2.1 Equipment setup

A PGNAA was used to detect the iron content in iron ore concentrate in the experiment. Fig. 1 schematically shows the equipment setup ^[15]. Two 20 μg ²⁵²Cf neutron sources were placed in the source chamber. Two 5 inch×5 inch (diameter × height) NaI detectors were used as the prompt gamma-ray detector. The experimental equipment was produced by DFMC, which was suitable for a one-meter-wide belt. The spectrum acquisition time of each sample was set to 3600 seconds. Because of the strong shielding ability of iron on gamma rays, the characteristic gamma ray of a sample containing iron should have strong gamma-ray self-absorption ^[21]. To measure the self-attenuation degree of gamma rays, one gamma-ray attenuation degree detection system was installed after the PGNAA, which included a ¹³⁷Cs gamma radiation source installed below the belt and a γ-ray detector installed above the belt, as shown in Figure 2.

Fig.1.Full-screen View

PGNAA device structure

Fig. 2.Full-screen View

System structure diagram

2.2 Sample preparation and experimental load

Six calibration samples and nine validation samples, with differing iron contents, were prepared for the experiment. Silicon, magnesium, calcium, and chlorine interference elements were added in sample 2-1#~2-9# to simulate a real test. The compositions of the calibration samples are shown in Table 1, and the composition of the verification samples are listed in Table 2.

An inflection curve is observed for the analytical coefficient between the deconvolution coefficient of iron and the sample load owing to the gamma-ray self-attenuation effect, as shown in Figure 3. In Figure 3, the linear region is between 60 to 130 kg. To obtain more rational results, 110 kg was selected as the experimental load in this study.

Fig.3.Full-screen View

Analytic coefficients of iron with different loads

2.3 Gamma-ray self-absorption correction

The following compensation formula ^[22] for gamma-ray self-absorption is used to correct for self-attenuation:

where $I_0{}_{E_i}$ is the energy spectrum without attenuation, $I_{E_i}$ is energy spectrum obtained by the PGNAA detector, ${\mu }_{m{E}_i}$ is the characteristic gamma-ray mass attenuation coefficient with energy $E_i$, ${\mu }_{m{E}_i}$ is related to the atomic number of the material and the energy of the gamma ray, $N$ is the detector count rate of the gamma-ray attenuation degree detection system when there is material on the belt, N₀ is the detector count rate of the gamma-ray attenuation degree detection system with no material on the belt, ${\mu }_0$ is the mass attenuation coefficient of the ¹³⁷Cs radioactive source with energy equal to 0.662 MeV.

The linear absorption coefficient, $\mu$, of the material is defined as follows:

where N_i is the atomic density of each element, and ${\sigma }_i^{\gamma }$ stands for the total microscopic photon atomic cross-section.

The calculation formula of parameter N_element is defined as follows:

where m_ρ is the mass density of the material being measured, M_i is the atomic weight of each element, f_i is the proportion of each element, $f_{\text{element}}$ is the proportion of current element, and N_A is Avogadro’s constant.

The characteristic gamma rays are not all produced at the bottom of the detection area. They are generated at every location in the detection area, thus, the final correction formula, with a correction factor k, can be rewritten as follows:

The main materials in the iron ore concentrate are calcium oxide, silicon dioxide_, ferrous oxide, ferric oxide, magnesium oxide, and chlorine. The corresponding composition of each material is listed in Table 3. Iron ore contains six elements: oxygen, magnesium, silicon, calcium, iron, and chlorine; the atomic proportions (f_i) of each element are listed in Table 4. The linear absorption coefficient, μ, of iron ore concentrate can be calculated from Eqs. 2 and 4, and the atomic proportions in Table 4. The $\frac{-{\mu }_{mE}}{{\mu }_0}$ data for each element is listed in Table 5.

Using the characteristic energy spectrum, $I_{E_i}$ (1 MeV≤$E_i$≤10 MeV), constant $\frac{-{\mu }_{m{E}_i}}{{\mu }_0}$ (1 MeV≤$E_i$≤10 MeV), and count rate $N$ and N₀ in Equation 4, the energy spectrum after compensation, $I_0{}_{E_i}$ (1 MeV≤$E_i$≤10 MeV), is obtained.

The gamma-ray self-absorption compensation parameters and data of the six calibration samples are listed in Table 6. The energy spectra before and after gamma-ray self-absorption compensation are shown in Figs. 4a and 4b, respectively. The relationship between the analytical coefficient and iron content, before and after gamma-ray self-absorption compensation, are shown in Figures 5a and 5b, respectively.

