Introduction

In high-sensitivity elemental analysis of historical heritage samples, X-ray analytical techniques, such as particle-induced X-ray emission (PIXE) and X-ray fluorescence (XRF), are generally regarded as non-destructive. Particularly, benchtop and handheld XRF devices are widely used in this field of research.

However, in PIXE analysis, the MeV protons directed to the sample induce not only the desired X-ray emission, but also a finite undesired radiation damage that can develop into detectable macroscopic effects, such as discoloration [1] and increased brittleness [2], in the irradiated sample. Considering this, a guideline has been provided for cultural heritage sample characterization by ion beam analysis, including PIXE [24]. However, this spot size is approximately 10 times larger than those of the benchtop micro-XRF instruments [34]. Therefore, if the aforementioned system is used practically, only plain and large areas can be analyzed, as in the case of handheld XRF devices; it would not be possible to analyze, e.g., cross-sections of paintings with many paint layers.

Comparison of the performances between the PIXRF setup presented above and, e.g., a commercially available benchtop device is very complex, because many factors including the X-ray source and X-ray detector, are different. Therefore, we built an equivalent of the PIXRF setup employing an X-ray tube (Mini-X, AMPTEK, Inc.) for comparison. The anode voltage and current were 20 kV and 100 µA, respectively. A 15 µm-thick aluminum foil was attached to the window of the X-ray tube to manipulate the energy spectrum, such that its peak could be exactly at the absorption edge energy of Cu. In this setup, the X-rays were also focused onto the sample by the X-ray lens in the same manner as in the PIXRF experiment.

Detector system

The fluorescence X-rays from the sample were detected by a Si-PIN semiconductor detector (XR-100CR, AMPTEK, Inc.). The detector size was 13 mm2 (sensitive area) × 0.5 mm (thickness). The Be-window thickness was 25.4 µm. The distance between the Be-window and the sample was 11 mm. The signal from the detector amplifier was processed by a 2048-channel pulse height analyzer. The spectrum measurement time per sample ranged from 30 min to 2 h depending on the samples. The total primary X-ray fluence to the sample was determined from the total proton charge measured by a current integrator (ORTEC 439) connected to the target.

For the absolute measurement of the energy spectra of the primary X-rays, the 90° attachment with the sample holder in Fig. 2 was removed, and the Si-PIN detector was put exactly at the focal position of the X-ray lens. In this measurement, the X-ray intensity was decreased by a factor of ≈ 102 by reducing the proton beam current to prevent the X-ray pulse pile-ups.

Sample preparation

In East Asian paintings, animal glue is used as common base binding material for inorganic pigments. Glues are also used, mixed with alum, as a sizing agent (dosa) for preparing the paper before painting. As another binding material, starch paste has been used mostly for lining and mounting [35, 36]. Although all these organic materials can be affected by incident X-ray radiation, the present study focuses on the damage to the paint layer, which is commonly regarded as a mixture of mineral pigment and animal glue.

Table 1 summarizes the details of the samples prepared in this study. Thick samples with low Cu concentrations were prepared (samples #1 to #3) to evaluate the LOD of the system. Copper(II) sulfate pentahydrate (CuSO4·5H2O, FUJIFILM Wako Pure Chemical Corp.) was used as the Cu compound. Gelatin (C65H102N18O21), which simulated the animal glue (collagen) used in traditional Japanese paintings, was used as the base binder material [37]. A small amount of CuSO4·5H2O was dissolved to an aqueous gelatin (FUJIFILM Wako Pure Chemical Corp.) solution. After completely drying this solution in a mortar, the residue was crushed by a pestle and filtered by a 200 µm stainless steel mesh. Subsequently, 1 g powder was pressed into a cylindrical pellet using a hydraulic press with 2 ton/cm2 pressure. The pellet size was 12 mm in diameter and ≈ 7 mm in height. We prepared pellets with Cu concentrations (w/w) of 0, 1000, and 10,000 ppm.

