Simultaneous Crystallization Testing in a Laboratory Furnace

A previous paper1 described a model of an air-cooled test tube with a series of sockets and plugs (crystallization socket-outlet adaptor) installed in a laboratory chamber furnace, the goal of which was to regulate the crystallization fronts and rates in columns of crucibles. The current paper discusses the improvement to the interior of the cooler, an air-cooled toothed tube (crystallization shelf) (see Figure 1). The improved cooler is simple to build and handle, is able to be lengthened and curved into different shapes, and can be used in crucible or tube furnaces. The cooler allows easy regulation of simultaneous crystallization tests of different crystallization parameters and substances, with the purpose of obtaining crystals from a family of newly synthesized compounds with a layered crystal structure (see Cabric in Tables 3.1-5 and 3.1-8 in Ref. 2) in a laboratory furnace.

Figure 1 - Crystallization cooler in a chamber furnace (crystallization shelf): 1) laboratory chamber furnace, 2) continuously changeable transformer, 3) air-cooled toothed tube (crystallization shelf), 4) mounting holes, 5) movable plugs, 6) columns of crucibles, 7) air-cooled toothed tube (crystallization finger), 8) movable mounting rings, and 9) Tamman test tubes.2,3

The procedure involves first increasing the voltage until the substances are completely melted. Then, while a constant furnace voltage is maintained, a small amount of airflow is introduced into the cooler. As a result, crystallization starts on the surface of the melts for the lower row and at the bottom of the melts for the upper row. With the increase in airflow, the crystallization front reaches the bottom and surface of the melt.2,3

The crystallization rate interval in each Tamman test tube is regulated by the cross-section of the airflow, a, i.e., the position on the cooler (see Eq. [2] in Ref. 4). The shapes of the crystallization fronts in the crucible columns are regulated by the plug fronts, i.e., the plug head (crystallization seals). The crystallization rate interval in each crucible can be regulated by the plug height, δp, and the distance of the plug head from the surface of the melt, δa. The temperature gradient is regulated by the distance, h.

Using the assumption that the liberated latent heat of solidification is equal to the heat removed by the airstream through the cooler, the following expression for the crystallization rate, R, is derived4:

where ΔT denotes the difference between the temperature of the melt and that of the airstream; λ is the latent heat of solidification; ρ represents the crystal density; α is the coefficient of heat transfer from the cooler wall to the airstream; and kp, ka, and kc are the heat conductivity of the plug, air, and crystal, respectively (Figure 1). The coefficient of heat transfer from the cooler wall to the airstream can be calculated using the following expression5:

where t is the temperature of the airstream in °C, w0 = (273/273 + t), w is the velocity of the airstream, and d is the diameter of the tube.

Figure 2 - Crystallization rate, R, as a function of the difference between the temperature of the melt and that of the airstream, ΔT, when α = 20 W/m2K, δc = 1 cm, –♦– δp = 0.5 cm, –■– δp = 1 cm, and –▲– δp = 1.5 cm.

Figure 3 - Crystallization rate, R, as a function of the height of the plug, δp, when δ = 1 cm, α = 20 W/m2K, –♦– ΔT = 100 K, –■– ΔT = 150 K, and –▲– ΔT = 200 K.

Figure 4 - Crystallization rate, R, as a function of the velocity of the airstream, w, when δc = 2 cm, δp = 2 cm, d = 2 cm, –♦– ΔT = 100 K, –■– ΔT = 150 K, and –▲– ΔT = 200 K.

In accordance with Eqs. (1) and (2), the authors obtained the numerical values of crystallization rate, R, as a function of the ΔT (Figure 2); δp (Figure 3); and w (Figure 4). In the case of bismuth: λ = 52,300 J/kg, ρ = 9800 kg/m3, and kc = 7.2 W/mK, when δa = 0 and kp = 0.756 W/mK (borosilicate glass).

Different temperature gradients in the crucibles can be tested simultaneously using an inclined cooler. Tamman test tubes and plugs of various shapes and dimensions can be mounted and thus tested at the same time. By varying the internal and external shapes and the dimension of the cooler, a set of crystallization shelves can be modeled for tests over a wider range of crystallization parameters and substances. The cooler can be installed in a crucible furnace in the horizontal position (crystallization key) or modified into a rectilinear shape and installed in a tube furnace (crystallization test bench). Several coolers (cold fingers) or a planar air cooler (cold board) with several columns of plugs can be installed in a chamber furnace (crystallization board). This increases the number of simultaneous tests, using a device that is economical, easy to build and handle, modular, and portable for rapidly obtaining crystals from substances with unknown crystallization parameters.

References

  1. Cabric, B.; Danilovic, N. J. Appl. Cryst. 2009, 42, 1205.
  2. Wilke, K.-Th.; Bohm, J. Growing Crystals; Verlag Harri Deutsch: Thun, Frankfurt/Main, 1988.
  3. Vilke, K.-T. Virashchivanie Kristallov; «Nedra». Leningradskoe odelenie: Leningrad, 1977 (in Russian).
  4. Cabric, B.; Zizic, B. et al. Lj. Eur. J. Phys. 1990, 11, 233–5.
  5. Schramek, E.-R. Handbook for Heating and Air Conditioning; Oldenbourg Industrieverlag GmbH: München, 2007; p 152.

Dr. Cabric and Mr. Danilovic are with the Faculty of Natural Sciences and Mathematics, University of Kragujevac, P.O. Box 60, 34000 Kragujevac, Serbia; tel.: +381 34 300 267; fax: +381 34 335 040; e-mail: bcabric@kg.ac.rs. Dr. Janicijevic is with the Faculty of Technology and Metallurgy, University of Belgrade, Belgrade, Serbia.

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