The physical chemistry of the formation of fluorescence centres in ZnSCu

Physica XVI, no 3

THE

M a a r t 1950

PHYSICAL CHEMISTRY OF THE FORMATION OF FLUORESCENCE CENTRES IN ZnS-Cu b y F. A. K R O G E R and N. W. SMIT Philips Research Lahoratories, Eindhoven-Netherlands

Summary O n t h e b a s i s of a m o d e l for t h e c e n t r e s of f l u o r e s c e n c e in Z n S - C u a r r i v e d a t in p r e v i o u s p u b l i c a t i o n s , t h e f o r m a t i o n of c e n t r e s w i t h p r o d u c t s p r e p a r e d in c o n t r o l l e d a t m o s p h e r e s of H 2 S - HC1 is discussed, a s s u m i n g e q u i l i b r i u m t o e x i s t b e t w e e n t h e solid a n d t h e gas p h a s e .

Introduction. In a previous paper 1) it has been shown that when ZnS-Cu phosphors are prepared by firing in a controlled atmosphere of H a S - HC1 the proportion between blue and green bands in the fluorescence depends on the composition of the atmosphere. The phenomena observed could be explained qualitatively b y the assumption that green copper centres are formed when copper is incorporated in ZnS as CuC1, while blue copper centres are formed when copper dissolves as Cu2C1. Blue zinc centres finally come into existence b y incorporation of chlorine with the simultaneous reduction of divalent to monovalent zinc (ZnS-ZnC1), while killer centres are assumed to consist of Cu2S. In a later paper 2) it has been shown that although chlorine aids in the incorporation of the activator it does not belong to the centre proper, the centres being Cu +, Cua+ and Zn +, surrounded by sulphur ions *); or in other words, the copper chlorides dissolved dissociate in the lattice, and the positivily charged dissociation products act as centres. In the present paper the formation of centres in dependence of the composition of the atmosphere is treated quantitatively, assuming equilibrium to exist between the solid and the gas phase. *) These models for the two types of copper centres resemble those proposed by LenardT) a long time ago. - -

317

- -

318

F . A . KR/JGER AND N, W. SMIT

Theoretical. S c h e m e I. In a first model it is assumed that centres of fluorescence are formed at the reaction temperature (1200°C) to the extent required by the equilibrium existing between the concentration of the reaction partners in the ZnS and in the atmosphere, and between the various centres within the ZnS; this situation is assumed to remain fixed during rapid cooling to room temperature, and therefore to determine the properties of the samples. Only reheating at elevated temperatures (1200 °C > T > 300°C) for a considerable time will cause adjustment to the new conditions (lower temperature, different atmosphere) and consequently a variation of the fluorescence properties. Such processes, however, will not be considered here. For the sake of simplicity it will further be assumed that the halides incorporated are totally dissociated; a finer treatment should of course allow for a partial dissociation regulated by a dissociation constant. Further the formation of ZnC12 by the reaction ZnS + 2HC1---> ZnC12 + H2S is ignored. The error thereby introduced is not serious, for although this reaction leads to an increase of the partial pressure of H2S and a decrease of that of HC1, the ZnC12 formed also participates in the reactions leading to the formation of centres, be it with a different reaction constant. In the following parentheses will be used to indicate that the particular molecule or ion is incorporated in the ZnS; brackets indicate concentrations, while partial pressures in the gas phase are indicated by Pi; concentrations are expressed in molar fractions, partial pressures in atmospheres. The formation of green and blue copper centres and killer centres can be described by the following equilibrium equations"

Cu2S + 2HC1 ~ 2(Cu +) + 2(C1-) + H2S

(1)

Cu2S +

(2)

HC1 ~_ (Cu +) + (C1-)+½H2S + ¼S2

cu s Z (Cu S)

(3)

By subtracting (2) and (3) from (1) we obtain the equilibria which must exist within the ZnS between the blue and the green copper centres (4) and between the green centres and the killer centres (5)" 2(Cu +) + (C1-) + ½H2S Z (Cu+) + HC1 + tS 2 (Cuss) + 2HC1 ~ 2(Cu +) + 2(Cl-) + H2S

(4) (5)

PHYSICAL CHEMISTRYOF ZnS-Cu

319

These reactions lead to an equilibrium governed by equilibrium constants, defined in the usual way: [Cu+] Psi. PHcx KGB = [Cu+] 2 [C1-] P~os

