METHOD FOR EVALUATION OF FUEL ELECTRON SPECTRA

Description

Field of the invention

[0001] The invention relates to methods for the ab initio evaluation of a core electron spectrum of a chemical sample, and in particular of a spectrum generated by X-ray photoelectron spectroscopy (XPS, ESCA) by constructing a fitting function based on the elemental chemically conceivable phase spectra and approximating the fitting function to the measured core electron spectrum to determine the phases contained in the sample and their concentration fractions. The invention also relates to a computer program product that can be loaded directly into a memory unit and comprises software sections with which the inventive method can be carried out.

[0002] The scientific article ISSN:0022-3093, DOI: 10.1016 / J.JNONCRYSOL.2011.02.005 describes the approximation of a fitting function of a core electron spectrum by evaluating peak positions. Background of the invention

[0003] X-ray photoelectron spectroscopy (XPS, often also electron spectroscopy for chemical analysis, ESCA) is an established and widely used method from the group of photoelectron spectroscopy (PES) for non-destructively determining the chemical composition of solids or their surfaces. This method initially provides an answer to the question of qualitative elemental analysis, i.e., which chemical elements the solid consists of. Furthermore, the collected data also provides an indication of the electronic and chemical status of the elements present, so that, in principle, the structural composition of complex solids or solid surfaces, for example, those exhibiting multiple phases, can also be determined.While the qualitative analysis of elements can be obtained relatively easily from the measured data, the chemical-structural interpretation of high-resolution XPS data is still very complex and often leads to incorrect results. The evaluation involves extensive fitting procedures and the comparison of extracted fitting parameters (such as core electron binding energies or chemical shifts for the respective chemical environment) with literature data, data obtained by simulation, or with self-collected measurement data. The procedure is therefore highly dependent on the user's experience and therefore cannot be automated. Furthermore, collecting one's own measurement data with sufficient accuracy is labor-intensive and time-consuming. Further complicating the process is the fact that the corresponding databases only contain reference data for approximately 5% of known structures.There is therefore a need for improved methods for the evaluation of core electron spectra, which can preferably also be automated. Summary of the invention

[0004] It is an object of the present invention to provide an improved method for evaluating core electron spectra.

[0005] According to a first aspect of the invention, a method for away initio evaluation of a core electron spectrum, the method comprising the following steps: a. Providing a core electron spectrum for a sample with known elemental composition; b. Constructing a fitting function S Theo ( E ) by concentration-weighted linear combination of phase spectra Φ comp,i ( E), which are calculated for each phase possibly present in this sample using the known binding energies and chemical shifts of the core electrons of this phase; c. Approximation of the core electron spectrum by the fitting function S Theo ( E ) from step (b); d. In case of insufficient approximation in step (c) exclusion of those phases whose phase spectrum does not contribute to the core electron spectrum or is spectrally indistinguishable and subsequent reconstruction of the fitting function S Theo ( E ) according to step (b) using a linear combination of the remaining phases; e. Iterative approximation according to steps (b) to (d) until the residual deviations are minimal.

[0006] Further embodiments are the subject of the further independent or dependent claims.

[0007] The evaluation method according to the invention combines several decisive advantages over the evaluation methods known from the prior art.

[0008] The method according to the invention interprets core electron spectra using a "reverse engineering" approach, in which a constrained approximation (so-called "constrained fit") is performed based on the physical information. Based on the possible phases, the respective phase spectra are calculated, and a fitting function is created through linear combination, which is then used to approximate the core electron spectrum.

[0009] In contrast to the state of the art, the individual binding energies and chemical shifts are not used for spectrum comparison, but rather physically motivated phase spectra are created, which can be significantly more complex than the normal peak functions and cannot lie in the same functional space. The concentration-weighted linear combination of these phase spectra results in a fitting function that can thus represent any mixed spectrum from these phases.

