Determination of total x-ray absorption coefficient using non-resonant x-ray emission

0.44 MB·English

by  A. J. Achkar

Determination of total x-ray absorption coefficient using non-resonant x-ray emission
A. J. Achkar1, T. Z. Regier2, E. J. Monkman3, K. M. Shen3,4 and D. G. Hawthorn*1
1Department of Physics and Astronomy, University of Waterloo, Waterloo, N2L 3G1, Canada
2Canadian Light Source, University of Saskatchewan, Saskatoon, Saskatchewan S7N 0X4, Canada
3Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, NY 14853
4Kavli Institute at Cornell for Nanoscale Science, Cornell University, Ithaca, NY 14853
(Dated: January 18, 2013)
Analternativemeasureofx-rayabsorptionspectroscopy(XAS)calledinversepartialfluorescence
yield (IPFY) has recently been developed that is both bulk sensitive and free of saturation effects.
Here we show that the angle dependence of IPFY can provide a measure directly proportional to
2 thetotal x-ray absorption coefficient, µ(E). In contrast, fluorescence yield (FY) and electron yield
1 (EY)spectraareoffsetand/ordistortedfromµ(E)byanunknownanddifficulttomeasureamount.
0
Moreover,ourmeasurementcandetermineµ(E)inabsoluteunitswithnofreeparametersbyscaling
2
toµ(E)atthenon-resonantemissionenergy. Wedemonstratethistechniquewithmeasurementson

n NiOandNdGaO3. Determiningµ(E)acrossedge-stepsenablestheuseofXASasanon-destructive
a measureofmaterialcomposition. InNdGaO3,wealsodemonstratetheutilityofIPFYforinsulating
J samples,whereneitherEYorFYprovidereliablespectraduetosamplechargingandself-absorption

5 effects, respectively.

] PACSnumbers: 78.70.Dm,78.70.En,61.05.cj
l
e
-
r X-rayabsorptionspectroscopy(XAS)iswidelyusedin influence on the energy dependence of the fluorescence
t
s biology, the physical sciences and materials engineering yield.11
t. asapowerfulprobeofspatialandelectronicstructure.1–4 Second,themagnitudeoftheEYandFYbothdepend
a
m In XAS, the by-products of the absorptionprocess, elec- on the relative probability, ωfl, that an excited atom
tron yield (EY) and fluorescence yield (FY), are com- willdecaybyemittingphotonsasopposedtoelectrons.12
d- monly used as measures of the x-ray absorption5,6 since This relative probability differs from atom to atom and
n transmissionexperimentsoftenrequireimpracticallythin edge to edge and is generally not known with great pre-
o samples. The principle behind EY and conventional FY cision.
c measurements(whichmeasurethe fluorescencefromres- Third, the emissionis distributed overa range of elec-
[
onant emission processes and shall henceforth be simply tron and photon energies. A given detector will not de-

2 referred to as FY) is that the electron and fluorescence tect all electron or photon energies with equal efficiency.
v yieldsbearsomeproportionalitytotheabsorptioncoeffi- InthecaseofEY,magneticorelectrostaticfieldswillalso
9 cient – the number of electrons or photons emitted from influence the efficiency of detection in the system, which
5
decaying atoms in a giventhickness of sample is propor- may vary between experiments. In addition, the quan-
2
tional to the number atoms that are excited. However, tumefficiencyofEY(thenumberofelectronsemittedper
0
. the measured FY or EY spectra are not strictly propor- incidentphoton)willalsovarywithphotonenergy.3 The
4 tional to the total absorption coefficient for several rea- consequence of all these factors is that the magnitude of
0
sons. the EY or FY signal will generally have a value that is
1
1 First, the thickness of sample probed depends on the not proportional to the total absorption coefficient but
: relativepenetrationdepth(attenuationlength)ofthein- is rather offset or distorted by some often unknown or
v
cidentphotons andthe escape depthof the emitted elec- difficult to calculate factors.
