The Mechanical and Electronic Properties of Ternary Rare-Earth Hexaboride LaxNd8-xB6 (x = 0, 1, 7, 8) Materials


We have carried out density functional theory to study the lattice constants and electronic properties of LaB6, NdB6, Nd-doped LaB6, and La-doped NdB6. The lattice constant, intra-octahedral bond, inter-octahedral boron bond, and positional parameter (z) were calculated for LaB6, La7Nd1B6, La1Nd7B6, and NdB6. Our results show that the doped Nd increases the lattice constant of La7Nd1B6. Likewise, La-doping leads to an increase in the lattice constant of the La1Nd7B6. The PDOSs of LaB6, B of LaB6, La7Nd1B6, B of La7Nd1B6, La1Nd7B6, B of La1Nd7B6, NdB6, and B of NdB6 were calculated. La d-electron bands cross the Fermi energy, showing classical conductor behavior. The charge density results indicate that light and dark colors show high and low-intensity zones, respectively. La1Nd7B6 has a low-density region and LaB6 has a high-density region. The LaB6 midpoint has strong charge density peaks. Weak peaks are also observed for La1Nd7B6. Thus, ternary REB6 has good potential for many applications. This article reports an investigation of the electronic features and structural parameters of binary and ternary hexaborides.

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Bozada, C. (2022) The Mechanical and Electronic Properties of Ternary Rare-Earth Hexaboride LaxNd8-xB6 (x = 0, 1, 7, 8) Materials. Modeling and Numerical Simulation of Material Science, 12, 1-11. doi: 10.4236/mnsms.2022.121001.

1. Introduction

Rare-earth hexaborides (REB6) are commonly used in various high-energy optical devices and field electron emitter systems because of their superior properties such as high chemical stability, high melting point, high mechanical strength, high brightness, low work function, low volatility, conductibility, small visual dimensions and long lifetimes [1]. REB6 is commonly used as cathode material. REB6 has a cubic CsCl-type structure with a space group of Pm-3m symmetry, in which a rare-earth (RE) ion occupies the Cs site, and the B6 octahedron is located on the Cl site. REB6 compounds include LaB6, CeB6, PrB6, NdB6, PmB6, SmB6, EuB6, GdB6, TbB6, DyB6, HoB6, ErB6, TmB6, YbB6, LuB6, ScB6 and YB6. LaB6 has low volatility, CeB6 indicates a typical dense Kondo behavior, PrB6 shows high density, NdB6 has low magnification, SmB6 is a typical valence semiconductor and GdB6 has the lowest work function among REB6 compounds [2].

The electronic structures of the doped and binary REB6 were calculated using density functional theory (DFT). The position of the Fermi energy level and DOS were adjusted by doping with REB6 to improve the electron emission characteristics. The high-density d-orbital electrons play a crucial role in considerably decreasing the work function of REB6 and contributing to the electronic states of electron emission near the Fermi level. This ensures excellent emission characteristics [3]. The second-order elastic constants (SOECs) and third-order elastic constants (TOECs) of LaB6 and CeB6 were studied by first-principles calculations. The effect of increased pressure on the elastic anisotropy, mechanical characteristics and structural stability of LaB6 and CeB6 has attracted considerable attention. When the pressure increases, the mechanical stability decreases and the ductility and anisotropy increase [1]. Lanthanum hexaborides (LaB6) are superb thermionic and field electron emission cathode materials in the field of electron emission. LaB6 has several applications in high-power electronics owing to its long lifetime and high luminosity. LaB6 attracts attention by its low work function between 2.6 and 2.8 eV, its high melting point of 2715˚C, and its stable chemical and physical characteristics. Compared to polycrystalline and single-crystal applications of LaB6, it has better potential for single-crystal applications [4]. LaB6 works well as a thermal-field emitter. It is easily degradable and stable in air. LaB6 was reactive at 2715˚C. LaB6 is a violet-colored metal and its electron conductivity is approximately 1/5 that of copper [5]. Lu et al. [6] successfully fabricated LaB6 nanocubes with an average dimension of 94.7 nm using a low- temperature molten salt technique at 800˚C. LaB6 nanocubes exhibited high near-infrared (NIR) adsorption. As mentioned in [7], LaB6 nanocrystalline preparation routes include many synthesis routes, such as the floating zone method, aluminum flux, molten salt, high-temperature reaction, chemical vapor deposition (CVD), direct solid-phase reaction and carbothermal reduction. It is because of its wonderful characteristics that LaB6 is commonly used in some electrical devices, including free-electron laser, thermionic electron cathode, electron microscope, vacuum, and electron beam welder [8].

