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Film formation and sintering of colloidal monoclinic zirconia
]OURNA
Journal of Non-Crystalline Solids 147&148(1992) 503-507 North-Holland
L OF
NON-C STALLINESOLIDS
Film formation and sintering of colloidal monoclinic zirconia H. V e s t e g h e m , A. L e c o m t e a n d A. D a u g e r Laboratoire Matdriaux C~ramiques et Traitements de Surface, URA 320 CNRS, ENSCI, 47 ave. A. Thomas, 87065 Limoges, France
Hydrothermal processing was used to produce colloidal monoclinic zirconia suspensions from zirconium carboxylate solutions. The colloidal suspensions exhibit high stability with respect to aggregation and films can be obtained by solvent evaporation. The as-prepared films yield dense monocliniczirconia ceramics with average grain sizes of 60 nm after firing at a temperature of 1100°C. The distribution of colloidal zirconia particles in aqueous suspension was investigated by small-angle X-ray scattering. The scattering curves showed a broad peak, the position of which shifted to higher angles with increasing particle volume fraction. The average interparticle distance was estimated using this interference peak position. Sintering of the colloidal films was monitored by dilatometry, scanning electron microscopyand small-angle X-ray scattering.
1. Introduction Ceramists are interested in processing fine particles to improve uniformity of ceramic microstructures and to decrease sintering temperatures. Slurries, i.e., ceramic particle suspensions, are convenient for forming technologies such as slip casting, tape casting and electrophoretic deposition used to produce green ceramic bodies. Ceramic nanostructure materials exhibit specific characteristics due to their nanoscale microstructure and the usefulness of these materials has become increasingly evident [1]. Preparation of stable colloidal monoclinic zirconia suspensions and their use as ceramic slurries for the fabrication of nanoscale ceramic materials are described. The concentration dependence of the colloidal zirconia particle distribution was investigated by small-angle X-ray scattering (SAXS).
2. Experimental The precursor of colloidal zirconia was a zirconium oxyacetate previously described [2]. Colloidal zirconia was prepared by hydrothermal treatments of the zirconium oxyacetate solutions in an autoclave system of 600 cm 3 volume at temperatures from 150 to 270°C. Hydrolysis of
zirconium oxyacetate has been shown to be incomplete during hydrothermal treatment. The amount of unreacted acetate of the as-obtained colloidal zirconia was determined by thermogravimetry and the hydrolysed molar fraction, a, of zirconium oxyacetate was deduced. Colloidal suspensions were cast in P T F E plates and films were prepared by slow evaporation of the solvent. Small-angle X-ray scattering data were obtained with a slit laboratory camera using Cu Ko~ 1 radiation provided with a double channel cut germanium monochromator. The detector was a position sensitive proportional counter with an effective length of 55 mm and a sample to detector distance of 500 ram. The scattering vector H = 4"rrA- 1 sin 0, where 0 is the Bragg angle and A the X-ray wavelength, was ranging from 0.06 to 2 nm-~. Experimental results were corrected for parasitic scattering and normalised to equivalent sample thickness, intensity and counter efficiency. Colloidal zirconia particles and their thermal evolution were studied with scanning electron microscopy (SEM) and transmission electron microscopy (TEM) to evaluate particle size and microstructure, X-ray diffraction (XRD) and electron diffraction, respectively, to examine the films and to identify crystallinity of individual particles. Shrinkage to 1300°C was measured directly from the thickness of the films in a vertical
0022-3093/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
H. Vesteghem et al. / Colloidal monoclinic zirconia
504
dilatometer with alumina as a reference at a heating rate of 3°C m i n - i .
