EFFECT OF CRYSTALLOGRAPHIC ORIENTATION ON THE DISSOLUTION RATE OF NaCl-TYPE CRYSTALS

A. F. NAUMOV, P. A. SAVINTSEV

The anisotropy of the dissolution rate of alkali-halide single crystals in their aqueous solutions has been determined by many authors (for example, [1–4]), who obtained contradictory data. The experimental results presented in [1] cast doubt on the dependence of the dissolution rate of crystals on their crystallographic orientation. In [2–4], a slight change in the dissolution rate (on the order of 2–5%) was obtained in going from one face of a crystal to another, and the data of one author contradict the results of other works.

The kinetics of dissolution of NaCl-type crystals in their aqueous solutions, far from saturation and weakly stirred, is described in [4]. Crystals of NaCl, KCl, KBr, and KJ dissolve under these conditions in the diffusion regime, in which the dissolution rate depends linearly on the magnitude of the relative undersaturation of the solution

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

where \(C_0\) is the concentration of the equilibrium solution above the crystal, and \(C\) is the concentration of the solution.

The use of the diffusion-dissolution method, when the dissolution rate is not a structurally sensitive quantity, can explain the conclusion that there is no anisotropy in the dissolution rate of NaCl single crystals [1, 5]. Although M. Towbin and O. Baham [2] found that, with weak stirring of the solution, during the first 1–2 min different faces of an NaCl crystal have different dissolution rates, subsequent experimental investigations [3] did not confirm their results.

At a rate of stirring of an NaCl crystal in water and in aqueous NaCl solutions equal to 0.4 m/sec, Davon [3] determined that the (110) face dissolves 3–5% faster than the (100) face. This ratio of the rates, according to Davon’s conclusion, does not depend on the concentration of the solution. One cannot agree with the latter assertion, since according to theoretical considerations [6] the sensitivity of the dissolution rate to the structure of the dissolving surface should increase with decreasing undersaturation of the solution. Accordingly—

with an increase in the concentration of the solution, the anisotropy of the dissolution rate will increase. In the limiting case, the dissolution rate of a crystal in the mother aqueous solution may become as structurally sensitive a quantity as the rate of etching of solids by various reagents.

Increasing the intensity of stirring of the solvent, by increasing the rate at which dissolved particles are carried away from the crystal, can likewise change the diffusion regime of dissolution into a diffusion–kinetic one, correspondingly increasing the sensitivity of the dissolution rate to the structure of the dissolving surface [4].

In the present work, we investigate the conditions under which the dissolution rate of KBr, NaCl, KJ, and LiF crystals in water and in their aqueous solutions depends on the crystallographic orientation of the dissolving surface.

The (100) face of an NaCl crystal is a repeatedly growing smooth face belonging to the equilibrium form [7, 8]. All the other faces are formed by steps that are bounded by portions of smooth faces. On the (100) face of an ideal defect-free NaCl single crystal, at slight undersaturation of the solution, there are no dissolution sites. They appear as a result of statistical fluctuations in the form of two-dimensional ruptures of the flat lattice network.

The probability of formation of such active dissolution centers increases with increasing undersaturation of the solution. On all other faces, or regions of the surface not belonging to the equilibrium form, the sites from which particles leave are active dissolution centers at any magnitude of undersaturation. This is one of the reasons leading to anisotropy of the dissolution rate. The dissolution rate of pure crystals of the NaCl type should be smallest on the (100) face, since this face has the lowest density of active dissolution centers. Lattice disturbances on the (100) face increase the number of dissolution sites. The appearance of new lattice defects on other faces plays a smaller role in dissolution, since even in those cases when they have an “ideal” structure, any region of them may be a center of outflow of matter from the crystal into the solution. Analogous conclusions have been drawn regarding the process of growth of faces belonging and not belonging to the equilibrium form of the crystal [6, 7, 9].

The mechanism of dissolution and growth [7] of roughened faces that do not belong to the equilibrium form is probably always determined by the influence of impurities. In the present work we did not specifically consider the influence of impurities on the anisotropy of dissolution. However, it must be remembered that, for heteropolar substances, the solvent should be regarded as an “impurity,” the action of which depends on the concentration of the dissolved substance [7, 10].

For the experiments, single crystals grown from melts of “KhCh” grade salts by the Kyropoulos method were used. Before dissolution, the specimens were annealed for 4² hours at 870°K, followed by cooling at a rate of 10°/h.

