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X-ray induced luminescence in single crystals of pure potassium iodide Usiskin, Sidney Robert 1955-12-31

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X-RAY INDUCED LUMINESCENCE IN SINGLE CRYSTALS OF PURE POTASSIUM IODIDE  by  SIDNEY ROBERT USISKIN  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE  REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in PHYSICS  We accept t h i s t h e s i s as conforming t o the standard r e q u i r e d from  candidates  f o r the degree o f DOCTOR OF PHILOSOPHY.  Members o f t h e Department o f P h y s i c s .  THE  UNIVERSITY OF BRITISH COLUMBIA October,  1955.  Faculty of Graduate Studies  P R O G R A M M E OF T H E  Jffittai ©ml |Lxmttitrati*mfori\\ e P g g r e *  SIDNEY ROBERT USISKIN B.Sc. (Hons.) (Manitoba) 1948 THURSDAY, OCTOBER  20th, 1955, at 3:00 p.m.  I N R O O M 303, P H Y S I C S  BUILDING  COMMITTEE IN CHARGE H . F. ANGUS, G.  Chairman  M . SHRUM  H . M . DAGGETT  A. M . CROOKER  M . KIRSCH  K.  C  PING-TI H O  G.  M . VOLKOFF  MANN  External  Examiner—A  J . DEKKER  Dept. of Electrical Engineering University of Minnesota  X-RAY INDUCED  LUMINESCENCE  in SINGLE CRYSTALS OF PURE K l ABSTRACT  T h e luminescent decay of pure potassium iodide has been measured under various conditions of temperature,  annealing and x-ray  irradiation time. T h e decay curves are found to be approximately of the form I (t) = "> p a exp (-a t) n where I (t) is the luminescent intensity at the time t. n  n  11  Using a method that has been developed for the analysis of decay curves, the decay constants, estimated.  and the trap populations p , have been n  T h e decay constants are found to be simple temperature  functions of the form a = s exp (-E / k T )  n  n  n  with the activation energies, E , lying between 0.4 and 0.8 ev and escape probabilities, s^, between 10 and 10 sec.- . 4  s  T h e temperature dependence of the p  1  is complicated and" indicates  that radiationless transitions strongly contribute to the emptying of traps at high temperatures. A n irreversible increase i n luminescent output produced by repeated x-irradiation without intermediate annealing has been discovered; it points to considerable deviation from a first order decay mechanism i n the case of slowly decaying traps.  T h e mechanism of the irreversible  effect has been discussed on a semi-quantitative basis.  LIST OF PUBLICATIONS Thermal Decay of the Luminescence of K B r , G . W . Williams, S.R. Usiskin, and A . J . Dekker, Phys. Rev. 92, 1398, 1953. X-Ray Induced Luminescence i n Single Crystals of Pure K l , S. R. Usiskin and O. Theimer, Phys. Rev. (in the press).  GRADUATE STUDIES Field of Study: Physics Electromagnetic Theory  W . Opechowski  Theory of Measurements  A . M . Crooker  Quantum Mechanics Special Relativity Chemical Physics Physics of the Solid State  G . M . Volkoff W . Opechowski A . J . Dekker H . Koppe  Other Studies: Differential Equations Advanced Differential Equations Radiochemistry  T. E. Hull T . E. H u l l M . Kirsch and K . Starke  v  ACKNOWLEDGMENTS I am indebted  t o Dr. 0. Theimer f o r v a l u a b l e  d i s c u s s i o n s during the course of these experiments and f o r h e l p i n i n t e r p r e t i n g the experimental r e s u l t s . indebted  I am a l s o  t o Dr. A . J . Dekker, under whose s u p e r v i s i o n  this  work was s t a r t e d and whose e n l i g h t e n i n g d i s c u s s i o n s have g i v e n me a f u l l e r a p p r e c i a t i o n o f t h e problems i n v o l v e d i n the study o f luminescence. I wish t o acknowledge the kind a s s i s t a n c e other  s t a f f members o f the P h y s i c s  laboratory  o f the  Deoartment and the e x c e l l e n t  f a c i l i t e s s u p p l i e d by t h e U n i v e r s i t y o f B r i t i s h  Columbia P h y s i c s  Department.  I would l i k e t o express my thanks t o Dr. G.W. Williams  f o r . h i s assistance  i n the design  and c o n s t r u c t i o n  o f the apparatus. T h i s work was made p o s s i b l e by r e s e a r c h  g r a n t s to  Dr. A . J . Dekker and t o Dr. 0. Theimer from the U n i v e r s i t y o f B r i t i s h Columbia.  A B r i t i s h Columbia Telephone  t o t h e author i s g r a t e f u l l y acknowledged.  Scholarship  ABSTRACT  The  l u m i n e s c e n t decay  o f pure  potassium  been m e a s u r e d u n d e r v a r i o u s c o n d i t i o n s o f annealing t o be  and  x-irradiation  approximately of the  time.  The  iodide  has  temperature,  decay  curves are  found  form  i  where I ( t ) i s t h e l u m i n e s c e n t U s i n g a method t h a t analysis  o f decay  constants,  V  k  temperature  f u n c t i o n s o f the  decay  w i t h the a c t i v a t i o n  and  t o t h e emptying  produced annealing from  decay  t o be  $t , b e t w e e n 10** and dependence o f the  of t r a p s at high  10^  and  O.fct ev  sec "^. 0  i s complicated  radiationless transitions  irreversible  simple  , l y i n g between 0.4  strongly  contribute  temperatures.  increase i n luminescent  by r e p e a t e d x - i r r a d i a t i o n w i t h o u t  output  intermediate  i s d i s c o v e r e d ; i t p o i n t s to c o n s i d e r a b l e d e v i a t i o n  a first  o r d e r decay  decaying traps. discussed  f o r the  form  energies,  temperature  indicates that  An  been d e v e l o p e d  c o n s t a n t s are found  probabilities, The  time t .  , and t h e t r a p p o p u l a t i o n s ^; , h a v e b e e n  The  escape  has  at the  curves, numerical values f o r the  estimated.  and  intensity  The  mechanism i n t h e  mechanism o f t h e  case o f s l o w l y  irreversible  on a s e m i - q u a n t i t a t i v e b a s i s .  effect  is  TABLE OF CONTENTS. Page ACKNOWLEDGMENTS. ABSTRACT. I.  INTRODUCTION. 1.  The Band Model of S o l i d s . . . .  2.  Previous Work on Alkali-Halides  1 v.  II.  DESCRIPTION OF APPARATUS.  III.  THEORY OF THE DECAY AND EXCITATION PROCESS. 1.  The Luminescent Decay Process  2.  The E x c i t a t i o n Process  1 3 6 11 11 « 13  IV.  THE ANALYSIS OF DECAY CURVES.  15  V.  EXPERIMENTAL RESULTS.  24  VI.  DISCUSSION OF EXPERIMENTAL RESULTS. 1. The Temperature Dependence of the ^«wia,jt Values 2. Effect of I r r a d i a t i o n Time on the Decay 3. The Temperature Dependence of the Populations „ 4. Irreversible Effects of X-Irradiation  27  5. VII.  Experiments at Low Temperatures  CONCLUSIONS.  APPENDIX I A Mechanical Device For F a c i l i t a t i n g The Graphical Analysis APPENDIX II A n a l y t i c a l Methods For Resolving A Decay Curve Into A Sum Of Exponentials..., REFERENCES.  27 29 29 31 3&* 42  44 46  L I S T OF  TABLES Facing  Table  I.  Test-of Graphical Analysis  20  Table  II.  Irreversible Effects X-Irradiations  25  of Successive  Table I I I .  E  Table  T e m p e r a t u r e Dependence o f t h e P o p u l a t i o n and C a p t u r e C r o s s Sections ( i n arbitrary units)  IV.  ;  And S; V a l u e s  27  30  Page  LIST OF ILLUSTRATIONS.  Facing Page F i g . 1.  D.C. Amplifier  6  F i g . 2.  Phptomultiplier Supply....,  7  F i g . 3.  C r y s t a l Holder (High Temp.)  8  F i g . 4.  C r y s t a l Holder (Low Temp.)  9  F i g . 5.  A Typical ^(E) Spectrum  24  F i g . 6.  Log  24  F i g . 7.  Decay Dependence on t *  25  F i g . 8.  Glow Curve f o r K l  26  F i g . 9.  Versus l / T  Dependence on t * .  F i g . 10. Graphical Analysis of a Decay Curve....  28 44  1 I. The  INTRODUCTION  emission of v i s i b l e  h a v i n g been exposed t o r e g i o n has halides,  l o n g ! b e e n an  because of  system, p r o v i d e Also,  radiation  since  the  apparent  a g o o d means o f  these c r y s t a l s a f f o r d  the  of  results  of the  o t h e r known p r o p e r t i e s , etc,^  For  t h e s e r e a s o n s , an  x-ray  induced  light  by  light  which i s emitted  is  of  light  or  excitation  termed  any  sec.  an  isolated  phenomenon.  at  least  in principle,  luminescence glow  i n t o the  crystals  its  curves,  seemed to  emission by,  That  i n a t i m e up  seconds a f t e r  to  10"^  the  promising.  excitation  1  with  decay o f  general term applied after  studies,  ionizing radiation.  the  portion  of  A l l subsequent  the  instant  of  1.  The  Band M o d e l o f  sec.  natural  i s b a s e d on  life-time of  between the  emission of  the  the light  an  instant  the  the  of  experi-  excited  10~9  to  10"^  excitation  o p t i c a l luminescence  photon.3  Solids.  When i n d i v i d u a l the  10~&  n o n - m e t a s t a b l e atom i s a b o u t  transitions  and  into  luminescent  this  study of  pure K l  alkali-  phosphorescence.  for dipole  crystal,  The  x-ray  various other  i s called fluorescence.  mental o b s e r v a t i o n t h a t of  of  investigation  This demarcation at  state  the  a c r y s t a l d u r i n g and  u-v  end  investigating object  after  u l t r a v i o l e t or  photoconductivity,  luminescence o f  e.g.,  crystal  s i m p l i c i t y of the  of  Luminescence i s the of  a  phenomenon.  opportunity,  e.g.  by  i n the  interesting  t h e y have b e e n t h e  correlation  light  energy l e v e l s  ions  are  of the  b r o a d bands b e c a u s e o f t h e  brought together to isolated  i o n s become  interactions  among t h e  form  a  converted ions.  2 T h e s e bands e x t e n d are  free  throughout  the entire  t o move i n any s i n g l e  most band filled  conduction o f charge  the difference  may be e x p l a i n e d .  the c r y s t a l  neighboring levels  insulating  crystal,  electrons  i s completely f i l l e d ,  moving i n a g i v e n d i r e c t i o n  the uppermost  filled  crystal,  of charge. an e l e c t r o n  In above T«=0 K o  f  oppositely  t h e appearance  For conduction to must be r a i s e d  electron  i n the f i l l e d  levels  crystal  from  i nthe  band  may  a t a temperature  structure w i l l of localized  and c o n d u c t i o n bands.  t h e i r way t o t h e s e l o c a l i z e d in  natural  defects i n the crystal  between t h e f i l l e d  directed  of charge.  any n o n - c o n d u c t i n g  These d e f e c t s cause  electron  a l l o w e d empty b a n d ,  c o n d u c t i o n band and t h e " h o l e " r e m a i n i n g to a transfer  I n an  f o r every  ( c o n d u c t i o n band) i n w h i c h c a s e b o t h t h e s i n g l e  contribute  f o r a net  i n which there are  so t h a t  band t o t h e n e x t  partially  of transitions to  there i s another  p r e v e n t i n g any n e t t r a n s f e r  occur i n a n ' i n s u l a t i n g  i s only  i n t h e same b a n d .  t h e u p p e r m o s t band  between  I f the upper-  i s a conductor,  c a n o c c u r by v i r t u e  unoccupied  thus  picture,  i n which there are e l e c t r o n s present  with electrons,  and e l e c t r o n s  band.  