DISSOLUTION OF IRRADIATED ALKALI-HALIDE CRYSTALS

A. F. Naumov, P. A. Savintsev

The widespread view that the majority of natural salts are characterized by a diffusion type of dissolution process \[1, 2\] is valid for the case when crystals of these salts dissolve in weakly stirred solutions far from saturation. In this case the dissolution rate, calculated per unit surface area of the crystal, is

\[ V = K(C_0 - C), \tag{1} \]

where \(C_0\) is the concentration of the equilibrium solution over the crystal, \(C\) is the concentration of the solution; \(K\) is a constant depending on the intensity of stirring of the solution and on the diffusion coefficient of the substance in the solution. Usually \[1\] one takes

\[ K = \frac{D}{\delta}, \]

where \(\delta\) is the thickness of the thin boundary layer of the stirred solution adjacent to the crystal. It should be noted that the real existence of a resting diffusion layer is doubtful, but the concept of it is introduced in order to simplify the picture of dissolution \[1, 2\]. The dissolution rate is determined by equation (1) when the assumption that near the surface of the crystals, in a very thin layer, the solution is always saturated is justified with sufficient accuracy. In reality, at small undersaturations and vigorous stirring of the solution, the concentration fields formed near the centers of outflow of substance from the crystal into the solution do not overlap. The dissolution of the crystal proceeds by a diffusion-kinetic mechanism. To describe it, use is made of the concept of the reduced concentration \(C_p\) of the dissolved substance in the solution at the crystal–solution phase boundary, derived under the assumption that the entire surface of the crystal participates uniformly in exchange of particles with the solution. Then the dissolution rate is

\[ v = \beta(C_0 - C_p) = \frac{D}{\delta}(C_p - C) \tag{2} \]

or

\[ v = \frac{1}{\dfrac{1}{\kappa} + \dfrac{1}{\beta}}\,(C_0 - C), \tag{3} \]

where \(K\) is the constant from equality (1), and \(\beta\) is the coefficient of exchange by particles between the crystal surface and a solution of reduced concentration \(C_p\).

The coefficient \(\beta\) is the greater, the higher the density of active dissolution centers on the dissolving surface. In diffusional dissolution of crystals, \(\beta\) is large and \(1/\beta \to 0\). In this case equation (3) passes into equation (1). In the diffusion–kinetic mechanism of dissolution, the number of centers of sink of substance from the crystal into the solution is comparatively small: \(\beta\) and \(K\) are quantities of the same order.

In [3, 4] it is shown that the sink of substance from the crystal into the solution proceeds through active, moving dissolution centers, whose sources may be crystal edges, pores, boundaries of large macrodefects, screw and edge dislocations; nuclei formed on a surface that remains flat (on the atomic scale). At a very small undersaturation of the solution, the process of crystal dissolution begins from its edges, large macrodefects and pores, along the boundaries of mosaic blocks, or from steps formed by screw dislocations. With an increase in the undersaturation of the solution, etch pits formed at the sites where dislocations emerge become active sources of steps on the dissolving faces of the crystal. And the dissolution rate of the entire crystal depends on the density of dislocations. Clusters of interstitial defects, too, can probably be active dissolution centers in this region of undersaturation of the solution. With a still greater increase in the undersaturation of the solution, dissolution begins with the formation of active dissolution centers over the entire surface of the dissolving face. The lower the energy of formation of a defect, the greater the undersaturation of the solution required for this defect to manifest itself as an active dissolution center. Thus, at different undersaturations of the solution, different types of defects in the crystal structure will influence the dissolution rate. As a result, the effect of irradiation on the dissolution rate of a given crystal may depend on the undersaturation of the solution.

To verify these assumptions, the dissolution rates of irradiated and unirradiated plates of alkali-halide single crystals were compared in solutions of different concentrations. The plates \((3 \times 20 \times 20\ \mathrm{mm})\) were preliminarily annealed at \(873^\circ\mathrm{K}\) for 42 hours, followed by cooling (10 degrees/hour). With the aid of a radium–beryllium source, the specimens were irradiated with neutrons of mean energy \(4.5\ \mathrm{MeV}\) and \(\gamma\)-quanta of energy about \(2\ \mathrm{MeV}\). The activity of the source in neutrons was \(4.8 \cdot 10^6\) neutrons/sec. Irradiation with protons of energy \(4.5\ \mathrm{MeV}\) was carried out on the cyclotron of the Tomsk Polytechnic Institute. The intensity of the proton beam was \(6 \cdot 10^{14}\) protons/\(\mathrm{m}^2\) sec.

