Study of electronic structure, charge density, Fermi energy and optical properties of Cs2KTbCl6 and Cs2KEuCl6

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Study of Electronic Structure, charge density, Fermi energy and Optical properties of Cs2KTbCl6 and Cs2KEuCl6 Sikander Azam, A.H. Reshak

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S0921-4526(13)00528-0 http://dx.doi.org/10.1016/j.physb.2013.08.048 PHYSB307868

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Physica B

Received date: 6 March 2013 Revised date: 20 May 2013 Accepted date: 29 August 2013 Cite this article as: Sikander Azam, A.H. Reshak, Study of Electronic Structure, charge density, Fermi energy and Optical properties of Cs2KTbCl6 and Cs2KEuCl6, Physica B, http://dx.doi.org/10.1016/j.physb.2013.08.048 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Study of Electronic Structure, charge density, Fermi energy and Optical properties of Cs2KTbCl6 and Cs2KEuCl6 Sikander Azam1 ,A. H. Reshak1,2 1 Institute of complex systems, FFPW, CENAKVA, South Bohemia University in CB, Nove Hrady 37333, Czech Republic 2 Center of Excellence Geopolymer and Green Technology, School of Material Engineering, University Malaysia Perlis, 01007 Kangar, Perlis, Malaysia Abstract: Through the assist of the full-potential linear augmented plane wave (FPLAPW) method, the calculations of the electronic band structure, density of states, charge density, Fermi energy and regularity dependent dielectric functions of Cs2KTbCl6 and Cs2KEuCl6 are reported. This study shows that the nature of both these compounds is metallic. The generalized gradient approximations (GGA) exchange correlation potential was applied. The densities of states around Fermi level are frequently subjugated by Eu/Tb-f and DOS below Fermi level are subjugated by Eu/Tb-s/d, Cs-s, Cl-s and K-s/p. The value of the DOS at Fermi level N(EF) is 17.02 and 4.86 (states per unit cell per eV) for Cs2KEuCl6 and Cs2KTbCl6. The bare electronic specific heat coefficient, is found to be 2.95 and 0.84 mJ/mol-K2 for Cs2KEuCl6 and Cs2KTbCl6, respectively. Three bands crossing the Fermi level along the Γ−A direction of Brillion zone of Cs2KTbCl6 compound and one band crossing along the Γ−A direction of Brillion zone of Cs2KEuCl6 compounds, to form the Fermi surface. There exists a strong hybridization between Tb/Eu-K-p and Cl-s K-s and at -5.0 and -4.0 eV.

Keywords: Terbium Compound; Europium Compounds; GGA, DFT *Corresponding author at: institute of Complex Systems, FFPW-South Bohemia University, Nove Hrady 37333, Czech Republic. Fax: +420 386 361255. E-mail address: [email protected] (Sikander Azam)

1. Introduction The elpasolites form an interesting family of cubic symmetry compounds. The magnetic, spectroscopic and the electric properties of the cubic elpasolite system have been the subject of frequent studies conveyed over the last 20 years (1). One of the biggest 1

benefits is that, that they present the Li3+ ions which are very important in studying the spectroscopic properties in the solid state. The Li3+

ions are situated on high sites

symmetry. Generally Li3+ ions exist in unlike symmetry sites and generally trivalent rare earth ions are not found in sites of octahedral symmetry [2]. In the elpasolite compounds the Li3+ site is cubic with accurate octahedral symmetry i.e. as the case for monovalent A and B ions [3, 4]. In Centro symmetric environments the relaxation times of the excited states of lanthanide ions would be much longer than those localized in noncentrosymmetric sites. This recommends interesting aptitude for optical pumping and for transferring and storing of energy (5). When exchange takes place in a crystalline compound, substantial structural changes distressing the chemical and spectroscopic properties are shaped. The majority of the elpasolites possess important spectroscopic properties when the cubic crystals occupy the octahedral sites by lanthanide ions, where they can be excited to disparate spectroscopic states (6). The europium and terbium ions are famous due to their easy excitation. One can expect the intrinsic fluorescence reaction in the detectable region in small compounds because of the high symmetry site of the octahedral which they inhabit in a crystal. The predictable transitions possibly will be for 4fn → 4f

n-1

5d. The consequence of this

prospect is to employ these compounds as light absorbing emitting devices. This is recognized that doping this system with further lanthanide ions enhances the quantum yields and amends the wavelength of the wrought radiations (7). This work plans to study the total density of state along with the partial density of states, the optical properties, band structure and the charge density for the compounds Cs2KTbCl6 and Cs2KEuCl6 using the full potential linear augmented plane wave (FPLAPW) method within the framework of the density functional theory (DFT). In the coming section we are going to talk about the computational method. In the next segment we shall present the calculated results and conclusion will be presented in the last segment.

