The influence of multiple ionization and chemical effects on magnesium Kα X-ray spectra in high-resolution proton and alpha PIXE measurements

Abstract

High-resolution wavelength-dispersive (WD) X-ray emission spectra of the Mg Kα band were measured for metallic Mg and selected Mg compounds under excitation with 2–3 MeV proton (H) and 1.5–5 MeV alpha (He) ion beams. The study investigated the influence of chemical state as well as ion beam type and energy on the positions and relative intensities of Mg Kα spectral line components. In addition to the characteristic X-ray emission line, H-induced spectra revealed KL¹ multiple ionization satellite (MIS) lines, while He excitation produced both KL¹ and KL² MIS groups with strong energy-dependent relative intensities. Small but measurable peaks' energy shifts were observed among different Mg compounds. Statistically significant variations in the relative intensities of KL¹ group's components, correlating with chemical bonding, were also detected. The use of He excitation resulted in enhanced sensitivity for chemical speciation.

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Introduction

Particle-Induced X-ray Emission (PIXE) spectroscopy is a widely used Ion Beam Analysis (IBA) technique for determining elemental compositions in materials.^1,2 PIXE is typically performed simultaneously with other IBA techniques, such as Rutherford Backscattering Spectrometry (RBS), Particle-Induced Gamma-ray Emission (PIGE) spectroscopy, and Nuclear Reaction Analysis (NRA). When performed with focused MeV ion beams, micro-PIXE spectrometry, used alongside these other techniques, serves as a powerful tool for studying the distribution of major, minor, and trace elements in micro-samples with micron-level spatial resolution.³

Most PIXE experiments are conducted using proton (H) ion beams in the 2–3 MeV energy range. Typically, RBS spectra are recorded simultaneously to help identify matrix elements within a sample. RBS is commonly carried out with alpha (He) ion beams in the 0.5–3 MeV energy range. He-induced PIXE offers several advantages over the H-induced PIXE, such as a reduced secondary electron background and a lower energy threshold for this background.⁴ Consequently, simultaneous use of PIXE and RBS with He ion beams is a highly attractive approach, as it yields more comprehensive data than either method used independently.⁵

Characteristic X-rays in PIXE experiments are commonly recorded with energy-dispersive (ED) silicon drift detectors (SDDs). The energy resolution of such conventional Si detectors ranges from FWHM ≈ 80 eV for Mg K to FWHM ≈ 120 eV for Mn Kα. Analysis of ED PIXE spectra is usually performed using dedicated software packages such as GUPIXWIN,⁶ which is based on the fundamental parameter approach. Accurate analysis requires careful energy calibration of the measured spectra.

Specific distortions have been reported in ED PIXE spectra of geological standards, especially in the low-energy region, when measured with SDD detectors, complicating proper energy calibration.⁷ Moreover, PIXE spectra include satellite peaks arising from multiple ionization of target atoms. In the case of K-shell X-ray excitation, one or more L-shell vacancies may also be created, resulting in multiple ionization satellites (MISs), denoted KLⁱ, where the K vacancy is accompanied by i L vacancies. These satellites appear at slightly higher energies than their parent K lines and further distort the measured ED spectra.

The MIS effect is more pronounced for He excitation. However, its influence on the shape of K X-ray lines in lighter elements, such as Na, Mg, and Al, is non-negligible even with H ion beams. Therefore, both detector-related distortions and multiple ionization effects must be accounted for in spectral analysis.

Recently, we investigated the impact of multiple ionization K X-ray satellites on the accuracy of He-induced PIXE spectra.⁵ For that purpose, high-resolution wavelength-dispersive (WD) PIXE spectra were measured for elements ranging from Mg to Cr, using pure elemental samples and their compounds. Properly designed WD spectrometers may provide high energy resolution comparable to natural X-ray line widths.

Furthermore, it is well known that X-ray spectra are sensitive to chemical effects. When measured using high-resolution spectrometers, K X-ray spectra reveal clearly resolved MIS lines and chemically induced satellite peaks, which cannot be reliably studied with a conventional ED X-rays spectrometer.

Quantitative data on relative intensities and energy shifts of individual components within the Kα and Kβ bands are therefore valuable for assessing the impact of MIS lines on PIXE accuracy, as well as for conducting chemical speciation studies. Although Kβ lines are more sensitive to chemical effects, their intensities relative to Kα are quite low for low-Z elements such as Mg. In particular, the relative intensity of Mg Kβ to Kα is only 1.4%.⁸ This is why investigating Kα chemical effects in low-Z elements is particularly important.

