Department of Physics, Anna University, Sardar Patel Road, Guindy, Chennai -25, India.

Transcription

1 Advanced Materials Research Online: ISSN: , Vol. 665, pp doi: / Trans Tech Publications, Switzerland Electronic Structure and Ground State Properties of A 4 [Ag 4 O 4 ] (A=Na, K and Rb): A First-Principles Study R.Umamaheswari, M.Yogeswari and G.Kalpana* Department of Physics, Anna University, Sardar Patel Road, Guindy, Chennai -25, India. *g_kalpa@yahoo.com, g_kalpa@annauniv.edu Keywords: Electronic structure, bulk modulus, cohesive energy, TB-LMTO method, non centrosymmetric oxides. Abstract: The first-principles calculation within density functional theory is used to study in detail the electronic structure and ground state properties of alkali-metal oxoargenates A 4 [Ag 4 O 4 ] (A= Na, K and Rb). The total energies calculated within the atomic sphere approximation (ASA) were used to determine the ground state properties such as equilibrium lattice parameter, c/a ratio, bulk modulus and cohesive energy. The theoretically calculated equilibrium lattice constants values are in well agreement with the available experimental values. The electronic band structures, total and partial density of states are calculated. The result of electronic band structure shows that the KAgO and RbAgO are direct band gap semiconductors with their gap lying between the Γ-Γ points, whereas NaAgO is found to be an indirect band gap semiconductor with its gap lying between Z-Γ points. 1. Introduction Noncentrosymmetric (NCS) oxide compounds are of particular interest because of their symmetry-dependent properties such as pyroelectricity, piezoelectricity, ferroelectricity and secondorder nonlinear optical (NLO) behaviour are the basis of numerous applications. Classification of NCS compounds and the categories coming under these classes are given in literature [1]. A 4 [M 4 O 4 ] (A= Li, Na, K and Rb; M=Ag and Cu) compounds coming under NCS nonpolar crystal category and they have the symmetrically-dependent properties such as piezoelectric and optical activity. During last two decades, a particular attention has been paid to piezoelectric materials due to their wide technological applications where piezoelectric materials are used as the basis materials for actuators as well as sensors. A 4 [Ag 4 O 4 ] (Na, K and Rb) compounds have both noncentrosymmetric and centrosymmetric structure. In 1968, H.Sabrowsky and R.Hoppe prepared and determined the crystal structure of KAgO and CsAgO [2] which has tetragonal body centred structure with I-4 space group. During 1980 s they reinvestigated the structure of A 4 [M 4 O 4 ] (A= Li, Na, K and Rb; M=Ag and Cu) compounds and revised structure of these compounds A 4 [M 4 O 4 ] found to crystallize in tetragonal body centred structure with two different space groups I-4m2(noncentrosymmetric) and I4/mmm(centrosymmetric). The difference between these two structure is that the M 4 O 4 ring is not planar in space group I-4m2 and exactly planar in I4/mmm [3-5]. In I-4m2 space group, the two O 2- ions are rather 0.02 Å above or below the plane of the ring. A novel feature of this structure is the formation of closed M 4 O 4 four-membered rings. In this paper we present a detailed description of the electronic structure of A 4 [Ag 4 O 4 ] (A=Li, Na, K and Rb) compounds which would bring us the thorough understanding of physical properties of these compounds. The calculations are performed for both the structures of all these compounds using the tight binding linear muffin-tin orbital (TB-LMTO) method, within the atomic sphere approximation (ASA). To the best of our knowledge there are no theoretical and experimental results explaining the electronic structure of these compounds. On application of pressure, these compounds exhibit an interesting phenomenon of band overlap metallization. The rest of the paper is organized as follows. Section 2 describes the details of the theoretical background. Results and discussions are given in section 3. The paper ends with a conclusion in section 4. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (# , Pennsylvania State University, University Park, USA-17/09/16,05:12:50)

