Synthesis of ultrafine titanium diboride particles by rapid carbothermal reduction in a particulate transport reactor

Article abstract of DOI:10.1023/A:1018664832203

Ultrafine TiB₂ powders were synthesized by rapid carbothermal reduction in a vertical tubular reactor through which the particles fell freely. The starting materials were TiO₂, H₃BO₃ and cornstarch, which were mixed and calcined at 400°C for 1 h. The calcined precursor was milled, sieved and then fed into the top of the reactor. The reduction was carried out between 1786-1791°C in a downward flow of argon. Product particles were recovered at the bottom of the reactor. When the precursor molar composition ratio was TiO₂:B₂O₃:C = 1:2:5.5, the carbon content in the product was 5 wt % and the crystallite size was 80 nm. The carbon content in the product was reduced to 2.9 wt % by a heat treatment in an H₂ atmosphere for 9 h.

Full text of DOI:10.1023/A:1018664832203

JOURNAL OF MATERIALS SCIENCE 32 (1997) 3933 — 3938
Synthesis of ultrafine titanium diboride particles
by rapid carbothermal reduction in a particulate
transport reactor
TAKEYAS U S AITO , TO M O YU KI FU KU DA, HIDEAKI M AEDA,
KATS U KI KU S AKABE, S HIG EHARU M O RO O KA*
Departm ent of Chem ical Science and Technology, Kyushu University, 6-10-1 Hakozaki,
Higashi-ku, Fukuoka 812-81, J apan
Ultrafine TiB
tubular reactor through which the particles fell freely. The starting m aterials were TiO
BO and cornstarch, which were m ixed and calcined at 400 °C for 1 h. The calcined
2
powders were synthesized by rapid carbotherm al reduction in a vertical
2
,
H
3
3
precursor was m illed, sieved and then fed into the top of the reactor. The reduction was
carried out between 1786—1791 °C in a downward flow of argon. Product particles were
recovered at the bottom of the reactor. When the precursor m olar com position ratio was
TiO
was 80 nm . The carbon content in the product was reduced to 2.9 wt % by a heat treatm ent
in an H atm osphere for 9 h.
2
: B
2
O
3
: C"1: 2 : 5.5, the carbon content in the product was 5 wt % and the crystallite size
2
1
. Introduction
Recently the group of Weimer [10—12] succeeded in
Titanium diboride (TiB ) possesses superior thermal,
producing B C particles containing a small amount of
ꢀ
ꢂ
mechanical and chemical properties and, as a result,
has broad applications in cutting tools, wear parts and
TiB particles via rapid carbothermal reduction. The
ꢀ
overall reactions of the carbothermal reduction are
jet engine components [1]. Normally, TiB is produc-
ed by reducing titanium oxide with either (1) boron
oxide and carbon, (2) boron and carbon, (3) boron
carbide or (4) an alkali metal and boron oxide. These
processes typically require long reaction periods, dur-
expressed as follows:
ꢀ
2
B O (l)#7C(s)PB C(s)#6CO(g)
(1)
ꢀ
ꢁ
ꢂ
TiO (s)#B O (l)#5C(s)PTiB (s)#5CO(g) (2)
ꢀ
ꢀ ꢁ
ꢀ
ing which the TiB particles are sintered. A sub-
sequent size-reduction step results in product con-
tamination. Doi [2] has reported that the impurity
The starting materials, TiO , H BO and cornstarch,
ꢀ
ꢀ
ꢁ
ꢁ
with TiO and carbon as the limiting components,
ꢀ
were calcined at 400 °C in a N atmosphere. After
ꢀ
content in TiB powders was approximately 35 wt %
pulverization, the precursor particles with a particle
ꢀ
after a size reduction from 7 to 1 lm in a WC—Co
size less than 44 lm were fed into a vertical tubular
reactor by a screw feeder. Dispersion of the precursor
particles in the gas phase and a short residence time in
the reactor prevented the particles from sintering.
Stanley et al. [13] used titanium isopropoxide as the
metal source, boron triethoxide as the boron source
and furfuryl alcohol as the carbon source. The precur-
alloy ball mill. Nishiyama [3] has reported that the
impurity content in TiB powders was approximately
ꢀ
2
0 wt % when the average particle size was decreased
from 6 to 2.5 lm by a 3 h ball milling in a WC/Co pot
with WC/Co balls.