2

2. Methodology The crystal structure of Cs2KEuCl6 and Cs2KTbCl6 compounds has been shown in Fig. 1. Both the compounds [8] have the cubic structure with space group number 225 (Fm-3m). The lattice constants are a = 11.122(3)Α 0 for terbium elpasolite compound and a = 11.1633(3)Α 0 for the europium compound. The Atomic-positions of Cs2KTbCl6 are

Tb (0, 0, 0), Cs (0.25, 0.25, 0.25), K (0.50, 0.50, 0.50) and Cl (0.2257, 0, 0) and for Cs2KEuCl6 are Eu (0, 0, 0), Cs (0.25, 0.25, 0.25), K (0.50, 0.50, 0.50) and Cl (0.2317, 0, 0). The electronic structure calculation for Cs2KTbCl6 and Cs2KEuCl6 has been calculated by using the FP-LAPW techniques as employed in the wein2k package [9] using the Generalized Gradient approximation (GGA) [10] The Kohn Sham equations are detected by using the starting point meaning of the linear APW`s. For achieving the Eigen-values convergence, the wave function in interstitial were distended in plane wave with a cutoff RMTkmax=7.0 where RMT shows the smallest atomic sphere radius while kmax gives the extent of the main k vector in plane wave spreading out up to Gmax=12 (a.u)-1 the charge density was Fourier expanded. The electronic band structure, densities of states and optical properties of Cs2KTbCl6 and Cs2KEuCl6 compounds were performed by means of DFT calculations. From the result of the structural and optoelectronic nature of the studied compounds we will be aware to say about its technological importance. For the cubic compounds only one component of the optical dielectric tensor is needed to absolutely describe the optical properties. This is the imaginary part ε 2 (ω ) which can be calculated using the expression given in Ref.11:

ε 2 (ω ) =

8 3πω

2

ds ∑ ∫ Ρ (k ) ∇ω (k ) mn′ ΒΖ

nn′

2

k

nn′

Ρnn′ (k) is the dipole matrix elements sandwiched between early nk and closing n′k

with Eigen-values Ε n (k ) and Ε n′ (k ) correspondingly.

3

The real part can be deduced from the imaginary part by using the Kramers-Kronig equations [12].

ε1 (ω ) = 1 +

ω ′ε 2 (ω ′) dω ′ π 0 ω ′2 − ω 2 2

∞

Ρ∫

3. Results and Discussion 3.1 Band structure and density of states The electronic band structure which has been calculated for Cs2KTbCl6 and Cs2KEuCl6 compounds are given in Fig. 2.

As noted in the shown Figs that Cs2KTbCl6 and

Cs2KEuCl6 compounds exhibit a metallic characters. With the information that there is no experimental data on the band structure of Cs2KTbCl6 and Cs2KEuCl6 compounds are available in literatures to be compared with our results, by due to successful application of FP-LAPW methods for Cs2KTbCl6 and Cs2KEuCl6 we can discuss the behavior of the energy band structure for this particular material under the current study. Here we set the energy scale is in eV, and arbitrarily the energy origin is set to be there at the Fermi level. Following Fig. 3, the bands situated in the range -3.0 eV to 0.0 (EF) is due to the admixture of Eu/Tb-f and Cl-s/p with small contribution Cs-s and k-p states. The structure localized above EF is due to the contribution of Eu/Tb-s/d with small admixture of K-s/p and Cl-s. The value of the DOS at Fermi level N(EF) is 17.02 (states per unit cell per eV) for Cs2KEuCl6 and for Cs2KTbCl6 is 4.86 (states per unit cell per eV). The metallic character of the two inter metallic is clearly seen from the finite DOS at the Fermi level. It is clear from Figures 3, that the total DOS at the Fermi level is the highest for Cs2KEuCl6 as compared to Cs2KTbCl6. The electronic specific heat coefficient (γ), which is function of DOS, can be calculated using the expression