For this purpose, we recently measured high-resolution WD Kα X-ray emission spectra induced by 2 MeV H and 3 MeV He ions in Al metal and four Al compounds.⁹ The results demonstrated that PIXE, when performed with a WD X-ray spectrometer of sufficient energy resolution, can efficiently explore chemical effects through the Kα emission band. The work also contributed to the development of a more extensive and accurate database required for improving the fitting and interpretation of H- and He-induced ED X-ray spectra in PIXE analysis software. Building such a database necessitates experimental data across various H and He ion energies and a broad range of elements.

Our focus is shifted now to even lower-Z elements, such as Na and Mg, as their Kα X-ray production cross sections can exceed that of Al. This suggests that the influence of MIS and chemical satellite lines may be even more significant for Na and Mg, offering new opportunities for chemical analysis via X-ray spectroscopy. In the present study, we aimed to measure high-resolution spectra of the Mg Kα X-ray emission band using selected Mg compounds excited by H and He ions at a few selected energies.

Experiment and analysis

The high-resolution PIXE measurements were performed using a modular end-station equipped with a WD X-ray spectrometer, developed for use with focused MeV ion beams at the Tandem Accelerator Facility of the Ruđer Bošković Institute.¹⁰ The main components of the spectrometer include a motorized sample holder, a flat diffraction crystal, and a charged-coupled device (CCD) X-ray camera. When an ion beam, focused to approximately 10 µm in diameter, strikes the target, the emitted X-rays are diffracted by the crystal and directed toward the CCD, where two-dimensional signal images are recorded. A detailed explanation of the spectrometer's working principle and the conversion of CCD images into X-ray spectrum can be found elsewhere.^11,12

The accessible energy window, and consequently the energy resolution, depend on the element being analyzed and the crystal being used. For measurements of Mg Kα emission band, two different crystals were used: Beryl (1010), with twice the lattice spacing 2d = 15.954 Å, which provided an energy window of ΔE ≈ 150 eV and relative resolution of FWHM(E)/E ≈ 9.5 × 10⁻⁴ and ADP (101), with 2d = 10.64 Å, which provided an energy window of ΔE ≈ 40 eV and relative resolution of FWHM(E)/E ≈ 5.6 × 10⁻⁴.

Compressed pellets made up of high-purity powders were used as irradiation targets. To investigate chemical effects in X-ray emission spectra, the following materials were irradiated across three separate measurement sets: Mg, Mg₂Si, Mg₃N₂, MgB₂, MgBr₂, MgO, MgSO₄, and MgWO₄. In the first set, mixtures of all materials with Ge powder were irradiated with a 2 MeV H beam. In the second and third sets, all materials were irradiated with 2 MeV H and 3 MeV He beams. To examine the influence of varying ion beam energies on X-ray emission, two additional measurement sets were performed. In the fourth set, Mg and MgO targets were irradiated with H ions at 2.5 MeV and 3 MeV. In the fifth set, the Mg target was irradiated with He ions at 1.5 MeV, 4 MeV, and 5 MeV. A summary of all measurements is provided in Table 1. In all cases, the ion beam current was maintained between 1 and 3 nA.

Table 1 Summary of all performed measurements. ✗ presents measurement performed on pure target. ^Ge✗ presents measurement performed on target mixed with Ge

Irradiation		Targets
Ion beam	Energy (MeV)	Mg	Mg2Si	Mg3N2	MgB2	MgBr2	MgO	MgSO4	MgWO4
H	2	^Ge✗✗	^Ge✗✗	^Ge✗✗	^Ge✗✗	^Ge✗✗	^Ge✗✗	^Ge✗✗	^Ge✗✗
	2.5	✗					✗
	3	✗					✗
He	1.5	✗
	3	✗	✗	✗	✗	✗	✗	✗	✗
	4	✗
	5	✗

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The first measurement set was required to perform energy calibration of measured spectra. A straightforward equation relates the CCD channel, where a diffracted X-ray is detected, to the energy of that X-ray. The equation is given in ref. 10 as eqn (1) and it shows that two known energy–channel pairs are necessary to perform energy calibration. Mg Kα components span the energy range of 1250–1290 eV. The tabulated X-ray energies reported by Deslattes et al.¹³ were inspected and the Ge Lα and Ge Lβ peaks, located at 1188.01 eV and 1218.5 eV, were identified as the most suitable reference lines for the energy calibration. These lines served as internal standard for all Mg compounds. Using Beryl (1010) as the diffraction crystal provided a sufficiently wide energy window to record both Ge L lines and Mg Kα lines of interest in the same spectrum. All the other measurements, focused solely on detecting Mg Kα components with the highest possible resolution, were performed using the ADP (101) crystal.

