DISTRIBUTION COEFFICIENTS OF ADMIXTURES IN TiN

DISTRIBUTION COEFFICIENTS OF ADMIXTURES IN TiN

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