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Journal of Radioanalytical and
Nuclear Chemistry
An International Journal Dealing with
All Aspects and Applications of Nuclear
Chemistry
ISSN 0236-5731
J Radioanal Nucl Chem
DOI 10.1007/s10967-016-4903-5
Rare earths analysis of rock samples by
instrumental neutron activation analysis,
internal standard method
I.Silachyov
1 23
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Rare earths analysis of rock samples by instrumental neutron
activation analysis, internal standard method
I. Silachyov
1
Received: 12 January 2016
ÓAkade
´miai Kiado
´, Budapest, Hungary 2016
Abstract The application of instrumental neutron activa-
tion analysis for the determination of long-lived rare earth
elements (REE) in rock samples is considered in this work.
Two different methods are statistically compared: the well
established external standard method carried out using
standard reference materials, and the internal standard
method (ISM), using Fe, determined through X-ray fluo-
rescence analysis, as an element-comparator. The ISM
proved to be the more precise method for a wide range of
REE contents and can be recommended for routine
practice.
Keywords Neutron activation analysis Rare earths
Rock samples
Introduction
Mineral resources analysis for individual rare earth element
(REE) content is still a difficult task in the field of ele-
mental analysis which can only be solved by spectroscopic
(instrumental) methods. Recent reviews of spectroscopic
techniques revealed the most common methods being used
at present for geological sample analysis for REE content
are inductively coupled plasma atomic emission spec-
trometry and mass spectrometry (ICP-AES and ICP-MS),
X-ray fluorescence (XRF) analysis, and instrumental neu-
tron activation analysis (INAA) [1,2]. The basic restriction
of the first two methods is that only solutions can be
analyzed. Complete sample dissolution is required and this
may be a problem in the case of REE determination since,
like the other lithophilic elements, they are associated with
silicate rocks. The main disadvantages of ICP-AES are the
poor sensitivity of REE analysis, a substantial matrix
effect, the intricacy of the REE individual spectra and
spectral interferences. To avoid most of these disadvan-
tages, efficient pre-concentration and separation procedures
need to be employed [3,4]. The ICP-MS method is much
more appropriate for REE analysis, but it is also subject to
spectral interferences including difficult to correct for
polyatomic ions which the lanthanides usually form in
plasma. The typically low content of REEs in rock means
careful sample preparation is essential to avoid analyte loss
and/or solution contamination, making the entire procedure
a crucial part of the analysis [5,6]. As a result, the ICP-MS
technique becomes the most expensive one for REE
determination [1].
Unlike ICP-AES and ICP-MS, XRF is commonly used
for nondestructive analysis, however in the case of REE
measurement it suffers from insufficient sensitivity both in
the energy dispersive (isotope excitation of K-series [7])
and the wave dispersive (X-ray tube excitation of L-series
[8]) variants. Only some light lanthanides (La, Ce, Pr and
Nd) can be analyzed by XRF due to their higher average
crustal contents. To determine heavier lanthanide content, a
time- and reagent-consuming procedure of sample
decomposition followed by chemical separation from the
major matrix elements and concentration on a target should
be applied [9]. Spectral interferences and a substantial
matrix effect present a serious problem in XRF, so high
resolution spectrometers and sophisticated algorithms must
be used, increasing the complexity of the whole analysis.
In contrast to XRF, neutron activation analysis is
‘‘physically fully described and understood’’, and that is
&I. Silachyov
silachyov@inp.kz
1
Institute of Nuclear Physics, Ibragimov str.1, Almaty,
Republic of Kazakhstan 050032
123
J Radioanal Nucl Chem
DOI 10.1007/s10967-016-4903-5
Author's personal copy
considered its main strength [10]. Compared to the other
methods, rock analysis for REE content is where INAA
shows its best advantages. The most important of these
advantages are nondestructive sample treatment and hence
a virtual absence of analytical blank, high sensitivity
making possible all REE measurements at levels much
lower than average crustal contents, relative freedom from
the matrix effect and few spectral interferences (mainly
caused by the U fission products) [11]. Repeated compar-
ison of the precision of INAA and ICP-MS methods with
the help of geological reference materials showed the for-
mer to give, in general, better results, especially for the
middle and heavy REEs [12,13]. INAA is characterized by
a relatively low price for REE determination [1] due to the
wide-spread accessibility of research reactors around the
world. All these advantages promote the broad application
of INAA to geological sample analysis for major and trace
elements [14], noble metals [15], and REE [16–22] content.
