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Thermal decay of the luminescence of KBr Williams, Gerald 1953

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THERMAL DECAY OF THE LUMINESCENCE OF KBr by GERALD WILLIAMS A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in PHYSICS We accept t h i s thesis as conforming to the standard required from candidates for the degree of DOCTOR OF PHILOSOPHY. Members of the Department of Physics. THE UNIVERSITY OF BRITISH COLUMBIA September, 1953. Y ABSTRACT. An apparatus for the measurement of the lumin-escent decay of phosphors has been designed. Decay times 4 in the range 2 to 10 seconds may be recorded. The decay of pure single crystals of KBr has been observed at six-teen temperatures in the range -77°C. to 240°C. Lumines-r cence disappears at higher temperatures. The decay curves were analyzed graphically into a sum of exponentials. The half-lives of these components were found to be independant of the intensity of excitat-ion of the crystal. The half-lives varied v/ith temperature according to the relation ^n ~ ^ The decay is then interpreted as being governed by a series of trapping levels in the crystal, which would pro-duce a variation of decay constant with temperature given by Applying this interpretation to the observed decay, seventeen trapping levels, with thermal activation energies Cpn have been obtained. The values of Cf>„ range from 0.42 e.v. to 1.05 e.v. The spectrum of the luminescence at room tempera-ture has been measured, and is found to be a wide band with a peak at 5100 A°. 'v. 1 ACKNOWLEDGMENTS. I am greatly indebted to Dr. Dekker for his ad-vice and encouragement during the course of t h i s work. His help has continued since his departure to the University of Minnesota, for which I am sincerely g r a t e f u l . I wish to thank Mr. S. R. Usiskin for his c o l -laboration i n the design and construction of the appara-tus. I also wish to acknowledge the assistance of the members of the shop s t a f f of the Physics Department. This work was supported by research grants made to Dr. Dekker and a Scholarship awarded to the au-thor (1951-52) by the National Research Council. The author also received a Scholarship (1949-50) from the B r i t i s h Columbia Telephone Company. These grants are gr a t e f u l l y acknowledged. T H E : U N I V E R S I T Y O F B R I T I S H C O L U M B I A Faculty of Graduate Studies PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of GERALD WDODBURN WILLIAMS B.Sc. (Saskatchewan) 1946? M.Sc. (Saskatchewan) 1949 WEDNESDAY, September 30th, 1953 at 2:30 p.m. in ROOM 303 PHYSICS BUILDING COMMITTEE IN CHARGE: H.F. Angus, Chairman W. Opechowski K.C. Mann G.M. Volkoff G.M. Shrum T.E. Hull M. Kirsch H.M. Mcllroy B.P. Wisnicki External Examiner - A.J. Dekker LIST OF PUBLICATIONS Magnetic Field Stabilization Circuit, L.. Kats, P.A. Forsyth, E,.F. Cudney, G.W. Williams, H.E. Johns and R. N.H. Haslam, Can. Jour. Res. A, 28, 67, 1950 Ultraviolet Photon Counting with an Electron Multiplier, A.H. Morrish, G.W. Williams and E..K. Darby. Rev. Sci. Inst. 21, 884, 1950 Thermal Decay of the Luminescence of KBr, G.W. Williams, S.R. Usiskin and A.J. Dekker, Phys. Rev. (in the press) THESIS THERMAE, DECAY OF THE LUMINESCENCE OF KBr. An apparatus for the measurement of the decay of luminescence from excited crystals has been designed and constructed. It has been used to measure the luminescent decay of single crystals of KBr at several temperatures i n the range -77°C to 240°C. The measurements have been graphically analyzed and may be represented by the formula The form of the decay is attributed to the existence of electron traps i n the crystal, with thermal activation energies (D^ . Seventeen values of (p^ are observed, ranging from 0.42 to 1.05 ev. The value of the constant S i s found to be 10 ,9.3- sec. -1 GRADUATE STUDIES Field of Study: Physics Special Relativity —, W. Opechowski Quantum Mechanics — ' G. M. Volkoff Quantum Theory of Radiation F...A. Kaempffer Chemical Physics ~ A. J. Dekker Electronics -- A. Van der Z i e l Theory of Measurements — A. M. Crooker Other Studies: Differential Equations — T. E, Hull Radiochemistry -- M. Kirsch and K. Starke TABLE OF CONTENTS. Page ACKNOWLEDGMENTS. ABSTRACT. I. INTRODUCTION. 1 I I . PREVIOUS WORK ON ALKALI-HALIDES. 6 II I . APPARATUS. 8 IV. RESULTS. 14 V. DISCUSSION. I 9 1. Energy Storage and Decay 19 2. The Frequency Factor S 22 3. Thermal Act i v a t i o n Energy 24 4. Population of Trapping Levels 26 5. Emission Spectrum 27 6. Retrapping 29 7. Conclusions 30 APPENDIX I. Li n e a r i t y of Response to Light Of A Photomultiplier and Pulse Counting System 32 APPENDIX I I . Electronic Apparatus. 37 REFERENCES. LIST OF ^ TABLES. Page Table I. Luminescence Spectrum 17 Table II. Thermal Activation Energies 24 LIST OF ILLUSTRATIONS. Facing Page Fig. 1. Fluorescence and Phosphorescence.. 1 Fig. 2. Bloch Band Model of A Crystal.... 2 Fig. 3. Schematic Diagram of D.C. Amplifier....... 9 Fig. 4. Crystal Holder for Low Temperatures 11 Fig. 5. Crystal Heater 12 Fig. 6. Analysis of Decay Curve at 195°C 14 Fig. 7. Plot of Log 1 0 T h against 1/T°K......... 15 Fig. 8. Luminescence Spectrum at 23°C. 18 Fig. 9. Energy Storage Models 19 Fig. 10. Potential Energy Curves 27 Fig. 11. Schematic Diagram of Pulse Counting Detector System 32 Fig. 12. Effect of Discriminator Setting on Nonlinearity 33 Fig. 13. Fatigue Effect at Constant Light Inten-sity 35 Fig. 14. D.C. Amplifier Power Supply 37 Fig. 15. D.C. Amplifier 38 Fig. 16. Photomultiplier High Voltage Supply 40 i Exciting Radiat ion (a) Emi t ted L ight Intensity (b) Emit ted L ight Intensity (c ) Time T ime T i m e Fig.' 1. Fluorescence and phosphorescence; To face page 1 I. INTRODUCTION. The emission of light was the f i r s t phenomenon observed in excited crystals, but i t is proving to be one of the most d i f f i c u l t to reduce to a theoretical interpre-tation. A large variety of data has been gathered on lumi-nescence, which by definition includes the light emitted by a crystal both during and after excitation by some energy source. The majority of the presently available information deals with substances f i r s t developed for commercial pur-poses (oscilloscope screens, etc.) which are uniformly sub-stances containing some impurity. The luminescence of pure substances has not yet been investigated in detail, largely because of the scarcity of efficient phosphors in that class. A qualitative description of the behaviour of a luminescent material w i l l best define the terms in use. Consider exciting radiation with a variation of intensity with time as shown in f i g . 1(a), f a l l i n g on such a material. The light emitted by the material may have a variation as illustrated in f i g . 1(b), i.e. light is emitted only during excitation. This is referred to as fluorescence. The variation may also be as shown in f i g . 1(c), in which the light intensity builds ;up to a maximum during excitation F i g . 