The energy calibration procedure began with the spectrum of the Mg and Ge mixture, shown in Fig. 1. Experimental X-ray energies reported by Deslattes et al.¹³ were assigned to channel centroids (defined in the following paragraph) of the two most prominent peaks – Ge Lα at 1188.01 eV and Mg Kα_1,2 at 1253.604 eV. Using these two reference points, the energy of the Ge Lβ peak was calculated via the energy-calibration equation. The known energies of the two Ge L peaks were then used to determine the Mg Kα_1,2 and Mg Kα₃ energies in all other spectra of Mg compounds and Ge mixtures. Finally, these calculated energies were paired with the corresponding channel centroids in all measured spectra of pure Mg compounds, enabling the determination of energies for all other resolved X-ray peaks.

Fig. 1 Measured X-ray emission spectrum of the Mg and Ge mixture excited by 2 MeV H used for energy calibration.

It is worth mentioning the higher-energy satellite lines (Lα′, Lα″ and Lα‴) accompanying the Ge Lα characteristic line present in Fig. 1. For an atom with a singly ionized L₃ state, a transition from M_4,5 to L₃ state contributes to the Lα main line. If an atom is in a doubly ionized state, with an electron missing from both L₃ and one of the five M subshells, higher-energy satellite lines are emitted.¹⁴ While the positions of these MIS lines do not depend on the excitation source, their relative intensities are influenced by ion beam energy and type. Selecting the H ion beam rather than the He ion beam for energy calibration ensured that intensities of the Ge Lα MIS lines were sufficiently low and did not distort the characteristic Ge Lα line, thereby preventing calibration errors.

The channel centroids of the peaks were calculated using the formula:

where ch denotes the channel number and I_ch the corresponding intensity. It is worth noting that the uncertainty of each centroid can be straightforwardly determined by propagating the Poisson uncertainty of the counts in each channel. Different choices can be made for defining the upper and lower channel limits around the peak maximum in the centroid calculation. A common approach is to include intensities down to a specific percentage of a peak maximum.¹⁵ However, we observed significant variations in the calculated centroid depending on the percentage of maximum intensity used to define these limits. Therefore, when possible, we avoided relying on a single percentage threshold. Instead, the most probable centroid was calculated as the average of the centroids obtained over a range of threshold values. Specifically, we used all intensity thresholds starting from the lowest one that clearly exceeds the background and excludes neighbouring peak regions, up to 60% of the peak maximum, in increments of 5%. For well-defined Mg Kα₁,₂ peaks, the lower threshold reached as low as 20%. However, for less well-resolved peaks, such as Mg Kα₃ in spectra of Mg compounds and Ge mixtures, as well as Mg Kα₄, Kα₅, and Kα₆ in the remaining spectra, a fixed threshold of 60% had to be used.

Peaks' energy uncertainties were estimated using Monte Carlo-based uncertainty propagation. For each known energy–channel pair, new samples were drawn from a Gaussian distribution, with means defined by the original centroids and energies, and standard deviations equal to their respective uncertainties. The energy-calibration equation was solved for every sampled pair, generating a distribution of calculated energies. The energy uncertainty was then determined as the standard deviation of this resulting distribution.

Besides energy calibration, the measured spectra were subjected to intensity correction. There are three reasons why the raw intensity data requires adjustment. First, the above-described energy calibration involves a transformation of the intensity scale, as described in ref. 16. Second, the intensity must be corrected for the variation in the solid angle that covers each CCD channel. Third, the intensity correction should account for the energy dependence of X-ray transmission through a 2 µm graphite-coated Mylar foil, which is placed in front of the CCD to eliminate the possible influence of ion-beam-induced luminescence. Together with energy calibration, these intensity corrections ensure that the final spectra precisely reflect the physical X-ray emission characteristics.

In order to accurately inspect intensities of all peaks' components, the spectra from pure Mg and its compounds recorded using the ADP (101) diffraction crystal were fitted, as demonstrated in Fig. 2. Each resolved peak was modelled using the Voigt function – a convolution of the Gaussian instrumental profile and the Lorentzian X-ray line shape. Only the initial value of the Gaussian width, as previously determined in ref. 10, was defined. The parameter was then allowed to vary freely during the fitting process, along with all other peak parameters (area, center and Lorentzian width). A linear background was included, which provided a suitable approximation given the narrow energy range. Fig. 2 presents two examples of fitted spectra, together with all their components, for both 2 MeV H and 3 MeV He irradiation. As previously noted, MISs are more pronounced under He excitation, resulting in a larger number of resolved Kα lines.

Fig. 2 Fitted Kα X-ray emission spectra of Mg excited by (a) 2 MeV H and (b) 3 MeV He, normalized with respect to the KL⁰ line. Spectra include all peaks' components and linear background.

