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Thermodynamic properties and In-Sn-Sb phase diagram

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Thermodynamic properties and In-Sn-Sb phase diagram
 ISSN 0020-1685, Inorganic Materials, 2007, Vol. 43, No. 8, pp. 803–815. © Pleiades Publishing, Inc., 2007.
Original Russian Text © V.P. Vasil’ev, B. Legendre, 2007, published in Neorganicheskie Materialy, 2007, Vol. 43, No. 8, pp. 903–916.
803
INTRODUCTION
In an earlier study [1], In–Sn–Sb alloys were pro-
posed as an alternative to (CdTe)
x
(HgTe)
1 – x
alloys for
the fabrication of far-IR detectors. Indeed, the
(Sn
2
)
1 −
x
(InSb)
x
solid solution containing 5.1 at % Sn,
with a band gap E
g
= 0.11–0.12 eV, is a candidate mate-
rial for IR detectors [2]. Also attractive in this regard are
thermodynamically stable solid solutions on the
β
-SnSb (53.12 at % Sb)–InSb join. In addition, β
-SnSb
was proposed as an anode material for rechargeable
lithium batteries [3].
The thermodynamic properties of In–Sn, In–Sb, and
Sn–Sb alloys and some liquid In–Sn–Sb alloys were
investigated in [1, 4–7].
Thermodynamic evaluation of the Sn–Sb phase dia-
gram was reported in [6]. In the subsolidus region, this
system contains several stoichiometric intermediate
phases rather than one phase (
β
) with a wide homoge-
neity range [8]. We believe that the β
solid solution in
the Sn–Sb system is in a metastable state and relaxes to
equilibrium through a series of intermediate phases
very close in lattice parameters, which have little effect
on their energetics. The room-temperature thermody-
namic stability of these phases is insignificant. The sta-
bilization of solid phases in the Sn–Sb system is of
practical interest since indium-doped Sn–Sb materials
are potentially attractive for optoelectronic applica-
tions.
This article presents the continuation of a systematic
study of In–Sn–Sb alloys.
EXPERIMENTAL
Preparation of In–Sn–Sb alloys.
The alloys were
prepared from high-purity (5N) indium, tin, and anti-
Thermodynamic Properties of Alloys
and Phase Equilibria in the In–Sn–Sb System
V. P. Vasil’ev
a and B. Legendre
b
a
Moscow State University, Vorob’evy gory 1, Moscow, 119899 Russia
b
Laboratoire E.A. 401, Université de Paris XI, Ch tenay-Malabris, France
e-mail: vas@td.chem.msu.ru
Received September 6, 2006
Abstract
—We report the thermodynamic properties of alloys and phase equilibria in the In–Sn–Sb system
studied by emf measurements at temperatures from 600 to 830 K. Different types of exchange reactions in the
electrochemical cell (–) W
|
In
|
In
+
in electrolyte |
I
n
x
Sb
y
Sn
z
|
W (+) are considered, and the ways of reducing
their influence on the accuracy of emf measurements are analyzed. A number of T
–
x
sections of the In–Sn–Sb
phase diagram are refined.
DOI: 10.1134/S0020168507080018
a
^
Table 1. Compositions of the In–Sn–Sb alloys studied by emf measurements
Sample no.
x
In
x
Sn
x
Sb
Sample no.
x
In
x
Sn
x
Sb
1 0.3335 0.3331 0.3334 10 0.2500 0.1231 0.6268
2 0.2997 0.2995 0.4008 11 0.5000 0.2499 0.2501
3 0.2502 0.2498 0.5000 12 0.1999 0.2001 0.6000
4 0.3332 0.1669 0.4991 13 0.1401 0.2866 0.5733
5 0.1666 0.3333 0.5001 14 0.2501 0.4994 0.2505
6 0.1002 0.3996 0.5003 15 0.4001 0.3999 0.2000
7 0.0503 0.4497 0.5000 16 0.4000 0.2000 0.4000
8 0.0500 0.4751 0.4749 17 0.4501 0.0999 0.4500
9 0.1112 0.4444 0.4444
804
INORGANIC MATERIALS
Vol. 43
No. 8
2007
VASIL’EV, LEGENDRE
mony. Weighed mixtures (
~1.6
g) of the metals were
sealed in Pyrex tubes under a vacuum of ~10
–4
Pa and
were reacted at 800 K for 48 h. The resultant ingots
were up to 5 mm in diameter and 10 mm in length. In
each experiment, a whole ingot was used. The differ-
ence in weight between the starting mixtures and ingots
was within 0.05%. The compositions of the alloys stud-
ied are listed in Table 1.
130
620 670
E
, mV
T
, K
1
2
3
4
120
110
100
90
720
770
820
Sb
DTA
EMF
(9)
In Sn
at %
(1) 6.66 at
% In
(2) 80 at
% Sb
(3) 66.66 at
% Sb
(10) 50 at
% Sb
(4) 30 at
% Sb
(5) 6.66 at
% Sb
(11) 20
(8)
33.33
(12)
50
(7)
66.66
(13)
80
(6)
(14)
Fig. 1.
Compositions of the In–Sn–Sb alloys characterized by DTA [7] and emf measurements (figures in parentheses are the num-
bers of the composition lines).
Fig. 2.
Temperature-dependent emf data for Sn
x
(In
0.5
Sb
0.5
)
1 – x
alloys (Fig. 1, line 14): x
Sn
= (
1
) 0.10, (
2
) 0.20, (
3
) 0.333, (
4
) 0.499.
