First-Principles Study on the Half-Metallicity of New MXene Materials Nd2NT2 (T = OH, O, S, F, Cl, and Br)

This work systematically studied the structure, magnetic and electronic properties of the MXene materials Nd₂N and Nd₂NT₂ (T = OH, O, S, F, Cl, and Br) via first-principles calculations based on density functional theory. Results showed that Nd₂NT₂ (T = OH, O, S, F, Cl, and Br) have half-metallic characteristics whose half-metallic band gap width is higher than 1.70 eV. Its working function ranges from 1.83 to 6.50 eV. The effects of strain on its magnetic and electronic structures were evaluated. Results showed that the structure of Nd₂NT₂ (T = OH, O, S, and Br) transitions from a ferromagnetic half-metallic semiconductor to a ferromagnetic metallic and ferromagnetic semiconductor under different strains. By contrast, the structures of Nd₂NF₂ and Nd₂NS₂ were observed to transition from a half-metallic semiconductor to a ferromagnetic metallic semiconductor under different strains. Calculations of the electronic properties of different proportions of the surface functional groups of Nd₂NT_x (T = OH, O, and F; x = 0.5, 1(I, II), and 1.5) revealed that Nd₂NO_1.5 has the characteristics of semiconductors, whereas Nd₂NO(II) possesses the characteristics of half-metallic semiconductors. The other structures were observed to exhibit the characteristics of metallic semiconductors. Prediction of Nd₂NT₂ (T = OH, O, S, F, Cl, and Br) increases the types of lanthanide MXene materials. They are appropriate candidate materials for preparing spintronic devices.

1 Introduction

As candidate materials for preparing spintronic devices with a high-density, a high read/write speed, and an ultra-small volume, two-dimensional ferromagnetic half-metallic materials are the key to the development of spintronic devices (Wolf et al., 2001; Hu et al., 2014; Kent and Worledge, 2015; Wang et al., 2021a). Ferromagnetic half-metallic materials have 100% spin polarization. In a spin state, they have metallic properties at the Fermi level. In another spin state, they exhibit semiconductor or insulator properties at the Fermi level. Since 2004, graphene has been experimentally prepared successfully (Novoselov et al., 2004). Graphene is a semiconductor with a zero band gap, a feature limits its application in magnetic equipment (Novoselov et al., 2004; Geim and Novoselov, 2007). Graphene can be applied to spintronic devices by improving graphene or developing graphene-like materials. Extensive research on graphene-like materials, such as hexagonal boron nitride, silicon, phosphorus, transition-metal dichalcogenides and transition-metal carbon (nitrogen) compounds (MXenes), is being conducted (Denk et al., 1994; Sevik, 2013; Liu et al., 2014; Naguib et al., 2014; Kranthi Kumar et al., 2015). MXenes have received increased attention because they have abundant types.

Two-dimensional MXene materials have been developed using HF corrosion body phase material Ti₃AlC₂ to remove Al atom experimentally and obtain Ti₃C₂ materials with a few layers (Naguib et al., 2011). MXene materials are represented by the formula M_n+1X_nT_x (n = 1, 2, 3), where M is a transition metal, X is either C or N, and T_x is a surface functional group. MXenes are becoming popular two-dimensional materials. Theoretical and experimental studies revealed that various MXene materials have intrinsic ferromagnetic half-metallicity, such as Cr₂C, Cr₂NO₂, Fe₂NO₂, Co₂NO₂, Ni₂NT₂ (T = O, F, OH), and Mn₂NT₂ (T = O, OH, F) (Si et al., 2015; Wang, 2016; Wang and Liao, 2017; Frey et al., 2018). External conditions can be applied to induce Ti₂NO₂, Cr₃C₂, and Hf₂MnC₂O₂ and obtain ferromagnetic half-metals (Chen et al., 2017; Zhang and Li, 2017; Siriwardane et al., 2019). However, several MXene materials have semiconductor properties, such as Sc₂CO₂, Ti₂CO₂, and Cr₂CT₂ (T = F, OH, O, Cl) (Lee et al., 2014; Si et al., 2015; Zhou et al., 2016). Therefore, MXenes have rich magnetic and electronic properties that must be harnessed.

