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Daisuke Shibata, Toshiaki Ohta, Yuki Orikasa, [Kimihiko Ito](https://orcid.org/0000-0003-0611-9590), Kiyotaka Asakura

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[A Voxel Method for Correcting the Self-absorption Effect in Fluorescence X-ray Absorption Fine Structure Spectra](https://mdr.nims.go.jp/datasets/4916677d-973f-4dab-b74c-6a90b0b86679)

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A Voxel Method for Correcting the Self-absorption Effect in Fluorescence X-ray Absorption Fine Structure Spectrae-Journal of Surface Science and Nanotechnology 23, 36–43 (2025)A Voxel Method for Correcting the Self-absorption Effectin Fluorescence X-ray Absorption Fine Structure SpectraDaisuke Shibata,a, † Toshiaki Ohta,a Yuki Orikasa,b Kimihiko Ito,c Kiyotaka Asakura a, ‡a SR Center, Research Organization of Science and Technology, Ritsumeikan University, 1-1-1 Noji-Higashi, Kusatsu, Shiga 525-8577, Japanb College of Life Sciences, Ritsumeikan University, 1-1-1 Noji-Higashi, Kusatsu 525-8577, Japanc National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan† Corresponding author: dshibata@fc.ritsumei.ac.jp‡ Corresponding author: kytkaskr@fc.ritsumei.ac.jpReceived: 15 November, 2024; Accepted: 27 January, 2025; J-STAGE Advance Publication: 1 March, 2025; Published: 1 March, 2025Partial fluorescence yield X-ray absorption fine structure (PFY-XAFS) spectroscopy in the soft X-ray region is important for obtain-ing information about the bulk region of a sample. However, the self-absorption effect is a serious problem that causes distortions to the finestructure of PFY-XAFS spectra. This self-absorption can be analyti-cally corrected for flat surfaces but not for arbitrary shapes such asthose of particles in powders. In this study, we propose a voxel methodwhere we divide the sample with arbitrary shapes into small boxes(called voxel) to calculate the self-absorption effect. By comparing theO K-edge PFY-XAFS spectra of a CoO single crystal, a thin layerLi2CO3 on a NiO substrate, and a CoO powder sample, we investigatethe validity of the voxel method, along with its merits and limitations.Keywords Soft X-ray PFY-XAFS; Self-absorption; Voxel methodI. INTRODUCTIONX-ray absorption fine structure (XAFS) spectroscopy is apowerful technique used to characterize the local structureand electronic states around X-ray-absorbing atoms in bothcrystalline and amorphous materials [1, 2]. The key featureof XAFS spectroscopy is its element specificity, which ispossible because each element has a characteristic absorptionedge energy. In particular, hard X-rays with an energy greaterthan 4 keV exhibit high penetration ability and allow XAFSexperiments to be conducted in a transmission mode evenunder ambient conditions. Operando XAFS under high pres-sure provides information about catalyst chemical reactionmechanisms [3]. However, transmission-mode XAFS analy-sis of light elements, such as carbon, oxygen, and fluorine, isdifficult because the K edges of these elements correspond tothe soft X-ray region (<1000 eV), and soft X-rays have muchless penetration ability than hard X-rays. The penetrationability is estimated by the attenuation length. For example,carbon materials, oxides, and fluorides typically have anattenuation length of 100, 280, or 350 nm, respectively, afterthe K-absorption edges [4]. Electron-based detection meth-ods, such as total electron yield (TEY) and partial electronyield (PEY), are usually used in soft X-ray XAFS measure-ments [5, 6]. However, because these electron-yield detectionmethods are surface sensitive, the obtained spectra arestrongly affected by the surface state, and obtaining informa-tion about the bulk region is difficult.Partial fluorescence yield XAFS (PFY-XAFS) is an im-portant method for obtaining XAFS information about low-concentration target elements in the bulk region of a sample.However, PFY-XAFS for concentrated samples suffers froma self-absorption effect, which reduces the intensity of theXAFS spectra and causes spectral distortion. For a flat sub-strate of uniform concentration with thickness d, the fluores-cence intensity (IF) including self-absorption can be obtainedvia the following analytical equation with incidence angle �and emission angle � from the flat surface [see Figure 1(d)][7–9]:Regular Papere-J. Surf. Sci. Nanotechnol. 