INORGANIC MATERIALS
Vol. 43
No. 8
2007
THERMODYNAMIC PROPERTIES OF ALLOYS AND PHASE EQUILIBRIA
805
Figure 1 indicates the compositions of the In–Sn–Sb
alloys characterized by emf measurements and differ-
ential thermal analysis (DTA).
Isothermal electrochemical cell.
In emf measure-
ments, we used the concentration cell
(–) W |
I
n
|
In
+
in electrolyte
|
In
x
Sb
y
Sn
z
|
W (+).(I)
In
+
ions were formed in situ, in contact with the metals
in the cell, owing to a small amount of hydrogen chlo-
ride dissolved in the electrolyte.
Potentiometric studies.
The emf was measured at
30-min intervals at constant temperature. The system
was thought to be in equilibrium if the measured emf E
varied by no more than ±
5
µ
V over the last three or four
measurement cycles. The E
(
T
)
data obtained during the
first week of measurements were thought of as corre-
sponding to a quasi-equilibrium state and were, as a
rule, left out of consideration. The reproducibility in
each series of measurements (two or three heating
cycles) was ±
0.7
mV or better. Measurements with each
cell took two to three months.
RESULTS AND DISCUSSION
The experimental E
(
T
)
data for homogeneous liquid
alloys and heterogeneous solid alloys in the In–Sn–Sb
system are presented in Figs. 2–6 and Tables 2 and 3.
Thermodynamic evaluation of liquid In–Sn–Sb
alloys.
The excess Gibbs energy of mixing for liquid
In–Sn–Sb alloys is given by
∆
mix
G
E
(
T
, x
) = x
In
x
Sb
[(–25631.2 + 102.9324
T – 13.45816
T
ln
T
) + (–2115.4 – 1.31907
T
)(
x
In
– x
Sb
) + 2908.9(
x
In
– x
Sb
)
2
]
+ x
In
x
Sn
[(–769 – 0.1312T) Table 2. Coefficients in E(T) = a + bT best fit equations for In–Sn–Sb alloys
Sample no.ı
In
a b × 10
2
l
, K
, mV
× 10
2
, mV
2
T
min
–T
max
, K
7 0.050 2.67 32.095 16 702.2 228.05 0.03 665–739
8 0.050 –1.91 31.864 15 694.8 219.48 0.02 660–730
8* 0.500 –528.89 10.873 46 648 175.95 58 630.1–668.5
8* 0.500 –1.96 25.394 23 614.7 154.15 6.8 599.7–630.6
6 0.100 36.40 23.042 30 742.8 207.56 0.12 675–796
9 0.111 32.69 21.590 36 728.7 190.02 0.08 648–796
13 0.140 59.04 18.177 37 766.4 197.90 0.43 702–814
13* 0.140 274.78 –15.240 19 688.5 169.85 3.2 679.9–969.8
5 0.167 51.30 16.339 39 745.9 173.17 1.0 670–814
12 0.200 58.15 15.216 91 776.8 176.35 5.35 715–821
12* 0.200 –251.37 57.029 18 713.1 155.31 14 676–737.5
14 0.250 20.40 12.762 135 749.3 116.03 0.26 640–822
3 0.250 51.88 12.157 96 767.3 145.17 5.89 672–821
3* 0.250 591.24 –61.564 21 703.8 157.94 0.02 683–730.7
10 0.250 74.61 11.711 116 789.4 167.05 1.84 719–835
10* 0.250 293.15 –17.830 62 709.7 166.62 0.57 682.3–742
10* 0.250 –241.17 53.75 5 706.1 138.34 0.3 698.2–714.2
2 0.300 37.45 10.782 98 765.9 120.03 6.85 672–821
1 0.333 28.39 10.171 114 757.8 105.47 0.26 659–822
4 0.333 55.80 9.344 121 788.9 129.52 2.03 698–835
16 0.400 36.72 8.311 76 766.0 100.39 0.46 707–822
15 0.400 12.62 8.276 140 740.2 73.88 8.30 632–821
17 0.450 43.30 7.145 74 780.1 99.04 0.18 732–822
11 0.500 25.36 5.622 46 719.3 65.80 37 660–796
Note:l is the number of data points in the experiment.
* Heterogeneous alloys (see Figs. 3–6).
T
E
S
0
2
806
INORGANIC MATERIALS Vol. 43 No. 8 2007
VASIL’EV, LEGENDRE
(1)
+ 108.3456(x
Sb
– x
Sn
) + 146.9628(x
Sb
– x
Sn
)
2
– 105.224(x
Sb
– x
Sn
)
3
+ 78.3754(x
Sb
– x
Sn
)
4
] + x
In
x
Sb
x
Sn
[(13001 + 5.1593T)x
In
+ (–24547 27.8447T)x
Sb
+ (89047 – 94.0796T)x
Sn
],
where R = 8.31451 J/mol.
Figure 7 shows the surface of the excess Gibbs
energy of mixing according to Eq. (1) for liquid In–Sn–
Sb alloys at 900 K.
The data in Figs. 2–6 and Tables 2 and 3 can be used
to determine the phase transition temperatures in the
range 600–760 K for all of the alloys studied by emf
measurements (Table 4).
The enthalpies of mixing determined in this study
for In–Sn–Sb alloys using emf measurements can be
compared to the calorimetry data reported by Gather
et al. [9] (Fig. 8), who studied Sb
x
(In
0.2
Sb
0.8
)
1 – x
,
Sb
x
(In
0.4
Sb
0.6
)
1 – x
, Sb
x
(In
0.6
Sb
0.4
)
1 – x
, and Sb
x
(In
0.8
Sb
0.2
)
1 – x
alloys at 936 K. The uncertainty in their data was
+ (–119 – 0.3902T)(x
In
– x
Sn
)] + x
Sb
x
Sn
R[–681.4821 reported to be ±100 J [9], but in effect it might be higher
because of the vaporization of antimony, whose vapor
pressure at 936 K is 30 Pa. As seen in Fig. 8, the heat
effect in calorimetric studies is smaller in comparison
with the emf data. The difference is particularly large,
up to ~400 J, for the Sb
x
(In
0.4
Sb
0.6
)
1 – x
alloys. The
enthalpies of mixing were determined for 900 K using
Eq. (1).