3. Preparation and characterisation of colloidal zirconia suspensions Precipitation of colloidal zirconia is achieved by two-step hydrolysis of the zirconium oxyacetate precursor. Dissolution of the precursor in water, at room temperature, produces a homogeneous system according to the reaction [2] ZrO1.35(OAc) 1.30, AcOHcryst.+ H 2 0 --> [ZrO1.35(Oac)1.30] aq.+ a c O H a q : Hydrolysis of the acetate ligands, which leads to zirconium oxide formation, is obtained by heating the zirconium oxyacetate solution to 270°C. This reaction can be represented as [ZrOt.35(Oac)1.30] aq.+ H 2 0 --* ZrO2cryst + AcOHaq.. Figure 1 shows the plot of hydrolysed fraction, a, against temperature. It illustrates that the hydrolysis of the acetate groups according to the latter reaction begins suddenly. Since the solubility of zirconia in the hydrothermal conditions used in this work is supposed to be very low, we conclude that nucleation occurs in a very short time interval. Consequently, the main requirement for monodispersed colloidal suspension, a single burst of nucleation, is met [3]. Figure 2 shows the T E M micrograph of the colloidal zirconia particles. Lattice imaging and electron diffraction pattern characterize single crystals of monoclinic ZrO 2. This result is verified by X R D measurements (fig. 3). The mean crystal size as determined by the Scherrer relation is 2R = 11 nm, in good agreement with the size evaluated from TEM. Colloidal zirconia suspensions were examined by the SAXS technique. The scattering curves of the as-obtained suspension with a 20 wt% concentration (5.1 vol.%) show a single broad peak which suggests that the zirconia particles are distributed in an ordered manner [4,5]. The interparticle interference effect can be removed from
0,8
z 0
to< re
0,6
LI-
a LU
¢/3 0,4
O re tm >32 0,2
0
1 O0
A
• I 150
--0 I 200
I 250
300
TEMPERATURE, °C
Fig. 1. Hydrolysed fraction, ~, of zirconium oxyacetate as a function of temperature for a 1 min (o) and a 9 h (A) hydrothermal treatment. the SAXS curve by decreasing the concentration to 0.4 wt%. In this case, the scattering intensity is proportional to single particle scattering and a
2 0 nm Fig. 2. T E M m i c r o g r a p h of the colloidal z i r c o n i a particles.
505
H. Vesteghem et a L / Colloidal monocfinic zirconia
Guinier analysis can be applied to the small angle region. A radius of gyration, Rg of 9 nm was measured and, using the relation R 2 = ~Rg 5 2 for spherical particles whose radius is R, the size of the colloidal particles was found to be 2 R - - 2 4 rim. The Log I ( H ) versus Log H plot showed slight departure from the Porod law. A power law I ( H ) c ~ H -D was clearly distinguished but the D value was 3.6 instead of 4. The results of the SAXS, X R D and T E M studies can be interpreted in the following way. We can describe colloidal zirconia particles as aggregates (2R = 24 rim) of a few smaller crystallites of monoclinic ZrO 2 (2R = 11 nm). In addition, we can assume that the crystallites in a colloidal particle are cemented together by the amorphous zirconium oxyacetate which has not reacted during hydrolysis. This assumption fully agrees with the measured D value of 3.6 which characterises a rough colloid [6]. Therefore, it is worth noting that remaining acetate groups are supposed to cover the colloidal particle and appear to work as a protective agent against coarsening. The as-prepared col-
200.000
Volume fraction a:0.051 b:0.092 c:0.20 d'0.28 e:0.40 f:film
150.000
O9 Z 100,000 LU I-Z
50.000 -
:: / C :/ / /."
_ d / ...~."/./ f
e' 0 0
0,2
0,4
0,6
0,8
H (nm "1)
Fig. 4. Concentration dependence of the SAXS curves of the colloidal zirconia suspensions.
I N T E N S I T Y (A.U.)
loidal suspensions are stable with respect to coarsening. Neither aggregation nor coalescence of the particle occurred in a period of three years.
4. Film formation and sintering
25
30
35 ANGLE (2e)
Fig. 3. T e m p e r a t u r e e v o l u t i o n of the X R D p a t t e r n s of colloidal zirconia.
Since an interparticle interference effect was observed in the SAXS experiment, the colloidal particles are not considered to be distributed randomly. However, because of the lack of a second-order peak, the particles form a highly distorted array in the suspension. Matsuoka et al. [5] demonstrated that the position of the firstorder peak is not affected by the distortion and can serve to evaluate the nearest-neighbour interparticle distance, d, using the Bragg equation. Figure 4 shows the concentration dependence of the scattering curve of colloidal zirconia suspensions. As expected, the peak position shifted
H. Vesteghem et al. / Colloidal rnonoclinic zirconia
506
-51
0,5
.0 •e-i
03
E //I~
E
-r" 0,2 n" O
.•.'/• ...'"
