TEMPERATURE CHANGES IN THE ELASTIC PROPERTIES OF SINGLE CRYSTALS OF THE NaCl—NaBr SOLID SOLUTION

A. V. SHARKO, A. A. BOTAKI

(Recommended for publication by the Department of General Physics, TPI)

Using the pulsed ultrasonic method, measurements of the elastic constants of single crystals of the NaCl—NaBr solid solution of different concentrations were carried out in the temperature range 80–300 K. Regularities in their variation over the investigated temperature interval were established.

In the present work, by the pulsed ultrasonic method at a frequency of 2.5 MHz, according to the procedure of [1–4], measurements were made of the elastic properties of single crystals of the NaCl—NaBr solid solution of different concentrations in the temperature range 80–300 K. The concentration of the solid solution was measured by the method of potentiometric titration on samples taken from different parts of the specimen. For the concentration of a solid solution of a given composition, the mean value from three measurements was adopted. The density of the samples, needed for determining the elastic constants, was calculated from the measured values of the density at room temperature and the temperature coefficient of linear expansion [5].

The results of measurements of the constants \(C_{ik}\) and the elastic coefficients \(S_{ik}\), as well as the values calculated from them of the anisotropy factor

\[ A=\frac{2C_{44}}{C_{11}-C_{12}} \]

and of the coefficient

\[ B=\frac{C_{44}}{C_{12}}, \]

which characterizes the deviation from the Cauchy relation, for different concentrations of the NaCl—NaBr solid solution and for its pure components NaCl and NaBr, are given in Tables I–VII. The concentration of the NaCl—NaBr solid solutions in the tables is expressed in mole percent.

To estimate the accuracy of the measurements, the linear temperature dependences \(C_{11}\), \(C_{44}\), and

\[ \frac{C_{11}-C_{12}}{2} \]

were treated by the method of least squares and yielded the following maximum values of the coefficients of variation: 0.6% for \(C_{11}\); 1.4% for \(C_{11}\); and 2.4% for

\[ \frac{C_{11}-C_{12}}{2}. \]

Analyzing the measurement data, the following conclusions may be drawn:

1. The elastic constants \(C_{11}\) and \(C_{44}\) of the NaCl—NaBr solid solutions increase linearly with decreasing temperature over the investigated temperature interval.

2. As the temperature of the substance decreases, the values of \(C_{11}\) and \(C_{44}\) increase the more rapidly, the greater the concentration of NaCl in the solid solution.

1. The temperature dependences of \(C_{11}\), \(C_{44}\), \(\dfrac{C_{11}-C_{12}}{2}\) for the NaCl—NaBr solid solution of different concentrations occupy an intermediate position between the pure components.

2. The dependence of the constants \(C_{ik}\) on the concentration of the components of the solid solution, expressed in mole percent, has a clearly pronounced negative nonadditivity.

3. The single crystals of the solid solution for all investigated concentrations, as the temperature is increased from 80 to 300 K, monotonically tend toward the isotropic state; however, none of the solid-solution crystals reaches complete isotropy \(A=1\) over the investigated temperature interval.

4. The coefficient \(B=\dfrac{C_{44}}{C_{12}}\), characterizing the deviation from the Cauchy relation, with decreasing temperature from 300 to 80 K monotonically

Table 1

100% NaCl

approaches unity. The value \(B=1\) over the investigated temperature interval is attained only for compositions containing more than 45 mol% NaCl.

Table 2

88.5% NaCl

Table 3

74% NaCl

Elastic constants: $\times 10^{-11}\ \mathrm{dyn}/\mathrm{cm}^2$
Elastic coefficients: $\times 10^{11}\ \mathrm{cm}/\mathrm{dyn}$

Table 4

49.5% NaCl

Table 5

37% NaCl

Table 6

21.5% NaCl

Table 7

100% NaBr

References

1. A. V. Sharko, A. A. Botaki. Izv. vuzov AN. “Fizika”, 6, 22, 1970.
2. A. V. Sharko, A. A. Botaki. FTT, 5, 1559, 1970.
3. A. V. Sharko, A. A. Botaki. FTT, 8, 2247, 1970.
4. A. V. Sharko, A. A. Botaki. FTT, 9, 2701, 1970.
5. M. S. Ivankina. Dissertation. Tomsk, 1959.