Table 1 Samples prepared in this study
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To demonstrate the applicability of the present setup to the artefact samples, we prepared samples simulating actual paintings. Japanese hemp paper (thickness = 4.5 mg/cm2, Ohnao Co., Ltd.) was used as the support material. The commercially available powder of the azurite (Cu3(CO3)2(OH)2, Iwa-gunjo in Japanese) blue pigment (#731, Nakagawa gofun enogu Co., Ltd.) and the same mass of gelatin were dissolved in warm water. The hemp paper was then painted with this pigment solution using a brush (Sample #4). Similarly, a sample with smalt (fine powder of SiO2·K2O·CoO glass, Hana-konjo in Japanese) (#860, Nakagawa gofun enogu Co., Ltd.) was prepared for the Co measurement (Sample #5). The CoO content (w/w) was assumed to be 10% [38]. The mass thicknesses or areal densities of azurite and smalt paint, including glue on the paper after drying, were 6.1 mg/cm2 and 42 mg/cm2, respectively. These thicknesses were determined such that the areal concentrations of Cu and Co were equal (1.7 mg/cm2).

A sample with a mixture of azurite and smalt was also prepared to demonstrate the element-selection capability (Sample #6). The mixing ratio for this sample was 1:1 in pigment-weight basis. The mass thickness of the mixed paint including glue on the paper after drying was 16 mg/cm2. The corresponding areal densities of Cu and Co on the hemp paper support were 2.2 mg/cm2 and 0.31 mg/cm2, respectively.

The geometrical thicknesses of the painted layers of the simulated cultural samples (samples #4 to #6) can hardly be measured due to permeation of the pigment solution into the paper support. Therefore, Table 1 demonstrates the whole thicknesses of the paper permeated with the pigment solution (after drying) measured with a micrometer caliper.

Results and discussion

Primary X-ray spectra

Figure 3a shows the measured energy spectrum of the primary X-rays produced by irradiating the Ge target with protons. The mass energy absorption coefficient of Cu as a function of the X-ray energy [39] is plotted, as well. As expected, only the Ge-KX-rays are clearly visible. Almost no continuous emission caused by Bremsstrahlung, which is the main component of emission from X-ray tubes, can be found. The Ge-KαX-ray energy was slightly higher than the absorption edge energy of Cu. Therefore, the XRF yield was expected to be nearly maximum. Figure 3b depicts the spectrum for the Cu target for the Co measurement, where the Cu–KX-ray energy is well-suited for the Co K-shell excitation.

Fig. 3
figure 3

a Measured energy spectra of the primary X-rays from the Ge target for PIXRF (blue) and the X-ray tube for conventional XRF (green). The absorption characteristics of Cu as the sample element were plotted as a function of the X-ray energy (red). b Measured energy spectra of the primary X-rays from the Cu target for PIXRF (blue). The absorption characteristics of Co as the sample element were plotted, as well (red). The proton and electron charges shown in the ordinates indicate the total charges (current × time) of these particles im**ed on the targets for PIXRF and the anode in the X-ray tube, respectively

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The measured energy spectrum of the X-rays from the X-ray tube is also plotted in Fig. 3a for comparison. Different from the proton-induced X-ray, the spectrum was continuous. Nevertheless, thanks to the anode voltage adjustment and the Al filter insertion, the spectrum peak could be tuned exactly at the absorption edge energy of Cu. Although the anode material of this tube was silver (Ag, Z = 47), no Ag-KX-ray peak (Kα at 22.1 keV, Kβ at 24.9 keV) was observed because the anode voltage was 20 kV.

LOD for Cu

Figure 4a–c show the PIXRF energy spectra measured for the thick targets with 0 ppm (Blank, background) (Sample #1), 1000 ppm (Sample #2), and 10,000 ppm Cu (Sample #3), respectively, using the Ge primary target. Together with the peaks caused by the scattering of the primary Ge-KX-rays, the peaks of the Cu–K emissions are clearly visible in Fig. 4b, c. The peak at ≈ 3.4 keV was caused by the electronic noise that appeared, even when the primary X-ray was off. This peak unfortunately overlapped the potassium (K) KX-ray peaks observed to be caused by K in gelatin as a minor element. The background continuum in Fig. 4a was very weak. From these spectra, the net count Nnet of the Cu–KαX-ray could be evaluated and plotted as a function of the Cu concentration Ccu in Fig. 5. In the upper graph, the vertical error bars indicate statistical errors evaluated by Nnet and background counts NBG under the peaks. The widths of the horizontal error bars were determined by the errors due to the multiple dilution process of the CuSO4·5H2O solution during the standard sample preparation. The LOD for Cu in the mass concentration unit was calculated as follows [40]:

