Dual-Gate Chemometric Spectral-Line Selection with Multi-Acid Digestion for ICP-OES Determination of HREEs in Complex Ores

Abstract

Reliable determination of heavy rare earth elements (HREEs) in ores with multiple components through ICP-OES analysis is limited by their complex spectral signatures and dependency on the chemical matrix of each sample. A double gate-line selection method was developed that utilizes both correlation between candidate ICP-OES line intensity values and ICP-MS reference concentration values for 24 geological samples and standard addition recovery screening. The multi acid decomposition of all samples utilized HNO₃, HCl, HF, HClO₄, and H₂O₂. The eight selected lines were Gd at 335.048 nm, Tb at 350.914 nm, Dy at 353.171 nm, Ho at 345.600 nm, Er at 369.265 nm, Tm at 313.125 nm, Yb at 369.419 nm, and Lu at 291.139 nm. Limits of detection for the blank-derived data range from 0.02 to 0.10 mg/kg; the limit of quantification ranges from 0.07 to 0.32 mg/kg. However, the lower bound of calibration standards represents 2.00 mg/kg in the solid phase. Therefore, any results that fall below this threshold will be represented as estimated (extrapolated) rather than measured (quantitatively determined). CRM recoveries for the eight target analytes fell within the range of 91.67 to 105.78 percent; however, the two CRM comparisons where the analytical result for one or more target analytes exceeded the two-sided critical T-value (two tailed) of 2.31 were Tb in OREAS 465 and Er in OREAS 461. Due to the fact that the 24 samples analyzed for ICP-OES/ICP-MS correlation analysis were also used for the initial selection of candidate ICP-OES lines, the demonstrated correlations represent internal validity versus independent prediction. Single interferent controlled experiments and matrix-matched calibration experiments were not completed.

1. Introduction

Heavy rare earth elements (HREEs) include elements from Gd to Lu [1], and their magnetic, optical, luminescence, and catalytic characteristics support a wide range of applications in the fields of advanced electronics, defense technology, and low-carbon energy systems [2,3]. Therefore, an increasing demand for some HREEs is anticipated, while at the same time, there are limited economic recoverable sources and supply chain for these HREEs. This has resulted in many of the HREEs being classified by international agencies as “critical” or “strategic” raw materials [4].

The geologically diverse environment of Morocco makes it one of the most attractive areas in terms of discovering areas rich in HREE. In the context of these varied geologic systems, the area around Twihinate, also known as Bir Gandouz in the Saharan portion of Morocco, has become an emerging frontier in terms of discovery of alkaline silicate and carbonate complexes [5]. For evaluating commercially viable opportunities associated with such deposits, creating geochemical maps related to local deposits and establishing a strong national R.E. supply chain will require developing reliable, standard, and accurate geo-analytic methodologies [6]. A major source of improving local abilities for mineral prospecting and enhancing domestic resources mapping is generating high-quality, censored-free datasets describing the distribution of rare earth elements within various types of matrices found throughout Morocco [7].

Geochemists characterize the HREEs based upon how trace-to-ultra-trace amounts occur throughout the Earth’s crust. They typically occur as part of stable, structurally complex accessory minerals like monazite, xenotime, apatite, and carbonatites [8]. Consequently, extracting and determining the amount of HREEs contained in the various minerals represents significant challenges in terms of analytical methods [8]. In general, Inductively Coupled Plasma Mass-Spectrometry (ICP-MS) is considered one of the most viable methods for measuring trace and ultra-trace concentrations of lanthanides [9]. However, due to high costs associated with purchasing and maintaining equipment, the need for experienced operators, and susceptibility to interference from the matrix being analyzed, ICP-MS does not represent a practical solution for many mining laboratories. Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES) represents a relatively more accessible alternative when compared to ICP-MS. For example, ICP-OES can be performed with much lower capital and operational costs than ICP-MS. In addition, ICP-OES generally provides faster sample throughput and better resistance to effects of dissolved solids. As a result of the increased sensitivity required to measure the lanthanide series elements, ICP-OES tends to provide slightly less sensitive results than those provided by ICP-MS [10].

Both ICP-OES and ICP-MS utilize similar sample preparation approaches. These include both wet acid digestion and microwave-assisted digestion. Wet digestion is utilized in this investigation and provides significantly lower equipment costs and higher sample throughput per batch. Microwave-assisted digestion may provide more uniform temperature control during digestion and reduced reagent usage. However, microwave-assisted digestion generally requires higher capital investment and lower sample throughput than wet digestion. A comparative study of lithium borate fusion versus four-acid digestion approaches for analyzing whole-rock geochemical samples emphasizes the trade-off that exists among different approaches to digesting geological materials for lithogeochemistry and mineral exploration purposes [11].

The purpose of this research is to evaluate a chemometric dual gate workflow that will allow researchers to choose the best ICP-OES emission lines for analysis of the eight heavy rare earth elements (HREE) present in complex mineral matrices. A total of 24 geological samples were analyzed as candidate lines using two different methods to screen potential lines. These included the relationship between ICP-OES signal intensity and ICP-MS reference concentration. Following initial screening, these candidate lines were further assessed using a standard addition recovery protocol. Due to the fact that all 24 samples used during line selection were also used for evaluation of the analytical procedure, the statistical results from both experiments are intended to provide insight into how consistent the results are within each experiment and should not be considered evidence for or against external validity [12]. Evaluation of the analytical procedure included the use of three types of quality control material: blank solutions; multiple analyses of certified reference materials (CRM); and spiked CRM samples. The tests conducted in this research are referenced against those found in ISO/IEC 17025:2017; ICH Q2(R2); and NF T90-210:2018 [13,14]. However, due to the fact that complete validation was not performed, no conclusion can be made about the applicability of this work outside of the sample set tested in this study. Therefore, while a line selection process has been demonstrated in this study, and an internally validated analytical procedure developed, its transferability to other sample sets is yet to be determined [15].

2. Materials and Methods

2.1. Standards and Reagents

In this research, we employed the individual standard solutions of the examined heavy rare earth elements, Dy, Ho, Er, Tm, Yb, Lu, Gd, and Tb, with a declared concentration of 1000 µg/mL in an acidic matrix of 5% (v/v) HNO₃ (prepared by SPEX CertiPrep, Metuchen, NJ, USA). The next step included preparing the multi-element intermediate solution at 100 µg/mL through suitable dilution of the stock solutions of the previously mentioned heavy rare earth elements in the same acidic matrix. To assess the accuracy and dependability of the developed analytical method for this analysis, we applied three certified reference materials: OREAS 460, OREAS 461, and OREAS 465 (OREAS, Ore Research & Exploration Pty Ltd, Bayswater North, VIC, Australia). For plasma generation, high-purity argon gas (>99.99%) was utilized as plasma gas. In this analysis, the argon gas was obtained from Air Liquid Maroc (Casablanca, Morocco). Ultrapure water with conductivity <2 µSm⁻¹ was drawn from Milli-Q water purification system (Millipore SAS, Molsheim, France) for preparation of all solutions and dilutions. All acids were of analytical grade and were employed for digestion of samples (HF (40%), HClO₄ (70%), HNO₃ (68%), and HCl (32%).

2.2. Apparatus

Heavy Rare Earth Element (HREE) concentrations were determined using Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES), provided by Agilent Technologies, Mulgrave, VIC, Australia; Model: Agilent 5900. The ICP-OES was outfitted with an Autosampler; model ASX-560, supplied by Teledyne CETAC Technologies, Omaha, NE, USA. The Sample Introduction System included a SeaSpray U-Series concentric glass nebulizer (Agilent Technologies, Mulgrave, VIC, Australia; part no. G8010-60255); a double pass glass cyclone spray chamber compatible with the (Agilent Technologies, Mulgrave, VIC, Australia) systems; and a one-piece ICP-OES torch for aqueous samples; p/n G8010-60228.

The ICP-OES operating conditions are presented in Table 1.

Table 1. ICP-OES operating conditions.

Parameter	Value
Chamber	Cyclonic
RF power	1200 W
Nebulizer	Concentric
Plasma flow rate	12 L/min
Nebulizer flow rate	0.70 L/min
Auxiliary flow rate	1 L/min
Mixed gas flow rate	0 L/min
Pump speed	17 rpm (fast pump enabled)
Number of replicate readings	3
Stabilization time	10 s
Measurement time	5 s
Sample uptake delay	10 s
Viewing mode	Axial
Viewing height	8 mm
Rinse solution	Ultrapure water (>18 MΩ·cm) with 5% HNO3 (v/v)
Rinse time	25 s

All Mass determinations on the samples were made on an analytical balance; RADWAG AS220; RADWAG Wagi Elektroniczne, Radom, Poland; maximum capacity: 220 g; readability: 0.1 mg. The digestion of the samples was completed using an electrical Sand Bath; SD type, supplied by Harry Gestigkeit GmbH; Düsseldorf, Germany [16].

2.3. Preparation of the Samples

In the present study, an optimal multi-acid-digestion scheme has been established to effectively extract HREEs and hard rock mineral phases from complex geological matrices. All of the geological samples were dried; they were all milled to a fine powder (<75 µm); a representative portion of each was accurately measured out (0.25 g). They were placed in a 150 mL PTFE beaker. A small amount (1 mL) of ultrapure deionized water was added to each beaker to assist in dissolving the mineral phase. The water was allowed to remain on the sample for 1 min before adding 5 mL of 68% nitric acid. The suspension containing the sample was then heated for 30 min at 95 °C. The heat promoted the oxidation of any organic or readily oxidizable material that may have existed in the mineral phase [16]. Following the heating process, 1 mL of 30% H₂O₂ was added dropwise while maintaining the temperature at 95 °C for 5 min. Hydrogen peroxide assisted in further oxidation of any remaining organic material, as well as sulfide bearing phases [17]. Next, 5 mL of 37% Hydrochloric (HCl) were added. The mixture remained at 95 °C for 15 min. HCl helped break down carbonates, oxides, sulfides, and other minerals that contained metals [18]. Then, 5 mL of 40% hydrofluoric acid (HF) were added gradually to the mixture, which had now cooled slightly. The mixture was heated again at 110 °C for 30 min. In addition to promoting further breakdown of the silicate matrix, it produced volatile fluorosilicon compounds. To avoid producing insoluble fluoride phases that could prevent complete dissolution of the sample matrix, HF is added last [19]. Once the digestion was completed, the mixture was treated with 2 milliliters of 70% perchloric acid (HCLO₄). The mixture was heated between 180 and 190 °C for approximately 50 to 60 min. These conditions permitted any remaining organic material and the hardest, most resistant mineral phases to undergo decomposition [20]. Additionally, it permitted removal of any excess fluoride species that would otherwise interfere with analysis [1]. Heating was discontinued once a concentrated, solidified paste like residue had formed. Care was taken to avoid evaporating the mixture completely until such time as the residue was ready to be dissolved. The residue was then treated with seven 7.5 mL of fresh aqua-regia. The mixture was warmed so as to facilitate dissolution of any remaining metallic phases [21]. Once dissolved, the resultant solution was quantitatively transferred to a 50 mL polyethylene volumetric flask and brought to full volume with de-ionized water. A blank was made up using the same procedures for digestion and dilution as described above. This blank served as a means of assessing any possible contaminants that may arise from the reagents and/or during sample handling. Final solutions were analyzed using Inductively Coupled Plasma Optical Emission Spectrometry (ICP-OES) for determining HREE content. Corresponding digests were also analyzed using Inductively Coupled Mass Spectrometry (ICP-MS), and these results were utilized as references for selecting analytical lines and evaluating the method.

