SETUP FOR REMOTE MEASUREMENT OF ELASTIC CONSTANTS AND INTERNAL FRICTION OF ALKALI METAL HALIDE SINGLE CRYSTALS

A. A. Botaki, I. N. Gyrbu, A. V. Sharko

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

When studying the effect of radiation on the mechanical properties of ionic crystals, measurements performed on specimens located directly in the irradiation zone acquire the greatest value.

For measuring the elastic constants and internal friction of alkali metal halide single crystals located in the irradiation zone, a setup has been assembled that allows the operator to perform measurements at a distance safe from the irradiation zone. The operating principle of the setup is based on the resonance method for measuring the elastic characteristics of solids by means of a two-component quartz vibrator [1]. The block diagram of this setup is shown in Fig. 1. The voltage taken from sinusoidal-oscillation generator III, of type G3-33, is fed through a coaxial cable to piezoquartz transducer VI, which excites ultrasonic oscillations in the specimen. Next, the signal from the sensor is sent to oscilloscope IV, type S-35, which serves as an indicator

Fig. 1. Block diagram of the setup for remote measurement of elastic constants and internal friction of alkali metal halide single crystals: I — voltage stabilizer; II — heterodyne wavemeter RFT-121; III — generator G3-33; IV — oscilloscope S1-35; V — tube voltmeter V3-14; VI — two-component quartz vibrator (a — quartz transducer, b — specimen under investigation)

resonance. By varying the frequency of the driving generator, resonance of the piezoquartz transducer–specimen system is gradually achieved. The voltage on the oscilloscope, proportional to the current passing through the piezotransducer, is recorded at the moment of resonance and antiresonance by a V-type VZ-14 tube voltmeter. The resonance frequency of the vibrator is measured with a type II RFT-121 heterodyne wavemeter. The piezotransducer is connected to the measuring setup by means of two coaxial cables. In this arrangement only the central conductors of the cables are used, and the shielding parts are grounded. This significantly reduces the capacitance between the wires. The setup is powered by a stabilized alternating voltage from the 220 V mains.

Electrical contact between the piezotransducer and the coaxial cable is made through special mechanical holders, constructed as collets of spring bronze, which are mounted on an electrical-insulating base made of Teflon. To reduce the capacitance between the collet tabs, the latter were placed as far apart as possible, and a grounded electrostatic shield was placed between them. On such a setup, measurements were made of the change in internal friction \(Q^{-1}\) and Young’s modulus \(E_{100}\) of predeformed NaCl single crystals during irradiation with soft X-rays on a URS-55A unit with a tube having a copper anticathode, as well as measurements of the elastic constants of NaCl, KCl, and KBr single crystals at room temperature.

The specimens for measurements of Young’s modulus were rectangular parallelepipeds with a cross section of \(3 \times 1.5\) mm, and for measurements of the shear modulus \(3 \times 3\) mm. The orientation of the specimens with respect to the cleavage planes was determined on a large instrumental microscope, which gave an error in determining the angles of no more than \(10'\). To obtain reliable acoustic contact between the transducer and the specimens during the measurements, the specimens were glued to the transducer with shellac. Before measurement, the resonance frequency of the specimen was adjusted to the resonance frequency of the piezoquartz, for which purpose the specimen was shortened in length. In this case the deviation of the resonance frequency of the composite vibrator from the resonance frequency of the specimen did not exceed 0.1% when measuring the shear modulus and 0.7% when measuring Young’s modulus.

The quartz piezotransducers intended for measuring Young’s modulus had, at room temperature, natural frequencies of longitudinal vibrations of 73770 Hz and 84400 Hz. To determine the shear modulus, quartz piezotransducers in torsional vibration, made in the form of round rods [2], were used. The natural frequencies of these piezotransducers were 102800 Hz and 104770 Hz. Young’s and shear moduli were calculated from the measured values of the resonance frequency of the composite vibrator using the following formulas [3]:

\[ E=\frac{4\rho l^{2} f^{2}}{n^{2}}, \qquad G=\frac{4.77 \rho l^{2} f^{2}}{n^{2}}, \]

where \(\rho\) and \(l\) are the density and length of the specimen under test, and \(f\) is its resonant frequency, determined from the expression \(f=f_{1}+\frac{m}{m_{1}}(f_{1}-f_{2})\), where

