Hydrogen reduction of ammonium paratungstate into tungsten blue oxide—Part II: Experimental

Refractory Metals & Hard Materials l0 (1991) 123 131

Hydrogen Reduction of Ammonium Paratungstate Into Tungsten Blue Oxide--Part II: Experimental J. W. van Put, T. W. Zegers* & H. Liu Department of Raw Materials Technology, Delft University of Technology, PO Box 5028, 2600 GA Delft, The Netherlands (Received 20 June 1991 ; revised version received 29 July 1991 ; accepted 12 August 1991)

Abstract: To determine the feasibility of the direct processing route, the variability

of the TBO properties resulting from changes in operating parameters was studied. The operating parameters were: reduction time, reduction temperature, hydrogen gas flow rate and the amount of powder. The factors all influence the ammonia content, the oxygen index and the specific surface area of TBO. The Fisher average particle size, however, cannot be altered sufficiently by changing one of these operating parameters.

1

INTRODUCTION

2

Part I of this paper, an extensive literature survey on the hydrogen reduction of APT to TBO, showed the basis for typical TBO characteristics. These characteristics are: the ammonia content, the oxygen content, i.e. oxygen index OI, the specific surface area and the Fisher average particle size. These specifications are currently used in industrial practice to characterize TBO. One of the options considered for the use of a m m o n i u m paratungstate as a raw material for the manufacturing of lamp filament tungsten wire is the so-called direct processing route. 1 The procedure would be to buy APT with approved chemical and physical specifications and to process it to tungsten metal under standard conditions. This paper aims at identifying operating parameters for controlling TBO specifications which are currently used in industry. Whether these specifications are indeed essential to obtain tungsten wire of approved quality has, however, not been investigated.

2.1

EXPERIMENTAL

Experimental procedures

Samples of 100 g standard APT were placed in boats with a semi-circuJar cross-section to simulate the shape of the industrial containers. The samples were reduced in a horizontal tube furnace with an internal diameter of 45 mm. The powder bed height was approximately 22 mm. Two chromel/alumel thermocouples were fixed within the sample: one at 12 mm and another at 5 m m below the surface of the sample. A third chromel/alumel thermocouple was positioned in the centre of the tube measuring and thereby defining the experimental temperature. The furnace temperature was 100°C at the start of the experiment. The rate of increase of the furnace temperature during heat-up was approximately 3"7°C/rain. Preheated, technically pure hydrogen with a dew point of - 6 0 ° C was used as a reductant. After the samples had reached the desired temperature they were maintained at this level for a predetermined reduction period. After reduction the samples were cooled to room temperature in a nitrogen atmosphere.

* To whom correspondence should be addressed at: Delft University of Technology, Faculty of Mining and Petroleum Engineering, Raw Waterials Technology, Mijnbouwstraat 120, 2628 RX Delft, The Netherlands. Present address: BHP-Utah Minerals International, USA. 123

Refracto O, Meta& & Hard Mater&& 0263~4368/91 $5.00 © 1992 Elsevier Science Publishers Ltd, England. Printed in Great Britain.

124

2.2

J. W. van Put, T. W. Zegers, H. Liu

Selection of experiments by factorial design

Two series of factorially designed experiments were carried out to obtain a better insight into the effect of changes in operating parameters on TBO characteristics. Attention was focused on the following parameters or factors: reduction temperature, reduction time, hydrogen flow rate and powder bed height. In addition experiments were carried out to study the powder quality over the bed height as a function of the above-mentioned factors. Because of the limited number of variables to be investigated, a 'full factorial' number of experiments was selected, in which each variable was tested at two levels. This allows evaluation of possible interaction of variables as well as the determination of the main effects of the variables. An analysis of variance of all effects with the F-test makes it possible to assign probabilities to the significance of the observed effects. Detailed information on the statistical data treatment is presented in the appendix of this paper.

2.3

comparison between the slope of the powder temperature and the furnace temperature as a function of time shows that the reduction occurs in four steps. The first three steps are endothermic and Table 1. Test series no. 1: conditions

Factor

3

3.1

RESULTS

Unit

1 2 3 4

T, reduction temperature C, amount of powder Q, hydrogen flow rate t, reduction time

Test series no. 1

°C g 1/h min

+

480 25 50 30

540 100 200 60

Table 2. Test series no. 1 : measured responses

Experiment (no.)

