Journal of Materials Science: Materials in Electronics

, Volume 22, Issue 6, pp 631–638

Electrical conductivity and viscosity of liquid Sn–Sb–Cu alloys

Authors

    • Department of Metal PhysicsIvan Franko National University
  • V. Sklyarchuk
    • Department of Metal PhysicsIvan Franko National University
  • A. Yakymovych
    • Department of Metal PhysicsIvan Franko National University
  • P. Svec
    • Slovak Academy of SciencesInstitute of Physics
  • D. Janickovic
    • Slovak Academy of SciencesInstitute of Physics
  • E. Illekova
    • Slovak Academy of SciencesInstitute of Physics
Article

DOI: 10.1007/s10854-010-0188-6

Cite this article as:
Plevachuk, Y., Sklyarchuk, V., Yakymovych, A. et al. J Mater Sci: Mater Electron (2011) 22: 631. doi:10.1007/s10854-010-0188-6
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Abstract

Tin-antimony-copper alloys are under intense consideration as favourable lead-free solders for consumer electronics and telecommunications. The electrical conductivity and viscosity studies were carried out in a wide temperature range above the liquidus. A melting-solidification region was investigated by Differential Scanning Calorimetry (DSC). The scaling relations have been proposed. A comparison with data available in literature is given.

1 Introduction

Strict performance requirements exist for high-temperature solder alloys (melting temperatures exceed 500 K) used in the electronics industry for advanced packing technologies [1]. In the multi-chip modeling technology, there is a need in a family of lead-free solder alloys with different melting temperature (the upper limit is around 620 K), which can substitute the toxic high-temperature Pb-Sn solders (>85 wt% Pb). The Sn-based alloys with Sb can be used for this purpose due to the improvement of wetting properties, thermal fatigue resistance and creep strength [2]. Tin-Antimony alloys with different melting points are often used in the step soldering technology, where soldering is applied more than once during the manufacturing. The solders used at the early steps should be characterized by higher melting temperatures in order to prevent melting of the existing solder joints during the subsequent soldering [3].

In general, the solder alloy must meet the expected levels of reliability, as well as electrical and mechanical performance [3]. Since the properties of the binary Pb-free solders cannot fully meet the requirements for applications in electronic packaging, additional alloying elements were added to improve the performance of these alloys. Small quantities of copper are often added to the solder alloys for improvement of their electrical characteristics, changing of the melting temperature, and prevention of the whisker formation. Also, Cu is introduced into the solder due to the dissolution of Cu substrate. Therefore, it is important to know the effect of Cu on the solderability and thermophysical properties, when selecting a particular Sn-Sb-Cu solder alloy.

The solidification process of a liquid alloy has a profound impact on the structure and properties of the solid material. Therefore, the knowledge of the physical properties of the molten alloys prior to solidification becomes very important for the development of solders with predetermined characteristics. Among all physical properties, the structure-sensitive characteristics of the liquid phase play a prominent role. Reliable information about the structural heterogeneity of the melt can also be obtained from studies considering the temperature dependence of the electrical conductivity and the viscosity. Solder joints in the electronic devices are electrical as well as structural connections. They should provide the lowest possible electrical resistance between mounted electronic components and the substrate. At the same time, the values of the thermoelectric power, which usually appear at the points of electric junctions between different materials, should be low.

The solder’s fluidity influences its wetting capability; hence knowledge of the viscosity is important. Particularly, the knowledge of the viscosity is of particular importance for considering the relationship between melt convection and solidification.

Experimental data on these properties are scarce in the literature and rather contradictory [46]. The discrepancy between the reported results, different investigated temperature ranges, and sometimes a very limited number of measuring points require new precise measurements in order to obtain reliable data on the temperature and concentration dependences of the above mentioned thermophysical properties over a wide temperature range. Finally, increasing influence of the computational modeling in technological processes generates a higher demand for accurate values of the physical properties of applied materials. Experimental studies of various systems in liquid state showed that at the temperatures much higher than the melting temperature they exhibit large concentration inhomogeneities, which are not incorporated in the phase diagrams [7]. It is a question, how the physical properties of the molten alloys vary with the temperature? Therefore, investigations of the electrical conductivity, and shear viscosity of liquid tin-rich binary Sn–Sb, and ternary Sn–Sb–Cu alloys have been performed in a wide temperature range in the present work.

