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DOI: 10.1039/D4JA00199K (Paper) J. Anal. At. Spectrom., 2024, Advance Article

Novel application of silicon multi-vacancy satellite peaks for silicate minerals analysis in igneous rocks using WD-XRF coupled with chemometrics analysis†

Ashok Kumar Maurya*
Geological Survey of India, Northern Region, Aliganj Sector E, Lucknow, 226024, India. E-mail: ashok.maurya@gsi.gov.in

Received 29th May 2024 , Accepted 29th August 2024

First published on 30th August 2024

Abstract

X-ray spectra are pivotal for understanding chemical bonding and atomic interactions in materials. Particularly, valence-to-core (VtC) electronic transitions and satellite peaks within X-ray spectra provide insights into valence states and chemical environments. This study focuses on the multi-vacancy satellite peaks, Si KβIII and KβIV, and their application in analyzing silicate minerals in igneous rocks. A wavelength dispersive X-ray fluorescence (WD-XRF) spectrometer, commonly employed for chemical analysis of geological samples, was utilized in this study. The Si KβIII and KβIV peaks were selected due to their VtC transitions and multi-vacancy origin, offering enhanced sensitivity to the chemical environment. We examined 41 certified reference materials (CRMs) of igneous rocks, demonstrating the capability of these satellite peaks to reveal detailed chemical and structural information. A strong correlation was found between the chemical composition of silicate minerals and the intensities along with chemical shifts of the Si KβIII and KβIV peaks. We developed a regression model to predict mineral concentrations, validating the method with CRMs. The results suggest that the spectral region of the Si KβIII and KβIV peaks serves as a distinctive fingerprint for identifying silicate minerals in igneous rocks.

1. Introduction

X-ray spectra offer a valuable insight into the characteristics of chemical bonding and interactions among atoms in the investigated materials.1–5 Within the spectrum of electron transitions, valence-to-core shell (VtC) electronic transitions exhibit heightened sensitivity, particularly in the analysis of valence states and chemical bonding.5–8 Another important feature of X-ray spectra are the satellite peaks, which are additional peaks that appear near the main peaks due to various effects.5,9–11 The satellite peaks can have higher or lower energy than the main peaks, and their intensity and shape depend on several factors, such as the crystal structure, the chemical environment, and the X-ray experimental conditions. The satellite peaks can be classified into three types10 according to their origin: (1) multi-vacancy satellites, which result from multiple core-hole creation; (2) charge-transfer satellites, which result from charge transfer between the core-hole atom and its neighbors; (3) molecular-orbital splitting satellites, which result from the splitting of molecular orbitals due to the core-hole potential. The multi-vacancy satellites have higher energy than the main peaks, and their intensity is related to the ionic character of X-ray emitting atom.5,10 They are strong for ionic character and weak for covalent, unless there is a resonance effect at the core-hole state.9–11

Silicon is one of the most abundant elements in the Earth's crust, and it occurs in various forms, such as silica (SiO2) and silicates (SiO4)n.12–15 The identification and quantification of these forms are important for various geological and environmental applications, such as mineralogy, petrology, geochemistry, and soil science.16–19

In this paper, we propose a method for analyzing silicate minerals in igneous rock using silicon multi-vacancy satellite peaks KβIII and KβIV fluorescence lines. Due to the significantly lower intensity of Si Kβ1,3 compared to Si Kα1,2, previous studies on satellite peaks have primarily focused on Kα satellites, with only a few exceptions. Notably, Baun and Fischer20 reported two high-energy peaks near the main Kβ1,3 peak, initially labeled Kβ′′ and Kβ′′′. Later, Soni21 renamed them KβIII and KβIV, respectively, and attributed them to specific transitions within the 1s–1 2p–1 – 2p–1 v(p)–1 array. However, since their discovery, these satellite lines have not been utilized in any studies concerning the analysis of rocks and minerals.

By measuring these lines using a wavelength dispersive X-ray fluorescence (WD-XRF) spectrometer, we were able to estimate silica and various silicate minerals in different igneous rocks. WD-XRF spectrometers have been employed for the elemental analysis of geological samples since the early 1950s.22 This method is nondestructive, yet it is suitable for complex geological samples.23–26 In addition to determining concentrations, these spectrometers are also used for elemental speciation.27–31 Recent advancements in XRF technology32–34 have enhanced its usability and acceptability, although it has not yet been employed for direct mineral characterization.