uJ > (.9
o~
•.••'o
•
..••""
5
mz ~" 10 'IO3 rr < IJ.l Z
•
z LU 0,1
,--I 15 O'3
20 0,05 I
I
0,03
I
0,05
I
I
0,1 0,2 0,3 V O L U M E FRACTION
I
__
o,5
Fig. 5. L o g - L o g plot of the position of the SAXS peak versus the volume fraction. T h e dashed line is the theoretical curve for an fcc a r r a n g e m e n t of 24 n m particles•
25
0
200
400
600
800
1,000
1.200
1.400
T E M P E R A T U R E , °C
Fig. 7. Densification curve for a colloidal zirconia film. 500.000
f
Temperature a:25°C b:400°C c:600°C d:800°C e:900°C f: 1000°C
\ i
400.000
to higher scattering vectors H, with increasing concentration. Figure 5 illustrates the relationship between the peak position, //max, and the
300.000
I,
z p.z
f
i I.
el
ii
200,000
'
d
i\
i'i,
!
100.000,
\ \,, '.~:)~......
....................."-..:"-'.L ............... 0
~ ~ = = ~ - - _ 0,1
0,2
0,3
0,4
0,5
0,6
H (nm -1)
Fig. 6. T e m p e r a t u r e evolution of the SAXS curves of colloidal zirconia films.
Fig. 8. SEM micrograph of the top surface of a monoclinic zirconia film fired in air at 1100°C for 1 h. (Bar = 100 nm.)
H. Vesteghem et al. / Colloidal monoclinic zirconia
concentration (volume fraction, q~). Assuming a continuous distribution array and a constant particle size, a linear regime should be obtained with a slope of 1 / 3 as represented in fig. 5 for an fcc array and a particle size of 24 nm. We observe that the experimental points fit this theoretical behaviour when the volume fraction of the suspension increases. Moreover, the position of the interference p e a k for the film sample leads to an interparticle distance of 24 nm which is the same as the colloidal particle diameter (2R = 24 nm). We conclude that no aggregation occurs during the increase in the volume fraction of the suspension and a nearly perfect compact packing of the initial particles is obtained. Coarsening of the zirconia particles during thermal treatment was evidenced by SAXS study. The particle size deduced from the position of the interference p e a k (fig. 6) increases markedly above 500°C. As expected [2], the same behaviour was observed for the crystallite size measured from broadening of X R D peaks (fig. 3). However, for the same temperature the crystallites were always found to be smaller than the particles; for example, 22 ram and 58 nm, respectively, at 800°C. Figure 7 shows the densification behaviour of a zirconia film sample p r e p a r e d by drying the colloidal suspension. It is shown that, first, the remaining acetate groups are removed between 250 and 400°C as was confirmed by thermogravimetry and, second, the densification begins below 1000°C and is nearly complete when the martensitic transforma-
507
tion M-ZrO2--* T - Z r O 2 occurs. Figure 8 illustrates the ability of a colloidal monoclinic zirconia film to densify completely at 1100°C and to give a regular nanoscale microstructure.
5. Conclusion
Small-angle X-ray scattering measurements demonstrate the stability of the colloidal monoclinic zirconia suspensions p r e p a r e d by thermohydrolysis of a zirconium oxyacetate precursor. Very efficient packing of initial colloidal particles was observed in green films obtained by evaporation of the solvent and zirconia materials with strongly decreased sintering t e m p e r a t u r e and consequently small grain size were fabricated.
References
[1] A.J. Burggraff, K. Keizer and B.A. Van Hassel, Solid State Ionics 32&33 (1989) 771. [2] T. Merle-Mejean, T. Jaccon and H. Vesteghem, in: Ceramic Powder Science III, ed. G.L. Messing, S. Hirano and H. Hausner (American Ceramic Society, Westerville, OH, 1990) p. 41. [3] T. Sugimoto, Adv. Colloid Interf. Sci. 28 (1987) 65. [4] J.D.F. Ramsay, Chem. Soc. Rev. 15 (1986) 335. [5] H. Matsuoka, H. Murai and N. Ise, Phys. Rev. B37 (1988) 1368. [6] D.W. Schaefer and K.D. Keefer, in: Better Ceramics Through Chemistry II, ed. C.J. Brinker, D.E. Clark and D. Ulrich (Materials Research Society, Pittsburgh, PA 1986) p. 277.