Effect of exchange reactions on emf measure-
ments in the ternary system In–Sn–Sb. Consider a
spontaneous exchange reaction in a cell which contains
four indium-poor alloys (samples 6–9, x
In
= 0.05–0.11),
one indium-rich alloy (sample 11, x
In
= 0.50), and two
reference electrodes of pure indium. Note that the mea-
sured E(T, x
In
) values of alloys 6–9 and, to a lesser
extent, that of alloy 11, were affected by the exchange
reaction, so we used only the first E(T) data points,
which were less affected. The exchange reaction is
more active for alloys 7 and 8. Figures 9 and 10 illus-
trate the dynamics of the variation in emf for alloys 7
and 11.
The data points in Figs. 9 and 10 can be divided into
two groups. The difference in emf between these
Table 3. Coefficients in E(T) = a + bT + cT
2
best fit equations for heterogeneous In–Sn–Sb alloys (see Figs. 3–6) in different
temperature ranges
Sample no.x
In
x
Sn
x
Sb
a b c l ±2S
0
, mV T
min
–T
max
, K
1 0.333 0.333 0.333
451.21
–0.8911 0.56125 × 10
–3
30 0.05 630.8–713.8
2 0.300 0.299 0.401 708.34 –1.2979 0.66173 × 10
–3
40 0.05 631.7–721.2
3 0.250 0.250 0.500 187.20 –0.3394 0.46307 × 10
–3
19 0.09 631.7–678.3
4 0.333 0.167 0.499 248.05 0.3460 –0.66903 × 10
–3
66 0.06 686–756.8
4 0.333 0.167 0.499 341.99 –0.8254 0.84629 × 10
–3
29 0.05 598–676.1
5 0.167 0.333 0.500 –6238.38 19.1376 –0.01428 17 0.30 681–694
5 0.167 0.333 0.500 386.01 –0.9623 0.95214 71 0.05 599–679.9
6 0.100 0.400 0.500 841.90 –3.1817 3.27195 × 10
–3
29 0.09 631–678.3
6 0.100 0.400 0.500 425.75 –1.1234 1.11000 × 10
–3
55 0.07 599–658.1
9 0.111 0.444 0.444 318.00 –1.5101 1.95152 17 0.08 615.3–664.6
9 0.111 0.444 0.444 408.58 –1.0668 1.06280 × 10
–3
49 0.08 599–653.2
10 0.250 0.123 0.627 368.47 –0.8890 0.88258 × 10
–3
36 0.05 598–679.1
11 0.500 0.250 0.250 669.53 –2.0924 1.76323 × 10
–3
60 0.05 601–689
12 0.200 0.200 0.600 548.59 –0.8981 0.50065 × 10
–3
19 0.10 680.7–721.2
12 0.200 0.200 0.600 993.96 –2.7072 2.19960 × 10
–3
10 0.20 654.1–678.3
12 0.200 0.200 0.600 –1735.56 6.1867 –5.02090 × 10
–3
5 0.30 634–650.1
13 0.140 0.287 0.573 732.19 –2.1893 1.98290 × 10
–3
28 0.08 677–729.3
12 0.140 0.287 0.573 332.24 –0.7946 0.82168 × 10
–3
60 0.05 598.8–679.9
14 0.250 0.499 0.251 541.67 –1.1854 0.79800 × 10
–3
14 0.10 630–669.4
16 0.400 0.200 0.400 471.37 –0.9493 0.60366 × 10
–3
52 0.03 630–750.5
17 0.450 0.100 0.450 490.30 –0.9868 0.62096 × 10
–3
69 0.03 630–727.7
Note:l is the number of data points in the experiment.
INORGANIC MATERIALS Vol. 43 No. 8 2007
THERMODYNAMIC PROPERTIES OF ALLOYS AND PHASE EQUILIBRIA
807
groups is related to low-temperature studies of hetero-
geneous phases, which were not described in this paper.
The numbers at the curves specify the experiment dura-
tion (in days). It can be seen from Figs. 9 and 10 that the
exchange reaction depends on time and temperature.
Two main types of exchange reactions in cell (I) are
(a)
In pure( ) InSnSb samples 6–9( ),
a
In
1 a
In
'
1<=
In
Sn
(b)
Reactions (a) and (b) reduce the emf of alloys 6–9,
and reaction (b) increases the emf of alloy 11 relative to
the indium reference electrode. The rate of exchange
reaction (a) is higher than that of reaction (b). The
kinetics of exchange reactions in liquid alloys at 755 K
were analyzed elsewhere [1].
InSnSb sample 11( ) InSnSb samples 6–9( ).
a
In
''
a
In
'
.>
In
Sn
1
2
3
4
5
6
250
590 640
E, mV
T, K
90
230
210
190
170
150
130
110
690
740
790
840
890
240
590 630
E, mV
T, K
40
200
160
120
80
670
710
750
790
830
1
2
3
4
Fig. 3. Temperature-dependent emf data for InSb–SnSb alloys (Fig. 1, line 10): x
In
= (1, 2) 0.005 (samples 7 and 6, respectively),
(3, 4) 0.250 (samples 5 and 3, respectively), (5) 0.333 (sample 4), (6) 0.500 (liquid InSb).
