Linear and Nonlinear Optical Susceptibilities of Ag3PS4 and Ag5PS4Cl2 Compounds

Linear and Nonlinear Optical Susceptibilities of Ag3PS4 and Ag5PS4Cl2 Compounds

,

Sikander Azam 1, Wilayat khan 1, Saleem Ayaz Khan 1 A. H. Reshak1,2

1 New Technologies – Research Center, University of West Bohemia, Univerzitni 8, 306 14 Pilsen, Czech Republic

2Center of Excellence Geopolymer and Green Technology, School of Material Engineering, University Malaysia Perlis, 01007 Kangar, Perlis, Malaysia

Abstract The complex density functional theory (DFT) calculations of linear and nonlinear optical susceptibilities for the Ag3PS4 and Ag5PS4Cl2 compounds have been reported, using the full potential linearized augmented plane wave (FP-LAPW) method. We have employed the local density approximation (LDA), generalized gradient approximation (GGA-PBE). In additional the Engel Vosko generalized gradient approximation (EVGGA) formalism, which optimizes the corresponding potential for the spectral features of the linear and nonlinear optical susceptibilities, was employed. We have calculated the frequency-dependent complex (, its zero-frequency limit 1(, refractive index n(, the reflectivity R( and electron energy loss function L(. Calculations are also reported for the frequency-dependent complex second-order nonlinear optical susceptibilities. We find opposite signs of the contributions of the 2( and 1( inter/intra-band to the imaginary part for the dominant component through the optical frequency range.

Keywords linear optical susceptibilities; nonlinear optical susceptibilities; DFT

in the texts, e.g. Ag4P2S6 [6], Ag4P2S7 [7], Ag7P3S11 [8,9], Cu3PS4 [10] and CuPS2 [11].

In this manuscript we have computed the linear and nonlinear optical properties of Ag3PS4 and Ag5PS4Cl2 compounds.

1. COMPUTATIONAL METHODOLOGY

   The Ag3PS4 and Ag5PS4Cl2 crystal structure has been exposed in Fig. 1. Both has the orthorhombic structure with space group # 31 (P m n 21) and # 38 (A m m 2). The lattice constants for the Ag3PS4/Ag5PS4Cl2 compounds are a = 7.647(3)/ 7.409(1) Ã…, b = 6.858(2)/ 11.143(2) Ã…, c = 6.506(1)/

   6.258(1) Ã…, [12].

   Fig. 1: Unit cell structure

   1. INTRODUCTION

      Numerous investigations have been conducted to know the standpoint philosophy presently existing in the analyses of nonlinear optical properties (NLO) of semiconductors. With the aim to get better production in the industrial area. It is accomplished that a substantial correlation subsist between the electro-negativity and the band gap in semiconductors [1].

      Therefore it is remarkable to exploit the influence of physical and chemical trends for instance the electro-negativity on the NLO in semiconductors [1]. Innovative compounds having appropriate features such as phase matching for applications in the area of laser or in devices based on optical parametric oscillators (OPO) are investigated [1].

      When the electro-negativity of the materials increases or decreases it influences the second harmonic generation. Many efforts has been made to get the relations between band gaps, single bond energy, atomic numbers, electro-negativities and refractive indices [2,3].

      The thiophosphates (transition metal) configured a broad and attractive class of compounds that have been the area of studies due to their different structural chemistries [4] and their physical properties. Only the AuPS4 [5] is the ternary thiophosphate of gold, a number of compounds appropriating to the ternary Ag-P-S and Cu-P-S system have been described

      Self-consistent FP-LAPW [13] calculations on Ag3PS4 and Ag5PS4Cl2 compounds has been conducted using the WIEN2k package [14]. The unit cell structure for both compounds has been shown in Fig.1. An adequate trade-off between accuracy and cost was achieved by taking a number of basic functions up to RMT_Kmax=9), whereas the RMT is the minimum radius of the muffin-tin spheres and Kmax provides the scale of the largest K vector in the plane wave basis. The muffin-tin radii RMT were chosen for Ag3PS4 compound as following; RMT (Ag) =2.37 a.u. and RMT (S and P) =1.82 a.u., whereas for Ag5PS4Cl2 compound as; RMT (Ag) =2.39 a.u., RMT (S and P)

      =1.84 a.u. and RMT (Cl) =2.16 a.u.