Journal of Non-Crystalline Solids 147&148(1992) 503-507 North-Holland
L OF
NON-C STALLINESOLIDS
Film formation and sintering of colloidal monoclinic zirconia H. V e s t e g h e m , A. L e c o m t e a n d A. D a u g e r Laboratoire Matdriaux C~ramiques et Traitements de Surface, URA 320 CNRS, ENSCI, 47 ave. A. Thomas, 87065 Limoges, France
Hydrothermal processing was used to produce colloidal monoclinic zirconia suspensions from zirconium carboxylate solutions. The colloidal suspensions exhibit high stability with respect to aggregation and films can be obtained by solvent evaporation. The as-prepared films yield dense monocliniczirconia ceramics with average grain sizes of 60 nm after firing at a temperature of 1100°C. The distribution of colloidal zirconia particles in aqueous suspension was investigated by small-angle X-ray scattering. The scattering curves showed a broad peak, the position of which shifted to higher angles with increasing particle volume fraction. The average interparticle distance was estimated using this interference peak position. Sintering of the colloidal films was monitored by dilatometry, scanning electron microscopyand small-angle X-ray scattering.
1. Introduction Ceramists are interested in processing fine particles to improve uniformity of ceramic microstructures and to decrease sintering temperatures. Slurries, i.e., ceramic particle suspensions, are convenient for forming technologies such as slip casting, tape casting and electrophoretic deposition used to produce green ceramic bodies. Ceramic nanostructure materials exhibit specific characteristics due to their nanoscale microstructure and the usefulness of these materials has become increasingly evident [1]. Preparation of stable colloidal monoclinic zirconia suspensions and their use as ceramic slurries for the fabrication of nanoscale ceramic materials are described. The concentration dependence of the colloidal zirconia particle distribution was investigated by small-angle X-ray scattering (SAXS).
2. Experimental The precursor of colloidal zirconia was a zirconium oxyacetate previously described [2]. Colloidal zirconia was prepared by hydrothermal treatments of the zirconium oxyacetate solutions in an autoclave system of 600 cm 3 volume at temperatures from 150 to 270°C. Hydrolysis of
zirconium oxyacetate has been shown to be incomplete during hydrothermal treatment. The amount of unreacted acetate of the as-obtained colloidal zirconia was determined by thermogravimetry and the hydrolysed molar fraction, a, of zirconium oxyacetate was deduced. Colloidal suspensions were cast in P T F E plates and films were prepared by slow evaporation of the solvent. Small-angle X-ray scattering data were obtained with a slit laboratory camera using Cu Ko~ 1 radiation provided with a double channel cut germanium monochromator. The detector was a position sensitive proportional counter with an effective length of 55 mm and a sample to detector distance of 500 ram. The scattering vector H = 4"rrA- 1 sin 0, where 0 is the Bragg angle and A the X-ray wavelength, was ranging from 0.06 to 2 nm-~. Experimental results were corrected for parasitic scattering and normalised to equivalent sample thickness, intensity and counter efficiency. Colloidal zirconia particles and their thermal evolution were studied with scanning electron microscopy (SEM) and transmission electron microscopy (TEM) to evaluate particle size and microstructure, X-ray diffraction (XRD) and electron diffraction, respectively, to examine the films and to identify crystallinity of individual particles. Shrinkage to 1300°C was measured directly from the thickness of the films in a vertical
0022-3093/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
H. Vesteghem et al. / Colloidal monoclinic zirconia
504
dilatometer with alumina as a reference at a heating rate of 3°C m i n - i .
