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The structure of colour centers in photochromic glass
Journal of Non-Crystalline Solids 34 (1979) 393-403 © North-Holland Publishing Company
THE STRUCTURE O F COLOUR CENTERS IN PHOTOCHROMIC GLASS A.A. ANIKIN and V.K. MALINOVSKY Institute o f Automation and Electrometry, Novosibirsk 90, USSR 630090
Received 21 November 1978 Revised manuscript received 10 April 1979
An ellipsoidal model of colour centers in photochromic glass was proposed to explain an additional absorption spectrum. Absorption spectra of small (R K 100 A) silver particles involving oblong and oblate ellipsoids of rotation have been analysed. The splitting of the absorption spectrum of the small silver particles with non-spherical form resulted in an absorption spectrum different from that for spherical particles. Calculation of the absorption spectra of the system of oblate ellipsoids with considerable dispersion in eccentricity and of about 20 A in size was in good agreement with experiment. Absorption spectra of the system of oblong ellipsoids differed significantly from experimental findings, indicating that oblong particles were absent. To verify the basic theory of the colour center model, advanced experiments have been carried out on the bleaching of photochromic glass by monochromatic polarized light. The so called photo-adaptation effect has been found, that is, the absorption decreased faster at the wavelength of the bleaching light. The photo-adaptation spectral width indicated that the particle size was nearly 20 A. The ratio of changing absorption for perpendicular and parallel orientations of bleaching and reading polarization vectors was about 0.7 in the longwave visable range, indicating that the colour centers were substantially anisotropic. In the thermal recovery of photochromic glass the shortwave and longwave absorptions were bleached faster, indicating the lower stability of the strong oblate particles, which specifies absorption in those parts of the spectrum.
1. Introduction Photochromic properties o f glasses are due to the minute particles of silver halide which are suspended in the host glass. Photochromic glass darkens when exposed to ultraviolet or shortwave light. In contrast to the photolysis o f silver halide crystals in photographic emulsion, where the halogen diffuses away from the particle during the development process, in photochromic glass the halogen is captured within the glass matrix. It is therefore available for recombination with the silver. A sample is bleached either thermally or b y red light. Figure 1 shows the typical additional absorption spectrum (AAS) of AgC1 photochromic glass. The form o f the AAS is similar to those o f exposed silver halide crystals. The absorption spectrum o f spherical silver particles suspended in the silver halide indicates that particles o f 5 0 0 - 6 0 0 A in size should explain the absorption 393
394
A.A. Anikin, V.K. Malinovsky / Colour centers in photochromic glass
0.25. 020
al$ 010 0.05 O. qoo
5oo
600
700 /],t2
Fig. 1. The typical absorption spectrum of AgHal photochromic glass.
spectrum of the exposed AgHal [1]. Meiklar [2] directly acknowledged that the maximum in the absorption spectrum is related to spherical silver particles with the proper size. Electron microscopic examination of photochromic glass has shown the average size of AgHal particles is in the range of 50-300 A [3]. Thus, it excludes formation of large silver particles which would explain the form of AAS. It has been shown in this paper that the features of AAS can be explained quite well within the bounds of the model which is based on the assumption of the nonsphericity of the silver particles. Numerical computation of absorption spectra in oblate ellipsoids of revolution which have considerable dispersion in eccentricity and size of about 20,8, are in good agreement with experimental AAS.
2. The model of colour centres
Let us suppose that along with circular silver particles there are ellipsoidal ones in photochromic glasses. For small particles (R ~ 100 A) the absorption constant K can be calculated using Mie's Theory [4], which gives the following simple expression when the field vector is in line with one of the ellipsoid axis: K = (2rre2/~,)/[(1 + (el - 1)nl 2 + e~n2),
(1)
where X is the light wavelength, e 1 and e2 are the real and imaginary parts of the dielectric constant of silver (e = e 1 + ie2) and n is depolarization coefficient along the proper ellipsoid axis. Here and below the volume of the particles is equal to
A.A. Anikin, V.K. Malinovsky / Colour centers in photochromic glass
unity. For an oblate ellipsoid o f revolution with l
=
[(t//c)
2 -
395
1] 1/2.
nil = (1 + 12)(l _ arctan l)fl a is the rotation axis in line with the field vector n± = (1 - n11)/2 is the rotation axis perpendicular to field vector. For an oblong ellipsoid of revolution with l = [ 1 - (ale) 2 ] 1/2 nil = (1 - 12)(ln[(1 +/)/(1 - / ) ] - 21)/2l 3 , n± = (1 - n 0 / 2
(2) (3)
.
