Article
Quantitative Analysis of Iron and Silicon
Concentrations in Iron Ore Concentrate
Using Portable X-ray Fluorescence (XRF)
Applied Spectroscopy
2020, Vol. 74(1) 55–62
! The Author(s) 2019
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DOI: 10.1177/0003702819871627
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Shubin Zhou1 , Zhaoxian Yuan2, Qiuming Cheng1,
David C. Weindorf3, Zhenjie Zhang1, Jie Yang1,
Xiaolong Zhang4, Guoxiong Chen5, and Shuyun Xie5
Abstract
As a technique capable of rapid, nondestructive, and multi-elemental analysis, portable X-ray fluorescence (pXRF) has
applications to mineral exploration, environmental evaluation, and archaeological analysis. However, few applications have
been conducted in the smelting industry especially when analyzing the metal concentration in ore concentrate samples.
This research analyzed the effectiveness of using pXRF in determining the metal concentration in Fe concentrate. For this
proof of concept study, Fe ore samples dominated by Fe and Si were collected from the Northeastern University Mineral
Processing Laboratory (Shenyang, China) and directly analyzed using pXRF, laboratory-based XRF, and titration methods.
The compactness (density) of the ore concentrate was found to have very little effect on pXRF readings. The pXRF
readings for Fe and Si were comparative to laboratory-based XRF results. Based on the strong correlations between the
pXRF and XRF results (Fe: R2 > 0.99, Si: R2 > 0.96), linear calibrations were adopted to improve the accuracy of pXRF
readings. Linear regression equations derived from the relations between XRF results and pXRF results of 21 Fe ore
concentrate samples were used to calibrate the pXRF, and then validation was performed on five additional samples.
Results from this preliminary study suggest that ordinary least squares (OLS) regression improves the accuracy dramatically, especially for Fe with relative errors (REs) decreasing to 0.03%–3.27% from 4.26%–8.32%. Consequently, pXRF
shows strong promise for rapid, quantitative analysis of Fe concentration in Fe ore concentrate. Based on the results
obtained in this study, a larger, more comprehensive study is warranted to confirm the results obtained.
Keywords
Portable X-ray fluorescence spectra, pXRF, quantitative analysis, compactness effect, calibration method, ore concentrates
Date received: 5 March 2019; accepted: 16 July 2019
Introduction
Iron concentrates are common commercial products used
in the steel smelting industry. The concentrations of Fe in
the Fe concentrate not only establish the values and prices
of concentrate but also affect the smelting process and the
quality of smelting products.1 Presently, titration is commonly used to determine the Fe concentrations in Fe ore
concentrates.2 However, the traditional titration method is
both time-consuming and uneconomical. Considering this,
several researchers previously applied X-ray fluorescence
(XRF) spectrometry and prompt gamma–neutron activation analysis system in the analysis of metal concentrations
in ore concentrates.1,3–8 XRF spectrometry was suggested
as a viable option for determining the concentration of
major, minor, and trace elements in ore concentrates
using proper calibration methods. By comparison,
1
State Key Lab of Geological Processes and Mineral Resources, China
University of Geosciences, Beijing, China
2
Institute of Resource and Environmental Engineering, Hebei Geo
University, Shi Jiazhuang, China
3
Department of Plant and Soil Science, Texas Tech University, Lubbock,
TX, USA
4
School of Resources & Civil Engineering, Northeastern University,
Shenyang, China
5
State Key Lab of Geological Processes and Mineral Resources, China
University of Geosciences, Wuhan, China
Corresponding author:
Zhaoxian Yuan, No. 136, Huaian East Road, Shijiazhuang City, Hebei
Province 050031, China.
Email: sdyzx86@126.com
56
inductively coupled plasma–mass spectrometry is an alternate approach for the determination of minor and trace
elements in ore concentrates.9 These analytical methods
made multi-elemental analysis possible and simplified the
analysis process to some extent.
