Round-Robin Interlaboratory Study on Rare-Earth Elements in U.S.-Based Geologic Materials

Abstract

In a study funded by the U.S. Department of Energy (DOE) National Energy Technology Laboratory (NETL), the University of North Dakota (UND) Energy and Environmental Research Center (EERC) performed a first-of-its-kind round-robin interlaboratory study (RRIS) to determine lab-to-lab and method-to-method variability in analyzing the rare earth element (REE) content of domestic resources. Analyses of REEs on eleven different materials were accomplished by the laboratories using four different procedures: ASTM D6357 (Procedure A), ASTM D4503 (Procedure B), an alternate in-house procedure for digestion and REE analysis (Procedure C), and neutron activation analysis (NAA). The results of the RRIS suggest that NAA is the most accurate and reliable method for many of the REEs in these types of materials; however, the method is limited in that it is able to determining only ten of the sixteen REEs. Five of the seven labs reporting data for Procedure A and three of the five labs reporting for Procedure B showed excellent performance in terms of repeatability, reproducibility, agreement with NAA, and SRM recoveries based on AOAC International guidelines on method performance. This indicates that when strictly followed these methods are suitable for REE determination in most materials, although are subject to the overall capabilities and experience of individual laboratories.

1. Introduction

Rare-earth elements (REEs), which include the fourteen naturally occurring lanthanide elements of lanthanum (57) through lutetium (71) plus scandium (21) and yttrium (39), are crucial materials in an incredible array of consumer goods, energy system components, and military defense applications because of their unique properties. However, their global production and entire value chain are dominated by China [1]. While the United States currently mines and concentrates REEs, the concentrate must be shipped out of the country for further processing into discrete metals and alloys, making the United States essentially 100% import-reliant for these critical materials. Traditional mineral ores, including previously mined deposits in the United States, have several challenges. Chief among these is that the content of the most critical and valuable REEs is deficient, making mining uneconomical. Further, the supply of these critical REEs is nearly 100% produced in China from a single resource (ion-adsorbed clays) that is projected by experts to only last another 10–20 years [2,3,4]. The United States currently considers the REE market an issue of national security [5,6,7]. It is imperative that alternative domestic sources of REE be identified and that methods be developed to produce them. Recently, coal and coal byproducts have been identified as among these promising alternative resources.

The U.S. Department of Energy (DOE) has been pursuing alternative sources for REEs and critical minerals (CMs), funding multiple projects aimed at building the knowledge base and capabilities needed to advance the technology for REE and CM extraction and processing. Part of this work involves locating promising REE and CM sources and developing estimates of resources available for processing [8]. As part of this function, determination of the precision and accuracy of commonly utilized analytical laboratory methods is an identified need. In a study funded by DOE’s National Energy Technology Laboratory (NETL), the University of North Dakota (UND) Energy and Environmental Research Center (EERC) focused on identifying and quantifying REE resources associated with coal and coal-related materials in the United States. A portion of that work included a round-robin interlaboratory study (RRIS) to determine lab-to-lab and method-to-method variability in analyzing the REE content of domestic-based resources. To accomplish this, thirteen laboratories participated in an RRIS focused on analyzing REEs, a first-of-its-kind study in the United States. Analyses of REEs performed on eleven different materials were accomplished by the laboratories using four different procedures: ASTM D6357 mixed acid (i.e., hydrochloric, nitric, and hydrofluoric) digestion with heat followed by either inductively coupled plasma–mass spectrometry (ICP–MS) or ICP–optical emission spectroscopy (ICP–OES) [9]; ASTM D4503 high-temperature lithium borate fusion digestion followed by ICP–MS analysis (although this method was withdrawn by ASTM in 2012, the process has been utilized in many laboratories, and subsequent to this study ASTM has added it as an alternative preparation and analysis method to ASTM D6357) [10]; an alternate in-house procedure routinely used by one of the laboratories for digestion and REE analysis; and neutron activation analysis (NAA). This paper discusses the results of the RRIS and the statistical analysis of the results.

2. Materials and Methods

2.1. Laboratory Participants

Thirteen laboratories with the capabilities and experience to digest and analyze samples for REEs participated in the interlaboratory study. The goal was to obtain enough laboratories to provide a minimum of six datasets for each of the methods in order to meet the minimum requirement specified in ASTM E691 for determining adequate statistical precision [11]. One additional lab was selected to perform NAA as a reference method.

2.2. Sample Selection

Eleven materials were selected for the RRIS, which included a variety of sample types and matrices with varying REE concentrations. Among them were four standard reference materials (SRMs) to help determine method bias. The study materials are listed in

Table 1. RRIS materials.

RRIS Code	Sample Type	Origin	TREE 1, ppm, Dry Mass Basis	Ash Content, %
Material A	Lignite coal	North Dakota/Harmon seam	400	25–30
Material B	Subbituminous coal	Wyoming/PRB 2	200	6–8
Material C	Bituminous coal	Central Appalachian	125	6–8
Material D	Bituminous fly ash	Kentucky power plant/Central Appalachian coal	700	98–100
Material E	Subbituminous fly ash	Wisconsin power plant/PRB coal	400	98–100
Material F	Clay parting	Texas/subbituminous	280	95–98
Material G	AMD 3 anthracite	Pennsylvania/Central Appalachian anthracite coal	200	50–55
Material H	Bituminous fly ash	NIST 4 SRM 5—Pennsylvania power plant/bituminous	600	90–93
Material I	Shale	USGS 6 SRM—Pennsylvania Bush Creek shale	315	90–93
Material J	Bituminous coal	NIST SRM—Pennsylvania/Northern Appalachian coal	40	8–9
Material K	Mine waste material	NIST SRM—Colorado/Rocky Mountain Basin coal	190	88–92

¹ Total REE. ² Powder River Basin. ³ Acid mine drainage. ⁴ National Institute of Standards and Technology. ⁵ Standard reference material. ⁶ U.S. Geological Survey.

, and the SRMs with their respective reference values are in

Table 2. SRMs included in the RRIS and REE reference values, mg/kg, dry mass basis.

Element	Symbol	NIST 1633c Fly Ash	NIST 1632e Coal	NIST 2780a Mine Waste	USGS SBC-1 Bush Creek Shale
Cerium	Ce	180	12.24	67.7	108 ± 0.9
Dysprosium	Dy	19	1	3.1	7.1 ± 0.09
Erbium	Er	–	0.7	2.0	3.8 ± 0.05
Europium	Eu	4.7	0.246	0.9	1.98 ± 0.02
Gadolinium	Gd	–	1	3.2	8.5 ± 0.1
Holmium	Ho	–	0.2	0.7	1.4 ± 0.02
Lanthanum	La	87.0	7	34.4	52.5 ± 0.6
Lutetium	Lu	1.3	0.1	0.33	0.54 ± 0.01
Neodymium	Nd	87	6	28.3	49.2 ± 0.5
Praseodymium	Pr	–	1.5	8	12.6 ± 0.1
Samarium	Sm	19	1	4.7	9.6 ± 0.1
Scandium	Sc	37.6	3.58	15.6	20 ± 0.2
Terbium	Tb	3.1	0.2	0.5	1.2 ± 0.02
Thulium	Tm	–	0.1	0.31	0.56 ± 0.01
Ytterbium	Yb	7.7	6	18	3.6 ± 0.04
Yttrium	Y	–	0.6	2	36.5 ± 0.3

.