Optical constants of silver particles of 200 A and less in size are significantly dependent on the size. Kreibig [5] has pointed out that the effect o f the electron free path agrees better with experiments than the Kawabata-Kubo theory [6]. We have
[5]: e(~, R) = el (~o) + i(e2(eo) + (co~,V v ) / ( ~ 3 R ) ) ,
(4)
where R is the particle radius and ~ p is the plasma frequency (Wp = 1.38 X 1016 s -1 and V R is the Fermi velocity (V v = 1.4 × 108 sm s - l ) . Spectra of e 2 for the particles of various sizes calculated from eq. (4) are shown in fig. 2. Optical constants of the bulk silver have been taken from [7]. We now turn to the analysis of eq. (1). For large enough particles (R ~ 100 A) a relation el > > e2 is fulfilled. A maximum in K is achieved when the first addend
= 2/2/7/.
10
6 q
goo
zoo
,joo A , n ~
Fig. 2. Spectra o f the imaginary part o f silver dielectric constant as a function o f the particle radius R.
396
A.A. Anikin, V.K. Malinovsky / Colour centers in photochromic glass
/f.tff~ S m "t
I
f.5"
l.O'
\
0.5.
~'oo
5bo
6~o
7bo
~, ~M
Fig. 3. Absorption bands of silver ellipsoidal particles in AgCI. The ratio of larger to smaller axis is 2.5. Optical constants correspond to R = 100 A. Oblate ellipsoid of rotation: the axis of rotation is parallel with the vector of field - 2 , the axis is perpendicular -1. Oblong ellipsoid of rotation is parallel with the vector of field - 4 , the axis is perpendicular -3.
in the d e n o m i n a t o r b e c o m e s zero. F o r spherical particles nil = n± = ~ corresponding to the position o f the absorption peak at 470 n m (silver dispersion in AgC1 was taken into account). F o r an oblate ellipsoid w i t h the relation a/c = 2.5 we have nil = 0.59 and n± = 0.21. Difference in n II and n I result in the splitting o f the absorption spectrum. The ellipsoid w i t h r o t a t i o n axis parallel to the field vector will have an absorption peak
/£.10 "7
/ g=lOnm f.0
a5
I
-...< R:la~ qOff
500
6bO ~,nm
Fig. 4. Spherical silver particle absorption in AgCt. Particle size is R = 100 A and R = 10 A.
qO0
~
(c)
~
~
500
600
_
G=~5
~:1.5
G=/.5
700
A, n.m
G':t,O ~ c'=of
v ~ ~ ~ ~ ~ ¢ = 1 . 5
(a )
2"
8'
~00
.5OO
f.O r=0.5
rbO A,nra
C=I.O ~'--"'-G=O..,q
~G=
6OO
++
(a)
Fig. 6. Absorption s p e c t r u m KZ: o f the s y s t e m o f oblong silver ellipsoidal particles in AgC1. (a) - R = 100 A; (b) - R = 20 A; (c) - R = 10 A.
Fig. 5. Absorption spectrum K Z o f the s y s t e m o f oblate silver ellipsoidal particles in AgC1. (a) - R = 100 A; (b) - R = 20 A; (c) - R = 10 A.
2 ° j/
•
+t
0
2'
6
Kz.ff 8 .~m"
~O
398
A.A. Anikin, V.K. Malinovsky / Colour centers in photochromic glass
2 /L<
q
0 ~bo
5bo
660 ,~, f~m
Fig. 7. Absorption spectrum K s of the system of oblate silver ellipsoidal particles in glass. 1 R = 2 0 A , 2 - R = 1 0 A ; t r = 1.0. at 370 nm, perpendicularly oriented to 590 nm (fig. 3). It is obvious that the system consisting of ellipsoids with various ratios will have a wide absorption band. Calculation shows that the splitting of the absorption spectra is different for oblate and oblong ellipsoids (see fig. 3). A longwave peak of an oblong ellipsoid shifts towards the IR region faster than that of an oblate one. As for a shortwave peak it moves slower towards the UV region. This remark will help to make clear some features of the absorption spectra of systems of oblate and oblong ellipsoids. Decrease of the particle size is followed by decrease in the peak height, broadening of the absorption band and the slight shift of the peak towards the shortwave region. This is illustrated in fig. 4. For the system of non-interacting ellipsoids absorption may be expressed as a sum of the absorption of the separate ellipsoids, taken with the proper weight: X
Kz =f
K(a/c)f(a/c) d(a/c),
(5)
1
where f(a/c) is a distribution function, K(a/c) is an average absorption of an isotropically oriented ellipsoid. The restriction on the upper limit of integration is imposed from geometrical considerations. The parameters are the volume of a particle present and average size of a microcrystal AgHal. Introducing designations for the absorption of ellipsoids with rotation axis parallel or perpendicular to the field vector and averaging over all orientations, we have:
K(a/c) = KII/3 4- 2K.L/3.