Compared with conventional analysis methods, portable
XRF (pXRF) not only provides the advantages of nondestructive and multi-elemental analysis, but also simplifies the
analysis process and reduces the expense by offering field
portability.10–15 To date, it is widely accepted as a tool for
data collection in mineral exploration, environmental quality
assessment, and archaeological analysis.10,11,13,15–21 The
results of pXRF measurements are influenced by many factors. For example, particle size, matrix effect, beam (dwell)
time, moisture content, and sample homogeneity can all
influence reported results.18,22–28 Thus, the pXRF analyzer
may produce different results when analyzing samples with
different physical properties (e.g., matrix density) such
as rocks, soil, water, or plants.15,18,29–32 The calibration or
response of pXRF to different sample types is dependent on
the analytical mode used in various pXRF models; hence,
several approaches, including ordinary least squares (OLS)
regression calibration, nonlinear, and segmented calibration
have been proposed to calibrate the pXRF readings
for improved accuracy.29,30–33 Generally, pXRF is capable
of quantitatively determining the elemental concentration
of homogeneous samples with a higher degree of certainty
such as polluted waters.28,31 Even for soil analysis, pXRF
provides strong correlation with conventional analysis methods.12,34 Furthermore, predictive accuracy in soils can be
improved using rudimentary sample preparation such as
homogenizing, drying, grinding, and sieving.26
Ore concentrates are commonly dry, with fine particle size
and a high degree of homogeneity. Given the demonstrated
effectiveness of pXRF in analyzing water and soil samples, the
purpose of this study is to develop a quantitative analysis
method to obtain elemental information of Fe concentrates
via pXRF and establish its effectiveness for industrial practices.
Materials and Methods
Applied Spectroscopy 74(1)
Laboratory Analysis
Analytical Instrument
The instrument employed in this study was a Niton XL3t
950 (Thermo Fisher Scientific). The instrument is equipped
with a silicon drift detector and an X-ray tube with a maximum voltage/current of 50 kV/40 mA and an Ag anode
target excitation source. The diameter of the detection
window is 8 mm. Three test modes, the mining mode,
soil mode, and ‘‘test all’’ mode, are available for analyzing
different types of samples. The mining mode is suitable for
analyzing elements at higher concentrations (i.e., for major
elements >0.2–0.5%), and soil mode is for minor and trace
elements.21 According to Thermo Fisher Scientific (USA),
the producer of the Niton XL3t 950 analyzer, the ‘‘test all’’
mode more rapidly obtains a comprehensive result than the
other two modes, but with relatively poor accuracy. In this
study, the ‘‘mining mode’’ was used since the concentrations of Fe were very high in ore concentrates.
Film Analysis
Due to the extremely small size of Fe concentrate particles,
the particles can easily attach to other objects. Thus, the
polyethylene films or paper bags needed to be used to
prevent the ore concentrates from contaminating the
pXRF detecting window. The effect of polyethylene films
and paper bags on pXRF readings has been previously investigated by many scholars.23,28,32,35 The attenuation is generally linear with respect to concentration but highly
dependent on the element.32 Polyethylene films generally
deliver lower attenuation than paper packet and Mylar
films. The penetration depth of the fluorescence signal is
also affected by film thickness. For example, at a thickness
of 2.5 mm, the Mylar film transmits 79% of the Si signal,
which decreases to 57% at a thickness of 6.0 mm.23
Considering the X-ray transmission rate, availability, and
economy, the same thin polyethylene film used in a previous
study (tens of mm, with nearly no compositional interference), causing little attenuation of X-rays,28 was employed
in this study.
Sample Collection
A total of 29 Fe ore samples were collected from the
Northeastern University Mineral Processing Laboratory
(Shenyang, China). These samples were mineral products
produced in different mineral processing experiments of Fe
ores with different ore grades. Thus, these Fe concentrates
represent those commonly produced in an industrial setting. Due to the drying and grinding process during the
mineral processing period, the collected Fe ore samples
were dry and the particle size was very small (80% passing
74 mm). The Fe concentrates were stored in plastic bags to
preserve desiccation and sent to the China University of
Geosciences, Beijing, China, for further analysis.
Compaction Effect
Even though the fine particle size of ore concentrates was
optimal for pXRF analysis, the compactness (density) of the
sample was still of concern. Due to the particle size of ore
concentrates, the volume of a certain weight of ore concentrate may vary significantly. Specifically, the compactness
of ore concentrates could vary considerably when exposed
to different levels of pressure in processing. Moreover, this
kind of difference is very common and unavoidable in an
industrial setting. For example, the ore concentrate stored
at the bottom of the packing bags is generally more compacted than ore concentrates in the upper section due to
Yuan et al.
simple, gravitational effects. Thus, an experiment was conducted in this paper in order to determine whether the
compactness of ore concentrates would affect the pXRF
readings. In the first step, the three loose Fe ore concentrates were analyzed 20 times using pXRF. Next, pressure
was applied, and the volumes of Fe ore concentrate were
compacted to approximately one-third of their previous
volumes. The compacted Fe ore concentrates were again
analyzed 20 times using pXRF and used to evaluate the
effect of compaction on pXRF elemental readings.
