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UBC Theses and Dissertations

The phosphorescent decay of Srs.CeSm Hamilton, Donald Ross 1952

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THE PHOSPHORESCENT DECAY OF SrS.CeSm by D o n a l d R o s s H a m i l t o n A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREES OF MASTER OF ARTS i n t h e D e p a r t m e n t o f PHYSICS We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e s t a n d a r d r e q u i r e d f r o m c a n d i d a t e s f o r t h e d e g r e e o f MASTER OF ARTS Members o f t h e D e p a r t m e n t o f P h y s i c s THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1952 ABSTRACT The general c h a r a c t e r i s t i c s of i n f r a r e d s e n s i t i v e phosphors are d i s c u s s e d , with p a r t i c u l a r emphasis on S r S . CeSm, known as Standard V I I , which i s the subject o f t h i s r e s e a r c h . The apparatus i s d e s c r i b e d , and c o n s i s t s of an i n f r a r e d spectrometer, a p h o t o m u l t i p l i e r and a d i r e c t coupled a m p l i f i e r . The performance i s discussed i n some d e t a i l . Curves of the decay of phosphorescence f o r Standard VII are d e s c r i b e d ; i t i s found that on a log-t ime l o g -brightness p l o t , these curves are s t r a i g h t l i n e s f o r times greater than ten minutes. The l i m i t i n g slope depends on the time of e x c i t a t i o n , and i s r e l a t e d to i t by a simple law. I t i s a l s o e s t a b l i s h e d that there are two types of colour centers a c t i v e during phosphorescent^decay, cerium and samarium. The emission of cerium i s a band with peak at .4$5 microns, and that of samarium a s e r i e s of l i n e s i n the r e d . A number of s i m p l i f i e d theories are developed or d e s c r i b e d , no one of which exactly f i t the d a t a . I t i s suggested that the curves can probably be f i t t e d by an exponential d i s t r i b u t i o n of shallow traps i f absorption and s c a t t e r i n g are considered. CONTENTS A b s t r a c t I I n t r o d u c t i o n . . . . • . . . . 1 I I The : A p p a r a t u s . . . . . .' . . • . 6 I I I The E x p e r i m e n t a l P r o c e d u r e 11 I V The E x p e r i m e n t a l R e s u l t s . • . .• . . 13 V C o n c l u s i o n . . . 24 A p p e n d i x . 2 6 R e f e r e n c e s ILLUSTRATIONS DIAGRAM 1 Band Scheme f o r SrS.CeSm 2 O p t i c a l Diagram 3 Globar Jacket and F l a t Mounting 4 Three P o s i t i o n F l a t " 5 Spheroid Mounting 6 . D i r e c t - c o u p l e d A m p l i f i e r 7 H.T. Set a Pulse A m p l i f i e r 9 P r e - A m p l i f i e r 10 Power Supply 11 P h o t o m u l t i p l i e r Response and F i l t e r T r a n s m i s s i o n 12 Decay,-: of SrS.CeSm: T o t a l E mission 13 Decay of SrS.CeSm: Cerium E m i s s i o n 14 L i m i t i n g Slope a g a i n s t Time of E x c i t a t i o n X5 I n i t i a l Values of B 0 a g a i n s t Time o f E x c i t a t i o n 16 R i s e of S t i m u b i l i t y a g a i n s t Time o f E x c i t a t i o n 1 I . INTRODUCTION I n f r a r e d s e n s i t i v e phosphors are c r y s t a l l i n e s o l i d s whose phosphorescent emission i s e i t h e r enhanced or decreased on a b s o r p t i o n of i n f r a r e d energy. The former c l a s s of phos-phors emit r a d i a t i o n of short wavelengths i n apparent v i o l a t i o n of Stoke's p r i n c i p l e and are consequently s a i d to be capable of considerable " l i g h t s torage". The l a t t e r c l a s s show a decrease of normal phosphorescence or a f t e r glow on i r r a d i a t i o n ; they are the "contriglow" or "quenching" phosphors, and w i l l not be discussed here. Before e i t h e r process can occur, the l a t t i c e must be ex ci ted by higher energy r a d i a t i o n than that emitted. The most s e n s i t i v e phosphors of t h i s f i r s t s o r t are the a l k a l i n e earth sulphides and s e l e n i d e s . Discovered by Urbach"'-and h i s c o l l a b o r a t o r s at the U n i v e r s i t y of Rochester, these host c r y s t a l s must be a c t i v a t e d or s e n s i t i z e d by i n c l u s i o n i n t o the matrix of small q u a n t i t i e s of two r a r e earths known as a c t i v a t o r s . Since the i n i t i a l emphasis i n such research was to compound phosphors s u i t a b l e f o r wartime a p p l i c a t i o n s , the m a t e r i a l s developed possess low backgrounds combined with high i n f r a r e d s e n s i t i v i t i e s and emissions favorable to the dark adapted eye. Phosphors of strontium sulphide or s e l e n i d e , with samarium and europium or c,erium a c t i v a t o r s , have the d e s i r e d c h a r a c t e r i s t i c s ; f u r t h e r d i s c u s s i o n w i l l be r e s t r i c t e d to these systems. The o p t i c a l constants of these m a t e r i a l s are of unusual i n t e r e s t . For example, the spectrum emitted during i n f r a r e d i r r a d i a t i o n (hereafter termed stimulation) i s determined almost e n t i r e l y by one of the activators which as a consequence i s known as the dominant activator; the second a c t i v a t o r ' independently determines the inf r a r e d stimulation spectrum, and i s c a l l e d the a u x i l i a r y a c t i v a t o r . The emission spectrum due to the dominant a c t i v a t o r i s well-nigh independent of changes i n matrix material and a u x i l i a r y activator; likewise the stimulation spectrum i s independent of changes i n the matrix composition or dominant a c t i v a t o r . Samarium i s the best a u x i l i a r y a c t i v a t o r because of the remarkable s t i m u b i l i t y of the one micron response band and the high value of the " l i g h t storage" c o e f f i c i e n t ; as dominant a c t i v a t o r cerium i s moist suitable, since i t s green emission peak f a l l s i n the sen s i t i v e region of the dark-adapted eye. The samarium emission spectrum does not generally appear during eit h e r stimulation or phos-phorescence, although i t i s found i n the spontaneous afterglow of one phosphor and at low temperatures. Three doubly-activated a l k a l i n e earth compounds are of 2 m i l i t a r y importance: Standard VI: lOOSrS + 7.5Sr04 + .02Eu2 + .02Sm3 Standard BI: 100 SrSe + 7.5Sr04 + 7.5CaF2 + 7.5SrS + .005Eu2 + .017Sm3 Standard VII: lOOSrS + 7.5SrSO/,, + J02Ce2 + .02Sm3 Of these, Standard VII i s the most suitable f o r detection of inf r a r e d and i s the subject of t h i s research. A summary of i t s c h a r a c t e r i s t i c s follows. 3 The emission of Standard VII under stimulation i s the cerium band with a main peak at . 4 $ 5 microns and a shoulder at . 