(6)
With the (ale - 1) distribution considered to be normal: f(a/c) " exp [ - ( a / c - 1)2/2o2 ],
(7)
Spectra K s were determined through numerical integration with regard to eqs. (6) and (7). In figs. 5 - 7 spectra K z are shown for various parameters o and sizes R.
A.A. Anikin, V.K. Malinovsky /Colour centers in photochromic glass
399
3. Experimental When photochromic glass is bleached with longwave monochromatic visible radiation the so-called photo-adaptation effect must be observed, that is, the primary destruction of colour centers responsible for absorption at the given wavelength. The narrower absorption bands of separate colour centers are signs of heavier photoadaptation. Photo-adaptation of the systems of spherical particles or spherical shells [9] should not depend on whether the bleaching radiation was polarized or not. For the system of ellipsoidal particles which is isotropic in total but consists of anisotropic elements, the polarization state of the exciting light is significant. To verify up the basic theory of the colour center model, experiments have been carried out on the bleaching of photochromic glass by monochromatic polarized light. A specimen 1 mm thick was darkened to saturation point with UV radiation. An AAS was taken on a spectrophotometer CF-14. A small amount of the bleaching radiation (k = 632.8 nm) was then given and the AAS taken again. Figure 8 shows the original absorption of the darkened sample AAS and the absorption spectra after a little bleaching AASII and AAS±. Signs II or / mean that the polarization vectors of bleaching and probing lightwaves are parallel or perpendicular to each other. In the same figure the dotted line show the normalized change of spectra (AAS o -AAStl)/AAS o. The normalized change gives a more correct estimation of the destruction value of colour centers which are responsible for the absorption at the proper wavelength.
015~ 0.I0. 005 qoo
3
560
6do
zbo A,nm
Fig. 8. Experiments on bleaching by h = 632.8 nm: l - initial AAS; 2 - AAS; following a small bleaching, polarization vectors o f the bleaching and probe waves are perpendicular; 3 - the same, but polarization vectors are parallel. Dashed line corresponds (AASII - AASo)/(AAS 0 in arbitrary units. Chain dotted line corresponds the thermal recovery rate of various parts o f spectrum, in arbitrary units.
400
A.A. Anikin, V.K. Malinovsky / Colour centers in photochromic glass
3 2" 1" 0
la)
q
i~
3 2. ! o
400
S6o
660
760
A, n m
Fig. 9. Photo-adaptation curves: (a) - h = 632.8 nm; (b) - h = 700 nm; 1 - (AASII - AAS0)/ (AAStO - AASo); 1 - (AAS± - AASo)/(AASto - AASo).
It follows from fig. 8 that the maximum o f the normalized bleaching rate has shifted towards the longwave area relative to the bleaching line. The lower stability o f colour centers absorbing in the longwave region was assumed. A chain-dotted curve in fig. 8 shows the experimental ratio (AAS o - AASto)/AASo (AASto is the additional absorption spectrum after a small amount of thermal relaxation). It followed from further experiments on the thermal bleaching o f photochromic glass that the curve ( A A S o - AASto)/AASo is not the only characteristic o f thermal bleaching but that it also depends on the shape of AASo. F o r samples o f glass having an AAS maximum at 700 nm a darkening is even observed at 5 2 0 - 5 7 0 nm while shortwave and longwave o f AAS are bleached in the process o f the thermal recovery. This association with colour center form change makes it difficult to treat the experimental data. But for sufficiently long waves o f bleaching (AAS o - A A S I I , a ) by ( A A S o - AASt o) normalizing gives quite good results. Experimental curves (AASo - AASII,a_)/(AASo - AASt o) for k = 632.8 nm and k = 700 nm are presented in fig. 9.