Si KβIII and KβIV satellite lines were selected for their advantageous properties: (1) they involve VtC electronic transitions, providing valuable insights into electronic structure, and (2) they originate from multi-vacancy, making them exceptionally sensitive to the chemical environment. The proposed method offers a novel tool for mineral characterization, utilizing chemometric analysis alongside XRF-spectral analysis. Chemometric analysis has been extensively studied by various researchers using laser-induced breakdown spectroscopy (LIBS) imaging for the geological characterization of minerals.35–37 We demonstrate the feasibility and accuracy of our method by applying it to various samples of igneous rock certified reference materials.

2. Experimental

2.1 Materials

We utilized 41 internationally recognized certified reference materials (CRMs) encompassing a variety of igneous rocks. These CRMs included: AGV-1, AN-G, BCR-1, BEN, BR, BHVO-1, CGL008, CGL013, DD-1, DNC1a, DR-N, DTS-1, G-1, G2, GSP-1, GUW-GM, JA1, JA2, JA3, JB-2A, JF-1, JF-2, JG-1A, JG-2, JG-3, JGb-1, JGb-2, JR-1, JR-2, JR-3, MK-1, MO 10, MRG1, NIM D, NIM P, OU-3, Sandstone, SARM 50, SW, UBN, and W2A. The exact rock type and chemical composition of each CRM can be found in the certificate of analysis that comes with the material and in the Geostandards Newsletter.38

2.2 Instrumentation

All Si Kβ spectra were recorded using a WD-XRF spectrometer (Model: Zetium; Manufacturer: PANalytical). A Rhodium (Rh) anode X-ray tube, operating at a power of 4 kW, was employed as the primary X-ray source with settings of 25 kV and 160 mA. The secondary X-ray beams were directed through a collimator of 300 μm to reach the diffracting crystal PE002 (2d = 0.8746 nm). The signals were captured by a gas flow detector. The entire X-ray path was maintained under high vacuum (<20 Pa). The instrument is provided with SuperQ 6.0 software for its smooth operation and spectral analysis.

2.3 Methods

2.3.1 Sample preparation. To circumvent the risks associated with sample dissolution, pressed powder pellets were employed for analysis. A non-reactive binder, a 10% (w/v) solution of poly(methyl methacrylate) in acetone, was added to the samples. Specifically, 0.5 mL of the binder was mixed with 3.0 g of sample in an agate mortar until homogeneous. The mixture was then compressed into a 40 mm diameter pellet within an aluminum cup using a boric acid bed. This process was conducted at 20 tons of pressure for 25 seconds. By eliminating the dissolution step, potential chemical reactions were prevented unlike fusion bead method. Moreover, the minimal binder addition (approximately 0.05 g of poly(methyl methacrylate)) ensured minimal sample dilution.
2.3.2 Registration of spectra for Si KβIII and KβIV satellite peaks and Si Kβ1,3. To achieve the best possible accuracy and precision for the Si Kβ peaks, the spectrum was acquired in two distinct regions instead of a single scan. Table 1 details the parameters employed for spectral recording.
Table 1 WD-XRF scan parameters for Si Kβ spectral lines
S. No. Parameter Region 1 Region 2
1 Lines Si KβIII and KβIV Si Kβ1,3
2 2θ 97–100° 100–104.5°
3 Channel mask 27 mm 27 mm
4 Step width 0.020° 0.060°
5 Time/point 2.00 s 0.80 s
6 Scan speed 0.010° s−1 0.076° s−1
7 kV 25 25
8 mA 160 160
9 Tube filter None None
10 Collimator 300 μm 300 μm
11 X-tal PE002 PE002
12 2d 0.8746 nm 0.8746 nm
13 Order 1 1
14 Detector Flow Flow
15 PHD levels 25–75 25–75

A combined spectra of both scans have been depicted in Fig. 1.


image file: d4ja00199k-f1.tif
Fig. 1 The XRF spectrum of the Si Kβ region of JA-3. The inset shows the multi-vacancy satellite peak region magnified approximately 10 times.
2.3.3 Processing of spectra. The photon-induced WD-XRF is not the optimal instrument for registering multi vacancy satellite peaks of SiKβ lines. Particle-Induced X-ray Emission (PIXE) techniques are more suitable for studying these multi-vacancy satellite lines. However, to ensure the accuracy and precision of the energy and intensity of these peaks, we implemented the following measures:

1. Scanning speed: We maintained a very low scanning speed (dwell time of 2.00 seconds per point), recording a total of 150 points with a step width of 0.020°.