i
X trons,inthecaseofelectronyield,orphotons,inthecase Fortunately, for many applications of XAS, the key
r of fluorescence yield. As the attenuation length varies features in absorption spectra measured by EY or FY
a overanabsorptionedge,itispossiblefortheattenuation are retained and can still be interpreted to glean im-
length to approach the electron escape depth, leading portant qualitative information about the electronic or
to saturation effects in EY and distorting the measured spatial structure. However, in many instances, such as
spectra.7InthecaseofFYmeasurementsofconcentrated correctingforself-absorptioneffects,calculatingresonant
species, both the total x-ray absorption coefficient and scattering cross-sections or determining x-ray penetra-
the absorption due to the edge of interest vary strongly, tion depth, it is important to know the magnitude of
leading to distortions of the spectra referred to as satu- the total absorption coefficient in absolute units. More-
ration effects or as “self-absorption effects.”8,9 Such FY over, knowing this could open the door to using XAS as
spectracansometimesbecorrectedforself-absorptionef- a quantitative tool for compositional analysis of materi-
fects using the angle dependence of the FY.8,9 However, als. In principle, the magnitude and energy dependence
this correction procedure can be unreliable since reso- of the total absorption coefficient contains information
nant x-ray emission processes10 that are not accounted about the compositionof a materialin addition to infor-
forintheself-absorptioncorrectioncanhaveasignificant mationabouttheelectronicandspatialstructure. Asthe
2
photon energy is increased through an absorption edge, RESULTS
theabsorptionincreasesinastep-wisefashionwhencore
electrons are photo-excited with enough energy to en-
A. Inverse partial fluorescence yield
ter the continuum of unoccupied states. The magnitude
of the edge-step relative to the pre-edge can provide a
IPFYoperatesonadifferentprinciplethanEYorFY,
measure of material composition. The various atomic
effectively measuring the attenuation length into a sam-
contributions can be determined using tabulated13 or
ple rather than the number of atoms that are excited
calculated14 values of the absorption cross-section that
and subsequently relax. With IPFY, an energy sensitive
areconvenientlyandfreelyavailableonlinefromtheCen-
detector is used to monitor non-resonant x-ray emission
terforX-rayOptics(CXRO)ortheNationalInstituteof
as the incident photon energy is scanned through an ab-
Standards and Technology (NIST).
sorptionedge. Thisnon-resonant(normal)emissionmay
With these inputs, the magnitude of the XAS, in par-
be from a different element or core electron than that
ticular the edge-step, can be used as a robust quanti-
associated with the absorptionedge under investigation.
tative measure of material composition. By fitting the
As the attenuation length decreases through an absorp-
availabletabulated or calculatedatomic absorptiondata
tion edge, the same number of atoms are excited (since
tothepre-andpost-edgeofameasuredabsorptionspec-
allphotons areabsorbedfor samples whichare thick rel-
trum, one can experimentally derive the stoichiometry
ativeto the x-raypenetrationlength), but fewerofthese
of a material in a non-destructive manner. Since they
excitations will correspond to non-resonant transitions.
do not measure the total absorption coefficient, FY and
Subsequently, the intensity of the non-resonant emission
EY are not well suited for this type of analysis. Trans-
will dip as the absorption coefficient peaks through an
mission measurements, however,do provide a direct and
absorption edge.
quantitative measure of the absorptioncross-sectionand
The intensity of the non-resonant emission will also
such measurements are routinely performed at hard and
depend on the absorption cross-section of the atom and
soft x-ray beamlines.15 However, transmission spectra
core electron corresponding to the non-resonant transi-
can be subject to “thickness effects” and should only be
tion and on the attenuation length of the emitted pho-
performed with sufficiently thin samples.16,17 Preparing
tons. However,these factorsare constantorvaryweakly
samples with appropriate thickness may be challenging
through an absorption edge, in the x-ray absorption
or impossible depending on the nature of the sample,
near edge structure (XANES). As a result, a straight-
particularly for soft x-rayswhere sample thicknesses less
forwardinversionof the partialfluorescence yield (PFY)
than 1 micron are typically required.
arising from a non-resonant emission process provides
The recent development of inverse partial fluorescence
an accurate measure of x-ray absorption cross-section
yieldallowsustoovercometheaforementionedshortcom-
in the XANES.18 As discussed in Ref. 18, since it is
ings of EY and FY.18 Unlike EYand FY measurements,
non-resonant emission processes that contribute to this
IPFY is both bulk sensitive and free of saturation ef-
measure of PFY, saturation (self-absorption) effects are
fects. In this paper, we demonstrate that the theory of
avoided. Moreover,thelargevariationofthefluorescence
IPFY can be extended and exploited to reliably obtain
decay rates observed across edge steps for resonant fluo-
a measure proportionalto the total x-ray absorption co-
rescenceprocesses,11asinconventionalFY,donotfactor
efficient, µ(E), with the proportionality constant being
into the measurement of IPFY, simplifying the analysis
thetotalabsorptioncoefficientatthenon-resonantemis-
and interpretation of IPFY relative to FY.
