Determination of total x-ray absorption coefficient using non-resonant x-ray emission
A. J. Achkar, T. Z. Regier, E. J. Monkman, K. M. Shen, D. G. Hawthorn
aa r X i v : . [ c ond - m a t . s t r- e l ] J a n Determination of total x-ray absorption coefficient using non-resonant x-ray emission
A. J. Achkar , T. Z. Regier , E. J. Monkman , K. M. Shen , and D. G. Hawthorn* Department of Physics and Astronomy, University of Waterloo, Waterloo, N2L 3G1, Canada Canadian Light Source, University of Saskatchewan, Saskatoon, Saskatchewan S7N 0X4, Canada Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, NY 14853 Kavli Institute at Cornell for Nanoscale Science, Cornell University, Ithaca, NY 14853 (Dated: August 29, 2018)An alternative measure of x-ray absorption spectroscopy (XAS) called inverse partial fluorescenceyield (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 tothe total x-ray absorption coefficient, µ ( E ). In contrast, fluorescence yield (FY) and electron yield(EY) spectra are offset and/or distorted from µ ( E ) by an unknown and difficult to measure amount.Moreover, our measurement can determine µ ( E ) in absolute units with no free parameters by scalingto µ ( E ) at the non-resonant emission energy. We demonstrate this technique with measurements onNiO and NdGaO . Determining µ ( E ) across edge-steps enables the use of XAS as a non-destructivemeasure of material composition. In NdGaO , we also demonstrate the utility of IPFY for insulatingsamples, where neither EY or FY provide reliable spectra due to sample charging and self-absorptioneffects, respectively. PACS numbers: 78.70.Dm,78.70.En,61.05.cj
X-ray absorption spectroscopy (XAS) is widely used inbiology, the physical sciences and materials engineeringas a powerful probe of spatial and electronic structure.
In XAS, the by-products of the absorption process, elec-tron yield (EY) and fluorescence yield (FY), are com-monly used as measures of the x-ray absorption sincetransmission experiments often require impractically thinsamples. The principle behind EY and conventional FYmeasurements (which measure the fluorescence from res-onant emission processes and shall henceforth be simplyreferred to as FY) is that the electron and fluorescenceyields bear some proportionality to the absorption coeffi-cient – the number of electrons or photons emitted fromdecaying atoms in a given thickness of sample is propor-tional to the number atoms that are excited. However,the measured FY or EY spectra are not strictly propor-tional to the total absorption coefficient for several rea-sons.First, the thickness of sample probed depends on therelative penetration depth (attenuation length) of the in-cident photons and the escape depth of the emitted elec-trons, in the case of electron yield, or photons, in the caseof fluorescence yield. As the attenuation length variesover an absorption edge, it is possible for the attenuationlength to approach the electron escape depth, leadingto saturation effects in EY and distorting the measuredspectra. In the case of FY measurements of concentratedspecies, both the total x-ray absorption coefficient andthe absorption due to the edge of interest vary strongly,leading to distortions of the spectra referred to as satu-ration effects or as “self-absorption effects.”
Such FYspectra can sometimes be corrected for self-absorption ef-fects using the angle dependence of the FY.