NH 3 (wt %)

OI (--)

BET (m2/g)

Fisher (/am)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

0-61 0-26 0"82 0"38 0"47 0"17 0-75 0"36 0"48 0-18 0-69 0"24 0"35 0-15 0"59 0"26

2'847 2'754 2'881 2'833 2'828 2'749 2.875 2"805 2'816 2'729 2"851 2'786 2'810 2'729 2"835 2"770

2"6 9'1 4-3 8"6 3"1 6-8 6"7 6'1 2.6 7'8 4"3 5'5 1'8 5-9 3"4 3"5

20.0 17.5 17-7 16-2 20"5 19"7 16"9 16"7 20-5 18"6 17"2 19"7 20"2 21.2 18"4 19'9

5OO

Temperature (°O)

400 F u r n a o e ~ u r ~

• : =:

3OO

"--.

Laboratory tests

3.1.1

Level -

Analyses

The OI was determined using the method of Kiss and Tisza) The principle of this method is to dissolve the reduced tungsten oxide or polytungstate in a solution containing K3[Fe(CN)6 ] and KOH, followed by the permanganometric titration of the hexacyano ferrate (II) ions which are formed in the oxidation-reduction reaction. The ammonia content of solid reaction products was determined with the Kjeldahl distillation method. The specific surface was determined with an area meter. X-ray diffraction analyses were performed on a Philips diffractometer using CuK~ radiation with a Ni filter. The X-ray diffraction pattern of Rb0.~TWO3 (PDF 5-0532) was used for determination of the ATB phases.

Description

(no.)

100 ~ ~

Powder temperature

The conditions for this first series of experiments are listed in Table 1 and the measured responses are listed in Table 2. i

Measurement o f the powder temperature

The furnace and powder temperature recorded during Experiment no. 1 is presented in Fig. 1. A

0 Q

i 20

i 40

i 60

i 80

Time (rain.)

i 100

i 12Q

14Q

Fig. 1. Furnace and average bed temperature during reduction.

Hydrogen reduction of ammonium paratungstate--Part H occur around 160-180, 220-240 and 270-290°C, respectively. The last step is exothermic and occurs around 420-440°C. These observations and conclusions are in good agreement with those of Dahl, s Bartha et al., 4 French and Sale s and Kiss et al. 6 who performed differential thermal analyses on the decomposition of ATP in various atmospheres. The temperature difference between the top and bottom layer was less than 5°C during the first three stages. In the fourth stage the temperature of the top layer becomes approximately 20°C higher than the bottom layer. This indicates that the exothermic reaction starts at the top of the powder bed. The difference between the top and bottom of the TBO bed decreases towards the end of this reaction. ii

Normal probability plots

A normal probability plot for the main effects of the reduction temperature, a m o u n t of APT powder, the hydrogen flow rate and the reduction time and their interactions on the ammonia content is shown in Fig. 2. This figure shows that the most significant change in ammonia content of TBO can be realized by changing the reduction temperature; the next significant variables are reduction time followed by the a m o u n t of powder. An increase in reduction temperature or time results in a lower ammonia content. An increase in the a m o u n t of APT results in an increase in the a m o u n t of ammonia in TBO. Increasing the gas flow rate results in a lower ammonia content. The F-test showed that all main effects are significant : the probability that the effects are just caused by experimental noise is for this series of experiments less than 0.2 %. Furthermore it was found that the effect of a change in temperature is influenced by the amount of powder reduced and by the flow rate used. The effect of changes in operating conditions on the OI is shown in Fig. 3. It was again found that all main effects are significant. In addition, it was found that the effect of the temperature on the OI is influenced by the amount of powder reduced. It can be seen in Fig. 3 that the powder is further reduced when the reduction temperature and time are increased. More APT powder results in a significantly lower degree of reduction. Figure 4 shows the effect of changes in operating conditions on the specific surface of the powder. The specific surface can mainly be controlled by changing the reduction temperature. The effect of the temperature change is influenced by the amount of powder reduced. The reduction time is also significant. The hydrogen flow rate and a m o u n t of

125

99.9

i

i

95 i................i"........... i ~ 8o

:

i

-0.35

-0.25

i

T

"~

°ti

01

o

i

~ " ~ i

i

i

0.15

B25

t

-015

-0.05 Effects

0.05

Fig. 2. N o r m a l p r o b a b i l i t y p l o t o f all effects o n t h e a m m o n i a c o n t e n t . T e s t series n o . 1, a v e r a g e [NH3] = 0.42 % .