5 4 microns. The emission during spontaneous afterglow should be the same, but has been found by Urbaeh^ e t a l . to be "....almost exclusively the samarium spectrum"; since samarium i s the a u x i l i a r y a c t i v a t o r , the appearance of i t s emission here i s unusual. However, i t has been found i n the present research that the spectrum of cerium does occur, e s p e c i a l l y i f ex c i t a t i o n has been i n the corresponding ( i . e . .36 micron) absorption band. Excited Standard VII i s sensitive to infrared from about to 1 . 2 5 microns, with a peak at 1 . 0 2 microns. VII can be excited i n the absorption band of the matrix or i n the cerium band, mentioned above, which occurs at the long wave-length l i m i t of the matrix band; the rate of e x c i t a t i o n and the saturation value of s t i m u b i l i t y reached are, however, functions of wavelength. When excited, an ad d i t i o n a l region of absorption appears at 1 micron, corresponding to the i n f r a -red s e n s i t i v i t y . The matrix absorption peak i s at about . 2 $ microns, and " . . . . f a l l s o f f rather sharply to a cutoff at about 3 2 0 0 A on the long wavelength side, and f a l l s gradually, on the short wavelength side to about 2 6 5 0 A from which point a rather uniform absorption continues at least as f a r as 2 0 0 0 A which was the l i m i t of the spectrometer used....The long wave-length ex c i t a t i o n band f o r Std. VII - the cerium band - i s only 1 0 0 A wide and peaks to about 36OO A". (Polytechnic In s t i t u t e of Brooklyn, F i n a l Report on Contract N 0 b s r 3 9 0 4 5 , hereafter referred to as I, p. $ 4 ) • From the e f f e c t s o f a c t i v a t o r s on o p t i c a l p r o p e r t i e s ( o u t l i n e d on page 2) a number of c o n c l u s i o n s can be drawn and a t h e o r e t i c a l model proposed. Because the a u x i l i a r y a c t i v a t o r i s r e s p o n s i b l e f o r the " l i g h t s t o r a g e " and i n f r a r e d s e n s i t i v i t y , i t i s p o s t u l a t e d t h a t a s s o c i a t e d w i t h each a u x i l i a r y a c t i v a t o r atom t h e r e i s a s t a b l e e l e c t r o n energy l e v e l , o f the order o f 1.2 e l e c t r o n v o l t s below the conduction band. The dominant a c t i v a t o r atoms are said t o behave as normal c o l o u r c e n t e r s , independent of the a u x i l i a r y a c t i v a t o r atoms; e l e c t r o n i c t r a n s i t i o n s between the two are b e l i e v e d t o take p l a c e through the conduction band. Thus, i n diagram 1, t h e r e are two separate c e n t e r s , cerium and sam-CONDUCTION BAND E x c i t e d s t a t e M u l t i p l e S m G r o u n d l e v e l C e l e v e l FULL BAND DIAGRAM 1 ' arium. E x c i t a t i o n r a i s e s e l e c t r o n s from e i t h e r the cerium l e v e l s or the f u l l band t o the condu c t i o n band ( t r a n s i t i o n s A and B); i n the l a t t e r case the cerium e l e c t r o n combines w i t h the f r e e h o l e w i t h the same end r e s u l t * B i s dominant i f the e x c i t i n g u l t r a v i o l e t quanta have e n e r g i e s equal to o r g r e a t e r than the Some of the e l e c t r o n s i n s e p a r a t i o n o f f i l l e d and empty bands, the conduction band then r e t u r n t o empty c e n t e r s , but the m a j o r i t y are trapped by the shallow samarium l e v e l s where th e y 5 are stable, having a l i f e t i m e of some weeks. The i n f r a r e d s e n s i t i v i t y i s explained by l i b e r a t i o n of such trapped electrons (G) through i n f r a r e d energy absorption with subsequent r a d i a t i v e t r a n s i t i o n s D. Phosphorescence or after glow i s accounted f o r by similar t r a n s i t i o n s D made by the electrons i n the conduction band after excitation; the samarium emission i n the spontaneous afterglow of Standard VII implies that t r a n s i t i o n s to and from excited states near the conduction band and the samarium ground state(s) also take place. Such t r a n s i t i o n s E are forbidden i n Standards VI and BI. Samarium emission probably does not occur i n the stimulated spectrum because the number of empty samarium centers i s small and the recombination p r o b a b i l i t y high during phosphorescence. Most of the recent experimental work has been directed towards understanding of the processes involved i n the decay of brightness during i n f r a r e d i r r a d i a t i o n . Under these circumstances a high f l u x of in f r a r e d energy i s used which gradually empties the occupied traps. This type of decay i s d i s t i n c t from phosphorescent decay i n which the energy supplied to the process i s s t r i c t l y room 3,4,5 temperature a g i t a t i o n . I t i s generally found that lim B = A f n l ^ n ^ 2 t — oo That i s , a plot of B against t on log log paper•in the l i m i t i s a l i n e of slope -n. To correlate t h i s with the bimolecular law, n = 2, corrections are made f o r absorption and scattering of ra d i a t i o n within the phosphor sample; although there are serious objections to such a scheme, exact f i t s of experimental data have been obtained. Some simultaneous observations have also been made on the decays of brightness and photocurrent under stimu-l a t i o n (I, p 101); these indicate that some degree of electron retrapping may be present i n Standard BI. This theory i s discussed i n greater d e t a i l i n section VI. The present research concerns i t s e l f with the decay of spontaneous afterglow of Standard VII f o r varying degrees of ex c i t a t i o n . Reports on t h i s phenomena are rather rare due to the low level s of emission experienced. They are: a) two curves published i n I, p 125, and b) a reference to an unpublished work of Schrader of R.C.A.6 I t was hoped that inve s t i g a t i o n of phosphorescence ( i n p a r t i c u l a r the emission processes to the cerium colour centers) would cor-3 4 ' roborate some of the r e s u l t s to be found i n I and other.papers. ' ' I I . THE APPARATUS The apparatus has two p r i n c i p l e parts - a Perkin-Elmer monochromator and a microphotometer. The Perkin-Elmer with i t s associated sources and optics i s shown i n diagram 2. Several types of prisms are available f o r the Perkin-Elmer but during these experiments one' of rock s a l t was f i t t e d ; the Littrow mirror M4 was adjusted so that the operating range was from .36 to 15. microns. As a consequence the monochromator i s us e f u l i n exciting the phosphor as well as i n stimulating i t with i n f r a r e d . The in f r a r e d source i s the Globar SI, a two hundred watt s i l i c o n carbide heater element enclosed i n a water-cooled jacket. (See work drawing 3). The r a d i a t i o n peak f a l l s at 2.25 microns, assuring a stable s i g n a l at one micron. A second source i s an air-cooled General E l e c t r i c AH.