Some approaches to the methods classification must be
mentioned. Both the relative and the non-relative (direct)
methods of concentration standardization are used in INAA
[11]. The latter comprises the absolute and the single
comparator methods (SCM). General definitions of the
relative and direct methods are cited by Greenberg [23]. If
one (the SCM) or more (the relative method) comparator
elements are separated from an analyzed sample, then both
methods use ‘‘the external standard method’’ of calibration
(external standardization) which is most often applied in
analytical chemistry. ‘‘The internal standard method’’
(ISM) is mainly used for liquid sample analysis and is
based on the known content of a comparator element in
every sample. A physical method must allow the calcula-
tion of other analyzed elements, and INAA is one such
method. In this case, internal standardization is an addi-
tional way of calibration in the SCM, but it cannot be
applied with the relative method. The interrelation between
INAA methods varying with concentration standardization
and the method of calibration is presented in Fig. 1. Grey
capsules denote reference material samples and the black
capsule denotes a single element comparator.
Methodologically rather simple and hence widely used,
relative INAA needs the rock reference materials certified
for REE content (CRMs)
1
in order to be used both as
calibration standards and for implementation of the ana-
lytical quality control procedures. The main disadvantages
of the relative method are additional time consumption,
considerable cost and limited choice of high-quality CRMs
with the uncertainties associated to REE not exceeding
8–10 % (e.g. by the Institute for Reference Materials and
Measurements (IRMM), Belgium). More accessible CRMs
do not guarantee adequate precision (e.g. fixed in [24]) due
to high uncertainties of REE certified values. Gamma-ray
intensity corrections for spectral interferences and U fission
products must often be made for the CRMs too, since U, Th
and other high element contents compete with REEs.
Additional analytical uncertainty may arise from reference
material heterogeneity since the CRM subsamples taken
for irradiation are frequently less than ‘‘the minimum
sample intake’’ recommended by the certificate. Lastly,
analytical results depend on the CRM manufacturer and
can vary more than 10 % without any apparent reason.
The single comparator method, including k
0
-INAA,
removes the majority of the disadvantages of the relative
method resulting from the use of CRMs, since the CRMs
are only used for analytical quality control. The basic
drawback of the SCM is a consequence of the comparator
method itself. Since generally the comparator material and
the samples present different features, the latter should be
considered when applying some corrections. In separate
cases, the SCM can result in lower performance if com-
pared to the relative method due to the effect of thermal
and epithermal neutron self-shielding. The SCM method is
commonly characterized by a more sophisticated calcula-
tion since it needs several parameters to be applied
[25,26].
If the SCM uses the internal standard method (an
internal comparator) it eliminates its main drawback by
taking into account the effects of different geometries and
the neutron self-shielding in every sample. In addition, the
neutron flux gradient inside the irradiation container should
be considered: if a source of mostly thermal neutrons is
used for irradiation, then the values of epithermal to ther-
mal neutron flux ratio, 1/f, in every sample can also be
estimated. However 1/fis assumed not to vary within an
irradiation container at all, not even from day to day [25].
Hence, when similar samples are irradiated in the same
channel position, the 1/fvalue can be considered as a
constant and there is no need to correct for it. The mass
fraction of any element of interest can be found using the
known content of a single element comparator only.
External standard
method
Internal standard
method
Relative
method
Single
comparator
method
a
bc
Fig. 1 Interrelation between two ways of concentration standardiza-
tion (a,b) and two ways of calibration (b,c) in INAA
1
Include SRMs, ERMs or any other national trademarks of certified
reference materials.
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123
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There are different ways to determine the internal
comparator content of a sample. The standard k
0
-method
with Al–Au foil or wire as a flux monitor is applied most
often [27,28]. For better accuracy and for bulk or irregular
geometry sample analysis, the INAA relative method is
used [29–32]. The internal comparator content can be also
found by an independent method. Matrix or major elements
are usually selected to implement internal standardization:
Ca for compositional characterization of cement samples
[31], Fe to measure element contents of meteorites [29],
uranium ore [30] and high-purity aluminum-clad samples
[32], and Na for large dross sample analysis for Au and Ag
content [33]. Sometimes other elements can be used, such
as Sc for the elemental analysis of ancient pottery samples
[34], Rb to analyze plant leave samples [27], and La for
INAA ISM verification by means of Soil-7 CRM [28].