2. Bloch band model of a c r y s t a l To face page 2 and persists for some time after the exciting radiation is removed. This delayed emission is referred to as phospho-rescence, hence the reference to a luminescent substance as a phosphor. The (arbitrary) lower time limit set on phos-_ o phorescence is 10 seconds, the order of relaxation time of an isolated excited ion. Phosphors usually exhibit both fluorescence and phosphorescence. The energy levels in a crystal may be described by a Bloch collective electron picture, in which the electrons are assumed to exist in orbits extending throughout the cry-s t a l . The discrete levels of the isolated ion then become bands in the crystal form, due to the interaction of neighbor ing ions. In an insulating crystal, a l l bands below a cer-tain level are completely f i l l e d , while a l l those above are completely empty, as shown in f i g . 2 . Electrons in these bands are free to move through the crystal, but in a com-pletely f i l l e d band, for every electron moving in one dir -ection there must be another moving in the precisely oppo-site direction, so there i s no resultant current in an elec-t r i c f i e l d . However, electrons may be excited from band B to the empty (conduction) band A, in which case conduction is possible (photoconduction). The "hole" in the f i l l e d band has an effective positive charge and may also contri-bute to the current. The excitation of such electrons by the absorption of light gives rise to the fundamental ultra-violet absorption band. In some cases (alkali-halides, and probably a l l ionic crystals at sufficiently low temperature), absorption in the long-wave length t a i l of this band produces no photoconduction, i.e. the electron and hole are s t i l l bound together (forming an "exciton") and are free to move through the crystal. This indicates an energy level below the conduction band. The most direct evidence of motion of excitons is provided by experiments on photoemission from alkali-halides by Apker and Taft*. The electrons raised to the conduction band by absorption of energy E may immediately f a l l back to the f i l l e d band with the emission of visible light, producing fluorescence. However, in any but an ideal crystal there w i l l exist in the crystal localized energy levels below the conduction band which can trap the electrons, (level D in f i g . 2). These may arise from impurities or defects in the crystal l a t t i c e . Assuming a direct transition from D to B is forbidden, the electron w i l l remain in an excited state until i t is released from D to the conduction band. This gives rise to phosphorescence i f the trap depth £ is small enough to permit excitation by thermal energy. Similar traps may exist for the holes in the f i l l e d band, i.e. normally f i l l e d levels just above the f i l l e d band. A further set of localized levels may exist in the crystal, where radiative transitions to the ground state are particularly favored. This type of level ( G in f i g . 2) is called a luminescent center and is the determining factor in phosphors dependant on activation by impurities. In such phosphors the probability of a radiative transition from the conduction band to the f i l l e d band is small, the energy being released as heat. The addition of (usually) metallic ions makes the emission of light probable, with the wave-length determined at least in part by the kind and concentration of impurity. As has been mentioned previously, the majority of work has been done on impurity-activated phosphors. Among these are included pure phosphors which are activated by heat treatment, producing a non-stdich^iometric crystal with the excess of one ion forming luminescent centers. Most pure substances show no luminescence, and of those that do, most exhibit pure fluorescence (e.g. uranyl sal t s ) . This involves excitation and emission restricted to i n d i v i -dual ions (no phcfcoconduction). Some pure substances do show phosphorescence, and mong these the alkali-halides show the greatest promise for a quantitative treatment. They possess a face-centered cubic structure, are obtainable in a highly purified form and large single crystals are easily grown. 5 The investigation of the alkali-halides has added a great deal to the knowledge of photoconductivity o and other a l l i e d problems , and the desirability of a simi-larly thorough investigation of the luminescence of these 3 materials has been pointed out by several authors . II. PREVIOUS WORK ON ALKALI-HALIDES. The luminescence of the pure alkali-halides has : been the subject of some investigations in the past. Edge emission, i.e. emission on the long wave-length side of the 4 ultra-violet absorption band, was reported by Kudriavzewa . Luminescence under X-ray excitation was observed by Katz 5, and the temperature dependance of this emission was measured 6 7 by Bose . He also observed the decay of the luminescence and gave a qualitative explanation in terms of electron traps. However, only alkali-halides activated by impuri-ties had been investigated in any detail, principally be-cause they show a f a i r l y strong luminescence. The effect of manganese, silver and copper activation has been repor-8 ted by a number of workers . Thallium-activated KC1 was 9 10 f i r s t observed by Bunger and Flechsig . Pringsheim later investigated the thallium-activated potassium-halides and found a temperature dependant exponential decay in the phosphorescence. Nal-Tl has been of some interest because of i t s application to s c i n t i l l a t i o n counters. In this connection Bonanomi and Rossel 1 1 have observed the fast *. phosphorescence in pure and thallium-activated a l k a l i -iodides. In every case they resolve the decay into a number of exponentials, either by direct analysis or by analysis of thermoluminescence curves. They observed some of these to be temperature independant, while others were temperature dependant. Using the newly available end-window photomulti-12 plier tubes, Dekker and Morrish measured the luminescent decay of KBr and LiF at -77°C, 0°C, and 20°C, after ex-citation by X-rays. They were able to follow the decay for several hours at the lowest temperature, so f a i r l y complete curves were obtained for the two materials. Their results gave a decay of the form. log I/Io = -1.17 log t (1) at room temperature, i.e. a straight line of slope -1.17 on a log I vs. log t plot. The lower temperatures produced a knee in the curve, with a steeper slope (~ 1.5) during the f i r s t few minutes. No quantitative explanation of the temperature dependance was attempted at the time, because of the preliminary nature of the experiment. At the suggestion of Dr. Dekker, the author em-barked on a programme of reproducing and expanding the above experiment, with suitable refinements on the temperature control, etc.. It was decided f i r s t to investigate KBr in detail, chiefly because of i t s Wronger luminescence. III. APPARATUS. 