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The application of the Plackett-Burman method for investigating SbSI vapour growth conditions
Materials Science and Engineering, 52 ( 1 9 8 2 ) 267 - 2 6 9
267
The Application of the Plackett-Burman Method for Investigating SbSI Vapour Growth Conditions ANDRZEJ
KIDAWA
Institute o f Physics, Silesian Technical University, ul. Krzywoustego 2, 44-100 Gliwice (Poland)
(Received M a r c h
30, 1 9 8 1 ; i n r e v i s e d f o r m J u l y 29, 1 9 8 1 )
SUMMARY
TABLE 1 Schematic representation of the
In this paper we describe the dependence o f crystal size on the following growth parameters: the temperature gradient; the gas in the ampoules, the pressure o f the gas, the time o f the crystal growth process; the heating power; the shape o f the ampoule in the crystallization zone; the composition o f the ingredients. To examine the influence o f the growth variables on crystal size, the Plackett-Burman method was used. The parameters which affect the crystal size most are the temperature gradient and the time o f the crystal growth process. 1. I N T R O D U C T I O N
SbSI grows mainly as needle crystals [1, 2]. In this paper we report an investigation on the way in which the growth conditions influence the needle morphology. The preparation of single crystals still remains mainly an art and is based essentially on empiricism. The development and refinement of the crystal growth process to achieve useful products have relied heavily on trial-and-error methods. The Plackett-Burman technique [3] seems to be useful for screening the large numbers of variables in a process such as crystal growth from the vapour phase, and thus it assures better control of crystallization.
2. E X P E R I M E N T A L
Experiment
3
4
0025-5416/82/0000-0000/$02.75
B
C
D
E
-+
+
+
+
+
+ +
+
--
--
+
--
+
5 6
+
7 8
--
+
F
G
Result R I 2
+
+ +
+
+
+
0
I
+
+ +
+ +
+ --
-+
3 0.5
+
+
--
+
--
0
0
each variable can have one of two states (high (+) or low (--)). The choice of variables, which were a result of the technical possibilities and limitations, and the experimental results are presented in Table 2. Eight Termisil ampoules were used to grow crystals. The ampoule dimensions were as follows: length, 17 cm; diameter, 3 cm. A schematic representation of the crystal growth equipment is shown in Fig. 1. The temperature T3 was stabilized at 360 + 5 °C. The temperature gradient inside the furnace was established using a metallic or a ceramic tube. The thermocouples T1 and T2 (3 cm apart) enabled us to control the temperature gradient in the growth zone. Using a metallic tube the temperature gradient was about 50 °C and using a ceramic tube about
DETAILS
The starting materials that we used were Sb2S3 and SbI3. The order in which the experiments were carried out is shown schematically in Table 1. To examine the effect of seven variables (A - G) on the crystal size using the Plackett-Burman m e t h o d , only eight experiments are necessary. In every experiment,
Variable A
1 2
experiments
? I: ii
" "::" " : " " "
" : l
Fig. 1. A s c h e m a t i c r e p r e s e n t a t i o n o f t h e f u r n a c e . © E l s e v i e r S e q u o i a / P r i n t e d in T h e N e t h e r l a n d s
268 TABLE 2 Results
Variable
Effect Ei
Levels
Relative significance t test
Code
Parameter
High (+)
Low (--)
A
Temperature gradient
B
Pressure of the gas in the ampoule Gas in the ampoule Time of the crystal growth process Composition of ingredients Heating power
Formed by placing a metallic tube inside the furnace --170 Tort
Formed by placing a ceramic tube inside the furnace --740 Tort
--0.375
0.45 (<40%)
Ar
N2
--0.625
1.24 (<80%)
13 - 14 days
5 - 6 days
0.875
2.45 (95%)
3 tool.% Sb2S 3 : 2 tool.% SbI 3 Heating current, llA With pipe in the growth zone
1 mol.% Sb2S 3 : 1 mol.% SbI 3 Heating current, 6A Without pipe in the growth zone
0.375
0.45 (<40%)
0.125
0.06 (<20%)
--0.125
0.06 (<20%)
C D
E F G
Ampoule placed inside the furnace
60 °C. When a " h i g h " heating power was used, the temperature T1 changed from about 410 to 350 °C. A " l o w " heating power changed the temperature T1 from 430 to 320 °C. To estimate the result o f each experiment a relative scale was introduced: 0, no crystals; 1, needle crystals; 3, bulk crystals (Fig. 2). The number defining the result was selected so as to arrange the crystals according to their sizes perpendicular to their c axis. Using this relative scale the influence of each variable on crystal size was estimated. The effect of a variable on the result is the difference between
Fig. 2. Single crystals of SbSI from experiment 5.
