Investigation of the critical region in monotectic systems by viscosity measurements

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1 Jounal o Physics: Coneence Seies Investigation o the citical egion in monotectic systems by viscosity measuements To cite this aticle: Yu Plevachuk et al 008 J. Phys.: Con. Se Recent citations - Electophysical and stuctue-sensitive popeties o liquid Ga In alloys Yuiy Plevachuk et al - Viscosity o liquid binay Pb Zn alloys in the miscibility gap egion Yu. Plevachuk et al View the aticle online o updates and enhancements. This content was downloaded om IP addess on /0/08 at 9:08

2 3th Intenational Coneence on Liquid and Amophous Metals Jounal o Physics: Coneence Seies 98 (008) 0007 doi:0.088/ /98//0007 Investigation o the citical egion in monotectic systems by viscosity measuements Yu Plevachuk, V Sklyachuk, O Alekhin, L Bulavin and O Bilous 3 Ivan Fanko National Univesity, Depatment o Metal Physics, 8 Kyylo and Mephodiy st., Lviv, Ukaine, plevachuk@mail.lviv.ua Kyiv National Taas Shevchenko Univesity, Faculty o Physics, Glushkova Ave. 030 Kyiv, Ukaine 3 National Aviation Univesity, Aeospace institute, Kosmonavta Komaova Ave Kyiv, Ukaine Abstact. Viscosity measuements wee peomed o liquid In-Se alloys in the tempeatueconcentation ange o a limited solubility. Citical paametes descibing the peculiaities o the viscosity in the citical egion ae evaluated. The dynamic theoy o phase tansitions was used o this evaluation. The esults ae compaed with peviously obtained data o immiscible dielectic solutions and metallic melts.. Intoduction Binay monotectic alloys with a micostuctue whee sot phases ae dispesed homogeneously in a had matix ae o special technical impotance []. These alloys ae miscible at tempeatues above the miscibility gap, but segegate into two liquids when they pass though the liquid miscibility gap. It is theeoe vey diicult to poduce those alloys. The Stokes motion caused by the dieence in densities o two liquids, and the Maangoni convection esulting om a tempeatue gadient (a liquid doplet moves to a highe tempeatue egion in ode to educe the inteacial enegy) ae two main actos causing the sepaation o two immiscible liquids. In ode to ovecome the segegation, seveal techniques have been poposed aiming at poducing a uniom dispesion o a sote phase in a hade matix [, 3]. The knowledge o the physical popeties o the molten alloys pio to segegation is vey impotant o the development o mateials with pedetemined chaacteistics. In this pape we pesent expeimental studies o the viscosity o liquid In-Se alloys in the concentation-tempeatue ange o the miscibility gap between 3 and 30 at. % o selenium. Viscosity essentially inluences the velocity o the dieent phases sepaation pocesses and om this point o view viscosity data ae o exceptional impotance. Special attention has been ocused on the behavio o the viscosity in the citical egion o phase sepaation. The esults ae compaed with peviously obtained data o immiscible liquid metallic alloys and dielectic solutions.. Expeimental A compute-contolled oscillating-cup viscomete was used o viscosity, h(t), measuements [4]. Weighed (to within 0-4 g) amounts o In and Se ( % puity) wee melted in evacuated and sealed quatz ampoules. The initial compositions o the samples wee accuate to 0.0 wt.%. The cylindical quatz cucibles with intenal diametes o 0 mm wee used. Ate melting, the samples wee homogenized o 4-5 h at the tempeatue o 0 K. A homogeneous tempeatue ield o 0.3 K has been ceated inside a unace. The tempeatue was measued with the Pt/PtRh themocouple aanged just below the cucible. The expeiments wee peomed in an atmosphee o 90% A and c 008 Ltd

