Wear of Crystals and Surface Energy of the Eutectic Systems KCl—K₂CrO₄, Bi—Sn during Mutual Grinding with Abrasive Powder

P. A. Savintsev and L. E. Abramovich

(Presented by Academician V. D. Kuznetsov)

In this work, the wear of crystals was determined by the method of mutual grinding, widely used by V. D. Kuznetsov [1] for determining the surface energies of brittle bodies.

We shall consider wear as one of the properties of an alloy. The relationship between the properties of alloys and their composition was formulated by N. S. Kurnakov [2] and is known as “Kurnakov’s rule.” As applied to eutectic alloys, this rule states that the change of a property as a function of composition is represented graphically by a straight line. This means that the eutectic point on the composition–property diagram does not manifest itself in any way, that is, it is not distinguished by any special properties from alloys close to it in composition. However, A. Sapozhnikov [3] observed an increase in the hardness of eutectic alloys of lead and tin in comparison with alloys close to them in composition.

A. Sapozhnikov and M. Sakharov [4, 5], studying the mechanical properties and microstructure of cadmium–zinc alloys, found that the eutectic alloy on the hardness–composition curve is distinguished by a maximum. These same authors found that the aluminum–zinc eutectic alloy differs from the alloys adjacent to it by greater hardness.

A. Sapozhnikov and Gaidukov [6], in measuring the hardness of antimony alloys with zinc, found that at a point close to the eutectic a clearly expressed minimum is obtained.

N. Kurnakov and his students [7] explained the increase in hardness of eutectic alloys by internal stresses arising during rapid crystallization. A necessary condition for the applicability of straight-line diagrams is that the solidified system must be in a stable (annealed) state. In this case the eutectic mixture is not distinguished by special properties from alloys close to it in composition. These conclusions of N. S. Kurnakov were confirmed by experiments with cadmium–zinc alloys by A. Glazunov and M. Matveev [8]. They annealed specimens for 72 hours (one batch) and 900 hours (another batch). It turned out that after annealing for 72 hours the hardness diagram is not represented by a straight line, but has a clearly expressed maximum corresponding to the eutectic. After annealing for 900 hours the hardness diagram is represented by a straight line. Straight-line dependences for annealed specimens were observed—

were also given by Kurnakov in plots of electrical conductivity—composition, and flow pressure—composition.

The opposite of N. S. Kurnakov’s assertion was maintained by P. Ya. Saldau [9]. He wrote that the compositions corresponding to the eutectic differ sharply from neighboring compositions by greater hardness, greater electrical resistance, and greater flow pressure. The special position of the eutectic points is preserved even after prolonged annealing. This is explained, according to P. Ya. Saldau, by the fact that a eutectic alloy is an alloy having a special structure and possessing special properties inherent only in it.

P. Ya. Saldau studied alloys of the lead—tin system; moreover, the composition of alloys close to the eutectic differed by 0.5%. The hardness of the alloys was determined before annealing, after two-week and six-week annealing at a temperature of 170°. It turned out that the hardness of a specimen with a eutectic structure always remains greater than the hardness of specimens having a concentration close to the eutectic one. It should be noted that the degree of difference in hardness of eutectic alloys from adjacent alloys decreases as the duration of annealing increases. However, even with prolonged annealing, the distinction of the eutectic point is preserved. These properties of eutectics, as P. Ya. Saldau indicates, are explained by their higher degree of dispersion in comparison with alloys of adjacent composition.

A. F. Kapustinskii and B. A. Shmelev [10] found the heat of activation \(Q\) of Bi—Sn alloys. To determine \(Q\), the equation

\[ K = ze^{-\frac{Q}{RT}}, \]

was used, where \(K\) is the reaction-rate constant, \(z\) is the proportionality coefficient, \(R\) is the universal gas constant, and \(T\) is the absolute temperature. By measuring the temperature dependence of the constant \(K\), it was possible to find the value \(Q\), characterizing the given process. The authors determined the rate of catalytic decomposition of hydrogen peroxide on Bi—Sn alloys. Specimens in the form of plates \(10 \times 10\ \text{mm}^2\) were fastened to a stirrer, which was immersed in a solution of hydrogen peroxide. The edge of the plate and the reverse side were protected with wax. The experiments were carried out in a thermostat at 30, 40, and 50° (\(\pm 0.1^\circ\)) at a constant rate of rotation of the stirrer. The decomposition was determined by taking samples of the given solution and measuring its concentration.

The authors found that the heat of activation \(Q\) of Bi—Sn alloys changes sharply with composition, reaching a maximum at the point corresponding to the eutectic concentration. It is unfortunate that in these interesting experiments the heat of activation for alloys of eutectic concentration was not measured by the authors, but was obtained by extending two curves to the eutectic point.