sion energy, µ(E ). This result is confirmed by excel-
f
The extraction of IPFY from the energy-resolved x-
lentagreementwithtabulatedorcalculatedvaluesofthe
rayemissionofNiOisdemonstratedinFig.1. Thex-ray
measuredIPFYofNiOandNdGaO singlecrystals. The
3
emission of NiO is measured as the incident photon en-
abilitytoderivequantitativeinformationfromXASwith
ergy, E , is scanned through the Ni L edge (Fig. 1a).
IPFY creates new opportunities for chemical speciation i
The Ni L absorption edge corresponds to exciting a Ni
and compositional analysis of materials.
2p electroninto unoccupied 3dstates near the edge (and
In addition, we demonstrate the applicability of IPFY
a continuum of states further above the edge), leaving
to XAS measurementsofstrongly insulating samples. In
behind a 2p core hole. The emission spectra (Fig. 1b)
NdGaO , neither EY or FY measurements provide re-
3 exhibit a peak atemissionenergyE ∼ 840eV that cor-
liable XAS spectra of the Nd M edges due to strong f
5,4 responds to resonant emission from Ni. This emission is
chargingandsaturationeffects,respectively. Incontrast,
duetotheelectronsmakingtransitionstofillintheNi2p
IPFYprovidesexcellentagreementwithpreviouslymea-
core-holeleftbehindbytheNiLedgeabsorptionprocess.
sured XAS on Nd metal.
The PFY from the Ni 2p emission (Fig. 1c, black curve)
sufferssignificantlyfromself-absorptioneffectsandbears
little resemblance to the absorption coefficient.
In addition to the Ni L absorption, the x-ray ab-
sorption and emission also have contributions from non-
resonanttransitionsofothercoreelectronsofNi(3s, 3p)
3
0 2 4 6 Intensity (arb. units) B. Geometry factor of IPFY in the XANES region
0 1 2 3 4
1,200
V) a b 845 eV (Pre-edge)
y (e 1,000 880 eV (Post-edge) It has been shown that the IPFY of thick, homoge-
g neousmaterialsisafunctionofthetotalx-rayabsorption
mission ener 864000000 Ni LOη ,Kℓα Ni Lα,β1 coefficientIµP(FEYi):1=8 I0(Ei) =A(µ(E )+B) (1)
E I(E ,E ) i
i f
y (arb. units) 64 c NOi KL PPFFYY d NiL3 Ni ITLPE2FYY 64 Intensity (a µwan(hEdefree)mssiiinnAsαsβi.on=,Hreers4epπeα/cηtai(vEnedfly),ΩβaωsaYrme(Eetafhs)euµrYaedn(Egflrie)osmoaftnhdiencsiBadmenpc=lee
Intensit 20 20 rb.units) istshuterhfeaemcceio,snηsit(orEnibfeu)ntiiesortnghyte,oqΩtuhiaesnttthoutemadleeaffitbesccoiteronprctsiyoonloifdctoaheneffigdlceei,teenµctYtfo(rrEoamit)
850 860 870 880 850 860 870 880
the excitation of core electron Y (ex. O 1s) and ω (E )
Incident photon energy (eV) Incident photon energy (eV) Y f
is the probability of fluorescence at energy E resulting
f
from electrons decaying to fill in the core hole left by Y.
