The field-assisted penetration of a silver film into glass

188

Journal of Non-Crystalline Solids 120 (1990) 188-198 North-Holland

T H E FIELD-ASSISTED P E N E T R A T I O N OF A SILVER F I L M I N T O GLASS T. K A N E K O NIKON Corporation Research Laboratory, Tokyo 140, Japan

The application of a DC field to a sodium-containing glass plate coated with a silver film causes Ag + and Na + ions to move toward the cathode, retaining the transparency of the glass. Characteristics of the process have been experimentally studied from various viewpoints: current and voltage versus time, fluorescence generation/annihilation, refractive index increase, spectral reflectivity characteristics, internal strain generation, volume increase, the weight of penetrated silver versus transported electric charge and concentration profiles. The dynamics of the process have been shown to be approximately linear. The linearity is considered to come from the following: (1) the resistance of a Ag-penetrated layer is m u c h smaller than that of the whole of a glass plate and (2) Na + ions are not piled up in the vicinity of the cathode-side surface.

1. Introduction More than 30 years ago, Hall and Hayes [1,2] reported the field-assisted penetration technique of a silver film into a glass plate (fig. 1). They showed that the transparency of the original glass was retained after the process was over. The technique was noteworthy in the sense that it could provide a simple means of producing a layer of high refractive index in the glass surface [3,4]. Recently, this and related processes have been of interest in integrated optics [5-21]. However, it seems that attention has been focused on the study of the refractive index profile a n d / o r the concentration profile of penetrated silver, al-

i < Graphite 1 Silver film G l a s s plate I Graphite Furnace

.VHjjj

Fig. 1. Experimental setup for the field-assisted penetration process.

though they are not yet well established. The purpose of this paper is to clarify various characteristics of the process experimentally: current and voltage versus time, fluorescence change, refractive index increase, spectral reflectivity characteristics, volume increase and concentration profiles of the exchanging ions.

2. Experimental procedure (see also ref. [I0]) 2.1. Glass sample Optical glasses CF 3 and BSC 7 and flat glass, which contain 10% or more N a 2 0 in weight, were used. Sample dimensions were 30, 33 and 49 mm diameter and 1.2 and 2.0 mm thick. ?.2. Diffusion source The diffusion source was a solid silver film deposited chemically or physically (vacuum evaporation) on the glass surface. The silver film was removed with nitric acid after the diffusion treatment. 2.3. Electrodes Graphite coatings (Aquadag, Acheson Colloids Co.) were applied as non-reacting electrodes on

0022-3093/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)

T. Kaneko / FieM-assistedpenetration (a) C o n s t a n t

applied

voltage

current

0 ....f time 0

(b) C o n s t a n t

t

appl

ed

0

189

(t) characteristics of current (i) and voltage (V) for those cases where silver penetrated over a wide area of the anode-side surface. The decrease of i and the increase of V after t o result from the depletion of A g + and N a + in the vicinity of the anode-side surface. A c c o r d i n g to the experiment of Carlson et al. [22], the ion-depleted region has a vitreous silica-like structure and therefore displays a lower refractive index c o m p a r e d with untreated glass.

current 3. Results

voltage 3.1. i - V characteristics for 0 < t < t o ( C F 3, 1.2 m m thick) V° .... t

/ time

0

0

Fig. 2. Schematic representation of current and voltage versus time. Depletion of the silver film beans at t = t 0. b o t h surfaces of the silver-coated glass and dried at a temperature < 50 o C. The main ingredients of A q u a d a g were graphite and water containing a small a m o u n t of N H 3, K, P, S, C1 and F, which were detected using an X R F spectrometer (Rigaku XRF-3080) and an ion c h r o m a t o g r a p h y system (Dionex 2010i). The graphite electrodes were rem o v e d by rubbing with hot water after diffusion treatment.

All the i - t characteristics exhibited profiles similar to that depicted in fig. 2. For every sample, i b e c a m e constant ( = i0) within several seconds. Figure 3 shows the linearity between i 0 and V obtained at 2 0 0 ° C (nominal value). However, i 0 did not take a single value a m o n g the treated samples, p r o b a b l y due to some scattering in the initial distribution of N a + ions, temperature, sample thickness, penetration area of silver and elec-

i

(mA/Scm 2 ) 0

©

2.4. Diffusion conditions

©

Temperature, < Tg. Applied voltage, < 200 V for 1.2 m m thick samples. Applied current, 3 m A for 2.0 m m thick samples. Preheating time, > 10 min. Atmosphere, in air.

