The structural phase transition, volume collapse and second order elastic constants of 5d-transition metal mononitride (IrN) have been investigated by using interaction potential model (IPM) which consists of Coulomb interaction, three-body interaction and short range overlap repulsive interactions. The present theoretical approach has predicted pressure-volume relationship curves which shows that IrN exhibits a zinc-blend (ZB) type structure at an ambient pressure and undergoes a structural phase transition from B3 to B1 phase at pressure 72 GPa. The equation of state shows volume collapse of 9.09 %. The phase transition pressure and associated volume collapses obtained from this model show a reasonable agreement with other theoretical results. The second order elastic constants are also investigated for ZB phase. Keywords: High Pressure, Phase Transition, Transition Metal Compound

Mir, Bashir Ahmed

Sarwan, Madhu

Shareef M, Faisal

Singh, Sadhna

Thakre, Vasudev

English

International Institute for Science, Technology and Education (IISTE): E-Journals

Advances in Physics Theories and Applications                                                                                                  www.iiste.org ISSN 2224-719X (Paper) ISSN 2225-0638 (Online) Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications  78 High Pressure Study of IrN in Zinc-Blende Structure  Madhu Sarwan (Corresponding author) Department of Physics, Barkatullah University, Bhopal, India 462026  E-mail: madhusarwan@gmail.com Bashir Ahmed Mir, Faisal Shareef M, Vasudev Thakre and Sadhna Singh Department of Physics, Barkatullah University, Bhopal, India 462026  E-mail: drsadhna100@gmail.com   Abstract The structural phase transition, volume collapse and second order elastic constants of 5d-transition metal mononitride (IrN) have been investigated by using interaction potential model (IPM) which consists of Coulomb interaction, three-body interaction and short range overlap repulsive interactions. The present theoretical approach has predicted pressure-volume relationship curves which shows that IrN exhibits a zinc-blend (ZB) type structure at an ambient pressure and undergoes a structural phase transition from B3 to B1 phase at pressure 72 GPa. The equation of state shows volume collapse of 9.09 %. The phase transition pressure and associated volume collapses obtained from this model show a reasonable agreement with other theoretical results. The second order elastic constants are also investigated for ZB phase.  Keywords: High Pressure, Phase Transition, Transition Metal Compounds  1. Introduction Transition metal nitrides have received much attention from experimental and theoretical workers in recent years because of their excellent properties such as hardness, superconductivity, photoluminescence and various type of magnetism [1]. The iridium mononitride (IrN) compound is the least studied among the family of these transition metal nitrides. Rached et.al. [2] investigated the elastic, structural and electronic properties of IrN by using first-principle calculation. The nature of interatomic forces is not well understood in these compounds and phenomenological model based on various interatomic interaction energies to determine stable structure becomes important.  In the present study, we have applied an interaction potential model (IPM) to study high pressure phase transition and elastic properties. In the present model we have included three-body interaction (TBI) forces [3-5]. This TBI approach has been extended to include the Hafemeister-Flygare (HF) type [6] overlap repulsion operative up to the second neighbour ions.   2. Present Potential Model The application of pressure on the crystal causes the decrease in their volume, which in turn leads to an increased charge transfer (or exchange) between the overlapping electron shells of the adjacent ions. This transferred charge modifies the ionic charge which when interacts with other distant charges gives rise to many body interactions (MBI), the dominant part of MBI is three-body interactions [3].   These TBP effects have been incorporated in the Gibbs free energy (G=U+PV-TS). Here, U is the internal energy which at T=0K is equivalent to the lattice energy, S is the vibrational entropy at absolute temperature T. At T=0K and pressure P, the Gibbs free energy for the zinc-blend (B3, real) and NaCl (B1, hypothetical) structures are given by                         333 )()( BBB PVrUrG +=                                    (1)                         111 )'()'( BBB PVrUrG +=                                 (2)  With V B3 (3.08 r³ )  and  VB1 ( 2.00 r’³)    as  unit  cell  volumes  for  B3  and  B1  phases,  respectively.    