On the Nature and Linear Rate of Contact Melting
Abstract Generated abstract
This paper investigates the mechanism of contact melting in alkali halide crystals and low melting metal systems, using high temperature X-ray diffraction, surface composition measurements after controlled contact, calorimetric data, and measurements of linear melting rate. The results indicate a preparatory stage in which mutual diffusion produces solid solution layers at the contact boundary, including in systems with limited solubility or eutectic behavior, followed by formation of a liquid interlayer and continued dissolution of the solid components. For metal pairs, the linear rate of contact melting above small superheatings follows an Arrhenius type temperature dependence, while pressure, contact area, and relative motion affect the rate but not the activation energy for a given pair.
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ON THE NATURE AND LINEAR VELOCITY OF CONTACT MELTING
L. A. Savintsev, V. E. Avericheva, V. Ya. Zelenko, A. V. Vyatkina
(Presented by the scientific seminar of the Radio Engineering Faculty)
Contact melting of substances has found application in practice as a method for obtaining new alloys [1] and as a method of physicochemical analysis [2]. However, the nature of contact melting has not yet been revealed.
It has been suggested that the contact melting of alkali-halide crystals forming continuous series of solid solutions is reduced to the formation of a low-melting solid solution as a result of mutual diffusion of the components [3].
Our experiments have shown that the mechanisms of contact melting of crystals with unlimited solubility and of crystals forming eutectic alloys are similar.
The method used was that of taking X-ray photographs at high temperatures, developed at the Institute of General and Inorganic Chemistry of the Academy of Sciences of the USSR [4].
The crystals under investigation were ground into a fine powder, poured into a thin-walled quartz capillary with an internal diameter of 0.4–0.6 mm, and placed in an X-ray camera of the design described in [4]. The samples were heated to the specified temperature and held at this temperature during an exposure of 1.3–2.5 hours.
On X-ray photographs of mixtures of KCl and NaCl powders taken at 20°, 300°, and 600°, only the lines of the components were found; but at 635°C, i.e., at a temperature 25° below the contact-melting temperature of these crystals, the lines of the components are absent, and in their place the lines of a solid solution appeared.
According to information available in the literature [5], KCl and KJ crystals form a system with limited solubility containing a simple eutectic. Contact melting of crystals of this system occurs at 600°C. We took X-ray photographs of KCl, KJ, the eutectic alloy, and the eutectic mixture of powders of these crystals at temperatures of 20°, 300°, 550°, and 580°. At no temperature was the formation of a homogeneous solid solution of the components detected on the X-ray photographs of the alloy and mixture. However, at a temperature \(t > 550^\circ\text{C}\), the lines of the X-ray photographs of the alloy and mixture are shifted relative to the lines of the X-ray photographs of pure KCl and KJ taken at the same temperatures; consequently, the lattice periods of KCl and KJ contained in the alloy
and in mixtures, differ from the lattice periods of the pure components. The data are given in Table 1.
At 300° the change in the lattice periods of the crystals occurs as a result of thermal expansion; however, at \(t > 550^\circ\) the action of the diffusion factor becomes appreciable, owing to which the period of KCl in the alloy increases more rapidly than in pure KCl, while the period of KI in the alloy decreases.
The diffusion process in KCl—KBr, NaCl—NaBr, and KCl—KI crystals brought into contact was studied at temperatures close to the temperature of contact melting.
The single crystals under investigation were heated separately to the specified temperature, then brought into contact and held at this same temperature for various times (from 6 to 260 minutes), after which the composition on the surface of each of the crystals was determined. The back-reflection X-ray method was used.
Table 1
Change in the lattice periods of KCl and KI as a function of temperature
| Crystals | Experimental temperature, °C | Lattice period, \(a\) (Å): pure component | Lattice period, \(a\) (Å): in alloy | Lattice period, \(a\) (Å): in mixture |
|---|---|---|---|---|
| KCl | 20 | 6.280 | 6.280 | 6.280 |
| KCl | 300 | 6.306 | 6.306 | 6.306 |
| KCl | 550 | 6.354 | 6.374 | 6.374 |
| KCl | 570 | — | 6.446 | — |
| KCl | 580 | — | 6.479 | — |
| KI | 20 | 7.050 | 7.050 | 7.050 |
| KI | 300 | 7.115 | 7.115 | 7.115 |
| KI | 550 | 7.213 | 7.080 | 7.080 |
| KI | 570 | — | 7.090 | — |
| KI | 580 | — | 7.010 | — |
In all cases, the formation of solid solutions was found on the surfaces of the crystals, the composition of which depended on the contact time and temperature. Thus, on the surface of a KCl crystal, at a contact temperature 50°C lower than the temperature of contact melting, in 200 minutes a solid solution of composition 60 mol % KBr + 40 mol % KCl is formed, which corresponds to the solid solution at the minimum of the melting diagram of the KCl—KBr system. On the surface of the second crystal (KBr), a solid solution of composition 30 mol % KCl—70 mol % KBr is formed.
The time required for the formation of solid solutions of such compositions decreases as the experimental temperature approaches the temperature of contact melting. At the contact-melting temperature the indicated layers are formed within several minutes.
Analogous results were obtained for NaCl and NaBr crystals. In the case of contact between KCl and KI crystals, limited solid solutions are formed on the surface of each of them. In the surface layer of KCl (of thickness \(3 \cdot 10^{-3}\) cm) at 550°, the maximum KI content was 32 mol %. Under the same conditions, only 12 mol % KCl was found in the surface layer of KI.
