First-principles investigations on electronic, elastic and thermodynamic

First-principles investigations on electronic, elastic and thermodynamicproperties of VN under high pressureAimin Hao 1, a , Xiaocui Yang 2, Lixin Zhang 3, Qizhou Zhang 31Department of Materials Science and Engineering, Northeastern University at Qinhuangdao, China2Department of Physics, Baicheng Normal College, China3College of Physics and Chemistry, Hebei Normal University of Science and Technology, China a email: aiminhao1991@Keywords: Structure transformation; Elastic property; Thermodynamic property; High pressure; Ab initio calculations.Abstract. An investigation on electronic, elastic and thermodynamic properties of VN under high pressure has been conducted using first-principles calculations based on density functional theory (DFT) with the plane wave basis set as implemented in the CASTEP code. At elevated pressures VN is predicted to undergo a structural phase transition from the relatively open NaCl-type structure into the denser CsCl-type atomic arrangement. The predicted transition pressure is 189 GPa. The elastic constants, Debye temperature as a function of pressure and temperature of VN are presented. IntroductionTransition-metal (TM) mononitrides, which have a simple rocksalt structure, continue to be studied because of their interesting physical and chemical properties. They have extreme hardness and high melting points, properties which are typical of covalent crystals, as well as metallic conductivities comparable to those of pure TMs. It is interesting that properties associated with covalent bonding are found in a system which displays a crystal structure normally associated with ionic bonding. These properties suggest that covalent, ionic, and metallic bondings are present simultaneously. Thus, these compounds are not only valuable technological materials, but are also of special theoretical interest. Among these compounds, in particular, there is increasing interest on VN as an important industrial catalyst known for its selectivity and stability [1].Harrison et al. [2] studied electronic structure and properties of d - and f -shell-metal compounds. Their results show that the simplest systems with 8 valence electrons per atom pair are almost insulating; and for the system with 9-12 valence electrons, the excess electrons occupy nonbonding bands making the compound metallic.To investigate electronic mechanism of hardness enhancement in TM carbonitrides, Jhi et al. [3] evaluated the shear modulus of various TM carbides and nitrides using ab initio pseudopotential calculations. Their results show that the behavior of these materials can be understood on a fundamental level in terms of their electronic band structure. It was confirmed that the unusual hardness originates from a particular band of σ bonding states between the non-metal p orbitals and the metal d orbitals, which strongly resists shearing strain or shape change. Filling of these states is completed at a valence-electron concentration of about 8.4, and any additional electrons would go into a higher band which is unstable against shear deformations.Stampfl et al. [4] investigated the bulk electronic and physical properties of a series of early TM mononitrides using first-principles density-functoinal theory calculations. They found that the bonding of these materials has a covalent-like character, however, there is also an ionic component with a significant charge transfer to the more electronegative nitrogen atom. Detailed study of the equation of state, elasticity, and hardness of selected superconducting TM nitrides reveals interesting correlations among their physical properties [5].Advanced Materials Research Vols. 550-553 (2012) pp 2805-2809Online:2012-07-26© (2012) Trans Tech Publications, Switzerland doi:10.4028//AMR.550-553.2805Materials properties of VN||TiN multilayers are studied focusing on the elastic and mechanical properties of the interface by Lazar et al. [6] using a density functional theory approach. The result shows that a distinct feature of VN is the very large value of C11, which reflects the strong covalent bonds between the vanadium d-like states and the nitrogen p-like states along [100] directions.Lattice dynamics of body-centered cubic VB-VIB group TMs, and B1-type monocarbides and mononitrides of IIIB-VIB TMs are studied by means of first-principles density functional perturbation theory [7]. The result shows that the superconductivity of TM carbides and nitrides is related to peculiarities of the phonon spectra, and the anomalies of the spectra are connected to the number of valence electrons in crystal.Ravi [8] systematically studied the ground-state properties and phase stability of VN using a series of density functional electronic structure total energy calculations.The result shows that higher bulk modulus is dominated by increased V-N bonds combined with low atomic volumes.Study on the electrochemical behavior of VN by Zhou et al. [9] indicates that VN belongs to the cubic crystal system with unit-cell parameter 4.15 Å, and that VN is a promising electrode material for electrochemical supercapacitors. The structural and electronic properties of three isostructural TM nitrides VN, NbN, and TaN have been calculated using the full-potential linearized augmented plane-wave method within a generalized gradient approximation scheme for the exchange-correlation potential [10].As stated above, different theoretical calculations of VN bulk electronic, elastic properties have been compared and discussed extensively. However, according to our knowledge, there is no report about the pressure-induced structural transition of VN up to now. Very few studies have been performed on the thermodynamic properties of VN. So, there is a need to investigate elastic and thermodynamic properties of VN under simulated extreme working conditions.In this paper, an investigation on electronic, elastic and thermodynamic properties of VN under high pressure was performed using first-principles calculations.Computational details and theoryComputational details. Our first-principles calculations are performed with the CASTEP code in MS modeling based on the plane wave basis set [11], the ultrasoft