
1 2
0
Correction for Multiple Correction for Multiple ScatteringScattering
A priori experimental “correction”A priori experimental “correction” (minimization):
A posteriori correctionA posteriori correction:
Level 0: use of “low”-scattering, “small” and beam-adapted samples, compatibly
Level 1: subdivide the sample in a series of smaller samples by using absorbing
with intensity requirements
spacers parallel to the beam direction.
It is based on the use of approximate models for (Models can be refined by an iterative procedure)
Given a model, a way is to simulatesimulate multiple scattering processes
dd
d
2
follow many neutron histories with a cutoff weight depending on attenuationconstruct a distribution function at the detector
Alternatively, calculatecalculateby Monte Carlo
integration
22 32 exps
exps I,I
(P1,P2,D) triplets are randomly sampled over the 8-dimensional space (Vs
ill + Vs + Sd). (in the elastic approximation)
(P1,P2,D) triplets are randomly sampled over the 8-dimensional space (Vs
ill + Vs + Sd). (in the elastic approximation)
1
12 1
0
1
1
11
2
1 sn
ns
n
ns
ms
s
sn
s
ns IIIIn,
I
I
I
I
A well known approximation (good for slab samples) is often used to avoid the calculation of I(3)…I(n):
A well known approximation (good for slab samples) is often used to avoid the calculation of I(3)…I(n):
Vineyard approximationVineyard approximation
Complication: Complication:
multiple scattering involving multiple scattering involving the containerthe container
cc,c cc,sc cc,c
As for the single scattering, the true multiple scattering contribution from the container in a s+c run is not that present in the empty cell measurement (attenuation due to the sample).
Moreover “cross” multiple scattering events can occur, involving both sample and container.
sc,sc cs,sc
222
2221
1
expmc
expc
expc
expmcs
expcs
expcs
IIBI
IIBI
Multiple scattering correction in a multi-Multiple scattering correction in a multi-element systemelement systemsample + container (+ cryostat/furnace + ...)sample + container (+ cryostat/furnace + ...)
While single scattering intensities are easily generalized and accounted for in the case of a multi-component system (it “only” requires the appropriate empty-“element” measurements and the calculation of the consequent
absorption coefficients), the same is not true for multiple scattering.
Complication arises from the cross contributions [which may not be negligible for some (forced) combinations of the sample and the container macroscopic scattering properties].
In the simplest case (s+c) we have (for each 2)
mc,cc
mc
msc,cc
msc,cs
msc,sc
msc,ss
mcs
II
IIIII
But we skip the details…..
Handling experimental quantities and Handling experimental quantities and calculations calculations
We have:
eb
Cd
c
cs
I
I
I
Iexp
exp
CdebcCd
CdebscCd
mcc
mcscs
IITIB
IITIB
IIB
IIB
expexp1
expexp1
exp2,
exp1
exp2,
exp2,
exp2,
exp2,
exp1exp1
cccc
scscsccsscccscsscs
IIB
IIIIIIB
EXP
calc
cccc
calcsccsccsscs
IAB
IAIAB
1
11
,
1,
1,
exp
exp
c
cs
I
I
with
calc
cc
calc
cccc
calc
sccscs
calc
scscsccsscccscsssc
I
I
II
IIII
1,
2,
1,
1,
2,
2,
2,
2,
The single-scattering The single-scattering intensity intensity IIss(1)(1)
sc,s
CdebcCdexp
ccalccc,c
sc,ccalcsc
CdebscCdexpsc
s A
IITIIA
AIITII
I
111
22
1
inccoh
ELASTIC
s
bQSbF
QS~
Fd
dFI
ELASTIC
If multiple scattering is neglected
If attenuation coefficients are approximated by the transmissions(As,sc ≈ Ac,sc ≈Tsc ≈Ts Tc and Ac,c≈Tc)
sc
Cdexp
csCdexpsc
s T
IITIII
1
F is the instrumental factor due to flux, solid angle, detector efficiency and sample density … we need to MEASURE it
VanadiumVanadiumVanadiumVanadium
Data normalization to Data normalization to absolute unitsabsolute units
To normalize the data we need to determine the experimental factor F = (0) N .