-4 mercury arc lamp; the .365 l i n e was used to excite the phosphors.. A helium lamp i s also a v a i l a b l e f o r c a l i b r a t i o n of the spectrometer and f o r c a l c u l a t i o n of f i l t e r transmission f a c t o r s . Sources are selected by rotation of Ml; (Work diagram 3 ) . The monochromatic output beam f a l l s on M8 and can be directed three ways by M9, a rot a t i n g f l a t with three spring-loaded stable positions. (Work diagram 4 ) . The spheroid M i l (Work diagram 5) i s set twenty degrees o f f angle; t h i s introduces s u f f i c i e n t l a t e r a l astigmatism into the image below M12 to evenly i l l u -minate the entire phosphor surface. This angle was calculated from the well-known formula 1 - 1 = s i n i tan i s i s£ f where s- arid s^ are the distances measured along the p r i n c i p a l ray from the mirror surface to the primary and secondary images, and i i s the angle of incidence. Standard VII i s available only as a pressure bonded button, 1.55 cm. i n diameter and .2 em. t h i c k . The sample i s held on the m u l t i p l i e r photocathode ( 2 4 . 8 cm. below M12) by a clear l u c i t e disk; above the phosphor i s mounted a small aluminized paraboloid which r e f l e c t s most of the sig n a l onto the cathode surface. This photomultiplier, i t s amplifier and power supply are the p r i n c i p l e photometer components. An R.C.A. 5$19 8 m u l t i p l i e r , was employed because of the h i g h s e n s i t i v i t y i n the b l u e and the l a r g e cathode a r e a . Three tubes were a v a i l a b l e and of these one had a phenomenally s m a l l and steady n o i s e c u r r e n t ( 3 x 10" 1 0 + 5 x 10""11 amperes a t 100 v o l t s per s t a g e ) . Although another of the t h r e e was 1.3:1 times more s e n s i t i v e , the s i g n a l n o i s e r a t i o s d i f f e r e d by a f a c t o r of 1:2.4 x 10 2 i n f a v o u r of the f i r s t . The e x c e l l e n c e of t h i s m u l t i p l i e r was i n s t r u m e n t a l i n the s a t i s f a c t o r y e x e c u t i o n o f t h i s r e s e a r c h . The dynodes are f e d by a 100k b l e e d e r c h a i n i n a c o n v e n t i o n a l c i r c u i t ; h i g h b leeder c u r r e n t i n s u r e s constant dynode v o l t a g e s d u r i n g h i g h s i g n a l s and a l s o reduces the u s u a l i n s t a b i l i t y when the H.T. i s f i r s t a p p l i e d to the m u l t i p l i e r . The photo-c u r r e n t o f the m u l t i p l i e r i s grounded through the (one:: per cent) p r e c i s i o n g r i d l e a k r e s i s t o r s of the i n p u t s t a g e . These r e s i s t o r s and the l e a d s between the anode and f i r s t g r i d are e n t i r e l y s e l f - s u p p o r t i n g except f o r the switch c o n n e c t i o n s ; the switch i t s e l f i s low-leakage s t e a t i t e . The a t t e n u a t o r , f i r s t stage and p h o t o m u l t i p l i e r i s mounted on p o l y s t y r e n e ; the e n t i r e assembly was washed i n a l c o h o l t o f u r t h e r reduce leakage c u r r e n t s . The c u r r e n t a m p l i f i e r (diagram 6) i s the s i m p l e s t d i r e c t -coupled s o r t . The f i r s t stage i s a 959 a c o r n tube connected i n the u s u a l e l e c t r o m e t e r c i r c u i t ; i n t h i s arrangement the p h o t o m u l t i p l i e r s i g n a l i s a p p l i e d to the suppressor g r i d i n o r d e r t o a v o i d g r i d c u r r e n t . The measured leakage c u r r e n t from a l l sources ( i n c l u d i n g g r i d c u r r e n t ) i s l e s s than 5 x 10~ 1 2 amperes. The 959 i s d i r e c t - c o u p l e d to a 1U4 m i n i a t u r e s h a r p c u t - o f f p e n t o d e ; t h e t e n megohm anode l o a d i s b y V p a s s e d t o g r o u n d by a .004 m i c r o f a r a d c o n d e n s e r t o i n c r e a s e s t a b i l i t y . The c a t h o d e l o a d o f t h e f i n a l 3S4 s t a g e i s a 10k p r e c i s i o n r e s i s t o r s h u n t e d b y a 5Q m i c r o a m p e r e o u t -p u t m e t e r a n d i t s a s s o c i a t e d z e r o - s e t t i n g p o t e n t i o m e t e r s ; one v o l t i n p u t g i v e s f u l l s c a l e m e t e r d e f l e c t i o n w i t h t h i s 10k r e s i s t o r i n t h e f e e d b a c k l o o p . C o n s e q u e n t l y , i n p u t r e s i s t a n c e s f r o m 10^ t o 10^ ohms e n a b l e measurement o f c u r r e n t s f r o m 10~3 t o 1 0 " ^ amperes, a l t h o u g h i n p r a c t i c e s i g n a l s l o w e r t h a n 10"*9 amperes a r e n o t u s e d ( s i g h a l - t o - n o i s e r a t i o o f t w o ) . A c a l c u l a t i o n b a s e d on s e n s i t i v i t y f i g u r e s q u o t e d i n t h e R.C.A. handbook i n d i c a t e s t h a t t h e u s e f u l r a n g e o f l i g h t i n t e n s i t y i s o f t h e o r d e r o f 10 t o 10~5 m i c r o l u m e n s . C h e c k s o f l i n e a r i t y ( l i g h t i n t e n s i t y v e r s u s o u t p u t s i g n a l ) were made o v e r t h i s r a n g e i n two ways: a) v e r i f i c a t i o n o f t h e i n v e r s e s q u a r e l a w u s i n g a s i n g l e s o u r c e and o p t i c a l b e n c h ; b) c o m p a r i s o n o f t h e sum o f two combined s o u r c e s w i t h t h e sum o f t h e s o u r c e s s i n g l y . I f a l l o w a n c e i s made f o r t h e n o i s e c u r r e n t on t h e l o w e r s c a l e s t h e p h o t o m e t e r i s l i n e a r o v e r t h e above r a n g e w i t h i n t h e l i m i t s {!%) o f t h e e x p e r i m e n t a l e r r o r . Long t e r m s t a b i l i t y o f t h e a m p l i f i e r i s 2% o f f u l l s c a l e ; s h o r t t e r m e x c u r s i o n s ( p e r i o d s o f f i v e t o t e n m i n u t e s ) o f t h e z e r o s e t t i n g do o c c a s i o n a l l y o c c u r b u t n e v e r amount t o more t h a n t h r e e p e r c e n t o f f u l l s c a l e and a r e u s u a l l y l e s s t h a n one p e r c e n t . T h e s e c h a n g e s a r e due t o s m a l l f l u c t u a t i o n s o f t h e anode c u r r e n t , t h e t o t a l v a l u e o f w h i c h i s 1.5 m i l l i a m p e r e s ; f i l a m e n t d r a i n i s 200 m i l l i a m p e r e s ; a s a c o n s e q u e n c e o f t h e s e f a c t s no a p p r e c i a b l e 10 change of b a t t e r y voltages has occurred over three months of o p e r a t i o n . Because miniature tubes are used the a m p l i f i e r i s small enough to be mounted underneath the p h o t o m u l t i p l i e r ; the B b a t t e r i e s , meters and switches are b u i l t i n t o a rack mounting. The'H.T. set (diagram 7) c o n s i s t s of a f o u r k i l o v o l t , f i f t e e n milliampere supply w i t h a three stage r e g u l a t o r . Since the output voltage i s set f o r 1.2 k i l o v o l t s , the t o t a l c o n t r o l v oltage a v a i l a b l e across the 807 s e r i e s r e g u l a t o r tube i s of the order of 3 k i l o v o l t s ; as a r e s u l t the r e g u l a t i o n f a c t o r i s l a r g e . A change i n l i n e voltage of 30 v o l t s produces a change i n output voltage of l e s s than £ of a v o l t , the experimental e r r o r . The average noise component i n the output was at one time 100 m i c r o v o l t s ; a d d i t i o n of a .05 microfarad condenser from the 6SL7 g r i d t o the 6J7 cathode reduced these t r a n s i e n t s t o 15 m i c r o v o l t s . D r i f t of output voltage i s 1.2. to 1.5 v o l t s per day, due to aging of the composition r e s i s t o r s i n the r e g u l a t o r c i r c u i t . As the e n t i r e supply i s f l o a t i n g , e i t h e r s i d e of the output can be grounded; a negative H.T. i s more convenient since the m u l t i p l i e r anode and the a m p l i f i e r i s then at ground p o t e n t i a l . The p r e l i m i n a r y experimental work was done w i t h the H.T. set and an A.C. pulse a m p l i f i e r r a t h e r than the d i r e c t coupled a m p l i f i e r now employed. The o r i g i n a l i n t e n t i o n was to r e g i s t e r m u l t i p l i e r output w i t h a d i s c r i m i n a t o r and s c a l e r , but t h i s was ^discarded when megacycle counting r a t e s were encountered. A counting r a t e meter, i n t e g r a t i n g the d i s -11 c r i m i n a t o r o u t p u t , p r o v e d more s u i t a b l e b u t was s a t i s f a c t o r y -o v e r an i n t e n s i t y r a n g e o f o n l y 1:5 x 10 2. D i s c o u r a g i n g a t -t e m p t s t o c a l i b r a t e t h i s i n s t r u m e n t b y t h e i n v e r s e s q u a r e l a w l e d t o . t h e c o n s t r u c t i o n o f t h e D.C. a m p l i f i e r d e s c r i b e d a b o v e . The c i r c u i t s o f t h e p u l s e a m p l i f i e r , p r e - a m p l i f i e r a n d a s s o c i a t e d power s u p p l y a r e i n c l u d e d f o r r e f e r e n c e . ( D i a g r a m s 8, 9 , 1 0 ) . C o n t r o l c i r c u i t s i n c l u d e a V a r i a c , v o l t a g e and c u r r e n t m e t e r s f o r G l o b a r S4; a V a r i a c and c u r r e n t m e t e r f o r t h e a r c s S2 and S3 a t t h e P e r k i n - E l m e r e n t r a n c e s l i t . An H.T. m e t e r and a m o n i t o r f o r p u l s e a m p l i f i e r p l a t e v o l t a g e c o m p l e t e t h e e l e c t r i c a l s y s t e m . I I I . THE EXPERIMENTAL PROCEDURE A c o m p l e t e e x p e r i m e n t on t h e d e c a y o f p h o s p h o r e s c e n c e i n a n i n f r a r e d s e n s i t i v e m a t e r i a l i n v o l v e s f o u r e x p e r i m e n t a l s t e p s : e x h a u s t i o n o f t h e p h o s p h o r , t h a t i s , l i b e r a t i o n o f a l l t r a p p e d e l e c t r o n s by h e a t i n g so t h a t t h e p h o s p h o r i s c o m p l e t e l y u n e x c i t e d ; e x c i t a t i o n o f t h e p h o s p h o r by m o n o c h r o m a t i c u l t r a -v i o l e t ; measurement o f t h e d e c a y o f p h o s p h o r e s c e n c e w i t h t h e p h o t o m e t e r ; f i n a l l y , a c h e c k on t h e i n f r a r e d s t i m u l a t i o n s p e c t r u m a f t e r t h e d e c a y o f a f t e r g l o w i s c o m p l e t e . S t a n d a r d V I I i s e x h a u s t e d o r d e - e x c i t e d b y h e a t i n g t h e p h o s p h o r b u t t o n i n an e n c l o s e d p y r e x d i s h t o 200°C a n d c o o l i n g i t s l o w l y t o room t e m p e r a t u r e ; i t must t h e n be t r a n s f e r r e d t o t h e a p p a r a t u s i n a b s o l u t e d a r k n e s s . The t h e r m o l u m i n e s c e n c e f t h e o r y o f R a n d a l l and W i l k i n s ^ i s t h e b a s i s o f t h i s p r o c e d u r e ; j u s t i f i c a t i o n o f t h e 200° f i g u r e i s g i v e n i n A p p e n d i x I . 12 The completeness o f exhaustion was always checked by i r r a d i a t i n g the sample 5 cm. d i s t a n t from a General E l e c t r i c 250 watt i n f r a r e d lamp, f i l t e r e d by a Corning 2450 heat f i l t e r ; the phosphor was considered f u l l y exhausted i f t h i s high energy f l u x produced no v i s i b l e e m i s s i o n . (T h i s corresponds zero •photometer s i g n a l when i r r a d i a t e d by monochromatic i n f r a r e d from the P e r k i n - E l m e r ) . E x c i t a t i o n was c a r r i e d out wit h the phosphor i n p l a c e on the p h o t o m u l t i p l i e r ; the .365 micron l i n e from the AH-4 a r c (S2, diagram 2) was used. The l i n e a r thermocouple and a m p l i f i e r o f the Perkin-Elmer spectrometer was used t o s e t the arc i n t e n s i t y b efore making a run; the "standard i n t e n s i t y " was d e f i n e d as a s i g n a l o f 1.8 m i c r o v o l t s with s l i t opening 1.5 mm., wave d r i v e 25.23 t u r n s , a m p l i f i e r g a i n a t 1 m i c r o v o l t = 20% d e f l e c t i o n on the Brown r e c o r d e r . Arc c u r r e n t under these c o n d i t i o n s was about .75 amperes, but v a r i e d s l i g h t l y as the AH-4 bulb blackened w i t h age. Since the thermocouple cannot be employed d u r i n g e x c i t a t i o n (M6 i s swung out of the mono-chromatic beam) a "Ssixtus" photographic exposure meter a l s o monitored the output. The photometer was t u r n e d on b e f o r e e x c i t a t i o n ; thus the s i g n a l r e f l e c t e d from the phosphor onto the photocathode provided another check on c o n d i t i o n s . T h i s was r e l i a b l e to about one p a r t i n t e n s i n c e v a r i a t i o n s i n phosphor p o s i t i o n sometimes allowed u l t r a v i o l e t t o " s p i l l o ver" d i r e c t l y onto the s e n s i t i v e s u r f a c e . A f t e r the e x c i t a t i o n had been shut o f f , ( t = 0 ) , 13 b r i g h t n e s s measurements were made against time; the decay was f o l l o w e d down to 10~9 amperes, or 300 minutes, whichever was s h o r t e r . Check of the zero s e t t i n g was o c c a s i o n a l l y made by swi t c h i n g the input attenuator to. ground and making the necessary potentiometer adjustments. S t i m u l a t i o n of an e x c i t e d phosphor was performed i n much the same f a s h i o n as e x c i t a t i o n , only the Globar (SI) was employed. Standard c o n d i t i o n s were a s i g n a l of 2.5 m i c r o v o l t s with s l i t opening .05 mm, wave d r i v e 13*90 (3 microns) g a i n as before. The i n f r a r e d spectrum from .63 to 1.8" microns was scanned with , s l i t openings .100 mm. and .250 mm.; the intensity;;" measured was, of course, the sum of the s t i m u l a t e d i n t e n s i t y and the r e s i d u a l phosphorescent i n t e n s i t y . Before the experimental r e s u l t s can be i n t e r p r e t e d , a number of f a c t o r s have to be considered. For example, the f i g u r e s on i n f r a r e d response must be corre c t e d f o r v a r i a t i o n s i n d i s p e r s i o n