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Formation of atomic solution in liquid eutectic alloys
Journal of Non-Crystalline Solids 353 (2007) 2982–2986 www.elsevier.com/locate/jnoncrysol
Formation of atomic solution in liquid eutectic alloys S. Mudry *, T. Lutsyshyn, I. Shtablavyi, A. Yakymovych, Yu. Plevachuk Ivan Franko National University, Physics of Metal Department, Kyrylo and Mephodiy str. 8, Ua-79005 Lviv, Ukraine Available online 10 July 2007
Abstract The influence of Pb, In, Bi and Ge on structure of tin within 0–12.5 at.% concentration range has been studied by means of X-ray diffraction method. Samples were prepared by melting in vacuum furnace filled with pure argon from ingots of Sn(99.999%), Pb(99.99), In(99.999), Bi(99.99), Ge(99.999) and checked by means of X-ray microanalysis The structure factors and pair correlation functions were analyzed. Concentration dependencies of structure parameters for liquid Sn-enriched melts in binaries with eutectic point are described. It is shown that atomic arrangement in tin-based molten alloy deviates from random atomic distribution within concentration range where these alloys can be considered as diluted solutions. Limited solubility in solid state in eutectic Sn-based systems is a precursor to deviation from random atomic distribution in liquid state. Ó 2007 Elsevier B.V. All rights reserved. PACS: 61.25.f Keywords: Liquid alloys and liquid metals
1. Introduction Binary eutectic alloys due to a low melting temperature attract the interest of researchers as materials for soldering and casting. In recent years interest to molten eutectic alloys significantly growth because many of them can be amorphised by rapid quenching. On other hand the low melting temperature of such alloys allows to use them for producing of Pb-free solders. On that reasons the studying of eutectic alloys in liquid state is of great importance. Most of binary eutectic systems have been widely studied in liquid state by means of X-ray diffraction method and physical property measurements. The concentration of melts including eutectic one had been chosen with large step and the temperatures of investigation were not far from the liquidus curve. Therefore the available data on structure and physical properties concentration dependencies are poor to make the conclusions about behavior of such molten alloys from the viewpoint of physics of solu-
*
Corresponding author. Tel.: +380 322 964 527. E-mail address: [email protected] (S. Mudry).
0022-3093/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2007.05.027
tions. It is of importance because the eutectic systems show the limited solubility in solid state. In this work we present the results on structure studies of liquid alloys, whose equilibrium phase diagrams show the limited solubility in solid state (Sn1xMx(M = In, Pb, Bi, Ge)). The second components of these systems are elements with different degree of metallicity in chemical bonding. The alloys, containing 2.5, 5.0, 7.5, 10.0 and 12.5 at.% of diluted element in Sn have been studied by means of Xray diffraction method at temperatures about 5 K above liquidus curve. 2. Experimental Samples were prepared in arc melting furnace filled with pure argon. The purity of the initial metals was 99.99% and 99.999%. The diffraction studies were carried out using a high-temperature diffractometer with a special attachment that allows to investigate the solid and liquid samples at different temperatures up to 1800 K. Cu Ka radiation monochromatized by means of LiF single crystal as a monochromator and Breg-Brentano focusing geometry
S. Mudry et al. / Journal of Non-Crystalline Solids 353 (2007) 2982–2986
were used. The scattered intensities as a function of the ˚ 1 < scattering angle were recorded within the range 1 A 1 ˚ k < 7 A , with different angular step, which was equal to 0.05° within the region of principal peak and 0.5° at rest values of wave vectors. The measuring of scattered intensity was done with accuracy, better then 2%. In order to obtain the more accurate scattered intensities, the scan time was equal to 100 s. The diffracted intensity was recorded using a NaI(Tl) scintillator detector in conjunction with an amplification system. The sample was placed in a rounded cup of 20 mm diameter. Intensity curves were corrected on polarization, absorption and incoherent scattering [1]. After this procedure they were normalized to electron units by Krogh–Moe method [2]. Obtained intensity curves were used to calculate the SF and than the pair correlation function PCF. Main structure parameters, obtained from SF and PCF were analyzed. 3. Results and discussion Experimental SF for Sn-based molten alloys with different content of diluted element are similar to one of pure
