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. 2024 Aug 14;9(34):36802–36811. doi: 10.1021/acsomega.4c05894

Structural and Electronic Properties of the Magnetic and Nonmagnetic X0.125Mg0.875B2 (X = Nb, Ni, Fe) Materials: A DFT/HSE06 Approach to Investigate Superconductor Behavior

Guilherme Bonifácio Rosa †, Luis Henrique da Silveira Lacerda ‡, Sergio Ricardo de Lazaro †,*
PMCID: PMC11359628  PMID: 39220542

Abstract

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MgB2 material has a simple composition and structure that is well-reported and characterized. This material has been widely studied and applied in the last 20 years as a superconductor in wire devices and storage material for H in the hydride form. MgB2 doped with transition metals improves the superconductor behavior, such as the critical temperature (Tcs) or critical current (Jsc) for the superconducting state. The results obtained in this manuscript indicate that Nb-, Fe-, and Ni-doping in the Mg site leads to a contraction of the unit cell through the spin polarization on the electronic resonance of the boron layer. Fe and Ni transition metals doping perturb the electronic resonance because of stronger dopant-boron bonds. The unpaired electrons are transferred from 3d orbitals to the empty 2pz orbitals of the boron atoms, locating α electrons in the σ bonds and β electrons in the π orbitals. The observed influence of magnetic dopants on MgB2 enables the proposal of an electronic mechanism to explain the spin polarization of boron hexagonal rings.

Introduction

The climate emergency raised by energy production from fossil sources is a critical topic affecting the thermic condition of life as we know it. Alternative clean energy sources such as photovoltaics, electrolysis, tide waves, geothermics, and others are more sustainable. However, the limitation on the efficiency of these processes can be related to energy dissipation or loss on the energy generator device or energy transmission from the energy source. Such narrowness has relevant consequences for the research on advanced inorganic and organic functional materials.1−5 In recent years, the search for functional materials with low energy dissipation or more efficiency in the transmission process has become the focus of several scientific investigations, and advanced functional materials have been proposed to overcome this challenge.6,7

In this context, materials with superconducting states have been broadly investigated since their discovery. However, the application of this class of materials is limited because of the low temperatures or extremely high pressures required to maintain the superconductivity.8−12 The superconductor state is accessible below a given temperature, called the superconducting critical temperature (Tcs), where the material transits from a normal state to a superconductor state. Since the H.K. Onnes first report on superconductors, the main challenge lies in the obtainment of materials with increased Tcs, being values closer to room temperature the goal.13,14 A significant advantage of superconducting materials is the absence of energy loss during transmission, which is relevant to current technological purposes. Hence, this is the main property responsible for the promising expectations of the superconductor materials to surpass recent environmental problems.15−18 In addition, scientific or commercial devices based on superconductor materials are more efficient due to their robustness and precision.19−21

The magnesium diboride, MgB2 (MB), is an example for electronic, energetic, and data transmission devices.22 This material is widely investigated as a superconductor due to its Tcs near 39.0 K, a higher temperature considering the simple composition forming a crystalline structure from Mg and B layers interspersed and unusual electronic properties.23−29 The MB crystallizes into a P6/mmm hexagonal space group organized as multilayers with a well-defined B lattice. The Mg sites, in particular, are an excellent option to be replaced by M2+ transition metals, tuning the materials properties.30 This material is applied on bulk,31 thin films,32,33 and superconductor wires (SCW).34−36 The SCW under cooling leads to no loss in the energy transport process.37 However, if high electrical currents exceed the value of critical current, then the superconductor state is suppressed. Thus, the chemical modification of the MB was broadly reported as always connected to increased critical currents (Jsc), avoiding such limitation.38 An usual experimental procedure to dope MB with transition metals is synthesizing them inside metallic tubes, such as Nb,39−43 Fe,44,45 and Ni46−48 on heat treatment to form a solid solution in Mg sites49. The synthesis of the MB has economic advantages regarding the YBa2Cu3O7−x (YBCO) material50.

Energy storage technologies are a very important electronic property in electronic transport, advanced computational devices, supercapacitors, and systems of SCW applied in superconductor coils in cryogenesis. These technologies are all based on superconductors materials, and this ensures the principal physical properties of stored charge do not decay.51,52

The study of MB material is attractive in materials science, especially with magnetic dopants, about the electronic nature of the boron lattice with high covalent behavior and the possibility of unpaired electron perturbation in the electronic structure of aromaticity of the B structure. The effect of unpaired electrons in superconductors is characterized in a shallow way even in current theoretical works, and this study is fundamental to understanding the electronic mechanism of magnetic impurities in high-ordered electronic structures. Lefcochilos-Fogelquist et al.53 reported the effect of the sp2 hybridization destabilization on the electronic resonance of the boron hexagonal lattice through Ti- and Ni-doping-induced the B–H hydrogenation process on the MB material. The unpaired electrons in 3d orbitals of the Ni atom were cited as a destabilization factor on sp2 hybridization, as observed on density of states (DOS) analysis. The strong bond between the transition metal and B atoms hinders the B–H bond formation; therefore, the hydrogenation process is not efficient. Wan and coauthors54 evaluated the MB as anodes for application in next-generation Li-ion batteries through DFT/PBE in the VASP code. The results discussed indicate the potential of MB based on the enhanced electronic resistivity and transport and low cost compared with other commercialized anodes.

The present study shows a DFT/HSE06 investigation on the electronic changes of the Nb-, Ni-, and Fe-doping in the Mg sites of the MB structure to clarify the role of the sp2-hybridized orbitals of the boron layers on the superconducting state.55−59

Computational Methodology

Structural Description for the MB and XMB Models

A periodic structural model for the lamellar MB was built from experimental data for the P6/mmm hexagonal group,60 yielding to MB (Figure 1a) and X0.125Mg0.875B2 (X = Nb, Ni, Fe) (XMB) materials (Figure 1b). The XMB models are a 2 × 2 × 2 bulk expansion, in other words, a growth of 2 cells in a, b, and c lattice parameters resulting in 8 cells to guarantee a X-doping concentration of 12.5% into the Mg site. Such proposed models include nonmagnetic and magnetic systems, with spin-polarized calculations required for the latter type. Thus, Nb0.125Mg0.875B2 (NbMB) are treated from closed-shell DFT calculations. At the same time, Ni0.125Mg0.875B2 (NiMB) and Fe0.125Mg0.875B2 (FeMB) were evaluated from restricted open-shell calculations assuming a collinear method to represent the magnetic ordering, describing the unpaired electrons as symmetrically distributed along the Cartesian coordinates (x, y, z).