A .A. Anikin, V.K. Malinovsky / Colour centers in photochromic glass
401
4. Discussion 4.1. Calculation based on the model
As seen from fig. 5 the increase in dispersion of ellipsoids results in the broadening of the absorption spectrum and its shift towards a longwave region. The splitring of the spectrum is displayed at first in the non-symmetry of the calculated AAS. When o increases the second maximum of AAS appears in the UV region. The maximum of AAS for photochromic glass in the UV region was discovered recently by Moriya [7]. The presence of the second maximum can be naturally explained within the bounds of the statistical model of the colour center. A shortwave maximum is produced by ellipsoids whose rotation axis is parallel to the field vector, and a longwave maximum by perpendicular ones. The spectrum of the oblong ellipsoid system differs considerably from the experimental AAS. The difference of splitting of the spectrum was indicated above for oblate and oblong ellipsoids. Oblong particles are probably absent, or there is a negligible amount of them. After comparison of experimental and calculated AAS one can conclude that the spectrum K2: of 2R = 20 A particle size gives the best agreement for the maximum position and width. Spectrum K2 for silver particles in glass (fig. 7) confirms Moruya's conclusion that silver is precipitated in the bulk of the AgHal crystal, rather than in the glass matrix. Some simplifications of the model have been carried out to facilitate calculation. The volume of the particles was considered to be equal and the electron free path length to be independent of the eccentricity of the ellipsoid and orientation. Taking into account these circumstances will not produce qualitative changes in the whole picture however. The choice of distribution function is arbitrary. In particular the third maximum in a AAS discovered by Moriya may have been explained by the peak in the distribution function. 4.2. Comparison with experiment
First of all note the qualitative differences of photo-adaptation spectral curves for parallel and perpendicular orientation of the polarization of bleaching and probing waves. To understand these differences turn to fig. 3. In the first instance ellipsoids whose axes are perpendicular to the polarization of the reading light are mostly destroyed. Accordingly larger variations of the spectrum are observed in the longwave region. In the second instance ellipsoids whose axes are parallel to the polarization of the reading light are mostly destroyed, variations are larger in the shortwave region. To gain some idea of the anisotropy of the colour centers we shall deal with the simplified model. The largest dichroism will occur if split spectra of ellipsoids do
402
A.A. Anikin, V.K. Malinovsky /Colour centers in photochromic glass
not overlap. Let us suppose that the shape of the particles does not change and that the rate of bleaching is proportional to the energy adsorbed. It may be shown that for such a system of ellipsoids the maximum of (AAS o - AASII)/(AASo - AASI) will be 4/3. The experimental ratio for longwave and shortwave regions is dose to this value thus confirming the significant anisotropy of colour centers. The halfwidth of the photo-adaptation peak should be considered to be an important experimental result. Above, the assumption of small (R ~ 10 A) colour center size was given, based on the maximum agreement between calculated and experimental AAS. The photo-adaptation experiment presents the experimental basis of this assumption. At this point it is desirable to discuss one more possible mechanism for the broadening of the absorption band. The absorption spectrum peak of a small ellipsoidal metal particle has a resonance character related to the negativity of the real part of the dielectric constant. The resonance being defined not by the size, but by the shape of the particle, as the field inside the ellipsoid is homogeneous and its magnitude is defined by the shape. The assumption may arise that the band broadening can occur due to the field inhomogeneity because of large departures of the shape from the eUipsoidal one. It is convenient to consider the influence of the internal field inhomogeneity of the particle on its absorption using as an example a spherical shell, the internal field of which is inhomogeneous. Polarizability of the spherical shell is: (e-1)(2e+l)+q3(2e+l)(1-e) ~3 a = (e + 2 ~ e + i-)~~ 2) (1 Z - ~ K '
(3)
where q is the ratio of the inner radius of the shell to the outer one. The denominator of eq. (8) is a square trinominal. If IM(e) = 0, we find that the sheel polarizability will approach infinity with two values. Thus, the field inhomogeneity has resulted in the appearance of a new absorption peak, but not in the broadening.
5. Conclusion The additional absorption spectrum of silver-halide photochromic glass can be explained by considering the absorption of oblate ellipsoidal particles of small size (R ~ 10 A), having a considerable dispersion of eccentricity. The optical bleaching of photochromic glass with monochromatic radiation revealed considerable differences in photo-adaptation spectral curves with regard to the parallel and perpendicular orientations of the polarization of the bleaching and reading waves: vectors. The results suggest the anisotropy of the colour centers and are completely explained within the bounds of the model of ellipsoids. The photoadaptation halfwidth indicates a particle size of about 2R ~ 20 A. The increase of thermal fading rate to the left and right of 500 nm indicates that the particle stability decreases with the increase of its non-sphericity.
A.A. Anikin, V.K. Malinovsky / Colour centers in photochromic glass
403
Though the results o f the given study are related to photochromic glasses, there is every reason to believe that photolytic silver particles forming in photo-emulsion crystals are o f similar structure.
Acknowledgement The authors wish to thank V.A. Tsekhomski and I.V. Tunimanova for the photochromic samples supplied for investigation.
References [ 1] M.V. Savostianova, Izv. Fiz. Matematic. Inst. V.A. Steklova 3 (1930) 169. [2] P.V. Meikliar, Fizicheskie Processi pri Obrazovanii Scritogo Fotograficheskogo lzobradgenia (Nauka, Moscow, 1972). [31 G.P. Smith, J. Mat. Sci. 2 (1967) 139. [4] R. Gans, Ann. Phys. 47 (1915) 270. [5] U. Kreibig, J. Phys. F: Metal Phys. 4 (1974) 999. [6] A. Kawabata and R. Kubo, J. Phys. Soc. Japan 21 (1966) 1765. [7] P.B. Johnson and R.W. Christy, Phys. Rev. B6 (1972) 4370. [8] Y. Moriya, J. Non-Crystalline Solids 21 (1976) 233. [9] A.V. Dotsenko and V.K. Zakharov, Opticheskie i Spectralnie Svoistva Stekol (Leningrad, 1974).
