PROCEEDINGS

of the Tomsk Order of the Red Banner of Labor Polytechnic Institute named after S. M. Kirov

Vol. 140
1965

ENSURING A PLANE FRONT OF INTERDIFFUSION OF BROMINE AND CHLORINE ANIONS THROUGH CONTACT OF KCl AND KBr CRYSTALS

V. Ya. Zlenko, A. M. Kostin

The conditions for applying Fick’s second law, used in the study of diffusion in binary solid-phase systems, require that the isoconcentration surfaces in the specimen remain parallel to one another throughout the entire period of diffusion annealing. In the case of specimens in the form of a plate, the surfaces of equal concentrations (the diffusion front) must be plane.

Theoretically, the condition of a plane diffusion front is fulfilled only in the presence of continuous contact between two crystals. In practice, however, continuous contact is not always necessary to ensure a plane diffusion front. A plane diffusion front will be obtained if the ion flux along the surface of the specimen \(j^s\) between the nearest contact points considerably exceeds the ion flux in the volume \(j^o\)

\[ j^s \gg j^o \]

or, for points of equal concentration,

\[ \frac{D^s}{l} \gg \frac{D^o}{a}, \tag{1} \]

where \(D^s\) and \(D^o\) are the coefficients of surface and volume diffusion, \(l\) is the distance between the nearest contact points, and \(a\) is the lattice parameter.

When the temperature changes, the principal influence on the magnitude of the distance \(l\) is exerted by the ratio \(D^s/D^o\). Its value at temperatures close to the melting temperature of the crystal is of the order of \(10^3\), while at lower temperatures it becomes greater than \(10^6\). A simple calculation from (1) shows that for \(a = 10^{-7}\) cm the distance \(l\) at high temperatures must be less than one micron, while at low temperatures \(l\) may be of the order of 1 mm.

For metals, the problem of creating the required density of the number of contacts is solved by several methods. For technical problems, the method of hot rolling plates of two metals is used, followed by the preparation of diffusion specimens from these plates [1].

Sometimes welding under slight pressure is used [1]. Much work has been carried out on metals, one of which was electrolytically coated with a layer of another [2, 3]. The listed methods of bringing specimens into contact are not acceptable for alkali-halide crystals.

A technique for ensuring a planar diffusion front in alkali-halide single crystals has not been developed. To study the interdiffusion of ions in alkali-halide single crystals, it is first of all necessary to solve the problem of bringing them into contact. We attempted to solve this problem by several methods. The possibility of ensuring a planar diffusion front in alkali-halide salts was studied on KCl and KBr single crystals grown by the Kyropoulos method from chemically pure salts.

Compression at High Temperature

At room temperature, KCl and KBr single crystals are brittle. As the temperature is raised, the plasticity of alkali-halide crystals increases; therefore one may hope that, by compressing them at elevated temperature, it is possible to increase the number of contacts. Bearing this possibility in mind, we set ourselves the task of studying the influence of external pressure on the change in the state of contact of KCl and KBr single crystals in the heated state.

Monocrystals of KCl and KBr, size \(15 \times 10 \times 3\) mm, were brought into contact with freshly cleaved surfaces, oriented so that the (100) faces of both crystals were parallel to one another, wrapped with nichrome wire 0.15 mm in diameter, and placed in a furnace (Fig. 1) on ceramic support 5. In the furnace the specimens were heated for 2 hours to \(700^\circ\)C and held at this temperature for 1 hour. After the specimens had been heated, a load was placed on the rod to create external pressure on the specimens. The specimens were kept under pressure for 30 to 60 minutes.

Fig. 1. Schematic of the apparatus for studying the behavior of KCl and KBr single crystals during heating.
1—light source, 2—load, 3—mirror, 4—single crystals, 5—ceramic support.

After cooling, the specimens were split along a plane perpendicular to their contact plane. One half of the specimen was examined under a microscope at magnification 90–480. On the other half, the dislocation density was determined by etching in methanol with an admixture of ammonium chloride [4].

Microscopic observations showed that changing the external pressure from 0 to \(2\ \text{kg}/\text{cm}^2\) at \(700^\circ\)C leads to a tenfold decrease in the gap between the crystals. At the same time, no dense joining of the crystals occurs, since after cooling they are freely separated. In addition, as a result of plastic deformation the external shape of the crystals is strongly distorted, and the dislocation density becomes 2–3 orders of magnitude higher than in the initial crystals. For these reasons, compression as a method of ensuring a planar diffusion front cannot be recommended for KCl and KBr single crystals.