1 3

γ = π 2 Ν (Ε F )K B 2 Where N(EF) is the DOS at the Fermi energy, EF and kB is the Boltzmann constant. The calculated densities of states at the Fermi energy N(EF) enables us to calculate the bare

4

electronic specific heat coefficient, which is found to be equal to 2.95 and 0.84 mJ/molK2 for Cs2KEuCl6 and Cs2KTbCl6, respectively. The total and partial densitiy of states for the compounds Cs2KTbCl6 and Cs2KEuCl6 were calculated using GGA scheme as illustrated in Fig. 3. The calculated total densities of states for Cs2KTbCl6 /Cs2KEuCl6 compounds have been illustrated in Fig. 3 and the partial densities of states s, p, d and f states of Cs, K Tb (Eu), and Cl have been illustrated in Fig.3. From Fig.3 one can see that for compounds Cs2KTbCl6/Cs2KTbCl6 the peak at -8.0 eV is due to Cl-s orbital. The peaks from -4.0 to -2.0 eV is due to Eu/Tb-s/p and K-p with feeble role of Cs/Cl/k-s orbital .It is clear from Fig.4 and 6 that DOS around the fermi level i.e. from -1.0 to 1.0 eV are frequently subjugated by Eu/Tb-f orbital. The peaks from 4.0 eV to 18.0 eV are due to Eu/Tb-s/d, and k-s/p with small contribution of Cl-s and Cs-s orbital. As we replace Tb by Eu the whole structure shifts towards lower energies. There is a strong hybridization between Tb/Eu-K-p and Cl-s K-s and at -5.0 and -4.0 eV.

3.2 Fermi surface:

We have computed the Fermi surface of the Cs2KEuCl6 and Cs2KTbCl6 for the theoretical lattice parameters. The highly anisotropic Fermi surface of Cs2KEuCl6 and Cs2KTbCl6 compounds calculated within the relativistic scheme as displayed in Fig. 4. We have enlarged the band structure near the Fermi level in order to get a deep understanding of the band crossing over the Fermi level as shown in Fig. 2 (c,d). The near-Fermi bands demonstrate (Fig. 2) a “mixed” character: the bands intersect the Fermi level between W and K. The calculations for Cs2KEuCl6/Cs2KTbCl6 compound reveal that there are four/one bands crossing along the W−K direction. These structures yield a multi-sheet Fermi surface of Cs2KEuCl6 and Cs2KTbCl6 compounds which consists of a set of holes and electronic sheets. The majority of them are hole-like, namely, concentric cylinders. The differences in FS topology of the two compounds are due to changes in inter-atomic distances, bonding angles and as well as to the degree of band filling. The shading is by velocity where the blue, green, and red colors corresponds to slow, intermediate, and fast electrons, respectively.

5

3.3. Electron charge Density:

Electron density denotes the nature of the bond character. In order to predict the chemical bonding and the charge transfer in Cs2KEuCl6 and Cs2KTbCl6 compounds, the chargedensity behaviors in 2D are calculated in the (101) plane and have been displayed in Fig. 5. To discuss the electronic charge density we calculated the bond lengths in unit lattices of Cs2KEuCl6 and Cs2KTbCl6 compounds as displayed in Table 1. The result demonstrates that the replacement of the Eu by Tb leads to redistribution of electron charge density. From table 1 as it is clear that there is a small change in bond length when we replace Eu by Tb. The plot shows there is ionic and partially covalent bonding between Eu/Tb and Cl, the Pauling electro-negativity of Eu/Tb atom is 1.2/1.3 and for Cl atom is 3.0. The calculated electron density shows that charge density lines are spherical in some areas of the plane structure which shows sign of ionic bond of K and Cs atoms and in some areas of structures Eu/Tb and Cl atoms shared electron that shows the strong covalent interaction between Eu/Tb and Cl. As a result, we examine a large Eu/Tb electronic charge transferred to Cl site. This can be seen clearly by color charge density scale, where blue color (+1.000) corresponds to the utmost charge gather ion site. This can also be noted that the majority of the charge is inhabited in the Eu/Tb - Cl bond direction, while the most charge inherent on the Eu/Tb and Cl site. The contact between Cl and Eu/Tb produces covalent-like bond due to the electro-negativity difference around (1.8/1.7). So Cs2KEuCl6 and Cs2KTbCl6 compounds has both ionic and covalent bond.