$${\mathrm{LOD}}_{\mathrm{Cu}}=\frac{3\sqrt{{N}_{\mathrm{BG}}}{C}_{\mathrm{Cu}}}{{N}_{\mathrm{net}}},$$
(1)

where \(\sqrt{{N}_{\mathrm{BG}}}\) represents the standard deviation of NBG. The ratio Nnet/CCu represents the sensitivity that is equal to the calibration line slope in Fig. 5, which was determined by a linear regression considering errors in both axes. By substituting the values of the calibration line slope above, we obtained LODCu = 80 ppm, while NBG was obtained from the measured spectra in Fig. 4. This LOD value was much higher than that of commercially-available conventional XRF devices [41, 42]. This result can be explained by the poorer signal-to noise ratio due to the lower primary X-ray intensity used.

Fig. 4
figure 4

PIXRF energy spectra measured for the thick samples with a 0-ppm (blank) (Sample #1), b 1000-ppm (Sample #2) and c 10,000-ppm (Sample #3) Cu using the Ge target. The asterisks (*) indicate the peaks of the scattered primary photons

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Fig. 5
figure 5

Net yield of the Cu–KαX-rays as a function of the Cu concentration (calibration line) for the PIXRF experiment in linear (upper) and logarithmic (lower) scales

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Figure 6a–c show the conventional XRF spectra for the 0-ppm (Blank, background) (Sample #1), 1000-ppm (Sample #2), and 10,000 ppm Cu (Sample #3) samples, respectively, measured using the X-ray tube. In contrast to that for PIXRF, the spectrum suffered from a continuous background due to the primary X-ray scattering. Nevertheless, at least for this Cu concentration, the Cu–KαX-ray yield was enough for the Cu quantification. Figure 7 illustrates the calibration line drawn in a similar manner to that in Fig. 5. From this graph, LOD = 32 ppm, which is 2.5-times better than that of PIXRF. This result is attributed to the better statistical accuracy of the spectrum measurement caused by the higher intensity of the primary X-rays in the conventional XRF experiment.

Fig. 6
figure 6

Conventional XRF spectrum measured for the thick samples with a 0-ppm (blank) (Sample #1), b 1000-ppm (Sample #2) and c 10,000-ppm (Sample #3) Cu using the X-ray tube

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Fig. 7
figure 7

Net yield of the Cu–KαX-rays as a function of the Cu concentration (calibration line) for the conventional XRF measurement in linear (upper) and logarithmic (lower) scales

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Radiation dose to the samples

Considering the energy dependence of the fluence–dose relationship, the radiation dose to the sample surface was calculated as follows based on the measured energy spectrum:

$$D = \Phi {\int}_{0}^{\infty } E_{{\text{X}}} \frac{{\mu_{{{\text{en}}}} \left( {E_{{\text{X}}} } \right)}}{\rho }f\left( {E_{{\text{X}}} } \right)dE_{{\text{X}}} ,$$
(2)

where \(\Phi\) is the total incident X-ray fluence (= photons per area); ρ is the target mass density; and µen(EX) is the energy absorption coefficient as a function of the photon energy EX. The samples consisted of many element species; thus, this quantity was calculated as

$${\mu }_{\mathrm{en}}\left({E}_{\mathrm{X}}\right)=\rho \sum_{i}{w}_{i}{\left.\frac{{\mu }_{\mathrm{en}}({E}_{\mathrm{X}})}{\rho }\right|}_{i},$$
(3)

where µen(EX)/ρ|i is the mass energy absorption coefficient [39] of the ith element, and wi is the mass fraction of the ith element satisfying

$$\sum_{i}{w}_{i}=1 .$$
(4)

In Eq. (2), the f(EX) function is the energy spectrum of the incident X-rays fulfilling the normalization condition that

$${\int }_{0}^{\infty }f({E}_{\mathrm{X}})d{E}_{\mathrm{X}}=1.$$
(5)

We determined f(EX) under the condition above using the measured spectra in Fig. 3a and the detector efficiency curve published by the manufacturer [43]. Using these formulas, we calculated the dose D in Gy (= J/kg) unit to the samples. Table 2 summarizes the result together with the LOD data for the PIXRF and conventional XRF experiments. In the present setup, the dose caused by PIXRF was 14 mGy, which was only ≈1/30 of the dose by the conventional XRF (i.e., 430 mGy). This result can be explained by the spectral shape of the primary X-rays shown in Fig. 3a, where the photon energy was tuned to ionize the Cu K-shell.