Contact Melting

The contact of KCl and KBr crystals melts at a temperature lower than the melting temperature of each of the crystals separately. This phenomenon, known as contact melting [5], was used by us to join KCl and KBr single crystals. The minimum temperature at which a liquid phase appears in the contact between KCl and KBr crystals is \(716^\circ\mathrm{C}\). Lowering the temperature of the contact liquid below \(716^\circ\mathrm{C}\) leads to its crystallization. When the liquid solidifies, solid solutions based on KCl and KBr are formed.

To join KCl and KBr single crystals, they were separately heated to a temperature of \(720^\circ\mathrm{C}\). After holding for half an hour at this temperature, the single crystals were brought into contact and kept in the furnace until the liquid that formed filled the entire gap between the single crystals. The single crystals were then removed from the furnace, cooled, and split along a plane perpendicular to their contact plane. On the cleavage plane of the single crystals, a scratch was made with the diamond indenter of a PMT-3 instrument. The width of the scratch in the region of the solid-solution interlayer proved to be considerably smaller than in the region of the KCl and KBr single crystals (Fig. 2).

As the width of the interlayer we took the length of the thinner part of the scratch. Measurements in 89 experiments showed that the width of the interlayer obtained by the method described varies from 30 to 300 microns.

Fig. 2. Interlayer between KCl and KBr single crystals.

We attempted to reduce the thickness of the interlayer by preliminary grinding followed by contact melting under a pressure of \(0.1\)—\(0.5\ \mathrm{kgf}/\mathrm{cm}^2\). However, this attempt did not give satisfactory results. The thickness of the interlayer at pressures below \(0.5\ \mathrm{kgf}/\mathrm{cm}^2\), within the scatter of the values, remained constant. Increasing the external pressure above \(0.5\ \mathrm{kgf}/\mathrm{cm}^2\) leads to plastic deformation of the KBr single crystal. The thickness of the interlayer is not the same at different points of contact of the KBr and KCl crystals. It increases smoothly from the middle toward the edges of the contact plane. Such an increase in the thickness of the interlayer is associated with an increase in temperature from the center toward the edges of the furnace.

By the method of potentiometric titration [6] of plane-parallel layers removed from KCl and KBr single crystals, the distribution of the bromine-ion concentration across the thickness of the interlayer was determined. It turned out

It was found that the concentration of bromine ions in the interlayer varies from 50 to 70 mol% (Fig. 3). The presence of such a concentration inhomogeneity in the interlayer prevents the use of contact melting for joining KCl and KBr single crystals, if interdiffusion is to be studied by the Matano method or by the metallographic method. The latter require that the phases in contact at the beginning of diffusion be homogeneous in composition.

Fig. 3. Chemical composition of the interlayer.

Annealing in Powder

In deriving the equation of Fick’s second law, it is assumed that the motion of impurity ions occurs only in the direction perpendicular to the contact plane. The directed flux of impurity ions along a plane parallel to the contact plane is taken to be zero. This condition may be violated if there is no continuous contact between the crystals.

If inequality (1) is not satisfied, then the fluxes \(j^s\) and \(j^0\) create a concentration distribution of the impurity in the crystal that is not planar, but rather as shown in Fig. 4. At point \(A\) the isoconcentration curve is parallel to the line of contact of the crystal. The flux of ions entering point \(A\) is directed along the \(OX\) axis. At point \(B\) the situation is different. The flux of ions entering point \(B\) changes its direction to a new one, \(BB'\), which must be opposite to the direction of the maximum concentration gradient. Resolving this flux into two components, \(j_x^0\) and \(j_y^0\), we obtain \(j^0 = j_x^0 + j_y^0\).

Fig. 4. Diagram of the leveling of the diffusion front.

Thus, the flux of ions entering the volume of the crystal goes partly toward decreasing the concentration gradient along the \(OX\) axis, and partly toward decreasing the concentration gradient along the \(OY\) axis, i.e., toward leveling the diffusion front. A decrease in the flux due to the appearance of \(j_y^0\) leads to a decrease in the rate of ion transfer along the axis

$OX$, and consequently to obtaining underestimated values of the diffusion coefficients in the experiment.

As was noted above, the diffusion front levels out with time and becomes practically flat. This circumstance may mislead the experimenter when deciding whether or not a flat diffusion front is present.