2983
liquid tin (Fig. 1). Main their features are an asymmetry of principal peak and a shoulder on its right side as well in SF for liquid tin. Obtained concentration dependencies of SF allowed us to note, that diluted elements does not change significantly the atomic distribution in liquid tin. Similar features are also observed in concentration dependencies for PCF. Main structural parameters – position of principal peaks and squares under them are close to corresponding values for liquid tin. In order to find the features of atomic distribution in Snenriched solutions we have analyzed the concentration dependencies of main structure parameters. It was found that first maximum position in SF of molten alloys changes with concentration in nonlinear way. At the same time it is should be noted that within some concentration interval there is linear-like dependence but with further addition of diluted elements the deviation from such dependence increases. Especially it is significant in case of Sn1x–Gex melts. Therefore it is possible to suggest that Sn-enriched molten alloys reveal the more complicated structure than suppose the ideal solution within concentration interval where CSn CM. In other words, Sn-based molten alloys
Sn1-xGex
S(q)
1
x=0.125
0
0.1
0
Sn1-xBix
S(q)
1
x=0.125
0.075
0
0.1
0
0.05
0
0.075
0
0.025
0
0.05
0
0.025
0
0
0
0
0
0
1
2
3
4
5
6
7
8
1
2
3
O -1
q, A
4 5 6 O -1 q, A
7
Sn1-xInx
S(q)
Sn1-xPbx
S(q)
1
x=0.125
0
0.1
0 0
1 0
0.1
0.075
0
0.075
0.05
0
0.05
0
0.025
0
0
0.025
0
x=0.125
0
0
1
2
3
4
5 O -1
q, A
6
7
8
1
2
3
4 5 6 O -1 q, A
7
8
Fig. 1. The structure factors of Sn1xMx molten alloys (M = Ge, In, Bi, Pb).
8
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S. Mudry et al. / Journal of Non-Crystalline Solids 353 (2007) 2982–2986
with Pb, In, Bi and Ge show the inhomogeneous atomic distribution. For analysis of structural inhomogeneities we also used the model interpretation method. According to random atomic distribution (RD) model and self-associated (SAD) one the most probable interatomic distances can be written: M M rRD ¼ ðC Sn K Sn þ C M K M ÞðC Sn rSn 1 1 þ C r1 Þ; 2
2
Sn M ¼ C Sn rSn þ C M rM ; rSAD 1 1 K 1 K M where rSn 1 , r1 – the most probable interatomicdistances for tin and diluted element respectively; CSn, CM, KSn, KM – their concentrations and scattering abilities, respectively. The data calculated according to these formulas were compared to experimental ones estimated from PCF. Results of such comparison (Fig. 2) indicate that in most binaries the deviation of experimental r1 values from model ones is significant. In case of Sn1xGex for small content of Ge(<5 at.%) the better agreement with SAD model is observed, whereas at higher content of this element departure from this model becomes more significant. It allowed us to suppose that existence of aggregated atomic groups of Ge makes more difficult the diluting process what is in result accompanied by r1 increase.
For Sn1xBix melts the model of self-associated distribution is in good agreement with experimental data over all chosen concentration range. In the case of Sn1xInx melts it is difficult to interpret this data because both models values are almost the same due to no significant difference in scattering abilities of In and Sn. But taking into account the concentration dependencies of other structure parameters we can suggest that atomic distribution in alloys of this system can be described by random atomic distribution model. In case of adding to tin Pb-atoms the experimental values of r1 are somewhat lower than ones predicted by the self-associated atomic distribution model whereas for random atomic distribution one they are significantly higher then r1. Analyzing these data it should be noted that at small content of lead the experimental values of r1 lie between ones for both models. Therefore the obtained data on structure parameters confirms our suggestion about existence of inhomogeneous atomic distribution in tin-based diluted solutions. The melts of eutectic systems, studied in this work show the significant difference in atomic radius values. Thus, if suppose that some tin atoms are substituted by another kind ones, the SF should be almost the same as for liquid tin. Such behavior must be also displayed in corresponding PCF.