8 The design requirements of the apparatus for the proposed investigations are f a i r l y straightforward. The crystal must be maintained at a fixed temperature for a considerable length of time over a temperature range above and below room temperature. It must be exposed at a f a i r l y short range to the excitation source, in this case a low voltage X-ray tube. The emitted light must be received by a detector with a reasonable geometric efficiency, and last, but probably most important, the detector must have a linear response over a range of light intensities of the order of 4 10 . A further requirement is that the detector have a reasonably fast response. It was f i r s t proposed that we use the existing detector used by Dekker and Morrish, with only incidental changes. Their system consisted of an RCA 5819 photomul-t i p l i e r operating into a 3Mc. wide-band amplifier. The resulting pulses were passed through a discriminator and recorded with a conventional scaling system. The only ap-parent drawback was the time required to record the count-ing rate, which could have been circumvented by adding a suitable counting rate meter. However, attempts to repeat their experiments produced conflicting results, which led Phototube col lector \ Input resistor 5 6 , 10 to 10 ohms 100% feedback zero adjust Amplifier volt, gain = I X 7 Record ing milliammeter F i g . 3. Schematic diagram of D.C. amplifier To face page 9 9 to an investigation of the linearity of such a detector. It was found that such a system strongly emphasized changes in gain in the photo-tube caused by (a) changing dynode volt-ages due to signal current drawn from the high impedance source and (b) fatigue of the secondary emission surfaces at high light intensities. The f i n i t e band-width of the amplifier also caused piling up of pulses, and the conse-quent counting of pulses normally below the discriminator level. These effects are discussed in detail in Appendix I. The above d i f f i c u l t i e s could be overcome by us-ing a D.C. detector (i.e. integrating the pulse output of the photo-tube) and using a low impedance voltage source for the photo-tube dynodes. The same photo-tube is used, operated at a reduced voltage to minimize fatigue. The D.C. detector chosen was an electronic am-p l i f i e r with a sufficiently low output impedance to operate a recording milliammeter. The amplifier is shown schemati-cally in f i g . 3 . The photo-tube current is fed to the grid of an electrometer tetrode (grid current 1 0 ~ 1 5 amp.) 8 5 which is connected to a resistor variable from 10 to 10 ohms. The resulting voltage signal is passed through a two-stage balanced amplifier with a low impedance output to the meter. The output signal is returned to the lower end of the electrometer grid resistor, supplying 100% feedback. I 10 An identical balanced amplifier supplies the balancing voltage for the meter. The type of feedback chosen serves a four-fold purpose. (a) It reduces the input time con-stant t>f the amplifier; (b) i t maintains the collector at a fixed voltage, independant of signal current; (c) i t re-duces the output impedance (to 1 ohm) and (d) i t makes the voltage gain (which is unity) independant of tube characteristics and supply voltage variations. The zero d r i f t of the amplifier is about 1 mv per hour, which is satisfactory compared to the minimum signal used (approxi-mately 200 mv.) The current gain of the amplifier is just the ratio of input and output resistances, which is easily variable over the required range of 10^ (10~^ amp. to 10"^ amps, f u l l scale). The low grid current of the input tube -13 allows a simple extension of the range to 10 amps. for possible future use with a liquid air cooled photo-tube. The amplifier is ful l y described in Appendix II. A low impedance source for the photo-tube dynodes was obtained by using a 1 ma. voltage divider, with the last four sections consisting of RCA 5651 gas tubes, which operate as voltage regulators. This gave a negligible im-pedance for the last 4 dynodes, where the signal current is appreciable. The power supply is a common regulator c i r c u i t , supplying 750 to 1250 volts, with a variation of 0.1%. \ Pyrtt w indow A / Glass double dewar Brass bar Vxte" Copper- Constanta n thermocouple KBr- c r y s t a l To vacuum system 1 O-ring seal A l . radiation shield .001" th. T A KBr crystal Brass outer shell i > ^ A l . w indow 1/ .oos"th. p<5lq*»Mn»m. tK. S e c t i o n A - A F i g . 4. Crystal holder for low temperatures. The brass pot for hold-ing the melting mixtures i s shown at the upper r i g h t . To face page 11 11 The detector system was checked by the same method used for the pulse system, and no departure from linearity could be observed. Fatigue was less than 1% at the highest signal current (10 /Ja..) used in the lumin-escence measurements. The meter used is an Esterline-Angus model AW recording milliammeter. The meter i s operated at a chart speed of 6"/min., switching to 6u/hour after the faster components of the decay have disappeared. The response time of this meter ( 1 sec.) means a time loss of about 5 sec. when changing the amplifier range. However, the readings of low signal levels near tube background is improved by the consequent smoothing of current fluctuat-i o n s . The crystal holder for measurements below room temperature (fig. 4), consists of a double Dewar at the top, with a radiation shield connected to the outer Dewar, and surrounding the narrow lower extension of the inner Dewar. (This makes i t possible to extend future experi-ments to liquid helium temperatures.) For the range of temperatures involved in this investigation, a brass pot is f i t t e d inside the glass system, a brass bar supplying thermal contact with the crystal. A cup stamped out of 2 mil. aluminum is placed around the crystal, covering / Leads to heater and V thermocouple A 4 V [FT Mycalex insulation copper-constantan thermocouple KBr crystal 3mm x 20mm d. 20mm hole tapered to hold crystal. 8 0 0 n Nichrome heater Fig. 5. Crystal heater. The heater is operated by an electronically regulated supply delivering up to 50 ma. To face page 12 12 the face exposed to the X-rays. This serves to reduce thermal gradients on that face of the c r y s t a l where the luminescence originates. A copper-constantan thermocouple i s fastened to the brass immediately next to the c r y s t a l . Five temperatures from 0°C. to -77°C. were obtained by placing melting mixtures i n the brass pot. (dry ice and acetone at -77°C.) The lower portion of the Dewar i s constructed of brass, and contains a 3 m i l . aluminum window facing the X-ray source and a Pyrex window facing the l i g h t de-tector. A pumping tube i s attached to t h i s portion, and the system i s evacuated with an o i l d i f f u s i o n pump. This portion was also used for measurement above room temperat-ure by replacing the Dewar with an e l e c t r i c a l l y heated holder ( f i g . 5). A brass spool wound with Nichrome wire holds the c r y s t a l i n i t s aluminum cup i n the vacuum. The surfaces of the spool are sheathed i n aluminum to reduce radiation. (Chiefly to prevent heating of the photo-tube cathode and consequently increasing i t s background). A copper-constantan thermocouple i s fastened inside the spool. Satisfactory temperature control was obtained by electronic regulation of the heater current. The c r y s t a l holder, photo-tube and i t s preampli-f i e r , and the excitation source are contained i n a l i g h t -13 tight box. A shutter in front of the photo-tube cuts off the relatively intense light during excitation of the cry-stal , and permits periodic observation of tube background during a measurement. The source of excitation is a Ferran 70 pkv, 15 ma. X-ray machine. 