However,this correction procedure can be unreliable since reso-nant x-ray emission processes that are not accountedfor in the self-absorption correction can have a significant influence on the energy dependence of the fluorescenceyield. Second, the magnitude of the EY and FY both dependon the relative probability, ω fl , that an excited atomwill decay by emitting photons as opposed to electrons. This relative probability differs from atom to atom andedge to edge and is generally not known with great pre-cision.Third, the emission is distributed over a range of elec-tron and photon energies. A given detector will not de-tect all electron or photon energies with equal efficiency.In the case of EY, magnetic or electrostatic fields will alsoinfluence the efficiency of detection in the system, whichmay vary between experiments. In addition, the quan-tum efficiency of EY (the number of electrons emitted perincident photon) will also vary with photon energy. Theconsequence of all these factors is that the magnitude ofthe EY or FY signal will generally have a value that isnot proportional to the total absorption coefficient butis rather offset or distorted by some often unknown ordifficult to calculate factors.Fortunately, for many applications of XAS, the keyfeatures in absorption spectra measured by EY or FYare retained and can still be interpreted to glean im-portant qualitative information about the electronic orspatial structure. However, in many instances, such ascorrecting for self-absorption effects, calculating resonantscattering cross-sections or determining x-ray penetra-tion depth, it is important to know the magnitude ofthe total absorption coefficient in absolute units. More-over, knowing this could open the door to using XAS asa quantitative tool for compositional analysis of materi-als. In principle, the magnitude and energy dependenceof the total absorption coefficient contains informationabout the composition of a material in addition to infor-mation about the electronic and spatial structure. As thephoton energy is increased through an absorption edge,the absorption increases in a step-wise fashion when coreelectrons are photo-excited with enough energy to en-ter the continuum of unoccupied states. The magnitudeof the edge-step relative to the pre-edge can provide ameasure of material composition. The various atomiccontributions can be determined using tabulated orcalculated values of the absorption cross-section thatare conveniently and freely available online from the Cen-ter for X-ray Optics (CXRO) or the National Institute ofStandards and Technology (NIST).With these inputs, the magnitude of the XAS, in par-ticular the edge-step, can be used as a robust quanti-tative measure of material composition. By fitting theavailable tabulated or calculated atomic absorption datato the pre- and post-edge of a measured absorption spec-trum, one can experimentally derive the stoichiometryof a material in a non-destructive manner. Since theydo not measure the total absorption coefficient, FY andEY are not well suited for this type of analysis. Trans-mission measurements, however, do provide a direct andquantitative measure of the absorption cross-section andsuch measurements are routinely performed at hard andsoft x-ray beamlines. However, transmission spectracan be subject to “thickness effects” and should only beperformed with sufficiently thin samples.
Preparingsamples with appropriate thickness may be challengingor impossible depending on the nature of the sample,particularly for soft x-rays where sample thicknesses lessthan 1 micron are typically required.The recent development of inverse partial fluorescenceyield allows us to overcome the aforementioned shortcom-ings of EY and FY. Unlike EY and FY measurements,IPFY is both bulk sensitive and free of saturation ef-fects. In this paper, we demonstrate that the theory ofIPFY can be extended and exploited to reliably obtaina measure proportional to the total x-ray absorption co-efficient, µ ( E ), with the proportionality constant beingthe total absorption coefficient at the non-resonant emis-sion energy, µ ( E f ). This result is confirmed by excel-lent agreement with tabulated or calculated values of themeasured IPFY of NiO and NdGaO single crystals. Theability to derive quantitative information from XAS withIPFY creates new opportunities for chemical speciationand compositional analysis of materials.In addition, we demonstrate the applicability of IPFYto XAS measurements of strongly insulating samples. InNdGaO , neither EY or FY measurements provide re-liable XAS spectra of the Nd M , edges due to strongcharging and saturation effects, respectively. In contrast,IPFY provides excellent agreement with previously mea-sured XAS on Nd metal. RESULTSA. Inverse partial fluorescence yield
