MAGNETIC AND ELECTRONIC PROPERTIES OF SIMPLE, TRANSITION, AND RARE EARTH LIQUID METALS

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1 Digest Journl of Nnomterils nd Biostructures Vol. 4, No., September, June 9, p MAGNETIC AND EECTRONIC ROERTIES O SIME, TRANSITION, AND RARE EARTH IQUID METAS J. K. BARIA, A. R. JANI b V.. & R.. T.. Science College, Vllbh Vidyngr 88, Gujrt, Indi b Deprtment of hysics, Srdr tel University, Vllbh Vidyngr 88, Gujrt, Indi In the present reserch pper we hve clculted the Mgnetic nd electronic properties of liuid simple, trnsition, nd rre erth metls t their melting temperture using recently proposed model potentil of Bri nd Jni. The prmeter of the potentil is determined through stndrd zero pressure techniue. The effect of exchnge nd correltion due to Ichimru nd Utsumi hs been incorported, while the structure fctor is derived through chrge hrd sphere pproximtion. The beuty of this pproximtion is tht it includes potentil in describing the structure fctor, so this gives better explntion of structure fctor thn other such pproximtions. A good greement between theoreticl investigtions nd experimentl findings proves the strength nd bility of the potentil. (Received June, 9; ccepted July 5, 9) Keywords: Mgnetic, Electronic, Knight-Shift, Electronic Susceptibility. Introduction Recently Bri nd Jni [,] hve reported lrge number of lttice mechnicl properties of d nd f-shell metls in the fcc phse very successively. In the present pper we thought to clculte some mgnetic properties such s Knight-Shift nd electronic property such s electronic susceptibility of liuid simple, trnsition, nd rre erth metls t their melting temperture to check the pplicbility of the pseudopotentil.. Mgnetic roperty (Knight- Shift) In the free electron pproximtion the temperture coefficient of the Knight- Shift t constnt volume in the liuid phse is given by [-7] lnk = T Z 4T E k m ( ) W( ) k ln k d k k () nd the knight-shift of liuid metl is given by [4,6] K K = Z 4E k ( ) W( ) k ln k d k k ()

2 46 Here () is the structure fctor derived through chrged hrd sphere pproximtion [8] nd depends only on the pcking frction η, W() is the screened form fctor recently proposed by Bri nd Jni [,], T m is the melting temperture, E is the ermi energy, k is the ermi wve vector nd K /K is the knight shift [4,6] of the liuid metls. The vlues of T m, pcking frction η,volume (Ω ) nd vlnce (Z) re given in tble while the vlue of ermi wve vector k cn be determined using the reltion K π Z = nd ermi energy Ω Tble. Input prmeters used in the present clcultions. E h k = from tble. m Metls r c (.u.) Z η ζ Ω (.u.) T m (in K) i N K Rb Cs Al b Cu Ag Au Ni d t Rh Ir Yb Ce Th Eutions () nd () were used to estimte the temperture coefficient of Knight shift of liuid metls t constnt volume nd Knight shift of liuid non-trnsition nd trnsition metls t melting point temperture. We hve performed the integrtion from to k. Very few experimentl nd theoreticl dt of Knight shift re vilble. Our present investigtion of temperture coefficient of Knight-shift t constnt volume of liuid metl, Knight-shift nd Knight-shift in percentge re shown in tble. It is the evident tht the present investigtions of Knight-shift in percentge for i, N, K, Rb, Cs, Al, Cu, Ag, Au, Rh nd Ir re very close to the experimentl findings while for rest of the metls the results re predictive in nture. The experimentl or theoreticl result of the temperture coefficient of the Knight-shit t constnt volume nd Knight-shift re not vilble so present investigtions hve the predictive men.. Electronic roperty (electronic susceptibility) The theoreticl investigtion, bsed on the pseudopotentil theory of the mgnetic susceptibility of liuid metls is very rre. Bltensperger [] clculted the correction due to the electron-ion potentil to the ndu dimgnetism in liuid metls by the theory of the free electron susceptibility of solid phse to the liuid phse by employing the pseudopotentil perturbtion techniue. Tkhshi nd Shimizu [] hve investigted the mgnetic susceptibility of liuid metls by tking ccount of the higher order terms due to the electron-ion potentil in

3 Green s function method. Srivstv [] hs lso reported electronic susceptibility of some simple liuid metls using n pproch followed by Timbie nd White [4]. The formultion of the electronic susceptibility is derived by employing pseudopotentil perturbtion theory nd mking use of lttice periodicity nd inverse plce trnsform reltionship between prtition function Z(β) nd thermodynmic potentil Φ per unit volume [4, 5]. 47 where Z(s) f Φ = ds Z(s) () s c i st Z(t) = dt e π i, c> (4) t c i nd f is the ermi function = β(s (e ) (5) f ξ) Here ξ is chemicl potentil nd β = k T. Using the stndrd techniues we write [4,5] c i B xt r e x Φ = dt θ(x) r π i =, Γ > (6) t Γ(r) c i Here Γ( r ) is the gmm function nd θ(x ) = x < = x > (7) The introduction of the potentil W() shifts the chemicl potentil ξ wy from the ermi energy. This shift my be clculted to second order in W using the reltion Φ ξ T, Ω = -n, where n being number density of electrons Ignoring the field dependence of ξ, the expression for ξ is given by [4, 5] = W() Ω S() W() ξ ξ d ln (8) / ξ 4 ξ ( π) E were / 4ξ = with E() E() = h m By knowing the chemicl potentil ξ, the first derivtive of thermodynmic potentil Φ gives the reltion for the electronic susceptibility s [4, 5]