Results and discussion

The calibrated and corrected Kα X-ray spectra, together with their corresponding fits, for Mg and its compounds irradiated with 2 MeV H and 3 MeV He are presented in Fig. 3a and b. In addition, Fig. 3c shows spectra related to Mg and MgO targets irradiated with 2, 2.5, and 3 MeV H, while Fig. 3d displays spectra for Mg metal target irradiated with 1.5, 3, 4, and 5 MeV He.

Fig. 3 Fitted Kα X-ray emission spectra of Mg and its selected compounds excited by (a) 2 MeV H and (b) 3 MeV He. (c) Fitted Kα X-ray emission spectra of Mg and MgO excited by H beam at three different energies: 2, 2.5 and 3 MeV. (d) Fitted Kα X-ray emission spectra of Mg excited by He beam at four different energies: 1.5, 3, 4 and 5 MeV. The intensities of spectral regions containing MIS lines in (a) and (c) are multiplied by a factor of 5 for plotting purposes. All spectra are normalized to their maximum intensity.

Energy shifts

Fig. 4 presents the energy shifts of the Kα_1,2 and Kα₃ lines in measured Mg compounds relative to pure Mg determined from 2 MeV H-induced X-ray spectra. The only previously reported energy shifts found in the literature are for MgO, measured by Fischer et al.¹⁷ for 10 keV electron excitation, which are also plotted in Fig. 4. Our measured energy shifts align well with ref. 17 values, differing by 13% for Kα_1,2 and 7% for Kα₃.

Fig. 4 Energy shift of the Kα_1,2 and Kα₃ lines in measured Mg compounds relative to pure Mg. Filled symbols represent shifts measured in this study, while open symbols represent shifts reported in ref. 17 for comparison.

These energy shifts arise from changes in valence electron density of an atom inside a compound, which reduce the effective nuclear potential experienced by its core electrons. As such, measuring these shifts should provide insight into the effective charge on Mg atoms within the solid and they do not depend on the atom's excitation mode.

For previously studied third-row elements, such as P, S, Cl and Al,^9,18 a negative linear correlation has been observed between Kα₁ energy shifts and calculated effective charges on the investigated atoms. It is reasonable to assume a similar relationship holds for Mg Kα₁,₂ energy shifts. Accordingly, similar energy shifts within different compounds suggest a similar effective charge on Mg atoms in those compounds. It is worth noting the similarity in the measured Kα₁,₂ energy shifts for MgSO₄ and MgWO₄, which is consistent with the fact that Mg is bound to tetrahedral XO₄²⁻ anions in both compounds. Also, this implies a trend in which the effective charge decreases from pure Mg toward the more oxidized compounds on the x-axis of Fig. 4, ending with MgSO₄ and MgWO₄.

The Kα₁,₂ and Kα₃ energy shifts were uniquely determined from 2 MeV H-induced X-ray spectra related to the selected mixtures of Mg compounds and Ge. In contrast, the energy shifts of the Kα₄ line were extracted from X-ray spectra of pure Mg compounds induced by both 2 MeV H and 3 MeV He. These values are listed in Table 2, together with the values for MgO from ref. 17. As expected, the two excitation modes yield consistent results. The average energy shift of the MgO Kα₄ line agrees well with the results from ref. 17, differing by 7%.

Table 2 Energy shifts of the Kα₄, Kα₅ and Kα₆ lines in measured Mg compounds relative to pure Mg. For comparison, the corresponding energy shifts reported in ref. 17 for electron excitation are also included

Compound	Energy shift (eV)
	Kα4 (2 MeV H)	Kα4 (3 MeV He)	Kα4 (10 keV e)	Kα5 (3 MeV He)	Kα5 (10 keV e)	Kα6 (3 MeV He)	Kα6 (10 keV e)
MgBr2	0.25 ± 0.06	0.26 ± 0.05		0.3 ± 0.1		0.1 ± 0.1
Mg2Si	0.31 ± 0.05	0.31 ± 0.05		0.22 ± 0.09		0.2 ± 0.1
Mg3N2	0.54 ± 0.04	0.54 ± 0.04		0.70 ± 0.09		0.6 ± 0.1
MgO	0.60 ± 0.05	0.57 ± 0.05	0.55 ^17	0.6 ± 0.1	0.5 ^17	0.7 ± 0.1	0.3 ^17
MgB2	0.65 ± 0.04	0.68 ± 0.05		0.79 ± 0.09		0.9 ± 0.1
MgSO4	0.72 ± 0.06	0.73 ± 0.05		0.70 ± 0.09		0.7 ± 0.1
MgWO4	0.75 ± 0.05	0.85 ± 0.05		0.9 ± 0.1		1.0 ± 0.1

