On the Kinetics of Interdiffusion in Alkali-Halide Crystals with the Formation of a Liquid Phase
Abstract Generated abstract
This paper examines interdiffusion in alkali halide crystal pairs when the phase diagram permits formation of an intermediate liquid layer, focusing on the NaCl, KCl system. Using contact melting experiments and comparison with interdiffusion data obtained without a liquid phase by Matano’s method, the authors relate the temperature dependence of liquid phase formation to activation energies and to the composition of saturated solid solutions at the crystal, liquid interface. The measured activation energies for liquid phase formation differ from bulk interdiffusion values but follow the same concentration dependence and agree, within experimental error, with about two thirds of the bulk activation energy. The results suggest that interdiffusion in the presence of a liquid phase is controlled by formation of solid solutions in a thin boundary layer, comparable to boundary diffusion rather than volume diffusion.
Full Text
On the Kinetics of Interdiffusion in Alkali-Halide Crystals with the Formation of a Liquid Phase
V. Ya. Zlenko, M. V. Kostyukevich
Two dissimilar crystals \(A\) and \(B\), brought into contact, constitute a nonequilibrium system [1]. The transition from a nonequilibrium state to an equilibrium one usually proceeds through the formation of single-phase layers, which are solid solutions of the \(A—B\) system.
If the \(A—B\) system has a fusibility diagram of the double-sigmoid type with a minimum (Fig. 1), then the transition from a nonequilibrium state to an equilibrium one at temperature \(T\) proceeds through the formation of three single-phase layers \(\alpha, L, \beta\), of which one, the \(L\)-layer, is liquid.
The rate at which equilibrium is established in the \(A—B\) system at temperature \(T\) is determined by the rate of formation of the \(\alpha\), \(L\), and \(\beta\) phases taken together. The rate of formation of the \(\alpha\) and \(\beta\) phases is determined by the rate of interdiffusion of components \(A\) and \(B\) in the solid phase. The rate of formation of the liquid \(L\)-phase is determined by the rate of interdiffusion of components \(A\) and \(B\) in the liquid phase.
Fig. 1. Fusibility diagram of the \(A—B\) system.
At temperature \(T\), the rate of interdiffusion of alkali-halide salts in the solid \(\alpha\) and \(\beta\) phases is significantly lower than the rate of interdiffusion of alkali-halide salts in the liquid \(L\)-phase. In this case, the rate of interdiffusion of alkali-halide salts in the presence of a liquid phase must be determined by the rate of formation of solid solutions in the \(\alpha\)- and \(\beta\)-phases, and the activation energy of interdiffusion of alkali-halide salts in the presence of a liquid phase must be equal to the activation energy of the process of formation of solid solutions of the \(\alpha\)- and \(\beta\)-phases.
When the temperature \(T\) changes (Fig. 1), the composition of the saturated solid solutions in the \(\alpha\)- and \(\beta\)-phases changes; as a result, the rate of interdiffusion in the presence of a liquid phase in the \(A—B\) system must be a function of composition.
We carried out a study of interdiffusion in the NaCl—KCl system in the presence of a liquid phase by the method of [4], known in the Soviet literature as contact melting. Interdiffusion without the presence of a liquid phase in the same system was studied by us by Matano’s method [8].
The results of studying the rate of formation of the liquid phase \(v\) at the contact of NaCl and KCl crystals are presented as the dependence of \(\lg v\) on \(10^3/T\) in Fig. 2. The tangent of the angle of inclination of the curve of the dependence
Fig. 2. Dependence of the melting rate of NaCl in contact with KCl on temperature.
of \(\lg v\) on \(10^3/T\) is related to the activation energy of the process \(Q_{\mathrm{l}}\) by the relation
\[ \tan \gamma = \frac{\Delta \lg v}{\Delta \left( \dfrac{10^3}{T} \right)} = -\frac{Q_{\mathrm{l}}}{2.3 \cdot R \cdot 10^3}, \tag{1} \]
where \(R\) is the universal gas constant.