Since single-component TiB particles are difficult
ꢀ
to sinter, additives such as Cr/C, Al O , ZrO , Ni/C,
sor particles contained TiO particles of 50—100 nm in
ꢀ
ꢁ
ꢀ
ꢀ
SiC and yttria stabilized zirconia (YSZ) are applied in
size that were reduced to TiB in a horizontal tubular
ꢀ
order to increase the density [4—8]. Baumgartner and
reactor. They obtained 1—3 lm sized TiB particles
ꢀ
Steiger [9] sintered a TiB powder with a 0.1—1 lm,
in the shape of well-defined hexagonal platelets and
ꢀ
particle size produced by an arc-plasma method from
claimed that the intimate mixture of reactants in the
precursor decreased the carbon content in the prod-
TiCl and BCl in H , and achieved a relative density
ꢂ
ꢁ
ꢀ
higher than 98% by pressureless sintering at 2000 °C.
Densification proceeded by self diffusion due to a high
grain-boundary area. Thus, it is essential to establish
uct. Maeda et al. [14] synthesized NbB powders by
ꢀ
rapid carbothermal reduction with a precursor pre-
pared from Nb O , H BO and cornstarch in a verti-
ꢀ
ꢃ
ꢁ
ꢁ
processes which produce TiB particles whose size is
cal particulate transport reactor. They concluded that
ꢀ
in the range of tens of nanometers.
the rate-determining step was NbB formation from
ꢀ
*
Author to whom correspondence should be addressed.
0
022—2461 ( 1997 Chapman & Hall
3933

TABLE I Reactions of rapid carbothermal reduction
Products
Overall reaction scheme
Temperature
Major reaction
Reaction type
b!SiC[15]
3C(s)#SiO (s)PSiC(s)#2CO(g)
1600—2000 °C
C(s)#SiO (s)PSiO(g)#CO(g)
Gas—solid
ꢀ
ꢀ
2
C(s)#SiO(g)PSiC(s)#CO(g)
C(s)#B O (1, g)PB O (g)
ꢀ
ꢁ
ꢀ ꢀ
#
CO(g)
B C [10—12]
7C(s)#2B O (1, g)PB C(s)
1500—1850 °C
1500—1800 °C
7C(s)#2B O (1)PB C(s)
Liquid—solid
(Gas—solid)
ꢂ
ꢀ
ꢁ
ꢂ
ꢀ
ꢁ
ꢂ
#
6CO(g)
#4CO(g)
C(s)#2B O (g)PB C(s)
5
ꢀ
ꢀ
ꢂ
#
4CO(g)
C(s)#B O (1, g)PB O (g)
ꢀ
ꢁ
ꢀ ꢀ
#
CO(g)
NbB [14]
Nb O (s)#2B O (1)#11C(s)
Nb O (s)#7C(s)P2NbC(s)
Liquid—solid—solid
(Gas—solid—solid)
ꢀ
ꢀ
ꢃ
ꢀ
ꢁ
ꢀ ꢃ
P2NbB (s)#11CO(g)
#5CO(g)
ꢀ
NbC(s)#B O (1, g)#2C(s)
ꢀ
ꢁ
PNbB (s)#3CO(g)
ꢀ
NbC(s)#B O (g)#C(s)
ꢀ
ꢀ
PNbB (s)#3CO(g)
ꢀ
AlN[16]
Al O (s)#3C(s)#N (g)
1400—1850 °C
1350—1550 °C
Al O (s)#3C(s)#N (g)
P2AlN(s)#3CO(g)
Gas—solid—solid
Gas—gas—solid
ꢀ
ꢁ
ꢀ
ꢀ
ꢁ
ꢀ
P2AlN(s)#3CO(g)
SiN [17, 18]
6C(s)#3SiO (s)#2N (g)
C(s)#SiO (s)PSiO(g)#CO(g)
ꢀ
ꢀ
ꢀ
PSi N (s)#6CO(g)
3C(s)#3SiO(g)#2N (g)
ꢁ
ꢂ
ꢀ
PSi N (s)#3CO(g)
ꢁ
ꢂ
TiN[19—21]
2TiO (s)#4C(s)#N (g)
1100—1250 °C
6TiO (s)#3C(s)
Gas—solid—solid
ꢀ
ꢀ
ꢀ
P2TiN(s)#4CO(g)
P2Ti O (s)#2CO(g)#C(s)
ꢁ
ꢃ
2
Ti O (s)#10C(s)#3N (g)
ꢁ ꢃ ꢀ
P6TiN(s)#10CO(g)
NbC, B O and C. The initial particle size of the
ꢀ
ꢁ
Nb O starting material was an important factor in
ꢀ
ꢃ
achieving a high conversion, whilst the calcination
temperature controlled the residual carbon content in
the products. The reaction temperature affected the
crystal size of the products. By optimizing the experi-
mental conditions, NbB particles 40—50 nm in size
ꢀ
were synthesized with a carbon content of 2.65 wt %.