Most MXene materials have different sensitivities to surface functional groups and external conditions. Therefore, MXene functional materials can be feasibly designed by exploiting functional groups or external conditions. However, current research on MXene materials mostly focuses on transition metals and largely ignores MXene materials with lanthanide elements. Tan et al. studied the strain piezoelectric coefficient of La₂CO₂, a lanthanide MXene material, under axial strain. They reported that strain piezoelectric coefficient of this material is up to 22.32 pm/V, which is substantially higher than that of other known piezoelectric materials, such as Sc₂CO₂, Y₂CO₂, BN, GaAs, and AlSb (Chen et al., 2021; Wang et al., 2021b). Bai et al. reported that the semiconductor MXene material Lu₂CT₂ (T = F, OH) has a low work function and a carrier mobility of about 105 cm²/V at room temperature (Zhang et al., 2021). Therefore, lanthanide MXene materials have excellent properties with great application potential in sensors, electromagnetic interference and catalysis.

M₂N (M = Cr, Mo, W), which belongs to the VIB group in MXene materials (Hou et al., 2021), has excellent properties whose surface functional groups can induce Cr₂NO₂ to exhibit stable half-metallicity (Wang, 2016). On the basis of the semimetal properties of VIB MXene materials reported thus far, this work explored the structural and electromagnetic properties of the lanthanide MXene material Nd₂NT₂ (T = OH, O, S, F, Cl, and Br) to increase the known types of lanthanide MXene materials. This study provides theoretical guidance and direction to the preparation of related spintronic devices.

2 Calculation Method

First-principles calculations based on density functional theory were conducted using the CASTEP calculation package (Lin and Wang, 2017). Perdew–Burke–Ernzerhof exchange correlation function under the generalized gradient approximation was applied and ultrasoft pseudopotentials were selected to describe the interaction between electrons and ions in a two-dimensional system (Tan et al., 2019; Bai et al., 2020). In the process of geometric optimization of the structure of Nd₂NT₂ (T = OH, O, S, F, Cl, and Br), the two-dimensional structure preliminarily assumed was a ferromagnetic structure, and spin polarization calculations were performed. After testing the preliminary calculation parameters, the truncation energy chosen was 420 eV, the self-consistent convergence standard was set to 1 × 10⁻⁶ eV/atom, the sampling at k point was 10 × 10 × 1, and the total energy convergence standard was set to 1 × 10⁻⁶ eV/atom. When the atomic structure was optimized, the force of each atom was not over 0.03 eV/Å, the maximum displacement of each atom was set to 0.001 Å, and the vacuum layer of the c axis was set to 20 Å.

The formation energy was calculated to describe the thermodynamic stability of two-dimensional MXene material systems with different surface functional groups by using the following formula (Bekaert et al., 2020):

$E_{\text{F}}=E_{\text{total}}({\mathrm{N}\mathrm{d}}_2{\mathrm{N}\mathrm{T}}_2)-E_{\text{total}}({\mathrm{N}\mathrm{d}}_2\mathrm{N})-E_{\text{total}}({\mathrm{T}}_2)(1)$

where E_total(Nd₂NT₂) is the total energy of Nd₂NT₂, E_total(Nd₂N) is the total energy of Nd₂N, and E_total(T₂) is the total energy of T₂ (T = OH, O, S, F, Cl, and Br) of functional groups.

3 Results and Discussion

3.1 Surface Functional Groups of the Structure

The top and side views of Nd₂N after structural relaxation are shown in Figures 1A, C, respectively. The optimization results showed that Nd₂N is a hexagonal crystal structure composed of Nd atoms on both sides and N atoms in the middle. This structure is similar to that of materials reported in the literature (Si et al., 2015; Zhang et al., 2021). Different methods for preparing MXene materials inevitably result in the formation of certain functional groups on their surface. In this study, six different functional groups present T₂ (T = OH, O, S, F, Cl, and Br) in the optimized structure of Nd₂N were investigated (Figures 1B, D). According to previous studies, the functional groups on the surface may be found at three sites, namely, on the top of Nd, on the top of N, and on the top of Nd at the bottom of both sides. In this study, the functional groups were observed to be located on the top of Nd at the bottom of both sides, similar to that reported in the literature (Wang and Liao, 2017; Zhang et al., 2021).