Table 2 Comparison of the observation area (A), detection limit of Cu (LODCu), radiation dose (D) and figure-of-merit (FOMD) performances among PIXRF, conventional XRF, and a commercially available handheld XRF device
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The trade-off between the LOD and the radiation dose was considered based on the following simple calculation: Nnet in Eq. (1) is proportional to the product of CCu and the number of incident primary X-ray photons IX, whereas NBG is proportional only to IX, that is,

$${N}_{\mathrm{net}}\propto {I}_{\mathrm{X}}{C}_{\mathrm{Cu}},$$
(6)
$${N}_{\mathrm{BG}}\propto {I}_{\mathrm{X}}.$$
(7)

In contrast, the dose D is proportional not to IX, but to the photon fluence \(\Phi\):

$$D\propto \Phi \propto \frac{{I}_{\mathrm{X}}}{A},$$
(8)

where A denotes the observation area equal to the primary X-ray spot area on the target. From Eqs. (6)–(8), LODCu in Eq. (1) becomes

$${\mathrm{LOD}}_{\mathrm{Cu}}\propto \frac{1}{\sqrt{DA}}, \quad \mathrm{or }\quad D\propto \frac{1}{A\times {{\mathrm{LOD}}_{\mathrm{Cu}}}^{2}}.$$
(9)

Thus, we can define the figure-of-merit FOMD in terms of the radiation dose given as

$${\mathrm{FOM}}_{D}\equiv DA\times {{\mathrm{LOD}}_{\mathrm{Cu}}}^{2}, \quad \mathrm{ or } \quad D=\frac{{\mathrm{FOM}}_{D}}{A\times {{\mathrm{LOD}}_{\mathrm{Cu}}}^{2}}.$$
(10)

It follows that the radiation dose is proportional to FOMD if A × LODCu2 is the same. Therefore, a smaller FOMD translates into better low-dose performance. Table 2 summarizes the data on LODCu, A, D, and calculated FOMD for the PIXRF and conventional XRF experiments. The FOMD performance of PIXRF was approximately five times better (i.e., D was approximately five times lower) than that of the conventional XRF setup. It is noted that the experimental D value of the PIXRF was 30 times lower than that of the conventional XRF. However, if the primary X-ray fluence (X-ray intensity × time) for PIXRF was increased to ensure that the LODCu values of both methods were equal, the dose by the PIXRF would have been only five times lower than that of conventional XRF.

For reference, we roughly estimated the FOMD for a commercially available handheld XRF device, namely the DELTA family handheld XRF analyzer from OLYMPUS INNOV-X. For this calculation, the A (25 mm2) and LODCu (5–7 ppm) values were obtained from the user manual [44] and brochure [42] of this product, respectively. The dose D was calculated from the data on these documents (dose rate = 20,000 mSv/h, measurement time = 2 min), assuming that 1 Sv was equivalent to 1 Gy. Table 2 also presents the calculated results and relevant data. Although a simple comparison is not appropriate, the FOMD of PIXRF herein is lower than those of the equivalent conventional XRF and the commercial product, i.e., the low-dose performance of the PIXRF is better than the other techniques examined. In this work, the conventional XRF experiment showed a better FOM performance than the commercial device. One possible reason for this is that the energy spectrum of the primary photons from the X-ray tube was tuned to efficiently induce Cu K-shell ionization (Fig. 3a).

In the actual painting sample analysis, not only organic binder materials, but also mineral-based pigment materials can be damaged by the incident X-ray. When the pigment particles are small, the low-energy secondary electrons from the Cu atoms, including Auger electrons, can give a high dose to the surrounding organic materials [45]. Hence, using Eq. (2), we re-examined the dose to the painted layer, where azurite and gelatin were mixed. Figure 8 plots the results as a function of the mixing ratio of azurite. In this figure, we adjusted the number of incident primary X-ray photons according to Eq. (9), such that the LODCu of both analytical methods were equal (80 ppm). For both analytical methods, the dose was very sensitive to and increased with the increasing azurite content because the primary X-ray energy was tuned to Cu detection in azurite. For example, Fig. 8 reveals that the dose to Sample #4 is 15 times higher than that to the pure gelatin sample (Sample #1). Thus the low-dose performance of PIXRF shown in Table 2 was degraded when actual painting samples were analyzed. Nevertheless, the radiation dose by PIXRF was still much smaller than that by the conventional XRF for any azurite concentration.