IPFY operates on a different principle than EY or FY,effectively measuring the attenuation length into a sam-ple rather than the number of atoms that are excitedand subsequently relax. With IPFY, an energy sensitivedetector is used to monitor non-resonant x-ray emissionas the incident photon energy is scanned through an ab-sorption edge. This non-resonant (normal) emission maybe from a different element or core electron than thatassociated with the absorption edge under investigation.As the attenuation length decreases through an absorp-tion edge, the same number of atoms are excited (sinceall photons are absorbed for samples which are thick rel-ative to the x-ray penetration length), but fewer of theseexcitations will correspond to non-resonant transitions.Subsequently, the intensity of the non-resonant emissionwill dip as the absorption coefficient peaks through anabsorption edge.The intensity of the non-resonant emission will alsodepend on the absorption cross-section of the atom andcore electron corresponding to the non-resonant transi-tion and on the attenuation length of the emitted pho-tons. However, these factors are constant or vary weaklythrough an absorption edge, in the x-ray absorptionnear edge structure (XANES). As a result, a straight-forward inversion of the partial fluorescence yield (PFY)arising from a non-resonant emission process providesan accurate measure of x-ray absorption cross-sectionin the XANES. As discussed in Ref. 18, since it isnon-resonant emission processes that contribute to thismeasure of PFY, saturation (self-absorption) effects areavoided. Moreover, the large variation of the fluorescencedecay rates observed across edge steps for resonant fluo-rescence processes, as in conventional FY, do not factorinto the measurement of IPFY, simplifying the analysisand interpretation of IPFY relative to FY.The extraction of IPFY from the energy-resolved x-ray emission of NiO is demonstrated in Fig. 1. The x-rayemission of NiO is measured as the incident photon en-ergy, E i , is scanned through the Ni L edge (Fig. 1a).The Ni L absorption edge corresponds to exciting a Ni2 p electron into unoccupied 3 d states near the edge (anda continuum of states further above the edge), leavingbehind a 2 p core hole. The emission spectra (Fig. 1b)exhibit a peak at emission energy E f ∼
840 eV that cor-responds to resonant emission from Ni. This emission isdue to the electrons making transitions to fill in the Ni 2 p core-hole left behind by the Ni L edge absorption process.The PFY from the Ni 2 p emission (Fig. 1c, black curve)suffers significantly from self-absorption effects and bearslittle resemblance to the absorption coefficient.In addition to the Ni L absorption, the x-ray ab-sorption and emission also have contributions from non-resonant transitions of other core electrons of Ni (3 s , 3 p ) E m i ss i o n e n e r g y ( e V ) I n t e n s i t y ( a r b . un i t s ) Incident photon energy (eV) I n t e n s i t y ( a r b . un i t s ) Ni L α , β O K α Ni L Ni L Ni L PFY O K PFY Incident photon energy (eV) IPFY TEY 845 eV (Pre-edge) 880 eV (Post-edge) c d Ni L η ,ℓ ba FIG. 1.
Energy sensitive fluorescence yield of NiO – a) Normalized x-ray fluorescence of NiO as the incident photonenergy is scanned through the Ni L and L edges. b) Theemission spectra in the pre- and post-edge regions at incidentphoton energies of 845 eV and 880 eV taken in 1-eV windows.Emissions corresponding to the resonant Ni 3 d to 2 p ( L α,β )and 3 s to 2 p ( L η,ℓ ) and non-resonant (normal) O 2 p to 1 s ( K α ) processes are observed. c) The Ni L and O K par-tial fluorescence yield extracted from panel a in 150-eV wideenergy windows centered on the respective emissions. Theresonant Ni L PFY shows strong distortions resulting fromsaturation effects. The normal O K PFY dips as the absorp-tion increases through the Ni L , absorption edges. d) TheIPFY is the inverse of the O K PFY shown in panel c. TheNiO IPFY is in good agreement with total electron yield datafrom Ref. 20 which has been scaled and offset to match theIPFY. and from oxygen (the total linear absorption coefficientis the sum of these contributions, µ ( E i ) = µ Ni ( E i ) + µ O ( E i ), where µ Ni ( E i ) = µ Ni, p ( E i ) + µ Ni, s ( E i ) + µ Ni, p ( E i )+ . . . ). As shown in Fig. 1a and 1b thereis a band of emission centred at 524 eV correspondingto the non-resonant emission of O 2 p valence electronsdecaying to fill in the O 1 s core hole (O K emission).The PFY from the O K emission (Fig. 1c, red curve) ex-hibits dips at the Ni L , absorption edges. The inverseof this spectrum, the IPFY = 1/PFY O K , is shown inFig. 1d along with total electron yield (TEY) measure-ments of NiO from Ref. 20 that have been scaled andoffset to match the IPFY. Similar to previous work onLa . Nd . Sr . CuO , the agreement between IPFYand TEY is very good, highlighting the ability of IPFYto measure the energy dependence of the absorption co-efficient of Ni without the strong self-absorption effectsexperienced with PFY. B. Geometry factor of IPFY in the XANES region
It has been shown that the IPFY of thick, homoge-neous materials is a function of the total x-ray absorptioncoefficient µ ( E i ): IP F Y = I ( E i ) I ( E i , E f ) = A ( µ ( E i ) + B ) (1)where A = 4 π/η ( E f )Ω ω Y ( E f ) µ Y ( E i ) and B = µ ( E f ) sin α sin β . Here α and β are the angles of incidenceand emission, respectively, as measured from the samplesurface, η ( E f ) is the quantum efficiency of the detector atthe emission energy, Ω is the detector solid angle, µ Y ( E i )is the contribution to the total absorption coefficient fromthe excitation of core electron Y (ex. O 1 s ) and ω Y ( E f )is the probability of fluorescence at energy E f resultingfrom electrons decaying to fill in the core hole left by Y .In Eq. (1), the constant B is independent of E i and A depends only weakly on E i over a narrow energyrange (XANES) so it can be treated approximately asconstant. This approximation fails over a large energyrange, requiring one to account for the energy depen-dence of µ Y ( E i ) and the quantum efficiency of the I measurement, which we demonstrate later. However, ina narrow energy range, it follows that IPFY is propor-tional to µ ( E i ) plus an offset proportional to B . Thecrucial feature of Eq. (1) is that the size of the offset B is determined by the geometrical factor sin α/ sin β . Thisallows one to determine µ ( E i ) /µ ( E f ) from experimentswith different measurement geometries.In Fig. 2, we demonstrate that the IPFY of NiO obeysthe expected dependence on the sample geometry as de-tailed in Eq. (1). First, the Ni L , PFY spectra mea-sured for various geometries (Fig. 2a) depict the strongangle-dependence of self-absorption effects in FY mea-surements. Notably, attempts to correct the PFY forself-absorption effects using the angle dependence (notshown) do not yield the correct spectra. In contrast,the IPFY spectra measured with the same geometries(Fig. 2b) are undistorted and offset from one another,in agreement with Eq. (1). The inset in Fig. 2b is aplot of the value of the IPFY spectra at a single valueof the incident photon energy [ E i = 845 eV (red cir-cles)] as a function of sin α/ sin β for the given experi-mental geometries. As expected, this offset fits well to astraight line with an intercept equal to Aµ (845 eV) and aslope equal to Aµ ( E f ). Subtracting Aµ ( E f ) sin α/ sin β for each of the spectra, we find that they collapse ontoa single curve (the slight variations in peak intensitiesare primarily due to magnetic linear dichroism in NiOdue to anti-ferromagnetic ordering of the Ni spins in the(111) plane ). The key point of this analysis is that theresulting spectra, derived entirely from experiment, aredirectly proportional to the total absorption coefficientwithout any offsets.The proportionality to µ ( E i ) is verified by comparing abc Ni L Ni L
210 210Incident photon energy (eV) μ ( E i ) ( / μ m ) I P F Y ( a r b . un i t s ) P F Y ( a r b . un i t s ) sin α /sin β I P F Y ( e V ) α =70°, β =24.6° α =90°, β =41.6° α =70°, β =56.3° α =50°, β =64.1° α =30°, β =59.2° α =10°, β =45.6° Linear fit CXRO μ ( E i ) NIST μ ( E i ) FIG. 2.