23, 36–43 (2025) | DOI: 10.1380/ejssnt.2025-010 36mailto:dshibata@fc.ritsumei.ac.jpmailto:kytkaskr@fc.ritsumei.ac.jphttps://doi.org/10.1380/ejssnt.2025-010IF ¼ kXI0�XðEÞ�totðEÞ þ �totðEFÞ sin �sin �× 1 � exp � �totðEÞsin �d � �totðEFÞsin �d� �� �; ð1Þwhere kX , I0, �XðEÞ, �totðEÞ, and �totðEFÞ are the branchingratio of the fluorescence to Auger decays, the intensity of theincident X-rays, the X-ray absorption coefficient for thetarget X-ray absorption edge of the X-ray-absorbing atomX at incident X-ray energy E, the total absorption coefficientat E, and the total absorption coefficient at fluorescence X-ray energy EF, respectively. The parameter �totðEÞ can beexpressed as �totðEÞ ¼ �BGðEÞ þ �XðEÞ, where �BGðEÞ is thebackground absorption coefficient at regions other than thetarget X-ray absorption edge for incident X-ray energy E. Ifthe sample has a flat surface and the appropriate assumptionsare made for �BG and �totðEFÞ, Eq. (1) can be used toestimate �XðEÞ from a spectrum, IF=I0, that is distorted bythe self-absorption effect. We refer to fluorescence correctionusing Eq. (1) as the flat-surface model.The thick samples have the term 1 � exp�� �totðEÞsin � d ��totðEFÞsin � d� � 1. When �BG � �X , Eq. (1) can be approximatedasIF ¼ kXI0�XðEÞ�BGðEÞ þ �totðEFÞ sin �sin �: ð2ÞThus, IF=I0 / �XðEÞ. It is called as thick and dilute case inwhich the fluorescence XAFS works well without any cor-rections [10].By contrast, in the thick and concentrated case,IF ¼ kXI0�XðEÞ�BGðEÞ þ �XðEÞ þ �totðEFÞ sin �sin �: ð3ÞThe �X terms in the numerator and denominator are canceledout, and the amplitude of the XAFS spectrum is reduced. Theraw IF=I0 is not directly proportional to �X , and the self-absorption correction using Eq. (1) is necessary.In the hard X-ray region, if the absorbance of the sample isnot large (or if the attenuation length is sufficiently large), aflat surface can easily be obtained by compacting the powderinto a disc. Creating a sufficiently flat surface in the soft X-ray region is difficult because the attenuation length is muchsmaller than that in the hard X-ray region and the surfaceroughness should be smaller than 100 nm. Consequently,applying the flat-surface model using Eq. (1) is not straight-forward. In this article, we present the results of a newsimulation method, referred to as the voxel method, in whichthe sample is divided into small cubes (voxels), and the self-absorption in each voxel is calculated to simulate �X for anarbitrarily shaped sample. In Section II, we describe thevoxel method and the experimental details. In Section III,we check the validity of the voxel method in two ideal cases:a flat CoO single crystal and a flat thin Li2CO3 layer on aNiO substrate. Finally, we apply the voxel method to apowder system.Figure 1: Schematic of (a) voxels and (b) subvoxels; dark and pale-gray boxes correspond to a full voxel and a border voxel, respectively. Theborder voxel is further divided into 8 × 8 × 8 subvoxels (b). (c) A three-dimensional drawing of a voxel. (d) CoO single crystal case. (e) Li2CO3/NiO film case; The green region in the subvoxel means Li2CO3 thin layer while the grey region in the subvoxel is the NiO substrate.Regular Papere-J. Surf. Sci. Nanotechnol. 