When the size of the powder grains is decreased, the distance between the nearest contact points decreases. This leads to a decrease in the flux $j_y^0$ that tends to level the diffusion front. At a certain value of $\delta$ the quantity $j_y^0$ becomes equal to zero, and $j^0 = j_x^0$. With a further decrease in $\delta$, the magnitude of the flux $j_x^0$ remains constant. By studying the dependence of the impurity-ion flux on the mean linear size of the powder grains, one can find such a value of $\delta$ below which the flux does not depend on the grain size. At these values of $\delta$ the diffusion front will be practically flat.

Table 1

Flux of chlorine ions into a KBr single crystal after annealing it in contact with KCl powder at a temperature of 640°C

Table 1 gives numerical values of the fluxes of chlorine ions through the contact plane of a KBr single crystal annealed in KCl powder. The number of chlorine ions that had diffused through a unit area of the contact during the entire diffusion time was determined by the method of potentiometric titration [6]. Table 1 shows that at $\delta \leqslant 30$ microns the chlorine-ion flux does not depend on the grain size. This indicates that at a temperature of 640°C a flat front occurs if the distance between the nearest contact points is less than 30 microns.

Discussion of the Results

The study of interdiffusion is usually carried out by the Matano method or by the method of B. Ya. Pines and E. F. Chaikovsky [3]. The first method requires that, at the beginning of diffusion, the composition of each of the contacting crystals be uniform throughout the entire volume of the crystal. The second method allows the presence of concentration inhomogeneity over the thickness of both crystals. However, the thickness of one of them is of the order of several microns [3]. Do the results we obtained satisfy the requirements of the named methods for studying diffusion?

A study of several methods for ensuring a flat diffusion front in KCl and KBr single crystals showed that none of these methods, in general form, gives a satisfactory solution of the problem. Compression of KCl and KBr crystals at high temperature leads to the appearance of plastic deformation and to an increase in the dislocation density. In this case continuous contact of the crystals is not obtained. In conne-

In this connection, the compression method as a method for ensuring a plane front of ion diffusion in KCl and KBr single crystals cannot be recommended.

Contact melting makes it possible to create a specimen with a continuous junction of KCl and KBr crystals. However, in this case an interlayer of solid solutions of variable concentration arises between them. The use of such a specimen for studying diffusion by the Matano method is impossible, since the latter requires that at the beginning of the diffusion anneal there be no interlayers with an intermediate concentration between the crystals.

A specimen made of KCl and KBr single crystals joined by an interlayer can be used for studying diffusion by the method of B. Ya. Pines and E. F. Chaikovsky. For this purpose it is necessary to try to obtain an interlayer of the greatest possible thickness (in order to reduce the concentration gradient in it), to cleave off one of the crystals, and by dissolving in water to reduce the thickness of the interlayer to several microns.

Annealing a single crystal in powder makes it possible to ensure a plane diffusion front provided that the mean linear grain size is less than 30 microns. This annealing should be continued until, over the thickness of the half-absorption layer of X-rays, a certain distribution of impurity concentration has been produced. After saturation of the surface layer of the crystal with the impurity, one may proceed to the study of diffusion by the method of B. Ya. Pines and E. F. Chaikovsky. The Matano method cannot be applied in this case, since the powder in which the crystal was annealed is scattered after the experiment, and it is then impossible to find the distribution of impurity concentration in the powder.

Thus, a check of the possibility of ensuring a plane front of anion diffusion in KCl and KBr single crystals has shown that, of all the methods we have studied, only two may find application: the contact-melting method and annealing in powder. Moreover, both methods of ensuring a plane diffusion front are applicable in the study of diffusion only by the X-ray method.

LITERATURE

1. V. Seith. Diffusion in Metals, Moscow, IIL, p. 51, 1958.
2. W. Seith, H. Wever, Zs. Elektrochem., 57, 891, 1953.
3. S. D. Gerzhriken and I. Ya. Dekhtyar. Diffusion in Metals and Alloys in the Solid Phase, Moscow, 1958.
4. S. V. Lyubents and N. F. Kostin. Crystallography, 7, No. 2, 328, 1962.
5. D. D. Saratovkin and P. A. Savintsev, DAN SSSR, 80, No. 4, 1951.
6. V. A. Kireev. Course of Physical Chemistry, Moscow, GNTI, 1956.