The Physical Properties of ThCr2Si2- Type Co-based Compound SrCo2Si2: An ab-initio Study

In this article, we have studied the mechanical, electronic, and optical features of ThCr2Si2type compound SrCo2Si2. The investigation has been done by using the first-principles method depend on the density functional theory (DFT) and the calculations were completed with the Cambridge Serial Total Energy Package (CASTEP) code. The optimized lattice parameters are well in accord with the existing synthesized values. The investigated elastic constants for this compound are positive which ensured the mechanical stability of this phase. The calculated values of Pugh’s ratio and Poisson’s ratio ensure the brittle character of SrCo2Si2. The universal anisotropic constant A ensures the anisotropic behavior of SrCo2Si2.The softness nature of SrCo2Si2 is confirmed by the bulk modulus calculations. The overlapping of the valence band and conduction band near the Fermi level indicates the metallic nature of SrCo2Si2. At the Fermi level the major contribution comes from Co-3d and Si-3p states. The large reflectivity in the high-energy region indicates that this compound might be useful as coating materials for reducing solar heating. The photoconductivity and absorption begin with zero photon energy which also ensures the metallic nature of SrCo2Si2.

perature 38K (Rotter et al., 2008). On the other hand, Pt, Ni and Pd-based ThCr 2 Si 2 type borocarbides (Nagarajan et al., 1994;Batlogg et al., 1994) have been discovered in the recent years with the transition temperature up to 23K which raises the hope to constitute a family of new high temperature superconductors. In ironbased compounds, the ternary intermetallic (122type compounds) in the company of ThCr 2 Si 2 type structure as example AFe 2 As 2 (A = Sr, Ca, Ba, etc.) are free from oxygen having metallic nature (Rotter et al., 2008;Sasmal et al., 2008;Torikachvili et al., 2008). These types of compounds have been comprehensively studied for interpreting their superconducting mechanism (Johnston 2010;Stewart 2011). These types of compounds have high chemical flexibility and abundance of substitution possibilities. In recent times concentration was given to a series of the iron based and arsenic-free AeT 2 X 2 compounds (Ae = alkaline earth metal, T = Ni, Pd; X = P, Ge) with very low transition temperatures (T c ~ 0.3 -3.0 K) (Mine et al., 2008). Undoped RT 2 Si 2 (R = La, Y, Th; T = Ir, Pt) type superconductors are predicted to CaBe 2 Ge 2 -type structures (Yang et al., 2011). However the compounds with alkaline earth metals having ThCr 2 Si 2 -type structure are inadequate (Ronning et al., 2009;Fujii and Sato, 2009;Shelton et al., 1984;Doerrscheidt et al., 1976;Rieger and Parthé, 1969;Bodak and Gladyshevskii, 1968;Palenzona et al., 1987).
In this work we have studied a new phase with alkaline earth metal on the A-site crystallizing in the ThCr 2 Si 2 -type structure are inadequate. The compound SrCo 2 Si 2 signifies the third ternary SrT 2 Si 2 compound (T = 3d-block transition metals) besides SrCu 2 Si 2 (Kranenberg et al., 2002) and SrZn 2 Si 2 (May and Schäfer, 1972). For SrT 2 Si 2 the isostructural compounds with T = Pd, Ag have been characterized and reported (Eisenmann et al., 1970). The compound SrCo 2 Si 2 is isoelectronic to the parent Fepnictide superconductors AeFe 2 As 2 at the X site, contrast to their electronic bonding situation will be of special interest. Here we have studied the detailed physical properties of Co-based material SrCo 2 Si 2 by using the DFT based calculations implemented in CASTEP code.

Computational details
The CASTEP code (Segall et al., 2002) written by FORTRAN 95 language is used to investigate the physical properties of SrCo 2 Si 2 . The calculations were done by DFT theory within GGA with the PBE exchange-correlation function (Clark et al., 2005; Materials Studio CASTEP, 2010; Hohenberg and Khon, 1964;Perdew et al., 2008). The pseudo atomic calculations were done for Sr-4s 2 4p 6 5s 2 , Si-3s 2 3p 2 and Co-3d 7 4s 2 valence electrons. The plane wave cut-off energy was set to 500 eV. The special k-point sampling of the Brillouin zone (BZ) was employed by using the Monkhorst-Pack method (Monkhorst and Pack, 1976) with special 10×10×10 grid points in the primitive cell of SrCo 2 Si 2 . The crystal structure of SrCo 2 Si 2 was optimized by the Broyden-Fletcher-Goldfarb-Shanno (BFGS) minimization technique (Pfrommer et al., 1997). For this optimization the criteria of convergence were set to 1.0×10 -5 eV/atom for energy, 0.03 eV/Å for force, 0.05 Gpa for stress and 0.001 Å for ionic displacement. The elastic stiffness constants of SrCo 2 Si 2 were obtained by the stress-strain method (Fan et al., 2006). Then the bulk properties were obtained by the elastic constant data of SrCo 2 Si 2 . In that case the criteria of convergence tolerance were set to 2.0×10 -6 eV/atom for energy, 2.0×10 -4 Å for maximum ionic displacement, 6.0×10 -3 eV/Å for maximum ionic force and 0.1 GPA for maximum stress component. The maximum strain amplitude was set to be 0.003 in the present calculation of SrCo 2 Si 2 .