3.30
3.35
3.25
1 2 3
3.30
r, A
r, A
3.20 O
O
3.15
3.25 3.20
3.10
3.15
3.05 3.00
1 2 3
0
5
10
aT. % Ge
3.10
15
5
aT. % In
10
15
3.40
1 2 3
3.3
0
1
3.35
2 3.30
r, A
r, A
3.2 O
O
3
3.25 3.20
3.1
3.15
3.0 -2.5
3.10
0.0
2.5
5.0
7.5
aT. % Bi
10.0 12.5
15.0
0
5
aT. % Pb
10
Fig. 2. The most probable distances for Sn1xMex (1 – experimental data, 2 – self-associated distribution model, 3 – random atomic distribution model).
S. Mudry et al. / Journal of Non-Crystalline Solids 353 (2007) 2982–2986
Taking into account the fact that atomic density with addition of diluted elements must be almost the same as for tin. It is possible to note that the height of SF principle peak must be unchangeable when diluted element content increases. Such behavior in concentration dependence of this parameter is not always observed for studied systems. This fact allowed us to suggest that introducing of diluted atoms into vacancies of liquid tin structure is possible. From analysis of obtained data follows that in some binaries the decrease of principal peak height with diluted element content is observed within some definite concentration range. Experimental total SF were used in order to calculate the partial SF by means of Reverse Monte Carlo Method [3]. For all binary systems the partial SF SSn–Sn(q) obtained in such way is similar to SF of liquid tin, whereas the SSn–M(q) and SM–M(q) show some features, especially the last (Fig. 3) It has an untypical for simple liquid metals profile and does not reveal any peaks. Upon increasing of diluted element content up to some values the profile of
SGe-Ge(q)
0.125
2985
SM–M(q) partial SF significantly changes and reveals the maxima as in simple liquids. Such behavior allowed us to conclude that correlation between diluted atoms occurs only at higher then some definite value concentration. Partial structure factors calculated by means of Reverse Monte Carlo method were used for obtaining of another kind structural functions – Bhatia–Thornton structure factors. One of them – SCC(q) is a measure of chemical short range order and indicates the deviation of structure from random atomic distribution. As it can be seen from Fig. 4 there are a small oscillations in SCC(q) for Sn1x–Gex molten alloys over all concentration range studied. SCC(q) structure factor shows no fluctuations of concentration in this case because the content of melt changes not only via changes of each kind atom fraction in structure units, but also via changes of these structure units fraction. The fluctuations concentration on the scale of structure units occur and it is the reason that peaks in SCC(q) for Sn1x–Gex molten alloys are not so resoluted
SIn-In(q)
1
0.125
0.1
1
0
0
0.1
0
0.075
0
0.05
0
x=0.025
0.075 0 0.05 0 x=0.025 0 0
0 1
2
3
4 5 -1 q, A
6
7
8
2
4
O
6 O
q, A
8
-1
SBi-Bi(q) 0.125
1
SPb-Pb(q)
0.1
0
0.125
0.05
1 0 0
x=0.025
0
0.05
0
0
x=0.025
0
0
0.075 0 0
0
1
2
3 4 -1 q, A O
5
6
7
8
0.1 0.075
0
1
2
3
4 5 6 -1 q, A O
Fig. 3. Partial structure factors (Reverse Monte Carlo method).