57
functions of concentration. The relative precision near
detection limits is low.36–38 The relative standard deviation
(RSD) of 20 measurements reflected the stability of the
pXRF readings (precision). The RSD is described per Eq. 1
RSD ¼
SD
100%
AM
ð1Þ
where SD is the standard deviation and AM is the arithmetical mean. Lower RSD values represent higher reliability of
the results.
Measurement of Iron Ore Concentrates
In total, 26 Fe ore samples were analyzed in the laboratory
via pXRF. The pXRF analyzer was placed vertically (aperture up) in the support stand. A small plastic tube (the
bottom was covered with one layer of polyethylene film)
was placed vertically on the pXRF aperture in the support
stand. According to previous studies,22,23 the penetration
depth was limited to a few hundred mm for different rocks,
and 5 mm of soil was considered to be infinitely thick. The
thickness of the Fe ore sample mass in the plastic tube was
>8 mm. All measurements were controlled using NDT
software. Mining mode was used to analyze the ore concentrates 20 times with a beam time of 60 s. Factory calibration, a self-calibration function of the Niton XL3t 950
analyzer, was performed after every 20 samples. The results
of 21 samples were used for model calibration, and the
remaining five samples were used for model validation.
These samples later underwent X-ray fluorescence
(ME-XRF21m) and titrimetric analysis (Fe-VOL82) at ALS
Minerals (ALS Chemex, Ltd., Guangdong, China). For the
X-ray fluorescence (ME-XRF21m) analysis, the Fe ore
sample was mixed with fusing agents (Li2B4O7 and
Li2CO3) and cobalt internal standard. The fusion pieces
were then prepared using a Vulcan Fusion Machine (IMP
Automation). The X-ray fluorescence spectrometer was a
PW2424 (Malvern Panalytical). In titrimetric analysis, the Fe
concentrates were dissolved in HNO3–HF and dissolved
with a mixture of sulfuric acid–phosphoric acid (H2SO4–
H3PO4). Fe3þ was then reduced to Fe2þ using stannous
chloride/titanium trichloride. The total Fe in Fe concentrate
was titrated using potassium dichromate standard solution
with sodium diphenylamine sulfonate as indicator.
Statistical Analysis
Accuracy and Precision
The accuracy in this study was the description of systematic
errors and a measure of statistical bias. Typically, accuracy
can be reflected in the linear regression equation between
certified values and pXRF readings. The precision was the
description of random errors, a measure of statistical variability. The precision (and to an extent accuracy) are
Calibration and Performance Verification
A linear regression model was used to establish the relationship between pXRF and XRF results. The linear regression model was described using Eq. 2:
y ¼ mx þ b
ð2Þ
where x is the Fe or Si concentration reported using XRF
and y is the pXRF reading for Fe. The value of m represents
the slope of the line and b is the y intercept; m and b are
used to calculate the response factor and the offset correction values, respectively.
Therefore, the regression equation can be expressed
as Eq. 3:
½pXRF readings ¼ m½certified concentrations þ b
ð3Þ
This equation enables calibration of the pXRF readings for
optimized accuracy. Following on, Eqs. 4 and 5 are given as
½calibrated pXRF reading ¼
1
ð½pXRF readings bÞ
m
ð4Þ
which we simplified to:
½calibrated pXRF reading ¼ p½pXRF reading þ c
ð5Þ
where p ¼ m1 and c ¼ mb
Measurement Times Versus Absolute Errors
The absolute error (AE) for n measurements is given as Eq. 6
"
#
n
1 X
AEn ¼ ð r i ci Þ n i¼1
ð6Þ
where ri is the pXRF reading after OLS calibration and ci
represents the results measured using XRF.
58
Applied Spectroscopy 74(1)
Results and Discussion
Compactness Effect
As shown in Table I, two groups of data which were produced by analyzing the same samples with different compaction (density) were compared. A paired-sample t-test
was also conducted to determine the significant difference
between the samples. The two groups of data revealed only
modest differences. The calculated P values (two-tail) for
G-0914-28 and T-0807-14-24 were 0.21 and 0.07,
Table I. Portable X-ray fluorescence of Fe content (%) of loose/
compacted Fe ore concentrate.
