Design and Calculation for Test Tube with the Aim of Regulation Simultaneous Crystallization Tests

doi:10.4236/jcpt.2012.23016

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Journal of Crystallization Process and Technology, 2012, 2, 121-123

http://dx.doi.org/10.4236/jcpt.2012.23016 Published Online July 2012 (http://www.SciRP.org/journal/jcpt)

121

Design and Calculation for Test Tube with the Aim of

Regulation Simultaneous Crystallization Tests

Aco Janicijevic1, Nebojsa Danilovic2, Branislav Cabric2*

1Faculty of Technology and Metallurgy, University of Belgrade, Belgrade, Serbia; 2Faculty of Sciences, University of Kragujevac,

Kragujevac, Serbia.

Email: *[email protected]

Received May 7th, 2012; revised June 11th, 2012; accepted June 19th, 2012

ABSTRACT

A design for an air-cooled test tube, with a series of modular and movable rings (cylindrical “crystallization comb”),

installed in a laboratory crucible furnace is presented. The setup allows easy regulation simultaneous crystallization

tests of a series of different crystallization rates in several columns (matrix) of test tubes, enabling fast studies of ob-

taining crystals. This low-budget, portable device (i.e. adjustable airstream with more simple control options), can also

be applied in tube and chamber furnaces. The relations between the crystallization rate and parameters of air-cooled test

tube are given and numerically analyzed.

Keywords: Technique for Crystal Growth; Design and Calculation; Test Tube—Cylindrical Crystallization Combs;

Crystallization Clusters—Obtaining Crystals from Melt

In a previous paper [1] we have described a design for

air-cooled test tube (bilateral “crystallization comb”),

installed in a laboratory chamber furnace with the aim of

regulating the crystallization fronts and rates in a two

columns of crucibles. In this paper, we describe the de-

velopment and improvement of the exterior of the cooler,

i.e. modular air-cooled test tube (cylindrical “crystalliza-

tion comb”) with several columns of test tubes (“crystal-

lization cluster”) (Figure 1), and a numerical study of

control options of matrix of new crystallization parame-

ters (Figures 2 and 3). The improved cooler is simpler to

build and handle, features regulation of different crystal-

lization fronts and rates in several columns of test tubes

[with the help of telescopic movable tube/sieve—see (5)

in Figure 1(a)] or rings—see (9) in Figure 1(b)]. This

stationary and adaptive device, with operating body air

(gas), allows easy regulation simultaneous crystallization

tests of different crystallization parameters and sub-

stances, enabling fast studies of obtaining single crystals

from substances with unknown crystallization parameters,

using a laboratory furnaces.

By the assumption that the liberated latent heat of so-

lidification is equal to the heat removed by the air stream

through the cooler, the following expression for the ma-

trix of crystallization rates Rij in the test tubes (see Fig-

ure 1(b)) is derived [4]:



ccijjc c

Rkk

 



 (1)

where i and j denote the indices of internal rings and ex-

ternal rings/plugs, c is the crystallization substance index,

ΔT denotes the difference between the temperature of the

melt and that of the air stream, λ is the latent heat of so-

lidification, ρ designates the crystal density, α is the co-

efficient of heat transfer from the cooler wall to the air

stream, k designates the heat conductivity.

Figure 1. Air-cooled test tube (cylindrical “crystallization

comb”) in a crucible furnace: (1) laboratory crucible fur-

nace, (2) air-cooled test tube (cylindrical “crystallization

comb”), (3) pipe (“draining shuttle”), (4) modular and

movable rings, (5) telescopic movable tube with mounting

holes (crystallization test sieve), (6) curved Tamman test

tubes [2,3] (“crystallization tests comb”), (7) mounting

plugs, (8) test tubes (“crystallization cluster”), (9) rings with

radial mounting holes (“junction rings”), and (10) cross

section of the air-cooled test tube.

*Corresponding author.

Design and Calculation for Test Tube with the Aim of Regulation Simultaneous Crystallization Tests

122

The coefficient of heat transfer from the test tube wall

to the air stream can be calculated using the following

expression (p. 152 of [5]):

0.75

0.25

4.130.23 100























(2)

where θ is average temperature of the airstream in ˚C (up

to 1000˚C), and

273





where wi is average velocity of the airstream next to the

ring i (0˚C, 1.013 bar) in m/s.

On the basis of the continuity and the cross section of

the airstream, the following expression for the velocity of

the airstream next to the ring i, wi, we obtain:















(3)

where wt denotes an average velocity of the airstream in

the test tube without ring, dt and dp is the diameter of the

test tube and the pipe respectively, di is diameter of the

ring—see (10) in Figure 1(b).

(a)

(b)

Figure 2. Crystallization rate Rij as a function of the posi-

tion of the ring along the test tube, lj, and the diameter of

the ring, di, when ΔT0 = 150˚C: –♦– wt = 0.6 m/s; –■– wt = 1.2

m/s, –▲– wt = 2 m/s. (a) di = 2 cm; (b) lj = 10 cm.

