Phase Quantification of Heterogeneous Surfaces Using DFT-Simulated Valence Band Photoemission Spectra

Quantifying the crystallographic phases present at a surface is an important challenge in fields such as functional materials and surface science. X-ray photoelectron spectroscopy (XPS) is routinely employed in surface characterization to identify and quantify chemical species through core line analysis. Valence band (VB) spectra contain characteristic but complex features that provide information on the electronic density of states (DoS) and thus can be understood theoretically using density functional theory (DFT). Here, we present a method of fitting experimental photoemission spectra with DFT models for quantitative analysis of heterogeneous systems, specifically mapping the anatase to rutile ratio across the surface of mixed-phase TiO2 thin films. The results were correlated with mapped photocatalytic activity measured using a resazurin-based smart ink. This method allows large-scale functional and surface composition mapping in heterogeneous systems and demonstrates the unique insights gained from DFT-simulated spectra on the electronic structure origins of complex VB spectral features.


Least-squares Fitting Methods
A least-squares refinement method was implemented to fit the XPS spectra with model spectra, whereby optimal parameters were obtained by minimising the residual sum of squares (Eq. S1) between the observed and calculated spectra.

Eq. S1
= ∑ ( -) Where and are the intensities observed and calculated in the spectra, respectively.

Refinement of Photoionization Cross-section Weightings
The simulated spectra from different methods of cross-section correction were compared and evaluated according to the least-squares fitting method described above. The photoionization cross-section values applied are shown in Table 1 and Table 2, and corresponding values are indicated in Table 3. The corresponding simulated spectra are shown in Figure S1. To optimize the cross-section weightings, the weightings were initially set to the YL tabulated crosssection values, with an estimate for the Ti 4p calculated by multiplying the Ti 4s by the Ge 4p/4s ratio, which gave the lowest compared to the other 'non-optimized' methods. The weightings were allowed to vary freely to achieve the best fit for both the anatase and rutile polymorphs. The average was then taken from the two phases to generate an optimised value for both phases. The individually optimised values and the final values applied are listed in Table 2. The Os contribution was rounded down to 0.5 as this reduced the value for rutile, without affecting the value for anatase. Figure S1. Simulated spectra resulting from different methods of photoionization cross-section correction for a) anatase and b) rutile. The different methods trialled are labelled i) to v) and correspond to the methods and RSS values listed in Table 3.   Table S3. Comparison of the RSS from fitting the experimental anatase and rutile VB spectra with simulated spectra using different methods of cross-section correction. Table 2.

Comparison of DFT and empirical fitting models
The DFT fitting model was compared to an empirical fitting model, using anatase and rutile XPS VB spectra measured from the single-phase films (Figure 1 main text). These models were fitted to VB spectra recorded from a 12 x 12 grid of points across mixed-phase r-corner and r-centre films, each point around 2 mm apart. During fitting, the binding energy positions of each component were allowed to vary freely, their intensity ratios were allowed to vary between 0 and 100 %, and a scale factor was applied such that the model total was equal to the maximum intensity of the experimental spectra. The anatase:rutile ratio with the minimum was used to estimate the surface phase fraction at that point.
The resulting fits from applying the models to 5 points on the r-centre sample are shown in Figure  S2. The same trend of increasing anatase composition was observed for the selected points in the r-centre sample for both the empirical and DFT-simulated models, with excellent agreement seen for the estimated phase fraction of anatase for all points across both samples ( Figure S3). The DFT-simulated fitting model tends to underestimate the phase fraction of anatase compared to the empirical fitting model. One potential cause is the disagreement between the experimental and simulated spectrum of anatase in the interpeak region (Figure 1 main text). This could be due to the higher reactivity of the anatase phase leading to more adventitious molecules adsorbed on the surface that may contribute to the experimental VB spectrum. Figure S2. Mixed-phase fitting models based on empirical fitting with XPS spectra (a-e) and fitting with DFT-simulated spectra (f-j), applied to VB XPS spectra taken from 5 points of mixed-phase composition from the r-centre sample. Each graph depicts the ratio of each phase that generates the lowest residual sum of squares ( ) and is labelled with the corresponding phase fraction of anatase. Figure S3. Comparison of the estimated surface phase fraction of anatase from fitting VB XPS spectra recorded on mixed-phase TiO 2 using an empirical fitting model and a DFT-simulated fitting model.