2 44 Condensed Matter and Materials Physics 2. Theoretical Framework The electronic structure of A4[Ag4O4] (A= Na, K and Rb) compounds has been investigated through first-principles calculations by using the efficient computational scheme offered by Andersen s tight binding linear muffin-tin orbital (TB-LMTO) method within the atomic sphere approximation (ASA). This method has been described well in the literature [6,7]. In this method, the total energy and electronic structure calculations were performed on the basis of the density functional theory (DFT) within the local density approximation (LDA) [8,9]. Exchange and correlation contributions to both the atomic and crystalline potentials have been included through the von Barth Hedin scheme [10]. The potential is taken to be spherically symmetric within the spheres. In this work, the Wigner Seitz sphere radii are chosen in such a way that the potential discontinuity at the sphere boundary is a minimum and the charge flow between the atoms is in accordance with the electro-negativity criteria. Without disturbing the crystal symmetry, empty spheres are included in appropriate positions to have close packing. We have kept the maximum overlap between the spheres as approximately 16%. The density of states (DOS) was calculated by the tetrahedron method [11]. The Brillouin zone (BZ) integration is performed by the usual tetrahedron technique. Energy as well as k-convergence is checked by increasing the k-points. In this calculation we use 349 k-points in the irreducible part of the Brillouin zone to construct the tetrahedrons in both the structures for all these compounds. In this work, we treat the core electrons fully relativistically and the valence electrons semi-relativistically. In the calculations, the following basis orbital were used: Li: 2s 1 2p 0 ; Na: 3s 1 3p 0 3d 0 ; K: 4s 1 3p 6 3d 0 ; Rb: 5s 1 4p 6 4d 0 ; Ag: 5s 1 5p 0 4d 10 ; O: 2s 2 2p 4 3d Result and Discussions 3.1 Total Energy Calculations and related properties. The total energies were calculated as a function of c/a ratio to minimize the c/a value. For each of these compounds using this minimized c/a ratio, we have calculated the total energy as a function of relative volume in tetragonal body centred structure with two different space groups I-4m2 and I4/mmm and the plots are given in Fig. 1. The total energy difference ΔE [E (I4/mmm) E (I-4m2)] between the two space group is given in Table 1. From the table 1, it can be seen that under ambient conditions all these compounds are stable in I4/mmm space group (ΔE = -ve). The calculated total energies were fitted to the Birch equation of state [12] as a function of reduced volume to obtain equilibrium properties such as equilibrium lattice constants (a and c/a), bulk modulus (B 0 ), and cohesive energy (E coh ). The calculated equilibrium lattice constant (a and c/a), bulk modulus (B 0 ), cohesive energy (E coh ), and ΔE are compared with the available results and are given in Table 1. From table 1, the comparison of calculated cohesive energy (E coh ) and Bulk modulus B 0 of these compounds shows that a clear decreases from NaAgO to RbAgO, i.e. from the lower to the higher atomic number. This suggests that RbAgO is more easily compressible than the others. 3.2 Electronic Structure and Density of States (DOS). The self-consistent scalar relativistic band structures for NaAgO, KAgO and RbAgO have been calculated at ambient pressure and to study the effect of pressure on the band gap, the band structures were calculated at high pressure region also. The energy band structure is calculated along the high symmetry directions in the Brillouin zone, as shown in Fig. 2. The appearances of band structures are due to four molecules per formula unit. The overall band profiles for these compounds are found to have same characteristic features with the variation only in the occupation of semicore states of K-3p and Rb-4p which are treated as relaxed valence band states. The band gap is due to the valence band maximum arising from the hybridisation of Ag d like and O p like states and the conduction band minimum arising from hybridisation of d like states of Ag with s like states of alkali metal (Na-Rb). There is no theoretical and experimental band structure calculations on these compounds, the band structure profiles were compared with KCuO [13] and they are similar to KCuO profile. The relative level positions for copper and silver in binary oxides and sulphides are given by Tossell and Vaughan in [14] and it explains that the d levels of Cu and Ag are above the p levels of oxides and sulphides. Therefore the top of the valence band (nearly at E F ) is mainly due to Ag d like states.

3 Advanced Materials Research Vol Figure 1. Variation of total energy with relative volume for AAgO compounds. Table 1. Lattice parameter (a) in Å, c/a ratio, cohesive energy (Ecoh), ΔE in ev and bulk modulus (B 0 ) in GPa of A 4 [Ag 4 O 4 ] compounds. NaAgO KAgO RbAgO Exp Present Exp Present Exp Present A c/a Bulk _ 69 _ 47 _ 34 Modulus E coh _ -53 _ -46 _ -43 ΔE _ _ _ From the partial DOS calculation ( not shown here), the lowest group which lies at the bottom of the valence band is due to O s like state and are well separated from other bands. The second group which lies at top of the valence band is composed of Ag d like states and O p like states. In the case of KAgO and RbAgO, there is K p and Rb p like states which lie above the O s like states in valence band and it is due to the consideration of semi core states as a relaxed valence states in K and Rb. This trend is observed in the case of A 2 O and A 2 S (A=K and Rb)[15,16]. The bottom of the conduction band is mainly due to hybridization of Cu d like states and alkali metals s like states. The uppermost conduction bands are due to complicated hybridization effects of anions and cations. At ambient condition, the band structure results show that KAgO and RbAgO are direct band gap semiconductors, with their band gap occurring at Γ points, whereas, NaAgO is indirect band gap semiconductor with a gap between Γ and Z points. This difference is due to the presence of K 3p and Rb 4p states in valence band which pushes the Ag d like states towards the Fermi level (E F ).