(6)

[Cu+] 2 [C1-] P.,.s = [CusS] P c,

(7)

Now it has been observed 1) that killers are only active in the range in which the copper blue predominates; further it is probable t h a t killers are much more effective than fluorescence centres 3). Therefore it is likely that the concentration of killer centres in the range in which green is still present is relatively small. As we are mainly interested in the relative concentrations of the fluorescence centres, killers will therefore be disregarded; if necessary they can be introduced by means of (7). Apart from the reactions leading to the formation of copper centres, we have also to reckon with the formation of zinc centres. These are formed in the reaction: ZnS + HC1 Z (Zn+) + (CI-) + {H2S + ¼S2 and the equilibrium constant corresponding to it is" Kzn = [[Zn+] C I - I P '~2s Ps2 ¼

(8)

(9)

PHCI The partial pressures appearing in the expressions (6) and (9) have been calculated for various compositions of the atmosphere consisting of a H 2 S - bHC1, assuming that HC1 is totally associated, while the dissociation of H2S is regulated by the dissociation constant KH~S _ PH~ P~,

(10)

PH2S which equals 0.228 at 1200°C 4). The expressions for the partial pressure of the various components of the atmosphere are listed in Table I, first column; a is the fraction of the H2S originally added which dissociates at 1200°C; d stands for the denominator in the expressions, and is introduced to shorten the formulae. Results for various compositions of the atmosphere are given in Table If. For the sake of simplicity we introduce the symbols

[Cu +] = x;

[Cu +] = y ;

[Zn +] = z

(ll)

320

F. A. KROGER A N D N. W. SMIT

TABLE I C o m p o s i t i o n of t h e a t m o s p h e r e a H ~ S - - bHC1

a H ~ S - - bHC1 --- n N ,

aH~.S - - bHCI - - hH~

K ~Ho.S= (0.225) 2 0.5a3a( l - - a ) - * d - l 0 . 5 ( a a + h ) ' c t a - ' ( l - - a ) - 2 d -~ O.SaSa( l - - a ) - * d - 1 d (l+0.5a)a + b 1+0.5a)a + b + h (1 + 0 . S a ) a + b + n PH2

aad-I

PH.S

(1 - - a ) a d - l

Pss

0"Saad-I

PHCI

bd- t

(aa + h)d-* ( 1 -- a)ad-t O.5aad - ~ bd-t

PN2 TABLE

98 95 90 80 70 60 50 40

2 5 10 20 30 40 50 60

( 0 . S a a + s)a*( l - - a ) - a d -~ (l+0.5a)a + b + s

aad-t

ctad-t

( 1 -- a)ad -I O.8aad -1

(1 - - a ) a d - l (0.5aa + s)d -t

bd-~ nd-t

bd-~

II

P a r t i a l p r e s s u r e s of HaS, Ha, S 2 a n d HC1 in H 2 S aH.,S - - bHCI

a H 2 S - - b H C I - - sS..

HCI a t 1200°C

PHi_

PS~

PH~S

PHCI

0.305 0.299 0.289 0.266 0.243 0.218 0.194 0.163

0.183 0.150 0.145 0.133 0.121 0.109 0.097 0.082

0.,520 0.500 0.481 0.426 0.372 0.316 0.260 0.204

0.018 0.042 0.0855 0.173 0.264 0.357 0.4,52 0.552

Then

[C1-] ---- x + y + z

(12)

and

[Cu]totaz = x + 2y

(13)

Replacing

[C1-] in (6) and (9) by (12) we obtain Y Psi2PHC, KGB = X2(X + y + Z) P~.~S

(14)

Kz. = z(x + y + z). P~s P~

(15)

PHCI

From (13), 14) and (15) x, y and z can be determined provided the constants KGn and Kz,, are known. Inversely these constants may be obtained from experimental data. The ratio green: blue found experimentally depends on the concentration of green and blue centres as given by the expression R

--

It(x)

(16)

12(Y) + I3(z) in which/1-3 indicate the weight the various centres have in producing fluorescence. For direct excitation in the centres these