For irradiation with X rays, BSV-type tubes with copper, molybdenum, and tungsten anodes were used.

To reveal the bulk radiation defects of interest to us, the near-surface layer [5, 10], destroyed during irradiation, with a thickness of 50 microns was removed by dissolution in water and polishing aqueous solutions. Two plates (irradiated and unirradiated) were subjected to dissolution simultaneously, by the incidence, normal to the surface, of two jets of aqueous solution having the same velocity \((7\ \mathrm{m/sec})\), concentration, and temperature \((293^\circ\mathrm{K})\). Preliminary experiments established that, at the indicated velocity of incidence of the jet, no washing-out of crystal particles occurs as a result of hydrodynamic impact.

The linear dissolution rate was taken to be the ratio of the thickness of the dissolved layer of substance at the point where the jet fell on the crystal to the dissolution time. The error from 10 measurements was 3% at low undersaturation and 1% at high undersaturation of the solution.

According to our experiments (Table 1), the dissolution rate of a NaCl crystal

along the (100) face

\[ v_{(100)} = K_1 \sigma^n, \tag{4} \]

where

\[ \sigma = \frac{C_0 - C}{C_0} \]

is the relative undersaturation of the solution, calculated in mole percent; \(C_0\) is the equilibrium concentration of the solution over the crystal; \(C\) is the concentration of the solution in the jet. For \(0.2 \le \sigma \le 1\), \(n = 1\). \(K_1\) is a constant for the indicated interval of undersaturations. For \(0.035 \le \sigma \le 0.090\), \(n = 1.65\). The deviation of \(n\) from unity indicates a transition to a diffusion-kinetic mechanism of dissolution.

Table 1

Dissolution rate of a NaCl single crystal along the (100) face and along the (110) face in an aqueous NaCl solution

The data obtained on the anisotropy of dissolution show that the lowest dissolution rate is exhibited by the (100) face, which belongs to the equilibrium form of the crystals.

Preliminary irradiation of the (100) face of a NaCl single crystal with x-rays of energy 8 keV, at a total absorbed-radiation dose of \(3.8 \cdot 10^5\) rad, significantly increases the dissolution rate (Fig. 1). The absolute difference in the dissolution rates of irradiated and unirradiated crystals increases with increasing relative undersaturation \(\sigma\) of the aqueous NaCl solution (Fig. 1). The ratio of these rates \(V_o/V_n\) tends to unity (Fig. 2, curve 4). This is associated, as the undersaturation increases, with a transition to that region of solution concentrations where the dissolution rate of the crystal becomes a structurally insensitive quantity, i.e., with a transition to a diffusion mechanism of dissolution.

From our investigations it may be approximately determined that, for NaCl, the structure-sensitive region of undersaturations lies at \(\sigma < 0.030\); for KCl at \(\sigma < 0.025\); for KBr at \(\sigma < 0.011\), and for KJ at \(\sigma < 0.007\).

Within the accuracy of the experiment, no increase in the solubility of crystals as a result of irradiation was detected. It follows from Fig. 2 that the effect of irradiation on the dissolution rate may be directly

opposite for solutions of different concentration within the structure-sensitive region of undersaturations.

At absorbed x-ray energy doses \(Q < 1.5 \cdot 10^5\) rad (curves 1 and 2, Fig. 2), irradiation causes an acceleration of dissolution at \(\sigma < 0.007\) and a slowing at \(\sigma > 0.007\). Such data confirm the assumption expressed above that, at different undersaturations of the solution, the rate of dissolution will be influenced by different kinds of defects in the crystal structure.

Fig. 1. Dissolution rate of an unirradiated (lower curve) and irradiated (upper curve) (100) face of a NaCl single crystal in an aqueous NaCl solution at different undersaturations of the solution. The dose of irradiation by x-rays of energy 8 keV is \(3.8 \cdot 10^5\) rad.