Neodymium hexaboride (NdB6) is black solid with good chemical stability, magnetic properties, electrical conductivity, and thermal conductivity characteristic. NdB6 is insoluble in hydrofluoric acid (HF) and hydrochloric acids (HCl). However, it can be dissolved in molten alkali, sulfuric acid (H2SO4) and nitric acid (HNO3). In addition, it exhibits very high antioxidant capability [9]. NdB6 crystallizes in a CsCl-type structure with a space group of Pm-3m symmetry, where the neodymium (Nd) occupies the Cs site and octahedral B6 molecules are located at the Cl site. NdB6 has a low work function (1.6 eV) [10]. NdB6 are an efficient field-emission cathode material. These excellent properties make NdB6 nanomaterials promising materials for use in vacuum electronic devices [11]. Thus, NdB6 is antiferromagnetical at TN = 7.74 K [12]. Ding et al. [13] successfully synthesized NdB6 nanowires (NWs) by a self-catalyst method. Nanowires with diameters of approximately 80 nm and lengths spanning several micrometers have monocrystalline structures. Xu et al. [14] successfully produced NdB6 nanostructures using a free-CVD process. The NdB6 nanostructures exhibited a good stability. The effect of temperature on NdB6 is important. When the temperature was increased, the turn-on and threshold electric fields decreased. The work function of NdB6 nanostructures is considerably decreased as the temperature increases, leading to much enhanced field emission characteristics.

Tsuji et al. [15], studied the magnetoresistance, magnetization and specific heat of NdxLa1-xB6 (x = 0. 9, 0.8, 0.7, 0) by a FZM method. The magnetoresistance, magnetization and specific heat are affected by temperature. As the temperature increased the others increase. Chaolong et al. [16] successfully investigated NdxLa1-xB6 bulks using spark plasma sintering (SPS) method. The work function of NdxLa1-xB6 was 2.72 eV. The Nd content enhanced thermionic emission characteristic and decreased the work function.

Li et al. [17] fabricated successfully high-quality, uniform LaxNd1-xB6 nanowires by catalyst-free CVD technique. LaxNd1-xB6 nanowires exhibit a superb field emission performance. Nanowires are used in optoelectronic devices such as nanoelectronic building blocks and flat panel displays.

2. Materials and Methods

Ab initio material modelling based on DFT was performed quantum espresso software (QE) packages based on modelling the material at nanoscales or on an atomic scale [18]. First-principles calculations were performed using the VASP. [19]. The projector augmented wave (PAW) method and the functional form of the generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) were preferred for exchange. The kinetic energy cut-off of the plane-wave basis set was 500 Ry. The Brillouin zone integration was performed at 3 × 3 × 3 k mesh points using methfessel-paxton smearing with a width of 0.02 Ry. A k-mesh 3 × 3 × 3 was used in the brillouin zone integration with Methfessel-Paxton smearing width of 0.02 Ry. Both LaB6 and NdB6 have cubic CsCl-type structures with a space group of Pm-3m symmetry [20].

3. Results and Discussion

The bulk unit cell of REB6 is simple cubic and is found in the symmetry of the space group Pm-3m. The lattice of NdB6 can be entirely defined using merely the lattice constant, a, and the positional parameter, z, as indicated in Figure 1. The lattice constant, a was 1, intra-octahedral boron bond was 2, and inter-octahedral boron bond was 3.

Figure 1. NdB6 structures with showing relevant bond lengths. NdB6 contains Nd (blue) and B atoms (purple) forming an octahedral structure.

Table 1 lists the positional parameters of the given REB6. The lattice constant of LaB6 (Pm-3m space group) was calculated as a value of 4.157 Å. This was consistent with the experimental consequences indicated in Table 1. Furthermore, parameters 2 and 3 were 1.766 and 1.660 Å, respectively, with a boron positional parameter of approximately z = 0.226 Å. Chen et al. [28] conducted a study on the structural refinement and thermal expansion of hexaborides. In this study, based on the X-ray powder diffraction technique, the intra-octahedral and inter-octahedral boron–boron distances were calculated as 1.766 and 1.659 Å, respectively. Xiao et al. investigated the optical features of LaB6 using first-principles DFT calculations. They calculated the LaB6 parameter to be 4.154 Å [33]. Hasan et al. [34] synthesized LaB6 via carbothermal reduction. The calculated value of the lattice parameter was 4.157 Å. Furthermore, other experimental studies [35], [36] are consistent with those of presidential study. Mackinnon et al. [37] calculated the lattice constant of LaB6 using DFT calculations. The calculated boron parameter (z) was 0.225 Å.

The doping of Nd instead of one La atom led to a slight increase in the lattice constant to 0.502 Å. In addition, 2 and 3 parameters were found to be 1.857 and 1.801 Å, respectively, which indicates an increase in these parameters while the z parameter remains nearly the same as that of LaB6. In a study related to LaxGd1-xBd6 synthesized by the SPS technique, the doping of Gd into LaB6 strengthened the lattice parameters of the structure [38]. In a similar study, Chao et al. [39] fabricated La7Sm1B6 by solid-state technique. Sm doping led to a decrease in the La7Sm1B6 lattice.

