THERMODYNAMIC MEASURES CALCULATION FOR Pb Sb BINARY ALLOY SYSTEM USING REDLICH KISTER THEORETICAL MODEL

Transcription

1 U.P.B. Sc. Bull., Seres B, Vol. 78, Iss., 06 ISSN THRMODYNAMIC MASURS CALCULATION FOR Pb Sb BINARY ALLOY SYSTM USING RDLICH KISTR THORTICAL MODL Floreta NICULSCU, Dragos Flor MARCU, Io CONSTANTIN 3, Iulus Dael Ştefa HICA 4 Ths aer ams to fd a ew thermodyamc model allowg the exermetal data rocessg for the Pb Sb bary system. The aer rooses a Redlch Kster model as a kck off ot for exermetal data aalysg. The obtaed thermodyamc fuctos for the thermodyamc characterzg of the bary alloy system of Pb ad Sb allowed the coverage of every terest ot of temerature cocetrato tercoecto, wth a hgh calculato recso. Keywords: thermodyamc actvty, actvty coeffcet, thermodyamc model, bary alloy system. Itroducto The ublcato umber the feld of bary alloys thermodyamc revealed the mortace of ths tye of bary system, Pb Sb. Recet vestgato o the Pb Sb system had bee realzed by S. Hassam, D. Boa, Y. Fouque et.all 009 []. Ths research gou measured the mxg ethaly of the Pb Sb bary system at 973K the terval x Sb = The tegral molar eerges values for the bary system I Sb, Pb Sb ad I Pb have bee also calculated by Asara resectvely Ohta et all [ 4] ad had bee used as a startg ot for the bary thermodyamc calculato. D. Maasjevc et all calculated the equlbrum hase terary I Sb Pb system [5 6]. The ma objectve of the aer s to fd ad aly a ew thermodyamc model whch allows a better exermetal data rocessg. There was a huge cocer regardg the determato of the thermodyamc measures of dfferet PhD eg., Det. of geerg ad Maagemet of Metallc Materals, Uversty POLITHNICA of Bucharest, Romaa, e-mal: flor.ereteau@yahoo.com PhD eg., Det. of geerg ad Maagemet of Metallc Materals, Uversty POLITHNICA of Bucharest, Romaa, e-mal: dragos.marcu@araset.ro 3 Prof., Det. of of geerg ad Maagemet of Metallc Materals, Uversty POLITHNICA of Bucharest, Romaa, e-mal: scremcosrl@yahoo.com 4 g., Cty Hall Bucharest, Romaa, e-mal: ulus_maxm@yahoo.com

2 40 Floreta Nculescu, Dragos Flor Marcu, Io Costat, Iulus Dael Ştefa Heca bary or terary [7-3] alloy system of Pb - Sb, resultg a seres of aers ublshed the scetfc lterature. It s well kow that the bary alloy system of the Pb Sb reset a hgh mortace the electro-techcal dustry, solder, hard lead, alloy for cable cover, used rtg, the automoble dustry as atfrcto alloy. The thermodyamcs of dfferet alloys had bee vestgated by dfferet researchers ad the develomet of comoste materals ad hgh etroy alloys was based o the alloys thermodyamcs ad ketcs [7, 8, 9, 0]. The Pb Sb wth 90% S are used for solderg ad for the tyograhy Pb S Sb sometmes wth.5%b creasg ther fludty lqud state ad tme servce. The most arecated are babbt alloys havg as a base Sb S Pb wth 0.7% Cu, babbt alloys Pb Sb wth 0.5% -.% Ca ad % Na. After a systematc study of the thermodyamc already kow models [4 6] ad usg both some results for the scetfc lterature ad the ow exermetal results the aer roosed a accurate aalyze of the theoretcal model Redlch Kster. Ths aer s ovelty cosst workg temerature (93K), a temerature ot foud the the secalty lterature. The deedece of the thermodyamcs roretes of the state arameter ca t be accurate theoretcal establshed, that s why the emrcal relatos (Margules formula) are used for descrbg these roretes the Pb-Sb system. Usg the emrcal relatos s helful the ractcal soluto of some elaborato roblems for the alloys or for the metal thermc affty, uderlg more the coformty betwee the model ad the exermetal data ad less the boud betwee the model ad the teracto of elemetary artcles.. The theoretcal model Redlch-Kster I the Redlch-Kster model, the correlato betwee the coeffcets s less tha the Margules model because the q x are all ull o x 0. = x = 5, ad ther absolute values are t at the x cocetrato. Ths s the reaso why the q coeffcets are t growg fast wth hgh values the same tme wth the growg of ad, as a result, the value of Δ G deeds less o the total umber of the terms of the seres. Accordg to ths model the Gbbs free eerges for the tegral molecular ad artal molecular s calculated based o the relatos (-3): x q j ( x ) j ΔG = x ()