Using relation (1), we calculated the values of the activation energy of the melting process of an NaCl crystal in contact with a KCl crystal at temperatures of \(680—750^\circ\mathrm{C}\). From the fusibility diagram of the NaCl—KCl system [9], using the experimental temperature \(T\), we found the composition of the saturated solid solutions \(c\) formed at the boundary of the NaCl crystal with the contact liquid. The results of determining the composition \(c\) and the activation energy of melting of an NaCl crystal in contact with KCl are given in Table 1. The same table also gives the experimentally found values of the activation energy of interdiffusion of NaCl and KCl without the presence of a liquid phase, \(Q_0\).
Table
Activation energy of melting of an NaCl crystal in contact with KCl and the activation energy of interdiffusion \(Q_0\) in the NaCl—KCl system
| \(t^\circ\mathrm{C}\) | \(c\), mol% KCl in NaCl | \(Q_{\ell}\), kcal/mol | \(Q_0\), kcal/mol |
|---|---|---|---|
| 750 | 13 | \(26 \pm 1\) | \(28 \pm 7\) |
| 740 | 16 | \(26 \pm 1\) | \(40 \pm 7\) |
| 735 | 18 | \(42 \pm 2\) | \(50 \pm 10\) |
| 725 | 21 | \(42 \pm 2\) | \(70 \pm 15\) |
| 712 | 26 | \(43 \pm 2\) | \(88 \pm 15\) |
| 705 | 29 | \(48 \pm 3\) | \(98 \pm 20\) |
| 700 | 30 | \(49 \pm 3\) | \(100 \pm 20\) |
| 697 | 31 | \(66 \pm 3\) | \(100 \pm 20\) |
| 680 | 40 | \(69 \pm 3\) | \(112 \pm 20\) |
It was shown above that the activation energy of interdiffusion in the presence of a liquid phase should be equal to the activation energy of interdiffusion in the absence of a liquid phase, i.e. \(Q_{\ell}=Q_0\).
From Table 1 it is evident that \(Q_{\ell} \ne Q_0\). This difference can be explained by the different experimental conditions. The values \(Q_0\) characterize the rate of formation of solid solutions of the NaCl—KCl system in the volume of an NaCl crystal. The values \(Q_{\ell}\), calculated from the rate of formation of the liquid phase, are determined by the rate of formation of solid solutions in a thin layer. If the thickness of this layer is of the order of the thickness of an intergrain boundary [10], then the activation energy of the process of formation of the liquid phase \(Q_{\ell}\) should be equal to the activation energy of boundary diffusion \(Q_{\mathrm{g}}\), which can be expressed according to [11] as \(Q_{\mathrm{g}}=2/3\,Q_0\); consequently,
\[ Q_{\ell}\simeq Q_{\mathrm{g}}\simeq 2/3\,Q_0, \]
\[ Q_{\ell}=2/3\,Q_0. \tag{2} \]
Figure 3 presents the dependences of the activation energy of diffusion processes in the NaCl—KCl system, constructed on the basis of the experimental data given in Table 1. The curve \(Q_0\) shows the dependence of the activation energy of volume diffusion on the concentration \(c\), and the curve \(Q_{\ell}\) the dependence of the activation energy of the process of formation
Fig. 3. Dependence of the activation energy of processes in the NaCl—KCl system. \(Q_0\)—volume heterodiffusion in the absence of a liquid phase; \(Q_{\ell}\)—volume heterodiffusion in the presence of a liquid phase.
of the liquid phase on the concentration \(c\) in the NaCl—KCl system. The hatched region represents the dependence of the activation energy of boundary diffusion on the concentration of the same system (constructed on the basis of relation (2), taking into account the scatter of the experimental values of \(Q_0\)).
The curves in Fig. 3 show that the nature of the dependence of the activation energy of the process of liquid-phase formation on the concentration \(c\) and the dependence of the activation energy of interdiffusion on the concentration \(c\) are identical.
The curves of the dependences \(Q_{\mathrm{l}}(c)\) and \(2/3\,Q_0(c)\) coincide within the experimental error.
Thus, the activation energy of interdiffusion in the presence of a liquid phase in the NaCl—KCl system can be determined as \(2/3\) of the activation energy of interdiffusion in the bulk of the crystal. Interdiffusion of alkali halide salts in the presence of a liquid phase occurs through the formation of solid solutions at the boundary between the liquid and the crystal in a thin layer.
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