Malhotra, B R

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Some ooservatifJ11&8 &,. flyn&miollZ vibration.! ate. 705 1''0 get. cIeIr idea aboat the nature of errors, let UI denote 1 =a + Z. I' _ a +1 " - ar " ,,= a;. r' 'M(B) _ 8· 1 a 4 I" == a-' +- -a - -, ,-- , r r' ... (9) The linear operators are defined on a set of functions having continuous derivative of the second order in [a, b] which, after topologising in the usual way, is denoted by D.[a,b] (Shilov, 1965), It is easy to see that I •• == ( I" _. ;-) ,I',. ==(/'" - ~.) I',. .,,(10) Relations (10) show that the .olutions of 11'" = ° and I" .. = ° are solutions of I., ,. = ° and Z'" u = 0, respectively. But the converse is not true. NOIl1lull images of the set points in D.[~, b I for which (11' - f ) .. = ° and ( 1'1' - f) u = 0, respectively, with respect to (I,,)-land, (1'1,)-1 are solutions of 1"u=O,andl,:,u=O,respectiveIV, but evidently 11,,,,p ° and 1', , .. ,pO. RBJlERBNCliS Chatterj ... D. 1968 Indo ... J. PhYI. n, 519. Cinelli, O. 1965 1""", Jour. E_g. 8.""... 3, 539. Clnoll!, O. 1966 Jo ..... API'~ MoIh., 825. D."., M. & Debnath, L. 1965 Slud. Un; •. Bob. 33.37. Love, A.a'H. 1944 0.. lhe MGlh_1 'l'h .. ,y of IIII .. tt,i/y, Dover Publication, N.Y. Shlloy, O. Ye. 1965 JI.IIt.moIiooI A''''IIiN, Pergamon Pr ... , Oxford 1.dio. J. N,.. ~4. 105-10' (1969) Decay characteristics of CaS (Zr, Oi) phosphors By B. R. MALHOTRA Omllral Road Re.gearoiJ bun/m', New D,/hi. (R1IJ8/wd 22 AUV"'/-Reviud 23 Deumber 1969) Phosphorescence decay characteristics of CaS phosphors activated with Zr and Di (pr+ Nd) impurit,ies. have been studied to gather inf~mation about the type of pbosphO\'eecence decay, value of time constlll!t of d~ay and the efective trap· depths contributing fO the phosphorescence in this l\'Item of phosphor.. . t 705 1 105 B. R. MaIholia Experimental results reveal that decay of phosphoteScence follows the hyperbolic relation 1- I •. ,-t with II varying from 0.77 to 0.92 and the kinetics being monomolecular. The vallie of decay constant II increases with the increase in concentration of DI impurity implying thereby that Oi atoms introduce shallow traps which get emptied soon. Group of traps with trap depth 0.7 ev contribute most effectively to the phos-phorescence. The close agreement between two values of trap depths E as obtained from phosphorescence decay and thermolijlllinescence justines the validity of the fundamental equation p = I. e-BliT in this system of phosphors. Blokhinsev (1937) and De Groot (1939) were the tirst among early workers who derived a theoretical time dependence of the decay of pho .. . ph~~escence from considerations of electron transitions between various energy levels. Lord et al (1947) identified these energy states as arising activators which have lost their electrons. The decay of phosphorescence is distinguished to be of two types depending on whether the kinetics involved in the luminescence process are of the first ordet or of the second order. Radiative transitions whicb are monomolecular in character, result in exponential decay of the form 1=1 •. exp( - pi), wbUe in the case of bimolecular mechanism involving recombination of the' free electrons and holes, the decay obeys the inverse square law, I=I./(I+.u)'. Phosphorescence decay charscteristics of CaS phosphors activated With zircomum and rare earth didymium (praesodymium+neodymlum) have been studied to gather information on the type of decay and trap <lepilis contnbutmg to phosphorescence. Phosphors were prepared by heating an intimate mIXture of CaSO, , a triple flux, activators ZlIconium and didymIUm in SUitable proportions at 950'C for two hours in a reduc-ing atmosphere of carbon. Four series of phosphors with different can .. tant concentratLOns 01 Zr in respective series were prepared and didymium ~ontent was varied from .001 to 0.4 percent by weight of CaSO, in each .erie •• Decay characteristics Were studied by plotting intensity measured in ar bltrary units against time on logarithmic scale. The deviation of the curve from the straight line eliminates the possibility of exponential decay. However the log I - log' curve shows a linear rehltionship sianifyil1~ a hyperbohc decay of the I ~ 10," where b is known as decay constant. The hyperbolic decay is supposed to result from the luperposltlon 'of intensities, each of which is varying exponentially with time, when different trap depths are involved in contributina to phosphorescence. The decay con~tant b has been calculated by introdUCing new varlablca to get a mor, workable rela-cLomhi", So taklni the logarithm of the abov. exprenion, " becay charactsriBioa of OaB (Zr. bi) phoaphor8 701 log I =logI, + b log! and putting 11 -log It :r: = log I and 0 = log I., weget,1I=b:r:+c The problem is simplified to, fitting a straight line to a set of points in the :r:1I plane and thus to a simple problem of least squares. b and G can be calculated from the following expressions: b = ~:EY_ - to1:ry _ (E"')" - n1:I:' c _ 1:y.E:r:' - E:r:.1:y - nExl - (Ex)' Value of b has been calculated for all the samples in the time interval from 5 seconds after excitation to the time when the intensity decayed to a negligibly small value. As b turns out to be a negative quantity, the equation becomes 1= [ •. ,- •. As shown by data collected for all the samples, value of decay constant varies from 0·77 to 0.92 with the increase in concentration of Di which implies that Di introduces shallow traps which get emptied soon, thus giving a higher value of the decay constant. Hyperbolic decay is considered to be the result of superposition of exponentials correspond. ing to different trap depths. To determine the different traps contributing to phosphorescence, the decay curves were broken into three exponen-tials and trap depths corresponding to these were determined. Trap depths as calculated from the three exponentials for most of the phosphors are 0.61, 0.65 and 0.69 ev From the limited number of ex-ponentials it is reasonable to assume the distribution to be Gaussian. Thus the group of traps contributing predominantly to phosphorescence may be aSSigned the value of trap depth corresponding to that of its maximum, i.s. 0'69. Thi~ value of trap depth is in dose agreement with that determined from glow-curve experiment implying thereby that the kinetics involved are mono-moleculAr and the validity of the equation p = 8 •• - B1ir holds good. RE?ERENCES Blokhin ... D. 19J1 J. E~p!l. flleo, Phy,jea. U.S.S.lI. 7, 1142. D, Groot W. 1949 P/'y •. 6, 27S. Lord, Roo. 81 WI •• 1941 Pr.c. Phy. S... 59, 4SS. 

Decay Characteristics of CaS (Zr, Di) Phosphors

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Decay Characteristics of CaS (Zr, Di) Phosphors

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