Fig. 4. Temperature-dependent emf data for In
x
(Sn
0.5
Sb
0.5
)
1 – x
alloys (Fig. 1, line 11): x
In
= (1, 4) 0.005 (samples 8 and 11, respec-
tively), (2) 0.111 (sample 9), (3) 0.333 (sample 1).
808
INORGANIC MATERIALS Vol. 43 No. 8 2007
VASIL’EV, LEGENDRE
180
580 620
E, mV
T, K
40
660
700
740
780
820
1
2
3
4
160
140
120
100
80
60
580 620
E, mV
T, K
80
220
660
700
740
780
820
1
2
3
200
180
160
140
120
100
x
In
0
Sb
∆
mix
G
E
, J/mol
–1000
–2000
–3000
–4000
0.2
0.4
0.6
0.8
In
0.5
Sn
Fig. 5. Temperature-dependent emf data for Sb
x
(In
0.667
Sn
0.333
)
1 – x
alloys (Fig. 1, line 12): x
Sb
= (1) 0.250, (2) 0.400, (3) 0.449,
(4) 0.627 (samples 11, 16, 4, and 10, respectively).
Fig. 6. Temperature-dependent emf data for Sb
x
(In
0.333
Sn
0.667
)
1 – x
alloys (Fig. 1, line 13): x
Sb
= (1) 0.250, (2) 0.500, (3) 0.573
(samples 14, 5, and 13, respectively).
Fig. 7. Surface of the excess Gibbs energy of mixing for liquid In–Sn–Sb alloys at 900 K.
INORGANIC MATERIALS Vol. 43 No. 8 2007
THERMODYNAMIC PROPERTIES OF ALLOYS AND PHASE EQUILIBRIA
809
We detected no exchange reactions for the alloys
with x
In
> 0.1, even in experiments run for longer than
two months at temperatures of up to 822 K (exchange
reactions with the participation of In–Sn–Sb ternary
alloys will be considered below).
Correlations between thermodynamic functions.
To assess the effect of exchange reactions on the emf,
we evaluated partial functions of mixing for indium,
∆
mix
(In) and ∆
mix
(In), using the a and b coefficients
of the linear best fit equations in Table 2 (E(x
In
, T)).
We obtained the following equations of ∆
mix
H(In) as
a function of x
Sb
and ∆
mix
S(In) as a function of x
In
for
In–Sn–Sb alloys:
(2)
(3)
∆µ(In) = ∆
mix
(In) – T∆
mix
(In),(4)
(5)
H
S
∆
mix
H In( )
= x
Sb
–3267.3 21275x
Sb
– 15342 x
Sb
( )
2
+( ),
2S
0
500 J;±=
∆
mix
S In( ) –9.241 1 x
In
/4–( ) x
In
( ),ln=
2S
0
0.9 J;±=
H
S
∆µ In( ) = x
Sb
–3267.3 21275x
Sb
– 15342 x
Sb
( )
2
+( )
+ 9.241 1 x
In
/4–( ) x
In
( ) J.ln
It follows from the data in Table 5 that the discrep-
ancy between E
calc
and E
meas
is largest for alloys 7 and
8, with x
In
= 0.05. The emf values obtained for alloy 7
during the second day of measurements differ from the
value calculated using Eq. (1) by 6 mV. In subsequent
measurements, the E
calc
– E
meas
difference increased
(Table 5). The possible influence of the third compo-
nent (antimony) on the rate of the exchange reaction
must be taken into account in emf measurements with a
significant difference in indium concentration across
the electrochemical cell.
For the other In–Sn–Sb and In–Sb alloys, Eq. (5) is
accurate to 2S
0
= ±4.3 mV (±400 J), except for alloys 6–9,
the data for which were not used in deriving correlation
equation (5).
We also determined ∆
mix
(In) as a function of x
In
in
the In–Sb, In–Sn, and In–Sn–Sb systems and
∆
mix
(Sn) as a function of x
Sn
in the Sn–Sb system
(Fig. 11). ∆ is close to zero in the In–Sb, In–Sn, and
In–Sn–Sb systems for 0 ≤ x
In
≤ 1 and in the Sn–Sb sys-
tem for 0 ≤ x
Sn
≤ 1.
Using Eq. (5) and the emf data obtained for the
alloys at the beginning and at the end of the measure-
ments (83 days), we can evaluate the amount of metals
transferred across cell (I) in opposite directions. The
metal transfer increases the indium concentration in
indium-poor alloys by 3–4% and enriches the indium
S
S
S
i
G
Table 4. Phase transition temperatures of In–Sn–Sb alloys inferred from emf data
Sample no.ı
In
ı
Sn
ı
Sb
T
liq
, K T
1
, K T
2
, K T
3
, K T
4
, K T
5
, K T
6
, K T
7
, K
1 0.3335 0.3331 0.3334 719.7
2 0.2997 0.2995 0.4008 724.0
3 0.2502 0.2498 0.5000 731.6 682.3 625
4 0.3332 0.1669 0.4991 757.1 682.2
5 0.1666 0.3333 0.5001 694.8 680.3
6 0.1002 0.3996 0.5003 681.7 660.7
7 0.0503 0.4497 0.5000 689.6 635.1 8 0.0500 0.4751 0.4749 685.6 632.7
9 0.1112 0.4444 0.4444 664.4 654.5
10 0.2500 0.1231 0.6268 739.8 679.7 746
11 0.5000 0.2499 0.2501 690
12 0.1999 0.2001 0.6000 739.2 723.2 678.5 652
13 0.1401 0.2866 0.5733 732.0 678.5
14 0.2501 0.4994 0.2505 668.9
15 0.4001 0.3999 0.2000 660
16 0.4000 0.2000 0.4000 749.2
17 0.4501 0.0999 0.4500 773.2
Note:The thermal effects are due to the secondary crystallization of alloy 12 (T
1
, see Fig. 14), Sn
15
Sb
17
(T
2
, β), Sn
4
Sb
5
(T
3
, β), liquidus
dome (T
4
, line 7), SnSb peritectic (T
5
), Sn
9S
Sb
7
peritectic (T
6
, metastable state), and metastable transformation of alloy 10 (T
7
).