X-ray investigation of mixtures of alkali-halide crystals, carried out at high temperatures, as well as the study of diffusion processes at temperatures close to the contact-melting temperature, showed the presence of a preparatory stage of the contact-melting process, consisting in the dissolution of the solid components.
This process occurs both in crystals forming a continuous series of solid solutions (NaCl—KCl, KBr—KCl, NaCl—NaBr) and in those forming eutectic alloys (KCl—KJ), and proceeds at a higher rate at temperatures close to the contact-melting temperature.
Evidently the same process also occurs in all other systems in which contact melting is observed.
The presence of contact melting may be regarded as evidence for the existence of mutual solubility of the components. This is confirmed by experiments on measuring the heat of formation of the eutectic alloy KCl—K\(_2\)CrO\(_4\), whose components are considered mutually insoluble. In addition, the heat of formation of the eutectic alloy KCl—KJ was measured. The method used was that developed and described by M. S. Ivankina [6]. The results are given in Table 2.
Table 2
Heat of formation of solid eutectic alloys
| Alloys | Holding time (h) | Heat of formation, kcal/mole |
|---|---|---|
| KCl—K\(_2\)CrO\(_4\) | up to 24 | \(0.250 \pm 0.080\) |
| KCl—K\(_2\)CrO\(_4\) | up to 72 | \(0.180 \pm 0.030\) |
| KCl—K\(_2\)CrO\(_4\) | up to 220 | \(0.08 \pm 0.01\) |
| KCl—KJ | up to 120 | \(0.18 \pm 0.07\) |
The heat of formation of the eutectic alloy KCl—KJ does not depend on time; the heat of formation of the eutectic alloy KCl—K\(_2\)CrO\(_4\) decreases sharply with holding time.
The rate of contact melting of low-melting metals as a function of temperature was determined.
The crystals were heated separately to a temperature exceeding the contact-melting temperature by a certain number of degrees (superheating \(\Delta t\)), and then brought into contact. The time during which the upper specimen, 1.5 mm high, melted completely at a constant superheating temperature was determined. The linear rate of contact melting \(v\) was taken to be the ratio of the specimen height to the melting time.
At a superheating exceeding \(5^\circ\), the linear rate of contact melting depends on the temperature \(t\) according to the law:
\[ v = A e^{-\frac{U}{RT}} . \tag{1} \]
The values of the activation energy \(U\) and of the contact-melting temperature are given in Table 3.
The linear rate of contact melting increases when the upper specimen is moved over the surface of the lower one, increases as the contact area of the components decreases, and increases
with increasing pressure on the specimens. The activation energy is independent of all the factors listed and remains constant for a given pair of metals. However, the activation energy increases with increasing molecular concentration of the components (Table 4) [7].
Table 3
Linear velocity of contact melting
| System | $t_{\mathrm{c.m.}}$ | $U\left(\dfrac{\mathrm{kcal}}{\mathrm{g\ atom}}\right)$ | $v\left(\dfrac{\mathrm{cm}}{\mathrm{s}}\right)$ | $\Delta t^\circ \mathrm{C}$ |
|---|---|---|---|---|
| Sn—In | 119 | 55.9 | $7.14\cdot 10^{-4}$ | 11 |
| Sn—Bi | 140 | 102.3 | $6.21\cdot 10^{-4}$ | 11 |
| Sn—Pb | 183 | 133.2 | $2.77\cdot 10^{-4}$ | 11 |
| Pb—Bi | 125 | 78.5 | $0.87\cdot 10^{-4}$ | 11 |
| Cd—Bi | 144 | 148.3 | $2.24\cdot 10^{-4}$ | 11 |
| (Sn—Pb)—Bi | 96 | 39.7 | $4.4\cdot 10^{-5}$ | 18 |
| (Sn—Pb)—Cd | 145 | 59.8 | $13\cdot 10^{-5}$ | 12 |
At superheating of less than $5^\circ\mathrm{C}$, a sharper dependence of the linear velocity of contact melting on temperature is observed than in formula (1).
Table 4
Comparison of activation energy with molecular concentration
| Components | Components | Molecular concentration | Molecular concentration | Molecular concentration | $U\left(\dfrac{\mathrm{kcal}}{\mathrm{g\ atom}}\right)$ |
|---|---|---|---|---|---|
| I | II | $a_1$ | $a_2>a_1$ | $a_2<a_1$ | |
| Sn | Bi | 61 | 47 | 102.3 | |
| Sn | Pb | 61 | 55 | 133.2 | |
| Sn | In | 61 | 64 | 55.9 | |
| Sn | Cd | 61 | 77 | 90.9 | |
| Bi | Pb | 47 | 55 | 78.5 | |
| Bi | Sn | 47 | 61 | 102.3 | |
| Bi | Cd | 47 | 77 | 148.3 |
The linear velocity of contact melting and the activation energy decrease as the number of components in the system increases (Table 3).
On the basis of all that has been set forth, the following conclusions may be drawn.
The first stage of the process of contact melting ends with the formation, at the boundary of contact of the crystals, of a layer corresponding to the alloy with the minimum melting temperature. Following this, a liquid interlayer appears, and the further course of the process of contact melting must be associated with the dissolution of the solid components in the liquid that has formed.
To characterize this stage of the contact-melting process, the linear velocity of contact melting may be used; it is related to the physicochemical characteristics of the components and of their melt.
References
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