2 Experimental details

2.1 Sample preparation

One of the targets of this work is to study and compare properties of selected alloys prepared both in the traditional bulk form and in the foil form by the rapid solidification technique. The shape of thin foil or ribbon is convenient for joining of large areas with well-defined joint dimensions, perspectively for joining the metallic matrix composites. The samples in the form of metallic ribbon (6 mm wide and 20–30 μm thick) were prepared by the method of planar flow casting with a quenching rate of 106 Ks−1 in air.

2.2 Electrical conductivity measurements

Two home-made experimental facilities based on the 4-point method, were used for electrical conductivity, σ(T), measurements.

The experiments in the liquid state were performed in an argon atmosphere. Graphite electrodes for current and potential measurements were placed in the wall of the vertical cylindrical boron nitride ceramic measuring cell along its vertical axis. The potential electrodes were provided with thermocouples for temperature measurements. Single thermoelectrodes of these thermocouples were used for electrical conductivity determination. The melt temperature was determined by WRe-5/20 thermocouples in close contact with the liquid. For further details of this method and its experimental realization we refer to [8]. Pure Sn, Sb and Cu (all 99.99) were melted and evacuated in sealed quartz ampoules at 10–15 Pa. Each sample was inserted into the cell directly inside a high-pressure vessel. Thus, the actual sample composition was accurate within a tolerance of 0.02 wt%. The resultant error of the electrical conductivity measurements is about 2%.

In the course of the conductivity measurements of the solid ribbons, the main difficulty was connected with determination of the ribbon cross-section, which was not uniform. For this reason, a density of the solid sample has been determined by using the Archimedes principle at room temperature. Knowing the length, width and mass of the ribbon sample, the volume and later the cross-section were determined. Finally, temperature dependence of the absolute electrical conductivity was found. Each composition was measured several times in order to get reliable data.

2.3 Viscosity measurements

The measurements of the melts viscosity were carried out using a computer-controlled oscillating-cup viscosimeter [9]. Using the Roscoe equation [10], the dynamic viscosity, η(T), has been calculated from the corresponding logarithmic decrement and the period of oscillations. The experiments were performed in a argon atmosphere under a negligible excess pressure of about 0.02–0.03 MPa. Each sample of about 30 g was weighed before and after the measurements, and no loss of mass was observed. Cylindrical graphite crucibles with internal diameter of 14 mm were used. A homogeneous temperature field up to 0.3 K in the range of absolute values between the melting temperature, Tm, and 800 K was created inside the furnace. The temperature was measured with a WRe-5/20 thermocouple arranged just below the crucible. The viscosity was determined with the accuracy of about 3%.

2.4 DSC

The Perkin-Elmer DSC7 differential scanning calorimeter calibrated for +10 K/min heating rate, always the same aluminum sample pan covered without restraint with the lid, no sample in the reference pan and flowing (20 ml/min) argon atmosphere were used. The sample mass was about 10 mg.

Always two independent ribbon shape samples and two independent bulk samples were measured, thus the reproducibility of each effect has been shown and the precision of each quantity might be calculated. The precision is ±0.5 K and ± 2 J/g. The instrument was calibrated for the heating regime therefore each temperature determined during the cooling should be corrected by adding of +5.1 K.

Each sample was measured in three subsequent heating and cooling cycles. Thus the reversibility and reproducibility of the eventual effects has been tested. Each eventual exothermal or endothermic effect (DSC peak) was characterized by its onset temperature (Tx), peak temperature (Tp), endset temperature (Te) and transformation enthalpy (ΔH). Temperature Tx is determined as a cross-section of two parallels. The first one is the prolonged baseline before the peak. The second one is constructed in the inflection point of the front-part of the peak. Temperature Te is the cross-section of two parallels, too. The first one is constructed in the inflection point of the back-side of the peak. The second one is the prolonged baseline after the peak. All deduced effects were consecutively numbered according to their appearance following the heating (e.g. R1, R2,…) and these numbers are used as the subscripts of the effect quantities as, e.g., Tx,1, Tp,1, Te,1, and ΔH1 in the case of the first effect.

3 Results and discussion

Electrical conductivity, \( \sigma (T) \), viscosity, η(T), and DSC measurements were performed for the binary Sn95Sb5, Sn90Sb10, Sn80Sb20 and ternary Sn90.8Sb7.4Cu1.8, Sn76.1Sb20.2Cu3.7 alloys (at.%).

