Research Journal of Recent Sciences _________________________________________________ ISSN 2277-2502 Vol. 4(IYSC-2015), 181-184 (2015) Res. J. Recent. Sci. International Science Congress Association 181 Analysis of Structural Phase Stability of Strontium Sulphide under High Pressure Shilpa Kapoor High pressure Research Lab, Department of Physics, Barkatullah University, Bhopal, MP, INDIAAvailable online at: www.isca.in, www.isca.me Received 27th July 2015, revised 27th August 2015, accepted 5th October 2015 AbstractA three body interaction potential (TBIPZpe) model is developed to study the structural phase stability of SrS having NaCl (B) structure at room temperature. This model consists of long range Columbic, three body interaction forces, short range overlap forces operative up to next nearest neighbors and zero point energy effects. We have reported the phase transition pressure, volume collapse and second order elastic constants and found results well agreed with available experimental data. Keywords: Phase transition, second order elastic constants, three body forces and zero point energy. Introduction The chalcogenides of strontium SrX (X = S, Se, Te) crystallize in the rock salt structure at normal temperature and forms a much closed shell ionic system with other alkaline earth chalcogenides. The majority of the compounds of strontium undergo a structural phase transition from the NaCl structure having coordination number 6 transforms to CsCl structure having coordination number 8 at a high pressure. Hence, in phase changes from NaClto CsCl the coordination number changes from 6 to 8. These chalcogenides are technologically important because of their applications in the area of luminescent devices, radiation dosimetry, fast high resolution, optically stimulated luminescence imaging and infrared sensitive devices2-5. SrS was found to undergo the structural phase transition by X-ray diffraction experiment at 18 GPa. The structural phase transition and elastic constants of SrS are also reported by Khenata et al.. B.Y.Thakore et al. found the structural phase transition of SrS at 17.95 GPa by using plane wave pseudopotential density functional theory. The electronic band structure and optical property of SrS are mainly discussed in other literatures8-10. In the present article, an effort has been devoted to develop an improved potential model, which has three-body interaction potential (TBIPZpe) and zero point energy effects. Due to this, our result shows a reasonable agreement with the available experimental data. The incorporation of zero point energy effects seems essential as it is the ground state energy of the compound which is the lowest energy a compound may acquire. It is well known that at T=0K the energy of a compound cannot be zero but ½ (h). This term, produces a very less effect, as far as Gibbs free energy is concerned, yet cannot be neglected completely. Material and Methods Pressure on materials causes a variation in volume which leads to an increased charge transfer (three body interaction effects)11due to deformation of the overlapping electron shells of the adjacent ions. This interaction becomes more important to consider because ions experience sufficient overlap due to the decrease in inter-ionic spacing of the lattice crystal when pressure gets increased. Besides, increase in overlap energy, the charge is transferred due to the overlap in electron shells, changes the ionic charge which in turn alters the coulomb energy by a factor () 1 fr nz    \n where and are respectively the number of electrons in outermost shell and ionic charge of the compound. The f(r) is the TBI parameter and it depends on the nearest neighbor distance (12 as (1) Where is a constant and is the range parameter. To achieve the stability for a crystal structure, the effect of TBI has been incorporated in the Gibbs free energy (G=U+PV-TS). Here U is the internal energy at T=0K, S is the entropy, pressure P and volume V. The Gibbs free energy for rock salt ( B1 ) and CsCl B2 ) structure at 0K can be stated by: PV (2) )')'PV (3) The first terms in the energies in equation (2) and (3) are lattice energies for B and B structures. Their expressions are: Research Journal of Recent Sciences ______________________________________________________________ ISSN 2277-2502Vol. 4(IYSC-2015), 181-184 (2015) Res. J. Recent. Sci. International Science Congress Association 182 exp())12(ijzf 2/1)5.0(414.1exp(414.1exp(jjii (4) exp())'(16(ijzf 2/1)5.0(154.1exp(154.1exp(jjii (5) ij is the Pauling coefficient, is the ionic radii of i(j) ions, and b are range and hardness parameters respectively. 