Fig. 8
figure 8

Radiation dose to the azurite–gelatin mixture sample as a function of the azurite content (w/w). The number of incident primary X-ray photons was adjusted, such that the LODCu for both the analytical methods were equal (80 ppm). For reference, the azurite concentration of Sample #4 is indicated by a vertical dashed line

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Measurement of the simulated painting samples

Figure 9 shows the PIXRF spectra measured for the test samples with azurite (Sample #4) and smalt (Sample #5) using the Ge and Cu targets. For the sample with azurite, the Cu-KX-ray peaks were clearly visible when the Ge target was used (Fig. 9a). However, no peak was observable when the Cu target was employed, except for the scattered primary X-rays (Fig. 9b). In contrast, for the sample with smalt, the Co-KX-ray peaks were observed both for the spectra obtained using the Ge (Fig. 9c) and Cu (Fig. 9d) targets. The Co-KX-ray yield obtained with the Cu target was higher than that acquired with the Ge target. One reason for this result is that the Cu-KX-ray energy (8.04 keV for Kα) as the primary X-ray was nearer to the Co absorption edge (7.71 keV) than the Ge-KX-ray energy (9.87 keV for Kα). Another reason is that, as the primary photon, the Cu-KX-ray intensity per incident proton charge (Fig. 3b) was higher than that of the Ge-KX-rays (Fig. 3a) because of the higher X-ray production cross-section [46]. The results suggest a high element selectivity of the PIXRF analysis.

Fig. 9
figure 9

PIXRF spectra of the simulated samples with azurite (a, b) and smalt (c, d) measured with the Ge and Cu targets. The asterisks (*) indicate the peaks of the scattered primary photons

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Figure 10a shows the X-ray spectra measured using the Ge target for the simulated painting sample, where the hemp paper support was painted with azurite and smalt mixture (Sample #6). Ge-KX-rays were used as the primary X-ray; thus, both Cu and Co could undergo K-shell ionization, emitting KX-rays of these elements. The peak intensity of the Co-KαX-ray was much lower than that of the Cu-Kα emission simply because of the low Co concentration in smalt. In this case, the overlap of the Cu-Kα and Co-Kα peaks was not that serious; hence, a quantitative evaluation of the Co peak area was still possible. However, if the Co concentration were a few orders of magnitude lower, the peak area quantification would have been difficult.

Fig. 10
figure 10

a PIXRF spectra measured using the Ge target for the simulated painting sample, where the hemp paper support was painted with a mixture of azurite and smalt. The height of the Cu–KαX-ray peak was ≈ 200 counts. b PIXRF spectrum measured for the same sample with the Cu target. The asterisks (*) indicate the peaks of the scattered primary photons

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Figure 10b depicts the result obtained when the target for the MeV protons was switched to Cu. In this case, except for the scattered primary photons, no Cu-KX-ray peaks appeared because the primary X-ray energy (8.04 keV for Cu-Kα) was lower than the K-absorption edge energy of Cu (8.98 keV). The primary X-ray energy was very near the absorption edge of Co (Fig. 3b). Consequently, the Co-Kα emission peak was more isolated, and the peak intensity was higher than those in Fig. 10a. This effect was applied to quantify low-concentration platinum (Z = 78) in gold (Z = 79) heritage objects [19].

In order to quantify minor element in the sample, the primary X-ray intensity should be increased. In conventional XRF, however, an increase in the power of the primary X-ray beam can cause serious pulse-pile ups due to X-rays from the major element. Comparatively, in PIXRF, we can increase the primary X-ray intensity without causing any serious pulse-pileups. Therefore, even if the peak of the element of interest (in this case Co) does not overlap with the peak of the major element, the suppression of the photon count caused by the major element (in this case Cu) is often advantageous. In addition, the primary X-ray intensity in PIXRF can be increased with less concern regarding the radiation dose received by the precious sample due to the larger margin for radiation dose to the sample compared to that in conventional XRF.