Most of these quantities are only approximately known, the flux at the sample mainly…( it depends on too many variables: source spectrum, monochromator, collimators… andtheir REAL performances).
Thus a specific measurement is required, using a REFERENCE sample of well-known scattering properties.
A solid is usually the choice because of its mostly elastic scattering, though this condition is not mandatory: it is only important that the differential cross-section of the reference sample is a known quantity (e.g. gaseous hydrogen).
An incoherent scatterer is the best choice, because a non-dramatic change in intensity with varying Q (Bragg peaks) is required for normalization purposes (flat diffraction pattern).
In MOST (not ALL) neutron experiments the reference sample is
To normalize the data we need to determine the experimental factor F = (0) N .
Most of these quantities are only approximately known, the flux at the sample mainly…( it depends on too many variables: source spectrum, monochromator, collimators… andtheir REAL performances).
Thus a specific measurement is required, using a REFERENCE sample of well-known scattering properties.
A solid is usually the choice because of its mostly elastic scattering, though this condition is not mandatory: it is only important that the differential cross-section of the reference sample is a known quantity (e.g. gaseous hydrogen).
An incoherent scatterer is the best choice, because a non-dramatic change in intensity with varying Q (Bragg peaks) is required for normalization purposes (flat diffraction pattern).
In MOST (not ALL) neutron experiments the reference sample is
Data normalization to Data normalization to absolute unitsabsolute unitsWhat we need is only a proportionality relation (… neglecting inelasticity
effects). In general, measurements on the sample and on the calibration sample (e.g. vanadium) may be synthetized as:
where different GEOMETRIES of the sample specimen and of the calibration sample are taken roughly into account through an overall “solid-angle” effect.
If we try to make the geometrical differences (between sample and reference) as small as possible, then REF SAMPLE (common) and therefore:
What we need is only a proportionality relation (… neglecting inelasticity effects). In general, measurements on the sample and on the calibration sample (e.g. vanadium) may be synthetized as:
where different GEOMETRIES of the sample specimen and of the calibration sample are taken roughly into account through an overall “solid-angle” effect.
If we try to make the geometrical differences (between sample and reference) as small as possible, then REF SAMPLE (common) and therefore:
)UNKNOWN(SAMPLE
SAMPLE)ILLUM(
SAMPLEs
)KNOWN(REFREF
)ILLUM(REFREF
d
dNI
d
dNI
01
0
2
2
)UNKNOWN(SAMPLE
)KNOWN(REF)ILLUM(REF
REF)ILLUM(
SAMPLE
s
)KNOWN(REF)ILLUM(REF
REF
d
d
dd
N
INI
dd
N
I
22
2
1
0
The data-analyzer endless The data-analyzer endless enigmaenigmaHow much should one push the refinement of the data
analysis and related calculations?
an “extremely accurate” analysiswould still be approximate and would never
end!It depends on…The physical effect
under investigationThe accuracy of the neutron
experimental data
and available TIME
Unavoidable measurements
BackgroundEmpty container
Reference sample (Vanadium)
Unavoidable estimatesattenuation
multiple scatteringVarious degrees of accuracythe sample features may allow for reasonable approximations down to:
use of transmissionsneglect of multiple scattering
Useful measurements
Transmissions
Riassumiamo un po’…Riassumiamo un po’…
La quantità fisica importante in esperimenti di diffrazione è S(Q), ma ciò che si misura non è connesso in modo diretto ad essa.L’intensità direttamente misurata soffre di vari effetti come il background, attenuazione, scattering multiplo, efficienza e, ovviamente, della risoluzione FINITA dello strumento. Molti di questi richiedono misure specifiche.
Anche in un caso ideale e ammettendo di liberarsi facilmente da fattori strumentali, la sezione d’urto differenziale NON è ciò che si cerca perché contiene ancora le sezioni d’urto e perché lo scattering NON E’ in generale ELASTICO.
In un esperimento reale, vanno ottimizzati i contenitori, il campione stesso, e predisposte varie misure, sia principali (campione nel contenitore e contenitore vuoto) che ancillari (vanadio, cadmio, trasmissioni). Ma dipende anche dal sample…
Altri step sono obbligatori in generale: e.g. normalizzazione delle intensità misurate nei vari run agli stessi conteggi di MONITOR
(cosa è fondamentale ricordare indipendentemente dallo specifico strumento)
Facciamo finta di arrivare Facciamo finta di arrivare sul D1A di ILL…sul D1A di ILL…
… e di dover fare delle misure su un liquido.
