Feasibility of SPPD for XAFS measurements

The Cu K-edge X-ray absorption spectrum of the Cu foil was first collected using the DD-SPPD detector combination in the conventional mode, as shown in Fig. 3(a). As a reference, the Cu K-edge X-ray absorption spectrum of the Cu foil was then collected with the IC-IC detector combination in the conventional sampling mode, as shown in Fig. 3(a). By comparing the two X-ray absorption spectra, it was found that the fine structures and oscillation amplitudes of IC-IC and DD-SPPD were nearly the same. Based on Figs. 3(b) and 3(c), these two XAFS spectra are highly consistent both in the k-space and R-space, further confirming the consistency of the spectral characteristics collected by the two detector combinations of IC-IC and DD-SPPD. Furthermore, the repeatability of the XAFS data was verified by comparing three independent XAFS scans of the Cu foil Cu K-edge, as shown in Fig. 3(d). From the three XAFS spectra repeatedly acquired using the DD-SPPD detector combination, the three Cu K-edge X-ray absorption spectra were found to be nearly the same, presenting excellent repeatability. This result indicates that in addition to the SPPD not being damaged by the continuous X-ray radiation, the XAFS data quality collected by the DD-SPPD detector combination was approximately the same as that collected by the widely used IC-IC detector combination. As indicated, the incident X-ray intensity was approximately 10¹² cps in the Cu K-edge XAFS spectra measurements. As a conservative estimate, a total of 20 min were required for acquiring a complete XAFS spectrum in the conventional XAFS sampling mode or step scanning mode. The SPPD was continuously exposed to the transmission X-ray beam for tens of minutes in a single XAFS scan; whereas in the HF sampling mode, the continuous exposure time of the SPPD was only for a dozen seconds. The reproducibility of the XAFS spectral characteristics in the conventional XAFS measurements clearly indicates that irradiation damage did not occur in the SPPD, as it was used to record the XAFS signals. The lifetime of SPPD depends on the exposure time in addition to the irradiation dosage. Namely, this type of photodiode can be stably used for the collection of transmission XAFS data if the incident X-ray flux is not higher than 10¹² cps. Based on these results, visible and infrared photodiodes can be sufficiently used for the acquisition of the transmission X-ray absorption spectra, verifying the feasibility of SPPD used for XAFS measurements.

Fig. 3Full-screen View

(Color online) Cu K-edge XAFS spectra of Cu foil in E-space (a), k-space, (b) and R-space (c) collected by different combinations of front and rear detectors (IC-IC and DD-SPPD) with the conventional XAFS transmission mode. Three independent absorption spectra of Cu K-edge (d), confirming the repeatability of XAFS data collected by the SPPD.

Comparison of detector combinations

The aforementioned results confirm the feasibility of the DD-SPPD detector combination for conventional transmission XAFS measurements. The IC-SPPD detector combination was also used to collect the Cu K-edge X-ray absorption spectrum of the Cu foil, and the obtained XAFS spectrum was labeled IC-SPPD. For comparison, the conventional Cu K-edge XAFS spectrum of the Cu foil collected with the IC-IC detector combination was used as a reference. The three Cu K-edge X-ray absorption spectra of the Cu foil are shown in Figs. 4(a) and 4(b). The three detector combinations can obtain nearly the same X-ray absorption spectra as that in the E-space or the XAFS curves in the k-space. Apparently, both DD and IC can be used as the front detectors when SPPD is used as the rear detector; the two-detector combinations of DD-SPPD and IC-SPPD are feasible for XAFS measurements.

Fig. 4Full-screen View

(Color online) Cu K-edge XAFS spectra of Cu-foil in E-space (a) and k-space (b) collected with IC-IC, DD-SPPD, and IC-SPPD detector combinations in a conventional transmission mode as well as their differences. (c) The X-ray intensity responses at different energies recorded by the IC, DD, and SPPD detectors. (d) The intensity response ratios of SPPD to IC and SPPD to DD at different energies.

To quantitatively evaluate the difference between the two XAFS curves, a deviation factor (Q) was defined as follows: $Q={\displaystyle \sum _i^N\left|Y_i-Y_{0i}\right|}/{\displaystyle \sum _{i=1}^N\left|Y_{0i}-{\overline{Y}}_0\right|}$ (1)

Here, Y0, Y, and ${\overline{Y}}_{\text{0}}$ indicate the reference function, function to be estimated, and mean value of the reference function, respectively, N indicates the number of data points, and subscript i denotes the i^th data point. The Q value calculated using Eq. 1 indicates the statistical average of the relative difference of a single data point between the curve to be estimated and the reference curve. A smaller Q value indicates a higher similarity between the two curves. After considering the possible errors, if the calculated Q value was less than 0.25, the two related curves were considered to be roughly the same. When the two curves were exactly the same, the Q value was equal to zero. Considering the data collected with the conventional IC-IC detector combination as the reference data, the calculated Q values for the three X-ray absorption curves shown in Fig. 4(a) are 0 (IC-IC), 0.024 (IC-SPPD), and 0.024 (DD-SPPD). The calculated Q values for the three XAFS curves shown in Fig. 4(b) are 0 (IC-IC), 0.121 (IC-SPPD), and 0.116 (DD-SPPD).

