High-accuracy analyses of key minor and trace elements in zircon by electron probe microanalysis

Abstract

Beyond its geochronological potential, zircon geochemistry is increasingly used not only for estimating formation temperature or identifying rock type and origin, but also for distinguishing magmatic, metamorphic and mineralization processes. Minor and trace elements (e.g., Al, P, Ti, Y, Yb, Lu, Hf, Th, and U) in zircon are informative, but high spatial resolution microanalysis techniques are urgently needed to address the limited size of zircon grains. Here, we developed a new EPMA method to determine minor and trace elements in zircon with high precision and accuracy. Detection limits and precision can be improved to several ppm level (e.g., Ti, 9 μg g⁻¹, 3σ) by using high acceleration voltage and high beam current combined with long counting time. The use of matrix-matched reference materials (GJ-1, Tanz, and Qinghu zircon) with well-characterized trace elements of interest is important for improving and monitoring the analytical accuracy. Careful background offsets and background regression models need to be obtained via high-sensitivity WDS scan on each target element. An exponential background regression model was applied to Ti, Al, Th, and U, whereas other elements required linear background regression. In addition, adjusting the calibration standard for Al and suppressing spectral interferences (e.g., P, Y, and Yb) enabled highly accurate EPMA measurements of trace elements below 1000 μg g⁻¹. The spatial resolution of EPMA in zircon analysis, even under extreme conditions (20 kV and 500 nA), remains below 3 μm, surpassing that of laser ablation inductively coupled plasma mass spectrometry. Using our protocols, we have successfully measured the contents of minor and trace elements in zircons from the Chang'E-6 lunar anorthosite sample. Overall, this improved EPMA method could broaden the applications of zircon composition to geological evolution processes of the Earth and the Moon.

---

1 Introduction

Zircon, a common accessory mineral in many rock types, is widely used in geological studies due to its ubiquity in different rock types, and geochemical relevance of its trace element and isotopic inventory. Beyond the applications in U–Pb dating, Hf and O isotopes,^1–5 minor and trace elements in zircon (e.g., P, Ti, Y, Lu, Hf, Th, and U) have sparked intense research on geochemical information related to the crystallization temperature,⁶ magma source,^7,8 magmatic evolution,^9,10 and metamorphic processes.^11,12 For example, Hofmann et al.¹³ suggested that micron-scale oscillatory zoning of Ti in zircons displayed a positive correlation to P, Y, and Ce, suggesting that Ti partitioning is influenced by non-equilibrium effects in addition to temperature. Therefore, the significance of key trace elements in zircon in understanding geological processes on the Earth and the Moon, particularly their distribution and mobility, merits further investigation.

A series of lunar samples have been collected from six Apollo missions, three Luna missions, and the Chang'E-5 and Chang'E-6 (CE-6) missions.^14–16 These samples have revolutionized our understanding of the Moon, e.g., the giant impact event, the lunar magma ocean (LMO), and the volcanism and thermal evolution,^17,18 which have significantly advanced planetary science.¹⁹ In particular, the CE-6 samples are the first lunar samples returned from the far side of history, ushering in a new era of lunar scientific research.^20,21 Zircon can be found in different types of lunar samples as small-size grains, such as in mare basalt or ferrous anorthosite (Fig. 1). Owing to the limitation of spatial resolution, minor and trace elements in small-grained zircons (<10 μm) are difficult to determine using laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). Although secondary ion mass spectrometry (SIMS) is capable of analyzing trace elements in zircon (e.g., P, Ti, and Y) at scales ranging from a few microns down to sub-microns,^13,22,23 its high cost and limited availability of instruments have resulted in the infrequent use of SIMS for trace element analysis. Most importantly, both LA-ICP-MS and SIMS are destructive analytical techniques, which may cause irreversible damage to the precious lunar samples, making them non-ideal choices for trace element analysis. Therefore, it is imperative to develop a non-destructive trace element analysis with high spatial resolution to support breakthroughs in zircon geochemical research.

Fig. 1 Selected back-scattering electron (BSE) images of the zircon grains from CE-6 anorthosite sample. Zrn, zircon; Pl, plagioclase.

Electron probe microanalysis (EPMA) is a powerful technique for measuring the content and distribution of major elements (>1.0 wt%) in minerals, offering high spatial resolution (micron-level) and non-destructive characteristics.^24–26 However, a significant limitation of EPMA is its inability in analyzing elements at contents below 1000 μg g⁻¹, where achieving adequate precision and accuracy becomes challenging. The contents of Hf, U, Y, and Th in zircon were analyzed at 25 kV and 100 nA using routine EPMA setting.²⁷ In addition, the beam current, analysis crystal, and monitoring standards were taken into account to improve the analytical precision of Hf and Ti in zircon, which corrects the underestimation of Ti content that occurs when using LA-ICP-MS.²⁸ The only drawback is that previous studies lack homogeneity verification for monitoring standards, high-precision background measurements, and simultaneous determination of multiple key trace elements.

In this study, we developed an optimized EPMA methodology to effectively reduce the detection limit and improve the analytical accuracy of Zr, Si, Al, P, Ti, Y, Yb, Lu, Hf, Th, and U in zircon. By comparing our results with the recommended values of three different zircon reference materials, we evaluated the effects of voltage, beam current, counting time, calibration standards, background measurement and regression models on the analytical accuracy of each measured element.

2 Experimental design and settings

A critical requirement for reliable quantitative analyses is the existence of reference materials (RMs) with known abundance and matrix, in which homogeneous elemental distribution is of primary importance.^29,30 The most commonly used zircon RMs are homogeneous in U–Pb or Hf and O isotopes, such as 91 500,^1,31 GJ-1,^32,33 Plešovice,³ Penglai,⁴ Qinghu,³⁴ Tanz,³⁵ SA01 and SA02,^36,37 but trace element homogeneity is not guaranteed. Therefore, the homogeneity of minor and trace elements (e.g., Al, P, Ti, Y, Yb, Lu, Hf, Th, and U) in zircon RMs should first be evaluated using LA-ICP-MS.

Minor and trace elements in zircon were measured using a Cameca SXFive EPMA instrument at the Institute of Geology and Geophysics, Chinese Academy of Sciences (IGGCAS). Different analytical conditions, such as accelerating voltage, beam current, counting time, analytical crystal, and calibration standards, were designed to lower the detection limit and improve data precision for each element measured in zircon. In addition, detailed wavelength dispersive spectroscopy (WDS) scans at different resolutions for different zircon RMs and CE-6 zircon were performed to optimize the background offsets and regression models, thereby increasing analytical accuracy. The detailed analytical conditions for Zr, Si, Al, P, Ti, Y, Yb, Lu, Hf, Th, and U in zircon are listed in Table 1.

