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The structural and lattice dynamical calculations are performed on ZrB2, NbB2, and MoB2 compounds using the first-principles of total energy calculations. Generalized gradient approximations (GGA) are used to model exchange-correlation effects. Structural results of these calculations are consistent with past experimental data and other theoretical...
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... calculated point frequencies: the infrared active (E 1u , A 2u ) and Raman active (B 1g , and E 2g ) modes are given Table 2 along with the available experimental data for the sake of comparison. The point frequencies of the E 1u , A 2u , and B 1g are, in general, in favor- able agreement with the experimental [22] ones. ...
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Citations
... The current results are compared with available experimental data [14,31], as well as reported calculated values [33][34][35][36][37]. Our results are in remarkable agreement with the data of Pei et al [14,31] at 90 GPa for both, the volume (a difference of around 0.3%) and also the c/a ratio (difference of 2.1%). ...
... Calculated p(V ) equation of state and optimized c/a parameter, as a function of applied pressure for α-MoB 2 obtained by two different band-structure methods (MBPP[27] and Elk [32]), compared with experimental data[14,31] (red triangles), and calculated results reported previously[33][34][35][36][37] (blue squares). ...
We have studied the lattice dynamics, electron-phonon coupling, and superconducting properties of α-MoB 2 , as a function of applied pressure, within the framework of density functional perturbation theory using a mixed-basis pseudopotential method. We found that phonon modes located along the A-H, H-L, and L-A high-symmetry paths exhibit large phonon linewidths and contribute significantly to the electron-phonon coupling constant. Although linewidths are particularly large for the highest-frequency optical phonon modes (dominated by B vibrations), their contribution to the electron-phonon coupling constant is marginal. The latter is largely controlled by the acoustic low-frequency modes of predominantly Mo character. It was observed that at a pressure of 90GPa, where α-MoB 2 forms, the phonon-mediated pairing falls into the strong-coupling regime, and the estimate for the superconducting critical temperature T c agrees well with experimental observations. When further increasing the applied pressure, a reduction of T c is predicted, which correlates with a hardening of the acoustic low-frequency phonon modes and a decrease of the electron-phonon coupling parameter.
... At the same time, the effects of B-B bond length and TM-B bond length on hardness were also comprehensively analyzed in figure 2(b). Since bonds lengths all have the same effect on hardness, the product of these two bond lengths is studied in relation to hardness [50,51,62,[93][94][95][96]. However, the results show that the relationships between hardness and atomic radius or bond lengths are complicated. ...
Transition metal diborides (TMdBs, P6/mmm, AlB2-type) have attracted much attention for decades, due to TMdBs can be conductors, superconductors, magnetism materials, and catalysts. The layered structure caused by borophene subunit is the source of functions, and also make TMdBs be a potential bank of Mbene. However, TMdBs also exhibit high hardness which is not supposed to have in layered structure. The high hardness of TMdBs arise from covalent bonds of Boron-boron (B-B) and strong p-d orbit hybridization of B and TM. While, strong B-TM bonds will eliminate the layered structure which may damage the functional properties. Understanding the basic mechanism of hardness and functional is significant to achieve optimal TMdBs. In this work, the basic properties of TMdBs include hardness, superconductor, and catalytic property are summarized. It can be found that Youngs modulus (E) and Shear modulus (G) are beneficial for the hardness of TMdBs and Poisson ratio is the opposite. The increasing of atomic radius of TM brings the improvement for the hardness of TMdBs before it reaches the highest value 1.47 Å, beyond which hardness decreases. Besides, TMdBs also have excellent activity comparable with some noble metal for hydrogen evolution reaction, which is closely related with d-band center. More importantly, higher valence electron concentrations were found to be adverse for hardness and superconductivity of TMdBs and greatly affect their catalytic properties. This review is of guiding significance for the further explore the relation between structures and properties of TMdBs.
... Our spectra are in good agreement with those calculated in Ref. [57] and slightly worse agree with the PHDOSs suggested in Refs. [58][59][60]. In Fig. 8f we also show the composition weighted average PHDOSs of MB 2 . ...
... The experimental PHDOSs [56] are denoted by red line. The phonon spectra calculated in other studies are denoted by green line [57] and blue line [58][59][60]. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) Fig. 9. Calculated heat capacity (C V ) as a function of temperature (T) (theor) and the comparison of the C V (T) dependences with the experimental curves [61] (exp) and [62] (exp1). ...
The stability, electronic and phonon structures, optical, mechanical and thermodynamic properties of the random high entropy (TiZrHfNbTa)B2 solid solution (alloy) were studied in comparison with those of TiB2, ZrB2, HfB2, NbB2 and TaB2 using first-principles calculations. The mixing enthalpy of −0.842 kJ/mol of atoms for the high entropy diboride points to that it is stable against decomposition into the constituting binary diborides. All the diborides studied are thermodynamically, mechanically and dynamically stable. The dielectric function, reflectivity and extinction coefficient of the diboride compounds were comprehensively studied. Both (TiZrHfNbTa)B2 and binary diborides are found to be good reflective materials in infrared, visible and ultraviolet regions. The calculated elastic moduli, B/G ratio, Vickers hardness, fracture toughness and Debye temperature of (TiZrHfNbTa)B2 are medium between largest and lowest ones of the constituents, approximately obey the rule of mixture. Calculations of the stress-shear strain relations for (TiZrHfNbTa)B2 point to the possibility of the activation of both basal and prismatic slip systems. The elastic moduli and linear compressibility exhibit the spatial anisotropy inherent to hexagonal structures. The thermodynamic characteristics of the diborides studied are well reproduced in a temperature range up to 800–1000 K.
