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Size effect on the Mie optical absorption of small sodium particles in sodium azide NaN3
Vol. 14, pp. 407—410, 1974.
Solid State Communications,
Pergamon Press.
Printed in Great Britain
SIZE EFFECT ON THE MIE OPTICAL ABSORPTION OF SMALL SODIUM PARTICLES IN SODIUM AZIDE NaN3 M.A. Smithard Laboratoire de Physique Exp~rimenta1e,*Ecole Polytechnique Fédérale de Lausanne (EPFL), 33, avenue de Cour, Lausanne, Switzerland (Received 1 October 1973 by F. Bassani)
The Mie optical absorption spectra of colloidal sodium particles in sodium azide NaN3 has been measured and compared with calculated spectra. The small particles were formed by X irradiating single crystals of the azide and then heating them at 280°C. The peak was observed to occur at about 5200 A compared to the calculated position of 5020 A. By comparing the measured and calculated spectra, the approximate particle size was deduced as a function of the heating time. For a given anneal time the size was found to be approximately independent of the irradiation dose, whilst the concentration of particles increased rapidly with increasing dose. After an anneal of 2 mm the particle size was between 10 and 20 A, increasing to about 100 A after 12 mm and about 1000 A after 30 mm. 1 that metal azides can be thermally IT IS WELL known decomposed to give the metal and nitrogen, and that this decomposition can be facilitated by previous itradiation of the sample. The metal precipitates in the form of small colloidal particles inside the azide lattice. With continued heating the decomposition increases rapidly until eventually the sample disintegrates. This disintegration can be explosive, especially in the heavy metal azides. The work reported here is a study of the Mie optical absorption or colouration produced by small colloidal sodium particles produced in partly decomposed sodium azide NaN 3 2 showed that a dispersion of small metal partides Mie in an insulating medium produces a characteristic absorption of light, causing the composite material to appear coloured. This absorption is due to an interaction between the plasma resonance of the conduction electrons in the metal particles and the oscillating electric vector of the incident light. For instance, Miller3 calculated an approximate value for the position
of the absorption peak due to sodium particles in sodium azide to be 4580 A. The peak was experimentally found to occur at 5200 A causing the azide to become red or violet in colour. More detailed calculations have been presented in the literature for the Optical absorption produced by silver particles in glass4’5 and for sodium particles in sodium chloride.5’6 These calculations were used to interpret measured spectra. For instance the size and concentration of the particles as a function of precipitation time were deduced. We have used the same model and the same values for the bulk optical constants of sodium, to azide, andthe used the results this calculation to sodium intercalculate absorption forofsodium particles in pret spectra observed in single crystal samples. The refractive index of sodium azide was taken as 1 .38.
-
*
In Fig. 1 the half height width of the calculated absorption spectrum is shown as a function of the particle size. The width is very size dependent and passes through a minimum for particles of about 250 A diameter. The increase in width for smaller particles may be thought of as being due to scattering of the metal conduction electrons by the particle surface.