and black body r a d i a t i o n w i t h wavelength i n order to reduce the experimental data to a set with constant energy f l u x f o r a l l wavelengths. Allowance must be made f o r f i l t e r t r a n s m i s s i o n s and p h o t o m u l t i p l i e r response i n measuring phos-phorescent decay. Such c o r r e c t i o n s have been c a r r i e d out f o r a l l data i n the f o l l o w i n g s e c t i o n , and d e t a i l s are i n c l u d e d t h e r e . •IV. EXPERIMENTAL RESULTS Data on phosphorescent decay has been obtained by the techniques o u t l i n e d i n the preceeding s e c t i o n . T h e o r e t i c a l 14 a n a l y s i s o f t h e r e s u l t s i s , however, g r e a t l y c o m p l i c a t e d by t h e f a c t t h a t the s p e c t r a l d i s t r i b u t i o n o f t h e e m i s s i o n i s n o t c o n s t a n t t h r o u g h o u t t h e c o u r s e o f a g i v e n e x p e r i m e n t . To c l a r i f y t h i s p o i n t a number o f p h o t o g r a p h s were t a k e n w i t h a s m a l l H i l g e r c o n s t a n t d e v i a t i o n s p e c t r o m e t e r . P r e l i m i n a r y i n v e s t i g a t i o n w i t h a d i r e c t v i s i o n s p e c t r o m e t e r had i n d i c a t e d t h a t t h e e m i s s i o n o f samarium d u r i n g b a c k g r o u n d decay was a s e r i e s o f weak l i n e s f r o m a b o u t .55 m i c r o n s i n t o t h e i n f r a -r e d ; d a t a o f G o b r e c h t and l a t e r P r e n e r (I p 48) f o r S r S . S m u n d e r d i r e c t u l t r a v i o l e t e x c i t a t i o n c o n f i r m e d t h i s o b s e r v a t i o n . U n f o r t u n a t e l y , t h e b r i g h t n e s s l e v e l s e n c o u n t e r e d d u r i n g p h o s -p h o r e s c e n t decay a r e s e v e r a l o r d e r s o f magnitude l o w e r t h a n , t h o s e d u r i n g d i r e c t e x c i t a t i o n ; c o n s e q u e n t l y some means o f e x c i t i n g t h e phosphor r e p e a t e d l y and e x p o s i n g i t d u r i n g t h e e a r l y (and hence b r i g h t e s t ) s t a g e s o f t h e decay had t o be d e v i s e d . A r o t a t i n g d i s k , s i m i l a r t o a B e c q u e r e l p h o s p h o r o -s c o p e , was employed f o r t h e f i r s t e x p o s u r e s ; s i n c e t h e a c t u a l t i m e o f e x c i t a t i o n and the e x p o s u r e a t t h e s l i t were o n l y a f r a c t i o n o f t h e t o t a l t i m e f o r one r e v o l u t i o n , t h i s p r o v e d u n s a t i s f a c t o r y . I n t h e f i n a l arrangement a m e r c u r y a r c ^ a h e a t f i l t e r , t h e phosphor and t h e s p e c t r o m e t e r were mounted c o l i n e a r l y ; t h e phosphor was r o t a t e d about a v e r t i c a l d i a m e t e r by a s m a l l m o t o r . The e x c i t i n g u l t r a v i o l e t beam was c o l l i m a t e d t o a w i d t h s l i g h t l y l e s s t h a n t h a t o f t h e phosphor b u t t o n when i t was edge o n ; t h e b u t t o n t h u s a c t e d as i t s own s h u t t e r . None o f t h e a r c r a d i a t i o n f e l l d i r e c t l y o n ' t h e s p e c t r o m e t e r s l i t , so t h e r e was no h a l a t i o n a t t h e s t r o n g e r m e r c u r y l i n e s . 15 C o n t i n u o u s e x p o s u r e t o b o t h t h e .365 m i c r o n e x c i t a t i o n a n d t o t h e s p e c t r o m e t e r were t h u s o b t a i n e d . TABLE I W a v e l e n g t h s o f Samarium E m i s s i o n i n SrS.Sm a n d SrS.CeSm ( i n t e n s i t i e s b r a c k e t e d ) P r e n e r 1 s D a t a SrS.Sm M e a s u r e d SrS.CeSm P r e n e r ' s D a t a . SrS.Sm M e a s u r e d SrS.CeSm 5550 (5) 5553 6068 (7) 6076 5586 (7) 5537 6107 (7) d i f f u s e 5621 (3) - 6315 (2) 5641 (10) 5640 6359 (4) a t l e a s t 5679 (10) 5676 6382 (4) t h r e e l i n e s 5706 (6) 6420 (4) n o t r e c o r d e d 5739 (5) 5734 6431 (4) 6460 (4) 6459 5935 (5) 5934 6544 ($) 6534 5 9 6 6 . ( 6 ) 5963 6579 (4) 6576 5994 (10) 5993 S p e c t r o m e t e r l i m i t 6036 (10) 6034 The m e a s u r e d w a v e l e n g t h s o f t h e l i n e s a r e t a b u l a t e d i n T a b l e I . a l o n g w i t h P r e n e r ' s d a t a f o r SrS.Sm; t h e r e c a n be l i t t l e d o u b t t h a t t h e r e c o r d e d e m i s s i o n i s t h a t o f Sm +^. In. h i s a n a l y s i s P r e n e r f i n d s s i x g r o u p s o f l i n e s , w h i c h ".;>..are e x p l a i n e d i n a c c o r d a n c e w i t h G o b r e c h t ' s scheme a s t r a n s i t i o n s b e t w e e n a 6 s i n g l e u p p e r t e r m and t h e components o f a H g r o u n d t e r m m u l t i p l e t w h i c h a r i s e s f r o m t h e f i v e ' e q u i v a l e n t 4f e l e c t r o n s o f a t r i v a l e n t samarium atom". ( F o u r g r o u p s a r e r e c o r d e d a b o v e ) . The a c c u r a c y o f t h e d a t a i n T a b l e I i s i n s u f f i c i e n t t o a l l o w e x a m i n a t i o n f o r a s h i f t ( i f any) due t o t h e s l i g h t v a r i a t i o n i n c o m p o s i t i o n . 16 Photographic evidence of cerium emission i s more d i f -f i c u l t , to obtain. Using an 0 plate (which i s more sen s i t i v e than the F plate at the cerium emission peak) a negative was taken which showed marked darkening up to .445 microns, the short wavelength l i m i t of the cerium band as found i n the 1 stimulated emission. Since the exposure was two days long and the s l i t opening ten times greater than i n Plate I, bad hala t i o n about the samarium l i n e s obscured the long wavelength part of the band. The general c h a r a c t e r i s t i c s of the cerium band (see Part I) were corroborated by exciting a sample at the entrance s l i t to. the Perkin-Elmer spectrometer and quickly scanning the decay with the photomultiplier. The procedure was marred by the low l e v e l and rapid decay of the s i g n a l . Possibly the best evidence f o r the presence of cerium emission has been obtained from the decay curves themselves. The measured response of the m u l t i p l i e r and the transmission of a blue f i l t e r are plotted on diagram 11. Using Urbach's curve f o r the cerium d i s t r i b u t i o n and a method of numerical integration i t was calculated that the f i l t e r would reduce the cerium sign a l to 37% of i t s former value. This c a l c u l a t i o n was checked by making stimulation runs with and without f i l t e r f o r an ex c i t a t i o n time of twenty minutes; since the stimulated emission i s e n t i r e l y that of cerium a si m i l a r transmission (34$) was found. However, the combination of f i l t e r and photomultiplier i s such that the response to the samarium l i n e spectrum is. n e g l i g i b l e ; hence decays with the f i l t e r are the response to the cerium component alone. Such curves were r e a d i l y obtained, 1 7 c o n f i r m i n g t h e p r e s e n c e o f t h e c e r i u m b a n d . N o t e t h a t t h e samarium t r a n s i t i o n i s o f t h e o r d e r o f one h u n d r e d t i m e s more f r e q u e n t t h a n t h e c e r i u m t r a n s i t i o n . e m i s s i o n ( d i a g r a m 1 2 ) and t h e c e r i u m e m i s s i o n ( d i a g r a m 1 3 ) . E a c h c u r v e r e p r e s e n t s t h e a v e r a g e o f f o u r i d e n t i c a l r u n s ; r e p e a t a b i l i t y was t h u s a s s u r e d t h r o u g h o u t t h e e x p e r i m e n t a l work. I n d i v i d u a l r u n s d i f f e r e d f r o m t h e a v e r a g e by p e r h a p s f i v e p e r c e n t . The i n t e r e s t i n g f e a t u r e o f b o t h s e t s o f d a t a i s t h e g r a d u a l change o f t h e l i m i t i n g s l o p b etween - 1 . 