ON THE PHYSICAL PROPERTIES OF CRYSTALS

P. A. SAVINTSEV

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

Crystals may be subjected simultaneously to considerable mechanical, thermal, and electrical influences. In such cases it is sometimes necessary to evaluate the totality of many properties of crystals.

The connection between the properties of ionic crystals and the energy of the crystal lattice has been shown [1,2]. However, experiments to determine the lattice energy are complicated, and data are lacking on the energy of crystals with impurities. It is therefore useful to find a physical quantity that is easily determined experimentally and is connected with many properties of a crystal: mechanical, thermal, electrical, etc.

We have found that a large number of constants characterizing the properties of a crystal depend on the molecular concentration. We denote this quantity by \(\alpha\) and find it from the formula: \(\alpha = \dfrac{D}{M}\cdot 10^3\),

where \(D\) is the density of the crystal, and \(M\) is the molecular weight.

The connection of \(\alpha\) with the properties of alkali-halide crystals is seen from Table 1. The designations in Table 1 are as follows: \(U\) is the energy of the crystal lattice in \(\mathrm{kcal}/\mathrm{mol}\), \(E_{\mathrm{pr}}\) is the electrical strength in \(\mathrm{mV}/\mathrm{cm}\), \(\varepsilon\) is the electronic component of the dielectric coefficient, \(\sigma\) is the ionic conductivity at the melting temperature, \(B\) is the constant entering into the conductivity equation \(\varepsilon = Ae^{-B/T}\), \(\beta\) is the coefficient of linear expansion, \(n_D\) is the refractive index of light. It should be noted that the value of the coefficient \(k\), which relates the constants to \(\alpha\), changes in going from compounds of one metal to compounds of another metal. Sometimes the values of \(k\) differ so little that they may be considered coincident. This is seen from Figs. 1, 2, 3.

In Table 2 we continue the comparison of mechanical characteristics and dielectric losses with the quantity \(\alpha\). In Table 2 the quantity \(\dfrac{\gamma}{\gamma_0}\) gives the relative values of the surface energy, determined by us by the method of mutual grinding [3]. From Table 2

it is evident that, with increasing \(\alpha\), the hardness of the crystals increases, while the dielectric losses (\(\operatorname{tg}\delta\) at a frequency of \(10^6\) Hz) and the flow pressure decrease. With increasing \(\alpha\), there is a tendency toward a decrease in the shear modulus and Young’s modulus.

Fig. 1. Relationship between the hardness of crystals and the molecular concentration \(\alpha\)

Fig. 2. Relationship between the compressibility coefficient of alkali-halide crystals and the molecular concentration \(\alpha\)

Table 3 compares the properties of oxides of metals of the second group with the value of \(\alpha\). From Table 3 it is evident that, as \(\alpha\) increases, the following quantities increase: heat of sublimation, melting temperature, lattice energy, hardness. Heat capacity, entropy,

the heat of hydration decrease with increasing $\alpha$. To construct Tables 1, 2, 3 we used data [1—12].

Let us note that the dependence of properties on $\alpha$ is also observed for some liquid organic dielectrics.

Fig. 3. Relation between the absorption maximum corresponding to the F-band and the molecular concentration $\alpha$

Fig. 4. Relation of the electric strength of a homologous series of liquid dielectrics to the molecular concentration $\alpha$

Fig. 4 shows a decrease in the electric strength of a homologous series of liquid dielectrics with increasing $\alpha$. In solid dielectrics the electric strength increases with increasing $\alpha$ (Tab-

1). This confirms the statements in [13] on the different mechanism of breakdown in solid and liquid dielectrics.

Let us establish the relation of \(\alpha\) with the properties of metals.

M. M. Khrushchov and M. A. Babichev [14], studying the abrasive wear of metals at low rates of displacement of the specimens, found a relation between the relative wear resistance \(i\) and the Vickers hardness \(H\).

Table 1

Relation of \(\alpha\) to the properties of alkali-halide crystals

Table 2

Comparison of mechanical characteristics and dielectric losses with the value of \(\alpha\)

Continuation of Table 2.

Table 3

Comparison of the properties of oxides of metals of the second group with the value of $\alpha$

The values of $i$ and $H$ are given in Table 4, from which it is seen that, with increasing $\alpha$, the relative wear resistance of the specimens and their hardness increase.

In Table 4 (column 5) we give the time $t$ for the amplitude of oscillation of V. D. Kuznetsov’s pendulum [4] to decrease from 3 to 2 cm. The reciprocal of $t$ may be regarded as the hardness by the method of damped oscillations $H_3$. From Table 4 it is seen that, with increasing $\alpha$, the hardness $H_3$ increases.

In column 6 of Table 4 are given the values of the shear modulus $N$, taken from the book [15]. It may be noted that for all the metals considered, except cadmium, the shear modulus increases with increasing $\alpha$.

Table 4

Comparison of the mechanical properties of metals with the value \(\alpha\)

Tonn [16] determined the wear resistance \(i\) of various metals during grinding on abrasive paper. The values of \(i\) are given in Table 5, from which it is evident that, with increasing \(\alpha\), the wear resistance of metals increases.

Table 5

Comparison of the relative wear resistance of metals
with the value \(\alpha\)

V. D. Kuznetsov, N. A. Bessonov, and M. F. Pichenin [17] determined the abrasive wear of zinc, bismuth, and antimony. Polycrystalline specimens of the indicated substances were abraded against emery paper No. 00, which was fixed on a disk rotating at a speed of \(2.3—3.6\ \mathrm{cm/sec}\). The authors found the quantity \(M_{0}\), which is numerically equal to the mass of the ground-off layer per unit of frictional work and for a specimen area equal to unity. The values of \(M_{0}\) are given in Table 6, from which it is seen that \(M_{0}\) increases with increasing \(\alpha\).

V. D. Kuznetsov, N. A. Bessonov, and M. F. Pichenin also studied the wear of certain alkali-halide salts. Table 6 gives the values they obtained for \(\dfrac{F}{M}\)—the ratio of the friction force to the mass ground off. It is not difficult to see that \(\dfrac{F}{M}\) increases with increasing \(\alpha\).

M. A. Bolshanina [4] relates the process of plastic deformation to the properties of the crystal lattice. Therefore it is advisable to seek a connection between the constants characterizing the plastic properties of metals and \(\alpha\). Table 7 gives, according to the data of [18], the values ...

of the absorbed energy under static deformation \(W\), the ratio of \(W\) to the work of deformation \(A\), the absorbed energy under dynamic compression \(W_g\) (relative deformation 20%), the polytropic exponent \(m\), and the hardening coefficient \(a\). From Table 7 it is seen that with increasing \(\alpha\), \(W\), \(W : A\), \(W_g\), \(m\), and \(a\) increase.

Table 6

Comparison of wear characteristics with the value of \(\alpha\)

Table 7

Comparison of absorbed deformation energy with \(\alpha\)

Thus, the molecular concentration \(\alpha\) is a combined characteristic of many properties of substances.

LITERATURE

1. Vorob’ev A. A. and Zavadovskaya E. K. Physical and electrical properties of ionic crystals, Izvestiya TPI, vol. 83, 1956.

2. Zavadovskaya E. K. On dielectrics with high electrical strength, Doklady Akademii nauk SSSR, vol. 82, No. 5, 1952.

3. Savintsev P. A. and Kutsepalenko V. V. Measurement of surface energies of single crystals of the potassium chloride—sodium chloride system by the method of drilling and mutual grinding, Izvestiya TPI, vol. 83, 1956.

4. Kuznetsov V. D. Physics of the Solid State, vol. 1, 1937; vol. 2, 1941; vol. 4, 1947. Tomsk.

5. Goldschmidt V. M. Krystallbau und chemische Zusammensetzung, Berichte d. Deutsch. Chem. Ges., 60, 1927.

6. R. Auerbach, Über die Oberflächenenergie fester Werkstoffe, Werkstoffe und Korrosion, 5, No. 6, 1954.

7. Kurnakov N. S. Collected Selected Works, vol. 1, ONTI, 1938; vol. 2, GONTI, 1939.

8. Collection of Physical Constants, ed. by Ya. G. Dorfman and S. E. Frisch, ONTI, 1937.

9. Technical Encyclopedia, Handbook of Physical, Chemical, and Technological Quantities, 1927.

1. Vodopyanov K. A., Vorob’ev A. A., and Krivov M. A. Dielectric losses, electrical strength of crystals of alkali-halide salts, and lattice energy, Izvestiya TPI, vol. 83, 1956.

2. Zeit V. Ionic conductivity in solid salts, Uspekhi fizicheskikh nauk, vol. 18, no. 4, 1937.

3. Zavadovskaya E. K. A note on the relation between the F-band of absorption in alkali-halide crystals and lattice energy, Izvestiya TPI, vol. 83, 1956.

4. Vorob’ev A. A. and Kalganov A. F. On the question of the relation between the electrical strength of liquid dielectrics and their physicochemical properties, Izvestiya TPI, vol. 83, 1956.

5. Khrushchov M. M. and Babichev M. A. Resistance to abrasive wear and hardness of metals, Doklady Akademii nauk SSSR, vol. 88, no. 3, 1953.

6. Slavinskii M. P. Physicochemical Properties of the Elements, Metallurgizdat, 1952.

7. W. Tonn. Beitrag zur Kenntnis der Verschleißvorganges beim Kurzversuch am Beispiel der reinen Metalle, Z. s. Metallkunde, 6, 1937.

8. Kuznetsov V. D., Bessonov A. A., and Pichenin M. F. Wearability of a surface under external friction depending on surface energy, Zhurnal prikladnoi fiziki, vol. 4, issue 3, 1927.