Table 1 Analytical conditions of major and trace element determination in zircon by EPMA

Cameca SXFive EPMA	Condition 1#			Condition 2#
Element	Zr	Si	Hf	Al		P	Ti	Y		Yb	Lu	Th	U
a Counting time on the peak position (s). b Counting time on the background position (s). c Standard deviation (μg g^−1). d Detection limit, based on repeated measurement of variation on the background (μg g^−1).
Acceleration voltage (kV)	20	20	20	20		20	20	20		20	20	20	20
Beam current (nA)	40	40	40	500		500	500	500		500	500	500	500
Analysis crystal	PET	TAP	LLIF	TAP_1	TAP_4	LPET	LPET	TAP_1	TAP_4	LLIF	LLIF	LPET	LPET
Line	Lα	Kα	Lα	Kα	Kα	Kα	Kα	Lα	Lα	Lα	Lα	Mα	Mβ
Calibration standard	Zircon	Zircon	Hf metal	Y3Al5O12	Y3Al5O12	Apatite	Rutile	Y3Al5O12	Y3Al5O12	Yb glass	Lu glass	Th glass	U glass
Peak time^a	10	10	10	240	240	240	240	240	240	240	240	240	240
Bg time^b	5	5	5	60	60	60	60	60	60	60	60	60	60
Bg^−	−1500	−2400	−600	−600	−550	None	−750	−300	−200	−530	−200	−500	−600
Bg^+	1500	1150	650	450	500	300	450	None	None	600	400	1400	1000
Bg method	Linear	Linear	Linear	Exp	Exp	Linear	Exp	Linear	Linear	Linear	Linear	Exp	Exp
SD^c			1132	16		23	9	42		51	52	45	58
DL (3σ)^d	917	458	1039	14		28	10	49		53	67	41	65

---

3 Analytical techniques

3.1 Back-scattered electron (BSE) imaging

BSE images for zircon RMs and CE-6 lunar samples were acquired with a Zeiss Gemini 450 field-emission scanning electron microscope equipped with an X-ray energy dispersive spectrometer and a pneumatically retractable BSE system with a six-segment multimode solid-state BSE detector at the IGGCAS. An acceleration voltage of 15 kV, a beam current of 5 nA, a spot size of 1 μm, and a working distance of 8.5 mm were applied.

3.2 Laser ablation inductively coupled plasma-mass spectrometry

Trace elements of the zircon RMs were determined using an Agilent 7500a quadrupole ICP–MS instrument (Agilent Technologies, USA) coupled with an Analyte G2 193 nm ArF excimer laser ablation system at the IGGCAS. The carrier gas, helium, was passed through the ablation cell, and argon was mixed downstream of the ablation cell. The spot size and frequency of the laser were set to 44 μm and 5 Hz, respectively. The laser energy density was ∼4.0 J cm⁻². The dwell time for different elements was consistent at 10 ms, and the sampling period for one cycle was 0.40 s. Each spot analysis included ∼20 s background and 60 s sample data acquisition. The trace element data were processed using multiple external standards and a normalization strategy without an internal standard.³⁸ US National Institute of Standards and Technology (NIST) standard reference material (SRM) 610 was the primary standard for data calibration, and BCR-2G and ARM-1 glass standards were analyzed for quality control. The standards were analyzed twice each at the beginning and end of data collection (after ten ablations) for unknown samples. For most trace elements (>0.10 μg g⁻¹), the accuracy was better than ±10% with analytical precision (relative standard deviation, RSD) of ±10%.

To further obtain more reliable trace element results of zircon standard, we conducted comparative experiments in two other LA-ICP-MS laboratories. (1) Analytical Laboratory Beijing Research Institute of Uranium Geology (IUG-ALBR). A Coherent Geolas 193 laser-ablation system was used in conjunction with a Thermo Scientific high resolution ICP-MS. The spot diameter was 44 μm with a laser pulse rate of 6 Hz. The energy density was 6 J cm⁻². Helium was used as the carrier gas and merged with argon via a T-connector before entering the ICP-MS. Each analysis incorporated an approximately 20 s background acquisition followed by 60 s data acquisition from the sample. NIST 610, 612, BHVO-2G, and 91 500 glass standards were used for data calibration and quality control. (2) Wuhan Sample Solution Analytical Technology Co., Ltd, Wuhan, China (WSSATC). A GeolasPro laser ablation system and an Agilent 7900 ICP-MS instrument were used to sample and acquire ion-signal intensities. Helium was applied as a carrier gas. Argon was used as the make-up gas and mixed with the carrier gas via a T-connector before entering the ICP. The spot size and frequency of the laser were set to 44 μm and 6 Hz, respectively. Excel-based software ICPMSDataCal was used to perform off-line selection and integration of background and analyzed signals, time-drift correction and quantitative calibration for trace element analysis.³⁸ Detailed operating conditions for the laser ablation system and the ICP-MS instrument and data reduction are the same as described by Zong et al. (2017).³⁹

3.3 Electron probe microanalysis

Minor and trace elements in zircon were determined using a Cameca SXFive EPMA at IGGCAS. Natural minerals, synthetic metals and oxides used for calibration purposes included: zircon (Si and Zr), Y₃Al₅O₁₂ (Al and Y), apatite (P), rutile (Ti), Yb glass (Yb), Lu glass (Lu), Hf metal (Hf), Th glass (Th), and U glass (U). Data were acquired by using five analyzing crystals: TAP for Si, Al (Kα) and Y (Lα), LLIF for Hf, Yb, Lu (Lα), LPET for Zr (Lα), P and Ti (Kα), Th (Mα), and U (Mβ). All data were obtained by Phi-Rho-Z matrix correction using CAMECA PeakSight software. Based on the abundances and spectral characteristics of key trace elements in zircon, a series of approaches have been designed to effectively reduce the detection limit, improve the analytical accuracy, and balance these factors with the spatial resolution and analysis efficiency.

4 Selection of zircon RMs

In situ microbeam analytical technologies (e.g., EPMA, LA-ICP-MS, and SIMS) are comparative methods, and the results need to be validated using matrix-matched reference materials to assess instrument reproducibility and control analytical deviations. In particular, for EPMA, the matrix-matched RMs are essential for measuring minor and trace elements. The detection limit of EPMA cannot be infinitely low, but it is possible to decrease down to a few parts per million under extreme analytical conditions.^24,40 Therefore, not only the homogeneous chemical composition of RM is considered, but also the abundances of the critical trace elements are taken into account.

Previous studies have identified a number of natural zircons as RMs suitable for geochronology and isotopic geochemistry, e.g., 91 500,⁴¹ BR266,⁴² Temora,⁴³ GJ-1,^32,33 Mud Tank,⁴⁴ M257,⁴⁵ Plešovice (PLE),³ Sri Lanka,⁴⁶ OG1/OGC,^47,48 Penglai,⁴ Qinghu,³⁴ GZ7/GZ8,⁴⁹ LKZ-1,⁵⁰ SA01/02,^36,37 and Tanz.³⁵ Among them, a series of key elements (e.g., Al, P, Ti, Y, Yb, Lu, and Hf) in some zircon RMs were either not published or not homogeneous. The GJ-1, 91 500, PLE, Penglai, Qinghu, and Tanz zircon RMs were selected to reevaluate the homogeneity of critical minor and trace elements. Among them, the visible inclusions were not seen in BSE images of GJ-1 and Tanz zircons, revealing no obvious compositional zoning (Fig. 2a and b). The sector zoning observed in Qinghu zircon reflects the potential existence of weak compositional heterogeneity (Fig. 2c).

Fig. 2 Selected cathodoluminescence (CL) images of the GJ-1 (a), Tanz (b), and Qinghu (c) zircon reference materials.

Minor and trace element abundances in zircon RMs at the μm to mm scale were further evaluated by LA-ICP-MS. Two fragments of every zircon RM were chosen randomly, and a section from the core to rim in each fragment was analyzed (SI, Fig. S1). Here, the relative standard deviation (RSD, %) was used as a measure of chemical variation. The GJ-1 zircon is the most homogeneous, with RSD values for Si, Zr, P, Y, Yb, Lu, Hf, Th, and U below 10%, while those for Al and Ti were 13.9% and 18.0%, respectively (Fig. 3a). The RSD values of most elements in Tanz zircon range from 0.68% to 12.0%, except for Al, which shows a higher RSD value of 31.0% owing to its low content. The Qinghu zircon exhibits homogeneous distributions of Si (0.99%), Zr (0.58%), and Hf (4.89%); moderately homogeneous distributions of Al (14.9%) and Ti (11.0%); and inhomogeneous distributions of other trace elements with variations exceeding 20%. Results are summarized in the SI, Table S1. The H index was proposed to evaluate the compositional homogeneity as described by Harries.³⁰ An index value of 1 implies that the sample is homogeneous within the analytical uncertainty of an individual measurement, while a value of greater than 3 indicates significant chemical heterogeneity.^25,51–53 The H-index for most trace elements in GJ-1 and Tanz zircons was below 3.0 (Fig. 3b). Most trace elements in Qinghu zircon were heterogeneous (H > 4.0), but Si, Zr, Al, Hf, and Ti displayed a lower H index.