7 a n d - 1 . a s t h e t i m e o f e x c i t a t i o n i n c r e a s e s . A g r a p h o f t h i s l i m i t i n g s l o p e a g a i n s t t h e r e c i p r o c a l o f t h e s q u a r e r o o t of' t h e t i m e o f I f one assumes t h a t e q u a l numbers o f e l e c t r o n s a r e e x c i t e d i n e q u a l t i m e s , t h e n t h e t o t a l number o f e x c i t e d e l e c t r o n s , n, i s d i r e c t l y p r o p o r t i o n a l t o t h e t i m e o f e x c i t a t i o n , n = k T x c t . . S i n c e B = - d n / d t , and t h e l i m i t i n g s l o p e i s ( I n B / l n t ) , where t i s t h e d e c a y t i m e , t h e n we h a ve t h e r e l a t i o n I n (-dn/dt) + 1 = - a / / n where a = . 3 6 5 . a n e q u a t i o n f o r t h e d e c a y c u r v e s i n t e r m s o f t h e t o t a l number o f e x c i t e d e l e c t r o n s . I t s h o u l d be v a l i d f o r s m a l l t i m e s o f Two s e t s o f d e c a y c u r v e s h a v e b e e n p l o t t e d : t h e t o t a l I n t T h i s r e d u c e s t o d n / d t = - t - f ^ " 1 } , e x c i t a t i o n , when thezassumption n = k T x c t h o l d s , f a i r l y r i g i d l y ; 18 i t i s s o l u b l e only by n u m e r i c a l methods. In the t h e o r e t i c a l development o u t l i n e d below a system with a s i n g l e type o f c o l o u r center w i l l be a n a l y s e d f i r s t : g e n e r a l equations are set up and c e r t a i n r e s t r i c t i n g assumptions made which s i m p l i f y the problem. The e f f e c t s o f a b s o r p t i o n a r e shown f o r the s i m p l i f i e d problem and the p o s s i b i l i t y of a d i s -t r i b u t i o n o f t r a p p i n g energies examined. Second, s i m i l a r r e s t r i c t i o n s w i l l be p l a c e d on the g e n e r a l equations d e r i v e d f o r a system with two types o f c o l o u r c e n t e r s ; i n even the most r e s t r i c t e d cases, complete s o l u t i o n i s i m p o s s i b l e because of the non-homogeneity of the equations and the m u l t i t u d e of a s s o c i a t e d parameters. A. The System with One Colour Center Let N be the number of t r a p s per u n i t volume o f depth E Let n i be those occupied by e l e c t r o n s Let n 2 be the number o f empty c o l o u r c e n t e r s , and n be the number o f f r e e e l e c t r o n s i n the c o n d u c t i o n band per u n i t volume. Let r,p be the r e s p e c t i v e p r o b a b i l i t i e s t h a t a f r e e e l e c t r o n w i l l recombine.with an empty t r a p or c e n t e r ; r = . v , where v i s the e l e c t r o n v e l o c i t y and o\ the capture c r o s s - s e c t i o n of an empty t r a p ; s i m i l a r l y p = c r 2 v • Suppose the n^ e l e c t r o n s a t an energy depth E have a Maxwellian d i s t r i b u t i o n of energy, i . e . exp^ E/ k T^; the number es c a p i n g per u n i t volume per u n i t time w i l l be s n i exp [-E/kt] where s i s the p r o b a b i l i t y of escape. C a l l sexp [-E/kTj = a. Assume t h a t t r a n s i t i o n s occur d i r e c t l y t o the empty c o l o u r c e n t e r s ; i f t h e r e i s a metastable l e v e l below the conduction band then the l i f e t i m e of an e l e c t r o n t h e r e i s c o n s i d e r e d t o be v e r y s h o r t . 19 Then dn/dt = -n(n+ni)p - n(N - n n j r + an^ ( l a ) d n i / d t = n(N - n^Jr - a n i . ( l b ) dn2/dt = -n(n + n^)p = -B (Ic) where n 2 = n + n-^  These g e n e r a l equations are not r e a d i l y s o l u b l e . I f , however, one assumes t h a t the number of e l e c t r o n s i n the conduction band i s s m a l l , i . e . t h a t the t r a n s i t i o n s occur almost i n s t a n -t a n e o u s l y , one can w r i t e , (n]_ >> n, n 2 » n, i n f a c t n = 0 ) d n i / d t = -ani_ . /the p r o b a b i l i t y of r e t r a p p i n g * - l \ \ the t o t a l p r o b a b i l i t y / » a n i . n2P / [n 2p + (N - n-jjr] dn£/dt = -an^ . n^p/ [n 2p + (N - n ^ J r ] . . . • (2) Two cases a r e e a s i l y s o l u b l e f o r n i n terms of t , i . e . f o r B = B ( t ) ; these are r = 0 and r = p. (Equation 2 i s d i r e c t l y i n t e g r a b l e but cannot be s o l v e d e x p l i c i t l y , f o r n i n terms o f t ) . I f r = 0 d n 2 / d t = -B = a n i and n i = C e ~ a t ; but a t t = 0 , ni_ = N 0 and B = B 0; thus B = -aN Q e " a t = B 0 e " a t . . . . ( 3 ) I f r = p. we have ( s o l u t i o n due t o Parker and E l l i c k s o n ) - 5 d n 2 / d t = - a n 2 2 / N , (n - 0) They show t h a t 9 B - aN Q /N (1 + a N 0 t / N ) 2 . . . . . (4) 20 Furthermore, f o r t h i s case Parker and E l l i c k s o n have c o n s i d e r e d the a b s o r p t i o n of l i g h t w i t h i n the d i f f u s i n g medium, of the phosphor. In t h e i r problem they t r e a t b r i g h t n e s s as a f u n c t i o n of time under constant i n f r a r e d s t i m u l a t i o n ; consequently a b s o r p t i o n of i n f r a r e d must be accounted f o r , making the parameter a o f t h e i r e quation a f u n c t i o n o f depth beneath the phosphor s u r f a c e . For phosphorescent decay, c e r t a i n changes must t h e r e f o r e be made i n t h e i r t h e o r y . For the s p e c i a l case r =0, the c o n t r i b u t i o n t o the t o t a l b r i g h t n e s s o f a l a y e r a d i s t a n c e x below the s u r f a c e of the phosphor w i l l be dB = -aN Q e ~ a t e " u l x dx where u i i s the c o e f f i c i e n t f o r l o s s by a b s o r p t i o n and s c a t -t e r i n g of the emitted r a d i a t i o n . But the e x c i t i n g r a d i a t i o n i s a l s o absorbed; hence N Q = N e ~ u 2 x dx . . . . . . . . (5) (For j u s t i f i c a t i o n of the use o f an e x p o n e n t i a l f u n c t i o n see I, page 92). B =-f D aN e " a t e ~ u l x e ~ u 2 x dx JO Since the sample i s t h i c k , D can be r e p l a c e d by i n f i n i t y . B = -aN e .CO - a t e - ( U l +.U12) x d x 0 aNe" a t u i + U 2 (6) So the presence of a b s o r p t i o n and s c a t t e r i n g do not a l t e r the nature of the decay curves i n any important f a s h i o n i f t h e r e i s no r e t r a p p i n g . 