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Table 2 also presents the energy shifts of the Kα₅ and Kα₆ lines. These were determined solely from X-ray spectra induced by 3 MeV He, where these MISs are clearly visible. The measured MgO energy shifts deviate from ref. 17 values by 20% for Kα₅ and 133% for Kα₆. The large deviation observed for the Kα₆ shift may be attributed to the lower energy resolution of ref. 17 spectra, as shown in Fig. 3 of ref. 17, where KL² group resolves only two peaks (Kα₅ and Kα₆). Fig. 3b of this work clearly shows four resolved peaks (Kα₅, Kα₆, Kα₇ and Kα₈) for both Mg and MgO, which enables a more accurate determination of peaks' centroids.

Peak intensities

Fig. 5 shows the relative intensity ratios of KL¹ to KL⁰ for measured combinations of Mg targets and H ion beam energies. The intensity of each KLⁿ group was calculated as the sum of individual fitted peak areas within each group (see Fig. 2). The shown uncertainties were calculated from statistical errors, as the square root of the number of counts within each KLⁿ group.

Fig. 5 Intensity ratio of KL¹ to KL⁰ X-ray emission lines of Mg and its compounds excited by H beam.

Irradiation with H ion beam did not result in significant variation in the relative KL¹ intensities across the different Mg compounds. For 2 MeV H excitation, the KL¹-to-KL⁰ intensity ratios of different Mg targets differ from the average ratio by less than 5%. These differences could be explained by thick target self-absorption of Mg Kα X-rays.

With increasing H ion beam energy from 2 to 3 MeV, a downward trend in the KL¹-to-KL⁰ intensity ratio was observed. Specifically, an energy increase from 2 to 2.5 MeV resulted in a ratio decrease of 8% for Mg and 10% for MgO. For further energy increase to 3 MeV, the ratio decreased by 18% for Mg and 14% for MgO. This behaviour reflects the dependence of inner-shell ionization cross sections on the ion beam energy.

Fig. 6 shows the relative intensity ratio of KL¹ and KL² to KL⁰ for measured combinations of Mg targets and He ion beam energies, alongside with the related intensity ratios reported by Heirwegh et al.¹⁹ for Mg and MgO excited by He beams of similar energies.

Fig. 6 Intensity ratio of (a) KL¹ to KL⁰ and (b) KL² to KL⁰ X-ray emission lines of Mg and its compounds excited by He beam. Filled symbols represent measured ratios, while open symbols represent values reported in ref. 19 for comparison.

3 MeV He excitation led to more observable variations in the relative KL¹ and KL² intensities across different Mg compounds. The KL¹-to-KL⁰ ratios of Mg and MgWO₄ differ from the average ratio by 11% and 17% respectively, while differences for the other compounds remain below 8%. For the KL²-to-KL⁰ ratios, Mg and MgWO₄ differ from the average ratio by 18% and 21%, while the remaining compounds show differences of up to 13%. Determining whether these variations are influenced by chemical effects is not straightforward. However, the major source of the differences is probably the combined influence of thick-target self-absorption of Mg Kα X-rays and the higher stopping power of He ions compared with H ions. Because the relative intensities of MIS lines depend on ion energy, the measured spectrum represents a superposition of spectral contributions from all ion energies along its path in the target. For He excitation this ion-energy-loss effect is likely more pronounced than for H excitation.

In agreement with H excitation results, a strong negative correlation was found between He ion beam energy and the relative KL¹ and KL² intensities of metallic Mg. Specifically, an energy increase from 1.5 to 3 MeV resulted in the KL¹-to-KL⁰ ratio decrease of 45%. For further energy increase to 4 MeV the ratio decreased by 63%, and at 5 MeV it decreased by 69%. The KL²-to-KL⁰ ratio decreased by 66% between 1.5 and 3 MeV, by 82% at 4 MeV, and by 87% at 5 MeV.

In Table 3, the KL¹-to-KL⁰ intensity ratios for Mg and MgO excited by H and He ion beams are compared with corresponding ratios obtained for X-ray and electron excitation reported in the literature.^17,19–24 For H excitation in the 2 to 3 MeV energy range, the relative KL¹ satellite intensities fall within a similar range as those observed for X-ray and electron excitation.