The products and rapid carbothermal reduction
schemes are summarized in Table I.
The present study describes the production of sub-
micrometre sized TiB particles via rapid carbother-
ꢀ
mal reduction, using precursors prepared from TiO ,
ꢀ
H BO and cornstarch. The carbon content in the
ꢁ
ꢁ
product is decreased by a heat treatment in a hydro-
gen atmosphere.
2
. Experimental procedure
2
.1. Precursor synthesis
Fig. 1 shows the TiO particles (supplied by Ishihara
ꢀ
Sangyo Co.) used as the titanium source. The average
Figure 1 Morphology of the TiO particles.
ꢀ
size was 40—50 nm as measured by field-emission
scanning electron microscopy (SEM, Hitachi S-900)
and approximately 30 nm by X-ray diffraction (XRD,
Shimadzu XD-D1). The latter was calculated from the
black flakes were pulverized in a ball mill for 4—12 h.
The carbon content in the precursor was determined
width of the main TiO (110) peak. Reagent grade
by elementary analysis after removal of the B O by
washing with methanol. The boron oxides in the pre-
cursors and products were dissolved in methanol, and
the boron concentration was evaluated by inductively
coupled plasma spectrometry (Seiko, SPS 1200VR).
ꢀ
ꢀ ꢁ
TiO , H BO and cornstarch (Wako Pure Chemical)
ꢀ
ꢁ
ꢁ
were mixed at prescribed ratios in deionized water at
ambient temperature, and the mixture was evaporated
by boiling with stirring. After the mixture became
viscous, it was placed in an oven at 95 °C and dried
overnight. The white flakes obtained were calcined at
4
00°C for 60 min in an argon atmosphere. Thus, the
2.2. Carbotherm al reduction
starting materials were converted to a mixture of
TiO , B O and carbonaceous matter. The calcined
Fig. 2 shows the continuously operated reactor
used for the rapid carbothermal reduction. The outer
ꢀ
ꢀ ꢁ
3
934

Figure 3 Morphology of the precursor particles.
Figure 2 The particulate transport reactor used for the rapid car-
bothermal reduction.
column was a 1.2 m long alumina tube having
a 36 mm internal diameter. The inner one was
a 19 mm internal diameter graphite pipe which was
used to protect the alumina tube from any reaction
with the boron oxides. The pulverized precursor pow-
der was stored in a 235 mesh metal sieve on top of the
reactor and was introduced into the reactor through
the mesh by manual tapping. The reactor was heated
by LaCrO heaters, and the isotherm zone of
ꢁ
1
786—1791 °C was approximately 4—5 cm in length.
The product was collected in a flask fixed at the cooled
bottom of the reactor. The reaction was always carried
out in an Ar atmosphere at ambient pressure. The
average velocity of the Ar carrier gas was 4 cm s\ꢄ at
Figure 4 Formation of: (⅙) TiC and (E) TiB in a horizontal tubular
reactor at 1350 °C.
ꢀ
1
791 °C. Since the free fall velocity of the precursor
particles of 30 lm diameter was approximately
cm s\ꢄ, the residence time in the isotherm zone was
1
TiO crystallites in the precursor was determined by
XRD and was found to be approximately 30 nm,
ꢀ
approximately 1 s. To decrease the carbon content the
particles of the product were treated in a H atmo-
sphere at 800 °C for 3—18 h. The reaction rate was also
which is equal to that of the initial TiO particles. Fig.