RESULT AND DISCUSSION:
3.1 Structural properties -At normal temperature and pressure, SrCo 2 Si 2 possesses a tetragonal crystal structure with the space group of I4/mmm (no.139) (Hoffmann et al., 2012). The conventional and optimized crystal structures of SrCo 2 Si 2 are shown in Fig   1. The unit cell contains two formula units (Z=2) with ten atoms that means one formula unit for each primitive cell with five atoms. The atomic position of Sr, Co, and Si in the unit cell of SrCo 2 Si 2 tetragonal crystal are 2a (0 0 0), 4d (0 0.5, 0.25) and 4e (0 0 0.3606) respectively.  The unit cell dimensions including equilibrium lattice parameters for tetragonal phase a 0 and c 0 , bulk modulus B 0 and the equilibrium cell volume V 0 of SrCo 2 Si 2 intermetallics at ambient temperature are charted in Table 1 with the experimentally evaluated values. From Table 1 it is obvious that the calculated lattice parameters are exceedingly close to the experimental data which ensure the dependability of the DFT-based investigations. From Table 1 we have seen that, our calculated lattice parameters are slightly deviated from the experimental results. The motive is due to the temperature dependence of the lattice parameters and GGA route (Zhu et al., 2016). The elastic constants were achieved from a linear fit of the calculated stress-strain function according to Hook's law (Nye, 1961). A crystal with the tetragonal phase belongs to six independent elastic constants (C 11 , C 12 , C 13 , C 33 , C 44 and C 66 ).The estimated elastic constants of SrCo 2 Si 2 are listed in Table 2.

Elastic properties -
According to the stability criteria (Pokunov et al., 2004) of tetragonal phase (Eq. 1) the com-pounds under consideration have good stability in nature. C 11 >0, C 33 >0, C 66 >0, C 44 >0 C 11 +C 33 -2C 13 >0, C 11 -C 12 >0 2(C 11 +C 12 ) +4C 13 +C 33 >0 (1) By utilizing the evaluated data of C ij , the most important mechanical features such as bulk modulus B, shear modulus G, Young's modulus Y, anisotropy factor A and Poisson's ratio ν of intermetallic SrCo 2 Si 2 have been calculated by using the Voigt-Reuss-Hill (VRH) averaging scheme (Hill, 1952). Which are listed in Table 3. The Voigt and Reuss bounds of B and G for cubic systems can be represented by the following expressions. = 2 11 +2 12 + 33 +4 13 9 (2) = + 3 11 − 3 12 + 12 44 Where, M and C 2 can be written as, M = C 11 +C 12 +2C 33 -4C 13 and C 2 = (C 11 +C 12 ) C 33 -2C 13 2 The arithmetic mean value of the Voigt (B V , G V ) and the Reuss (B R , G R ) bounds which is used to calculate the polycrystalline modulus is given by in terms of Voigt-Reuss-Hill approximations: Using the following expressions we have also calculated the Young's modulus (Y) and Poisson's ratio (ν), The Young's modulus is specified by the ratio of the tensile stress to tensile strain, which measure the stiffness for solid material. The larger value of Y point outs the more stiffness of a compound (Chen, et al., 2011). The higher value makes the solid better stiffer. The calculated Young's modulus is shown in Table 3 along with available similar type of compounds. From Table 3, we can say that the value of Young's modulus of SrCo 2 Si 2 is larger than SrRu 2 As 2 and SrRh 2 Ge 2 compounds indicating that the compound SrCo 2 Si 2 is stiffer than SrRu 2 As 2 and SrRh 2 Ge 2 compounds.
The Poisson's ratio is another useful parameter to understand the nature of bonding force in a material (Cao et al., 2013). The smaller value of ν (ν = 0.1) indicates the covalent materials whereas for ionic crystal ν = 0.25. The larger value of Poisson's ratio ( > 0.26) indicates that the compound will be ductile and the compound will be brittle when the value of Poisson's ratio is ( < 0.26). From Table   3, we see that the value of ν is 0.18 which refers the brittle nature of SrCo 2 Si 2 . The ratio between bulk and shear modulus (B/G) is known as Pugh's ratio which is applied to understand the brittleness and ductility manner of solid material (Pugh, 1954  The universal anisotropic factor of a solid material is specified by the subsequent relation (Ranganathan, et al., 2008).
A U = 0 indicates completely isotropic crystal and the deviation from this value shows the degree of anisotropy in a material. Chung and Buessen suggests two new relations (Chung and Buessem, 1967) to determine the anisotropy indexes of bulk modulus and shear modulus given as follows, For an isotropic crystal the value of A is 1 and for anisotropic crystal the values of A are either smaller or greater than unity. From Table 3 we see that the value of A is less than unity which represents the anisotropic nature of this compound.