2. Noise reduction: Each spectrum was recorded five times to reduce noise. Outliers, if present, were manually removed from the 5 × 150 points dataset. The remaining data points were averaged to produce a smooth spectrum.

3. Smoothing: To ascertain the precise position and intensity of the Si KβIII and KβIV satellite peaks, each spectrum was meticulously replotted and processed using the graphic software Origin Pro 2022b. We applied two additional successive second-order Savitzky–Golay smoothing39,40 processes to improve the intensity and energy position of the peaks. After applying the Savitzky–Golay smoothing, no shift was observed in either the energy or the intensity (Fig. S1 and S2†). Comparisons between the smoothed and raw spectra are provided in the ESI file (Fig. S1†).

In accordance with both classical and quantum theories, the inherent shape of the emission line on the energy scale manifests as a Lorentzian.41 Consequently, all spectra of Si KβIII and KβIV satellite peaks were fitted with a Lorentz function during spectral processing. The detailed spectral processing is discussed in the ESI.†

3. Result and discussion

Quartz is a highly symmetrical mineral composed of robust, interconnected SiO4 tetrahedra. Other silicate minerals can be considered derivatives of quartz. Introducing a metal into the SiO4 network disrupts the symmetry of the tetrahedra and changing the chemical environment of the Si atoms. Despite this, direct chemical bonding between Si and metal atoms within silicate minerals is never observed. We analyzed fifteen silicate igneous rock CRMs to measure the intensities of the Si Kα1,2 and Si Kβ1,3 fluorescence lines. The CRMs analyzed included CGL008, CGL013, GUW GM, JA2, JA3, JF1, JG1A, JG3, JGB1, JR1, JR3, MO10, NIM P, Quartz, and W2A. Remarkably, the intensity ratio of Si Kβ1,3 to Si Kα1,2 exhibited exceptional consistency across all CRMs, averaging 2.24 ± 0.03%. This suggests that the oxidation state and local bonding environment of Si remain largely unchanged across these materials, leading to minimal variation in the relative intensities of the Si Kα1,2 and Si Kβ1,3 lines. This is the why these diagram lines cannot differentiate silica and silicates.

Among the most common silicate minerals found in igneous rocks are quartz (SiO2), orthoclase KAlSi3O8, albite NaAlSi3O8 anorthite CaAl2Si2O8, diopside Ca(Mg,Fe)Si2O6, hypersthene (Mg,Fe)SiO3 and olivine (Mg,Fe)2SiO4. To compare the intensity of Si KβIII and KβIV across different silicate minerals, we aim to normalize their intensities. Three options exist for this purpose: elemental Si concentration, intensity of Si Kα1,2 and intensity of Si Kβ1,3 fluorescence lines. The latter two options are indirectly related to the first. Measuring Si concentration requires a separate application program and calibration, so we focus on the other two alternatives. In XRF, absorption and enhancement matrix effects significantly impact intensity.23–25 Consequently, we choose the intensity of Si Kβ1,3 fluorescence lines for normalization. Since satellite peaks Si KβIII and KβIV closely coincide with Si Kβ1,3, the matrix effects remain consistent across these lines. For instance, if a matrix element (such as Fe) enhances the intensity of Si Kβ1,3, it will similarly affect the intensity of satellite peaks Si KβIII and KβIV. Si Kα1,2 lacks this privilege and is therefore excluded from normalization. However, as already discussed, the intensity ratio of Si Kα1,2 and Si Kβ1,3 remains constant across different igneous rocks, suggesting that the matrix has consistent absorption and enhancement effects on all four peaks. Thus, intensity of Si Kα1,2 can also be used for normalization. We normalize the intensity of satellite peaks Si KβIII and KβIV according to the defined eqn (1).