Table 3 Intensity ratio of KL¹ to KL⁰ X-ray emission lines of Mg and MgO. Bold values represent the present measurement, while non-bold values correspond to literature data reported in ref. 17 and 19–24 for comparison

Excitation		I(KL^1)/I(KL^0)
		Mg	MgO
He ion beam	1.5 MeV	2.79 ± 0.04
	2.5 MeV^19	1.67 ± 0.07	1.62 ± 0.05
	3 MeV	1.53 ± 0.01	1.38 ± 0.01
	3.6 MeV^19	1.10 ± 0.02	1.09 ± 0.03
	4 MeV	1.048 ± 0.006
	4.6 MeV^19	0.83 ± 0.02	0.80 ± 0.03
	5 MeV	0.865 ± 0.005
H Ion beam	2 MeV	0.161 ± 0.001	0.156 ± 0.001
	2.5 MeV	0.1494 ± 0.0008	0.141 ± 0.001
	3 MeV	0.1320 ± 0.0009	0.136 ± 0.001
X-rays	Cr K^21	0.140 ± 0.003	0.158 ± 0.002
	Rh L^22	0.139 ± 0.006
	Cr K^23	0.114 ± 0.001
Electrons	4–5 keV^17	0.161 ± 0.005	0.159 ± 0.005
	6 keV^24	0.155 ± 0.003
	12 keV^20	0.161 ± 0.007

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In contrast to KL¹-to-KL⁰ and KL²-to-KL⁰ ratios, the relative intensities of X-ray emission lines within the same group are not expected to be affected by thick target self-absorption, but only by chemical effects. Within the KL¹ group, clear differences in the relative intensities of the Kα₃ and Kα₄ lines, which are separated by less than 2 eV, are evident across different Mg targets in the measured spectra. It can be seen in Fig. 3a and b that the increase in the Kα₄ intensity in going from Mg metal to Mg oxides is accompanied by a decrease in the Kα₃ intensity. These differences are illustrated in Fig. 7, which presents the Kα₄-to-Kα₃ intensity ratios for both 2 MeV H and 3 MeV He excitation. The intensities and associated uncertainties of Kα₃ and Kα₄ peaks were derived from the fitted peak areas.

Fig. 7 Intensity ratio of Kα₄ to Kα₃ X-ray emission lines of Mg and its compounds excited by H and He ion beams.

Differences in Kα₄-to-Kα₃ intensity ratios for metal and its compounds when excited by light ions are in previous works^25–27 attributed to the effect of Coster–Kronig transitions before the emission of Kα X-ray. Such transitions convert states that can deexcite via Kα₄ emission to states that can deexcite via Kα₃ emission. It has been proposed that Coster–Kronig transitions are available completely for a metal but are available to a lesser extent in compounds due to ionic binding energy. Our measurements agree with that interpretation. As shown in Fig. 7, there is a clear difference in Kα₄ to Kα₃ intensity ratios for Mg metal and all measured compounds, except for Mg₂Si. The similarity in this ratio between Mg and Mg₂Si could be explained by the significant covalent character of the Mg–Si chemical bond. A review of the literature reveals that X-ray Photoelectron Spectroscopy (XPS) data indicate that Mg–Si bond in Mg₂Si is far from purely ionic (i.e. in which Mg valence electrons are entirely transferred to Si). In fact, its ionicity is only 8%.²⁸ Under 3 MeV He excitation, where the intensities of the Kα₃ and Kα₄ peaks could be measured with higher precision, a statistically significant deviation in the Kα₄-to-Kα₃ intensity ratio was also observed for MgB₂ compared to the other compounds. Literature data²⁹ suggest that the Mg–B bond is likewise not purely ionic, but has a substantial metallic (delocalized) electron contribution. These results demonstrate that examining the Kα₄-to-Kα₃ intensity ratio via WD PIXE spectrometry, particularly under He excitation, can provide insight into the nature of chemical bonding in the measured compound.

Fig. 8 shows how Kα₄-to-Kα₃ intensity ratio varies with H and He ion beam energy. In addition to the measured data, the figure includes relevant values reported in the literature.^19,25,27

Fig. 8 Intensity ratio of Kα₄ to Kα₃ X-ray emission lines of: (a) Mg and MgO excited by H beam, and (b) Mg excited by He beam. Filled symbols represent ratios measured in this study, while open symbols represent values reported in ref. 19, 25 and 27 for comparison.

No statistically significant difference was observed in the measured Kα₄-to-Kα₃ intensity ratios for the H ion beam across the 2–3 MeV energy range. However, the measured ratios are lower than the corresponding literature values, by 16% for Mg and 22% for MgO. This discrepancy is likely due to differences in the methods used to determine peak areas.

Similarly, for the He ion beam in the 3–5 MeV range, the ratio remains largely unchanged. In this energy interval, the average of measured ratios is 10% higher than the literature values reported for 2.5–5.4 MeV. However, when the He beam energy is reduced to 1.5 MeV, the ratio drops significantly, by 17% compared with the average value at higher energies. A possible explanation lies in the larger variations between double K–Lⁱ ionization cross sections at lower He beam energies, close to 1 MeV, compared with higher energies between 2–5 MeV used in this work.