2.3. Materials Preparation

The coal samples were air-dried, ground to −60 mesh (150 μm), riffled, and split according to ASTM Methods D2234 and D2013. The splits were packaged in 4 oz amber glass jars. The ash and clay materials were ground to −200 mesh (75 μm), riffled, split according to ASTM D2013, and packaged in 2 oz high-density polyethylene (HDPE) jars. The SRMs were prepared, riffled, and split by the vendors.

2.4. Homogeneity Testing

The homogeneity of the SRMs was determined by the vendors who supplied them. For the remaining materials, ten jars of each coal material were analyzed in duplicate for sulfur content and ten jars of each ash and clay material were analyzed in duplicate for silica content. All materials passed the ANOVA (analysis of variance) criteria for homogeneity with a p-value > 0.05. The Kruskal–Wallis statistical technique was applied to the results as well, again with a p-value > 0.05 [12].

2.5. Procedures and Samples Distribution

Approximately 50 g of each coal and 20 g of each of the other materials, labeled Materials A–K, were provided to each participating laboratory along with study instructions. The laboratories were asked to prepare and analyze each sample in triplicate and record the results in an Excel template that was emailed to them. They had approximately 10 weeks to complete the analysis and report the results. The study instructions are included in Appendix A.

2.6. Analytical Methods

Other than the laboratory performing NAA, the participating laboratories were asked to perform one or more of the following methods: Procedure A, ASTM D6357, mixed acid (i.e., hydrochloric, nitric, and hydrofluoric) digestion with heat followed by either ICP–MS or ICP–OES; Procedure B, ASTM D4503, high-temperature lithium borate fusion digestion followed by ICP–MS analysis; or Procedure C, an alternate procedure routinely used by one of the laboratories for digestion and REE analysis.

2.7. Statistical Methods

The data reported by the laboratories for the various procedures and test materials were compiled and the following statistics applied in accordance with ASTM Method E691, Standard Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method:

($\overline{X}$) = average of three replicates.

s = standard deviation of triplicate test results.

RSD = ratio of the test results standard deviation (s) over the average ($\overline{X}$) × 100%.

S_r = repeatability standard deviation (i.e., within laboratory variability).

$$s_r=\sqrt{{\sum }_1^p{s}^2}/p$$

(1)

where p is the number of laboratories and s is the standard deviation of triplicate test results.

Here, S_R is the reproducibility standard deviation (i.e., between-laboratory variability):

$$s_R=\sqrt{{\left(s_{\overline{x}}\right)}^2+{\left(s{}_r\right)}^2\left(\frac{n-1}{n}\right)}$$

(2)

where $s_{\overline{x}}$ is the standard deviation of the test result averages, S_R is the repeatability standard deviation, and n is the number of test results per measurement.

3. Results

3.1. Repeatability and Reproducibility

According to ASTM Method E691, the repeatability standard deviation or within-laboratory variability is defined as the standard deviation of test results obtained among the labs using the same procedure, operator, and equipment. These are considered the most favorable conditions possible and to yield the best precision of the method (i.e., the smallest standard deviation).

The reproducibility standard deviation or between-laboratory variability is determined by comparing the test results obtained with the same method on identical test materials in different laboratories with different operators using different equipment. Thus, it takes into account many more sources of variation than the repeatability does. These are considered the least favorable conditions and typically yield the worst precision of a method (i.e., the greatest standard deviation).

The repeatability standard deviation (S_r) and reproducibility deviation (S_R) were calculated for Procedures A and B, which included all sixteen elements for all eleven materials. Although only five laboratories reported data for Procedure B, which did not meet the minimum requirement according to ASTM E691, the repeatability and reproducibility were still calculated. Because only one laboratory reported results on Procedure C, the repeatability and reproducibility standard deviation could not be calculated; however, the RSDs of the triplicate values were calculated and compared to those of the other methods. One laboratory that reported data for Procedure A withdrew from the study after it discovered problems with the analysis. The data from that lab were excluded; however, the minimum number of labs for Procedure A was met. The repeatability and reproducibility results are presented in

Table 3. Repeatability (within lab) and reproducibility (between lab) standard deviations, µg/g dry whole sample basis.