Figure 1.

Figure 1

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Crystalline representation in the P6/mmm group of the periodic models for MB (a) and XMB (X = Ni, Fe, Nb) (b) from the DFT/HSE06 approach. The orange, green, and purple colors represent Mg, B, and X-dopant atoms, respectively.

Chemical Bond Energy Calculation

The formation energies of the MB (EfMB) and XMB materials (EfX) were calculated from eqs 1 and 2, where EB is the energy of the boron atom, EMg is the energy of the magnesium atom, and EX is the energy of the doping atom. Meanwhile, eq 3 presents the formalism for calculating the X-doping bond energies (EbondX) in the XMB materials; factor 1/6 is the energy correction regarding the six chemical bonds found on the doping site. In eq 3, the binding energy (Ebind) is the necessary energy to break chemical bonds of the X dopants with positive values.

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Properties Analysis

Band structure (BS), DOS, and spin charge density maps (SCDM) analyses were performed from the wave functions for the fully relaxed MB and XMB materials. In particular, the band gap region of the materials was evaluated since the DOS and BS calculations take into account the last five energy levels of the valence band (VB) and the first five states of the conduction band (CB) and determine the data for the BS and DOS analysis. In the case of charge density maps, SCDM assesses the electronic density only for unpaired electrons in alpha and beta spins; therefore, the spin density maps for nonmagnetic NbMB and MB were not calculated. Such analysis carefully depicted the charge distribution in the dopant transition metal and the boron atoms within the boron layers since the (001) and (110) planes were investigated. VESTA61 and XCrysden62 packages were employed in this step.

Input Information

The three-dimensional periodic DFT quantum simulations performed in this study describe the exchange–correlation energies through the formalism proposed in the Heyd−Scuseria−Ernzerhof functional (HSE06)63−65 implemented in the CRYSTAL17 code.66 All simulations assume the following thermodynamic conditions: gas phase, zero Kelvin, and vacuum on a stationary position approximation. Mg, B, Fe, Ni, and Nb atoms were described by the 8−511G,67 m-6-311G(d),68 s86411p6411d4411,69 84−2111(6311d)(4111d)G,70 and 986-31(631)G71 Gaussian basis sets, respectively. A 8 × 8 × 8 point mesh filled the space on the symmetry k-points for the BS described by the Monkhrost–Pack approach.72 The self-consistent field convergence criterium was of 10−7 a.u., the total energy convergence for the structural relaxation was 10−8 a.u., and the factor of 10−8 a.u. in energy truncated the convergence of the mono- and bielectronic integrals.

Results and Discussion

Structural and Charge Density Analysis

Quantum simulation of the MB material calculated a = b = 3.073 Å and c = 3.553 Å lattice parameters, which agree with previous experimental73 and theoretical studies found in scientific literature.74,75 Thus, the obtained results show the efficiency of the employed methodology in predicting the material crystalline structure.

As expected, Fe-, Ni-, and Mg-doping is responsible for crystalline structural distortions of the MB material (Table 1). The NbMB showed an expansion of 0.016 Å in the a and b lattice parameters and a 0.018 Å contraction in the c lattice parameter. The unit cell angles indicate a low distortion of 0.002° in the γ angle. In FeMB, a contraction of 0.015 Å in the a and b lattice parameters and 0.033 Å for the c parameters without modifications on unit cell angles. The results for NiMB suggest a contraction of all lattice parameters, with the most pronounced decrease observed for the c lattice parameters; the angles were also affected. The modifications carried out from 3d (Ni and Fe) and 4d (Nb) metals in the Mg site preserved the P6/mmm crystalline structure since they are responsible only for point distortions, which affect the lattice parameters and unit cell angles. The chemical bonds directly influenced the volume of the cell unit, decreasing the volume following the order MB > NbMB > FeMB > NiMB.

Table 1. Lattice Parameters, Volume, and Lattice Angles for the MB, NbMB, FeMB, and NiMB Materials.

material a (Å) b (Å) c (Å) volume (Å3) α = β γ
MgB2 exp73 3.073 3.073 3.553 29.057 90.0° 120.0°
MgB2 3.067 3.067 3.436 27.985 90.0° 120.0°
Nb0.125Mg0.875B2 3.083 3.062 3.418 27.774 90.0° 120.002°
Fe0.125Mg0.875B2 3.052 3.052 3.403 27.448 90.0° 120.0°
Ni0.125Mg0.875B2 3.055 3.055 3.388 27.371 90.0° 120.068°
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The results indicate that Nb-, Fe-, and Ni-doping decreases the distance between the B and cation layers, distorting the c lattice parameter according to the X transition metals. The calculated distances are 2.467 Å (B, Mg), 2.453 Å (B, Nb), 2.429 Å (B, Fe), and 2.430 Å (B–Ni). Figure 2 shows the B–B bonds for the XMB materials. The B–B bond length within the boron layer is 1.770 Å for the MB material. After Fe, Ni, and Nb-doping, slight distortions created expansion and contraction effects on the B hexagons (Figure 2). Consequently, such distortions perturbed the electronic resonance on the boron layers.

Figure 2.

Figure 2

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Chemical bonds for the boron layers in NbMB (a), FeMB (b), and NiMB (c) materials indicating expansion and contraction effects. The orange, green, cyan, red, and silver colors represent Mg, B, Nb, Fe, and Ni atoms, respectively. The blue arrows represent an expansion of the B–B bond length, while the red arrows represent a contraction in the B–B bond length.

Formation energy is relative to an enthalpy connected to electronic energy under drastic thermodynamic conditions from the stationary state approximation accepted in quantum simulations. Such an approximation package determines good qualitative representativity for chemical properties, such as the chemical bond energies. The X–B and Mg–B bond energies were calculated to understand the interaction between boron and cations layers. The results presented regarding the Mg–B bond energy in the MB material (Figure 3) showed that the Ni–B and Fe–B bonds are more robust, corroborated by Figure 2. Consequently, the Fe- and Ni-doped materials showed more significant distortion of the boron ring in the direction of the dopant site. This structural effect indicates that Ni–B and Fe–B bonds are more effective than Nb–B and Mg–B bonds. For the MB, the Mg–B bond presents a weak covalent character because of the null overlap between Mg 2s orbitals and empty 2pz orbitals of the boron, causing charge density wave behavior for the electrons on the boron layers.

Figure 3.

Figure 3

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Calculated bond energies for the X-doped (X = Nb, Fe, Ni) MgB2 structure. The scale was referenced to the Mg–B bond energy in MgB2 material, represented by the red dash line at 0 eV.