Electronic properties -
The band structure and density of states (TDOS and PDOS) provide a clear concept about the electronic properties of a material. The electronic band structure provides vital information about a material to be metal, semiconductor or insulator. The bonding features of a material are obtained from the partial and total density of states calculations (Hu, et al., 2014). The full picture of energy bands and band gaps of a solid is known as electronic band structure or simply band structure. In solid-state and condensed matter physics, the band structure defines certain ranges of energy that are allowed for electrons within a solid, and the ranges of energy that are not allowed for any electrons. The investigated band structure for SrCo 2 Si 2 has been illustrated in Fig 2 in the energy range -10 eV to 10 eV which is observed along the high symmetry directions in the first Brillouin zone. The horizontal solid line at 0 eV indicates the Fermi level. From band structure it has seen that the valence bands and conduction bands are overlapped at Fermi level and there is no band gap indicating that this compound shows metallic manner. The metallic nature of SrCo 2 Si 2 signifies that this compound might be superconductor. The partial and total density of states of SrCo 2 Si 2 is plotted in Fig 3. From Fig 3 we have observed that the total density of states (TDOS) of SrCo 2 Si 2 is composed of four main peaks. The first peak in the valence band lies between -36.17 eV and -34.75 eV. In SrCo 2 Si 2 , Sr-5s states contribute the most to create the first peak. The second peak lies between -18.63 eV and -16.93 eV in SrCo 2 Si 2 . This peak is dominated by Co-3d and Si-3p states. The third peak lies between -11.42 eV and -7.46 eV. This peak is contributed by Si-3p states. The fourth peak lies from -6.32 eV to 8.65 eV. This peak is dominated by Si-3s and Si-3p states. We observe clear coincidence between the Co-3d and Si-3p states in SrCo 2 Si 2 , which suggests the covalent nature of Co-Si bonds in SrCo 2 Si 2 . This is a common feature of ThCr 2 Si 2 type compounds (Jeitschko et al., 1987). The calculated DOS at EF is 3.43 states/ eV-unit cell.

Optical properties -
The study of photon energy dependent optical function of a solid material is so essential due to the fact that it helps to get a clear conception concerning the electronic configuration of materials. The optical properties of SrCo 2 Si 2 with different photon energies are calculated by the frequency dependent dielectric function, ( ) = 1 ( ) + 2 ( ), which is closely correlated to the electronic configurations. The imaginary part 2 ( ) of dielectric function is obtained from the momentum matrix elements between the filled and the unfilled electronic state by utilizing the subsequent relation (Materials Studio CASTEP, 2010); Where, ω refers to light frequency, e indicates the electronic charge, û is the vector representing the polarization of the incident electric field, along with Where, denotes the light frequency and refers the principle value of the integral part.
The reflectivity spectra are derived from Fresnel's formula for normal incidence assuming an orientation of the crystal surface parallel to the optical axis using the relation (Fox, 2001).
We calculate the absorption coefficient I(ω), the real part of optical conductivity Re[σ(ω)] and the elec-tron energy-loss spectrum L(ω) using the following expressions (Delin et al., 1996). ( ) = 2 ( ) 1 ( ) 2 + 2 ( ) 2 (18) The optical spectra such as the refractive index, n( ), and the extinction coefficient, k( ), are easily calculated in terms of the components of the complex dielectric function as follows: The photon energy dependent ground state optical properties of SrCo 2 Si 2 are shown in

Reflectivity -
Reflectivity is a surface-sensitive analytical technique used in Physics, Chemistry and material science to characterize surfaces, thin films and multi layers. The optical reflectivity spectra are shown in Fig 4(a) as a function of incident photon energy. For SrCo 2 Si 2 the reflectivity spectrum starts with a value of 0.48, at the beginning it decreases and then rises again to reach maximum value of 0.79 at 13.22 eV obtained in the high energy region. This high value of reflectivity in high energy region reveals the characteristics of high conductance in the low energy region (Ali et al., 2016). Hence the compound shows promises as good was coating materials in the ultraviolet region.