The calculated Q values demonstrate that the DD-SPPD and IC-SPPD detector combinations can acquire XAFS data closer to the reference data collected by the IC-IC detector combination; however, the IC-SPPD detector combination presents slight glitches on the XAFS spectrum compared to that collected by the IC-IC detector combination. This is because the IC and SPPD exhibited slightly different responses to the X-ray energy, as shown in Fig. 4(c). Consequently, certain unnecessary and harmful glitches were not sufficiently removed and were superimposed on the XAFS spectrum. By comparing the responses of the IC, SPPD, and DD to the X-rays, nearly all the details can be found to have a one-to-one correspondence; however, the response ratio in pairs among the three detectors was only approximately linear, as shown in Fig. 4(d). The slightly different responses of the detectors to the X-ray leads to minor deviations between the X-ray spectra or the XAFS curves recorded by the different detectors. Regardless,, the IC-SPPD and DD-SPPD detector combinations for XAFS data acquisition remain feasible.

HF sampling XAFS data acquisition

In addition to the conventional XAFS measurement scheme, a new sampling scheme, HF sampling XAFS transmission, was tested when the beamstop-coupled SPPD was used as the rear detector. In the HF sampling scheme, the XAFS signals were collected in the transmission mode, and a high-speed counting module (NI 9223) was used for data collection. A high-speed counting module was used for the Cu K-edge XAFS measurements of the Cu foil at three sampling frequencies (1, 10, and 100 kHz). Here, the sampling frequency represents the number of times that an experimental signal (X-ray intensity) was repeatedly read in one second. Thus, the X-ray intensities in front and behind the sample were repeatedly read 10³, 10⁴, and 10⁵ times per second at the three respective sampling frequencies. Note, the sampling rate of this high-speed counting card was higher than that (5000 data points/s) of IK220^[21]. A higher sampling rate can significantly improve data quality by raising the statistics.

For a typical XAFS spectrum covering an energy range of 1000 eV, the total measurement time of the XAFS spectrum in the HF sampling scheme was controlled within a few seconds (8 s) in the transmission mode at BSRF. Namely, each XAFS spectrum contains 8000, 80000, and 800000 data points under the three sampling frequencies. Figure 5(a) presents the raw Cu K-edge XAFS spectra of the Cu foil collected using the DD-SPPD detector combination at sampling frequencies of 1, 10, and 100 kHz. Note, the HF sampling XAFS data are clearly different than that of the conventional XAFS data in appearance. It is difficult to determine the data qualities and features from the raw HF sampling XAFS data. To save time, the XAFS data are usually recorded in chronological order (time dimension) in these HF sampling XAFS measurements. The XAFS data is required to be converted from the time domain into the energy space for a subsequent data analysis. Another important issue is that the HF sampling scheme does not increase the energy resolution of the XAFS spectra, however drastically increases the number of data points. Therefore, in addition to the abscissa transformation, an appropriate statistical average for the HF sampling XAFS data is necessary. Typically, for an XAFS spectrum covering an energy range of approximately 1000 eV, it is sufficient to retain a few hundred data points. Under 10³, 10⁴, or 10⁵ sampling frequencies, the entire X-ray absorption spectrum recorded by the HF sampling scheme can be roughly divided into 800 time segments in chronological order. Each time segment had approximately 10, 100, or 1000 raw data points. These raw data points in each time segment must be summed and averaged to form one reduced data point. After data pre-processing, each XAFS spectrum was statistically averaged into 800 data points. Conservatively, this data preprocessing did not reduce the energy resolution. The 800 data points reserved for each XAFS spectrum were generally more than those for the traditional XAFS spectrum. The statistical average not only reduces the number of data points, but also significantly improves the SNR of the XAFS spectrum, as shown in Fig. 5(b). Note, all three HF sampling XAFS spectra had 8 s data acquisition times; however, their SNRs after the statistical average preprocessing were different. For an energy region with a span smaller than the energy resolution, the XAFS signal can be regarded as approximately constant if the sampling frequency is sufficiently high. Therefore, the HF sampling scheme is equivalent to the repeated measurements of an approximately constant quantity and different sampling frequencies correspond to different repetitive measurement times. A higher sampling frequency leads to a greater statistic and lower noise. When the sampling frequency was as low as 1 kHz, the XAFS spectrum after the statistical average remained too noisy, resulting in the failure of the XAFS spectrum, as shown in the curve at the bottom of Fig. 5(b).

Fig. 5Full-screen View

(Color online) Cu-foil raw (a) and pre-processed (b) HF sampling XAFS spectra collected with the DD-SPPD detector combination at three sampling frequencies (from bottom to top: 1, 10, and 100 kHz).

To convert the abscissa of the HF sampling XAFS spectra from chronological order (time domain) to the energy space, the absorption-edge position was first determined and marked as E₀, which corresponds to the first-derivative maximum of the XAFS spectrum. For a typical double-crystal monochromator, its rotation in the Bragg angle (θ) space is usually uniform. This indicates that the Bragg angle of the Si(111) monochromator linearly changed following the formula θ-θ₀ = ω (t-t₀). where θ₀ indicates the Bragg angle corresponding to the absorption edge of the element to be measured, t₀ is the time required for the monochromator to rotate to the absorption edge of the element, and ω is the rotation angular velocity of the monochromator. Based on the linear relationship between the Bragg angle (θ) and rotation time (t), the data point distribution of the HF sampling XAFS spectrum was also uniform in the Bragg angle space. The abscissa of the HF sampling XAFS spectra can be converted from the Bragg angle (θ) to the incident X-ray energy (E) using the following formula: $E(eV)=\frac{hc}{2d_{(111)}\sin \theta }=\frac{1977}{\sin \theta },$ (2) where h is the Planck's constant (6.626×10-34 J·s), c is the velocity of light (2.998×108 m·s-1), and d(111) is the interplanar spacing of the Si(111) crystal plane (3.1357 Å). For the Cu foil sample, the absorption edge energy of the Cu K-edge (E0) was 8979 eV. After reducing the number of data points and converting the abscissa to the energy space, the three XAFS spectra with sampling frequencies of 1, 10, and 100 kHz were also compared, as shown in Fig. 5(b). Evidently, within the sampling frequency range of our investigation, a higher sampling frequency improved the data quality and SNR. This is because a higher sampling frequency indicates a greater number of measurements, thus improved statistical data.

Comparison of HF sampling XAFS spectra

To verify the data quality of the HF sampling XAFS spectra acquired by the SPPD, the Cu K-edge XAFS spectrum collected with the DD-SPPD detector combination and the 100 kHz sampling frequency was compared to the reference spectrum that was collected by the IC-IC detector combination in the conventional sampling mode. The E-space X-ray absorption spectra and k-space XAFS spectra of the Cu foil are shown in Fig. 6 (a) and (b), respectively, which demonstrates that regardless of the E-space or k-space, the HF sampling XAFS spectrum collected within a few seconds was very similar to the conventional XAFS spectrum collected within a few minutes, except for the fact that the SNR of the HF sampling XAFS spectrum was slightly worse. Considering the data with the IC-IC detector combination as a reference, the calculated Q factor was 0.017 for the X-ray absorption spectrum with the DD-SPPD detector combination shown in Fig. 6(a), or 0.213 for the XAFS spectrum with the DD-SPPD detector combination shown in Fig. 6(b). This result demonstrates that in addition to the SPPD detector being used for the collection of conventional XAFS spectra, it can also be used for the data acquisition of HF sampling XAFS. Furthermore, the Fourier transform spectra in the R-space and the isolated single-shell XAFS oscillations in the k-space were extracted, as shown in Fig. 6 (c) and (d), respectively. Similarly, the calculated Q factors were 0.121 and 0.068 for the Fourier transform spectrum and single-shell XAFS curve, respectively. Although the Q factor was defined in Eq. (1) to describe the similarity between the two curves, it was found that the calculated Q values were slightly different for the same data in the E-space, k-space, and R-space. Evidently, the Q-value calculated for the data in the k-space was the most sensitive to the curve deviation. A quantitative comparison between the HF-sampling and conventional XAFS spectra was also performed by fitting the nearest-neighbour single-shell XAFS oscillations of the Cu foil. The fitting curves are shown in Fig. 6(c) and (d), and the fitting parameters are listed in Table 2.

Fig. 6Full-screen View

(Color online) Comparison of Cu K-edge XAFS spectra of the Cu-foil between the HF sampling scheme (solid line) with the DD-SPPD detector combination, and the conventional scheme (dot line) with the IC-IC detector combination in the E-space (a) and k-space (b) as well as their differences. Comparison of the Fourier transform spectra (solid line) and the fitting curves (circle line) in the R-space (c) between the 100 kHz HF sampling XAFS mode with the DD-SPPD detector combination, and the conventional XAFS mode with the IC-IC detector combination, as well as a comparison between the isolated nearest-neighbor XAFS spectra (solid line) and the fitting curves (circle line) in the k-space (d) between the 100 kHz HF sampling XAFS mode with the DD-SPPD detector combination, and the conventional XAFS mode with the IC-IC detector combination.

The XAFS fitting results indicate that the fitting parameters of the nearest-neighbor structure are nearly the same for the 100 kHz HF sampling XAFS and conventional XAFS spectra. This study demonstrates that the SPPD is not only capable of being sufficiently applied for conventional XAFS measurements, but can also be sufficiently used for HF sampling XAFS measurements. The small size of the SPPD and ease of assembly with a beamstop makes it capable for use in a combined technique, including the XAFS measurement. The good performance of this SPPD in the HF sampling XAFS measurements proves that it can be sufficiently applied to time-resolved experimental measurements within seconds.