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8
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Scc(q)
Scc(q)
Sn-Ge 1
Sn-In
0.125
0.125
0
1
0.1
0
0.1
0.075
0
0.075
0
0.05
0
0
x=0.025
0
0
0
0.05
0
x=0.025
0
2
4 O
6
2
4 O
-1
6
-1
q, A
q, A
Scc(q)
Sn-Pb
Scc(q)
0.125
Sn-Bi
1
0.125
0.1
0
1
0.1
0
0.075
0
0
0.075
0
0.05
0
x=0.025
0.05
0
x=0.025
0 0
0 0
2
4 O
6
0
2
4 O
-1
6
-1
q, A
q, A
Fig. 4. Partial Bhatia–Thornton SCC(q) structure factors.
as in other melts. Another shape of SCC(q) is observed in Sn1xBix molten alloys. Particularly, the principal peak increases with addition of Bi- atoms. If content of Bi reaches 12.5 at.%, the concentration fluctuations are significant and first peak position SCC(q) is practically the same that in total structure factor. Slight oscillations in SCC(q) occur for Sn1xInx liquid alloys. If the content of In is 10 at.% and higher the SCC(q) shows the typical shape, which is the evidence of significant concentration fluctuations. Concentration dependence of SCC(q) for Sn1xPbx molten alloys is similar to that in Sn1xBix. Only at small content of Pb the deviation from random atomic distribution can be neglected. At addition of Pb atoms up to 12.5 at.% the principal peaks show a good resolution. The reason of such behavior is the tendency to self-association of Pb-atoms, which aggregates in groups, diluted in tin matrix. Thus the analysis of SCC(q) partial structure factors for binary Sn-based eutectic melts shows that Bi and Pb- atoms
attempt to aggregate in small atomic groups. Therefore the real structure of diluted tin-based solutions deviates from ideal solutions model and can be considered as mixture of atoms and structural units of larger size. 4. Conclusions Tin-based alloys with Pb, In, Bi and Ge, containing 0– 12.5 at.% show the inhomogeneous short range order, whose topology is determined by structure of tin. Significant changes of atomic distribution in tin are no observed upon addition of diluted atoms up to some definite their content. Molten alloys of these systems can be considered as a mixture of atoms and aggregated atomic groups. References [1] D.T. Cromer, J.T. Waber, Acta Cryst. 18 (15) (1965) 104. [2] J. Krogh-Moe, Acta Cryst. 9 (1956) 951. [3] R.L. McGreevy, L. Pusztai, Mol. Simulat. 1 (1988) 359.
Formation of atomic solution in liquid eutectic alloys S. Mudry *, T. Lutsyshyn, I. Shtablavyi, A. Yakymovych, Yu. Plevachuk Ivan Franko National University, Physics of Metal Department, Kyrylo and Mephodiy str. 8, Ua-79005 Lviv, Ukraine Available online 10 July 2007
Abstract The influence of Pb, In, Bi and Ge on structure of tin within 0–12.5 at.% concentration range has been studied by means of X-ray diffraction method. Samples were prepared by melting in vacuum furnace filled with pure argon from ingots of Sn(99.999%), Pb(99.99), In(99.999), Bi(99.99), Ge(99.999) and checked by means of X-ray microanalysis The structure factors and pair correlation functions were analyzed. Concentration dependencies of structure parameters for liquid Sn-enriched melts in binaries with eutectic point are described. It is shown that atomic arrangement in tin-based molten alloy deviates from random atomic distribution within concentration range where these alloys can be considered as diluted solutions. Limited solubility in solid state in eutectic Sn-based systems is a precursor to deviation from random atomic distribution in liquid state. Ó 2007 Elsevier B.V. All rights reserved. PACS: 61.25.f Keywords: Liquid alloys and liquid metals
1. Introduction Binary eutectic alloys due to a low melting temperature attract the interest of researchers as materials for soldering and casting. In recent years interest to molten eutectic alloys significantly growth because many of them can be amorphised by rapid quenching. On other hand the low melting temperature of such alloys allows to use them for producing of Pb-free solders. On that reasons the studying of eutectic alloys in liquid state is of great importance. Most of binary eutectic systems have been widely studied in liquid state by means of X-ray diffraction method and physical property measurements. The concentration of melts including eutectic one had been chosen with large step and the temperatures of investigation were not far from the liquidus curve. Therefore the available data on structure and physical properties concentration dependencies are poor to make the conclusions about behavior of such molten alloys from the viewpoint of physics of solu-
*
Corresponding author. Tel.: +380 322 964 527. E-mail address: [email protected] (S. Mudry).