On t h e b a s i s o f t h i s c o n d u c t o r s and n o n - c o n d u c t o r s  crystal,  occur.4  energy  levels  E l e c t r o n s which  a r e n o t f r e e t o move  find about  the c r y s t a l . Direct  the ground  electronic  transitions  s t a t e a r e very improbable,  localization  from these l e v e l s t o  mainly because  o f the  o f t h e t r a p s and o f t h e " h o l e s " i n t h e f i l l e d  O n l y when a h o l e i s a c l o s e  n e i g h b o r o f an e l e c t r o n  in a  band. level,  .  3 is  there  a chance f o r a t r a n s i t i o n  then, provide metastable s t a t e s to  as  to occur.  These  f o r e l e c t r o n s and a r e  interpretation  o f the r e s u l t s  o f the  experiments  described  i n t h i s work i s b a s e d upon t h e a s s u m p t i o n  existence  of traps  i n pure K l  P r e v i o u s Work on  Alkali-Halides.  about m a t e r i a l s o f t e c h n i c a l o n l y the i m p u r i t y - a c t i v a t e d  importance.  luminescence application subject  and F l e c h s i g 5 were t h e f i r s t  i n thallium-activated in scintillation  of considerable  alkali-halides,  investigated i n  KC1.  to observe  Because  ofi t s '  c o u n t e r s , K a l - T l has been  the  research. Bose^»  7  first  measured  t e m p e r a t u r e dependence o f t h e x - r a y i n d u c e d l u m i n e s c e n c e .  He  gave  of  electron  a qualitative  KBr  and  e x p l a n a t i o n o f t h e decay  and M o r r i s h ^ ' 9  L i F using  a new  photomultiplier tubes.  dependence of the The  Because  resolved their  o f the  decay  end-window  preliminary nature of  made t o e x p l a i n t h e  temperature  decay.  phosphorescence  a l k a l i - h a l i d e s was  measured t h e l u m i n e s c e n c e  technique employing  e x p e r i m e n t , no a t t e m p t was  direct  process i n terms  traps.  Dekker  the  Of t h e  c r y s t a l s have b e e n  As f o r t h e p u r e a l k a l i - h a l i d e s ,  of  mainly centered  detail. Bunger  the  of the  crystals.  P r e v i o u s work on l u m i n e s c e n c e h a s b e e n  any  referred  traps. The  2.  levels,  o f p u r e and  thallium-activated  m e a s u r e d by Bonanomi and R o s s e l . ^ O  decays  into  They  a number o f e x p o n e n t i a l s e i t h e r  by  a n a l y s i s o r w i t h t h e a i d o f i n f o r m a t i o n g a i n e d by means  4  of  the thermoluminescence  technique f i r s t  i n t r o d u c e d by  U r b a c h ^ and t h e o r e t i c a l l y d i s c u s s e d by R a n d a l l and W i l k i n s . ^ ^ H i l l and S c h w e d ^ have i n v e s t i g a t e d t h e of  x-rayed NaCl.  exist  luminescence  They found t h a t d i f f e r e n t types o f t r a p s  i n the c r y s t a l each h a v i n g the same a c t i v a t i o n The author, i n c o l l a b o r a t i o n w i t h G.W.  energy.  W i l l i a m s and  A . J . Dekker, i n v e s t i g a t e d the luminescent decay o f pure KBr-^. I t was  found t h a t a l a r g e number o f t r a p s e x i s t e d i n the  crystal.  The d i f f e r e n t a c t i v a t i o n e n e r g i e s f o r 17 o f these t r a p s were determined  on the assumption  e s s e n t i a l l y o f the f i r s t  t h a t t h e decay process i s  order.  These d e t a i l e d r e s u l t s l e a d t o the hope t h a t the a n a l y s i s o f luminescent decay curves might prove t o be s u p e r i o r to  such other standard methods as the glow curve a n a l y s i s , or  the i n v e s t i g a t i o n o f p h o t o c o n d u c t i v i t y . These hopes have not been f u l l y confirmed by investigations.  later  N e i t h e r the monomolecular c h a r a c t e r o f the  decay nor the d e t a i l e d numerical r e s u l t s c o n c e r n i n g the p r o p e r t i e s o f the t r a p s can be c o n v i n c i n g l y proven.  In a  manner s i m i l a r t o o t h e r methods, the a n a l y s i s o f luminescent decay curves g i v e s o n l y s e m i - q u a n t i t a t i v e i n f o r m a t i o n and o n l y a combination  o f d i f f e r e n t experiments  may  finally yield  r e l i a b l e q u a n t i t a t i v e knowledge o f the mechanism o f It  i s the purpose  luminescence.  of t h i s work t o c a r r y out  i n v e s t i g a t i o n s designed t o d i s c o v e r t h e p o s s i b i l i t i e s l i m i t a t i o n s o f the decay curve method.  a  and  5 Potassium i o d i d e has p r o v i d e d the experimental material. the  T h i s substance was  chosen f o r i n v e s t i g a t i o n  because  a b s o r p t i o n band o f the x-rayed c r y s t a l l i e s i n a d i f f e r e n t  s p e c t r a l r e g i o n than the response o f the RCA multiplier  5819  photo-  tube used as the d e t e c t o r o f the emitted l i g h t .  A l s o , the luminescent decay o f K l had not yet been i n v e s t i g a t e d w i t h the s e n s i t i v e apparatus which had been designed for. the purpose o f measuring the weak l i g h t i n t e n s i t i e s w i t h the decay o f the luminescence o f the pure  associated alkali-halides.  A s i n g l e c r y s t a l o f pure K l has been s u b j e c t e d t o v a r i o u s temperatures at which the luminescent decay o c c u r r e d , to d i f f e r e n t irradiation.  a n n e a l i n g times and to d i f f e r e n t  times of  Preamplifier  FIG. 1.  D.C. A m p l i f i e r  F a c i n g Page 6  II.  "DESCRIPTION OF APPARATUS  In order to perform the experiments proposed, an apparatus having the following c h a r a c t e r i s t i c s was required: (a)  Maintenance of the c r y s t a l at various fixed  temperatures f o r considerable periods of time. (b)  Proximity of the c r y s t a l to the e x c i t i n g source,  in t h i s case, a low-voltage x-ray tube. (c)  Good geometrical e f f i c i e n c y f o r the acceptance  of emitted l i g h t from the c r y s t a l by the detector, an endwindow RCA 56*19 photomultiplier tube. (d)  S t a b i l i t y of the detecting system over long  periods of time. (e)  Linearity of the detecting system i n responding  to light i n t e n s i t i e s that may vary by as much as 105. It was found that the detecting device best suited for the requirements (d) and (e) indicated above, was one using a photomuliplier tube as the i n i t i a l l i g h t detecting stage and integrating i t s pulse output to get a D.C. response.  The  photo-tube was operated at reduced voltage to eliminate the p o s s i b i l i t y of fatigue. The D.C. amplifier used was one whose p.utput impedance was s u f f i c i e n t l y low so that i t could operate a recording milliammeter. i n . f i g . 1.  The c i r c u i t diagram f o r this amplifier i s shown  The output of the photomultiplier was fed to the  variable (105 to 10^ ohms) grid r e s i s t o r of a Victoreen 5300 electrometer tetrode.  The voltage developed across t h i s  r e s i s t o r by the output current of the photomultiplier was amplified by a 2 stage balanced amplifier, and passed to the meter.  The output signal from the amplifier was also l e d to  FIG.  21.  P h o t o m u l t i p l i e r Supply  F a c i n g Page 7  the An  lower end  o f the  grid resistor,  supplying 100$  feed-back.  i d e n t i c a l a m p l i f i e r s u p p l i e d the b a l a n c i n g v o l t a g e f o r the  meter. The  l a r g e amount o f feed-back u t i l i z e d i n the  a m p l i f i e r served  D.C.  a 4 - f o l d purpose:  (1)  Reduction o f the input time constant  of  (2)  Maintenance o f the c o l l e c t o r at a f i x e d  the  amplifier. voltage  independent o f s i g n a l c u r r e n t . (3)  Reduction of output impedance (~ 1  (4)  The  ohm).  v o l t a g e g a i n of the a m p l i f i e r ( u n i t y ) i s  made independent of tube c h a r a c t e r i s t i c s and  supply  voltage  variation. An E s t e r l i n e - A n g u s was  model A-W  u t i l i z e d to r e c o r d the decays.  speed o f 6" curve and  per minute f o r the  switched t o 6"  The  recording  milliammeter  c h a r t was  run at a  i n i t i a l p o r t i o n o f the decay  per hour t o r e c o r d the l a t t e r ,  v a r y i n g , p o r t i o n of the decay.  The  slowly  response time o f the meter  (^ 1 sec.) meant t h a t about 5 sec. of the r e c o r d i n g were l o s t when the range o f the a m p l i f i e r was time, however, improved the r e a d i n g s  changed.  T h i s response  at the lowest  intensities  smoothing out the c u r r e n t f l u c t u a t i o n s . The  p h o t o m u l t i p l i e r supply  shown i n f i g . 2,  is a  common, r e g u l a t o r c i r c u i t with an output v a r i a b l e from 750 1200  volts.  The  v o l t a g e d i v i d e r s u p p l y i n g the  dynode v o l t a g e s draws 1 ma. c o n s i s t of RCA  5651  The  to  photomultiplier  l a s t 4 s e c t i o n s o f the d i v i d e :  v o l t a g e r e f e r e n c e tubes which act  as  L e a d s to h e a t e r and thermocouple  h V  6 [ F T Mycalex insulation  Kl crystal 3 m m x 2 0 m m d.  A l . cup  -20mm hole tapered to hold c r y s t a l . copper-constantan thermocouple FIG.  "3..  8 0 0 n Nichrome heater  C r y s t a l Holder (High Temp.) F a c i n g Page #  d v o l t a g e r e g u l a t o r s f o r c u r r e n t s In the range from 0.5 T h i s reduces the source  t o 1.2  ma.  impedance to a n e g l i g i b l e value f o r the  l a s t dynodes where t h e c u r r e n t i s a p p r e c i a b l e and  consequently  the g a i n o f the phototube>which i s s e n s i t i v e t o changes i n the dynode v o l t a g e S j i s u n a f f e c t e d by even l a r g e output  currents.  To check t h a t the g a i n o f the d e t e c t i n g system r e t u r n e d t o the same value a f t e r s w i t c h i n g the system o f f , a "standard"  light  source was  introduced.  c o n s i s t e d of a 6 v o l t lamp.  The  This l i g h t  c u r r e n t was  source  s u p p l i e d by  a  storage b a t t e r y , and the v o l t a g e a c r o s s the lamp maintained a f i x e d value w i t h the use o f a potentiometer.  The  used f o r short p e r i o d s of time o n l y , t o prevent  c r y s t a l was  maintained  operation.  i n a vacuum between the  x-ray tube and the p h o t o m u l t i p l i e r tube. was  was  changes i n  amount o f r a d i a t i o n which might occur a f t e r l o n g The  lamp  at  The  vacuum chamber  as narrow as the p h y s i c a l s i t u a t i o n would a l l o w , and had  3 m i l t h i c k aluminum window f a c i n g the x-ray window f a c i n g the l i g h t d e t e c t o r . (b) and  (c) t o be met.  The  source  T h i s allowed  a  and a pyrex  requirements  thermal i n s u l a t i n g p r o p e r t i e s o f  the vacuum meant t h a t t h e p h o t o m u l t i p l i e r tube could be kept i n c l o s e p r o x i m i t y t o the c r y s t a l even when the c r y s t a l temperature was  relatively  high.  The requirement  (a) was  s a t i s f i e d by having  c r y s t a l h e l d i n the vacuum i n a brass s p o o l which had wire h e a t e r wound about i t .  (see f i g . 3 )  o f the c u r r e n t to t h i s heater provided control.  