Measurement of the Surface Energies of Single Crystals of the Potassium Chloride–Sodium Chloride System by the Method of Drilling and Mutual Grinding

P. A. Savintsev and V. V. Kutsepalenko

Surface particles of a crystal possess greater potential energy than particles located inside the crystal. This excess potential energy, referred to a unit surface of the crystal, is called the surface energy \(\sigma\). The determination of \(\sigma\) can also be approached in the following way. Let us mentally divide a certain crystal into two parts by a plane of area \(S\). In this case the energy of the crystal may be represented as the sum of the energies of its parts, that is,

\[ U = U_1 + U_2 . \]

If, however, this crystal is actually divided into two parts, two crystals are obtained with a total energy

\[ U' = U_1 + U_2 + U_{12}. \]

The total energy has increased by \(U_{12}\) because, as a result of cleavage, some of the internal particles have become surface particles. In such an experiment the surface energy \(\sigma\) is found from the formula

\[ \sigma = \frac{U_{12}}{2S}. \]

This definition of surface energy, developed by V. D. Kuznetsov [1], gives grounds for regarding \(\sigma\) as a measure of the strength of a crystal along the plane \(S\).

The surface energy of crystals has been calculated by a number of authors. Some results obtained for the crystals of interest to us, NaCl and KCl, are given in Table 1.

Table 1

Surface energy of KCl and NaCl crystals in \(\dfrac{\text{erg}}{\text{cm}^2}\) for the face of a cube

For NaCl crystals, the surface energies of the faces \((110)\) and \((111)\) have also been calculated. It has been established that \(\sigma_{(110)} = 2.5\,\sigma_{(100)}\), and \(\sigma_{(111)} = 5.81\,\sigma_{(110)}\). These values of \(\sigma\) are confirmed by experiments on cleavage of rock salt carried out by V. D. Kuznetsov and V. M. Kudryavtseva [1]. V. D. Kuznetsov also showed that a NaCl crystal cannot be cleaved along the planes \((110)\) and \((111)\). In all cases, cleavage proceeds along the surface \((100)\).

Later V. D. Kuznetsov [1, 2, 3] developed a number of additional methods for determining surface energy, namely: grinding on an emery wheel, drilling, and mutual grinding of crystals. In the theory of the drilling method, for two crystals with surface energies \(\sigma_1\) and \(\sigma_2\), a relation was obtained—

\[ \frac{\sigma_1}{\sigma_2}=\frac{\alpha_2}{\alpha_1}, \]

where \(\alpha\) are the angular coefficients in the drilling diagrams: the diameter of the conical pit—the number of revolutions of the drill at constant load. The coefficients \(\alpha_1\) and \(\alpha_2\) are easy to determine if one finds the difference between the diameters of the pits, for example, at 50 and 100 revolutions of the drill. If for the first crystal a difference in diameters \(\Delta d_1\) is obtained, and for the second crystal \(\Delta d_2\), then

\[ \frac{\sigma_1}{\sigma_2}=\frac{\Delta d_2}{\Delta d_1}. \]

By the method of mutual grinding of two crystals, the surface energy is determined from the formula \(\sigma_1 v_1=\sigma_2 v_2\), where \(v\) is the ground-off volume.

As indicated above, the surface energy of pure single crystals was determined by V. D. Kuznetsov by the methods of chipping, grinding on an abrasive, and damped oscillations. By the method of mutual grinding, he also determined the surface energy of pure polycrystals. The results gave good confirmation of the theory of this method.

It was of interest to determine the surface energy of single crystals of solid solutions by the grinding method and to compare the results obtained by this method and by the drilling method.

This problem was solved by us for the KCl—NaCl system.

Sodium chloride and potassium chloride form solid solutions (Fig. 1), formed with absorption of heat and decomposing at temperatures below \(495^\circ\mathrm{C}\) [4,5]. By the Kyropoulos method [6], using a seed, NaCl single crystals with an admixture of KCl (up to 12 mol %) and KCl single crystals with an admixture of NaCl (up to 12 mol %) were obtained.

Fig. 1. Phase diagram of the KCl—NaCl alloy.

The crystals were annealed at a temperature of \(620^\circ\mathrm{C}\), after which the surface energy was determined by the drilling method and by mutual grinding. Drilling was carried out on a hand drilling machine at a constant load of 2.5 kg. The drill was a hardened steel rod, sharpened in the form of a four-sided pyramid with an apex angle of \(90^\circ\).

The experimental results for the crystals of solid solutions are given in Table 2 and in Figs. 2 and 3.

In calculating the surface energies of KCl single crystals with an addition of NaCl, we proceeded from the theoretical value

\[ \sigma_{0\mathrm{KCl}}=108\ \frac{\mathrm{erg}}{\mathrm{cm}^2}, \]

and in determining the surface energy of NaCl single crystals with an admixture of KCl we used the theoretical value

\[ \sigma_{0\mathrm{NaCl}}=150\ \frac{\mathrm{erg}}{\mathrm{cm}^2}. \]

These numerical results were obtained by Born and Stern and confirmed by the experiment of V. D. Kuznetsov.

Fig. 2. Δ—drilling, x—mutual grinding of annealed specimens, o—mutual grinding of unannealed specimens.

The surface energy of a KCl single crystal, determined relative to NaCl, is found to be \(113 \ \frac{\text{erg}}{\text{cm}^2}\), while \(\sigma\) for NaCl relative to KCl is equal to \(143 \ \frac{\text{erg}}{\text{cm}^2}\).

Fig. 3. x—mutual grinding of annealed specimens, o—mutual grinding of unannealed specimens, Δ—drilling.

Table 2

Surface energy of single crystals of sodium chloride–potassium chloride

In the mutual grinding of crystals, an annealed KCl single crystal was taken as the standard. Each time, the mass of the ground-off layer of KCl and of the specimen under study, which was tested before annealing and after annealing, was determined with an accuracy of up to 1 mg. The results of the experiments are given in Table 2 and in Figs. 2 and 3. In the table, the quantities $v_0, \sigma_0, \Delta d_0$ refer to the standard, and the quantities $v, \sigma, \Delta d$ to the specimens under investigation.

Our experiments provide grounds for drawing the following conclusions:

1. The results given by the method of mutual grinding are comparable with the results obtained by the drilling method.

2. In the KCl—NaCl system the surface energy $\sigma$ decreases with an increase in the percentage of the second component. The decrease of $\sigma$ with concentration, expressed in a decrease of the disintegration energy, is evidently connected with a weakening of the forces of interaction between the particles of the lattice.

3. The change in $\sigma$ is especially large at the initial impurity concentrations (in our case, 2.5%). Evidently, a more considerable weakening of the bonds in the lattice occurs here.

4. Annealing of single crystals of solid solutions did not have a noticeable effect on the value of $\sigma$. It may be assumed that, along with the removal of stresses during annealing, in this system there also occurs a process of decomposition of the solid solution.

LITERATURE

1. Kuznetsov V. D. Physics of the Solid State. Tomsk, vol. 1, 1937.

2. Kuznetsov V. D. Physics of the Solid State. Tomsk, vol. 4, 1947.

3. Kuznetsov V. D. Mutual grinding of brittle bodies. Zhurn. TF, 22, 9, 1952.

4. Kurnakov N. S., Zhemchuzhnyi S. F. Isomorphism of potassium and sodium compounds. Collected Selected Works, vol. 1, 186, ONTI, Khimteoretizdat, 1938.

5. Anosov V. Ya. and Pogodin S. A. Fundamentals of Physicochemical Analysis. 330, Publishing House of the Academy of Sciences of the USSR, 1947.

6. Kubanskii A. M. and Toporets A. S. Artificial Single Crystals. Publishing House of the Academy of Sciences of the USSR, 1935.