The electrical conductivity of all Sn–Sb alloys in the solid state decreases gradually with heating according to the linear law (see Fig. 1). The melts were heated and cooled several times with different rates, but the change of the rate did not affect noticeably the electrical conductivity behavior. A very good agreement between heating and cooling curves has been observed. Heating as well as cooling is accompanied by small almost linear changes in the electrical properties, and the temperature dependence of σ(T) can be well fitted by linear functions of type:
$$ \sigma (T) = \sigma_{R} - {\frac{{{\text{d}}\sigma }}{{{\text{d}}T}}}T, $$
(1)
where σR is conductivity at 300 K and \( {\frac{d\sigma }{dT}} \) in a temperature coefficient of conductivity.
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Fig. 1

Electrical conductivity versus temperature for Sn–Sb alloys in the solid ribbons and liquid bulks

Similar conductivity behavior in the solid state was observed for ternary Sn90.8Sb7.4Cu1.8 and Sn76.1Sb20.2Cu3.7 alloys (see Fig. 2). Table 1 gives the parameters of linear fits for the experimental data plotted in Figs. 1 and 2. As seen, the electrical conductivity at room temperature and the temperature coefficient of conductivity of the binary Sn–Sb alloys decrease with an increase of the antimony content. The absolute conductivity value σRof Sn90.8Sb7.4Cu1.8 is somewhat higher than σR of Sn90Sb10, while the conductivity of Sn76.1Sb20.2Cu3.7 is slightly lower than that of Sn80Sb20 at the room temperature.
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Fig. 2

Electrical conductivity versus temperature for Sn–Sb–Cu alloys in the solid ribbons and liquid bulks

Table 1

The temperature dependences of the electrical conductivity for the solid ribbons: linear fits to the experimental data plotted in Figs. 1, 2

Alloy composition

\( \sigma (T) = \sigma_{R} - {\frac{{{\text{d}}\sigma }}{{{\text{d}}T}}}T\left( {{\text{Ohm}}^{ - 1} \cdot {\text{cm}}^{ - 1} } \right) \)

\( \sigma_{R} \left( {{\text{Ohm}}^{ - 1} \cdot {\text{cm}}^{ - 1} } \right) \)

\( {\frac{{{\text{d}}\sigma }}{{{\text{d}}T}}}\left( {{\text{Ohm}}^{ - 1} \cdot {\text{cm}}^{ - 1} \cdot {\text{K}}^{ - 1} } \right) \)

Sn95Sb5

58,770

8.79

Sn90Sb10

52,120

7.47

Sn80Sb20

50,770

7.14

Sn90.8Sb7.4Cu1.8

53,800

8.65

Sn76.1Sb20.2Cu3.7

49,440

8.46

Temperature dependence of conductivity of liquid binary Sn–Sb alloys is presented in Fig. 3 together with results of previous works for the same compositions and compared with conductivity of pure Sn [11] as well as conductivity of binary Pb–Sn solder alloys from the lead-reach side [12]. The results obtained for the Sn95Sb5 composition are in good agreement with data reported earlier [4], while the electrical conductivity of the Sn90Sb10 is slightly lower than data presented in [5]. The conductivity of all lead-free melts is higher than that of the Pb–Sn alloys, which is favourable.
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Fig. 3

Electrical conductivity as a function of temperature for liquid Sn–Sb alloys

A scattering of the electrical conductivity data σ(T) of the investigated alloys in the liquid state is more pronounced than in solids (see Figs. 1, 2 and 3). The measurements were carried out during heating and cooling. The electrical conductivity of all studied melts decreases gradually with heating. The melting and solidification processes are accompanied by a hysteresis.

There are a limited number of studies in the literature on the electrical conductivity of Sn–Sb liquid alloys and the data are rather contradictory. A smooth linear resistivity rise with heating up to almost 1,300 K in the liquid Sn95Sb5 alloy was reported in [4]. In compositions with higher content of antimony (Sn90Sb10 and Sn70Sb30) the anomalous variation of the resistivity at certain temperatures was observed [5] (not shown in figures).