1.625
8.40 (99%)
the average value o f the result for the four runs at the high (+) level and the average value of the result for the four runs at the low (--) level, e.g.
R(+) EA
-
-
R(--)
-
4
4
(1)
Table 2 shows the effects for each of the variables. The significance of each effect was determined using a t test, in which all variables were treated as d u m m y variables which do not influence the result. The effect of a d u m m y variable is zero. The fact t h a t the
269
effect is n o t equal to zero is assumed to be a measure of the error. To evaluate the variance S of the error, we used the well-known formula G
2. /
$2 = Z E~ 'In i=A
(2)
/
The t parameter for an effect E i (i = A - G) was calculated from
A>
E i(n -- 1)1/2 ti -
S
variable of all. The next most important variable is t h a t there should be a long time for the growth process. On the assumption that the confidence levels are 80%, it is shown that the remaining variables have an insignificant effect on crystal size. The results in Table 2 show that the parameters have a decreasing effect in the following order:
(3)
where the number n of d u m m y variables (which is equal to the n u m b e r of degrees of freedom) is 7.
D>
C> B=E>
F =G
(4)
To grow single bulk crystals of SbSI the most important factor is that a small temperature gradient should be established in the crystal growth zone.
REFERENCES
3. SUMMARIZINGREMARKS Single bulk crystals of SbSI can be grown using a vapour growth technique. The small temperature gradient, which limits the nucleation rate, seems to be the most important
1 K. Nassau, J. W. Shiever and M. Kowalchik, J. Cryst. Growth, 7 (1970) 237. 2 A. S. Bhalla, K. E. Spear and L. E. Cross, Mater. Res. Bull., 14 (1979) 423. 3 R. A. Stowe and R. P. Mayer, Ind. Eng. Chem., 58 (2) (1966) 36.
267
The Application of the Plackett-Burman Method for Investigating SbSI Vapour Growth Conditions ANDRZEJ
KIDAWA
Institute o f Physics, Silesian Technical University, ul. Krzywoustego 2, 44-100 Gliwice (Poland)
(Received M a r c h
30, 1 9 8 1 ; i n r e v i s e d f o r m J u l y 29, 1 9 8 1 )
SUMMARY
TABLE 1 Schematic representation of the
In this paper we describe the dependence o f crystal size on the following growth parameters: the temperature gradient; the gas in the ampoules, the pressure o f the gas, the time o f the crystal growth process; the heating power; the shape o f the ampoule in the crystallization zone; the composition o f the ingredients. To examine the influence o f the growth variables on crystal size, the Plackett-Burman method was used. The parameters which affect the crystal size most are the temperature gradient and the time o f the crystal growth process. 1. I N T R O D U C T I O N
SbSI grows mainly as needle crystals [1, 2]. In this paper we report an investigation on the way in which the growth conditions influence the needle morphology. The preparation of single crystals still remains mainly an art and is based essentially on empiricism. The development and refinement of the crystal growth process to achieve useful products have relied heavily on trial-and-error methods. The Plackett-Burman technique [3] seems to be useful for screening the large numbers of variables in a process such as crystal growth from the vapour phase, and thus it assures better control of crystallization.