99.9

99

9s

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b so

.

20

.

.

.

.

.

.

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1

0.1 .i ......... i ......... i............

i........... i............ i..

I

-008

-0.05

0.02

001

004

0.07

Effects

F i g . 3. N o r m a l p r o b a b i l i t y p l o t o f all effects o n t h e o x y g e n i n d e x . T e s t series n o . 1 ; a v e r a g e O I = 2.806.

powder do not significantly influence the specific surface. Figure 5 shows the influence of operating conditions on the Fisher average particle size. It can be seen that this size can be influenced by changing the amount of powder reduced. The change in the Fisher average particle size is, however, relatively small: the Fisher size could be changed from 16.1 to 21.0/tm. 3.1.2

Test series no. 2

As in Test series no. 1, the experiments in Test series no. 2 were performed at 420 and 480°C. The upper and bottom layers in the powder were sampled to get an impression of the powder quality over the powder bed height. Furthermore, the experiment

126

J. W. van P u t , T. W. Zegers, H . L i u Table 4. Test series no. 2: measured responses

9g, g

95

~

5o

i

i

i

i

d.

................................................

2°

i ................... ..................... i .................... t ...................

0,1 ............................................................................................................... -1.9

-0,

0.1

1.1

2.1

.1

Effects

Fig. 4. N o r m a l probability plot of all effects on the specific surface area. Test series no. 1; average BET = 5'1 m~/g.

99,9

....................................................................................

Experiment (no.)

NH 3 (wt %)

OI (--)

BET (m2/g)

Fisher (,urn)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

0'75 0'59 0.71 0.52 0.64 0"43 0'60 0'37 0"89 0-70 0"83 0'60 0'74 0.48 0'74 0'43

2-977 2"913 2"971 2"880 2'898 2"798 2"871 2'780 2'982 2'903 2'974 2"873 2.877 2'800 2"862 2"775

3"0 1-9 2"4 1"7 2.2 1.8 1"9 1"7 5'7 3.4 5'3 3"1 3-6 3'3 3"4 3"3

18'0 18.1 17"5 18-2 18.2 18.0 18-0 17-8 17-0 17.6 16"0 18-4 17.8 17.5 17.9 17.8

i ..............................

99 ................................................................................... i............................

*~

95 i

i

80

i ......

4 ..........................

i i.... 5o

% 28

20 " i .......................... ~.......... t~-........... i .......................... i .......................... ~....

'+d ..................... t .......................... i .......................

i ...........

1 .. o,1

s i

i

.i..-

4 ........................

a. 1 ..............................:i..........Z .......................................................................

...................................................................................

I

I

-2

-1

i

0 Effects

-0.23

Fig. 5. N o r m a l probability plot of all effects on the Fisher average particle size. Test series no. 1; average Fisher size 18'8 pm.

Table 3. Test series no. 2: conditions Factor

Description

Unit

(no.) 1 2 3 4

°~

T, reduction temperature Q, hydrogen flow rate t, reduction time P, position of powder

°C 1/h min --

Level -

+

420 50 0 upper

480 200 60 bottom

was either finished directly after the sample had reached the reduction temperature or after 60 min. The conditions for this test are listed in Table 3 and the measured responses are listed in Table 4.

-0.13

-0.03 Effects

0.07

0.17

Fig. 6. N o r m a l probability plot of all effects on the ammonia content. Test series no. 2; average ammonia content 0.63 %.

The effect of changing operating conditions and position of the powder on the ammonia content is shown in Fig. 6. As in test series no. 1, all main effects are significant. For this test an interaction between reduction temperature and time was found. The effect of changes in operating conditions on the oxygen index is shown in Fig. 7. The effects of changes in the reduction temperature, reduction time and hydrogen gas flow are significant for the OI. It can be seen that changes in reduction time and temperature have a pronounced effect on the degree of reduction. The powder is also more or less homogeneously reduced as there is no apparent effect of the position of the powder on the degree of reduction. If one compares Figs 6 and 7 it can be seen that the change in reduction time has a

Hydrogen reduction of ammonium paratungstate--Part H 99,9

127

99.9

99

gg i

i¸ i

i

95

95 . . . . . . . . . . . . . . . . . . . . . . . . . . . .