Based on the fact that the heat removed from the test

tube wall is equal to the heat accepted by the air stream,

we have derived the following expression (integral equa-

tion) for the difference between the temperature of the

melt and that of the air stream ΔTj at the point lj:

tt aa

TT Td

wd c





 

l

l (4)

where ΔT0 denotes the difference between the tempera-

ture of the melt and that of the air stream at the point lj =

0, (Figure 1(b)), αt is the coefficient of heat transfer from

the test tube without ring to the air stream [Equations (2)

and (3) when di = dp], ΔTl denotes the difference between

the temperature of the melt and that of the air stream at

the point l, ρa and ca designates density and heat capacity

of the air stream, respectively.

In accordance with Equations (1)-(4), the authors ob-

tained the numerical values of crystallization rate, Rij, as

function of lj and di (Figure 2), and wt and ΔT0 (Figure 3),

(a)

(b)

Figure 3. Crystallization rate Rij as a function of the velocity

of the airstream in the test tube, wt, and difference between

the temperature of the melt and that of the air stream at the

point l = 0 – ΔT0, when lj = 10 cm: –♦– di = 1 cm, –■– di = 2

cm, –▲– di = 2.4 cm. (a) T0 = 150˚C; (b) wt = 1 m/s.

Design and Calculation for Test Tube with the Aim of Regulation Simultaneous Crystallization Tests

123

in the case of bismuth: Tmelt = 271˚C, λc = 52300 J/kg, ρc

= 9800 kg/m3 and kc = 7.2 W/mK. In all numerical cal-

culation is taken that: dt = 3 cm, dp = 1 cm, δj = 0.5 cm, kj

= 0.756 W/mK (pyrex i.e. borosilicate glass, softening

point ≈ 600˚C), δc = 0 cm (Figure 1(b)), ρa = 0.682

kg/m3 and ca = 1.035 kJ/kgK.

The shape of crystallization front in each test tube can

be regulated by the plug or ring front (Figure 1). The

crystallization rate in each test tube can be regulated by

the position of the ring along the test tube (Figure 2(a))

and by the diameter of the ring (Figure 2(b)); and/or by

the velocity of the air stream and the difference between

the temperature of the melt and that of the air stream at

the point lj = 0—Figures 3(a) and (b), respectively. The

crystallization rate in tests tubes can also be regulated by

the thickness of the ring δj (Equation (1)). Different

crystallization rates in the test tubes in one ring (“wreath”)

can be simultaneous tested using asymmetric ring. The

temperature gradient is regulated by the distance air-

cooled test tube from the furnace wall δt. Different tem-

perature gradients in the test tubes in one ring can be

simultaneous tested using air-cooled test tube dislocation

to the axis of the furnace, i.e. asymmetric position of the

key.

Tamman test tubes (Figure 3.1.-8 of [2]; Figure 3.1-2.

of [3]), plugs and rings of various numbers, shapes and

dimensions can be mounted and thus simultaneously

tested (fineness of the comb). By varying the internal and

external shapes and dimensions of the cooler, a set of

“crystallization combs/keys” can be modeled for tests

over a different range of crystallization fronts and rate

intervals. The air cooled test tube can be installed into a

tube furnace in a horizontal position (“crystallization

shelf”—Figures 16 and 17 in [6]) or vertical position

(“crystallization corncob”—Figure 13 in [6]). Several

different air-cooled test tubes (a family group of “crystal-

lization keys/combs”) can be installed in the chamber

furnace (Figure 11 in [6]. This increases the number of

simultaneous crystallization tests (comb) of different

crystallization parameters, using a low-budget, modular,

easy to install and remove, portable (“pocket”) device, i.e.

airstream with more simple control options. This pro-

vides a way (“crystallization cluster”) for fast studies of

obtaining crystals from substances with unknown crys-

tallization parameters, and the economic expansion ap-

plication of laboratory furnaces.

REFERENCES

[1] B. Cabric and N. Danilovic, “Test Tube for Obtaining

Crystals,” Journal of Applied Crystallography, Vol. 42,

2009, p. 1205. doi:10.1107/S0021889809036188

[2] K.-Th. Wilke and J. Bohm, “Kristallzüchtung,” Verlag

Harri Deutsch, Frankfurt, 1988.

[3] K.-T. Vilke, “Virashchivanie Kristallov,” Nedra Lenin-

gradskoe odelenie, Leningrad, 1977.

[4] B. Cabric, N. Danilovic and A. Janicijevic, “Tube for

Obtaining Crystals in a Laboratory Furnaces,” Instru-

ments and Experimental Techniques, Vol. 54, No. 2, 2011,

pp. 282-283.

[5] E.-R. Schramek, “Taschenbuch für Heizung + Klimatech-

nik,” Oldenbourg Industrieverlag GmbH, München, 2007.

[6] A. Janćijević and B. Čabrić, “New Class of Apparatus for

Crystal Growth from Melt,” In: N. Kolesnikov and E.

Borisenko, Eds., Modern Aspects of Bulk Crystal and

Thin Film Preparation, InTech—Open Access Publisher,

Rijeka, 2012, pp. 3-24.