THE STRUCTURE O F COLOUR CENTERS IN PHOTOCHROMIC GLASS A.A. ANIKIN and V.K. MALINOVSKY Institute o f Automation and Electrometry, Novosibirsk 90, USSR 630090
Received 21 November 1978 Revised manuscript received 10 April 1979
An ellipsoidal model of colour centers in photochromic glass was proposed to explain an additional absorption spectrum. Absorption spectra of small (R K 100 A) silver particles involving oblong and oblate ellipsoids of rotation have been analysed. The splitting of the absorption spectrum of the small silver particles with non-spherical form resulted in an absorption spectrum different from that for spherical particles. Calculation of the absorption spectra of the system of oblate ellipsoids with considerable dispersion in eccentricity and of about 20 A in size was in good agreement with experiment. Absorption spectra of the system of oblong ellipsoids differed significantly from experimental findings, indicating that oblong particles were absent. To verify the basic theory of the colour center model, advanced experiments have been carried out on the bleaching of photochromic glass by monochromatic polarized light. The so called photo-adaptation effect has been found, that is, the absorption decreased faster at the wavelength of the bleaching light. The photo-adaptation spectral width indicated that the particle size was nearly 20 A. The ratio of changing absorption for perpendicular and parallel orientations of bleaching and reading polarization vectors was about 0.7 in the longwave visable range, indicating that the colour centers were substantially anisotropic. In the thermal recovery of photochromic glass the shortwave and longwave absorptions were bleached faster, indicating the lower stability of the strong oblate particles, which specifies absorption in those parts of the spectrum.
1. Introduction Photochromic properties o f glasses are due to the minute particles of silver halide which are suspended in the host glass. Photochromic glass darkens when exposed to ultraviolet or shortwave light. In contrast to the photolysis o f silver halide crystals in photographic emulsion, where the halogen diffuses away from the particle during the development process, in photochromic glass the halogen is captured within the glass matrix. It is therefore available for recombination with the silver. A sample is bleached either thermally or b y red light. Figure 1 shows the typical additional absorption spectrum (AAS) of AgC1 photochromic glass. The form o f the AAS is similar to those o f exposed silver halide crystals. The absorption spectrum o f spherical silver particles suspended in the silver halide indicates that particles o f 5 0 0 - 6 0 0 A in size should explain the absorption 393
394
A.A. Anikin, V.K. Malinovsky / Colour centers in photochromic glass
0.25. 020
al$ 010 0.05 O. qoo
5oo
600
700 /],t2
Fig. 1. The typical absorption spectrum of AgHal photochromic glass.
spectrum of the exposed AgHal [1]. Meiklar [2] directly acknowledged that the maximum in the absorption spectrum is related to spherical silver particles with the proper size. Electron microscopic examination of photochromic glass has shown the average size of AgHal particles is in the range of 50-300 A [3]. Thus, it excludes formation of large silver particles which would explain the form of AAS. It has been shown in this paper that the features of AAS can be explained quite well within the bounds of the model which is based on the assumption of the nonsphericity of the silver particles. Numerical computation of absorption spectra in oblate ellipsoids of revolution which have considerable dispersion in eccentricity and size of about 20,8, are in good agreement with experimental AAS.
2. The model of colour centres
Let us suppose that along with circular silver particles there are ellipsoidal ones in photochromic glasses. For small particles (R ~ 100 A) the absorption constant K can be calculated using Mie's Theory [4], which gives the following simple expression when the field vector is in line with one of the ellipsoid axis: K = (2rre2/~,)/[(1 + (el - 1)nl 2 + e~n2),
(1)
where X is the light wavelength, e 1 and e2 are the real and imaginary parts of the dielectric constant of silver (e = e 1 + ie2) and n is depolarization coefficient along the proper ellipsoid axis. Here and below the volume of the particles is equal to
A.A. Anikin, V.K. Malinovsky / Colour centers in photochromic glass
unity. For an oblate ellipsoid o f revolution with l
=
[(t//c)
2 -
395
1] 1/2.
nil = (1 + 12)(l _ arctan l)fl a is the rotation axis in line with the field vector n± = (1 - n11)/2 is the rotation axis perpendicular to field vector. For an oblong ellipsoid of revolution with l = [ 1 - (ale) 2 ] 1/2 nil = (1 - 12)(ln[(1 +/)/(1 - / ) ] - 21)/2l 3 , n± = (1 - n 0 / 2
(2) (3)
.