2/1 is known as the mean square frequency related to Debye temperature as /)/1 (6) Here can be expressed by Blackman’s formula12. rB (7) where and are the bulk modulus and reduced mass of the compounds. The first term in equations (4) and (5) are long- range Columbic, second terms are three body interaction forces for B and B phases , third terms are the short range overlap repulsion for (i, j) ions, fourth and fifth terms are overlap repulsive term extended up to next nearest neighbor ions within Hafemeister and Flygare approach13 and the last term is zero point energy12 Here, VB1 (=2.00 3) and VB2 (=1.54 ) represent the unit cell volumes for B and B phases, respectively. The Gibbs free energy is equivalent to enthalpy at 0K.The relative stability condition of the two phases may be expressed as G = GB2 ~ B1 where GB1 and GB2 are the Gibbs free energies for rock salt B1) and CsCl ( B2 ) structure. The pressure at which 0 is the phase transition pressure P which is associated with a sudden collapse in volume. This shows that the phase transition is of first order. To understand the elastic properties, we have to calculate the second order elastic constants (SOECs), (C11, C12 and C44) at room temperature 0 K. For calculating the value of SOECs we have to determine the value of three model parameters (b, , f(r)) namely hardness, range and three body force parameter. The values of b, and f(r) have been determined by solving the equilibrium conditions using the measured values of the equilibrium inter-ionic separation (r). 0= dr dU and kB dr Here, BT is isothermal bulk modulus and k=2 for B phase. Results and Discussion The relative stability of the two phases were obtained by minimizing the lattice energies in both real and hypothetical phases at different pressures corresponding to equilibrium inter-ionic separation r(r’) using the model parameters as listed in table-1. The phase transition pressure and volume collapse are listed in table-2. The second order elastic constants are listed in table-3. The calculated value of phase transition pressure (P= 17.97 GPa) is in reasonable agreement with experimental value(P= 18 GPa). The variation of G with pressure for SrS is shown in figure-1. Table-1 Input data and model parameters Input parameters Model parameters r B (GPa) b(×10 - 12ergs) (Å) f(r) 3.01258a 10.7592 0.475 -0.049972 Ref. [4] Table-2 alculated transition pressure and volume collapse Transition Transition Pressure (GPa) Volume collapse (%) -B17.97 (present) 11.1 (present) 18 (exp)a 11.4 (exp)b 18.3 (other)c 10.8 (other)d Ref. [4] , Ref. [14] ,Ref. [15], Ref. [16] Table-3 alculated elastic constants Elastic constants (GPa) Present Others 11 132.9 113.9 a 12 25.7 19.4 a 44 38.95 30.3 a Ref. [17] The values of relative volume change (Vp/Vo) associated with various compressions have been obtained and plotted against pressure in figure-2 for SrS. The calculated value of volume collapse is in good agreement with other theoretical values. We have plotted the variation of elastic constant with pressure in figure-3. The calculated values of, C11, C12 and C44 is in good agreement with other theoretical values. Research Journal of Recent Sciences ______________________________________________________________ ISSN 2277-2502Vol. 4(IYSC-2015), 181-184 (2015) Res. J. Recent. Sci. International Science Congress Association 183 Figure-1 Variation of Gibb’s free energy with pressure 0.750.80.850.90.951.0505101520Vp/VoPressureNaCl (B CsCl(B=17.97 GPaFigure-2 Variation of Vp/V0 with pressure 20406080100120140 0 5 10 15 20 25 Elastic constants114412Figure-3 Variation of SOECs with pressureConclusion Finally, we can conclude that the three body interaction potential (TBIPZpe) model has yielded more precise predictions of the structural, elastic and phase transition of SrS from NaCl to CsCl structure. 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