0 • 1 1 1 1 1 1 1 1 1 I 1 1 1 1 I • . I I 5 10 15 ZO 10 40 60 g 0 50 100 150 t 0 o Time in seconds Fig. 6. Graphical analysis of decay curve at 195°C. 1 - original dscay curve. 2 - curve plotted after subtraction of 61 sec. half-l i f e . 3 - curve plotted after subtraction of 61 and 10 sec. half-lives. To face page 14 14 IV. RESULTS. The luminescent decay of KBr was measured using the above apparatus over the temperature range -77°C. to 240°C. Lower temperatures in steps of about 20° are not easily obtained by using melting mixtures, and higher tempera-tures showed no luminescence. The crystal was always i r -radiated at the temperature at which the decay was obser-ved, and the crystal was bleached with room light before each run. The decay curves were f i r s t plotted on log-log graph paper in ah attempt to establish a power-law decay as tentatively assigned by Dekker and Morrish. However, the increased accuracy and range of the measurements showed that such a decay did not occur. The decay was then plotted on semi-log graph paper, the logarithm of intensity against the time after irradiation. It was found possible to analyze a curve graphically at a given temperature i n -to a sum of exponentials, i.e. the decay is of the form - t lug where t„ are the measured half-lives of the component decays. An example of such an analysis i s shown in f i g . 6. The original curve, corresponding to the decay at 195°C, in this case leads to three decay times: = 61 s e c , ^ = 10 sec. and T3 = 2.6 s e c , W w The energy scale i s based on the assumption that the obser-ved v a r i a t i o n of t with tem-perature i s a Boltzmann func-ti o n e */",T > i . e . the energy <p i s proportional to the slope (see page 22). ~ " "• K in AS' u|" qjdap dDj_L ' I I I I I I I I I 9J!HIDt| jo UJM^JD6OH F i g . 7. Plot of l o g ^ Q ^ against 1/T°K. To face page 15 which are independant of irradiation time. Such an analysis was used for each of the 16 temperatures in the range, and the results were found to be reproducible to about 10%. At lower temperatures five or six exponentials v/ere required. The shortest decay time i s somewhat in doubt since i t is comparable with the response time of the meter. The longest decay time could not be determined from the decay curve at lower temperat-ures, and was predicted from the results at the next high-est temperature (see below). Its amplitude was adjusted to straighten out the t a i l of the difference curve. This procedure is thought to be valid because the value chosen for the largest h a l f - l i f e affects essentially only the next shortest h a l f - l i f e . In f i g . 7, the logarithms of the half-lives have been plotted against the inverse of the absolute temperature for the 16 temperatures used. The experimental -y -4/0 points are found to l i e on straight lines given by c n " r > where A is a constant (10"®*^) independant of n. It is this analysis of the temperature dependance of the • which j u s t i f i e s the method of analysis. One would hesi-tate to base a physical interpretation on an analysis of the type expressed by (2) for a single temperature, but the consistent results obtained for the whole range of temperatures indicates the procedure is valid. It should be noted that while no luminescence was normally observed above 240°C., faint emission was observed at temperatures as high as 350°C. after prolonged heat treatment of the crystal. This emission disappeared i f the crystal was returned to room temperature for 24 hours prior to a high temperature run. This effect has not been investigated in any further detail. It should also be noted that the X-ray excitation necessary to ob-tain a given i n i t i a l intensity of luminescence depends strongly on temperature, varying by a factor 100 between room temperature and -77°C. It is known that the emission band of KBr is broad, so i t was deemed advisable to discover whether the wave length of the emitted light is different for different half-lives. Consequently a series of decay curves were taken at room temperature with a series of band pass f i l t e r s before the photo-tube. The intensity of each curve as a fraction of the unfiltered curve was determined for various times after irradiation. This ratio was found to be independant of time for a l l f i l t e r s , showing the emission to be independant of h a l f - l i f e . It was also observed that the fraction of the luminescence detected through each f i l t e r was the same 17 TABLE I. Spectrometer mm. Setting A° Detector Current ^Relative Sensitivity Corrected Intensity 6.5 7100 0.02xl0~8a 0.077 0.16 7 6670 0.07 0.246 0.28 7.5 6320 0.21 0.545 0.39 8 6030 0.80 1.33 0.60 8.5 5750 1.93 2.87 0.67 9 5550 2.68 3.35 0.80 9.5 5370 3.36 3.70 0.91 10 5220 3.81 3.82 1.00 10.5 5090 3.66 3.72 0.98 11 4970 3.46 3.46 1.00 12 4770 2.76 3.13 0.88 13 4600 2.09 2.72 0.77 14 4450 1.36 2.2 0.62 15 4320 0.95 1.9 0.50 16 4220 0.57 1.7 0.34 17 4120 0.34 1.5 0.23 18 4050 0.18 1.3 0.14 19 3980 0.08 1.2 0.07 20 3930 0.03 1.0 0.03 A The relative sensitivity was measured by observing the spectrum of a tungsten bulb operating at 1750°C, and c a l -culating i t s spectrum considering i t as a black body. 4 0 0 0 5 0 0 0 6000 7 0 0 0 A° W a v e l e n g t h F i g . 8. Luminescence spectrum of KBr at 23°C. To face page 18 during decay as during excitation of the crystal, indicat-ing that the spectrum of the decaying crystal is the same as that from the excited crystal. The spectrum was then measured during excitation at room temperature using a direct vision spectroscope, an RCA 1P21 photomultiplier replacing the eye piece. The instrument was calibrated using a- tungsten lamp source. The results are given in Table I. The corrected spectrum (fig. 8), shows a broad band with a peak at 5100,A° (2.4 ev) and a relatively sharp cutoff at 3900 A° (3.15 ev). At the long wave length side i t f a l l s off more slowly, but the lack of res-ponse of the photomultiplier tube prevented measurements beyond 7100 A° (1.74 ev). B (a) B (b) B Z A (c) F i g . 9. Energy storage models. (a) Temperature indepen-dant exponential decay. (b) Temperature dependant expon-e n t i a l decay. (c) Temperature dependant complex decay. To face page 19 1 •' V. DISCUSSION 19 Summarizing the results stated in Section IV, the luminescent decay of KBr may be represented by the expression for the light intensity - t l ug . r- |i„a ^ ( 2 ) The variation of decay "half-lives" with temperature i s of the form ^ A io ' C n (3) Further, the wave length of emitted light (at least at room temperature) is independant of the h a l f - l i f e ob-served. The emission is a broad band extending from $ 3900 A° past 7100A0, with the intensity maximum at 5100 A°. 