In the first series of experiments, the solvent flowed through a cylindrical through-hole in the crystal, oriented perpendicular to the (100) and (110) faces. By varying the length and diameter of the hole and the velocity of the solvent jet passing through it, one can obtain the desired regime of dissolution of the walls of the cylindrical hole. Under these dissolution conditions, we have a set of surfaces of the most varied orientations dissolving under identical conditions.

From the resulting dissolution forms one can judge the anisotropy of the dissolution rate. The hydrodynamics of the process of passage of a solution through cylindrical tubes has been well studied. At a solution-flow velocity of about \(1—5\) m/sec and a cylindrical-opening diameter on the order of \(1—2\) mm, the thickness of the laminar sublayer adjacent to the dissolving surface is much smaller than the diameter of the opening. Then the dissolution rate \(v\) along any direction perpendicular to the longitudinal axis of the opening, and the radius vector \(r\), of the same direction, are related (at constant jet velocity) by the relation \(r = r_0 + v\tau\), where \(r_0\) is the initial radius of the cylindrical opening and \(\tau\) is the dissolution time.

In another series of experiments, two crystal plates oriented in different ways were subjected simultaneously to dissolution by the normal incidence on their surfaces of two jets of aqueous solution having the same velocity, concentration, and temperature. The diagram of the apparatus for dissolving crystals is shown in Fig. 1.

The solvent is fed by a centrifugal pump (6) into the upper vessel (2), from which, through a tube, it enters the divider (3), where it is divided into two streams. These streams pass through calibrated tubes and fall normally on the faces of the reference and test specimens (4). After the specimens, the solvent passes through the drain funnel (5) and again enters the reservoir of the centrifugal pump. One and the same amount of solution continuously circulates along the described circuit. The increase in the concentration of the solution due to dissolution of the crystals is so insignificant that it may be neglected. The temperature of the solvent is maintained constant to an accuracy of \(\pm 0.05\) deg by a contact thermometer (1). Flowing water from the heater (7) enters the heat exchanger (8), where it cools or heats the solvent passing through the same heat exchanger. The interlock device (9) switches off the electric circuit of the heater if the water supply to the heater stops. The diameter of the solution jets is changed by replacing the calibrated tubes in the divider (3). The jet velocity depends on the height of the hydrostatic head produced by the column of solution above the calibrated tubes, and is changed by lengthening or shortening the tube connecting the upper vessel (2) with the divider (3).

Fig. 1. Apparatus for dissolving crystals.

The hydrodynamics of the dissolution process for the reference and test specimens is completely identical. This is achieved by the identical velocity of normal incidence of the jets onto the dissolving crystal surfaces, by the identical dissolution temperature and solution concentration. The calibrated tubes, which impart a definite direction to the motion of the jets, are structurally rigidly connected—

…with sockets for the nozzles into which the specimens are placed, in order to ensure that the jets fall on the dissolving surface exactly along the normal. The jet velocities used in the work do not lead to mechanical washing-out of crystal particles by the solvent owing to hydrodynamic impact. Thus, for example, jets of saturated solutions of NaCl, KCl, KBr, etc., 2 mm in diameter, falling for three hours at a velocity of \(7\ \mathrm{m/sec}\) onto the surface of the corresponding single crystals of sodium chloride, potassium chloride, potassium bromide, etc., lead neither to dissolution nor to destruction of their surfaces. In this case the place where the jet falls differs in no way from the neighboring regions of the crystal.

As the linear dissolution rate \(v\), the ratio of the thickness of the dissolved layer of substance at the place where the jet falls on the crystal to the dissolution time was taken. The error from 10 measurements was 3% at low and 1% at high undersaturation of the solution.

In dissolving crystals having a through cylindrical hole, the same apparatus was used. Only the calibrated tubes were replaced by glass tubes 0.02 m in diameter, to which the crystals were glued from below. Two crystals with differently oriented holes could be glued at once to two glass tubes and dissolved simultaneously under identical conditions. The temperature at which all experiments were carried out was \(293^\circ\mathrm{K}\).

Cylindrical holes in crystals, when an undersaturated solution is passed through them, increase in diameter and are transformed into prismatic angular dissolution forms (Figs. 2, 3). Study with an instrumental microscope of transverse

Fig. 2. Dissolution form obtained from an initially cylindrical hole in an NaCl single crystal oriented along the direction \([001]\). Dissolution time \(\tau = 20\ \mathrm{min}\), \(\sigma = 0.05\), \(w = 1\ \mathrm{m/sec}\). \((\times 20)\).

