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.  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,
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.
Cabric, B.; Danilovic, N. J. Appl. Cryst. 2009, 42, 1205.
- Wilke, K.-Th.; Bohm, J. Growing Crystals; Verlag Harri Deutsch:
Thun, Frankfurt/Main, 1988.
- Vilke, K.-T. Virashchivanie Kristallov; «Nedra». Leningradskoe odelenie:
Leningrad, 1977 (in Russian).
- Cabric, B.; Zizic, B. et al. Lj. Eur. J. Phys. 1990, 11, 233–5.
- 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: firstname.lastname@example.org. Dr. Janicijevic is with the Faculty of Technology and Metallurgy, University
of Belgrade, Belgrade, Serbia.