1. ENERGY STORAGE AND DECAY The storage of energy evinced by phosphores-cence may occur in several ways. The absorption of i n -cident radiation may l i f t an electron to a metastable state (f i g . 9(a)), with a subsequent exponential decay with a life-time characteristic of that state. The life-time in such a state w i l l be only slightly dependant on tempera-ture. There may also exist below the excited level B (fig . 9(b)), a second level C into which some of the elec-trons may f a l l . If then a transition of level C to the 20 ground level A is forbidden, the electron w i l l remain in C unless excited (thermally or otherwise) into level B. Such a situation w i l l give rise to an exponential decay whose life-time is strongly dependant on temperature. If, as i s the case in a crystal exhibiting photoconductivity, the excited level B is the conduction band, the level C may be represented by localized levels (i.e. traps) throughout the crystal, arising from defects and/or im-purities (fig. 9 ( c ) ) . In such a case we w i l l observe a phosphorescence consisting of as many different exponen-t i a l decays as there are different trapping levels, with the life-times characteristic of the level being strongly temperature dependant. This corresponds to the observed behaviour of KBr in this investigation. Thus we can des-cribe the luminescence of KBr as an excitation of elect-rons from the f i l l e d band to the conduction band. A por-tion of these are trapped in levels just below the conduc-tion band before they can return to the ground state. Transitions from these traps to the ground state being for-bidden, these electrons emit luminescence only after their release by thermal energy, which occurs at a rate depen-dant on the depth of the trap. (The process may also be dependant on the release of trapped holes to the f i l l e d band). The fact that the emitted wave-length i s indepen-21 dant of the h a l f - l i f e is further evidence that a l l elec-trons emitting luminescence do so in f a l l i n g from a com-mon level, i.e. the conduction band. Consider the case of a set of trapping levels of depth (p below the conduction band, After the cessa-tion of the exciting radiation, there w i l l be N Q electrons in these traps. If the crystal i s at the absolute tem-perature T, the probability per unit time that the elec-trons w i l l be thermally excited w i l l be proportional to the Boltzman factor <2 . The decay constant w i l l then be given by A - S E 5 e c ' (4) where S is the so-called "frequency of attempt to escape". Thus we have M " > N * " N S 8 ' * " (5) In terms of the i n i t i a l population, NQ, the observed light intensity w i l l be given by I - - *jr a N o S e e <6) Comparing this to the observed behaviour of KBr, - t U2 I a ? I o . e (2) where ^ h r ^ l o (3) -3r/r - * W r we can write Since the constant A is observed to be the —9 5 same (10 * sec.) for a l l trap depths, we obtain the 1 22 "frequency factor" S = i n 9 * 3 5 sec." 1 and the set of ther-mal activation energies <p„ * talO k : 8 n # 1>ke levels obtained are l i s t e d in Table II. It w i l l be noted that the deepest level is 1.05 e.v. below the conduction band, the absence of deeper ones being indicated by the disappearance of phosphorescence above 240°C. 2. THE FREQUENCY FACTOR S The magnitude observed for the frequency factor S i s not at present explainable in terms of other charac-te r i s t i c s of the crystal. The frequency one would expect in such an expression would be of the order of the fre-quency of vibration of the ions in the l a t t i c e , which is 13 -1 about 10 sec. . However, the values reported in the literature are uniformly less than this by several orders 13 of amgnitude. (A summary is given by Bube ). Further-more, no account has been taken of the possible variation of (jfV, with temperature. This would reduce the value of S s t i l l further. The F-band in KBr (absorption band arising from electrons trapped at negative ion vacancies) 14 does change with temperature . The peak of the band appears to have a temperature coefficient of the order of -3x10""4 e.v./deg. The probability of release of a trapped electron then becomes ^ z 5 e e ( 8 ) In this case i t would change the frequency factor to the g order of 10 . A further consequence of this i s of course that the actual thermal activation energy is not observed, rather (f0 , the value at T = o, is obtained from the experiment. 15 Ellickson has discussed the problem of inter-pretation of the magnitude of S, and beyond pointing out the necessity for the correction given above, he comes to no positive conclusion. In the case of ZnS, he mentions that there had been some prospects of connecting S with the observed dielectric relaxation time of 10 s e c , un-t i l the effect was shown to be due to the separation of photoconducting grains separated by insulating boundaries. A further factor affecting the observed value of S is the possibility of retrapping of the thermally, released electrons. If the probability of this is p, the observed value of S could be decreased by the factor (1-p). To make a significant change p would need to be nearly unity, and would have to be independant of the number of f i l l e d traps to retain an exponential decay. (Retrapping i s dis-cussed in a later section). At any rate the value of S obtained in this experiment (2.2 x 10 9 s e c " 1 ) corresponds closely to previously measured values for the alkali-halides. Bunger 24 16 q and Flechsig reported 2.9 x 10 for thallium activated KC1, which appears to possess traps of a single depth. 17 9 Bonanomi and Rossel reported 3; x 10 for one of the ob-served trapping levels in NaI:Tl (the only level for which they were able to observe directly the life-time of the de-cay over a range of temperatures). 3. THERMAL ACTIVATION ENERGY The seventeen thermal activation energies (Table II) observed in the temperature range of this TABLE II. n n T n 1 530 1.05 10 310 0.61 2 495 0.98 11 290 0.57 3 470 0.93 12 270 0.54 4 445 0.88 13 255 0.52 5 415 0.82 14 245 0.49 6 390 0.77 15 240 0.48 7 370 0.73 16 220 0.44 8 350 0.69 17 210 0.42 9 330 0.65 experiment range from 0.42 to 1.05 e.v. Traps of lower activation erfergy would undoubtedly be observed at lower temperatures. The immediate question is what, i f any, correlation exists between these energies and other mea-surements on KBr. However, thermal activation energies have not been directly measured by any other method (e.g. thermoluminescence curves). Optical activation energies have been investigated quite thoroughly by ob-servations on absorption, photoconduction and "bleaching" of colored alkali-halide crystals. Several bands have been located and attributed to trapped electrons or holes. The correlation of an absorption band with one or more thermal activation energies is s t i l l not possible with the information available. For example, the width of the F-band (corresponding to the deepest electron traps) cannot be ascribed to a distribution of trapping levels, since monochromatic illumination anywhere in the band w i l l bleach the entire band. Furthermore, 18 Pringshium has shown that F-centres with the same op-t i c a l activation energy may have different thermal ac-tivation energies. These experiments showed that, es-pecially at low temperatures, a large fraction of the F-centres formed by X-ray excitation were thermally un-stable. For example, the F-band when formed at -185°C. bleaches almost completely at room temperature, while the 2 6 F-band formed at room temperature i s quite stable. This seems to indicate that the F-centres formed at or above room temperature have a thermal activation energy close 19 * to the value reported by Smakula , v i z . 