... The electrical and magnetic properties largely depend on the number of electrons in the valence band. Calculations have shown that the electron-phonon coupling of the s and p bonds is highly anisotropic with a dominant role due to optical in-plane phonons [107] and phonon dispersion around the Gsymmetry point in the Brillouin zone of ZrB2 [108]. ...
We review the thin film growth, chemistry, and physical properties of Group 4-6 transition-metal diboride (TMB2) thin films with AlB2-type crystal structure (Strukturbericht designation C32). Industrial applications are growing rapidly as TMB2 begin competing with conventional refractory ceramics like carbides and nitrides, including pseudo-binaries such as Ti1-xAlxN. The TMB2 crystal structure comprises graphite-like honeycombed atomic sheets of B interleaved by hexagonal close-packed TM layers. From the C32 crystal structure stems unique properties including high melting point, hardness, and corrosion resistance, yet limited oxidation resistance, combined with high electrical conductivity. We correlate the underlying chemical bonding, orbital overlap, and electronic structure to the mechanical properties, resistivity, and high-temperature properties unique to this class of materials. The review highlights the importance of avoiding contamination elements (like oxygen) and boron segregation on both the target and substrate sides during sputter deposition, for better-defined properties, regardless of the boride system investigated. This is a consequence of the strong tendency for B to segregate to TMB2 grain boundaries for boron-rich compositions of the growth flux. It is judged that sputter deposition of TMB2 films is at a tipping point towards a multitude of applications for TMB2 not solely as bulk materials, but also as protective coatings and electrically conducting high-temperature stable thin films.
... The electrical and magnetic properties largely depend on the number of electrons in the valence band. Calculations have shown that the electron-phonon coupling of the σ and π bonds is highly anisotropic with a dominant role due to optical in-plane phonons [107] and phonon dispersion around the Γ-symmetry point in the Brillouin zone of ZrB 2 [108]. ...
We review the thin film growth, chemistry, and physical properties of Group 4–6 transition-metal diboride (TMB2) thin films with AlB2-type crystal structure (Strukturbericht designation C32). Industrial applications are growing rapidly as TMB2 begin competing with conventional refractory ceramics like carbides and nitrides, including pseudo-binaries such as Ti1-xAlxN. The TMB2 crystal structure comprises graphite-like honeycombed atomic sheets of B interleaved by hexagonal close-packed TM layers. From the C32 crystal structure stems unique properties including high melting point, hardness, and corrosion resistance, yet limited oxidation resistance, combined with high electrical conductivity. We correlate the underlying chemical bonding, orbital overlap, and electronic structure to the mechanical properties, resistivity, and high-temperature properties unique to this class of materials. The review highlights the importance of avoiding contamination elements (like oxygen) and boron segregation on both the target and substrate sides during sputter deposition, for better-defined properties, regardless of the boride system investigated. This is a consequence of the strong tendency for B to segregate to TMB2 grain boundaries for boron-rich compositions of the growth flux. It is judged that sputter deposition of TMB2 films is at a tipping point towards a multitude of applications for TMB2 not solely as bulk materials, but also as protective coatings and electrically conducting high-temperature stable thin films.
... Oguchi [9] studied the systematic trend in lattice constants and heat of formation of these compounds. Deligoz et al. [10,11] investigated the structural and lattice dynamic properties of TiB 2 and ZrB 2 together with VB 2 , ScB 2 , NbB 2 , and MoB 2 . They reported lattice parameters, phonon dispersion curves, and some thermodynamic properties such as internal energy, entropy, heat capacity etc. Waskowska et al. [12] grew single crystals of ScB 2 , TiB 2 , YB 4 , and HoB 4 and determined their bulk modulus, thermal expansion, and other thermoelastic properties. ...
Based on the density functional theory and using GGA and GGA + so approximations, the electronic and optical properties of bulk TMB2 (TM = Cr, Mn, and Fe) are calculated. We calculate the electronic properties of these compounds in the presence of spin-orbit interaction. The highest and lowest spin-orbit effects are observed in MnB2 and FeB2 compounds respectively; this effect also causes degeneration disappear in these compounds and its greatest effect is on the orbital p of transition metals at low energy levels. In the up spin state and near the Fermi level, the energy levels are shifted to higher energies, which is not commonly observed in down spin state. Moreover, the optical properties of TMB2 including the real and imaginary parts of ε(ω), energy loss function, absorption coefficient, reflectivity, and refraction are calculated for two directions. The spin-orbit effect has significant influence on the optical coefficient of these compounds. Energy loss of the emitted photons is significantly reduced in these compounds at both directions in the presence of spin-orbit effects. Also, the spin-orbit effect in both directions increases the plasmon frequency and eliminates the transparency of the material at higher energies than the plasmon frequency.