In this paper the precision of INAA for long-lived REE
using the relative method (Fig. 1a) and using the internal
standard method (Fig. 1c) with XRF as an independent ana-
lytical technique is compared for a wide range of REE content
in geological samples covering several orders of magnitude.
Theory
Any element content of the analyzed sample C
a
(%) by the
internal standard method can be calculated using the
equation of the single comparator method of standardiza-
tion [35,36] (lower case indices aand cmean an analyzed
element and the comparator, respectively):
Ca¼Cc
kcJaeðEcÞðfþQc
0ÞðSDCÞcGcFc
kaJceðEaÞðfþQa
0ÞðSDCÞaGaFa
Ka;c;ð1Þ
where C
c
is the element comparator content of the sample
(%), Jis the full-energy peak count rate of the corre-
sponding radionuclide analytical gamma-ray (cps), e(E)is
the relative detection efficiency of the analytical gamma-
ray (%), Q
0
is the resonance integral I
0
(cm
2
) to thermal
neutron cross-section r0(cm
2
) ratio, fis the thermal to
epithermal neutron flux ratio, Sand Dare, respectively,
saturation and decay factors, Cis the correction for mea-
surement time, Gis the correction factor for neutron self-
shielding by the sample, Fis the correction factor for
analytical gamma-ray self-absorption by the sample, and
the k-factor is composed of nuclear constant product:
k¼r0hPcM1
;ð2Þ
where his isotopic abundance (%), Pcis the yield of the
analytical gamma-line (%), Mis the atomic mass (Da). The
empirical correction factor K
a,c
compensates for a bias
which may be caused by the errors of the detector cali-
bration for relative detection efficiency.
In the case of the long-lived radionuclide analysis,
counting correction Cis always \1 % and can be neglec-
ted. Correction factor Gis very close to unity in most
samples and also can be ignored [36]. If the internal
comparator is determined by an independent technique,
INAA ISM may be used to analyze materials suffering
from thermal neutron self-shielding since it affects all the
elements in the sample to the same degree [27]. Even in the
case of REE high content analysis, self-shielding can be
usually kept to a negligible value (no more than 5 %) by
diminishing the sample mass. Correspondingly, the Ffac-
tor must be taken into account only in the case of large
sample analysis [37] or a heavy matrix [38], and can be
neglected when irradiating small samples with a common
Al–Si matrix.
To evaluate the 1/fratio in rock samples, the content of
at least two easily detectable elements with respectively a
low and high Q
0
value must be known. Considering Fe as
the element with a low Q
0
value, the second element could
be Rb, Sr, Ba, Cs, Th or U, depending on its content. The
values of 1/fcan be calculated solving the system of two
elements using Eq. (1). Then, keeping the ordinary con-
ditions of rock analysis such that the correction factors
mentioned above can be neglected, the epithermal to
thermal neutron flux ratio equals to ðQ0;1\\ Q0;2Þ:
1
f¼C2r0;2C1Br0;1
C1BI0;1C2I0;2
;ð3Þ
where
B¼J2eðE1ÞM2h1Pc;1ðSDÞ1
J1eðE2ÞM1h2Pc;2ðSDÞ2
lower indices in both Eq. 3are valid. This method is
effective where the neutron flux is not highly thermalized.
If the neutron flux is highly thermalized then the uncer-
tainty of the calculated value of 1/fwould be too high; in
this case the cadmium ratio method should be used.
Experimental
Following the approach above, it was decided to use
58
Fe
as the internal standard for the determination of REE in
geological samples. Iron was chosen as it is widely spread
in all rock types with high crustal abundance, and the
radionuclide
59
Fe is characterized by suitably low value of
resonance integral to thermal neutron cross-section ratio
and a rather long half-life time. The Fe content of the rock
samples was determined by an independent method, XRF
analysis, using a portable energy dispersive X-ray spec-
trometer RLP-21T (Republic of Kazakhstan). The ascribed
uncertainties of such measurements are 2–8 % [39], com-
parable with the uncertainties associated with REE in the
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high quality CRMs. The mass of an ordinary rock sample
(Al–Si matrix) measured with RLP-21T is 5–7 g, much
greater than if INAA is applied to analyze the same
material. The larger sample mass is an important advantage
of XRF, since the representativeness of the small geolog-
ical material subsamples typically used for trace element
analysis may be questionable [40]. Then, using the Fe
content measured by XRF as the internal standard, the
reproducibility of rock analysis for REE content should be
improved compared with the INAA relative method.