ICP-MS Reference Measurements

A Thermo Scientific iCAP MSX single quadrupole ICP-MS was used to determine reference HREE concentrations. The monitored isotopes included 157Gd, 160Gd, 159Tb, 163Dy, 165Ho, 166Er, 170Er, 169Tm, 172Yb, and 175Lu. Calibration over the range 0.5–100 ppb was achieved through external calibration. Rhodium and rhenium were added as internal standards at a final concentration of 10 ppb. All samples were initially digested in an acidic solution consisting of HClO₄, HF, and HNO₃. High concentration samples required a dilution of 1:50 prior to ICP-MS analysis, while lower concentration samples required a dilution of 1:10 using a diluent of 2% v/v HNO₃. No collision gas was employed during measurement, and therefore no mathematical interference correction was necessary. Quality control was assessed by using OREAS 460 and a reagent blank. All results that fell below the method quantification limit are reported as <LOQ rather than as zero.

• Safety guidelines:

All heated HClO₄ digestions took place inside of an appropriate, wash-down hood for the use of perchloric acid. In addition, organic materials were prohibited from being located near any areas where hot HClO₄ was used. Also, all lab workers involved in the preparation of all of the vessels that contained either HClO₄ or HF had to have their hands properly washed before they left the hood; otherwise, they would be required to leave immediately and obtain proper hand washing [22,23].

2.4. Sampling Context and Confidentiality Notice

The 24 geochemical samples (TWH_01–TWH_24) were taken over two separate field campaigns. These campaigns took place in the Twihinate Complex. This is a complex that includes both alkaline carbonatites and silicates, located near the town of Bir Gandouz in the northwestern region of Morocco. Because these samples originated from property with license agreements, exact location information was withheld due to company policies regarding confidentiality. In addition, the major element analysis for all samples is contained within Table 2, and HREE concentration results via ICP-MS are provided in Table 3.

Table 2. Sample set (TWH_01–TWH_24): major-oxide composition (wt.%).

Sample	SiO2	Al2O3	Fe2O3	CaO	MgO	K2O	MnO	TiO2	P2O5	Na2O	SO3
TWH_01	57.79	15.67	6.91	0.15	0.38	12.16	0.02	0.44	0.29	0.47	0.15
TWH_02	56.67	15.12	9.56	0.11	0.48	11.97	0.05	0.56	0.22	0.47	0.10
TWH_03	54.85	15.80	9.27	0.13	0.43	11.41	0.04	0.80	0.19	0.48	0.10
TWH_04	56.62	15.04	9.42	0.14	0.48	11.62	0.03	0.66	0.24	0.44	0.08
TWH_05	55.87	16.14	7.92	0.25	0.46	11.09	0.02	0.74	0.40	0.66	0.12
TWH_06	55.98	17.24	5.41	0.30	0.59	11.16	0.02	1.24	0.93	0.57	0.16
TWH_07	53.61	15.52	10.67	0.13	1.18	11.90	0.03	0.68	0.23	0.57	0.11
TWH_08	59.16	15.83	5.56	0.16	0.28	11.39	0.02	0.66	0.36	0.44	0.11
TWH_09	57.04	16.78	5.72	0.19	0.50	11.65	0.02	0.78	0.34	0.55	0.11
TWH_10	56.56	17.44	5.45	0.30	0.58	11.34	0.03	1.26	0.94	0.58	0.15
TWH_11	55.87	19.23	4.93	0.25	0.61	11.70	0.02	0.90	0.68	0.54	0.10
TWH_12	60.21	17.36	3.77	0.17	0.49	12.11	0.01	0.74	0.45	0.40	0.08
TWH_13	57.42	16.74	5.96	0.15	0.76	13.25	0.02	0.75	0.46	0.43	0.09
TWH_14	54.38	17.21	6.28	0.28	1.05	11.76	0.02	1.10	1.16	0.50	0.16
TWH_15	59.50	17.07	3.58	0.14	0.43	13.23	0.01	0.71	0.28	0.49	0.15
TWH_16	98.95	0.11	0.59	0.03	0.01	0.01	0.00	0.00	0.01	0.02	0.01
TWH_17	60.53	16.58	3.11	0.16	0.29	13.02	0.01	1.42	0.52	0.42	0.18
TWH_18	58.96	16.28	6.40	0.13	0.23	12.55	0.03	0.81	0.31	0.41	0.09
TWH_19	58.58	15.74	7.16	0.11	0.36	12.62	0.03	0.70	0.22	0.38	0.08
TWH_20	62.47	16.42	2.56	0.23	0.05	13.19	0.01	0.87	0.22	0.38	0.09
TWH_21	52.31	18.88	3.91	0.41	0.57	9.89	0.02	3.61	1.28	0.50	0.11
TWH_22	48.11	14.63	11.52	0.53	0.18	10.29	0.01	1.72	2.42	0.41	0.19
TWH_23	55.87	20.44	3.42	0.35	0.49	11.61	0.02	1.26	0.85	0.50	0.12
TWH_24	58.69	18.55	4.26	0.27	0.42	12.58	0.01	0.91	0.57	0.43	0.10

Table 3. Sample set (TWH_01–TWH_24): ICP-MS reference HREE concentrations (mg kg⁻¹).

Sample	Dy	Ho	Er	Tm	Yb	Lu	Gd	Tb
TWH_01	0.16	<LOQ	<LOQ	<LOQ	<LOQ	<LOQ	0.34	<LOQ
TWH_02	8.92	1.45	4.19	0.58	3.85	0.51	18.73	2.05
TWH_03	5.27	0.87	2.32	0.36	2.47	0.37	10.15	1.12
TWH_04	14.42	2.30	5.95	0.87	5.65	0.84	27.33	3.05
TWH_05	20.45	3.38	8.71	1.33	8.75	1.26	33.21	3.97
TWH_06	27.94	6.19	18.52	3.61	24.11	3.34	23.09	3.72
TWH_07	6.36	1.05	2.80	0.41	2.75	0.42	13.79	1.47
TWH_08	16.57	2.50	6.19	0.84	5.44	0.74	31.64	3.48
TWH_09	10.17	1.56	4.09	0.54	3.50	0.47	21.50	2.33
TWH_10	32.59	6.95	20.52	3.79	25.63	3.70	25.76	4.03
TWH_11	7.49	1.25	3.27	0.45	2.86	0.39	11.85	1.45
TWH_12	10.49	1.72	4.25	0.65	4.02	0.70	14.04	1.83
TWH_13	6.84	1.04	2.70	0.35	2.27	0.32	13.73	1.50
TWH_14	17.61	2.72	7.01	0.89	5.59	0.76	34.19	3.79
TWH_15	10.31	1.55	3.95	0.54	3.40	0.47	19.31	2.25
TWH_16	1.00	<LOQ	<LOQ	<LOQ	<LOQ	<LOQ	<LOQ	<LOQ
TWH_17	84.48	18.02	53.91	9.70	63.72	8.97	55.32	10.54
TWH_18	19.33	3.71	9.92	1.70	11.06	1.57	19.56	2.83
TWH_19	8.31	1.35	3.67	0.51	3.34	0.46	15.94	1.74
TWH_20	10.64	1.69	4.09	0.63	4.00	0.56	19.64	2.18
TWH_21	21.08	3.56	9.27	1.36	8.64	1.14	31.67	3.90
TWH_22	210.64	32.88	76.06	11.59	70.71	9.27	303.54	40.81
TWH_23	9.70	1.71	4.82	0.85	5.52	0.83	14.83	1.98
TWH_24	9.63	1.73	5.24	0.82	5.62	0.84	13.87	1.78

Silica content ranged from 52.31 to 62.47 wt.%, alumina content varied in a range from 14.63–20.44 wt.%, potash oxide (K₂O) content varied within a range from 9.89 to 13.25 wt.%, and ferric iron oxide (Fe₂O₃) content varied from 2.56–11.52 wt.% (Table 2), while calcium oxide, sodium oxide, titanium dioxide, magnesium oxide, manganese oxide, and phosphorous pentoxide were all less than 1.0 wt.%. Some samples had elevated levels for those elements listed above. High potassium oxide (K₂O) percentages indicate an abundance of K-feldspar, while variations in the percentage of iron oxide (Fe₂O₃) can be attributed to varying amounts of biotite and/or iron bearing oxides. As such, the composition of the studied materials indicates that they are primarily alkaline silicate rocks. A mineralogical verification of the data would have been beyond the scope of this study [7].

Alkaline rock types that contain low amounts of SiO₂ (silica undersaturated) like Nephelinite, Ijolite, phonolite, and Nephelinesyenite have been associated with carbonatites, whereas association of silica saturated rock types is generally rarer [24,25]. This type of geological setting supports the necessity for evaluating the analysis technique on chemically different alkaline samples.

2.5. Preparation of Calibration Standards

The calibration standards for ICP-OES were made from stock solutions of individual elements that had been certified. These stock solutions were diluted into nitric acid; each standard’s concentration can be found in Table 4. The ICP-OES standards were not matched to the multi-acid digests. No internal standard was included in the ICP-OES analysis. A 0.250 g portion of sample was added to 5 mL of 68% HNO₃, 5 mL of 37% HCl, 5 mL of 40% HF, 2 mL of 70% HClO₄, and 1 mL of 30% H₂O₂. The residue was then reconstituted with 7.5 mL of aqua regia and diluted to 50.0 mL; this corresponded to a nominal sample equivalent load of 5.0 g/L prior to any additional dilutions. Since digestion involved both evaporation and reconstitution, neither the final composition of acids nor the amount of dissolved solids was determined. Variations in acid concentration, viscosity, surface tension, and dissolved solid loads could potentially impact solution uptake, aerosol generation/transport, nebulizer performance, plasma loading, and the production of excited states for the analytes. While the CRM and spike recovery data provide evidence regarding the overall effects of the procedure being evaluated on the two sample types analyzed, these data also will not substitute for a comparison using either matrix-matched calibrants, standard additions, or an ICP-OES internal standard method. Therefore, residual matrix-dependent biases cannot be eliminated [26].