Procedure A
		Sc	Y	La	Ce	Pr	Nd	Sm	Eu	Gd	Tb	Dy	Ho	Er	Tm	Yb	Lu
Material A	$\overline{X}$	15.86	34.58	31.95	80.86	10.09	42.19	8.82	1.996	8.713	1.305	8.212	1.655	4.911	0.713	4.709	0.746
	sr	0.468	0.658	0.716	1.60	0.193	1.16	0.279	0.0288	0.212	0.033	0.219	0.0321	0.101	0.015	0.0765	0.014
	sR	1.91	3.44	2.55	5.69	0.827	2.39	0.560	0.227	1.32	0.233	0.934	0.183	0.436	0.056	0.340	0.13
Material B	$\overline{X}$	1.844	2.224	2.815	4.613	0.623	2.387	0.432	0.126	0.577	0.073	0.422	0.085	0.252	0.040	0.233	0.039
	sr	0.0446	0.0332	0.0428	0.108	0.013	0.0343	0.0117	0.0027	0.0093	0.001	0.0054	0.002	0.0045	0.001	0.0023	0.0005
	sR	0.790	0.418	0.334	1.51	0.057	0.185	0.130	0.036	0.327	0.010	0.043	0.011	0.026	0.009	0.030	0.006
Material C	$\overline{X}$	4.426	18.98	19.74	42.10	4.784	18.00	3.722	0.381	3.500	0.569	3.379	0.702	2.020	0.313	1.824	0.256
	sr	0.187	0.539	0.813	1.86	0.204	0.808	0.163	0.015	0.152	0.018	0.110	0.022	0.0615	0.010	0.0633	0.0088
	sR	0.530	2.57	3.16	6.46	0.763	3.06	0.490	0.055	0.66	0.075	0.431	0.066	0.219	0.072	0.2268	0.023
Material D	$\overline{X}$	53.61	121.48	95.55	201.73	23.65	92.55	20.61	4.391	20.49	3.325	21.31	4.406	12.45	1.929	10.88	1.589
	sr	2.22	9.298	1.92	17.70	0.647	7.05	0.897	0.130	0.778	0.107	0.519	0.0758	0.399	0.0488	0.351	0.0411
	sR	7.78	16.71	7.20	20.48	1.91	8.43	1.64	0.420	2.42	0.415	1.39	0.274	1.03	0.432	0.986	0.154
Material E	$\overline{X}$	27.67	51.98	54.04	105.03	13.23	51.54	9.907	2.712	12.85	1.546	8.998	1.824	5.309	0.742	5.062	0.749
	sr	2.31	0.633	1.17	2.541	0.212	0.820	0.133	0.0436	0.246	0.0243	0.228	0.0534	0.0795	0.019	0.0686	0.013
	sR	18.2	7.44	14.5	30.12	3.35	13.9	3.40	0.912	7.79	0.402	2.19	0.473	1.37	0.199	0.396	0.249
Material F	$\overline{X}$	5.323	31.30	53.11	110.73	11.49	41.52	7.615	0.515	6.338	0.927	5.840	1.124	3.388	0.521	3.402	0.545
	sr	0.545	0.717	2.96	4.977	0.433	2.09	0.267	0.022	0.229	0.041	0.225	0.0489	0.128	0.022	0.123	0.026
	sR	1.44	4.56	5.46	9.545	1.71	3.47	0.619	0.145	1.42	0.25	0.713	0.194	0.445	0.062	0.408	0.15
Material G	$\overline{X}$	11.56	10.37	23.18	48.38	5.558	20.60	4.206	0.938	2.991	0.437	2.401	0.457	1.496	0.219	1.461	0.260
	sr	0.228	0.201	0.542	0.769	0.0856	0.457	0.0593	0.013	0.0520	0.018	0.0795	0.014	0.0431	0.0078	0.0339	0.011
	sR	3.81	3.56	7.06	13.2	1.66	6.00	1.29	0.071	1.07	0.085	0.565	0.096	0.456	0.055	0.273	0.14
Material H	$\overline{X}$	38.53	102.01	82.10	191.29	21.91	91.26	20.52	4.465	20.11	3.124	18.31	3.348	10.02	1.456	8.608	1.549
	sr	1.34	9.848	10.0	14.99	0.635	8.47	0.580	0.141	0.749	0.106	0.611	0.132	0.309	0.0501	0.343	0.0603
	sR	4.29	17.09	11.2	18.02	2.05	11.2	2.19	0.502	2.66	0.373	1.79	0.669	1.03	0.274	0.878	0.798
Material I	$\overline{X}$	22.02	29.48	51.26	103.86	12.78	49.31	10.10	1.969	8.277	1.221	6.590	1.108	3.576	0.505	3.361	0.633
	sr	0.439	0.919	1.66	4.501	0.309	1.70	0.343	0.0588	0.253	0.0376	0.246	0.0504	0.110	0.023	0.0679	0.033
	sR	2.39	4.15	4.25	16.81	0.890	3.50	0.678	0.173	1.50	0.170	0.594	0.248	0.405	0.054	0.306	0.35
Material J	$\overline{X}$	3.513	5.271	5.684	11.89	1.424	5.543	1.192	0.246	1.086	0.182	1.018	0.202	0.588	0.0895	0.557	0.123
	sr	0.0794	0.237	0.234	0.542	0.0412	0.127	0.0209	0.0045	0.0179	0.0047	0.0186	0.0038	0.013	0.0017	0.0096	0.0022
	sR	0.382	0.832	0.616	0.997	0.0884	0.255	0.181	0.013	0.166	0.042	0.0671	0.013	0.032	0.016	0.042	0.106
Material K	$\overline{X}$	14.76	6.203	29.31	53.27	6.658	23.31	4.223	0.710	2.347	0.406	1.838	0.238	1.017	0.112	0.949	0.432
	sr	0.366	0.350	1.33	3.11	0.237	0.998	0.155	0.034	0.0871	0.070	0.0797	0.016	0.0307	0.012	0.034	0.012
	sR	3.27	1.75	5.24	10.9	1.75	4.45	1.76	0.143	1.12	0.315	1.37	0.074	0.795	0.034	0.508	0.733
Procedure B
		Sc	Y	La	Ce	Pr	Nd	Sm	Eu	Gd	Tb	Dy	Ho	Er	Tm	Yb	Lu
Material A	$\overline{X}$	21.40	44.18	37.34	79.44	11.95	44.32	8.549	1.987	10.54	1.376	8.539	2.150	5.134	0.924	4.882	0.732
	sr	1.27	4.04	2.56	2.22	0.870	2.93	0.280	0.0709	0.505	0.0454	0.262	0.115	0.172	0.046	0.142	0.023
	sR	11.6	15.1	11.9	7.66	4.54	26.2	0.861	0.194	3.67	0.136	0.925	0.968	0.630	0.42	0.573	0.075
Material B	$\overline{X}$	2.103	2.992	3.335	6.246	0.626	3.027	0.501	0.140	0.593	0.088	0.566	0.117	0.358	0.052	0.329	0.049
	sr	0.313	0.202	0.107	0.237	0.0065	0.126	0.0069	0.0096	0.045	0.003	0.020	0.016	0.026	0.009	0.021	0.005
	sR	1.50	0.662	0.902	1.78	0.074	1.07	0.035	0.048	0.233	0.035	0.241	0.057	0.169	0.025	0.132	0.010
Material C	$\overline{X}$	5.049	23.29	22.72	48.85	5.771	19.40	4.616	0.464	4.362	0.711	4.306	0.903	2.097	0.376	2.350	0.275
	sr	0.398	1.37	1.35	1.02	0.348	1.62	0.347	0.045	0.256	0.059	0.339	0.061	0.193	0.025	0.147	0.0067
	sR	2.05	4.92	6.43	13.5	1.96	1.62	1.87	0.17	1.56	0.31	1.82	0.43	0.245	0.19	1.07	0.018
Material D	$\overline{X}$	61.85	125.86	91.53	191.56	23.32	80.79	21.03	4.568	22.09	3.643	22.85	4.695	13.64	1.911	12.23	1.869
	sr	2.53	5.917	4.13	9.346	1.20	5.35	1.12	0.209	1.08	0.199	1.33	0.306	0.852	0.104	0.753	0.0302
	sR	31.3	15.86	7.48	15.71	2.22	37.1	2.81	0.640	1.91	0.584	3.77	0.909	2.61	0.393	2.38	0.405
Material E	$\overline{X}$	29.16	53.01	60.41	117.49	14.70	50.73	12.25	2.818	11.64	1.703	10.31	2.051	5.979	0.848	5.487	0.850
	sr	1.48	0.954	1.03	1.984	0.266	0.944	0.263	0.0760	0.288	0.0631	0.230	0.0553	0.146	0.029	0.178	0.028
	sR	21.1	6.23	4.85	8.754	1.44	23.2	1.49	0.410	1.07	0.293	1.88	0.409	1.17	0.17	1.02	0.18
Material F	$\overline{X}$	4.616	32.55	53.16	107.19	11.88	43.48	7.774	0.575	6.811	1.030	6.476	1.287	3.855	0.568	3.858	0.576
	sr	0.212	0.864	0.909	1.519	0.214	0.805	0.161	0.051	0.139	0.0196	0.121	0.0375	0.0709	0.025	0.102	0.025
	sR	1.58	4.32	5.86	11.36	1.42	4.80	1.20	0.11	0.544	0.237	1.23	0.256	0.789	0.12	0.871	0.14
Material G	$\overline{X}$	16.80	19.35	25.15	50.31	5.921	19.54	4.553	0.966	4.288	0.625	3.881	0.776	2.267	0.325	2.153	0.326
	sr	0.748	0.753	0.640	1.17	0.108	0.702	0.194	0.049	0.190	0.041	0.143	0.043	0.123	0.011	0.132	0.010
	sR	12.2	3.28	3.18	5.59	0.661	9.88	0.654	0.15	0.316	0.15	0.557	0.13	0.381	0.0534	0.348	0.050
Material H	$\overline{X}$	44.36	101.57	79.57	176.61	21.86	80.43	20.64	4.619	21.57	3.242	19.61	3.885	10.94	1.479	9.307	1.416
	sr	2.86	2.688	2.07	4.515	0.562	1.05	0.408	0.168	0.573	0.105	0.576	0.113	0.302	0.0339	0.144	0.0345
	sR	22.5	11.32	8.51	18.27	2.86	35.0	3.68	0.816	2.83	0.684	4.19	0.907	2.41	0.345	2.08	0.370
Material I	$\overline{X}$	26.83	33.19	49.40	103.57	12.38	51.20	9.884	1.996	8.726	1.258	7.309	1.399	4.091	0.578	3.813	0.584
	sr	0.725	0.884	1.02	2.479	0.310	1.35	0.238	0.0586	0.198	0.0366	0.298	0.0653	0.164	0.039	0.169	0.029
	sR	17.9	4.02	4.58	8.175	1.19	4.35	1.40	0.283	0.824	0.195	1.29	0.272	0.753	0.12	0.635	0.13
Material J	$\overline{X}$	3.669	5.384	5.226	10.46	1.258	4.973	1.022	0.248	1.065	0.188	0.995	0.228	0.622	0.118	0.553	0.085
	sr	0.530	0.172	0.243	0.470	0.068	0.184	0.106	0.076	0.099	0.087	0.076	0.087	0.110	0.094	0.079	0.002
	sR	2.05	1.78	1.38	2.83	0.251	1.17	0.195	0.068	0.167	0.082	0.163	0.082	0.109	0.103	0.090	0.006
Material K	$\overline{X}$	24.82	16.99	34.43	65.17	7.531	29.69	4.714	0.907	3.435	0.496	3.164	0.684	2.156	0.327	2.175	0.375
	sr	1.41	0.595	0.878	1.56	0.177	0.788	0.102	0.033	0.109	0.043	0.0969	0.032	0.109	0.016	0.0322	0.022
	sR	20.8	2.14	3.32	5.22	0.770	2.96	0.687	0.136	0.335	0.090	0.614	0.150	0.413	0.088	0.445	0.093