This work was supported by the Swiss National Fund for Scientific Research No. 2.666.72. 407
408
MIE OPTICAL ABSORPTION OF SODIUM AZIDE NaN3 TIilJ
3000
‘I
I
6500
it,,1
IIIIiJ
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Vol. 14, No.5 I
IIIII1J
—
6000
2000 0<
10000
—
~5500 5000
i~I~III~IIIflIJ
10
100
1000
0
d(A) FIG. 1. The calculated width AX of the optical absorption peak shown as a function of particle diameter. The width is seen to pass through a minimum value for particles of about 250 A diameter. The increase in width for larger particles comes out of the Mie theory directly. The increase for smaller particles is due to scattering of the metal particle conduction electrons by the particle surface. Figure 2 shows the calculated peak position of the absorption to be 5020 A for the smallest particles and shows that the peak begins to move to longer wavelength for particles greater than about 100 A diameter. 46 In the found earlier that workthe onmeasured silver andpeak sodium particles it was width did pass through a minimum as the particle size increased but that the value of the minimum width was always a little larger than that calculated. This was attributed to the existence of a spread in the particle sizes present. The peak position for the smallest particles was found to occur at longer wavelength than the calculated value but approached the calculated value as the particle size increased to about 100 A. This difference was attributed to an insufficiently good theoretical model. For sodium particles in sodium azide, the same sort of experimental result should be expected, with both the width and the position of the absorption peak decreasing, passing through a minimum and then increasing again as the particle size increases, Single crystals of the azide were prepared using the precipitant infusion method of Richter and Haase,7 starting with ‘Merck’ grade powder. The samples were removed from the water—methanol solution after a maximum precipitation time of two weeks and were typically leaf.like plates of surface area 1 cm2 and of
I
—
unit 10
i
I
lull
100
I I
liii
1000
d (A) FIG. 2. The calculated position X~,of the absorption peak as a function of particle diameter. Previous work on silver and sodium colloids showed that in fact the measured peak occured at longer wavelength than calculated, to give the sort of size dependence represented approximately by the broken line. thickness 0.2—0.5 mm. The purity was expected to be approximately that measured by Richter and Haase, namely 99 .96%. Sodium azide has a hexagonal (or rhombohedral) structure at room temperature with the three nitrogen atoms lying along the C axis. birefringent. Samples which were examined withIta is polarising microscope were found to be single crystals with the C axis perpendicular to the large surface. The crystals were X irradiated at about 8 cm from a tungsten tube operating at 40 kV and 30 mA. The total dose was varied by varying the length of exposure. At the end of the exposure the samples were slightly yellow in colour. The origin of this colour was not known. It was not thought to be associated with colloidal centres. After irradiation the crystals were annealed at 280°C when they became red, violet or blue in colour. This colouration was not completely evenly distributed through the thickness of the sample, but tended to be more concentrated towards the sample surface. The total intensity of the colour across a sample was approximately uniform even if the sample thickness was not uniform. The optical absorption spectra of the samples were measured at intervals during the annealing process. A wide absorption band was observed. The parameters of this band were found to depend on the irradiation dose and the anneal time. The width and the position of the band were measured as functions
Vol. 14, No.5
2400 2000
MIE OPTICAL ABSORPTION OF SODIUM AZIDE NaN3
I ~
~°
again annealing time. The minimum value measured for the peak position was 5200 A which is quite close
I A.
l~0,
to the calculated value of 5020 A. This comportment
~,
1600 1200
A
~‘
800
-
particles the identified thesize band of which as coming increased from colloidal with increasing sodium annealing. By comparing the curves of Figs. 3 and 4
-
with the calculated curves in Figs. 1 and 2 the particle size of the colloid as a function of anneal time could be estimated. The resulting curve is shown in Fig. 3
28
that the minimum width of the absorption was about 1100 A which is much greater than the calculated
~
I
400 0
4
6
12
16 20
24
t(min)
-
FIG. 3. The measured width ~X of the optical absorp. tion as a function of anneal time at 280°C. As the anneal progressed the width decreased, passed through a minimum then increased again, suggesting a progressive increase in the average particle size. The symbols a Lu. x ci represent irradiation doses of: 10, 15, 30,60, 180 mm respectively. The pomts (except per haps for the 180 mm dose) all lie on approximately the same curve, indicating that the particle size was approximately independent of the X-ray dose received by the sample. The results shown are for about three samples for each dose.
value of 300 A (the mmimum width measured for any sample was about 800 A). This discrepancy was attributed to a large range of particle sizes or perhaps to slightly non spherical particles. It introduced an ambiguity in the deduction of the particle sizes and this ambiguity is reflected in the rather large error bars in Fig. 5. Nevertheless the results show that the average -________________________ 1000 I I I ~ : ~ —
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-
100 I
o
5600
I
I
I
~5200 5000
/ -
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o~5400
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•
~..‘,.
•~
~
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-
V
/
10
°
—
I
I
0481216202428 t(min)
-
FIG - 4. The measured position of the absorption X~,
0
as a function of the anneal time at 280 C.