Summary and conclusions

In this work, high-resolution WD X-ray emission spectra of the Mg Kα band were systematically investigated in metallic Mg and a series of Mg compounds excited by H and He ion beams of various MeV energies. The study focused on two aspects: the influence of chemical bonding and the effects of ion beam type and energy on the Mg Kα spectral line components. These aspects were examined through peak energy shifts and relative intensities of specific MIS lines within the overall spectral profile.

The Mg Kα X-ray spectra exhibit statistically significant variations in peak positions depending on the measured compound. The energy shifts of Kα_1,2 and MIS peaks among selected Mg compounds relative to metallic Mg are all less than 1 eV, yet remain measurable. Based on previous findings, we suggest that the relationship between Kα_1,2 shifts provides insight into the effective charge on Mg atoms in these compounds. Nevertheless, verifying this relationship in future studies would be valuable. In addition, analysis of the relative Kα₄ peak position in spectra induced by both 2 MeV H and 3 MeV He confirmed that the two excitation modes yield consistent results.

For 2–3 MeV H ion beam excitation, only KL¹ MIS group could be measured, with a KL¹-to-KL⁰ intensity ratio of about 15%, showing a slight negative correlation with ion beam energy. In contrast, for 1.5–5 MeV He ion beam excitation, both KL¹ and KL² MIS groups were observed. The KL¹-to-KL⁰ and KL²-to-KL⁰ intensity ratios varied strongly with He ion beam energy, ranging from 279% to 87% and from 202% to 27%, respectively. Measured trends reflect the dependence of inner-shell ionization cross sections on the ion beam type and energy.

Selected Mg compounds irradiated with 2 MeV H showed no significant variation in the KL¹-to-KL⁰ intensity ratios. Small differences observed could be attributed to thick target self-absorption of Mg Kα X-rays. Observed variations in the KL¹-to-KL⁰ and KL²-to-KL⁰ intensity ratios for 3 MeV He excitation were more noticeable. It remains challenging to determine whether these differences come from chemical effects or are primarily due to enhanced ion-beam-energy-loss and related X-ray self-absorption in thick targets.

Statistically significant variations were observed in the relative intensities of the KL¹ group components. The Kα₄-to-Kα₃ intensity ratios, measured for both 2 MeV H and 3 MeV He excitation, showed a strong dependence on the chemical bonding within the target. Since MIS components are more pronounced with 3 MeV He excitation, it allows chemical speciation via the Kα₄-to-Kα₃ intensity ratio with higher precision compared to H excitation. Changes in ion beam energy produced no statistically significant differences in the measured Kα₄-to-Kα₃ intensity ratios for H beam in the 2–3 MeV range nor for He beam in the 3–5 MeV range. In contrast, the ratio decreased remarkably when the He beam energy was reduced to 1.5 MeV.

The results of this study confirm that PIXE performed with a WD spectrometer having adequate energy resolution can be efficiently used to study chemical effects in Kα X-ray band of Mg using H and He ion beams in MeV energy range. Also, this work will contribute to constructing a more extensive and accurate database of MIS X-ray lines for H and He ions, which is needed to improve fitting and interpretation of standard ED X-ray spectra in PIXE analysis software.

Conflicts of interest

There are no conflicts to declare.

Data availability

Data for this article are available at Fulir DATA Ruđer Bošković Institute Research Data Repository at https://data.fulir.irb.hr/.

Acknowledgements

AM, IBM, SF and MRR acknowledge the support from the Croatian Science Foundation project Hi-REXS [Grant Number 9429].