.

As expected, the between-laboratory standard deviations (S_R) were higher than the within-laboratory standard deviations (S_r). The highest (S_R) values were observed for scandium and lutetium for both procedures. In certain cases these values were as high as or even higher than the mean values. For example, the mean value ($\overline{X}$) from Procedure B for scandium (Sc) on Material K was 24.82 ppm and the (S_R) value was 20.8 ppm, while for lutetium (Lu) on Material K using Procedure A the mean value ($\overline{X}$) was 0.432 ppm and the (S_R) value was 0.733 ppm.

The repeatability or reproducibility standard deviation can be expressed as a fraction of the element concentration, which is the RSD, defined above as the ratio of the test results standard deviation (s) in ppm over the mean ($\overline{X}$) in ppm × 100%. Although the RSDs for Procedure C are based on only three replicates obtained from one laboratory, this can nonetheless provide information on the within-laboratory precision of the method.

The mean repeatability (within-laboratory) relative standard deviations for Procedures A, B, and C are summarized and compared in

Table 4. Mean repeatability RSD for all RRIS materials and elements (%).

	Sc	Y	La	Ce	Pr	Nd	Sm	Eu	Gd	Tb	Dy	Ho	Er	Tm	Tb	Lu	Mean—All Elements
Material A	2.0	1.7	2.1	1.7	1.7	2.1	2.1	1.3	1.9	2.5	2.0	1.8	1.8	2.0	1.4	1.7	1.9
Material B	2.2	1.0	1.3	2.6	1.9	1.6	2.0	1.6	1.6	1.4	1.0	2.0	1.7	3.2	0.9	1.1	1.7
Material C	3.3	2.6	3.5	3.7	3.4	3.6	3.6	3.5	3.6	7.2	2.9	10.0	2.6	7.6	2.7	2.7	4.2
Material D	3.5	5.3	1.8	5.0	2.0	5.4	3.4	2.3	3.3	2.7	2.0	1.5	2.4	2.1	2.6	2.0	3.0
Material E	4.7	2.2	1.3	1.6	1.6	1.6	1.5	1.6	1.8	1.5	2.3	2.1	1.7	2.7	1.7	1.8	1.9
Material F	5.3	2.0	4.3	3.5	2.6	3.5	2.6	4.6	2.5	4.3	2.7	3.6	2.7	3.5	2.4	3.5	3.4
Material G	1.7	1.6	2.2	1.3	1.4	2.0	1.7	1.3	1.7	2.2	2.3	2.4	2.0	1.6	1.5	1.8	1.8
Material H	2.6	4.6	7.6	4.0	2.2	5.0	2.1	2.1	2.8	2.4	2.6	2.6	2.2	2.6	2.7	3.2	3.2
Material I	1.8	2.7	2.4	3.9	2.0	2.5	2.8	2.5	3.0	2.5	2.9	4.5	2.7	3.4	1.7	3.1	2.8
Material J	2.2	3.9	3.3	3.1	2.3	2.1	1.7	1.6	1.7	2.0	1.6	4.2	2.1	1.6	1.5	1.6	2.3
Material K	2.2	5.0	3.3	4.9	2.8	3.1	3.1	4.0	3.5	5.3	4.2	6.4	2.6	7.6	3.6	5.2	4.2
Mean—All Materials	2.9	3.0	3.0	3.2	2.2	3.0	2.4	2.4	2.5	3.1	2.4	3.7	2.2	3.4	2.1	2.5
	Sc	Y	La	Ce	Pr	Nd	Sm	Eu	Gd	Tb	Dy	Ho	Er	Tm	Tb	Lu	Mean—All Elements
Material A	5.0	4.3	3.9	3.4	3.8	3.8	4.3	4.4	3.0	3.9	3.2	3.4	3.9	3.1	3.2	3.6	3.8
Material B	11.8	3.6	1.9	2.0	0.9	6.2	2.3	4.0	2.9	3.6	2.5	4.4	3.1	7.6	3.8	5.8	4.1
Material C	7.0	3.4	3.6	3.3	3.4	5.8	3.6	4.3	3.3	3.6	3.6	3.1	3.7	3.3	3.5	4.7	3.9
Material D	4.0	3.7	3.0	3.0	3.0	4.1	3.3	3.2	3.5	3.6	3.0	3.4	3.4	3.2	3.0	3.8	3.4
Material E	2.2	1.7	1.5	1.5	1.6	2.6	2.0	2.6	2.2	3.2	2.2	2.4	2.1	3.0	2.8	2.6	2.3
Material F	3.8	2.1	1.6	1.3	1.7	1.8	1.9	6.6	2.0	1.8	1.9	2.6	1.6	4.1	2.7	3.9	2.6
Material G	4.8	3.5	2.0	1.8	1.7	5.0	2.9	3.4	3.3	5.1	2.5	3.7	3.3	3.1	3.5	2.7	3.3
Material H	4.3	2.5	2.2	2.2	2.2	1.4	1.6	3.2	2.2	2.7	2.7	2.7	2.3	2.1	1.5	2.2	2.4
Material I	2.5	2.3	1.8	2.0	2.1	3.0	2.2	2.3	2.1	2.3	2.8	3.7	2.4	5.0	3.2	4.1	2.8
Material J	21.5	3.9	4.6	4.8	4.8	4.5	7.5	13.5	6.5	15.9	6.0	14.8	9.5	18.8	8.3	22.9	10.5
Material K	4.6	3.3	2.4	2.3	2.2	10.5	2.2	3.2	3.0	6.5	2.7	4.5	3.7	4.4	1.0	4.7	3.8
Mean—All Materials	6.5	3.1	2.6	2.5	2.5	4.4	3.1	4.6	3.1	4.7	3.0	4.4	3.6	5.2	3.3	5.5
	Sc	Y	La	Ce	Pr	Nd	Sm	Eu	Gd	Tb	Dy	Ho	Er	Tm	Tb	Lu	Mean—All Elements
Material A	30.9	19.0	24.3	17.2	25.6	20.7	24.5	24.4	23.0	23.4	23.7	23.9	23.5	22.6	20.6	25.1	23.3
Material B	47.3	37.8	26.2	22.9	24.9	22.8	21.1	20.4	17.3	18.4	17.3	17.4	17.1	16.3	16.3	21.7	22.8
Material C	23.3	4.5	20.7	20.4	22.4	38.1	22.5	15.8	17.6	17.3	15.1	13.6	11.8	12.3	10.1	14.1	17.5
Material D	40.6	10.6	5.9	6.9	7.4	7.6	7.5	7.5	10.8	13.1	8.5	11.9	11.8	7.2	6.6	12.4	11.0
Material E	26.5	12.1	10.6	4.7	8.9	8.0	6.4	7.8	2.7	4.1	2.9	2.3	2.0	2.3	4.3	5.2	6.9
Material F	29.5	20.4	16.4	13.4	17.9	16.9	15.7	14.0	11.2	13.2	11.9	11.4	10.8	10.9	12.2	14.7	15.0
Material G	53.2	32.5	24.9	23.1	27.1	25.3	23.9	24.8	17.1	17.6	15.2	14.7	14.5	14.7	15.5	19.9	22.7
Material H	27.6	30.6	7.7	9.4	11.0	7.6	15.2	16.8	22.3	20.1	23.0	24.1	25.9	27.3	28.6	23.5	20.1
Material I	23.8	16.7	13.8	10.5	13.0	12.0	11.3	10.3	7.9	9.4	7.9	7.7	7.2	6.8	7.5	11.1	11.1
Material J	47.3	39.1	29.6	31.0	29.0	28.3	26.4	25.8	20.7	22.4	21.1	20.7	19.9	19.0	18.3	24.1	26.4
Material K	24.1	19.5	25.2	23.7	24.6	25.4	23.0	22.1	19.9	22.0	21.9	22.5	22.2	22.6	76.6	27.1	26.4
Mean—All Materials	34.0	22.1	18.7	16.7	19.3	19.3	17.9	17.3	15.5	16.5	15.3	15.5	15.2	14.7	19.7	18.1