4
8
12
16 20
24 28
(mm) FIG 5. The deduced particle diameter as a function of the anneal time at 280°C. The points marked with circles were obtained from the width of the optical absorption and the crosses from its position. -
of the dose and anneal time for a large number of samples. Some typical results are shown in Figs. 3 and 4. The mtensity of the absorption was initially zero, then increased rapidly with annealing until it eventually became too intense to measure. Hence for a given dose there was a range of anneal times during which the absorption peak could be measured; for shorter or longer anneals, it was either too weak or too strong to measure. This range was extended somewhat by thinning the samples in the later stages of the anneal. Samples which received higher doses of irradiation developed very intense absorption peaks which were strong enough to measure after only short anneal times. From Figs. 3 and 4 ii can be seen that the width and position of the peak passed through a minimum value then increased -
-
.
.
.
-
particle size increased from between 11 and 17 A after 2 min of annealing, to about 100 A after 12 min annealing and then to approximately 1000 A after 30 mm annealing. This interpretation was confirmed by the fact that the samples scattered light only in the later stages of annealing (only particles greater than a few hundred A diameter give appreciable light scattering). Furthermore if the measured peak position is plotted against the particle size as deduced from Fig. 5, then the form of the resulting curve is very similar to the corresponding curves obtained earlier for silver and
410
MIE OPTICAL ABSORPTION OF SODIUM AZIDE NaN3
sodium particles, The concentration of metal particles present in the samples was deduced from the area under the op. tical absorption peak. The value varied greatly according to the dose and anneal to which the sample had been submitted,but for instance a sample irradiated for one hour and annealed for 4~min contained a volume fraction of metal of 6 i0~,in other words 3. Forthe an sample anneal contained 1.6 corresponding 1018 sodium atoms/cm of 12 mist the figures were 5 i04 and 1.3 iO’9. The type of experiments described here may give some clues as to the mechanism of particle formation and growth in this material. For instance it was noted that the colloid concentration varied more rapidly with X-ray dose than would be expected from a simple proportionality. On the other hand, as can be seen in Figs. 3 and 4, the anneal curves for samples given different X-ray doses were more or less superimposed on each other. This suggests the approximation which we have used in interpreting the results, namely that the particle size was approximately independent of the -
.
.
-
Vol. 14, No. 5
irradiation dose and depended only on the anneal time and temperature. For doses greater than about one hour this approximation was not valid, the partide size seemed to increase more rapidly with annealing. Attempts to correlate the deduced particle size with the measured concentration suggested that some agglomeration of the particles occured during the growth process. The evolution of the optical absorption was alsoand studied thebetemperatures 260, 300 and 320°C foundatto very temperature dependent. For instance at these temperatures the times taken to reach a particle size of about 100 A were respectively 40, 4 and less than 1 min. High resolution electron microscopy measurements were carried out on some samples to try and observe the sodium particles directly. Suitably thin samples were prepared but the microstructure observed was too complicated to interpret. -
Acknowledgements The author would like to thank Dr W. Garrett of the Explosive Research Laboratory, Picatinny Arsenal, for helpful communications concerning the preparation of single crystal samples. —
1.
REFERENCES See for example YOFFE A.D., Developments in Inorganic Nitrogen Chemisrry.(edited by COLBURN C.B.) Elsevier, New York (1966).
2.
MIE G.,Ann. Phys. 25, 377 (1908).
3.
MILLER B.S.,J. Chem. Phys. 33,3,889 (1960).
4. 5.
SMITHARD M.A., Solid State Commun. 13, 2, 153 (1973). SMITHARD M.A. and TRAN M.Q.,Proc. Second Cairo Solid State Conference (1973).
6.
SMITHARD M.A., TRAN M.Q., He/v. Phys. Acta (in press) (1974).
7.
RICHTER T.A. and HAASE 0., Mat. Res. Bull. 5, 511(1970).
L’absorption optique (théorie de Mie) due a des petits cristaux de sodium dans du NaN 3 a été mesurée et comparée aux previsions theoriques. Les petits cristaux ont été formés dans du NaN3 1,par une irradiation aux rayons X suivie d’un recuit a Ia temperature de 280 C. La position du pic a été mesurée a 5200 A et calculée a 5020 A. La taille des petits cristaux en fonction de la durée de recuit a été déduite par des comparaisons entre les spectres mesurés et calculés. La taile ëtait approximativement indépendante de la dose pour un temps de recuit donné, cependant Ia concentration des cristaux augmentait fortement avec Ia dose. La taille des cristaux était entre 10 Ct 20 A après un recuit de 2 min, passant a 100 A après 12 min et a 1000 A après 30 mm’
Solid State Communications,
Pergamon Press.