Fig. 3. Dissolution form obtained from an initially cylindrical hole in an NaCl crystal oriented along the direction \([1\bar{1}0]\). \(\tau = 20\ \mathrm{min}\), \(\sigma = 0.05\), \(w = 2\ \mathrm{m/sec}\). \((\times 15)\).

cleavages and cuts of the resulting dissolution figures gives the necessary data on the dependence of the crystal dissolution rate on crystallographic orientation.

The anisotropy of dissolution is more clearly expressed at low undersaturations of the solution and with its intensive stirring. Table 1…

data are given on the dissolution of plates of a NaCl single crystal of different orientation by means of jets of solution falling normally onto the plates.

It follows from Table 1 that the ratio \(\rho=\dfrac{V_{(110)}}{V_{(100)}}\) increases as the relative undersaturation \(\sigma\) of the solution decreases and as the velocity of incidence of the jet of \(W\)-solution increases. Davon’s conclusion [3] on the independence of \(\rho\) from \(\sigma\) is apparently due to the comparatively low intensity of stirring of the solution in his experiments.

Table 1

Ratio of the dissolution rate of the (110) face of a NaCl single crystal to the dissolution rate of the (100) face of the same single crystal, \(v_{(110)}/v_{(100)}\), at various values of the relative undersaturation \(\sigma\) of an aqueous NaCl solution and various velocities of incidence of the solution jet \(W\)

In Fig. 4 and in Table 2, using a NaCl single crystal as an example, it is shown that, although in absolute value the rate \(v_{(110)}\) approaches \(v_{(100)}\) as the relative undersaturation \(\sigma\) decreases, their ratio \(\rho\) increases greatly in this case. The dissolution process of KBr and KJ single crystals is characterized by the same regularities (Table 2).

The (110) face of a LiF single crystal, at a jet incidence velocity \(W=7\ \mathrm{m/sec}\), even in pure water dissolves 2.8 times faster than the (100) face.

The data obtained show that the coefficient \(\rho\) for the series of crystals investigated, at constant undersaturation of the aqueous solution, increases from KJ to LiF, i.e., \(\rho\) is larger the higher the melting point of the crystals and the lower their solubility in water.

Fig. 4. Dependence of \(v_{(110)}\) (curve 1), \(v_{(100)}\) (curve 2), and \(\rho=v_{(110)}/v_{(100)}\) (curve 3) for a NaCl crystal on the undersaturation of an aqueous NaCl solution \((w=7\ \mathrm{m/sec})\).

In Figs. 5 and 6 are shown the results of experiments in which an aqueous NaCl solution is passed at a velocity of \(0.6\ \mathrm{m/sec}\) through a cylin-

Table 2

Effect of the relative undersaturation of the solution on the dissolution rate of NaCl, KBr, and KJ crystals in their aqueous solutions ($W = 7$ m/sec)

a cylindrical hole in an NaCl single crystal, oriented in the direction [001] (Fig. 5) and in the direction $[1\bar{1}0]$ (Fig. 6). The initial diameter of the cylindrical hole was 0.004 m, the length—

Fig. 5. Plot of the dependence of the linear dissolution rate of an NaCl crystal on the direction of the radius vector in the plane {001}.

Fig. 6. Plot of the dependence of the linear dissolution rate of an NaCl crystal on the direction of the radius vector in the plane $\{1\bar{1}0\}$.

0.04 m. The relative undersaturation $\sigma$ was taken equal to 0.02. Under these conditions, the dissolution rates of the various faces of an NaCl single crystal are arranged in the series

\[ v_{(100)} < v_{(111)} < v_{(210)} < v_{(110)}. \]

A similar series of dissolution rates characterizes KBr and LiF crystals. In KJ crystals, in contrast to crystals of other salts, $v_{(111)} > v_{(110)}$.

The fact that the most slowly dissolving face of the crystals studied is the (100) face serves as further evidence of the small number of dissolution sites on smooth faces belonging to the equilibrium form of the crystal, as compared with roughened-

faces (or imperfect faces) that do not belong to the equilibrium form. Smooth faces are also distinguished by the lowest growth rate [7, 9, 11]. On dissolution figures (Figs. 2, 3), the (100) face appears in the form of mirror planes, while the (111) and (110) faces pass smoothly into neighboring ones. Let us note that the described method for obtaining dissolution figures can be used to determine the faceting of the equilibrium form of a crystal.