and Figure 1 and Figure 2.

The repeatability RSD results show that Procedures A and B well outperformed Procedure C, with Procedure A slightly better than Procedure B. The overall mean RSDs by material and by element were all less than 5% for Procedure A and in all but two values (scandium at 6.5% and Material J at 10.5%) for Procedure B. All mean RSDs calculated for Procedure C exceeded 5%, ranging from 6.9% to 34%. AOAC International reproducibility guidelines range from 15% for analyte concentrations near 100 ppb to 5% for analyte concentrations near 100 ppm [13].

The mean reproducibility (between-laboratory) RSDs for Procedures A and B are summarized and compared in

Table 5. Mean reproducibility RSD for all RRIS materials and elements (%).

	Procedure A
	Sc	Y	La	Ce	Pr	Nd	Sm	Eu	Gd	Tb	Dy	Ho	Er	Tm	Yb	Lu	Mean—All Elements
Material A	12.1	10.0	8.0	7.0	8.2	5.7	6.3	11.4	15.1	17.9	11.4	11.0	8.9	7.8	7.2	17.4	10.3
Material B	42.8	18.8	11.9	32.7	9.1	7.7	30.1	28.6	56.7	13.7	10.2	13.0	10.3	22.3	12.9	15.5	21.0
Material C	12.0	13.6	16.0	15.3	15.9	17.0	13.2	14.4	18.9	13.2	12.8	9.4	10.8	22.9	12.4	8.9	14.2
Material D	14.5	13.8	7.5	10.2	8.1	9.1	8.0	9.6	11.8	12.5	6.5	6.2	8.2	22.4	9.1	9.7	10.4
Material E	65.8	14.3	26.8	28.7	25.3	27.0	34.3	33.6	60.6	26.0	24.3	25.9	25.7	26.8	7.8	33.2	30.4
Material F	27.0	14.6	10.3	8.6	14.9	8.4	8.1	28.2	22.3	27.2	12.2	17.3	13.1	11.9	12.0	26.9	16.4
Material G	33.0	34.3	30.5	27.3	29.9	29.1	30.7	7.5	35.8	19.5	23.5	20.9	30.5	24.9	18.7	52.4	28.0
Material H	11.1	16.8	13.7	9.4	9.4	12.3	10.7	11.2	13.2	11.9	9.8	20.0	10.3	18.8	10.2	51.5	15.0
Material I	10.9	14.1	8.3	16.2	7.0	7.1	6.7	8.8	18.1	13.9	9.0	22.4	11.3	10.7	9.1	55.5	14.3
Material J	10.9	15.8	10.8	8.4	6.2	4.6	15.2	5.3	15.3	23.0	6.6	6.4	5.4	17.9	7.5	86.0	15.3
Material K	22.2	28.2	17.9	20.5	26.3	19.1	41.8	20.2	47.8	77.7	74.4	31.0	78.2	30.6	53.5	169.8	47.4
Mean—All Materials	23.8	17.6	14.7	16.8	14.6	13.4	18.6	16.3	28.7	23.3	18.2	16.7	19.3	19.7	14.6	47.9
	Procedure B
	Sc	Y	La	Ce	Pr	Nd	Sm	Eu	Gd	Tb	Dy	Ho	Er	Tm	Yb	Lu	Mean—All Elements
Material A	54.1	34.1	31.7	9.6	38.0	59.1	10.1	9.8	34.8	9.9	10.8	45.0	12.3	45.9	11.7	10.2	26.7
Material B	71.3	22.1	27.0	28.5	11.8	35.4	7.0	34.3	39.3	39.7	42.6	48.6	47.2	48.3	40.1	20.3	35.2
Material C	40.5	21.1	28.3	27.7	34.0	8.4	40.5	37.3	35.8	43.3	42.3	47.5	11.7	49.3	45.6	6.4	32.5
Material D	50.7	12.6	8.2	8.2	9.5	45.9	13.4	14.0	8.6	16.0	16.5	19.4	19.1	20.6	19.5	21.7	19.0
Material E	72.4	11.8	8.0	7.5	9.8	45.7	12.2	14.5	9.2	17.2	18.2	20.0	19.6	20.5	18.6	21.1	20.4
Material F	34.2	13.3	11.0	10.6	12.0	11.0	15.4	19.3	8.0	23.0	19.0	19.9	20.5	21.5	22.6	24.7	17.9
Material G	72.6	16.9	12.6	11.1	11.2	50.6	14.4	15.7	7.4	23.2	14.4	16.6	16.8	16.4	16.2	15.4	20.7
Material H	50.7	11.1	10.7	10.3	13.1	43.5	17.8	17.7	13.1	21.1	21.4	23.3	22.0	23.3	22.3	26.1	21.7
Material I	66.7	12.1	9.3	7.9	9.6	8.5	14.2	14.2	9.4	15.5	17.6	19.4	18.4	20.4	16.7	22.1	17.6
Material J	55.8	33.1	26.5	27.0	19.9	23.5	19.1	27.5	15.7	43.4	16.4	36.1	17.6	87.6	16.2	7.6	29.6
Material K	84.0	12.6	9.6	8.0	10.2	10.0	14.6	14.9	9.8	18.2	19.4	22.0	19.2	26.8	20.4	24.8	20.3
Mean—All Materials	59.4	18.3	16.6	14.2	16.3	31.1	16.2	19.9	17.4	24.6	21.7	28.9	20.4	34.6	22.7	18.2

and Figure 3 and Figure 4. As with the S_r and S_R results, these results show that the between-laboratory RSDs are much higher than the within-laboratory RSDs. The mean between-laboratory RSDs all exceeded 13%, with the highest mean value being 59% for scandium for Procedure B. AOAC International reproducibility guidelines range from 22% for analyte concentrations near 100 ppb to 8% for analyte concentrations near 100 ppm [13].