0.84 e.v. This value l i e s in the range of thermal energies observed here, but without further information, identification i s not possible. 4 . POPULATION OF TRAPPING LEVELS. The population of the levels involved in the experiment would be a useful piece of information, and an attempt was made to measure them. This was done by extrapolating the component exponential to t=0, the population of the level at zero time then being propor-tional to t* h -^ on . However, the error involved in determining I Q by extrapolation on a logarithmic plot i s considerable, and consequently only a qualitative state-ment may be made. Almost invariably, the population i n -creased with increasing value of at a given tem-perature, i.e. the deepest traps are most densely popu-lated at t=0. A further effect i s observed, namely the greatly increased intensity at low temperatures. A fac-tor of about 100 occurs between room temperature and -77°C. This latter effect may be due to the formation at low temperatures of large numbers of F-centers from i n -I >-Generalized coordinate F i g . 10. Energy l e v e l diagram. The potential energy i plotted as a function of a generalized coordinate repre senting the positions of a l l ions. To face page 27 I cipient vacancies in the vi c i n i t y of jogs in dislocation lines. Such a process has been proposed by Markham after a suggestion by S e i t z 2 1 . 5. EMISSION SPECTRUM. The spectrum of the luminescence is observed to extend from 3J. e.v. to below 1.8 e.v. The energy absor-bed in raising an electron from the f i l l e d band to the conduction band is 8.4 e.v. (the second maximum of the fundamental absorption). The equivalent amount of energy must be dissipated in the return of the excited electrons to the ground state. Some of the discrepancy might be re-moved by postulating recombination of free electrons and trapped holes, or trapped electrons and free holes. The deepest electron trap has an optical absorption peak of about 2.0 e.v. (F-band) while the deepest hole trap has an optical depth of 3.0 e.v. (V^-band). Consequently the two processes postulated would release 5.4 e.v. and 6.4 e.v. of energy, respectively. Aside from this, the energy difference may be attributed to the Frank-Condon principle, which states that an electronic transition occurs in a time short Compared to the time required for reorientation of ionic positions. This is i l l u s t r a -ted in Fig.10, where the energy is shown as a function , of a generalized coordinate, defining the positions of 28 a l l the ions. (This model is used extensively by Seitz in 22 his treatment of various solid state problems ). Curve I represents the ground state and curve II the excited state. The minima of the two curves w i l l in general not occur at the same value of the general coordinate. An electronic transition w i l l be represented by a vertical line, e.g. fundamental absorption A B. If the excited electron does not return immediately to the ground state, the ions w i l l change their position to C, with the energy difference B C appearing as heat. Now a transition to the ground state w i l l release an amount of energy C D, with a release of the further quantity D A in the form of heat. Aside from the influence of heat motion on these levels, the emitted quan-tum w i l l in general be less energetic than the absorbed quantum. The above argument does not obviate the possi-b i l i t y that some of the emitted light may be due to the retrapping of electrons and/or holes. Such a process might be detected in a crystal containing a stoichimetric excess of one of the constituents. A crystal containing an excess of the metal is colored, i.e. contains F-centers which are stable. Heating such a crystal would thermally excite some of the trapped electrons, and the light emitted by retrapping ( i f any) could be detected by a photomultiplier. 29 6 . RETRAPPING In some of the foregoing discussions, i t has been taci t l y assumed that the electrons, once they are thermally excited from traps to the conduction band, are not retrapped 23 before f a l l i n g to the ground state. Garlick has considered the case where the probability of recapture by an empty trap is the same as the probability of luminescent emission. He obtains the decay law I = n * P N [ l + ( V t j ) P t ] 1 (9) where P = S exp. ( - <P /*T ); ° o= number of trapped electrons at t = o; U = number of traps in the crystal. In deriving this equation, he also assumes that there are as many places in the crystal where an electron may f a l l to the ground state as there are excited electrons. (A more general treatment due to Klasens and Wise2'* leads to the same type of decay law). Judging from the above treatment, retrapping must be negligible in order to allow the observed exponential de-cay. A simple experiment, however, seemed to show that there is some retrapping. A crystal was irradiated at room temperature and allowed to decay. It was then exposed to room light, and replaced in front of the photo tube. A 30 small amount of decaying luminescence was detected, i n d i c a -ted that trapped electrons had been released by v i s i b l e l i g h t from deep traps, and retrapped i n shallower traps which were unstable at room temperature. (A s i m i l a r re-25 s u i t i s reported by Garlick and Mason ). At present then the only conclusion that can be drawn i s that, although re-trapping does exi s t i n KBr, i t i s not s u f f i c i e n t Ito cause a departure from an exponential decay. A quantitative i n -vestigation of retrapping i s being attempted i n t h i s labora-tory . 7. CONCLUSIONS In summary, the luminescent decay of KBr has been observed to consist of a sum of exponentials. The v a r i a t i o n with temperature of the decay constants i n these exponentials has made possible the determination of seven-teen thermal a c t i v a t i o n energies. The deepest trap i n the c r y s t a l has an a c t i v a t i o n energy of l.Ose.v. (cf. Smakula's 1 9 figure of 0.84 e.v. from the mobility of F-centers). The wavelength of the emitted l i g h t i s independant of the trap producing the phosphorescence (at least at room temp-erature). The information i s s t i l l i n s u f f i c i e n t to describe the complete luminescence process, but i t i s a considerable advance i n the d e t a i l available on pure luminescent sub-31 s t a n c e s . T h e a d d i t i o n o f t h e r m a l a c t i v a t i o n e n e r g i e s t o o t h e r d a t a o n t h e p h y s i c a l c h a r a c t e r i s t i c s o f c r y s t a l s d e -f e c t s may s e r v e t o f a c i l i t a t e t h e t h e o r e t i c a l t r e a t m e n t o f t h e p r o b l e m . R C A 5 8 1 9 Phototube to * Prff-d mp. 3 Mc. B a r v d w i d t h A m p l r t i e r D i s c r i -mind tor S c a l e of 6 4 0 & Meek reqtster -1500 V . R e g u l a t e d P w r . S u p p l y 10 meg. bWeder F i g . 