Moreover, XRF complements INAA well in mineral
resources exploration, enabling the Fe content of rock
samples to always be available [41,42].
To assess 1/fand K
a,Fe
values, the archive of INAA
measurements relative to different multi-element CRMs
carried out over an eighteen month period was consulted.
Correction coefficients K
a,Fe
used for the determination of
REE content with respect to Fe as the internal standard
were evaluated, based on a total number of 50–70 mea-
surements; 5–10 different types of CRMs—rocks, soil,
flying ash, and bottom sediments were used. Some CRMs
were rejected since they resulted in K
a,Fe
values for cer-
tain REEs being incompatible with other ones within a
reasonable discrepancy (10 %), or with insufficient
reproducibility of separate K
a,Fe
estimations. Apart from
low gamma-ray intensities, the discordance was related to
cases of high uncertainty in the REE certified values and
to cases of significant spectral interferences. Substantial
scattering of individual K
a,Fe
values was marked for the
CRMs with poor small subsample representativeness.
Both cases were mentioned above as drawbacks to the
relative method.
The relative bias of REE content measurement by INAA
ISM was evaluated using CRMs certified only for REE
contents, but not for Fe content: BCR-667 (estuarine sed-
iment, IRMM), CC-690 (calcareous soil, ERM), and SL-3
(river sediments, IAEA). The Fe content of these CRMs
was measured using an RLP-21T X-ray spectrometer. The
samples were prepared, irradiated and measured as
described below.
The RLP-21T spectrometer by JSC ‘‘Physicist’’,
Almaty, was designed to analyze powdered geological
samples (rocks, ores, soil, sediments) and ore concentrates.
In order to get maximum accuracy, the elemental content
of the samples was calculated using a reference-free
modified method of the fundamental parameters. The
spectrometer is enrolled in the State Register of Measuring
Devices, and the certified analytical technique is registered
by the National Body for Certification of Kazakhstan. The
accuracy of calculations by the spectrometer software was
repeatedly confirmed with the help of appropriate, different
CRMs. E.g., the Fe content of rock reference materials is
determined with a systematic error of no more than 4–5 %.
To evaluate the relative standard deviation of INAA for
long-lived REE by the ISM, the archive data on the results
of independent measurements of rock samples by the rel-
ative standardization method were used. These data were
obtained in the course of certified analytical technique [43]
elaboration and corresponded to all concentration ranges of
REE analysis by this technique. The data were replenished
later with additional measurements to provide some con-
tent intervals with minimum numbers of replicates.
Most of the rock samples used for the investigation were
collected from Kundybai REE deposit, Northern Kaza-
khstan, and prepared for instrumental analysis according to
the routine technique with a particle size \0.074 mm. The
CRMs used were certified for REE content and obtained
from different manufacturers such as IAEA, IRMM, China,
Poland, and the Russian Federation.
50–200 mg of rock samples, depending on the expected
REE content, and 100 mg of CRMs were used. Samples
were sealed in small double polyethylene bags, packed in
Al foil and placed in an irradiation container. Up to 23 bags
were irradiated at the same time for 1–2 h in position §3
inside ‘‘wet’’ channel §8–9 of the research reactor WWR-
K with a typical neutron flux density 10
13
cm
-2
s
-1
.No
flux monitors were used because the relative method was
applied.
Irradiated samples were measured twice: first after
7 days of the decay time for the determination of La, Nd,
Sm, Ho, Yb, Lu and secondly about 30 days after the
irradiation for the determination of Sc, Ce, Eu, Gd, Tb, and
Tm. Both measurements were performed using an exten-
ded-range HPGe detector GX5019 with a relative effi-
ciency of 50 % and an energy resolution of 1.86 keV at the
1332 keV peak of
60
Co, connected to a Canberra multi-
channel analyzer DSA-1000. Detector calibration for rel-
ative detection efficiency was made with the help of a
multi-gamma ray standard (
152
Eu,
154
Eu,
155
Eu) and an
isotopic source
133
Ba, both by Canberra. Spectra collection
and subsequent treatment were carried out by the special
software developed in the INP to provide gamma-ray
spectrometric analysis. The coefficients to
239
Np full-en-
ergy peak intensities to correct La, Ce, Nd and Ho ana-
lytical line count rates for U fission products were
calculated by counting a specially prepared sample made
from a uranium standard solution by Perkin Elmer. No
corrections for neutron self-shielding, gamma-ray self-ab-
sorption or true-coincidence effects were applied.