3 3th Intenational Coneence on Liquid and Amophous Metals Jounal o Physics: Coneence Seies 98 (008) 0007 doi:0.088/ /98//0007 0% H ate initially pumping out the unace woking volume in ode to avoid the oxidation o the sample. Ate the measuement the loss o the mateials by vapoization did not exceed 0.4 %. Measuements wee made stating om the maximal tempeatue with a cooling ate o 0 K/h, which was educed to K/h appoaching to the segegation egion. Using the modiied Roscoe equation, h(t) was calculated om the logaithmic decement and the peiod o oscillations [4]. The densities wee calculated om the tempeatue dependences o the densities o pue components [5]. The viscosity values wee obtained with an accuacy o about 3 %. 3. Results The viscosity h(t) was measued o binay In x Se 00-x alloys thoughout the concentation ange o the miscibility gap (3<x<30 at.%) between the binodal and 0 K by ive-pecent steps. The esults ae shown in igue. Beoe the measuements the samples wee kept 5-6 h at 0 K o homogenization. Cooling the completely mixed melts is accompanied by an incease o the viscosity. h(t) adopts a maximum value i a gavitational phase sepaation o the melt in two liquid layes occus. The obseved cups coespond to the binodal tempeatues, T S. The data obtained by uthe cooling should be undestood as eective values and ae omitted, o the sake o claity. The absolute h(t) value in the high tempeatue egion above the binodal is detemined by the initial sample composition and incease when a Se content inceases. The T S values ae pesented in table togethe with data detemined ealie om the electical conductivity [6], o compaison. Figue epesents the statiication cuve o the In-Se system detemined using viscosity and conductivity [6] data. The binodal tempeatues detemined by viscosity measuements ae lowe that those obtained ealie om the conductivity data [6]. Simila dieences wee noticed ealie o othe monotectic systems (In-Te, Ga-Pb, In-Te-Tl), and possible souces o such dieences wee discussed in details in [7]. Table. Binodal tempeatues, T S, o the In-Se alloys In 00-x Se x, x = T S, K, el.cond ,5 949,3 946, T S, K, visc Figue. Viscosity as a unction o tempeatue o In-Se liquid alloys Figue. Miscibility gap o the In-Se system 4. Discussion Accoding to the dynamic theoy o the citical phenomena [8-0], the viscosity o a liquid in the citical egion is descibed by the ollowing expession: Zh Zh Zh h ( T ) = h ( T ) + h ( T ) = h ( T )( qr ) = h ( T )( 0 q) t () c

4 3th Intenational Coneence on Liquid and Amophous Metals Jounal o Physics: Coneence Seies 98 (008) 0007 doi:0.088/ /98//0007 whee h (T ) = A exp(b/t) is a egula pat o viscosity and h (T ) is a luctuation viscosity. R c = 0 t is a coelation length o the concentation luctuations, 0 is a system-dependent amplitude. n denotes a citical exponent o the coelation length, and z h is a citical exponent o viscosity. q is a wave numbe, t = (T - T c )/T c. As is seen om equation (), h(t) o a liquid tends to ininity i T appoaches to T c (t 0). The analysis o this omula eveals that the tempeatue egion o its application is limited. It cannot be applied in the hydodynamic egion, whee qr c <<. On the othe hand, a tempeatue egion o its eliable application as t 0 is also not detemined. Moeove, the analysis o the available expeimental data indicates that viscosity takes a inite value at the citical point [-4]. This suggestion ollows also om the model o Fixman developed in his studies as ealy as 960th [5], whee a spatial dispesion nea citical point was taken into account. Nevetheless, a athe complicated Fixman viscosity equation as well as othe analytical expessions o tanspot coeicients poposed late (e.g. in [6]) can hadly be applied o metallic melts, as they oten contain a numbe o unknown paametes like diusion constants, chemical potentials, osmotic pessues etc. [5]. In a simpliied solution o the viscosity equation [5], the luctuation viscosity h (T ) is connected to the compessibility b and the coelation length as h (T ) ~ b / ~ R c ~ t -/. Based on the Fixman theoy, a semiempiical viscosity equation has been poposed []. In the pesent wok we use a modiied expession o the luctuation viscosity which takes account o the spatial dispesion o the system nea T c by a quadatic tem (qr c ) [7]: ( ÀR ) é é ù ( 0 ) ( ) ( ) ú ú ù c Dh t h = ê ú = ê () ë + qrc û êë + qrc û whee D h0 is an amplitude o the singula viscosity. This omula agees with the Fixman equation, assues viscosity initeness at the citical point and was aleady appoved o dieent binay immiscible systems [-4]. Ove a wide ange o tempeatues, including the vicinity o the T c, the viscosity can be appoximated by: B é ( Dh t ) ù è T ø êë + ( qr c ) úû The viscosity o the citical composition In 80 Se 0 is pesented in igue 3. h ( T) = h ( T) + h ( T) = æ ö 0 A expç + ê ú (3) Figue 3. Tempeatue dependence o the viscosity in liquid In 80 Se 0 : o expeimental, - calculated by Eq. (3) with itting paametes om Table, --- backgound viscosity obtained with A = 0.37 mpa s, B = 7 K. The application o equations () and (3) allows to calculate impotant paametes chaacteizing the viscosity nea T c : D h0, q 0, ν, z h, and h c being deined as Δh 0 / q 0. As a ist step, the paametes A and B o the backgound viscosity wee deduced om the high tempeatue egion (t > 0 - ) whee h (T) >> h (T ). This contibution is epesented by the dashed line in igue 3. With the help o the 3