FIGURE 1

FIGURE 1. Diagram of the structure of the 2 × 2×1 supercell of the two-dimensional MXene materials (A,C) Nd₂N and (B,D) Nd₂NT₂ (T = OH, O, S, F, Cl, and Br). (A,B) top views; (C,D) side views.

The lattice constants of Nd₂N and Nd₂NT₂ and the bond lengths of Nd–N and Nd–T are listed in Table 1. The lattice constant of Nd₂NT₂ and the bond length of Nd–N are larger than those of Nd₂N, indicating that the functional groups on the surface can change the structure of Nd₂N. Nd₂NS₂ has the largest lattice constant (4.232 Å), whereas Nd₂NO₂ has the smallest lattice constant (3.755 Å). Moreover, the Nd–N and Nd–T bond lengths of Nd₂NS₂ are longer than those of Nd₂NO₂ because both O and S belong to the VIA family and have similar properties. The radius of the S atom is greater than that of the O atom. The lattice constants of Nd₂NF₂, Nd₂NCl₂, and Nd₂NBr₂ are 3.796, 3.911, and 3.971 Å, respectively. The lattice constants increase with the increase in the atomic radius of the VIIA family, and the bond lengths of Nd–N and Nd–T gradually increase. However, the bond length of Nd–T is quite different. Nd–Br has the maximum bond length (3.015 Å), whereas Nd–O has the minimum bond length (2.280 Å), indicating that the bonding intensity of Nd and O is greater than that of Nd–Br. However, the bond length of Nd–N is 2.62–2.69 Å, indicating that although the different surface functional groups have an effect on the structure of the monolayer Nd₂N, their effect on the bond length of this structure is less than that on its lattice constant.

TABLE 1

TABLE 1. Lattice constants of the two-dimensional MXene materials Nd₂N and Nd₂NT₂ and bond lengths of Nd–N and Nd–T (T = OH, O, S, F, Cl, and Br).

3.2 Magnetic and Thermodynamic Stability

The atomic resolution magnetic moments and formation energies of Nd₂N and Nd₂NT₂ (T = OH, O, S, F, Cl, and Br) were calculated to assess their magnetic and thermodynamic stability (Table 2). The magnetic moments of monolayer Nd₂N (up to 8.95 μ_B) are higher than those of Nd₂NT₂ (T = OH, O, S, F, Cl, and Br). However, the magnetic moments of Nd₂N(OH)₂, Nd₂NF₂, Nd₂NCl₂, Nd₂NBr₂, Nd₂NO₂, and Nd₂NS₂ are 7.01, 7.01, 7.00, 7.00, 5.00, and 4.98 μ_B, respectively. The magnetic moment of Nd₂N mainly comes from two Nd atoms, and the contribution of the N atom to the total magnetic moment is small. The Nd atom is still the main contributor to the magnetic moment of Nd₂N(OH)₂. However, with the addition of –OH, the total magnetic moment is reduced to 7.01 μ_B. The magnetic moment of the nonmagnetic elements is also reduced because of the strengthening of hybridization between the atoms that strengthened the magnetic coupling effect and reduced the magnetic moment. In the structures of Nd₂NO₂ and Nd₂NS₂, the total magnetic moment is substantially reduced primarily because of the fact that the magnetic moment of the N atom of the Nd atom is remarkably smaller. Moreover, the magnetic moments of the nonmagnetic elements O and S in the induced surface functional groups are considerably smaller than those of the magnetic elements, indicating that the bonds between the O and S atoms and Nd atom are relatively intense, resulting in a sharp decrease in atomic localization. In addition, the total magnetic moment of the structures of Nd₂NF₂, Nd₂NCl₂, and Nd₂NBr₂ remains 7.00 μ_B. The increase in the amplitude of Nd and the F, Cl, and Br atoms is the same as that in the decrease in their amplitude. By comparison, the magnetic moment of the N atom remains low.

TABLE 2

TABLE 2. Total atomic magnetic moment (M_total) and atomic resolution magnetic moment (M), and formation energy (E_F) of the two-dimensional MXene materials Nd₂N and Nd₂NT₂ (T = OH, O, S, F, Cl, and Br).