FIG.1. Energy sensitivefluorescence yieldof NiO–a)
Normalized x-ray fluorescence of NiO as the incident photon
energy is scanned through the Ni L3 and L2 edges. b) The In Eq. (1), the constant B is independent of Ei and
emissionspectrainthepre-andpost-edgeregionsatincident A depends only weakly on E over a narrow energy
i
photonenergiesof845eVand880eVtakenin1-eVwindows. range (XANES) so it can be treated approximately as
Emissions corresponding to the resonant Ni 3d to 2p (Lα,β1) constant.18 This approximation fails over a large energy
and 3s to 2p (L ) and non-resonant (normal) O 2p to 1s
η,ℓ range, requiring one to account for the energy depen-
(Kα) processes are observed. c) The Ni L and O K par- dence of µ (E ) and the quantum efficiency of the I
tial fluorescence yield extracted from panel a in 150-eV wide Y i 0
measurement, which we demonstrate later. However, in
energy windows centered on the respective emissions. The
a narrow energy range, it follows that IPFY is propor-
resonant Ni L PFY shows strong distortions resulting from
saturation effects. ThenormalOK PFYdipsastheabsorp- tional to µ(Ei) plus an offset proportional to B. The
tion increases through the Ni L3,2 absorption edges. d) The crucial feature of Eq. (1) is that the size of the offset B
IPFY is the inverse of the O K PFY shown in panel c. The isdeterminedbythegeometricalfactorsinα/sinβ. This
NiOIPFYisingoodagreementwithtotalelectronyielddata allows one to determine µ(E )/µ(E ) from experiments
i f
from Ref. 20 which has been scaled and offset to match the with different measurement geometries.
IPFY.
InFig.2,wedemonstratethattheIPFYofNiOobeys
the expected dependence on the sample geometry as de-
tailed in Eq. (1). First, the Ni L PFY spectra mea-
3,2
sured for various geometries (Fig. 2a) depict the strong
angle-dependence of self-absorption effects in FY mea-
surements. Notably, attempts to correct the PFY for
self-absorptioneffectsusingtheangledependence8,9 (not
shown) do not yield the correct spectra. In contrast,
and from oxygen (the total linear absorption coefficient the IPFY spectra measured with the same geometries
is the sum of these contributions, µ(E ) = µ (E ) + (Fig. 2b) are undistorted and offset from one another,
i Ni i
µ (E ), where µ (E ) = µ (E ) + µ (E ) + in agreement with Eq. (1). The inset in Fig. 2b is a
O i Ni i Ni,2p i Ni,3s i
µ (E )+ ...).19 As shown in Fig. 1a and 1b there plot of the value of the IPFY spectra at a single value
Ni,3p i
is a band of emission centred at 524 eV corresponding of the incident photon energy [Ei = 845 eV (red cir-
to the non-resonant emission of O 2p valence electrons cles)] as a function of sinα/sinβ for the given experi-
decaying to fill in the O 1s core hole (O K emission). mental geometries. As expected, this offset fits well to a
The PFYfromthe OK emission(Fig.1c,redcurve)ex- straightlinewithaninterceptequaltoAµ(845eV)anda
hibits dips at the Ni L3,2 absorption edges. The inverse slope equal to Aµ(Ef). Subtracting Aµ(Ef)sinα/sinβ
of this spectrum, the IPFY = 1/PFY , is shown in for each of the spectra, we find that they collapse onto
OK
Fig. 1d along with total electron yield (TEY) measure- a single curve (the slight variations in peak intensities
ments of NiO from Ref. 20 that have been scaled and are primarily due to magnetic linear dichroism in NiO
offset to match the IPFY. Similar to previous work18 on due to anti-ferromagnetic ordering of the Ni spins in the
La Nd Sr CuO , the agreement between IPFY (111)plane21). The key point of this analysis is that the
1.475 0.4 0.125 4
and TEY is very good, highlighting the ability of IPFY resulting spectra, derived entirely from experiment, are
to measure the energy dependence of the absorption co- directly proportional to the total absorption coefficient
efficient of Ni without the strong self-absorption effects without any offsets.
experienced with PFY. The proportionality to µ(E ) is verified by comparing
i
4
α=70°, β=24.6° α=90°, β=41.6° α=70°, β=56.3° (µ(E =524eV)=3.14×106 m−1 forNiO fromRef. 13)
f
α=50°, β=64.1° α=30°, β=59.2° α=10°, β=45.6°
tonormalizethesubtractedoffsetanddeterminethepro-
Linear fit CXRO μ(Ei) NIST μ(Ei)
portionality constant A. Note that the O K emission is
6 a due primarily to 2p valence electrons decaying to fill the
1s core hole and is peaked at a photon energy below the
s)
unit 4 absorptionthreshold. ThedatashowninFig.2chasbeen
b. scaled using µ(Ef) (a non-arbitrary scaling factor) and
FY (ar 2 cisalschuolawtneda1l4on(rgedwsitqhuatrhees)taxb-rualyataebds1o3rp(gtiroenencoceuffirvceie)nat.nd
P
Using this single scaling parameter, we find that the
0 measuredspectraareinexcellentagreementwiththetab-
b V) 2 ulatedcoefficientsinboththepre-andpost-edgeregions,
6 45 e 1 capturingboththeenergydependenceandtheedge-step.