Fig. 3 Relative standard deviation (RSD) values and homogeneity index (H) of major and trace elements in the GJ-1, Tanz, and Qinghu zircon RMs.

In summary, the LA-ICP-MS results demonstrate that the GJ-1, Tanz, and Qinghu zircon RMs exhibit homogeneity in specific minor and trace elements: Al, P, Ti, Y, Yb, Lu, and Hf in GJ-1, P, Ti, Y, Yb, Hf, Th, and U in Tanz, and Al, Ti, and Hf in Qinghu, which are therefore suitable for quality control of zircon trace element measurement by EPMA. To obtain reliable recommended values of trace elements for zircon RMs, we conducted LA-ICP-MS measurements on one GJ-1 zircon fragment in three laboratories. The LA-ICP-MS results are consistent with solution ICP-MS and LA-ICP-MS data from previous studies, indicating that these GJ-1 zircon fragments originated from the same grain (Liu et al., 2010).⁵⁴ As shown in Fig. 4, the relative deviation [100 × (C_solution − C_LA)/C_solution] for key trace elements is less than 10% (SI, Table S2), with the exception of Ti owing to its low concentration. This agreement further validates the LA-ICP-MS calibration and analytical reproducibility achieved for three zircon standards in this study. Consequently, we propose that the LA-ICP-MS results obtained under these controlled conditions can serve as recommended values for assessing the accuracy of EPMA measurements of trace elements in zircon (Table 2).

Fig. 4 Comparison of trace elements in the GJ-1 zircon RM determined using different methods (a) and relative deviation (%) values (b) between LA-ICP-MS and solution ICP-MS data.

Table 2 Comparison of EPMA and LA-ICP-MS results for the Qinghu, GJ-1 and Tanz zircon reference materials^a

Element	SiO2 wt%	ZrO2 wt%	Hf μg g^−1	Lu μg g^−1	Al μg g^−1	Y μg g^−1	Yb μg g^−1	P μg g^−1	Ti μg g^−1	Th μg g^−1	U μg g^−1
a SD, standard deviation. LA_Aver, average value obtained using LA-ICP-MS. RSD, relative standard deviation. RE, relative error. bd, below detection limit.
GJ-1_S (10)	33.32	65.76	7353	18	7	254	48	183	5	bd	310
GJ-1_E (5)	32.75	66.27	7552	25	8	246	51	183	8	bd	322
GJ-1_Aver	33.03	66.01	7419	21	7	251	49	183	6	bd	314
SD	0.19	1.38	705	53	13	40	54	41	10	bd	57
LA_Aver (49)	33.10	65.80	7492	13	4	252.6	62.3	183.7	4	9.6	327.4
2σ	1.430	3.310	270	0.6	1	12.4	3.4	10.1	1	0.5	16.9
RSD (%)	2.68	1.39	2.70	4.25	13.9	3.59	1.97	4.33	18.0	2.5	1.7
RE (%)	0.20	−0.33	0.97			0.50	21.8	0.25			4.1
Tanz_S (10)	32.87	64.59	13 193	16	7	210	1	212	23	65.2	400.4
Tanz_E (5)	33.96	63.32	13 714	27	7	208	−3	219	22	63.2	409
Tanz_Aver	33.42	63.95	13 367	20	7	209	−1	214	23	64.5	406
SD	0.20	1.39	815	55	11	33	45	23	10	46	57
LA_Aver (20)	32.87	65.46	13 197	5	2	181	28	219.2	18	66.9	400.9
2σ	0.65	1.66	306	0.2	0.5	8	2	10.3	2	5.8	18.1
RSD (%)	1.22	0.68	1.98	4.34	35.2	5.21	7.94	3.65	7.80	12.0	6.0
RE (%)	−1.66	2.30	−1.28			−15.7		2.27	−26.2	3.6	−1.2
Qinghu_S (10)	32.61	65.39	12 576	18	80	436	36	559	68	71.5	750.4
Qinghu_E (5)	32.53	65.51	12 972	11	81	521	55	582	72	41.0	700.4
Qinghu_Aver	32.57	65.45	12 708	15	81	464	42	567	70	61.3	733.7
SD	0.19	1.36	804	53	22	80	51	44	19	46.0	58.0
LA_Aver (20)	32.15	65.91	12 322.4	11	75.2	524	79	689	78.9	138.6	1186
2σ	0.61	1.47	400.2	0.4	8.5	19	3	6	9.4	4.7	36.0
RSD (%)	0.99	0.58	4.89	29.4	14.9	28.4	33.6	32.4	13.1	83.3	73.5
RE (%)	−1.31	0.69	−3.13		−7.01	11.3		17.7	10.8

---

5 Development of a high-accuracy EPMA method

Over the last decade, EPMA has been successfully used to determine minor and trace elements in various minerals, including olivine,^55–57 ilmenite,²⁶ spinel,⁵⁸ rutile,^59,60 quartz,^24,40,61 monazite,^62,63 zircon (Hf and Ti),⁶⁴ and glass.⁶⁵ These studies have provided valuable experience and established diverse analytical protocols. In the following discussion, the precautions and protocols for measuring minor and trace elements in zircon using EPMA are established to balance the spatial resolution, detection limit, analytical precision and accuracy.

5.1 Practical spatial resolution

One of the great strengths of trace element analysis by EPMA is the capability for very high spatial resolution, particularly for extremely small samples or those with complex growth zoning. The spatial resolution depends on the X-ray emission volume, sample composition, beam energy, and beam diameter,⁶² and can be estimated by Monte Carlo interaction models, such as CASINO software.⁶⁶

Firstly, we tested the spatial resolution of the routine analytical method (15 kV, 2–3 min per spot), close to the time of 10 000 electron trajectories. We used a density of 4.56 g cm⁻³ for zircon composition (ZrSiO₄), a 15 nm thick carbon coating, and a focused beam with a diameter of 100 nm. The spatial resolution can be approximately defined by the 5% contour because X-rays are not effectively generated beyond the 5% contour. As a result, the spatial resolution of EPMA was close to 1 μm (Fig. 5a), which was reasonable under this analysis condition.

Fig. 5 Monte Carlo simulations of the electron energy distributions in zircon bombarded by electrons accelerated to 15 kV (a and b), 20 kV (c), and 25 kV (d) with a focused normal incidence beam. The simulations were performed using the CASINO program, with 10 000 electron trajectories (equivalent to 2–3 minutes per spot) or 100 000 electron trajectories (equivalent to 10–12 minutes per spot). The spatial resolution can be approximately defined by the 5% contour on account of X-rays not being effectively generated beyond this threshold.

To achieve the goal of trace element determination by EPMA, high count rates are usually needed via increasing the accelerating voltage and/or analytical time, which directly compromises spatial resolution. In our simulation for trace element analysis, a total of 100 000 electron trajectories (equivalent to 12–14 min per spot) were simulated to model the interactive volume at 15 kV, 20 kV, and 25 kV, using a focused beam (100 nm). At 15 kV, the spatial resolution drops to ∼1.5 μm by increasing the number of electron trajectories from 10 000 to 100 000 (Fig. 5b). Furthermore, the increase in accelerating voltage markedly affects the spatial resolution, which drops from 1.5 μm at 15 kV to 2.0 μm at 20 kV and 3.0 μm at 25 kV (Fig. 5c and d).