[0010] By approximating this fitting function (so-called "curve fitting" or "fitting" for short), a complete interpretation of complex core electron spectra can be performed quickly and automatically without any user-specific assumptions.

[0011] Amazingly, the values ​​for binding energies and chemical shifts obtained by simulation are so precise that they allow the complete chemical interpretation of a complex multiphase surface and even lead to the identification of a previously unsuspected phase. Furthermore, the temperature-dependent change in a core electron spectrum can also be chemically decoded.

[0012] The present method is flexible in that further boundary conditions can be introduced or the fitting parameters can be varied. For example, based on the known stoichiometric composition of the sample, by varying the concentration fitting parameter λ i The adjustment function allows the method to be specifically adapted to the measurement method, the measurement results, or the underlying sample.

[0013] The data-based method according to the invention has the additional advantage that the adaptation requires fewer free parameters than conventional evaluation methods.

[0014] Another major advantage of this procedure compared to conventional methods is that one can now systematically incorporate further physically or experimentally motivated restrictions (e.g. the measured stoichiometry) into the fitting function.

[0015] Furthermore, spectral components which arise from additional physical phenomena (such as surface states, excitations, Coster-Kronig effect, etc.) can either be removed in the spectrum pretreatment or the construction of the spectral components can be extended accordingly in the method according to the invention.

[0016] Since numerous simulation methods for calculating binding energies and chemical shifts are known (e.g. the method of density functional theory), the phase spectra and thus also the fitting function can be calculated in a simple manner and accordingly a generally usable database of phase spectra can be built up very quickly.

[0017] Overall, the present method represents a decisive breakthrough in the evaluation of complex core electron spectra and thus has the potential to open up completely new areas of application for photoelectron spectroscopy. The invention in detail

[0018] The method according to the invention is a ab initio procedure, since it can be carried out without knowledge of the results of the corresponding measurement, insofar as for each phase possibly present in the sample the corresponding phase spectrum Φ comp,i ( E) is calculated using the known binding energies and chemical shifts of the core electrons of this phase. By concentration-weighted linear combination of the thus calculated phase spectra Φ comp,i ( E ) an adjustment function S Theo ( E ) is constructed. In the next step, the core electron spectrum is approximated by this fitting function S Theo ( E) to determine the individual phases hidden in the complex envelope of the core electron spectrum. Since the fitting function contains the combination of all conceivable phases, it is very likely that some of these phases and thus also the phase spectra derived from them are not represented in the spectrum. This becomes apparent through an insufficient approximation, so that in the next step those phases whose phase spectrum does not contribute to the core electron spectrum, or is spectrally indistinguishable, are excluded and the fitting function S Theo ( E) is constructed again using a linear combination of the remaining phases. This optimized fitting function is used again for the approximation and can be further optimized by phase exclusion and reconstruction if the approximation is still inadequate. This is an iterative approximation procedure that is repeated until the fitting function S Theo ( E ) shows a sufficient approximation to the core electron spectrum. A sufficient approximation is defined as an approximation for which the approximation method used no longer shows any further approximation to the core electron spectrum when applied iteratively. In the least squares method (LQ method), this is the case when the residual deviations are minimal.

[0019] The method according to the invention is, in principle, applicable to all spectroscopic methods that involve recording core electron spectra (so-called core-level spectra). Thus, the core electron spectrum to be evaluated can be generated by one of the following spectroscopic methods: i. X-ray photoelectron spectroscopy (XPS, ESCA), ii. X-ray absorption spectroscopy (XAS), iii. Auger electron spectroscopy (AES), or iv. X-ray emission spectroscopy (XES).

[0020] Preferably, this is a core electron spectrum recorded by X-ray photoelectron spectroscopy (XPS, ESCA).

[0021] The core electron spectrum to be evaluated can be subjected to a pretreatment prior to the actual application of the method according to the invention. Such pretreatments of spectra are known to those skilled in the art and can be specifically applied here. This preferably involves determining and subtracting background values ​​or identifying and considering shake-up stellites and shake-off satellites in the spectrum.