Angle dependence of PFY and IPFY – a) TheNi L PFY for various experimental geometries. The spectraare distorted by strong self-absorption effects that depend onthe angle of incidence ( α ) and angle of emission ( β ). b) TheIPFY extracted from the O K PFY for the same experimentalgeometries as panel a. The spectra are offset by a geometrydependent constant, but are otherwise not distorted. Theinset plots the IPFY at E i = 845 eV (red circles) as a functionof sin α/ sin β , which varies linearly as predicted by Eq. (1). c) The linear absorption coefficient, µ ( E i ), obtained from IPFYspectra. As described in the text, the offsets in the IPFYspectra are subtracted, collapsing the IPFY spectra onto asingle curve proportional to µ ( E i ). The spectra shown herehave been scaled using a single tabulated value for µ ( E f )and plotted against the tabulated (green) and calculated (red squares) absorption coefficients. our measurement to tabulated and calculated val-ues of µ ( E i ). The calculated and tabulated data cap-ture the transitions from the core electron to the con-tinuum, accurately reproducing the edge-step, but donot include the multiplet physics associated with the2 p to 3 d transition. We use the calculated value ofthe absorption coefficient at the O K emission energy ( µ ( E f = 524eV) = 3 . × m − for NiO from Ref. 13)to normalize the subtracted offset and determine the pro-portionality constant A . Note that the O K emission isdue primarily to 2 p valence electrons decaying to fill the1 s core hole and is peaked at a photon energy below theabsorption threshold. The data shown in Fig. 2c has beenscaled using µ ( E f ) (a non-arbitrary scaling factor) andis shown along with the tabulated (green curve) andcalculated (red squares) x-ray absorption coefficient.Using this single scaling parameter, we find that themeasured spectra are in excellent agreement with the tab-ulated coefficients in both the pre- and post-edge regions,capturing both the energy dependence and the edge-step.This demonstrates that IPFY provides a measure directlyproportional to the total absorption coefficient with theproportionality constant being µ ( E f ). In contrast, quan-titative analysis of EY or FY spectra requires scaling andoffsetting data to calculated values of the absorption co-efficient above and below the edge, essentially fixing theedge-step. This latter procedure requires prior knowl-edge of the material composition and is subject to uncer-tainties in the tabulated or calculated values which areestimated at 5-20% between 500 and 1000 eV and evenhigher near absorption edges. Moreover, XAS measure-ments often still have significant structure above an ab-sorption edge in the form of extended x-ray absorptionfine structure (EXAFS) that is not accounted for in thetabulated or calculated values, resulting in additional er-rors in normalizing data above an absorption edge. Incontrast, with IPFY, we obtain the energy dependence of µ ( E i ) directly from measurement and can scale the dataat a single point well below the absorption edge. The re-sult of this normalization can be independently checkedagainst the absorption above and below the absorptionedge in question and multiple angles can be measured toensure self-consistency, resulting in a reliable and accu-rate normalization of the data. C. IPFY beyond the XANES
In the NiO measurements shown above, the describedoffsetting procedure works well over the narrow energyrange covered, giving a quantity approximately propor-tional to µ ( E i ). However, over a larger energy win-dow, the energy dependence of µ Y ( E i ) can be significant.An example of this effect is shown in measurements ofNdGaO over a wide energy range. In Fig. 3a, the IPFYmeasured using the O K emission of NdGaO is shownfor three measurement geometries over an extended en-ergy range covering the Nd M edge.The spectra are not rigidly offset, instead appearingto be subject to a sloping background in addition to anoffset. This background is due to the energy dependenceof µ O K ( E i ) and also to the energy dependence of ourmeasurement of the incident photon flux, I .In our measurement, and many XAS measurements, I is measured using a Au grid with 85% transmis- μ ( E i ) ( / μ m ) ( a r b . un i t s ) S ( E i ) ( a r b . un i t s ) I P F Y ( a r b . un i t s ) S ( E i ) S ( E i ) Linear FitIncident photon energy (eV) α = 30°, β = 59.2° α = 90°, β = 41.6° α = 70°, β = 24.6° abcd S ( E i ) I P F Y α = 30°, β = 59.2° α = 90°, β = 41.6° α = 70°, β = 24.6° α = 30°, β = 59.2° α = 90°, β = 41.6° α = 70°, β = 24.6° FIG. 3.
