The Modified Born-Mayer Potential in Layered-Cuprate-High-Tc Superconductors: An Analytic Approach

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1 ISSN(Online): ISSN (Pint): (An ISO 397: 007 Cetified Oganization) Website: Vol. 6, Issue 7, July 017 The Modified Bon-Maye Potential in Layeed-Cupate-High-Tc Supeconductos: An Analytic Appoach Hempal Singh 1, B. D. Indu Assistant Pofesso, Depatment of Physics, Cental Univesity of Hayana, Jant-Pali, Mahendegah, Hayana, India 1. Pofesso, Depatment of Physics, Indian Institute of Technology Rookee, Rookee, Haidwa, Uttaakhand, India. ABSTRACT: The theoy of modified Bon-Maye-Huggins potential is futhe advanced to exploe the best suitable inteaction potential fo high tempeatue supeconducting layeed cupates by developing the analytical expessions to find the Bon-Maye-Huggins (BMH) paametes themodynamically. The citical analysis eveals that BMH paametes depend upon vaious physics quantities, e.g., chages, inte-ionic distance, volume and Guneisen paamete, which is the stength of anhamonic effects in a layeed systems. A laye wise study fo the inteaction of Y- O and Y-Cu(+3) of a model supeconducto YBaCu3O 7 (YBCO) have been caied out within a new fame wok and the theoy is applicable to othe high tempeatue and layeed supeconductos. KEYWORDS: High tempeatue supeconductos, Anhamonic Effects, Guneisen paamete, Bulk Modulus. I. INTRODUCTION Afte seven Decades of the discovey of supeconductivity by Dutch physicist H. Kammelingh Onnes [1], new ea of eseach was healded with the beakthough discovey of fist high tempeatue supeconducto (HTS) by Bednoz and Mulle though thei famous publication Possible High T C Supeconductivity in Ba-La-Cu-O system [] in They found evidence of supeconductivity in Ba-La-Cu-O ceamics at 30K. Since then high tempeatue supeconductivity (HTSC) has been one of the inteesting and fascinating phenomenon fo theoetical as well as expeimental physicists. A suitable inteacting potential is needed to study the vaious dynamical and stuctual popeties of HTS as they have lage numbe of atoms pe unit cell. Even the simple empiical models exhibit vey inteesting qualitative account of seveal stuctual and dynamical popeties of high tempeatue supeconductos establishing that the inteatomic foces ae ionic in natue. In this jouney, BMH potential is found one of the favouable potential to descibe the vaious laye wise inteactions in HTS [3, 4, 5, 6]. As YBCO has collected of stacked (layeed stuctues) planes, hence due to the dual attactive (stong-, long ange- and cental-) and epulsive (weak-, shot ange-) natue of BMH potential it appeas easonably justified to adopt it fo the study of lattice spectum of HTS in a new fame wok which can be witten as [3, 4, 5, 6] b qi q j V ( ) ae (1) Hee a and b ae the ange and softening paametes, espectively; i and j label the ions distant apat. The fist tem in the above potential is the BMH potential tem is epulsive in natue and keeps the atoms apat fom collapsing and behaves as a shot ange potential. The second tem is the Coulomb tem may be eithe attactive o epulsive as pe dissimila o simila natue of chages qi and q maintaining the stability of the cystal and is also called the long j Copyight to IJIRSET DOI: /IJIRSET

2 ISSN(Online): ISSN (Pint): (An ISO 397: 007 Cetified Oganization) Website: Vol. 6, Issue 7, July 017 ange potential. In this wok taking the themodynamic appoach the new foms of a and b have been investigated with the poof that they ae no longe constants but depend upon vaious physical quantities. II. THEORETICAL BACKGROUND OF THE PRESENT PROBLEM In the pesent wok we found that a and b ae not constants but paametes as have been taditionally consideed, and thei dependence on vaious physical quantities is descibed. (a) Pessue dependence: Conside the simple dependence of volume V on lattice mode fequencies as V and the well known elation fo Guneisen paamete [7] d(ln ) / d(ln V ) one can easily obtain d / dv / V The use of themodynamic elation between pessue and potential enegy [8] P dv ( ) / dv and some algebaic simplification yields [6] dv ( ) P () V d Now using the eq (1) in above equation () of pessue its expession can be obtained in the following fom [6] P a b e V q q b i j (3) This expession is the leading esult to study the pessue dependence on Bon-Maye paametes. (b) Dependence on Bulk Modulus: The volume compessibility VdP / dv enables us to obtain the bulk modulus in the fom b qi q j B ab (1 b ) e V (4) Following the equilibium condition ( ) / 0 o dv d and Eq. 1, one can obtained e b q / 1q ab o o. Without any loss of geneality we can eplace by o o in Eq. 4 which yields the Bon-Maye paametes in the following fom as [6] o 1 1 BV b o qi q j (5) a 1 i j o BV o o BV exp o o qi q j o qi q j q q (6) Fom equations (5) and (6) we can conclude that the BMH paametes a and b show a complicated dependence on, B, V, and q i and hence cannot be taken as constant quantities as has been consideed in the ealie woks. Copyight to IJIRSET DOI: /IJIRSET