      Furthermore, inside muffin-tin spheres, the valence wave functions are extended up to lmax=10. The exchange and correlation effects are treated by the local density approximation (LDA), generalized gradient approximation (GGA-PBE) and EVGGA functional [15-18]. The energy dependence on k points in the irreducible wedge of the Brillouin zone (IBZ) has been checked, and the mesh size has been set to 10×10×10 points.

2. RESULTS AND DISCUSSION

   1. Linear optical properties

      In this section we will talk about the dielectric function (complex quantity) ( of Ag3PS4 and Ag5PS4Cl2 compounds. These properties are resolute by the dielectric function ( as specified by the following expression

      Fig. 2: Average imaginary part dielectric function of both compounds

      As it is clear from the (average) spectra of both compounds that, as we move from Ag3PS4 compound to Ag5PS4Cl2 compound, though there is a small shift in the structure towards the higher energy and also the magnitude of the peaks decreases.

      As our investigated compounds has the orthorhombic symmetry, hence the dielectric functions are resolved into three components xx( yy( and zz(. The investigated

      2

      2

      2

      spectra of the imaginary part xx , yy and zz of the

      ( 1( i2(. The dielectric function absorptive part, 2( contingents on the momentum matrix elements and the joint density of states. The optical properties can be illustrated through the transverse dielectric function (. For (, there exist two impacts i.e. the intraband and interband transitions. The contribution of first one is only vital for metals. While the former one, can be torn apart in to direct and indirect transitions. Here in this article we overleap the indirect interband transitions, that implicate the scattering of phonons assuming a small contribution to the frequency dependent dielectric functions. For calculating the direct interband contribution to the absorptive part, so this is obligatory to summarize all conceivable transitions from valence band to the conduction band taking the suitable transition dipole matrix elements into description.

      The spectra of the optical properties have been evaluated for an energy range 014 eV, this spectra of both compounds enclose numerous peaks which communicate to electronic transitions from the occupied band to unoccupied band. We firstly calculated the average dielectric function of both compounds as shown in Fig. 2.

      frequency dependent dielectric function are shown in Fig. 3 (a and b) for both compounds. We can explain the different structures, we divide the optical spectra into two major groups, the first from 2.0 to 6.0 eV and the second from 6.0 eV and above. The first group is subjugated by S-p and P-s/p transitions, the first interband transition arises between the valence band maximum (VBM) and conduction band

      2

      2

      minimum (CBM), and the first peaks of xx , yy and

      2

      zz for Ag3PS4 (Ag5PS4Cl2) compounds are at 3.72, 4.05 and 4.09 eV (4.04, 3.98 and 4.01 eV). The next group of the peaks is construed from the transitions from either S-p or P-p states to Ag-s or Ag-p states for Ag3PA4 compounds while in Ag5PS4Cl2 compound these peaks can be deduced from either

      2

      2

      2

      S-p or P-p states to Ag-s or Ag-p or Cl-s states, where th main peaks of xx , yy and zz for Ag3PS4

      (Ag5PS4Cl2) compounds are located at 8.47, 6.87 and 8.77 eV (8.20, 8.31 and 7.49 eV).

