LEAD-CHALCOGENIDES UNDER PRESSURE: AB-INITIO STUDY

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International Conference on Ceramics, Bikaner, India International Journal of Modern Physics: Conference Series Vol. 22 (2013) 612 618 World Scientific Publishing Company DOI: 10.

1 International Conference on Ceramics, Bikaner, India International Journal of Modern Physics: Conference Series Vol. 22 (2013) World Scientific Publishing Company DOI: /S X LEAD-CHALCOGENIDES UNDER PRESSURE: AB-INITIO STUDY DINESH C. GUPTA Condensed Matter Theory Group, School of Studies in Physics, Jiwaji University, Gwalior (M.P.), India IDRIS HAMID Condensed Matter Theory Group, School of Studies in Physics, Jiwaji University, Gwalior (M.P.), India ab-initio calculations using fully relativistic pseudo-potential have been performed to investigate the high pressure phase transition, elastic and electronic properties of lead-chalcogenides including the less known lead polonium. The calculated ground state parameters, for the rock-salt structure show good agreement with the experimental data. The enthalpy calculations show that these materials undergo a first-order phase transition from rock-salt to CsCl structure at 19.4, 15.5, 11.5 and 7.3 GPa for PbS, PbSe, PbTe and PbPo, respectively. Present calculations successfully predicted the location of the band gap at L-point of Brillouin zone as well as the value of the band gap in every case at ambient pressure. It is observed that unlike other lead-chalcogenides, PbPo is semi-metal at ambient pressure. The pressure variation of the energy gap indicates that these materials metalized under high pressures. For this purpose, the electronic structure of these materials has also been computed in parent as well as in high pressure phase. Keywords: Lead-chalcogenides; Electronic structure; Phase transition. 1. Introduction Lead chalcogenides (PbX : X = S, Se, Te, Po) have attracted the experimental and theoretical attention due to pressure and temperature dependence of the energy gap in them. Under high pressure, PbS, PbSe, and PbTe were observed to transform into the eightfold-coordinated CsCl structure at pressures of 25.3, 18.76, and GPa, 1-3 respectively. Numerous theoretical calculations have been performed to study the pressure-induced structural transformations, electronic, elastic and optical properties of PbS, PbSe, and PbTe compounds using density functional calculations 3 5 and potential models. 6 However, a very scant amount of attention has been devoted to study the theoretical computation of energy band structure, phase transition and various physical properties of these materials, particularly less studied compound PbPo at normal and high pressures. A common phase transition sequence (RS CsCl) is expected in PbPo with pressure below that of PbTe. Bencherif et al. 7 have theoretically predicted a RS CsCl transition 612

2 Lead-Chalcogenides under Pressure: ab-initio Study 613 in PbPo at 8.5 GPa by generalised gradient approximation (GGA) using both fullpotential linearized augmented plane wave (FP-LAPW) and plane wave pseudo-potential methods. However, they have not computed detailed properties of PbPo in high pressure phase. The aim of the present work is to perform a unified study of the electronic, structural, phase transition and mechanical properties of lead-chalcogenides in parent (B1) as well as in high pressure (B2) phase using OpenMX code. 8 The high pressure phase of PbPo has yet not been reported. 2. Computational Methods The calculations have been performed using Ceperly-Alder local density approximation (LDA) exchange-correlation functional used in OpenMX package for DFT calculations. The package includes fully relativistic pseudo-potentials (PP), same can be generated using ADPACK with demanded number of valence electrons. The PPs with primitive basis sets have been considered for Pb, Po, S and Te. However, for PbSe calculations, an optimized set of basis sets (s2p2d1 for Pb and s2p1d1 for Se) were used. The cut-off radii of confinement potentials were set to 8.0 a.u. for Pb and Po and 7.0, 7.5 and 7.5 a.u. for S, Se and Te, respectively. We have used cut-off energy of 100 Ry in every case with 4x4x4, and 3x3x3 k-point grids for PbS and PbTe, respectively and 4x3x3 for both PbSe and PbPo for the Brillouin zone summation. The calculations were performed in B1 and B2 phases by repeating them several times at varying lattice constant to optimize the total energy. The optimized lattice parameters are close to the experimental values. The results were fitted to Murnaghan s equation of state to get the values of the equilibrium bulk modulus (B 0 ) and its first pressure derivative (B 0 ). These values are used to calculate the electronic properties of present set of materials. 3. Results and Discussions The structural optimizations were performed by variation of unit cells and atomic positions. Fig.1(a-d) present the total energy variations with volume (E V) for PbX in B1 and B2 phases, together with the static equation of state (EOS) and the phase stability data. By exploiting the curves of minimization, it is found that the most stable phase at Energy (Ry) Volume (a.u. 3 ) Fig. 1: Energy vs. volume plots for Pb-chalcogenides.