3.2. SRM Recovery

Four SRMs, described in Table 2, were included in the study to help determine the overall accuracy and bias of the methods based on the recovery of the analyte from the matrix. The recovery was calculated by taking the average mean values ($\overline{X}$) reported by the labs for each of the elements and dividing by the reference value reported in the SRM certificates multiplied by 100%. The results are presented in

Table 6. REE recovery from SRMs (%).

Material H										Material I
NIST 1633c Fly Ash										USGS SBC-1 Bush Creek Shale
		NAA		Procedure A		Procedure B		Procedure C				NAA		Procedure A		Procedure B		Procedure C
Element	Reference Value	$\overline{\mathit{X}}$, µg/g	Recovery, %	$\overline{\mathit{X}}$, µg/g	Recovery, %	$\overline{\mathit{X}}$, µg/g	Recovery, %	$\overline{\mathit{X}}$, µg/g	Recovery, %	Element	Reference Value	$\overline{\mathit{X}}$, µg/g	Recovery, %	$\overline{\mathit{X}}$, µg/g	Recovery, %	$\overline{\mathit{X}}$, µg/g	Recovery, %	$\overline{\mathit{X}}$, µg/g	Recovery, %
Sc	37.6 ± 0.6	36.5	97%	40.7	108%	44.4	118%	32.8	87%	Sc	20 ± 0.2	20.2	101%	24.4	122%	26.8	134%	34.2	171%
Y	NA 1	NR 2	NR	89.6	NA	102	NA	107.8	NA	Y	36.5 ± 0.3	NR	NR	25.3	69%	33.2	91%	45.7	125%
La	87.0 ± 2.6	82.6	95%	72.5	83%	79.6	91%	71.7	82%	La	52.5 ± 0.6	52.2	99%	44.0	84%	49.4	94%	57.1	109%
Ce	180	186	103%	181	101%	177	98%	172	96%	Ce	108 ± 0.9	110	102%	93.9	87%	104	96%	120	111%
Pr	NA	NR	NR	19.0	NA	21.9	NA	17.9	NA	Pr	12.6 ± 0.1	NR	NR	11.0	87%	12.4	98%	13.5	108%
Nd	87	88	101%	81	93%	80	92%	78	90%	Nd	49.2 ± 0.5	47.5	96%	42.4	86%	42.0	85%	52.7	107%
Sm	19	21	109%	18	93%	21	109%	15	79%	Sm	9.6 ± 0.1	10.3	107%	8.7	90%	9.9	103%	9.8	102%
Eu	4.67 ± 0.07	4.43	95%	3.86	83%	4.62	99%	3.20	69%	Eu	1.98 ± 0.02	1.94	98%	1.97	99%	2.00	101%	1.90	96%
Gd	NA	NR	NR	17.5	NA	21.6	NA	15.2	NA	Gd	8.5 ± 0.1	NR	NR	7.1	84%	8.7	103%	8.1	95%
Tb	3.12 ± 0.06	3.21	103%	2.71	87%	3.24	104%	2.26	72%	Tb	1.2 ± 0.02	1.2	102%	1.2	102%	1.3	105%	1.1	95%
Dy	18.70 ± 0.30	17.93	96%	15.83	85%	19.61	105%	13.26	71%	Dy	7.1 ± 0.09	6.6	93%	5.7	80%	7.3	103%	6.4	90%
Ho	NA	NR	NR	2.92	NA	3.88	NA	2.61	NA	Ho	1.4 ± 0.02	NR	NR	0.96	68%	1.4	100%	1.2	88%
Er	NA	NR	NR	8.66	NA	10.9	NA	7.40	NA	Er	3.8 ± 0.05	NR	NR	3.1	81%	4.1	108%	3.6	94%
Tm	NA	NR	NR	1.26	NA	1.48	NA	0.90	NA	Tm	0.56 ± 0.01	NR	NR	0.44	78%	0.58	103%	0.50	89%
Yb	7.7	8.6	111%	7.4	97%	9.3	121%	5.5	71%	Yb	3.6 ± 0.04	3.6	100%	2.9	80%	3.8	106%	3.2	88%
Lu	1.32 ± 0.03	1.25	94%	1.55	117%	1.42	107%	0.81	62%	Lu	0.54 ± 0.01	0.55	101%	0.63	117%	0.58	108%	0.47	86%
Min			94%		83%		91%		62%	Min			93%		68%		85%		86%
Max			111%		117%		121%		96%	Max			107%		122%		134%		171%
Average			100%		95%		104%		78%	Average			100%		88%		102%		103%
Material J										Material K
NIST 1632e Coal										NIST 2780a Mine Waste
		NAA		Procedure A		Procedure B		Procedure C				NAA		Procedure A		Procedure B		Procedure C
Element	Reference Value	$\overline{\mathit{X}}$, µg/g	Recovery, %	$\overline{\mathit{X}}$, µg/g	Recovery, %	$\overline{\mathit{X}}$, µg/g	Recovery, %	$\overline{\mathit{X}}$, µg/g	Recovery, %	Element	Reference Value	$\overline{\mathit{X}}$, µg/g	Recovery, %	$\overline{\mathit{X}}$, µg/g	Recovery, %	$\overline{\mathit{X}}$, µg/g	Recovery, %	$\overline{\mathit{X}}$, µg/g	Recovery, %
Sc	3.583 ± 0.088	3.302	92%	3.513	98%	3.669	102%	5.354	149%	Sc	15.6	16.1	103%	19.5	125%	24.8	159%	28.1	180%
Y	6	NR	NR	4.7	78%	5.4	90%	7.9	131%	Y	18	NR	NR	5.51	31%	17.0	94%	18.7	104%
La	7	6.1	87%	5.0	72%	5.2	75%	6.0	86%	La	34.4	35.5	103%	26.0	76%	34.4	100%	27.7	80%
Ce	12.24 ± 0.27	12.38	101%	11.17	91%	10.46	85%	12.42	101%	Ce	67.7	68.7	102%	50.3	74%	65.2	96%	52.7	78%
Pr	1.5	NR	NR	1.2	83%	1.3	84%	1.37	92%	Pr	8	NR	NR	5.82	73%	7.53	94%	5.8	72%
Nd	6	5.6	93%	4.9	82%	4.1	69%	5.3	89%	Nd	28.3	28.6	101%	20.9	74%	23.9	85%	20.7	73%
Sm	1	1.2	118%	1.0	104%	1.0	102%	1.0	100%	Sm	4.7	4.9	105%	3.8	80%	4.7	100%	3.1	67%
Eu	0.2457 ± 0.0063	0.2428	99%	0.2142	87%	0.2483	101%	0.2086	85%	Eu	0.9	0.86	95%	0.64	72%	0.91	101%	0.6	61%
Gd	1	NR	NR	1.0	95%	1.1	107%	0.9	91%	Gd	3.2	NR	NR	2.15	67%	3.44	107%	1.9	61%
Tb	0.2	0.2	82%	0.2	79%	0.2	94%	0.1	68%	Tb	0.5	0.45	89%	0.36	71%	0.50	99%	0.3	51%
Dy	1	1.0	103%	0.9	89%	1.0	100%	0.8	83%	Dy	3.1	2.9	95%	1.6	53%	3.2	102%	1.5	49%
Ho	0.2	NR	NR	0.2	101%	0.2	114%	0.2	84%	Ho	0.7	NR	NR	0.24	34%	0.68	98%	0.3	46%
Er	0.7	NR	NR	0.5	73%	0.6	89%	0.5	71%	Er	2.0	NR	NR	0.90	45%	2.2	108%	1.0	52%
Tm	0.1	NR	NR	0.1	78%	0.1	118%	0.1	68%	Tm	0.31	NR	NR	0.10	32%	0.33	106%	0.2	50%
Yb	0.6	0.541	90%	0.5	81%	0.6	92%	0.4	72%	Yb	2	2.0	99%	0.83	41%	2.2	109%	1.9	94%
Lu	0.1	0.085	85%	0.1	123%	0.1	114%	0.1	65%	Lu	0.33	0.45	135%	0.43	131%	0.37	114%	0.17	52%
Min			82%		72%		69%		65%	Min			89%		31%		85%		46%
Max			118%		123%		118%		149%	Max			135%		131%		159%		180%
Average			95%		88%		96%		90%	Average			103%		67%		104%		73%