...... /

................

- %

i

"

i

a

8

80

80

"'i

....i..........

U

o_ ~>

50

i

uq 50

.......... i. . . .

4~

............... :: .

oi ............. i

}

El i

i

i

.

.

.

.

.

........... ~. . . . . . .

i

20 N o

!° T

5 ° t

!

5

i

1

I

0.1

01 -011

009

007

-0.05 Effects

-0,03

-001

0.01

Fig. 7. Normal probability plot of all effects on the OI. Test series no. 2; average O I 2 - 8 8 .

larger effect on the degree of reduction than on the ammonia content. The effect o f changes in operating conditions and the position o f the powder in the boat on the BET specific surface area can be seen in Fig. 8. It can be seen that the specific surface area of the powder largely depends upon the position of the powder within the boat. Furthermore, the temperature has a significant effect on the specific surface as has the reduction time. The effect of a change in temperature is influenced by the reduction time. The change of the specific surface area within the boat was found to be larger than the change which can be realized by changing operating conditions. A plot of the effect o f operating parameters and powder position on the Fisher size is shown in Fig. 9. It can be seen that the Fisher average particle size is hardly affected by a change in operating conditions. It was found that none of the main effects was significant.

-0.9

-04

06 Effects

11

1

21

Fig. 8. Normal probability plot of all effects on the specific surface area. Test series no. 2; average BET 2 . 9 7 m ~ / g .

....~:.........

! ................. i. . . . . . .

..................... !o

~

"

~:

c)_

50

........................................

%

20 :: i

o

n

.

~

'

:.

!

5

3.1

-0.58

0.38

-018

002

022

042

Effects

Fig. 9. Normal probability plot of all effects on the average Fisher size. Test series no. 2; average Fisher particle size 17.7/tin.

Reduction

3.1.3 Observation of reaction front From the factorially designed experiments it can be concluded that the quality of TBO varies over the bed height. It is postulated that this variation is the result o f the reduction proceeding from top to bottom. To get an impression of the proceeding reduction reaction as a function o f time, the boat was sampled at distinct time intervals during reduction. A reaction front was observed. This reaction front could be identified by a small green rim which separated the blue reduced TBO from the white unreduced APT. The front moved downward during reduction. The reaction front after a certain reduction time is shown in Fig. 10.

0.1

'

~

~

"

~

/

front Fig. 10. Moving reduction front.

The green rim had the same colour as APT decomposed in a nitrogen atmosphere. 7 This green colour was found to be typical for APT calcined at a temperature of 260-300°C in a nitrogen atmosphere. Based on these observations and the measurement of the powder temperature during reduction, it is concluded that the reduction starts as soon as a certain degree of decomposition is achieved. It has, however, not yet been possible to determine the exact degree of decomposition. From

J. W. van Put, T. W. Zegers, H. Liu

128

Table 5. Industrial TBO, properties of various sieve fractions

Fraction (um)

Fisher (ltm)

Specific surface (m2/g)

32-45 45~53 63-90 90-125 > 125

13"9 17"8 23-5 23"8 26-3

4"0 4"3 4'5 5"6 7-3

this it can be concluded that the reduction does not occur instantaneously, but occurs stepwise.

3.2

Full-scale testing

The important characteristics for APT are not well established. The desired properties of TBO, however, are usually specified by the user. Therefore, a laboratory reduction test where the conditions for industrial reduction are simulated can provide better insight into the relations between APT and TBO characteristics. 1 F r o m the knowledge of these relations, specifications for APT can be derived. To get a better insight into the occurring reduction, and in order to develop the reduction test procedure, an experiment was performed on full industrial scale. In this experiment an extension tube, which was flushed with nitrogen gas, was attached to the feed end of the reactor tube. At a point in time, when steady state conditions had been reached, all boats were pushed into the extension tube to 'freeze' the reduction products. This enabled subsequent determination of the reaction profile. The boats were sampled in layers of approximately 1-cm thickness. During the industrial-scale test, samples were taken from the boats at the product end of the tube. The largest spread in quality was observed for the specific surface area: approximately 4 m~/g at the bottom of the boat and approximately 6.5 m~/g at the top. It was furthermore observed, contrary to what normally could be expected, that small TBO particles have a smaller specific surface than large TBO particles. The Fisher average particle size and the specific surface area of various TBO fractions are listed in Table 5.

3.3

X-ray diffraction

X-ray diffraction analyses of the laboratory samples showed that the TBO product is X-ray amorphous when produced between approximately 220 and

300°C; at around 300°C small reflections of a hexagonal tungsten phase appear and at around 400°C fl-oxide reflections begin to show. The ATB phase was dominantly present in all samples. The industrial TBO samples contained ATB and floxide. No other crystalline phases could be detected with certainty. 4

CONCLUSIONS

Based on published information (see Part I) and confirmed by our own observations, it can be concluded that the reduction of APT to TBO takes place in four major steps. The first three steps are endothermic, the fourth step is an exothermic one. The following reduction path for APT is proposed. The transition temperatures may shift depending upon the reduction time, PH2, amount of APT reduced and so on. APT T ~ 220°C Amorphous APT or amorphous bronze + T ~ 300°C y(NH4)20. WOz. zH20 {(x/2)(NH4)20 } . WO~_x/~ (reduced bronze) x has a fixed value between 0.33 and 0.25 2.9 < OI < 3 + T .,~ 420°C {(x/2)(NH,)~)}. WOz_x/~ + Wz0058 2-83 < OI < 2.9 + T ,,~ 480°C {x/2(NH4)zO } . WO3_x/2 + W20058 + lower oxides OI < 2"83 A non-reduced phase y(NH4)20. WO z . zH~O with a hexagonal crystal structure, forms during the recrystallization of the amorphous phase. A crystalline reduced ATB, {(x/2)(NHa)~O}. WO3_~/~ with a low ammonia content, forms from this nonreduced hexagonal phase. Both phases co-exist in the temperature range 300-400°C. More reduced tungsten bronze forms during reduction as more bronze-forming W4 + ions are formed during reduction. The amount of ammonia that is actually captured by the bronze will depend upon the heating rate relative to the reduction rate. If the heating rate is high, compared to the reduction rate, WO 3 will form s before reduction can actually take place. The r-oxide will start to form when the OI of the mixture of the non-reduced tungsten phase and the reduced ATB reaches 2-9. As the reduction proceeds, y-W, WO 2, fl-W and ~-W will form.

Hydrogen reduction of ammonium paratungstate--Part H

Concerning the control of TBO properties that have to meet certain specifications, it can be concluded that: 1. The ammonia content can be decreased most significantly by increasing the reduction temperature. Increasing the reduction time also results in a decreased ammonia content. The effect of a change in reduction time on the ammonia content is less than the effect of a change in reduction temperature. 2. The OI is mainly influenced by the furnace temperature and the reduction time, the higher the temperature and the longer the reduction time, the lower the OI. An increase of the hydrogen flow rate results in a lower OI, but this effect is less pronounced than an increase of the former operating parameters. 3. The specific surface area of TBO depends significantly upon the position of the sample in the boat; it increases towards the bottom of the boat. A longer reduction time gives a smaller specific surface area. A higher reduction temperature results in a higher specific surface area. Some interaction between reduction time and temperature exists. 4. The Fisher size cannot sufficiently be controlled by changing one of the operating conditions. Most likely the Fisher size of TBO is related to the initial physical characteristics of APT. As long as the Fisher size is believed to be an essential property of TBO for the production of high-quality lamp filament tungsten wire, the direct processing route will only be feasible for purchased APTs meeting preset physical specifications. ACKNOWLEDGEMENTS

variable. This approach has two negative aspects. In the first place it is inefficient; in the second place interactions between variables are not detected. Variables interacting may have a greater or smaller effect than the individual ones. In a factorialdesigned experiment the effect of variables and the interaction between variables on a response can be tested in a minimal number of experiments. In this study use is made of a so-called full factorial design. This type of factorial design allows an analysis of variance. In our experiments four factors are tested at two levels, i.e. a 2 4 factorial design matrix is used. The experimental design matrix is presented in Table A1. Let the responses of experiment 1 to 16 be Yl to Yw The main effect of a factor, i.e. the change in the response y if we move from the - to the + version of that factor, can be calculated as follows. The main effect of factor 1 is: {(Y2 --Yl) j- (.]24--Y3) ~-''" j- (Y16 --Y15)}/8 (Al) Interactions between factors can be calculated in a similar way by using Table A2. 9 This table is generated from Table A1, for each experiment, by multiplying the signs of the appropriate factors. No direct estimate of the variance, a 2, is available from these 16 runs because there were no replicates. An indirect estimate can, however, be obtained from three- and four-factor interactions. If all three- and four-factor interactions are supposed to be insignificant, these higher-order interactions would measure differences arising principally from Table

A1.2 4 experimental

calculating

main

Experiment (no.)