0022-3093/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2007.05.027
tions. It is of importance because the eutectic systems show the limited solubility in solid state. In this work we present the results on structure studies of liquid alloys, whose equilibrium phase diagrams show the limited solubility in solid state (Sn1xMx(M = In, Pb, Bi, Ge)). The second components of these systems are elements with different degree of metallicity in chemical bonding. The alloys, containing 2.5, 5.0, 7.5, 10.0 and 12.5 at.% of diluted element in Sn have been studied by means of Xray diffraction method at temperatures about 5 K above liquidus curve. 2. Experimental Samples were prepared in arc melting furnace filled with pure argon. The purity of the initial metals was 99.99% and 99.999%. The diffraction studies were carried out using a high-temperature diffractometer with a special attachment that allows to investigate the solid and liquid samples at different temperatures up to 1800 K. Cu Ka radiation monochromatized by means of LiF single crystal as a monochromator and Breg-Brentano focusing geometry
S. Mudry et al. / Journal of Non-Crystalline Solids 353 (2007) 2982–2986
were used. The scattered intensities as a function of the ˚ 1 < scattering angle were recorded within the range 1 A 1 ˚ k < 7 A , with different angular step, which was equal to 0.05° within the region of principal peak and 0.5° at rest values of wave vectors. The measuring of scattered intensity was done with accuracy, better then 2%. In order to obtain the more accurate scattered intensities, the scan time was equal to 100 s. The diffracted intensity was recorded using a NaI(Tl) scintillator detector in conjunction with an amplification system. The sample was placed in a rounded cup of 20 mm diameter. Intensity curves were corrected on polarization, absorption and incoherent scattering [1]. After this procedure they were normalized to electron units by Krogh–Moe method [2]. Obtained intensity curves were used to calculate the SF and than the pair correlation function PCF. Main structure parameters, obtained from SF and PCF were analyzed. 3. Results and discussion Experimental SF for Sn-based molten alloys with different content of diluted element are similar to one of pure
2983
liquid tin (Fig. 1). Main their features are an asymmetry of principal peak and a shoulder on its right side as well in SF for liquid tin. Obtained concentration dependencies of SF allowed us to note, that diluted elements does not change significantly the atomic distribution in liquid tin. Similar features are also observed in concentration dependencies for PCF. Main structural parameters – position of principal peaks and squares under them are close to corresponding values for liquid tin. In order to find the features of atomic distribution in Snenriched solutions we have analyzed the concentration dependencies of main structure parameters. It was found that first maximum position in SF of molten alloys changes with concentration in nonlinear way. At the same time it is should be noted that within some concentration interval there is linear-like dependence but with further addition of diluted elements the deviation from such dependence increases. Especially it is significant in case of Sn1x–Gex melts. Therefore it is possible to suggest that Sn-enriched molten alloys reveal the more complicated structure than suppose the ideal solution within concentration interval where CSn CM. In other words, Sn-based molten alloys
Sn1-xGex
S(q)
1
x=0.125
0
0.1
0
Sn1-xBix
S(q)
1
x=0.125
0.075
0
0.1
0
0.05
0
0.075
0
0.025
0
0.05
0
0.025
0
0
0
0
0
0
1
2
3
4
5
6
7
8
1
2
3
O -1
q, A
4 5 6 O -1 q, A
7
Sn1-xInx
S(q)
Sn1-xPbx
S(q)
1
x=0.125
0
0.1
0 0
1 0
0.1
0.075
0
0.075
0.05
0
0.05
0
0.025
0
0
0.025
0
x=0.125
0
0
1
2
3
4
5 O -1
q, A
6
7
8
1
2
3
4 5 6 O -1 q, A
7
8
Fig. 1. The structure factors of Sn1xMx molten alloys (M = Ge, In, Bi, Pb).