¹ Not available. ² Not reported.

. In terms of average recoveries, all methods showed acceptable recoveries (±15%) for all four SRMs, with the exception of Procedure C for Material H (78%) and Procedures A and C for Material K (67% and 73%, respectively). Although the average recoveries were reasonable, the ranges (max. and min.) for several of the procedures were large. The largest variation for all procedures was observed with Material K (46%–180%). AOAC International recovery guidelines range from 80% to 110% for analyte concentrations ranging from 100 ppb to 10 ppm and 90%–107% for analyte concentrations near 100 ppm [13].

3.3. Comparison of Methods with NAA

The results reported by the NAA reference method were compared to the data generated from the three procedures (A, B, and C). For various reasons, which include low gamma ray energies, long decay time, low sensitivity to neutrons, and no stable isotopes produced, NAA is only able to quantitatively measure ten of the sixteen REEs. These ten elements are Sc, La, Ce, Nd, Sm, Eu, Tb, Dy, Yb, and Lu.

Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14 show the mean concentrations and standard deviations obtained from the four procedures for each of the eleven materials. The standard deviations were calculated from the following number of observations (i.e., test results): NAA (n = 3), Procedure A (n = 21), Procedure B (n = 15), and Procedure C (n = 3). Each element is presented in a separate figure.

Table 7. Calculated difference from NAA reference method (%); shaded cells indicate results within ±15% of the reference method.

Material	Sc	La	Ce	Nd	Sm	Eu	Tb	Dy	Yb	Lu
A	4.5%	−5.7%	−5.6%	0.3%	−8.7%	−0.8%	−7.8%	−5.9%	−6.0%	−13.9%
B	52.3%	−4.1%	−18.3%	3.0%	−14.1%	13.4%	−25.9%	0.8%	−17.4%	−5.9%
C	6.8%	−6.1%	−6.7%	−11.1%	−10.6%	−5.9%	−5.3%	−6.8%	−11.1%	−8.0%
D	2.6%	−1.7%	−2.7%	1.0%	−7.4%	−1.6%	−11.7%	−0.9%	−7.0%	−11.8%
E	40.4%	−12.3%	−5.5%	−6.8%	−17.4%	9.2%	−4.9%	−3.9%	12.0%	5.5%
F	35.1%	−5.7%	−5.2%	−6.9%	−16.9%	−7.2%	−11.2%	−7.3%	−8.7%	−35.0%
G	−6.1%	−6.7%	−0.9%	−6.6%	−14.3%	−3.0%	−39.8%	−39.6%	5.8%	−15.1%
H	5.7%	−0.6%	2.9%	4.3%	−0.5%	0.7%	−2.6%	2.1%	0.4%	24.3%
I	9.1%	−1.9%	−5.8%	3.9%	−1.8%	1.3%	−0.6%	0.2%	−6.9%	16.0%
J	6.4%	−6.7%	−3.9%	−1.0%	0.6%	1.4%	10.8%	−1.6%	2.9%	44.8%
K	−8.5%	−17.5%	−22.5%	−18.5%	−14.4%	−17.3%	−9.1%	−37.5%	−52.0%	−3.4%
Material	Sc	La	Ce	Nd	Sm	Eu	Tb	Dy	Yb	Lu
A	41.1%	−4.8%	−7.3%	5.4%	−11.5%	−1.3%	−2.8%	−2.1%	−2.6%	−15.5%
B	70.7%	13.6%	−2.5%	30.5%	−0.3%	26.2%	−10.4%	9.9%	17.0%	19.3%
C	21.8%	8.1%	8.3%	−4.2%	10.9%	14.6%	18.4%	18.8%	−8.5%	−1.2%
D	18.3%	−5.8%	−7.6%	−11.9%	−5.5%	2.4%	−3.3%	6.3%	4.6%	3.7%
E	48.0%	−1.9%	−2.1%	−8.2%	2.1%	13.5%	4.8%	10.0%	21.4%	19.7%
F	17.1%	−5.6%	−8.3%	−2.5%	−15.1%	3.6%	−1.3%	2.8%	3.6%	−31.5%
G	36.6%	−7.9%	−9.0%	−11.5%	−7.3%	−0.1%	−13.8%	−2.4%	−5.2%	6.5%
H	21.7%	−3.7%	−5.0%	−8.1%	0.1%	4.2%	1.1%	9.4%	8.5%	13.6%
I	32.9%	−5.4%	−6.1%	7.9%	−4.0%	2.6%	2.4%	11.1%	5.6%	7.0%
J	11.1%	−14.2%	−15.5%	−11.2%	−13.7%	2.2%	14.5%	−3.8%	2.2%	−0.5%
K	53.9%	−3.1%	−5.2%	3.8%	−4.5%	5.6%	11.1%	7.5%	9.9%	−16.1%
Material	Sc	La	Ce	Nd	Sm	Eu	Tb	Dy	Yb	Lu
A	32.1%	10.2%	7.9%	3.6%	−10.7%	−4.4%	−3.6%	−3.4%	−8.9%	−24.8%
B	77.7%	−0.2%	−0.5%	−0.8%	−9.1%	−6.3%	−34.6%	−6.7%	−21.8%	−13.1%
C	−22.7%	1.1%	6.1%	−14.9%	−5.4%	−6.9%	−8.3%	−9.0%	−20.8%	−22.8%
D	−24.9%	2.8%	2.0%	6.5%	−11.2%	−8.5%	−16.6%	−6.2%	−21.1%	−27.6%
E	171.1%	−0.2%	6.9%	−4.7%	−18.3%	−12.7%	−26.9%	−25.6%	−24.8%	−27.8%
F	38.9%	0.1%	−8.8%	−6.6%	−21.2%	0.9%	−11.6%	−11.6%	−15.0%	−48.6%
G	24.5%	23.4%	23.0%	29.9%	4.0%	4.3%	−26.2%	−23.5%	−21.7%	−14.9%
H	−10.1%	−13.2%	−7.5%	−10.5%	−27.5%	−27.8%	−29.6%	−26.0%	−36.2%	−34.8%
I	69.3%	9.4%	8.4%	11.0%	−4.9%	−2.4%	−7.5%	−2.5%	−12.5%	−14.4%
J	62.1%	−1.2%	0.4%	−4.9%	−15.2%	−14.1%	−16.9%	−19.6%	−20.6%	−23.8%
K	74.3%	−22.1%	−23.3%	−27.5%	−36.3%	−35.9%	−43.1%	−48.7%	−5.0%	−61.7%