Sample
description
Fe content
(G-0914-28)
Fe content
(G-0116-15)
Fe content
(T-0807-14-24)
Loose
Compacted
47.73
47.86
9.84
9.67
51.05
50.85
Figure 1. Scatter plots of Fe contents reported using XRF
versus Fe content reported using titration for Fe ore concentrate
in China.
respectively, which indicates no significant difference
between loose and compacted samples with relatively
high Fe concentrations. However, the P values (two-tail)
for G-0116-15 was 0.00, suggesting a significant difference
for loose and compacted ore concentrate with low Fe concentration. Even so, the average mean of Fe readings
for loose and compacted samples was generally the same,
indicating that it is not necessary to control the compactness of homogeneous Fe ore samples for pXRF measurements. This is likely due to the inherent high particle
density of Fe oxides (e.g., hematite 5.3 g cm–3) and relatively
uniform, small particle size. Undoubtedly, the study of compactness effects broadens the potential application of pXRF
in industrial practices, suggesting only simple sample preparation methods are needed.
Accuracy and Precision
According to the laboratory analysis, the Fe ore concentrate was Fe and Si dominated. As shown in Fig. 1, the XRF
data were in perfect correlation with elemental data produced by titration. The Fe content reported using titration
is generally slightly higher (0.17%–0.66%) than that
reported using XRF. Due to the relatively high detection
limit of titration, e.g., ciron > 10%, elemental data for five
samples (G-0914-27, G-2714-27, G-0116-8, G-0714-29,
and G-1111-29) was not possible through titration.
Therefore, the data produced using XRF (in perfect correlation to titration) were used for comparison with pXRF
results.
Prior to model development, five samples of different Fe
ore concentration ranges were chosen as the validation set.
The relationship between the pXRF readings of the remaining 21 samples and the XRF results is displayed in Figs. 2a
and b. Linear regression analysis was used to compare the
pXRF data with the XRF data. The slope and the square of
the correlation coefficient (R2) of the regression line close
to 1 indicate accurate pXRF results. As shown in Fig. 2a,
Figure 2. Scatter plots of pXRF readings versus XRF-determined Fe or Si concentrations (a, b) display the results for Fe and Si,
respectively, in Fe ore concentrate from China.
Yuan et al.
the slope of the regression line for Fe is 1.042 and the R2
value is 1.000, which indicates robust pXRF performance.
The pXRF data for Fe were comparable with certified
values and calibrated through the linear regression.
However, as shown in Fig. 2b, the slope of the regression
line for Si is 0.858 and the R2 value is 0.963, suggesting
slightly less accurate results for Si compared to Fe. Such
results were expected, as pXRF is more sensitive for heavier elements due to its higher excitation energy.39,40
Twenty replicate measurements were conducted for
each sample, making it possible to calculate the RSD of
pXRF data. Thus, the RSD values reflect the stability of
pXRF results. Yuan et al.16 reported that pXRF offers
good performance when analyzing samples with relatively
high elemental concentrations. Figure 3 illustrates the variation in RSDs with increasing Fe and Si concentrations. The
RSD values for Si generally decrease with the increasing Si
concentrations. Even so, all RSD values are <8%. In contrast, RSD values for Fe were mostly <2% (except one with
a RSD of 2.16), which indicates relatively better stability.
59
The solid stability results obtained likely reflect high homogeneity of the ore concentrate.
Calibration and Performance Verification
Considering the good correlation between pXRF readings
and XRF results for both Fe and Si, an attempt was made to
calibrate the pXRF readings through the formulas obtained
from the measurements of the 21 samples. According to the
equations described in Figs. 4a and 4b, the calibration formulations for Fe and Si are given as Eqs. 7 and 8, respectively.
yFe ¼
xFe 0:057
1:042
ð7Þ
ySi ¼
xSi 0:75
0:858
ð8Þ
The xFe and xSi values represented original readings for
Fe and Si, respectively. The yFe and ySi represent calibrated
readings for Fe and Si, respectively. To determine the effectiveness of the calibration, the REs for original errors and
errors after calibration were compared. The REs were
defined per Eq. 9.