\(f_{1}\) is the resonance frequency of the composite vibrator, \(f_{2}\) is the resonance frequency of the piezotransducer, \(m\) is its mass, \(m_{1}\) is the mass of the specimen, and \(n\) is the number of half-waves fitting along the specimen. For a half-wave

vibrator \(n = 1\). The calculation of the coefficients and elastic constants was carried out using the following equations [4]:

\[ C_{44}=G_{100}=\frac{1}{S_{44}},\quad S_{11}=\frac{1}{E_{100}},\quad S_{12}=\frac{2}{E_{110}}-S_{11}-\frac{S_{44}}{2}, \]

\[ C_{11}-C_{12}=\frac{1}{S_{11}-S_{12}},\quad C_{11}+2C_{12}=\frac{1}{S_{11}+2S_{12}}, \]

where \(C_{ik}\) are constants, and \(S_{ik}\) are elastic coefficients; \(E_{100}\) and \(E_{110}\) are the values of Young’s modulus in the \(\langle 100\rangle\) and \(\langle 110\rangle\) directions.

The error in determining the resonance frequency of the compound vibrator in measurements with the RET-121 heterodyne wavemeter did not exceed 0.1%, which made it possible to determine the constants \(E_{110}\), \(E_{100}\), \(G_{100}\), \(S_{11}\), and \(S_{44}\) with an accuracy of about 0.5%. The results of measurements of the elastic constants of single crystals of the alkali-metal halides NaCl, KCl, and KBr, performed at room temperature, as well as the values of ultrasound propagation velocities in various crystallographic directions, found from the formula \(C = \frac{2lf}{n}\), are presented in Table 1.

A comparison of the obtained results with data from other authors [5–7], obtained at room temperature for the same single crystals, shows good agreement. Figure 2 presents the dependences of Young’s modulus \(E_{100}\) and the internal friction \(Q^{-1}\) of NaCl single crystals on the irradiation time of a specimen by soft X-rays in a URS-55A unit. The internal friction in the single crystals studied was determined by the formula [7]:

Fig. 2. Dependence of Young’s modulus and internal friction of preliminarily deformed NaCl single crystals on the time of irradiation by soft X-rays

\[ Q^{-1}=\frac{m\delta+m_{1}\delta_{1}}{\pi(m+m_{1})} =2\frac{f_{a}-f_{p}}{f_{1}}\sqrt{\frac{U_{a}}{U_{p}}}, \]

where \(U_{p}\) and \(U_{a}\) are the voltages at resonance and antiresonance at the terminals of oscilloscope IV, \(m\) and \(m_{1}\) are the masses of the quartz and the specimen, \(f_{1}=f_{p}+(f_{a}-f_{p})\times\)

\(\times \dfrac{U_a}{U_p+U_a}\) is the resonance frequency of the composite rod; \(f_a\) and \(f_p\) are the frequencies at antiresonance and resonance.

Table

\(\delta\) and \(\delta_1\) are the logarithmic decrements of damping of the piezoelectric transducer and of the specimen under study, respectively. The measurements are first carried out only on the piezoelectric transducer \((m_1=0)\), and then on the composite rod. This makes it possible to find the logarithmic damping decrement of the specimen \(\delta_1\).

The dependences obtained are in good agreement with analogous measurements by Gordon and Nowick [9].

REFERENCES

1. Physical Acoustics. Edited by W. Mason. Vol. 3, Part A. Moscow, Mir, 1963.
2. L. Bergmann. Ultrasound. Moscow, Foreign Literature Publishing House, 1956.
3. A. V. Stepanov, I. M. Eidus. ZhETF, 29, 699, 1955.
4. Elasticity and Anelasticity of Metals. Edited by S. V. Vonsovskii. Moscow, Foreign Literature Publishing House, 1964.
5. S. Haussühl. Zeitschrift für Physik, 159, 223—29, 1960.
6. G. Huntington. UFN, 74, 3, 1961.
7. A. V. Sharko, A. A. Botaki. Izv. vuzov. “Fizika”, 6, 1970.
8. V. S. Postnikov. Internal Friction in Metals. Metallurgiya, 1969.
9. Gordon R. B., Nowick A. S. Acta Met., 4, 514, 1956.