3 614 D. Gupta & I. Hamid zero pressure is B1phase which has lowest total energy as compared to CsCl (B2) structure in all the cases. The equilibrium lattice parameter, bulk modulus and its firstorder pressure derivative along with total energy for PbX compounds in both the phases have been obtained by Murnaghan EOS and presented in Table 1. Our calculated lattice parameters and other values for the RS phase are in good agreement with experimental values. 9 The trend of E V curves in Fig. 1(a-d) suggests the occurrence of phase transition from the RS to the CsCl structure under compression in each material. As is known, at zero temperature, the thermodynamically stable structure under a given pressure (P) is the one with the lowest enthalpy, H = E-PV. Therefore, the static transition pressures (P T ) between the RS and CsCl structures of PbX compounds can be estimated from the usual condition of equal enthalpies, i.e., H B1 (P T ) = H B2 (P T ). Fig. 2(a-d) displays the enthalpy as a function of pressure in B1 and B2 phases for all materials under consideration. It may be seen from these figures that PbX solids show transition from B1 to B2 phase at 19.4, 15.5, 11.5 and 7.3 GPa. Table 1: Values of the calculated lattice parameter, the bulk modulus (GPa) and its pressure derivative at equilibrium volume in RS and CsCl phase. Rock-salt structure Solids a (Å) B 0 PbS PbSe PbTe CsCl structure ' B 0 a (Å) B 0 ' B 0 References Present work Theory [17] Expt. Ref. [11] Present work Theory [17] Expt. Ref. [11] Present work Theory [17] Expt. Ref. [11] PbPo Present work Enthalpy (Ry) Pressure (GPa) Fig. 2: Enthalpy vs. pressure for Pb-chalcogenides.

4 Lead-Chalcogenides under Pressure: ab-initio Study 615 Table 2: Values of elastic constants (in GPa) for RS phase. Solids C 11 1 C 12 C 44 4 The present values are close to the available values. 6-9 The variation of reduced volume (V(P)/V(0)) with pressure has been studied to obtain the equation of state (EOS) of these materials to understand the mechanism of transformation. We found that the volume of these materials decreases smoothly up to P T. At P T, an abrupt change in volume is observed, which is associated with first-order phase transformation showing structural change from B1 to B2 phase. The elastic constants of solids provide a link between the mechanical and dynamical behaviour of crystals, and give important information concerning the binding characteristic between adjacent atomic planes, anisotropic character of binding and, in particular, structural stability and stiffness of the materials. 10 To study the stability of these compounds in the RS (B1) and CsCl (B2) structures, we have calculated the elastic constants C 11, C 12, C 44 and the aggregate bulk modulus [B = (C 11 +C 12 )/3] at equilibrium lattice constants. It is found that our values satisfy correctly the elastic stability criteria (C 11 C 12 > 0, C 44 > 0 B0 >0). The elastic constants in case of PbPo are being reported for the first time. The calculated and experimental 11 values for the RS structure are listed in Table 2. From these results, we conclude that these compounds are stable against elastic deformation in RS structure. The calculations in the CsCl structure also show stability against elastic deformation. On comparing our theoretical values for elastic constants to experimental data, we find overall a good agreement. Energy (ev) PbS Present Expt.[11] (a) PbS (c) PbTe PbSe PbTe PbPo Reference Present Expt.[11] Present Expt.[11] (b) PbSe (d) PbPo Wave Vector Fig. 3: Band structure of Pb-chalcogenides in rock-salt phase (Fermi level is set to zero).

