Structure and electrical properties of liquid Sn, Sn0.962Ag 0.038, Sn0.987Cu0.013, and Sn 0.949Ag0.038Cu0.013

Article abstract of DOI:10.1007/s10789-008-2008-4

We have studied the structure, electrical conductivity, and thermopower of liquid Sn, Sn_0.962Ag_0.038, Sn_0.987Cu _0.013, and Sn_0.949Ag_0.038Cu_0.013 alloys, which are used as lead-fr

Full text of DOI:10.1007/s10789-008-2008-4

ISSN 0020-1685, Inorganic Materials, 2008, Vol. 44, No. 2, pp. 129–133. © Pleiades Publishing, Ltd., 2008.
Original Russian Text © S.I. Mudry, V.M. Sklyarchuk, Yu.O. Plevachuk, I.I. Shtablavyi, 2008, published in Neorganicheskie Materialy, 2008, Vol. 44, No. 2, pp. 171–175.
Structure and Electrical Properties of Liquid Sn, Sn Ag ,
0.962
0.038
Sn Cu , and Sn Ag Cu
0
.987
0.013
0.949
0.038
0.013
S. I. Mudry, V. M. Sklyarchuk, Yu. O. Plevachuk, and I. I. Shtablavyi
Franko National University, ul. Kirila i Mefodiya 8, Lviv, 79005 Ukraine
e-mail: sihor@ukr.net
Received November 9, 2006; in final form, April 4, 2007
Abstract—We have studied the structure, electrical conductivity, and thermopower of liquid Sn, Sn0.962Ag0.038
,
Sn0.987Cu0.013, and Sn0.949Ag0.038Cu0.013 alloys, which are used as lead-free solders. Diffraction data have been
used to develop structural models of the melts. The conductivity and thermopower data have been interpreted
in terms of the proposed structural models and resonance s–d scattering.
DOI: 10.1134/S0020168508020088
INTRODUCTION
components of the alloys. The structure factors were
also used to calculate radial distribution functions, from
which we inferred the most probable interatomic dis-
tances and coordination numbers.
Many alloys have been proposed to date as lead-free
alloys [1–3]. The principal properties determining their
performance parameters are electrical resistivity, ther-
mopower, surface tension, corrosion resistance, and
mechanical strength. Extensive data on these properties
of the alloys in question are presented in [4, 5]. At the
same time, there has been little work on their structure.
The relationships between their structure and physical
properties are unexplored.
Tin-based eutectic alloys are the most attractive
lead-free low-melting solders from the viewpoint of the
working temperature range. The composition of most
of such alloys is dominated by Sn, while solutes change
the solidification temperature and performance charac-
teristics.
Electrical measurements were carried out up to
20 K at an excess argon pressure. The experimental
7
technique and setup were described in detail elsewhere
8]. Note that small amounts of impurities may have a
[
rather weak effect on the conductivity of the melt,
which can only be assessed at a high measurement
accuracy.
The uncertainty in conventional conductivity mea-
surements is 2% or slightly smaller. This accuracy may
however be insufficient for our purposes. By carefully
calibrating each measuring cell and collecting a large
data set, we were able to reduce the uncertainty in con-
ductivity to a level no higher than 0.3–0.4%, which
allowed us to obtain reliable experimental data.
In this paper, we report the structure and electrical
properties of liquid Sn0.962Ag0.038, Sn0.987Cu0.013, and
Sn0.949Ag0.038Cu0.013 alloys.
RESULTS AND DISCUSSION
Structural models of the melts. The XRD patterns
of liquid Sn, Sn0.962Ag0.038, Sn0.987Cu0.013, and
Sn0.949Ag0.038Cu0.013 were obtained near the correspond-
ing liquidus temperatures and also at temperatures 100
and 200 K above the melting points of the alloys. Since
the Sn concentration far exceeded the concentrations of
the other elements in the melts, these can be considered
dilute solutions, and the atomic distribution can be
assumed to be governed by the Sn structure. In earlier
studies of the short-range order in liquid Sn, its struc-
ture was concluded to be microinhomogeneous [4, 5].
A noteworthy feature of the present data (Figs. 1–3) is
EXPERIMENTAL
Samples for this investigation were prepared from
9.999%-pure tin, silver, and copper. X-ray diffraction
9
(
XRD) measurements were performed on a high-tem-
perature diffractometer intended for studies of liquids
Bragg–Brentano geometry [6], diffracted-beam graph-
ite monochromator, scintillation counter). The samples
were mounted in a chamber filled with high-purity
helium. Angle-dependent scattered x-ray intensity data
were corrected for the sample absorption and incoher-
ent scattering.
(
After conversion to electronic units, the intensity the weak shoulder on the large-k side of the first peak,
curves were used to calculate structure factors [7]. which indicates that the melt inherits some structural
These were analyzed to determine peak positions, features of the crystalline alloy. This behavior of the
which were then compared to those for the constituent structure factor is typical of liquid semimetals (Bi, Ga,
1
29