In our measurements, the conductivity of the Sn95Sb5 melt did not reveal noticeable deviation from linearity up to 1,100 K. The heating and cooling curves almost coincide keeping the same slope. More pronounced spread of experimental points takes place in the Sn90Sb10 and Sn80Sb20 melts. Although we did not reach temperatures of the so-called “turning points of anomalous resistivity variations” [5], the \( \sigma (T) \) curves were not smooth even at lower temperatures. We do not consider some \( \sigma (T) \)data scattering as anomalous variation of the resistivity in the liquid state. We suggest that it could be due to the remaining covalent bonds in Sn and Sb, which partly break after melting and appear again before solidification.

Electrical conductivity of liquid ternary Sn90.8Sb7.4Cu1.8, Sn76.1Sb20.2Cu3.7 alloys decreases gradually with heating revealing some data scattering similar to that in the binary alloys.

The dynamic viscosity, \( \eta (T) \), of the binary Sn95Sb5, Sn90Sb10, Sn80Sb20 and ternary Sn90.8Sb7.4Cu1.8, Sn76.1Sb20.2Cu3.7 liquid alloys was measured during heating and cooling over a wide temperature range above the liquidus. All samples were subjected to at least 2 heating–cooling cycles. Several experiments with different samples of the same composition revealed good reproducibility of the results. The dynamic viscosity as a function of temperature for the binary alloys is presented in Fig. 4 together with data for pure tin and results of previous studies for almost the same compositions [6]. It should be noted that the present data are higher than those found in [6]. At the same time, our experimental data for pure Sn are in a good agreement with those reported earlier [13, 14].
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Fig. 4

Viscosity versus temperature for liquid Sn–Sb alloys

The viscosities of Sn and Sn95Sb5 melts are consistent within the limits of experimental error in the high temperature region. Further increasing of the Sb content leads to an increase of the absolute viscosity values. Such increase of the viscosity with addition of a small quantity of solute is in agreement with the experimental data on other dilute binary alloys (1–5 per cent increase of η with addition of 1 at.% solute [15]) as well as with the theoretical estimations (7–8 per cent increase of η with addition of 1 at.% solute [16]). One of commonly used theoretical descriptions is based on the correlation between the viscosity and interchange energy, which can be expressed through the enthalpy of mixing [17]. In this case, viscosity of a real melt is:
$$ \eta = \eta^{id} + \Updelta \eta . $$
(2)
where \( \eta^{id} \) is an ideal viscosity and \( \Updelta \eta \) is an excess viscosity. Viscosity of a two-component ideal system can be written as:
$$ \eta^{id} = x_{1} \eta_{1} + x_{2} \eta_{2} $$
(3)
where η1, η2, x1, x2 are the viscosities and concentrations of the melt components 1 and 2, respectively.The excess viscosity Δη is given by [17]:
$$ \Updelta \eta = - 2\left( {x_{1} \eta_{1} + x_{2} \eta_{2} } \right){\frac{{{{\Updelta}}H}}{RT}} $$
(4)
The sign of the excess viscosity depends only upon that of the integral enthalpy of mixing ΔH. It has been shown that Δη tends to become negative as the difference in atomic size increases [15]. Viscosity is expressed in terms of some basic physical quantities (ionic radius, mass of an atom, coefficient of activity) and consists of the hard and soft parts of the friction constant for viscous movements of atoms. It was shown that the hard part tends to become less negative as the difference between ionic radii increases. On the other hand, the soft part tends to become positive as the difference between the mass of atoms increases. A model proposed in Ref. [16] is similar, but the integral enthalpy of mixing is taking into account only in the soft component.
It is known that the enthalpy of mixing of the Sb–Sn binary system is negative over the whole concentration range, and reveals small positive values for the Cu–Sn and Cu–Sb systems in the Sn-rich and Sb-rich regions, respectively [1821]. According to Eq. (4), the negative enthalpy of mixing leads to increase of viscosity, as we observed for the binary Sn–Sb alloys (Fig. 4). Additions of copper also increase the viscosity of tin, but viscosity of the ternary Sn–Sb–Cu liquid alloys reveals the intermediate values between those of liquid Sn and Sn80Sb20 (Fig. 5).
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Fig. 5

Viscosity versus temperature for liquid Sn–Sb–Cu alloys

Cooling of the pure liquid Sn is accompanied by an increase of the viscosity according to an Arrhenius-type empirical equation:
$$ \eta (T) = \eta_{0} \exp \left( {{\frac{{E_{A} }}{RT}}} \right) $$
(5)
where η0 is a constant (mPas), R is the gas constant (J mol−1 K−1), T is the absolute temperature (K), EA is the flow activation energy (J mol−1). At the same time, addition of antimony results in the deviation from the Arrhenius law. Approaching the liquidus, the viscosity curves become steeper (Fig. 4), which could be explained by remaining covalent bonds and also the difference in bonding ability between Sn and Sb atoms, which might yield temperature-induced structure changes in some Sn–Sb alloys.