The  first  term  in  (1) and  (2)  are  lattice  energies  for  B3  and  B1  structures  and  they  are  expressed  as                 (3)               (4)  With  αM  and  α’M  as  the  Madelung   constants  for  ZnS  and  NaCl  structures,  respectively.  βij ( i,j = 1,2 )  are  the  Pauling  coefficients  )/exp(4)(4)(2223 ρβααijjiijMMB rrrbrrZferZerU −++−−=)/'exp(6')('6'')(2221 ρβααijjiijMMB rrrbrrZferZerU −++−−=Advances in Physics Theories and Applications                                                                                                  www.iiste.org ISSN 2224-719X (Paper) ISSN 2225-0638 (Online) Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications  79 defined  as  βij = 1 + (Zi/ni) +(Zj/nj)  with  Zi (Zj ) and  ni (nj )  as  the  valence  and  the  number  of  electrons  of  the  i (j)th  ion.  Ze  is  the  ionic  charge  and b (ρ)  are  the  hardness (range) parameters,  r(r’)  are  the   nearest  neighbour  separation  for  ZnS (NaCl)  structure.  f(r)  is  the three-body  force  parameter   ri (rj)  are  the  ionic  radii  of  ions i (j). These lattice energies  consist  of  long  range  Coulomb  energy (first  term ),   three-body  interactions  corresponding  to  the  nearest  neighbour  separation  r (r’)   (second  term ),  energy  due  to  the  overlap  repulsion  represented  by  Hafemeister  and  Flygare ( HF)  type  potential  (third term).  3. Result and Discussions The present interaction potential model (IPM) contains three model parameters b, ρ and f(r), namely hardness, range and three-body interaction parameter. These parameters are calculated by using the first derivative of cohesive energy (U) and equilibrium condition expressed as:          00== rrdrdU                                                               (5)                                                                                                   B1+B2=-1.261Z[Z+8f(r)]                                                   (6)                                                                                          The input data and model parameters are given in table 1.  As the stable phase is always associated with minimum of energy, we have minimized GB3 (r) and GB1 (r’) at different pressures in order to obtain inter ionic separations r and r’ for B3 and B1 phases respectively associated with minimum energies.  We have evaluated the corresponding GB3 (r) and GB1 (r’) and their respective differences ∆G=GB3(r)-GB1 (r’). A positive value of ∆G at zero pressure justifies the stability of B3 phase. As the pressure is increased the value of ∆G decreases and approaches to zero at the transition pressure (Pt). Beyond this pressure ∆G becomes negative as the phase B1 become stable. The Gibb’s free energy difference ∆G =GB3(r)-GB1 (r’) has been plotted as a function of pressure (P) in Fig. 1. The pressure corresponding to ∆G approaching zero is the phase transition pressure (Pt). The phase transition pressures so obtained are presented in Table 2 along with the other theoretical results [1]. Fig. 1 shows the phase transition from ZB to RS structure in IrN at 72 GPa. The phase transition pressure is illustrated by arrow in Fig. 1.  Under pressures, the materials transform from one structure to another structure with a sudden change in arrangement of atoms. These atoms are rearranged in new position and give rise to the new structure. Experimentally one usually studies the relative volume change associated with compressions. The discontinuity in volume at the transition pressure is obtained from the phase diagram. The values of relative volume associated with various compressions have been computed by using the interaction potential model. Deduced the pressure dependent radii r and r’ for both the structures (B3 and B1) have been used to compute the relative volume changes and are plotted against the pressure (P) in Fig. 2. The magnitude of the discontinuity in volume change at the transition pressure has been obtained from the phase diagram and the value is listed in Table 2. The elastic constants are important properties of solids which provide a link between the mechanical and dynamic behaviors of crystals. They provide information on the elasticity, stability and stiffness of crystals and give important information about nature of forces operating in solids. While studying the high pressure elastic behavior of IrN we have computed the second order elastic constants (SOECs) C11, C12 and C44 as they provide physical insight into the nature of binding forces between different constituents of a crystal. In the present model we have included three body interaction forces. The inclusion of three body interaction forces was emphasized by Sims et al. [7]. Earlier calculations were based on two-body potential mainly. They concluded that possible reasons for disagreements include the failure of the two body potential model. Since these studies were based on two body potentials and could not explain Cauchy violations C12  ≠  C44.  