The main nuclear parameters of the analytical gamma-
ray lines of the radionuclides used to calculate REE content
and the interferences which were taken into account are
presented in Table 1.U(n,f) means the same radionuclide
as a U fission product, whereas
133
Xe by the U fission
reaction appears as a spectral interference. Some minor
interferences in an ordinary rock matrix were regarded as
J Radioanal Nucl Chem
123
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inessential and neglected. The partly resolved peaks, where
possible, were divided by the software.
Results and discussion
The epithermal to thermal neutron flux ratio and its time
stability in the selected position of the irradiation channel
were estimated using the 1/fvalues calculated according to
Eq. (3) with the help of several CRMs irradiated at dif-
ferent times. Rb and Cs were chosen for the determination
of 1/fsince they presented the higher number of indepen-
dent measurements (respectively 50 and 46) among the
elements with a high Q
0
value. The determined 1/fvalues
are presented in Fig. 2, where they are reported in
chronological order. No time trends were revealed for
either of them, as expected.
As they were composed of independent data, the ranges
can be treated as stochastic variables with mathematical
statistics methods applicable to them. First, the strict non-
parametric Mann–Whitney U-test for independent samples
[44] insensitive to variable distributions was employed to
compare the two ranges. Since the calculated value of the
standard normal variable (SNV) ^z¼0:87 did not exceed its
critical value z0:05 ¼1:96 for the two-tailed test, it was
concluded that these two datasets came from the same
population and were combined. The nonparametric Kol-
mogorov–Smirnov test showed the distribution of the
combined dataset did not contradict the Gaussian one (the
calculated value of D-statistics
^
D¼0:0616; the critical
value D0:05 ¼0:139; n=96). Thus the combined dataset
parameters can be described in the terms of normal dis-
tribution, i.e. the 95 % confidence interval embraces two
standard deviations raround the mean. The epithermal to
thermal neutron flux ratio in the selected irradiation posi-
tion appeared to be: 1/f=0.028 ±0.004 (P=0.95,
r=0.002).
In spite of a great number of measurements, the uncer-
tainty of this value is rather high, about 14 %. Hence, this
approach apparently cannot be applied to evaluate 1/fin
distant positions of the irradiation channels with a more
thermalized neutron flux. In this case the cadmium ratio
method must be used.
The evaluated neutron flux ratio made possible the
estimation of relative bias values (trueness) of the REE
content measurement of the selected CRMs: D
rel
=
(C
INAA
/C
CRM
–1)9100 %, where C
INAA
is the REE
content measured by INAA using the internal standard
method, and C
CRM
is the corresponding certified value. The
rounded D
rel
values are presented in Table 2. Blanks mean
an absence of certified values.
The acceptable |D
rel
| values of no more than 10 %
supported further comparison of the precision of INAA for
these REEs by the relative and internal standard method.
Selected results of REE analysis in rock samples by the
relative method were reinterpreted using the Fe contents of
these samples obtained by XRF as the internal standard.
Based on 5 replicas, 12 pairs of the mean REE values C
m
and the relative standard deviations s/C
m
characterizing
reproducibility of each REE measured by both methods
were calculated. The uncertainties of the single measure-
ments derived by the relative method are fixed, [43],
ranging within 12–22 % for all the REE presented in
Table 2, with the exception of Gd and Ho (16–28 %).