21 I f t here i s r e t r a p p i n g , r = p, Parker and E l l i c k s o n ' s 5 development can be a l t e r e d to f i t the present s i t u a t i o n . dB = a N e -(ux + 2u 2)x (1 + a e~u2X t) B = aN ]Q e - ( u i + 2u 2)x dx (1 + a e- u2 x t ) 2 By s e t t i n g y = a t e ~ U 2 x and m = U T / U 2 + 1 the e q u a t i o n becomes B = aN (at) m X y / (1 + y ) 2 . dy . . (7) u 2 Jo Parker and E l l i c k s o n set G(m,at) = m + 1 f a t r i T - e t c . , and ( a t ) m + 1 JO t a b u l a t e d G f o r v a l u e s of m between zero and i n f i n i t y . They found t h a t l i m (InB / In at) = -2 m-l i m (InB / In at) = -1 m—-0 Thus the long time behavior under the s p e c i f i e d c o n d i t i o n s approximates the experimental c u r v e s . The f i t I s , however, poor f o r t S 1. Note that m = U T / U 2 + 1; hence m > 1 u n l e s s u l o r u2 i s ^ g a t i v e * A l s o , t o t a l v a r i a t i o n of e i t h e r u 2 o r u i i s c e r t a i n l y not more than one order of magnitude from f u l l e x c i t a t i o n ; consequently the v a r i a t i o n i n slope of cerium e m i s s i o n alone cannot be accounted f o r by a b s o r p t i o n alone, although a b s o r p t i o n w i l l a l t e r the curve o b t a i n e d . I t i s a l s o p o s s i b l e t h a t the i n t e r p r e t a t i o n of the parameters i s i n c o r r e c t , but t h i s i s u n l i k e l y . F i n a l l y , l e t t h e r e be some d i s t r i b u t i o n of the number 22 of t r a p s with energy. Let, f o r example, 1 0 N(E) = A e ~ b E dE (8) dB = - a e " U 2 x N(E) e " a t e " u l x dx, where a = s e " E / k T dB = - A s e " E / k t e " S t 6 X p ~ E / k T e " ( u l + U 2 , X e " b E dEdx -E/kT Put y = se J then B = -0 Ay e~ ty ( y / s ) b k T kT dy/y s - ( u i + U 2 ) x e dx 0 • AkT t - ( b k T + 1 ) p e - y y b k T d y s b k T ( u 1 + u 2 ) J ° where y has been r e - d e f i n e d . The i n t e g r a l on the r i g h t (st—*-«*») i s the gamma f u n c t i o n o f bkT + 1, so B = C t - ( b k T + 1 » [TbkT+1) . . ( 9 ) Again we have a r r i v e d at a s o l u t i o n f o r t » 1. The c o n d i t i o n f o r the v a r i a t i o n o f s l o p e s i s e a s i l y met with, i . e . O ^ b ^ l / k T . Note t h a t N(E) i s e x p o n e n t i a l o n l y f o r E ~ 1/50 e l e c t r o n v o l t s ; t o i n c l u d e the deep, i n f r a r e d s e n s i t i v e t r a p s , a term f o r a s i n g l e l e v e l E = 1.2 e l e c t r o n v o l t s must be added to ( £ ) . B. The System wi t h Two Colour Centers Let the second c o l o u r center have parameters n^ and q = cr-jv. Then the equations analogous to ( l a , b and c) are dn/dt = -nn^p - n n 2 q - n(N - n ^ ) r + an-j_ . . . (10a) d n i / d t = n(N - n ^ r - a n x (10b) d n 2 / d t = -nn xp = -B» . . . (10c) dn^/dt = -nn 2q = -B" •• • . • • . • • (10d) where n + n^ = n 2 + 23 I f , as b e f o r e , we d i s r e g a r d t h e e q u a t i o n i n n, we c a n r e d u c e t h e s e t o a s e t s i m i l a r t o e q u a t i o n (4): d n j / d t - -anx . ^ ( N - n x ) r / [ n 2 p + n 3 q +. (N - n x ) r ] - l ) (11a) d n 2 / d t = - a n x . n 2 p / [ ] ( l i b ) d n 3 / d t = -an-L . n 3 q / [ ] (11c) T h e s e . e q u a t i o n s a r e n o t s o l u b l e b y o r d i n a r y methods; some s o r t o f a n a l y s e r would be r e q u i r e d t o o b t a i n t h e r e q u i r e d s o l u t i o n . Once t h i s was done, e q u a t i o n (5) c o u l d be added t o t h e s y s t e m a l o n g w i t h exp [-u-^x] t o a l l o w f o r t h e e f f e c t s o f a b s o r p t i o n . I t must be e m p h a s i z e d t h a t t h e s e h o l d f o r some v a l u e o f a , some v a l u e o f E i n o t h e r w o r d s . To o b t a i n a c o m p l e t e s o l u t i o n an i n t e g r a t i o n o v e r t h e t r a p d i s t r i b u t i o n w o u l d have t o be. made. A l s o n o t e t h a t t h e t r a p s t h a t a r e a c t i v e i n p h o s p h o r e s -c e n c e a r e v e r y s h a l l o w t r a p s , o f t h e o r d e r o f 1/50 o f a n e l e c t r o n v o l t b e l o w t h e c o n d u c t i o n band; t h u s t h e p r o p o s e d i n t e g r a t i o n must be o v e r t h e s e t r a p s and t h e s i n g l e d e e p s e t w h i c h a r e r e s p o n s i b l e f o r t h e i n f r a r e d s e n s i t i v i t y . The d e e p t r a p s w i l l n o t c o n t r i b u t e a p p r e c i a b l y t o t h e p h o s p h o r -e s c e n c e b u t w i l l e n t e r i n t o t h e s y s t e m i n t e r m s o f t h e i r r e t r a p p i n g c o e f f i c i e n t . T hus i t has b e e n shown t h a t t h e c a s e s r = 0 w i t h a n e x p o n e n t i a l t r a p d i s t r i b u t i o n a n d r » p w i t h a s i n g l e t r a p p i n g e n e r g y f o r one t y p e o f c o l o u r c e n t e r l e a d t o s o l u t i o n s w h i c h a p p r o x i m a t e t h e r e q u i r e d s o l u t i o n a t l o n g t i m e s i f a b s o r p t i o n i s c o n s i d e r e d . I t i s f e l t t h a t t h e c o r r e c t s o l u t i o n f o r two t y p e s o f c o l o u r c e n t e r s w i l l be a n a l o g o u s t o t h e s e s i m p l i f i e d c a s e s , and w i l l have 0 ^ r / p ^ 1 . B e c a u s e t h e 24 process o f phosphorescent, decay i s predominantly t h a t of the samarium c e n t e r s , i t i s b e l i e v e d t h a t the t h e o r y f o r one c o l o u r c e n t e r w i l l be a c l o s e approximation t o f a c t ; s i n c e an exponen-t i a l d i s t r i b u t i o n of t r a p s (Equation (&)) i s found t o have a reasonable range o f parameter v a r i a t i o n , i t i s suggested t h a t t h i s i s a c t u a l l y the case. An accounting of the r e t r a p p i n g t r a p p i n g c o e f f i c i e n t must be made bef o r e the model can be d e f i n i t e l y e s t a b l i s h e d . V. CONCLUSION The phosphorescent decay of Standard V I I , SrS.CeSm, has a l i m i t i n g s l o p e on log-time l o g - b r i g h t n e s s p l o t s between -2 and -1, the a c t u a l slope being d i r e c t l y p r o p o r t i o n a l t o the r e c i p r o c a l of the square r o o t of the e x c i t a t i o n time f o r times g r e a t e r than .5 minutes. T h i s r e s u l t l e a d s to the c o n c l u s i o n t h a t the processes i n v o l v e d are n e i t h e r simple b i m o l e c u l a r nor e x p o n e n t i a l ; examination o f the v a r i a t i o n s i n the curves due t o a b s o r p t i o n and to an assumed d i s t r i b u t i o n o f t r a p s f u r t h e r c o n f i r m the c o n c l u s i o n t h a t experiments of t h i s s o r t cannot be f i t t e d by any simple, pre-conceived t h e o r y . The e x i s t e n c e of two types o f c o l o u r c e n t e r s has been e s t a b l i s h e d which f u r t h e r complicates the s i t u a t i o n , even though the