8 ThisdemonstratesthatIPFYprovidesameasuredirectly
5 Y(
units) 4 IPF 00 1 2 pprrooppoorrttiioonnaallittyoctohnesttaontatlbaebinsogrµp(tEiofn).coIenfficcoinetnrtaswt,itqhutahne-
b. sin α/sin β titativeanalysisofEYorFYspectrarequiresscalingand
ar
Y ( 3 offsetting data to calculated values of the absorption co-
F
IP efficient above and below the edge, essentially fixing the
2 edge-step.3 This latter procedure requires prior knowl-
edgeofthematerialcompositionandissubjecttouncer-
1
tainties in the tabulated or calculated values which are
0 estimated at 5-20% between 500 and 1000 eV and even
c Ni L highernearabsorptionedges.22Moreover,XASmeasure-
3
30 ments often still have significant structure above an ab-
m) sorption edge in the form of extended x-ray absorption
μ
E) (1/i 20 Ni L2 fitanbeuslatrtuedctourreca(lEcXulAatFeSd)vtahluaetsi,srensoutltaicncgoiunnatedddiftoironinaltehre-
(μ rors in normalizing data above an absorption edge. In
10
contrast,withIPFY,weobtaintheenergydependenceof
µ(E ) directly from measurementand can scale the data
0 i
850 860 870 880 atasingle pointwellbelow the absorptionedge. The re-
Incident photon energy (eV) sult of this normalization can be independently checked
against the absorption above and below the absorption
FIG. 2. Angle dependence of PFY and IPFY – a) The edge in questionandmultiple angles canbe measuredto
Ni L PFY for various experimental geometries. The spectra ensure self-consistency, resulting in a reliable and accu-
aredistortedbystrongself-absorption effectsthatdependon rate normalization of the data.
the angle of incidence (α) and angle of emission (β). b) The
IPFYextractedfromtheOKPFYforthesameexperimental
geometries as panel a. The spectra are offset by a geometry
C. IPFY beyond the XANES
dependent constant, but are otherwise not distorted. The
insetplotstheIPFYatEi=845eV(redcircles)asafunction
ofsinα/sinβ,whichvarieslinearlyaspredictedbyEq.(1). c) In the NiO measurements shown above, the described
Thelinearabsorption coefficient, µ(Ei),obtained from IPFY offsetting procedure works well over the narrow energy
spectra. As described in the text, the offsets in the IPFY range covered, giving a quantity approximately propor-
spectra are subtracted, collapsing the IPFY spectra onto a tional to µ(E ). However, over a larger energy win-
i
single curve proportional to µ(Ei). The spectra shown here dow,theenergydependenceofµ (E )canbesignificant.
have been scaled using a single tabulated13 value for µ(E ) Y i
f An example of this effect is shown in measurements of
and plotted against the tabulated13 (green) and calculated14
NdGaO overa wide energy range. In Fig. 3a,the IPFY
(red squares) absorption coefficients. 3
measured using the O K emission of NdGaO is shown
3
for three measurement geometries over an extended en-
ergy range covering the Nd M edge.
our measurement to tabulated13 and calculated14 val- The spectra are not rigidly offset, instead appearing
ues of µ(E ). The calculated and tabulated data cap- to be subject to a sloping background in addition to an
i
ture the transitions from the core electron to the con- offset. This backgroundis due to the energy dependence
tinuum, accurately reproducing the edge-step, but do of µOK(Ei) and also to the energy dependence of our
not include the multiplet physics associated with the measurement of the incident photon flux, I0.