The b r a s s s p o o l was  the a Nichrome  Electronic regulation  satisfactory  temperature  suspended i n the p a r a l l e l e p i p e d  .glass to Kovar seal  rubber  gasket  //,,,7////iM brass  Pare* window  >|  Al window  Kl cmtdl  FIG.  4'.  C r y s t a l H o l d e r (Low Temp.) F a c i n g Page 9  vacuum chamber from a cover t h a t made a vacuum-tight rubber gasket at the t o p o f the chamber.  s e a l on a  The chamber was  c o n t i n u a l l y pumped from an arm a t r i g h t angles t o t h e l i n e running through the x-ray tube, c r y s t a l and p h o t o m u l t i p l i e r tube. The c r y s t a l was p l a c e d i n an aluminum cup b e f o r e b e i n g put i n t o t h e i n t e r i o r o f the b r a s s s p o o l .  T h i s cup, which  covered the face o f t h e c r y s t a l toward t h e x - r a y tube served a d u a l purpose: (a)  I t maintained the face o f t h e c r y s t a l from which  the luminescence was mainly o r i g i n a t i n g , at a u n i f o r m temperature (b)  I t served t o r e f l e c t t h e l i g h t  i n t o t h e photo-  • c a t h o d e o f t h e p h o t o m u l t i p l i e r tube and thus i n c r e a s e d the g e o m e t r i c a l e f f i c i e n c y f o r d e t e c t i o n o f the l i g h t . For purposes o f measuring the temperature o f the c r y s t a l , a copper constantan thermocouple, whose e.m.f. was recorded on a potentiometer, was f a s t e n e d t o the i n s i d e o f t h e brass spool. For the measurements taken at l i q u i d oxygen temperatures, the c r y s t a l h o l d e r d e s c r i b e d above was r e p l a c e d by a pyrex Dewar v e s s e l , whose i n n e r p o r t i o n was made o f metal, (see f i g . 4.)  T h i s Dewar made a vacuum s e a l on the same rubber  gasket as t h e one d e s c r i b e d above.  The i n n e r metal p o r t i o n o f  the Dewar was made o f Kovar and a g l a s s - t o - m e t a l s e a l was thus easily effected.  The c r y s t a l was h e l d . i n a b r a s s s p o o l and  t h i s was f a s t e n e d t o t h e metal i n t e r i o r o f the Dewar by means  10 o f a heavy b r a s s bar. i t s ' temperature was  The c r y s t a l was  c o o l e d by conduction  and  measured by a thermocouple attached t o the  b r a s s spool i n very c l o s e p r o x i m i t y to i t .  III.  THEORY OF THE DECAY AND EXCITATION PROCESS. It  i s generally'assumed  phosphorescence the  ground  In (filled  i s due t o e l e c t r o n s i n t r a p s r e t u r n i n g t o  state  most p r o b a b l y  v i a h i g h e r energy  v i athe conduction a pure c r y s t a l ,  b a n d ) may be e x c i t e d  absorption of x-rays. move t h r o u g h  than 1.  e l e c t r o n s i n t h e ground to the conduction  ^  and e v e n t u a l l y f a l l  band, w i t h t h e e m i s s i o n o f l i g h t , o r  process  i s terminated,  leave the traps per unit  be t e m p e r a t u r e  band i s l e s s  i n t h e t r a p s o f depth  I f thermal  energy  time  then  and r e a c h t h e  fluctuations  cause f o r the d i s c h a r g e o f the t r a p s , the decay will  i n the  Process.  e l e c t r o n s are present  c o n d u c t i o n band.  band  to the fluorescence.  Decay  after the excitation electrons w i l l  speed  r e t u r n i n g t o the f i l l e d  10"^ s e c . g i v e r i s e The L u m i n e s c e n t  state  band by t h e  Those e l e c t r o n s whose l i f e - t i m e  band b e f o r e  If  o f the c r y s t a l ,  band.  the c r y s t a l with great  the t r a p s .  conduction  levels  These e l e c t r o n s i n t h e c o n d u c t i o n  b a c k e i t h e r t o the. f i l l e d into  that the l o n g - l i v i n g  are the only constants  f u n c t i o n s o f t h e form  A. * s e" VtiT  i d )  ;  where T = t e m p e r a t u r e , k = B o l t z m a n n ' s c o n s t a n t , S ^ = t r a n s i t i o n probability. The  emitted  light  intensity  i s proportional t o the  number o f r a d i a n t t r a n s i t i o n s t h a t a r e made p e r u n i t the  transition  probabilities  the  c o n d u c t i o n band t o t h e f i l l e d  time.  f o r the radiant transitions b a n d a r e v e r y much  If from  larger  12 than f o r r e t r a p p i n g and f o r the thermal d i s c h a r g e o f the t r a p s , the l a t t e r , then, are the r a t e - d e t e r m i n i n g process, and lead to a luminescent decay o f the f i r s t  order (monomolecular decay):  IIK2) It  i s obvious t h a t the simple monomolecular decay  law, as g i v e n by equation 111(2),can never be f u l l y r e a l i z e d i n nature.  The reason f o r t h i s i s t h a t the number o f " h o l e s " or  empty p l a c e s i n the ground s t a t e o f the c r y s t a l matrix i s approximately equal to the number o f e l e c t r o n s i n the conduction band and i n the t r a p s .  I f the l a t t e r number i s s m a l l , and i t i s  n e c e s s a r i l y so toward the end o f a decay p r o c e s s , the number of empty e l e c t r o n a c c e p t o r s i n the ground s t a t e becomes e q u a l l y s m a l l , and the t o t a l t r a n s i t i o n p r o b a b i l i t y f o r r a d i a n t t r a n s i t i o n s becomes dependent not o n l y upon the thermal d i s c h a r g e of  the t r a p s but upon the number of h o l e s i n the f i l l e d band as  w e l l . . The decay constants  X;, w i l l t h e r e f o r e become time  dependent toward the end o f a decay. In  t h i s s i t u a t i o n , r e t r a p p i n g of the e l e c t r o n s  becomes i n f l u e n t i a l , and the decay g r a d u a l l y becomes transformed i n t o one of 2nd order ( b i m o l e c u l a r d e c a y ) . c o m p l i c a t i o n i s unavoidable, i t may  Although t h i s  final  be n e g l i g i b l e f o r the major  p o r t i o n o f the decay, and c o n t r i b u t e s u b s t a n t i a l l y o n l y to those l a s t p o r t i o n s o f the decay which, at moderate are unobservable  temperatures  anyway, because o f the s m a l l luminescent  intensity. A f e a t u r e which has u n t i l now  been n e g l e c t e d , i s the  p o s s i b i l i t y that r a d i a t i o n l e s s t r a n s i t i o n s from the t r a p s , as  13 w e l l as those g i v i n g r i s e t o the observed  luminescence,  are  allowed. If radiationless  t r a n s i t i o n s are c o n s i d e r e d , t h e r a t e  o f d i s c h a r g e o f a t r a p w i l l be d e s c r i b e d by  A, r e p r e s e n t s t h e escape p r o b a b i l i t y g i v i n g r i s e t o  where  radiant transitions, r e p r e s e n t s the escape p r o b a b i l i t y g i v i n g r i s e t o radiationless X*"  and  i s  t h e  transitions  " e f f e c t i v e " escape  probability.  I n t e g r a t i n g e q u a t i o n 111(3) g i v e s t> "= The  IIIU)  :  observed  l i g h t i n t e n s i t y at any g i v e n t i m e i s  g i v e n by t h e product o f t h e p o p u l a t i o n i n the t r a p a t t h a t time and  "X  t  , the r a d i a n t escape p r o b a b i l i t y . IW'  2.  fc*.*  The E x c i t a t i o n  IIK5)  Process.  I n o r d e r t o make a study o f t h e t e m p e r a t u r e dependence o f the i n i t i a l p o p u l a t i o n s i n t h e t r a p s , a mechanism f o r f i l l i n g t h e t r a p s must be assumed. Cl)  X-rays l i f t  The assumptions made were: g r e a t numbers o f e l e c t r o n s f r o m t h e  f i l l e d band t o the c o n d u c t i o n band. (2)  Most o f t h e s e e l e c t r o n s f a l l d i r e c t l y back t o t h e  f i l l e d band g i v i n g r i s e t o t h e i n t e n s e f l u o r e s c e n c e  observed.  14 (3)  The number o f e l e c t r o n s which a r e caught i n  t r a p s , per u n i t time, i s only a very small f r a c t i o n o f t h e t o t a l number o f e l e c t r o n s i n the conduction  band a t any time d u r i n g  the e x c i t a t i o n . (4)  The c o n c e n t r a t i o n o f e l e c t r o n s i n the conduction  band d u r i n g t h e e x c i t a t i o n process  remains constant,  being  determined c h i e f l y by t h e r a t e at which e l e c t r o n s are r a i s e d from the f i l l e d t o conduction  band by the x - r a y s a n d t h e }  i  fluorescent t r a n s i t i o n s . filling  'With these  assumptions, the r a t e o f  o f t r a p s may be d e s c r i b e d by  U < - r ^ - ( where  = the "charging  k  *  +  ,  >  ; %  ni(6)  constant", which i s p r o p o r t i o n a l t o  the i n t e n s i t y o f the x-rays  and i s , most  probably,  very s l i g h t l y temperature dependent, i f at a l l . i  = number o f t r a p s c h a r a c t e r i z e d by t h e s u b s c r i p t ^* = discharge  "constant"  i . e . r a t e a t which the x-rays  e j e c t e l e c t r o n s t h a t a r e caught i n the t r a p s . k * < * K  likely ^  v  = t h e p o p u l a t i o n i n t h e t r a p a t the time If  \-0  L  and  equation  Most  t*  111(6) i s i n t e g r a t e d between the l i m i t s  t s *t*s charging time and  and ^  one o b t a i n s  111(7)  •Equation  111(7) g i v e s t h e p o p u l a t i o n i n the t r a p s a t  the end o f the i r r a d i a t i o n time "t*.  15 IV.  THE  ANALYSIS OF  Assuming t h e valid,  equation n i ( 2 )  resolved  into  a sum  DECAY CURVES  simple monomolecular decay process r e q u i r e s that every  of exponentials.  The  decay curve  be  question of  the  to  be  •' IK • >'.. I  uniqueness, o f such  a resolution  i s t h e main p r o b l e m t o  be  investigated. In  those  c a s e s where t h e d e c a y  constants, \  components o f a d e c a y c u r v e  are o f r a t h e r d i f f e r e n t  e.g.  o f two  the  decay  different  of a m i x t u r e  intensity  radio-isotopes with  occur  be  I f , however, t h e d e c a y c o n s t a n t s ,  v a l u e s t h a t are not different  components w i l l  approximately If decay curve different be  equal  the  by two  I n the end  o f the  made f r o m  large values of  time.  they  case  plot  produced  will  be  curved  spacings the  of  the  widely  a  t-»»)  single  spaced  decay  since i t w i l l Thus,  of the decay c o n s t a n t s  curvature of t h i s  any  components.  (i.e. by  the  At  intensity  of the  plot  thus  the  o r more  o f many c l o s e l y  plot  can  ,have  composed o f  o r more o f t h e d e c a y c o n s t a n t s .  measure o f t h e r e l a t i v e be  be  of t h i s  essentially case  different  contributions of  l o g a r i t h m of the  d e c a y c o n s t a n t s t h e end  constants,  principle  will  i s made, i n t h e  line,  and  overlap to a great extent.  o f the  vs. time  decay c o n s t a n t .  the  c o n t r i b u t i o n s f r o m two  a plot  a straight  produced  separate times  very d i f f e r e n t ,  given time the t o t a l i n t e n s i t y  will  greatly  which i s experimentally  measured, w i l l separated.  at w i d e l y  the  values,  h a l f - l i v e s , t h e maximum c o n t r i b u t i o n s o f t h e  components t o t h e t o t a l  of  t  at  be  a can  very  in  The  resolution  may be a c c o m p l i s h e d Log the  curve  o f any d e c a y c u r v e  into  exponentials  i n t h e f o l l o w i n g manner:  I(t) i splotted  v s . t and a t a n g e n t  at a point corresponding  i s drawn t o  t o a large t value,  where I(t') i s s o s m a l l t h a t f o r t>t', t h e d i f f e r e n c e the tangent  and t h e curve  fluctuations  i s s m a l l e r than  a n d , hence n o t o b s e r v a b l e .  