Some Properties of Eutectic Alloys and Molecular Concentration
Abstract Generated abstract
This paper examines whether the molecular concentration, defined from density and molecular weight, can serve as a parameter characterizing properties of eutectic alloys and related low melting solid solutions. Using published and tabulated data for binary and ternary systems, it compares molecular concentration with contact melting temperature, superconducting transition temperature in lead eutectic alloys, and the temperature coefficient of Brinell hardness. The analysis indicates that higher molecular concentration is associated with higher contact melting temperatures in binary and ternary eutectics, while superconducting transition temperature and the absolute value of the hardness temperature coefficient decrease with increasing molecular concentration. The paper argues that these correlations support treating molecular concentration as a useful descriptive quantity for several physical and mechanical properties of eutectic alloys.
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SOME PROPERTIES OF EUTECTIC ALLOYS AND MOLECULAR CONCENTRATION
P. A. SAVINTSEV
(Presented by the Scientific Seminar on Dielectrics)
Eutectics have extensive practical applications. Many technically important alloys contain one or several eutectics.
One of the interesting properties of eutectics is their low melting point: eutectics have a melting temperature lower than the melting temperature of the components. It was believed that this feature of eutectics is explained by the properties of eutectic structures, which are formed from a liquid melt during its solidification [1].
Experiments [2] showed that eutectic melting can also be observed when there are no preexisting eutectic structures. Melting occurs at the contact of two or more substances possessing mutual limited solubility in the solid state and dissolving in one another in the liquid state, when the contact is heated to a temperature much lower than the melting temperatures of the components. This phenomenon was called [3] the phenomenon (effect) of contact melting. Investigations showed that the temperature of contact melting coincides with the temperature of eutectic melting.
The phenomenon of contact melting was used in [4] to determine the melting temperature of a large number of organic eutectics. The authors of [4] point out that the usual method for determining the melting temperatures of eutectics by observing the cooling curves of alloys of the reacting components proved unsuitable, owing to the fact that, when the components are fused, systems complex in composition are formed, containing, in addition to the principal reaction products, also substances formed as a result of further successive transformations, and substances released in the course of the reaction.
We have shown [5] the relation of certain properties of crystals and alloys to the molecular concentration
\[ a=\frac{D}{M}10^3, \]
where \(D\) is the density, and \(M\) is the molecular weight of the substance. It is of interest to investigate the relation of the contact-melting temperature to the quantity \(a\). In the experiments [2], contact melting was observed for any ratio of the components. This gives grounds for understanding, by the value \(a\) of eutectics, a quantity proportional to \((a_1+a_2)\), where \(a_1\) and \(a_2\) are the molecular concentrations of the substances forming the eutectic.
Comparison of the temperature of contact melting with \((\alpha_1+\alpha_2)\) in the case of a large number of pairs is better if one of the components remains constant and, consequently, the value \(\alpha_1\) remains unchanged. In Table 1 a comparison is made of the temperature of contact eutectic melting with the value \((\alpha_1+\alpha_2)\). From Table 1 it is seen that, with an increase in the molecular concentration \((\alpha_1+\alpha_2)\), the temperature of contact melting rises. In the comparisons carried out in Table 1, cases are distinguished in which \(\alpha_1>\alpha_2\) and in which \(\alpha_1<\alpha_2\).
Table 1
Comparison of the temperature of contact melting with the molecular concentration \((\alpha_1+\alpha_2)\)