Thus, the relative uncertainties of C
m
values should be a
factor of ffiffiffi
5
plower, i.e. approximately 6–10 and 7–13 %
correspondingly. Although it would be done for certified
analytical techniques, there was not a systematic
Table 1 Main nuclear parameters and interferences of the radionu-
clides used to calculate REE by INAA internal standard method
Radionuclide Half-life
(days)
Energy
(keV)
Quantum
yield (%)
Interferences
59
Fe 44.5 1099.2 56.5
46
Sc 83.8 889.3 99.9
140
La 1.7 1596.2 95.4 U(n,f)
141
Ce 32.5 145.4 48.3 U(n,f)
147
Nd 11.0 91.1 28.1 U(n,f)
153
Sm 1.9 103.2 29.3
239
Np,
153
Gd
152
Eu 4943 121.8 28.7
153
Gd 240.4 103.2 21.1
153
Sm,
233
Pa
160
Tb 72.3 298.6 26.1
166
Ho 1.1 80.6 6.7
133
Xe
170
Tm 128.6 84.3 2.5
182
Ta
175
Yb 4.2 396.3 13.2
177
Lu 6.6 208.4 10.4
0.020
0.025
0.030
0.035
0.040
01020304050
1/ f
Number
a
0.020
0.025
0.030
0.035
0.040
0 1020304050
1/ f
Number
b
Fig. 2 Calculated values of epithermal to thermal neutron flux ratio
using respectively Fe-Rb (a) and (Fe-Cs) (b) determined in the CRMs
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assessment made of REE measurement uncertainties by
INAA ISM. However these values can be assumed not to
exceed the ones derived by the relative method, since the
internal standardization is specifically used to increase
reproducibility and accuracy of a quantitative analysis [45].
The dependency of s/C
m
values on REE content
approximated by nonlinear power law trends are plotted in
Figs. 3,4in semi-logarithmic coordinates. These graphs
show that all the trends corresponding to the ISM are
located below the trends corresponding to the relative
method. Such an order supposes reproducibility of the ISM
to be better in all the cases, but due to the random character
of the variables this must be proved by mathematical sta-
tistical methods.
If highly homogeneous powder or water samples are
analyzed, the experimental dependence of s/C
m
on analyte
content appears as a hyperbola-like descending curve. Such
behavior was not shown for Sc, La, Eu, Yb analysis by the
relative method and La, Nd, Yb analysis by the ISM; the
empirical trends are slopeless or not sufficiently sloped, as
could be expected. This effect was explained by the
increasing heterogeneous REE distribution within the
samples collected from the real REE deposit. It appears, in
this case, the usual grinding to a particle size \0.074 mm
Table 2 Rounded relative bias
of REE analysis in CRMs by
INAA internal standard method
(%)
Sc La Ce Nd Sm Eu Gd Tb Ho Tm Yb Lu
BCR-667 4 9 0 -49 8-7149 510
CC-690 0 1 -6-11 -3-275
SL-3 -21 2-36 -5-5-7-8
0
1
2
3
4
5
6
5E-05 0.0005 0.005 0.05
s/C
m
[%]
Content [%]
Internal standard method Relative method
a
0
1
2
3
4
5
6
7
8
0.0002 0.002 0.02 0.2
s/C
m
[%]
Content [%]
Internal standard method Relative method
d
0
1
2
3
4
5
6
7
0.0002 0.002 0.02 0.2
s/C
m
[%]
Content [%]
b
0
1
2
3
4
5
6
7
8
5E-05 0.0005 0.005 0.05
s/C
m
[%]
Content [%]
e
0
1
2
3
4
5
6
7
8
0.0002 0.002 0.02 0.2
s/C
m
[ %]
Content [%]
c
0
1
2
3
4
5
6
7
5E-06 5E-05 0.0005 0.005
s/C
m
[%]
Content [%]
f
Fig. 3 Relative standard deviation values of light REE analysis by INAA: Sc (a), La (b), Ce (c), Nd (d), Sm (e), Eu (f)
J Radioanal Nucl Chem
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was not sufficient to provide the necessary homogeneity in
small samples.
To establish the quantitative distinction between trend
behavior for every REE, two statistical tests were applied
using different approaches. The first test is ‘‘comparison of
one empirical curve with another after some interference in
the process’’ [44] (‘‘ECC’’). It is based on the construction
of the standard normal variable (SNV) ^zin the following
way:
^z¼Pn
i¼1ðy1;iy2;iÞ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
nðs2
1þs2
2Þ
p;
where, for the case under discussion, y
1,i
and y
2,i
are the
pairs of s/C
m
values for the same REE content (see Figs. 2,
3), n=12, s
1
and s
2
are the standard deviations of y
1
and
y
2
respectively. The test implies Gaussian distribution of
the independent s/C
m
variables forming each trend, and this
hypothesis was confirmed by effective nonparametric
Shapiro–Wilk W-test applicable for restricted samples. As
an alternative, the nonparametric Mann–Whitney U-test
was applied to each of twelve pairs of s/C
m
stochastic
samples to verify their belonging to the same general
population.