After the structural and magnetic properties of the materials were determined, the phonon spectrum of monolayer Nd₂N and the formation energy of Nd₂NT₂ (T = OH, O, S, F, Cl, and Br) were further calculated. According to the phonon spectrum of Nd₂N, it has good dynamic stability (Figure 2). Equation 1 was also used to calculate the formation energy of Nd₂NT₂ (T = OH, O, S, F, Cl, and Br). Nd₂N(OH)₂ has the smallest formation energy of –25.92 eV, whereas Nd₂NBr₂ has the largest formation energy of –9.016 eV (Table 2), indicating an intense interaction between the metals and the surface functional groups. When the surface functional groups are F, Cl, and Br (VIIA group), the formation energy gradually decreases (Table 2). However, the surface functional groups O and S (VIA group) also show a similar rule. According to previous studies, on the surface functional groups of MXene structures, the formation energy can easily change from high to low under certain conditions. The formation energy of the –OH structure with surface functional groups is smaller than that of the O, S, F, Cl, and Br structures with surface functional groups (Table 2), suggesting that MXene materials with O, S, F, Cl, and Br as functional groups should not be washed or stored in H₂O during preparation to prevent them from being converted into –OH MXene materials (Perdew et al., 1996).

FIGURE 2

FIGURE 2. Phonon spectrum of Nd₂N structure.

3.3 Electronic Properties

The electronic properties of Nd₂N and Nd₂NT₂ (T = OH, O, S, F, Cl, and Br) were evaluated by calculating and plotting the energy band structure diagram (Figure 3). The spin up and the spin down of the energy band structure of Nd₂N pass through the Fermi level, indicating that it has ferromagnetic characteristics. In the spin down channel, the energy band density near the Fermi level is relatively sparse, indicating that the energy band structure can be changed under certain conditions, which are described below.

1) In the energy band structure of Nd₂NT₂ (T = OH, F, Cl, and Br), the spin up energy band at the Fermi level passes through the Fermi level, whereas the spin down energy band has an energy band gap, indicating that it has semimetal characteristics. The spin up energy band has an energy band gap near the Fermi level, indicating that the structure may change from a semimetal to a semiconductor under certain conditions.

2) In the band structure of Nd₂NT₂ (T = O and S), the spin up band at the Fermi level passes through the Fermi level, suggesting that it has metal characteristics. However, the spin down band has an energy band gap at the Fermi level, reflecting the nature of a semiconductor. Therefore, there is 100% spin polarization at the Fermi level, indicating that it has semimetal characteristics. According to the energy band structure, the band gap width between the spin down valence band and the Fermi surface is approximately 0.2–0.6 eV, and the band gap width between the spin down conduction band and the Fermi surface is greater than 3 eV, indicating that the structure does not readily change from a half-metal to a metal. Theoretically, the half-metallicity remains stable under certain external conditions.

3) The spin down band gap width of the semimetal was counted. Nd₂N(OH)₂ has the smallest band gap width (1.72 eV), whereas Nd₂NO₂ has the largest band gap width (4.61 eV) (Figure 3H). Therefore, the half-metallicity can remain stable within a certain range.

FIGURE 3

FIGURE 3. Energy band structure and band gap width diagram of the two–dimensional MXene materials Nd₂N and Nd₂NT₂ (T = OH, O, S, F, Cl, and Br). (A) Nd₂N, (B) Nd₂N(OH)₂, (C) Nd₂NO₂, (D) Nd₂NS₂, (E) Nd₂NF₂, (F) Nd₂NCl₂, (G) Nd₂NBr₂, and (H) band gap width diagram.

The calculated total density of states (TDOS) of Nd₂N and Nd₂NT₂ (T = OH, O, S, F, Cl, and Br) are provided in Figure 4. As can be seen from the TDOS graphs, the polarization peak of Nd₂N(OH)₂ appears at 1.5 eV, but this phenomenon is not observed in Nd₂N. Moreover, the spin down band gaps of Nd₂NO₂ and Nd₂NS₂ move to the high energy region, and their band gap width increase. However, the spin down band gaps of Nd₂NF₂, Nd₂NCl₂, and Nd₂NBr₂ exhibit similar behavioral changes, and the only differences are in the energy range of spin polarization peaks, which gradually move to the high-energy region.

