CRYSTALLIZATION SUPPORT TUBE IN A LABORATORY FURNACE

Design of modular, simple to build and handle air c ooler (“crystallization support tube”) installed in a laboratory tube furna ce is presented. The setup allows easy regulation and simultaneous crystallization tests o f different temperature gradients, shapes of crystallization fronts and rate intervals in crucibles and Tamman test tubes, enabling fast studies of obtaining crystals. The re lationship between the crystallization parameters has been derived and numerically analyze d. This method can also be applied in crucible or tube furnaces.


INTRODUCTION
In principle, monocrystals can be obtained by crystallization from solid, liquid or gas phases. Within these possibilities a number of methods have been developed (TARJAN and MATRAI, 1972;WILKE and BOHM, 1988). Selection of the proper method for growing monocrystals of a given substance depends upon many factors, primarily on the nature of the substance and its physicochemical properties, quality desired and intended application of crystals as well as on available laboratory possibilities.
In many cases, monocrystals are obtained by growing from the melt, which is in essence a controlled cooling growth; in comparison with other methods for monocrystal preparation this method is simpler and easilier to control. When crystals are growing from the melt a higher crystallization rate than by other methods can be achieved. With the exception of crystal growth from water solutions, this process has been most thoroughly investigated from the technical standpoint. Crystal growth from the melt is widely applicable (ČABRIĆ and JANIĆIJEVIĆ, 2012).
The preparation of crystals of good quality (containing a small concentration of impurities and defects) requires crystallizing substances of a high purity, vacuum or an inert atmosphere (vacuum is not suitable if the substance has a high vapour pressure at the melting temperature), crucibles made of materials which do not react chemically with the melt, a high temperature stabilization in the furnace and the absence of mechanical shocks (TARJAN and MATRAI, 1972).

APPARATUS
In the previous papers (CABRIC et al., 2011;CABRIC et al., 2013), models of air coolers in a laboratory tube furnace, for regulating the crystallization fronts and rates in a several crucibles and Tamman test tubes are shown. In this paper, we show the development and improvement of the interior and exterior of the coolers, with movable cold plugs and cold thresholds (Fig. 1). The improved coolers are simple to build and handle. The coolers allows easy regulation of simultaneous crystallization tests of different number of crystallization parameters, with the purpose of obtaining single crystals from a family of newly synthesized compounds with a layered crystal structure (WILKE and BOHM, 1988) in a laboratory tube furnace.

BASIC EQUATIONS FOR COMPUTATIONS
The rate of melt solidification depends upon extracting the latent heat of solidification. For a time interval t, a crystal layer of thickness δ is formed (Fig. 1). During the formation of an elementary crystal layer of thickness dδ per unit area, the amount of heat released is Lρ dδ (L denotes the latent heat of solidification and ρ the crystal density); the latter is being extracted through the cooler for a time interval dt. On this basis the following equation may be written (ČABRIĆ et al., 1990): where ∆T denotes the difference between the temperature of the melt and that of the air stream, α is the coefficient of heat transfer from the cooler wall to the air stream, b denotes the plug height, kb designates the heat conductivity of the plug and k is the heat conductivity of the crystal. Introducing the parameter a = 1/α + b/ kb and transforming equation (1) we obtain ( ) The quotient dδ/dt denotes the rate of crystal layer growth which is usually represented by the symbol R; it is greatest at the beginning (δ = 0) and decreases with increasing thickness of the solidified layer.
Integration of equation (2) within the limits from 0 to δ and from 0 to t, and solving from δ gives the relation by means of which one can calculate also the time needed for the solidification front to reach the surface of bottom of the melt.

RESULTS AND DISCUSSION
In accordance with equation (2), we obtained numerical values of crystallization rate R in function of the difference between the temperature of the melt and that of the airstream ΔT, in the case of tin (Sn) (Fig. 2). Also, in accordance with equation (3), we obtained numerical values of thickness of crystal layer δ as a function of the height of the plug b, in the case of tin (Sn) (Fig. 3). The crystallization rate interval in each crucible and Tamman test tube is regulated by the cross section of the airflow a (Fig. 1) and by the difference between the temperature of the melt and that of the airstream ΔT (Fig. 2). The crystallization rate interval in crucibles can also be regulated by the plug height b (Fig. 1 and Fig. 3) and the distance of the plug head from the surface of the melt c (in the crucibles below the cooler) (Fig. 1). The temperature gradient is regulated by the distance d (Fig. 1). Plugs of various shapes and dimensions can be mounted on the air-cooled tube and thus simultaneously tested. By varying the internal and external shapes and dimensions of the cooler, a set of crystallization tubes can be modeled for tests in a wider range of crystallization parameters and substances. The shapes and dimensions of crystallization front in crucibles can be regulated by the plug fronts, i.e. plug heads (Fig. 1).

CONCLUSIONS
The improved cooler ("crystallization support tube") is simple to build and handle, and enable mounting different number of crucibles and Tamman test tubes. This enables easy regulation and simultaneous crystallization tests of different number of crystallization parameters, with the purpose of obtaining single crystals from a family of newly synthesized compounds with a layered crystal structure in a laboratory tube furnace.
The cooler can be modified and installed into a crucible furnace. Also, the cooler can be applied in a chamber furnace.