number of cerium centers a c t i v e d u r i n g phosphorescent decay i s found t o be much s m a l l e r than the number of a c t i v e samarium c e n t e r s . In c o n c l u s i o n , the author wishes to thank Dr. A.M. Crooker f o r d i r e c t i n g the work, and Dr. A . J . Dekker f o r r e a d i n g 25 and c r i t i c i z i n g the t h e s i s . The author i s a l s o i n d e b t e d to the O n t a r i o Research C o u n c i l f o r two s c h o l a r s h i p s granted d u r i n g t h i s work, and to the Defence Research Board f o r f i n a n c i n g the p r o j e c t . APPENDIX I Exhaustion and Thermoluminescence The theory which f o l l o w s i s based on the equations developed by R a n d a l l and Wilkins'''; the data on t r a n s i t i o n s i s from I . The b r i g h t n e s s of a phosphor a t a gi v e n time i s B = -G dn/dt where n i s the number of trapped e l e c t r o n s , a l l of which are assumed t o make r a d i a t i v e t r a n s i t i o n s d i r e c t l y to an empty c o l o u r center v i a the conduction band. The number of such e l e c t r o n s r a i s e d to the conduction band by thermal energy i s p r o p o r t i o n a l to the temperature, so t h a t B = -C dn/dt = • C s n e ~ E / ' k T where s i s the p r o b a b i l i t y o f t r a n s i t i o n t o the conduction' & -1 band and i s of the order o f 10 sec. . Suppose t h a t the phosphor i s b e i n g heated at a r a t e o f /2> degrees per second. Then dn/n = - s e ~ E / k T dt/dT . dT and n = n Q e Mo S//3 . e " " E / k T dT J B = n0CeHo • //» . e - E A T 4 s e - E A T Now dB/dT = 0 a t some T m a x^' t h a t i s , the b r i g h t n e s s reaches a maximum as the phosphor i s heated. A p p l y i n g t h i s c o n d i t i o n we get E A T m a x . + 2 l o g e T m = l o g e s k / £ E which can be slolved f o r T m a x # s i n c e E = 1.2 e l e c t r o n v o l t s i s known f r o m s t i m u l a t i o n d a t a . Thus f o r /fl =20 d e g r e e s p e r m i n u t e , T m Q V . . = 1 1 0 ° C . The glow c u r v e i s e s s e n t i a l l y s y m m e t r i c a b o u t T „ _ v Thus d n / d t = 0 a t room t e m p e r a t u r e i m p l i e s t h a t d n / d t i s a l s o z e r o a t 2 0 0 ° C , i . e . t h e e q u i l i b r i u m c o n d i t i o n i s one w i t h n = 0. REFERENCES 1. F. Urbach, D. Pearlman,' H. Hemmendinger, J . O p t i c a l Soc. Am., 36, 372, 1946 2. B r i a n O'Brien, J . O p t i c a l Soc. Am., 36, 369, 1946 . 3. F. Urbach et a l . , " S o l i d Luminescent Materials'! Wiley, N.Y., 279, 194"5 '. 4. F. Urbach, N. N a i l , D. Pearlman, J . O p t i c a l Soc. Am. 39, 675, 1949 5. R.T. E l l i c k s o n , W.L. Parker, Phys. Rev. 70, 290, 1946 6. F.E. W i l l i a m s , " S o l i d Luminescent M a t e r i a l s " . Wiley, N.Y., 337, 1943 : : : ~~~ " 7. R a n d a l l and W i l k i n s , Proc. Royal Soc. A184, 336, 1945 8. Gobrecht, Ann. der Physik 28, 673, 1937 9. R.C. Herman, C.F. Meyer, H.S. H o p f i e l d , J . O p t i c a l Soc. Am. 38, 999, 1948 10. R a n d a l l and W i l k i n s , Proc. Roy. Soc. A184, 390, 1945 For f u r t h e r i n f o r m a t i o n , see: R.H. Thompson and R.T. E l l i c k s o n , Phys. Rev. 73, 185, 1948 ( E x c i t a t i o n of I n f r a r e d Phosphors by Alpha and Beta P a r t i c l e s ) S c o t t , Thompson and E l l i c k s o n , J . O p t i c a l Soc. Am. 39, 64, 1949 ( I n e r t i a E f f e c t s i n I n f r a r e d S e n s i t i v e Phosphors) R.T. E l l i c k s o n , J . O p t i c a l Soc. Am. 36, 264, 1946 ( L i g h t Sums of Phosphors Under Thermal and I n f r a r e d S t i m u l a t i o n ) P. Brauer, J . O p t i c a l Soc. Am. 40, 353, 1950 (The R i s e of B r i g h t n e s s of I n f r a r e d S e n s i t i v e Phosphors) F.W. Paul, J . O p t i c a l Soc. Am. 36, 175, 1946 (Experiments on the use o f I n f r a r e d S e n s i t i v e Phosphors i n Photography of the Spectrum) M l ,M4,K45,M6,M0,MI(yvll2, are flats M2 .M8 .M 11, are ,spheroids , M3 is parabolic M 7 is e l l ipt ic Rectangle indicates m on ochrom at or Diagram 2 1/5 scale Aluminizcd f lat Mount — i - ^ - M f - ^ T — r - - ^  - J l i im i t r t i f i tn i r i .•>*•-. FffTiffjjlijjf ifII 4 Support block -Rotating Spring loaded Sliding f i t Note : The mount is shown in one stable p o s i t i o n ; a s the flat and bearings rota te , the catch and notch engage for a second posit ion. The third i s analogous to the f i rst , but on l e f t hand s t o p . b o t t o m view Sliding catch Notch Lef tstop o o -Freely rotating -Flat -Mount -Support block -Central bearing -Lower bearing Right stop Diagram 4 M9 Mounting; full scale. dept. physics u-b-c/bxii-1/4-20 6/32 Parts A,B,C are cylindrically symetrical, D is "rounded off" with radius I |/4",centre xx HZ , Press fit D e ,1/4-20 ST 6/32 a l, 3-*&%l%li i -W44 . Z 3/8 -i3/g Diagram 5 Spherical mirror mount. Mater ia l : aluminum Full scale dept. physics u.b.c/d.r.h. 5819 -1.2 k v i lOOk't IP8T I k I OK lOOk im lOm lOOm 45v 2 0 0 k cf o x— cr o us' cf 0 o o o Di ag ram 6 D C Ampl i f i e r aN resistors 1/2 watt un less o therwise specified dept physics u.b.c /dr.h. 2/2X2 8 0 7 6 J7 6 S L 7 Diagram 7 . H.T. Supply all res is tors 1/2 watt unless otherwise specified dept. pf&ics u.b.c/o.r.h. 6 A C 7 6 A C 7 6 A C 7 6 A G 7 6 A L 5 T , _ _ 4 0 m f d y 5 k •—»2SOv \ I O w l O k 2w lOtc 2w I Ok 2w - T - 2 0 Q p _ _ _ , , . I Ok 2w > l m 2 C O \ _ _ < o h m s < 15 ohms woe....,,. 1 V •'I j 8mfd | j 4S 51 5k I O w 3 0 0 v l O O O p OJnVd \ - 2 5 m 2 5 0 ohms . 4 S O v X 5m 2 0 0 ^ I O p ohms, 1 004 m« . 5 m 3.3 k |w I . 0 5 < 2 0 0 mt d ^ o h m s 2 5 m f d - — I f - r so o h m s D i a g r a m S Pulse A m p l i f i e r a l l r e s i s t o r s t / 2 watt unless o t h e r w i s e s p e c i f i e d d e p t p h y s i c s u . b . c / d . r . h . 6AK5 Input I SOP 5 0 k P i — U >k < ISO < • r j ohms> • Olmfl-u 500P-l O O k ^ I2AT7 6 A K 5 8.5k Iw pr 3k SOOp-r-Ik C lOOk SOOP-4 0 m M I I 5 0 v 8 0 0 ohms KDOk 4 0 0 S. ohms ^ Output IOO ^ ohms \ Ik / A Diagram 9 Pulse Pre-amplif ier all res is tors 1/2 watt unless otherwise specified dept. phjics ab.c/d.rh. Hammond 5Y3 I67£ 6AS7 6SJ 7 6SL7 ^ 3 0 0 \ Diagram IO Low V o l t a g e P o w e r S u p p l y a l l r e s i s t o r * 1 /2 w a t t u n l e s s o t f i w i s c s p e c i f i e d d e p t . p h y s i c s u . b x / d . r . h . Decay of Phosphorescence for SrS.CeSm Total emission, excitation time i n d -icated in minutes. SOO IOOO Time of Decay in Minutes D i ag r am 12 dept. physics ubc/drh T 1 1 r — - — i 1 r Decoy of Phosphorescence for SrS.CcSm Ce emission alone, excitation time ind-Time of Decay in Minutes Diagram 13 dept physics ubc / drh I • 7Y I .6 1.5 s® Cerium / emission / 4 / m c 8 I 4 o. o <7> c £ I I . 3 I .2 T o t a l emission Diagram 14 dept .physics u t c / drh 

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