Table 4. Calibration-solution concentrations (mg L⁻¹) used for the investigated HREEs.

Element	Blank	STD1	STD2	STD3	STD4	STD5	STD6
Dy	0.00	0.01	0.05	0.10	0.50	1.00	5.00
Ho	0.00	0.01	0.05	0.10	0.50	1.00	5.00
Er	0.00	0.01	0.05	0.10	0.50	1.00	5.00
Tm	0.00	0.01	0.05	0.10	0.50	1.00	5.00
Yb	0.00	0.01	0.05	0.10	0.50	1.00	5.00
Lu	0.00	0.01	0.05	0.10	0.50	1.00	5.00
Gd	0.00	0.01	0.05	0.10	0.50	1.00	5.00
Tb	0.00	0.01	0.05	0.10	0.50	1.00	5.00

• Quality-control sequence and background correction:

The quality-assurance process involved a blank calibration solution, a blank solution containing reagents, certified reference materials (CRM), and duplicate samples. Calibration linearity was examined based on an R² value greater than 0.995 as the acceptable criterion. A blank reagent solution was utilized to assess if contaminants were present during the sample preparation. Each batch of 10 samples contained one CRM that was analyzed to assess instrument drift. Duplicate samples consisted of 30 percent of all the samples. Duplicate samples were placed throughout the sequence of 20 samples [27]. Based on Table 5, background corrections were made by selecting the appropriate correction method for each analyte and its corresponding peak position. Left-side corrections were applied to Gd, Tb, and Dy; Fitted Interpolation was applied to Ho; Right-Side Corrections were applied to Er, Tm, Yb, and Lu.

Table 5. Background-correction modes used for the selected HREE emission lines.

Analyte	Background Correction Mode
Gd	Left side
Tb	Left side
Dy	Left side
Ho	Fitted (Interpolated)
Er	Right side
Tm	Right side
Yb	Right side
Lu	Right side

2.6. Chemometric Optimization and Cloud-Based Dual-Gate Line Selection Workflow

To find candidate ICP-OES emission lines that would be free from interference by major rock forming oxides (Fe₂O₃, Al₂O₃, SiO₂, TiO₂ and P₂O₅), as well as vanadium and light rare earths, a dual-gate workflow was utilized. All data processing for this study was completed with use of Python 3 via Google Colab. The key steps for data processing are detailed below in Table 6 [28].

Table 6. Data Processing and Metrological Validation Pipeline.

Stage	Main Function	Tools/Libraries
Parsing & Cleaning	Decimal harmonization, unit conversion, NaN handling, and background noise removal	Pandas (v2.2.1), numpy (v1.26.4), io
Metrology & Selection	Linearity assessment (R2, r), automated filtering, and selection of top ICP-OES lines (r ≥ 0.95)	numpy.polyfit (v1.26.4), pandas.corr (v2.2.1)
Visualization	Generation of multi-panel dashboards (2 × 3), regression fits with 95% CI, interference heatmaps, and bar charts	Matplotlib (v3.8.3).pyplot, seaborn (v0.13.2)

The workflow comprised two sequential screening gates (Figure 1):

Figure 1. Modular flowchart of the proposed dual-gate (Gate 1/Gate 2) spectral line screening workflow for HREE analysis.

Gate 1 compared 10 possible atomic/ionic emissions for each heavy rare earth element (HREE) as determined by net ICP-OES intensities for 24 different geological samples representative of earth’s crust; the intensities for these possible lines were then correlated to the reference values for HREE (obtained via ICP-MS) from those same 24 samples; those possible lines whose correlation coefficients (r) were ≥0.95 were selected for consideration. Gate 1 also looked into how other elements in each sample affected the intensity correlations, as well as whether this indicated the presence of a matrix effect [29].

Gate 2 continued evaluation on the remaining lines using standard additions. Lines producing recoveries of 90–110% under the test spike conditions were selected for use. This assessment did not provide absolute protection from all plasma and/or matrix effects; it only provided a measure of performance under the testing conditions [30].

The overall wavelength selection strategy can be mathematically expressed as:

$$L_{Optimized}=\{{\lambda }_i\in L\mid r_i\ge 0.95; 90\%\le R_i\le 110\%\},$$

(1)

• L: Initial set of candidate analytical emission wavelengths evaluated for each.
• L_optimized: Final chemometrically optimized set of analytical emission wavelengths
• selected for HREE determination.
• λ_i: The ith candidate analytical emission wavelength belonging to L.
• r_i: Correlation coefficient of the calibration curve at wavelength λ_i, used to assess linearity.
• R_i: Recovery (%) obtained at wavelength λ_i, used to evaluate method accuracy.

3. Results and Discussion

3.1. Spectral Line Selection and Statistical Optimization Strategy

The candidate emission line intensities from ICP-OES have been compared to the ICP-MS reference concentrations for the 24 geological samples. The correlation coefficient, Pearson’s r, has been applied as a within-dataset screening criterion where r values greater than 0.95 indicate retention. Because the same samples are used for further comparisons, the use of this screening method is intended to provide no measure of performance when using an independent sample set [31,32].

3.1.1. Linear Tracking and Within-Dataset Screening

There were significant differences among the candidate emission lines tested via correlation analysis (Figure 2) relative to each other. Both the Gd and Dy lines that were tested met the specified screening criteria for r values > 0.95 in the data set of 24 samples. These results suggest that there is a linear relationship between the ICP-MS reference concentrations and the samples examined in these studies. Therefore, they do not represent any predictive capability regarding how well these lines would perform on unknown samples or completely eliminate potential plasma- or matrix-related influences [33].

Figure 2. Pearson Correlation Coefficients (r) of Candidate ICP-OES Emission Lines vs. Corresponding Reference Concentration Values from ICP-MS for Each Investigated Heavy Rare Earth Element: (a) Gadolinium; (b) Dysprosium; (c) Ytterbium; (d) Thulium; (e) Terbium; (f) Lutetium; (g) Holmium; (h) Erbium. For each panel, Emission Lines were Ranked in Order of Highest to Lowest r. Bar Color Indicates Ranking. Red Dashed Vertical Line Indicates Acceptance Threshold (r = 0.95).

The strong wavelength dependence of the measured laser wavelengths for Yb, Er, Ho, Tb, Lu, and Tm is demonstrated by their significantly higher r-values. Of the three erbium values reported, two are strongly dependent upon concentration with an r-value of 0.1708, and one value does not meet the defined correlation as it has a poor r-value of 0.142. Two of the holmium values have very high r-values (0.997 and 0.998) and therefore correlate well to the reference concentrations. All three Lutetium values that are greater than 290 nm track reference concentrations very well, but one value at 289.484 nm tracks the reference concentrations very poorly (r ≈ 0.09). Only one Thulium value (at 313.125 nm) approaches the correlation threshold (r ≈ 0.98). However, another Thulium value (at 384.802 nm) shows a negative relationship (r ≈ −0.40) to reference concentrations. Since each element’s spectral line strength was determined from the same dataset, we could not use our results to determine if there is interference between different spectral lines. Therefore, poor correlation values (weakly or negatively correlated) can be due to either spectral interferences between elements, background contamination, unstable signals, or some form of geochemical covariance [34,35].

3.1.2. Geochemical Covariation and Candidate Matrix Effects

The correlation patterns identified in Figure 3 show which elemental combinations are worthy of investigation. However, these patterns do not provide a means to separate direct spectral interferences from covariation due to differences in mineralogy or geochemistry [36].

Figure 3. Lower-triangular Pearson correlation matrices mapping the interactions between potential interfering elements and candidate HREE emission lines: (a) Gd; (b) Dy; (c) Yb; (d) Tm; (e) Tb; (f) Lu; (g) Ho; (h) Er. Red and blue color gradients represent positive and negative Pearson correlation coefficients, respectively.

In Figure 3, the patterns observed within the correlations are considered to be associations with respect to each element pair identified; therefore, these associations do not prove the existence of a particular mechanism responsible for an interaction. For example, a pattern may indicate that there is either spectral overlap occurring (due to atomic emission spectra being similar) or that continuum background effects are present due to overlapping absorption features of other minerals. Mineral host sharing, major phase dilution, or geochemical covariance may also explain the presence of certain patterns. Atomic-line proximity in combination with application of the recovery screen can provide a basis for identifying potential interference risk; however, independent variation of Fe, Ti, V, Al, and P was not performed while maintaining constant HREE concentrations. Therefore, the potential interference mechanisms outlined in Table 7 are offered as possible explanations that require verification through controlled single-interferent experiments and local spectral profile analysis [37].

Table 7. Candidate spectral-interference assignments for the retained HREE lines and rejected Er 337.271 nm line).

Analyte	λ (nm)	Major Interferences	Minor Interferences
Gd	342.247	Ti at 342.246 nm (Δλ = 0.001 nm, critical)	Ce at 342.250 nm; Fe (baseline elevation near 342 nm)
Gd	335.047	V at 335.042 nm	Sm at 335.040 nm
Tb	350.917	Fe at 350.911 nm (very strong); V at 350.930 nm	Ho at 350.937 nm; Th at 350.910 nm
Tb	384.873	—	Ce at 384.870 nm
Dy	353.170	V at 353.164 nm	Nd at 353.172 nm
Dy	387.211	Fe at 387.203 nm + overall background elevation	La at 387.205 nm
Ho	345.600	Fe at 345.602 nm (direct); Ti at 345.590 nm	Gd at 345.605 nm
Ho	379.675	—	Ce at 379.670 nm
Er (rejected candidate)	337.271	Ti at 337.280 nm (massive overlap)	Ce at 337.270 nm; V (mid-UV peak wings)
Tm	313.125	Ti at 313.08 nm; V at 313.03/313.20 nm; Fe at 313.08 nm	Th, U, Zr
Yb	369.419 *	Fe at 369.40 nm; V at 369.43 nm; Er at 369.265 nm (the Er line used in this same method)	Ce, Cr, Th
Lu	291.139	Fe at 291.21 nm; Cr at 291.15 nm; Ti at 291.07 nm	V, Th, Zr

* Note: the selected Yb line (369.419 nm) lies close to the Er line used in this same method for Er quantification (369.265 nm, Δλ ≈ 0.15 nm). Because Er and Yb commonly co-occur in HREE-bearing samples, a degree of mutual spectral overlap between these two method analytes cannot be excluded and was not directly quantified in this study Section 3.1.3. Internal Consistency Comparison with ICP-MS Reference Values.