      Fig. 3: Calculated imaginary 2

      (a)

      (b)

      We have investigated the real part of the dielectric function

      1 , using the KramersKronig relations [19]. The investigated spectra of 1 for both compounds are exposed in Fig. 4 (a and b). The zero frequency limit 1 0is the mainly imperative quantity, known as the electronic part of the static dielectric constant which is greatly influenced by the band

      Fig.4: Real part 1 of dielectric tensor (d and e)

      (a)

      (b)

      The absorption coefficient can be evaluated from the and . The Ixx Iyy and Izz spectra has been shown in Fig. 5 (a and b), at 2.0 (2.5) eV the first absorption peak is originated for the Ag3PS4 (Ag5PS4Cl2) compounds. The absorption coefficient of the band at 3.6 (4.3) eV are anticipated by our computing to be 45.0 (70.0) ×104cm-1 for

      Ag3PS4 (Ag5PS4Cl2) compounds. Seeing as that the absorption coefficient in the fundamental region is exalted almost

      gap. The static values

      xx 0, yy 0 and zz 0

      for Ag3PS4

      4 -1

      4 -1

      1 1 1

      200×10 cm Ag3PS4 compound and more than 200×10 cm

      (Ag5PS4Cl2) compounds are 5.71 (5.17), 5.82 (5.43) and 6.06 (5.12). We note that a smaller energy gap (Eg) acquiesces a larger 1 0value [20-24]. This could be cleared through Penn

      model [25]. This model is based on this formula

      for Ag5PS4Cl2) compound at high energy.

      The reflectivity spectra Rxx Ryy and Rzz for Ag3PS4 and Ag5PS4Cl2 compounds has been shown in Fig. 5 (c and d).

      It shows a weak anisotropy between the three components but

      0 1 p

      / E 2 . From this expression it is apparent that

      this anisotropy increases a little when we move from Ag3PS4

      g

      that 0 is inversely proportional to Eg. The value of the Eg

      can be find out from this expression by using the values of both 1 0 and p (plasma energy).

      compound to Ag5PS4Cl2 compounds The energy loss function (Lxx Lyy and Lzz (see Fig. 5(e and f) shows the main peak in the energy loss function, which defines the screened plasma frequency p [26], are located at 8.70eV. This main peak corresponds to the abrupt reduction of the reflectivity spectrum (Rxx Ryy and Rzz) and to the zero crossing of (Fig. 4(a and b). From the reflectivity spectrum, one can say that these compounds show small reflectivity at low energies then a rapid increase in the reflectivity occurs at intermediate and high energies. The reflectivity maxima take

      place from inter-band transitions. They occurred between the energy range 10.014.0 eV for both compounds, which is in the ultraviolet. i.e. both compounds can be therefore serve as a possible shield for ultraviolet radiation.

      The calculated refractive indices nxx nyy and nzz for Ag3PS4 and Ag5PS4Cl2 compounds are shown in Fig. 5 (g and h). The peaks that appears in the refractive index spectra are narrated to the peaks emerged in the imaginary part of the dielectric function. At low energies, the refractive index for both compounds assorted between 2.0 and 2.5. But a rapid decreasing occurs at high energies, in the refractive indices of both compounds.

      This phenomena is significant physical parameter linked to the microscopic atomic interactions. Through theoretical stance, there exist two different approaches in screening this subject: the refractive index is associated to the density and the local polarizability of these individuals are related to the energy gap Eg of the material [27,28].

      Hervé and Vandamme proposed an empirical formula, in order to be motivated by simple physics of light refraction and dispersion, as follows [28]:

      (b)

      A

      n 1

      E

      • B

      g

      where A=13.6eV and B=3.4 eV and Eg is the band gap. The calculated refractive indices of our investigated compounds are 2.79 and 2.73 for Ag3PS4 and Ag5PS4Cl2 compounds. This is confirmed by the computation of the optical dielectric constant , which depends on the n.

      The refractive index spectra nxx nyy and nzz for the investigated compounds, shows a difference in the anisotropy as one goes from Ag3PS4 and Ag5PS4Cl2 compound. We may conclude, frankly, that the static value of n(0) decreases as the band gap increases. The static values nxx nyy and nzz for Ag3PS4 (Ag5PS4Cl2) compounds are 2.30 (2.27), 2.41

      (2.33) and 2.46 (2.26).

