by investigation of elastic constants

Transcription

1 Journal of Physics: Conference Series PAPER OPEN ACCESS Comparison between layering NbSe 2 and rod characteristic of MgB 2 by investigation of elastic constants To cite this article: Asiye Shokri et al 2018 J. Phys.: Conf. Ser View the article online for updates and enhancements. This content was downloaded from IP address on 08/10/2018 at 19:37

2 Comparison between layering NbSe 2 and rod characteristic of MgB 2 by investigation of elastic constants Asiye Shokri, Ahmad Yazdani* and Behrad Barakati Department of Physics, Tarbiat Modares University, P.O. Box , Tehran, Iran *yazdania@modares.ac.ir Abstract. The delicate balancing of strong anisotropy on strength of hybridisation resulted to CDW- order T CDW =33K and finally emerging superconductivity at T c = 7.2K are the most intriguing question in characteristic behaviour of NbSe 2. On other hand, the original mechanism of MgB 2 old superconductor, which has unlike the cuprates a lower anisotropy on strength hybridisation is still unknown. We believe this could result to bond exchange and larger coherence length of the grain boundary to current. Since the cause and the mechanism of band strengths of two original layering and rod structures are consequence of bond- rupturingatomic displacement, here the stability of crystalline structure of inter atomic potential through the elasticity-compressibility is investigated. Consequently, in order to clear out the strong difference between the layering NbSe 2 and domination of rod-character of MgB 2 the stability of both crystal structures through the cohesive energy c/a, c zz and c 33 are investigated. The proposed investigations are more evident on different characteristic behaviour of calculated parameters. 1. Introduction As a member of transition metal dichalcogenids, it has been more than fifty years that 2H-NbSe 2 has attracted many attentions due to its electronic properties and phase transition [1]. 2H-NbSe 2, a hexagonal structure with space group P6 3 /mmc and structural parameters of a=3.6å, and c=12.6å contains two NbSe 2 units as ABAB stacking and it is a type II superconductor under 7.1K [2,3]. On other hand electronic instabilities driven by Fermi surface nesting, are because of the two dimensional nature of materials like 2H-NbSe 2. The interplay between charge density wave order (T CDW =33K [4]) and superconductivity (T c =7.1K) and also coexistence of these properties has attracted so many attentions [5]. In 2015, a group showed the decrease of critical temperature of superconductivity in this material by decreasing the layers to T c =3.1K in achieving a monolayer. It is while they found that by decreasing the layers, T CDW is increasing to 145K for the monolayer [6]. H. Suderow et al. in 2005 measured critical temperature up to 19GPa and found a maximum at 10.5GPa [7]. It is while different works on MgB 2 show that the critical temperature decrease with increasing of the pressure [8]. MgB 2 with the highest critical temperature among conventional BCS and intermetallic compounds (T c =39K) [9], has hexagonal structure with space group P6/mmm (a=3.08 and c=3.52å) [10]. Wires and thin films of this material have been constructed for decades [11]. Although the Be and Mg belong to a same column in periodic table, but the different stiffens [12] made MgB 2 rod and wire shape unlike BeB 2 which is to be a layered material like NbSe 2. Relative to layering of low T c =0.7 of BeB 2, as it is presented by others [12], and because of the different behavior of critical temperature in presence of Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by Ltd 1

3 the pressure, the difference between layering character of NbSe 2 and rod-formation character of MgB 2 superconductors could be the intriguing question. The directional bond formation or a strong anisotropy of different B-B length do to smaller- intro- layer to the inter-layer distance of B-B could be the cause where we are following characteristic behavior of MgB 2 for the cause of rod/wire character. Insignificancy of T c =0.7 in BeB 2 is surprisingly in a challenge which could be due to its layering- character as its common feature with NbSe 2. In this work, we have compared the structural properties of these two materials. For the best of our knowledge there is no study, comparing the structural properties of NbSe 2 and MgB 2 from the elastic constants point of view 2. Calculation methods Calculations of the electronic structure were carried out using the linearized augmented plane wave(lapw) method as performed in the WIEN2k package [13]. Calculating the elastic constants of these hexagonal structures were performed using Hex-elastic package [14] based on the second-order derivative (E ( δ)) of the polynomial t of energy (E=E(δ)) vs strains, at zero strain (δ=0). The generalized gradient approximation exchange- correlation function of Perdew et al [15] was used in the present work. 3. Result and discussion As a starting point of discussion, the calculated equilibrium lattice parameters of MgB 2 (NbSe 2 ) were calculated to be a=3.06å(3.38å) and c=3.54å(12.96å). Diagram of density of states for both structures are shown in figure 1. The c/a optimization calculations were done and c/a for constant volume was optimized to find the optimized a and c lattice parameters (figure 2). Elastic constants of crystals provide a link between the mechanical and dynamical behaviors of solids, give important information about the elastic response of a crystal to an external pressure and also can predict the anisotropic character of binding. Five independent elastic constants are listed in table 1. To investigate the stiffness, hardness and structural anisotropy of these structures, bulk, shear and young modulus based on voigt, Reuss and Hill approximations are presented in table 2. Young s modulus, the ratio of stress and strain, indicates the stiffness. It means the material with larger Young s modulus is stiffer. As can be seen from table 2, MgB 2 is stiffer than NbSe 2. If we want to know how much a material is resistant against shape changes, we should discuss about the hardness which is related to bulk modulus (resistance against volume changes) and shear modulus (resistance against reversible deformations). Then, it can be seen that MgB 2 is more resistant. Strain vs energy in figure 3 shows the C zz elastic constant diagram which says by this strain, volume and symmetry will not change. The structural anisotropy can have different definitions. The amount of deviation from 1 can be a criterion for anisotropy according to equation (1). It shows that MgB 2 has anisotropic structure due to f=1.86. f = C!! + C!" 2C!" C!! C!" 1 Table1: The calculated elastic constants C ij (in GPa) for MgB 2 and NbSe 2. C11 C12 C13 C33 C55 MgB NbSe