The comparison in Figure 4 is a consistency check with respect to the data (geological samples), as well as methods (wavelength screening and regression using ICP-OES/ICP-MS). As such, it is not a statistically independent test set since all 24 geological samples were used throughout both steps. Therefore, estimates of coefficient of determination (the determination) and regression error may also be overly optimistic for matrices that have never been seen prior to testing. Therefore, no claim of externally validated predictions on additional samples, nor of broad robustness and/or general applicability of these results can be made. These claims will only be possible when a group of independent samples has been collected, or alternatively through nested cross-validation techniques where spectral line selection occurs within each “fold” of the cross-validation process.

Figure 4. Internal-consistency comparison of ICP-OES data obtained from retained emission lines using reference values for the same 24 geological samples that were compared in the screening by ICP-MS (a) Gd, (b) Dy, (c) Yb, (d) Tm, (e) Tb, (f) Lu, (g) Ho, and (h) Er. The colored points represent each individual measurement as a different wavelength. Solid lines through these points correspond to the best fit line of the individual wavelengths and the light-gray dashed line is the one-to-one equivalence line. The French labels in (e,h) denote multi-wavelengths linearity against the Tb reference and inter-method correlation for Er, respectively. However, these comparisons are not intended to be an independent validation.

Priori coefficients of determination and regression error may be overly optimistic when applied to previously unobserved matrices. No claims of externally validated predictions (beyond this study), wide-ranging robustness, or generalized application are being made using this benchmarking method. To estimate out-of-sample predictive performance, independent samples or nested resampling where the same spectral lines are randomly selected from the full set into each training fold will be required. The selected analytical lines and their internal performance assessment are summarized in Table 8.

Table 8. Selected analytical emission lines and internal performance assessment for HREE determination by ICP-OES.

Element	Status	Primary Line	Secondary Lines	Excluded Lines
Gd	Internally supported	335.048	301.013; 376.840	310.050; 303.284
Dy	Internally supported	353.171	353.602; 387.211	364.540
Er	Internally supported	369.265	349.910	390.631; 323.058; 337.275; 291.036
Yb	Internally supported	369.419	328.937; 211.667; 212.674	222.447; 265.375; 275.048; 297.056
Tb	Internally supported	350.914	332.440	370.285 and other lines
Ho	Internally supported	345.600	339.895; 341.644	Remaining lines
Lu	Conditionally supported	291.139	261.541; 219.556	289.484 and remaining lines
Tm	Conditionally supported	313.125	None	Remaining lines

3.1.3. Spectral-Line Specificity and Matrix Response Evaluation by Standard Addition

Standard-addition recovery was therefore applied as a second screening criterion to select among candidate lines presented in Figure 5 due to the high density of the emission spectra of lanthanides, making it impossible to determine the optimal candidate lines using absolute emission intensity alone.

Figure 5. Recovery of candidate HREE emission lines using standard addition: (a) Gd, (b) Tb, (c) Dy, (d) Ho, (e) Er, (f) Tm, (g) Yb, and (h) Lu. Blue indicates that a measured value is within the defined acceptable range (90–110%); Red indicates that a measured value is outside this acceptable range. The Solid Line represents 100% recovery, and Dashed Lines represent the upper/lower acceptable range limits; The Shaded Area represents the total accepted range.

Recovery in standard addition experiments were variable among candidate lines. Only those lines whose recovery values fell within ±10% of 100% for the spike amounts examined were selected to compare against the correlations found during the screening phase. Values outside of the range of 90–110% could represent either interference due to overlapping signals, errors in placing background measurements, or simply changes in how the analyte responds based upon the matrix. Since each individual interference was not separately varied, it is not possible to attribute a specific mechanism to each excluded line [38,39].

The exclusion of lines that failed to meet the specified recovery criteria in the final comparison eliminated dependence upon the inter-element corrections used in testing these samples. However, it was not established that the remaining lines contained no interference.

3.1.4. Combined Dual-Gate Selection Framework for Final Line Constellation

Final line selection compared standard addition recoveries in Table 9 to within-dataset regression metrics from Table 9. Agreement of the two selections (not independent validation) was used to select lines for final qualification. For example, a line may have met the criteria for good recovery at the spiked level, but it failed to demonstrate consistent tracking over all concentrations tested [40,41]:

Table 9. Standard-addition recovery, wavelength selection, and candidate spectral-interference assignments.

Element	Selected λ	Recovery	Rejected λ	Main Mechanism/Comments
Gd	335.048	Acceptable (109.6%)	310.050, 335.048, 358.496	Spectral overlap leading to signal overestimation (>110%) or suppression (<90%)
Tb	350.914	Acceptable (100.0%)	321.998, 332.440, 384.873	Background drift/spectral interferences (>110%)
Dy	353.171, 364.540	Acceptable (91.8%/99.8%)	338.501, 340.780, 407.797	Matrix effects: signal suppression or enhancement
Ho	345.600	Acceptable (98.3%)	347.425, 348.484, 351.559	Matrix-induced attenuation and quenching effects
Er	369.265	Acceptable (106.3%)	300.241, 323.058, 389.623	Continuum background variations and spectral distortions
Tm	313.125, 336.261	Acceptable (92.5%/100.3%)	329.100, 384.802	Line overlap and spectral coincidences
Yb	369.419	Acceptable (106.3%)	211.667, 265.375, 297.056, 289.138	Strong matrix effects and signal variability
Lu	291.139, 339.707	Acceptable (95.4%/106.0%)	261.541, 289.484, 547.668	Matrix variability and local interferences

• Tb with 350.914 nm gave a slope of 1.000 and a recovery of 100.0%, whereas Tb at 370.285 nm had a slope of 4.097 and was eliminated as non-compliant. The Gd 335.048 nm and Tm 313.125 nm lines were also compliant due to meeting the pre-defined compliance standards for both slope and recovery; these data provide evidence that the selected wavelengths are appropriate within the test matrices. However, this does not establish resistance to quenching by the plasma or interference from an iron band mechanism.
• The compliant wavelengths used in independent geological samples include Gd 335.048 nm, Tb 350.914 nm, Dy 353.171 nm, Ho 345.600 nm, Er 369.265 nm, Tm 313.125 nm, Yb 369.419 nm, and Lu 291.139 nm.

The final retained emission lines and their within-study support status are summarized in Table 10.

Table 10. Final retained emission lines for HREE determination by ICP-OES.

Element	Primary λ (nm)	Validation Status
Gd Gadolinium	335.048	Internally supported
Tb Terbium	350.914	Internally supported
Dy Dysprosium	353.171	Internally supported
Ho Holmium	345.600	Internally supported
Er Erbium	369.265	Internally supported
Tm Thulium	313.125	Conditionally supported (internal consistency)
Yb Ytterbium	369.419	Internally supported
Lu Lutetium	291.139	Conditionally supported (internal consistency)

3.2. Internal Analytical Performance Evaluation

Instrumental background corrections had to be made prior to assessing instrument linearity, precision, and trueness. The instrumental background correction addresses two types of issues with baseline positioning and known local background effects. This does not represent complete removal of all spectral overlap or matrix effects; thus, the subsequent metrics reflect the performance that was achieved for the specific conditions and matrices that were tested in this study [42,43].

3.2.1. Linearity

The calibration was assessed at seven levels, which included a calibration blank and five non-zero standards ranging from 0.01 to 5.00 mg L⁻¹. There were five replicate responses for each level (total N = 35 per analyte), which were used to estimate the calibration equation, parameter confidence intervals, residual error, and lack of fit.

For each analyte, net emission intensity (y) was modeled as a linear function of calibration concentration (x): y = ax + b, where a is the slope and b is the intercept:

$$y=ax+b$$

(2)

Calibration Equations and R² Values are Summarized in Table 11. The R² values were all greater than 0.99998. However, R² is not sufficient to establish that there was no lack of fit. Therefore, a 95% confidence interval for the slope and y-intercept, as well as the residual root mean squared error (RMSE) and lack of fit tests, were calculated using the five replicates generated for each of the seven calibration levels reported in Table 12 [44].

Table 11. Calibration ranges, equations, and coefficients of determination for the selected HREE lines.

Element	Wavelength (nm)	Range (mg L−1)	Linear Equation	R2
Dy	353.171	0.00–5.00	y = 30,346.6585x + 150.8012	0.999992
Er	369.265	0.00–5.00	y = 49,740.1805x − 136.4074	0.999998
Ho	345.600	0.00–5.00	y = 18,280.7040x + 78.4617	0.999988
Tm	313.125	0.00–5.00	y = 130,213.7089x + 543.4882	0.999993
Yb	369.419	0.00–5.00	y = 433,538.2921x + 1770.9069	0.999993
Lu	291.139	0.00–5.00	y = 16,896.5842x + 21.6895	1.000000
Gd	335.048	0.00–5.00	y = 50,816.4776x + 241.2264	0.999989
Tb	350.914	0.00–5.00	y = 35,534.8786x − 42.5339	0.999997

Note: All the regression models include both the calibration blank and six non-Zero standards. The Negative fitted intercepts for Er and Tb represent the background-correction responses to the samples and are not a representation of concentration.

Table 12. Calibration-parameter uncertainty, residual error, and lack-of-fit tests based on five replicate responses at seven concentration levels.

Element	Slope	Slope 95% CI	Intercept	Intercept 95% CI	R2	RMSE	FLOF	pLOF
Dy	30,346.6585	29,803.3997–30,889.9173	150.801	−901.467–1203.070	0.999992	2665.27	0.017	1.000
Er	49,740.1805	48,875.1545–50,605.2064	−136.407	−1811.925–1539.110	0.999998	4243.89	0.006	1.000
Ho	18,280.7040	17,860.2430–18,701.1650	78.462	−735.953–892.876	0.999988	2062.82	0.016	1.000
Tm	130,213.7089	128,027.1377–132,400.2802	543.488	−3691.805–4778.781	0.999993	10,727.51	0.018	1.000
Yb	433,538.2921	427,050.3019–440,026.2822	1770.907	−10,796.047–14,337.861	0.999993	31,830.63	0.022	1.000
Lu	16,896.5842	16,385.4036–17,407.7648	21.690	−968.445–1011.824	1.000000	2507.90	0.000	1.000
Gd	50,816.4776	50,097.3235–51,535.6318	241.226	−1151.744–1634.197	0.999989	3528.23	0.037	0.999
Tb	35,534.8786	34,932.9998–36,136.7575	−42.534	−1208.347–1123.279	0.999997	2952.87	0.007	1.000

Inspecting residual Plots for concentration-dependent structure was completed (see Figure 6), calculating the parameter intervals and lack-of-fit results were based on replicate response values rather than rounded R² values. Diagnostics for evaluating the nitric-acid standard fitted calibration functions do not address mismatches between the calibration standards and digest Matrix [45].