4 46 Condensed Matter and Materials Physics Figure 2. Electronic band structure (left panel) and density of states (right panel) of AAgO compounds at ambient pressure. When these compounds are compressed by reducing the cell volume, the broadening of the bands occurs. The band gap of these compounds reduces by shifting of Cu d like states in valence band towards E F. At high pressure region, metallization occurs due to the overlapping of lowest conduction band and highest valence band. In A 2 S and A 2 O (A= Li-Rb) band gap increases with pressure [15,16]. But in A 4 [Ag 4 O 4 ] compounds, band gap decreases with pressure and it is mainly due to the broadening of bands in Ag and alkali metals. The calculated band gap values, interatomic distances d(ag-o), d(a-o) at ambient pressure and metallization volume are given in Table 2. From the table 2, the interatomic distance d(a-o) increases from NaAgO to RbAgO and it depends upon the size of alkali metal atoms.

5 Advanced Materials Research Vol Table 2. Energy band gap (E g ) in ev, interatomic distances d(ag-o), d(a-o)in Å at ambient pressure and metallization volume (V/V 0 ) of AAgO compounds. NaAgO KAgO RbAgO Exp Present Exp Present Exp Present E g _ 1.37 _ 1.25 _ 1.14 d(ag-o) d(a-o) _ _ V/V 0 _ 0.69 _ 0.52 _ 0.48 Figure 3. Electronic band structure (left panel) and density of states (right panel) of AAgO compounds at high pressure.

6 48 Condensed Matter and Materials Physics 4. Conclusions In the present work, we have calculated the electronic structure and ground state properties of AAgO (A=Na, K and Rb) compounds using the TB-LMTO method. From the total energy calculations, the ground state properties were calculated for both the structures. The calculated equilibrium lattice constant a and c/a ratio are found to be in agreement with the experimental results. From the electronic structure calculations at ambient conditions, we find that KAgO and RbAgO are direct band gap semiconductors, whereas, NaAgO is a indirect band gap semiconductor. At high pressure the band gap decreases and metallization occurs. To the best of our knowledge, this is the first ever band structure calculations reported for these compounds. References [1] P. Shiv Halasyamani, R. Kenneth, Poeppelmeier, Chem. Mater, 10 (1998) [2] H. Sabrowsky, R. Hoppe, Z.anorg. allg. Chem, 358 (1968) [3] H. Von Klassen, R.Hoppe, Z.anorg. allg. Chem, 485 (1982) [4] W. Losert, R.Hoppe, Z.anorg. allg. Chem, 524 (1985) [5] D. Fischer, W. Carl, H. Glaum, R. Hoppe, Z.anorg.allg. Chem, 585 (1990) [6] O. K. Andersen, O. Jepsen, Phys. Rev. Lett. 53 (1984) [7] H.L. Skriver, The LMTO Method (Heidelberg: Springer),1984. [8] P. Hohenberg, W. Kohn, Phys. Rev. B 136 (1964) [9] W. Kohn, L. J. Sham, Phys. Rev. 140 (1965) A1133-A1138. [10] U. Von Barth, L. Hedin, J. Phys. C: Solid State Phys.5 (1972) [11] O. Jepsen, O.K. Andersen, Solid State Commun. 9 (1971) [12] F. J. Birch, Geophys. Res. 83 (1978) [13] Etienne Gaudin, Florent Boucher & Michel Evain, J. Solid State chem. 160 (2001) [14] J. A Tossel, D. J. Vaughan, Inorg. Chem. 20 (1981) [15] R. D. Ethiraj, G. Jaiganesh, G. Kalpana, Physica B, 396 (2007) [16] R. D. Ethiraj, G. Jaiganesh, G. Kalpana, M. Rajagopalan, Phy. Stat. Solidi B, 244 (2007)