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Materials science is concerned with the development of novel materials that possess specified physical characteristics. In this work, we study MP₂ (M = Co, Rh, Ir) compounds which crystallize in the monoclinic structure with formation energy equal to −11.72eV, −11.62eV, and −11.13eV for CoP₂, RhP₂, and IrP₂, respectively. These materials in high temperature present an important advance for thermoelectric applications. First-principles calculations with density functional theory (DFT) are employed to investigate the electrical, optical, thermoelectric, and thermodynamic properties of MP₂ (M = Co, Rh, and Ir) compounds. All computations are performed using DFT and the WIEN2k method. By combining the modified Becke–Johnson of Tran-Blaha potential (TB-mBJ) with the approximated gradient généralisé (GGA), the precision of the restricted band has been optimized. This approach, in conjunction with tools like GIBBS2 and Boltzmann’s theory of transport, has made it possible to ascertain the thermodynamic and thermoelectric properties of the materials under study. The results show that these materials have a straight band gap of CoP₂ is 4.78eV, whereas the indirect band gaps of RhP₂ and IrP₂ are 0.575eV and 0.875eV, respectively. The optical characteristics indicated good optical absorption and conductivity in the ultraviolet and visible ranges. Furthermore, using Boltzmann’s theory, it was revealed that the figure of merit ZT is more than 1.7 at a temperature of $T=700$K, notably for CoP2. In fact, our study demonstrates that MP2 (M = Co, Rh, and Ir) compounds might be effective in ultraviolet and visible photoelectric applications, as well as thermoelectric applications.

First-principles calculations were carried out to study the stability and electronic properties of native vacancy defects in the semiconducting ZnIn₂Te₄ (ZIT) and CdIn₂Te₄ (CIT). The Zn/Cd and In vacancies are acceptor defects, while the Te vacancy is donor defect. However, the In and Te vacancies dominate in the $n$-type and $p$-type semiconducting environments, respectively. The Te vacancy is not excited, so it could not compensate the majority of free carriers. The In vacancy prefers to be excited, which generates free hole carriers to compensate the majority of electron carriers. The Zn vacancy is rare in a typical semiconducting environment. Furthermore, all the vacancies induce localized defect states which may be trap centers for the free carriers. Accordingly, these native vacancy defects are destructive for the development of solar cells based on ZIT and CIT, so they should be avoided as much as possible during the growth process.

In this paper, the effect of Co and Ni in AerMet100 steel on the structure stability for Fe₃C was investigated using first-principles calculations based on generalized gradient approximation (GGA) density function theory. The internal positions of atoms within the unit cell were optimized and the ground state properties such as lattice parameter, the formation energy and density of states for Fe₃C structure without and with Co or Ni((Fe, M)₃C, M=Fe, Co, Ni) were calculated. The calculated results show that the equilibrium structural parameters of Fe₃C agree with the experimental ones. The formation energy of Fe₃C is negative, while that of Fe₃C with Co or Ni are positive. The Fe₃C with the substitution of Co or Ni for Fe at the 4c sites are metastable or unstable at ambient conditions. The effect of Co and Ni on the structural stability for Fe₃C is discussed in terms of their electronic structure and chemical bonding.

In this paper, the formation energies and elastic constants of $\alpha$-Al₂O₃, MgO and AlN in both rock salt (cubic) and wurtzite (hexagonal) structures were investigated by first principles calculations. The results show that the formation energy being −17.8, −6.3, −3.06 and −3.46 eV/formula unit for $\alpha$-Al₂O₃, MgO, AlN (rock salt) and AlN (wurtzite). It suggests that in the ground state, $\alpha$-Al₂O₃ is relatively more stable than MgO and AlN. The elastic properties for a polycrystalline in the ground state were calculated with the obtained elastic constants, the elastic properties reveal the rock salt structure AlN is the hardest particles among all the inclusions, and all of these inclusions are classified as brittle materials, which is detrimental to the ductile nature of aluminum matrix. The calculated anisotropy index shows that the AlN (wurtzite) and $\alpha$-Al₂O₃ have a lower degree of anisotropy compared with MgO and AlN (rock salt). The calculated results are in good agreement with the values of experimental and other works.

Using the first-principles methods, we study the formation energetics and charge doping properties of the extrinsic substitutional defects in montmorillonite. Especially, we choose Be, Mg, Ca, Fe, Cr, Mn, Cu, Zn as extrinsic defects to substitute for Al atoms. By systematically calculating the impurity formation energies and transition energy levels, we find that all Group II defects introduce the relative shallow transition energy levels in montmorillonite. Among them, Mg_Al has the shallowest transition energy level at 0.10 eV above the valence band maximum. The transition-elemental defects Fe_Al, Cr_Al, and Mn_Al are found to have relatively low formation energies, suggesting their easy formation in montmorillonite under natural surrounding conditions. Our calculations show that the defects Cu_Al and Zn_Al have high formation energies, which exclude the possibility of their formation in montmorillonite.

By using the first-principles methods based on density function theory (DFT), the effects of boron(B)/phosphorus(P) pair co-doping on the electrical properties of zigzag single-walled carbon nanotubes (SWNTs) have been investigated. We calculated the formation energies and band structures of (6, 0) metallic and (8, 0) semiconducting SWNTs with different B/P co-doping sites and concentrations. The obtained formation energies suggest that the B/P co-doping configurations are energetically stable structures and the B and P tend to form a B–P bond. It shows that an energy gap is opened by B/P co-doping in (6, 0) metallic SWNTs and the metallic carbon nanotubes are converted into semiconductors. For the (8, 0) semiconducting SWNTs, B/P co-doping influences the band structure, but it does not change the attributes essentially and the SWNTs are still semiconducting. It was also found that the band structures depend on the doping concentration as well as the doping site of B/P pair.

