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A programmable temperature controller for crystal growth experiments

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1977 J. Phys. E: Sci. Instrum. 10 142

(http://iopscience.iop.org/0022-3735/10/2/009)

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A programmable temperature controller for crystal growth experiments

M GrubiC. and R Strey Max-Planck-Institut fur Biophysikalische Chemie (Karl-Friedrich-Bonhoeffer-Institut), D-3400 Gottingen- Nikolausberg, Germany

Received 5 July 1976, in final form 1 September 1976

Abstract A thermostat has been developed for the study of the behaviour of crystals in aqueous solutions under the influence of periodic and non-periodic temperature programs. A temperature stability of If: 2 x 10-3 "C is obtained over the range 5-5OT for several weeks. The temperature programs around the set point with a maximal nonlinearity of 1 % for I 2 " C variations in the range 20-30°C are controlled by an electronic program unit. As an application, the growth and dissolution rates of a KAI(S04)2 single crystal are measured.

1 Introduction A strong dependence of aging (Ostwald ripening) of disper- sions of crystals upon temperature variations has been found (Hohmann and Kahlweit 1972). In order to improve the experimental conditions, a thermostat has been developed which is capable of (i) keeping the temperature constant to within millidegrees Kelvin for weeks and hence permitting investigations of isothermal processes, and (ii) changing the temperature according to a given program with temperature change rates of up to 2°C min-1. In addition, the growth and dissolution rates of a single crystal have been measured.

2 The apparatus 2.1 The cell The cell (figure 1) comprises two cylindrical vessels, the inner one being the growth vessel (450 ml). A coolant liquid thermo- stated to within 0.1 "C by a constant-temperature thermostat (Lauda Thermostat, West Germany) is circulated through the space between the vessels. The inner glass wall thickness is approximately 1 mm and the outer wall (separating the cell from the environment) approximately 2 mm. The top plate of the cell is made of PVC (15 mm in thickness) and supports the conductivity cell, glass stirrer, thermistor temperature sensor, crystal holder and heater. The stirrer A (two-bladed glass paddle) is driven by an induction motor of adjustable speed in the range 100-1500 rev min-I.

The temperature of the solution is sensed by means of a glass-encapsulated thermistor B (2322 6271, Valvo) and regulated by a heater E. The heater wires are mounted into the glass tube (wall thickness 0.5 mm) in close contact with the

Figure 1 Diagram of the glass cell. A, stirrer; B, thermistor; C, conductivity cell; D, crystal holder; E, heater

wall. The tube is filled with silicone oil in order to improve the thermal conductivity between the heater wires and stirred solution. To avoid evaporation, the connections through the top plate are sealed by silicone rubber and the connection between the top plate and vessels by a rubber ring.

2.2 Electronics The principle of operation of the temperature controller can be seen from figure 2. The temperature sensor is a thermistor of relatively small B25 constant (B25=2360 K, R25= 1270 n) placed in one arm of a conventional DC Wheatstone bridge. Due to the small B25 constant, the slope of the resistance- temperature curve is rather low. The variable arm of the bridge is composed of an adjustable resistor (R42) and a constant resistor Rql that determines the upper temperature limit of the device. Two equal resistors, RI and Rz, constitute the ratio arms of the bridge. The bridge error signal amplified by a stable instrumentation amplifier is fed to a summing amplifier. The summing amplifier output signal, which is equal to the difference between the amplified bridge unbalance signal U B and program voltage U P is conditioned by a PID regulator. A burst control circuit (integral half-cycle) provides additional signal amplification and zero-crossing synchronized triggering of a triac.

The Wheatstone bridge is linearized on balance at the temperature TI (Bowman 1970) for values of

where R T ~ is the thermistor resistance at T I , Using expressions obtained by Bowman, it can be shown that the position of the inflection point in the plot of bridge output voltage against temperature, for balance temperature TZ different from TI and bridge linearized on balance at TI, remains at the temperature TI. This results in an almost symmetrical decay of the bridge sensitivity and symmetrical increase of the nonlinearity of the bridge around TI. The bridge of the controller was linearized at 2 5 T . The calculated and measured nonlinearity, defined as the deviation from the linear temperature change determined by the ratio of bridge unbalance voltage to bridge sensitivity, showed good agreement and did not exceed 1 % for ? 2°C bridge temperature deviations from the balance temperature in the region of 20-30°C.