11. Schematic diagram of pulse counting detector system. To face page 32 f APPENDIX I. LINEARITY OF RESPONSE TO LIGHT OF A  PHOTOMULTIPLIER AND PULSE COUNTING SYSTEM. The l i g h t detection system used by Dekker and Morrish i n the o r i g i n a l experiments i s i l l u s t r a t e d schema-t i c a l l y i n f i g . 11;. It consists of conventional pulse coun-tin g system following an RCA 5819 photomultiplier. The d i f f i c u l t y of reproducing t h e i r r e s u l t s prompted an i n -vestigation into the l i n e a r i t y of such a system. The f i r s t attempts consisted of mounting the photo-tube on an o p t i c a l bench, along with a point source of l i g h t . Move-ment of the l i g h t source along the bench presumably gave an inverse square v a r i a t i o n of in t e n s i t y with distance. P l o t t i n g the detector response versus distance to the l i g h t source on log-log paper should have given a straight l i n e with a negative slope of two. Slopes both greater and less than two were recorded, but the method proved too cumbersome for systematic investigation of the possible causes. ^Further, there was some doubt as to whether the l i g h t i n t e n s i t y actually followed the inverse-square law (ra d i a l non-uniformity, r e f l e c t i o n from walls, etc.).. The second method used to measure l i n e a r i t y was a two source system. Two l i g h t sources of approximately o T i F i g . 12 . E f f e c t of discriminator s e t t i n g on nonlinearity of a pulse counting system. To face page 33 33 equal intensity, were mounted before the photomultiplier with a remotely controlled shutter before them. The sources could be exposed individually or together to the photo-tube. The counting rate was recorded for the separate sources and for the sum. The ratio of counting rate for the two sources to the sum of the rates for the separate sources was then a measure of the linearity of the detector system. This proved a convenient method for investigating linearity at various light intensities and discriminator settings. The effect of changing light intensity at three different discriminator settings i s shown in f i g . 12. The departure from linearity is seen to increase rapidly with both increasing intensity and increasing bias. Even at the lowest usable bias and light intensity, the system s t i l l showed a significant error. The foregoing effects may be explained, at least in part, by the resolving time of the system. Pulses entering the system may only be distinguished as individual pulses i f they are separated by a time interval greater than t r , the resolving time of the system. Two pulses se-parated by a shorter time interval w i l l be added in the amplifier system and registered as a single larger pulse. The number of such larger pulses w i l l be proportional to t r , and to the square of the counting rate. The result is 1 a non-linearity of response, increasing with light inten-sit y . The effect is aggravated by the fact that the dis-criminator is operated at such a level as to count only about 5% of the pulses from the photo-tube. (This i s neces-sary to keep the counting rate within the operating range of the scalers). Since the pulses distorted by addition in the amplifier w i l l be twice the normal average size, a larger fraction of them w i l l be recorded. The resolving time of the system was shortened by a factor of 3 to check the validity of this argument. The linearity was improved considerably, but a further decrease in t r would have re-quired excessively complicated electronic c i r c u i t s . A second contributing cause to non-linearity was found in the method of obtaining the dynode voltages for the photomultiplier. As shown in f i g . 11, the source of these voltages i s a ten megohm resistance chain supplied by a regulated power supply. The collector and the last few dynodes draw a current through this chain of s u f f i -cient mangitude (up to one microamp.) to cause an appre-ciable increase in the voltages between the f i r s t seven or eight dynodes. The increase in gain caused by this increase is not balanced out by the decrease in gain in the last two or three dynodes. As a consequence, the gain of the photo-tube increases slightly with increasing 2o<H 0-| 1 1 1 1 1 1 y 10 lo is" 3 0 F i g . 13. Fatigue e f f e c t i n a photomultiplier with constant l i g h t input. To face page 35 35 l i g h t input. The pulse counting technique emphasizes t h i s change. The discriminator i s operating on a steep pulse d i s t r i b u t i o n curve, i . e . a small change i n discriminator voltage produces a large change i n counting rate. A change i n photo-tube gain produces the same eff e c t as a change i n discriminator voltage, consequently the counting rate i s not a d i r e c t function of the photo-tube gain. This devia-ti o n may e a s i l y be remedied by using a low impedance source for the l a s t few dynodes. A t h i r d and more serious e f f e c t was observed at r e l a t i v e l y high l i g h t i n t e n s i t i e s . The counting rate for a constant l i g h t i n t e n s i t y changed with time, the rate of decrease being quite rapid when the photo-tube was f i r s t exposed to the l i g h t . The photo-tube eventually recovered i t s i n i t i a l s e n s i t i v i t y a f t e r the l i g h t was removed. To determine where t h i s fatigue was occurring, the counting rate was recorded for the same l i g h t i n t e n s i t y with the tube.operating at two d i f f e r e n t voltages. The consequent change i n gain was compensated by a change i n gain of the amplif i e r . The resultant fatigue curves are plotted i n f i g . 13. They show c l e a r l y that the fatigue occurs i n the secondary emission surfaces, and not i n the photo-cathode. Here again, the decrease i n photo-tube gain due to fatigue i s emphasized by the pulse counting technique. (After the completion of t h i s work, the same eff e c t was reported for s c i n t i l l a t i o n counters by R e i f f e l , 27 Stone and Brauner ". . It was obvious from these re s u l t s that a pulse counting system was not suitable for the proposed experi-ment. I t appeared that a dir e c t current amplifier would be far superior, since i t s response would be j u s t d i r e c t l y proportional to changes of gain i n the photo-tube. Such an apparatus was constructed and tested by the above me-thods. The ef f e c t of resolving time, of course, i s e l i -minated by integrating the pulse output of the photo-tube. A low impedance dynode source was used, as des-cribed elsewhere. No departure from l i n e a r i t y was obser-ved for t h i s system mp to the highest l i g h t i n t e n s i t i e s that were expected to be used. Fatigue at the highest signal current (10 microamps.) was less than 1%. To face page 37 APPENDIX II. ELECTRONIC APPARATUS. 