3 ISSN(Online): ISSN (Pint): (An ISO 397: 007 Cetified Oganization) Website: Vol. 6, Issue 7, July 017 III. RESULTS AND DISCUSSIONS Let us citically investigate the natue of epesentative layeed high tempeatue supeconducto YBCO to study the vaious esponses of BMH paametes. Taking Y(1) ion at the cente of the system a mesh of 38 atoms/lattice sites (Ba(), Cu(16) and O(0) ions) is obseved fo the model calculations in which Cu-O laye has Cu(8) and O(4), Cu-O laye has Cu(8) and O(8) and Ba-O laye has Ba() and O(8) atoms. The digits appeaing in backets with elements stand fo thei numbe taken up fo numeical estimation. The following physical constants used in numeical analysis a 3.8Å, b 3.9 Å, c Å, 11 B Dyne / cm, 1.4, 4 3 V cm [9, 10, 11]. The natue of a fo Y-Cu 3+ and Y-O inteaction with inteionic distance has been depicted in fig (1). and fig (), espectively. The softening paamete b has been potayed fo Y-Cu 3+ and Y-O inteaction with inteionic distances in fig (3) and fig (4). Fig.1 The Vaiation of ange paamete a with distance fo Y- Cu 3 inteaction in YBCO Supeconducto. Fig. The Natue of a with distance fo Y-O inteaction in YBCO Supeconducto. Copyight to IJIRSET DOI: /IJIRSET

4 ISSN(Online): ISSN (Pint): (An ISO 397: 007 Cetified Oganization) Website: Vol. 6, Issue 7, July 017 Fig. 3 Behaviou of b with distance fo Y- Cu 3 inteaction in YBCO Supeconducto. Fig.4 Natue of b with distance fo Y-O inteaction in YBCO Supeconducto. Up to 3 Å, thee is shap decease in both a and b with inteionic distance and the ange paametes becomes steady faste than softening paamete. It is evident that within the inteaction ange 0Å 3Å the effect inteaction ange falls off steadily and not dissipate if the inteionic distances of the ions ae lage. The natue of Bulk Modulus has been citically analysed fo Y-Cu 3+ and Y-O inteaction with inteionic distances in fig (5) and fig (6) fo YBCO supeconducto. In Fig (5), < Å Bulk modulus shaply down upto minimum and gain its maximum nea Å and get satuated nea 6 Å. But fo Y-O inteaction Bulk modulus is minimum nea 6.5 Å and stats to ise afte this point. Copyight to IJIRSET DOI: /IJIRSET

5 ISSN(Online): ISSN (Pint): (An ISO 397: 007 Cetified Oganization) Website: Vol. 6, Issue 7, July 017 Fig. 5 The Vaiation of B with distance fo Y- Cu inteaction in YBCO Supeconducto. Fig 6. Behavio of B with distance fo Y-O inteaction in YBCO Supeconducto. IV. CONCLUSIONS It emeges fom the pesent study that by taking a and b as paametes adds up new featues to the theoy of layeed high tempeatue supeconductos evealing it as a moe ealistic appoach. The BMH potential found the best potential to study the vaious inteactions in the layeed and othe high tempeatue supeconductos. REFERENCES [1] H. Kamelich Onnes. Comm. Phys. Lab. Uni. Leiden, 1B, 140, 1911 [] J.G. Bednoz and K.A. Mulle, Z. Phys. B 64, (1986) 189. [3] J.M. Delaye, V. Louis-Achille, D. Ghaleb, J. Non-Cyst. Soli., 10, (1997) 3. [4] John P. Rose and R. Stephen Bey, J. Chem. Phys., 98, (1993) 346. [5] T. P. Matin, J. Chem. Phys.,67, (1977) 507. Copyight to IJIRSET DOI: /IJIRSET

6 ISSN(Online): ISSN (Pint): (An ISO 397: 007 Cetified Oganization) Website: Vol. 6, Issue 7, July 017 [6] Hempal Singh, Anu Singh and B. D. Indu, Mod. Phys. Lett. B., 30, (016), [7] J. R. Hook and H. E. Hall, Solid State Physics, second ed., John Wiley & sons, New Yok, [8] M. Bon, K. Huang, Dynamical Theoy of Cystal Lattices, fist ed., Oxfod Univ. Pess, London, [9] D. P. Almond, E. Lambson, G. A. Saundes, and W. Hong, J. Phys. F: Met. Phys., 17, (1987) L1. [10] C. Haetinge et al., Supecond. Sci. Technol., 9, (1996) 639 [11] D. Vashney, A. Yogi, N. Dodiya and I. Mansui, J. Mod. Phys.,, (011) 9. Copyight to IJIRSET DOI: /IJIRSET