| System | \(t_{\mathrm{melt}}\), °C | \((\alpha_1+\alpha_2)\ \mathrm{cm}^{-3}\,\mathrm{mol}\), \(\alpha_1>\alpha_2\) | \((\alpha_1+\alpha_2)\ \mathrm{cm}^{-3}\,\mathrm{mol}\), \(\alpha_1<\alpha_2\) | System | \(t_{\mathrm{melt}}\), °C | \((\alpha_1+\alpha_2)\ \mathrm{cm}^{-3}\,\mathrm{mol}\), \(\alpha_1>\alpha_2\) | \((\alpha_1+\alpha_2)\ \mathrm{cm}^{-3}\,\mathrm{mol}\), \(\alpha_1<\alpha_2\) |
|---|---|---|---|---|---|---|---|
| Bi—Pb | 125 | — | 102 | Cu—Sb | 535 | 195 | — |
| Bi—Sn | 139 | — | 108 | Cu—P | 707 | 210 | — |
| Bi—Cd | 144 | — | 124 | Cu—Ag | 779 | 238 | — |
| *Cu—Mn | 862 | 274 | — | ||||
| Sn—Cd | 177 | — | 138 | Fe—S | 985 | 203 | — |
| Sn—Zn | 199 | — | 166 | Fe—Ti | 1430 | 233 | — |
| *Fe—V | 1442 | 253 | — | ||||
| n—B | 139 | 108 | — | Fe—C | 1145 | 330 | — |
| n—Pb | 183 | 116 | — | Fe—B | 1165 | 352 | — |
| Cd—Bi | 144 | 124 | — | *LiCl—NaCl | 552 | 86 | — |
| Cd—Sn | 177 | 138 | — | LiCl—KCl | 352 | 75 | — |
| LiCl—RbCl | 312 | 45 | — | ||||
| Zn—Sn | 199 | 171 | — | *KCl—KBr | 716 | 48 | — |
| Zn—Cd | 266 | 182 | — | *KCl—KJ | 584 | 45 | — |
| Pb—Sn | 183 | — | 116 | RbCl—NaCl | 541 | — | 60 |
| Pb—Cd | 248 | — | 132 | *RbCl—CsCl | 440 | — | 47 |
| Ag—Bi | 262 | 145 | — | *KBr—KJ | 589 | 41 | — |
| Ag—Ti | 287 | 156 | — | KBr—KF | 581 | — | 63 |
| Ag—As | 540 | 160 | — | KBr—LiBr | 348 | — | 62 |
| Ag—Si | 830 | 183 | — | ||||
| Ag—Cu | 779 | — | 238 | KOH—KBr | 300 | 60 | — |
| Ag—Be | 878 | — | 303 | KOH—KJ | 250 | 57 | |
| Au—Tl | 120 | 156 | — | ||||
| Au—Si | 370 | 183 | |||||
| *Au—Cu | 895 | 238 | — | ||||
| Au—Ni | 950 | 247 | — |
* Solid solutions with a descending liquidus.
Contact melting is explained [6] with the aid of the hypothesis of interaction between like and unlike atoms: at a temperature below the eutectic temperature, interaction between like atoms predominates, while at a temperature above the eutectic temperature, conversely, interaction between unlike atoms predominates. The temperature of transition from one type of interaction between particles to another type of interaction depends on the concentration of the particles forming the crystals: the greater the concentration of particles, the higher the temperature at which the change in the type of interaction takes place.
It should be noted that Table 1 also presents solid solutions that have a melting temperature lower than the melting temperature of the components. In this respect, the given solid solutions are similar in their properties to eutectics. The majority of solid solutions formed by alkali-halide salts belong to the class of solid solutions considered.
Table 2
Comparison of the temperature of contact melting at the boundary “binary eutectic—third component,” forming a ternary eutectic, with the molecular concentration of the third component
| System | \(t_{\text{melt. eut.}}\), °C | \(a_3\), \(cm^{-3}\, mol\) |
|---|---|---|
| \((\mathrm{Bi—Cd})—\mathrm{Pb}\) | 92.6 | 55 |
| \((\mathrm{Bi—Cd})—\mathrm{Sn}\) | 104.4 | 61 |
| \((\mathrm{Bi—Sn})—\mathrm{Pb}\) | 97.5 | 55 |
| \((\mathrm{Bi—Sn})—\mathrm{Cd}\) | 104.4 | 77 |
| \((\mathrm{Sn—Cd})—\mathrm{Bi}\) | 104.4 | 47 |
| \((\mathrm{Sn—Cd})—\mathrm{Pb}\) | 146.4 | 55 |
| \((\mathrm{Sn—Cd})—\mathrm{Zn}\) | 164.7 | 105 |
| \((\mathrm{Pb—Cd})—\mathrm{Bi}\) | 92.6 | 47 |
| \((\mathrm{Pb—Cd})—\mathrm{Sn}\) | 146.4 | 61 |
| \((\mathrm{Pb—Sn})—\mathrm{Bi}\) | 97.5 | 47 |
| \((\mathrm{Pb—Sn})—\mathrm{Cd}\) | 146.2 | 77 |
Contact melting was also observed for substances forming ternary eutectics. In these experiments [3], powders of three substances were brought into contact, or else pieces of binary eutectics were contacted with a third substance, which together formed a ternary eutectic. When comparing molecular concentration with the contact-melting temperature of three substances, the presence of a binary eutectic is assumed. In this case, the contact-melting temperature can be related to the molecular concentration of the third component. It follows from Table 2 that, with increasing \(a_3\), the contact-melting temperature rises.
In Table 3 the temperature of transition of binary eutectic lead alloys into the superconducting state is compared with the molecular concentration \((a_1 + a_2)\).
For constructing Table 3, data from [7] were used. It follows from Table 3 that, with increasing \((a_1 + a_2)\), the transition temperature decreases.
The molecular concentration \((a_1 + a_2)\) is connected with the mechanical properties of eutectic alloys. V. P. Shishokin and co-workers [8–10] determined the Brinell hardness of the alloys bismuth–tin, cadmium–bismuth, cadmium–lead, cadmium–tin, lead–tin, tin–zinc, cadmium–zinc. The relation between the hardness of the alloys \(H\) and the test temperature \(t\), established in [8], has the form:
\[ H = \varkappa e^{-\beta t}, \]
where \(\kappa\) is a constant for the given alloy,
\(\beta\) is the temperature coefficient of hardness.
Table 3
Comparison of the transition temperature of binary eutectic lead alloys into the superconducting state with the molecular concentration \((\alpha_1+\alpha_2)\)
| Alloys | Pb—As | Pb—P | Pb—Ag | Pb—Au |
|---|---|---|---|---|
| \(T\), °abs. | 8.4 | 7.8 | 7.2 | 7.0 |
| \((\alpha_1+\alpha_2)\ \mathrm{cm}^{-3}\ \mathrm{mol}\) \(\alpha_1<\alpha_2\) |
117 | 125 | 152.6 | 152.8 |
V. P. Shishokin and V. A. Ageeva [9] found for alloys of the lead–bismuth system that the temperature coefficient of hardness has its greatest value for an alloy having the eutectic composition. They explain these results by the assumption that there is a dependence between the temperature coefficient of hardness and the melting temperature of the alloy: the lower the melting temperature, the higher the temperature coefficient.
V. P. Shishokin, I. R. Kogan, and P. A. Vikhoreva [10] carried out a study of the zinc–cadmium system under conditions of preliminary prolonged annealing of the specimens (460 h). In this system the alloy of eutectic composition has the greatest temperature coefficient of hardness.
In Table 4 the Brinell temperature coefficient of hardness \(\beta\) of binary eutectic alloys is compared with the molecular concentration of the components \((\alpha_1+\alpha_2)\). It is seen from Table 4 that, with increasing molecular concentration, the absolute value of the temperature coefficient of hardness decreases.
V. P. Shishokin and I. D. Zaporozhets [11] determined the Brinell hardness at various temperatures of several ternary and one quaternary eutectics. They found that the temperature coefficient of hardness of ternary eutectic alloys exceeds the temperature coefficient of hardness of the components to an even greater degree than does the temperature coefficient of binary alloys. If for binary eutectic alloys the coefficient \(\beta\) is 2–3 times greater than \(\beta\) of pure metals, then for ternary eutectic alloys it is 3–4 times greater, and for the quaternary eutectic alloy 4–5 times greater than \(\beta\) of pure metals. As a result of annealing, which lasted 120–240 hours at a temperature 20–30° below the eutectic temperature, the hardness and the temperature coefficient of hardness decreased; however, the decrease was not very large.
In Table 4 the Brinell temperature coefficient of hardness of ternary eutectic alloys is compared with the molecular concentration \(\alpha_3\) of the third component.
It is seen from Table 4 that in each group of alloys, with increasing \(\alpha_3\), the absolute value of the Brinell temperature coefficient of hardness decreases.
Thus, molecular concentration may be regarded as a quantity characterizing many properties of eutectic alloys. With increasing molecular concentration, the melting temperature of binary and ternary eutectics increases, and the temperature decreases
transition to the superconducting state of binary eutectic lead alloys, the absolute value of the temperature coefficient of Brinell hardness of binary and ternary eutectic alloys decreases.
Table 4
Comparison of the temperature coefficient of Brinell hardness of eutectic alloys with molecular concentration
| Alloys | $-\beta \cdot 10^4$ | $(z_1+z_2)\ \mathrm{cm}^{-3}\ \mathrm{mol}$, $z_1 > z_2$ | $(z_1+z_2)\ \mathrm{cm}^{-3}\ \mathrm{mol}$, $z_1 < z_2$ | $z_3\ \mathrm{cm}^{-3}\ \mathrm{mol}$ |
|---|---|---|---|---|
| Pb—Cd | 57 | — | 132 | — |
| Pb—Sn | 75 | — | 116 | — |
| Cd—Sn | 53 | 138 | — | — |
| Cd—Pb | 57 | 132 | — | — |
| Cd—Bi | 88 | 124 | — | — |
| Bi—Cd | 88 | — | 124 | — |
| Bi—Sn | 117 | — | 108 | — |
| Sn—Pb | 77 | 116 | — | — |
| Sn—Bi | 117 | 108 | — | — |
| (Bi—Cd)—Pb | 128 | — | — | 55 |
| (Bi—Cd)—Zn | 63 | — | — | 105 |
| (Pb—Bi)—Sn | 131 | — | — | 61 |
| (Pb—Bi)—Cd | 128 | — | — | 77 |
| (Pb—Sn)—Bi | 131 | — | — | 47 |
| (Pb—Sn)—Cd | 73 | — | — | 77 |
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