3.3 Optical properties

Fig. 6, illustrates the imaginary part of the dielectric function for both the compounds. As the investigated compounds are metallic so we have to take the intra band transitions (Drude term) into account [13]

ε 2 (ω ) = ε 2 int er (ω ) + ε 2 int ra (ω ) Where

ω P2τ ε 2 int ra (ω ) = ω (1 + ω 2τ 2 ) 6

Where ω p and τ is mean plasma frequency and mean free time respectively among the collisions [14] usually written as:

ω p2 =

8π 3

∑ϑ

2

δ (ε kn )

kn

kn

Where ε kn is Ε n (k ) − Ε F and ϑ kn is the velocity of electron. The effect of Drude term is significant for less than 1.0 eV. We have calculated the imaginary parts of the dielectric functions ε 2 (ω ) for the compounds Cs2KTbCl6 and Cs2KEuCl6 using GGA scheme whose results are illustrated in Fig 6. So far we know there is no experimental and theoretical data for the optical properties of these compounds available in literature to be compared with our results. As shown in Fig. 6 that there alters of structure forwards to the elevated energies by around 0.5 eV for both the compounds. There are some humps in the structure from the start to the last of the graph. The larger peak for Cs2KEuCl6 compound is at 6.55 eV and for Cs2KTbCl6 compound is at 6.40 eV. The peaks in the optical properties can be determined by the electric dipole transition among the unoccupied and occupied bands and we can determine these peaks by the band structures. The first peak is due to the transition from Eu/Tb-f to C-s, the second peak is due to the transition from either K-p or Cl-p state to C-s or Cl-s states. The other peaks are due to the transition from Eu/Tb-p, K-s/p and Eu/Tb-s states to K-p and Eu/Tb-d states. From the imaginary part of the dielectric functions ε 2 (ω ) are the real parts ε1 (ω ) were Computed using the Kramers–Kronig relations [12]. The results of our calculated ε1 (ω ) dissemination are shown in Fig. 7 for both compounds.

4. Conclusion

The electronic structure, electronic charge density and linear optical properties of the Cs2KEuCl6 and Cs2KTbCl6 compounds are studied using the FP-LAPW method based on the density functional theory with the GGA for the exchange-correlation functional. The investigated compounds possess metallic nature. The value of the DOS at Fermi level N(EF) is 17.02 and 4.86 (states per unit cell per eV) for Cs2KEuCl6 and Cs2KTbCl6. The bare electronic specific heat coefficient, which is found to be equal to 2.95 and 0.84

7

mJ/mol-K2 for Cs2KEuCl6 and Cs2KTbCl6, respectively. Corresponding density of states are presented and the major structures in them are identified. It is clear that DOS around the Fermi level are frequently subjugated by Eu/Tb-f and DOS below the Fermi level are subjugated by Eu/Tb-s/d, Cs-s, Cl-s and K-s/p. As we replace Tb by Eu the whole structure shifts towards lower energies. There is a strong hybridization between Tb/Eu-Kp and Cl-s K-s and at -5.0 and -4.0 eV. The Fermi surface of Cs2KEuCl6 and Cs2KTbCl6 is composed of four/one bands crossing along the W−K direction of BZ. The bonding features are analyzed by using the electronic charge density contour in the (101) crystallographic plane. The result demonstrates that the replacement of the Eu by Tb causes a small change in bond length. There is ionic and partially covalent bonding between Eu/Tb and Cl. Using the projected DOS and band structure we have analyzed the interband contribution to the optical properties of Cs2KEuCl6 and Cs2KTbCl6. The real and imaginary parts of dielectric function are calculated. . AKNOWLEDEGMENT

This work was supported by the project CENAKVA (No. CZ.1.05/2.1.00/01.0024), the grant No. 152/2010/Z of the Grant Agency of the University of South Bohemia. School of Material Engineering, Malaysia University of Perlis, P.O Box 77, d/a Pejabat Pos Besar, 01007 Kangar, Perlis, Malaysia.