The 1, 2, 3 and z parameters; 1 of La1Nd7B6 were found as 4.449, 1.812, 1.801, and 0.223 Å respectively. Compared to LaB6, the ratio of Nd/La increased in parameters 1 2, and 3 but the parameter z didn’t change considerably. On the other hand, Li et al. [17] conducted a study of single-crystal LaxNd1-xB6 nanowires to investigate the field emission performance and characterization. In this study, when Nd-doped into LaB6, the lattice parameter of LaxNd1−xB6 was decreased. In a similar study, Chao et al. [39] produced LaxSm1−xB6 by solid-state reaction. They employed DFT to describe the characteristic of Sm-doped LaB6. They obtained the lattice parameters of La0.2Sm0.8B6 and La0.4Sm0.6B6 as 4.123 and

Table 1. The lattice constant (1), intra-octahedral boron bond (2), inter-octahedral boron bond (3), and positional parameter (z) of REB6. z = 3/2 × 1.

4.128, respectively. Their results showed that doping LaB6 with Sm decreases the lattice parameter of LaxSm1−xB6. When the La content was doped into BaB6, the calculated value of the lattice constant of La1Ba7B6 was increased [40]. Luo et al. [41] studied La1Ca7B6 by first-principles calculations. Ca doping provides increases in the lattice strength of La1Ca7B6.

The lattice constant of NdB6 was calculated as a value of 4.118. Ali et al. [12] studied the thermoelectric power of NdB6 by using the floating zone method. They measured the lattice constant was 4.126 Å. In other studies, Ping et al. [42] conducted a study of NdB6 by using the first principle method. The lattice parameter of NdB6 was calculated as 4.069 Å. Sandeep et al. [35] calculated the lattice parameter of NdB6 (4.157 Å) using the full-potential linearized augmented plane wave (FP-LAPW) technique. Furthermore, parameters 2 and 3 were found to be 1.750 and 1.643 Å, respectively, and the z parameter was 1.643 Å. Mackinnon et al. [37] determined the z parameter as 0.226 Å.

Figure 2 illustrated PDOS of LaxNd8-xB6 (x = 0, 1, 7, 8). As explicated in Figure 2(a) and Figure 2(c) PDOS curves. La d-electron bands show typical conductive behavior as they pass fermi energy. The lowermost conduction bands (CBs) consisted of B s and the uppermost valence bands (VBs) have consisted of B p are indicated in Figure 2(b). La d-electron band passing Fermi energies are shown in Figure 2(c). The calculation converged with great intensity to a metallic ground state at the EF, at the Fermi level, as shown in the figure. The zone near EF is contributed mostly by La d states as explicit in Figure 2(b) and Figure 2(c). Besides that, EF is contributed generally by Nd d states as shown in Figure 2(e) and Figure 2(g). This is obvious that the energy division of the La d states and Nd d states additives look alike to B 2p additives, which is a signature of hybridization between La d-Nd d - B 2p states.

Figure 3 shows the charge density of LaB6, La7Nd1B6, La1Nd7B6 and NdB6. Light and dark colors show high and low-intensity zones respectively. Dark and light colours indicate low and high-density regions, respectively. La1Nd7B6 has a low-density region and LaB6 has a high-density region. There are six boron atoms on the plane. The center of the figure was seen the strong B-B bonds. The LaB6 midpoint has strong charge density peaks. La1Nd7B6 has weak peaks.

(a) La of LaB6 (b) B of LaB6 (c) La and Nd of La7Nd1B6 (d) B of La7Nd1B6 (e) La and Nd of La1Nd7B6 (f) B of La1Nd7B6 (g) Nd of NdB6 (h) B of NdB6

Figure 2. The partial density of states (PDOS) of (a) LaB6 (b) B of LaB6 (c) La7Nd1B6 (d) B of La7Nd1B6 (e) La1Nd7B6 (f) B of La1Nd7B6 (g) NdB6 (h) B of NdB6.

(a) LaB6 (b) La7Nd1B6 (c) La1Nd7B6 (d) NdB6

Figure 3. The charge density of (a) LaB6 (b) La7Nd1B6 (c) La1Nd7B6 (d) NdB6.

4. Conclusion

We comprehensively studied the mechanical and electronic properties of LaB6, NdB6, Nd-doped LaB6 and La-doped NdB6 using the density functional theory. The lattice constant of LaB6 was lower than that of Nd-doped LaB6. In addition, La doping increased the lattice constant of La-doped NdB6. We calculated the PDOS of LaB6, B for LaB6, La7Nd1B6, B for La7Nd1B6, La1Nd7B6, B of La1Nd7B6, NdB6, and B of NdB6. We found that the La d-electron bands pass the Fermi energy as shown in Figure 2(c). The light color in the charge density indicates that LaB6 has a high-density region. Similarly, dark color in the charge density shows that La1Nd7B6 has a low-density region.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.


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