Printed in Great Britain
SIZE EFFECT ON THE MIE OPTICAL ABSORPTION OF SMALL SODIUM PARTICLES IN SODIUM AZIDE NaN3 M.A. Smithard Laboratoire de Physique Exp~rimenta1e,*Ecole Polytechnique Fédérale de Lausanne (EPFL), 33, avenue de Cour, Lausanne, Switzerland (Received 1 October 1973 by F. Bassani)
The Mie optical absorption spectra of colloidal sodium particles in sodium azide NaN3 has been measured and compared with calculated spectra. The small particles were formed by X irradiating single crystals of the azide and then heating them at 280°C. The peak was observed to occur at about 5200 A compared to the calculated position of 5020 A. By comparing the measured and calculated spectra, the approximate particle size was deduced as a function of the heating time. For a given anneal time the size was found to be approximately independent of the irradiation dose, whilst the concentration of particles increased rapidly with increasing dose. After an anneal of 2 mm the particle size was between 10 and 20 A, increasing to about 100 A after 12 mm and about 1000 A after 30 mm. 1 that metal azides can be thermally IT IS WELL known decomposed to give the metal and nitrogen, and that this decomposition can be facilitated by previous itradiation of the sample. The metal precipitates in the form of small colloidal particles inside the azide lattice. With continued heating the decomposition increases rapidly until eventually the sample disintegrates. This disintegration can be explosive, especially in the heavy metal azides. The work reported here is a study of the Mie optical absorption or colouration produced by small colloidal sodium particles produced in partly decomposed sodium azide NaN 3 2 showed that a dispersion of small metal partides Mie in an insulating medium produces a characteristic absorption of light, causing the composite material to appear coloured. This absorption is due to an interaction between the plasma resonance of the conduction electrons in the metal particles and the oscillating electric vector of the incident light. For instance, Miller3 calculated an approximate value for the position
of the absorption peak due to sodium particles in sodium azide to be 4580 A. The peak was experimentally found to occur at 5200 A causing the azide to become red or violet in colour. More detailed calculations have been presented in the literature for the Optical absorption produced by silver particles in glass4’5 and for sodium particles in sodium chloride.5’6 These calculations were used to interpret measured spectra. For instance the size and concentration of the particles as a function of precipitation time were deduced. We have used the same model and the same values for the bulk optical constants of sodium, to azide, andthe used the results this calculation to sodium intercalculate absorption forofsodium particles in pret spectra observed in single crystal samples. The refractive index of sodium azide was taken as 1 .38.
-
*
In Fig. 1 the half height width of the calculated absorption spectrum is shown as a function of the particle size. The width is very size dependent and passes through a minimum for particles of about 250 A diameter. The increase in width for smaller particles may be thought of as being due to scattering of the metal conduction electrons by the particle surface.
This work was supported by the Swiss National Fund for Scientific Research No. 2.666.72. 407
408
MIE OPTICAL ABSORPTION OF SODIUM AZIDE NaN3 TIilJ
3000
‘I
I
6500
it,,1
IIIIiJ
I
Vol. 14, No.5 I
IIIII1J
—
6000
2000 0<
10000
—
~5500 5000
i~I~III~IIIflIJ
10
100
1000
0
d(A) FIG. 1. The calculated width AX of the optical absorption peak shown as a function of particle diameter. The width is seen to pass through a minimum value for particles of about 250 A diameter. The increase in width for larger particles comes out of the Mie theory directly. The increase for smaller particles is due to scattering of the metal particle conduction electrons by the particle surface. Figure 2 shows the calculated peak position of the absorption to be 5020 A for the smallest particles and shows that the peak begins to move to longer wavelength for particles greater than about 100 A diameter. 46 In the found earlier that workthe onmeasured silver andpeak sodium particles it was width did pass through a minimum as the particle size increased but that the value of the minimum width was always a little larger than that calculated. This was attributed to the existence of a spread in the particle sizes present. The peak position for the smallest particles was found to occur at longer wavelength than the calculated value but approached the calculated value as the particle size increased to about 100 A. This difference was attributed to an insufficiently good theoretical model. For sodium particles in sodium azide, the same sort of experimental result should be expected, with both the width and the position of the absorption peak decreasing, passing through a minimum and then increasing again as the particle size increases, Single crystals of the azide were prepared using the precipitant infusion method of Richter and Haase,7 starting with ‘Merck’ grade powder. The samples were removed from the water—methanol solution after a maximum precipitation time of two weeks and were typically leaf.like plates of surface area 1 cm2 and of