In our experiments, relative wear was determined by the method of mutual grinding of crystals with abrasive powder KZ-100. The theory of this method was given by V. D. Kuznetsov [1]. He also carried out an experimental verification of the theory on crystals of halide salts of alkali metals. It turned out that the energy expended on mutual grinding of brittle metals is distributed equally between the crystals; it is also interesting that the ratio of the ground-off masses depends little on the grade of abrasive powder and the rate at which it is fed. A necessary condition for the application of this method is the absence of chipping of large particles of the crystals, i.e., the powders obtained during grinding must consist of small particles of approximately identical size.

Let us regard one of the crystals as the standard and denote its ground volume by \(V_0\), while the ground volume of the alloy under investigation will be \(V\). Then, as the relative wear one may choose the ratio

\[ \frac{V}{V_0}. \]

In our experiments the volumes were calculated from determinations of the masses of the crystals \(M\) before and after the experiment. The densities of the crystals were found by weighing the crystals, with an accuracy of up to 1 mg, in air and in a liquid that does not dissolve the crystal.

As the standard crystal in the study of the system KCl—K\(_2\)CrO\(_4\), we chose a single crystal of KCl grown by the Kyropoulos method [11]. Grinding was carried out on a cube face of the above-mentioned crystal. The experimental results are given in Table 1, from which it is seen that the alloy of eutectic concentration differs sharply in relative wear from alloys of neighboring concentrations. The eutectic alloy corresponds to the maximum relative wear.

Table 1

Relative wear of alloys of the system KCl—K\(_2\)CrO\(_4\)

Note to Table 1. \(M_0\) and \(V_0\) are the ground mass and volume of the standard (KCl); \(M\) and \(V\) are the ground mass and volume of the alloy.

In the study of the Bi—Sn system, we chose a Bi crystal as the standard. The results obtained in the mutual grinding of Bi—Sn alloys against a Bi crystal are given in Table 2, from which it is seen that the alloy of eutectic concentration has a wear almost 2 times greater than that of alloys of neighboring concentrations.

It is known that V. D. Kuznetsov related relative wear to the surface energy of brittle crystals [1]. We shall use his theory in order to estimate the surface energy \(\sigma\) of the crystals we investigated.

The surface energy of crystals of the system KCl—K\(_2\)CrO\(_4\) can be calculated from the magnitude of the relative wear

\[ \frac{V}{V_0} \]

and the surface energy \(\sigma_0\) of the standard single crystal.

\(^1\) Eutectic.

Table 2

Relative wear of bismuth–tin alloys

The surface energy \(\sigma_0\) of a KCl single crystal has been calculated theoretically by a number of researchers [1, 12]. The results of these calculations are given in Table 3, from which it is evident that the values of \(\sigma_0\) obtained by different authors differ considerably from one another.

Table 3

Surface energy of a KCl crystal for the (100) face

In his works V. D. Kuznetsov [1] gives preference to the surface-energy calculations carried out by Born and Stern.

We calculated the surface energy of KCl–K\(_2\)CrO\(_4\) alloys on the basis of these same data; that is, we took the surface energy of the reference KCl crystal to be \(\sigma_0 = 108\) erg/cm\(^2\). The results of determining \(\sigma\) in this way are given in Table 4, from which it is evident that the eutectic alloy (31.5% K\(_2\)CrO\(_4\) + 68.5% KCl) has a surface energy several times lower than the \(\sigma\) of alloys of neighboring concentrations.

Table 4

Surface energy of KCl–K\(_2\)CrO\(_4\) alloys

By the method of mutual grinding we also determined the surface energy of a KCl polycrystal. It turned out that the $\sigma$ of the KCl polycrystal is 1.5 times greater than the surface energy of the cube face of a KCl single crystal. These results agree with the following calculations by V. D. Kuznetsov [1], which were carried out for NaCl crystals but are also valid for crystals similar to them in structure, i.e., for KCl crystals.

Let us denote the surface energy of the faces (100), (110), and (111) of a KCl crystal and similar halides by $\sigma_0$, $\sigma_1$, and $\sigma_2$. From cleavage experiments on NaCl single crystals it was found that $\sigma_2 = 1.73\sigma_0$, and $\sigma_1 = 1.41\sigma_0$. We shall assume that in cutting a polycrystal we encounter one of the above three groups of faces. In the crystal there are 6 faces (100), 12 faces (110), and 8 faces (111), for a total of 26 faces. The probabilities of encountering the faces (100), (110), and (111) will therefore be, respectively, $6:26 = 0.23$, $12:26 = 0.46$, and $8:26 = 0.31$.