Fig. 2. Dependence of the ratio of the dissolution rate of an irradiated (100) face to the dissolution rate of an unirradiated (100) face of a NaCl single crystal on the relative undersaturation of the aqueous NaCl solution. Doses of irradiation by x-rays of energy 8 keV are: 1—\(4.8 \cdot 10^4\) rad; 2—\(1.2 \cdot 10^5\) rad; 3—\(1.9 \cdot 10^5\) rad; 4—\(3.8 \cdot 10^5\) rad; 5—\(8 \cdot 10^5\) rad.

At a relative undersaturation of the solution greater than 0.006–0.007, at the point where the jet of solution falls on the (100) face of the crystal, a depression in the form of a saucer is formed, often with stepped edges.

In this case the dissolution rate does not depend on the dimensions of the face. At smaller undersaturation of the solution, no depression is formed at the point where the jet falls, and the dissolution rate depends on the dimensions of the face. Here the dissolution of layers of the crystal lattice, beginning from the edges of the crystal, plays the greater role. This indicates the small number of defects that can serve in this undersaturation region as active centers of dissolution. To exclude the possibility of dissolution beginning from the edges of the crystals, they had to be coated with lacquer. Two-dimensional disturbances causing fragmentation of the crystal [5], micro- and macropores, and large clusters of vacancies [6, 7] are responsible in this region for the increase in dissolution rate upon irradiation of the crystals. The energy of the disturbances created by them in the regular crystal lattice is comparable with the increase in the potential energy of the lattice layers at the edges and ribs of the crystal. As the dose of absorbed x-rays increases, the number of two-dimensional disturbances in the NaCl crystal increases and the dissolution rate increases (Fig. 2, curves 1, 2, 3, 4). Curve 5 of Fig. 2, characterizing crystals that received an irradiation dose \(Q = 5.8 \cdot 10^5\) rad, lies below curve 4 for crystals

with a dose \(Q = 3.8 \cdot 10^5\) rad. This indicates the possibility of radioactive annealing processes, accompanied by coarsening of defects and a decrease in their total number. No influence of the storage time of the crystals after irradiation with x-rays on the dissolution rate was observed for storage times up to 2 weeks.

For the region \(\sigma > 0.007\), the change in the dissolution rate upon preliminary irradiation of the crystals should be attributed to a change in the number of clusters of point defects of various kinds, which cause the appearance of roughness on the etched surface of the irradiated crystal [5, 8]. Small irradiation doses \((Q < 1.5 \cdot 10^5\ \text{rad})\) cause a decrease in the dissolution rate of the (100) face of the NaCl crystal, while larger doses \((Q > 1.5 \cdot 10^5\ \text{rad})\) cause an increase (Fig. 2).

Irradiation with harder x-rays does not change the general picture described above. The characteristic radiation of copper (energy 8 keV) and molybdenum (energy 17.5 keV) anodes gives analogous dependences.

Fig. 3 shows the dependence of the dissolution rate of the (100) face of a NaCl single crystal on the irradiation dose by unfiltered radiation from a tungsten anode at a voltage of 57 kV applied to the x-ray tube. The first curve was obtained at \(\sigma = 0.0036\), i.e., in the region of slight undersaturation of the solution. It shows that irradiation of the crystal followed by dissolution in the region of solutions close to saturation gives an increase in the dissolution rate. The third curve was obtained at \(\sigma = 0.010\), i.e., in the region of large undersaturation of the solution. At this undersaturation, small irradiation doses cause a decrease in the dissolution rate, and large doses cause an increase. The general picture is qualitatively analogous to that shown in Fig. 2.

Fig. 3. Dependence of the dissolution rate of the (100) face of a NaCl single crystal on the irradiation dose \(Q\) by unfiltered x-radiation from a tungsten anode at a voltage of 57 kV applied to the x-ray tube.
\(1—\sigma = 3.6 \cdot 10^3;\quad 2—\sigma = 5.8 \cdot 10^3;\quad 3—\sigma = 0.01.\)

Fig. 4. Dependence of the ratio of the dissolution rates of the irradiated and unirradiated (100) faces of a KCl single crystal on the magnitude of the undersaturation of an aqueous KCl solution. Doses of irradiation by x-rays of energy 8 keV are equal to:
\(1—2.5 \cdot 10^6\ \text{rad};\quad 2—1.2 \cdot 10^5\ \text{rad};\quad 3—8 \cdot 10^4\ \text{rad}.\)