4 shows the changes in the XRD peaks assigned to
ꢀ
ꢀ
determined using a horizontal tubular reactor of 1 cm
diameter. The precursor was placed in a molybdenum
boat and was maintained at a temperature of
TiC (200) and TiB (101). The initial molar composi-
ꢀ
tion of the precursor was TiO : B O : C"1:5:12.5,
ꢀ
ꢀ ꢁ
and the reaction temperature was 1350 °C. The TiO
peaks rapidly disappeared and those due to TiC
reached a maximum at 30 s after the start of the
ꢀ
1
350—1500 °C for a prescribed period. The sample was
then analysed by XRD.
reaction. The TiB peaks gradually increased with
ꢀ
time, and no peaks that could be assigned to TiB,
3
. Results and discussion
.1. Effects of reaction conditions on
product particles
Ti B and Ti B were observed. The reaction was
conducted at 1400, 1450 and 1500 °C, and the initial
ꢁ
ꢂ
ꢀ ꢃ
3
reaction rate of TiB formation was determined for
ꢀ
Fig. 3 shows the morphology of the precursor particles
each temperature. From an Arrhenius plot of this
after calcination at 400 °C for 1 h. The precursor was
data, the activation energy was calculated to be
prepared at a molar composition of TiO : B O : C" 340 kJ mol\ꢄ, which is in agreement with the value
ꢀ
ꢀ ꢁ
1
: 2 : 5.5 and a milling period of 4 h. The average size
for the production of NbB by carbothermal reduc-
ꢀ
of the agglomerates was 1.5—30 lm. The size of the
tion [14]. The formation of B C is negligible at
ꢂ
3
935

1
400—1500 °C due to chemical equilibrium con-
straints. The present results suggest that carbothermal
reduction of TiO to TiB proceeded as described by
ꢀ
ꢀ
the reaction shown as Equation 2, which consists of
the following steps:
TiO (s)#3C(s)PTiC(s)#2CO(g)
(3)
ꢀ
B O (l)#TiC(s)#2C(s)PTiB (s)#3CO(g) (4)
ꢀ
ꢁ
ꢀ
At higher temperatures, B O (g), which is formed by
ꢀ
ꢀ
the reaction shown as Equation 5, may participate in
the carbothermal reductions shown in Equations 6
and 7.
B O (l)#C(s)PB O (g)#CO(g)
ꢀ ꢀ
(5)
ꢀ
ꢁ
B O (g)#TiC(s)#C(s)PTiB (s)#2CO(g) (6)
ꢀ
ꢀ
ꢀ
2
B O (g)#5C(s)PB C(s)#4CO(g)
(7)
ꢀ
ꢀ
ꢂ
In the presence of TiO , the following reaction occurs:
ꢀ
B C#2TiO #3CP2TiB #4CO(g)
(8)
ꢂ
ꢀ
ꢀ
The Gibbs free energy for B C forming via the reac-
ꢂ
tion shown as Equation 1 at 1790 °C is —200 kJ mol\ꢄ,
and that for TiB forming by the reaction shown as
ꢀ
Equation 8 is —211 kJ mol\ꢄ [22]. This suggests that
TiB is preferentially formed rather than B C.
ꢀ
ꢂ
Weimer et al. [11] expressed the carbon conversion
due to the reaction shown as Equation 1 as follows,
when carbon was the limiting component.
[
B C]
1
![
ꢂ
"1!X"exp+!(kt)ꢁ, (9)
B C]#0.1429[C]
ꢂ
where the brackets refer to the molar concentration of
reactants, and t is the reaction period. The reaction
rate coefficient k at 1790 °C was given as 0.48 s\ꢄ [11].
The conversion, X, defined by Equation 9 is then
calculated as 0.11 under the experimental conditions
of the present study, i.e., 1790 °C and t"1 s. This
corresponds to a B C fraction of 8 wt % in the prod-
ꢂ
uct. To examine the validity of the estimation, a pre-
cursor was prepared from H BO and cornstarch
ꢁ
ꢁ
(
B O : C"1 : 4) which was subjected to carbother-
ꢀ ꢁ
mal reduction using the vertical particulate transport
reactor. The product recovered at the bottom of the
reactor was washed with methanol to remove unreac-
ted B O , and the B C content was determined by the
XRD method. No substantial peaks of B C were de-
tected in this experiment. If the reaction rate estimated
Figure 5 Morphology of the TiB particles formed by rapid car-
ꢀ
bothermal reduction at 1791°C. Milling period; (a) 4 h, (b)12 h.
