DISTRIBUTION COEFFICIENTS OF ADMIXTURES IN TiN

cta Metallurgica Slovaca, 10, 2004, 1 (59-66) 59 DISRIBUION COEFFICIENS OF DMIXURES IN in Drápala J., Kuchař L. Department of Non-ferrous Metals, Refining and Recycling; Faculty of Metallurgy and Materials Engineering, Vysoká škola báňská echnical University of Ostrava, 708 33 Ostrava, e-mail: Jaromir.Drapala@vsb.cz, Czech Republic ROZDĚLOVCÍ KOEFICIENY PŘÍMĚSÍ V CÍNU Drápala J., Kuchař L. Katedra neželezných kovů, rafinace a recyklace; Fakulta metalurgie a materiálového inženýrství, Vysoká škola báňská echnická univerzita Ostrava, 708 33 Ostrava, e-mail: Jaromir.Drapala@vsb.cz, Česká republika bstract In the paper the results of the systematic study of tin - admixture binary systems are presented. he values of distribution coefficients of admixtures in give us information about distributing ability of the individual admixtures and impurity elements in tin by zone melting. he correlation periodical dependence of the distribution coefficients of admixtures in tin on atomic number of the admixtures was determined. Key words: Distribution coefficient, tin, binary systems bstract V práci jsou uvedeny výsledky systematického studia binárních systémů cín - příměs. Hlavním materiálovým parametrem rozdělování příměsí mezi tekutou a tuhou fází je rozdělovací koeficient k o příměsi B v základní látce definovaný jako izotermní poměr koncentrace příměsi na křivce solidu X SB (at. %) ke koncentraci na křivce likvidu X LB (at. %) v binárním systému kov-příměs (1). Rovnovážný rozdělovací koeficient k o nabývá hodnot větších nebo menších než 1 podle toho, zda příměs snižuje teplotu tání m základní složky (k o <1) pro eutektické systémy nebo zvyšuje teplotu tání základní složky (k o >1) pro peritektické typy binárních systémů -B. Pro výpočet křivek solidu a likvidu v binárních soustavách byla autory již dříve vypracována metodika [1,2], podle které mohou být křivky solidu a likvidu vyjádřeny polynomem druhého řádu (2) tak, aby odpovídaly realitě zejména v oblasti přilehlé k základní složce. Průběh křivek je v oblasti nízkých koncentrací příměsí kontrolován termodynamicky [4]. Extrapolací funkčního průběhu křivek solidu a likvidu do oblasti zředěných roztoků (X 0) lze vyjádřit limitní hodnotu k o lim dle (4). Jako vstupní termodynamické hodnoty byly pro výpočty použity: teplota tání M = 232 C, molární entalpie tání H M = 7029 J.mol -1. Binární fázové diagramy cín příměs lze rozdělit do pěti typů - viz obr. 1 [5-15]. Z obr. 1 ke patrné, že všechny příměsi teplotu tání cínu snižují, kromě antimonu, který má k o >1. V tab. I jsou shrnuty parametry rovnic křivek solidu a likvidu (2) včetně teplotního rozsahu jejich platnosti od M až po udanou teplotu. Dále jsou zde uvedeny význačné body fázových transformací eutektických či peritektických reakcí a vypočtené limitní hodnoty rovnovážných rozdělovacích koeficientů pro 15 vybraných příměsí v cínu ko lim, jakož i hodnoty rozdělovacích koeficientů při eutektické či peritektické teplotě k o EP. Z hodnot k o lim a hodnot

cta Metallurgica Slovaca, 10, 2004, 1 (59-66) 60 rozdělovacích koeficientů dle různých autorů shrnutých v tab. II byla sestavena periodická korelační závislost rozdělovacích koeficientů příměsí v cínu na protonovém čísle příměsí viz obr. 2. ato korelační závislost vykazuje pravidelná maxima a minima vzájemně oddělená hodnotami k o inertních plynů. Hodnoty rozdělovacích koeficientů příměsí v nám dají důležité informace o rozdělovací schopnosti jednotlivých příměsí a nečistot v cínu při zonálním tavení a směrové krystalizaci. Rozdělovací koeficienty jsou hlavním materiálovým parametrem chemických nestejnorodostí vznikající při krystalizaci a známých jako dendritická segregace. 1. Introduction During refining crystallization processes the distribution of admixtures and impurities at the phase interface occurs. he distribution of admixtures and impurities between solidus and liquidus phases is characterized by equilibrium distribution coefficient. Knowledge of the distribution coefficient is important for the choice of the convenient crystallization method of refining, preparation of single crystals and the study of segregation micro- and macroinhomogeneities in real alloys. he equilibrium distribution coefficient represents the main material parameter for the preparation of high pure materials by refining processes as zone melting and directional crystallization. In these selected crystallization processes the distribution of admixture (impurity) B in basic substance occurs at the liquidus and solidus phase boundary of the materials. he distribution is result of the different concentration admixture (impurity) in the liquidus and solidus phase at the thermodynamic equilibrium. he concentration conditions can be determined by means of the equilibrium binary diagrams. 2. Distribution coefficient he equilibrium distribution coefficient is defined as an isothermal ratio of admixture concentration on the solidus curve X SB and the liquidus curve X LB in binary systems of basic metal admixture B: X SB k o = ( = const.) (1) X LB he equilibrium distribution coefficient takes the values k o >1 for systems, in which the admixtures (impurities) causes a temperature rise of the basic component, and the values k o <1 for those admixtures (impurities) causing a temperature drop of the basic component. he equilibrium distribution coefficients characterize the behavior and segregation of admixtures during crystallization at the solidus-liquidus interface, refining processes, preparation of single crystals and the study of inhomogeneities in real alloys. Some gave us reliable information about the distributing ability of individual admixture elements in the basic metal by crystallization processes during which the admixture with k o >1 are enriched on the axes of crystallizing dendrites or cells, and vice versa, the admixture with k o <1 are enriched in interdendritic spaces and in the finally solidifying mother melts during the dendritic or cellular segregation which always accompanies solidification of substance in reality. Knowledge of distribution coefficient values is important for the prediction of the refining efficiency in view of the fact that the purity can be influenced. he used thermodynamic values for [3]: Melting point of : M = 232 C, transformation enthalpy of : H M = 7029 J.mol -1. Binary phase diagrams of tin - admixture systems it is possible to divide into five types - see Fig. 1 [5-15]. From the fig. 1 is seen, that all admixtures increase the melting point of tin, except for antimony, that has k o >1.

cta Metallurgica Slovaca, 10, 2004, 1 (59-66) 61 Diagram ype k o dmixture element Me L IV.a k o > 1 232 S Peritectic Sb 232 L IV. k o < 1 S Peritectic Cd, Hg, In 232 S L V. k o < 1 Eutectic l, Bi, Ga, Pb, Zn 232 L V.a k o << 1 Eutectic with very small solubility in solidus g, u, Ca, Ce, Co, Cu, Dy, La, Li, Mg, Na, Pt, Sm, Sr, h, i, l, Yb L 232 M s, B, Ba, Be, Cl, Cr, Cs, Er, F, Fe, Gd, Ge, Hf, K, Monotectic Lu, Mn, Mo, Nb, Nd, Ni, O, P, Pd, Pr, Pu, Rb, Re, Rh, Ru, S, Sc, Se, Si, b, e, m, U, V, Y, Zr Fig.1 ypes of tin - admixture binary phase diagrams

cta Metallurgica Slovaca, 10, 2004, 1 (59-66) 62 o calculate the solidus and liquidus curves in binary - B systems we have used the authors method [1,2] by help of which these curves are especially in the region adjacent to the basic component expressed in the form of the second grade polynoms - eq. (2): 2 = a X + b X +, (2) SL, SL, SLB, SL, SLB, M where M is the melting point of the basic element, XS,LB is the concentration of B admixture in atomic percent. he parameters a S,LB, b S,LB can be calculated by the method of last squares of the deviations. he curves are thermodynamically controlled by Hayes-Chipman s thermodynamical formula [4]. In the able I are summarized these parameters inclusive the range of their validity from M to temperature for tin admixtures. able I Regresní parametry rovnic křivek solidu a likvidu, rozsah jejich teplotní platnosti od teploty tání, vypočtené hodnoty rovnovážných rozdělovacích koeficientů příměsí v cínu, složení význačných bodů solidu a likvidu při eutektické či peritektické reakci Regression parameters of solidus System k o lim k o EP X S EP X L EP EP Validity and liquidus curves [at. %] [at. %] [ C] a S b S a L b L to [ C] - g 0,034 0,024 0,09 3,8 221-434,8330-83,2897-0,0043-2,8704 221 - l 0,43 0,42 1,0 2,4 228-0,1202-3,8862 0,0087-1,6864 228 - u 0,036 0,033 0,2 6,3 217 21,1894-78,9926 0,0677-2,8689 217 - Bi 0,27 0,30 13,1 43,0 139 0,0599-7,8641 0,0002-2,1524 139 - Cd 0,21 0,15 0,63 4,3 223-4,4581-11,4412 0,0700-2,3929 223 - Cu 0,0060 0,0078 0,01 1,3 227-0,1195-499,9989-0,6934-2,9820 227 - Ga 0,17 0,12 7,1 91,5 20,5-0,6825-14,3850 0,0082-2,4949 150 - Hg 0,20 0,17 0,5 3,0 224-7,8586-12,0096-0,0955-2,3855 224 - In 0,39 0,40 0,8 4,3 224 0,0396-4,7014-0,0125-1,8378 224 - Ni 0,013 0,015 0,005 0,33 231,15 11999,6084-229,9992 1,3467-3,0202 231,15 - Pb 0,058 0,053 1,4 26,1 183 10,8133-49,9606 0,0394-2,8846 183 - Sb 1,95 1,54 10,0 6,5 250 0,0299 1,5006-0,0238 2,9237 250 - i 0,063 0,040 0,02 0,5 231-250,6338-44,9873 1,6667-2,8333 231 - l 0,058 0,052 1,6 31,0 172 7,1228-49,0177 0,0284-2,8257 172 - Zn 0,032 0,04 0,6 14,9 198,5 58,3334-90,8333 0,0438-2,8963 198,5 k o lim - limit value of the equilibrium distribution coefficient k o EP - equilibrium distribution coefficient of admixture in tin at EP EP - eutectic ev. peritectic temperature X S EP - max. solubility of admixture in tin at EP X L EP liquid concentration of admixture at EP Validity of equations is from up to temperature M Based on the dependence on temperature or concentration from the course of distribution coefficient is possible to express by parameters a S,L and b S,L from equation (2) in the shape: k a X + b L LB L o = (3) as X SB + bs

cta Metallurgica Slovaca, 10, 2004, 1 (59-66) 63 By extrapolation of the course solidus and liquidus curves to the area of dissolved solution (X S,LB 0), ie for X get near to zero from equation (3) the limit value of the equilibrium distribution coefficient k olim : b k o lim = b L S, (4) which is possible in the limit areas to ± 10 K from the melting temperature and is the main material parameter which express segregation ability of admixture B in base element during crystallization. his is very important especially in the edge areas of the binary diagrams where are limited amounts of admixtures and in those mentioned areas ko lim might be accepted as constant value. In the able II there are the values of k o lim and k o EP calculated by authors together with the predicted values of k o. In the same table you can see the values of k o and k ef those obtained from different authors [16-23]. M 3. Periodical correlation dependence of equilibrium distribution coefficients of admixtures on atomic number of admixtures he distribution coefficient introduce characteristics of admixture element, those influence material when are used as alloying element of the base metal. he important function of distribution coefficients are their implementation into the different dependencies based on amount of some physical properties of admixtures or on maximum solubility of admixture in solid and so on. On the Fig. 2 is shown the periodical correlation dependence of the distribution coefficients of admixtures in tin (from ab. II) on the atomic number of admixtures. In mentioned graphical dependence the minimum of k o are the values of inert gases He, Ne, r, Kr, Xe and Rn, those are practically not dissolvable in tin and separate one from another different periods. In the second and third periods are the maximums of k o created by the values of admixtures Li and l. In the fourth doubled period there are seeable two maximums of k o, lower for i and higher for s. In the fifth period is the maximum created by Sb (k o >1), in the sixth period by Bi (k o <1). For group of RE metals is till now known very small amount of binary diagrams. he similar periodical correlation dependencies of equilibrium distribution coefficients of admixtures on atomic number of admixtures were as well constructed for more then 55 basic elements [2]. Periodical correlation dependence of the equilibrium distribution coefficients of admixtures in the basic metals on atomic number usually allow: the determination of unknown values of k o and supposition of the distribution coefficients during crystallization processes the information about the suitability and direction of the zone melting or directional crystallization for preparation of high pure materials, the choice of the optimum input materials for such refining processes and evaluation of the acceptable grade of refining the controlled microalloying and dotting of admixture during growing of crystals even from technical alloys, those increase by that way their physical characteristics the calculation of concentration undercooling in the solidified materials on the boundary crystal melt the prognosis of the distribution ability and enrichment of the foreign admixtures with k o >1 in the axes of dendrite, accumulation of admixtures with k o <1 in the inter-dendritic

cta Metallurgica Slovaca, 10, 2004, 1 (59-66) 64 areas, in the mother melt during dendritic segregation. s more far away is k o from 1, as more higher is the efficiency of the admixtures distribution the prognosis of the basic types of the unknown binary diagrams the calculation of decreasing or increasing the melting temperature of the base element during given concentration of admixture the determination of the width of interval solidification, which is important to know for control of the production processes at technical alloys during classical or continuous casting and directional solidification of materials. able II Equilibrium k o, k o lim and effective values k ef of distribution coefficients of admixtures in No Element uthors [2] [16] [17] [18] [19] [20] [21] [22] [23] k o lim k o lim k o k ef k o k ef k ef k ef k ef k o 2 He <0.001 <0.001 3 Li 0,01 10 Ne <0.001 <0.001 11 Na 0,24 0,6 0,24 12 Mg 0,05 0,06 0,05 13 l 0,43 0,42 0,01 0,01 0,22 14 Si 0,1 18 r <0.001 <0.001 19 Ca 0,02 22 i 0,063 26 Fe 0,03 28 Ni 0,013 0,1 29 Cu 0,006 0,01 0,08 0,01 0,01 0,02 30 Zn 0,032 0,09 0,14 0,04 0,12 0,12 31 Ga 0,17 0,34 0,07 0,12 0,07 32 Ge 0,53 33 s 0,76 36 Kr <0.001 <0.001 47 g 0,034 0,022 0,015 0,1 0,01 48 Cd 0,21 0,23 0,26 0,3 0,48 49 In 0,39 0,18 0,4 0,25 0,36 50 1,00 1,00 1,00 51 Sb 1,95 2,01 2,8 1,65 54 Xe <0.001 <0.001 79 u 0,036 0,031 0,03 0,03 0,08 80 Hg 0,20 0,13 0,1 0,1 81 l 0,058 0,052 0,034 0,03 82 Pb 0,058 0,13 0,09 0,1 0,09 0,1 0,14 83 Bi 0,27 0,26 0,28 0,3 0,26 0,27 0,3 86 Rn <0.001 <0.001 k ef Experimental determined effective distribution coefficient Conclusion In this paper we present the distribution coefficients of admixtures k o in tin and their periodical dependence of equilibrium distribution coefficients of admixtures in tin on the atomic number of impurities. his dependence allow us to predict the behaviour of the admixture in the interface boundary crystal melt during the crystallization processes as well as the prediction

cta Metallurgica Slovaca, 10, 2004, 1 (59-66) 65 for other admixtures, those binary systems are not yet known. ll the admixtures increase the melting point of tin, except antimony (k o >1) that will be concentrated in the end part of refined ingot. he paper gives our contribution to theory and praxis of high purity materials preparation by crystallization methods. k o 10 1 0.1 Na Mg l Si Ca s Ge G i Fe Zn Sb Cd g In Hg u Bi Pb l uthors [2] [16] [17] [18] [19] [20] [21] [22] [23] 0.01 Li Ni Cu 0.001 He Ne r Kr Xe Rn 0 10 20 30 40 50 60 70 80 90 100 tomic number Fig.2 Periodical correlation dependence of distribution coefficients of admixtures in tin on the atomic number of admixtures cknowledgement his work was solved in the frame of the project COS 531 "Lead-free solder materials" and was supported by the Ministry of Education of the Czech Republic within the project Nr. MSM273600002 New materials prepared by crystallization processes. Literature [1] Barthel, J., Buhrig, E., Hein, K., Kuchař, L.: Kristallisation aus Schmelzen. VGI Leipzig 1983 [2] Kuchař, L., Drápala, J.: Metallurgy of pure metals. Nadácia R. Kammela, Košice, 2000 [3] Hayes,., Chipman, J.: rans. IME, 135, 1939, p. 85 [4] SGE Date for Pure Elements. NPL Reports DM (), 195, 1989. Binary lloy Phase Diagrams on CD-ROM SM International Materials Park, Ohio, 1996 [5] Hansen, M.: Constitution of Binary lloys. McGraw-Hill Company, New York, 1958 [6] Elliott, R.P.: Constitution of Binary lloys. McGraw-Hill Company, New York, 1965 [7] Shunk, F..: Constitution of Binary lloys. McGraw-Hill Company, New York, 1969 [8] Massalski,.D.: Binary lloy Phase Diagrams. SM Metals Park, Ohio, 1987 [9] Massalski,.D.: Binary lloy Phase Diagrams. Second Edition Plus Updates on CD ROM, SM International, Metals Park, Ohio, 1996

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