The NbMB material presents a low bond energy of 4.9 meV, which is very similar to that observed for the Mg–B bond in pure material. The Fe- and Ni-doping increased the bond energy to 15.7 and 115.1 meV because of the unpaired electrons. This behavior justifies a more efficient overlap between the 3d orbitals of the transition metals and the 2pz orbitals of the boron layer.

The spin populations for the FeMB and NiMB materials are listed in Table 2, showing significant differences for each material. The total magnetic moment (μtotal) of the FeMB material is 2.539 |e−| in the alpha orientation on the Fe 3d orbitals. However, the Fe atomic spin moment (μFe) is 3.094 |e−| in alpha, while the spin moments on the boron atoms (μB) are 0.576 alpha and 1.092 beta |e−|. The boron spin moments with Fe and Mg atoms were μB–Fe = 0.091 beta |e−| and μB–Mg = 0.144 alpha |e−|. In NiMB, the μtotal is precisely 2.0 |e−| with the alpha spin ion, which is 1.244 alpha |e−| on the Ni atoms and 0.712 alpha electrons in B atoms. The simulation does not present a significant beta electron population on boron atoms. In different sites of boron only, there are magnetic moments for alpha electrons, while the μB–Mg is higher than μB–Ni. The same tendency occurs for the FeMB material. Then, it is possible to classify two different boron sites, i.e., boron bonded directly with dopant atoms (B–Fe and B–Ni) and boron without direct bond with such dopants (B–Mg). Consequently, there is a different spin population for each B–Fe, B–Ni B, and B–Mg sites because of the chemical environment in the boron lattice.

Table 2. Results for the Total Spin Momentum (μtotal) for FeMB and NiMBa.

FeMB NiMB
μtotal 2.539α μtotal 2.000α
μFe 3.094α μNi 1.244α
μB 0.576α μB 0.712α
  1.092β   0.0β
μB–Fe 0.091β μB–Ni 0.020α
μB–Mg 0.144α μB–Mg 0.120α
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a

Atomic spin moment for the Fe atom (μFe) on B atom (μB); B atoms bonded with magnetic dopants (μB–Fe, μB–Ni), and B atoms connected to the Mg atoms (μB–Mg).

Figure 4 shows the SCDM for the FeMB magnetic system, demonstrating that the boron lattice presents alpha spin density on the 2px orbitals involved in the formation of the boron ring found in the (001) plane (Figure 4a). The evaluation of the beta channel for the same plane (Figure 4c) suggests that such unpaired electrons occupy the B 2py orbitals, which connect two different boron rings. In the case of (110) planes, the unpaired electron occupation depends on the B distance to the Fe dopant, being alpha electrons found in the 2pz orbitals of the furthest sites and beta electrons observed at the B 2pz orbitals for the sites close to the doping site. It is important to note that the orbitals containing the beta electrons are strongly influenced by the Fe atoms, resulting in 2pz orbitals aligned in the direction of the inserted transition metal. The spin canting creates a deformation on the spin density, which is found in the internal and peripheral regions of the boron rings (Figure 4c), indicating that unpaired electrons have an anisotropic magnetic effect on the B 2pz orbital in both alpha and beta channels.

Figure 4.

Figure 4

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SCDM for the Fe0.125Mg0.875B2 material in the electronic channels (a) alpha channel in the (001) plane; (b) alpha channel in the (110) direction; (c) beta channel in the (001) plane; and (d) beta channel in the (110) plane. The green, orange, and red colors represent the B, Mg, and Fe atoms, respectively.

An important detail in FeMB spin-charge density maps is the measure of the spin canting on the pz orbitals with beta electrons. The spin canting for the B 2pz orbital oriented to the Fe atom has a torsion of 35°, while the same orbital oriented to the Mg atom shows 22° of torsion (Figure 4d). The result indicates a charge attractor behavior of the Fe dopant in the material structure, behavior coherent with the structural distortions on the boron ring in Figure 2b.

The Fe atoms are responsible for the magnetic moment created within the boron hexagonal rings, affecting the electronic resonance in the B–B bond. In summary, Fe atoms within the MgB2 structure are responsible for the change of 2p orbital energies of all boron, creating a magnetic moment for such species, as evidenced by the spin-charge values in Table 2. More specifically, the unpaired electrons in 2pz orbitals of the boron lattice present an increased overlap with the Fe atoms, leading to a stronger Fe–B bond regarding the Mg–B bond.

For NiMB, the alpha electrons show a low spin density located in the boron ring bonds in the (001) plane (Figure 5a). Meanwhile, for the (110) plane, there is a high spin density on the 2 pz orbital of the boron. The difference between NiMB and FeMB can be attributed to the characteristic spin moments for unpaired electrons in the d orbitals of the Ni (1.244 |e−|) and Fe (3.094 |e−|) atoms. NiMB spin density is less ordered regarding FeMB material. This fact is evident in the (001) plane of material in B–B bonds, in which alpha electrons present a distorted spin density (Figure 5b). Such electronic behavior is a consequence of different magnetic moments between Fe and Ni atoms. The Fe atom presents 3.094 |e−| alpha in 3d orbitals, while Ni presents 1.244 |e−| alpha in 3d orbitals. The strong magnetic moment on the Fe atom provides a more spin distribution of the alpha electrons in B–B bonds and beta electrons in the 2 pz orbital of the boron atoms. NiMB material does not present beta unpaired electrons in the electronic structure, indicating that the Ni unpaired electrons are insufficient to provide an effective spin polarization on the boron layer in the MB material.

Figure 5.

Figure 5

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Spin Charge Density Map of the Ni0.125Mg0.875B2 material in (a) alpha channel in the (001) plane; (b) alpha channel in the (110) direction; (c) beta channel in the (001) plane and (d) beta channel in the (110) plane. in electronic channels. The colors green, orange, and red represent the B, Mg, and Fe atoms, respectively.

Electronic Profile

The DOS and BS electronic properties evaluated the MB and XMB materials. The BS for the MB (Figure 6a) presented a metallic behavior in direct bandgaps of 0.05 eV at the L point and 0.12 eV at the M point. The NbMB (Figure 6b) is a nonmagnetic material exhibiting a metallic profile structure with Dirac cones located explicitly at the Γ and A points. The FeMB and NiMB materials have unpaired electrons displacing the electronic bands in the alpha and beta states. Figure 6c,d shows the BS for FeMB where Dirac-cones are at the Γ point in both alpha and beta spins. On the other hand, NiMB (Figure 6e,f) indicates two Dirac cones at the Γ point of the alpha spin and one cone at the A high-symmetry point of the beta channel. It is essential to highlight that doping causes punctual defects responsible for the repetition of the M and L high-symmetry points in the electronic structure of NbMB, FeMB, and NiMB.

Figure 6.

Figure 6

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Band structures for MB (a), NbMB (b), alpha FeMB (c), beta FeMB (d), alpha NiMB (e), and beta NiMB (f). The blue lines represent the last energy level on the VB, while the green lines represent the first energy level of the CB. Red dot lines refer to the Fermi level referenced in 0 eV. The coordinates for the k points in BS analysis were Γ(0,0,0), M(1/2,0,0), M(0, 1/2,0), M(1/2, 1/2, 0), L(1/2, 0, 1/2), A(0, 0, 1/2), L(0, 1/2, 1/2), L(1/2, 1/2, 1/2).

The electronic behavior reported for materials based on the MB structure presents the Mg atoms as electron donors to the boron atoms. The B layers have σ-bond features from px and py orbitals and π-bond features in the pz orbitals.76 Then, the orbital DOS analysis (Figure 7) demonstrates the contributions of the atomic orbitals, specifying the overlap among B 2p orbitals, the 2p and 3s orbitals from Mg, the 4d orbitals from Nb, and the 3d orbitals from Fe and Ni atoms. In Figure 7a, the DOS for the MB material shows that the px and py orbitals for boron are degenerated, while the pz orbital contribution is found mainly at 0 eV.

Figure 7.

Figure 7

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DOS per orbital for MB (a), NbMB (b), FeMB alpha channel (c), FeMB beta channel (d), NiMB alpha channel (e), and NiMB beta channel (f).

In other words, the 2pz orbitals are predominant in the Fermi energy region, being overlapped with the 2p and 3s orbitals of the Mg atom; such energy levels create an interaction between the Mg and B layers. The boron layer in the NbMB material (Figure 7b) interacts with Nb through linear (2pz−4dz2) or parallel (Inline graphic and 2pz–4dxy) orbitals. The 4dz2 orbital Nb presents a high electronic state density on the top of the VB and bottom of the CB overlapping with the 2pz orbitals from boron. In turn, the 4dxz and 4dyz orbitals have a small contribution to the formation of the VB and CB.

For the FeMB (Figure 7c,d), the behavior is opposite regarding the NbMB material. The Fe atoms present distinct 3d−2p overlap in alpha and beta channels. In the alpha spin channel (Figure 7c), there is an overlap between 3d (3dxz and 3dyz) orbitals Fe and 2p (2px and 2py) orbitals boron. Meanwhile, in the beta channel, overlap occurs between the 3dz2 and 2pz orbitals. These results corroborate the SCDM analysis since σ-bonding orbitals were found in the alpha channel (Figure 4a) and π-bonding orbitals are observed in the boron layer (Figure 4b). In the case of NiMB, the orbital overlap is less pronounced than in FeMB. The alpha and beta channels in Figure 7e show the overlap between Ni (3dxz and 3dyz) and boron (2px and 2py) orbitals. The lack of overlap between 3dz2 orbital Ni and 2pz orbital boron is the reason behind the significant spin charge density in the alpha channel (Figure 4a) and the spin absence in the beta channel (Figure 4b) for the NiMB.

The results enable us to better understand the influence of magnetic dopants on π resonance in the boron layers, creating spin polarization. The high spin moment localized in the dopant site is sufficient to perturb the px and py overlap responsible for forming the boron layer. As previously mentioned, the perturbation of electron resonance occurs only for magnetic dopants, the magnitude of the spin polarization being proportional to the impurity magnetic moment. Therefore, the magnetic moment uncouples the alpha and beta spins in σ-bond B–B, locating alpha electrons in the σ-bond region and β electrons in π orbitals, creating the electronic coupling between α2pz–β3d orbitals (Figure 8). In the investigated materials, the Ni atom has two unpaired electrons, while the Fe atom presents four unpaired electrons. The SCDM (Figure 5) indicated that only alpha-unpaired electrons are in the boron lattice of the NiMB. In contrast, alpha and beta electronic densities are well-defined in the boron lattice in FeMB. Thereby, the high spin moment is essential to locate the unpaired electrons on the empty 2pz orbitals in the boron layer. This observation is coherent with previous theoretical results, which determine the electronic effect of the Fe- and Ni-doping on the MB material, suggesting that the boron atom presents a stronger chemical bond with the magnetic atom than the nonmagnetic atom.53

Figure 8.

Figure 8

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Mechanism of spin polarization for the FeMB and NiMB. Green and purple spheres refer to the boron ring and magnetic dopants. The red and blue arrows represent the alpha and beta spins, respectively.

Based on the destabilization of the B–B bond caused by the presence of the magnetic transition metal and the M–B bond energies analysis (Figure 3), an electronic mechanism for spin polarization was proposed (Figure 8). The mechanism agrees with other ideas previously reported in the literature, contributing to clarifying the decrease in Jc and Tc values from Fe and Ni doping in MB materials. In other words, the doped materials lose superconductor efficiency because the localization of the alpha and beta electrons harms the cooper pair formation.44,53,77 In addition to the spin polarization effect, an electronic transfer process is observed since the Fe atom transfers 3dz electrons to empty 2pz orbitals in the boron atoms, making a strong chemical bond. Magnetic dopants behave as quantum charge attractors in MB structures, with a selection to attract the beta electrons from the boron layer electronic resonance and pair them with alpha electrons in the 3d orbitals.

The Spin Polarization Mechanism is theoretical evidence to explain the loss of superconductivity efficiency of the FeMB and NiMB reported in experimental works. The break of electronic pairing in the boron layer makes Cooper pair formation difficult. Furthermore, magnetic dopants create magnetic centers with the behavior of quantum charge attractors because they separate electrons per spin in different orbitals of boron atoms.

Conclusions

The present work investigates the influence of Fe-, Ni-, and Nb-doping on the properties of MgB2. The results obtained for the MgB2 material, with a crystalline structure that aligns with experimental reports, demonstrate the potential and promise of the employed theoretical methodology. The doping with 3d and 4d transition metals induces a contraction of the crystalline structure, maintaining the P6/mmm space group. The electronic structure results suggest that the superconductivity in doped MgB2 materials can potentially offer a more accessible superconducting state due to the presence of Dirac cones in the Γ and A points. Therefore, modifying MgB2 materials with the investigated dopant species is a promising alternative for various applications, sparking excitement and anticipation for future possibilities in the field.

In particular, Fe- and Ni-doping showed structural and electronic modifications connected to the unpaired electron population in the 3d orbitals, promoting an effective bond with the boron layer. The results enable the proposal of an electronic mechanism for spin polarization of boron layers through the unpaired electron transfer from the Fe atom, causing a perturbation of π resonance on boron rings. Furthermore, the magnetic doping in the MgB2 material increases chemical bonds between boron atoms and transition metal dopants because of the spin polarization.

The Spin Polarization Mechanism presented a strong spin separation on the boron ring from magnetic induction of the Fe atoms.

Acknowledgments

The authors acknowledge the financial support from the Coordination of Superior Level Staff Improvement (CAPES). The authors are thankful to the National Laboratory for Scientific Computing (LNCC/MCTI, Brazil) for providing HPC resources for the SDumont supercomputer, which contributed to the research results reported in this work (URL: http://sdumont.lncc.br).

Author Contributions

Guilherme Bonifacio Rosa: writing−original draft, investigation, formal Analysis, methodology, and visualization. Luis Henrique da Silveira Lacerda: supervision, validation, and writing−review and editing. Sergio Ricardo de Lazaro: supervision, resources, validation, conceptualization, writing−review and editing, and project administration.

The Article Processing Charge for the publication of this research was funded by the Coordination for the Improvement of Higher Education Personnel - CAPES (ROR identifier: 00x0ma614).

The authors declare no competing financial interest.