[0022] The method according to the invention can be used to interpret all chemical samples that yield a core electron spectrum. This particularly applies to solids and solid surfaces. Metals and alloys are particularly amenable to analysis.

[0023] According to the invention, the phase contained in the sample is understood to be a spatial region with similar physical and chemical properties. This region is preferably selected from the group consisting of element, molecule, material, material compound, surface, surface state, and nanoparticle.

[0024] To calculate the phase spectra, the binding energies or chemical shifts of the core electrons must be known. If available, experimentally collected data or published data (e.g., as an entry in the NIST database) can be used. However, according to the invention, such data sources are not required, since the phase spectra can also be determined using ab initio simulations. Numerous methods are available to the person skilled in the art, such as density functional theory (DFT), many-body methods, or machine learning based on ab initio-Simulation data.

[0025] In a particularly preferred manner, the simulation is carried out according to the density functional theory (DFT) method.

[0026] According to the invention, a calculated phase spectrum is used in the method. The phase spectrum Φ comp,i ( E ) consists of a linear combination of M peak functions V j , where these M peak functions are each multiplied by an intensity factor aj be weighted.

[0027] The phase spectrum Φ comp,i ( E ) is preferably calculated according to the following formula: ϕ comp , i E = ∑ j = 1 M α j V j E μ j f G f L Here: Mthe number of chemical environments in the phase; aj the respective intensity factor for the respective peak function V j ; V j the peak function, which is, for example, a Voigt profile, a pseudo-Voigt profile, a Lorentz curve, or a Gaussian curve; E the binding energy as a function variable; µ j the core electron binding energy of this chemical environment; and f L , f G Parameters of the peak function that describe the width of the profiles.

[0028] The phase spectrum can also be constructed from chemical shifts if the absolute binding energies µ j are unknown. The binding energies can be calculated from the chemical shifts C j,lm using the known elementary binding energy reference EB,ref of the core state under consideration according to: μ j = E B , ref − C j , l m

[0029] By linear combination of the individual phase spectra one obtains the fitting function S Theo ( E ). Preferably, the fitting function is constructed according to the following formula: S theo E = ∑ i = 1 N λ i ϕ comp , i E Here: λ i the concentration fit parameter of the respective phase i; Φ comp,i ( E)the respective phase spectrum i; Nthe number of potentially existing phases used for the adaptation.

[0030] When performing the approximation, a person skilled in the art can draw on numerous state-of-the-art approximation methods. The preferred approximation method is the least squares method (LS method).

[0031] In one embodiment of the invention, the approximation is carried out using a concentration fit parameter λ i per phase or component spectrum. When constructing the phase spectrum from chemical shifts, it may be useful, depending on the accuracy of the data used, to vary the elementary binding energy reference EB,ref in the approximation. In some cases, it may even be useful to allow a small variation in the reference binding energy per phase.

[0032] During the approximation, the further adjustment can be performed not only on the basis of the phase spectra, for example, by excluding phases without a phase contribution, but the phase spectra underlying the adjustment function can also be varied. This additional adjustment increases the quality of the approximation. In one embodiment, the peak function parameters are also adjusted. In the case of the Voigt profiles, these are the parameters f L and f G .

[0033] In one embodiment of the invention, in the method, if two phases have indistinguishable contributions to the spectrum, one of these phases is excluded from further fitting if the phase concentration fit parameter is zero in accordance with its standard deviation and does not indicate phase indistinguishability.

[0034] If there are more than two phases with indistinguishable contributions, one of these phases is excluded from further adjustment one after the other and it is determined for which phase exclusion the adjustment is optimal.

[0035] In a further embodiment of the invention, the method takes into account the known measurement uncertainties of the experimental data during the adjustment.