I
—
unit 10
i
I
lull
100
I I
liii
1000
d (A) FIG. 2. The calculated position X~,of the absorption peak as a function of particle diameter. Previous work on silver and sodium colloids showed that in fact the measured peak occured at longer wavelength than calculated, to give the sort of size dependence represented approximately by the broken line. thickness 0.2—0.5 mm. The purity was expected to be approximately that measured by Richter and Haase, namely 99 .96%. Sodium azide has a hexagonal (or rhombohedral) structure at room temperature with the three nitrogen atoms lying along the C axis. birefringent. Samples which were examined withIta is polarising microscope were found to be single crystals with the C axis perpendicular to the large surface. The crystals were X irradiated at about 8 cm from a tungsten tube operating at 40 kV and 30 mA. The total dose was varied by varying the length of exposure. At the end of the exposure the samples were slightly yellow in colour. The origin of this colour was not known. It was not thought to be associated with colloidal centres. After irradiation the crystals were annealed at 280°C when they became red, violet or blue in colour. This colouration was not completely evenly distributed through the thickness of the sample, but tended to be more concentrated towards the sample surface. The total intensity of the colour across a sample was approximately uniform even if the sample thickness was not uniform. The optical absorption spectra of the samples were measured at intervals during the annealing process. A wide absorption band was observed. The parameters of this band were found to depend on the irradiation dose and the anneal time. The width and the position of the band were measured as functions
Vol. 14, No.5
2400 2000
MIE OPTICAL ABSORPTION OF SODIUM AZIDE NaN3
I ~
~°
again annealing time. The minimum value measured for the peak position was 5200 A which is quite close
I A.
l~0,
to the calculated value of 5020 A. This comportment
~,
1600 1200
A
~‘
800
-
particles the identified thesize band of which as coming increased from colloidal with increasing sodium annealing. By comparing the curves of Figs. 3 and 4
-
with the calculated curves in Figs. 1 and 2 the particle size of the colloid as a function of anneal time could be estimated. The resulting curve is shown in Fig. 3
28
that the minimum width of the absorption was about 1100 A which is much greater than the calculated
~
I
400 0
4
6
12
16 20
24
t(min)
-
FIG. 3. The measured width ~X of the optical absorp. tion as a function of anneal time at 280°C. As the anneal progressed the width decreased, passed through a minimum then increased again, suggesting a progressive increase in the average particle size. The symbols a Lu. x ci represent irradiation doses of: 10, 15, 30,60, 180 mm respectively. The pomts (except per haps for the 180 mm dose) all lie on approximately the same curve, indicating that the particle size was approximately independent of the X-ray dose received by the sample. The results shown are for about three samples for each dose.
value of 300 A (the mmimum width measured for any sample was about 800 A). This discrepancy was attributed to a large range of particle sizes or perhaps to slightly non spherical particles. It introduced an ambiguity in the deduction of the particle sizes and this ambiguity is reflected in the rather large error bars in Fig. 5. Nevertheless the results show that the average -________________________ 1000 I I I ~ : ~ —
-
-
100 I
o
5600
I
I
I
~5200 5000
/ -
:
00’
o~5400
409
AO
•
~..‘,.
•~
~
A
-
V
/
10
°
—
I
I
0481216202428 t(min)
-
FIG - 4. The measured position of the absorption X~,
0
as a function of the anneal time at 280 C.
4
8
12
16 20
24 28
(mm) FIG 5. The deduced particle diameter as a function of the anneal time at 280°C. The points marked with circles were obtained from the width of the optical absorption and the crosses from its position. -
of the dose and anneal time for a large number of samples. Some typical results are shown in Figs. 3 and 4. The mtensity of the absorption was initially zero, then increased rapidly with annealing until it eventually became too intense to measure. Hence for a given dose there was a range of anneal times during which the absorption peak could be measured; for shorter or longer anneals, it was either too weak or too strong to measure. This range was extended somewhat by thinning the samples in the later stages of the anneal. Samples which received higher doses of irradiation developed very intense absorption peaks which were strong enough to measure after only short anneal times. From Figs. 3 and 4 ii can be seen that the width and position of the peak passed through a minimum value then increased -
-
.