The structural and electronic properties of neutral oxygen vacancies in (Mo + C)-doped anatase TiO₂ were investigated using frozen-core projector-augmented wave (PAW) method within GGA +U approximation. Six possible oxygen vacancy sites were considered in the present work. The results show that the octahedral vertex adjacent to Mo and opposite from C is the most stable position for oxygen vacancy based on the results of the formation energy. The Fermi level is located at above the bottom of the conduction band and a typical n-type metallic behavior occurs as a result of the oxygen vacancy appeared in (Mo + C) doped TiO₂.

Exploring the next generation of invincible energy materials with fascinating properties is vital in the challenge of energy crisis. In this paper, we extract T-carbon as a potential candidate and have an insight into the electronic and optical properties by means of first principles. It is found that S1 position doping system is relatively more stable with the formation energy of 0.323 eV, and has the smallest bandgap value of 1.228 eV. Charge density difference maps show that the electron loss is obvious near the S atom and the covalent bond is weakened. The population analysis shows that the S atom will obtain electrons through competition, while the Se atom will lose electrons. Additionally, the peak values of $𝜀$2 in the doped systems decrease significantly, especially for S2 doping system, indicating that S2 doping can effectively improve the service life in related devices. Compared with the instinct system, the absorption coefficient is lower in the UV region and greater in the visible region. The peak of energy loss spectrum reduces after doping, especially for Se1 doping. The results provide a theoretical basis for the industrial application of T-carbon in the energy microdevice fields.

The structural, stability, and electronic properties and optimized inter-wall distances of double-walled boron nitride nanotubes (DWBNNTs) are investigated based on density functional theory (DFT) with the SIESTA code. The computations are done on the zigzag ($m$,0)@($n$,0) DWBNNTs with chirality of ($m=6$, 7 and $n=10$–18) and the armchair ($m,m)@(n,n)$ with chirality of ($m=5$, 6 and $n=7$–15). The calculated binding and formation energies revealed that the armchair and the zigzag DWBNNTs with chirality differences of ($n-m=6$ and 9) ($m,m)@(m+6,m+6$), ($m,0)@(m+9,0$) and inter-layer spacing of about 4.22Å and 3.62Å are the best favorable nanotubes, respectively. Analyzing the electronic structures revealed that all considered armchair and zigzag BNNTs are semiconductors. Furthermore, it is concluded that with increasing diameters of the tubes and the spaces between walls, the value of the band gap rises, and the change process is almost constant at larger distances between the walls. Also, compared to single-walled nanotubes, DWBNNTs have a narrower bandgap. Future empirical investigations can definitely benefit from the implications of this research.

With a hexagonal (honeycomb) network of mono-layered carbon atoms, graphene has demonstrated outstanding electronic properties. This work describes the impact of deliberately introduced single, double and triple carbon vacancies in grapheme monolayer. In addition, these carbon vacancies were then substituted with gold atoms and their influence on the electronic properties of the two-dimensional (2D) graphene layers was investigated. In this regard, a first principle calculation was performed to examine electronic properties and formation energy of 2D graphene layer by applying density functional theory (DFT). Introduction of such defects appeared to increase the stability of the graphene sheet as confirmed by formation energy calculations. Moreover, decrease of formation energy was noticed to be significant with an increase in the number of defects. Band structure calculations described the shifting of localized states from valance to conduction bands which caused the transformation of semiconducting behavior into metallic one on the filling of carbon vacancies by gold atoms. Comparing this behavior with that of partial density of states (PDOS) it was noted that a lot of states existed in the valance band in the case of C-vacancies yielding charge free region around the vacancy. On the other hand, filling of C-vacancies by gold generated a large number of energy states in the conduction band illustrating the accumulation of charges near gold atom. Width of the peak across the Fermi level indicated the accumulative energy of electron to be almost 0.15eV. These calculated DOS and PDOS demonstrated metallic like behavior of the graphene monolayer with typical defect states.

Geometric and electronic properties and vacancy formation energies for two kinds of oxygen-vacancy Cu₂O (111) surfaces have been investigated by first-principles calculations. Results show that the relaxation happens mainly on the top three trilayers of surfaces. Two vacancies trap electrons of -0.11e and -0.27e, respectively. The effects of oxygen vacancies on the electronic structures are found rather localized. The electronic structures suggest that the oxygen vacancies enhance the electron donating ability of the surfaces to some extent. The energies of 1.75 and 1.43 eV for the formation of oxygen vacancies are rather low, which indicates the partially reduced surfaces are stable and easy to produce.

In this paper, structural, elastic, electronic and magnetic properties of half-Heusler XSrC ($\mathrm{\text{X}}=\mathrm{\text{Li}}$ and Na) compounds have been investigated utilizing full potential linearized augmented plane wave (FP-LAPW) method based on density functional theory (DFT). For exchange-correlation potentials, the generalized gradient approximation (GGA) has been used. The calculated cohesive and formation energy values showed that these compounds can be experimentally synthesized. The elastic properties were analyzed in detail and reveal that LiSrC and NaSrC compounds are mechanically stable. The spin-polarized band structure and density of states illustrate that LisrC and NaSrC alloys have a half metallic character. The total magnetic moment is 1$\mu \mathrm{\text{B}}$ per formula unit that confirms the half metallic behavior and follows the Slater-Pauling rule $M_T=(8-Z_{\mathrm{\text{tot}}}){\mu }_B$. For half-Heusler XSrC ($\mathrm{\text{X}}=\mathrm{\text{Li}}$ and Na) compounds, there are no available experimental or theoretical studies, our calculations are considered as first predictions.