... According to the design principle, Nb-based borides have attracted attention because of their low cost, high hardness, high elastic modulus, and excellent thermal stability. 12,13 For those Nb−B binary compounds, early studies have focused on the structure and mechanical properties of NbB 2 . For example, the electronic structure and bonding state of NbB 2 have been investigated by Vajeeston and Ravindran. ...
Synthesizing and designing novel hard material is still a huge challenge to industrial applications. In this paper, the influence of B concentration on the structural stability, elastic properties, hardness, and chemical bonding of Nb-B compounds has been investigated by using a first-principles approach. Two previously unreported crystal structures of Nb2B and Nb2B3 were predicted. In particular, the hard mechanism of TMBs has been explored in detail. The convex hull has indicated that the NbB with an orthorhombic structure is the most stable structure among those Nb-B compounds. The bulk modulus of Nb-B compounds is related to the B concentration. However, Nb2B3 shows the highest shear deformation resistance and the strongest elastic stiffness. The calculated theoretical hardness of Nb2B3 is 33.5 GPa and can be considered as a potential superhard material. The high hardness and elastic properties are attributed not only to the B concentration and orientation of bonds but also to the chemical bonding between layer-layer. Finally, we concluded that the bond strength at layer-layer plays a crucial role for hardness and elastic properties.
... A number of studies [29][30][31][32][33][34][35][36][37] exist in the literature dealing with lattice dynamical properties of borides and diborides. The results of these works showed that diborides and borides are dynamically stable for AlB 2 and WC structures, respectively. ...
... The obtained phonon dispersion curves along the high-symmetry directions and the corresponding phonon DOS for these compounds are illustrated in Fig. 1. The overall features of the phonon dispersion curves are similar to those of the other transi-tion-metal and rare earth borides [6,32,33]. The unit cell of AlB 2type structure contains three atoms, which give rise to a total of nine phonon branches, which contains three acoustic modes and six optical modes. ...
We have tried to theoretically predict the lattice dynamical and thermodynamic properties of rare earth diborides (XB2, X = Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm) in AlB2-type structure based on density functional theory within generalized gradient approximation. The calculated equilibrium lattice parameters are in overall agreement with the available experiment and other theoretical results. The phonon dispersion curves are derived by using the direct method. The lattice dynamical results are showed that these compounds are dynamically stable for the considered structure, and these properties exhibits, almost, similar trend for these compounds. In addition, thermodynamic properties such as the free energy, enthalpy, entropy and heat capacity are, also successfully predicted and analyzed with the help of phonon dispersion.
... 13 Interestingly, candidate ground states hR24-MoB 3 and hP10-MoB 4 were theoretically presented. 19 In addition, some modeling works on Mo-B compounds has given insights into their dynamical, thermodynamic, mechanical properties and high-pressure structure transitions, [25][26][27] but these different and even contradictory reports about their structures and compositions have not been solved. Therefore, it is highly urgent to explore structural stabilities and mechanical behaviors of MoB x . ...
Molybdenum borides are currently raising great expectations for superhard materials, but their crystal structures and mechanical behaviors are still under discussion. Here, we report an unexpected reduction of stability and hardness from porous hP16-MoB3 and hR18-MoB2 to dense hP20-MoB4 and hR21-Mo2B5, respectively. Furthermore, we demonstrate that this anomalous variation has its electronic origin. These findings not only manifest that the long-recognized hP20-MoB4 (hP3-MoB2) and hR21-Mo2B5 should be hP16-MoB3 and hR18-MoB2, respectively, but also challenge the general design principle for ultrahard materials only pursuing the dense transition-metal borides with high boron content.
... This high frequency region results from optical phonon modes, and is dominated by the movements of the Si, Si, Sn atoms for SiGe, SiSn, and GeSn, respectively. This is expected because the cation atom is lighter than the anion atoms, which leads to comparatively weaker electron-phonon interactions [30]. In Fig. 4, the two regions of PHDOS curves SiGe and SiSn are also separated by phonon band gaps, which are same as the gaps between the optical and acoustic branches in the phonon dispersion spectra. ...
A first-principles calculations, based on the norm-conserving pseudopotentials and the density functional theory (DFT) and the density functional perturbation theory (DFPT) as implemented in the ABINIT code, have been performed to investigate the structural stability, elastic, lattice dynamic and thermodynamic properties of the ordered SiGe, SiSn and GeSn cubic alloy in zinc-blende (B3) structure. The calculated lattice parameters and bulk modulus agree with the previous results. The second-order elastic constants have been calculated and other related quantities such as the Young’s modulus, shear modulus, anisotropy factor are also estimated. We also obtain the data of lattice dynamics and the temperature dependent properties currently lacking for SiGe, SiSn and GeSn. Findings are also presented for the temperature-dependent behaviors of some thermodynamic properties such as the internal energy, Helmholtz free energy, entropy and heat capacity.