Figure 6. Calibration and residual plots for the selected HREE emission lines: (a) Yb 369.419 nm, (b) Dy 353.171 nm, (c) Er 369.265 nm, (d) Ho 345.600 nm, (e) Gd 335.048 nm, (f) Lu 291.139 nm, (g) Tb 350.914 nm, and (h) Tm 313.125 nm. Points show mean ± SD for five replicate responses at each level; lines show ordinary least-squares fits. Residuals are displayed below each calibration plot.

• Calibration lack-of-fit and parameter uncertainty.

Pure Error was estimated as a result of the variability in the response to the five replicates at each of the seven calibration levels. Lack-of-fit was determined through comparison of deviations of the level means from the fitted line, using pure error (within levels), with this lack-of-fit being compared against (df₁ = 5; df₂ = 28). Confidence limits for slope and intercept parameters were constructed two-sided at α = 0.05 and with 33 residual degrees of freedom using the residual mean square.

The Lack of Fit statistics were found to be between 0.000 and 0.037, with corresponding p-values between 0.999 and 1.000. None of these results demonstrated a statistically significant lack of fit for α = 0.05. Therefore, these data are consistent with the assumption that there is a linear relationship among the calibration standards that have been tested. However, it also indicates no evidence to support an equivalency between the Nitric-acid standardization solution and multi-acid sample digestions.

3.2.2. Precision

Repeatability and Intermediate Precision for each of the tested analytes were evaluated via repeated analysis on OREAS 460, OREAS 461, and OREAS 465 over a period of three separate measurement days, with nine replicate analyses performed for each day (nine total replicates per analyte CRM pair). One-way ANOVA was used to evaluate variance components as described in ISO 5725-3:2023; (Accuracy (trueness and precision) of measurement methods and results—Part 3: Intermediate precision and alternative designs for collaborative studies [46]. International Organization for Standardization: Geneva, Switzerland, 2023). Concentration values ranged from approximately 0.33 mg kg⁻¹ for Lu to 578.67 mg kg⁻¹ for Gd. Therefore, these data represent an evaluation of precision of the CRM matrixes and the tested concentrations but are not representative of all other complex geologic materials [47]. The individual concentration measurements for each analyte–CRM pair across the three days are presented in Table 13.

Table 13. Raw HREE concentrations measured in three certified reference materials over 3 days, with three replicate measurements per day (mg kg⁻¹).

Analyte	CRM	Day 1 R1	Day 1 R2	Day 1 R3	Day 2 R1	Day 2 R2	Day 2 R3	Day 3 R1	Day 3 R2	Day 3 R3
Dy	OREAS 460	18.16	18.40	18.52	17.76	17.96	18.07	17.82	18.14	18.17
Dy	OREAS 461	33.42	32.58	33.05	33.80	33.21	32.80	33.73	32.85	33.26
Dy	OREAS 465	213.84	215.65	214.56	214.63	213.90	213.07	213.70	215.94	214.60
Ho	OREAS 460	2.45	2.34	2.44	2.43	2.43	2.34	2.38	2.32	2.47
Ho	OREAS 461	4.13	4.08	3.98	4.11	4.08	4.06	4.14	4.20	4.05
Ho	OREAS 465	27.11	26.15	26.80	26.73	26.33	26.86	26.67	26.32	26.85
Er	OREAS 460	4.61	4.70	4.60	4.64	4.74	4.66	4.66	4.81	4.65
Er	OREAS 461	7.21	8.16	7.93	7.33	8.16	7.93	7.28	8.19	8.02
Er	OREAS 465	46.86	46.64	47.50	47.15	46.77	47.62	47.35	47.07	47.28
Tm	OREAS 460	0.40	0.62	0.52	0.44	0.53	0.49	0.57	0.55	0.64
Tm	OREAS 461	0.80	0.76	0.69	0.74	0.73	0.64	0.78	0.75	0.67
Tm	OREAS 465	4.11	3.91	3.78	3.88	3.91	3.73	4.05	4.04	3.84
Yb	OREAS 460	2.61	2.50	2.75	2.65	2.60	2.79	2.67	2.57	2.82
Yb	OREAS 461	3.41	3.17	2.92	3.42	3.10	2.93	3.42	3.21	2.92
Yb	OREAS 465	14.38	15.47	15.62	14.32	16.45	15.59	14.36	16.13	15.65
Lu	OREAS 460	0.40	0.39	0.30	0.28	0.33	0.31	0.38	0.17	0.41
Lu	OREAS 461	0.42	0.45	0.45	0.28	0.46	0.50	0.33	0.42	0.18
Lu	OREAS 465	1.55	1.38	1.73	1.79	1.77	1.77	1.83	1.73	2.00
Tb	OREAS 460	4.41	4.47	4.58	4.44	4.65	4.60	4.49	4.57	4.62
Tb	OREAS 461	8.85	9.03	8.84	9.07	9.13	8.99	9.20	9.04	9.07
Tb	OREAS 465	58.00	57.10	56.91	57.31	56.99	57.27	57.53	56.92	57.78
Gd	OREAS 460	47.50	48.32	48.83	47.88	48.43	49.03	47.62	48.47	48.62
Gd	OREAS 461	97.35	98.50	98.21	97.89	99.29	99.50	96.31	97.46	98.05
Gd	OREAS 465	581.62	574.01	572.61	579.79	577.37	582.92	574.59	584.62	580.53

• Homogeneity of Intra-day Variances (Cochran’s Test).

Cochran’s C test was used to examine whether any daily variance was disproportionately large before the variance estimates were pooled. For p = 3 days and n = 3 replicates, the critical value was 0.871 at α = 0.05. The observed values in Table 14 ranged from 0.341 to 0.823; none exceeded the critical value. The test therefore did not identify a daily variance outlier among the analyte–CRM combinations evaluated [48].

Table 14. Cochran’s C test for homogeneity of within-day variances (α = 0.05; C_critical = 0.871).

Analyte	CRM Matrix	Mean Grade (mg kg−1)	Maximum Day Variance (Vmax)	Calculated Cobs	Statistical Decision
Gd	OREAS 460	48.30	0.4502	0.4200	Acceptable
	OREAS 461	98.06	0.7830	0.4107	Acceptable
	OREAS 465	578.67	25.4354	0.4487	Acceptable
Tb	OREAS 460	4.54	0.0120	0.5063	Acceptable
	OREAS 461	9.02	0.0114	0.4845	Acceptable
	OREAS 465	57.31	0.3390	0.5999	Acceptable
Dy	OREAS 460	18.11	0.0376	0.3923	Acceptable
	OREAS 461	33.19	0.2527	0.4051	Acceptable
	OREAS 465	214.43	1.2705	0.4688	Acceptable
Ho	OREAS 460	2.40	0.0057	0.4711	Acceptable
	OREAS 461	4.09	0.0058	0.4795	Acceptable
	OREAS 465	26.65	0.2400	0.6171	Acceptable
Er	OREAS 460	4.67	0.0080	0.5793	Acceptable
	OREAS 461	7.80	0.2456	0.3703	Acceptable
	OREAS 465	47.14	0.1996	0.4964	Acceptable
Tm	OREAS 460	0.53	0.0121	0.7398	Acceptable
	OREAS 461	0.73	0.0032	0.3452	Acceptable
	OREAS 465	3.92	0.0276	0.5422	Acceptable
Yb	OREAS 460	2.66	0.0158	0.3840	Acceptable
	OREAS 461	3.17	0.0630	0.3408	Acceptable
	OREAS 465	15.33	1.1482	0.4698	Acceptable
Lu	OREAS 460	0.33	0.0171	0.8234	Acceptable
	OREAS 461	0.39	0.0147	0.5116	Acceptable
	OREAS 465	1.73	0.0306	0.6201	Acceptable

• Assessment of Repeatability (Short-Term Precision)

Repeatability results were summarized in Table 15. Twelve of the 24 Analyte–CRM combinations had Cv_r values below 1.5%, primarily at medium to high concentration levels. The largest Cv_r values occurred for Tm and Lu at low concentration levels. They were 13.95% and 25.24%, respectively. This illustrates that relative imprecision increased as one approached the lower end of the concentration range [49].

Table 15. Repeatability standard deviations (Sr) and coefficients of variation (CVr) for the HREE–CRM combinations.

Analyte	CRM Standard	Pooled Mean (mg kg−1)	Sum of Variances	Repeatability Standard Deviation, (Sr) (mg kg−1)	Repeatability CVr (%)
Gd	OREAS 460	48.30	1.0719	0.5977	1.24
	OREAS 461	98.06	1.9068	0.7972	0.81
	OREAS 465	578.67	56.6868	4.3469	0.75
Tb	OREAS 460	4.54	0.0238	0.0890	1.96
	OREAS 461	9.02	0.0236	0.0887	0.98
	OREAS 465	57.31	0.5651	0.4340	0.76
Dy	OREAS 460	18.11	0.0959	0.1788	0.99
	OREAS 461	33.19	0.6238	0.4560	1.37
	OREAS 465	214.43	2.7102	0.9505	0.44
Ho	OREAS 460	2.40	0.0121	0.0635	2.65
	OREAS 461	4.09	0.0122	0.0637	1.56
	OREAS 465	26.65	0.3890	0.3601	1.35
Er	OREAS 460	4.67	0.0139	0.0680	1.45
	OREAS 461	7.80	0.6634	0.4702	6.03
	OREAS 465	47.14	0.4021	0.3661	0.78
Tm	OREAS 460	0.53 *	0.0164	0.0739	13.98
	OREAS 461	0.73 *	0.0094	0.0559	7.67
	OREAS 465	3.92	0.0510	0.1303	3.33
Yb	OREAS 460	2.66	0.0412	0.1172	4.40
	OREAS 461	3.17	0.1850	0.2483	7.84
	OREAS 465	15.33	2.4442	0.9026	5.89
Lu	OREAS 460	0.33 *	0.0208	0.0832	25.21
	OREAS 461	0.39 *	0.0287	0.0979	25.24
	OREAS 465	1.73 *	0.0494	0.1283	7.43

* Denotes a value less than the minimum quantifiable amount of approximately 2.0 mg/kg in the solid sample; blank derived LOQs indicate no confidence in the data at lower concentrations. Values for Yb of 2.66 and 3.17 mg/kg are above the demonstrated calibration range and thus are marked as such.