FIGURE 4

FIGURE 4. Total density of states (TDOS) of Nd₂N and Nd₂NT₂ (T = OH, O, S, F, Cl, and Br). The red line represents Nd₂N, whereas the black line denotes is (A) Nd₂N(OH)₂, (B) Nd₂NO₂, (C) Nd₂NS₂, (D) Nd₂NF₂, (E) Nd₂NCl₂, (F) Nd₂NBr₂, respectively.

3.4 Work Functions of Nd₂NT₂ (T = OH, O, S, F, Cl, and Br)

Work function, as a reference for charge transfer, is a key parameter. The definition of work function (φ_wf) is as follows (Vanderbilt, 1990):

${\phi }_{\text{wf}}=E_{\text{vacuum}}-E_{\text{F}}(2)$

where E_vacuum represents the energy of the surface electron energy level in the vacuum, and E_F is the Fermi level of the MXene material. The electrostatic potentials of Nd₂NT₂ (T = OH, O, S, F, Cl, and Br) are calculated using Eq. 2 and plotted in Figure 5. The work function of Nd₂N is approximately 1.186 eV, whereas that of Nd₂N(OH)₂, Nd₂NO₂, Nd₂NS₂, Nd₂NF₂, Nd₂NCl₂, and Nd₂NBr₂ is 1.83, 5.38, 6.50, 2.22, 4.33, and 4.40 eV, respectively. The work function of –OH is 1.6–2.8 eV, similar to that reported in the literature (Khazaei et al., 2013). Moreover, the work function of Nd₂NT₂ (T = OH, F, Cl, and Br) increases as VIIA atoms are introduced. The work function of Nd₂NO₂ is evidently lower than that of Nd₂NS₂. The work functions indicate that lanthanide MXene materials have potential applications in spintronic devices.

FIGURE 5

FIGURE 5. Calculated electrostatic potentials along the Z direction of Nd₂NT₂ (T = OH, O, S, F, Cl, and Br), while (A) Nd₂N(OH)₂, (B) Nd₂NO₂, (C) Nd₂NS₂, (D) Nd₂NF₂, (E) Nd₂NCl₂, (F) Nd₂NBr₂, respectively. The black arrow indicates the difference from vacuum level to the Fermi level. The black dashed line denotes the Fermi level.

3.5 Strain Effect

The effects of strain on the magnetic and electronic structure of monolayer Nd₂NT₂ (T = OH, O, S, F, Cl, and Br) were evaluated by calculating the magnetic moment under different biaxial strains (Figure 6). Theoretical studies indicated that the electronic and magnetic properties of the monolayer MXenes Ti₂C and Ti₂N are tunable by strain (Clark et al., 2005; Sternik and Wdowik, 2018). Thus, biaxial strain was applied to monolayer Nd₂NT₂ (T = OH, O, S, F, Cl, and Br) by using the following formula:

$\epsilon =\frac{L-L_0}{L_0}(3)$

where L and L₀ are the lattice constants of strain and the equilibrium, respectively. Positive and negative ɛ values correspond to tensile and compressive strain, respectively. Under different strains, both Nd₂NF₂ and Nd₂NCl₂ transition from a ferromagnetic half-metallic structure to a ferromagnetic metallic structure (Figure 6), and their total magnetic moment is maintained is from 6.5 to 9.0 μ_B. By comparison, Nd₂N(OH)₂, Nd₂NO₂, Nd₂NS₂, and Nd₂NBr₂ transition from a ferromagnetic half-metallic structure to a ferromagnetic metallic structure and a ferromagnetic semiconductor under different strains. Notably, the total magnetic moments of the transition of Nd₂NO₂ and Nd₂NS₂ range from 5 to 7 μ_Bunder strain.

FIGURE 6

FIGURE 6. Total magnetic moments of monolayer Nd₂NT₂ (T = OH, O, S, F, Cl, and Br) under biaxial strain. (A) Nd₂N(OH)₂, (B) Nd₂NO₂, (C) Nd₂NS₂, (D) Nd₂NF₂, (E) Nd₂NCl₂, (F) Nd₂NBr₂. FM, FHM, and FS denote ferromagnetic metallic, ferromagnetic half-metallic, and ferromagnetic semiconductor, respectively.

