Structural, Electronic and Elastic Properties of Be2B Compound. Venu Mankad, Sanjeev K Gupta, Prafulla K Jha Department of Physics, Bhavnagar University, Bhavnagar, Gujarat- 364022. Email:
[email protected] Abstract. A detailed theoretical study of structural, electronic and elastic properties of Be2B compound is presented by performing ab-initio calculations based on density-functional theory using the ABINIT. The calculated value of lattice constant and bulk modulus are compared with the available experimental and other theoretical data and agree reasonably well. The calculated elastic constants satisfy the mechanical stability criteria. Zener anisotropy factor (A), Poisson’s ratio (v),Young’s modulus (E), shear modulus (C’), elastic wave velocities for Be2B compound is also reported.
Keywords: Electronic band structure, Elastic properties, Lattice dynamics, Ab-initio calculation. PACS: 61.50.Ks, 63.20.Dj, 63.20.Ry The equilibrium lattice constant, bulk modulus, and its total energy of the crystal are calculated at different volumes by means of Murnaghan’s equation of state [6]. The total energy versus lattice constant graph is presented in Fig.1.
INTRODUCTION In recent years Beryllium semi-boride (Be2B) has attracted great attention as a potential superconductor [1]. Theoretical prediction of changes in the electrophysical properties of Be2B caused by electron, isoelectron or hole doping as a result of partial substitution of beryllium by Al, Mg, and Na, respectively, is reported in [1]. The potential of this system for materials science is substantially dependent on their mechanical properties. Be2B crystallizes in cubic crystal lattice (CaF2-type space group: Fm3m ) [2]. The present paper reports a systematic study on the first principles study of elastic and electronic properties of Be2B compounds.
Be2B Rocksalt-Phase
Total energy(eV)
-150.90 -150.95 -151.00 -151.05 -151.10 -151.15 -151.20 -151.25 8.2
8.4
8.6
8.8
9.0
9.2
Lattice constant(Bohr)
Figure1. Energy versus lattice parameter curve
METHOD OF CALCULATION
The present value of lattice constant for rock salt (B1) structure of Be2B compound is in good agreement with experimental and other theoretical values (TableI) The present value of optimized lattice parameter for Be2B is 1.47 % higher than the available experimental result [6]. It is worth noting that C11 coefficients are much higher than C44 ones (Table-I). This indicates that the Be2B in cubic structure is less resistant to the applied shear. The traditional mechanical stability conditions on the elastic constants are satisfied at zero pressure. The calculated shear modulus ,Young’s modulus, Poisson’s ratio, Shear wave modulus and Anisotropic factor is presented in Table-II.The present value of Anisotropic factor suggests that the present Be2B is less anisotropic compound .
In this article, all calculations were performed within the framework of DFT using a basis set consisting of plane waves, as implemented in the ABINIT [3]. The electron–ion interactions were described by pseudopotentials and electron exchange and correlation energies were calculated with the gradient-corrected functionals in the form of the generalized-gradient approximation (GGA) by Perdew and Wang [4]. The kinetic energy cutoff 19 Ha of the plane wave basis was used throughout and the Brillouin zone was sampled with a 8x8x8 grid of special k-points as proposed by Monkhorst and Pack [5].
RESULT AND DISCUSSION Solid State Physics, Proceedings of the 55th DAE Solid State Physics Symposium 2010 AIP Conf. Proc. 1349, 863-864 (2011); doi: 10.1063/1.3606131 © 2011 American Institute of Physics 978-0-7354-0905-7/$30.00
863
Downloaded 12 Jul 2011 to 117.211.84.58. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/about/rights_permissions
DOS (electrons/eV/cell)
100 80 60 40 20 0
-10
-5
0
5
10
15
20
E-EF Figure 2.Calculated electronic band structure of Be2B
Figure 3. Calculated electronic density of states of Be2B
Table I. Calculated static and elastic properties for Be2B compound Material
Reference
Bulk Modulus B(GPa) 133.80
Pressure derivative(B’)
C11(GPa)
C12(GPa)
C44(GPa)
Present(LDA)
Lattice Constant ao(Å) 4.57
Be2B
3.49
272.38
64.52
144.20
Theory(LDA)a
4.51
154.88
3.27
243.72
110.46
168.42
other data. The compound is not a high anisotropic
Table II. Different Moduluses and Anisotropic factor(A)
Present(LDA)
Shear modulus(G) 126.47
Youngs’s modulus(E) 288.51
Poisson’s ratio (v) 0.14
Anisotropic factor(A) 1.38
Theory(LDA) a
116.12
278.7
0.2
2.52
Material
Reference
Be2B
Shear wave modulus(C’) 103.93 177.09
compound. The mechanical stability is satisfied. The dispersive and flat band suggest this compound to be a potential superconductor.
The calculated electronic band structure and electronic density of states are presented in Fig 2 and 3 respectively. Band structure reveals that the two electronic bands cross the Fermi surface, but the band
REFERENCES
dispersions are rather weak, in particular, along the toL to X direction. There is also relatively flat conduction band in the direction near the Fermi level. The simultaneous occurrences of dispersive and flat bands have been suggested as being a favorable for potential superconductivity [7].
1
I. R. Shein et.al Phys. Status Solidi A, 227, No. 2, R1-R3 (2001).; Neorg. Mater., 39, No. 7,(2003), 820. 2 Yu.B.Kuzma,Crystal Chemistry of Borides(Vyssha Shkola,Lviv,1983) (in Russian) 3. The ABINIT Code is a Common Project of Universite Catholique de Louvain,Corning Incorporated and Other Contributors . 4. J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244. 5. H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. 6. M. T. Kadri,N.E.Derradji,H. Belkhir physica status solidi (b) 41-47(2010) 247. 7. Simon, Angew. Chem., Int. Ed. Engl. 36 (1997) 1788.
CONCLUSIONS In this work we have presented the structural, electronic and mechanical properties of cubic Be2B compound. The calculated lattice constant and mechanical properties are in good agreement with
864
Downloaded 12 Jul 2011 to 117.211.84.58. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/about/rights_permissions