One of the factors limiting the high spatial resolution of EPMA in trace element measurements is secondary fluorescence (SF) across phase boundaries.^67–69 The SF effect is small and can generally be neglected, but the analytical accuracy may be reduced when analyzing a minor or trace element in a phase surrounded by another phase that contains higher content of the same element. For example, Fournelle (2007)⁷⁰ estimated the SF effect in Ti quantification in zircon using EPMA, which caused spurious reporting of Ti content ranging from >10 μg g⁻¹ at 100 μm distance to >250 μg g⁻¹ at 25 μm distance from a large Ti-rich phase. Although the SF effect can be calculated theoretically^71,72 or empirically evaluated,^68,73,74 it is tedious and not always feasible. Therefore, it is imperative to address the root cause of the SF under the analytical conditions. Low accelerating voltage has two major advantages: (1) improved spatial resolution; and (2) inefficient production of the fluorescence-inducing radiation.⁵⁸ Based on the Monte Carlo simulation results, the accelerating voltage of 20 kV, corresponding to a spatial resolution of ∼2.0 μm, was optimal for determining minor and trace elements in small-sized zircon using EPMA.

5.2 Precision and detection limit

The immediate challenge of trace element analysis by EPMA is to decrease detection limit (DL) and improve analytical precision. Since the analytical precision of EPMA depends on X-ray counting statistics for both the peak and background, approaches to improve DL primarily focus on enhancing precision, which is typically quantified by the standard deviation (3σ).^56,75–78 Batanova et al. (2018)⁷⁹ suggested that the DL of an element is negatively correlated with the analytical precision, and lower detection limits mean higher data precision. There are, of course, several approaches to increase the characteristic X-ray signal, including the accelerating voltage, beam current, counting time, and/or a combination of the above. In addition, some other strategies, such as large analytical crystals (e.g., LPET and LLIF) and aggregate intensity counting software, can also improve counting statistics to optimize the DL and precision.

In general, the extremely high counting rates of high-content elements would result in oversaturation of counters at high accelerating voltage and high beam current. Thus, we simultaneously applied the double beam current mode to the analysis of major and trace elements using a Cameca SXFive EPMA. In order to lower DL and improve precision, the following approaches were implemented in this study: (1) a higher acceleration voltage of 20 kV was applied to balance spatial resolution (∼2 μm) and high counting intensity; (2) four large Bragg crystals were utilized for enhanced sensitivity and counting rates: specifically, two LLIF for Lu, Hf, and Yb, and two LPET for P, Ti, Th, and U; (3) the aggregate counting intensity software was employed, such as by using two TAP crystals in spectrometers 1 and 4 for Al measurement (Fig. 6a); (4) a beam current of 500 nA and a peak time of 240 s were identified as the optimal conditions through detection limit simulations (Fig. 6b and c), since higher currents and longer peak times would not significantly reduce the detection limit (SI, Table S3); (5) a shorter background time of 60 s than half peak counting time (240 s) was adopted for trace elements, which enhances analytical efficiency without substantially compromising the detection limit (Fig. 6d).

Fig. 6 Comparison of detection limits (ppm, 3σ) for Al, Th, and Ti under different analytical conditions using EPMA.

As a result, the detection limit is 14 μg g⁻¹ for Al, 28 μg g⁻¹ for P, 10 μg g⁻¹ for Ti, 49 μg g⁻¹ for Y, 53 μg g⁻¹ for Yb, 67 μg g⁻¹ for Lu, 41 μg g⁻¹ for Th, and 65 μg g⁻¹ for U (3σ), and the corresponding standard deviation is 16 μg g⁻¹ for Al, 23 μg g⁻¹ for P, 9 μg g⁻¹ for Ti, 42 μg g⁻¹ for Y, 51 μg g⁻¹ for Yb, 52 μg g⁻¹ for Lu, 45 μg g⁻¹ for Th, and 58 μg g⁻¹ for U, respectively. The single-point analysis using this method took approximately 14 minutes. The detailed results are provided in Table 1. It is noteworthy that the detection limit (3σ) is comparable to the analytical precision for each element, which aligns with trace element measurement results reported for olivine.⁷⁹

5.3 Accuracy improvement

Although the analytical precision of EPMA can be enhanced through improved counting statistics, the accuracy of X-ray background characterization remains limited by systematic errors, which cannot be mitigated solely by increasing measurement precision. The primary cause of most analytical deviation is spectral interference of different elements and/or background measurement.^24,78,80 To avoid beam damage caused by multiple WDS scans on small and precious lunar zircons, the GJ-1, Tanz, and Qinghu zircon RMs were used to define protocols for accurate measurements of minor and trace elements by evaluating the effects of background offsets, regression models, and calibration standard selection. A program based on the X-PHI matrix correction procedure applied the Phi–Rho-Z model to integrate X-rays for the whole excitation volume.^81,82 Analytical accuracy was tested by comparing repeated measurements of the zircon RMs obtained using LA-ICP-MS. In the following discussion, the accuracy improvement and assessment processes for each element were conducted sequentially. The recommended background offsets, calibration settings, and related results are presented in Table 1.

5.3.1 Titanium. The Qinghu zircon has higher Ti content (78.9 μg g⁻¹) than other zircon RMs, which makes it suitable as a quality control material. To identify optimal background positions for Ti, a high-sensitivity wavelength dispersive spectrometer (WDS) scan on each side of the peak was performed on Qinghu zircon at 20 kV and 200 nA. A routine background offset (AC1: −500, +500) was applied to Ti, but the result yielded a lower deviation from the recommended value. Slight changes in the background offsets of Ti in AC2–7 did not improve data accuracy. Incorrect measurement of continuum curvature near the peak region may reduce apparent peak intensities by tens of parts per million.^24,53,58 As shown in Fig. 7a, the detailed WDS of Ti Kα revealed some curvature, in which the linear background regression (two-point interpolation) yielded a significantly overestimated background value, resulting in lower contents. Therefore, the exponential background regression was performed for zircon Ti analysis, significantly improving the analysis accuracy (AC8, −650, +650). Using this analytical condition to measure the CE-6 lunar zircons, negative Ti contents were obtained (AC9). Hence, the high-sensitivity WDS scan of Ti Kα was acquired on lunar zircon at 20 kV and 500 nA, resulting in more obvious peak and background positions (Fig. 7b). We applied a new background setting (AC10, −750, +450) to measure the CE-6 and Qinghu zircons, and the latter's results were closer to the recommended value, with a 10.8% deviation (Fig. 7c).

Fig. 7 Accuracy evaluation on Ti and P using Qinghu and GJ-1 zircon RMs. (a) WDS scan of Ti element in Qinghu zircon at 20 kV and 200 nA; (b) WDS scan of Ti element in Qinghu zircon at 20 kV and 500 nA; (c) measured Ti contents compared to the recommended value of the Qinghu zircon RM; (d) WDS scan of P element in GJ-1 zircon at 20 kV and 200 nA; (e) WDS scan of Ti element in GJ-1 zircon at 20 kV and 500 nA; (f) measured P contents compared to the recommended value of the GJ-1 zircon RM. The error bars reflect the analytical uncertainties for each individual analysis.