2p to 3d transition. We use the calculated value of In our measurement, and many XAS measurements,
the absorption coefficient at the O K emission energy I is measured using a Au grid with 85% transmis-
0
5
20 (thenumberofelectronsgeneratedperincidentphoton),
a
α1= 70°, β1= 24.6° which in general will be energy dependent. As such,
s) 15 α2= 90°, β2= 41.6° IGrid(Ei) = I0(Ei)ν(Ei) and Eq. (1) should be modified
nit α3= 30°, β3= 59.2° to:
u
b. 10
ar I (E ) I (E )ν(E )
Y ( IPFY = Grid i = 0 i i
IPF 5 I(Ei,Ef) I(Ei,Ef) (2)
Dν(E )
i
≈ (µ(E )+B)
0 µ (E ) i
Y i
b
S1,3 (Ei)
nits) 2 LSi2n,3e (aEri) Fit dwehnecreeoDf b=othAµν(YE(Ei)i)a.ndFµorYt(uEnia)teclayn, tbheeuennaemrgbyigdueopuesnly-
u
b. eliminated from the data by subtracting IPFY spec-
ar trameasuredwithdifferentmeasurementgeometriesand
E) (i 1 normalizingto the geometry(ν(E ) generallyalso enters
S( i
into EY and FY measurements, but is typically not cor-
rected for). From Eq. (2) it follows that
0
c
10 α1= 70°, β1= 24.6° Dν(E )
nits) αα32== 3900°°,, ββ23== 4519..62°° Sj,k(Ei)= µY(Eii)µ(Ef)
arb. u = IPFY(αj,βj)−IPFY(αk,βk) (3)
IPFY (SE()i 5 ssiinnαβjj − ssiinnαβkk
where j and k correspond to different measurement ge-
0 ometriesand S(E )is independent ofthe choice ofj and
i
α1= 70°, β1= 24.6° d k. We can now write
30 α2= 90°, β2= 41.6°
m) α3= 30°, β3= 59.2° IPFY = 1 µ(E )+µ(E )sinα , (4)
1/μ 20 S(Ei) µ(Ef)(cid:18) i f sinβ(cid:19)
E) (i
(μ which is simply rearranged to yield the total x-ray ab-
10
sorption coefficient:
0
IPFY sinα
800 850 900 950 1,000 1,050 1,100 µ(E )=µ(E ) − . (5)
i f
(cid:18)S(E ) sinβ(cid:19)
Incident photon energy (eV) i
FIG.3. WideenergyrangeIPFYofNdGaO3–a)IPFY
of NdGaO3 for several measurement geometries. The IPFY 40
ismeasuredusingtheOK emission ina150eVwindowcen- 35 α=30°, β=59.2°
tredabout524eV.Themeasurementsatdifferentgeometries NIST μ(Ei)
30
exhibit different sloping backgrounds due to the energy de-
pendence of µOK(Ei) and the quantum efficiency of the I0 m)μ 25
tmheeadsuiffreemreennttm, νe(aEsui)r.embe)nSt(gEeio)mceatlrciuelsatdeedpiuctseindginEqt.he(3l)egweinthd E) (1/i 2105
of panel a. The black line is a linear fit to S(Ei). c) The (μ
10
IPFY(Ei)/S(Ei)spectraarerigidlyoffsetbyB. d)Thetotal
absorption coefficient, µ(Ei), determined using Eq. (5) (the 5
dataarescaledtoµ(524eV)fromRef.14). Thespectramea- 0
sured with different geometries collapse onto a single curve 800 850 900 950 1,000 1,050 1,100
overthe entireenergy range. Incident photon energy (eV)
FIG.4. NormalizedIPFYcomparedtoatomiccalcula-
tions–TheabsorptioncoefficientofNdGaO3 extractedfrom
the O K IPFY and corrected for the energy dependence of
sion that is placed between the sample and the last theOKabsorptionandthequantumefficiencyoftheI0mea-
optical component. The total electron yield from the surement. Theincidentphotonenergywasscannedacrossthe
grid, IGrid, is used to measure the incident photon flux. Nd M5 and M4 edges. The data agrees well with calculated
This measurement, however, depends not only on I , XAS14 over a wide energy range.