Philips Lighting BV is acknowledged for financially supporting this work. We thank Ir. I. K. van Hoof, manager at Philips Lighting, for his permission to publish this work. W. P. C. Duyvesteyn and G. M. van Rosmalen are acknowledged for checking and correcting the manuscript. APPENDIX: FACTORIALLY DESIGNED EXPERIMENTS

The classical approach to experimentation is to study one variable at a time, varying its level over a certain range, while holding all other variables constant and observing the effect of the response

129

+

design matrix,

settings

and signs for

effects

Factor 1 (+/-)

Factor 2 (+/-)

.

.

Factor 3 (+/-)

Factor 4~ (+/-)

1

.

2

+

--

. --

--

3

--

+

--

--

4

+

+

-

-

5

--

--

+

--

6

+

--

+

--

7

-

+

+

-

8

+

+

+

-

9

-

-

-

+

10

+

-

-

+

11

-

+

-

+

12

+

+

-

+

13

-

-

+

+

14

+

-

+

+

15

-

+

+

+

16

+

+

+

+

low setting

of a

represents

variable.

high setting;

-

represents

J. W. van Put, T. W. Zegers, H. Liu

130

A2. Signs

Table

for calculating

interaction

e f f e c t s f o r a 24 f a c t o r i a l

Experiment

Interactions

(no.) Second order 12

13

14

23

Third order 24

34

123

124 .

134

234

.

1234

1

+

+

+

+

+

+

.

2

-

-

-

+

+

+

+

+

+

-

-

-

-

+

+

+

-

+

-

+

-

-

+

+

+

+

.

Fourth order

+

3

-

+

4

+

.

5

+

--

+

--

+

--

+

--

+

+

--

6

-

+

-

-

+

-

-

+

-

+

+

7

-

--

+

+

-

-

-

+

-

+

8

+

+

--

+

--

--

+

.

-

.

.

.

+

.

.

.

9

+

+

-

+

-

-

-

+

+

+

10

-

-

+

+

-

-

+

-

-

+

+

11

--

+

--

--

+

--

+

--

+

--

+

12

+

--

--

+

--

--

+

--

--

--

13

+

.

+

+

+

--

-

+

14

--

+

+

--

--

+

--

-

+

--

-

15

--

--

--

+

+

+

--

--

--

+

--

16

+

+

+

+

+

+

+

+

+

+

+

Table

A3. Main

effects and

+ .

.

interactions

.

of test no.

1 : ammonia

Effect

S = V

F

W

(= v/ao

F(1,S) two sided

T

- 0-345

0.119025

1322-50

< 0-2 %

0-1775

0-031506

350-07

< 0-2 %

TC

- 0-0575

0'003306

37.74

Q

- 0'07

0.0049

54-44

TQ

0.04

0.0016

17.77

CQ

0'0275

0-000756

8"40

--

TCQ

0'0025

0"000006

0"07

--

C

t

-0'11

Tt

0"0121

0-025

< 0'2% <

10 %

0.000506

5.63

--

TCt

- 0"0125

0"000156

1.74

--

Qt

0.01

0.0001

1.11

--

TQt

0.015

0.000225

2.50

--

0-000056

0.63

--

0000006

0-07

- 0-0075 0.0025 a ~ = (0"000006 + 0-000156

that

6"94

- 0.0225

TCQt

Note

< 2 %

134"44

0-000625

1%

0-2 %

Ct

CQt

variance

< <

the F-tables

in the numerator,

present

data

V, and

for one-sided

the dominator,

+ 0"000225 + 0-000056

confidence

the numbers

= 0"00009

(1,5) signify

the degrees

of freedom

for the

a2, respectively.

experimental error. Thus, they provide an appropriate reference set for the remaining effects. 9 The a s is equal to the sum of squares divided by the degrees of freedom and can be calculated from the third- and fourth-order interactions by applying eqn (A2). a s = {E (effect)2}/5

levels;

--

+ 0.0000062)/5

(A2)

where 5 is the degrees of freedom. Second-order effects smaller than a, 2s calculated from higherorder effects, could subsequently be used for a new

estimate of a s. The sums of squares of an individual effect, S, is given by (effect)2. The degrees of freedom of a single effect is equal to 1. The variance, V, of an effect is therefore equal to (effect)S/1. The thus-calculated variance of an effect can be tested against the estimated variance to determine whether the effect comes from experimental error or whether it is really significant. This can be done with the Ftest. A condition for the use of the F-test is that the data come from a normal distribution. This condition is met: the effects which are unimportant

Hydrogen reduction of ammonium paratungstate--Part H Table A4. Probabilities for ranked effects

Effect (ascending order)

P (%)

(no.) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

3"33 10-00 16-67 23"33 30"00 36"67 43.33 50-00 56"67 63"33 70"00 76"66 83"33 90'00 96'67

should actually behave as if they came from a normal distribution. This is because averages, effects and contrast sums tend to be normally distributed even though the original data may be non-normal. 10 As an example, the main effects and the interactions of the factors reduction temperature T, amount of APT powder C, hydrogen gas flow rate Q and the reduction time t on the ammonia content of the TBO produced in the 16 experiments of Test no. 1 are given in Table A3. The main effects and their interactions were calculated with the computer program STATGRAPHICS. 11 All effects which are significant on a two-sided significance level of 5 % were considered to be significant. It can therefore be concluded with a two-sided significance level o f 0.2 % that the most significant effects for the residual ammonia content of TBO are in decreasing order: T, C, t, Q. The interaction between temperature and amount of powder and the interaction between the temperature and the hydrogen gas flow are also significant. Because the effects come from a normal distribution, they can be plotted on normal probability

131

paper: those effects which represent noise will lie on a straight line, whereas those effects which are significant will not lie on this line because they do not belong to the population of effects which represent noise. The effects should be in ascending order to make a normal probability plot. The probability is given by" P = 100. ( i - 1 ) / m , 9 where i is the ranked order of the effect to be plotted and m is equal to the n u m b e r of effects, i.e. 15. Table A4 presents the fixed probabilities for the 15 effects. REFERENCES 1. van Put, J. W., Ammonium paratungstate as a raw material for the manufacturing of lamp filament tungsten wire. PhD thesis, Delft University of Technology, May 1991. Delft University Press, Delft, 1991. 2. Kiss, A. B. & Tisza, F., Determination of the oxygen index of non-stoichiometric tungsten oxides and compounds of bronze type. Acta Chim. Acad. Sci. Hung., 104 (3) (1980) 211 21. 3. Dahl, M., Reduction of ammonium paratungstate to tungsten metal in different atmospheres. Proc. 5th Europ. Symp. Powd. Metal, 2 (1978) 143-8. 4. Bartha, L., Kiss, A., Neugebauer, J. & N6meth, T., Reaction parameters and intermediate products of the reduction of ammonium paratungstate (APT) in the production of tungsten powder. High Temp. High Press., 14 (1982) 1-10. 5. French, G.J. & Sale, F.R., A re-investigation of the thermal decomposition of ammonium paratungstate. J. Mat. Sci., 16 (1981) 3427-36. 6. Kiss, A. B., Gad6, P. & Hegedfis, A. J., Investigations on the thermocondensation of ammonium paratungstate pentahydrate by a combined thermoanalytical and I.R. spectrometric method, and additional methods. Acta Chim. Acad. Sci. Hung., 72 (4) (1972) 371-91. 7. van Put, J. W., Duyvesteyn, W. P. C. & Luger, F. G. J., Calcination of ammonium paratungstate into an ammonia soluble product. Hydromet., 26 (1991) 1-18. 8. Zou Zhiqiang, Wu Enxi, Tan Aichun & Qian Chungliang, Formation of tungsten blue oxide and its hydrogen reduction. Proc. llth Plansee Seminar '85, Vol. 1, RM42. Metallwerk Plansee GmBH, Reutte, Austria, 1985, pp. 337~J,8. 9. Box, E.P., Hunter, W. & Hunter, J.S., Statistics .for Experimenters," An Introduction to Design, Data Analysis and Model Building. John Wiley, Chichester, 1978. 10. Hendrix, C.D., What every technologist should know about experimental design. Chemtech., 9 (1979). 11. STATGRAPHICS release 3.01. Registered trademark of: the Statistical Graphics Corporation. Rockville, Maryland, USA, 1988.