shows the calculated percent difference of each of the Procedures A, B, and C from the reference method NAA. The difference was calculated by subtracting the mean value of all observations obtained by each procedure from the mean value obtained by NAA divided by the mean value of NAA multiplied by 100%. A positive value shows that the mean value resulting from that procedure was higher than that of NAA, while a negative value shows that the value was lower. Values that agree within ±15% of the reference method are highlighted.

These results show that Procedures A and B performed significantly better than Procedure C in terms of overall agreement with NAA. Of the 110 results (10 elements × 11 materials), Procedures A and B met the ±15% limit for 100 (83%) and 98 (81%) results, respectively. Procedure C performed the worst, meeting the limit for only 50 (41%) results. Scandium and lutetium were observed to have relatively high RSDs of over 60% for either Procedure A or B with respect to reproducibility of the measured quantities, whereas the RSDs for the reproducibility of the other eight REEs were less than 35%. The high RSD of these methods for lutetium can be explained by the low concentrations found in all of the materials, which impact the effectiveness of lutetium recovery, instrument detection, and quantification accuracy. Lutetium quantification values ranged from 0.04 to 1.8 μg/g. On the other hand, scandium levels were much higher, ranging from 1.2 to 61.8 μg/g, which should rule out detection limit problems.

The materials that showed the greatest RSDs for reproducibility appear to be Material B (bituminous coal) and Material K (mine waste material), with RSD values > 35% for one or the other of Procedures A and B. Several other materials were close to 30% RSD with respect to reproducibility. Again, the higher RSD of Material B could be explained by the low concentrations of all elements found in that material. Although Material K had much higher concentrations of REEs, that particular matrix was possibly more challenging to analyze for the three methods.

3.4. Total Rare Earth Elements

The mean values reported by each of the laboratories, including all procedures except NAA, were totaled and the frequency distributions by material were calculated. The TREE results are summarized in

Table 8. TREE * data distribution by material.

	Material A	Material B	Material C	Material D	Material E	Material F	Material G	Material H	Material I	Material J	Material K
	244	14.7	97.5	650	170	251	147	533	291	38.0	104
	238	19.9	118	638	398	264	143	575	280	42.5	171
	131	17.2	40.3	206	436	83.0	165	673	346	39.2	150
	287	17.8	147	776	381	321	151	629	317	39.8	153
	266	18.5	123	713	381	290	156	633	325	38.2	165
	259	29.9	137	706	379	299	190	610	308	42.7	192
	260	20.6	133	709	415	287	150	547	359	20.9	182
	280	17.3	130	690	398	286	164	665	316	39.1	185
	481	17.8	225	689	371	306	138	599	309	33.5	197
	261	18.2	133	671	335	310	160	493	267	40.6	200
	227		105	602	398	275	174	619	328	42.1
	276		133	722	394	292		629
	272		136	733
n	13	10	13	13	12	12	11	12	11	11	10
Min.	131	14.7	40.3	206	170	83.0	138	493	267	20.9	104
Max.	481	29.9	225	776	436	321	190	673	359	42.7	200
Median	261	18	133	690	388	289	156	615	316	39.2	177
Mean	268	19.2	128	654	371	272	158	600	313	37.9	170
No. of Outliers	2	1	2	1	3	1	0	0	0	1	0

* TREE reported in µg/g (ppm), dry whole sample basis.

and plotted in Figure 15 and Figure 16. The plots are split between TREEs < 300 ppm and TREEs > 300 ppm. Although the TREE mean value of Material F was slightly less than 300 ppm, it is grouped with the materials greater than 300 ppm because several of the values used to calculate the mean exceeded 300 ppm. The × within the box indicates the mean value, the horizontal bar within the box is the median value, the lower and upper horizontal bars outside the box are the min. and max. values, respectively, and the circles outside the box are outliers. The laboratory that was excluded from the reproducibility and repeatability calculations is included here in order to provide an overall look at all the data reported in the study.

These data show that the reported TREE results for several of the materials analyzed varied significantly, as can be seen from the large range between the minimum and maximum values. Of particular interest are Materials F and I, where the mean values are close to 300 ppm (272 and 313, respectively); in both cases, the minimum values were much less than 300 ppm and the maximum values were much higher. This is a significant difference when qualifying resources based solely on a >300 ppm TREE content.

4. Summary and Conclusions

Thirteen laboratories participated in an RRIS focused on analyzing REEs, a first-of-its-kind study in the United States. Analysis of REEs from eleven different materials was accomplished by the laboratories using four different procedures. The results of the RRIS suggest that NAA is the most accurate and reliable method for many of the REEs in these types of materials; however, the method is limited to determining only ten of the sixteen REEs, and is not commonly available in most laboratories. Of the other three methods in the study, Procedure A (D6357) and Procedure B (D4503) both had acceptable repeatability (within-lab) performance as well as relatively good agreement with NAA. Procedure C showed the poorest performance in these categories. The reproducibility (between-lab) results indicated a high level of variability among the labs for Procedures A and B. Scandium and lutetium were observed to have relatively high RSDs of over 60% for either Procedure A or B with respect to reproducibility of the measured quantities, whereas the RSDs for the other fourteen elements were less than 35%. The materials that showed the greatest RSDs with respect to quantification reproducibility of REEs were Material B (bituminous coal) and Material K (mine waste material), the only materials having RSD >35% for Procedures A or B. The data showed that some of the reported TREE results varied significantly based on the large range between the minimum and maximum values. Of particular interest were two materials where the mean values were close to 300 ppm (272 and 313 ppm, respectively), which is a significant difference when qualifying resources based solely on a >300 ppm TREE content.

Although the overall between-laboratory variability was relatively higher than the within-laboratory RSDs, exceeding 13%, it is worth noting that five of the seven labs reporting data for Procedure A and three of the five labs reporting for Procedure B showed excellent performance in terms of repeatability, reproducibility, agreement with NAA, and SRM recoveries as based on AOAC international guidelines on method performance. This indicates that if strictly followed these methods are suitable for REE determination in most materials, although are subject to the overall capabilities and experience of the individual laboratories.

As of the start of this study, the ASTM D4503 method had been withdrawn as an ASTM-supported procedure in 2012. However, subsequent to this study ASTM has added this as an alternative preparation and analysis method to ASTM D6357.

In addition, the National Institute for Standards and Technology (NIST) provided four reference materials for this study which did not have certified values for many of the REEs, with the intent of using the study results after statistical review by NIST to upgrade its certificates with more certified values. This provides NIST with more CRM to provide to the public.