Fig.4Full-screen View

(Color online) Energy spectra of different samples before (a) and after (b) gamma self-absorption compensation

Fig.5.Full-screen View

Relationship between the analytical coefficient and iron content Before (a) and after (b) gamma self-absorption compensation

2.4 Neutron self-absorption correction

Self-absorption in the PGNAA technique is comprised of two parts: gamma-ray self-absorption and neutron self-absorption ^[16-18]. A bigger neutron-absorption cross-section will result in more neutron self-absorption. The neutron capture reaction cross-section and characteristic gamma-ray energy of different materials are listed in Table 7^[19].

Previous work regarding neutron self-absorption correction ^[20] by Professor Wen-bao Jia is compared with the current iron ore concentrate detection experiment in Table 8. It is clear that the total neutron capture cross-section of iron is quite strong in the iron ore concentrate detection experiment, contrasting with the experiment by Professor Jia, which means the influence of sample thickness on detection results is higher than that of previous evaluation.

The experimental samples contain silicon, calcium, magnesium, chlorine, and other interfering elements. The test results of iron can be disturbed by these elements. The iron element test result, found by a PGNAA, can be expressed by the following formula:

where ${m^{\prime }}_{\text{Fe}}$ is the iron grade, as detected by the PGNAA, and K is a constant representing all other contributing factors. ${\sigma }_i^{\text{n}}$ is the neutron-absorption cross-section of each element listed in Table 7.

The formula for the contribution of each element (excluding iron) to the measurement error of iron is as follows:

The contribution of iron to the measurement error of the iron grade is:

The formula for the total error in iron grade detection is:

Formula 9 shows that the changes in the content of chlorine will cause the greatest error in the result. Because chlorine has a large neutron absorption cross-section, the neutron field of the entire system will change considerably when the content of chlorine changes, and, furthermore, it induces more error in the detection of other elements.

The concentration of iron, $m_{\text{Fe}}$, and chlorine, $m_{\text{Cl}}$, can be expressed as follows ^[20]:

where ${\Phi }_0$ and ${\Phi }_1$ are the neutron flux upon it entering (0) and leaving (1) the sample, $A_{\text{Fe}}^0$ is the analytical coefficient of the energy spectrum of iron when the iron content is $m_{\text{Fe}}$, $A_{\text{Cl}}^0$ is the analytical coefficient of the energy spectrum of chlorine when the content is $m_{\text{Cl}}$; $k_{\text{Fe}}$ and $k_{\text{Cl}}$ are scaling factors between the concentration and analytic coefficient, $f$ is the geometric factor of the NaI scintillation detector, and $\eta$ is the detection efficiency.

When the measured sample changes, the iron and chlorine contents become multiples of the original content; $p$ and k, respectively. The corresponding formulas are

where ${\Phi }_1^{\text{'}}$ represents the corresponding neutron flux exiting from the surface of the sample, when the iron content of the sample becomes $p{m}_{\text{Fe}}$, the chlorine content of the sample becomes $k{m}_{\text{Cl}}$. $A_{\text{Fe}}^1$ is the analytical coefficient of the energy spectrum of iron when the iron content is $p{m}_{\text{Fe}}$; $A_{\text{Cl}}^1$ is the analytical coefficient of the energy spectrum of chlorine when the chlorine content is $k{m}_{\text{Cl}}$; ${k^{\prime }}_{\text{Fe}}$ and ${k^{\prime }}_{\text{Cl}}$ are scaling factors.

From Equations (10)–(13), the expressions of p and k can be rewritten as:

The linear correction factor $g\left(p,k\right)$ is defined as:

To determineφ₀, φ₁, andφ' 1, a ³He neutron detector was added over the material to detect the neutron flux as shown in Figure 2. Because the measured material itself slows fast neutrons, φ₀ is not the thermal neutron flux when the belt is empty. In this experiment, φ₀, the thermal neutron flux, was defined when 20 kg carbon powder was placed on the belt.

The final analytical coefficient $A_{\text{Fe}}^{\text{Final}}=A_{\text{Fe}}^1\times g\left(p,k\right)$. The data used in the calculation of the calibration samples are listed in Table 9. The calibration data are listed in Table 10. The final total iron calibration curve is shown in Figure 6.

Fig. 6.Full-screen View

Iron calibration curve

2.5 Calculation of check samples

To verify the reliability of the method, nine validation samples were prepared. The experimental data of each sample are listed in Table 11. The total iron content comparison curve of the validation samples is shown in Figure 7.

Fig. 7.Full-screen View

Check samples comparison curve