3 Thermodyamc measures calculato for Pb Sb bary alloy system usg Redlch Kster...4 j [( j jx )( x ) ] = x q j Δ G () j [( jx )( x ) ] = x q j Δ G (3) For the calculato of the coeffcets q the relato (), for examle, s trasformed to the relato (4), as below: Δ G = qz + q z + + q z, (4) I whch: z = x, z = x ( 3 4x ),, z = x ( x )( x ) (5) It results the fucto: where y~ = q j z j, ( y~ y ) Φ = (6) s gve by the relato (4) ot, ad y s referrg to the exermetal value of the excess molar artal quattes of the free eergy ( Δ ) ot. G, ( qz, + qz, + + q z, ΔG, ) Φ = (7) The artal dervate of the (7) fucto coecto wth q, t s cacelled Φ = Φ q = q z z ( q z + q z + + q z Δ ) j j =,,..., = 0 (8),,,, G, ( q z + q z + + q z Δ ) = 0 (9),,,, G, ( q z + q z + + q z ΔG ) Φ = z,,,,, = 0 (0) q Ad t s obtaed a system of equatos wth ukows: q z, + q z, z, + + q z, z, = z, ΔG, q z, z, + q z, + + q z, z, = z, ΔG, () ()

4 4 Floreta Nculescu, Dragos Flor Marcu, Io Costat, Iulus Dael Ştefa Heca q z, z, + q z, z, + + q z, = z,δg, (3) of whch solutos q j, j =,,..., s allowg the determato of the excess thermodyamc measures. 3. The exermetal method For the determato of the thermodyamc actvtes the bary alloy system of Pb-Sb the authors used the measuremet of the electromotve force. The choce to use ths method s made due to ts hgh recso ad reroducblty of the rove exermetal data other researches cocerg the thermodyamc of the metallurgcal melts. The method s based o the measuremet of the electromotve force a galvac cell havg a reversble cocetrato wth a lqud or sold electrolyte at a temerature whch were t foud avalable data the scetfc lterature (93K). After the achevemet of the measuremet the data obtaed were comared wth the data obtaed through the measuremet of the electromotve force method of Seltz ad DeWtt at 900 K ad the data were certfed wth the Cochra measure. For ths crtera I obtaed the calculate value G = 0.05 less tha the tabled value Ths result dcates a better recso of the measuremets ad the relatve average error s oly of 4.09%, rovdg a adequate cofdece the used values. 4. Results ad dscussos For the alloy system Pb-Sb the system solutos ()-(3) leads to the followg measuremets of the actvty coeffcets ( Pb; Sb): ( 3 4xSb ) ( 5 6xSb )( xsb ) + ( )( ) 7 8xSb xsb lγ Pb = xsb (4) ( 4xSb ) ( 6xSb )( xsb ) + ( )( ) 8xSb xsb lγ Sb = xpb (5) The values of the actvty coeffcets for Pb ad Sb are measured wth (4-5) ad showed the table. Average square error of the Redlch-Kster 6 model s MP γ = Pb

5 Thermodyamc measures calculato for Pb Sb bary alloy system usg Redlch Kster...43 Tabel The values of the actvty coeffcets of Pb ad Sb calculated wth the Redlch-Kster model Sb Pb Sb γc Pb 0.95 γpb Fg.. Grahcal comarso betwee the actvty coeffcet of Pb, exermetal ad calculate value c realzed wth the hel of the Redlch - Kster at temerature of 93K x γc Sb 0.9 γsb x Fg.. Grahcal comarso betwee the actvty coeffcet of Sb, exermetal ad calculate value c realzed wth the hel of the Redlch-Kster at temerature of 93K