1
30
MUDRY et al.
3
2
1
0
1
2
1
2
(a)
(
a)
2
1
0
1
2
(
b)
1
2
(
b)
2
1
2
1
0
0
2
1
2
1
2
(c)
(
c)
2
1
0
1
0
0
1 2 3 4 5 6 7 8
0
1 2 3 4 5 6 7
8
k, Å–1
k, Å–1
Fig. 1. Structure factors of liquid (1) Sn and (2)
Sn0.962Ag0.038 at (a) 505, (b) 605, and (c) 705 K.
Fig. 2. Structure factors of liquid (1) Sn and
(2) Sn0.987Cu0.013 at (a) 505, (b) 605, and (c) 705 K.
Sb) and is better defined in semiconductors (Si, Ge) [4, 5]. 2.87 Å, coordination number ZAg = 11.3), we conclude
Our experimental data demonstrate that the shoulder that the formation of an atomic solution would increase
persists even if the structure factor of the solute has a the coordination number, in contrast to what we
symmetrical first peak. The effect of silver on the shape observed. In light of this, it is reasonable to assume that
of the structure factor becomes stronger with increasing silver atoms dissolve between clusters in the structure
temperature, as evidenced by the variation in the shape of liquid Sn. This dissolution mechanism stabilizes
of the shoulder, which is less sensitive to temperature in microinhomogeneities in the Sn structure, which shows
comparison with the structure factor of liquid undoped up in the temperature dependences of r and Z. At the
1
Sn. On the other hand, in the presence of Ag, the height same time, the dissolved silver atoms may also be
of the first peak decreases less rapidly with increasing assumed to be clustered, thereby contributing to the
temperature in comparison with liquid Sn. The shape of microinhomogeneity of the melt. The first peak of sil-
the atomic pair distribution functions and the parame- ver influences the shape of the shoulder in the structure
ters evaluated from them are temperature-dependent factor of the melt.
(
table). In particular, the nearest neighbor distance in
The Sn0.987Cu0.013 eutectic alloy was investigated in
the same temperature range as above. The addition of
copper has little or no effect on the structure factor of
Sn. The main structural parameters evaluated from the
structure factor and radial distribution function (table)
vary insignificantly. The structure factor is more sensi-
tive to temperature (Fig. 2). In particular, the addition of
liquid Sn0.962Ag0.038 increases with temperature, while
that in liquid Sn decreases in the same temperature
range. The addition of Ag reduces the average coordi-
nation number, but at a slower rate in comparison with
pure Sn. Taking into account the main structural param-
Ag
eters of Ag (average nearest neighbor distance r1
=
INORGANIC MATERIALS Vol. 44 No. 2 2008