The calculated SNV values for both approaches are
presented in Table 3. Comparing them with the critical
value z0:05 ¼1:96, a conclusion was drawn that for Gd, Ho
and Lu the application of the relative method or the ISM do
not present any difference in terms of analytical perfor-
mance. This is not valid for the other REEs: in these cases
the application of the ISM offers an advantage.
A further comparison of the ability of the INAA ISM
and the relative methods to analyze the REE content of
geological objects was made in terms of their precision
assessment. The next three CRMs by Ore Research &
3
4
5
6
7
8
9
10
0.0005 0.005 0.05
s/C
m
[%]
Internal standard method Relative method
a
2
3
4
5
6
7
8
5E-06 5E-05 0.0005 0.005
s/Cm[%]
Content [%]
Internal standard method Relative method
d
1
2
3
4
5
6
7
8
5E-06 5E-05 0.0005 0.005
s/C
m
[%]
Content [%]
b
1
2
3
4
5
6
7
0.00002 0.0002 0.002 0.02
s/Cm[%]
Content [%]
e
3
4
5
6
7
8
9
2E-05 0.0002 0.002
s/C
m
[%]
Content [%]
c
2
3
4
5
6
7
8
2E-06 2E-05 0.0002 0.002
s/Cm[%]
Content [%]
f
Content [%]
Fig. 4 Relative standard deviation values of heavy REE analysis by INAA: Gd (a), Tb (b), Ho (c), Tm (d), Yb (e), Lu (f)
J Radioanal Nucl Chem
123
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Exploration, Australia, were used to that end: OREAS 24b
(granodiorite), OREAS 100a (uranium-bearing multi-ele-
ment reference material) and OREAS 463 (REE-Nb ore).
Sample preparation and measurement were carried out
basically as described above. Three replicas of each CRM
were irradiated simultaneously for 2 h:100 mg of the first
two and 10 mg of OREAS 463. The subsample masses of
the third CRM were substantially diminished to reduce the
neutron self-shielding effect (due to high REE content) to a
negligible value.
All measurements were carried out using the main
GX5019 detector and the additional GLP36360 planar
detector (energy resolution is 585 eV at 122 keV peak of
57
Co) by ORTEC. GLP36360 was used for Gd analysis
since it partly resolves the 103.18 keV analytical peak of
153
Gd from the 103.86 keV interference line of
233
Pa.
GLP36360 does not discriminate between the energies of
166
Ho (80.57 keV) and
133
Xe (81.00 keV) lines, but it
resolves the sum peak and thus made Ho analysis in
OREAS 100a more reliable. In this case
233
Pa (311.9 keV)
was used as the internal standard instead of
59
Fe, since the
count rate of the 192.3 keV line of
59
Fe (quantum yield is
3.1 %) measured by the planar detector was too low. The
Th content of OREAS 100a was determined by INAA ISM
with the help of GX5019 and using Fe as the internal
standard. Thus, to analyze Ho in OREAS 100a the ISM was
applied twice. The same detector was used to analyze Ho in
OREAS 24b due to insufficient count rate by the planar
detector. Tm and Ho were not determined in Oreas 463
because of severe overlapping by
182
Ta and the corre-
sponding absence of the analytical signal against the
background.
The REE content of the OREAS samples by the relative
method was calculated using the following CRMs: GBW-
07110 (trachyte andesite) and GBW-07159 (rare earth ore),
both from China.