References

1. B. Schmidt and K. Wetzig, Ion Beams in Materials Processing and Analysis, Springer, 1st edn, 2013, pp. 301–376..
2. Y. Wang and M. Nastasi, Handbook of Modern Ion Beam Materials Analysis, Materials Research Society, 2nd edn, 2009, pp. 285–305..
3. S. Fazinić, I. Božičević Mihalić, G. Provatas, T. Tadić, M. Rubel, E. Fortuna-Zaleśna and A. Widdowson, Nucl. Fusion, 2020, 60, 126031.
4. L. Beck, in X-Ray Spectrometry, John Wiley and Sons Ltd, 2005, vol. 34, pp. 393–399.
5. D. J. T. Cureatz, M. Kavčič, M. Petric, K. Isaković, I. Božičević Mihalić, M. Rodriguez Ramos, S. Fazinić and J. L. Campbell, Spectrochim. Acta, Part B, 2022, 194, 106483.
6. J. L. Campbell, D. J. T. Cureatz, E. L. Flannigan, C. M. Heirwegh, J. A. Maxwell, J. L. Russell and S. M. Taylor, Nucl. Instrum. Methods Phys. Res., Sect. B, 2021, 499, 77–88.
7. C. M. Heirwegh, J. L. Campbell and G. K. Czamanske, Nucl. Instrum. Methods Phys. Res., Sect. B, 2016, 366, 40–50.
8. Y. Ito, T. Tochio, M. Yamashita, S. Fukushima, T. Shoji, K. Słabkowska, Ł. Syrocki, M. Polasik, J. P. Gomilsek, J. P. Marques, J. M. Sampaio, M. Guerra, J. Machado, J. P. Santos, A. Hamidani, A. Kahoul, P. Indelicato and F. Parente, Int. J. Mol. Sci., 2023, 24, 5570.
9. S. Fazinić, I. Božičević Mihalić, A. Mioković, M. Rodriguez Ramos and M. Petric, J. Anal. At. Spectrom., 2023, 38, 2179–2187.
10. I. Božičević Mihalić, A. Mioković, M. Rodriguez Ramos, D. Cosic, D. Mudronja, M. Tkalčević and S. Fazinić, Measurement, 2024, 238, 115325.
11. I. Božičević Mihalić, S. Fazinić, T. Tadić, D. Cosic and M. Jakšić, J. Anal. At. Spectrom., 2016, 31, 2293–2304.
12. S. Fazinić, I. Božičević Mihalić, T. Tadić, D. Cosic, M. Jakšić and D. Mudronja, Nucl. Instrum. Methods Phys. Res., Sect. B, 2015, 363, 61–65.
13. R. D. Deslattes, E. G. Kessler, P. Indelicato, L. De Billy, E. Lindroth and J. Anton, Rev. Mod. Phys., 2003, 75, 35–99.
14. H. S. Kainth, J. Alloys Compd., 2019, 782, 404–412.
15. S. Lafuerza, A. Carlantuono, M. Retegan and P. Glatzel, Inorg. Chem., 2020, 59, 12518–12535.
16. A. Iwata, K. Yuge and J. Kawai, X-Ray Spectrom., 2013, 42, 16–18.
17. D. W. Fischer and W. L. Baun, Spectrochim. Acta, 1965, 21, 448–450.
18. M. Petric and M. Kavčič, J. Anal. At. Spectrom., 2016, 31, 450–457.
19. C. M. Heirwegh, M. Petric, S. Fazinić, M. Kavčič, I. Božičević Mihalić, J. Schneider, I. Zamboni and J. L. Campbell, Nucl. Instrum. Methods Phys. Res., Sect. B, 2018, 428, 9–16.
20. E. Mikkola, O. Keski-Rahkonen, J. Lahtinen and K. Reinikainen, Phys. Scr., 1983, 28, 188–192.
21. J. Utriainen, M. Linkoaho, E. Rantavuori, T. Aberg and G. Graeffe, Z. Naturforsch., 1968, 23, 1178–1182.
22. K. Parthasaradhi, G. R. Babu, V. Radha, K. Murty, M. V. R. Murti and K. S. Rao, Nucl. Instrum. Methods Phys. Res., Sect. A, 1987, 255, 54–55.
23. O. Mauron, J.-C. Dousse, J. Hoszowska, J. P. Marques, F. Parente and M. Polasik, Phys. Rev. A, 2000, 62, 062508.
24. M. O. Krause and J. G. Ferreira, J. Phys. B: At., Mol. Opt. Phys., 1975, 8, 2007–2014.
25. R. L. Watson, A. Langenberg and F. E. Jenson, Jpn. J. Appl. Phys., 1978, 17, 93–96.
26. V. Radha Krishna Murty, V. Gopalakrishna, M. L. N. Raju, B. Mallikarjuna Rao, K. Parthasaradhi, M. V. R. Murti and K. S. Rao, Phys. Rev. A, 1988, 38, 2171–2173.
27. A. Langenberg and R. L. Watson, Phys. Rev. A, 1981, 23, 1177–1187.
28. Z. Fan, H. N. Ho, R. Szczęsny, W. R. Liu and D. H. Gregory, CrystEngComm, 2022, 24, 5801–5809.
29. J. M. Osorio-Guillén, S. I. Simak, Y. Wang, B. Johansson and R. Ahuja, Solid State Commun., 2002, 123, 257–262.

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Footnote

† Present address: Centro Nacional de Aceleradores (U. Sevilla, CSIC, J. de Andalucia), 41092 Seville, Spain.

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