In linear steady state operation, due to the high gain of the PID regulator and burst control circuit, the controller keeps the difference in the UB and U P voltages practically equal to zero. Since

U g = A i S ( T )AT= UP (2) where Ai is the instrumentation amplifier gain, S( T ) the bridge sensitivity and AT the temperature deviation from the

142

Temperature controller for crystal growth experiments

Instrumen- 2 ' tation amplifier amplifier -

jz----l regulator

U

1 voltage generator

.L

balance temperature, the controlled temperature is adjusted around the balance temperature T by applying the appropriate voltage U P . The dynamic linear response of the temperature deviation to the changes of U P is adjusted by the gain and time constants of the PID regulator.

The duty cycle adjustment is performed by adjustment of the heater voltage (TR1). By providing an internal time base of the burst control circuit of approximately 400 ms, a compromise between the time constant of the controlled cell and power resolution is made. Radio frequency interference is eliminated by the zero-voltage firing of the triac.

The controller errors (drift, noise), cell ambient temperature variations and heater power supply voltage variation cause the instabilities of the cell temperature. Due to the large time constant of the controlled cell and high gain of the feedback loop, an investigation of the controller errors is practically reduced to that of the static errors of the controller input circuits (Forgan 1974).

The worst case of drift of the cell temperature is given by

The first term describes the drift of the balance temperature setting of the Wheatstone bridge, the second term de- scribes the drift due to the instrumentation amplifier offset voltage and bias currents drift, the third the net influence of the induced thermovoltages and the fourth the influence of the cell ambient temperature variations and power supply instabilities reduced by the controller; ~ T B A is the bridge ambient tem- perature variation, 0141, 0142 and ~ N T C are the temperature coefficients of the corresponding resistors, ROB the bridge output resistance, eos and id the input offset voltage and difference current change, Zb the input bias current change, and CMR the common mode rejection. A contribution of the long- term instability of the input parameters is negligible in com- parison to their temperature drifts. The calculated drift, due to the f i s t and second terms at the controlled temperature of 2 5 T , for the bridge thermostated to i 0.1 "C, AD610 amplifier (Analog Devices) thermostated to k 0*5"C, and element values given by figure 4, is 0.5 x "C. The third term is reduced to the same order of magnitude by using the copper leads, solder of low thermal EMF, and good thermal contact between oppos- ing soldering points, while the gain of the feedback loop and its frequency characteristics decide A TCA.

The program voltage generator (figure 3) incorporates an oscillator of adjustable frequency, reversible (up and down) counter, 10-bit bipolar DAC, and function module producing sinusoidal output (5010, Optical Electronics Inc.).

The detailed circuit diagram of the controller is given in

Figure 2 Schematic diagram of the controller. R42 set temperature; Rw, heater; TR1, duty cycle adjustment

figure 4. The bridge resistors, bridge power supply circuit (AD580, Analog Devices) and instrumentation amplifier are thermostated at 40°C by two simple on-off controllers. The input of the burst control circuit L121B (SGS-ATES) is

dKb Periodic enerator z:F

Periodic 3 triangular

out Oscillator

Periodic erectangular out

Decoder

-10 v--l +,o v r M a n u a 1

Figure 3 Schematic diagram of the program voltage generator

protected from overvoltage. Its internal ramp width of 400 ms is determined by values of R5 = 100 ki2 and C5 = 4.7 pF. Since the program generator output voltages are of the constant amplitude k 10 V, the range of the temperature amplitude (f 5"C, k 0 . 5 T and rt: 0.05T) is adjusted by the gain of the instrumentation amplifier (see equation (2)). The feedback loop gain is kept constant by simultaneous change of the OA1 amplifier gain. The fine regulation of the amplitude and correc- tion for S(T) changes are performed by attenuation of the program voltage.

3 System performance The first step in evaluating the performance of the controller was to measure its static errors. To separate the temperature variations caused by these errors from the temperature insta- bilities caused by the ambient temperature and heater power supply variations, a brass block of great thermal capacity was thermostated by the controller at 45°C. Its temperature was measured by a precision platinum thermometer (Leeds and Northrup 81 63QC) and Leeds and Northrup ER thermometer bridge. The room temperature variations were below k 5°C. The readings, as measured at the output of the instrumentation amplifier, gave a maximum value of the temperature variation of k 2 x 10-4 "C/week. Since the independent measurement by the bridge showed variations of rt K/week, this value is attributed to the drift of the input circuits.

A typical linear dynamic response of the cell temperature to the periodic rectangular input program, as measured at the output of the instrumentation amplifier, is shown in figure 5.