 
image file: d4ja00199k-t1.tif(1)
where Ii(N) is normalized intensity of i line (i.e. either Si KβIII and KβIV), Ii is intensity of i line in kcps and IKβ intensity of Si Kβ1,3 in kcps. Spectra were recorded for 41 silicate igneous rock CRMs. The energy and normalized intensity values of both peaks are included in Table 2 for 41 igneous rock CRMs. A notable shift in the energy and intensity of Si KβIII and KβIV multi-vacancy satellite peaks was observed as we transitioned from quartz to various silicate minerals. Fig. 2 illustrates stacked normalized spectra of different CRMs, including Quartz, JF2 (76% orthoclase), JGb1 (60% anorthite), and NIM-D (96.6% olivine), specifically for Si KβIII and KβIV lines. The introduction of metals into the interconnected SiO4 tetrahedral framework led to an evident increase in the energies and intensities of the satellite peaks. In most cases, both peaks exhibited a similar pattern of changes, except for a few exceptions. To address these exceptions, we utilized the sum of normalized intensities (ΣI) and the sum of chemical shifts (Σδ) for these peaks, rather than relying on individual peak values. The chemical shift was calculated in relation to the quartz mineral. Our efforts focused on correlating various types of silicate igneous rocks with the intensities and chemical shifts of Si KβIII and KβIV. Fig. 3 presents a 3D plot with Σδ (x-axis), rock type (y-axis), and ΣI (z-axis) for these silicate rocks. The strong correlation between Σδ, ΣI, and rock type is evident. Transitioning from quartz to gabbro generally resulted in an increase in both Σδ and ΣI, with some exceptions. Notably, ΣI exhibited greater consistency compared to Σδ with rock type. Chemically similar rocks clustered together in the plot, emphasizing that the spectral region of multi-vacancy satellite peaks Si KβIII and KβIV serves as a distinctive fingerprint region for each silicate rock.