ꢀ
ꢁ
ꢂ
ꢂ
described in Fig. 5. The peaks that correspond to TiC
disappear when the milling time was greater than
8 h. A longer milling period increased the fraction of
smaller agglomerates in the precursor, although the
volume-averaged size of the particles remained un-
changed. Thus, milling may increase the contact be-
from the result of Weimer et al. [11] is applied, then
the B C weight fraction is, at most, 7 wt %. Thus, in the
ꢂ
present study, the total carbon content in the product
consisted predominantly of residual free carbon.
Fig. 5 (a and b) shows the morphology of the prod-
uct particles after a carbothermal reduction at 1790°C.
tween the reactant TiO and C particles. Fig. 7 shows
ꢀ
The precursor molar composition was TiO :
the effect of carbon content in the precursor on the
ꢀ
B O : C"1 :2 : 5.5, and the milling periods were 4
ratio of the relative intensity of the TiC (200) and TiB
(101) XRD peaks. The milling period was fixed at 4 h
ꢀ
ꢁ
ꢀ
and 12 h. The average crystal-like size of the product
particles was approximately 80 nm, which is larger
in this case. When the precursor molar composition
than the original TiO size of 30 nm, and the size was
not significantly affected by the milling period.
was TiO : B O : C " 1 : 2 : 6, the yield of TiC reach-
ꢀ
ꢀ
ꢀ ꢁ
ed its minimum.
Fig. 6 shows XRD patterns of the products as
a function of milling period. The preparation method
for the precursors and the reaction conditions were as
To increase the conversion, the particles recovered
at the reactor bottom were remixed with H BO ,
calcined (as described in the experimental section),
ꢁ
ꢁ
3
936

Figure 8 Effect of C/Ti atomic ratio in precursor on residual carbon
content. Keys are the same as in Fig. 7.
Figure 6 XRD patterns of products formed by rapid carbothermal
reduction at 1791 °C. Milling period, (a) 4 h, (b) 8 h, (c)12 h. Key:
(E) TiBꢀ and (⅙) TiC.
Figure 9 Effect of hydrogen treatment time on residual carbon
content. Precursor molar composition, TiO : B O :C"1 : 2 : 5.5,
ꢀ
ꢀ ꢁ
milling period, 8 h.
Figure 7 Effect of C/Ti atomic ratio in precursor on XRD intensity
ratio of TiC to TiB . TiO : B O in precursor, (᭝) 1 : 1.5, (E) 1 : 2.0,
ꢀ
ꢀ
ꢀ ꢁ
(
ᮀ) 1 : 2.5, on a molar basis.
indicated by Weimer et al. [11] and Xiang et al. [12].
An improvement in the milling of precursors, on the
other hand, was effective in that the residual carbon
content was reduced from 10 to 5 wt % by extending
the milling period from 4 to 12 h. This suggests that
pulverized and then fed into the reactor a second time.
No differences were observed in the XRD patterns
between the resulting product and the initial product.
The conversion of TiO to TiB was practically com-
plete after the initial reaction, and free carbon conver-
sion was negligible at this temperature.
the contact between the solid reactants (TiO and C)
ꢀ
in the precursor is important for rapid carbothermal
ꢀ
ꢀ
reduction. In the case of B C production by the reac-
ꢂ
tion (shown as Equation 1), carbon is the limiting
component and reacts with liquid or gaseous boron
oxides. Unreacted boron oxides are easily removed by
3
.2. Carbon content in product particles
washing with methanol. In the case of TiB produc-
ꢀ
tion, solid-solid reactions are involved, TiO particles
ꢀ
The content of residual carbon in the product particles
was not greatly changed by repeating the reaction. An
increase in the reaction temperature is effective in
reducing residual carbon content by enhancing the
reaction (shown as Equation 1), but a high reaction
temperature gives sintering of the product particles as
rapidly react with carbon to give TiC, which then
reacts with carbon to give TiB . Thus, the initial
ꢀ
carbon content should be controlled in order to maxi-
mize the TiB yield and to minimize any residual
ꢀ
carbon.
3
937

As described in the former section, the major por-
tion of carbon in the product particles existed as
amorphous free carbon. In the expectation of decreas-
ing the carbon content, product particles were heat-
3. K. NISHIYAMA, J. Jpn. Soc. Powder Metall. 37 (1990) 906 (in
Japanese).