[0036] It is useful to further restrict the evaluation procedure, for example by adjusting the parameters for the approximation parameter, or based on the known stoichiometric composition of the sample by changing the concentration fit parameters λ i the adjustment function changes.

[0037] It is a further object of the present invention to provide an improved computer program product for carrying out an evaluation method for core electron spectra.

[0038] According to a further aspect, a computer program product is provided. The computer program product comprises computer code means that can be stored in a memory unit of an evaluation computer. The computer code means are configured such that the method steps according to an embodiment of the method described above can be executed on a processor of an evaluation computer.

[0039] In particular, the steps of calculating the phase spectra and constructing the fitting function can be performed on a separate or external evaluation computer. The actual evaluation can then be performed using the fitting function on an evaluation computer optimized for this purpose.

[0040] The memory unit comprises any suitable storage device, in particular digital storage devices such as optical or solid-state memory. The processor comprises any type of microprocessor or application-specific integrated circuit (ASIC). Examples of implementation 1. XPS analysis of a beryllium-titanium (Be-Ti) solid 1.1 Basic procedure

[0041] In this example, two beryllium 1s XPS spectra from a beryllium-titanium sample are analyzed and interpreted. The spectra were measured and published at the Forschungszentrum Jülich GmbH, Institute of Energy and Climate Research - Plasma Physics (IEK-4) (Helfer, N., (2017), "Comparative Investigation of Beryllides with Photoelectron Spectroscopy," Master's thesis, Chair of Experimental Physics I, TU Dortmund University). The spectral background of these spectra was determined.

[0042] For Be-Ti compounds, there are currently no literature data on 1s binding energies and chemical shifts (see NIST XPS database). Therefore, in order to apply the invention, all binding energies of all known Be-Ti phases had to be determined using Ab initio Simulations can be calculated.

[0043] The invention presented here is applied to these XPS measurement data as an example and the spectra are interpreted. 1.2 Binding energies of ab initio Simulation

[0044] For the ab initio Simulation was carried out using density functional theory (DFT) according to the full-potential linearized augmented plane wave (FLAPW) method with the FLEUR program (www.flapw.de). The generalized gradient approximation according to the Perdew-Burke-Enzerhof form was applied to the exchange-correlation potential. The core electrons are stored in the "all-electron FLEUR"The program treats the system relativistically. For the simulations, all experimentally known Be-Ti crystal structures were extracted from the ICSD database of inorganic crystal structures. From the previously known structure of the unit cell, it is known how many atom types (M) of an element exist and how many electrons (scatterers) contribute to the spectrum from the respective core level.

[0045] For all Be-Ti phases, the chemical shifts were calculated using the "initial state" approximation. This approximation, which is much simplified compared to other approaches, proved sufficient for the Be-Ti phases. The core-level shift C i,lm of a core state (l,m) for an atom type (i) corresponds approximately to the difference between two Kohn-Sham energies of this core state and the respective Fermi energy, according to the following equation: C i , l m Be ≈ ΔE i , l m = ϵ i , l m Be x Ti y − ϵ Fermi Be x Ti y − ϵ l m Be + ϵ Fermi Be

[0046] Accordingly, three self-consistency calculations using an all-electron method are required to determine all core-level shifts of a given binary compound. Experience has shown that the initial shifts can converge below 0.05 eV, allowing comparison to the experimentally determined chemical shifts. The results are summarized in Table 1 below: Ab initio Table 1: Results of all core-level shifts of the most stable compounds of the Be-Ti system. Depending on the respective crystal symmetry, there are different chemical environments that result in different chemical shifts. All of these shifts have not yet been determined experimentally. Based on these shifts and the number of electrons in the chemical environments, all Be 1s XP spectra of the Be-Ti system can be constructed. material Be 1s electrons Be 1s DFT CLSs [eV] Be 12 Ti 8 8 8 1.02, 0.79, 0.32 Be 17 Ti 2 α 6 12 12 4 1.03, 0.97, 0.82, 0.48 Be 17 Ti 2 β 6 12 12 4 1.08, 0.98, 0.81, 0.65 Be 3 Ti 2 14 4 1.52, 1.36, 0.84 Be 2 Ti 4 1.29 BeTi 2 0.88 From the calculated chemical shifts for beryllium C j,lm become absolute binding energies µ j calculated according to: μj=EB,ref−Cj,lmBe where, E B,ref in this case the experimentally determined core electron binding energy of elemental beryllium.