Similar η(T) behavior has been revealed also in ternary Sn90.8Sb7.4Cu1.8 and Sn76.1Sb20.2Cu3.7 liquid alloys (Fig. 5). The absolute viscosity value of Sn76.1Sb20.2Cu3.7 is very close to viscosity of Sn80Sb20 in the high temperature region but deviates upon cooling. Viscosity of Sn90.8Sb7.4Cu1.8 is close to that of Sn90Sb10. As in the case of the binaries, a deviation from the Arrhenius law approaching the liquidus has been observed.

The results of the DSC measurements for binary Sn–Sb alloys are shown in Figs. 6, 7 and 8. Principally the heating and cooling curves reflect the reversibility of the observed phenomena. Besides generally, the DSC signal in the cooling regime is more sensitive than that in the heating regime due to the well-defined surface and volume morphology of the measured substances. Also the differences between the ribbon shape and the bulk shape samples have been minimized after the preceding melting. Our XRD analysis in Fig. 9 shows that the as-prepared Sn95Sb5 sample consists of the Sn (Sb) solid solution. This sample manifests one massive endothermic peak R1 which starts at Tx1 = 513.8 K during the continuous heating or one reversed sharp exothermic peak starting at Tx1 = 503.5 K in the case of continuous cooling. These temperatures, after their extrapolation to the zero heating rate in the case of heating and both to the zero cooling rate and taking into account the undercooling due to the nucleation it the case of the continuous cooling, well coincide with the solidus and liquidus temperatures of Sn95Sb5 solution in the actual phase diagram [22]. The as-prepared Sn90Sb10 and Sn80Sb20 samples consist of solid Sn (Sb) and also SnSb (stistaite) phases, (see Fig. 9).
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Fig. 6

Details of the heating and cooling DSC curves of Sn95Sb5 alloy. Complete melting peaks are in the inset. Full lines—as-prepared ribbon-shape sample, dashed lines—as-prepared bulk-shape sample, short-dashed lines represent the second heating after the first heating and cooling in DSC. Heating and cooling rates were ± 10 K/min

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Fig. 7

Details of the heating and cooling DSC curves of Sn90Sb10 alloy. Complete melting peaks are in the inset. Full lines—as-prepared ribbon-shape sample, dashed lines—as-prepared bulk-shape sample. Heating and cooling rates were ± 10 K/min

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Fig. 8

Details of the heating and cooling DSC curves of Sn80Sb20 alloy. Complete melting peaks are in the inset. Full lines—as-prepared ribbon-shape sample, dashed lines—as-prepared bulk-shape sample. Heating and cooling rates were ± 10 K/min

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Fig. 9

X-ray diffraction patterns using Cu Kα radiation of binary Sn–Sb alloy ribbons in as-prepared state, showing the presence of Sn(Sb) solid solution in the Sn95Sb5 alloy and increased presence of stistaite with increased Sb content. The diffraction pattern of pure Sn is shown for convenience

Increasing the temperature, the SnSb phase via a peritectic transformation reacts into the Sn3Sb2 phase and the liquid Sn(Sb) solution start to be formed in the first intense endothermic peak R1 at Tx1 = 519.9 ± 0.6 K. R1 is subsequently followed by the second shallow but wide endothermic R2, which finishes at Te2 = 546.5 K for Sn90Sb10, however, at much higher temperature Te2 = 607.5 K in the case of Sn80Sb20. Again, the cooling DSC curves show the reversibility of both R1 and R2 effects. These DSC results and their interpretation coincide well with the Sn–Sb phase diagram. The characteristic temperatures and heats of all mentioned effects for both ribbon and bulk shape alloys are summarized in Table 2.
Table 2

Characteristic temperatures and enthalpies of the melting and solidification of both ribbon shape (R) and bulk shape (B) Sn–Sb alloys as measured in DSC at 10 K/min

Regime

Sample

Tx,1 K

Tp,1 K

Te,1 K

H1 J/g

Tx2 K

Tp2 K

Te2 K

H2 J/g

Heating

Sn95Sb5/R

513.8

517.4

518.4

57.9

    