STRUCTURE AND ELECTRICAL PROPERTIES OF LIQUID
131
copper markedly reduces the height of the first peak.
1
2
Analysis of these results suggests that the dissolved
copper atoms are clustered in vacancy zones in the
structure of liquid Sn. As the temperature is raised, the
clusters dissociate, and the copper atoms tend to be
incorporated into structural groups of Sn atoms,
increasing the difference between the structure factors
of Sn and Cu-doped Sn above the melting point.
(
a)
2
1
0
The assumed mechanism of copper dissolution in
tin correlates well with experimental thermodynamic
data, which attest to a negative enthalpy of mixing and
the existence of compositionally ordered phases in the
equilibrium phase diagram of this system [9, 10].
Interesting data were obtained for tin codoped with
silver and copper. As seen in Fig. 3, the structure factors
in this system vary more significantly. In particular,
doping changes the shape of the shoulder and reduces
the height of the first peak in the structure factor. The
difference is more pronounced at higher temperatures
1
2
(b)
2
1
0
2
(
T = 705 K), which also refers to the second and third
1
2
peaks. This shows up in the structural parameters
extracted from radial distribution functions (table).
Analysis of the structural data indicates that codoping
of tin with copper and silver has a stronger effect on the
short-range order in the melt.
(c)
1
0
Thus, the assumed presence of copper in the form of
isolated atoms and clusters reduces the topological
microinhomogeneity of the melt but increases its chem-
ical microinhomogeneity, which must show up in the
physical properties of the melt.
0 1 2 3 4 5 6 7 8
k, Å–1
Electrical properties. The electrical conductivity
σ) data are presented in Fig. 4. The conductivity of
(
Fig. 3. Structure factors of liquid (1) Sn and
2) Sn0.949Ag0.038Cu0.013 at (a) 505, (b) 605, and (c) 705 K.
(
pure liquid Sn is ~21000 S/cm and decreases linearly
with increasing temperature over the entire temperature
range studied. Cu doping increases the conductivity
only slightly, by ~200 S/cm, while Ag doping leads to
a marked increase in σ. Codoping with Cu and Ag
reduces σ. The conductivity of the codoped material
decreases nonlinearly with increasing temperature over
the entire range studied.
Thermopower α, a function of the carrier effective
mass, was expected to be more sensitive to structural
microinhomogeneities (Fig. 5). The temperature
dependence of α for pure Sn is featureless. The α of liq-
uid Sn is about –1 µV/K and varies little with tempera-
ture. The thermopower of the Sn–Cu eutectic is at a
level of –7 µV/K and is also a very weak function of
temperature. The α of the Sn–Ag eutectic at its melting
point is –5 µV/K and passes through a maximum.
thereby symmetrizing the arrangement of scattering
centers. This leads to an increase in carrier mobility
and, accordingly, in conductivity and results in a small
magnitude of thermopower. With increasing Cu and Ag
concentration (Sn–Cu–Ag eutectic), Sn vacancies dis-
appear, and the solute atoms undergo short-range order-
ing on their own, thereby distorting the symmetry of the
melt. As a result, the conductivity drops, and the ther-
mopower rises in magnitude.
In the free-electron approximation [11], the conduc-
tivity of the alloys is given by
2
n e
ꢀk
e
σ = ---------L,
(1)
f
The curve for the Sn–Cu–Ag eutectic differs mark-
edly from those above. After melting, α is –20 µV/K;
with increasing temperature, it decreases nonlinearly in
magnitude, to –12 µV/K.
where L is the electron mean free path.
Resonance s–d scattering can be thought of as a
change in mean free path [12, 13]:
Taking into account the proposed structural models
of the melts studied here and the conductivity and ther-
mopower data, we believe that small Cu and Ag addi-
tions dissolve via incorporation into the loose structure
1
L
1
L
0
C
-
- = --- -- + ------------- -- ,
(2)
v τ
F s–d
where L is the electron mean free path in undoped
0
of Sn, densifying the short-range order in the melt and Sn, v
is the Fermi velocity, τs–d is the relaxation time
F
INORGANIC MATERIALS Vol. 44 No. 2 2008