[0047] For the Be 1s spectra to be evaluated, this reference energy is 111.82 ± 0.06 eV according to the NIST database (J. Electron Spectrosc. Relat. Phenom. 185, 1 (2012)). 1.3 Evaluation according to the state of the art

[0048] A state-of-the-art evaluation was performed in (Helfer, N., (2017). Comparative investigation of beryllides using photoelectron spectroscopy, Master's thesis, Chair of Experimental Physics I, TU Dortmund University). Parts of this master's thesis are outlined here as follows.

[0049] The Unifit 2016 fitting software was used to evaluate the spectra. All fitted features have a Voigt profile, and the Shirley-type background is adjusted numerically during the approximation.

[0050] The penetration depth at a kinetic energy of 1370 eV was determined to be approximately 73.3 Å. A sample cleaned by a sputtering-annealing cycle was measured with high resolution at room temperature. The corresponding spectrum is shown in Figure 4 The spectrum shows a clear shoulder on the high-energy side, and the absence of the beryllium oxide signal at 114 eV was noted.

[0051] An approximation was performed using three Voigt functions for three different chemical environments of Be 12 Ti. The full width at half maximum of all three signals was varied as a variable, which is 0.49 eV for the Gaussian contribution and 0.10 eV for the Lorentz contribution. The binding energies resulting from the fitting are listed in Table 2 below: Table 2: Binding energies of the approximated peaks in the beryllium 1s spectrum from N. Helfer’s master thesis. Peak I Peak II Peak II Binding energy 1 / eV 110.9376 111.4076 111.7376 Half-width Gauss 1 / eV 0.48991 0.48991 0.48991 Half-width Lorentz 1 / eV 0.10286 0.10286 0.10286 Peak height / cps 5605.8 0.30233 / PeakI 0.10636 / PeakI Relative area 0.7095 0.2149 0.0756 Shift to 111.85 eV 0.91 0.44 0.11

[0052] The choice of three Voigt contributions was made for several reasons. First, it was the smallest number of contributions that allowed a correct description of the recorded spectra. Second, three shifts were expected due to the three atom types in Be 12 Ti. Since the Be-Ti system has rarely been analyzed using XPS, no information on binding energy shifts is available in public databases. Since the three atom types of Be 12 Ti were expected to contribute equally to the spectrum, this approximation could not be satisfactorily interpreted based on the current state of the art.

[0053] Since there is no good agreement between the ab initio calculated shifts (from Table 1) to the shifts resulting from the approximated signal positions (Table 2), these could not help with the interpretation either.

[0054] The determined stoichiometry for Be-Ti in the measurement area was found to be 86 ± 2 % Be to 7 ± 1 % Ti to 6.9 ± 0.9 % O for an emission angle of Φ = 0.

[0055] Remarkably, the temperature treatment at 1100°Kelvin leads to a decrease in the Gaussian half-width and the stoichiometry decreases to 60% Be to 28% Ti to 6.9 ± 12% O. A shift in the binding energy and a strong deformation of the spectrum is observed at the 1100°Kelvin temperature value, this spectrum with approximation of four Voigt profiles is shown in Figure 5B shown. 1.4 Application of the method presented in the invention

[0056] With the prior knowledge of the crystal structure, the number of atom types M originating from an element and the number of electrons with their contribution to the spectrum ajFrom the information of the atom types (intensity information) and the core-level shifts together, theoretical individual phase spectra Φ comp,i ( E ) according to the following formulas: ϕ comp , i E = ∑ j = 1 M α j V j E μ j f G f L