A prioriavrete scelto un contenitore adatto al vostro liquido in termini di:
Potere di scattering del campione corrispondente…
Ps S / T (1-T) con T dipendente da n e dallo spessore di campione illuminato (cambia con la forma del contenitore e del fascio…)
Il potere di scattering vi dice anche quanto multiplo vi potete aspettare. In genere si cerca di non superare il 20%....
Proprietà di scattering del materiale della cella (min. scattering, min. assorbimento, possibilmente INCOERENTE)
Compatibilità di materiali fra cella e campione (ci sono campioni corrosivi…)
Facciamo finta di arrivare Facciamo finta di arrivare sul D1A di ILL…sul D1A di ILL…
A posteriori (in genere, ma dipende…):
Preparate la cella(schermi di Cadmio, se necessario)
Adattate con diaframmi la dimensione del fascio alla parte utile della cella
Posizionate al meglio la cella sul fascio(se è slab va cercata la posizione ortogonale al fascio)
Verificate la posizione coprendo completamente la celladi Cadmio (prendete vari riferimenti geometrici per poterla riposizionare bene, ma solo con Cd esterno)
Facciamo finta di …Facciamo finta di …A posteriori (in genere, ma dipende…):
Va scelta l’energia incidente di lavoro e la collimazione(cercando il solito compromesso fra intensità, assorbimento e risoluzione…: ma dipende dal campione e dalla proprietà cercata!!)
Vanno scelti i tempi di misura di campione+cella, cella vuota, assorbitore, campione di riferimento… in base a:tempo assegnato sullo strumentoaccuratezza che si desidera raggiungere sull’intensità dal solo sample (cioè dopo la sottrazione della cella)potere e proprietà di scattering di cella e campione
Vanno eseguiti vari sottorun per ciascun gruppo di misure (in modo da controllare la stabilità del campione e dello strumento)
I sottorun compatibili (normalizzati allo stesso conteggio di monitor e in accordo fra loro) vanno raggruppati tramite una media pesata: questi saranno i file RAW necessari per la successiva analisi. Ne avremo uno per tipo: sample+cella, cella, assorbitore, campione di riferimento etc….
I file raw… che aspetto I file raw… che aspetto hanno?hanno?Per esempio, da un gas poco strutturato come il Cl2 a 405 K
e con densità numerica (molecolare) di 1.7 molecole/nm-3
(per confronto, un liquido denso può raggiungere densità dell’ordine di 20 molecole/ nm-3) dà profili del tipo:
0 20 40 60 800
2000
4000
6000
8000
ClCl22 sample + sample + cellcell
Empty cellEmpty cell
Cell + Cell + 33He He (matched)(matched)
Empty Empty furnacefurnace
Bragg peak Bragg peak from the from the
cell….cell….
Feeble sign Feeble sign of of
STRUCTURESTRUCTURE
A spike in all A spike in all measurementsmeasurements
(some problem at that detector (some problem at that detector tube…)tube…)
A slightly A slightly different different
slopeslope
Sign of Sign of DIRECT DIRECT beambeam
2 [degrees]
Intensity[arb. units]
I file raw del campione di I file raw del campione di riferimento… riferimento… (H(H22, per esempio. …, per esempio. …
non Vanadio!)non Vanadio!)
0 20 40 60 80 1000
1000
2000
3000
4000
5000
2 [degrees]
Intensity[arb. units]
Dilute HDilute H22
(inside the cell!)
Sign of Sign of DIRECT DIRECT beambeam
0 20 40 60 80 1000
2000
4000
6000
8000
2 [degreces]
Intensity[arb. units]
ClCl22 sample - sample - IIHeHeIIss
(1)(1)
Dopo un po’ di correzioni….Dopo un po’ di correzioni….
Dopo normalizzazione e Dopo normalizzazione e correzionecorrezione
anelasticaanelastica
0 1 2 3 4-2
0
2
4
6
8
Q [Å-1]
D(Q)barn/sr
~
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