1. D.C. AMPLIFIER The amplifier designed for these experiments is briefly described in Section III. However, construction of such an amplifier requires considerable attention to 2 6 detail. Similar designs have been published , but not generally in sufficient detail to permit straightforward duplication. The power supply for the amplifier (fig. 14) is the usual type using a series regulator tube. There are a few variations from the normal practice. A separate plate transformer was found necessary. The supply i s not grounded, and coupling to ground in the transformer introduced r i p -ple on the whie supply. This coupling is much larger in the conventional multi-winding power transformer than in a plate transformer. The voltage reference is a 67J volt battery, which does not have the fluctuations and tempera-ture sensitivity of gas regulator tubes. The heaters of the tubes amplifying the error signal are in series with a resistor chain draining 150 ma from the output of the power supply. (The same chain supplies the tube heaters in the amplifier i t s e l f ) . There is no ground connection F i g , 15, D. C. Amplifier. -To face page 38, i 38 in the power supply proper. The basic characteristics of the amplifier are described in Section III. The f u l l c i r c u i t diagrams (fig.15) requires further explanation. The heaters of a l l tubes (except the electrometer tube) are supplied by a resistor chain from the regulated high voltage supply. The ground point in the cir c u i t is also obtained from this resistor chain, and is adjusted to such a point that the electro-meter grid is at ground potential. The filament current for the electrometer tube is obtained by a 12 ma bleeder chain across the high voltage. The electrometer plate and screen voltages, as well as various fixed grid voltages are also obtained from the chain. The resistors are wire wound, and operate at a small fraction of their ratings, to reduce d r i f t . The various resistors in the remainder of the circ u i t are uniformly a precision wire wound type with the exception of the 3 meg coupling resistors between V 2 and V 3, and between V 5 and Vg. These are precision metallized resistors. The potentiometers used for coarse and fine adjustment of amplifier zero, and for adjustment of the electrometer filament current to the rated value, are altered slightly. They are ordinary one watt wire-wound models, with the contact arm changed from a f l a t contact 39 to a knife edge contact. The contact then s i t s between adjacent wires, and makes the contact point insensitive to shock. The high gain triodes used in the amplifier are mechanically sensitive. The grid operating point for a given plate current may change several millivolts when the tube is jarred. This d i f f i c u l t y was overcome by mounting the tube sockets on sponge rubber supports, and making a l l electrical connections to the tube socket with loops of fine wire.. (With this alteration, the amplifier chassis may be severely jarred without affecting the zero point). The switching arrangement i s designed to reduce transient voltages when turning the amplifier on. The power supply is turned on with Si in position 1. This places only the tube heaters across the high voltage, since there is a considerable overvoltage before the volt-age regulator gains control. In the second position of S-^ , voltage i s applied to a l l the amplifier tubes except the electrometer tube. The third ppsition then turns on the filament current for the electrometer tube. After a pause of at least one second, S2 is closed to supply plate and screen grid voltages to the electrometer tube. S3, of course, disconnects the output meter while the amplifier is being turned on. F i g . 16. Photomultiplier high voltage supply. To face' page 40 The preamplifier (containing the electrometer tube) i s , of course, situated at the base of the photo-multiplier tube. Connection to the amplifier is made by a six-conductor shielded cable. The switch for the four grid resistors was made of Lucite. The switch arm operates on the lower end of the grid resistors (i.e. at a low impe-dance point) so i t need not be well insulated. 2. PHOTOMULTIPLIER SUPPLY The 1,000 volt supply for the photomultiplier (fi g . 16) has a negative output. Regulation i s by a two stage difference amplifier and series regulator tube. Plate voltages for the amplifier, and screen voltage for-"', the tetrode series tube are supplied by a separate low volt-age power supply (regulated by gas tubes). The design is such that the only tube with higher than normal plate volt-age is the series tube (6V6), which was found to give good service under these conditions. The voltages for the ten dynodes are supplied from a divider chain consisting of seven 100,0P0 ohm resistors and four RCA 5651 gas tubes. These tubes are in the lower end of the chain, supplying the last stages in the photomultiplier. With a 1 ma current flowing in the chain, these tubes act as excellent voltage regulators, producing a low impedance voltage source for the-last four dynodes. ft REFERENCES. 1. Imperfections in Nearly Per-fect Crystals, p. 246, Wiley & Sons, New York, 1948. 2. Mott, N.F. and Gurney, Electronic Processes in Ionic 3. 4. 5. 6. 7. 8. 9. 10. 11, 12, R.W. Seitz, F. Cornell Symposium Garlick, G.F.J. Kudriavzewa, W. Katz, M.L. Bose, H.N. Bose, H.N. Kato, M. Weyl, W.A., Schulman, J.H., Ginther, R.J. and Evans, L.W. Crystals. Clarendon Press, Oxford, 1940. Rev.Mod.Physles, 18, 384, (1946) Solid Luminescent Materials. Wiley & Sons, New York, 1948. Luminescent Materials. Clar-endon Press, Oxford, 1949. Z.Phys. 90, 861, 1934. Phys.Z.der Sowjet, 12, 273, 1937. Ind.J.Phys., 20, 21, 1946. Ind.J.Phys., 21, 29, 1947. Sci.Papers Inst.Phys.Chem. Research (Tokyo), 41, 113, 1943; ibid 42_, 35 and 95, 1944. J. Electrochem.Soc. 915, 70, 1949. Bunger, W. and Flechsig, Z.Phys. 67, 42, 1931. W. Pringsheim, P. Pringsheim, P. Rev.Mod.Phys. 14, 132, 1942. J.Chem.Phys. 16, 241, 1948. Bonanomi, J. and Rossel, J. Helv.Phys.Acta 25,v 725, 1952. Dekker, A.J. and Morrish, A.H. Phys.Rev. 78, 301, 1950; ibid . 80, 1 0 3 0 7 1950. t 13. Bube, R.H. Phys.Rev. 80, 655, 1950. 14. Pohl, R.W. Proc.Phys.Soc. 49 (extra part), 3 (1937). 15. Ellickson, R.T. J .Opt .Soc .Ani. 43, 196, March 1953. 16. Bunger, W., and Flechsig, W. Z.Phys. 67, 42, 1931. 17. Bonanorai, J. and Rossel, J. Helv.Phys. Acta 25, 725, * 1952. 18. Casler, R., Pringsheim, P, J.of Chem.Phys. 18, 887, and Yuster, P. 1950. 19. Smakula, A., Gottinger Nachrichten, 1, 55, 1934. ~ 20. Markham, J.J. Phys.Rev. 88_, 500, 1952. 21. Seitz, F. Phys.Rev. 80, 239, 1950. 22. Seitz, F. The Modern Theory of Solids. McGraw-Hill, 1940. 23. Garlick, G.F.J. Luminescent Materials, p.37. Oxford, Clarendon Press, 1949. 24. Klasens, H.A. and Wise, M.E. Nature, 158, 483, 1946. 25. Garlick, G.F.J, and Mason, D.E. J.Electrochem. Soc. 96, 90, 1949. 26. Miller, S.E. A Sensitive D.C. Amplifier. Electronics, Nov. 1941. Johns, H.E., Darby, E.K. Am.J. of Roentgenology and and Hamilton, J.J.S, Radium Therapy, 61, 550, 1949. 27. Reiffel, L., Stone, C.A. Nucleonic, 9, 13, 1951. and Brauner, A.R. 

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