PHYSICAL C H E M I S T R Y OF Z n S - C u

321

factors are d e t e r m i n e d b y the oscillator s t r e n g t h of the absorption b a n d for the exciting radiation, while t h e y f u r t h e r d e p e n d on the efficiency in the centre itself. The oscillator s t r e n g t h of the absorption is directly related to the transition p r o b a b i l i t y of the fluorescence. F r o m m e a s u r e m e n t s m a d e with excitation b y cathode rays, there are indications t h a t 10/2, 10/3 > /l > /2,/4. We shall t e n t a t i v e ly assume t h a t /l = 3/2 = 3/3 and therefore R = 3 x / ( y + z)

.(17)

W i t h the aid of (17) it is possible to determine KGI~ and Kz, , from the c o p p e r c o n c e n t r a t i o n s at which, for a certain composition of the a t m o s p h e r e , R = 1. W i t h 80 H 2 S - 20 HC1 this is the case for [Cu]to,a~ : 9 . 1 0 -5 and 5. I0 --6 (Fig. 1)1). At the u p p e r green-blue b o u n d a r y z m a y be ignored in a first app r o x i m a t i o n *), so t h a t R = 1 = 3 x / y , while [Cu]tota, ---- x + 2y ---- 9. l0 -5,

f r o m which it follows t h a t x ---- 1.29.10-5; y = 3.86.10 -5. Inserting these values in (14), t o g e t h e r with the partial pressures according to table II, we obtain KGB :

7.3" 108

(18)

At the l o w e r green-blue b o u n d a r y y m a y be ignored in a first app r o x i m a t i o n ; this leads to x o~ 5.10--* and z - ~ 3 x ==:_15.10--*. F u r t h e r calculations show t h a t actually y is of the order of 0.2x; using this value we find x o~ 3.6.10 --6, z = 3x + 0 . 2 x ___ 10- s and K z . = 3.10 -1°. K z . can also be o b t a i n e d more directly from the concentrations of blue centres in ZnS-ZnC1. According te recent estimations b y B r i 1, based on the s a t u r a t i o n of the cathodofluorescence of ZnS-ZnC1, in comparison with t h a t of Z n S AgC1, z = 8.10 -6 for p r o d u c t s m a d e in 80 H2S - - 20 HC1 at 1200°C. This value is a little lower t h a n t h a t which B r i 1 arrived at before s). Chemical d e t e r m i n a t i o n of the chlorine c o n t e n t indicates a slightly higher value, viz z = 3.10 - s 6); it being e x t r e m e l y difficult to m a k e sure t h a t all e x t e r n a l chloride is e x t r a c t e d , this value only constitutes an u p p e r limit. T h e value z = 8.10 -6 leads to K :

1.45"10 -1°,

(19)

*) The results arrived at farther on show that this is actually the case. Physica XVI

21

322

F.A.

KROGER

AND N. W. SMIT

which is of the same order of magnitude as that arrived at above. For the further calculations the latter value has been chosen. Using the values (18) and (19) for KGB and Kzn the concentration of blue and green centres has been calculated for products containing various amounts of copper, made in various atmospheres; the green" blue ratio (R) was obtained from (17). The results are tabulated in tables n I and IV; calculated values of R are compared with the experimental data in Figs. 1 and 2. TABLE III C o n c e n t r a t i o n s of g r e e n c o p p e r c e n t r e s (x), blue c o p p e r e e n t r e s (y) a n d b l u e z i n c c e n t r e s (z) a n d t h e g r e e n : blue r a t i o of f l u o r e s c e n c e (R) c a l c u l a t e d f o r p r o d u c t s c o n t a i n i n g 0, 10- 5 or 10- 4 C u as a f u n c t i o n of t h e c o m p o s i t i o n of t h e H . S - - HCI a t m o s p h e r e . ( S c h e m e I) atmosphereaH2S --

~[

bHC]

99 98 95 90 80 70 60 40

[Cu]=0

1 2 5 10 20 30 40 60

[Cu] = 1 0 - 5

lO.x 1.7 2.4 3.7 5.4 8 0.3 2.7

2.4 3.1 4.1 5.0 5.9 6.4 6.8

8.2

7.2 5

I

l°'yl

I06~' I 0.4 1.7 2.24 0.8 2.7 1.6 2.8 2.83 4.95 2.53 2.18 7.0 1.87 9.3 1.39 I 14.2

3.8 3.4 : 2.951 2.5 2.05 1.8 1.6 1.4

[Cu] = 10 -6

I0 e x I I 0 6 y ] lOSz ] 3.2 4.4 6.6 912 13 15.5 18 23

48.4 47.8 46.7 45.4 43.8 42.3 41 38.5

0.06 0.11 0.25 0.50 1.14 1.7 2.6 5.1

TABLE IV C o n c e n t r a t i o n s of g r e e n c o p p e r ¢ e n t r e s (x), b l u e c o p p e r e e n t r e s (y) a n d blue z i n c e e n t r e s (z), a n d t h e g r e e n : b l u e r a t i o (R) c a l c u l a t e d f o r p r o d u c t s c o n t a i n i n g v a r i o u s c o n c e n t r a t i o n s of c o p p e r m a d e i n 80 H2S - - 20HC1 a t 1200°C ( S c h e m e I) 106 [Cu]

106 x

1 2 4 FO 15 20 30 40 50 80 90 100 300 lO00

1 1.8 3.1 5.9 7.4 8.4 9.9 10.8 I 1.4 12.8 12.7 12.9 14 14.8

10 e y m

0.1 0.4 s 2.05 3.8 5.8 10.-14.6 19.3 33.8 38.6 43.5 143 497

10 8 z 7.9 7.1 6.4 4.9 s 4.2 3.5 2.8 2.3 1.9 s 1.3 1.2 1.1 0.4

R 0.38 0.75 1.36 2.53 2.77 2.70 2.31 1.915 1.60 1.07 0.96 0.87 0.29 0.09

R 0.20 0.27 s 0.42 0.60 0.876 1.06 1.24 1.9

PHYSICAL CHEMISTRY OF Z n S - C u

323 i

From Fig. 1 it is seen that the theory gives a curve with a maximum, but this maximum is too low, while the decrease of the curve at the side of high copper concentrations is too slow. The former discrepancy can be removed b y chosing ]1-----4]2 = 4/s, and therefore taking R = 4x (y + z) -1, instead of (17). The weak R 5

Fig. 1. C a l c u l a t e d a n d experim e n t a l v a l u e s for t h e g r e e n : blue r a t i o (R) for Z n S - C u , p r e p a r e d at 1200°C in an a t m o s p h e r e of 80 H2S - - 20 HC1, as a f u n c t i o n of t h e c o p p e r c o n c e n t r a t i o n . T h e experim e n t a l p o i n t s are t a k e n f r o m reference 1.

t%

t ~ 0 ~ l $0U2S-20UC~

t,

[cuI~

slope, however, cannot be improved. Similar discrepancies are revealed b y Fig. 2: the curve for a low copper concentration fits comparatively well, but the curve for 10--~ Cu is much too flat. Attempts to obtain better agreement between theory and experiment b y 5

Fig. 2 . C a l c u l a t e d a n d experim e n t a l v a l u e s for t h e g r e e n : blue r a t i o (R) for Z n S - C u c o n t a i n i n g 10 - s or 10--4Cu, p r e p a r e d at 1200°C in v a r i o u s a t m o s p h e r e s aH2S - bHC1; t h e e x p e r i m e n t a l p o i n t s are t a k e n f r o m reference 1.

i,

• .....

er~mental(rtq..~) colcul~f~I)

/

. . . . . .

4Cu

3

2

~0

20

30

40 50 60 J- ~.tCI in H~S-t4Cl

using different values of the constants Kc~ and Kz,, combined with different values o f / l : /2 :/a have failed; also the introduction of partial association of the incorporated halides did not give any improvement. Apparently the model has to be changed more fundamentally. S c h e m e II. In a second model it is assumed that Cu +, Zn + and C1- are incorporated in the lattice in equilibrium with the atmosphere at 1200°C, but that blue centres (Cu +) cannot exist at this temperature because they are totally dissociated into Cu + (green centres) and atomic copper (Cu°). Blue centres are formed b y association of fhese copper atoms with Cu + during the cooling from

324

1~. A. KROGER AND N. W. SMIT

1200°C to room temperature. This amounts to assuming that the equilibrium between the atmosphere and the solid phase is frozen in at its 1200°C-value, but that the internal dissociation equilibrium (Cu +) ~- Cu ° + Cu ÷ adjusts itself to a lower temperature at which association is more complete. For all centres the dissociation from C1- is assumed to remain complete. For the calculation it is not necessary to know in what form Cu ° is present, i.e. as an atom in the inter-lattice or as a monovalent ion at a lattice site next to a sulphur vacancy containing an electron 1), 3). If then

[Cu +] = x ,

[Cu °] = y

[Cu]taa ~ = x + y

and [Zn +] = z

and

[C1-] = x + z

(20)