810
INORGANIC MATERIALS Vol. 43 No. 8 2007
VASIL’EV, LEGENDRE
reference electrodes and alloy 11 by the same amount
of Sn. In measurements in electrochemical cells, the
ideal emf difference between two indium electrodes
must be close to zero. An increase in this difference to
2 mV attests to some processes in the cell (oxidation,
exchange reaction, reaction between the alloy and elec-
trolyte, and others). For alloys 7 and 8, the emf differ-
ence between the indium reference electrodes in the
cell was 1 to 3 mV, whereas for the other alloys this dif-
ference was between 0 and 0.3 mV.
Comparison of the present results with the data
reported by Emi and Shimoji [10], who used emf mea-
surements in molten alkali chlorides (Table 6), indi-
cates that exchange reactions have a strong effect on
emf data. We evaluated E
calc
– E
meas
[10] using Eq. (5).
It can be seen from Table 6 that the E
calc
– E
meas
dif-
ference is rather large for x
In
≤ 0.3. The emf data do not
agree with our results for 7 alloys (out of the 21 stud-
ied). The possible sources of experimental errors are
analyzed in Table 7.
–2000
0 0.2
(a)
x
Sb
0.4
0.6
0.8
1.0
∆
mix
H, J/mol
–2500
0 0.2
(b)
x
Sb
0.4
0.6
0.8
1.0
–3000
(c)
∆
mix
H, J/mol
0
(d)
–400
–800
–1200
–1600
–500
–1000
–1500
–2000
–1000
–2000
–3000
0
–1000
–2000
Fig. 8. Enthalpies of mixing for liquid In–Sn–Sb alloys: (a) Sb
x
(In
0.2
Sn
0.8
)
1 – x
, (b) Sb
x
(In
0.4
Sn
0.6
)
1 – x
, (c) Sb
x
(In
0.6
Sn
0.4
)
1 – x
,
(d) Sb
x
(In
0.8
Sn
0.2
)
1 – x
; the points represent the calorimetry data from [9] and the lines represent the best fit to the present emf data
with Eq. (1).
640 680
E, mV
T, K
200
720
760
800
840
260
240
220
20
58
84
72
11
2
6
Fig. 9. Temperature-dependent emf data for alloy 7; the
numbers at the curves specify the experiment duration (in
days); the filled data points represent the most reliable data.
INORGANIC MATERIALS Vol. 43 No. 8 2007
THERMODYNAMIC PROPERTIES OF ALLOYS AND PHASE EQUILIBRIA
811
The presence of oxide compounds of indium in dif-
ferent valence states in the electrolyte leads not only to
oxidation of the electrodes but also to spontaneous
indium transfer according to the scheme
cathode (pure indium): (m – n)In + nIn
m+
mIn
n+
,
anode (indium–tin alloy): mIn
n+
(m − n)In + nIn
m+
,
where m > n.
40
0 0.2
∆
mix
S(In, Sn), , J/(K mol)
x(In, Sn)
0.4
0.6
0.8
1.0
–40
20
0
–20
1
2
3
4
I
II
III
∆
S
i
G
–
75
600 650
E, mV
T, K
55
700
750
800
70
65
60
72
2
6
84
58
22
20
Fig. 10. Temperature-dependent emf data for alloy 11; the
numbers at the curves specify the experiment duration (in
days); the filled data points represent the most reliable data.
Table 5. Measured and calculated emf values (mV) in the In–Sn–Sb system
Sample no.
x
In
x
Sn
x
Sb
T
min
, K T
max
, K
E
meas
(T
min
)
E
meas
(T
max
)
E
calc
(T
min
)
E
calc
(T
max
)
E
calc
– E
meas
(T
min
)
E
calc
– E
meas
(T
max
)
7
0.0503 0.4497 0.5 665 739 216.1 239.8 240.2 261.1 24.1 21.2
8 0.05 0.4751 0.4749 660 730 208.4 230.7 235.8 255.6 27.4 24.9
6 0.1002 0.3996 0.5003 675 796 191.9 219.8 197.2 223.2 5.3 3.4
9 0.1112 0.4444 0.4444 648 796 172.6 204.5 177.2 207.4 4.6 2.9
13 0.1401 0.2866 0.5733 702 814 186.7 207.0 189.4 209.8 2.7 2.8
5 0.1666 0.3333 0.5001 670 814 160.8 184.3 162.4 186.1 1.6 1.8
12 0.1999 0.2001 0.6 715 821 167 183.1 170.1 185.6 2.9 2.5
14 0.2501 0.4994 0.2505 640 822 102.1 125.3 99.5 122.1 –2.6 –3.2
3 0.2502 0.2498 0.5 672 821 133.6 151.7 135.8 154.3 2.2 2.6
10 0.25 0.1231 0.6268 719 835 158.8 172.4 158.2 172.6 –0.6 0.2
2 0.2997 0.2995 0.4008 672 821 109.9 126.0 110.5 126.4 0.6 0.4
1 0.3335 0.3331 0.3334 659 822 95.4 112.0 93.4 109.2 –2.0 –2.8
4 0.3332 0.1669 0.4991 698 835 121 133.8 119.4 132.6 –1.6 –1.2
16 0.4 0.2 0.4 707 822 95.5 105.0 94.5 103.6 –1.0 –1.4
15 0.4001 0.3999 0.2 632 821 64.9 80.6 64.2 79.1 –0.7 –1.5
17 0.4501 0.0999 0.45 732 822 95.6 102.0 95.1 101.2 –0.5 –0.8
11 0.5 0.2499 0.2501 660 796 62.4 70.1 58.1 66.0 –4.3 –4.1
Note:The most reliable calculated values are set in bold.