[0057] Here, for each atom type j, the Voigt profiles are added according to the Faddeeva representation according to the following formula, where each atom type j is considered with an area for the total number of electrons contributing to this atom type: V j E μ j f G f L = Re ω ln 2 2 E − μ j − i f L f G f G π 2 ln 2

[0058] A superposition of N spectra constructed according to the following formula leads to the fitting function, which is directly approximated (after adding the background obtained from the experiment) to the experimentally determined core electron spectrum. S theo E = ∑ i = 1 N λ i ϕ comp , i E

[0059] This fit consists of a concentration fit parameter λ i per phase or component spectrum and another fit parameter for the elementary Be 1s binding reference energy EB,ref (Be,1s).

[0060] The reference energy of 111.82 / 111.85 ± 0.06 eV was used for approximation, taking the experimental uncertainty into account. Here, the same reference energy is fitted for all phase spectra, and additionally, a single Lorenz and Gaussian broadening is varied for all Voigt profiles.

[0061] All constructed Be-Ti phase spectra are in Figure 3 scaled in direct comparison to the experimentally measured spectrum.

[0062] Spectral analysis using this physically based approximation can be easily automated by initial approximation with all phases and successive deletion of phases not belonging to the spectrum using iterative approximation. If phase spectra cannot be clearly assigned (e.g., Be 17 Ti 2 α and β are barely distinguishable), all possible chemical interpretations for the spectrum are obtained. An approximation with a large spectrum contribution from BeTi can be ruled out due to the experimentally determined stoichiometry.

[0063] The used ab initio chemical shifts are listed in Table 1. The final regression result is shown in Figure 4BThe contribution to the Be 1s signal is comprised of 51% Be 12 Ti, 47% Be 17 Ti 2, and 2% Be within the XPS information depth. These contributions result in a stoichiometry of 10.21 Be to 1 Ti. In addition to the three phase contributions, the approximation yielded a global reference binding energy of 111.85 eV, a Lorentzian half-width of 0.10 eV, and a Gaussian half-width of 0.43 eV for all Voigt profiles, which is plausible. Thus, a concrete, complete interpretation of the spectrum could be performed.

[0064] Analogous with the same Ab initio data, the spectrum of the heated Be-Ti sample was also evaluated. The result is shown in Figure 5A The sample now appears to consist of Be 2 Ti and Be 12 Ti. 1.5 Summary of the results

[0065] In summary, a novel and improved strategy for the complete chemical interpretation of XP spectra is provided, which turns the previous evaluation approach on its head by constructing a fitting function based on the physical properties of the sample that encompasses all phases and can therefore consider all phases in their contributions during the approximation. Remarkably, this includes not only experimentally known phases, but also entirely new, only theoretically predicted phases can be included in the fitting. This was demonstrated using Be-Ti measurements, where a complete set of ab initioSpecific core-level shifts for the known Be-Ti phases were constructed and used for the approximation. This approach is based on prior physical knowledge of the material and results in a reduced number of fitting parameters, allowing the approximation to lead to a clear chemical interpretation of the spectra. Remarkably, this successful interpretation was achieved for a system where conventional approximation methods do not allow for a valid interpretation. Short description of the figures

[0066] These and other aspects of the invention are shown in detail in the figures as follows: Fig. 1 shows a flow chart for the evaluation of XPS spectra according to the state of the art. Fig. 2 shows a flow chart for the evaluation method according to the invention. Fig. 3 shows Be 1s phase spectra for all known stable Be-Ti phases constructed from Ab initioChemical shifts calculated using methods. Fig. 4 shows a measured Beryllium 1s XP spectrum at 300°K, which was approximated in A with three Voigt profiles of the same Lorentz and Gaussian broadening and in B were approximated by means of the method according to the invention. Fig. 5 shows a Beryllium 1s XP spectrum measured based on a second, chemically different Be-Ti compound, where the spectrum is B with four Voigt profiles of the same Lorentz and Gaussian broadening and in A was approximated by means of the method according to the invention. Detailed description of the implementation examples