4
.
.
J. MATSUSHITA, S. HAYASHI and H. SAITO, J. Ceram.
Soc. Jpn. 97 (1989) 1206.
J. MATSUSHITA, H. NAGASHIMA and H. SAITO, ibid. 99
5
treated in an H atmosphere at 800°C for 3—18 h.
(1991) 78.
ꢀ
Fig. 9 shows the effect of the treatment period on
6. J. MATSUSHITA and A. SANO, ibid. 100 (1992) 593.
7
.
S. TORIZUKA, J. HARADA, H. YAMAMOTO, H.
residual carbon content. The precursor possessed a
NISHIO, A. CHINO and Y. ISHIBASHI, ibid. 100 (1992) 259.
8. Idem, ibid. 100 (1992) 691.
molar composition of TiO : B O : C"1 : 2 : 5.5 and
ꢀ
ꢀ ꢁ
was prepared with an 8 h milling. The free carbon in
the product was reduced from 6.4 to 2.9 wt % as a
result of a hydrogen treatment for 9 h.
9
.
H. R. BAUMGARTNER and R. A. STEIGER, J. Amer. Ce-
ram. Soc. 67 (1984) 207.
10. A. W. WEIMER, R. P. ROACH, C. N. HANEY, W. G.
MOORE and W. RAFANIELLO, AIChE J. 37 (1991) 759.
1
1. A. W. WEIMER, W. G. MOORE, R. P. ROACH, J. E. HITT,
R. S. DIXIT and S. E. PRATSINIS, J. Amer. Ceram. Soc. 75
4
. Conclusions
(1992) 2509.
Ultrafine TiB particles were synthesized by rapid
1
1
2. Y. XIONG, S. E. PRATSINIS and A. W. WEIMER, AIChE
J. 38 (1992) 1685.
3. D. R. STANLEY, J. D. BIRCHALL, J. N. K. HYLAND, L.
THOMAS and K. HODGETTS, J. Mater. Chem. 2 (1992) 149.
ꢀ
carbothermal reduction of precursor particles pre-
pared with TiO , H BO and cornstarch. When the
precursor was composed of TiO : B O : C"1:2:5.5,
the carbon content was 5 wt %, and the crystalline
particle size was 80 nm. The free carbon content in the
product was reduced to 2.9 wt % by a heat treatment
ꢀ
ꢁ
ꢁ
ꢀ
ꢀ ꢁ
14. H. MAEDA, T. YOSHIKAWA, K. KUSAKABE and S.
MOROOKA, J. Alloys. Comp. 215 (1994) 127.
5. A. W. WEIMER, K. J. NILSEN, G. A. COCHRAN and R. P.
ROACH, AIChE J. 39 (1993) 493.
6. Y. BAIK, K. SHANKER, J. R. McDERMID and R. A. L.
DREW, J. Amer. Ceram. Soc. 77 (1994) 2165.
1
1
in an H atmosphere at 800 °C for 9 h.
ꢀ
1
1
7. M. EKELUND and B. FORSLUND, ibid. 75 (1992) 532.
8. T.-H. LIOU and F.-W. CHANG, Ind. Engng Chem. Res. 34
Acknowledgements
(1995) 118.
This study was supported by the Ministry of Educa-
19. G. V. WHITE, K. J. D. MACKENZIE and J. H. JOH-
NSTON, J. Mater. Sci. 27 (1992) 4287.
tion, Science, Sports and Culture. The TiO particles
were supplied by Ishihara Sangyo Co. The help of
Mr. Tomohisa Yoshikawa during the experimental
work is deeply appreciated.
ꢀ
20. G. V. WHITE, K. J. D. MACKENZIE, I. W. M. BROWN,
M. E. BOWDEN and J. H. JOHNSTON, ibid. 27 (1992) 4294.
21. G. V. WHITE, K. J. D. MACKENZIE, I. W. M. BROWN
and J. H. JOHNSTON, ibid. 27 (1992) 4300.
2
2. ‘‘JANAF thermochemical tables’’, 3rd Edn (American Chem-
ical Society, American Institute for Physics, and National
Bureau of Standards, 1986).
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.
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2
.
H. DOI, Boundary 2 (1986) 33.
and accepted 28 January 1997
.
3
938