say t '  between  the noise T h i s tangent,  which  may be r e p r e s e n t e d f o r m a l l y b y t h e e q u a t i o n :  iv(i)  U^ICO« lo^VA-O"**)*.* t  c a n be c o n s i d e r e d a s f o r m i n g In the ^  k  first  difference  obtains a discrete  t h e observed  plotted  into  decay  equation  ^(A)  of the  i s displayed, i fthe ^  T h i s spectrum and A  k  energy  will  values are  have a d i s c r e t e  values obtained  line  i n t h e g r a p h i c a l >.  Since A i s a f u n c t i o n  o f the t r a p s , s u c h  represents the electronic  a  spectrum  population distribution  i n the  traps o f the c r y s t a l . The  the  values  h a s been f o u n d t o  curve w i t h i n t h e l i m i t s  spectrum  i f the ^  the activation  various  111(2)  and  i n t h e same  s e t o f |\ a n d  manner d e s c r i b e d a b o v e , a r e u t i l i z e d . of  yields  error.  against ^ .  character  logjjT(,i) - T , w Q  curve,  w h i c h , when s u b s t i t u t e d  A  t o the t a i l o f  member o f t h e sum and p r o c e e d i n g  way, one f i n a l l y  experimental  o f t h e sum 1 1 1 ( 2 ) .  e x a c t l y t h e same way, a t a n g e n t  f o r a second  yield  one member  statement  that the  above method y i e l d s t h e o b s e r v e d  spectrum  o b t a i n e d by  d e c a y c u r v e when  17 s u b s t i t u t e d i n t o 111(2), does not imply t h a t i t i s the o n l y possible  spectrum. In f a c t , because  the e x p e r i m e n t a l l y observed  I ( t ) , becomes l e s s r e l i a b l e as the n o i s e background and because  decay  i s reached  l o g I ( t ) always appears to have some c u r v a t u r e  even when t h e n o i s e background  i s reached, a d i f f i c u l t y  i n t h e drawing o f the tangent t o t h i s curve.  arises  I f the tangent  i s drawn to the observed part o f the decay c u r v e , equation IV(1) does not y e t a f f o r d a good approximation, s i n c e t h e r e i s never a s t r a i g h t p o r t i o n o f the observed curve.  I f , on the o t h e r  hand, one attempts t o e x t r a p o l a t e the observed curve t o reach a s t r a i g h t p o r t i o n , the d i f f i c u l t y a r i s e s anew, s i n c e p o l a t i o n i s no unique p r o c e s s .  The same ambiguity a r i s e s when  p l o t t i n g the tangents t o a l l the d i f f e r e n c e c u r v e s . because  extra-  Further,  o f the l a c k of knowledge o f the decay curves f o r times  10"^ sec; < t < 2 sec., the decay curve must a l s o be e x t r a p o l a t e d t o zero- time, and because  o f the e x c e e d i n g l y r a p i d  r a t e o f change o f t h e i n t e n s i t y a t these t i m e s , l a r g e e r r o r s may be i n t r o d u c e d . I t i s thus obvious t h a t many d i f f e r e n t  spectra  may be found f o r a s i n g l e e x p e r i m e n t a l curve, each-of  which,  when s u b s t i t u t e d i n t o e q u a t i o n 111(2), reproduce t h a t  curve  equally well. (a)  T h i s has the f o l l o w i n g  consequences:  The number o f l i n e s i n a spectrum  i s rather  meaningless, p h y s i c a l l y , s i n c e t h i s number can be a r b i t r a r i l y  18 i n c r e a s e d by superimposing n d i f f e r e n t  lw»£ L  h  .  »  >  .  i  allowed s p e c t r a : k  Only t h e s m a l l e s t number o f l i n e s s u f f i c i e n t  I  V  (  2  )  t o reproduce t h e  decay curve i s p o s s i b l y o f some i n t e r e s t , as i n d i c a t i n g t h e s m a l l e s t number o f t r a p s which w i l l g i v e r i s e t o t h e observed luminescent  decay.  (b)  The i n d i v i d u a l ^  w  and A; v a l u e s o f a spectrum  are r a t h e r meaningless i f c o n s i d e r e d s e p a r a t e l y . of displacements o f l i n e s by amounts  The e f f e c t s  AX^on t h e r e p r o d u c t i o n  o f I ( t ) can e f f e c t i v e l y be compensated by s u i t a b l e changes A^>; i n the magnitudes  o f the l i n e s .  Only i f t h e l e n g t h and  p o s i t i o n o f t h e l i n e s i n a spectrum a r e j o i n t l y c o n s i d e r e d , can t h e r e s u l t  o f an a n a l y s i s be g i v e n i n a manner which i s  reasonably i n v a r i a n t a g a i n s t t h e a r b i t r a r y c h o i c e o f t a n g e n t s to l o g I ( t ) . T h i s can be understood from t h e f o l l o w i n g argument: Consider two e q u i v a l e n t decay c u r v e s IV(3a)  r  Z-V^  VA;K  '  IV(3b)  which are i d e n t i c a l w i t h i n e x p e r i m e n t a l e r r o r although produced by two d i f f e r e n t t h a t t o each l i n e  k  l i n e spectra.  and A  t  The n o t a t i o n  indicates  o f e q u a t i o n IV(3a), corresponds  19 a group o f one or s e v e r a l l i n e s  and  the symbols w i t h the double  ^ i k and X-^  Here,  index  which are denoted - \  by  +  i s the s e p a r a t i o n o f the l i n e s i n the q-spectrum  from the c o r r e s p o n d i n g l i n e i n the p-spectrum. v a l u e s as g i v e n and  Consider a c e r t a i n set o f attempt  t o determine  t  the ^ ^ i n such a manner t h a t , a c c o r d i n g  t o the r e q u i r e d e q u i v a l e n c e o f the decay c u r v e s , I ( t ) and  lit),  t h e i r mean square d e v i a t i o n i s a minimum, i . e . '  f*  X  -mow.  IV(4)  I n s e r t i n g the v a l u e s d e f i n e d i n equations IV(3) d i f f e r e n t i a t i n g with r e s p e c t t o one  i n t o IV(4),  o f the ^ C K ^ a y fyi'** > <  i n t e g r a t i n g over the time and p u t t i n g the r e s u l t equal t o zero gives:  r  The denominators are now powers o f A ^  *  21  =  expanded and the second  i.v i v ( and  5  )  higher  are n e g l e c t e d .  This gives:  ) This r e l a t i o n s h i p i s v a l i d approximation  that  ^ V^c  for ^  L  allA^ » "the  ^ t h e r e f o r e i n the must s a t i s f y the  following conditions:  L  r  <T M i  I V ( 7 a )  IV(7b)  TABLE I (continued) H  X  0  M]  S L  Facing Page 20  _  I^:  M  M3  2  Ifc>;  s  a  lK\  §  Analysis I I I  p -4d  V I . 02-10-3  p -111.0  \«4.2S.10~  2  P =114  ^=9.04-IO-  2  1  2  3  273  15.09  1.134  0.0929  252  13.04  0.912  0.0691  Analysis IV p -48"  A=1.02.10-3  P =50.ct  \=3.54«10-2  P -110  V ^ '  V  \-9.-57*lCT  2  3  4  3  6  3  1  0  "  2  2  Average over the 4 analyses.  BT o 254  . MT 1 13.55  MT c 0.993  MT 3 .0799  TABLE I.  Facing Page 20  TEST OF GRAPHICAL ANALYSIS M  ^  x  0  M  x  M  2  ^  M  3  g *f K  Actual Spectrum P =50  A , »10-3  p =50  ^=4-10-  2  p «50  *,«5-10-  2  p^»50  "X.,-7'10-  x  2  3  250  13.05  0.95  0.0766  245  12.82  .9139  0.0693  24^  13.27  1.016  0.0886  2  V '  P »50 5  1  0  "  1  Analysis I p =48  \ =1.02.10-3  P -S1.5  \=4.11'10-  P =115.5  ^,=8.2-10-  1  2  2  2  3  Analysis II p -48  X -1.02* IO"  3  t  p =135.5  \-4.79-10-  p =64.5  -A^l.05-10-1  2  3  2  20  From these f o l l o w the a d d i t i o n a l c o n d i t i o n s IV(7c) IV(7d) C o n d i t i o n s I V ( 7 a ) and I V ( 7 d ) t o g e t h e r show t h a t the " c e n t e r o f g r a v i t y " o f the spectrum  as a f u n c t i o n o f X  i s i n v a r i a n t ; and  equations I V ( 7 b ) and I V ( 7 c ) t o g e t h e r show t h a t t h i s i s t r u e not only f o r the spectrum as a whole, but a l s o f o r p a r t s o f the spectrum w i t h a width o f the o r d e r o f magnitude o f  .  I t must be emphasized t h a t these r e s u l t s a r e v a l i d f o r the c o n d i t i o n  &\<^/x^  < <  I  , and s t r o n g d e v i a t i o n s from the  equations I V ( 7 ) may be expected from l a r g e v a l u e s o f /\\^ From these c o n s i d e r a t i o n s , i t can be seen t h a t i n s p i t e o f the a m b i g u i t i e s i n v o l v e d i n t h e r e s o l u t i o n o f an experimental decay curve i n t o a sum o f e x p o n e n t i a l s , c e r t a i n properties of the  |>fa)  s p e c t r a obtained should prove t o be  rather invariant. An a r t i f i c i a l decay curve was mathematically c o n s t r u c t e d and then analyzed by t h e g r a p h i c a l  procedure  o u t l i n e d above, i n o r d e r t o see whether t h i s method o f r e s o l v i n g a decay curve i n t o e x p o n e n t i a l s i s capable o f o b t a i n i n g r e s u l t s t h a t are compatible w i t h equation Four d i f f e r e n t first  j>(>)  f o u r moments  IV(7).  s p e c t r a were found f o r t h i s curve, and the  fVXb; i M , I ^ S  ;  i  ^\=  were c a l c u l a t e d f o r each o f these s p e c t r a . t h i s procedure a r e g i v e n i n t a b l e  1.  x  E  ;  The r e s u l t s o f  21 In a n a l y z i n g the t o t a l p o p u l a t i o n  a c t u a l decay curves,  o f a l l traps,JL^i  i t was found t h a t  was n e a r l y i n v a r i a n t b(x")  when c a l c u l a t e d from d i f f e r e n t p o s s i b l e  spectra.  By t h e very nature o f the g r a p h i c a l a n a l y s i s described  above, the i n i t i a l  c o r r e c t l y reproduced by the ^  intensity, c  and X  v  values  i s always of a possible  spectrum i f the decay curve i s known f o r a l l times i n c l u d i n g the very  short times f o r which t->0.  was not f u l f i l l e d  This l a t t e r  condition  i n t h e experiments performed, and hence,  the v a r i a t i o n i n Jlb-'A;, f o r the d i f f e r e n t s p e c t r a was g r e a t e r than normally expected. I t must be p o i n t e d out, however, that t h i s u n c e r t a i n t y does not depend upon t h e a n a l y t i c a l method used, but i s due t o the l a c k o f knowledge o f t h e i n i t i a l p o r t i o n o f the curve. The individual  f a c t t h a t the i n v a r i a n t p r o p e r t i e s o f the  ^(X) s p e c t r a a r e t h e f i r s t  few moments o f these  s p e c t r a means t h a t no d e t a i l e d knowledge o f the number, depth and  populations  o f the t r a p s can be obtained  i n t h i s way.  A  b e t t e r p h y s i c a l d e s c r i p t i o n o f t h e luminescent system was t h e r e f o r e looked  for.  I f the assumption i s made t h a t the  distribution  i s continuous r a t h e r than d i s c r e t e , one a r r i v e s at the s t a r t i n g p o i n t o f t h e method o f a n a l y s i s which proved t o be the most u s e f u l i n l e a d i n g t o r a t h e r d e t a i l e d knowledge o f the t r a p s i n the  crystal. If n different line  s p e c t r a which are a l l compatible  w i t h a g i v e n decay a r e superimposed a f t e r d i v i d i n g t h e l e n g t h  22 o f each single  l i n e by many-line  decay.  n i n the  manner o f IV(2)  spectrum  Such a many-line  which i s a l s o spectrum  one  then  obtains a  compatible  c a n be  with  transformed  equivalent  continuum  i f the  condition that  the  g r a v i t y be  conserved  w i t h i n s m a l l r e g i o n s o f the  the  into  an  center of spectrum  is  observed. T h i s may procedure:  first,  be  achieved,  one  in practice,  c o n s t r u c t s a "sum  o f r e p l a c i n g t h e v a l u e o f b.  a t *V  by  curve".  