23, 36–43 (2025) | DOI: 10.1380/ejssnt.2025-010 37https://doi.org/10.1380/ejssnt.2025-010II. EXPERIMENTAL ANDANALYTICAL METHODSA. XAFS measurementsThe XAFS measurements were performed at beamline BL-11 at the SR Center, Ritsumeikan University (RSRC). The X-rays emitted from the ultra-compact storage ring Aurora-1(Sumitomo Heavy Industry) operated at 150mA with0.575GeV were monochromatized by a 1200Lmm−1 gratingand focused on the sample by a toroidal mirror. The TEYandPFY data were acquired simultaneously using the samplecurrent and a silicon drift detector (SDD) (TechnoAP), re-spectively. The SDD has an effective detection area of50mm2 and a sample-detector distance of 25mm. The anglebetween the SDD and the incident X-ray beam was set to90°. Consequently, � ¼ 90° � �.The five samples (a CoO single crystal, a thin Li2CO3layer on a NiO substrate, CoO powder, Co3O4 powder, andLi2CO3 powder) were measured. The CoO single crystal wasmechanically polished with Al2O3 powder with a particle sizeof 0.05 µm. The Li2CO3 was deposited onto a 1000 nm-thickNiO film on a silicon wafer. It is hereafter denoted as Li2CO3/NiO. The thickness of the Li2CO3 thin film was 10 nm,determined by X-ray reflectivity measurements. CoO powderwas purchased from Kojundo Chemical and stored underatmospheric conditions. A typical SEM (scanning electronmicroscopy) picture and particle size distribution by the lightscattering are given in Figures S1 and S2 (SupplementaryMaterial). SEM picture was obtained by JSM-7800F (JEOL).The CoO powder was put on the carbon conducting tape withextra powder removed. The particle size distribution wasobtained using a laser scattering particle analyzer (LA-950V2, HORIBA). The CoO powder was dispersed in etha-nol solution.Li2CO3 powder was purchased from FUJIFILM WakoPure Chemical. Co3O4 was prepared by the calcination ofCoO at 800°C in air because the decomposition temperatureof Co3O4 is 890°C in air [11]. The powder samples were puton the conductive tape. The extra powder particles werecarefully removed not to create particle overlap. The acquireddata were processed in the Athena software for backgroundremoval and normalization [12].B. Voxel methodThe voxel method is a numerical computational method inwhich the material body is divided into small cubes calledvoxels. Each voxel at the relative coordinate, ~r ¼ ðx; y; zÞ,holds various parameters such as density, molar fraction, andcomposition, together with absorption coefficients for all ofthe component elements (Figure 1). To express the bordermore precisely, we introduce subvoxels with a smaller size,as shown in Figure 1(b), and calculate the absorption coef-ficients at the border. The sample was typically divided into16 × 16 × 16 voxels and the voxel at the border was furtherdivided into 8 × 8 × 8 subvoxels as shown in Figure 1(a, d).In the thin layer (10 nm thick Li2CO3) system the sample wasdivided into 32 × 32 × 32 voxels and then the voxel wasdivided into 8 × 8 × 8 subvoxels as shown in Figure 1(e) tocalculate the borders more precisely. The calculation timedepends on the number of divisions. For example, we need 8times longer calculation time for the 32 × 32 × 32 voxelsthan that for the 16 × 16 × 16 voxels. Because the synchro-tron radiation exhibits only a small amount of divergence, thelight emitted from the storage ring is considered parallel. Thevoxel is placed with its edge parallel to the incident X-raybeam. The total fluorescence signal is calculated asIF ¼Z~r2�dIF¼ i0Z~r2�kXð~rÞTinð~r; EÞ�Xð~r; EÞToutð~r; EFÞd~r¼ i0X~rnkXð ~rnÞTinð ~rn; EÞ�Xð ~rn; EÞvnToutð ~rn; EFÞ; ð4Þwhere i0, vn, Tinð ~rn; EÞ, and Toutð ~rn; EFÞ are the incident X-rayintensity per unit area, the voxel volume (=l3), and thetransfer operators expressing the absorption of incident X-rays traveling through the sample to voxel n and the absorp-tion of the outgoing X-rays from voxel n to the detector,respectively. Because the voxels are set with their side edgesparallel to the incident X-rays (Figure 1), Tinð ~rn; EÞ can besimply expressed asTinð ~rn; EÞ ¼ exp��Xso on s!rn�totðrso; EÞlso�Xi on s!rn�totðri; EÞl�;where l and lso are the edge lengths for a voxel and subvoxel,respectively,Pi on s!n indicates the summation of all i-thvoxels along the optical path from the source to the n-thvoxel, andPso on s!rnis similarly summed over the subvox-els along the optical path. However, Toutð ~rn; EFÞ is somewhatcomplex because the outgoing fluorescence X-ray beamdiverges and the X-rays travel to the detector in an obliquedirection (Figure 1). The optical path length l0j;rn� is not equalto the voxel edge length l; it depends on the fluorescenceemission point, rn, and the detection point of the detector, �.We use Siddon’s algorithm to evaluate l0j;rn� [13]. Similarly,we introduce l0so;rn� as the optical path length in a subvoxel onthe path:Toutð ~rn; EFÞ ¼ZSexp��Xj on rn!