      Fig. 5: Calculated absorption co-efficient (a and b), reflectivity (c and d), energy-loss spectrum (e and f) and the refractive index (g and h)

      (a)

      (c)

      (d)

      (e) (h)

   2. Nonlinear optical properties (NLO)

   Since nonlinear optical properties are more sensitive to small changes in the band structure than the linear ones, and because of its mechanism itself, any anisotropy in the linear optical proper- ties lead to improve the second harmonic generation effect (SHG).

   131

   232

   311

   322

   This is apportioned to the actuality that the second harmonic response involves 2( resonance additionally to the customary resonance. Since Ag3PS4 and Ag5PS4Cl2 compounds possess orthorhombic structure belongs to the space group # 31 (P m n 21) and # 38 (A m m 2). Thus these compounds having five independent non-zero tensor

   components; namely

   (2) ,

   (2) ,

   (2) ,

   2

   and

   333

   322

   (2) . Here, the calculations predict that

   (2)

   is the

   333

   (f)

   (g)

   dominant component for Ag3PS4 compound and Ag5PS4Cl2 compound as shown in Fig. 6 (a and b).

   ijk

   Fig. 6: Calculated 2

   2 for

   (a)

   (b)

   The calculated imaginary part of the second harmonic generation (SHG) is shown in Fig. 7a. It is clear that the imaginary part of the second harmonic generation is zero below half the band gap. The terms 2( start to conduce at energies ~1/ 2Eg and the terms for energy values above Eg.

   (b)

   333

   322

   Fig. 8 shows the 2 and inter/intraband contributions to the imaginary parts of (2) for Ag3PS4 compound and 2

   for Ag5PS4Cl2 compound. Note the opposite signs of the two contributions throughout the frequency range. This fact may

   Fig.7b shows the

   2

   and

   2

   of Ag3PS4 and

   be useful for molecular engineering of the crystals in the

   322

   333

   Ag5PS4Cl2 compounds. Following Fig.7b, we point out that moving from Ag3PS4 compound to Ag5PS4Cl2 compound, guides to decrease the amplitude and shift all the structures of

   desirable directions.

   333

   Fig. 8: Calculated total

   2 2;; and

   322

   2 2;; spectrum

   ijk

   2 towards higher energies. Following Fig. 7b, we found

   and on linear optical properties

   that the value of

   2 0

   is 0.05 pm/V for Ag3PS4 compound

   333

   322

   and the value of pm/V.

   2 0 for Ag5PS4Cl2 compound is 0.02

   Fig. 7: (a) Calculated imaginary part of the second harmonic generation

   ijk

   (SHG) and (b) Calculated 2 pm/V

   (a)

   (a)

   (b)

3. CONCLUSION

The full potential linearized augmented plane wave technique has been used for the theoretical investigation of the Ag3PS4 and Ag5PS4Cl2 compounds. We have calculated and analyzed their linear and nonlinear optical properties. We analyzed the real and imaginary part of the dielectric tensor with other related properties like reflectivity, refractive index, extension co-efficient and energy loss function of the linear optical properties. We concuded that the reflectivity maxima occur from inter-band transitions. They occurred between the energy range 10.014.0 eV for both compounds, which is in the ultraviolet. i.e. both compounds can be therefore serve as a possible shield for ultraviolet radiation.

Further to the linear properties we computed the second order nonlinear optical properties namely the SHG. We calculated the total complex susceptibility of all nonzero components of

ijk

333

(2) and we found that that (2) is the dominant

322

component for Ag3PS4 compound and 2 for Ag5PS4Cl2 compound.

AKNOWLEDEGMENT

The result was developed within the CENTEM project, reg. no. CZ.1.05/2.1.00/03.0088, co-funded by the ERDF as part of the Ministry of Education, Youth and Sports OP RDI programme.

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