pseudopotential for electron-ion interaction, and the exchange correlation potential of Perdew et al. [12] in the generalized gradient approximation (GGA) for electron-electron interaction. The typical configurations are 3s23p63d34s2 and 2s23p3for V and N, respectively. Integrations in the Brillouin zone (BZ) is performed using special k points generated with 14×14×14 for the B1 and B2 structures, which make the separation of the reciprocal space to be less than 0.02 Å-1. One-electron valence states are expanded on a basis of plane waves with a cutoff energy of 700 eV in the electronic property calculations. Such parameters have been tested to be sufficient for convergence (<10-3eV). During the structure optimization, the total energy is minimized by varying cell parameters and atomic positions under the restriction of the given symmetry. In the geometrical optimization, all forces on atoms were converged to less than 0.001eV/ Å, and the total stress tensor was reduced to the order of 0.005 GPa by using the finite basis-set corrections [13].Elastic and thermodynamic properties. The theory of the elastic and thermodynamics properties was described in earlier works [14].Results and discussionElectronic and structural properties. The total energy as a function of volume is calculated to determine the equilibrium volume and bulk modulus by parabolic fitting to a third Birch-Murnaghan equation of state [15].Calculated equilibrium lattice constant and bulk modulus of VN in the B1and B2 structures are illustrated in Table 1. It can be clearly seen that the calculated structural parameters are in excellent agreement with experimental results [16] and other theoretical investigation [7,8,10]. Since the bulk modulus is inversely proportional to the bond length, the smaller atomic size ofnitrogen and the shorter bond lengths cause the bulk modulus to be larger, and consequently the elastic constants, which in turn are related to hardness, are larger. For bulk modulus of VN-B1, the calculated result is consistent with experimental data [17] and previous theoretical results [7,8].Table 1 Calculated equilibrium lattice constant (a0), energy gap (E g) and bulk modulus (B) of VN, together with previous theoretical results and the available experimental data.a0 (Å)E g (eV)B (GPa)B′VN-B1 VN-B2 4.119; 4.12a4.12b;4.11c;4.13d2.544311; 333a; 313c;317d; 327e; 268f3144.244.21a Ref. [5];b Ref. [10];c Ref. [7];d Ref. [8];e Ref. [2];f Ref. [17].Our computational approach is based on constant-pressure static quantum mechanical calculations at T = 0 K, so the relative stability of different structures can be deduced from the pressure dependence of the enthalpy instead of the Gibbs free energy [18]. Our calculation suggests that there exists a transition from the B1 to B2 structure, which is a second-order phase. The pressure corresponding to ∆H=H B2-H B1approaching zero is the transition pressure (p t). The calculated transition pressure and volume collapse are 189 GPa and 5.6%, respectively.Elastic properties. The elastic constants of solids provide a link between the mechanical and dynamics and provide important information concerning the nature of the forces operating in solids. In particular, they provide information on the stability and stiffness of materials. The total energy of the system depends on volume more strongly than on strain. In this work, the volume contribution to total energy can be eliminated using volume conserving strains[19].We investigate the high-pressure elastic behavior of VN-B1, by computing the second-order elastic constants (SOECs) and their variation with pressure, as shown in Fig. 1. It is noticed that C44 decreases linearly with pressure, while C11and C12increase linearly with pressure. C11is more sensitive to the change of pressure compared to C12. The similar features were reported for YN [20]. The calculated bulk modulus B increases gradually with pressure, indicating it becomes more and more difficult to be compressed with increasing pressure.Fig. 1 The elastic constants as a function of pressure of VN-B1.Thermodynamic properties. The pressure and temperature dependence of the isothermal bulk modulus for VN-B1 is shown in Fig. 2. It demonstrates that dramatic volume variation leads to the rapid decrease in the isothermal bulk modulus. These results indicate that B increases with P at a given temperature and decreases with T at a given pressure. It shows the fact that the effect of increasing pressure on VN is the same as that of decreasing temperature. However, the effect of temperature on the bulk modulus is less important than that of pressure.Fig. 2. Pressure and temperature dependence of the isothermal bulk modulus of VN-B1.The pressure and temperature dependence of Debye temperature for VN-B1 is shown in Fig. 3. It demonstrates that dramatic volume variation leads to the rapid decrease in Debye temperature. These results indicate that Debye temperature increases with P at a given temperature and decreases with T at a given pressure. It shows the fact that the effect of increasing pressure on VN is the same as that of decreasing temperature. However, the effect of temperature on the bulk modulus is less important than that of pressure.Fig. 3. Pressure and temperature dependence of Debye temperature of VN-B1.ConclusionsIn this paper, electronic, elastic and thermodynamic properties of VN are studied using first-principles calculations. The calculated structural and elastic parameters agree well with the available experimental results and the previous theoretical data. It is predicted that the B1 to B2 phase transition pressure of VN is 189 GPa. The fundamental physical properties, such as elastic constants, Debye temperature, and heat capacity as a function of pressure and/or temperature of VN are reported.AcknowledgementsThis work was supported by the Project of Science and Technology of Jilin Province in 11th-Five Years Plan (2010217) and China Postdoctoral Science Foundation funded project (Grant no. 20090450924).References[1] H. Kwon, S. Choi and L.T. Thompson; J. Catal. 184 (1999) 236.[2] W. A. Harrison and G.K. Straub: Phys. Rev. B 36 (1987) 2695.[3] S. Jhi, J. Ihm, S.G. Louie and M.L. 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