• Evaluation of Inter-day Variance Contributions (Fisher’s F-Test)

A single-way ANOVA was performed to compare both the between-day variation and within-day variations of the same dataset for 3 days that were each replicated three times (df₁ = 2; df₂ = 6). For a given alpha level of 0.05, the critical value of F at this degree of freedom was 5.14. None of the 24 values of F_obs shown in Table 16 had a F_obs greater than 5.14. Therefore, there was no evidence based on the statistical test of whether or not the means differed by day [50].

Table 16. One-way ANOVA evaluation of between-day effects (α = 0.05; F_critical = 5.14).

Analyte	CRM	SS_Between	SS_Within	MS_Between	MS_Within	F_obs	F_crit	p-Value	Decision
Dy	OREAS 460	0.30	0.19	0.15	0.03	4.66	5.14	0.06	Acceptable
Dy	OREAS 461	0.13	1.25	0.07	0.21	0.32	5.14	0.74	Acceptable
Dy	OREAS 465	2.41	25.96	1.20	4.33	0.28	5.14	0.77	Acceptable
Ho	OREAS 460	0.00	0.02	0.00	0.00	0.07	5.14	0.93	Acceptable
Ho	OREAS 461	0.01	0.02	0.00	0.00	0.87	5.14	0.47	Acceptable
Ho	OREAS 465	0.01	0.78	0.00	0.13	0.03	5.14	0.97	Acceptable
Er	OREAS 460	0.01	0.03	0.00	0.00	0.81	5.14	0.49	Acceptable
Er	OREAS 461	0.01	1.33	0.00	0.22	0.01	5.14	0.99	Acceptable
Er	OREAS 465	0.09	0.80	0.04	0.13	0.33	5.14	0.73	Acceptable
Tm	OREAS 460	0.02	0.03	0.01	0.01	1.47	5.14	0.30	Acceptable
Tm	OREAS 461	0.00	0.02	0.00	0.00	0.54	5.14	0.61	Acceptable
Tm	OREAS 465	0.03	0.10	0.01	0.02	0.86	5.14	0.47	Acceptable
Yb	OREAS 460	0.01	0.08	0.00	0.01	0.29	5.14	0.76	Acceptable
Yb	OREAS 461	0.00	0.37	0.00	0.06	0.01	5.14	0.99	Acceptable
Yb	OREAS 465	0.14	4.89	0.07	0.81	0.09	5.14	0.92	Acceptable
Lu	OREAS 460	0.01	0.04	0.00	0.01	0.38	5.14	0.70	Acceptable
Lu	OREAS 461	0.03	0.06	0.01	0.01	1.48	5.14	0.30	Acceptable
Lu	OREAS 465	0.15	0.10	0.07	0.02	4.43	5.14	0.07	Acceptable
Tb	OREAS 460	0.01	0.05	0.01	0.01	0.71	5.14	0.53	Acceptable
Tb	OREAS 461	0.06	0.05	0.03	0.01	4.12	5.14	0.07	Acceptable
Tb	OREAS 465	0.08	1.13	0.04	0.19	0.20	5.14	0.82	Acceptable
Gd	OREAS 460	0.10	2.14	0.05	0.36	0.14	5.14	0.88	Acceptable
Gd	OREAS 461	3.94	3.81	1.97	0.64	3.10	5.14	0.12	Acceptable
Gd	OREAS 465	30.28	113.37	15.14	18.90	0.80	5.14	0.49	Acceptable

• Intermediate precision

Intermediate precision combined the pooled within-day variance with the estimated between-day variance component (Table 17). Negative between-day variance estimates, which arise when the between-day mean square is smaller than the within-day mean square, were set to zero for variance-component reporting. The largest CVR occurred for Lu in OREAS 461 (27.17%), consistent with its low concentration. The remaining values describe the CRM matrices and concentration levels tested and should not be extrapolated to all ore matrices [51].

Table 17. Intermediate-precision standard deviations (SR) and coefficients of variation (CVR) for HREE analysis.

Analyte	CRM Matrix	Total Reproducibility Variance	Intermediate Precision Standard Deviation (SR)	Global CVR (%)
Gd	OREAS 460	0.3573	0.5977	1.24
	OREAS 461	1.0812	1.0398	1.06
	OREAS 465	18.8956	4.3469	0.75
Tb	OREAS 460	0.0087	0.0931	2.05
	OREAS 461	0.0160	0.1267	1.40
	OREAS 465	0.1884	0.4340	0.76
Dy	OREAS 460	0.0710	0.2664	1.47
	OREAS 461	0.2087	0.4568	1.38
	OREAS 465	4.3259	2.0799	1.01
Ho	OREAS 460	0.0040	0.0635	2.65
	OREAS 461	0.0041	0.0637	1.56
	OREAS 465	0.1297	0.3601	1.35
Er	OREAS 460	0.0053	0.0731	1.56
	OREAS 461	0.2211	0.4702	6.03
	OREAS 465	0.1335	0.3654	0.78
Tm	OREAS 460	0.0063	0.0795	15.01
	OREAS 461	0.0031	0.0559	7.67
	OREAS 465	0.0170	0.1303	3.33
Yb	OREAS 460	0.0137	0.1172	4.41
	OREAS 461	0.0617	0.2483	7.84
	OREAS 465	0.8147	0.9026	5.89
Lu	OREAS 460	0.0069	0.0832	25.21
	OREAS 461	0.0111	0.1054	27.17
	OREAS 465	0.0353	0.1878	10.86

3.2.3. Assessment of Method Trueness (Bias, Recovery, and Student’s t-Test)

Trueness of results was determined through comparison to the certified values using a t-test. A t-test (Table 18) is conducted when evaluating whether there is a statistically significant difference between the mean of nine replicate measurements for each analyte–CRM pair compared to the certified value. Relative bias and recovery are also considered in this process. Only two pairs were found to exceed the alpha level of 0.05, which represents a critical t-value of 2.31. These included Tb in OREAS 465 (t-obtained = 2.41) and Er in OREAS 461 (t-obtained = 2.51) [32]. CRM recovery, relative bias, and Student’s t-test results are summarized in Table 17.

Table 18. CRM recovery, relative bias, and Student’s t-test results for HREE determination (α = 0.05; t_critical = 2.31).

Analyte	CRM Standard	Certified Value, Vc (mg kg−1)	Experimental Mean, M (mg kg−1)	|Vc − M| (mg kg−1)	Recovery (%)	Relative Bias (%)	tobs	Decision
Gd	OREAS 460	48.20	48.30	0.10	100.21	+0.21	0.57	Compliant
	OREAS 461	98.00	98.06	0.06	100.06	+0.06	0.19	Compliant
	OREAS 465	581.00	578.67	2.33	99.60	−0.40	1.65	Compliant
Tb	OREAS 460	4.60	4.54	0.06	98.62	−1.38	2.22	Compliant
	OREAS 461	9.09	9.02	0.07	99.28	−0.72	1.66	Compliant
	OREAS 465	57.00	57.31	0.31	100.55	+0.55	2.41	Non-compliant (p < 0.05)
Dy	OREAS 460	18.00	18.11	0.11	100.62	+0.62	1.35	Compliant
	OREAS 461	33.50	33.19	0.31	99.07	−0.93	2.25	Compliant
	OREAS 465	215.00	214.43	0.57	99.74	−0.26	1.84	Compliant
Ho	OREAS 460	2.37	2.40	0.03	101.27	+1.27	1.62	Compliant
	OREAS 461	4.06	4.09	0.03	100.79	+0.79	1.54	Compliant
	OREAS 465	26.80	26.65	0.15	99.43	−0.57	1.47	Compliant
Er	OREAS 460	4.65	4.67	0.02	100.53	+0.53	1.11	Compliant
	OREAS 461	7.46	7.80	0.34	104.57	+4.57	2.51	Non-compliant (p < 0.05)
	OREAS 465	47.30	47.14	0.16	99.66	−0.34	1.46	Compliant
Tm	OREAS 460	0.50	0.53 *	0.03	105.78	+5.78	1.11	Compliant
	OREAS 461	0.70	0.73 *	0.03	104.13	+4.13	1.65	Compliant
	OREAS 465	3.82	3.92	0.10	102.53	+2.53	2.26	Compliant
Yb	OREAS 460	2.64	2.66	0.02	100.84	+0.84	0.63	Compliant
	OREAS 461	3.06	3.17	0.11	103.49	+3.49	1.48	Compliant
	OREAS 465	14.90	15.33	0.43	102.89	+2.89	1.63	Compliant
Lu	OREAS 460	0.36	0.33 *	0.03	91.67	−8.33	1.18	Compliant
	OREAS 461	0.39	0.39 *	0.00	99.43	−0.57	0.06	Compliant
	OREAS 465	1.72	1.73 *	0.01	100.45	+0.45	0.13	Compliant

* The smallest amount of a calibration solution by ICP-OES that contained non-zero amount of Yttrium was 0.01 mg/L. As for 0.250 g of sample diluted into 50.0 mL, this equates to 2.00 mg kg⁻¹ in the solid: (0.01 mg L⁻¹ × 0.0500 L)/(0.000250 kg) = 2.00 mg kg⁻¹. Values under 2.00 mg kg⁻¹ are estimated and marked with an asterisk. Blank-derived Limits of quantification (LOQs) do not determine quantitative performance at concentrations greater than the LOQ and less than or equal to 2.00 mg kg⁻¹. Since the two Yb values of 2.66 and 3.17 mg/kg fall well within the demonstrated calibration range, they are NOT marked as being extrapolated.

The analysis of the nine replicates in Table 12 (Section 3.2.2) supported that 22 out of 24 of the analyte CRM comparisons yielded an absolute t_obs value equal to or less than 2.31. Only two comparisons were outside the critical values for both sides of the t-test: Tb in OREAS 465 (t_obs = 2.41) and Er in OREAS 461 (t_obs = 2.51); these two indicated detectably biased results based on this test and therefore cannot be classified as compliant. The En evaluation(Table 19) provides an answer to a completely different question since it evaluates the magnitude of the observed differences relative to the combined expanded uncertainty; thus, |En| ≤ 1 may exist even when there is a statistically significant t test [52].

Table 19. Uncertainty-aware trueness cross-check using En values and method-specific certified values from the four-acid digestion sections of the OREAS 460, 461, and 465 certificates. |En| ≤ 1 indicates compatibility within the combined expanded uncertainties (k = 2).