Sn95Sb5/B

510.2

525.0

525.1

58.8

    

Cooling

Sn95Sb5/R

503.5

502.2

499.8

−58.4

    

Sn95Sb5/B

506.2

504.5

501.2

−58.4

    

Heating

Sn90Sb10/R

520.5

522.6

523.9

54.4

523.9

531.0

546.5

5.3

Sn90Sb10/B

526.1

527.1

528.0

55.9

527.8

533.1

553.5

4.5

Cooling

Sn90Sb10/R

519.9

516.3

509.2

−56.9

533.2

529.2

520.8

−4.8

Sn90Sb10/B

519.2

516.4

508.9

−58.6

533.3

529.1

523.2

−2.5

Heating

Sn80Sb20/R

519.3

521.8

523.5

29.6

523.5

587.6

607.5

34.3

Sn80Sb20/B

514.6

528.1

529.6

43.3

529.6

567.7

595.0

19.4

Cooling

Sn80Sb20/R

519.4

518.2

514.8

−49.6

592.6

586.9

578.4

−21.7

Sn80Sb20/B

519.4

514.2

507.5

−47.9

573.3

568.0

545.8

−19.2

Tx,i—the onset temperatures, Tp,i—the peak temperatures, Te,i—the end temperatures, Hi—the transformation enthalpies of the R1 effect (i = 1) and the R2 effect (i = 2)

The phase compositions of the ribbon shape and bulk shape alloys as well as their DSC curves are the same, revealing only minor but non-negligible disagreements. Namely, the small differences in the widths of both R1 and R2 peaks might reflect certain deviations in the phase compositions, while the small sharp exothermal overshoot, which separates the R1 and R2 effects in the case of the ribbons, might suggest that the melting and solidification processes are accompanied by more complicated structure rearrangements with phase transformations, which are probably not reflected at the corresponding phase diagram. These deviations are irreversible; they vanish after the completed melting. Also the differences between the DSC traces of the ribbon and bulk shaped samples upon subsequent cooling or the following heating cycles become smaller.

According to the DSC results, the melt should be completely homogeneous above the Te2 value. Nevertheless, a deviation of viscosity from the exponential law, seen in Figs. 4 and 5, suggests that the molten metallic alloys undergo a number of structural transformations between the initial microheterogeneous state just after melting and the true solution state. It was also discussed, that regions of different thermodynamic stability exist in the liquid state [23]. The anomalous temperature dependencies of some physical properties are connected with the structure transition of local short-range orders, when the previous bonds are broken to form new bonds or a more disordered high-temperature liquid. Cooling of the melt is accompanied by formation of nuclei of future solidified phases and gradual precipitation of the solid phases; thus, a two-phase liquid is formed. We suggest that similar structure rearrangements are reflected on the viscosity polytherms.

The Sn–Sb and Sn–Sb–Cu ribbons are not brittle. A shape of thin foil/ribbon of all the compositions studied are elastic enough and convenient for joining of large areas with well-defined joint dimensions, prospectively for joining the metallic matrix composites.

4 Summary

Investigations of the melting-solidification region of the Sn–Sb–Cu alloys revealed that a unique melting temperature can be expected only for eutectic compositions or for compositions that melt congruently. Other compositions can be expected to melt over a range of temperatures, with melting beginning at the solidus temperature and being complete at the liquidus temperature. The anomalous variation of the resistivity in the liquid state and viscosity at certain temperature ranges for the Sn–Sb–Cu melts may be due to the remaining covalent bonds and also the difference in bonding ability between Sn and Sb atoms, which might yield temperature-induced structure changes in some compositions of liquid Sn–Sb alloys. The increase of the viscosity of liquid Sn with additions of Sb and Cu correlates with the theoretical predictions derived with the relationship between the excess viscosity and integral enthalpy of mixing. The observed features of structure point to atomic rearrangement in the alloy in the temperature region close to the melting point.

Acknowledgments

This work was carried out within the framework of the COST Action MP0602, joint Slovak-Ukrainian project APVV-SK-UA-0043-09, projects APVV-0102-07 and VEGA 2/0157/08 and supported by the National Scholarship Programme of the Slovak Republic (Minerva) and the Fundamental Researches State Fund of Ukraine (projects F28-255, F28-329).

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