8
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S. Mudry et al. / Journal of Non-Crystalline Solids 353 (2007) 2982–2986
with Pb, In, Bi and Ge show the inhomogeneous atomic distribution. For analysis of structural inhomogeneities we also used the model interpretation method. According to random atomic distribution (RD) model and self-associated (SAD) one the most probable interatomic distances can be written: M M rRD ¼ ðC Sn K Sn þ C M K M ÞðC Sn rSn 1 1 þ C r1 Þ; 2
2
Sn M ¼ C Sn rSn þ C M rM ; rSAD 1 1 K 1 K M where rSn 1 , r1 – the most probable interatomicdistances for tin and diluted element respectively; CSn, CM, KSn, KM – their concentrations and scattering abilities, respectively. The data calculated according to these formulas were compared to experimental ones estimated from PCF. Results of such comparison (Fig. 2) indicate that in most binaries the deviation of experimental r1 values from model ones is significant. In case of Sn1xGex for small content of Ge(<5 at.%) the better agreement with SAD model is observed, whereas at higher content of this element departure from this model becomes more significant. It allowed us to suppose that existence of aggregated atomic groups of Ge makes more difficult the diluting process what is in result accompanied by r1 increase.
For Sn1xBix melts the model of self-associated distribution is in good agreement with experimental data over all chosen concentration range. In the case of Sn1xInx melts it is difficult to interpret this data because both models values are almost the same due to no significant difference in scattering abilities of In and Sn. But taking into account the concentration dependencies of other structure parameters we can suggest that atomic distribution in alloys of this system can be described by random atomic distribution model. In case of adding to tin Pb-atoms the experimental values of r1 are somewhat lower than ones predicted by the self-associated atomic distribution model whereas for random atomic distribution one they are significantly higher then r1. Analyzing these data it should be noted that at small content of lead the experimental values of r1 lie between ones for both models. Therefore the obtained data on structure parameters confirms our suggestion about existence of inhomogeneous atomic distribution in tin-based diluted solutions. The melts of eutectic systems, studied in this work show the significant difference in atomic radius values. Thus, if suppose that some tin atoms are substituted by another kind ones, the SF should be almost the same as for liquid tin. Such behavior must be also displayed in corresponding PCF.
3.30
3.35
3.25
1 2 3
3.30
r, A
r, A
3.20 O
O
3.15
3.25 3.20
3.10
3.15
3.05 3.00
1 2 3
0
5
10
aT. % Ge
3.10
15
5
aT. % In
10
15
3.40
1 2 3
3.3
0
1
3.35
2 3.30
r, A
r, A
3.2 O
O
3
3.25 3.20
3.1
3.15
3.0 -2.5
3.10
0.0
2.5
5.0
7.5
aT. % Bi
10.0 12.5
15.0
0
5
aT. % Pb
10
Fig. 2. The most probable distances for Sn1xMex (1 – experimental data, 2 – self-associated distribution model, 3 – random atomic distribution model).
S. Mudry et al. / Journal of Non-Crystalline Solids 353 (2007) 2982–2986
Taking into account the fact that atomic density with addition of diluted elements must be almost the same as for tin. It is possible to note that the height of SF principle peak must be unchangeable when diluted element content increases. Such behavior in concentration dependence of this parameter is not always observed for studied systems. This fact allowed us to suggest that introducing of diluted atoms into vacancies of liquid tin structure is possible. From analysis of obtained data follows that in some binaries the decrease of principal peak height with diluted element content is observed within some definite concentration range. Experimental total SF were used in order to calculate the partial SF by means of Reverse Monte Carlo Method [3]. For all binary systems the partial SF SSn–Sn(q) obtained in such way is similar to SF of liquid tin, whereas the SSn–M(q) and SM–M(q) show some features, especially the last (Fig. 3) It has an untypical for simple liquid metals profile and does not reveal any peaks. Upon increasing of diluted element content up to some values the profile of