4 48 μ n Ω = d S() W() () ξ 8 ξ ( π) (9) where / x y (5 ) / () = ln ln () 8( ) 6 Here μ n = is ndu-uli free electron susceptibility ξ Assuming tht W() depends only on the mgnitude of, the bove volume integrl cn be solved using ()=N S() nd the integrtion vrible is chnged to the dimensionless prmeter k=/k. the liuid metl nlog of Glsser s [5] result for the totl electronic susceptibility is thus obtined s = ( ) () where Z = dk (k) W (k) G(k) () ξ nd G(k) k k k 8 7k k (k 4) = (k ) ln () The orbitl susceptibility in the liuid phse my be clculted seprtely in much the sme wy by omitting the spin term from the Hmiltonin, the reltion is given by = ( ) (4) Z = dk (k) W (k) G (k) (5) ξ nd G (k) k k k 8 4 k k (k 4) 4 = (k ) ln (6) = ( ) (7)

5 49 Z = dk (k) W (k) G (k) (8) ξ nd k 8k G (k) = (k ) ln (9) k (k 4) Now, including exchnge nd correltion due to Brueckner nd Swd [6], we get the reltion for totl electronic susceptibility for liuid metls [7], ele = o ( δ ex. corr. ) o ( ) () with reltion δ ex. corr. = [.66 rs.4 rs ( ln rs )] () The vlue of ζ is given in tble while the vlue of r s cn be determined using the Ω s = from tble.the obtined vlues of electronic susceptibilities re r 4 Z π displyed in tble with vilble other such experimentl s well s theoreticl findings. It is seen tht present findings for i, N, K, Rb, Cs nd l grees very well with the experimentl results s well s theoreticl results of Jnk [8] while for Cu, Ag, d nd Rb re very similr to the results of Jnk [8]. or rest of metls no theoreticl s well s experimentl dt re vilble for the untittive comprisons, so they re predictive in nture. The effect of exchnge nd correltion due to Ichimru nd Utsumi [9] is incorported while clculting structure fctor (). Tble. The temperture coefficient of Knight-shift t constnt volume, Knight shift nd Knight-shift in % of some liuid simple, trnsition, nd rre erth metls t melting temperture. Metl ln K in K K% Expt. Others T K% K [9,] [-7,9] -4 K - i ,. N ,.,.6 K ,.96 Rb ,.54 Cs ,.54 Al ,.7 b Cu Ag Au Ni d t Rh

6 4 Ir Yb Ce Th Tble. Electronic susceptibility ( ele / ) of some liuid simple, trnsition, nd rre erth metls t melting temperture. Metl resent Expt. work [4] Others [4] Others [8] i N K Rb Cs Al b Cu Ag Au Ni d t Rh Ir Yb Ce Th It is n evident from Tble nd tht the presently proposed pseudopotentil hve reproduced promising results of the Knight-Shift nd susceptibility of liuid simple, trnsition, nd rre erth metls nd hence the potentil cn be exploited further to study the other metllic properties. Acknowledgements One of the uthors (JKB) is thnkful to the University Grnts Commission (UGC-WRO, une) for providing finncil support under minor reserch project grnt (. No.: 47-79/8). References [] J. K. Bri nd A. R. Jni, hysic B 8, 7 (). [] J. K. Bri nd A. R. Jni, rmn J. of hys. 6, (). [] J. Behri, hil. Mg. 6, 77 (97).

7 [4] A.. Ritter nd J. A. Grdner, hys. Rev. B, 46 (97). [5] M. Wtbe, M. Thk, H. Endo nd B. K. Jones, hil. Mg., 47 (965). [6] N. C. Hlder, J. Chemicl hys. 5, 545 (97). [7] B. Mishr,. K. Ds, T. Shu, G. S. Tripthi,. K. Mishr, J. hys.: Condensed Mtter, 989 (99). [8] R. V. Gopl Ro nd U Bndyopdhyy, Ind. J. hys. 65A, 86 (99). [9] G. A. Styles nd G. Trnfield, J. hys. : Metl hys. 8, 5 (978). []. Seitz nd D. Turnbull, Solid Stte hysics, Vol., Acdemic ress, New York, (956). [] W. Bltensperger, J. hys.: Condensed Mtt. 5, 5 (966). [] Y. Tkhshi nd M. Shimizu, J. hys. Soc. Jpn 4, 94 (97). J. hys. Soc. Jpn 5, 46 (97). [] S. K. Srivstv, J. hys. Chem. Solids 6, 99 (975). [4] J.. Timbie nd R. M. White, hys. Rev. B, 49 (97). [5] M.. Glsser, hys. Rev. 4, A96 (964). [6] R. K. Bruckner nd K. Swd, hys. Rev., 8 (958). [7] A. R. Jni,. N. Gjjr nd H. K. tel, hys. Stt. Sol. (b) 69, K5 (99). [8] J.. Jnk, hys. Rev. 6, 55 (977). [4] S. Ichimru nd K. Utsumi, hys. Rev. B, 5 (98)., hys. Rev. B, 5 (98), hys. Rev. B, 9 (98)., hys. Rev. B 4, (98)., hys. Rev. B 4, 785 (98). 4

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