3. Preparation and characterisation of colloidal zirconia suspensions Precipitation of colloidal zirconia is achieved by two-step hydrolysis of the zirconium oxyacetate precursor. Dissolution of the precursor in water, at room temperature, produces a homogeneous system according to the reaction [2] ZrO1.35(OAc) 1.30, AcOHcryst.+ H 2 0 --> [ZrO1.35(Oac)1.30] aq.+ a c O H a q : Hydrolysis of the acetate ligands, which leads to zirconium oxide formation, is obtained by heating the zirconium oxyacetate solution to 270°C. This reaction can be represented as [ZrOt.35(Oac)1.30] aq.+ H 2 0 --* ZrO2cryst + AcOHaq.. Figure 1 shows the plot of hydrolysed fraction, a, against temperature. It illustrates that the hydrolysis of the acetate groups according to the latter reaction begins suddenly. Since the solubility of zirconia in the hydrothermal conditions used in this work is supposed to be very low, we conclude that nucleation occurs in a very short time interval. Consequently, the main requirement for monodispersed colloidal suspension, a single burst of nucleation, is met [3]. Figure 2 shows the T E M micrograph of the colloidal zirconia particles. Lattice imaging and electron diffraction pattern characterize single crystals of monoclinic ZrO 2. This result is verified by X R D measurements (fig. 3). The mean crystal size as determined by the Scherrer relation is 2R = 11 nm, in good agreement with the size evaluated from TEM. Colloidal zirconia suspensions were examined by the SAXS technique. The scattering curves of the as-obtained suspension with a 20 wt% concentration (5.1 vol.%) show a single broad peak which suggests that the zirconia particles are distributed in an ordered manner [4,5]. The interparticle interference effect can be removed from
0,8
z 0
to< re
0,6
LI-
a LU
¢/3 0,4
O re tm >32 0,2
0
1 O0
A
• I 150
--0 I 200
I 250
300
TEMPERATURE, °C
Fig. 1. Hydrolysed fraction, ~, of zirconium oxyacetate as a function of temperature for a 1 min (o) and a 9 h (A) hydrothermal treatment. the SAXS curve by decreasing the concentration to 0.4 wt%. In this case, the scattering intensity is proportional to single particle scattering and a
2 0 nm Fig. 2. T E M m i c r o g r a p h of the colloidal z i r c o n i a particles.
505
H. Vesteghem et a L / Colloidal monocfinic zirconia
Guinier analysis can be applied to the small angle region. A radius of gyration, Rg of 9 nm was measured and, using the relation R 2 = ~Rg 5 2 for spherical particles whose radius is R, the size of the colloidal particles was found to be 2 R - - 2 4 rim. The Log I ( H ) versus Log H plot showed slight departure from the Porod law. A power law I ( H ) c ~ H -D was clearly distinguished but the D value was 3.6 instead of 4. The results of the SAXS, X R D and T E M studies can be interpreted in the following way. We can describe colloidal zirconia particles as aggregates (2R = 24 rim) of a few smaller crystallites of monoclinic ZrO 2 (2R = 11 nm). In addition, we can assume that the crystallites in a colloidal particle are cemented together by the amorphous zirconium oxyacetate which has not reacted during hydrolysis. This assumption fully agrees with the measured D value of 3.6 which characterises a rough colloid [6]. Therefore, it is worth noting that remaining acetate groups are supposed to cover the colloidal particle and appear to work as a protective agent against coarsening. The as-prepared col-
200.000
Volume fraction a:0.051 b:0.092 c:0.20 d'0.28 e:0.40 f:film
150.000
O9 Z 100,000 LU I-Z
50.000 -
:: / C :/ / /."
_ d / ...~."/./ f
e' 0 0
0,2
0,4
0,6
0,8
H (nm "1)
Fig. 4. Concentration dependence of the SAXS curves of the colloidal zirconia suspensions.
I N T E N S I T Y (A.U.)
loidal suspensions are stable with respect to coarsening. Neither aggregation nor coalescence of the particle occurred in a period of three years.
4. Film formation and sintering
25
30
35 ANGLE (2e)
Fig. 3. T e m p e r a t u r e e v o l u t i o n of the X R D p a t t e r n s of colloidal zirconia.
Since an interparticle interference effect was observed in the SAXS experiment, the colloidal particles are not considered to be distributed randomly. However, because of the lack of a second-order peak, the particles form a highly distorted array in the suspension. Matsuoka et al. [5] demonstrated that the position of the firstorder peak is not affected by the distortion and can serve to evaluate the nearest-neighbour interparticle distance, d, using the Bragg equation. Figure 4 shows the concentration dependence of the scattering curve of colloidal zirconia suspensions. As expected, the peak position shifted
H. Vesteghem et al. / Colloidal rnonoclinic zirconia
506
-51
0,5
.0 •e-i
03
E //I~
E
-r" 0,2 n" O
.•.'/• ...'"
uJ > (.9
o~
•.••'o
•
..••""
5
mz ~" 10 'IO3 rr < IJ.l Z
•
z LU 0,1
,--I 15 O'3
20 0,05 I
I
0,03
I
0,05
I
I
0,1 0,2 0,3 V O L U M E FRACTION
I
__
o,5
Fig. 5. L o g - L o g plot of the position of the SAXS peak versus the volume fraction. T h e dashed line is the theoretical curve for an fcc a r r a n g e m e n t of 24 n m particles•
25
0
200
400
600
800
1,000
1.200
1.400
T E M P E R A T U R E , °C
Fig. 7. Densification curve for a colloidal zirconia film. 500.000
f
Temperature a:25°C b:400°C c:600°C d:800°C e:900°C f: 1000°C
\ i
400.000
to higher scattering vectors H, with increasing concentration. Figure 5 illustrates the relationship between the peak position, //max, and the
300.000
I,
z p.z
f
i I.
el
ii
200,000
'
d
i\
i'i,
!
100.000,
\ \,, '.~:)~......
....................."-..:"-'.L ............... 0
~ ~ = = ~ - - _ 0,1
0,2
0,3
0,4
0,5
0,6
H (nm -1)
Fig. 6. T e m p e r a t u r e evolution of the SAXS curves of colloidal zirconia films.
Fig. 8. SEM micrograph of the top surface of a monoclinic zirconia film fired in air at 1100°C for 1 h. (Bar = 100 nm.)
H. Vesteghem et al. / Colloidal monoclinic zirconia
concentration (volume fraction, q~). Assuming a continuous distribution array and a constant particle size, a linear regime should be obtained with a slope of 1 / 3 as represented in fig. 5 for an fcc array and a particle size of 24 nm. We observe that the experimental points fit this theoretical behaviour when the volume fraction of the suspension increases. Moreover, the position of the interference p e a k for the film sample leads to an interparticle distance of 24 nm which is the same as the colloidal particle diameter (2R = 24 nm). We conclude that no aggregation occurs during the increase in the volume fraction of the suspension and a nearly perfect compact packing of the initial particles is obtained. Coarsening of the zirconia particles during thermal treatment was evidenced by SAXS study. The particle size deduced from the position of the interference p e a k (fig. 6) increases markedly above 500°C. As expected [2], the same behaviour was observed for the crystallite size measured from broadening of X R D peaks (fig. 3). However, for the same temperature the crystallites were always found to be smaller than the particles; for example, 22 ram and 58 nm, respectively, at 800°C. Figure 7 shows the densification behaviour of a zirconia film sample p r e p a r e d by drying the colloidal suspension. It is shown that, first, the remaining acetate groups are removed between 250 and 400°C as was confirmed by thermogravimetry and, second, the densification begins below 1000°C and is nearly complete when the martensitic transforma-
507
tion M-ZrO2--* T - Z r O 2 occurs. Figure 8 illustrates the ability of a colloidal monoclinic zirconia film to densify completely at 1100°C and to give a regular nanoscale microstructure.
5. Conclusion
Small-angle X-ray scattering measurements demonstrate the stability of the colloidal monoclinic zirconia suspensions p r e p a r e d by thermohydrolysis of a zirconium oxyacetate precursor. Very efficient packing of initial colloidal particles was observed in green films obtained by evaporation of the solvent and zirconia materials with strongly decreased sintering t e m p e r a t u r e and consequently small grain size were fabricated.
References
[1] A.J. Burggraff, K. Keizer and B.A. Van Hassel, Solid State Ionics 32&33 (1989) 771. [2] T. Merle-Mejean, T. Jaccon and H. Vesteghem, in: Ceramic Powder Science III, ed. G.L. Messing, S. Hirano and H. Hausner (American Ceramic Society, Westerville, OH, 1990) p. 41. [3] T. Sugimoto, Adv. Colloid Interf. Sci. 28 (1987) 65. [4] J.D.F. Ramsay, Chem. Soc. Rev. 15 (1986) 335. [5] H. Matsuoka, H. Murai and N. Ise, Phys. Rev. B37 (1988) 1368. [6] D.W. Schaefer and K.D. Keefer, in: Better Ceramics Through Chemistry II, ed. C.J. Brinker, D.E. Clark and D. Ulrich (Materials Research Society, Pittsburgh, PA 1986) p. 277.