©

at 200 2.5. Principle of the penetration process A high refractive index layer was formed in the glass surface according to the setup shown in fig. 1; in some cases a silver film was also coated on the cathode-side of the glass. Figure 2 shows time

0

I

I

100

200

V (V/l.2mm) Fig. 3. Current versus applied voltage. ©; silver was coated on anode- and cathode-side surfaces, ><; silver was coated on the anode-side surface only.

T. Kaneko / Field-assisted penetration

190

>,

Ag-containing

,(a)

anode

surface

¢)

e. , , . , . ,

I

300

I

400

500 X(/am)

(b) °•°°°*o

"o

Cathode-side

"surface Fig. 5. Fringes obtained using a Tolansky-type interferometer. A rings-patterned film of silver was used as a diffusion source. • ° °

,

,

•° •°

Ag-containing I

300

anode

surface I

400

500

x(um) Fig. 4. Generation and vanishment of fluorescence: 2~ex= 254 ~m. (a) flat glass, (b) CF 3.

trode resistivity; the higher the temperature, the larger the scatter [10].

3.2. Fluorescence generation / vanishment (CF 3, BSC 7, flat glass) Figure 4 shows fluorescence changes due to the silver penetration (2~ex= 254 I~m). BSC 7 showed an increase in fluorescence after treatment.

3. 3. Optical path increase Figure 5 shows an interference fringe pattern obtained between two surfaces of a sample after treatment using a Tolansky-type interferometry system. A fringe shift can be seen due to an

optical path difference (OPD) between silverpenetrating and silver-free regions. Table 1 compares OPD in the sample measured using different wavelengths. Figure 6 shows OPD versus t and V characteristics estimated from refractive index profiles which were obtained by Chartier et al. [5]; specimens were 0.7 mm thick plates of a soda-lime glass. It appears that OPD is proportional to t and V.

3.4. Visible reflection spectra (CF 3, 1.2 rmn thick) 1101 The interfaces where the Ag+-containing layer meets the Na+-only-containing region and the

Table 1 Optical path differences (OPD) measured using different wavelengths (7~) (see fig. 5) Laser

2~ (rtm)

O P D (~tm)

He-Ne Ar Ar Ar

632.8 514.5 476.5 457.9

= = = =

261 268 268 270

T. Kaneko / Field-assisted penetration 0 P D

~ m)

~'d

191

(Urn) O

.

94 0

•

10

0

0.5

0 at I

0

I

I

10

20

1

I

I

I

30 40 50 60

I

50

I

I

80 90 1 ~

70 t

250 ~ , I

V

82 I

80 ~ 0

llO 120 78

(min)

123 ~

(.m)

OPD

84

at

1 18

230

°C

85i

--0

125 ~ 119 /

•

(~81 (~.

79 ~ - ~

o

~*111 ~ . . . . .

~ ,

i

p

r

i

i

91X~

/

0.5

0

1

2

3

4 > q/

5

6

( C / 8 c m 2)

Fig. 7. Optical path length (~d) of a reflecting layer versus transported charge (numbers indicate sample names). Silver film was undepleted (©), depleted ( × ) and uncoated (A).

o Q

•

at I

0

I

0

I

I

250 I

°C, I

30 min I

I

50

I

100 V (V)

Fig. 6. Optical path difference (OPD) versus time and voltage (calculated from the data of Chartier et al. [5]).

Table 2 Refractive index data (see fig. 8) No.

nD

1 2 3 4 5 6 7 8

1.60225 1.59705 1.59165 1.58615 1.58035 1.5741 1.5680 1.5610

1.6011 1.5960 1.5906 1.5851 1.5793 1.5734 1.5669 1.5600

ion-depleted layer meets the Ag+-containing layer have fairly steep changes in Ag + concentration; this tendency is not surprising considering that the treatment temperature is low. These steep changes display distinct interference curves in visible reflection spectra. Figure 7 shows an approximately linear relation between optical path lengths (~d) and total charges (q') transported through sam-

No. No.

nD

9 10 11 12 13 base

1.5528 1.5449 1.5369 1.5278 1.51855 1.5151

Cathode-side surface: 1.51495. Every fringe separates into two because of birefringence due to anisotropic stress. However, it was difficult to separate each fringe above No. 8, because it was too vague.