Table 2 Peak position and normalized intensity of Si KβIII and Si KβIV satellites lines in various igneous rock CRMs
S. No. CRM Rock type38 Si KβIII energy (eV) Si KβIII intensity (%) Si KβIV energy (eV) Si KβIV intensity (%)
1 BCR-1 Basalt 1858.6 ± 0.1 1.95 ± 0.03 1867.5 ± 0.1 2.58 ± 0.03
2 BEN Basalt 1859.3 ± 0.1 2.51 ± 0.06 1868.4 ± 0.1 8.58 ± 0.06
3 BHVO-1 Basalt 1858.6 ± 0.1 2.10 ± 0.03 1867.6 ± 0.1 2.68 ± 0.03
4 BR Basalt 1859.3 ± 0.1 2.55 ± 0.04 1868.6 ± 0.1 8.71 ± 0.04
5 AGV-1 Andesite 1857.8 ± 0.1 1.88 ± 0.04 1867.3 ± 0.1 2.49 ± 0.04
6 JA1 Andesite 1857.9 ± 0.1 1.99 ± 0.03 1867.5 ± 0.1 2.40 ± 0.03
7 JA2 Andesite 1857.8 ± 0.1 1.77 ± 0.03 1867.3 ± 0.1 2.42 ± 0.03
8 JA3 Andesite 1857.0 ± 0.1 2.17 ± 0.02 1866.6 ± 0.1 2.54 ± 0.02
9 MO10 Anorthosite 1858.6 ± 0.1 2.40 ± 0.04 1867.8 ± 0.1 3.44 ± 0.04
10 AN-G Anorthosite 1858.7 ± 0.1 2.82 ± 0.04 1867.8 ± 0.1 3.78 ± 0.04
11 JB2A Basalt 1858.1 ± 0.1 2.14 ± 0.04 1867.3 ± 0.1 2.82 ± 0.04
12 W2A Diabase 1858.5 ± 0.1 2.45 ± 0.04 1867.8 ± 0.1 2.77 ± 0.04
13 SARM 50 Dolerite 1858.5 ± 0.1 2.35 ± 0.04 1867.7 ± 0.1 2.86 ± 0.04
14 DNC1A Dolerite 1858.5 ± 0.1 2.29 ± 0.05 1867.5 ± 0.1 2.77 ± 0.05
15 DR-N Dolerite 1858.3 ± 0.1 2.43 ± 0.03 1867.7 ± 0.1 3.10 ± 0.03
16 DTS-1 Dunite 1858.6 ± 0.1 2.68 ± 0.04 1867.5 ± 0.1 3.10 ± 0.04
17 NIM D Dunite 1858.7 ± 0.1 2.78 ± 0.05 1867.5 ± 0.1 3.11 ± 0.05
18 DD-1 Dunite 1857.9 ± 0.1 4.23 ± 0.04 1867.3 ± 0.1 4.45 ± 0.04
19 CGL013 Gabbro 1858.8 ± 0.1 2.34 ± 0.05 1868.1 ± 0.1 4.56 ± 0.05
20 JGb1 Gabbro 1858.5 ± 0.1 2.55 ± 0.03 1867.8 ± 0.1 3.38 ± 0.04
21 JGb2 Gabbro 1858.6 ± 0.1 2.48 ± 0.02 1867.8 ± 0.1 3.54 ± 0.02
22 MRG1 Gabbro 1858.8 ± 0.1 2.55 ± 0.05 1867.8 ± 0.1 3.60 ± 0.05
s23 CGL008 Granite 1857.7 ± 0.1 1.69 ± 0.04 1866.9 ± 0.1 2.07 ± 0.03
24 G1 Granite 1857.5 ± 0.1 1.75 ± 0.03 1867.0 ± 0.1 2.21 ± 0.03
25 G2 Granite 1857.6 ± 0.1 1.81 ± 0.03 1866.9 ± 0.1 2.13 ± 0.03
26 GUMGW Granite 1857.5 ± 0.1 1.71 ± 0.03 1867.0 ± 0.1 2.18 ± 0.03
27 OU3 Granite 1857.5 ± 0.1 1.70 ± 0.04 1866.9 ± 0.1 1.85 ± 0.03
28 MP1A Granite 1857.8 ± 0.1 1.70 ± 0.04 1866.9 ± 0.1 2.09 ± 0.04
29 GSP-1 Granodiorite 1857.6 ± 0.1 1.73 ± 0.04 1867.3 ± 0.1 2.26 ± 0.04
30 JG1a Granodiorite 1857.6 ± 0.1 1.85 ± 0.03 1867.3 ± 0.1 2.17 ± 0.03
31 JG3 Granodiorite 1857.8 ± 0.1 1.91 ± 0.03 1867.6 ± 0.1 2.45 ± 0.03
32 MK1 Granodiorite 1857.8 ± 0.1 1.94 ± 0.02 1867.6 ± 0.1 2.74 ± 0.02
33 70A Granodiorite 1857.9 ± 0.1 1.93 ± 0.03 1867.2 ± 0.1 2.13 ± 0.03
34 JF2 K-Feldspar 1857.8 ± 0.1 2.00 ± 0.03 1867.5 ± 0.1 2.34 ± 0.03
35 JF1 K-Feldspar 1857.9 ± 0.1 1.97 ± 0.03 1867.5 ± 0.1 2.25 ± 0.03
36 NIM P Pyroxenite 1858.6 ± 0.1 2.47 ± 0.04 1867.5 ± 0.1 2.66 ± 0.04
37 Sandstone Quartz 1857.2 ± 0.1 1.21 ± 0.04 1866.4 ± 0.1 1.46 ± 0.03
38 JR1 Rhyolite 1857.8 ± 0.1 1.72 ± 0.03 1866.9 ± 0.1 1.94 ± 0.03
39 JR3 Rhyolite 1857.6 ± 0.1 1.59 ± 0.04 1866.7 ± 0.1 1.93 ± 0.04
40 UBN Serpentine 1858.4 ± 0.1 2.48 ± 0.04 1866.6 ± 0.1 2.88 ± 0.04
41 SW Serpentine 1858.3 ± 0.1 2.49 ± 0.03 1866.8 ± 0.1 2.82 ± 0.03


image file: d4ja00199k-f2.tif
Fig. 2 Stacked normalized spectra of various CRMs for comparison of Si KβIII and KβIV peak. The a.u. stands for arbitrary unit.

image file: d4ja00199k-f3.tif
Fig. 3 This 3D plot illustrates the variation of the Σδ and ΣI across different rock types. The a.u. stands for arbitrary unit.

3.1 Chemometric analysis

Some CRMs, employed in this study, exhibits distinct primary mineral compositions. These included:

Sandstone: Composed primarily of quartz (q).

Potassium feldspar (JF2): Composed mainly of orthoclase (or).

Dunite (NIM D): Dominated by olivine (ol).

Anorthosite (MO-10): Characterized by a high concentration of anorthite (an).