0
but also on the quantum efficiency of the mesh, ν(E )
i
6
InFig.3,thissubtractionisshown,givingS(E )thatis 12
i
a
a smooth function of energy. As shownin Fig. 3c, divid-
960 to 1020 eV
10
ingthespectrainFig.3abyS(E ),providesspectrathat
i 1020 to 960 eV
arerigidlyoffsetoverawiderangeinenergy. Subtracting
s) 8
sinα/sinβ from the spectra provides µ(Ei)/µ(Ef), col- nit
u
lapsingthe dataontoasinglecurve,whichisthenscaled b. 6
usingacalculatedvalue14 ofµ(E =524eV)asshownin ar
f Y (
Fig.3d. Whennormalizedinthis way,the spectraarein E 4
T
excellent quantitative agreement with the calculated ab-
sorption coefficient over a wide energy range above and 2
below the Nd M absorption edge, as shown in Fig. 4.
5,4
0
5 b α=90°
D. IPFY in strong insulators β=41.6°
Finally,wewouldliketoemphasizetheroleofIPFYto units) 4 αβ==5390.°2°
b. 3
studyinsulatingsamplesthatcanbedifficultorimpossi- ar
ble to measurecorrectlyusing FY orEY.An example of Y (
F 2
P
such a system is NdGaO . This material is an insulator
3
commonly usedas a substratefor oxide film growth. EY 1
measurements of the Nd M edge in NdGaO , shown in
3
Fig. 5a, exemplify issues one can encounter when mea- 0
suringtheEYofsamples. HeretheEYhasanunphysical c
NdGaO IPFY
negativeedge jump atthe absorptionedge. The unusual 3
6
Nd TEY
behaviour is attributed to a build-up in positive charge s)
near the surface of the sample that effectively reduces nit
u
the numberofemittedelectrons. Wewereabletoreduce arb. 4
the effect by recording the spectra by scanning the inci- y (
dentphotonenergyinthenegativedirection(1020eVto sit
n
e
980 eV) or measuring different spots on the sample, but nt 2
I
ultimately these spectra are not reliable.
PFYandTFYinthismaterialarealsounreliable. The
NdedgePFYmeasurements,showninFig.5b,areheav- 0
960 970 980 990 1,000 1,010 1,020
ilydistortedbyself-absorptioneffects, similarto NiO.In
Incident photon energy (eV)
contrast, the IPFY (Fig. 5c) provides the correct XAS
spectrumforNd3+. Thisisevidencedbyexcellentagree-
ment with XAS in pure Nd, which like NdGaO has FIG. 5. XAS of NdGaO3 – a) The TEY of NdGaO3 ex-
Nd3+ characterandisdescribedwellbyatomicmul3tiplet hibits an anomalous negative edge-jump across the Nd M5,4
edges (red curve). A spectrum collected with the incident
calculations.23 In this case, both EY and FY provide er-
photonenergy scanned in thenegative direction (bluecurve)
roneous results and transmission measurements are not soon after has positive edge-jumps. This difference is at-
possible due to the thickness of the sample. As such, tributed to a charge up of the sample surface, affecting the
IPFY provides the only means to measure the correct TEYmeasurement. NeitherspectrummatcheswellwithTEY
XAS spectrum. We anticipate IPFY to be widely appli- onpuremetallicNdfromRef.23. b)Thepartialfluorescence
cable to similar cases. yield from the Nd emission of NdGaO3 is strongly distorted
by saturation effects. c) The IPFY extracted from the O
K PFY of NdGaO3 agrees remarkably well with the TEY of
pureNdfrom Ref.23which isscaled andoffset tomatchthe
DISCUSSION
IPFY.
Experimental studies that require accurate knowledge
of optical constants or atomic scattering form factors,
suchasinmodellingofresonantreflectivityorx-rayscat- extend sufficiently above absorption edges to avoid EX-
tering, stand to benefit substantially from angle depen- AFS resonances. It is not always possible to meet these
dent IPFY since it provides a measure of the total ab- requirements,andinsuchcases the determinationof op-
sorption coefficient. In such studies, it is common to ticalconstantsoratomicscatteringformfactorswillnec-
scaleandoffsetXASspectraaboveandbelowanabsorp- essarilybesubjecttosystematicerrors. Incontrast,with
tion edge to tabulated atomic calculations or absorption angle dependent IPFY, µ(E ) and µ(E ) can be deter-
i f
data.24 This procedure requires knowledge of the com- mined with a simple fitting approach that does not de-
position of a material and requires measurements that pend on prior knowledge of material composition. Con-
7
sequently, scaling the measured absorption to absolute experiments with varied geometry to provide data di-
units using µ(E ) enables the determination of atomic rectly proportional to µ(E ) and undistorted by satura-
f i
form factors with the appropriate edge-step even if sam- tionorself-absorptioneffects. Byscalingtoasinglevalue
ple composition is not previously known or if the XAS of µ(E ), µ(E) is obtained in absolute units. We antici-
f
spectra do not extend sufficiently above the EXAFS. patethistechniquetohavewideapplicabilityinmanyar-
As an accurate measure of µ(E ), IPFY spectroscopy eas of science and engineering, potentially opening XAS
i
could become a powerful tool in non-destructive quan- up to non-destructive, quantitative analysis of material
titative analysis of material composition, which can be composition.