[0067] Fig. 1shows a flow chart for the evaluation of XPS spectra according to the state of the art. First, a measured spectrum to be analyzed is prepared to enable approximation. In this preparation step, for example, the background is determined and satellite peaks are removed. After preparation, a regression with as few parameters as possible, including peak functions, is performed on the spectrum. Appropriate software is available for this. Additional peak functions are added until the cumulative curve of the peak functions approximates the data well enough and, for example, no systematic pattern can be seen in the residuals of the fit, which would suggest another contribution. The choice of the number of peak functions is up to the evaluator. Finally, an attempt is made to identify the positions of the peaks with known literature values ​​in order to deduce which phases / components are present in the sample.For more complex spectra, this approach does not always lead to success because the data available is insufficient or certain peaks simply do not match the literature data.

[0068] Fig. 2shows a flow chart for the evaluation method according to the invention. First, the spectrum must be prepared, analogous to the prior art. With the knowledge of the elements present in the sample and what type of spectrum it is, a fitting function is then constructed from the available literature data, which is composed of individual phase spectra. Further known boundary conditions can optionally be incorporated into this. The fitting function is therefore physically motivated and only as good as the data available. In the next step, the experimental spectrum is approximated with the fitting function using regression method(s). In this process, phases and components that do not contribute are iteratively excluded. If the approximation with this composite fitting function works, a complete interpretation of the spectrum is immediately obtained from the result.

[0069] Fig. 3 shows all constructed Be 1s phase spectra from the Be-Ti system compared to measured data from a sample. The phase spectra were scaled to the maximum measured intensity. This representation shows that no phase spectrum alone matches the measured core electron spectrum.

[0070] Fig. 4 shows a measured beryllium 1s XP spectrum at 300°K. In A, the spectrum was approximated with three Voigt profiles of the same Lorentz and Gaussian broadening using eight fit parameters. In B, the spectrum was approximated using the inventive method and six fit parameters, with contributions from Be 12 Ti, Be 17 Ti 2, and elemental beryllium being determined. Remarkably, this superposition of these contributions results in a very good fit to the measured spectrum defined by the cross-shaped measurement points ("component fit" = solid line). The contributions represent a selection of a total of eight Voigt profiles of the participating atom types (not shown) with the same Lorentz and Gaussian broadening and Be 1s reference binding energy. It should be noted that a Be 12 Ti contribution alone is not able to approximate the measured spectral curve.

[0071] Fig. 5shows a beryllium 1s XP spectrum measured based on a second, chemically different Be-Ti compound. In B, the spectrum was approximated with four Voigt profiles of the same Lorentzian and Gaussian broadening using 10 fit parameters. In A, the spectrum was approximated using the inventive method and five fit parameters, with contributions from Be 12 Ti and Be 2 Ti being determined. Remarkably, this superposition of these contributions results in a very good fit to the measured spectrum defined by the cross-shaped measurement points ("component fit" = solid line). The contributions represent a selection of a total of seven Voigt profiles of the participating atom types (not shown) with the same Lorentzian and Gaussian broadening and Be 1s reference binding energy.

[0072] Further variants of the invention and their implementation will become apparent to the person skilled in the art from the preceding disclosure, the figures and the patent claims.

[0073] Terms used in the claims such as "comprise," "have," "include," "contain," and the like do not exclude further elements or steps. The use of the indefinite article does not exclude a plurality. A single device may perform the functions of several units or devices mentioned in the claims. Reference numerals indicated in the claims are not to be construed as limitations on the means and steps employed.