by t h e  smooth c u r v e a t e a c h  continuous  function  The  many-lined  more t h a n about |*(x)  continuous  .  25  lines  shape.  Since a single  yielded  5 or 6 l i n e s ,  at a  least  This leads to the  The decay curves  o b t a i n e d from  the  The  each  different  A  decay  found  to require  range,  i t t o be  c u r v e had line  ^(^)  physical  t o be  that  survive repeated  f o r the  invariant  in  curve  analyzed  into  spectra i n order to obtain  i n the many-lined  spectrum.  continua obtained f o r d i f f e r e n t  distinct  situation,  the  formulae  maxima and  minima.  These  c o n t i n u a p r o b a b l y g i v e t h e most a c c u r a t e d e s c r i p t i o n real  points  derivative  g r a p h i c a l a n a l y s i s o f a decay  number o f l i n e s  exhibited  I V ( 2 ) , was  i n the observable  5 or 6 d i f f e r e n t  sufficient  .  consists  p o i n t g i v e s the magnitude o f  spectrum,  spectrum  following  This  sum t-  t h u s o b t a i n e d a r e j o i n e d by a smooth c u r v e and of t h i s  the  s i n c e any  maxima i n  s u p e r p o s i t i o n i n g and  of  the  distributions  a v e r a g i n g when  another new  l i n e spectrum i s added, should be r e a l and not i.  due t o the mode o f a n a l y s i s .  24 V.  EXPERIMENTAL RESULTS.  Decay curves f o r a single c r y s t a l of pure (Harshaw) Kl were obtained for temperatures between 66°C and 200°C. Between each experimental determination of the decay curves, the c r y s t a l was annealed at a high temperature about 30 hours.  (*^300°C) f o r  The c r y s t a l was always irradiated at the  temperature at which the decay was The continuous f>(^  observed.  d i s t r i b u t i o n s f o r the range of  temperatures from 66°C to 200°C was determined from the experimental decay curves by the method described i n section IV. found.  In every case, d i s t i n c t maxima and minima were  Thus the l i n e spectra of Williams et a l ^ are here 1  replaced by continuous spectra with the l i n e s replaced by bands.  A t y p i c a l spectrum, i n which s i n equation I I I ( l ) has  been a r b i t r a r i l y chosen as 10$, may be seen i n f i g . 5.  The  h a l f width of the bands may represent the uncertainty i n our knowledge of the peak positions, A^v.> situation:  °  r  the r e a l physical  that traps of a certain class (responsible for a  certain band) are not completely i d e n t i c a l . The values of A.^^ scale vs. l/T i n f i g . 6.  are plotted i n a logarithmic  The point marked with a double arrow  represents a missing point (perhaps a non-resolved broad band i n the b(x)  d i s t r i b u t i o n ) , while the brackets indicate an  excess point. In order to obtain a greater amount of information as to the mechanism of decay, a study of the dependence of the jit  decay curve on the i r r a d i a t i o n time t  was made.  F i g . 7 shows  a t y p i c a l result where the i r r a d i a t i o n times f o r the curves  TABLE I I .  F a c i n g Page 25  IRREVERSIBLE EFFECTS OF SUCCESSIVE  t(sec.)  40  X-IRRADIATIONS..  I (t) I (t) I (t) I (t) ^ ( t j / l i t t ) x  2  3  4  ^(tj/lxlt)  ^(tj/litt)  269  386  412  424  1,438  1.530  l 575  100  64.4  91.6  103  '111  1.418  1.600  1.725  150  38.4  54.6  62.3  67.2  1.422  1.622  1.75  200  27.6  39.6  45.7  55.6  1.435  1.660  2.02  300  17.0  26.5  30.2  33.8  1.560  1.775  1.98  Ii(t)  are the i n t e n s i t i e s o f the i  t  n  decay a t the time t„  c  '5  2  * . shown were t  • 5, 15, 45 seconds.  A series of experiments of the following nature was made:  the c r y s t a l was x-rayed, and the decay recorded.  Then,  when the luminescent l i g h t had disappeared into the noise background, the c r y s t a l was re-irradiated  with x-rays and the  consequent decay of luminescence recorded.  This procedure  was repeated a number of times without benefit ,of intermediate annealing of the c r y s t a l .  The r e s u l t s of t h i s experiment are  summarized i n table I I . It was found that t h i s " i r r e v e r s i b l e " increase i n luminescent intensity could be removed by annealing the c r y s t a l f o r long periods of time (up to 60 hours at~300°C). In other words, two successive decay experiments were completely reproducible i f and only i f the c r y s t a l was f u l l y annealed between experiments. Since there are arguments f o r believing that the decay curve i s most c l o s e l y approximated by a simple monomolecular mechanism at low temperatures, an experimental determination of the decay curve for K l was made at l i q u i d a i r temperatures.  One of the features of t h i s experiment was the  fact that i t was found possible to re-excite luminescence i n the c r y s t a l at t h i s low temperature by means of v i s i b l e l i g h t a f t e r the o r i g i n a l l i g h t i n t e n s i t y had dropped to the noise level.  After an i r r a d i a t i o n with v i s i b l e l i g h t of 1 s e c , an  appreciable amount of luminescence was observed.  The c r y s t a l  was then exposed to white l i g h t f o r about 90 minutes.  At the  FIG. 8.  Glow Curve f o r K l  F a c i n g Page  26  26 end  o f t h i s t i m e , no  the c r y s t a l . temperature function indicated  The and  luminescent  c r y s t a l was  intensity  of time.  The  i n f i g . 6*.  l i g h t c o u l d be d e t e c t e d f r o m  t h e n a l l o w e d t o warm up  o f e m i t t e d l i g h t r e c o r d e d as  results  o f t h i s glow curve  are  and a  the  TABLE I I I  E^ AND  S  L  F a c i n g Page 27  VALUES.  i n ev  log  i n ev  l o g s:  0.68  4.8  0.69  7.1  0.74  5.0  0.67  7.4  0.70  6.1  0.59  6.9  0.69  6.4  0.45  5.7  27  IV. 1.  DISCUSSION OF EXPERIMENTAL RESULTS.  The Temperature Dependence o f the A-w,m.  Values.  In t h e r e s u l t s obtained f o r K l by t h e procedure o f s u p e r p o s i t i o n o f many "allowed" l i n e s p e c t r a and t r a n s f o r m a t i o n i n t o an e q u i v a l e n t continuum, no attempt  was made t o choose, a  p r i o r i , the v a l u e s o f s appearing i n equation 111(1), o r t o L  impose a temperature  dependence on the A > *  w  The v a l u e s o f  the ^*, .were p l o t t e d i n a l o g a r i t h m i c s c a l e a g a i n s t l / T , fcK  (see f i g . 6) and an attempt  made t o f i n d a s e t o f s t r a i g h t  l i n e s which would cover a l l the p o i n t s so obtained i n accordance w i t h t h e requirements  o f equation I I I ( l ) .  The only  p o s s i b i l i t y o f doing so, i s i n d i c a t e d i n f i g . 6; a l l other p o s s i b i l i t i e s were excluded f o r p h y s i c a l reasons. for  Ej,  and S  t  The values  can be c a l c u l a t e d from equation I I I ( l ) with the  h e l p o f f i g . 6, and these v a l u e s are e x h i b i t e d i n t a b l e I I I . • I t must be emphasized t h a t these v a l u e s r e p r e s e n t crude approximations quantities.  for rather questionable physical  The approximate c h a r a c t e r o f the values i s  r e v e a l e d by t h e l a r g e s c a t t e r i n g o f p o i n t s about the l i n e s , which i n d i c a t e s e i t h e r l a r g e experimental and a n a l y t i c a l e r r o r s o r a wrong p h y s i c a l i n t e r p r e t a t i o n o f the p o i n t s .  The  l a r g e s c a t t e r o b v i o u s l y prevents q u a n t i t a t i v e statements as to  a s l i g h t c u r v a t u r e o f the l i n e s or a common p o i n t o f i n t e r -  s e c t i o n a t l / T • 0, o r l / T = o» , which have been proposed by other authors.^-3 >  ^  There are other arguments a g a i n s t an o v e r - o p t i m i s t i c i n t e r p r e t a t i o n o f f i g . 6.  These i n c l u d e the f a c t t h a t there  2$  may  be  e f f e c t s due  l i g h t by the  t o the  s e l f - a b s o r p t i o n o f the  luminescence  c r y s t a l which i s c o l o r e d by x - i r r a d i a t i o n .  Also,  i t has been found t h a t the X.*, ^ . v a l u e s c o r r e s p o n d i n g t o decays which occur under i d e n t i c a l c o n d i t i o n s , v a r y w i t h i r r a d i a t i o n time (see f i g . 9 ) .  This also points  the to  d e f i c i e n c i e s e i t h e r i n the a n a l y t i c method used i n f i n d i n g the Xv,a.^. v a l u e s or i n the  p h y s i c a l p i c t u r e o f the  decay  process. I t should be p o i n t e d between the El^  out, too, that the  differences  and S v a l u e s o f i n d i v i d u a l t r a p s as g i v e n  in  t  the t a b l e are o f the  same o r d e r of magnitude as the  broadening o f these q u a n t i t i e s .  thermal  This f a c t j u s t i f i e s  the  i n t r o d u c t i o n o f a continuous d i s t r i b u t i o n f u n c t i o n renders s l i g h t l y q u e s t i o n a b l e  the r e a l i t y and  but  exact l o c a t i o n  o f i n d i v i d u a l bands i n t h i s d i s t r i b u t i o n . The  p o s s i b i l i t y that r a d i a t i o n l e s s t r a n s i t i o n s  help t o empty f i l l e d  traps introduces  further  may  complications.  Equation 111(5) i n d i c a t e s t h a t i f r a d i a t i o n l e s s t r a n s i t i o n s are allowed, the observed l i g h t i n t e n s i t y must be X*  i n terms o f  the  " e f f e c t i v e " decay constant as w e l l as  the r a d i a n t t r a n s i t i o n p r o b a b i l i t y . y i e l d s the may  o f the  the temperature dependence o f  p o i n t s about the  t h i s f a c t , since uncertain  Since  decay constant appearing i n the  represent  X.*  described  graphical  l i n e s i n t h i s f i g u r e may  i s a rather  temperature dependence.  analysis  exponential, X*.  X,  The  scatter  be due  complex q u a n t i t y with  fig. 6  to an  29 2.  E f f e c t o f I r r a d i a t i o n Time on t h e D e c a y . E q u a t i o n 111(7) i n d i c a t e s t h a t i f ( b ^ r *  i s g r e a t e r t h a n 4, of  s a y , t h e |* become i n d e p e n d e n t  charging, i . e . reach  u p o n t h e l u m i n e s c e n t d e c a y was  the  decay  7.  of the time  saturation.  A study o f t h e e f f e c t o f d i f f e r e n t  shown i n f i g .  irradiation  made, a t y p i c a l r e s u l t  I f the assumption  being  i s made t h a t a t t h e t i m e t ,  X(0~^>A> t h e n t h e s e e x p e r i m e n t s i n d i c a t e d  t h a t even f o r t h e l a r g e s t o b s e r v a b l e X - v a l u e s , n o t r e a c h e d f o r a n e x c i t a t i o n t i m e o f 30  saturation  seconds.  seconds.)  T h i s t h e n a l l o w e d an upper  n u m e r i c a l v a l u e of Temperature  (K*  C)  30  l i m i t t o be p u t u p o n t h e  such t h a t (MIC)  *  d sec.