EFFECT OF IRRADIATION WITH $\gamma$-QUANTA ON THE TEMPERATURE COEFFICIENT OF LINEAR EXPANSION OF SOLID SOLUTIONS OF THE KCl—KBr SYSTEM

M. S. Ivankina, I. V. Yanshen

(Presented by the scientific seminar of NIIYaFEA)

Irradiation of crystals leads to the appearance in them of a large number of disturbances in their structure. Irradiation with heavy particles of high energies causes displacement of ions from the sites of the crystal lattice as a result of elastic collisions of the latter with accelerated particles, and also as a result of ionization effects. The mechanism of ion displacement under irradiation of alkali-halide crystals with X-rays and $\gamma$-quanta has not been established. Possible explanations of this mechanism have been proposed by Seitz [1], Varley [2], and others [3, 4, 5].

Under the action of radioactive radiation the density of crystals changes [6, 7, 8], the crystal-lattice parameter [9], the volume [10, 11, 12], and other properties [13—16] change.

The change in the physical properties of alkali-halide crystals under the action of radiation is due to disturbance of their structure, which is accompanied by a weakening of the bond between the particles of the crystal and an increase in the free energy of the system—$F$ [17, 18] by the amount $\Delta F = nw - T \Delta S_{\text{conf}} - T \Delta S_{\text{vib}}$, where

$n$ is the number of introduced disturbances of the type of Schottky or Frenkel defects,

$w$ is the free energy of defect formation,

$\Delta S_{\text{conf}}$ and $\Delta S_{\text{vib}}$ are the changes in configurational and vibrational entropy, respectively,

$T$ is the temperature. Since the magnitude of the temperature coefficient of linear expansion is determined by the thermodynamic relation

\[ \alpha = -\frac{1}{k}\,\frac{\partial^2 F}{\partial V \cdot \partial T}, \]

($k$ is the compressibility coefficient, $V$ is the volume), a change in the free energy of the crystal must affect the magnitude of the temperature coefficient of linear expansion—$\alpha$. A change in $\alpha$ was experimentally established for crystals of NaCl, KCl, KBr, and KI under irradiation with neutrons [13], protons [14], and for NaCl crystals under X-ray irradiation [19]. However, very few studies devoted to measuring the temperature coefficient of linear expansion of irradiated crystals of solid solutions of alkali-halide salts have been carried out to date [20].

In the present work, the effect of isodose irradiation by $\gamma$-quanta on the temperature coefficient of linear expansion of solid solutions of the KCl—KBr system is considered as a function of their composition, and the effect of the irradiation dose on $\alpha$ of solid solutions of different compositions is also investigated.

The measurements were performed on a capacitive dilatometer by the beat method [21] with an accuracy of up to $\pm 10^{-7}\,1/\mathrm{deg}$. Irradiation was carried out with a Co$^{60}$ source of $\gamma$-quanta with a radiation intensity of 450 roentgens/sec.

The experimental results showed (Fig. 1) that the temperature coefficient of linear expansion, measured at a temperature of 100°C, is greater for crystals of solid solutions irradiated with $\gamma$-quanta at a dose of $4\cdot 10^8$ roentgens than for unirradiated ones. The smallest increase in the temperature coefficient of linear expansion is found in irradiated crystals of solid solutions of compositions 75 mol.% KCl + 25 mol.% KBr and 50 mol.% KCl + 50 mol.% KBr.

Fig. 1. Dependence of the relative change in the temperature coefficient of linear expansion — $\dfrac{\Delta\alpha}{\alpha}$ — on the composition of solid solutions of the KCl—KBr system irradiated with Co$^{60}$ $\gamma$-quanta at a dose of $4\cdot 10^8$ roentgens.

It is known that in solid solutions of alkali-halide salts the bonding forces between lattice ions are smaller than in crystals of the initial components [21, 22, 23]. In this connection, the relative increase in radiation-induced defects in solid solutions should be smaller than in pure alkali-halide crystals and, consequently, the change in their properties after irradiation should also be smaller [18].

Our data (Fig. 1) confirm this proposition. More defective crystals, with reduced bonding forces between particles, are the most radiation-resistant; their relative change in $\alpha$, caused by irradiation, proved to be the smallest.

Figure 2 presents curves for the change in the relative temperature coefficient of linear expansion in pure crystals and their solid solutions of different compositions as a function of the irradiation dose (from $3\cdot 10^6$ to $4\cdot 10^8$ roentgens). From Fig. 2 it is seen that at comparatively small irradiation doses ($3\cdot 10^6$ roentgens), $\dfrac{\Delta\alpha}{\alpha}$ for equimolar solid solutions is close to zero, i.e., the temperature coefficient of linear expansion in the more defective crystals of equimolar composition almost does not change. This gives grounds to suppose that radiation annealing of the structural disturbances present in the crystal of the crystalline...

...lattice with the effect of creating defects by irradiation; therefore, a certain equilibrium defect state is preserved and \(\alpha\) does not change. It is possible that \(\alpha\) even decreases at still lower doses of irradiation by \(\gamma\)-quanta [20]. At high irradiation doses \((8 \cdot 10^7—4 \cdot 10^8\) roentgens)

\[ \frac{\Delta \alpha}{\alpha}=\frac{\alpha_{\mathrm{irr}}-\alpha_{\mathrm{unirr}}}{\alpha} \]

increases, and the more so the less defective the crystal is. The greatest change in \(\frac{\Delta \alpha}{\alpha}\) is observed in pure KBr crystals, and the change in \(\frac{\Delta \alpha}{\alpha}\) increases with increasing irradiation dose. Consequently, on the basis of our experiment studying the influence of \(\gamma\)-irradiation on the temperature coefficient of linear expansion of solid solutions, it may be said that the most radiation-resistant crystals are indeed those with a reduced bond strength between ions [18].

Fig. 2. Dependence of the relative change in the temperature coefficient of linear expansion, \(\frac{\Delta \alpha}{\alpha}\), of solid solutions of the KCl—KBr system of different compositions on the dose of irradiation by \(\gamma\)-quanta from Co\({}^{60}\). \(\times\)—50 mol% KCl + 50 mol% KBr; ●—10 mol% KCl + 90 mol% KBr; ○—KBr.

Thus, on the basis of the investigations carried out, the following conclusions may be drawn.

1. The rate of the process of annealing of defects produced by irradiation is determined by the bonding forces of the ions in the crystal lattice. The resulting concentration of defects after irradiation is lower in solid solutions of alkali-halide salts that, before irradiation, have a greater defectiveness of structure in comparison with pure components. As a result, the temperature coefficient of linear expansion of solid solutions increases to a lesser degree than in pure crystals.

2. With increasing irradiation dose, the concentration of defects produced by irradiation increases more rapidly in the less defective pure crystals than in the uniformly irradiated solid solutions.

In this connection, a more rapid relative increase of the temperature coefficient of linear expansion is observed in pure components in comparison with the increase of \(\frac{\Delta \alpha}{\alpha}\) for crystals of solid solutions.

The authors consider it a pleasant duty to thank Prof. E. K. Zavadovskaya for discussion of the results and for her constant interest in the work, and postgraduate student N. M. Timoshenko for irradiating the crystals with a Co\(^{60}\) source.

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