Analyte	CRM	Measured (mg kg−1)	Certified (mg kg−1)	U_cert (mg kg−1; k = 2)	En
Gd	460	48.30	48.16	4.93	0.03
Gd	461	98.06	97.60	6.97	0.07
Gd	465	578.67	581.07	71.62	−0.03
Tb	460	4.54	4.60	0.34	−0.18
Tb	461	9.02	9.09	1.01	−0.07
Tb	465	57.31	57.08	6.66	0.03
Dy	460	18.11	18.03	0.87	0.09
Dy	461	33.19	33.51	1.72	−0.18
Dy	465	214.43	215.19	18.52	−0.04
Ho	460	2.40	2.37	0.27	0.12
Ho	461	4.09	4.06	0.23	0.14
Ho	465	26.65	26.78	1.87	−0.07
Er	460	4.67	4.65	0.43	0.04
Er	461	7.80	7.46	0.51	0.57
Er	465	47.12	47.27	5.02	−0.03
Tm	460	0.53	0.50	0.10	0.25
Tm	461	0.73	0.70	0.09	0.30
Tm	465	3.92	3.82	0.55	0.17
Yb	460	2.66	2.64	0.38	0.04
Yb	461	3.17	3.06	0.30	0.31
Yb	465	15.33	14.90	1.91	0.22
Lu	460	0.33	0.36	0.09	−0.23
Lu	461	0.39	0.39	0.13	0.03
Lu	465	1.73	1.72	0.56	0.02

3.2.4. Detection and Quantification Limits (LOD and LOQ)

Ten procedural blanks that were treated with the identical multi-acid treatments as the samples and analyzed by ICP-OES were used to provide an estimation of the instrumental detection limit (LOD) and quantification limit (LOQ) for the selected emission lines. The instrument’s LOD and LOQ values based on blank variability (Equation (3)) and instrumental LOD and LOQ values were determined from Equation (4) [53].

$$\mathrm{L}\mathrm{O}\mathrm{D}=\left(\right(3\ast {\mathsf{\sigma }}_{\mathrm{b}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{k}})/\mathrm{S})\ast \mathrm{D}\mathrm{F}$$

(3)

$$\mathrm{L}\mathrm{O}\mathrm{Q}=\left(\right(10\ast {\sigma }_{blank})/\mathrm{S})\ast \mathrm{D}\mathrm{F}$$

(4)

Instrumental LOD and LOQ values are derived from blank-derived values via the use of sample mass (0.250 g) and final sample solution volume (50.0 mL). Thus, they provided a dilution factor of 200 mL g⁻¹. Therefore, these blank-derived LOD and LOQ values do not define quantitative accuracy or precision between the LOQ and the lowest calibration concentration that provided experimental data (i.e., 2.00 mg kg⁻¹) [54]:

$$\mathrm{D}\mathrm{F}={\displaystyle \frac{\mathrm{V}}{\mathrm{m}}}=0.05\mathrm{L}0.25\mathrm{g}=200\mathrm{m}\mathrm{L}{\mathrm{g}}^{-1},$$

(5)

The results of this determination are presented in Table 20.

Table 20. Blank-derived limits of detection and quantification for the selected HREE emission lines (n = 10 procedural blanks).

Element	Sensitivity S (cps·L·mg−1)	σblank (cps)	LODinst (mg kg−1)	LOQinst (mg kg−1)
Gd	50,816.48	8.16	0.10	0.32
Tb	35,534.88	2.50	0.04	0.14
Dy	30,346.66	2.62	0.05	0.17
Ho	18,280.70	1.52	0.05	0.17
Er	49,740.18	3.69	0.04	0.15
Tm	130,213.71	11.23	0.05	0.17
Yb	428,771.27	15.65	0.02	0.07
Lu	16,896.58	1.13	0.04	0.13

3.2.5. Quantified HREE Concentrations by ICP-OES

HREE concentrations in the 24 geological samples are reported in Table 21. Gd ranged from 1.54 to 389.83 mg kg⁻¹, and Dy reached 217.74 mg kg⁻¹ in TWH_22. Values below 2.00 mg kg⁻¹ are reported as extrapolated estimates because they fall below the experimentally demonstrated calibration range. The observed concentration range de-scribes the samples analyzed in this study and does not establish negligible spectral interference or general robustness across other geological matrices.

Table 21. HREE concentrations in the 24 geological samples determined using the retained ICP-OES emission lines (mg kg⁻¹).

Sample	Dy_AES	Er_AES	Gd_AES	Ho_AES	Lu_AES	Tb_AES	Tm_AES	Yb_AES
TWH_01	0.81 *	0.42 *	1.54 *	0.13 *	0.01 *	0.15 *	0.01 *	0.29 *
TWH_02	8.89	4.28	18.26	1.32 *	0.72 *	2.01	0.54 *	3.47
TWH_03	4.25	2.97	10.14	0.91 *	0.33 *	2.38	0.52 *	2.08
TWH_04	14.66	7.34	28.87	2.65	0.34 *	1.88 *	0.97 *	5.36
TWH_05	19.88	9.72	33.52	3.15	0.31 *	2.33	1.37 *	8.11
TWH_06	29.21	25.27	25.51	6.47	3.53	3.81	3.68	25.86
TWH_07	6.58	3.53	14.12	1.19 *	0.17 *	1.69 *	0.21 *	1.86 *
TWH_08	18.75	6.45	35.90	2.97	1.01 *	1.79 *	0.75 *	5.16
TWH_09	11.29	4.13	24.20	2.00	0.60 *	1.93 *	0.41 *	3.51
TWH_10	27.35	23.04	25.38	6.01	3.59	3.84	3.59	24.09
TWH_11	5.81	3.13	14.28	1.04 *	0.34 *	2.09	0.38 *	2.41
TWH_12	11.70	4.63	23.12	2.08	0.73 *	0.56 *	0.54 *	3.88
TWH_13	6.96	3.29	11.84	1.09 *	0.85 *	2.08	0.57 *	2.50
TWH_14	16.22	5.73	31.71	2.44	<LOQ	1.74 *	<LOQ	4.63
TWH_15	10.32	4.82	14.89	1.80 *	1.14 *	1.95 *	0.62 *	4.12
TWH_16	<LOQ	<LOQ	<LOQ	<LOQ	<LOQ	<LOQ	<LOQ	<LOQ
TWH_17	85.67	63.77	62.47	17.40	7.21	9.96	9.65	65.41
TWH_18	17.27	10.91	20.44	3.36	1.54 *	2.81	1.04 *	9.97
TWH_19	8.17	4.92	15.73	1.54 *	0.72 *	1.99 *	0.22 *	3.09
TWH_20	10.70	4.44	21.17	1.75 *	0.53 *	1.15 *	0.45 *	3.03
TWH_21	21.81	9.93	44.75	4.75	1.43 *	2.61	1.12 *	8.13
TWH_22	217.74	73.93	389.83	31.21	9.78	40.48	11.82	68.77
TWH_23	9.44	4.80	14.07	1.27 *	0.86 *	1.90 *	1.25 *	4.45
TWH_24	9.85	5.21	14.52	1.48 *	0.83 *	1.70 *	0.27 *	5.48

* Extrapolated estimate below the demonstrated calibration range (2.00 mg kg⁻¹ lower boundary).

The summary in Figure 7 is a measure of consistency for all concentrations measured in the study. The experimental calibration curve for ICP-OES ranges from 2.00 mg kg⁻¹ in solids. Therefore, any concentrations lower than 2.00 mg kg⁻¹ should be treated as an estimate based on the data collected, and no conclusions can be made that these estimated low concentrations are accurate. As the concentration in samples increases, dispersion also increases, with the highest number of results found to be within ±15% of the acceptance limits found near 5 mg kg⁻¹.

Figure 7. Agreement profile for HREE measurements by ICP-OES across the observed concentration range. Blue Line is Mean Relative Bias of all values. Shaded Region between Dashed Teal Lines are ±95% Expectation Tolerance Interval. Red Dotted Lines are ±15% Acceptable Limits for All Values.

4. Limitations and Future Work

There are several factors that define the boundaries of this study. (1) The same 24 geological samples were analyzed using both the spectral-line screening procedure and as part of the ICP-OES/ICP-MS comparison. Therefore, this comparison evaluates the internal consistency of the ICP-OES/ICP-MS comparison results, which can result in overly optimistic regression statistics for previously untested samples. An evaluation based on new sampling must perform the line selection process again for each data subset and, most importantly, evaluate external validation against geologically different samples. (2) Calibration standards were made by dissolving certified reference materials in nitric acid and did not contain an internal standard or were matrix-matched to the multi-acid digested samples. The sample-equivalent amount of digestion material prior to additional dilution was approximately 5.0 g L⁻¹. However, the final composition of acids and the total dissolved solids were not determined, and potential matrix-dependent biases could exist. (3) The lowest non-zero calibration standard corresponds to 2.00 mg kg⁻¹ HREE in the solid phase. All values less than this value are estimated values using extrapolation and are also above the lower limit of detection (LOD), which is calculated from blanks. (4) Although there are correlations between HREE and Fe, Ti, V, Al, and P, it does not indicate what mechanism(s) cause the interferences among these elements since these elements have been evaluated at varying concentrations relative to one another while keeping the concentration of HREE constant. As such, the assignments shown in Table 20 represent a possible explanation for the interference patterns observed and will require independent variable control studies along with local spectra to validate.

Within-dataset regression parameters and calibration status for the candidate HREE emission lines are summarized in Table 22.

Table 22. Candidate HREE emission lines and within-dataset regression parameters.