6 44 Floreta Nculescu, Dragos Flor Marcu, Io Costat, Iulus Dael Ştefa Heca The actvty coeffcet of Sb ad Pb at 93K were calculated ad a grahcal comaros was realzed wth the data already kow at the temerature of 900K I Fg. ad the grahcal comarso betwee the actvty coeffcets exermetally determed ad calculated wth Redlch Kster temerature at 93K of Pb ad Sb are show. The exermetal data are followg the calculated data meag that the model used s very accurate. Ths way of solvg the roblem s very useful for ractcal solvg of some alloys roducto roblems, to obta comoste materals, hgh etroy alloys or to thermal refg of the metals whe the cocordace betwee the model ad the exermetal data s very mortat. 5. Coclusos The obtaed Redlch Kster models gvg a better descrto of the thermodyamc roretes of Pb ad Sb ad from the thermodyamc ot of vew both elemets are actg smlar. The Redlch Kster model s more recse for Pb ad could be used as a referece model for other aers ths feld. The obtaed thermodyamc fuctos for the thermodyamc characterzg of the bary alloy system of Pb ad Sb, allow coverg every terest ot of temerature-cocetrato wth a hgh recso through calculato. R F R N C S []. Hasam et al., Joural of Alloys adcomouds 476 (009) []. I. Asara, C. Chatllo, H.L. Lukas, T. Nshzawa, H. Ohta, K. Ishda, M. Hllert, B. Sudma, B.B. Arget, A. Watso, T.G. Chart, T. Aderso, CALPHAD 8 (994) 77. [3]. H. Ohta, K. Ishda, Phase qulbra 6 (995) 46. [4]. A. Bolcavage, C.R. Kao, S.L. Che, Y.A.Chag, Proceedgs of the Symosum o Alcato of Thermodyamcs the Sythess ad Processg of Materals, P. Nash, B.Sudma, ds., TMS, Warredale, PA, 995,. 7. [5]. D. Maasjevć, D. Žvkovć, M. Cocć, D. Jajć, Ž. Žvkovć, Thermochm. Acta 49 (004) 95. [6]. D. Mć, D. Maasjevć, D. Žvkovć, Ž. Žvkovć, J. Serb, Chem. Soc. 7 (006) 843. [7]. A. Aloma, D.Talo, Comuterzed aalytcal thermodyamcs of the B-Cd alloys, edtura Prtech, 999. [8]. G. Petzow ad G. ffeberg, Terary Alloys: A Comrehesve Comedum of valuated Costtutoal Data & Phase Dagrams, -5, ed. (Wehem, Germay: VCH Verlagsgesellscahft, ). [9]. Sha-hua Che, Jag Su, Yua Wag, Y-qag Tag, X-kou He, Thermodyamc assemssemet of BO3-MgO bary system. Calhad 5 (05) [0]. D.Talo, Thermodyamc model for bary alloy systems. UPB. Scetfc Bullet, Seres B: Chemstry ad Materals Scece. 65. (.)

7 Thermodyamc measures calculato for Pb Sb bary alloy system usg Redlch Kster...45 []. T.B. Massalsk. s.a., (ds) Bary alloy hase dagrams, Vol.-3, Metals Park, Oho, ASM Iteratoal, 990. []. R. Hultgre s.a., Selected values of the thermodyamc roertes of the elemets, Metals Park. Oho. ASM [3]. Fl. Pereţeau, D. Talo, I. Costat, Thermodyamc study of bary Pb Sb systemusg the POSS model, UPB Scetfc Bullet, Sees B Chemstry ad Materals Scece, 7(), 67 74, 00, ISSN [4] J.O. Adersso et al., Acta Metall., 34 (986), Asara, B. Sudma, ad P. Wllem, Acta Metall., 36 (988), I. Asara et al., J. Alloys Comd., 47 (997), [5]. B. Predel, Phase qulbra, Crystallograhc ad Thermodyamc Data of Bary Alloys, 5, subvol. A-g, ed. O. Madelug (Berl, Germay: New Seres, Srger, ) [6]. P. Vllar, A. Prce, ad H. Okamoto, Hadbook of Terary Alloy Phase Dagrams, -0 (Materals Park, OH: ASM, 995). [7]. S.L. Che, C.R. Kao, ad Y.A. Chag, Itermetallcs, 3 (995), [8]. R. Ştefăou, V. Geată, I. Voculescu, I. Csak, N. Ghba, Researches regardg the fluece of chemcal comosto o the roertes of AlxCrFeCoN alloys, Revsta de chme, Vol. 65, No. 7, 04. [9]. V. Geată, I. Voculescu, R. Ştefăou, D. Savastru, I. Csak, D. Patro, L.Leoat, Processg ad characterzato of advaced mult-elemet hgh etroy materals fro AlCrFeCoN system. Otoelectrocs ad advaced materals rad commucatos, Vol. 7, No. -, , 03. [0]. I. Csak, G. Poescu, R. Ştefăou, I stu Reacto Ifluece o Hybrd Alumum/Tta Alumde ad Aluma Comoste Hardess. RVISTA D CHIMI, Volume 64, Issue 7, , 0, FI = 0,677, ISSN: