DISTRIBUTION COEFFICIENTS OF ADMIXTURES IN TiN

Acta Metallurgica Slovaca, 10, 2004, 1 (59 - 66)

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DISTRIBUTION COEFFICIENTS OF ADMIXTURES IN TiN Drápala J., Kuchař L. Department of Non-ferrous Metals, Refining and Recycling; Faculty of Metallurgy and Materials Engineering, Vysoká škola báňská – Technical University of Ostrava, 708 33 Ostrava, e-mail: [email protected], Czech Republic ROZDĚLOVACÍ KOEFICIENTY PŘÍMĚSÍ V CÍNU Drápala J., Kuchař L. Katedra neželezných kovů, rafinace a recyklace; Fakulta metalurgie a materiálového inženýrství, Vysoká škola báňská – Technická univerzita Ostrava, 708 33 Ostrava, e-mail: [email protected], Česká republika Abstract In the paper the results of the systematic study of tin - admixture binary systems are presented. The values of distribution coefficients of admixtures in Sn give us information about distributing ability of the individual admixtures and impurity elements in tin by zone melting. The 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 Abstract V práci jsou uvedeny výsledky systematického studia binárních systémů cín - příměs. Hlavním materiálovým parametrem rozdělování příměsí mezi tekutou a tuhou fází je rozdělovací koeficient ko příměsi B v základní látce A definovaný jako izotermní poměr koncentrace příměsi na křivce solidu XSB (at. %) ke koncentraci na křivce likvidu XLB (at. %) v binárním systému kov-příměs (1). Rovnovážný rozdělovací koeficient ko nabývá hodnot větších nebo menších než 1 podle toho, zda příměs snižuje teplotu tání TmA základní složky (ko<1) pro eutektické systémy nebo zvyšuje teplotu tání základní složky (ko>1) pro peritektické typy binárních systémů A-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 A. 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 ko lim dle (4). Jako vstupní termodynamické hodnoty byly pro výpočty použity: teplota tání Sn TMSn = 232 °C, molární entalpie tání Sn ∆H MSn = 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 ko>1. V tab. I jsou shrnuty parametry rovnic křivek solidu a likvidu (2) včetně teplotního rozsahu jejich platnosti od TMSn 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 ko EP. Z hodnot ko lim a hodnot


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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. Tato korelační závislost vykazuje pravidelná maxima a minima vzájemně oddělená hodnotami ko inertních plynů. Hodnoty rozdělovacích koeficientů příměsí v Sn 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. The 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. The 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 A occurs at the liquidus and solidus phase boundary of the materials. The distribution is result of the different concentration admixture (impurity) in the liquidus and solidus phase at the thermodynamic equilibrium. The concentration conditions can be determined by means of the equilibrium binary diagrams. 2. Distribution coefficient The equilibrium distribution coefficient is defined as an isothermal ratio of admixture concentration on the solidus curve XSB and the liquidus curve XLB in binary systems of basic metal A – admixture B: X (T = const.) (1) k o = SB X LB The equilibrium distribution coefficient takes the values ko>1 for systems, in which the admixtures (impurities) causes a temperature rise of the basic component A, and the values ko<1 for those admixtures (impurities) causing a temperature drop of the basic component A. The 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 Sn by crystallization processes during which the admixture with ko>1 are enriched on the axes of crystallizing dendrites or cells, and vice versa, the admixture with ko<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. The used thermodynamic values for Sn [3]: Melting point of Sn: TMSn = 232 °C, transformation enthalpy of Sn: ∆H MSn = 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 ko>1.

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Diagram

Admixture element Me

Type

ko

IV.a

ko > 1

T L 232

Peritectic

S

Sn

Sb

at. % Me

T

IV.

L

232

ko < 1

Peritectic

S

Cd, Hg, In

at. % Me

Sn T 232

Eutectic

S

Sn

V.a

232

L

Sn 232

Al, Bi, Ga, Pb, Zn

at. % Me

T

T

ko < 1

V.

L

ko << 1

Eutectic with very small solubility in solidus

Ag, Au, Ca, Ce, Co, Cu, Dy, La, Li, Mg, Na, Pt, Sm, Sr, Th, Ti, Tl, Yb

at. % Me

M L

Monotectic

Sn

As, B, Ba, Be, Cl, Cr, Cs, Er, F, Fe, Gd, Ge, Hf, K, Lu, Mn, Mo, Nb, Nd, Ni, O, P, Pd, Pr, Pu, Rb, Re, Rh, Ru, S, Sc, Se, Si, Tb, Te, Tm, U, V, Y, Zr

at. % Me

Fig.1 Types of tin - admixture binary phase diagrams

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To calculate the solidus and liquidus curves in binary A - 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 Sn expressed in the form of the second grade polynoms - eq. (2):

TS , L = a S , L X S2, LB + bS , L X S , LB + TMA ,

(2)

where TMA is the melting point of the basic element A, XS,LB is the concentration of B admixture in atomic percent. The parameters aS,LB, bS,LB can be calculated by the method of last squares of the deviations. The curves are thermodynamically controlled by Hayes-Chipman´s thermodynamical formula [4]. In the Table I are summarized these parameters inclusive the A range of their validity from TM to temperature T for tin – admixtures. Table I Regresní parametry rovnic křivek solidu a likvidu, rozsah jejich teplotní platnosti od teploty tání Sn, vypočtené hodnoty rovnovážných rozdělovacích koeficientů příměsí v cínu, složení význačných bodů solidu a likvidu při eutektické či peritektické reakci Regression parameters of solidus Validity System ko lim ko EP XS EP XL EP TEP and liquidus curves Sn - Ag

0,034

0,024

[at. %]

[at. %]

[°C]

aS

0,09

3,8

221

-434,8330

bS -83,2897

aL -0,0043

bL

to T [°C]

-2,8704

221

Sn - Al

0,43

0,42

1,0

2,4

228

-0,1202

-3,8862

0,0087

-1,6864

228

Sn - Au

0,036

0,033

0,2

6,3

217

21,1894

-78,9926

0,0677

-2,8689

217

Sn - Bi

0,27

0,30

13,1

43,0

139

0,0599

-7,8641

0,0002

-2,1524

139

Sn - Cd

0,21

0,15

0,63

4,3

223

-4,4581

-11,4412

0,0700

-2,3929

223

Sn - Cu 0,0060

0,0078

0,01

1,3

227

-0,1195 -499,9989

-0,6934

-2,9820

227

Sn - Ga

0,17

0,12

7,1

91,5

20,5

-0,6825

-14,3850

0,0082

-2,4949

150

Sn - Hg

0,20

0,17

0,5

3,0

224

-7,8586

-12,0096

-0,0955

-2,3855

224

224

0,0396

-4,7014

-0,0125

-1,8378

224

231,15 11999,6084 -229,9992

1,3467

-3,0202

231,15

-49,9606

0,0394

-2,8846

183

Sn - In

0,39

0,40

0,8

4,3

Sn - Ni

0,013

0,015

0,005

0,33

Sn - Pb

0,058

0,053

1,4

26,1

183

10,8133

Sn - Sb

1,95

1,54

10,0

6,5

250

0,0299

1,5006

-0,0238

2,9237

250

Sn - Ti

0,063

0,040

0,02

0,5

231

-250,6338

-44,9873

1,6667

-2,8333

231

Sn - Tl

0,058

0,052

1,6

31,0

172

7,1228

-49,0177

0,0284

-2,8257

172

Sn - Zn

0,032

0,04

0,6

14,9

198,5

58,3334

-90,8333

0,0438

-2,8963

198,5

ko lim - limit value of the equilibrium distribution coefficient ko EP - equilibrium distribution coefficient of admixture in tin at TEP TEP - eutectic ev. peritectic temperature XS EP - max. solubility of admixture in tin at TEP XL EP – liquid concentration of admixture at TEP Validity of equations is from TMSn up to temperature T

Based on the dependence on temperature or concentration from the course of distribution coefficient is possible to express by parameters aS,L and bS,L from equation (2) in the shape:

ko =

aL X LB + bL aS X SB + bS

(3)

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By extrapolation of the course solidus and liquidus curves to the area of dissolved solution (XS,LB → 0), ie for X get near to zero from equation (3) the limit value of the equilibrium distribution coefficient kolim :

k o lim =

bL , bS

(4)

which is possible in the limit areas to ± 10 K from the melting temperature TMA and is the main material parameter which express segregation ability of admixture B in base element A during crystallization. This 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 Table II there are the values of ko lim and ko EP calculated by authors together with the predicted values of ko. In the same table you can see the values of ko and kef those obtained from different authors [16-23]. 3. Periodical correlation dependence of equilibrium distribution coefficients of admixtures on atomic number of admixtures The distribution coefficient introduce characteristics of admixture element, those influence material when are used as alloying element of the base metal. The 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 Tab. II) on the atomic number of admixtures. In mentioned graphical dependence the minimum of ko are the values of inert gases He, Ne, Ar, 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 ko created by the values of admixtures Li and Al. In the fourth doubled period there are seeable two maximums of ko, lower for Ti and higher for As. In the fifth period is the maximum created by Sb (ko>1), in the sixth period by Bi (ko<1). For group of RE metals is till now known very small amount of binary diagrams. The 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 ko 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 ko>1 in the axes of dendrite, accumulation of admixtures with ko<1 in the inter-dendritic

64


• • •

areas, in the mother melt during dendritic segregation. As more far away is ko 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.

Table II Equilibrium ko , ko lim and effective values kef of distribution coefficients of admixtures in Sn No Element Authors [2] [16] [17] [18] [19] [20] [21]

ko lim

ko lim

<0.001

<0.001

<0.001

<0.001

ko

kef

ko

2 3 10 11 12 13 14 18 19 22 26

He Li Ne Na Mg Al Si Ar Ca Ti Fe

28

Ni

0,013

29 30 31 32

Cu Zn Ga Ge

0,006 0,032 0,17

33

As

36

Kr

<0.001

<0.001

47

Ag

0,034

0,022

0,015

48

Cd

0,21

0,23

0,26

0,3

49

In

0,39

0,18

0,4

0,25

50

Sn

51

Sb

1,00 1,95

1,00 2,01

1,00 2,8

54

Xe

<0.001

<0.001

79

Au

0,036

0,031

0,03

0,03

80 81 82

Hg Tl Pb

0,20 0,058 0,058

0,13 0,052 0,13

0,1 0,034 0,09

0,1 0,1

0,09

0,28

0,3

0,26

kef

kef

[22]

[23]

kef

ko

0,01

0,43

0,42

<0.001

<0.001

0,24 0,05 0,01

0,6 0,01

0,24 0,05

0,06 0,22 0,1 0,02

0,063 0,03 0,1 0,09 0,34

0,01 0,14 0,07

0,08

0,01 0,04 0,12

0,01

0,02

0,12

0,12 0,07

0,53 0,76

83

Bi

0,27

0,26

86

Rn

<0.001

<0.001

kef

kef

0,1

0,01 0,48 0,36 1,65 0,08 0,03 0,1 0,27

0,14

0,3

Experimental determined effective distribution coefficient

Conclusion In this paper we present the distribution coefficients of admixtures ko in tin and their periodical dependence of equilibrium distribution coefficients of admixtures in tin on the atomic number of impurities. This 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

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for other admixtures, those binary systems are not yet known. All the admixtures increase the melting point of tin, except antimony (ko>1) that will be concentrated in the end part of refined ingot. The paper gives our contribution to theory and praxis of high purity materials preparation by crystallization methods. 10

Authors [2] [16] [17] [18] [19] [20] [21] [22] [23]

Sb

Sn

1

As Ge

Al

ko

Na

In

Bi

Cd

G

Hg

Si

0.1

Ti

Mg Ca Li

Fe

Zn

Au

Ag

Tl

Pb

Ni

0.01

Cu

0.001 0

He

10

Ne

Ar 20

30

Kr

40

50

Xe

60

70

80

Rn

90

100

Atomic number Fig.2 Periodical correlation dependence of distribution coefficients of admixtures in tin on the atomic number of admixtures

Acknowledgement This work was solved in the frame of the project COST 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, A., Chipman, J.: Trans. AIME, 135, 1939, p. 85 [4] SGTE Date for Pure Elements. NPL Reports DMA (A), 195, 1989. Binary Alloy Phase Diagrams on CD-ROM ASM International Materials Park, Ohio, 1996 [5] Hansen, M.: Constitution of Binary Alloys. McGraw-Hill Company, New York, 1958 [6] Elliott, R.P.: Constitution of Binary Alloys. McGraw-Hill Company, New York, 1965 [7] Shunk, F.A.: Constitution of Binary Alloys. McGraw-Hill Company, New York, 1969 [8] Massalski, T.D.: Binary Alloy Phase Diagrams. ASM Metals Park, Ohio, 1987 [9] Massalski, T.D.: Binary Alloy Phase Diagrams. Second Edition Plus Updates on CD ROM, ASM International, Metals Park, Ohio, 1996


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[10] Baker, H., Okamoto, H.: ASM Handsbook. Alloy Phase Diagrams. ASM International, Materials Park, Ohio, Vol. 3, 1999 [11] Okamoto, H.: Phase Diagrams for Binary Aloys. Desk Handbook. ASM International, Materials Park, Ohio, 2000 [12] Peretti, E.A., Paulsen, J. Kevin, M.: Contribution to the system tin-arsenic. J. LessCommon Metals, 17, 1969, No. 3, pp. 283-290 [13] Dric, M.E., Fridman, A.S., Zusman, L.L., Kusikov, V.A.: Diagramma sostojanija olova s kaliem, rubidiem i ceziem. Faz. ravnovesija v met. splavach. Moscow, 1981, pp. 176-178 [14] Charlesworth, J.P. Macphail, I., Madsen, P.E.: Experimental work on the niobium - tin constitution diagram and related studies. J. Mater. Sci., 5, 1970, No. 7, pp. 580-603 [15] Predel, B., Schwermann, W.: Constitution and thermodynamics of the antimony - tin system. J. Inst. Metals. 1971, 99, pp. 169-173 [16] Vigdorovič, V.N., Volpjan, A.E., Kurdjumov, G.M.: Napravlennaja kristallizacija i fizikochimičeskij analiz. Izd. Chimija, Moskva, 1976, p. 22 [17] Kirgincev, A.N., Selivanov, I.M.: Izv. SO AN SSSR. Ser. chim. nauk., vyp. 2, 1970, p. 57 [18] Aleksandrov, B.N., Udovikov, V.I., Usenko, L.E. Fizika kondensirovannogo sostojanija. Nauchnye trudy FTINT AN USSR, Charkov, vyp. 25, 1973, p. 85 [19] Kirgincev, A.N.: Upravljajemaja kristallizacija v trubčatom kontejnere. Nauka, Novosibirsk, 1978 [20] Kirgincev, A.N., Gorbačeva,,I.I., Judelevič, I.G.: Izv. SO AN SSSR. Ser. chim. nauk. vyp. 3, 1967, No. 4, p. 35 [21] Kirgincev, A.N., Gorbačeva, I.I.: Izv. SO AN SSSR. Ser. chim. nauk. vyp. 2, 1969, No. 4, p. 30 [22] Hoshino, Y., Utsunomiya,T. J.: Chem. Eng. Data. 27, 1982, No. 2, p. 144 [23] Vigdorovič, V.N., Morochovec, M.A.: Izv. AN SSSR. Ser. Metally. 1971, No. 6, p. 97

DISTRIBUTION COEFFICIENTS OF ADMIXTURES IN TiN

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