- . x  Dependence o f t h e P o p u l a t i o n s  Decay e x p e r i m e n t s g i v e i n f o r m a t i o n about t h e A;  constants are, the  was  (For a l l  o t h e r e x p e r i m e n t s p e r f o r m e d , t h e i r r a d i a t i o n t i m e was  The  times  c o n s t a n t X - /-t i s t h e m a i n c o n t r i b u t o r t o t h e  i n t e n s i t y and t h a t  3.  "t*  *t)  as w e l l as t h e p o p u l a t i o n s ^ .  decay  These p o p u l a t i o n s  i n p r i n c i p l e , as c h a r a c t e r i s t i c o f t h e decay mechanism as .  T h e r e f o r e , the b e h a v i o u r o f t h e ^  temperature  as a f u n c t i o n  of  s h o u l d a l s o be t a k e n i n t o c o n s i d e r a t i o n when an  e x p l a n a t i o n o f t h e decay mechanism i s a t t e m p t e d .  This  has  b e e n done i n f e w p r e v i o u s i n v e s t i g a t i o n s . The t e m p e r a t u r e d e p e n d e n c e o f t h e p o p u l a t i o n s t h a t was  e x p e r i m e n t a l l y f o u n d i n t h i s work w i l l  t e r m s o f an e x t r e m e  be e x p l a i n e d i n  m o d e l where t h e e x c i t a t i o n and  mechanisms a r e o f t h e f i r s t  order (monomolecular).  decay The  F a c i n g Page 30  TABLE IV.  TEMPERATURE DEPENDENCE- OF THE POPULATION AND CAPTURE•CROSS-SECTIONS (in arbitrary units) •  T°cN 200  173  147  i  l  K h A;  2  3  154 0 . 0 0 3 0  185 0.0121  190 0.0555  5.5 7 . 9  7.2  12.6  7.8  11.7  105 0.005  300  460  0.002  0.015  0.055  1 3 . 8  4 . 0  12.4  3.30  13.6  7.7  31.0 4.66  1200  400 0.0036 13.5 3.6  400  650  0.0036  0.0135  260 0.0436  400  *L  0.0004 40 1  117  1470 0.0002 49 1  A;  AV*. 92  .  A;  •  15.5  3.73  2.66  5.14  950  960  400  0.0009 31.7  0.0029 32  620 0.0128  24  2.45  2.64  25 1.2  1902  1132 0.0012 37.7 1.36  906 0.0046  2535 0.0003 84.5 1  800 0.0007  63.5 1.3 66  2364 0.00005  i  210  26.6  0.0003  79 1  9  0.15 32  5.85  13.5  8  7  110 0.147  16.6 20.8  .  6  5  4  32  0.897.  2 6 . 6 1  220  0.164  0.0444  36 •>  3.34  282  386  0.0185 20 3.22  466  .  0.0764  0.27  24  100  1620 0.003 54 1  750  522  0.014  0.119  0.447  65  258  1.93  31  1  .  576  30 possibility traps  o f r a d i a t i o n l e s s e l e c t r o n i c t r a n s i t i o n s from  t o the  ground  If allows  the  state  values  o f k;N;  the  continuous  J>(A)  the  decay curve. JbOOdA  (which s h a l l  definition  the  that  values  In t h i s  case, the  taken over the  An  IV  t e n d to  must be  t  ^  a considerable and  have b e e n  ,K;I^, ;  capture  f o r these traps  occurs i n analysis  by  of  by  •  an  By  arbitrariness in assumption  traps  are  \ ^* 5  possible)  calculated. of t h i s  f o r the  table  slowly  i s that  decaying  have a t e m p e r a t u r e d e p e n d e n c e s u c h t h a t  sections  III(?)  replaced  w i t h the  escapes from the  interesting feature  capture cross-sections  Jp  from the  band and  band l i m i t s  radiant  of table  termed the  d i s t r i b u t i o n obtained  o f the  only  be  c a l c u l a t e d f o r e a c h band t h a t  t h i s method, w h i c h i n v o l v e s  (I.e.  equation  <-  t o be  the  excluded.  i t i s assumed t h a t K «  cross-sections)  integral  i s , h o w e v e r , not if-  the  strongly  increase  traps  the  with  the  cross-  decreasing  temperature. This cross-sections temperature of these  i s a r a t h e r unexpected r e s u l t . f o r a l l the  independent.  cross-sections  The  could  found t h a t remove t h e The  with  no  most p r o b a b l y  due  to  the  assumption that  other  constant  temperature  i n c r e a s i n g temperature  o f the  they is  have  zero.  sum  i n luminescence i n t e n s i t y  i s i n d i c a t e d i n t a b l e IV  i n the  decrease i n i n t e n s i t y could  value  dependence  fact that (Ki^W*)  be  dependence.  observed decrease  corresponding decrease  should  capture  observed temperature  i s not  been c a l c u l a t e d under the I t was  traps  The  capture  a l s o be  cross-sections.  explained,  as  a This  i f i t were  31  assumed that  r a d i a t i o n l e s s t r a n s i t i o n s become  increasingly  important as the temperature i s r a i s e d . The p o s s i b i l i t y that r a d i a t i o n l e s s t r a n s i t i o n s occur was  n e g l e c t e d i n the c a l c u l a t i o n o f the v a l u e s o f t a b l e  and t h i s n e g l e c t  cross-sections.  The p o s t u l a t e  made t h a t the capture c r o s s - s e c t i o n s  to s a t i s f y t h i s p o s t u l a t e .  was  are c o n s t a n t s  independent o f temperature and t h e r a t i o s A * / * , ;  t a b l e IV.  IV  lead t o t'he unexpected r e s u l t o f the  temperature dependent therefore  may  calculated  These r a t i o s a r e a l s o l i s t e d i n  They were c a l c u l a t e d on the assumption t h a t  f o r the lowest temperature o f o b s e r v a t i o n . t h i s assumption i s t h a t  A*/A,=  I  The reason f o r  r a d i a t i o n l e s s t r a n s i t i o n s p l a y a minor  r o l e at lower temperatures and may  therefore  be n e g l e c t e d at  these temperatures. I t can be seen from the r a t i o s X * / ^ , ; cross-sections  t h a t capture  which are temperature independent are  o n l y i f r a d i a t i o n l e s s t r a n s i t i o n s become p r e v a l e n t with i n c r e a s i n g temperature.  possible  increasingly This represents a  s t r o n g argument f o r t h e assumption t h a t t r a p s a r e p a r t i a l l y d i s c h a r g e d by r a d i a t i o n l e s s t r a n s i t i o n s . though, i m p l i e s the  a d i f f e r e n c e between  This  \n  and ^  assumption, and  complicates  i n t e r p r e t a t i o n o f e q u a t i o n I I I ( l ) which has been s *  e x p e r i m e n t a l l y found t o be v a l i d f o r Aj 4.  .  I r r e v e r s i b l e E f f e c t s of X - I r r a d i a t i o n . Reproducible r e s u l t s c o u l d be obtained f o r a decay  curve produced under i d e n t i c a l c o n d i t i o n s  o n l y i f the c r y s t a l  32 was  annealed  experiment effect.  f o r about  , the An  decay then  30 h o u r s a t **300°C.  results  annealed recorded  c r y s t a l was until  the c r y s t a l immediately and  this  process The  table  I I , the  o f w h i c h s h a l l be  effect  i t disappeared  a number o f  of t h i s  c a l l e d the  i r r a d i a t e d with  re-irradiated,  repeated  T h i s prompted  into  seen  increases the  intensity  a t any  that  i s i l l u s t r a t e d by  repeated  time  t after  excitation  time  decay o f the  first  of the  excitation,  successive i r r a d i a t i o n s tends  twice the  a f t e r the  end  the  intensity  initial To  emitted  by  the  the  g a i n more i n f o r m a t i o n a b o u t t h e d e c a y  the e x p e r i m e n t a l  before they  after  irradiation.  them may  be  process,  caused  Three e x p l a n a t i o n s a r e  c o n c l u s i o n s drawn f r o m  If  about  c r y s t a l at t h i s time  x-irradiations.  by r e p e a t e d  At t h e .  intensity  toward a value o f  repeated  i)  the  annealed  increase i n  have b e e n made t o e x p l a i n t h e e f f e c t s  the  and  of. t h e d e c a y .  attempts  and  similar  x-irradiation  end  corresponding to the  etc.  times.  amount o f i n c r e a s e i s g r e a t e r a t t h e  with  background,  values given being t y p i c a l of a l l other I t can be  the  t h e decay r e c o r d e d ,  procedure  experiments.  crystal  irreversible  x-rays,  the  an  by  considered  checked  against  results.  Changes o f t h e  initial  p o p u l a t i o n s ^>  i0  produced  x-irradiation. the t r a p s are r e f i l l e d have had  p o p u l a t i o n s found  a chance t o be  by  successive  completely  i n the t r a p s immediately  irradiations  emptied,  after  the  excitation  may  i n c r e a s e w i t h s u c c e s s i v e i r r a d i a t i o n s and thus l e a d t o an  i n c r e a s e i n luminescence The  intensity.  c r y s t a l was r e - i r r a d i a t e d w i t h x - r a y s  only  after  the luminescence i n t e n s i t y had dropped each time t o the same s m a l l value where i t became unobservable because o f the background n o i s e f l u c t u a t i o n s . t o t a l trap populations  Thus, i t may be assumed t h a t  j u s t before the 2nd and  i r r a d i a t i o n s were equal t o one t h a t before the i n i t i a l  another, and  the  subsequent  also higher  than  excitation.  T h i s assumption would e x p l a i n an i n c r e a s e i n o n l y f o r the 2nd e x c i t a t i o n ,  luminescence output x-irradiations  a l l subsequent  o c c u r r i n g w i t h the same t r a p p o p u l a t i o n s ,  l e a d i n g to decay curves o f the same i n t e n s i t y as t h a t  thus  after  the 2nd i r r a d i a t i o n . T h i s i s c o n t r a r y to the observed behaviour, alternative  and an  explanation i s required.  ii)  The  p r o d u c t i o n o f new t r a p s by x - i r r a d i a t i o n .  By combining equations 111(2) and 111(7) i t can be seen that the i n t e n s i t y of the luminescence i s p r o p o r t i o n a l t o the n u m b e r , ,  o f t r a p s present  i n the c r y s t a l .  i r r e v e r s i b l e i n c r e a s e o f luminescence output attributed  could be  t o the p r o d u c t i o n o f new t r a p s by the This explanation  i s c o n s i s t e n t w i t h the  t h a t luminescence i n a pure c r y s t a l matrix  Hence, the  i s due  x-irradiation. suggestion t o the  e l e c t r o n t r a p s a s s o c i a t e d with l a t t i c e d e f e c t s . C r e a t i o n o f such d e f e c t s by x-rays  i s suggested by v a r i o u s  observations;  34  e.g. the volume d i l a t a t i o n that accompanies the of  alkali-halides. The  x-irradiation  2  p r o d u c t i o n o f new  t r a p s by x - i r r a d i a t i o n  may  e x p l a i n the i r r e v e r s i b l e e f f e c t s o f such i r r a d i a t i o n on the luminescent  decay, but i t f a i l s to e x p l a i n i n a simple manner  the r e l a t i v e l y quick s a t u r a t i o n o f t h i 3 e f f e c t and prevalence  its*  i n the t a i l o f the decay. i i i ) - I n d i r e c t changes of the decay c o n s t a n t s  by x - i r r a d i a t i o n s . As has been mentioned i n ' s e c t i o n I I I , the decay " c o n s t a n t s " may  become time dependent toward the end o f a  decay when d e v i a t i o n s from a  raonomolecular  decay process  are  most l i k e l y to occur. I f the observed decay process o f the  luminescence  i n part by a  second o r d e r , then i t i s c o n c e i v a b l e t h a t  s u c c e s s i v e x - i r r a d i a t i o n s may constants X .  i s caused  T h i s may  be  a f f e c t the v a l u e s o f the decay  seen from the f o l l o w i n g argument:  Suppose there e x i s t i n the c r y s t a l a number o f very deep t r a p s ; i . e . t r a p s w i t h a l a r g e a c t i v a t i o n energy and which e l e c t r o n s cannot be d i s c h a r g e d by thermal  from  fluctuations.  