Optical constants of silver particles of 200 A and less in size are significantly dependent on the size. Kreibig [5] has pointed out that the effect o f the electron free path agrees better with experiments than the Kawabata-Kubo theory [6]. We have
[5]: e(~, R) = el (~o) + i(e2(eo) + (co~,V v ) / ( ~ 3 R ) ) ,
(4)
where R is the particle radius and ~ p is the plasma frequency (Wp = 1.38 X 1016 s -1 and V R is the Fermi velocity (V v = 1.4 × 108 sm s - l ) . Spectra of e 2 for the particles of various sizes calculated from eq. (4) are shown in fig. 2. Optical constants of the bulk silver have been taken from [7]. We now turn to the analysis of eq. (1). For large enough particles (R ~ 100 A) a relation el > > e2 is fulfilled. A maximum in K is achieved when the first addend
= 2/2/7/.
10
6 q
goo
zoo
,joo A , n ~
Fig. 2. Spectra o f the imaginary part o f silver dielectric constant as a function o f the particle radius R.
396
A.A. Anikin, V.K. Malinovsky / Colour centers in photochromic glass
/f.tff~ S m "t
I
f.5"
l.O'
\
0.5.
~'oo
5bo
6~o
7bo
~, ~M
Fig. 3. Absorption bands of silver ellipsoidal particles in AgCI. The ratio of larger to smaller axis is 2.5. Optical constants correspond to R = 100 A. Oblate ellipsoid of rotation: the axis of rotation is parallel with the vector of field - 2 , the axis is perpendicular -1. Oblong ellipsoid of rotation is parallel with the vector of field - 4 , the axis is perpendicular -3.
in the d e n o m i n a t o r b e c o m e s zero. F o r spherical particles nil = n± = ~ corresponding to the position o f the absorption peak at 470 n m (silver dispersion in AgC1 was taken into account). F o r an oblate ellipsoid w i t h the relation a/c = 2.5 we have nil = 0.59 and n± = 0.21. Difference in n II and n I result in the splitting o f the absorption spectrum. The ellipsoid w i t h r o t a t i o n axis parallel to the field vector will have an absorption peak
/£.10 "7
/ g=lOnm f.0
a5
I
-...< R:la~ qOff
500
6bO ~,nm
Fig. 4. Spherical silver particle absorption in AgCt. Particle size is R = 100 A and R = 10 A.
qO0
~
(c)
~
~
500
600
_
G=~5
~:1.5
G=/.5
700
A, n.m
G':t,O ~ c'=of
v ~ ~ ~ ~ ~ ¢ = 1 . 5
(a )
2"
8'
~00
.5OO
f.O r=0.5
rbO A,nra
C=I.O ~'--"'-G=O..,q
~G=
6OO
++
(a)
Fig. 6. Absorption s p e c t r u m KZ: o f the s y s t e m o f oblong silver ellipsoidal particles in AgC1. (a) - R = 100 A; (b) - R = 20 A; (c) - R = 10 A.
Fig. 5. Absorption spectrum K Z o f the s y s t e m o f oblate silver ellipsoidal particles in AgC1. (a) - R = 100 A; (b) - R = 20 A; (c) - R = 10 A.
2 ° j/
•
+t
0
2'
6
Kz.ff 8 .~m"
~O
398
A.A. Anikin, V.K. Malinovsky / Colour centers in photochromic glass
2 /L<
q
0 ~bo
5bo
660 ,~, f~m
Fig. 7. Absorption spectrum K s of the system of oblate silver ellipsoidal particles in glass. 1 R = 2 0 A , 2 - R = 1 0 A ; t r = 1.0. at 370 nm, perpendicularly oriented to 590 nm (fig. 3). It is obvious that the system consisting of ellipsoids with various ratios will have a wide absorption band. Calculation shows that the splitting of the absorption spectra is different for oblate and oblong ellipsoids (see fig. 3). A longwave peak of an oblong ellipsoid shifts towards the IR region faster than that of an oblate one. As for a shortwave peak it moves slower towards the UV region. This remark will help to make clear some features of the absorption spectra of systems of oblate and oblong ellipsoids. Decrease of the particle size is followed by decrease in the peak height, broadening of the absorption band and the slight shift of the peak towards the shortwave region. This is illustrated in fig. 4. For the system of non-interacting ellipsoids absorption may be expressed as a sum of the absorption of the separate ellipsoids, taken with the proper weight: X
Kz =f
K(a/c)f(a/c) d(a/c),
(5)
1
where f(a/c) is a distribution function, K(a/c) is an average absorption of an isotropically oriented ellipsoid. The restriction on the upper limit of integration is imposed from geometrical considerations. The parameters are the volume of a particle present and average size of a microcrystal AgHal. Introducing designations for the absorption of ellipsoids with rotation axis parallel or perpendicular to the field vector and averaging over all orientations, we have:
K(a/c) = KII/3 4- 2K.L/3.