References

1. R. W. Schwartz, S. F. Watkings, Ch. J. OÔConnor, and R. L. Carlin, J. Chem. Soc. Faraday ¹rans. II. 72 (1976) 565Ð570. 2. R. W. Schwartz and N. J. Hill, J. Chem. Soc. Faraday II. 70 (1974) 124Ð131. 3. L. R. Morss and J. Fuger, Inorg. Chem. 8 (1969) 1433Ð1439. 4. D. Babel, R. Haegle, G. Pausewang, and F. Wall, Mater. Res. Bull. 1371Ð1382 (1973).

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5. A. K. Banerjee, F. Stewart-Darling, C. D. Flint, and R. W. Schwartz, J. Phys. Chem. 85 (1981) 146Ð148 6. R. Nevald, F. W. Voss, O. V. Nielsen, H. D. Amberger, and R. D. Fischer, Solids State Commun. 32 (1979) 1223Ð1225. 7. M. Bertinelli and C. D. Flint, J. Phys.: Condens. Matter. 2 (1990) 8417Ð8426. 8. M. E. Villafuerte-Castrejon, M. R. Estrada, J. Gomez-Lara, J. Duque,à and R. Pomes . J. of solid state chemistry. 132 (1997) SC977382. 9. Blaha,p.; Schwarz, k.; Madsen, G. K. H.; Kvasnicka, D. Luitz, j. WEIN2K, an augmented plane wave + local orbital programme for calculating crystal properties; Technische Universitat, Wein: Vienna, Austria,; ISBN 3-9501031-1-2 (2001). 10. J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. 11. Ali Hussain Reshak, Z. Charifi, H. Baaziz, Current Opinion in Solid State and Material Science. 12 (2008) 39-43. 12 Khan MA, Kashyap A, Solanki AK, Nautiyal T, Alluck S,. Phys Rev B. 23 (1993) 16974. 13. Wooten F. Optical Properties of solids. Newyork and London: Acdmic press (1972). 14. Chakraborrty B, Pickett WE, Allen PB. Phy Rev B.14 (1972) 3227.

Table Caption Table 1: Some relevant Eu1/Tb1-Cl4 and Cl–K interaction distances in Cs2KEuCl6 and

Cs2KTbCl6 compounds

Figs Caption Fig. 1: Unit cell structure for Cs2KEuCl6 and Cs2KTbCl6compounds. Fig. 2: Calculated band structure for compound Cs2KEuCl6 and Cs2KTbCl6 Fig. 3 : Calculated total and partial densities of states (States/eV unit cell) for

Cs2KEuCl6and Cs2KTbCl6. Fig. 4: Calculated Fermi surface for Cs2KEuCl6 and Cs2KTbCl6. Fig. 5: Calculated electron charge density for Cs2KEuCl6 and Cs2KTbCl6.

9

Fig. 6: Calculated value of imaginary part (ε 2 (ω )) of dielectric function for Cs2KEuCl6

and Cs2KTbCl6. Fig. 7: Calculated value of real part of dielectric function (ε 1 (ω )) for Cs2KEuCl6 and

Cs2KTbCl6. Table 1

Cs2KEuCl6

Cs2KTbCl6 Distance(Å)

Atomic pair

Distance(Å)

Eu1-Cl4

2.585(Ǻ)

Tb1-Cl4

2.577(Ǻ)

Eu1-Eu1

7.893(Ǻ)

Tb1-Tb1

7.864(Ǻ)

Cl4-Cl4

4.236(Ǻ)

Cl4-Cl4

4.220(Ǻ)

Cl4-K3

2.995(Ǻ)

Cl4-K3

2.984(Ǻ)

K3-K3

7.893(Ǻ)

K3-K3

7.864(Ǻ)

Atomic pair

(a)

(b)

10

Fig. 1: Unit cell structure for Cs2KEuCl6 and Cs2KTbCl6compounds

(b)

(a)

(c)

(d)

Fig. 2: Calculated band structure for compound Cs2KEuCl6 and Cs2KTbCl6

11

(a)

(b)

12

(c)

(d)

13

(e)

(f)

14

(g)

(h)

15

(i)

(j)

16

(k)

(l) Fig. 3:

17

(a)

(b) Fig. 4

18

(a)

(b) Fig. 5: Calculated electron charge density for Cs2KEuCl6 and Cs2KTbCl6.

19

(a)

(b) Fig. 6:

20

(a)

(b)

Fig. 7:

21

22