1
32
MUDRY et al.
Structural parameters of liquid Sn, Sn0.962Ag0.038, Sn0.987Cu0.013, and Sn0.949Ag0.038Cu0.013
k1, Å–1
k2, Å–1
k2/k1
S(k1)
r1, Å
r2, Å
r2/r1
Z
T, K
Sn
5
6
7
05
05
05
2.23
2.23
2.22
4.35
4.34
4.38
1.95
1.95
1.97
2.52
2.39
1.98
3.22
3.19
3.18
6.19
6.14
6.13
1.92
1.92
1.93
9.67
9.37
9.04
Sn0.962Ag0.038
5
6
7
05
05
05
2.23
2.25
2.26
4.35
4.35
4.40
1.95
1.93
1.95
2.54
3.18
3.19
3.21
6.10
6.15
6.14
1.92
1.93
1.91
9.38
9.21
9.23
2.40
2.23
Sn0.987Cu0.013
5
6
7
05
05
05
2.23
2.25
2.23
4.29
4.30
4.36
1.92
1.91
1.95
2.49
3.20
3.24
3.17
6.25
6.11
6.13
1.95
1.89
1.93
9.95
10.01
8.87
2.11
1.93
Sn0.949Ag0.038Cu0.013
5
6
7
05
05
05
2.23
2.23
2.26
4.31
4.32
4.34
1.93
1.94
1.92
2.65
2.26
1.75
3.19
3.18
3.19
6.16
6.03
5.98
1.93
1.90
1.87
9.91
10.34
9.07
of s–d resonance scattering, and ë is the solute con- shielding of impurity centers by free carriers. There-
centration. fore,
At low C (approaching zero), Eq. (2) takes the form
0
e
n = n ± ∆n .
(4)
e
e
L
0
L = ------------------------.
(3) Substituting Eqs. (3) and (4) in (1), we obtain
CL
0
1
+ ---------------
2
v τ
L
0
F
s–d
0
e
e
ꢀ
σ = (n ± ∆n )-------------------------------.
(5)
e
k
CL
0
f
The electron density can change both in response to
changes in carrier concentration and owing to the
1 + ---------------
v τ
F
s–d
0
2
2
1
1
2000
0000
8000
6000
–10
1
2
3
4
1
2
3
4
–
20
5
50
600
650
700
T, K
5
00
550
600
650
700
750
T, K
Fig. 4. Conductivity as a function of temperature for (1) Sn,
2) Sn0.962Ag0.038 (3) Sn0.987Cu0.013 and (4)
Sn0.949Ag0.038Cu0.013
Fig. 5. Thermopower as a function of temperature for
(1) Sn, (2) Sn0.962Ag0.038 (3) Sn0.987Cu0.013 and
(4) Sn0.949Ag0.038Cu0.013
(
,
,
,
,
.
.
INORGANIC MATERIALS Vol. 44 No. 2 2008

STRUCTURE AND ELECTRICAL PROPERTIES OF LIQUID
133
It is clear from Eq. (3) that the electron mean free path
can only decrease. Therefore, an increase in conductiv-
ity on doping can only be accounted for by an increase
in electron density. Moreover, the electron density must
rise more rapidly than the mean free path decreases. A
reduction in conductivity on doping can be understood
in terms of changes in mean free path.
Solders, Colorado: NIST & Colorado School of Mines,
002, p. 77.
4. Wilson, J.W., Structure of Liquid Metals and Alloys,
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Melts), Moscow: Nauka, 1980.
2
6
7
8
9
. Kaplow, R. and Averbach, B.L., X-ray Diffractometer
for the Study of Liquid Structures, Rev. Sci. Instrum.,
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1
963, vol. 34, pp. 579–581.
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We studied the structure, electrical conductivity, and
thermopower of liquid Sn, Sn0.962Ag0.038, Sn0.987Cu0.013
,
and Sn0.949Ag0.038Cu0.013
.
The proposed structural models adequately describe
the structure of the melts studied. The scattering mech-
anism for charge carriers depends not only on the short-
range order in the solute distribution but also on the
clustering behavior of the solute.
1
1
0. Binary Alloy Phase Diagrams, Massalski, Th.B., Ed.,
Metals Park: Am. Soc. for Metals, 1998.
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INORGANIC MATERIALS Vol. 44 No. 2 2008