The OREAS CRMs’ certified values (±1 standard
deviation) of long-lived REEs, Th and U along with their
Table 3 Values of standard normal variable of ‘‘ECC’’ test and Mann–Whitney U-test to compare reproducibility of REE analysis by INAA
relative and internal standard methods
Sc La Ce Nd Sm Eu Gd Tb Ho Tm Yb Lu
^z, ECC 12.4 3.81 4.65 4.67 3.51 6.23 1.88 4.04 1.74 4.16 2.65 1.67
^z,U-test 4.07 2.98 3.49 3.50 2.66 4.01 1.82 3.41 1.59 3.29 2.58 1.45
Table 4 Comparison of REE, Th, U certified and measured values by
INAA internal standard and relative methods in OREAS 24b (in ppm
except where % indicated)
Element Certified
value
INAA
Relative method ISM
Fe, % 4.45 ±0.12 4.80 ±0.10 4.53 ±0.10
a
Sc 14.1 ±0.7 16.6 ±1.0 15.6 ±0.9
La 44.0 ±1.5 46.4 ±2.6 46.6 ±2.6
Ce 86.0 ±2.5 86.2 ±6.4 84.5 ±6.3
Nd 38.7 ±0.8 41.5 ±3.5 39.4 ±3.3
Sm 7.17 ±0.28 8.14 ±0.64 7.49 ±0.59
Eu 1.39 ±0.09 1.53 ±0.09 1.44 ±0.09
Gd 6.27 ±0.37 6.6 ±1.0
b
6.3 ±1.0
b
Tb 0.98 ±0.05 1.12 ±0.09 1.01 ±0.08
Ho 1.17 ±0.06 1.10 ±0.14 1.23 ±0.15
Tm 0.50 ±0.03 0.56 ±0.13 0.52 ±0.12
Yb 3.24 ±0.14 2.87 ±0.23 3.20 ±0.26
Lu 0.49 ±0.05 0.52 ±0.12 0.52 ±0.12
Th 16.5 ±0.7 17.5 ±2.6 16.6 ±2.5
U 3.31 ±0.14 3.0 ±0.8 3.3 ±0.9
a
By XRF
b
With GLP36360
Table 5 Comparison of REE, Th, U certified and measured values by
INAA internal standard and relative methods in OREAS 100a (in ppm
except where % indicated)
Element Certified
value
INAA
Relative method ISM
Fe, % 4.66 ±0.11 4.95 ±0.10 4.72 ±0.10
a
Sc 7.25 ±0.50 6.90 ±0.48
La 260 ±13 297 ±32 250 ±27
Ce 463 ±29 471 ±26 462 ±26
Nd 152 ±14 159 ±12 152 ±12
Sm 23.6 ±0.7 25.5 ±3.2 22.9 ±2.9
Eu 3.71 ±0.36 4.03 ±0.27 3.83 ±0.26
Gd 23.6 ±2.2 24.0 ±2.0
b
23.8 ±2.0
b
Tb 3.80 ±0.34 4.00 ±0.24 3.70 ±0.22
Ho 4.83 ±0.21 4.60 ±0.36
b
4.88 ±0.38
b
Tm 2.31 ±0.18 2.19 ±0.36 2.23 ±0.36
Yb 14.9 ±0.5 14.3 ±1.2 15.2 ±1.3
Lu 2.26 ±0.16 2.50 ±0.31 2.38 ±0.31
Th 51.6 ±4.3 54.0 ±7.5 52.4 ±7.5
U 135 ±11 131 ±16 135 ±16
a
By XRF
b
With GLP36360
J Radioanal Nucl Chem
123
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measured mean values by INAA ISM and relative methods
calculated using three replicas are presented in Tables 4,5
and 6. A blank means the absence of a certified value. The
Sc content of OREAS 463 is an indicative one.
A quantitative comparison of precision between the two
INAA methods versus the certified values showed a
noticeable advantage using the INAA internal standard
method for REE analysis in geological samples of different
composition. Together with the demonstrated higher
reproducibility of small rock sample analysis, INAA, using
Fe as the internal standard with the content determined by
an up-to-date XRF technique, can be successfully used for
long-lived REE analysis in routine practice.
Conclusions
The experimentally-proven stability of neutron spectra in
the same irradiation position of the research reactor WWR-
K enabled the application of the simplified approach to
INAA of geological samples for rare earth element deter-
mination using the internal standard method. Taking
account of its nuclear properties and wide abundance in
rocks and minerals, Fe looks to be the most suitable inter-
nal comparator. An independent up-to-date instrumental
method such as energy dispersive XRF can be a convenient
means of Fe content determination. The absence of a range
of drawbacks inherent in the relative method is the most
attractive feature of INAA ISM. Its main disadvantage is
the same as for SCM, in that they are both strictly bound to
experimental counting conditions.
The estimated precision, high reproducibility of small
sample analysis, and other advantages, enables INAA ISM
to be recommended for routine analysis of a large series of
similar rock types for REE content.
Acknowledgments The author is greatly thankful to Dr
John W. Bennett and Ms Gillian Blackburn, Australian Nuclear Sci-
ence and Technology Organization, for valuable remarks and cor-
rections in the course of manuscript preparation.
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