��totðrj; EFÞl0j;rn��Xso on rn!��totðrso; EFÞl0so;rn��d�;where S is an individual detection area on the detector, andthe integral is performed over all detection areas. In thecalculation, �totð~r; EÞ is necessary: �totð~r; EÞ ¼ �BGð~r; EÞ þ�Xð~r; EÞ. For each voxel, �BG can be evaluated using theCromer–Liberman method [14].Regular Papere-J. Surf. Sci. Nanotechnol. 23, 36–43 (2025) | DOI: 10.1380/ejssnt.2025-010 38https://doi.org/10.1380/ejssnt.2025-010III. RESULTS AND DISCUSSIONA. CoO single crystalTo check the validity of the voxel method, we comparedspectra constructed from experimental PFY-XAFS data for aflat CoO single crystal with those constructed from calculateddata. The calculated PFY-XAFS spectra were obtained fromTEY data after the background was removed and normal-ization was carried out. Figure 2(a) shows O K-edge PFY-XAFS spectra of the CoO single crystal for different incidenceangles. Although CoO has a highly symmetric NaCl structurewith oxygen atoms occupying the 4b sites and no polarizationdependence is expected, we find a strong angular dependence.Especially for � ¼ 5°, all peaks are suppressed, which weattribute to the self-absorption effect. According to Eq. (1),when � becomes small, � becomes nearly 90°. Consequently,the first term in the denominator of Eq. (1), �totðEÞ½¼ �BGðEÞ þ �XðEÞ� becomes dominant and the �XðEÞ termsin the numerator and the denominator are canceled so that thepeaks are strongly suppressed. However, for � ¼ 90°, thesecond term in the denominator becomes dominant and IF isapproximately proportional to �X , although the intensity islow because of the long path length for fluorescence X-rays.Figure 2(b) shows the self-absorption-simulated spectra ofCoO using Eq. (1) under the assumption that �XðEÞ is thesame as that for the TEY-XAFS spectrum shown in Fig-ure 2(c). We found the same behavior of the simulated andthe observed spectra as shown in Figure 2(a, b). The self-absorption-simulated PFY-XAFS spectra at � ¼ 5° arestrongly affected while the self-absorption-simulated PFY-XAFS spectra at � ¼ 90° appear similar to the originalTEY-XAFS spectrum [Figure 2(b, c)]. The spectra in Fig-ure 2(d) have been corrected using Eq. (1) (red line) fromPFY-XAFS data acquired at an incidence angle of 50° andusing the voxel method (blue line). Although small differ-ences are observed in the peak intensities because of thefinite size of the voxel, the spectrum corrected by the voxelmethod generally agrees well with that based on the flat-surface model [Eq. (1)], indicating that the voxel methodcalculation works well.The PFY-XAFS structures appear clearer and sharper thanthe TEY-XAFS structures. Suppose the fluorescence XAFSdata are acquired with high energy resolution (less than1 eV). In that case, high-energy-resolution XAFS spectraare expected, which is known as the high-energy-resolutionfluorescence detection (HERFD) method. However, we usedan SDD in this work, which has an energy resolution of80 eV [15]. Thus, the SDD’s energy resolution is insufficientto produce a HERFD spectrum. We speculate that the surfaceof the polished single crystal was somewhat oxidized orreconstructed. These effects were detected in the surface-sensitive TEY-XAFS spectra.Figure 2: (a) PFY spectra of CoO single crystal. (b) Self-absorption-simulated spectra of CoO single crystal using its TEY spectrum. (c) TEYspectrum of CoO scaled by edge jump. (d) PFY spectra were corrected using the flat-surface model and the voxel method.Regular Papere-J. Surf. Sci. Nanotechnol. 23, 36–43 (2025) | DOI: 10.1380/ejssnt.2025-010 39https://doi.org/10.1380/ejssnt.2025-010B. Li2CO3/NiO filmWe tested the performance of the voxel method in a mixedLi2CO3/NiO system containing several components. For thelayer-on-layer flat surface, the fluorescence signal IF is givenin Eq. (5), where O fluorescence is emitted from each layerof the sample:IF ¼ k1XI0�1XðEÞ�1totðEÞ þ �1totðEFÞ sin �sin �× 1 � exp � �1totðEÞsin �d1 � �1totðEFÞsin �d1� �� �þ exp � �1totðEÞsin �d1 � �1totðEFÞsin �d1� �×k2XI0�2XðEÞ�2totðEÞ þ �2totðEFÞ sin �sin �× 1 � exp � �2totðEÞsin �d2 � �2totðEFÞsin �d2� �� �:ð5ÞThe upper Li2CO3 film with a thickness d1 (= 10 nm) isdenoted as 1 and the NiO substrate with a thickness d2(= 1000 nm) is denoted as 2.Equation (5) is composed of two terms. The first term isthe fluorescence signal from the thin overlayer 1, and thesecond term is that for the thick substrate film 2 afterabsorption of incident X-rays and emission of fluorescenceby the overlayer 1. Because oxygen atoms are present in bothfilms, the IF signal is generated in a complex manner viainterference between 1 and 2.Figure 3(a) shows the observed O K-absorption edge PFY-XAFS spectra of Li2CO3/NiO acquired at different incidenceangles. Figure 3(c, d) shows a TEY-XAFS spectrum ofLi2CO3 powder and a reference NiO single crystal. Theraw PFY-XAFS spectrum is similar to the TEY-XAFS spec-trum of the NiO single crystal [Figure 3(d)]. The angulardependence of the PFY-XAFS spectrum can be understoodbased on the PFY-XAFS spectra of the CoO single-crystal.When � is small, the PFY-XAFS spectra are strongly dis-torted, whereas a weaker self-absorption effect is observedwhen � � 90°. However, an extra peak appears at 533 eVwhen � ¼ 5° and 85°. By comparison of the spectra with theTEY-XAFS spectrum of Li2CO3 powder, we assign this tothe �� peak of CO2�3 in Li2CO3. The appearance of the peakin the � ¼ 85° spectrum can be understood from the follow-ing term in Eq. (5):exp � �1totðEÞsin �d1 � �1totðEFÞsin �d1� �: ð6ÞIn Eq. (6), the first and second terms represent absorption ofincident X-rays by the thin overlayer 1 and absorption of theoutgoing X-ray fluorescence emitted from the substrate 2 bythe thin overlayer 1, respectively. For � ¼ 5°, the first termacts as previously described, whereas at � ¼ 85°, the secondterm reduces the fluorescence signal from the substrate 2. AsFigure 3: (a) PFY spectra of Li2CO3/NiO film. (b) Self-absorption-simulated spectra of Li2CO3/NiO film, as calculated from TEY. TEY-XAFSspectra of (c) Li2CO3 powder and (d) a NiO single crystal.Regular Papere-J. Surf. Sci. Nanotechnol. 23, 36–43 (2025) | DOI: 10.1380/ejssnt.2025-010 40https://doi.org/10.1380/ejssnt.2025-010a result, the contribution from the substrate 2 is reduced forboth � ¼ 5° and 85°.Figure 3(b) shows the self-absorption-simulated spectrausing the voxel method and Eq. (5). We estimated the �Xvalues for the Li2CO3 powder and NiO from their TEY-XAFS spectra shown in Figure 3(c, d). We assumed thatk1X and k2X were equal and that O was homogeneouslydistributed in each film. The solid and dotted lines in Fig-ure 3(b) correspond to the simulated spectra obtained by thevoxel method and the flat-surface model, respectively. Thespectral trend are roughly reproduced by both methods. Inthe voxel method, the fitting is not so good in a low � regionbecause of the limitation of the machine power not to makethe further smaller subvoxel.C. CoO powderFinally, we analyze the PFY-XAFS spectra of CoO powderby the voxel method. Figure 4(a) shows TEY-XAFS andPFY-XAFS spectra of Co3O4 and CoO powders. The TEY-XAFS and PFY-XAFS spectra of Co3O4 exhibit similarfeatures and correspond well with the spectrum in the liter-ature [16]. The PFY-XAFS spectra of Co3O4 have lower peakintensities than the corresponding TEY-XAFS spectra, re-flecting the effect of self-absorption.The TEY-XAFS spectrum of the CoO powder is similar tothat of Co3O4, indicating that surface of the CoO powdersample is oxidized to Co3O4. Compared with the TEY-XAFSspectrum of the CoO powder, the PFY-XAFS spectrum ismore similar to the TEY-XAFS of a CoO single crystal.Figure 4(b) shows the self-absorption-simulated spectra ofCoO powder with various sizes using the voxel method. Weassumed a single spherical particle. The �X used for thesimulation was estimated from the PFY-XAFS spectrumof CoO single crystal after self-absorption correction[Figure 2(d)]. For a particle with a radius of ~10 nm, theself-absorption-simulated spectrum is unaffected by self-absorption. In Eq. (1) for the flat-surface model, theterm 1 � exp ð� �totðEÞsin � d � �totðEFÞsin � dÞ can be approximated asð� �totðEÞsin � d � �totðEFÞsin � dÞ and is canceled by the denominator.When the particle radius is greater than 500 nm, the self-absorption-simulated spectrum no longer varies with particlesize, indicating saturation of the self-absorption effect, whichcorresponds to Eq. (3) in the flat-surface model. The particlesize of CoO powder was about a 2–20 µm as shown inFigure S1 and its average size determined by light scatteringwas 7 µm in Figure S2 (Supplementary Material). Conse-quently, we can consider the self-absorption effect of thePFY signal as saturated.Figure 4(c) shows the spectrum after self-absorption cor-rection assuming a particle radius of 1000 nm. This spectrumagrees well with the TEY-XAFS spectrum of the CoO singlecrystal. The peak intensities are reduced compared with thosein the PFY-XAFS spectrum of the CoO single crystal afterself-absorption correction. This difference is due to the pres-ence of a Co3O4 thin layer on the surface, which is observedin the TEY-XAFS of the CoO powder.We performed calculations for different thicknesses of theCo3O4 shell around the CoO core. Figure 5(a) shows the self-absorption-simulated spectra of CoO particles with core radiiof 100, 500, and 1000 nm, where the particles are coveredFigure 4: (a) Experimental spectra (TEY and PFY) of Co3O4 and CoO powders. (b) Self-absorption-simulated spectra of CoO with differentparticle sizes, as calculated using the voxel method. A sphere with radius r is assumed. (c) Corrected PFY-XAFS spectra of the powder andsingle crystal of CoO and the TEY-XAFS spectrum of the single crystal of CoO.Regular Papere-J. Surf. Sci. Nanotechnol. 23, 36–43 (2025) | DOI: 10.1380/ejssnt.2025-010 41https://doi.org/10.1380/ejssnt.2025-010with a Co3O4 shell with different thicknesses. The overalldegree of self-absorption changes with the CoO core radius,whereas the shape of the spectra changes with the thicknessof the Co3O4 shell. The PFY-XAFS spectrum of the CoOpowder is well reproduced by a CoO core with a radius of1000 nm covered with a Co3O4 shell with a thickness of lessthan 50 nm. We performed calculations with the radius of theCoO core set at 1000 nm and with the thickness of the Co3O4shell varied in 10 nm steps. As shown in Figure 5(b), thespectrum of CoO with a thickness of 10 nm agrees with thePFY-XAFS spectrum of the CoO powder. We evaluated thesimilarity of the two spectra using the Pearson correlationcoefficient (¼ cov½XY��X�Y), where cov½XY� and �X �Y are thecovariance and standard deviation of spectra X and Y , re-spectively. Figure 5(c) shows the similarity of the spectra,indicating that the Co3O4 shell thickness is approximately10 ± 5 nm. This result is reasonable considering the TEYmeasurement depth (~5 nm [17]).D. Fluorescence XAFS for bulkmeasurements in the soft X-ray regionXAFS is an important technique for the analysis of localstructure. In the hard X-ray region, the advantage of XAFS isits deep penetration ability, which enables easy transmission-mode acquisition of the structural information about the bulkregion of a sample. In contrast, transmission-mode XAFS inthe soft X-ray region is difficult to carry out because itrequires a special device and windows to prepare a thinand homogeneous sample [18]. TEY-XAFS is usually used;however, it is still surface sensitive. Its