5.3.2 Phosphorus. The GJ-1 and Tanz zircon RMs have P contents of 183.7 ± 10.1 μg g⁻¹ and 219.2 ± 10.3 μg g⁻¹, respectively, and can be used as monitoring standards for P in zircon. As shown in Fig. 7d and e, the P Kα X-ray peak is very close to Zr Lα, causing the lower background to rise and producing negative values when using wide background offset ranges on one side of the Zr Lα peak (AC1–2, Fig. 7f). While using wider background ranges on both sides of the Zr Lα peak (AC3–5), the analysis results were positive but much higher than the recommended value. This may be due to Zr Lα interference in the P Kα analysis. Therefore, we applied the upper single background measurement (AC6–8, e.g., none, +800) to minimize Zr Lα interference, thereby slightly improving the analytical accuracy. In addition, the high-sensitivity WDS was obtained on GJ-1 zircon at 20 kV and 500 nA, the X-ray peak shape of P Kα was more obvious (Fig. 7d). Changing background offset in AC10 (none, +300) resulted in the P content of the GJ-1 zircon RM being closer to the recommended value, with 1.62% deviation, compared to 17.8% deviation for AC9 (none, +400).

5.3.3 Aluminum. To improve the total counting statistics, the aggregate intensity counting approach was performed for Al analysis using two TAP crystals simultaneously. As shown in Fig. 8a, the Al Kα X-ray peak was weak at 20 kV and 200 nA. The analysis data obtained by wide background offsets of Al Kα peak (AC1–5) were obviously lower than the recommended value in Qinghu zircon. After replacing the primary standard (Al₂O₃ oxide) with YAG (Y₃Al₅O₁₂), the average value of 79.4 μg g⁻¹ was consistent with the recommended value. The large Al content variations (AC6) measured by EPMA could be caused by the heterogeneity of the Al content in Qinghu zircon. However, the Al results of CE-6 zircons determined were negative, revealing the inaccurate background acquisition. As shown in the WDS curvature of Al Kα on lunar zircon at 20 kV and 500 nA (Fig. 8b), the background measurement of AC7 (−150, +350) was overestimated, resulting in the negative values. We applied a more appropriate background setting (AC8, −550, +500) to determine the Qinghu zircon, which yielded consistent data with a deviation of 7.01% (Fig. 8c).

Fig. 8 Accuracy evaluation on Al and Y using Qinghu, CE-6, and GJ-1 zircon RMs. (a) WDS scan of Al element in the Qinghu zircon at 20 kV and 200 nA; (b) WDS scan of Al element in CE-6 zircon at 20 kV and 500 nA; (c) measured Al contents compared to the recommended value of the Qinghu zircon RM; (d) WDS scan of Y element in GJ-1 zircon at 20 kV and 200 nA; (e) WDS scan of Y element in GJ-1 zircon at 20 kV and 500 nA; (f) measured Y contents compared to the recommended value of the GJ-1 zircon RM.

5.3.4 Yttrium. Similar to Al analysis, Y content in zircon was measured simultaneously on two TAP crystals to achieve higher peak/background ratios. The interferences of Zr Lα, Zr Ln, and Si Lβ on Y Lα are notable, as shown in Fig. 8d, making the intensities at both side background positions overestimated. Slight underestimation or negative values (AC1-5) were observed. To select more accurate background positions, we acquired high-sensitivity WDS scan of Y Lα on GJ-1 zircon at 20 kV and 500 nA (Fig. 8e). However, the analytical results were still low using a narrow background offset in AC6–7, with a deviation of 55.7%. Significant improvement of Y analysis accuracy was shown after applying the single lower background offset in AC8. Finally, changing background offset in AC9 (−200, none) resulted in Y contents closer to the reference value, with 0.50% deviation (Fig. 8f).

5.3.5 Ytterbium. The GJ-1 zircon has a high and homogeneous Yb content of 62.3 μg g⁻¹, which is suitable as a monitoring standard for measuring trace Yb in zircon using EPMA. The detailed WDS scan of Yb Lα on GJ-1 zircon was acquired at 20 kV and 200 nA, with linear background regression, as shown in Fig. 9a. Changing background offsets in AC5–7 resulted in consistent Yb average contents ranging from 40.0 μg g⁻¹ to 47.7 μg g⁻¹, with deviations of 23.6–35.9%, compared to deviations of 35.1–74.4% for AC1–4 with other background settings. The Yb content measured in AC8 (−530, 600) was closer to the reference value, with 21.9% deviation (Fig. 9b). The underestimation in our study may be accounted for the current precision (51 μg g⁻¹) and detection limit (65 μg g⁻¹, 3σ) for Yb under this analytical condition. The accuracy of EPMA decreases at low contents because most random and systematic errors are magnified at trace level and specific errors appear.^25,75,79 It follows that increasing the accuracy of EPMA trace element measurement largely depends on the improvement of analytical precision and detection limit.

Fig. 9 Accuracy evaluation on Yb and Hf using GJ-1, Tanz, and Qinghu zircon RMs. (a) WDS scan of Yb element in the GJ-1 zircon at 20 kV and 200 nA; (b) measured Yb contents compared to the recommended value of the GJ-1 zircon; (c) WDS scan of Hf element in Tanz zircon at 20 kV and 100 nA; (d) measured Hf contents compared to the recommended values of the GJ-1, Tanz, and Qinghu zircon RMs.

5.3.6 Hafnium. Due to the high content in zircon, the determination of Hf yields highly accurate data. The measured Hf results are consistent with the recommended values of Qinghu, GJ-1, and Tanz zircon RMs (Fig. 9c), with analytical relative deviations of 3.13%, 0.97%, and 1.28%, respectively (Fig. 9d).

5.3.7 Lutetium. High-precision WDS scanning for Lu was conducted in GJ-1 zircon at 20 kV and 500 nA, showing very weak peak intensity because of its low content. Under the analytical conditions in Table 1, the detection limit for Lu was 67 ppm, with a precision of 52 ppm. However, the Lu content in three zircon reference materials (5–13 ppm) was below the detection limit. To balance analytical efficiency and spatial resolution, there is no need to deliberately achieve such a low detection limit under the current analytical conditions, except for cases requiring low Lu content analysis.

5.3.8 Thorium. Among the studied zircon standards, the Qinghu zircon has the highest Th content of 138.6 μg g⁻¹ with the worst RSD value of 83.3%, and the GJ-1 zircon displays the lowest Th content of 9.6 μg g⁻¹ with the best RSD value of 2.5%. Therefore, the Tanz zircon with homogeneous Th content (66.9 μg g⁻¹) and a good RSD value (5.8%) is suitable as monitoring standard for EPMA. Since the atomic numbers of Th and U are both greater than 72, the M line with high diffraction efficiency and peak-to-back ratio is therefore preferred for EPMA. The detailed WDS scan of Th Mα on Tanz zircon was acquired at 20 kV and 500 nA, as shown in Fig. 10a. Th average contents ranging from 14 to 53 μg g⁻¹ were lower than the recommended value (66.9 μg g⁻¹), with 19.7–78.8% deviation. The linear background regression for Th determination may reduce the net peak intensities because of the continuum curvature near the peak region. The exponential background regression was used for Th measurement, showing better results than those obtained using linear background regression. After changing the background offsets (AC5–AC7), the Th content measured in AC8 (−500, 1400) was closer to the reference value, with 3.59% deviation (Fig. 10b).

Fig. 10 Accuracy evaluation of Th and U using Tanz zircon RM. (a) WDS scan of Th element in the Tanz zircon at 20 kV and 500 nA; (b) measured Th contents compared to the recommended value of the Tanz zircon RM; (c) WDS scan of U element in the Tanz zircon at 20 kV and 500 nA; (d) measured U contents compared to the recommended value of the Tanz zircon RM. The error bars reflect the analytical uncertainties for each individual analysis.