Therefore, the average surface energy of the section plane of a polycrystal, with a random arrangement of crystallite faces, will be

\[ \sigma = \frac{23 \cdot 1 + 46 \cdot 1.41 + 31 \cdot 1.73}{100}\,\sigma_0 = 1.46\sigma_0 . \]

Such a ratio, writes V. D. Kuznetsov [1], will be valid for any crystal among the alkali-metal halides.

Our experiments with KCl confirm these calculations. In addition to calculations in which we took $\sigma_0 = 108$ erg/cm$^2$, we also made other calculations, determining simply the relative values of the surface energies $\dfrac{\sigma}{\sigma_0}$. The results of such calculations are also given in Table 4, from which it is seen that the eutectic point differs sharply from alloys adjacent in concentration by the minimum value of the relative surface energy $\dfrac{\sigma}{\sigma_0}$.

In calculating the surface energy $\sigma$ of Bi—Sn alloys, as the reference crystal having surface energy $\sigma_0$ we chose a Bi crystal and calculated the relative values of the surface energies $\dfrac{\sigma}{\sigma_0}$. The results of these calculations are given in Table 5, from which it is seen that the eutectic alloy differs from alloys of neighboring concentrations by the minimum value of the relative surface energy.

It is of interest to compare the surface-energy values $\sigma$ found by us with those obtained in determining $\sigma$ of liquid bismuth—tin melts [13].

The notation in Table 5 is as follows: $M_0$ is the ground mass of Bi, $M$ is the ground mass of the alloy, $D$ is the density of the alloy, $D_0$ is the density of Bi, $\dfrac{\sigma}{\sigma_0}$ is the ratio of the surface energy of the alloy to the surface energy of bismuth.

Yu. Ya. Klyachko and A. L. Kunin [13] measured the surface tension of liquid tin—bismuth alloys by the ring-detachment method [14]. They found that, with considerable superheating above

Table 5

Surface energy of Bi—Sn alloys

of the crystallization temperature, the eutectic point does not affect the course of the dependence of surface tension on alloy concentration. The surface tension of eutectic alloys at a temperature somewhat above the melting temperature of the eutectic is lower than the surface tension of each of the components of the alloy.

The authors believe that with slight overheating the eutectic structure is preserved, and therefore the alloy exhibits a minimum surface tension. With sufficient overheating this structure is destroyed, and the alloy behaves “normally.”

Yu. A. Klyachko and L. L. Kunin point out that the special properties of eutectic structures are explained by the fact that they are not simply mixtures, but are chemical compounds.

However, the chemical nature of solid eutectics and liquid eutectic melts under slight overheating has been refuted by many experiments, including the X-ray studies of V. I. Danilov [15]. He showed that, near the eutectic point, an analogy may be drawn between the structure of liquid and solid eutectic alloys. Later K. Bunin [16] reached the same conclusions from experiments on the centrifugation of liquid bismuth–tin eutectic alloys. Hence it becomes clear why the eutectic point, which is distinguished in solid alloys, is also distinguished in the case of melts under slight overheating.

Conclusion

Experiments on the mutual grinding of KCl—K\(_2\)CrO\(_4\) and Bi—Sn crystals show that eutectic alloys have maximum wear in comparison with alloys close to them in composition.

An evaluation of the values of the surface energy of the above systems, carried out on the basis of V. D. Kuznetsov’s theory developed for brittle bodies, indicates that eutectic alloys must have minimum surface energy.

E. M. Simagina took part in the experiments on the mutual grinding of crystals.

¹) Eutectic.

References

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8. Glazunov, A. I., and Matveev, M. M. Hardness and electrical conductivity of zinc alloys with cadmium. Proceedings of the Petrograd Polytechnic Institute, vol. 19, 1913.

9. Sal’dau, P. Ya. Special properties of eutectic and eutectoid metallic alloys. Domez, No. 7 (13), 1930.

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11. S. Kurokoulos. Ein Verfahren zur Herstellung grosser Kristalle. Z. s. f. anorg. und allgem. Chem., 154, 1926.

12. B. M. Dent. The effect of boundary distortion on the surface energy of a crystal. Phil. Mag., 8, 1929.

13. Klyachko, Yu. A., and Kunin, L. M. On the surface tension of eutectic alloys. DAN SSSR, vol. 64, No. 1, 1949.

14. Kunin, L. L., and Klyachko, Yu. A. An apparatus for measuring the surface tension of liquid metals. Zavodskaya laboratoriya, vol. 14, No. 6, 1948.

15. Danilov, V. I. X-ray studies of liquids. Izv. AN SSSR, Physical Series, vol. 5, No. 1, 1941.

16. Bunin, K. On the question of the structure of metallic eutectic alloys. Izv. AN SSSR, OTN, No. 2, 1946.

1. Eutectic. ↩↩↩↩