done separately or in conjunction with XANES or EX- METHODS
AFS measurements of electronic and spatial structure.
Without prior knowledge of material composition, it is The XAS measurements were performed at the Cana-
possible to fit µ(Ei)/µ(Ef) to a sum of the tabulated dian Light Source’s 11-ID SGM beamline. All mea-
atomic absorption coefficients in order to determine the surements were made at room temperature. The drain
relative weights of each atomic species in a sample. Fur- current of the sample provided the electron yield. An
thermore,µ(Ef)canbedeterminedbythefittingroutine energy-dispersivesilicondriftdetector(SDD)withanen-
asittooistheweightedsumoftheatomiccontributions. ergy resolution of ∼120 eV was used to collect the emis-
Thus,inafullyself-consistentway,itispossibletoutilize sionspectraasafunctionofincidentphotonenergy. The
IPFYspectratoestimatethecompositionofanunknown SDD was fixed in position (25.8◦ below the plane and
sample. Even if a quantitative estimate is not needed, 42.5◦ from the beam axis) and the sample was rotated
the magnitude of the pre-edge relative to the post-edge about the vertical axis to vary α and β, the angles of
bears a distinct signature of the quantity of an element incidence and emission,respectively. Dark counts onthe
relative to the other elements in the material. A simple detector were negligible. However, a small background
comparison of the magnitude of the edge-step compared in the 200-2000 eV region of the NiO emission spectra
to calculations or to IPFY on similar materials can then wasobserved,likelyduetoaslightmis-calibrationofthe
be used as a clear measure of sample composition. We detector electronics. This background potentially intro-
believe this kind of non-destructive estimate of sample duced an error of up to 20% at the Ni L peak and 3%
3
composition will be very useful to XAS practitioners as in the post-edge.
a simple means to verify the stoichiometry of a given
The single crystal of cubic NiO was polished to a
sample.
surface roughness less than 0.03 µm. Its dimensions
Finally, wewouldliketo commentonthe applicability were 5×5 by 0.5 mm thick and it was oriented such that
of IPFY to the hard x-ray regime. Thus far, IPFY has the h100i direction was perpendicular to the sample
only been demonstrated using soft x-rays. However, we surface. The NdGaO single crystal was a 10×10 mm
3
feel IPFY would likely also be useful for XAS at hard x- by 0.5 mm thick, polished substrate oriented with the
ray energies. In order to measure IPFY in this case, one h100i direction perpendicular to the sample surface.
wouldrequirethe appropriateselectionofemissionlines.
While low energy emission lines would exist, their exci-
tation cross-section would be quite small and the pres-
ence of air and/or windows between the sample and the
detector may make it impossible to detect these. How-
ever, in compounds with multiple elements, one could ACKNOWLEDGMENTS
in principle utilize non-resonant K or L emission lines
(at intermediate to hard x-ray energies) to study the K This research is supported by the Natural Sciences
edge absorption of another element. Hence, we believe andEngineeringResearchCouncilofCanadaandby the
thatIPFYstudiesathardx-rayenergiesarefeasibleand NationalScienceFoundationthroughDMR-0847385and
could be performed using a similar detection scheme as theMRSECprogramunderDMR-0520404(CornellCen-
we have used at soft x-ray energies. ter for Materials Research). The research described in
In conclusion, we have demonstrated a measure of the this paper was performed at the CanadianLight Source,
total x-ray absorption coefficient using angle dependent whichissupportedbyNSERC,NRC,CIHR,andtheUni-
IPFY. Unlike in EY or conventional FY measurements, versity of Saskatchewan. E.J.M. acknowledges NSERC
theoffsetinIPFYcanbesubtractedunambiguouslyfrom for PGS support.
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