Wide energy range IPFY of NdGaO – a) IPFYof NdGaO for several measurement geometries. The IPFYis measured using the O K emission in a 150 eV window cen-tred about 524 eV. The measurements at different geometriesexhibit different sloping backgrounds due to the energy de-pendence of µ O K ( E i ) and the quantum efficiency of the I measurement, ν ( E i ). b) S ( E i ) calculated using Eq. (3) withthe different measurement geometries depicted in the legendof panel a. The black line is a linear fit to S ( E i ). c) TheIPFY( E i ) /S ( E i ) spectra are rigidly offset by B . d) The totalabsorption coefficient, µ ( E i ), determined using Eq. (5) (thedata are scaled to µ (524 eV) from Ref. 14). The spectra mea-sured with different geometries collapse onto a single curveover the entire energy range. sion that is placed between the sample and the lastoptical component. The total electron yield from thegrid, I Grid , is used to measure the incident photon flux.This measurement, however, depends not only on I ,but also on the quantum efficiency of the mesh, ν ( E i ) (the number of electrons generated per incident photon),which in general will be energy dependent. As such, I Grid ( E i ) = I ( E i ) ν ( E i ) and Eq. (1) should be modifiedto: IP F Y = I Grid ( E i ) I ( E i , E f ) = I ( E i ) ν ( E i ) I ( E i , E f ) ≈ Dν ( E i ) µ Y ( E i ) ( µ ( E i ) + B ) (2)where D = Aµ Y ( E i ). Fortunately, the energy depen-dence of both ν ( E i ) and µ Y ( E i ) can be unambiguouslyeliminated from the data by subtracting IPFY spec-tra measured with different measurement geometries andnormalizing to the geometry ( ν ( E i ) generally also entersinto EY and FY measurements, but is typically not cor-rected for). From Eq. (2) it follows that S j,k ( E i ) = Dν ( E i ) µ Y ( E i ) µ ( E f )= IP F Y ( α j , β j ) − IP F Y ( α k , β k ) sin α j sin β j − sin α k sin β k (3)where j and k correspond to different measurement ge-ometries and S ( E i ) is independent of the choice of j and k . We can now write IP F YS ( E i ) = 1 µ ( E f ) (cid:18) µ ( E i ) + µ ( E f ) sin α sin β (cid:19) , (4)which is simply rearranged to yield the total x-ray ab-sorption coefficient: µ ( E i ) = µ ( E f ) (cid:18) IP F YS ( E i ) − sin α sin β (cid:19) . (5) μ ( E i ) ( / μ m ) α =30°, β =59.2° NIST μ ( E i ) FIG. 4.