(6)
With the (ale - 1) distribution considered to be normal: f(a/c) " exp [ - ( a / c - 1)2/2o2 ],
(7)
Spectra K s were determined through numerical integration with regard to eqs. (6) and (7). In figs. 5 - 7 spectra K z are shown for various parameters o and sizes R.
A.A. Anikin, V.K. Malinovsky /Colour centers in photochromic glass
399
3. Experimental When photochromic glass is bleached with longwave monochromatic visible radiation the so-called photo-adaptation effect must be observed, that is, the primary destruction of colour centers responsible for absorption at the given wavelength. The narrower absorption bands of separate colour centers are signs of heavier photoadaptation. Photo-adaptation of the systems of spherical particles or spherical shells [9] should not depend on whether the bleaching radiation was polarized or not. For the system of ellipsoidal particles which is isotropic in total but consists of anisotropic elements, the polarization state of the exciting light is significant. To verify up the basic theory of the colour center model, experiments have been carried out on the bleaching of photochromic glass by monochromatic polarized light. A specimen 1 mm thick was darkened to saturation point with UV radiation. An AAS was taken on a spectrophotometer CF-14. A small amount of the bleaching radiation (k = 632.8 nm) was then given and the AAS taken again. Figure 8 shows the original absorption of the darkened sample AAS and the absorption spectra after a little bleaching AASII and AAS±. Signs II or / mean that the polarization vectors of bleaching and probing lightwaves are parallel or perpendicular to each other. In the same figure the dotted line show the normalized change of spectra (AAS o -AAStl)/AAS o. The normalized change gives a more correct estimation of the destruction value of colour centers which are responsible for the absorption at the proper wavelength.
015~ 0.I0. 005 qoo
3
560
6do
zbo A,nm
Fig. 8. Experiments on bleaching by h = 632.8 nm: l - initial AAS; 2 - AAS; following a small bleaching, polarization vectors o f the bleaching and probe waves are perpendicular; 3 - the same, but polarization vectors are parallel. Dashed line corresponds (AASII - AASo)/(AAS 0 in arbitrary units. Chain dotted line corresponds the thermal recovery rate of various parts o f spectrum, in arbitrary units.
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A.A. Anikin, V.K. Malinovsky / Colour centers in photochromic glass
3 2" 1" 0
la)
q
i~
3 2. ! o
400
S6o
660
760
A, n m
Fig. 9. Photo-adaptation curves: (a) - h = 632.8 nm; (b) - h = 700 nm; 1 - (AASII - AAS0)/ (AAStO - AASo); 1 - (AAS± - AASo)/(AASto - AASo).
It follows from fig. 8 that the maximum o f the normalized bleaching rate has shifted towards the longwave area relative to the bleaching line. The lower stability o f colour centers absorbing in the longwave region was assumed. A chain-dotted curve in fig. 8 shows the experimental ratio (AAS o - AASto)/AASo (AASto is the additional absorption spectrum after a small amount of thermal relaxation). It followed from further experiments on the thermal bleaching o f photochromic glass that the curve ( A A S o - AASto)/AASo is not the only characteristic o f thermal bleaching but that it also depends on the shape of AASo. F o r samples o f glass having an AAS maximum at 700 nm a darkening is even observed at 5 2 0 - 5 7 0 nm while shortwave and longwave o f AAS are bleached in the process o f the thermal recovery. This association with colour center form change makes it difficult to treat the experimental data. But for sufficiently long waves o f bleaching (AAS o - A A S I I , a ) by ( A A S o - AASt o) normalizing gives quite good results. Experimental curves (AASo - AASII,a_)/(AASo - AASt o) for k = 632.8 nm and k = 700 nm are presented in fig. 9.