Conclusions

In this study, we found that PIXRF analysis can potentially provide a low-LOD and -dose performance for the measurement of specific element species. This result can be of help in preventing the possible sensible radiation damage, even as a late effect on the precious historical heritage samples. The experiments using a mixed pigment sample also successfully demonstrated the selective measurement of a minor element mixed with major elements. This can be a powerful tool when the Z-numbers of these elements are near each other.

However, our results do not mean that PIXRF can be used as a substitute for conventional XRF because its advantages are available only for the analysis of particular single element species. In this sense, PIXRF is not anymore considered as a multi-elemental analytical technique. Thus PIXRF cannot be used for completely unknown samples; the samples must be analyzed with other techniques in advance. Such a two-step analysis is time consuming. Moreover, if the first measurement is implemented with a radiation-based technique such as conventional XRF or PIXE, the dose due to the first measurement must also be considered. For example, by simply repeating the same measurement by using the same method, the overall LOD can be reduced to \(1/\sqrt{2}\), and the total dose becomes twice of the original value. However, if PIXRF is applied as the second measurement and the overall LOD of a specific element becomes \(1/\sqrt{2}\), the total dose can be less than twice of the original value. Nevertheless, to include such a case, the application of PIXRF as the second step should be determined by weighing the cost (increase of measurement time and total dose) versus the benefits (lower overall LOD for the specific element).

The local radiation dose also increases with the increasing Cu concentration, although this occurs also in conventional XRF. The size of the whole system, including a MeV proton accelerator, is much larger than conventional XRF devices like portable ones, although the setup in Fig. 2 is palm sized. Thus, PIXRF could be used as a simple inexpensive supplementary technique to substitute well-established conventional multi-elemental analytical techniques only when we focus on a low-concentration specific element contained in very precious cultural heritage samples. Compatibility with the ordinary PIXE facility would be the best because both methods use MeV proton beams. Although large and/or extremely precious cultural heritage samples cannot be moved from museums, small and/or less precious artefacts are being routinely moved, for example, to dedicated PIXE facilities [47, 48] at distant locations. Therefore, PIXRF can be used in combination with PIXE analysis for cultural heritage samples.

Note that the selective detection of particular elements through PIXRF cannot be applied to arbitrary element pairs. In this study, we only considered Cu and Co for the selective detection of the element of interest. However, in historical materials, discrimination of element pairs, such as Ca (K-edge at 4.04 keV) and Sb (LIII-edge at 4.13 keV); S (K-edge at 2.47 keV) and Pb (MV-edge at 2.48 keV); and Ti (K-edge at 4.96 keV) and Ba (LIII-edge at 5.25 keV), is often difficult owing to spectral overlap**. Among these pairs, the Ca-Sb pair can be separated by using Sc (EKα = 4.09 keV) as the primary target. In contrast, S-Pb and Ti-Ba pairs cannot be resolved using PIXRF because there exists no appropriate primary target element whose KαX-ray energy lies between the absorption edges of each pair.

Also, low Z elements, such as Na, Mg, and Al, are often of interest in heritage samples. K-absorption edge energies of Na, Mg, and Al are 1.07, 1.30, and 1.56 keV, respectively. Therefore, the best targets for protons would be Mg (EKα = 1.25 keV), Al (EKα = 1.49 keV), and Si (EKα = 1.74 keV), respectively, which are easily available. However, owing to the low fluorescence yield of these low-Z elements [40], the primary X-ray intensity is insignificant. Therefore, the PIXRF of these low-Z elements is, in principle, expected to not be very effective.

In the present study, typically a 30-min acquisition time was employed for spectral data. The relatively long measurement time was selected due to the low primary proton beam current available in the beam line used. It should be mentioned that other MeV proton accelerator facilities can routinely deliver much higher beam current (1–10 µA). Provided that higher current beams from such a facility were used, and the primary target was adequately cooled, we could increase the beam current by 10–100 times, dramatically reducing the measurement time.

Among many elements used in pigments, we selected Cu as the sample element in our experiment. Note that Cu is not the only subject of evaluation. In addition, for the experiment, the selection of the sample element species is not very critical because the cross-sections of atomic processes relevant to PIXRF do not change sensitively with the valence state, but change slowly with respect to the atomic numbers of the sample and primary target elements. As a result, the experimentally confirmed low-dose performance for Cu can be extrapolated to other elements.