Our model is able to explain Cauchy violation C12  ≠  C44    in second order elastic constants. One common approach is to assume that the atoms are connected with springs and that the resulting forces are only in the direction of the nearest neighbours (central force model). The deviation from the Cauchy violation δ=C12-C44-2P is a measure of the contribution from the non central many-body force. Our calculations give negative C12-C44 values (Table 3). C44>C12 inequality is observed in the present work. The method for their calculations is same which we have reported in our earlier work [4]. The values of SOECs are given in Table 2. We note that the values of C11, C12 and C44 are better matching with others [1].  4. Conclusion We have applied interaction potential model (IPM)) to investigate the structural phase transition and elastic properties of IrN compounds. An overall assessment shows that, our values of IPM near to available are in general matching with other theoretical results. Our results where no experimental results are available may be tested with different theoretical and experimental methods in future.    Advances in Physics Theories and Applications                                                                                                  www.iiste.org ISSN 2224-719X (Paper) ISSN 2225-0638 (Online) Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications  80 Acknowledgement  The authors are thankful to the U.G.C.(SAP) New Delhi for the financial support.       References [1] Chen W. and Jiang J. Z. (2010) Elastic properties and electronic structures of 4d and 5d transition metal mononitrides, J. of Alloys and compounds, 499, 243.  [2] Rached H, Rached D, Khenata R, Benalia S, Rabah M, Semari F and Righi H (2011) Structural stabilities, elastic and electronicmononitride: A first-principles study, Phase Transitions, 84, 269-283. [3] Singh R. K. (1982) Many body interactions in binary ionic solids, Phys Rep. 85, 259-401. [4] Singh R.K. and Singh S. (1989) Structural phase transition and high pressure elastic behavior of III-V semiconductors, Phys. Rev. B, 39, 671-676. [5] Bhardwaj P., Singh S. and Gaur N. K. (2009) Structural, elastic and thermophysical properties of divalent metal oxides with NaCl structure, Mater. Res. Bull., 44, 1366-1374. [6] Hafemiester D. W. and Flygare H. F. (1965) J. Chem. Phys. 43, 795.  [7] Sims C. E., Barrera G. D. and Allan N. L. (1998) Thermodynamics and mechanism of the B1- B2 phase transitionin group-I hailides and group-II oxides, Phys. Rev. B, 57, 11164-11172.  Figure 1. The Trend of Economic Development Description for the above figure.               Table 1 Input and model parameters of IrN.        Input parameters                               Model parameters          r1 (Å)      r2(Å)     a(Å)             b(10-12 ergs)            ρ (Å)            f(r)                                0.82     1.47       4.64[1]          0.8297                  0.402         -0.0962  Table 2 Input and model parameters of IrN.         Phase transition          Volume collapse                Elastic constants                Pressure (GPa)                 (%)                                    (GPa)                                                                              C11              C12             C44                                                                  IPM       72                                9.09                  326.54        213.09          50                           Exp.       -                                     -                         -                 -                  - Other [1]  72                                                       322              256                34  Advances in Physics Theories and Applications                                                                                                  www.iiste.org ISSN 2224-719X (Paper) ISSN 2225-0638 (Online) Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications  81                     Fig. 1 Variation of change in Gibbs free energy with pressure.           0 20 40 60 80-20020406080100120IrNPt=72 GPa∆∆ ∆∆G (kJ/mol)Pressure (GPa)Advances in Physics Theories and Applications                                                                                                  www.iiste.org ISSN 2224-719X (Paper) ISSN 2225-0638 (Online) Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications  82 0 20 40 60 80 1000.700.750.800.850.900.951.00RS phaseZB phaseV/V0Pressure (GPa)                            Fig. 2 Variation of V/V0 with pressure.  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High Pressure Study of IrN in Zinc-Blende Structure

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High Pressure Study of IrN in Zinc-Blende Structure

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