Irradiation with x-rays of the (100) face of a KCl single crystal in the region of small undersaturations of the solution, just as irradiation of NaCl, causes an increase in the dissolution rate (Fig. 4). In the region of larg—

...undersaturations of the solution, the dissolution rate of irradiated KCl crystals over the entire investigated range of irradiation doses up to \(Q = 1.5 \cdot 10^{6}\) rad is lower than the dissolution rate of unirradiated crystals (Fig. 4). Table 2 gives, for comparison, data on the dissolution rate of the (100) face of NaCl, KCl, KBr, and KJ crystals in the corresponding aqueous solutions at various undersaturations. All crystals received the same dose \(Q = 1.2 \cdot 10^{5}\) rad of X-rays with an energy of 8 keV. It is seen from Table 2 that irradiation has less effect on the dissolution rate of KBr and KJ at the undersaturations indicated in the table than on the dissolution rate of NaCl and KCl crystals. At \(\sigma > 0.009\) this is associated with the KBr and KJ crystals passing beyond the structurally sensitive region of undersaturations. The lattice energy of the crystals listed in the first column of Table 2 increases from KJ to NaCl. At \(\sigma < 0.006\) the change in the dissolution rate increases with the energy of the crystal lattice. The dependence obtained is probably explained by the fact that the concentration of radiation defects established in an ionic crystal at a given irradiation dose may depend on the lattice energy.

Ratio of the dissolution rate of an irradiated (100) face to the dissolution rate of an unirradiated (100) face, \(\dfrac{v_{0}}{v_{\mathrm{H}}}\), for various alkali-halide crystals that received an irradiation dose \(Q = 1.2 \cdot 10^{5}\) rad from X-rays with an energy of 8 keV.

Table 2

The destruction of accumulated radiation defects is hindered in crystals with a high binding energy. Therefore, in the region of small undersaturations of the solution, at the same irradiation dose, the greatest increase in the dissolution rate will occur for crystals with the higher crystal-lattice energy. Thus, in the chlorine series, as is evident from Table 2 and Figs. 2 and 4, the increase in the dissolution rate of NaCl is considerably greater than the increase in the dissolution rate of KCl. From Table 2 (\(\sigma = 0.003\)) it is seen that, in the potassium series, of the crystals studied the greatest increase in the dissolution rate is shown by the KCl crystal, as the crystal with the highest crystal-lattice energy.

Small doses of ionizing radiation, by breaking up accumulations of vacancies [6], should decrease the dissolution rate of crystals in the region of large undersaturation of solutions.

This process, as applied to a single series of alkali-halide crystals, will proceed more actively in crystals with lower crystal-lattice energy, owing to the less strong bond between the particles in the crystals and the vacancies in their clusters.

Therefore, for example, at \(\sigma > 0.009\) and \(Q = 1.2 \cdot 10^{5}\) rad (Table 2, Figs. 2 and 4), the dissolution rate of KCl decreases by a larger amount than the dissolution rate of NaCl. An increase in the irradiation dose may lead to an increase in the dissolution rate even in the region of large undersaturations, owing to an increase in the number of interstitial defects and their clusters, which may be active in this region of solution concentrations.

centers of dissolution. Such an increase in the dissolution rate is more probable for crystals with a higher lattice energy, since in them the destruction of the accumulated radiation defects is hindered. This explains why increasing the dose of irradiation by X rays of energy 8 keV above \(1.5\cdot 10^{5}\) rad (Fig. 2) leads in this region of undersaturation of the solution to an increase in the dissolution rate of the NaCl crystal. No such effect was observed for KCl, KBr, and KJ crystals, which is apparently connected with the greater ease of destruction of the radiation disturbances accumulated in the course of irradiation.