Claims

1. A method for ab initio evaluation of a core electron spectrum, comprising the following steps: a. provision of a core electron spectrum for a sample of known elemental composition; b. construction of a fitting function Stheo(E) by concentration-weighted linear combination of phase spectra Φcomp,i(E) calculated for each phase possibly present in said sample from the known bond energies and chemical shifts of the core electrons of said phase, wherein each of the at least one phase contained in the sample is defined as a spatial region having similar physical and chemical properties and structure of the elementary cell, preferably selected from the group consisting of element, molecule, material, material compound, surface, surface state and nanoparticle; c. approximation of the core electron spectrum by the fitting function Stheo(E) from step (b); d. if the approximation in step (c) is insufficient, exclusion of those phases whose phase spectrum does not contribute to the core electron spectrum or is spectrally indistinguishable and, thereafter, reconstruction of the fitting function Stheo(E) according to step (b) with linear combination of the remaining phases; e. iterative approximation according to steps (b) to (d) until the residual deviations are minimal.

2. The method according to claim 1, wherein the core electron spectrum was generated by one of the following spectroscopic methods: i. X-ray photoelectron spectroscopy (XPS, ESCA), ii. X-ray absorption spectroscopy (XAS), iii. Auger electron spectroscopy (AES), or nv. X-ray emission spectroscopy (XES), where XPS is preferred.

3. The method according to any one of the preceding claims, wherein the core electron spectrum is subjected to one or more of the following pretreatments: i. determination and subtraction of background values; ii. consideration of shake-up and shake-off satellites in the spectrum.

4. The method according to any one of the preceding claims, wherein the known bond energies or chemical shifts of the core electrons are determined by means of ab initio simulations, preferably by the methods of density functional theory, many-particles methods or machine learning based on ab initio simulation data.

5. The method according to one of the preceding claims, wherein each of the phase spectra Φcomp,i(E) consists of a linear combination of M peak functions (vj) multiplied by an intensity factor (aj) for the respective peak function and is calculated as follows: ϕ comp , i E = ∑ j = 1 M α j V j E μ j f G f L wherein M is the number of chemical environments in the phase; aj is the respective intensity factor for the respective peak function Vj ; Vj is the peak function, which is, for example, a Voigt profile, a pseudo-Voigt profile, a Lorentz curve or a Gaussian curve; E is the bond energy as a function variable; µj is the core electron bond energy of this chemical environment; and fL and fG are parameters of the peak function that describe the width of the profiles.

6. The method according to any one of the preceding claims, wherein the fitting function constructed in step (b) is constructed as follows: wherein S theo E = ∑ i = 1 N λ i ϕ comp , i E λi is the concentration fit parameter of the respective phase i, Φcomp,i (E) is the respective phase spectrum i, N is the number of phases possibly present, which are used for the fitting.

7. The method according to any one of the preceding claims, wherein the approximation method used in step (c) is the least squares method (KQ method).

8. The method according to any one of the preceding claims, wherein the approximation in step (c) is performed using a concentration fit parameter λi per phase or component spectrum, and the approximation in step (c) optionally includes, in the case of construction from chemical shifts, a fit parameter for the variation of the element core electron state bond energy reference.

9. The method according to one of the preceding claims, wherein during the approximation in step (c) the peak function parameters, which in the case of Voigt profiles are the parameters fL and fG, are also adapted.

10. The method according to any one of claims 8 or 9, wherein in step (d), in the case of two phases with indistinguishable contributions to the spectrum, one of these phases is excluded from further fitting if the phase concentration fit parameter is zero in accordance with its standard deviation and does not indicate phase indistinguishability.

11. The method according to one of the preceding claims, wherein, based on the completed approximation in step (e), the phases present in the sample are indicated with their concentration fraction.

12. A computer program product comprising computer code means which can be stored in a memory unit of an evaluation computer, wherein the computer code means are configured such that the computer code means, when executed on the evaluation computer, cause the evaluation computer to perform the method steps of the method according to any one of claims 1-11.