SGe-Ge(q)
0.125
2985
SM–M(q) partial SF significantly changes and reveals the maxima as in simple liquids. Such behavior allowed us to conclude that correlation between diluted atoms occurs only at higher then some definite value concentration. Partial structure factors calculated by means of Reverse Monte Carlo method were used for obtaining of another kind structural functions – Bhatia–Thornton structure factors. One of them – SCC(q) is a measure of chemical short range order and indicates the deviation of structure from random atomic distribution. As it can be seen from Fig. 4 there are a small oscillations in SCC(q) for Sn1x–Gex molten alloys over all concentration range studied. SCC(q) structure factor shows no fluctuations of concentration in this case because the content of melt changes not only via changes of each kind atom fraction in structure units, but also via changes of these structure units fraction. The fluctuations concentration on the scale of structure units occur and it is the reason that peaks in SCC(q) for Sn1x–Gex molten alloys are not so resoluted
SIn-In(q)
1
0.125
0.1
1
0
0
0.1
0
0.075
0
0.05
0
x=0.025
0.075 0 0.05 0 x=0.025 0 0
0 1
2
3
4 5 -1 q, A
6
7
8
2
4
O
6 O
q, A
8
-1
SBi-Bi(q) 0.125
1
SPb-Pb(q)
0.1
0
0.125
0.05
1 0 0
x=0.025
0
0.05
0
0
x=0.025
0
0
0.075 0 0
0
1
2
3 4 -1 q, A O
5
6
7
8
0.1 0.075
0
1
2
3
4 5 6 -1 q, A O
Fig. 3. Partial structure factors (Reverse Monte Carlo method).
7
8
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S. Mudry et al. / Journal of Non-Crystalline Solids 353 (2007) 2982–2986
Scc(q)
Scc(q)
Sn-Ge 1
Sn-In
0.125
0.125
0
1
0.1
0
0.1
0.075
0
0.075
0
0.05
0
0
x=0.025
0
0
0
0.05
0
x=0.025
0
2
4 O
6
2
4 O
-1
6
-1
q, A
q, A
Scc(q)
Sn-Pb
Scc(q)
0.125
Sn-Bi
1
0.125
0.1
0
1
0.1
0
0.075
0
0
0.075
0
0.05
0
x=0.025
0.05
0
x=0.025
0 0
0 0
2
4 O
6
0
2
4 O
-1
6
-1
q, A
q, A
Fig. 4. Partial Bhatia–Thornton SCC(q) structure factors.
as in other melts. Another shape of SCC(q) is observed in Sn1xBix molten alloys. Particularly, the principal peak increases with addition of Bi- atoms. If content of Bi reaches 12.5 at.%, the concentration fluctuations are significant and first peak position SCC(q) is practically the same that in total structure factor. Slight oscillations in SCC(q) occur for Sn1xInx liquid alloys. If the content of In is 10 at.% and higher the SCC(q) shows the typical shape, which is the evidence of significant concentration fluctuations. Concentration dependence of SCC(q) for Sn1xPbx molten alloys is similar to that in Sn1xBix. Only at small content of Pb the deviation from random atomic distribution can be neglected. At addition of Pb atoms up to 12.5 at.% the principal peaks show a good resolution. The reason of such behavior is the tendency to self-association of Pb-atoms, which aggregates in groups, diluted in tin matrix. Thus the analysis of SCC(q) partial structure factors for binary Sn-based eutectic melts shows that Bi and Pb- atoms
attempt to aggregate in small atomic groups. Therefore the real structure of diluted tin-based solutions deviates from ideal solutions model and can be considered as mixture of atoms and structural units of larger size. 4. Conclusions Tin-based alloys with Pb, In, Bi and Ge, containing 0– 12.5 at.% show the inhomogeneous short range order, whose topology is determined by structure of tin. Significant changes of atomic distribution in tin are no observed upon addition of diluted atoms up to some definite their content. Molten alloys of these systems can be considered as a mixture of atoms and aggregated atomic groups. References [1] D.T. Cromer, J.T. Waber, Acta Cryst. 18 (15) (1965) 104. [2] J. Krogh-Moe, Acta Cryst. 9 (1956) 951. [3] R.L. McGreevy, L. Pusztai, Mol. Simulat. 1 (1988) 359.