Fig. 11. (I) Partial entropies of mixing as functions of
(1−3) x
In
and (4) x
Sn
for (1) In–Sn–Sb, (2) In–Sb, (3) In–Sn,
and Sn–Sb alloys; (II) ∆ values in the same systems;
(III) ideal component.
S
i
G
812
INORGANIC MATERIALS Vol. 43 No. 8 2007
VASIL’EV, LEGENDRE
Note two points of key importance in designing liq-
uid-electrolyte cells for liquid A–B–C alloys (A = In,
Ga, Zn, …; B = Cd, Sn, Pb, …; C = Sb, Ag, Cu, …) in
which the A and B components are close in electro-
chemical potential (systems In–Sn–Sb, Ga–Sn–Sb, In–
Sn–Ag, Zn–In–Cu, and others):
1. Avoid using electrode materials one of which is
very poor and the other is very rich in A.
Table 6. Experimental data [10] for In–Sn–Sb alloys in comparison with correlation equation (5)
Series x
In
x
Sn
x
Sb
a b
∆ (In), J/K
∆ (In),
J
E, mV (770 K)
E, mV (900 K)
E
calc
, mV (770 K)
E
calc
, mV (900 K)
E
calc
– E
meas
, mV (900 K)
I 0.1 0.225 0.675 3.20 0.248 23.928 –309 194.16 226.4 240 267.9 41.5
0.2 0.20 0.60 25.90 0.169 16.306 –2499 156.03 178 178.1 191.7 13.7
0.3 0.175 0.525 39.10 0.113 10.903 –3773 126.11 140.8 137.7 151.5 10.7
0.4 0.15 0.45 32.50 0.094 9.070 –3136 104.88 117.1 106.2 116.5 –0.6
0.5 0.125 0.375 13.70 0.084 8.105 –1322 78.38 89.3 80 87.6 –1.7
0.6 0.10 0.30 7.10 0.063 6.079 –685 55.61 63.8 57.7 63.1 –0.7
0.7 0.075 0.225 3.10 0.045 4.342 –299 37.75 43.6 38.7 42.3 –1.3
II 0.1 0.45 0.45 –25 0.258 24.893 2412 173.66 207.2 211 238.9 31.7
0.2 0.40 0.40 12.7 0.168 16.209 –1225 142.06 163.9 151.4 170.4 6.5
0.3 0.35 0.35 22.9 0.114 10.999 –2210 110.68 125.5 114.2 128 2.5
0.4 0.30 0.30 14.5 0.092 8.877 –1399 85.34 97.3 86.5 96.8 –0.5
0.5 0.25 0.25 9.7 0.072 6.947 –936 66.04 74.5 64.5 72 –2.5
0.6 0.20 0.20 7.1 0.057 5.500 –685 50.99 58.4 46.3 51.7 –6.7
0.7 0.15 0.15 3.7 0.042 4.052 –357 36.04 41.5 31.2 34.9 –6.6
III 0.1 0.675 0.225 –51.4 0.271 26.147 4959 157.27 192.5 182.5 210.5 18
0.2 0.60 0.20 –26.1 0.20 19.297 2518 127.9 153.9 127.1 146.1 –7.8
0.3 0.525 0.175 1.8 0.135 13.025 –174 105.75 123.3 93.6 107.8 –15.5
0.4 0.45 0.15 –2.4 0.104 10.034 232 77.68 91.2 70.3 80.6 –10.6
0.5 0.375 0.125 –4.6 0.087 8.394 444 62.39 73.7 52.1 59.6 –14.1
0.6 0.30 0.1 2.2 0.059 5.693 –212 47.63 55.3 37.5 42.9 –12.4
0.7 0.225 0.075 4.3 0.037 3.570 –415 32.79 37.6 25.4 29.1 –8.5
Note:The most reliable experimental data from [10] are set in bold.
S
H
Table 7. Possible sources of experimental errors in [10]
Report This work [10]
Cell Isothermal Nonisothermal
Preparation of the elec-
trolyte and the way it was
introduced into the cell
Transparent electrolyte, treated with dry
HCl and sealed in ampules. Introduction
into the cell and evacuation take 5–10 s.
The preparation of the electrolyte and the way it was introduced into the cell are not described.
InCl synthesis In the cell; reaction of indium with the hy-
drogen chloride absorbed by the electrolyte:
2In + 2HCl(g) = 2InCl + H
2
.
Introduction of 5 wt % InCl into the electrolyte. InCl reacts with humid air according to the scheme InCl + O
2
+ H
2
O In(OH)Cl
2
+ In(OH)
2
Cl + In(OH)Cl + InOCl + ….
Atmosphere Turbomolecular pump.
Evacuation to 0.01 Pa.
Fore pump (100 Pa).
The purity of the argon is not specified.