4 Table2: Calculated bulk(b), shear modulus(s) and Young s modulus E (all in GPa), in Voigt (V) Reuss (R) Hill (H) approximations B(V) B(R) B(H) S(V) S(R) S(H) E(V) E(R) E(H) MgB NbSe b) Figure 1: density of states for a) MgB 2 and b) NbSe 2 3

5 a) b) Figure 2: C zz diagram for a) MgB 2 and b) NbSe 2 structures 4

6 a) b) Figure 3: c/a vi energy for a) MgB 2 and b) NbSe 2 4. Conclusion As a consequence, due to Young, Bulk and shear modulus our results show that in compare with NbSe 2, because of having larger E, B and S, MgB 2 is stiffer, more resistant against volume changes 5

7 and reversible deformations. Accordingly, more especially due to Bulk modulus, it is clear that MgB 2 has a continuous and anisotropic structure, while someone could access to a monolayer of NbSe 2 easier because of more easily shearing. Finally, it could be a predictable reason for different (rod and layering) structures of these two materials. References [1] Withers RL, Wilson JA. An examination of the formation and characteristics of charge-density waves in inorganic materials with special reference to the two-and one-dimensional transition-metal chalcogenides Sep 10 Journal of Physics C: Solid State Physics. 19(25):4809. [2] Mattheiss LF. Band structures of transition-metal-dichalcogenide layer compounds Oct 15. Physical Review B. 8(8):3719. [3] Lee HN, McKinzie H, Tannhauser DS, Wold A. The Low Temperature Transport Properties of NbSe Feb. Journal of Applied Physics. 40(2): [4] Xi X, Zhao L, Wang Z, Berger H, Forró L, Shan J, Mak KF. Strongly enhanced charge-densitywave order in monolayer NbSe Sep 1. Nature nanotechnology. 10(9): [5] Le Tacon M, Bosak A, Souliou SM, Dellea G, Loew T, Heid R, Bohnen KP, Ghiringhelli G, Krisch M, Keimer B. Inelastic X-ray scattering in YBa2Cu3O6. 6 reveals giant phonon anomalies and elastic central peak due to charge-density-wave formation Jan 1. Nature Physics. 10(1):52-8. [6] Xi X, Zhao L, Wang Z, Berger H, Forró L, Shan J, Mak KF. Strongly enhanced charge-densitywave order in monolayer NbSe Sep. Nature nanotechnology. 1;10(9): [7] Suderow H, Tissen VG, Brison JP, Martínez JL, Vieira S. Pressure Induced Effects on the Fermi Surface of Superconducting 2 H NbSe Sep. Physical review letters. 9;95(11): [8] Buzea C, Yamashita T. Review of the superconducting properties of MgB Nov. Superconductor Science and Technology. 5;14(11):R115. [9] Nagamatsu J, Nakagawa N, Muranaka T, Zenitani Y, Akimitsu J. Superconductivity at 39 K in magnesium diboride Mar. Nature. 1;410(6824):63-4. [10] Mijatovic D, Brinkman A, Oomen I, Veldhuis D, Rijnders G, Hilgenkamp H, Rogalla H, Blank DH. MgB 2 thin films and Josephson devices Jun. IEEE transactions on applied superconductivity. 13(2): [11] Grasso G, Penco R, Braccini V, Putti M, Fanciulli C, Tumino A, Brisigotti S, Berta S, Demencik E, Pietranera D, Vignolo M. Current MgB 2 wire performance and their industrial development.tromans D. Elastic anisotropy of HCP metal crystals and polycrystals Mar. Int. J. Res. Rev. Appl. Sci. 6(4): [12] Tromans D. Elastic anisotropy of HCP metal crystals and polycrystals Mar. Int. J. Res. Rev. Appl. Sci. 6(4): [13] Blaha P, Schwarz K, Madsen GK, Kvasnicka D, Luitz J wien2k. An augmented plane wave+ local orbitals program for calculating crystal properties. [14] M. Jamal, 2012, Hex-elastic, [15] Perdew JP. Kieron Burke and Matthias Ernzerhof Phys. Rev. Lett.77: