CONTACT MELTING OF MULTICOMPONENT ORGANIC SYSTEMS

P. A. Savintsev, B. F. Ufimtsev

(Presented by the scientific seminar of the Radio Engineering Faculty)

Low-melting eutectic alloys, whose melting temperature is lower than the melting temperatures of the initial components, find broad application in science and technology. Binary and ternary eutectic alloys are known; eutectics of four and five components occur much more rarely. Low-melting alloys of six or more components are unknown.

The production of alloys from a large number of components would be of considerable theoretical and practical interest, since this would broaden the range of alloys possessing useful properties.

In a number of works [1, 3], opinions have been expressed that eutectics of five or more components do not exist and cannot be obtained.

Ieneke [1] proved the impossibility of the existence of multicomponent eutectic systems on the basis of geometrical considerations: eutectics are a mixture of heterogeneous crystals. Therefore, in an \(m\)-phase eutectic there must be contact of \(m\) different substances. At one and the same point, at most 4 crystals can be in contact. Consequently, only two-, three-, and four-component eutectic systems are possible.

S. V. Avakyan and N. F. Lashko [2] criticized Ieneke’s statements. They present a geometrical scheme illustrating the possibility of contact of six heterogeneous crystals. The limited number of phases in a eutectic follows, in their opinion, from the principle according to which the formation of a eutectic is determined by the probability of formation of contact of \(m\) phases. To find the probability of such an event, S. V. Avakyan and N. F. Lashko propose the formula

\[ p_m = C_N^m p^m(1-p)^{N-m}, \]

where \(N\) is the number of possible objects of investigation (for eutectics of elements it coincides with the number of chemical elements).

\(p\) is the probability of the occurrence of a nucleus of any one of the \(m\) phases in any of the unit volumes.

\[ p=\frac{\kappa}{N}, \]

where \(\kappa\) is the average number of objects per unit volume.

\(C_N^m\) is the number of combinations of \(N\) taken \(m\) at a time.

If \(N\) is sufficiently large and \(p=\dfrac{\kappa}{N}\) is sufficiently small, then we arrive at the Poisson equation

\[ p_m=\frac{\kappa^m}{m!}\exp(-\kappa) \]

and for \(\kappa=1\) we obtain

\[ p_m=\frac{1}{e m!}. \]

It follows from this that the probability of coexistence of elements decreases markedly as the number of phases increases. The relative probability of the occurrence of an \(m\)-phase eutectic as compared with a two-phase eutectic will be

\[ \frac{p_m}{p_2}=\frac{2!}{m!}=\frac{1}{3\cdot 4\cdot 5\ldots (m-1)m}. \]

Calculations performed using this formula gave the following:

From the values given, it is evident that the probability of existence of a eutectic with more than four phases is very small. S. V. Avakyan and N. F. Lashko explain by this the absence in the reference literature of data on multicomponent eutectics with more than four phases. M. Kh. Gluzman and V. P. Rubtsova [3] use the conclusions of S. V. Avakyan and N. F. Lashko to deny entirely the possibility of determining the melting temperature of systems of five or more components by the method of contact melting.

The conclusions of Gluzman and Rubtsova are untenable. The small probability of existence of multicomponent eutectics by no means implies their complete absence. Experiments [4] have revealed eutectics of seven components.

In applying the method of contact melting to multicomponent systems, an interesting feature of the liquid droplets obtained was used. If a particle of crystal \(B\) is placed on the surface of crystal \(A\) and heating is carried out, then, upon reaching the contact-melting temperature, a liquid will form that will spread over the surface of crystal \(A\) [5]. This is explained by the fact that the surface tension of the liquid eutectic droplet \(\sigma\) at the melting point \(t\) is less than the sum of the surface tensions of the crystals \(\sigma_A+\sigma_B\) at the same temperature.

To find a ternary eutectic, one may place a grain of component \(C\) on the film of the solidified binary eutectic on crystal \(A\) and carry out heating in the same manner until droplets of the ternary eutectic appear. Then, in this way, four-component, five-component, six-component, etc. alloys can be obtained.

To obtain a large amount of melt, the crystals \(A\), \(B\), \(C\), etc., must be of large size.

The low-melting multicomponent alloys discovered by us by the method of contact melting are given in Table 1. There is reason to expect the existence of low-melting alloys with a number of elements greater than that indicated in Table 1.

Table 1

Temperature of contact melting of organic systems

Thus, contact melting is also possible in systems consisting of a large number of components.

LITERATURE

1. Janecke E., Kurzgefasstes Handbuch aller Legierungen, 1937.

2. Avakyan S. V. and Lashko N. F., On the nature of eutectic alloys. ZhFKh, vol. 23, no. 3, 315, 1949.

3. Guzman M. Kh. and Rubtsova V. P., Determination of eutectic melting of three- and four-component organic systems. ZhOKh, vol. 27 (89), no. 3, 704, 1957.

4. Savintsev P. A. and Vyatkina A. V., Multicomponent low-melting alloys. Izvestiya vuzov MVO SSSR, Fizika, no. 4, 1958.

5. Saratovkin D. D. and Savintsev P. A., Capillary phenomena during contact melting. DAN SSSR, vol. 80, no. 4, 1951.