References

  1. Lewis L. H.; Jiménez-Villacorta F. Perspectives on Permanent Magnetic Materials for Energy Conversion and Power Generation. Metall. Mater. Trans. A 2013, 44 (S1), 2–20. 10.1007/s11661-012-1278-2. [DOI] [Google Scholar]
  2. Liu J.; Xue Y.; Zhang M.; Dai L. Graphene-Based Materials for Energy Applications. MRS Bull. 2012, 37 (12), 1265–1272. 10.1557/mrs.2012.179. [DOI] [Google Scholar]
  3. Mori T.; Priya S. Materials for Energy Harvesting: At the Forefront of a New Wave. MRS Bull. 2018, 43 (3), 176–180. 10.1557/mrs.2018.32. [DOI] [Google Scholar]
  4. Liu C.; Li F.; Ma L.; Cheng H. Advanced Materials for Energy Storage. Adv. Mater. 2010, 22 (8), E28 10.1002/adma.200903328. [DOI] [PubMed] [Google Scholar]
  5. Wang D.-G.; Qiu T.; Guo W.; Liang Z.; Tabassum H.; Xia D.; Zou R. Covalent Organic Framework-Based Materials for Energy Applications. Energy Environ. Sci. 2021, 14 (2), 688–728. 10.1039/D0EE02309D. [DOI] [Google Scholar]
  6. Badgujar D. M.; Talawar M. B.; Asthana S. N.; Mahulikar P. P. Advances in Science and Technology of Modern Energetic Materials: An Overview. J. Hazard. Mater. 2008, 151, 289–305. 10.1016/j.jhazmat.2007.10.039. [DOI] [PubMed] [Google Scholar]
  7. Meyer J.; Hamwi S.; Kröger M.; Kowalsky W.; Riedl T.; Kahn A. Transition Metal Oxides for Organic Electronics: Energetics, Device Physics and Applications. Adv. Mater. 2012, 24, 5408–5427. 10.1002/adma.201201630. [DOI] [PubMed] [Google Scholar]
  8. Zhang J.; Wu H.; Zhao G.; Han L.; Zhang J. A review on strain study of cuprate superconductors. Nanomaterials 2022, 12 (19), 3340. 10.3390/nano12193340. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. van Delft D. History and Significance of the Discovery of Superconductivity by Kamerlingh Onnes in 1911. Phys. C 2012, 479, 30–35. 10.1016/j.physc.2012.02.046. [DOI] [Google Scholar]
  10. Ginzburg V. L. High-Temperature Superconductivity (History and General Review). Phys.-Usp. 1991, 34 (4), 283–288. 10.1070/PU1991v034n04ABEH002361. [DOI] [Google Scholar]
  11. Orenstein J.; Millis A. J. Advances in the Physics of High-Temperature Superconductivity. Science 2000, 288 (5465), 468–474. 10.1126/science.288.5465.468. [DOI] [PubMed] [Google Scholar]
  12. Arunachalam V. S.; Fleischer E. L. The Global Energy Landscape and Materials Innovation. MRS Bull. 2008, 33 (4), 264–288. 10.1557/mrs2008.61. [DOI] [Google Scholar]
  13. Bi J.; Nakamoto Y.; Zhang P.; Shimizu K.; Zou B.; Liu H.; Zhou M.; Liu G.; Wang H.; Ma Y. Giant Enhancement of Superconducting Critical Temperature in Substitutional Alloy (La,Ce)H9. Nat. Commun. 2022, 13 (1), 5952. 10.1038/s41467-022-33743-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Tresca C.; Profeta G.; Marini G.; Bachelet G. B.; Sanna A.; Calandra M.; Boeri L. Why Mercury Is a Superconductor. Phys. Rev. B 2022, 106 (18), L180501. 10.1103/physrevb.106.l180501. [DOI] [Google Scholar]
  15. MacManus-Driscoll J. L.; Wimbush S. C. Processing and Application of High-Temperature Superconducting Coated Conductors. Nat. Rev. Mater. 2021, 6 (7), 587–604. 10.1038/s41578-021-00290-3. [DOI] [Google Scholar]
  16. Buchholz A.; Noe M.; Kottonau D.; Shabagin E.; Weil M. Environmental Life-Cycle Assessment of a 10 Kv High-Temperature Superconducting Cable System for Energy Distribution. IEEE Trans. Appl. Supercond. 2021, 31 (5), 1–5. 10.1109/TASC.2021.3070703. [DOI] [Google Scholar]
  17. Godeke A. High Temperature Superconductors for Commercial Magnets. Supercond. Sci. Technol. 2023, 36 (11), 113001. 10.1088/1361-6668/acf901. [DOI] [Google Scholar]
  18. Nishijima S.; Eckroad S.; Marian A.; Choi K.; Kim W. S.; Terai M.; Deng Z.; Zheng J.; Wang J.; Umemoto K.; Du J.; Febvre P.; Keenan S.; Mukhanov O.; Cooley L. D.; Foley C. P.; Hassenzahl W. V.; Izumi M. Superconductivity and the Environment: A Roadmap. Supercond. Sci. Technol. 2013, 26 (11), 113001. 10.1088/0953-2048/26/11/113001. [DOI] [Google Scholar]
  19. McCaughan A. N.; Verma V. B.; Buckley S. M.; Allmaras J. P.; Kozorezov A. G.; Tait A. N.; Nam S. W.; Shainline J. M. A Superconducting Thermal Switch with Ultrahigh Impedance for Interfacing Superconductors to Semiconductors. Nat. Electron 2019, 2 (10), 451–456. 10.1038/s41928-019-0300-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Bussmann-Holder A.; Keller H. High-Temperature Superconductors: Underlying Physics and Applications. Z. Naturforsch., B 2020, 75 (1–2), 3–14. 10.1515/znb-2019-0103. [DOI] [Google Scholar]
  21. Frolov S. M.; Manfra M. J.; Sau J. D. Topological Superconductivity in Hybrid Devices. Nat. Phys. 2020, 16 (7), 718–724. 10.1038/s41567-020-0925-6. [DOI] [Google Scholar]
  22. Ramdane W. Self-Propagating High-Temperature Synthesis of MgB2 Superconductor: A Review. Int. J. Self-Propag. High-Temp. Synth. 2023, 32 (1), 41–59. 10.3103/S1061386223010065. [DOI] [Google Scholar]
  23. Agrestini S.; Metallo C.; Filippi M.; Campi G.; Sanipoli C.; De Negri S.; Giovannini M.; Saccone A.; Latini A.; Bianconi A. Sc Doping of MgB2: The Structural and Electronic Properties of Mg1−xScxB2. J. Phys. Chem. Solids 2004, 65 (8–9), 1479–1484. 10.1016/j.jpcs.2003.09.033. [DOI] [Google Scholar]
  24. Karpinski J.; Zhigadlo N. D.; Katrych S.; Puzniak R.; Rogacki K.; Gonnelli R. Single Crystals of MgB2: Synthesis, Substitutions and Properties. Phys. C 2007, 456 (1–2), 3–13. 10.1016/j.physc.2007.01.031. [DOI] [Google Scholar]
  25. Aksan M. A.; Yakıncı M. E.; Güldeste A. Co-Addition into MgB2: The Structural and Electronic Properties of (MgB2)2−xCox. J. Alloys Compd. 2006, 424 (1−2), 33–40. 10.1016/j.jallcom.2005.12.066. [DOI] [Google Scholar]
  26. Floris A.; Sanna A.; Lüders M.; Profeta G.; Lathiotakis N. N.; Marques M. A. L.; Franchini C.; Gross E. K. U.; Continenza A.; Massidda S. Superconducting Properties of MgB2 from First Principles. Phys. C 2007, 456 (1−2), 45–53. 10.1016/j.physc.2007.01.026. [DOI] [PubMed] [Google Scholar]
  27. Buzea C.; Yamashita T. Review of the Superconducting Properties of MgB2. Supercond. Sci. Technol. 2001, 14 (11), R115–R146. 10.1088/0953-2048/14/11/201. [DOI] [Google Scholar]