INORGANIC MATERIALS Vol. 43 No. 8 2007
THERMODYNAMIC PROPERTIES OF ALLOYS AND PHASE EQUILIBRIA
813
2. In studies of alloys poor in A, the reference elec-
trode must be from an A–B alloy close in the activity of
the A component to A–B–C alloys.
DTA data for the In–Sn–Sb system. A DTA study
of the In–Sn–Sb system was reported in [7]. Alloys
(123) were prepared from high-purity (99.9999%) ele-
ments. Weighed mixtures (0.2–0.3 g) were melted in
silica ampules sealed off under a vacuum of 1 Pa. After
holding at 910 K, the alloys were annealed for 15 days
at temperatures from 370 to 670 K, depending on com-
position. Measurements were performed with a differ-
ential scanning calorimeter (SETARAM DSC 121).
Sb
In Sn
InSb
[Sb]
InSb + [β-SnSb]
[Sb] + [β-SnSb]
InSb + [Sb]
[In]
[Sn]
[β-SnSb] + [Sn]
InSb + [β-SnSb] + [Sn]
InSb + [Sn]
InSb + [β-InSn] + [γ-InSn] InSb + [β-InSn]
[In] + InSb
[β-InSn] + [In] + InSb
[In] + [β-InSn]
[β-InSn] [γ-InSn]
[Sn] + [γ-InSn]
[Sn] + InSb + [γ-InSn]
InSb + [γ-InSn]
900
800
700
600
T, K
1
2
3
6
7
8
5
13
9
10
11
12
14
15
16
17
18
19
597
623
680
600
4
0 0.2 0.4 0.6 0.8 0.9333
x
Sn
EMF
DTA
InSb + [β-SnSb] + [Sb]
634
Fig. 12. 298-K section of the In–Sn–Sb phase diagram.
Fig. 13. In
0.066
Sb
0.933
–In
0.066
Sn
0.933
phase diagram (line 1) inferred from emf and DTA data [7]: (1) L, (2) [Sb] + L, (3) [Sb] +
InSb + L, (4) [Sb] + InSb, (5) [β-SnSb] + [Sb] + L, (6) [Sb] + [β-SnSb] + InSb, (7) [Sb] + [Sn
4
Sb
5
] + InSb, (8) [Sb] + [Sn
3
Sb
4
] +
InSb, (9) [Sn
4
Sb
5
] + [β-SnSb] + InSb, (10) [Sn
3
Sb
4
] + InSb, (11) [Sn
3
Sb
4
] + [β-SnSb] + InSb, (12) [β-SnSb] + InSb, (13) [β-SnSb] +
InSb + L, (14) [SnSb] + InSb + L, (15) [Sn
17
Sb
15
] + InSb + L, (16) [SnSb] + [Sn
17
Sb
15
] + InSb, (17) [β-SnSb] + [SnSb] + InSb,
(18) [Sn
9
Sb
7
] + [Sn
17
Sb
15
] + InSb, (19) [Sn
17
Sb
15
] + InSb + L.
814
INORGANIC MATERIALS Vol. 43 No. 8 2007
VASIL’EV, LEGENDRE
Consider the 300-K section of the In–Sn–Sb phase
diagram (Fig. 12), which has a relatively simple phase
compatibility diagram. In the system, no ternary com-
pounds have been identified. In this system, the [β-
SnSb–InSb triangle is of special interest ([β-SnSb] rep-
resents a series of homologous phases separated by nar-
row two-phase regions). Each of these phases may form
an In
z
Sn
x
Sb
y
solid solution with indium, whose mole
fraction is within 0.05. Under nonequilibrium conditions,
the [β-SnSb] phase fields merge into the β-In
z
Sn
x
Sb
y
solid-solution region.
Figures 13–16 show four T–x sections obtained
using earlier data [6].
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
x
Sb
900
800
700
600
500
400
EMF
DTA
T, K
1
1'
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
26
252423
22
17
18
19
20
723
634
623
21
519
488
653
680
600
0 0.1 0.2 0.3 0.5 0.6 0.7 0.8
x
Sb
900
800
700
600
500
400
EMF
DTA
T, K
252423
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
26
22
27
29
28
21
17
18
19
20
680
653
600
634
597
519
488
392
597
Fig. 14. In
0.5
Sn
0.5
–Sb phase diagram (line 9) inferred from emf and DTA data [7]: (1) L, (1') L' + L'' (immiscibility region), (2) [Sb] + L,
(3) [Sb], (4) [Sb] + InSb, (5) [Sb] + InSb + L, (6) InSb + L, (7) β-SnSb + InSb + [Sb], (8) [Sb] + [Sn
4
Sb
5
] + InSb, (9) δ + InSb +
[Sb], (10) β-SnSb + InSb + L, (11) [SnSb] + InSb + L, (12) [Sn
17
Sb
15
] + InSb + L, (13) [Sn
9
Sb
7
] + InSb + L, (14) [Sn
9
Sb
7
] +
[Sn
17
Sb
15
] + InSb, (15) [Sn
17
Sb
15
] + [SnSb] + InSb, (16) β-SnSb + [SnSb] + InSb, (17) β-SnSb + InSb, (18) β-SnSb + [Sn
4
Sb
5
] +
InSb, (19) δ + β-SnSb + InSb, (20) δ + InSb, (21) InSb + [Sn] + L, (22) InSb + [γ-InSn] + L, (23) InSb + [γ-InSn], (24) InSb +
[γ-InSn] + [Sn], (25) InSb + [Sn], (26) InSb + [Sn
17
Sb
15
] + [Sn]; δ is an Sn
3
Sb
4
-based solid solution containing 56 to 57.5 at % Sb.