Such deep t r a p s w i l l be c h a r a c t e r i z e d by v e r y small v a l u e s o f the decay c o n s t a n t s and,  consequently,  by v i r t u e o f  equation 111(7), w i l l not be s a t u r a t e d a f t e r an of 30  x-irradiation  seconds (the time used i n these experiments) i f  i s a l s o assumed to have a v e r y s m a l l v a l u e . x - i r r a d i a t i o n s w i l l tend to f i l l extent u n t i l  +  Thus, s u c c e s s i v e  these deep t r a p s t o a g r e a t e r  s a t u r a t i o n i s reached  a f t e r the nP^  1  irradiation.  35 The  e l e c t r o n s caught i n these deep t r a p s w i l l remain  there u n t i l t h e c r y s t a l i s annealed, s i n c e a t t h e temperature o f t h e experiments thermal energy f l u c t u a t i o n s are i n s u f f i c i e n t to e j e c t them. filled  Since these e l e c t r o n s w i l l o r i g i n a t e from t h e  band, t h e i r t r a p p i n g i n t h e deep t r a p s w i l l i n c r e a s e  the number o f h o l e s i n the f i l l e d band at a l l times and thus a l l o w t h e d i s c h a r g e o f the shallower t r a p s t o remain monomolecular f o r longer p e r i o d s o f time, i . e . t h e A^ w i l l remain time-independent  for a longer  time.  Thus, x-rays may induce i n d i r e c t decay constants  changes i n t h e  A ; , t e n d i n g t o make them l e s s time-dependent  at the t a i l o f t h e decay curve.  In o t h e r words, i t i s  p o s s i b l e t h a t s u c c e s s i v e x - r a y i n g w i l l tend t o make the decay process more n e a r l y monomolecular i n c h a r a c t e r f o r a l o n g e r time. The with-x-rays  experimental  r e s u l t that successive i r r a d i a t i o n  causes s u c c e s s i v e i n c r e a s e s i n the luminescent  decay would be e x p l a i n e d , then, by the above arguments, i f i t could be shown t h a t i n the r e l e v a n t time i n t e r v a l s ,  a mono-  molecular decay leads t o h i g h e r i n t e n s i t i e s than a b i m o l e c u l a r decay. What i s meant by t h e r e l e v a n t time i n t e r v a l i s discussed f i r s t .  F o r a monomolecular decay process, t h e  d i s c h a r g e o f t r a p s i s d e s c r i b e d by which, when i n t e g r a t e d g i v e s  36 The  i n t e n s i t y o f t h e decay i s p r o p o r t i o n a l t o t h e r a t e o f  discharge  o f the t r a p s , i . e .  IJ^ - -& « For a bimolecular  frA** * 1  decay, t h e d i s c h a r g e  V I ( 1 )  of t h e t r a p s i s d e s c r i b e d  ie  1  xM  I n t e gi rn at te in ns gi t ty h iiss .egqiuvaetni oby n gives The  Introducing  s  |>.  o  ^this  It) •=  • X  a  equation  may be r e - w r i t t e n a s  VI(2)  .  E q u a t i o n s VT(1) and V I ( 2 ) , i f c o n s i d e r e d  as f u n c t i o n s o f X  and X' e x h i b i t maxima f o r  A = 'A: This f a c t  may be i n t e r p r e t e d a s f o l l o w s : At  any g i v e n t i m e ,  contribute the greatest will to  X ' = '/t say T, t h e v a l u e  amount t o t h e m o n o m o l e c u l a r  be X = X/T and s i m i l a r l y X * J p  the bimolecular  differences neglected.  o f "X w h i c h w i l l  intensity.  i n the i n i t i a l  will  be t h e m a j o r  This i s true only  populations  .  intensity contributor  i f the  of various traps are  37 In the case of a continuous t r a p d i s t r i b u t i o n , i n t e n s i t y at the time t w i l l be mainly c o n t r i b u t e d by (or A') ,which i s equal t o l / t .  value o f  p o s s i b l e t o compare t h e time t , corresponding considering  A-*X"  intensities  t h a t would r e s u l t , at  initial  intensity X  decay mechanisms. T  One  V o  corresponding  intensities  population  to the  two  different  finds  -'At  r—Ua, Equation  the  decay, by  i m p l i e s comparing the  o f t h e decay from a t r a p with a g i v e n i n i t i a l and  the  It i s therefore  to a mono- or b i m o l e c u l a r  '/t. This  the  ^  L  *  w  t =  VI(3)  l  V I ( 3 ) i n d i c a t e s t h a t i n the r e l e v a n t time i n t e r v a l a  monomolecular decay l e a d s to a h i g h e r bimolecular  light  output than a  d e c a y . s t a r t i n g from the same i n i t i a l  Returning  to the problem o f the  conditions.  irreversible  i r r a d i a t i o n e f f e c t s , t h e above f i n d i n g s may  be summarized  as  follows: The  luminescent decay o f f i l l e d  monomolecular i n c h a r a c t e r , owing to the electron acceptors  (or h o l e s  t r a p s i s not  l i m i t e d number o f  i n the f i l l e d band) and  r e s u l t i n g retrapping of released electrons. from the monomolecular decay process decaying  The  deviations quickly  p o r t i o n o f the  However, f o r the  t r a p s , i . e . those t h a t e s s e n t i a l l y  the ,  are s m a l l f o r the  t r a p s which produce the i n i t i a l  observed luminescence decay.  purely  slowly  decaying  produce the t a i l o f the  observed decay, these d e v i a t i o n s are l a r g e .  38 Repeated x - i r r a d i a t i o n provides This  a greater  increases  increases the  the  molecular  deep t r a p s  number o f e l e c t r o n a c c e p t o r s monomolecular c h a r a c t e r  effect  increase  initial  very  and  (or h o l e s ) .  of the  d e c a y and  so  luminescent i n t e n s i t y .  The intensity  the  fills  shows a q u i c k  o f a b o u t two,  p o r t i o n o f the  and  c a n n o t be  saturation after  and  i s least  an  pronounced  in  d e c a y w h i c h i s a l w a y s n e a r l y mono-  made much more m o n o m o l e c u l a r i n  character. These t h e o r e t i c a l p r e d i c t i o n s agree with experimental  results.  They p o i n t  to considerable  the deviations  f r o m a p u r e l y m o n o m o l e c u l a r d e c a y mechanism f o r s l o w l y  decaying  traps. 5.  Experiments at At  the that  Low  liquid  d e c a y c u r v e was  Temperatures.  a i r temperatures, the  initial  f o u n d t o be  times greater  a t room t e m p e r a t u r e .  decay f o r a g r e a t e r  disappeared  i n t o the  disappeared  c r y s t a l with luminescence. thermal caught  give  any  interesting feature  e x p e r i m e n t was had  length  background n o i s e .  however, d i d n o t An  the  fact  i n t o the  white l i g h t This  that  new  i t was  a f t e r the  possible  Analysis of the  i n d i c a t e s that  t r a p s and  that  to  low  temperature  original  luminescence of  sufficient  at t h i s  low  the  to  re-induce  temperature,  release a l l the their  decay  information.  background, i r r a d i a t i o n f o r 1 s e c . was  than  of time before i t  or u s e f u l  of the  energy f l u c t u a t i o n s cannot i n a l l of the  100  Consequently,  observe the  curve,  about  i n t e n s i t y of  release  electrons requires  the  39 g r e a t e r amount o f e n e r g y  c o n t a i n e d i n the l i g h t  This r e - a c t i v a t i o n with white l i g h t by one  o f the f o l l o w i n g (a)  transition  The  absorption  o f an e l e c t r o n  o f an  optical  from, a v e r y deep t r a p d i r e c t l y escape  a  to a  to the  give r i s e  to  re-induced luminescence. (b)  transition  energies,  The  quantum c a u s e s a  t o t h e c o n d u c t i o n band, f r o m whence the  become t r a p p e d t o be r e l e a s e d  or f a l l  "secondary  back  t o the  filled  band,  l a t e r by (giving  thermal rise  t o .a  fluorescence"). Since  irradiation  intensity  a b s o r p t i o n o f an o p t i c a l  directly  e l e c t r o n may  of  explained  quantum c a u s e s  c o n d u c t i o n b a n d by means o f t h e r m a l e n e r g y and  the  can be  mechanisms:  s h a l l o w e r t r a p , f r o m where t h e e l e c t r o n may  the  quanta.  i t was  i m p o s s i b l e t o view the c r y s t a l  with white  t h a t would  light  because  have b e e n r e f l e c t e d  t h e p h o t o m u l t i p l i e r t u b e , i t was  of the high upon t h e  not p o s s i b l e  during light  photo-cathode to  determine  whether "secondary f l u o r e s c e n c e " o c c u r s . A further result was  the  o f t h e low t e m p e r a t u r e  following: A f t e r the o r i g i n a l  irradiation of  time  of the c r y s t a l  could  irradiation 90  l u m i n e s c e n c e had d i s a p p e a r e d ,  with white l i g h t  induce f u r t h e r luminescence.  with white  l i g h t was  m i n u t e s , no l u m i n e s c e n c e c o u l d  crystal.  experiment  T h i s c a n be  thermal energy  and  However, when t h e  c o n t i n u e d f o r about t h e n be d e t e c t e d f r o m  t a k e n t o mean t h a t  fluctuations,  f o r short periods  also  a l l traps,  optical  quanta  the  f o r which i n the  v i s i b l e r e g i o n , are e f f e c t i v e i n causing a d e p l e t i o n of p o p u l a t i o n , had been  emptied.  A f t e r t h e 90 minute p e r i o d o f v i s i b l e i r r a d i a t i o n , t h e temperature  o f the c r y s t a l was  i n c r e a s e , t h e c r y s t a l b e i n g observed o f t h i s experiment  light a l l o w e d to  continuously.  are shown i n f i g .  temperature  I n a d d i t i o n , one o t h e r e x t r e m e l y b r o a d ,  v e r y weak i n c r e a s e i n i n t e n s i t y was temperature,  results  T h i s f i g u r e shows t h a t  three d i s t i n c t luminescent b u r s t s occurred i n the r e g i o n shown.  The  and  observed a t a h i g h e r  but i t appeared more as a g e n e r a l i n c r e a s e i n  i n t e n s i t y r a t h e r t h a n as a d i s t i n c t peak o f luminescence was  t h e r e f o r e not shown i n t h i s The  and  figure.  phosphor o p e r a t i n g temperature  T a t t h e peak o f  each glow curve band i s r e l a t e d t o t h e c o r r e s p o n d i n g t r a p depth E by t h e a p p r o x i m a t i o n  sc" / E  k T  -as  1 sec?1  Assuming v a l u e s o f s r a n g i n g from 10^* t o 10^ determined  as  by the method p r e v i o u s l y d e s c r i b e d , the range i n  a c t i v a t i o n e n e r g i e s f o r t h e t h r e e observed luminescence  peaks i n t h e .  output o f the warming c r y s t a l are g i v e n by:  f o r the peak a t  142°K ,  E = 0.112  - 0.225 ey  154°K , E » 0.122  - 0.244 ev  172°K,  - 0.272 ev  E = 0.136  These v a l u e s o f the a c t i v a t i o n e n e r g i e s , E i , l i e i n an e n t i r e l y d i f f e r e n t r e g i o n o f t h e energy range between  filled  and c o n d u c t i o n band than the v a l u e s as c a l c u l a t e d from the l u m i n e s c e n t decay c u r v e s .  I t should be mentioned here t h a t these v a l u e s o f E; were o b t a i n e d a f t e r the c r y s t a l was  allowed t o d e - e x c i t e  i t s e l f by thermal means and a l s o a f t e r i t was bleached w i t h white l i g h t .  T h i s may  completely  i n d i c a t e t h a t the t r a p s  r e s p o n s i b l e f o r the i n t e n s i t y observed i n the glow curve are of a d i f f e r e n t nature than those r e s p o n s i b l e f o r the luminescent  decay.  VII.  CONCLUSIONS.  