Additionally, granite CRMs (JG1, JG2, CGL008) were utilized, characterized by their dominant albite ab, q, and or content. Thus, the effect of each mineral concentration on chemical shift and intensity of Si KβIII and KβIV peaks can be estimated. In other CRMs, normative mineralogy was determined using a software tool called shinyNORRRM.42 This package, developed as a free and open-source resource, serves the geochemical community by providing a universal programming framework. The name shinyNORRRM derives from combining “shiny” (referring to the Web Application Framework for R) and “NORRRM” (an acronym representing “noRm,” “R language,” and “Reneé”). The shinyNORRRM package, implemented in R, operates as a shiny app. R, a widely used free software environment for statistical computing and graphics, facilitated our normative mineral calculations.

Following the acquisition of mineral composition, chemical shift, and peak intensity data for Si KβIII and KβIV in each CRM, a statistical correlation analysis was conducted. As already discussed, the introduction of metals into the SiO4 network is known to enhance the intensity of these peaks. Therefore, a non-negative linear regression model was employed, resulting in eqn (2), which establishes the correlation between ΣI and silicate mineral concentrations.

 
ΣI = 0.0174[or] + 0.0052[ab] + 0.0493[an] + 0.0125[di] + 0.0197[hy] + 0.0319[ol] + 2.88 (2)

Using such regression model, we determined the ΣI for minerals by leveraging a specific set of CRMs. For instance, the ΣI values for minerals ab and or were computed using CRMs from sandstone, granite (CGL008, OU-3), and rhyolite (JR-1 and JR-3). The ΣI value for an was further calculated using CRM ANG. The calculated ΣI for ab, or and an are 2.95, 5.06 and 9.4 respectively. Olivine's ΣI values were extracted from dunite CRMs NIM-D and DD-1, which differ in their iron (Fe) and magnesium (Mg) content. Notably, the ΣI follows the mineral sequence: q < ab < or < ol < an. This order is consistent with the coefficients of the corresponding minerals in eqn (2).

The nature of chemical bond affects the intensity of multi-vacance satellite line.9,10,43 In covalent compounds, the valence electrons are not confined to a single atom but are shared among atoms, leading to a small perturbation when a core-hole is created. This results in a low probability of multi-electron ionization in covalent compounds. Conversely, in ionic compounds, the valence electrons are localized, causing a large perturbation when a core-hole is created. This leads to strong satellites in ionic compounds. For instance, in solid NaCl, the chlorine X-ray spectra differ from those in solutions.44 This can be attributed to the strong multivacance satellites in an ionic solid like NaCl, which become weak in a water solution. This is because, in water, the chlorine atom is surrounded by hydrogen and oxygen molecules, making it highly covalent.44 The trend observed in this study aligns with the concept above. Quartz, with the most covalent character in its SiO4 network, displays the weakest Si KβIII and KβIV peak intensities among the studied silicate minerals. As the ionic character increases in other minerals, the peak intensities become progressively stronger. In the SiO4 framework, the metal atoms are not directly chemically bonded to Si. Instead, a metal is bonded to Si through an oxygen atom (Si–O–M). A cation with higher electronegativity introduces more ionic character into the Si–O bond, resulting in higher values of Σδ, and ΣI. It is a well-established fact that chemical shifts escalate with the oxidation state, or nuclear charge.5,25,29 Our findings corroborate this trend in silicate minerals. Furthermore, the heightened effective nuclear charge amplifies the ionic nature of the Si–O bond within the SiO4 network, culminating in an intensified intensity of Si KβIII and KβIV peaks. Fig. 4 illustrates a mineral distribution plot showcasing Σδ and ΣI. This plot highlights that a particular mineral composition correlates with distinct values of Σδ and ΣI. This figure highlights that each mineral composition has unique chemical shift and intensity values. Consequently, the spectral region encompassing these peaks serves as a distinct fingerprint for identifying igneous silicate rocks using XRF spectroscopy.


image file: d4ja00199k-f4.tif
Fig. 4 Silicate mineral profile with respect to Σδ and ΣI in different igneous rock CRMs.

The composition of igneous rocks is indeed specific and not random, a characteristic that can be traced back to the controlled process of their formation.45,46 As lava or magma cool gradually, the minerals crystallize in a systematic manner, influenced by the original chemical makeup of the lava or magma. This methodical cooling allows certain minerals to form at specific temperatures and pressures, resulting in a predictable and consistent composition within igneous rocks. The rate of cooling, along with the conditions present during solidification, dictates the mineralogy and texture of the rock, ensuring that each igneous rock type has a unique, yet definitive, composition. For instance, granite rock typically comprises quartz, albite, and orthoclase minerals. Therefore, we can anticipate the mineralogy of an igneous rock using XRF spectra from the Si KβIII and KβIV regions along with a statistical model. Various linear and nonlinear statistical models can be employed for multiple dependent and independent variables. Our analysis revealed that RandomForestRegressor regression model47 exhibits the best agreement between predicted values and actual values. Random forests are powerful tools used in machine learning. They combine the strengths of multiple decision trees to make more accurate predictions. Imagine a forest with many trees (decision trees), each predicting slightly different things. By averaging their predictions, we get a more robust and accurate result.

A careful examination of Table 2 indicates that the intensity ratio (R) of Si KβIII and KβIV peaks also exhibits variation across different rock types. Consequently, our methodology employs three independent variables: Σδ, ΣI, and R for the prediction of mineral concentration in igneous rocks. To train the prediction model, we utilize Fig. 3 to select CRMs with similar mineralogy to the unknown samples. We conducted analyses on five granite and two rhyolite samples for quartz mineral. The comparison between predicted values and calculated values42 are presented in Table 3. These results are highly promising, confirming the effectiveness and utility of the proposed technique.

Table 3 Comparison of predicted and calculated quartz concentrations in granite and rhyolite igneous rocks
Sample Predicted value (%) Calculated value (%) Relative error (%)
S1 30.68 ± 0.2 31.26 −1.86
S2 30.31 ± 0.2 29.53 2.64
S3 31.65 ± 0.2 32.35 −2.16
S4 30.36 ± 0.1 30.54 −0.59
S5 24.59 ± 0.2 23.47 4.77
S6 29.12 ± 0.2 28.71 1.43
S7 34.05 ± 0.2 33.35 2.10

3.2 Limit of estimation

The intensities of the multi-vacancy satellite peaks Si KβIII and Si KβIV are significantly lower compared to the primary Si Kβ1,3 peak. A higher silica content in igneous rocks is advantageous for the precise and accurate detection of these weak satellite lines. Among igneous rocks, ultramafic rocks exhibit the lowest silica content (<45%). Within the 41 certified reference materials (CRMs) analyzed, BEN, with the lowest silica content at 38.20%, demonstrated successful spectrum acquisition and suitability for applying the proposed technique.

Photon-induced wavelength dispersive X-ray fluorescence (WD-XRF) is suboptimal for registering multi-vacancy satellite peaks of Si Kβ lines due to the inherently low ionizing power of photons. Particles such as electrons, protons, or alpha particles are more effective in creating multiple vacancies. Particle-Induced X-ray Emission (PIXE) techniques, including Electron Probe Microanalysis (EPMA), are better suited for studying these satellite lines and would provide improved detection limits when employing the proposed method.

4. Conclusions

This study successfully demonstrates the feasibility and efficacy of a novel technique for analyzing silicate mineralogy of igneous rocks using XES. The method hinges on the analysis of very less explored multi-vacancy satellite peaks, specifically Si KβIII and Si KβIV, within the Si Kβ spectra. These peaks offer a distinct advantage due to their sensitivity to the chemical environment surrounding the Si atom. Our findings reveal a remarkable correlation between the intensity and chemical shift of Si KβIII and Si KβIV peaks, and the type of silicate mineral present. This correlation establishes the spectral region encompassing these peaks as a unique “fingerprint” for each silicate mineral. The intensity of these peaks increases with increasing ionic character of the Si–O bond within the silicate network.

Furthermore, we have done chemometric analysis that leverages the spectral information from Si KβIII and Si KβIV peaks to predict the mineralogy of igneous rocks. This analysis exhibits promising results, suggesting its potential application in rapid and non-destructive identification of silicate minerals in igneous rocks.

In conclusion, this research paves the way for a novel and powerful XES based approach for analyzing silicate mineralogy in igneous rocks. The utilization of Si KβIII and Si KβIV satellite peaks offers a sensitive and efficient means for characterizing these materials. The established correlations between peak properties and mineral composition, coupled with the effectiveness of the statistical model, hold significant promise for various geological and environmental applications.

Data availability

The data utilized in this article can be found in Table 2 of the manuscript.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The author sincerely thanks Dr Ashish Kumar Pandey for his valuable suggestion. The author is also grateful to Mrs Alpana Shahi for her constant support during the research and manuscript preparation.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4ja00199k
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