Temperature Changes in the Elastic Properties of the KCl—KBr Solid Solution

A. V. Sharko, A. A. Botaki

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

On single crystals of the KCl—KBr solid solution of various concentrations, the elastic constants were measured by the pulsed ultrasonic method in the temperature range 80—300 K. Regularities in their variation over the investigated temperature interval were established.

Slegel and McKinstry [1] experimentally determined the dependence of the elastic constants of the KCl—KBr solid solution for temperatures above room temperature. In studying the physical properties of solid solutions, the variation of these characteristics in the region of negative temperatures is of no less interest.

In the present work, by the pulsed ultrasonic method [2—7] at a frequency of 2.5 MHz, in the interval 80—300 K, measurements were made of the temperature changes in the elastic properties of single crystals of KCl—KBr solid solutions of various concentrations. The elastic constants $C_{ik}$ and the elastic compliances $S_{ik}$ were determined from the measured values of the propagation velocities of longitudinal elastic waves in the directions $<100>$ and $<110>$ and of transverse waves in the direction $<100>$. The specimens for measurements had dimensions in the sounding direction from 20 to 50 mm. Particular attention was paid to the quality of preparation of the surfaces and to the parallelism of the working faces of the specimens. The specimens intended for measuring the elastic constants $C_{11}$ and $C_{44}$ were made in such a way that the input and reflection surfaces of the ultrasonic vibrations coincided with the crystallographic planes $\{100\}$, while for determining the constant $C_{12}$ additional measurements were required on specimens whose working faces coincided with the crystallographic planes $\{110\}$. Measurements of the propagation velocities of ultrasound in single crystals of the KCl—KBr solid solution of various concentrations were carried out with a DUK-6V pulsed ultrasonic flaw detector with combined-type transducers, according to the procedure described earlier [4—7]. When obtaining the temperature dependences of the ultrasonic propagation velocities, the specimen was glued to the transducer with a mixture consisting of 88% ED-5 epoxy resin and 12% polyethylene polyamine and was placed in a cryostat. In order to prevent cracking of the specimen during the measurements, the cooling rate was kept to no more than 10 K per 1 h. The density of the specimens required for determining the elastic constants was calculated from the measured density values at room temperature and the temperature coefficient of linear expansion [8]. The concentration of the solid solution was measured by ...

by the method of potentiometric titration on samples taken from different parts of the specimen. The concentration of the solid solution of a given composition was taken to be the average value from three measurements. The results of measurements of the coefficients \(S_{ik}\) and the elastic constants \(C_{ik}\), as well as the values calculated from them of the anisotropy factor \(A=\dfrac{2C_{44}}{C_{11}-C_{12}}\) and of the coefficient \(B=\dfrac{C_{44}}{C_{12}}\), characterizing the deviation from the Cauchy relation for different concentrations of the KCl—KBr solid solution and for its pure components KCl and KBr, are placed in Tables 1—VI. The concentration of the solid solutions is expressed in mole percent.

Table 1

100% KCl

The elastic constants are in \( \times 10^{-11}\ \mathrm{dyn}/\mathrm{cm}^{2}\), and the elastic coefficients are in \( \times 10^{11}\ \mathrm{cm}^{2}/\mathrm{dyn}\).

For estimating the accuracy of the measurements, the linear temperature dependences \(C_{11}\), \(C_{44}\), and \(\dfrac{C_{11}-C_{12}}{2}\) were treated by the method of least squares; the following maximum values of the coefficien-

of the variation: 1.15% for \(C_{11}\), 1.78% for \(C_{44}\), and 2.1% for \(\dfrac{C_{11}-C_{12}}{2}\).

A comparison of the results of our measurements with the data of Slagle and McKinstry for room temperatures gives good agreement.

Table 2

74% KCl

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

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

2. The dependence of the elastic constants \(C_{ik}\) on composition has a negative nonadditivity.

3. The anisotropy factor \(A\) increases with increasing temperature, while the coefficient

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

decreases. Complete isotropy of the elastic properties (\(A=1\)) is not reached by any composition of the solid solution over the temperature interval studied. The coefficient \(B\), on the contrary, at low temperatures of the 80–300 K interval takes a value equal to unity for compositions containing more than 40 mol.% KBr.

Table 3

51% KCl

Table 4
39.5% KCl

Table 5
24.5% KCl

Table 6

100% KBr

REFERENCES

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8. M. S. Ivankina. Dissertation, Tomsk, 1959.