Experiments showed that preliminary irradiation of NaCl, LiF, KCl, KBr, and KJ crystals by X rays with quantum energies from 8 to 30 keV changes the dissolution rate only of the (100) face. The dissolution rate of irradiated crystals in all other directions, except \([100]\), proved to coincide, within the experimental error, with the dissolution rate of unirradiated crystals. These results indicate a slight relative increase in the density of dissolution centers on these faces when the integrity of the crystal lattice is disturbed, and the closeness of the mechanism of their dissolution to a diffusion mechanism. The change in the dissolution rate caused by irradiation of the crystal is much smaller than the change in the dissolution rate due to a change in crystallographic orientation at a constant value of undersaturation (Tables 1, 2; Figs. 1–5). A neutron flux changes the dissolution rate of alkali-halide crystals analogously to large doses of X-ray radiation. Protons of energy 4.5 MeV, already at doses of the order of \(10^{18}\) protons/\(\text{m}^{2}\), lead to a very strong increase in the dissolution rate. This is probably caused by the numerous displacement zones formed in the crystals [7, 9], along which the initial outflow of substance from the crystal into the solution takes place. The penetration depth of the protons, measured by the depth of coloration, was on the average, for the single crystals investigated, of the order of \(2\cdot 10^{-4}\) m. A layer 50 μ thick was removed before the experiment from the irradiated surface, as was stated above. In the course of experiments using jets of undersaturated solutions, a layer of about 150 μ dissolved. Thus the penetration depth of the protons was sufficient for investigating proton-irradiated crystals by the method described.

Fig. 5. Comparison of the effect of protons (curve 1), neutrons (curve 2), and X rays (curve 3) on the dissolution rate of the (100) face of a KCl single crystal. The irradiation dose by protons is \(10^{19}\) protons/\(\text{m}^{2}\), by neutrons—\(10^{14}\) neutrons/\(\text{m}^{2}\), and by X rays—\(10^{5}\) rad.

In Fig. 5 a comparison is made of the action of X rays, neutrons, and protons on a KCl single crystal. Crystals irradiated with X rays at a dose \(Q = 10^{5}\) rad and with neutrons at a dose of \(10^{14}\) neutrons/\(\text{m}^{2}\) (with accompanying irradiation by \(\gamma\)-quanta of energy 2 MeV at a dose of 18,000 roentgens) dissolve more slowly than unirradiated crystals at \(\sigma > 0.007\). Crystals irradiated with protons at a dose of \(10^{19}\) protons/\(\text{m}^{2}\) dissolve faster than unirradiated ones throughout the entire structurally sensitive region of undersaturations.

LiF crystals irradiated with protons dissolve in pure distilled water considerably faster than unirradiated ones; moreover, Table 3 shows that a small change in the experimental temperature does not affect the character of this dependence.

Table 3

Dependence of the dissolution rate of the (100) face of a lithium fluoride crystal, \(v \cdot 10^{7}\) m/sec in water, on the irradiation dose \(Q\) by protons of energy 4.5 MeV and on temperature

At the same time, LiF irradiated with neutrons to a dose of the order of \(2 \cdot 10^{13}\) neutrons/m\(^2\) dissolves under analogous conditions more slowly than unirradiated LiF by 10%. The qualitative character of the dependence of the dissolution rate of LiF and KCl crystals on irradiation by neutrons and protons is the same. Only the structure-sensitive region of undersaturations is shifted for LiF all the way to pure water.

Conclusions

1. Preliminary irradiation affects the dissolution rate of only one reproducibly growing smooth face (100) of the investigated single crystals NaCl, KCl, LiF, KBr, and KJ.

2. The change in the dissolution rate of alkali-halide crystals under the action of irradiation is considerably smaller than the change in the dissolution rate caused by a change in crystallographic orientation.

3. At small undersaturations (for NaCl, \(\sigma < 0.007\)), irradiation of alkali-halide single crystals leads to an increase in the dissolution rate of the (100) face. For the region of large undersaturations, the sign of the change in the dissolution rate of the crystals depends on the magnitude of the irradiation dose. Small irradiation doses (up to \(1.5 \cdot 10^{5}\) rad in the irradiation of NaCl by X-rays) cause a decrease in the dissolution rate. Large irradiation doses lead to an increase in the dissolution rate of the crystals.

4. For a number of alkali-halide salts, radiation annealing of defects proceeds at a lower rate in crystals with a larger crystal-lattice energy, which leads to a greater influence of irradiation on the dissolution rate of these crystals.

References

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4. Collected articles “Elementary Processes of Crystal Growth,” IL, Moscow, pp. 153—247, 1959.

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6. Collection “Vacancies and Point Defects.” Metallurgizdat, Moscow, pp. 123—159, 1961.

7. V. V. Penkovskii. The action of irradiation on metals and certain refractory materials. Publishing House of the Academy of Sciences of the Ukrainian SSR, Kiev, 1962.

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10. Van Buren, Defects in Crystals. IL, Moscow, p. 462, 1962.