Absorption Coefficient -
The absorption coefficient visualizes how far into a material light of a particular wave length can penetrate before it is absorbed. The absorption coefficient depends on the material and also on the wavelength of light which is being absorbed. The photon energy dependent absorption spectra of SrCo 2 Si 2 are shown in Fig 4(b).
For this compound the absorption spectra starts at zero photon energy which ensures the metallic manner of this phase. This phase exhibit quite good absorption coefficient in the energy ranges 4-22 eV. It supplies the information about the optimum solar energy conversion efficiency and point out the penetration depth of light of precise energy into the material before being absorbed (Ali et al., 2016). For this phase the strong absorption coefficients are observed in the UV region, however, they are weak in the visible region but continuously increase to-ward the UV region, and reach a maximum value at 9.11 eV. This result indicates that this compound is promising for absorbing materials in the UV region.

Refractive index -
Refractive index is a dimensionless quantity which determines how much light is bent or refracted when entering into material (Russell, 2003). The concept of refractive index of optical material is important for use in optical instruments like optical crystals, waveguides etc. Fig 4(c) shows the refractive index of SrCo 2 Si 2 which is one of the important optical properties. In the low energy region the highest refractive index of SrCo 2 Si 2 was found to 6.0 and this value rapidly decreases in the high energy region.

Conductivity -
Conductivity is an optoelectronic event where the conductivity rises due to absorbing of photons. It provides the information about a material will be semiconductor, conductor or insulator. The photo conductivity spectrum of SrCo 2 Si 2 shows in Fig   4(e). From Fig 4(e) it is obvious that the photoconductivity starts with zero photon energy which also ensures the metallic nature of this compound. The photoconductivity of SrCo 2 Si 2 increases due to the absorbing of photons (Sun et al., 2006). From Fig 4(e) we have seen that the photoconductivity spectra have a few maxima and minima peak in the calculated energy range.

Loss function -
The photon energy loss spectrum of SrCo 2 Si 2 is shown in Fig 4(f). The energy loss function is a significant matter to reveal the energy loss of a fast electron when it traversed in a material (Parvin et al., 2015). In loss function graph the peaks related with the plasma resonance and in which associated frequency is called the plasma frequency (Fox, 2002). The frequency connected to the upper limit of the energy loss spectrum is specified by the bulk plasma frequency  p of the material, which emerges at  2 < 1 and  1 = 0 (Saniz et al., 2006;Almeida et al., 2006). The peak in the energy-loss function arises when   goes through zero from below and  2 goes through zero from above. In the energy loss spectra we have seen that the effective plasma frequency of SrCo 2 Si 2 is equal to 14.42 eV. The highest peak is found at about 4.42 eV, which reveal the plasma frequency of SrCo 2 Si 2 . The material becomes transparent when the frequency of the incident light is higher than of plasma frequencies mentioned above. Furthermore, the peak in loss function corresponds to the trailing edges in reflection spectra.

CONCLUSION:
The different physical features such as mechanical, electronic and optical properties of intermetallic SrCo 2 Si 2 have been successively investigated by DFT simulation. The investigated optimized structural parameters are well accord with the available synthesized data. The calculated elastic constants have maintained the born stability criteria which ensure the theoretical mechanical stability of SrCo 2 Si 2 .
The calculated values of Pugh's ratio (B/G) and Poisson's ratio ensure the brittle nature of SrCo 2 Si 2 . The stiffer behavior of this phase is ensured by Young's modulus calculation. The analysis of universal anisotropic factor ensured the anisotropic nature of SrCo 2 Si 2 .The calculated band structure shows the metallic nature and major the part arrives from the Sr-4p states at Fermi level. High reflectivity is observed in the ultraviolet region energy site which ensure about the use of SrCo 2 Si 2 as a good coating material at ultraviolet energy region. The absorption quality is good in the ultraviolet region and high refractive index in the infrared region. This result ensured that this compound is promising for absorbing materials in the UV region. The effective plasma frequency of SrCo 2 Si 2 is found to 14.42 eV which ensures that this material becomes transparent when the frequency of the incident photon is higher than 14.42 eV.

ACKNOWLEDGEMENT:
Thanks to the Physics Department of Pabna University of Science and Technology for giving me opportunity to complete my research work.

CONFLICTS OF INTEREST:
The authors declared that there is no conflict of interest in this article.