HREE	Wavelength λ (nm)	r	R2	Slope	Intercept	Calibration
Dy	338.501	1.00000	1.00000	1088.08388002	7.00025064	Calibrated
Dy	340.780	1.00000	1.00000	6602.77145367	15.90439201	Calibrated
Dy	349.449	0.99999	0.99998	6661.31981692	−13.66157310	Calibrated
Dy	352.398	1.00000	1.00000	3037.35646707	32.88903649	Calibrated
Dy	353.171	1.00000	1.00000	9921.56077215	26.31375601	Calibrated
Dy	353.602	0.99999	0.99998	1553.02458933	3.62537031	Calibrated
Dy	353.852	1.00000	1.00000	967.59118424	16.20640774	Calibrated
Dy	357.625	0.99009	0.98028	58,881.72560535	216.16244102	Calibrated
Dy	364.540	0.99998	0.99996	24,186.26548857	146.76528726	Calibrated
Dy	387.211	1.00000	1.00000	7732.82211522	44.13236882	Calibrated
Dy	394.468	1.00000	1.00000	10,102.30116253	3.32693409	Calibrated
Dy	400.045	1.00000	1.00000	6997.41115113	25.13620916	Calibrated
Dy	407.797	1.00000	1.00000	8033.89591832	20.99759192	Calibrated
Er	291.036	1.00000	1.00000	581.34213337	5.40483907	Calibrated
Er	296.452	1.00000	1.00000	1016.68556441	34.89308995	Calibrated
Er	300.241	1.00000	1.00000	2720.82189283	3.41002117	Calibrated
Er	323.058	0.99999	0.99998	1712.99187834	21.25581535	Calibrated
Er	326.478	1.00000	1.00000	11,017.08123094	23.30919065	Calibrated
Er	331.243	1.00000	1.00000	4801.43044398	13.19368575	Calibrated
Er	334.603	1.00000	1.00000	2558.01735271	8.71423112	Calibrated
Er	337.275	0.99999	0.99998	8848.04545561	143.49828956	Calibrated
Er	338.507	1.00000	1.00000	1091.31885614	7.78408436	Calibrated
Er	339.199	0.99983	0.99966	5547.05254707	466.41791936	Calibrated
Er	349.910	1.00000	1.00000	14,670.39756489	28.57543432	Calibrated
Er	361.657	1.00000	1.00000	2556.19793281	13.97077043	Calibrated
Er	369.265	1.00000	1.00000	12,597.26996372	−7.48393501	Calibrated
Er	389.623	1.00000	1.00000	6903.26650643	17.53440619	Calibrated
Er	390.631	1.00000	1.00000	7971.67227484	80.92634714	Calibrated
Gd	301.013	1.00000	1.00000	3050.84163775	11.12982006	Calibrated
Gd	303.284	1.00000	1.00000	671.89844502	10.02499896	Calibrated
Gd	310.050	1.00000	1.00000	583.74691188	12.17211885	Calibrated
Gd	335.048	1.00000	1.00000	7988.78108219	24.38924354	Calibrated
Gd	335.863	0.99099	0.98206	5664.70390015	−13.00222084	Calibrated
Gd	336.224	1.00000	1.00000	5811.52475361	79.86786473	Calibrated
Gd	342.246	1.00000	1.00000	17,425.41209639	79.88029934	Calibrated
Gd	358.496	1.00000	1.00000	8042.84194407	10.74795605	Calibrated
Gd	364.620	1.00000	1.00000	4951.51894799	18.09059299	Calibrated
Gd	376.840	1.00000	1.00000	9702.52872205	32.85462444	Calibrated
Gd	379.638	1.00000	1.00000	3922.94854126	16.02714420	Calibrated
Gd	308.436	0.99999	0.99998	1073.99767304	30.05324727	Calibrated
Ho	339.895	0.99999	0.99998	10,646.60855679	66.35528663	Calibrated
Ho	341.644	1.00000	1.00000	10,757.02481486	14.94373525	Calibrated
Ho	342.534	0.99999	0.99998	2701.78940274	33.13706241	Calibrated
Ho	342.813	0.99999	0.99998	4571.15437101	111.49928678	Calibrated
Ho	345.314	1.00000	1.00000	1637.41661000	7.35658036	Calibrated
Ho	345.600	0.99999	0.99998	6307.27443409	1.85304554	Calibrated
Ho	347.425	1.00000	1.00000	8441.30371091	−24.53051521	Calibrated
Ho	348.484	1.00000	1.00000	13,493.38854635	48.17185046	Calibrated
Ho	349.476	0.99999	0.99998	5420.88547537	12.05328084	Calibrated
Ho	351.559	0.99999	0.99998	4183.21515388	49.80168049	Calibrated
Ho	379.675	1.00000	1.00000	6406.50210808	6.12918517	Calibrated
Ho	381.074	0.99999	0.99998	4383.01279209	18.73124493	Calibrated
Ho	389.094	0.99999	0.99998	21,064.99013300	33.95016491	Calibrated
Ho	404.547	0.99967	0.99934	10,076.16253718	−137.33309498	Calibrated
Lu	219.556	0.99999	0.99998	2362.87039624	15.71597738	Calibrated
Lu	261.541	0.99998	0.99996	60,762.30156799	88.66637317	Calibrated
Lu	265.780	0.99999	0.99998	3141.47962596	27.12118106	Calibrated
Lu	270.171	1.00000	1.00000	538.24771642	4.32208122	Calibrated
Lu	275.417	0.99099	0.98206	331.52197428	7.48146648	Calibrated
Lu	284.751	0.99999	0.99998	1790.34215252	2.17853542	Calibrated
Lu	289.484	0.99999	0.99998	6843.41088695	36.24769076	Calibrated
Lu	290.030	0.99099	0.98206	3364.61727200	303.97922308	Calibrated
Lu	291.139	0.99909	0.99818	1894.21301416	−0.20424836	Calibrated
Lu	296.332	0.99999	0.99998	2299.45398694	10.15896507	Calibrated
Lu	307.760	1.00000	1.00000	12,055.30614800	18.97440624	Calibrated
Lu	339.707	1.00000	1.00000	10,390.50524335	15.54303215	Calibrated
Lu	347.248	1.00000	1.00000	9568.98172274	51.61947850	Calibrated
Lu	350.738	0.99998	0.99996	10,898.44169077	6.00009189	Calibrated
Lu	547.668	1.00000	1.00000	42,793.41849343	190.72851022	Calibrated
Tb	321.893	0.99999	0.99998	1510.32838061	19.16047422	Calibrated
Tb	321.998	0.99999	0.99998	1305.64081688	6.75915641	Calibrated
Tb	329.307	1.00000	1.00000	792.50503875	12.35178003	Calibrated
Tb	332.440	0.99998	0.99996	5344.34291650	−2.37451556	Calibrated
Tb	350.914	1.00000	1.00000	9309.27370368	26.87398830	Calibrated
Tb	356.170	1.00000	1.00000	5557.03249989	130.30180913	Calibrated
Tb	356.851	0.99983	0.99966	ND	ND	Uncalibrated
Tb	360.044	0.99999	0.99998	2698.07131215	−22.36746955	Calibrated
Tb	367.636	1.00000	1.00000	7408.49182832	37.51600299	Calibrated
Tb	370.285	1.00000	1.00000	3206.68948431	14.53298594	Calibrated
Tb	370.392	1.00000	1.00000	2180.38584478	19.53937187	Calibrated
Tb	384.873	0.99999	0.99998	5836.14513475	5.00787575	Calibrated
Tb	387.417	1.00000	1.00000	6725.49167136	2.71814213	Calibrated
Tb	389.919	0.99999	0.99998	2636.73647196	23.29636177	Calibrated
Tm	313.125	0.99999	0.99998	19,709.57448303	28.35561507	Calibrated
Tm	313.389	1.00000	1.00000	5576.74012063	68.84726475	Calibrated
Tm	329.100	1.00000	1.00000	3501.20980580	22.87373677	Calibrated
Tm	336.261	1.00000	1.00000	8470.27164488	−2.82012715	Calibrated
Tm	342.508	1.00000	1.00000	18,561.41918636	51.52259741	Calibrated
Tm	344.150	1.00000	1.00000	7388.33338582	68.96282570	Calibrated
Tm	345.367	1.00000	1.00000	2223.75779468	23.22157406	Calibrated
Tm	346.220	1.00000	1.00000	2508.50504849	4.25630113	Calibrated
Tm	370.026	1.00000	1.00000	6971.23753862	49.53796821	Calibrated
Tm	376.133	1.00000	1.00000	16,750.11849223	155.31766102	Calibrated
Tm	376.191	1.00000	1.00000	13,253.19750595	86.90331072	Calibrated
Tm	379.576	1.00000	1.00000	10,293.71722114	40.93248130	Calibrated
Tm	384.802	1.00000	1.00000	21,447.75879630	114.70492857	Calibrated
Yb	211.667	0.99999	0.99998	692.62265850	10.32939709	Calibrated
Yb	212.674	1.00000	1.00000	1817.80157564	15.15066712	Calibrated
Yb	216.160	1.00000	1.00000	423.54173379	12.86688534	Calibrated
Yb	218.572	0.99999	0.99998	1812.13653089	12.43793209	Calibrated
Yb	222.447	1.00000	1.00000	3614.33449733	23.99155392	Calibrated
Yb	232.081	0.99997	0.99994	ND	ND	Uncalibrated
Yb	253.867	1.00000	1.00000	558.32462351	8.32040021	Calibrated
Yb	265.375	0.99997	0.99994	262.66100098	15.60515468	Calibrated
Yb	267.266	0.99999	0.99998	892.64235457	5.02362405	Calibrated
Yb	275.048	0.99997	0.99994	519.20726702	6.27538139	Calibrated
Yb	289.138	0.99999	0.99998	15,078.34657074	621.69074152	Calibrated
Yb	297.056	0.99999	0.99998	1186.71893388	72.56095706	Calibrated
Yb	303.111	0.99998	0.99996	618.75255216	8.48975825	Calibrated
Yb	328.937	0.99099	0.98206	82,552.81969114	74.23598048	Calibrated
Yb	369.419	0.99998	0.99996	108,056.93155803	32.11500466	Calibrated
Yb	398.799	1.00000	1.00000	9647.39303442	12.24485492	Calibrated

5. Conclusions

This research investigated a double-gate workflow to select suitable ICP-OES emission lines for determination of Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu in ore samples digested by multiple acids. The lines chosen for use were: Gd 335.048 nm; Tb 350.914 nm; Dy 353.171 nm; Ho 345.600 nm; Er 369.265 nm; Tm 313.125 nm; Yb 369.419 nm; and Lu 291.139 nm. Blank-derived limits of detection (LOD) and quantification (LOQ) were found to be between 0.02–0.10 and 0.07–0.32 mg/kg, respectively. However, it is important to note that although the experimental results demonstrate the lowest calibration range limit of quantification to be approximately 2.00 mg/kg. Values below this level are considered to be an extrapolation based on the original calibration curve. A second statistical evaluation using the CRM (Certified Reference Materials) data also revealed two instances where the TB—OREAS 465 sample and the ER—OREAS 461 sample exceeded their respective TB and ER t-tests. All 24 inter-day analysis of variance (ANOVA) F-values were less than the critical value of F-critical = 5.14. Because the ICP-OES/ICP-MS comparison utilized the same set of 24 samples from the initial line selection experiment, it can be concluded that there is internal validation within this group of samples. It should, however, be noted that correlation-based interference assessments are still tentative due to the fact that each individual matrix element could not be changed with a constant concentration of each respective analyte, and therefore it is possible that uncontrolled residual matrix effects may have existed during ICP-OES calibrations since calibration standards did not contain matching matrices and no internal standard was employed.