REFe=Si ¼
Figure 3. The RSDs of pXRF readings for Fe or Si versus XRFdetermined Fe or Si concentrations in Fe ore concentrate from
China.
j pXRFFe=Si XRFFe=Si j
XRFFe=Si
ð9Þ
The REs of the calibrated readings were calculated
through the same method. Figs. 4a and 4b display the
results. The line indicated by triangles and the line using
squares represent the errors after linear calibration and
original errors, respectively. As shown in Fig. 4a, the REs
for Fe decrease to 0.03%–3.27% from 3.81%–8.32%, suggesting that the OLS calibration for Fe can effectively
improve the accuracy. However, as shown in Fig. 4b,
Figure 4. Improvement in accuracy of portable X-ray fluorescence (pXRF) readings using OLS regression calibration, (a, b) display the
results for Fe and Si, respectively, for Fe ore concentrate in China.
60
Applied Spectroscopy 74(1)
Table II. Portable X-ray fluorescence replicate measurements versus absolute errors (%) for Fe ore concentrate in
China.
MT
AE-(G-2714-27)
AE-(G-0914-24)
AE-(G-0714-28)
AE-(G-2714-20)
AE-(G-1111-31)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0.17
0.20
0.23
0.25
0.26
0.24
0.24
0.26
0.26
0.26
0.26
0.27
0.27
0.27
0.27
0.27
0.26
0.26
0.26
0.27
1.28
0.65
0.51
0.34
0.43
0.27
0.22
0.24
0.34
0.33
0.26
0.20
0.24
0.21
0.20
0.18
0.23
0.23
0.22
0.22
0.50
0.63
0.64
0.40
0.38
0.52
0.44
0.46
0.52
0.46
0.46
0.46
0.41
0.42
0.41
0.40
0.36
0.36
0.33
0.31
0.54
0.29
0.06
0.13
0.09
0.19
0.19
0.20
0.14
0.19
0.10
0.13
0.11
0.17
0.16
0.12
0.10
0.09
0.10
0.10
0.19
0.05
0.00
0.31
0.35
0.33
0.24
0.12
0.09
0.03
0.04
0.04
0.02
0.15
0.13
0.05
0.03
0.00
0.00
0.02
MT: measurement time; AE: absolute error.
the effect of calibration for Si was less robust. The OLS
calibration improved the accuracy for four samples with Si
contents >8.8%. For sample G-1111-31 with a Si content of
5.6%, the OLS calibration failed to reduce the error probably due to the relatively low Si content.
Measurement Times versus Absolute
Errors
As shown in Table II, the AEs for one time of measurement
are from 0.17% to 1.28%. The results with such accuracy
are mostly attributed to the high homogeneity of the ore
concentrate. Generally, the AEs decrease with increasing
replicate measurements, suggesting the necessity to perform repeated measurements. The errors would keep relatively stable after certain minimum measurement times
(MTs). In fact, as shown in Fig. 1, different laboratorybased methods such as XRF or titration produce different
readings on the same sample with AEs ranging from 0.17%
to 0.66%. Thus, calibrated pXRF readings were found to be
comparable to the elemental data produced using XRF or
titration. Based on the consideration of both MT and accuracy, at least four replicate scans for averaging are recommended in further measurements of ore concentrates
which share similar physical properties (particle size,
moisture, and homogeneity) as the ore concentrates
described herein.
Conclusion
In this preliminary study, the feasibility of using pXRF to
quantitatively analyze Fe and Si concentrations was assessed.
The effect of the compaction of Fe ore concentrate on the
pXRF readings was also evaluated. Based on high correlations between pXRF readings and certified elemental data
reported using XRF, OLS calibration equations were built
and used to directly predict unknown samples. Results indicated that the OLS calibrations can substantively improve
pXRF predictive accuracy and provide reliable elemental
data in the rapid analysis of ore concentrate.
Declaration of conflicting interests
The authors declared no potential conflicts of interest with
respect to the research, authorship, and/or publication of this
article.
Funding
This research was supported by the National Key Research and
Development Program of China (No.2016YFC0600501), the
National Basic Research Program of China (2015CB452605),
Yuan et al.
61
the China Geological Survey Project (No.DD20160045, No.
DD20190459), the National Natural Science Foundation of
China (No. 41602338, No. 41302263, No. 41430320,
No.41702075, No. 41702355 No.51734005), the Research
Program of Hebei Education Department (No. ZD2017011), the
Fundamental Research Funds for the Central Universities, China
University of Geosciences, Wuhan (No. CUG170104), and the BL
Allen Endowment in Pedology at Texas Tech University.
ORCID iD
Shubin Zhou
https://orcid.org/0000-0003-4104-1688
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