Normalized IPFY compared to atomic calcula-tions – The absorption coefficient of NdGaO extracted fromthe O K IPFY and corrected for the energy dependence ofthe O K absorption and the quantum efficiency of the I mea-surement. The incident photon energy was scanned across theNd M and M edges. The data agrees well with calculatedXAS over a wide energy range. In Fig. 3, this subtraction is shown, giving S ( E i ) that isa smooth function of energy. As shown in Fig. 3c, divid-ing the spectra in Fig. 3a by S ( E i ), provides spectra thatare rigidly offset over a wide range in energy. Subtractingsin α/ sin β from the spectra provides µ ( E i ) /µ ( E f ), col-lapsing the data onto a single curve, which is then scaledusing a calculated value of µ ( E f = 524 eV) as shown inFig. 3d. When normalized in this way, the spectra are inexcellent quantitative agreement with the calculated ab-sorption coefficient over a wide energy range above andbelow the Nd M , absorption edge, as shown in Fig. 4. D. IPFY in strong insulators
Finally, we would like to emphasize the role of IPFY tostudy insulating samples that can be difficult or impossi-ble to measure correctly using FY or EY. An example ofsuch a system is NdGaO . This material is an insulatorcommonly used as a substrate for oxide film growth. EYmeasurements of the Nd M edge in NdGaO , shown inFig. 5a, exemplify issues one can encounter when mea-suring the EY of samples. Here the EY has an unphysicalnegative edge jump at the absorption edge. The unusualbehaviour is attributed to a build-up in positive chargenear the surface of the sample that effectively reducesthe number of emitted electrons. We were able to reducethe effect by recording the spectra by scanning the inci-dent photon energy in the negative direction (1020 eV to980 eV) or measuring different spots on the sample, butultimately these spectra are not reliable.PFY and TFY in this material are also unreliable. TheNd edge PFY measurements, shown in Fig. 5b, are heav-ily distorted by self-absorption effects, similar to NiO. Incontrast, the IPFY (Fig. 5c) provides the correct XASspectrum for Nd . This is evidenced by excellent agree-ment with XAS in pure Nd, which like NdGaO hasNd character and is described well by atomic multipletcalculations. In this case, both EY and FY provide er-roneous results and transmission measurements are notpossible due to the thickness of the sample. As such,IPFY provides the only means to measure the correctXAS spectrum. We anticipate IPFY to be widely appli-cable to similar cases.
DISCUSSION
Experimental studies that require accurate knowledgeof optical constants or atomic scattering form factors,such as in modelling of resonant reflectivity or x-ray scat-tering, stand to benefit substantially from angle depen-dent IPFY since it provides a measure of the total ab-sorption coefficient. In such studies, it is common toscale and offset XAS spectra above and below an absorp-tion edge to tabulated atomic calculations or absorptiondata. This procedure requires knowledge of the com-position of a material and requires measurements that I n t e n s i t y ( a r b . un i t s ) T E Y ( a r b . un i t s ) P F Y ( a r b . un i t s )
960 to 1020 eV 1020 to 960 eV NdGaO IPFY Nd TEY α =90° β =41.6° α =30° β =59.2° abc FIG. 5.
XAS of NdGaO – a) The TEY of NdGaO ex-hibits an anomalous negative edge-jump across the Nd M , edges (red curve). A spectrum collected with the incidentphoton energy scanned in the negative direction (blue curve)soon after has positive edge-jumps. This difference is at-tributed to a charge up of the sample surface, affecting theTEY measurement. Neither spectrum matches well with TEYon pure metallic Nd from Ref. 23. b) The partial fluorescenceyield from the Nd emission of NdGaO is strongly distortedby saturation effects. c) The IPFY extracted from the O K PFY of NdGaO agrees remarkably well with the TEY ofpure Nd from Ref. 23 which is scaled and offset to match theIPFY. extend sufficiently above absorption edges to avoid EX-AFS resonances. It is not always possible to meet theserequirements, and in such cases the determination of op-tical constants or atomic scattering form factors will nec-essarily be subject to systematic errors. In contrast, withangle dependent IPFY, µ ( E i ) and µ ( E f ) can be deter-mined with a simple fitting approach that does not de-pend on prior knowledge of material composition. Con-sequently, scaling the measured absorption to absoluteunits using µ ( E f ) enables the determination of atomicform factors with the appropriate edge-step even if sam-ple composition is not previously