Fig. 15. Sn
0.2
Sb
0.8
–Sn
0.2
In
0.8
phase diagram (line 8) inferred from emf and DTA data [7]: (1) L, (2) L + [Sb], (3) L + InSb, (4) L +
InSb + [Sb], (5) L + [Sb] + [β-SnSb], (6) [Sb] + β-SnSb, (7) β-SnSb + [Sb] + InSb, (8) Sn
4
Sb
5
+ [Sb] + InSb, (9) δ + [Sb] + InSb,
(10) β-SnSb + InSb + L and δ + InSb + L, (11) [SnSb] + InSb + L, (12) [Sn
17
Sb
15
] + InSb + L, (13) [Sn
9
Sb
7
] + InSb + L,
(14) [Sn
9
Sb
7
] + [Sn
17
Sb
15
] + InSb, (15) [Sn
17
Sb
15
] + [SnSb] + InSb, (16) β-SnSb + [SnSb] + InSb, (17) β-SnSb + InSb, (18) β-
SnSb + [Sn
4
Sb
5
] + InSb, (19) δ + β-SnSb + InSb, (20) δ + InSb, (21) InSb + [Sn] + L, (22) InSb + [γ-InSn] + L, (23) InSb + [γ-
InSn], (24) InSb + [γ-InSn] + [Sn], (25) InSb + [Sn], (26) InSb + [γ-InSn] + L, (27) InSb + [γ-InSn] + [β-InSn], (28) InSb + [β-
InSn], (29) InSb + [β-InSn] + L; δ is an Sn
3
Sb
4
-based solid solution containing 56 to 57.5 at % Sb.
INORGANIC MATERIALS Vol. 43 No. 8 2007
THERMODYNAMIC PROPERTIES OF ALLOYS AND PHASE EQUILIBRIA
815
CONCLUSIONS
The emf of 17 In–Sn–Sb ternary alloys was mea-
sured in concentration cell (I) at temperatures from 600
to 830 K, and the partial thermodynamic functions
∆µ(In), ∆ (In), and ∆ (In) of the alloys were deter-
mined for different phase fields.
The results were used to derive an analytical expres-
sion for the Gibbs energy of mixing of liquid In–Sn–Sb
alloys.
We determined ∆ (In) as a function of x
In
and
∆ (Sn) as a function of x
Sn
for liquid In–Sb, In–Sn, In–
Sn–Sb, and Sn–Sb systems. The results can be repre-
sented by a single equation. In these systems, ∆ is
close to zero (within the present experimental uncer-
tainty).
In the composition ranges studied, the partial and
integral enthalpies of mixing in the binary system In–
Sb coincide with those in the ternary system In–Sn–Sb.
Therefore, the Sn in the ternary system In–Sn–Sb acts
as a neutral diluent.
We considered different types of exchange reactions
in cell (I) and the possible ways of reducing their influ-
ence on emf results.
H
S
S
S
S
i
G
The present emf data were used to refine a number
of T–x sections of the In–Sn–Sb phase diagram.
Thermodynamically stable β-SnSb-based solid
solutions on the pseudobinary join β-SnSb (53.12 at %
Sb)–InSb appear potentially attractive for the use in IR
detectors.
ACKNOWLEDGMENTS
We are grateful to M. Sghaier (Laboratoire E.A.
401, Université de Paris XI, Ch tenay-Malabris,
France) and N. David (UMR CNRS 7555, Lab. de
Chimie et du Solide Minéral, Group Thermody-
namique Métallurgique, Université Henri Poincaré,
Nancy I, France) for their assistance with this study.
REFERENCES
1.Vassiliev, V., Feutelais, Y., Sghaier, M., and Leg-
endre, B., Thermodynamic Investigation in In–Sb, Sn–
Sb, and In–Sn–Sb Liquid Systems, J. Alloys Compd.,
2001, vol. 314, pp. 197–205.
2.Saidov, A.S., Ruzakov, A.Sh., and Saparov, D.V., Liquid
Phase Epitaxy of (Sn
2
)
1 – x
(InSb)
x
Solid Solutions,
Pis’ma Zh. Tekh. Fiz., 2002, vol. 28, no. 22, pp. 7–10.
3.Wachtler, M., Berenhard, J.O., and Winter, H., Anodic
Materials for Rechargeable Li-Batteries, J. Power
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endre, B., Liquid State Electrochemical Study of the
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7.Legendre, B., Dichi, E., and Vassiliev, V., The Phase Dia-
gram of the In–Sb–Sn System, Z. Metallkd., 2001,
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8.Predel, B. and Schwermann, W., Constitution and Ther-
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9.Gather, B., Schröter, P., and Blachnic, R., Mischun-
genthalpien in Ternären Systemen: IV. Das System
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no. 8, pp. 523–527.
10.Emi, T. and Shimoji, M., Thermodynamic Properties of
Indium–Tin–Antimony Liquid Alloys, Ber. Bunsen-Ges.
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11.Lühberg, K., Über das System Zinn–Antimon–Indium,
Metallwiss. Tech., 1968, no. 8, pp. 777–784.
a
^
Fig. 16. SnSb–InSb phase diagram (line 10): (1) L, (2) L' +
L'', (3) [Sb] + L, (4) [SnSb
2
] + L, (5) [Sn
7
Sb
11
] + L,
(6) [InSb] + L, (7) β-SnSb + L, (8) β-SnSb + [InSb] + L,
(9) [SnSb] + [InSb], (10) [SnSb]; 623 K is the temperature
of a metastable equilibrium.
800
700
600
T, K
0.1 0.2 0.3 0.4SnSb InSb
x
In
1
2
3
4
5
6
7
8
9
10
680
634
623
[11]
EMF
DTA
This
work
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