  28. Rogado N.; Hayward M. A.; Regan K. A.; Wang Y.; Ong N. P.; Zandbergen H. W.; Rowell J. M.; Cava R. J. Low Temperature Synthesis of MgB2. J. Appl. Phys. 2002, 91 (1), 274–277. 10.1063/1.1420771. [DOI] [Google Scholar]
  29. Doi T.; Kitaguchi H.; Hata S.; Fukuyama K.; Masuda K.; Takahashi K.; Yoshidome T.; Hakuraku Y.; Kuwano N. Monotonic Decrease of Tcs with Thinning of the Superconducting MgB2 Layer in MgB2/Ni and MgB2/B Alternately-Layered Thin Films. Supercond. Sci. Technol. 2007, 20 (12), 1223–1227. 10.1088/0953-2048/20/12/023. [DOI] [Google Scholar]
  30. Karpinski J.; Zhigadlo N. D.; Katrych S.; Puzniak R.; Rogacki K.; Gonnelli R. Single Crystals of MgB2: Synthesis, Substitutions and Properties. Phys. C 2007, 456, 3–13. 10.1016/j.physc.2007.01.031. [DOI] [Google Scholar]
  31. SavaşKan B.Strong Influence of Pressure on the Magnetic Properties of MgB2 Bulk Superconductors; Sakarya University Journal of Science, 2022. [Google Scholar]
  32. Yamasaki A.; Kambe H.; Kawayama I.; Ichinose A.; Doi T. MgB 2 Thin Films Fabricated on Fe Tape and Effects of Annealing on Their Properties. Appl. Phys. Express 2023, 16 (1), 013001. 10.35848/1882-0786/acb1eb. [DOI] [Google Scholar]
  33. Le T.; Pham H. H.; Nghia N. T.; Nam N. H.; Miyanaga T.; Tran D. H.; Kang W. N. Effects of Sn-Ion Irradiation on Local Structure and Flux Pinning Properties of MgB2 Thin Films. Ceram. Int. 2023, 49 (2), 2715–2720. 10.1016/j.ceramint.2022.09.252. [DOI] [Google Scholar]
  34. Glowacki B. A.; Majoros M.; Vickers M.; Evetts J. E.; Shi Y.; McDougall I. Superconductivity of powder-in-tube MgB2 wires. Supercond. Sci. Technol. 2001, 14 (4), 193–199. 10.1088/0953-2048/14/4/304. [DOI] [Google Scholar]
  35. Ye S.; Kumakura H. The Development of MgB2 Superconducting Wires Fabricated with an Internal Mg Diffusion (IMD) Process. Supercond. Sci. Technol. 2016, 29 (11), 113004. 10.1088/0953-2048/29/11/113004. [DOI] [Google Scholar]
  36. Giunchi G.; Ceresara S.; Ripamonti G.; Di Zenobio A.; Rossi S.; Chiarelli S.; Spadoni M.; Wesche R.; Bruzzone P. L. High Performance New MgB2 Superconducting Hollow Wires. Supercond. Sci. Technol. 2003, 16 (2), 285–291. 10.1088/0953-2048/16/2/328. [DOI] [Google Scholar]
  37. Ballarino A.; Flükiger R. Status of MgB2 wire and cable applications in Europe. J. Phys.: Conf. Ser. 2017, 871 (1), 012098. 10.1088/1742-6596/871/1/012098. [DOI] [Google Scholar]
  38. Zhang P.; Zhang Y.; Li C.; Zhang Y.; Shen S.; Ruan G.; Zhang J.; Noudem J. G. The Influence of Preparation Temperature on the Different Facets of Bulk MgB2 Superconductors. Micromachines 2023, 14 (5), 988. 10.3390/mi14050988. [DOI] [PMC free article] [PubMed] [Google Scholar]
  39. Kim J. H.; Dou S. X.; Matsumoto A.; Choi S.; Kiyoshi T.; Kumakura H. Correlation between Critical Current Density and N-Value in MgB 2/Nb/Monel Superconductor Wires. Phys. C 2010, 470, 1207–1210. 10.1016/j.physc.2010.05.075. [DOI] [Google Scholar]
  40. Kováč P.; Hušek I.; Melišek T.; Kulich M.; Štrbík V. MgB2 Composite Wires with Fe, Nb and Ta Sheaths. Supercond. Sci. Technol. 2006, 19 (6), 600–605. 10.1088/0953-2048/19/6/031. [DOI] [Google Scholar]
  41. Goldacker W.; Schlachter S. I.; Zimmer S.; Reiner H. High transport currents in mechanically reinforced MgB2wires. Supercond. Sci. Technol. 2001, 14 (9), 787–793. 10.1088/0953-2048/14/9/331. [DOI] [Google Scholar]
  42. Fu B. Q.; Feng Y.; Yan G.; Liu C. F.; Zhou L.; Cao L. Z.; Ruan K. Q.; Li X. G. High Transport Critical Current in MgB2/Fe Wire by in Situ Powder-in-Tube Process. Phys. C 2003, 392–396 (396), 1035–1038. 10.1016/S0921-4534(03)00858-X. [DOI] [Google Scholar]
  43. Kühberger M.; Gritzner G. Effects of Sn, Co and Fe on MgB2. Phys. C 2002, 370 (1), 39–43. 10.1016/S0921-4534(01)01130-3. [DOI] [Google Scholar]
  44. Dou S. X.; Soltanian S.; Zhao Y.; Getin E.; Chen Z.; Shcherbakova O.; Horvat J. The Effect of Nanoscale Fe Doping on the Superconducting Properties of MgB2. Supercond. Sci. Technol. 2005, 18 (5), 710–715. 10.1088/0953-2048/18/5/022. [DOI] [Google Scholar]
  45. Kováč P.; Hušek I.; Melišek T.; Martínez E.; Dhalle M. Properties of Doped Ex and in Situ MgB2Multi-Filament Superconductors. Supercond. Sci. Technol. 2006, 19 (10), 1076–1082. 10.1088/0953-2048/19/10/016. [DOI] [Google Scholar]
  46. Gong C.; Zhao Q.; Lan F.; Ping X.; Zhang P.; Liu Y.; Hao L. Effect of Ni Doping on Microstructure and Superconductivity of MgB2 Prepared by C - Coated B Powder. Phys. C 2019, 566, 1353540. 10.1016/j.physc.2019.1353540. [DOI] [Google Scholar]
  47. Novosel N.; Galić S.; Pajić D.; Skoko Ž.; Lončarek I.; Mustapić M.; Zadro K.; Babić E. Enhancement of the Critical Current Density in MgB 2 Wires Doped with Ni Nanoparticles. Supercond. Sci. Technol. 2012, 25 (9), 095018. 10.1088/0953-2048/25/9/095018. [DOI] [Google Scholar]
  48. Zhao Q.; Liu Y.; Penner S.; Yu L.; Dong Z.; Gao Z. Characterization and the Mechanism of Formation of the Ternary Compound MgNi2.5B2 in Ni-Doped MgB2 Bulk. Supercond. Sci. Technol. 2009, 22 (7), 075024. 10.1088/0953-2048/22/7/075024. [DOI] [Google Scholar]
  49. Filar K.; Morawski A.; Zaleski A.; Tran L. M.; Czujko T.; Gajda D. Superconducting Properties and Microstructure Changes after Heat Treatment of In Situ MgB2 Wires with Ex Situ MgB2 Barriers. J. Supercond. Nov. Magnetism 2022, 35 (6), 1491–1497. 10.1007/s10948-022-06296-4. [DOI] [Google Scholar]
  50. Kumar D.; Pennycook S. J.; Narayan J.; Wang H.; Tiwari A. Role of silver addition in the synthesis of high critical current density MgB2 bulk superconductors. Supercond. Sci. Technol. 2003, 16 (4), 455–458. 10.1088/0953-2048/16/4/306. [DOI] [Google Scholar]
  51. Khaleel M.; Yusupov Z.; Nassar Y.; El-khozondar H. J.; Ahmed A.; Alsharif A.. Technical Challenges and Optimization of Superconducting Magnetic Energy Storage in Electrical Power Systems. e-Prime-Advances in Electrical Engineering, Electronics and Energy; Elsevier, 2023; Vol. 5, p 100223. [Google Scholar]
  52. Papageorgiou P. G.; Oureilidis K. O.; Christoforidis G. C. A Systematic Review of Hybrid Superconducting Magnetic/Battery Energy Storage Systems: Applications, Control Strategies, Benefits, Limitations and Future Prospects. Renewable and Sustainable Energy Reviews 2023, 183, 113436. 10.1016/j.rser.2023.113436. [DOI] [Google Scholar]