sampling depth is lessthan 10 nm for an X-ray energy of <1000 eV [17, 19]. Thedifference in surface composition from the bulk stronglyaffects the spectra and gives erroneous results. BecausePFY-XAFS can be used to detect deeper regions, PFY-XAFSmeasurements are more suitable for acquiring bulk data inthe soft X-ray region. In addition, recently HERFD-XANES(X-ray absorption near edge structure) method has rapidlybeen developed, which provides high-energy-resolutionXANES spectra and fruitful information about the electronicstates of samples [20–26]. HERFD-XANES uses a fluores-cence detection and strongly suffers from the self-absorptioneffect if one measures the thick concentrated samples. Itis difficult to obtain the HERFD-XANES of referencecompounds without self-absorption correction. Thus, theHERFD-XANES method necessitates the self-absorptioncorrection. In the hard X-ray region, the flat-surface methodusing Eq. (1) is available using a flat disc sample prepared bycompacting a sample powder and the sample roughness isexpected to have a negligible influence. In the soft X-rayregion, Eq. (1) is limited because of surface roughness andinhomogeneity in the powder sample. The voxel methodproposed here is useful for the analysis of powder systemsto express the roughness and inhomogeneity in the samplemore precisely. We can obtain information about the samplecomposition and roughness by SEM, electron-probe micro-analysis (EPMA) and atomic force microscopy (AFM). Asshown in Section III.C, the TEY-XAFS measurement is pref-erably conducted simultaneously with PFY-XAFS to detectsurface contaminants and compositions. The voxel methodis still limited due to the high computational cost. It took30min for a Windows computer with i7-6700HQ CPU(clock = 2.6GHz) to calculate the 16 × 16 × 16 voxels. WeFigure 5: (a) Self-absorption-simulated spectra of particles with CoO core radii of 100, 500, and 1000 nm, where the cores are coated withCo3O4. The labels in the figure for example, 100 nm–50 nm mean the CoO core with 100 nm raius covered with 50 nm thick Co3O4 shell. (b)Self-absorption-simulated spectra of CoO samples with various thicknesses. (c) Pearson correlation coefficient between the PFY spectrum ofCoO powder and the self-absorption-simulated spectra with a model of a CoO core coated with Co3O4 shell.Regular Papere-J. Surf. Sci. Nanotechnol. 23, 36–43 (2025) | DOI: 10.1380/ejssnt.2025-010 42https://doi.org/10.1380/ejssnt.2025-010have to calculate many self-absorption-simulated spectrarepeatedly with different physical parameters such as thethickness of the surface layers and compare them with theobserved one to estimate the self-absorption correction. Thus,we spent a few weeks to obtain the final corrected spectraunder the appropriate model structure. However, the im-provement of the program and the increase in the computer’scalculation machine power will allow more realistic calcu-lations, and the voxel method will make the PFY-XAFS apowerful and practical bulk analysis tool in the soft X-rayregion.IV. CONCLUSIONThe voxel method enables us to correct for self-absorptionof PFY-XAFS for a sample with an arbitrary shape. Once thesample roughness, composition, distribution, and morphol-ogy are known, the PFY-XAFS data can be corrected evenfor inhomogeneous samples. We can determine the bulkinformation in the soft X-ray region using PFY-XAFS. Em-powered by the HERFD technique, PFY-XAFS will be amore conventional and powerful analysis tool in the soft X-ray regions.AcknowledgmentsThis study is supported by the New Energy and IndustrialTechnology Development Organization (NEDO; GrantNo. JPNP21006). The authors thank FORTE Science Communica-tions (https://www.forte-science.co.jp/) for editing the English lan-guage.AppendixThe SEM and light scattering data of CoO powder are availablein Supplementary Material at https://doi.org/10.1380/ejssnt.2025-010.References[1] Y. Iwasawa, K. Asakura, and M. 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