3.6 Electronic Properties of Different Proportions of the Surface Functional Groups of Nd₂NT_x (T = OH, O, F; x = 0.5, 1(I, II), and 1.5)

Surface functional groups have a great influence on the electronic properties of MXene materials (Xie et al., 2014). The influence of different proportions of the surface functional groups of the Nd₂NT_x materials on their electronic properties was assessed at proportions of x = 0.5, 1, and 1.5 (Figure 7). x = 1 has two types; in type I, the functional groups are distributed on both sides, whereas in type II, the functional groups are distributed on one side only. After geometry optimization, TDOS was calculated (Figure 8).

FIGURE 7

FIGURE 7. Top and side views of the 2 × 1×1 supercell of the structure of the two-dimensional MXene material Nd₂NT_x (T = OH, O, F; x = 0.5, 1, and 1.5). (A) Nd₂NT_0.5 (T = OH, O, F), (B) Nd₂NT (T = OH, O, F)(I), (C) Nd₂NT (T = OH, O, F)(II), and (D) Nd₂NT_1.5 (T = OH, O, F).

FIGURE 8

FIGURE 8. Total density of state(DOS) of (A) Nd₂N(OH)_x, (B) Nd₂NO_x, and (C) Nd₂NF_x, where x = 0.5, 1(I), 1(II), and 1.5.

The structures of Nd₂N(OH)_x and Nd₂NF_x exhibit metal characteristics because of the asymmetry of their surface functional groups. When the surface functional group is 100%, the material has half-metallic characteristics. This result provides a direction for detecting the richness of surface functional groups experimentally.

When x = 0.5 and 1 (type I), the structure of Nd₂NO_x exhibits metal characteristics. However, when x = 1 (type II), an obvious band gap is observed in the spin downward at the Fermi level, indicating that it has half-metal characteristics. Unexpectedly, when x = 1.5, both spin up and spin down have a symmetric band gap width at the Fermi level, indicating that it has the characteristics of a semiconductor. This result provides a reliable direction for the regulation of electronic properties by controlling the richness of surface functional groups experimentally.

4 Discussion

The structural, magnetic, and electronic properties of Nd₂N and Nd₂NT₂ (T = OH, O, S, F, Cl, and Br) were evaluated via first-principles calculations based on density functional theory. According to the calculated phonon spectrum and formation energies, Nd₂N and Nd₂NT₂ (T = OH, O, S, F, Cl, and Br) are stable. Owing to the effects of surface functional groups on the electronic properties of Nd₂NT₂ (T = OH, O, S, F, Cl, and Br), it exhibits the characteristics of a half-metal, and its band gap width is higher than 1.70 eV. The work function ranges from 1.83 to 6.50 eV, indicating that lanthanide MXene materials have potential applications in spintronic devices. Under different strains, Nd₂NT₂ (T = OH, O, S, and Br) transition from a ferromagnetic half-metallic structure to a ferromagnetic metallic structure and a ferromagnetic semiconductor. However, the structures of Nd₂NF₂ and Nd₂NS₂ transition from a half-metallic structure to a ferromagnetic metallic structure under different strains. Calculation of the electronic properties of different proportions of the surface functional groups of Nd₂NT_x (T = OH, O, F; x = 0.5, 1(I, II), and 1.5) revealed that Nd₂NO_1.5 has the characteristics of a semiconductors, whereas Nd₂NO(II) has the characteristics of a half-metal. The other structures show the characteristics of a metal. This study demonstrated that new lanthanide MXene materials have a high application potential in spintronic devices.

Data Availability Statement

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.

Author Contributions

Methodology, KY and BW; software, TZ and KY; data curation, SR; XL and KY; writing-original draft preparation, KY and HH; writing-review and editing, GS; BW and KY. All authors have read and agreed to the published version of the manuscript.

Funding

This work was financially supported by the Graduate Research Fund of Guizhou Province (YJSCXJH(2019)042), Major Research Projects for Innovative Groups of Guizhou Education Department (QJHKY(2020)025), Natural Science Foundation of Hainan Province (121MS032), Guizhou Science and Technology Plan Project (QKHJC-ZK(2021)029), Zunyi Science and Technology Plan Project (ZSKHHZ(2021)211), Key Laboratory of Clean Energy Materials and Devices in Guizhou Province (QJHKY(2019)055).

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s Note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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