U t i l i z i n g a method o f a n a l y s i s t h a t has been developed  f o r decay curves, i t has been p o s s i b l e t o a s c e r t a i n  the e x i s t e n c e o f ct d i f f e r e n t types o f t r a p s i n K l whose a c t i v a t i o n e n e r g i e s l i e i n the range 0.4 t o 0.8 ev and whose escape p r o b a b i l i t y , s, has been found t o vary from 10^ t o 10^. These v a l u e s f o r extremely  and S-  v  were c a l c u l a t e d on the b a s i s o f the  simple monomolecular decay process i n which a l l  t r a n s i t i o n s o f e l e c t r o n s l e a d t o observable That t h i s simple assumption approximation  to explain  behaviour o f t h e p o p u l a t i o n s i n the t r a p s  a f t e r x - i r r a d i a t i o n i n a manner which i s  compatible w i t h temperature the t r a p s .  i s only a f i r s t  i s i n d i c a t e d by t h e f a c t t h a t i t f a i l s  the temperature immediately  radiation.  independent  cross-sections for  Only by i n t r o d u c i n g the p o s s i b i l i t y t h a t  r a d i a t i o n l e s s t r a n s i t i o n s f o r e l e c t r o n s may occur and t h a t they become o f i n c r e a s i n g r e l a t i v e importance temperature  i s r a i s e d , can the behaviour  as t h e  o f the i n i t i a l t r a p  p o p u l a t i o n s be s a t i s f a c t o r i l y e x p l a i n e d . F u r t h e r arguments a g a i n s t the simple monomolecular decay process are found  i n the e x p l a n a t i o n o f the i r r e v e r s i b l e  effects of x-irradiation. assumption  T h i s e x p l a n a t i o n i s based  t h a t s u c c e s s i v e x - i r r a d i a t i o n s cause a p a r t o f the  decay process t o become transformed to  on the  a monomolecular one.  from one o f h i g h e r o r d e r  43 In s p i t e values represent  o f these  acceptable  facts,  approximations  i n f o r m a t i o n about t h e l u m i n e s c e n t The determination r e g i o n than  on  of  process.  and c o n t a i n  useful  system.  values which l i e i n a d i f f e r e n t determined  from the luminescent  alone,  o f t h e decay o f observed  give detailed  for this  b e e n d i s c u s s e d and when c o n s i d e r e d w i t h  the description  i n v o l v e d when 'a c r y s t a l  visible  x-rays.  luminescence  process  results  experiments should f a c i l i t a t e  excitation with  experiments  i n f o r m a t i o n about t h e decay  Some o f t h e p o s s i b i l i t i e s  emits  energy  decay.  work d e s c r i b e d above i n d i c a t e s t h a t  the determination  cannot,  v  e x p e r i m e n t s a t l o w t e m p e r a t u e s have e n a b l e d t h e  those  The  E- and S;  t h e determined  have  o f other  o f t h e mechanism  radiation  after  time (sec) FIG.  10.  G r a p h i c a l A n a l y s i s o f a Decay Curve F a c i n g Page 44  44 APPENDIX I A MECHANICAL DEVICE FOR  FACILITATING  ...THE GRAPHICAL ANALYSIS. In o r d e r t o o b t a i n a s u f f i c i e n t the many-lined derived  continuous  necessary sum  s p e c t r u m , g i v e n by |j>(>^  d i s t r i b u t i o n be  c o n s t r u c t i n g the was  introduced.  I , 1^  Lg.  logarithmic  10 A  same s c a l e a s t h e  tangent  1^  its'  o f ways.  on  i s based  use  i t was  decay curve  a mechanical  This device  illustrates  The  To  i s kept  always kept  in a vertical  a logarithmic  f o r the  curve  the t a n g e n t i a l r u l e r  by  be  guide  fixed  having long  i t slides  ruler, The  along frame.  at the upper  edge  graph. With t h i s d e v i c e , I2, which c o i n c i d e s with the  (x-1)  the  it.  a T-bar attache d t o i t s o u t e r  T h i s T-bar g l i d e s along a h o r i z o n t a l  three  I i n the  i n coincidence with as  relation  first  along t h i s  position  a  device f o r  inner part of a s l i d e - r u l e , glides  into  facilitate  upon t h e  i s drawn t o t h e  l o g paper used,  p o i n t "1.0"  slide-rule  of the  invariant,  s c a l e by means o f a l o n g r u l e r w h i c h may  position.  with the  the  logarithm of a difference  Figure  to t h i s  IV(2),so that  to resolve a s i n g l e experimental  the t e d i o u s g r a p h i c a l procedure,  lines  in  equation  of exponentials i n a large v a r i e t y  graph,  number o f l i n e s  on t h e  logarithmic  slide  rule,  s c a l e without  c a n be any  immediately  internsdiate  plotted  point  i n the  n u m e r i c a l work,  as  4 5  indicated i n f i g . 10. I'and l " r e p r e s e n t p o s s i b l e tangents t o the curve I, i n d i c a t i n g why  d i f f e r e n t a n a l y s e s are p o s s i b l e .  46 APPENDIX I I ANALYTICAL METHODS FOR RESOLVING A DECAY CURVE INTO A SUM OF EXPONENTIALS. Assuming t h a t the t r a p d i s t r i b u t i o n i n t h e A - s c a l e i s a continuous one, t h e a n a l y s i s o f a decay curve reduces t o the problem o f i n v e r t i n g a Laplace t r a n s f o r m : J-fr^-  1 ^©  b'(x>Ae~  A(l)  S e v e r a l methods have been attempted  f o r achieving the  inversion: i)  Introducing  c  o ^= too* (  equation A ( l ) may be r e - w r i t t e n as  where  C= a  constant.  and the problem reduces t o one o f determining the f u n c t i o n ^ ( * ) I f one d e f i n e s  I(t> =  then,  \\ix> e  where A * i s the n  ****  t n  =fj*C»  *  V  moment o f X w i t h r e s p e c t t o the f u n c t i o n  jWft^  , and I ( t ) , i(t), i'(t) etc. can in  p r i n c i p l e be found g r a p h i c a l l y from the decay curves. Any f u n c t i o n  may be r e o r e s e n t e d ^5 as  0  where t h e Hj.*)  xir  are the Hermite p o l y n o m i a l s , and  47  «»» \ H^OO^*)^*-.  C  s  The C ^ c a n  a s f u n c t i o n s o f t h e moments o f Thus  (A) c a n be r e p r e s e n t e d  where  the  ii)  Similarly,  respect to  a s a power  ^>Cx).  series, i n  the function  values  w h i c h c a n be o b t a i n e d  ^  A(^.  region  o f t h e moments  from the h i g h e r d e r i v a t i v e s o f I ( t )  r e q u i r e s an a c c u r a t e  knowledge o f I ( t ) i n t h e  at t » 0 . iii)  ^C>)  I f I ( t ) i s expressed  may be e x p r e s s e d ^  ^2.  O!  0  Introducing  t * '/^  +  as  may be c o n s t r u c t e d  t i m e t=0:  T h i s method  Thus  represented  p o p u l a t i o n f u n c t i o n , b(A) may be e x p r e s s e d  from t h e numerical  Then  with  be  a r e f u n c t i o n s o f t h e moments  Therefore.the  the  x  thus  as  a s ^  O Ma  I!  + a ^ x  XT  +  ...  at  All  t h e d e r i v a t i v e s o f I^t}  with respect  obtained from t h e d e r i v a t i v e s of I ( t ) with respect i.e.  power s e r i e s  linear  give  sufficient  (n+1) d e r i v a t i v e s  i n f o r m a t i o n t o s e t up  e q u a t i o n s i n t h e (n+1) unknowns, Note,  i n the at any  (n+1)  .  too, that -  Lim *r--*»o  o.  and i f a  0  o  i s known,  K  Lim  etc.  The v a l u e s o f a l l t h e 0 - ^ may, extrapolation  of similar  iiii)  i n principle,  function's t o  be o b t a i n e d by t h e  HzsO.  A n o t h e r method a t t e m p t e d  i n the a n a l y s i s of  d e c a y c u r v e s i s b a s e d upon t h e f o r m u l a  The f u n c t i o n N.  be  to t;  I f (n+1) t e r m s a r e u s e d  for'X('f) ,• t h e n t h e f i r s t  timet»VV  given  the  may  f r o m the h i g h e r d e r i v a t i v e s o f t h e e x p e r i m e n t a l d e c a y  curve a t any g i v e n v a l u e o f t .  then  to ^  Rosen.  Expressed  A-^C*) i  s  given  i n tabular  form i n a paper  by  1 7  i n terms o f  (for practical  purposes)  this  formula i s  and t h e p r o c e d u r e o f a n a l y s i s The e n t i r e is divided  A -range  i n t o a g i v e n number  i s as  follows:  of interest  (from  of intervals.  o t o %- X )  W i t h i n each  interval a  i t i s assumed t h a t  power s e r i e s  may be r e p r e s e n t e d by  of 3 terms,  say.  t h e n be r e p r e s e n t e d b y t h e power  The t a i l  o f t h e I ( t ) may  series  3  The  length o f the t  coefficients interval  is  i n t e r v a l must be c h o s e n  jf; r e m a i n  used.  invariant  i s then  t o a decrease  o f the f  Then,  constructed f o r a l l times  ^Lijt)  such t h a t t h e  (up t o t = « o  s u b s t r a c t e d from  i n principle)  and t h e d i f f e r e n c e  a n a l y z e d by t h e f o r m u l a  TCr> - I  -11U.  T h i s procedure covered. series  i s then repeated u n t i l  Thus  J>(>)  X  the entire  X-range  = C $(>)/A  r e p r e s e n t e d as  i s a constant.  t h e s e methods o f a n a l y s i s were a t t e m p t e d .  found  t h a t t h e l a c k o f knowledge o f t h e i n t e n s i t y  times  extremely  difficulties.  s h o r t and a l s o  extremely  ^OA} left  curve f o r decay  long, introduced various  by these  F u r t h e r , t h e r e p r o d u c t i o n o f the decay  distribution something  I t was  T h u s , t h e p o p u l a t i o n d i s t r i b u t i o n was f o u n d t o  h a v e some n e g a t i v e v a l u e s when d e t e r m i n e d methods.  is  r e g i o n and t h e p o p u l a t i o n d i s t r i b u t i o n  where C All  (V*)]  ^ ( ^ ) may be r e p r e s e n t e d a s a sum o f t h e power  f o r each  function  (>./r) - ^  t*'  determined  t o be d e s i r e d .  by t h e s e a n a l y t i c  analytic  curve u s i n g the methods  always  50 F o r t h e s e r e a s o n s , t h e g r a p h i c a l method was most  satisfactory,  possibility  since  obtained  t o . be  i t a v o i d s , from the s t a r t , the  of negative p-values.  t h e d e c a y c u r v e s was  found  found  Also, the reproduction o f  t o be much b e t t e r t h a n  by u s e o f t h e a n a l y t i c  methods.  that  REFERENCES 1.  B e c q u e r e l , E.  2.  . Seitz', F.  La Lumiere ( P a r i s  1867)  Rev. Mod. Phys. 26 7, (1954).  3..  Leverenz,  H.W.  4.  Mott, N.F. and Gurney,  5.  Bunger, W. and F l e c h s i g , Z.  Z. Phys. 62 42, ( 1 9 4 1 T 7  6.  Bose,  H.N.  Ind. J . Phys. 20 2 1 , (1946).  7.  Bose,  H.N.  Ind. J." Phys. 21 29, (1947). -~  Luminescence o f S o l i d s , John Wiley and Sons, Inc., New York, (1950). R.W. E l e c t r o n i c Processes i n I o n i c C r y s t a l s . (Clarendon P r e s s , ) Oxford, (1940).  8. • Dekker, A . J . and M o r r i s h , A.H.  Phys. Rev. 78 3 0 1 , (1950).  9.  Dekker, A . J . and M o r r i s h , A.H.  Phys. Rev. 80 1030, ( 1 9 5 0 7 7  10.  Bonanomi, J . And Rossell, J.  Helv. Phys. A c t a 2j> 725, (1952).  11.  Urbach, F.  Wien Ber. (IIA) 132 363, (1930).  12.  Randall., J.T. ani • W i l k i n s , M.H.F.  13.  Hill,  J . J . and Schwed, P  14.  Williams,G.W., U s i s k i n , S.R. and Dekker, A-.J.  Proc. Roy. Soc. A 184 366, (1945). J . Chem. Phys. 23 652, (1955). Phys. Rev. 92 1398, (1953T7  15.  Z e r n i c k e , F.  Handbuch der Physik, V o l . I l l , pp.. 448  16.  Churchill,  Modern O p e r a t i o n a l Mathematics i n E n g i n e e r i n g , McGraw H i l l Book Co. I n c . New York, 1944.  17.  Rosen,  N.  R.V.  Phys. Rev.  2|  255-276, (1931).  

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