2. E X P E R I M E N T A L
Experiment
3
4
0025-5416/82/0000-0000/$02.75
B
C
D
E
-+
+
+
+
+
+ +
+
--
--
+
--
+
5 6
+
7 8
--
+
F
G
Result R I 2
+
+ +
+
+
+
0
I
+
+ +
+ +
+ --
-+
3 0.5
+
+
--
+
--
0
0
each variable can have one of two states (high (+) or low (--)). The choice of variables, which were a result of the technical possibilities and limitations, and the experimental results are presented in Table 2. Eight Termisil ampoules were used to grow crystals. The ampoule dimensions were as follows: length, 17 cm; diameter, 3 cm. A schematic representation of the crystal growth equipment is shown in Fig. 1. The temperature T3 was stabilized at 360 + 5 °C. The temperature gradient inside the furnace was established using a metallic or a ceramic tube. The thermocouples T1 and T2 (3 cm apart) enabled us to control the temperature gradient in the growth zone. Using a metallic tube the temperature gradient was about 50 °C and using a ceramic tube about
DETAILS
The starting materials that we used were Sb2S3 and SbI3. The order in which the experiments were carried out is shown schematically in Table 1. To examine the effect of seven variables (A - G) on the crystal size using the Plackett-Burman m e t h o d , only eight experiments are necessary. In every experiment,
Variable A
1 2
experiments
? I: ii
" "::" " : " " "
" : l
Fig. 1. A s c h e m a t i c r e p r e s e n t a t i o n o f t h e f u r n a c e . © E l s e v i e r S e q u o i a / P r i n t e d in T h e N e t h e r l a n d s
268 TABLE 2 Results
Variable
Effect Ei
Levels
Relative significance t test
Code
Parameter
High (+)
Low (--)
A
Temperature gradient
B
Pressure of the gas in the ampoule Gas in the ampoule Time of the crystal growth process Composition of ingredients Heating power
Formed by placing a metallic tube inside the furnace --170 Tort
Formed by placing a ceramic tube inside the furnace --740 Tort
--0.375
0.45 (<40%)
Ar
N2
--0.625
1.24 (<80%)
13 - 14 days
5 - 6 days
0.875
2.45 (95%)
3 tool.% Sb2S 3 : 2 tool.% SbI 3 Heating current, llA With pipe in the growth zone
1 mol.% Sb2S 3 : 1 mol.% SbI 3 Heating current, 6A Without pipe in the growth zone
0.375
0.45 (<40%)
0.125
0.06 (<20%)
--0.125
0.06 (<20%)
C D
E F G
Ampoule placed inside the furnace
60 °C. When a " h i g h " heating power was used, the temperature T1 changed from about 410 to 350 °C. A " l o w " heating power changed the temperature T1 from 430 to 320 °C. To estimate the result o f each experiment a relative scale was introduced: 0, no crystals; 1, needle crystals; 3, bulk crystals (Fig. 2). The number defining the result was selected so as to arrange the crystals according to their sizes perpendicular to their c axis. Using this relative scale the influence of each variable on crystal size was estimated. The effect of a variable on the result is the difference between
Fig. 2. Single crystals of SbSI from experiment 5.
1.625
8.40 (99%)
the average value o f the result for the four runs at the high (+) level and the average value of the result for the four runs at the low (--) level, e.g.
R(+) EA
-
-
R(--)
-
4
4
(1)
Table 2 shows the effects for each of the variables. The significance of each effect was determined using a t test, in which all variables were treated as d u m m y variables which do not influence the result. The effect of a d u m m y variable is zero. The fact t h a t the
269
effect is n o t equal to zero is assumed to be a measure of the error. To evaluate the variance S of the error, we used the well-known formula G
2. /
$2 = Z E~ 'In i=A
(2)
/
The t parameter for an effect E i (i = A - G) was calculated from
A>
E i(n -- 1)1/2 ti -
S
variable of all. The next most important variable is t h a t there should be a long time for the growth process. On the assumption that the confidence levels are 80%, it is shown that the remaining variables have an insignificant effect on crystal size. The results in Table 2 show that the parameters have a decreasing effect in the following order:
(3)
where the number n of d u m m y variables (which is equal to the n u m b e r of degrees of freedom) is 7.
D>
C> B=E>
F =G
(4)
To grow single bulk crystals of SbSI the most important factor is that a small temperature gradient should be established in the crystal growth zone.
REFERENCES
3. SUMMARIZINGREMARKS Single bulk crystals of SbSI can be grown using a vapour growth technique. The small temperature gradient, which limits the nucleation rate, seems to be the most important
1 K. Nassau, J. W. Shiever and M. Kowalchik, J. Cryst. Growth, 7 (1970) 237. 2 A. S. Bhalla, K. E. Spear and L. E. Cross, Mater. Res. Bull., 14 (1979) 423. 3 R. A. Stowe and R. P. Mayer, Ind. Eng. Chem., 58 (2) (1966) 36.