5 3th Intenational Coneence on Liquid and Amophous Metals Jounal o Physics: Coneence Seies 98 (008) 0007 doi:0.088/ /98//0007 expeimental viscosity, the singula viscosity was calculated accoding to h (T ) = h(t ) - h (T ). The uthe analysis o this pat was conducted by consideing the tempeatue dependence o Δh - = (h - - h - c ) ~ t n in a double logaithmic scale. n was ound to be 0.63 ± 0.05 which is a value close to the univesal exponent o the coelation length 0.63 [8]. z h was detemined om the tempeatue dependence o h(t)/h (t) in a double logaithmic scale. Theewith it was possible to ind a value o z h n = Using now n = 0.64 the citical exponent o viscosity tuned out to be ± The citical paametes ound o In 80 Se 0 ae collected in table togethe with those o othe binaies. Table. Citical paametes o liquid In 80 Se 0 compaed to othe systems. System А Dh 0 h c В n (mpa s) (mpa s) (mpa s) (K) (q 0 ) z h In 80 Se , ± ± Ga 5.5 Pb ± ± In 40 Se 0 Tl ± ± In 30 Te 0 Tl ± ± Іn 80 Se 04 Te ± ± Methanol-heptane ± ± Methanol-hexane ± ± A physical meaning o the ecipocal value o the wave numbe q - can be now explained. As ound om the molecula light scatteing data, an amplitude o the coelation length 0 is equal to 3 Å []. Based on the q 0 values o dieent systems, collected in Table, q - tuned out to be»00 Å. It is suggested that q - is close to the coelation length o the liquid system at the bode o the hydodynamic egion at t» 0-3. Compaing the citical paametes, it is evealed that the univesality pinciple speads to such the dieent mateials as dielectic demixing solutions and metallic melts. Acknowledgments. The authos Yu. Plevachuk and V. Sklyachuk acknowledge the suppot o this wok by the Deutsche Akademische Austauschdienst (DAAD). Reeences [] Ratke L, Dieenbach S 995 Mate. Sci. Eng. R5 6 [] Pinz B, Romeo A and Ratke L 995 J. Mate. Sci [3] Somme F 996 Z. Metallkd. 87() 865 [4] Vollmann J, F. Hewig, M. Wobst. Expeimentelle Technik de Physik 39 (99) 57. [5] Iida T and Guthie R I L 993 The physical popeties o liquid metals (Oxod: Claendon Pess) [6] Didoukh V, Plevachuk Yu, Sokolovskii B 996 J. Phase Equilibia 7(5) 44 [7] Plevachuk Yu, Filippov V, Kononenko V et al. 003 Z. Metallkd. 94(9) 034 [8] Kadano L P, Swit 968 J Phys. Rev. 66() 89 [9] Halpein B I, Hohenbeg P C 969 Phys. Rev. 77() 95 [0] Feell R A 970 Phys. Rev. Lett [] Oleinikova A, Bulavin L, Pipich V 997 Chem. Phys. Lett. 78 [] Alekhin A, Bilous O 007 Uk. J. Phys (in pess) [3] Plevachuk Yu, Sklyachuk V, Alekhin O, Bulavin L 005 J. Phys. Studies, 9(4) 333 [4] Plevachuk Yu, Sklyachuk V, Alekhin O, Bulavin L 006 J. Mol.Liquids, 7 33 [5] Fixman M J. 96 Chem. Phys , ibidem 96 [6] Folk R, Moze G 996 Condens. Matt. Phys. 7 7 [7] Landau L D, Lishitz E M 980 Statistical physics (Oxod: Buttewoth-Heinemann) [8] Patashinskii A, Pokovskii V 98 Fluctuation theoy o phase tansitions (Мoskow: Nauka) 4