5.3.9 Uranium. The Tanz zircon, which has a homogeneous U content of 400.9 ± 18.1 μg g⁻¹ with RSD values of 6.0%, was used for quality control of EPMA. Similar to the Th element characteristics, the LPET crystal and Mα line were used to analyze the U content in Tanz zircon. The background intensities under AC1–AC4 settings were near or higher than the U peak intensity when using linear background regression (Fig. 10c), resulting in negative values or very low positive values. Although the results have improved after exponential background regression for U (AC5–AC6, SI, Table S4), they were still much lower than the recommended value (Fig. 10d). The analytical deviation might be due to interference from Th Mβ on U Mα, resulting in preference for U Mβ. Analytical accuracy improved under the AC7 (−600, 1000) using the Mβ line and linear background regression for U, but the measured values remained slightly lower than the recommended value. Therefore, we switched to exponential background regression, yielding a relative deviation of 1.18%.

In summary, these data demonstrate good agreement between EPMA and LA-ICP-MS methods (Fig. 11), confirming the appropriate selection of positions for background measurements. Zircon grains from the CE-6 anorthosite were analyzed using this optimized EPMA method, which showed major elemental contents of Zr and Si ranging from 47.3 to 48.5 wt% and 15.2 to 15.9 wt%. Minor and trace elements (Hf, Y, Yb, Lu, P, and Ti) exhibited contents of 11 336–12668 μg g⁻¹, 740–847 μg g⁻¹, 216–296 μg g⁻¹, 38–99 μg g⁻¹, 503–562 μg g⁻¹, and 51–102 μg g⁻¹, respectively (SI, Table S5). These results could provide critical insights into the formation temperature of the anorthosites, characteristics of the source region, and magmatic processes.

Fig. 11 Comparison of minor and trace element mass fractions in the GJ-1, Qinghu, and Tanz zircon RMs obtained using high-accuracy EPMA measurement with LA-ICP-MS results. The 1 : 1 line is provided for comparison. The bars shown for spots represent two times standard deviation.

6 Conclusions and future prospects

In this study, we focus on practical approaches for the measurement of minor and trace elements in zircon using EPMA. The spatial resolution of zircon analysis ranges from 1 to 3 μm at 15–25 kV, as simulated by Monte Carlo. Analytical conditions of the optimal method are: accelerating voltage of 20 kV, beam currents of 40 nA for major and minor elements, and of 500 nA for trace elements, total measurement time of ∼14 minutes for a single analysis, and beam size of ∼2 μm. The excellent precision and detection limits of 10–67 μg g⁻¹ (3σ) are achieved using a combination of aggregated intensity software, large Bragg crystals, and extreme analysis conditions. Three zircon reference materials are evaluated as the “monitoring standard” for quality control in EPMA measurement of minor and trace elements. The background measurement and regression model, calibration standard, and suppression of peak spectral interference are carefully considered, resulting in highly accurate EPMA trace element measurements in zircon. Although LA-ICP-MS shows better precision than EPMA at abundance levels of <1000 μg g⁻¹, the spatial resolution of EPMA is 5–10 times better than that of LA-ICP-MS. The reliable methodology presented here is potentially useful for elucidating the magmatic source and formation processes of zircon and associated host rocks.

Although EPMA exhibits unique advantages in trace element determination owing to its high spatial resolution and non-destructive analytical capabilities, it still faces unavoidable limitations: (1) the balance between element coverage, detection limit, and analytical efficiency; (2) variations in analytical accuracy; and (3) the trade-off between spatial resolution and secondary fluorescence effects. In practical analytical methodology research, it is essential to prioritize key trace elements based on specific scientific objectives and achieve an optimal balance among spatial resolution, detection limit, and analytical efficiency through dynamic adjustment of experimental parameters, development of reference materials, and algorithm-based corrections. With advancements in field-emission EPMA low-voltage operation mode and soft X-ray spectrometers, EPMA holds significant potential for micro-scale trace element analysis in minerals.

Author contributions

Lihui Jia: conceptualization, data curation, formal analysis, investigation, methodology, writing–original draft, and writing–review & editing; Yi Chen: investigation, methodology, resources, and visualization; Yu Li: formal analysis; Qian Mao: data curation and methodology; Hao Wang: project administration, resources, and methodology; Zeling Wang: formal analysis and data curation; Haojie Chen: formal analysis and data curation.

Conflicts of interest

No potential conflict of interest was reported by the authors.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information includes the following materials: Supplemental Table S1: Minor and trace element (μg g⁻¹) mass fractions of the GJ-1, Qinghu, and Tanz zircon RMs determined using LA-ICP-MS. Supplemental Table S2:e Element compositions of the GJ-1 zircon RM determined using different method. Supplemental Table S3: Variation of detection limits (ppm, 3σ) for Al, Th, and Ti under different analytical conditions. Supplemental Table S4: Major, minor and trace element results (wt%) in GJ-1, Qinghu, and Tanz zircon RMs analyzed using EPMA. Supplemental Table S5: Major, minor and trace element data of the zircon in CE-6 anorthosite determined using EPMA. Supplemental Fig. S1: Compositional variation plots for key trace elements in GJ-1, Qinghu, and Tanz zircon RMs analyzed using LA-ICP-MS. See DOI: https://doi.org/10.1039/d5ja00150a.

Acknowledgements

This study was funded by the National Natural Science Foundation of China (42441802), the Key Research Program of the Institute of Geology and Geophysics, Chinese Academy of Sciences (IGGCAS-202401), and the Experimental Technology Innovation Fund of the Institute of Geology and Geophysics, Chinese Academy of Sciences (E4518504).

References

1. M. Wiedenbeck, J. M. Hanchar, W. H. Peck, P. Sylvester, J. Valley, M. Whitehouse, A. Kronz, Y. Morishita, L. Nasdala, J. Fiebig, I. Franchi, J. P. Girard, R. C. Greenwood, R. Hinton, N. Kita, P. R. D. Mason, M. Norman, M. Ogasawara, R. Piccoli, D. Rhede, H. Satoh, B. Schulz-Dobrick, O. Skar, M. J. Spicuzza, K. Terada, A. Tindle, S. Togashi, T. Vennemann, Q. Xie and Y. F. Zheng, Geostand. Geoanal. Res., 2004, 28, 9–39.
2. Y. B. Wu and Y. F. Zheng, Chin. Sci. Bull., 2004, 49(15), 1554–1569.
3. J. Slama, J. Kosler, D. J. Condon, J. L. Crowley, A. Gerdes, J. M. Hanchar, M. S. A. Horstwood, G. A. Morris, L. Nasdala, N. Norberg, U. Schaltegger, B. Schoene, M. N. Tubrett and M. J. Whitehouse, Chem. Geol., 2008, 249, 1–35.
4. X. H. Li, W. G. Long, Q. L. Li, Y. Liu, Y. F. Zheng, Y. H. Yang, K. R. Chamberlain, D. F. Wan, C. H. Guo, X. C. Wang and H. Tao, Geostand. Geoanal. Res., 2010, 34, 117–134.
5. B. Schoene. Treatise on Geochemistry, 2^nd edn, New York, Elsevier, 2014.
6. E. B. Watson and T. M. Harrison, Science, 2005, 308, 841–844.
7. S. J. Mojzsis, T. M. Harrison and R. T. Pidgeon, Nature, 2001, 409, 178–181.
8. A. I. S. Kemp, C. J. Hawkesworth, B. A. Paterson and P. D. Kinny, Nature, 2006, 439, 580–583.
9. Y. Buret, A. von Quadt, C. Heinrich, D. Selby, M. Wälle and I. Peytcheva, Earth Planet. Sci. Lett., 2016, 450, 120–131.
10. Y. Buret, J. F. Wotzlaw, S. Roozen, M. Guillong, A. von Quadt and C. A. Heinrich, Geology, 2017, 45, 623–626.
11. P. W. O. Hoskin and L. P. Black, J. Metamorph. Geol., 2000, 18, 423–439.
12. R. J. M. Taylor, C. Clark, S. L. Harley, A. R. C. Kylander-Clark, B. R. Hacker and P. D. Kinny, J. Metamorph. Geol., 2017, 35, 759–775.
13. A. E. Hofmann, J. W. Valley, E. B. Watson, A. J. Cavosie and J. M. Eiler, Contrib. Mineral. Petrol., 2009, 158, 317–335.
14. F. M. McCubbin, C. D. K. Herd, T. Yada, A. Hutzler, M. J. Calaway, J. H. Allton, C. M. Corrigan, M. D. Fries, A. D. Harrington, T. J. McCoy, J. L. Mitchell, A. B. Regberg, K. Righter, C. J. Sbeadm, K. T. Tait, M. E. Zolensky and R. A. Zeigler, Space Sci. Rev., 2019, 245, 48.
15. C. L. Li, M. F. Yang, Z. Y. Pei, Q. Zhou, X. Ren, B. Liu, D. W. Liu, X. G. Zeng, G. L. Zhang, H. B. Zhang, J. J. Liu, Q. Wang, X. J. Deng, C. J. Xiao, Y. G. Yao, D. S. Xue, W. Zuo, Y. Su, W. B. Wen and Z. Y. Ouyang, Natl. Sci. Rev., 2022, 9, 21–33.
16. C. L. Li, H. Hu, M. F. Yang, J. J. Liu, Q. Zhou, X. Ren, B. Liu, D. W. Liu, X. G. Zeng, W. Zuo, G. L. Zhang, H. B. Zhang, S. H. Yang, Q. Wang, X. J. Deng, X. Y. Gao, Y. Su, W. B. Wen and Z. Y. Ouyang, Natl. Sci. Rev., 2024, 11, nwae328.
17. B. L. Jolliff, J. J. Gillis, L. A. Haskin, R. L. Korotev and M. A. Wieczorek, J. Geophys. Res.:Planets, 2000, 105(E2), 4197–4216.
18. L. R. Gaddis, K. H. Joy, B. J. Bussey, J. D. Carpenter, I. A. Crawford, R. C. Elphic, H. S. Halekas, S. J. Lawrence and L. Xiao, Rev. Mineral. Geochem., 2023, 89, 1–51.
19. S. Gou, Z. Y. Yue, Y. T. Lin, K. C. Di, P. C. Pinet, R. Buguilacchi, Y. Y. He, W. Wang, H. L. Lin, H. C. Tian and S. Hu, Earth Planet. Sci. Lett., 2024, 648, 119091.
20. Q. W. L. Zhang, M. H. Yang, Q. L. Li, Y. Liu, Z. Y. Yue, Q. Zhou, L. Y. Chen, H. X. Ma, S. H. Yang, X. Tang, G. Zhang, X. Ren and X. H. Li, Nature, 2025, 643, 356–360.
21. Z. X. Cui, Q. Yang, Y. Q. Zhang, C. Y. Wang, H. Y. Xian, Z. M. Chen, Z. Y. Xiao, Y. Q. Qian, J. W. Head III, C. R. Neal, L. Xiao, F. L. Luo, J. Y. Chen, P. L. He, Y. J. Cao, Q. Zhou, F. F. Huang, L. L. Chen, B. Wei, J. T. Wang, Y. N. Yang, S. Li, Y. P. Yang, X. J. Lin, J. X. Zhu, L. Zhang and Y. G. Xu, Science, 2024, 386, 1395–1399.
22. T. M. Harrison, E. B. Watson and A. B. Aikman, Geology, 2007, 35, 635–638.
23. A. E. Hofmann, M. B. Baker and J. M. Eiler, Contrib. Mineral. Petrol., 2014, 168, 1–21.
24. J. J. Donovan, H. A. Lowers and B. G. Rusk, Am. Mineral., 2011, 96, 274–282.
25. V. G. Batanova, J. M. Thompson, L. V. Danyushevsky, M. V. Portnyagin, D. Garbe-Schonberg, J. I. Hauri, E. Kimura, Q. Chang, R. Senda, K. Goemann, C. Chauvel, S. Campillo, D. A. Lonov and A. V. Sobolev, Geostand. Geoanal. Res., 2019, 43, 453–473.
26. L. H. Jia, Q. Mao, H. C. Tian, L. X. Li, L. Qi, S. T. Wu, J. Y. Yuan, L. L. Huang and Y. Chen, J. Anal. At. Spectrom., 2022, 37, 2351–2361.
27. X. Wang, Sci. China Earth Sci., 2000, 30(2), 180–187.
28. L. L. Li, B. Wang and C. J. Wei, Sci. China Earth Sci., 2023, 66(5), 985–996.
29. K. P. Jochum, D. B. Dingwell, A. Rocholl, B. Stoll, A. W. Hofmann, S. Becker, A. Besmehn, D. Bessette, H. J. Dietze, P. Dulski, J. Erzinger, E. Hellebrand, P. Hoppe, I. Horn, K. Janssens, G. A. Jenner, M. Klein, W. F. McDonough, M. Maetz, K. Mezger, C. Munker, I. K. Nikogosian, C. Pickhardt, I. Raczek, D. Rhede, H. M. Seufert, S. G. Simakin, A. V. Sobolev, B. Spettel, S. Straub, L. Vincze, A. Wallianos, G. Weckwerth, S. Weyer, D. Wolf and M. Zimmer, Geostand. Geoanal. Res., 2000, 24, 87–133.
30. D. Harries, Chem. Erde, 2014, 74, 375–384.
31. J. T. Caulfield, C. M. Allen, T. Ubide, A. Nguyen and H. E. Cathey, Chem. Geol., 2025, 674, 122580.
32. S. E. Jackson, N. J. Pearson, W. L. Griffin and E. A. Belousova, Chem. Geol., 2004, 211, 47–69.
33. M. L. A. Morel, O. Nebel, Y. J. Nebel-Jacobsen, J. S. Miller and P. Z. Vroon, Chem. Geol., 2008, 255, 231–235.
34. X. H. Li, G. Q. Tang, B. Gong, Y. H. Yang, K. J. Hou, Z. C. Hu, Q. L. Li, Y. Liu and W. X. Li, Chin. Sci. Bull., 2013, 58, 4647–4654.