Raman Spectroscopy Composition Mapping Method
Raman spectroscopy was applied to investigate the composition across the mixed-phase TiO 2 films along selected cross-sections of each sample. Phase quantification was achieved using a methodology described elsewhere. 2 The analysis region was confined to 310-750 cm -1 , with anatase modes 3 at 395 cm -1 (B 1g ), 515 cm -1 (A 1g +B 1g ) and 637 cm -1 (E g ) and rutile modes 4 at 438 cm -1 (E g ) and 605 cm -1 (A 1g ), respectively. The spectra were normalised and fitted with linear background functions before the fitting of Raman bands using Lorentzian functions. The frequencies of the individual modes were allowed to vary ± 5 cm -1 and the FWHM was limited to the average values recorded over 10 points on the single-phase anatase and rutile thin films. Examples of the deconvoluted Raman spectra for three points on the r-centre sample are shown in Figure S4. The relative intensities of the fitted Lorentzian components were used to estimate the compositions at each point, which are indicated in the figure. Comparison between composition cross-sections estimated from XPS and Raman analysis are shown in Figure S5.
From the Raman analysis, the reference samples were determined to be 100 % anatase and rutile, and the annealed areas in the r-centre and r-corner samples were found to contain regions of up to 89 % and 96 % rutile, respectively. The film quality was reduced at the edges of the samples, which is the probable cause for disagreement at these points. The discrepancies away from the edges arise from the different probing depth of the two techniques.  Photocatalytic Activity Mapping Method

S7
The photocatalytic properties of the TiO2 films were probed using a standard test, based on the photoreduction of resazurin dye (smart ink). 5 The underlying mechanism of the process Figure  S6a) 6 relies on the photo-oxidation of a sacrificial electron donor (SED) driven by positive holes (h + ) trapped at the photocatalyst surface upon light excitation. The SED used in this formulation is typically glycerol. In turn, the resulting electron-rich surface can irreversibly reduce the resazurin molecule (R z ) to resorufin (R f ), which is evidenced by a colour change from blue to pink. This transformation can be easily monitored visually and by photographic analysis. Selected photographs from the smart ink test monitoring the performance of pure and mixed-phase anatase and rutile films are shown in Figure S6b. The transformation of R z (blue) into R f (pink) was evidenced within the first minutes of irradiation for most films except for pure rutile, which is inactive in this process. Prolonged irradiation (t= 100 min) lead to the full degradation of the ink. To further quantify these transformations, colour mapping of the photographs was carried out averaging RGB values across a 1212 grid for the mixed phase samples for direct comparison with XPS mapping. Following the procedure described in the ISO test, 5 the RGB values were transformed into normalised RGB(red) component, R t , at irradiation time t, according to Eq. S2.
Where RGB(R,B,G) t correspond to red, blue and green components, respectively.

Figure S7
illustrates an example of this analysis after t= 100 s irradiation. Following the evolution of R t values as a function of irradiation time across the entire 1212 grid in the samples allowed for an estimation of dye photoreduction rates, k Rt . Examples of R t curves are plotted in Figure  S5. k Rt values were estimated from linear regression of the initial steps in these curves. To account for photon-energy gradients during the irradiation experiments, measured in the range of 1.8−2 mW cm -2 , formal quantum efficiencies,  (units, s -1 photon -1 ), were then estimated from k Rt values per incident photon, for a fair comparison among the samples (Figure 5). For simplicity, these calculations account for photons at λ= 365 nm (maximum of light emission band) only, since the UVX detector we used to measure irradiance has a broad detection sensitivity across 300-400 nm and the lamp has a broad emission spectrum within the same range. Nevertheless, this assumption affects all the samples equally and accurate comparison can still be established, albeit absolute  values will likely be underestimated. Figure S7. RGB mapping based on normalised red component, Rt (eq. S1) of (a) r-centre and (b) r-corner samples after t= 100 s irradiation under UV light. The pink and blue areas in the analysis correspond to anatase-and rutile-rich regions, respectively. The corresponding photographs of the samples are included for reference.