Yamamoto [12], by a phenomenological approach, taking into account the symmetry of crystals, established the following expression for the anisotropy of the etching rate of cubic crystals:

\[ v=v_{(100)}+4\left(v_{(110)}-v_{(100)}\right)\left(\alpha^{2}\beta^{2}+\beta^{2}\gamma^{2}+\gamma^{2}\alpha^{2}\right)+ \]

\[ +9\left(v_{(100)}-4v_{(110)}+3v_{(111)}\right)\alpha^{2}\beta^{2}\gamma^{2}, \]

where \(\alpha, \beta\), and \(\gamma\) are the direction cosines \((\cos\alpha,\ \cos\beta,\ \cos\gamma)\) of the direction of the velocity vector with the tetragonal axes of the cubic crystal. The relations obtained by him are also valid for the case of dissolution of alkali-halide crystals in their aqueous solutions. The calculated curves for the dependence of the dissolution rate on orientation approximately coincide with the curves shown in Figs. 5 and 6. Apparently, he obtained a general expression for the anisotropy of the dissolution rate and for the form of the dissolution figure in cubic crystals. In describing etch figures, for the example of a LiF crystal, Ives [13] successfully applied the topographic theory of the orientational dependence of dissolution of single crystals, developed by Frank [14]. In this case as well, the etching rate of the (100) face by special etchants is lower than the etching rate of other faces [13].

Fig. 7. Dependence of \(\rho=v_{(110)}/v_{(100)}\) for an NaCl crystal on the undersaturation \(\sigma\) of an aqueous NaCl solution at different doses of X-ray irradiation.
1—without irradiation; 2—\(1.8\cdot10^{5}\) rad; 3—\(4.6\cdot10^{5}\) rad; 4—\(1.5\cdot10^{6}\) rad; 5—\(2.2\cdot10^{6}\) rad.

The etching rate for the close-packed surface of a perfect crystal should be equal to zero. In real crystals, dissolution is associated with the formation of etch pits, the number of which can be increased by an artificial increase in the defectiveness of the crystal.

Figure 7 shows how \(\rho=\dfrac{v_{(110)}}{v_{(100)}}\) of an NaCl crystal depends on the undersaturation of the solution \(\sigma\) at different doses of X-ray irradiation. The rate of fall of the solution jet is \(W=7\) m/sec.

The X-ray irradiation doses used (up to \(2.2\cdot10^{6}\) rad) cannot cause a significant increase in the solubility of the crystal

\[ \Delta C_{0}\approx \frac{\Delta \Phi}{2RT}\,C_{0}, \]

where

\[ \Delta\Phi \]

is the increase in the thermodynamic potential of the crystal upon its irradiation,

$C_0$ — solubility of the NaCl crystal in water,
$R$ — universal gas constant,
$T$ — absolute temperature of the experiment.

Taking $\Delta \Phi < q$, where $q$ is the energy stored in the crystal upon irradiation, and $q \simeq 10^{-4}\cdot Q$ [15], where $Q$ is the dose of absorbed energy, we obtain

\[ \Delta C_0 < 1.4\cdot 10^{-4}\% \text{ by weight.} \]

Such a change in solubility cannot cause the noticeable change in the dissolution rate that is observed experimentally (Fig. 7). In all probability, the dissolution rate changes owing to a change in the density of defects in the crystal upon its irradiation. This leads to a change in the density of active dissolution centers on the dissolving faces. In this case the relative increase in the density of dissolution centers on the (100) face will be considerably greater than on the other faces, since the other faces possessed numerous dissolution centers even before irradiation. Indeed, the experiments show that the anisotropy coefficient of the dissolution rate $\rho$ changes only because of a change in the dissolution rate of the (100) face. The dissolution rate of the other faces does not depend on prior X-ray irradiation. This is additional evidence that the solubility of the crystals does not change under irradiation by the doses used, since otherwise the dissolution rate of all faces would change. Thus, the experiment on the dissolution of previously irradiated crystals also argues in favor of a special mechanism of dissolution of the (100) face, distinct from the mechanism of dissolution of the other faces.

Conclusions

1. The anisotropy of the dissolution rate of NaCl-type crystals in aqueous solutions is caused by an unequal number of dissolution centers on different faces and increases with increasing intensity of stirring of the solutions and with increasing concentration.

2. The cube face of NaCl, LiF, KBr, and KJ crystals has the lowest density of active dissolution centers, which determines the lowest dissolution rate of the crystal of this face. The mechanism of dissolution of the other faces is close to diffusion-controlled.

3. A change in the number of active dissolution centers due to irradiation of crystals with X-rays at a dose up to $2\cdot 10^6$ rad leads to a change in the anisotropy coefficient of the dissolution rate owing to a change in the dissolution rate of the crystal along the cube face.

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