known or if the XASspectra do not extend sufficiently above the EXAFS.As an accurate measure of µ ( E i ), IPFY spectroscopycould become a powerful tool in non-destructive quan-titative analysis of material composition, which can bedone separately or in conjunction with XANES or EX-AFS measurements of electronic and spatial structure.Without prior knowledge of material composition, it ispossible to fit µ ( E i ) /µ ( E f ) to a sum of the tabulatedatomic absorption coefficients in order to determine therelative weights of each atomic species in a sample. Fur-thermore, µ ( E f ) can be determined by the fitting routineas it too is the weighted sum of the atomic contributions.Thus, in a fully self-consistent way, it is possible to utilizeIPFY spectra to estimate the composition of an unknownsample. Even if a quantitative estimate is not needed,the magnitude of the pre-edge relative to the post-edgebears a distinct signature of the quantity of an elementrelative to the other elements in the material. A simplecomparison of the magnitude of the edge-step comparedto calculations or to IPFY on similar materials can thenbe used as a clear measure of sample composition. Webelieve this kind of non-destructive estimate of samplecomposition will be very useful to XAS practitioners asa simple means to verify the stoichiometry of a givensample.Finally, we would like to comment on the applicabilityof IPFY to the hard x-ray regime. Thus far, IPFY hasonly been demonstrated using soft x-rays. However, wefeel IPFY would likely also be useful for XAS at hard x-ray energies. In order to measure IPFY in this case, onewould require the appropriate selection of emission lines.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 thedetector may make it impossible to detect these. How-ever, in compounds with multiple elements, one couldin principle utilize non-resonant K or L emission lines(at intermediate to hard x-ray energies) to study the K edge absorption of another element. Hence, we believethat IPFY studies at hard x-ray energies are feasible andcould be performed using a similar detection scheme aswe have used at soft x-ray energies.In conclusion, we have demonstrated a measure of thetotal x-ray absorption coefficient using angle dependentIPFY. Unlike in EY or conventional FY measurements,the offset in IPFY can be subtracted unambiguously from experiments with varied geometry to provide data di-rectly proportional to µ ( E i ) and undistorted by satura-tion or self-absorption effects. By scaling to a single valueof µ ( E f ), µ ( E ) is obtained in absolute units. We antici-pate this technique to have wide applicability in many ar-eas of science and engineering, potentially opening XASup to non-destructive, quantitative analysis of materialcomposition. METHODS
The XAS measurements were performed at the Cana-dian Light Source’s 11-ID SGM beamline. All mea-surements were made at room temperature. The draincurrent of the sample provided the electron yield. Anenergy-dispersive silicon drift detector (SDD) with an en-ergy resolution of ∼
120 eV was used to collect the emis-sion spectra as a function of incident photon energy. TheSDD was fixed in position (25 . ◦ below the plane and42 . ◦ from the beam axis) and the sample was rotatedabout the vertical axis to vary α and β , the angles ofincidence and emission, respectively. Dark counts on thedetector were negligible. However, a small backgroundin the 200-2000 eV region of the NiO emission spectrawas observed, likely due to a slight mis-calibration of thedetector electronics. This background potentially intro-duced an error of up to 20% at the Ni L peak and 3%in the post-edge.The single crystal of cubic NiO was polished to asurface roughness less than 0.03 µ m. Its dimensionswere 5 × h i direction was perpendicular to the samplesurface. The NdGaO single crystal was a 10 ×
10 mmby 0.5 mm thick, polished substrate oriented with the h i direction perpendicular to the sample surface. ACKNOWLEDGMENTS
This research is supported by the Natural Sciencesand Engineering Research Council of Canada and by theNational Science Foundation through DMR-0847385 andthe MRSEC program under DMR-0520404 (Cornell Cen-ter for Materials Research). The research described inthis paper was performed at the Canadian Light Source,which is supported by NSERC, NRC, CIHR, and the Uni-versity of Saskatchewan. E.J.M. acknowledges NSERCfor PGS support. Lee, P., Citrin, P., Eisenberger, P. & Kincaid, B. ExtendedX-ray absorption fine structure - its strengths and limita-tions as a structural tool.
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