.
.
-
particle size increased from between 11 and 17 A after 2 min of annealing, to about 100 A after 12 min annealing and then to approximately 1000 A after 30 mm annealing. This interpretation was confirmed by the fact that the samples scattered light only in the later stages of annealing (only particles greater than a few hundred A diameter give appreciable light scattering). Furthermore if the measured peak position is plotted against the particle size as deduced from Fig. 5, then the form of the resulting curve is very similar to the corresponding curves obtained earlier for silver and
410
MIE OPTICAL ABSORPTION OF SODIUM AZIDE NaN3
sodium particles, The concentration of metal particles present in the samples was deduced from the area under the op. tical absorption peak. The value varied greatly according to the dose and anneal to which the sample had been submitted,but for instance a sample irradiated for one hour and annealed for 4~min contained a volume fraction of metal of 6 i0~,in other words 3. Forthe an sample anneal contained 1.6 corresponding 1018 sodium atoms/cm of 12 mist the figures were 5 i04 and 1.3 iO’9. The type of experiments described here may give some clues as to the mechanism of particle formation and growth in this material. For instance it was noted that the colloid concentration varied more rapidly with X-ray dose than would be expected from a simple proportionality. On the other hand, as can be seen in Figs. 3 and 4, the anneal curves for samples given different X-ray doses were more or less superimposed on each other. This suggests the approximation which we have used in interpreting the results, namely that the particle size was approximately independent of the -
.
.
-
Vol. 14, No. 5
irradiation dose and depended only on the anneal time and temperature. For doses greater than about one hour this approximation was not valid, the partide size seemed to increase more rapidly with annealing. Attempts to correlate the deduced particle size with the measured concentration suggested that some agglomeration of the particles occured during the growth process. The evolution of the optical absorption was alsoand studied thebetemperatures 260, 300 and 320°C foundatto very temperature dependent. For instance at these temperatures the times taken to reach a particle size of about 100 A were respectively 40, 4 and less than 1 min. High resolution electron microscopy measurements were carried out on some samples to try and observe the sodium particles directly. Suitably thin samples were prepared but the microstructure observed was too complicated to interpret. -
Acknowledgements The author would like to thank Dr W. Garrett of the Explosive Research Laboratory, Picatinny Arsenal, for helpful communications concerning the preparation of single crystal samples. —
1.
REFERENCES See for example YOFFE A.D., Developments in Inorganic Nitrogen Chemisrry.(edited by COLBURN C.B.) Elsevier, New York (1966).
2.
MIE G.,Ann. Phys. 25, 377 (1908).
3.
MILLER B.S.,J. Chem. Phys. 33,3,889 (1960).
4. 5.
SMITHARD M.A., Solid State Commun. 13, 2, 153 (1973). SMITHARD M.A. and TRAN M.Q.,Proc. Second Cairo Solid State Conference (1973).
6.
SMITHARD M.A., TRAN M.Q., He/v. Phys. Acta (in press) (1974).
7.
RICHTER T.A. and HAASE 0., Mat. Res. Bull. 5, 511(1970).
L’absorption optique (théorie de Mie) due a des petits cristaux de sodium dans du NaN 3 a été mesurée et comparée aux previsions theoriques. Les petits cristaux ont été formés dans du NaN3 1,par une irradiation aux rayons X suivie d’un recuit a Ia temperature de 280 C. La position du pic a été mesurée a 5200 A et calculée a 5020 A. La taille des petits cristaux en fonction de la durée de recuit a été déduite par des comparaisons entre les spectres mesurés et calculés. La taile ëtait approximativement indépendante de la dose pour un temps de recuit donné, cependant Ia concentration des cristaux augmentait fortement avec Ia dose. La taille des cristaux était entre 10 Ct 20 A après un recuit de 2 min, passant a 100 A après 12 min et a 1000 A après 30 mm’