The cooling and heating rates of the solute are, in general, functions of the mode of the controller operation (linear or

143

M GrubiC and R Strey

I 1

OC 25'0 1

t1

I I

Figure 4 Circuit diagram of the controller. Unless otherwise indicated, all resistors are 0.25 W; asterisk denotes thermostated elements; all operational amplifiers are

TP1321 (Teledyne Philbrick); TR3 1 : 1, 20 W; TR4 1 : 1 180 turns on ferrite core; bridge variable resistor, Helipot 7266 (20 ppm K-1)

nonlinear), the difference between the thermostated tempera- ture and reference coolant temperature, the stirring rate and adjusted duty cycle. For example, a settling time of 120 s within "C about 25°C due to the step change of UP was measured for 50 duty cycle at an initial temperature of 27"C, reference temperature of 21 "C, maximum stirring rate

- 100 5

Figure 5 Response of the cell temperature to a periodic rectangular program; duty cycle 507; at 25°C; reference temperature 23°C; stirring speed 1500 rev min-1; CD = 470 pF, CI = 5000 pF

144

(1500 rev min-1) and the time constants and gain of the PID

regulator adjusted to give a monotonic response. Under the same conditions, the settling time for the temperature change from 25 to 27°C was found to be 100 s. The temperature varia- tion around 25°C and 27°C steady state point, indicated at the instrumentation amplifier output, did not exceed I "C. Reducing the stirring rate to 300 rev min-l increased settling times for heating and cooling down to 160 s and 150 s respec- tively and reduced temperature stability to k 4 x

The linearity of the k 2°C off-balance temperature change was measured between 20 and 30°C by recording steady state off-balance temperatures for given program voltages and set temperature point. The measurement gave the maximum non- linearity of 1 %.

The temperature controller has been in continuous use for a year and proved to be reliable.

"C.

4 Experimental The growth and dissolution rates at 25°C of an almost perfect octahedral KAI(S04)z single crystal were measured. The crystal holder system used in the experiment was identical to the stirrer system. This construction permits the rotation of the single crystal under investigation and hence the uniform growth of the crystal faces. Solution concentration is measured

Temperature controller for crystal growth experiments

by determining its conductance. The glass conductivity cell (PW 9512/01, Philips, cell factor 1-39) showed a high stability and drifts were found to be below 0.5%,, for a day.

In the preparatory phase of the experiment, the crystal seed was glued on to the tip of the glass rod D and the crystal was allowed to grow to its final dimensions from slightly super- saturated solution. The geometric area of each (111) face was about 4 cm2, In the course of the experiment, the geometric area of the (100) and (110) faces did not exceed 5% of the total surface area. Throughout the experiment, the crystal holder and stirrer were rotated at constant speeds of 100 and 300 rev min-1 respectively. The super- and undersaturation were generated by step temperature changes from 27 and 23°C respectively, to the 25°C measuring point. Conductance is measured on a Wayne-Kerr autobalance precision bridge (B331 Mk 11) and recorded by a pen recorder after the tem- perature settling time. The growth and dissolution rates were obtained by graphical differentiation of the conductivity-time plots (figure 6).

1 1 x 10-8 1s / 112 x 1 V q

Figure 6 Growth (full curve) and dissolution (broken curve) rates of the crystal

Assuming the relation

E = k,(hc)m one finds

where b is the time derivative of the concentration (kilograms of hydrate per kilogram of solution per second) and h c is the concentration difference defined as the difference of solution concentration and saturation concentration (kilograms of hydrate per kilogram of solution). Further, the assumption that the change in concentration i is due to the growth of the (1 11) faces leads to

~1(111)=4*6 x 10-j(&)1*63(*0.03)

(where 2;<111) is the linear growth rate of the (111) face in metres per second) for a solution velocity of approximately 0.05 m s-l, which is in reasonable agreement with Mullin and Garside (1967, 1968). For the dissolution, the corresponding result is

i = - 1.2 x lo-'( 4c)l.o.

Acknowledgments The authors wish to thank Professor M Kahlweit and Dr U Wiirz for many stimulating discussions and Mr J Winkler for technical assistance.

References Bowman M J 1970 Radio Electron. Engnr 39 209-14 Forgan E M 1974 Cryogenics 14 207-14 Hohmann H H and Kahlweit M 1972 Ber. Bunsenges. Phys. Chem. 76 933-8 Mullin J W and Garside J 1967 Trans. Inst. Chem. Engrs 45

Mullin J W and Garside J 1968 Trans. Inst. Chem. Engrs 46 T285-90

T11-8

Journal of Physics E: Scientific Instruments 1977 Volume 10 Printed in Great Britain 0 1977

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