Fig. 8.

STi

Interference fringes observed in an Abbe-type refract•meter.

T. Kaneko / Field-assistedpenetration

192 R

(%)

4o

Anode side

No. ST8

30

o Ole•

."

o o. • •

20 10 0

i

"'"

1300

1400

1200

,

i

1100

i

1000

i

-~t~'-

900

i

800

i

1

v

i

700

v

600

•

i

500

tl00

~-1 (,:m-I) Fig. 9. Infrared reflection spectra. Anode-side surface; silver film was depleted during treatment. A

~-

57

nm

not piled up in the vicinity of the cathode-side surface.

3.5. Interference fringes observed in an Abbe-type refractometer (CF 3) Fig. 10. Dilation (zx) of a glass plate by field-assisted ion exchange.

Interference fringes due to a high index layer were observed using an A b b e - t y p e refractometer. O n the other hand, n o interference fringe was observed at cathode-side surfaces. The fringes were clear when the treatment temperature was rather high, or when t > t 0. Figure 8 shows an example (sample, No. ST8; q ' , 4 C / 6 . 1 6 cm 2, nominal treatment temperature, 278 o C). Index values mea-

pies at 2 3 0 ° C (nominal value); here, ~ is the average refractive index of a reflecting layer and d the thickness of the layer. N o interference curve was obtained f r o m the cathode-side surfaces of treated samples. This suggests that N a + ions are

(rim) 100

l

I

STI0

90 50 0

86

123

0

O

0

84

81

118

230 288 280

O"

83

ST2" ST10"

19 k"f~ S T 2

°C °C °C

O 0 125 I

0

!

0.1

I

i

I

0.2 >

i

I

0.3 q

i

0.4

I

i

I

0.5

( C / c m 2)

Fig. 11. Dilation versus transported charge (numbers indicate sample names).

|

0.6

T. Kaneko /Field-assistedpenetration

193

sured are shown in table 2, which does not suggest that the surface has a vitreous silica-like structure. This is p r o b a b l y because the time of t - t o (---2 min) was short and therefore the ion-depleted layer is very thin. Actually, the infrared reflection spectra ( I R R S ) (Hitachi Infrared Spectrophotometer 1-2000) suggest that the anode-side surface was changed to a vitreous silica-like structure (fig. 9).

3. 6. Volume change (CF 3, flat glass) The Ag-containing region of anode-side surfaces was dilated a little as c o m p a r e d to the Ag-free region [23]. This is because larger ions replaced smaller ions [6,24]. Figure 10 shows an example of this (CF 3, 2.0 m m thick, q ' : 2.3 C / 1 8 . 5 cm 2, penetration area of silver film: 0.8 c m 2, t > t 0, nominal treatment temperature, 290 ° C); a Talystep ( R a n k Taylor H o b s o n Co.) was used to measure the dilation (A). (For flat glass, similar dilation was observed using a multiple-beam interferometry system.) It should be noted that dilation tends to be a little larger near the Ag-free region. N o deformation was observed for cathode-side surfaces. Figure 11 shows a nearly linear relation between A and the transported charge density q when t < t o (CF 3, 1.2 and 2.0 m m thick). W h e n the silver film was uncoated, the graphite-coated regions of the anode-side surface were depressed c o m p a r e d with the regions which were not coated with graphite; this is in accordance with the experimental results of Carlson et al. [22]. A depression of about 8 n m was observed for a 2.0 m m thick C F 3 sample (No. S1642) treated as follows: t = 10 min, q = 0.10 C / c m 2 and 2 7 0 ° C (nominal temperature). The depletion of sodium near the anode-side surface was confirmed from

z<

i

I ne i dent

z< Glass

Fig. 12. Geometry between a sample and the electron beam in the EPMA experiment.

Fig. 13. Experimental concentration profiles for sample S1642: (a) anode-side surface treated with graphite coating, (b) anode-side surface treated without graphite coating, (c) cathode-side surface treated with graphite coating. See fig. 12 forz. 0 = 5 ° 30'.

T. Kaneko / Field-assistedpenetration

194 (%)

H

I

50

I

I

1

I

I

I

I

51642 anode side 40

30 )'..O%o

°%

20

°q

I0

!

1400

1300

1200

1100.

1000

900

800

700

600

500

400

X -1 ( c , "1) Fig. 14. Infrared reflection spectra. Silveris not penetrated for samples S1642 and 111.

E P M A analysis (Shimadzu EMX-SM7); fig. 12 shows the geometry of a sample and the electron beam. Figure 13 shows X-ray intensity profiles, i.e. concentration profles, of N a and Si at 8 = 5 o 30' (accelerating voltage V,c, 15 kV). Figure 14 compares the I R R S spectra of Agpenetrated surfaces (t < to, Nos. SBA2 and SBB2) and Ag-free surfaces (Nos. 111 and S1642) of CF 3. The treatment conditions were: q ' = 2.7 C/18.5 cm 2 for SBA2, 3.6 C/18.5 cm 2 for SBB2, 0.69 C / 8 cm 2 for 111 and 1.8 C / 1 8 cm 2 for S1642. The spectra for the ion-depleted surfaces show a distinct shift in the S i - O - S i vibrational mode toward the value observed for fused silica (~-1__ 1125 cm-1). The spectra for the Ag-containing surfaces show a small decrease in reflectivity at around X - l = 1075 cm -~ compared with the untreated surface.

analysis (Shimadzu AA-646) and X R F analysis (Rigaku XRF-3080). We see that eq. (1) is satisfied fairly well. W

(mg/om 2 )

0.5 124 .'" q=O.

• "'SBC1

0.3

."'~SBC 1 -" 83 .'"'(~380 -"(~ SBB I " 8t ..,'@ SBA 1, SBA2 120

0.2

3. 7. Weight of penetrated silver (CF 3) 0.1

...'0

If surface currents and the transference of N a + towards the anode-side surface can be ignored, q ( C / c m 2) is given by q = 0.892W

( F a r a d a y ' s law of electrolysis),

(1)

where W is the weight of penetrated silver (mg/cm2). Figure 15 shows the W - q relationships; W was measured from atomic absorption

892W

0.4

78

,-G'I 19 I

0

I

0.1

I

I

I

I

I

0.2 0.3 > q (C/em 2)

0.4

Fig. 15. The weight (W) of penetrated silver versus transported charge (numbers indicate sample names).

T. Kaneko / Field-assisted penetration

195

,~x

I

--~ Depth

'

5//m

~o 94

I--~ Depth

51zm

Fig. 16. Experimental concentration profiles. Silver film was depleted (No. 91) and undepleted (No. 94) during treatment. Applied voltage = 45 V, 0 -- 90 o.

3.8. Concentration profiles of penetrated silver (CF 3) Figure 16 shows step function-like EPMA profiles of silver for ion-depleted and -undepleted samples ( 0 = 9 0 °, Hitachi SEM X 560-Kevex 5100, Vac: 20 kV). The treatment conditions were: q ' = 5.1 C / 8 cm 2 for t < t o and 1.3 C / 8 cm z for t > t o for No. 91 and 4.8 C / 8 cm 2 for No. 94, Depletion of silver at the surface of No. 91 was confirmed by an ESCA spectrometer (YHP 5950A); fig. 7 also supports it. These concentra-

tion profiles are very similar to those obtained by Fauchey and Guigonis [25] and the refractive index (RI) profiles obtained by Chartier et al. [5]. However, they are different in shape from the concentration profiles obtained by Chen et al. [21] and the RI profiles obtained by Pitt et al. [7] and Voitenkov and Red'ko [11], which take rather Gaussian profiles. Forrest et al. [13] and Honkanen and Tervonen [19] reported the above two types of concentration and RI profiles, respectively. Figure 17 shows EPMA profiles measured at 0 = 4 ° for samples 80 and 82 (see fig. 7 for the

Fig. 17. Experimental concentration profiles: (a) No. 80, (b) No. 82. Applied voltage = 45 V, 0 = 4 °.

T. Kaneko /Field-assistedpenetration

196

M' ( a . u . )

piled up inside the glass. The relation (2b) shows that the treated glass is an ohmic conductor. The linearity between q and A was discussed previously [23]. The volume increase 8 produced by the penetration of an Ag + ion is estimated as 3 × 10 24 c m 3 from fig. 11. If the replacement of a N a + ion by an Ag ÷ ion is stress-free, and their ionic radii are assumed to be 0.097 nm and 0.126 nm, then 8 - 4.6 x 1 0 - 2 4 c m 3. The birefringence shown in table 2 shows that the above difference is significant. We see that the concentration (C), flux ( J ) and total penetrated amount ( M ) of Ag ÷ ions for t < t o will roughly be given by

.O "" 82

15

." 10

O" 80

,

78 Q~5 85 5

"" /"

• 0

" -"

"'i

q,(C/Scm2) ,

i

. . . .

0

v

. . . .

1

i

. . . .

>

i

2

. . . .

i

. . . .

C/Co, J/Jo = 1

for 0 < z < d = vt (o: constant)

i

(3a)

3

Fig. 18. Relative value {M ' ) oz tlae a m o u n t of penetrated silver versus transported charge (numbers indicate sample names). 0 = 5 ° 3 0 '.

treatment conditions) (Shimadzu EMX-SM7, Vac: 15 kV). Figure 18 is a plot of the total amount M ' of penetrated silver estimated from E P M A against q', the surface concentration being normalized. Linearity between 14" and M ' is derived from figs. 15 and 18; therefore, the concentration profiles measured at an angle of << 90 ° are reasonable.

=0 M -

for z > d,

(3b)

C dz = Cod cxt.

(4)

Here, Co and J0 are constant parameters, v is the advancing velocity of the A g / N a boundary and L is the substrate thickness ( L >> d). Since actual concentration profiles have smooth curves, some refined approximation for C is necessary. According to Kaneko's linear analysis, it is given by

C / C o = vt(~rDt)-l/2, e x p [ - (z - vt)2/(4Dt)] - o ( 2 D ) - a - (z + vt + D / v ) .

exp(vz/D)

× erfc[ (z + v t ) / 2 ( D t ) '/2]

4. Discussion

+ ( 1 / 2 ) " erfc[(z - v t ) / 2 ( D t ) ' / 2 ] ,

4.1. Linearity

(5)

The above results indicate that the field-assisted penetration of Ag has linear characteristics for t < to:

under the boundary condition of J(0, t) = J0 [26]. Here, CO= Jo/v = M / v t , D is the diffusion constant and erfc is the error function complement, which can be estimated by using the following new closed-form expression

di/dt = 0

(except for small t) for constant V, (2a)

erfc x = (1 + 0.35859x 2 - 0.07745x 3 + 0.04007X 4)

i cx V,

(2b)

8nd or. t, V,

(2c)

I c 1 < 3 . 9 × 10 - s for x > 0. On the other hand, the steadily advancing boundary solution which Abou-el-Leil and Cooper derived on the basis of a nonlinear analysis [27,28] is

q = 0.892Wcx ~d,

A,

(2d)

where 8n is an average increase in RI. Equation (2a) implies the following: (i) the resistance of a Ag-penetrated layer is much smaller than that of the entire glass plate and (ii) N a + ions are not

/ e x p ( x 2 + 2 x ~ -°'5) + ,,

(6)

C/Co = {1 + e x p [ ( o / D ' ) ( 1 - a)(z - vt)] } - ' ,

(7)

T. Kaneko / Field-assisted penetration

197

pearance of fluorescence pertaining to silver is unknown; it was impossible to distinguish between Ag +, Ag 2+ and Ag o from ESCA. When the silver source was deposited chemically, a small amount of Sn was introduced into the surface.

L .,a ~0

go ! ( i a ) ) ~ ~ d

')

(e) 5. Conclusions (am)

0 1 2 3 4 5 6 Fig. 19. Comparison of theoretical and experimental diffusion profiles. (a) No. 79, (b) No. 85, (c) No. 78, (d) No. 80, (e) No. 82. Applied voltage=45 V. v / D = 1 5 ~m-1; vt values (in ~m) = (a) 1.0, (b) 1.7, (c) 1.8, (d) 3.5, (e) 4.4. 0 = 5 ° 30'.

where a is the mobility ratio of Ag + to Na + (a < 1) and D' is the diffusion constant. It follows from eq. (7) that M/C o = L-

D ' / [ v ( 1 - a)]

X log{ [ e x p [ ( v / D ' ) ( 1 +exp[(v/D')(1

References

- a)C]] + 11}

- a)]

×log{exp[(v/D')(1

- a ) v t ] + 1}

(> --vt

The author thanks T. Yamaguchi (fig. 5), K. Ishii of Hitachi Co. (IRRS), H. Sugihara (Tokyo Institute of Technology) (ESCA), N. Mochizuki (AA, XRF) and T. Onagi (EPMA) for their kind cooperation. He is grateful to the referees for their comments.

- a ) vtl

/[exp[(v/D')(1-a)vt] -- D ' / [ v ( 1

Various characteristics of the field-assisted penetration of Ag film have been clarified. The dynamics of the process have been shown to be approximately linear.

for(v/D')(1-a)vt>>

l.

(8)

A rough agreement of eqs. (5) and (7) is obtained by taking D ' > D (see, for instance, ref. [29]). Figure 19 shows the concentration profiles obtained from eq. (5): v / D = 15 /,m -1 and vt = 1.0 (for No. 79), 1.7 (for No. 85), 1.8 (for No. 78), 3.5 (for No. 80) and 4 . 4 / , m (for No. 82). We see that the simulation is fairly good. 4.2. Positive ion penetration

The following should be noted. When an electric field was not externally applied, silver penetration was not observed at all; however, when the graphite coatings were eliminated penetration occurred in an oxidative atmosphere. At the present stage, the cause of the generation or disap-

[1] A.J.C. Hall and J.G. Hayes, Aust. J. Appl. Sci. 9 (1958) 207. [2] A.J.C. Hall and J.G. Hayes, Interstitial Patterns (Defence Standards Laboratories Technical Note 50) (Australian Defence Scientific Service, Victoria, 1958). [3] T. Kaneko and H. Yamamoto, in Proc. 10th Int. Congress on Glass, Kyoto (1974) p. 8. [4] T. Tsunashima, T. Kaneko and T. Ichimura, Soft-focus optical element (US Patent no. 3900249, 1975). [5] G.H. Chartier, P. Jaussaud, A.D. de Oliveira and O. Parriaux, Electron. Lett. 14 (1978) 132. [6] J. Viljanen and M. Leppihalme, J. Appl. Phys. 51 (1980) 3563. [7] C.W. Pitt, A.A. Stride and R.I. Trigle, Electron. Lett. 16 (1980) 701. [8] G. Chartier, in: Integrated Optics, eds. S. Martellucci and A.N. Chester (Plenum, New York, 1981) p. 49. [9] K. Kaede and R. Ishikawa, Electron. Lett. 20 (1984) 647. [10] T. Kaneko, Opt. Commun. 52 (1984) 17. [11] A.I. Voitenkov and V.P. Red'ko, Sov. Phys. Tech. Phys. 30 (1985) 112. [12] T. Findakly, Opt. Eng. 24 (1985) 244. [13] K. Forrest, S.J. Pagano and W. Viehmann, J. Lightwave Technol. LT-4 (1986) 140. [14] B1. Pantchev, Opt. Commun. 60 (1986) 373. [15] S. Honkanen, A. Tervonen, H. von Bagh and M. Leppihalme, J. Appl. Phys. 61 (1987) 52.

198

T. Kaneko / Field-assisted penetration

[16] S. Honkanen, A. Tervonen, H. von Bagh, A. Salin and M. Leppihalme, Appl. Phys. Lett. 51 (1987) 296. [17] A. Tervonen, S. Honkanen and M. Leppihalme, J. Appl. Phys. 62 (1987) 759. [18] A. Tervonen and S. Honkanen, Opt. Lett. 13 (1988) 71. [19] S. Honkanen and A. Tervonen, J. Appl. Phys. 63 (1988) 634. [20] H. Zhenguang, R. Srivastava and R.V. Ramaswamy, Appl. Phys. Lett. 53 (1988) 1681. [21] C.L. Chen, K. Daneshvar and S. Hinata, Proc. 1988 IEEE Southeast Conf., Knoxville (1988) p.674. [22] D.E. Carlson, K.W. Hang and G.F. Stockdale, J. Am. Ceram. Soc. 57 (1974) 295.

[23] [24] [25] [26] [27]

T. Kaneko, J. Mater. Sci. Lett. 5 (1986) 1011. D.K. Hale, Nature 217 (1968) 1115. S. Fauchey and J. Guigonis, Ind. C6ram. 641 (1971) 493. T. Kaneko, J. Phys. D 18 (1985) 2233. M. Abou-el-Leil and A.R. Cooper, J. Am. Ceram. Soc. 62 (1979) 390. [28] A.R. Cooper and M. Abou-el-Leil, Appl. Opt. 19 (1980) 1087. [29] H.-J. Lilienhof, E. Voges, D. Ritter and B. Pantschew, IEEE J. Quantum Electron. QE-18 (1982) 1877.