  53. Lefcochilos-Fogelquist H. M.; Wan L. F.; Rowberg A. J. E.; Kang S.; Stavila V.; Klebanoff L. E.; Allendorf M. D.; Wood B. C. Understanding Electronic Structure Tunability by Metal Dopants for Promoting MgB2 Hydrogenation. J. Appl. Phys. 2024, 135 (2), 025003. 10.1063/5.0175546. [DOI] [Google Scholar]
  54. Wan M.; Zhao S.; Zhang Z.; Zhou N. Two-Dimensional BeB2 and MgB2 as High Capacity Dirac Anodes for Li-Ion Batteries: A DFT Study. J. Phys. Chem. C 2022, 126 (23), 9642–9651. 10.1021/acs.jpcc.2c02563. [DOI] [Google Scholar]
  55. de Lazaro S. R.; Rosa G. B.; Ribeiro R. A. P.; Lacerda L. H. d. S.; de Oliveira M. C.; Longo E. Hybrid Exchange−Correlation Functionals for van Der Waals TiSe2Material: Parametrization versus a Posteriori D3 Dispersion Corrections. Comput. Mater. Sci. 2022, 214, 111672. 10.1016/j.commatsci.2022.111672. [DOI] [Google Scholar]
  56. He Q.; Yu B.; Li Z.; Zhao Y. Density Functional Theory for Battery Materials. Energy Environ. Mater. 2019, 2 (4), 264–279. 10.1002/eem2.12056. [DOI] [Google Scholar]
  57. Zhang X.; Zhang Z.; Wu D.; Zhang X.; Zhao X.; Zhou Z. Computational Screening of 2D Materials and Rational Design of Heterojunctions for Water Splitting Photocatalysts. Small Methods 2018, 2 (5), 1700359. 10.1002/smtd.201700359. [DOI] [Google Scholar]
  58. Zhao Y.; Zeng S.; Ni J. Superconductivity in Two-Dimensional Boron Allotropes. Phys. Rev. B 2016, 93 (1), 014502. 10.1103/PhysRevB.93.014502. [DOI] [Google Scholar]
  59. Rosa G. B.; da Rocha G. G.; Jurelo A.; de Lazaro S. R.. Electronic Structure of the Fe-Doped TiSe2Material: What Quantum Conditions Improve the Efficiency in the Energy Transmission Technology?; Springer, 2024; pp 101–117. [Google Scholar]
  60. Jin K.-H.; Huang H.; Mei J.-W.; Liu Z.; Lim L.-K.; Liu F. Topological Superconducting Phase in High-Tc Superconductor MgB2 with Dirac−Nodal-Line Fermions. npj Comput. Mater. 2019, 5 (1), 57. 10.1038/s41524-019-0191-2. [DOI] [Google Scholar]
  61. Momma K.; Izumi F.. An integrated three-dimensional visualization system VESTA using wxWidgets. In Atelier de Diffraction sur oudre Seventh Canadian Powder Diffraction Workshop; International Union of Crystallography, 2006; p 106. [Google Scholar]
  62. Blatov V. A.TOPOS, IUCr Compcomm Modeling Migration Paths in Fast-Ion Conductors View Project Cation Arrays in Inorganic Structures View Project. http://www-structmed.cimr.cam.ac.uk/ (accessed date July 30, 2024).
  63. Mohebbi E.; Pavoni E.; Mencarelli D.; Stipa P.; Pierantoni L.; Laudadio E. PBEsol/HSE Functional: A Promising Candidate for Vanadium Dioxide (B) Characterization. RSC Adv. 2022, 12 (48), 31255–31263. 10.1039/D2RA04322J. [DOI] [PMC free article] [PubMed] [Google Scholar]
  64. Deák P.; Aradi B.; Frauenheim T.; Janzén E.; Gali A. Accurate Defect Levels Obtained from the HSE06 Range-Separated Hybrid Functional. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81 (15), 153203. 10.1103/PhysRevB.81.153203. [DOI] [Google Scholar]
  65. Kohn W.; Sham L. J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965, 140 (4A), A1133–A1138. 10.1103/PhysRev.140.A1133. [DOI] [Google Scholar]
  66. Dovesi R.; Erba A.; Orlando R.; Zicovich-Wilson C. M.; Civalleri B.; Maschio L.; Rérat M.; Casassa S.; Baima J.; Salustro S.; Kirtman B. Quantum-Mechanical Condensed Matter Simulations with CRYSTAL. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2018, 8 (4), e1360 10.1002/wcms.1360. [DOI] [Google Scholar]
  67. McCarthy M. I.; Harrison N. M. Ab initio determination of the bulk properties of MgO. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 49 (13), 8574–8582. 10.1103/PhysRevB.49.8574. [DOI] [PubMed] [Google Scholar]
  68. Pernot P.; Civalleri B.; Presti D.; Savin A. Prediction Uncertainty of Density Functional Approximations for Properties of Crystals with Cubic Symmetry. J. Phys. Chem. A 2015, 119 (21), 5288–5304. 10.1021/jp509980w. [DOI] [PubMed] [Google Scholar]
  69. Heifets E.; Kotomin E. A.; Bagaturyants A. A.; Maier J. Thermodynamic Stability of Non-Stoichiometric SrFeO3-:δ: A Hybrid DFT Study. Phys. Chem. Chem. Phys. 2019, 21 (7), 3918–3931. 10.1039/C8CP07117A. [DOI] [PubMed] [Google Scholar]
  70. Vilela Oliveira D.; Laun J.; Peintinger M. F.; Bredow T. BSSE-Correction Scheme for Consistent Gaussian Basis Sets of Double- and Triple-Zeta Valence with Polarization Quality for Solid-State Calculations. J. Comput. Chem. 2019, 40 (27), 2364–2376. 10.1002/jcc.26013. [DOI] [PubMed] [Google Scholar]
  71. Dall’Olio S.; Dovesi R.; Resta R. Spontaneous polarization as a Berry phase of the Hartree-Fock wave function: The case of KNbO3. Phys. Rev. B 1997, 56 (16), 10105. 10.1103/PhysRevB.56.10105. [DOI] [Google Scholar]
  72. Chauhan S. S.; Srivastava P.; Shrivastava A. K. Band Gap Engineering in Doped Graphene Nanoribbons: An Ab Initio Approach. Solid State Commun. 2013, 154 (1), 69–71. 10.1016/j.ssc.2012.10.030. [DOI] [Google Scholar]
  73. Zhang Y.; Xu X. Predicting Doped MgB2 Superconductor Critical Temperature from Lattice Parameters Using Gaussian Process Regression. Phys. C 2020, 573, 1353633. 10.1016/j.physc.2020.1353633. [DOI] [Google Scholar]
  74. Kortus J.; Mazin I. I.; Belashchenko K. D.; Antropov V. P.; Boyer L. L. Superconductivity of Metallic Boron in MgB2. Phys. Rev. Lett. 2001, 86 (20), 4656–4659. 10.1103/PhysRevLett.86.4656. [DOI] [PubMed] [Google Scholar]
  75. Liu A. Y.; Mazin I. I.; Kortus J. Beyond Eliashberg Superconductivity in MgB2: Anharmonicity, Two-Phonon Scattering, and Multiple Gaps. Phys. Rev. Lett. 2001, 87 (8), 087005. 10.1103/PhysRevLett.87.087005. [DOI] [PubMed] [Google Scholar]
  76. Choi H. J.; Roundy D.; Sun H.; Cohen M. L.; Louie S. G. The Origin of the Anomalous Superconducting Properties of MgB2. Nature 2002, 418 (6899), 758–760. 10.1038/nature00898. [DOI] [PubMed] [Google Scholar]
  77. Lee J. M.; Jung S.-G.; Han Y.; Park T.-H.; Jang J.; Jeon H.; Yeo S.; Choi H.-Y.; Park T.; Kang W. N. Influence of Disorder Strength on the Superconducting Mechanism of MgB2. Supercond. Sci. Technol. 2022, 35 (1), 015001. 10.1088/1361-6668/ac392a. [DOI] [Google Scholar]

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