5 616 D. Gupta & I. Hamid As shown in Table 1, the equilibrium lattice constant is in closer agreement with the experimental values. We have calculated the band structure at the present values of lattice constant. The band gap is located at L point of the Brillouin zone as shown in Fig. 3(a-d). For the width of the band gap and overall ordering of bands, the present study shows good agreement with the experimental data [9] as mentioned in Table 3 and better than earlier calculated values for PbS, PbSe and PbTe. In Fig. 3(d) we have presented the band structure of PbPo. The main feature of the band structure is that the valence band maximum and the conduction band minimum occur at L point of the Brillouin zone as found for other compounds of this family. Table 3: calculated values of band gaps for RS phase (Fermi level is set to zero). Compounds Present work Expt. [11] Others [17] PbS PbSe PbTe Fig.4: PDOS and DOS of lead-chalcogenides Unlike other PbX compounds, PbPo is semimetal as established earlier by Rabii et al. 15,16 The total and partial density of states (DOS and PDOS) is shown in Fig. 4(a-d). It is shown that for each compound the bands just below the Fermi level (E F ) are predominately p states of chalcogen atom with a small contribution from 6p of Pb. The

6 Lead-Chalcogenides under Pressure: ab-initio Study 617 lowest bands have exclusively chalcogen atom s character, while the next bands have the s character of Lead and lies far below the gap. The conduction bands originate mainly out of p orbitals of Pb in PbS, PbSe and PbTe and p of Pb and Po with a small contribution of the d states of Pb and Po. We have also investigated the electronic band structure in B2 phase at high pressures. It was found that these solids metalize under pressure. The band structure of PbX in B2 phase is not reported here. We have also studied the pressure dependence of the band gap. The results are shown in Fig. 5(a-c). It is clear that with increasing pressure, the conduction band minimum further goes closer to the Fermi level. However, in B2 phase, no gap is observed, showing metallization. Energy (ev) 4. Summary Wave Vector Fig. 5: Band structure of lead chalcogenides near P T. We have studied the electronic band structure, and elastic properties of the lead chalcogenides from ab-initio self-consistent calculations based on fully relativistic pseudo-potential method within LDA. The present results show that the equilibrium lattice constants are in good agreement with experimental and other theoretical data. In general, our values of the mechanical properties of these compounds in the RS phase give the correct agreement with the experimental values. In addition, we found that unlike other lead chalcogenides, PbPo is semi-metal in the parent (RS) phase. We have also found the phase transition in PbX and the energy gap between conduction band and valence band varies with pressure. At ambient pressure, they are in semiconducting level, with increase in pressure, semiconducting behaviour goes towards the metallic behaviour and eventually overlaps at high-pressure. Acknowledgments (a) PbS (b) PbSe The authors are thankful to UGC, New Delhi for financial support. (c) PbTe References 1. J. Maclean, P.D. Hatton, R.O. Piltz, J. Grain, R.J. Cernik, Nucl. Instrum. Methods Phys. Res. B (1995). 2. A. Onodera, Y. Fujii, S. Sugai, Physica B and C , 240 (1986). 3. T. Chattopadhyay, H.G. Von Schnering, W.A. Grosshans, W.B. Holzapfel, Physica B (1986); Rev. Phys. Appl (1984).

7 618 D. Gupta & I. Hamid 4. Y. Fujii, K. Kitamura, A. Onodera, Y. Yamada, Solid State Commun (1984). 5. M. Ferhat, A. Zaoui, M. Certier, B. Khelifa, Phys. Lett. A (1996); Appl. Phys. Lett (2006). 6. R.K. Singh, D.C. Gupta, S.P. Sanyal, Phys. Stat. Sol. (b) 149, 121 (1988). 7. Y. Bencherif, A. Boukra, M. Ferhat, A. Zaoui, Physica B (2012). 8. [ 9. R. Dornhaus, G. Nimtz, B. Schlicht, Narrow-gap semiconductors, (Springer-Verlag, Berlin, 1985). 10. L.W. Shi, Y.F. Duan, L.X. Qin, Comput. Mater. Sci (2010). 11. O. Madelung, M. Schulz, H. Weiss (Eds.), Numerical Data and Functional Relationships in Science and Technology Landolt-Bornstei, New Series, vol. 17, Springer, Berlin, K. Hummer, A. Gruneis, G. Kresse, Phys. Rev. B 75, (2007). 13. Z. Nabi, B. Abbar, S. Mecabih, A. Khalfi and N. Amrane, Comp. Mat. Sc. 18, 127 (2000). 14. S. WEI, A. Zunger, Phys. Rev. B (1997). 15. S. Rabii, R.H. Lasseter, Phys. Rev. Lett (1974); Phys. Rev. B (1978). 16. M. Baleva, E. Mateeva, Phys. Rev. B (1994). 17. K. Hummer, A. Gruneis, G. Kresse, Phys. Rev. B 75, (2007).

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