A .A. Anikin, V.K. Malinovsky / Colour centers in photochromic glass
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4. Discussion 4.1. Calculation based on the model
As seen from fig. 5 the increase in dispersion of ellipsoids results in the broadening of the absorption spectrum and its shift towards a longwave region. The splitring of the spectrum is displayed at first in the non-symmetry of the calculated AAS. When o increases the second maximum of AAS appears in the UV region. The maximum of AAS for photochromic glass in the UV region was discovered recently by Moriya [7]. The presence of the second maximum can be naturally explained within the bounds of the statistical model of the colour center. A shortwave maximum is produced by ellipsoids whose rotation axis is parallel to the field vector, and a longwave maximum by perpendicular ones. The spectrum of the oblong ellipsoid system differs considerably from the experimental AAS. The difference of splitting of the spectrum was indicated above for oblate and oblong ellipsoids. Oblong particles are probably absent, or there is a negligible amount of them. After comparison of experimental and calculated AAS one can conclude that the spectrum K2: of 2R = 20 A particle size gives the best agreement for the maximum position and width. Spectrum K2 for silver particles in glass (fig. 7) confirms Moruya's conclusion that silver is precipitated in the bulk of the AgHal crystal, rather than in the glass matrix. Some simplifications of the model have been carried out to facilitate calculation. The volume of the particles was considered to be equal and the electron free path length to be independent of the eccentricity of the ellipsoid and orientation. Taking into account these circumstances will not produce qualitative changes in the whole picture however. The choice of distribution function is arbitrary. In particular the third maximum in a AAS discovered by Moriya may have been explained by the peak in the distribution function. 4.2. Comparison with experiment
First of all note the qualitative differences of photo-adaptation spectral curves for parallel and perpendicular orientation of the polarization of bleaching and probing waves. To understand these differences turn to fig. 3. In the first instance ellipsoids whose axes are perpendicular to the polarization of the reading light are mostly destroyed. Accordingly larger variations of the spectrum are observed in the longwave region. In the second instance ellipsoids whose axes are parallel to the polarization of the reading light are mostly destroyed, variations are larger in the shortwave region. To gain some idea of the anisotropy of the colour centers we shall deal with the simplified model. The largest dichroism will occur if split spectra of ellipsoids do
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A.A. Anikin, V.K. Malinovsky /Colour centers in photochromic glass
not overlap. Let us suppose that the shape of the particles does not change and that the rate of bleaching is proportional to the energy adsorbed. It may be shown that for such a system of ellipsoids the maximum of (AAS o - AASII)/(AASo - AASI) will be 4/3. The experimental ratio for longwave and shortwave regions is dose to this value thus confirming the significant anisotropy of colour centers. The halfwidth of the photo-adaptation peak should be considered to be an important experimental result. Above, the assumption of small (R ~ 10 A) colour center size was given, based on the maximum agreement between calculated and experimental AAS. The photo-adaptation experiment presents the experimental basis of this assumption. At this point it is desirable to discuss one more possible mechanism for the broadening of the absorption band. The absorption spectrum peak of a small ellipsoidal metal particle has a resonance character related to the negativity of the real part of the dielectric constant. The resonance being defined not by the size, but by the shape of the particle, as the field inside the ellipsoid is homogeneous and its magnitude is defined by the shape. The assumption may arise that the band broadening can occur due to the field inhomogeneity because of large departures of the shape from the eUipsoidal one. It is convenient to consider the influence of the internal field inhomogeneity of the particle on its absorption using as an example a spherical shell, the internal field of which is inhomogeneous. Polarizability of the spherical shell is: (e-1)(2e+l)+q3(2e+l)(1-e) ~3 a = (e + 2 ~ e + i-)~~ 2) (1 Z - ~ K '
(3)
where q is the ratio of the inner radius of the shell to the outer one. The denominator of eq. (8) is a square trinominal. If IM(e) = 0, we find that the sheel polarizability will approach infinity with two values. Thus, the field inhomogeneity has resulted in the appearance of a new absorption peak, but not in the broadening.
5. Conclusion The additional absorption spectrum of silver-halide photochromic glass can be explained by considering the absorption of oblate ellipsoidal particles of small size (R ~ 10 A), having a considerable dispersion of eccentricity. The optical bleaching of photochromic glass with monochromatic radiation revealed considerable differences in photo-adaptation spectral curves with regard to the parallel and perpendicular orientations of the polarization of the bleaching and reading waves: vectors. The results suggest the anisotropy of the colour centers and are completely explained within the bounds of the model of ellipsoids. The photoadaptation halfwidth indicates a particle size of about 2R ~ 20 A. The increase of thermal fading rate to the left and right of 500 nm indicates that the particle stability decreases with the increase of its non-sphericity.
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Though the results o f the given study are related to photochromic glasses, there is every reason to believe that photolytic silver particles forming in photo-emulsion crystals are o f similar structure.
Acknowledgement The authors wish to thank V.A. Tsekhomski and I.V. Tunimanova for the photochromic samples supplied for investigation.
References [ 1] M.V. Savostianova, Izv. Fiz. Matematic. Inst. V.A. Steklova 3 (1930) 169. [2] P.V. Meikliar, Fizicheskie Processi pri Obrazovanii Scritogo Fotograficheskogo lzobradgenia (Nauka, Moscow, 1972). [31 G.P. Smith, J. Mat. Sci. 2 (1967) 139. [4] R. Gans, Ann. Phys. 47 (1915) 270. [5] U. Kreibig, J. Phys. F: Metal Phys. 4 (1974) 999. [6] A. Kawabata and R. Kubo, J. Phys. Soc. Japan 21 (1966) 1765. [7] P.B. Johnson and R.W. Christy, Phys. Rev. B6 (1972) 4370. [8] Y. Moriya, J. Non-Crystalline Solids 21 (1976) 233. [9] A.V. Dotsenko and V.K. Zakharov, Opticheskie i Spectralnie Svoistva Stekol (Leningrad, 1974).