The formation of Zn + is again regulated b y (9) which m a y be written in the form:

Kz. = z(x + z) P~'--~-Ps2

(21)

PHCI

For the copper we are only dealing with the incorporation of Cu ÷ and Cu °, the incorporation of Cu2S killers being ignored for the same reasons as outlined above. The equations of the reactions involved are Cu2S + 2HC1 ~ 2(Cu +) + 2(C1-) + H2S

Cu2S

~ 2(Cu°) + ½S2

(Cu +) + (C1-) + ½H2S ~ (Cu °) + HC1 + iS 2 and therefore Kc u _ [ C u °] [Cu +] [C1-]

PHc] P62 _ P!~2s

Y

PHClPSi2

(22)

x(x+z) P~s

During cooling Cu ° combines with Cu ÷ to form Cu2+ ; if for the sake of simplicity, this association is assumed to be complete, then the y Cu ° atoms combine with y Cu + to from y blue Cu + centres, leaving (x - - y) green Cu + centres. Assuming further/1 = 3[2 = 3/3 as above, then. R -- 3(x - - y)

y+z

(23)

From (23) and (22), Kcu can be determined from the position of

PHYSICAL

CHEMISTRY

OF ZnS-Cu

325

the green:blue boundary as outlined above. Using again the value [Cuq,ta,~ = 9.10 -5 for 80 H2S - - 20 HC1 we obtain Kcu ----- 2.2.10 3

(24)

From (20), (21), (22) and (23) the concentrations of the various centres and the values of the ratio R between green and blue have been calculated, using the values (19) and (24) for the equilibrium constants. The results are given in tables V and VI and the values of R are compared with the experimental data in figs. I and 2. TABLE V Concentrations of green copper centres ( x - y). b l u e c o p p e r c e n t r e s (y) and blue z i n c c e n t r e s (z) and the green: blue ratio (R) calculated for products c o n t a i n i n g 10 - 5 or 10 -* Cu, a n d p r e p a r e d in various H 2 S - - H C I a t m o s p h e r e s ( S c h e m e I1) [Cu] =

a H , S - - bHCI 98

2

95

5

90 80

I0 20

70 60

30 40

50

50

10U(X

-

-

0.6 3.2 5.4 6.8

7.6 8.8.2

y)

10-~

[Cu] =

t lo.y

Ilo..I

R

4.7 3.4 2.3 1.6 1.2 1.--

0.93 1.62 2.84 4.66 6.2 I 8.9

0.84

111.3

0.32 1.92 3.15 3.25 3.08 2.44 2.04

10-4

lOs ( x - y ) l IO~y I looz I R m - - *) 12 28 40 48

44 44 36 30 26

0.67 1.13 1.65 2.28 2.95

0 0.79 2.23 3.7I 4.96

*) x < y T A B L E VI Concentrations of green copper centres (x - - y), blue c o p p e r eentres (y) and blue zinc centres (z) and the ratio green: blue (R) calculated for products c o n t a i n i n g various a m o u n t s of copper, and p r e p a r e d in 8 0 H , S - - 2 0 H C 1 a t 1200°C 10 e C u 1 5 10 20 30 50 80 100 150

10 6 ( x - - y ) 0.8 3.8 6.8 11.6 14.8 18 16 12 0

10 ~ y

10 6z

R

0.1 0.6 1.6 4.2 7.6 16 32 44 75

8 6.5 4.7 3.35 2.6 1.9 1.3 l.l 0.9

0,3 1.59 3.25 4.6 4.35 3 1.45 0.8 0

From the same equation we have also calculated the position of the green-blue boundary, i.e. the copper concentration at which, for a given composition of the atmosphere, R = I. The results are shown in Fig. 3, together with the experimental curves ac-

326

i¢. A. K R / J G E R A N D

N. W . SMIT

cording to ref. 1. In all cases the agreement is satisfactory. We are therefore inclined to believe that this model corresponds to reality. I0"; Z,S-Cu :1200"C: H~S-HCt Green-blue boundorles ( R . I ) experimental ( ref. I) ------colculoted (scheme,~)

CC,,

tO-a Cu -blue

JO~

fO-S

Za-/~e o

io

Fig. 3. C a l c u l a t e d a n d e x p e r i m e n t a l p o s i t i o n s of t h e b o u n d a r i e s b e t w e e n g r e e n a n d b l u e fields (R = 1) for Z n S - - x C u p r e p a r e d a t 1200 ° i n a H 2 S - bHC1; t h e e x p e r i m e n t a l c u r v e s h a v e b e e n t a k e n f r o m r e f e r e n c e 1 (Fig. 4).

It must be amphasized that this theory does not lead to acceptable results if Kzn is assumed to be much greater than (19). Conversely the satisfactory results of the theory using this value m a y be considered as an indication of the correctness of this value. On the basis of the theory we have also calculated the concentration of centres and the value R for methods of preparation in which !

--

[cu]:

a.to-~ - -

\\ / #oI.bs-20~CI

A

B

S~ H, N,

Fig. 4. V a r i a t i o n s of t h e g r e e n : b l u e r a t i o (R) u p o n a d d i t i o n of H 2, N 2 o r S 2 t o t h e a t m o s p h e r e of p r e p a r a t i o n (80 H2S - - 20 HCI) for [Cu]taa~ = 3.10 - s (A), or 8.10--5(B).

P H Y S I C A L C H E M I S T R Y OF Z n S - C u

''

~,

~do

ddo

o,

~

~

-

o o

~

'

~

327

'

"ddo

o o

~ o

~

~

~

~

~

m m m m m

~ ~ ~I

~ ddl

~ I ~ ....

~ o o

~

--

6

~

i a

~

~

~

-o-

o o o o

dd

~~ d

~~

_

o o - -

dd

-

o o o o o -

~

d

II~ 0

o d

o d

d

o d

o

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--

!

~i

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ol

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o~.~

o°~

-

~-

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~O

O

o o o o o o

> PQ f~ <

- - o o

co

I

o

o

I'o O O O O O

O O O O

O O O O O O

ddddd

dddd

dddddd

co.,~

~8o

~__ "~

~

O 0

O 0

ddddd

~o

0

0

0

~

dddd 0 0

0 0

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0 0

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dddddd 0 0

0 0

~ 0

~ 0

0 0

0 0

0 0

0 0

I

c~

o v

V

328

PHYSICAL CHEMISTRY OF Z n S - C u

more complex atmospheres are used, viz. H 2 S - - H C 1 - - N 2 , H2S HC1 - - H 2 and H2S - - HC1 - - S2. Expressions for the partial pressures of the various components of the atmopshere are given in table I. Partial pressures calculated for various cases, together with values for the concentration of centres and the green:blue ratio are assembled in Table VII and the values of R are represented in fig. 4, A and B. The. difference in behaviour for the two copper concentrations is caused by the fact that for preparation in 80 H2S - - 2 0 HC1 at 1200° the product with 8.10 -s Cu lies closer to the green-blue boundary than that with 3.10 -s Cu. It is seen that an addition of N2, H2 or S2 in high concentrations in all cases causes the fluorescence to turn blue. With H 2, and to a smaller extent also with N 2, the decrease of R sets in immediately, but with S2 the oxidizing influence of the sulphur first causes an increase of R. These results seem not to be at variance with the experimental results so far available 1), but the experimental data are insufficient to test the theory more precisely. The values of the equilibrium constants regulating the formation of the centres are determined by the thermodynamic potential of the components participating in the reactions. For preparation in H 2 S - HBr or H 2 S - HI the constants must therefore be different. The same is of course the case for methods of preparation in which the halogen is provided by halides (NaC1, CaC12 etc.) and for those in which the monovalent activator ions are incorporated with the aid of trivalent cations (A13+, Gd 3+ etc). In all these cases the situation will be quantitatively different, but the qualitative picture remains the same. The experimental evidence so far available indeed points in this direction 2). -

-

Received January 7th, 1950.

REFERENCES 1) F.A. K r 6 g e r , J . E . H e l l i n g m a n and N.W. S m i t , Physiea 15,990(19t9). 2) F . A . K r U g e r and J. D i k h o f f , Physica 16, 297 (1950). 3) H.A. K l a s e n s , W. R a m s d e n and C h o w Q u a n t i e , ]'.opt. Soe. Am. tlS, 60 (1948). 4) Critical Tables. 5) A. B r i l , Physiea 15, 361 (1949). 6) F.A. K r 6 g e r and J . E . H e l l i n g m a n , J. eleetroehem. Soe. 95,68 (1949). 7) P. L e n a r d , Ann. Physik 31, 661 (1910).