35. Z. C. Hu, X. H. Li, T. Luo, W. Zhang, J. Crowley, Q. L. Li, X. X. Ling, C. Yang, Y. Li, L. P. Feng, X. P. Xia, S. B. Zhang, Z. C. Wang, J. L. Guo, L. Xu, J. Lin, X. M. Liu, Z. A. Bao, Y. S. Liu, K. Q. Zong, W. Chen and Y. S. Hu, J. Anal. At. Spectrom., 2021, 36, 2715–2734.
36. C. Huang, H. Wang, J. H. Yang, J. Ramezani, C. Yang, S. B. Zhang, Y. H. Yang, X. P. Xia, L. J. Feng, J. Lin, T. T. Wang, Q. Ma, H. Y. He, L. W. Xie and S. T. Wu, Geostand. Geoanal. Res., 2020, 44, 103–123.
37. C. Huang, H. Wang, J. H. Yang, C. Yang, Z. X. Li, Y. H. Yang, L. J. Feng, L. W. Xie and S. T. Wu, J. Anal. At. Spectrom., 2021, 36, 368–374.
38. Y. S. Liu, Z. C. Hu, S. Gao, D. Günther, J. Xu, C. G. Gao and H. H. Chen, Chem. Geol., 2008, 257, 34–43.
39. K. Q. Zong, Y. S. Liu, C. G. Gao, Z. C. Hu, S. Gao and H. J. Gong, Chem. Geol., 2010, 269, 237–251.
40. J. Q. Cui, S. Y. Yang, S. Y. Jiang and J. Xie, Microsc. Microanal., 2019, 25, 47–57.
41. M. Wiedenbeck, P. Alle, F. Corfu, W. L. Griffin, M. Meier, F. Oberli, A. von Quadt, J. C. Roddick and W. Speigel, Geostand. Newsl., 1995, 19, 1–23.
42. R. A. Stern, Geological Survey of Canada (Ottawa), Radiogenic age and isotopic studies: Report 14, 2001, p. 120.
43. L. P. Black, S. L. Kamo, C. M. Allen, J. N. Aleinikoff, D. W. Davis, R. J. Korsch and C. Foudoulis, Chem. Geol., 2003, 200, 155–170.
44. J. D. Woodhead and J. M. Hergt, Geostand. Geoanal. Res., 2005, 29, 183–195.
45. L. Nasdala, W. G. Hofmeister, N. Norberg, J. M. Mattinson, F. Corfu, W. Dorr, S. L. Kamo, A. K. Kennedy, A. Kronz, P. W. Reiners, D. Frei, J. Kosler, Y. S. Wan, J. Gotze, T. Hager, A. Kroner and J. W. Valley, Geostand. Geoanal. Res., 2008, 32, 247–265.
46. G. E. Gehrels, V. Valencia and J. Rui, Geochem., Geophys., Geosyst., 2008, 9, Q03017.
47. R. A. Stern, S. Bodorkos, S. L. Kamo, A. H. Hickman and F. Corfu, Geostand. Geoanal. Res., 2009, 33, 145–168.
48. A. I. S. Kemp, J. D. Vervoort, K. E. Bjorkman and L. M. Iaccheri, Geostand. Geoanal. Res., 2017, 41, 659–673.
49. L. Nasdala, F. Corfu, B. Schoene, S. R. Tapster, C. J. Wall, M. D. Schmitz, M. Ovtcharova, U. Schaltegger, A. K. Kennedy, A. Kronz, P. W. Reiners, Y. H. Yang, F. Y. Wu, S. E. M. Gain, W. L. Griffin, D. Szymanowski, N. C. Chanmuang, M. Ende, J. W. Valley, M. J. Spicuzza, B. Wanthanachaisaeng and G. Giester, Geostand. Geoanal. Res., 2018, 42, 431–457.
50. A. C. S. Cheong, Y. J. Jeong, S. Lee, K. Yi, H. J. Jo, H. S. Lee, C. Park, N. K. Kim, X. H. Li and S. L. Kamo, Minerals, 2019, 9, 325.
51. P. J. Potts, A. G. Tindle and M. C. Isaacs, Am. Mineral., 1983, 68, 1237–1242.
52. M. J. Pankhurst, R. Walshaw and D. Morgan, Geostand. Geoanal. Res., 2017, 41, 85–91.
53. L. H. Jia, X. Ma, S. T. Wu, Y. L. Li, J. Y. Yuan, Q. Mao, X. G. Li and Y. Chen, Geostand. Geoanal. Res., 2024, 48, 207–225.
54. Y. S. Liu, S. Gao, Z. C. Hu, C. G. Gao, K. Q. Zong and D. B. Wang, J. Petrol., 2010, 51(1–2), 537–571.
55. A. V. Sobolev, A. W. Hofmann, S. V. Sobolev and I. K. Nikogosian, Nature, 2005, 434, 590–597.
56. V. G. Batanova, A. V. Sobolev and D. V. Kuzmin, Chem. Geol., 2015, 419, 149–157.
57. P. Jiang, M. Perfit, D. A. Foster and A. Trucco, Chem. Geol., 2022, 614, 121199.
58. L. H. Jia, Y. Chen, Q. Mao, D. Zhang, J. Y. Yuan, X. G. Li, S. T. Wu and D. P. Zhang, At. Spectrosc., 2022, 43, 42–52.
59. G. L. Luvizotto, T. Zack, H. P. Meyer, T. Ludwig, S. Triebold, A. Kronz, C. Münker, D. F. Stockli, S. Prowatke, S. Klemme, D. E. Jacob and H. von Eynatten, Chem. Geol., 2009, 261, 346–369.
60. J. Wang, Y. Chen, Q. Mao, Q. L. Li, Y. G. Ma, Y. H. Shi and C. Z. Song, Acta Petrol. Sin., 2017, 33(6), 1934–1946.
61. D. A. Wark and B. E. Watson, Contrib. Mineral. Petrol., 2006, 152, 743–754.
62. M. J. Jercinovic, M. L. Williams and E. D. Lane, Chem. Geol., 2008, 254, 197–215.
63. J. Allaz, M. J. Jercinovic, M. L. Williams and J. J. Donovan, Microsc. Microanal., 2014, 20, 720–721.
64. X. L. Li, J. Rock Miner. Anal., 2023, 42(1), 89–101.
65. D. Zhang, Y. Chen, W. Yang, J. H. Fournelle, J. L. Ji, B. Su, Q. Mao, L. H. Jia, J. Y. Yuan and X. G. Li, At. Spectrosc., 2022, 43, 28–41.
66. D. Drouin, A. R. Couture, D. Joly, X. Tastet, V. Aimez and R. Gauvin, Scanning, 2007, 29, 92–101.
67. X. Llovet and G. Galan, Am. Mineral., 2003, 88, 121–130.
68. X. Llovet, J. A. Proenza, N. Pujol-Solà, J. Farré-De-Pablo and M. Campeny, Microsc. Microanal., 2020, 26, 895–905.
69. R. Rinaldi and X. Llovet, Microsc. Microanal., 2015, 21, 1053–1069.
70. J. Fournelle, Microsc. Microanal., 2007, 13, 1390–1391.
71. G. F. Bastin, F. J. J. van Loo, P. J. C. Vosters and J. W. G. A. Vrolijk, Scanning, 1983, 5, 172–183.
72. X. Llovet, P. T. Pinard, J. J. Donovan and F. Salvat, J. Phys. D:Appl. Phys., 2012, 45, 225301.
73. A. A. Borisov, S. E. Borisovskiy and A. N. Koshlyakova, Petrology, 2023, 31(5), 576–579.
74. X. Llovet and F. Salvat, Microsc. Microanal., 2017, 23, 634–646.
75. S. J. B. Reed, Mikrochim. Acta, 2000, 132, 145–151.
76. J. I. Goldstein, D. E. Newbury, D. C. Joy, C. E. Lyman and J. R. Michael, Scanning Electron Microscopy and X-ray Microanalysis, 2003, p. 0306472929.
77. Y. G. Lavrent'ev, X-Ray Spectrom., 2010, 39, 37–40.
78. M. J. Jercinovic, M. L. Williams, J. Allaz and J. J. Donovan, Microsc. Microanal., 2011, 17, 576–577.
79. V. G. Batanova, A. V. Sobolev and V. Magnin, IOP Conf. Ser.:Mater. Sci. Eng., 2018, 304, 012001.
80. M. J. Jercinovic and M. L. Williams, Am. Mineral., 2005, 90, 526–546.
81. C. Merlet, Microchim. Acta, 1992, 107–115.
82. C. Merlet, Mikrochim. Acta, 1994, 114(115), 363–376.

---