Validity of repeated initial rise thermoluminescence kinetic parameter determinations

0735-245X/91 $3 00 + 0(3 Pergamon Press plc

Nucl Tracks Radtat Meas, Vol 18, No I/2, pp 19-25, 1991 lnt J Radlat Appl lnstrum, Part D Pnnted m Great Bntam

VALIDITY OF REPEATED INITIAL RISE THERMOLUMINESCENCE KINETIC PARAMETER DETERMINATIONS* J A Klr~slv_.ADand P W LEW Brookhaven National Laboratory, Upton, NY 11973, U S A Abstract--The vahdRy of thermolummescence (TL) glow curve analysts by repeated mmal rise (mmal slope) measurements has been studied by computer slmulauon Thermolun~nescence described by first order, second order, general one trap (GOT), and mteract~ve TL kmetmcs, were mvesUgated In the s~mulatmon, each of the repeated temperature mcrease and decrease cycles contams a hnear temperature mcrease followed by a decrease appropnate for "radmtwe" coohng, ~e the latter msapproximated by a decreasmg exponentml Plots showmg the actmvatmn energies, computed from each simulated en'assmn, agamst the correspondmg (mean) temperature are readdy compared vmh the known values used to compute the TL emission From such plots mt~s determmed that the repeated mmal rise techmque provides rehable results only for (I) stogie peak glow curves, or (2) glow curves contammng peaks that do not overlap, or (3) the lowest temperature peak tn multi-peak curves where the peaks are well separated In cases where ~t ms vahd to use the mmal nse method, the activation energy vs correspondmg mmal nse temperature plots contam plateaux of constant activation energy values that correspond to the known value Also, the mmal rise temperatures correspondmg to "'correct" activation energies occur on the low temperature s~de of the normal glow curve, often well below the peak temperature In cases where the mmal rise method gives mcorrect results, plateaux do not occur and/or they correspond to activation energies not used m the simulation Consequently, a vanety of misleading and/or mcorrect "results" can be obtamed when the repeated mmal nse techmque ~s apphed to TL systems that produce overlappmg peaks in the usual glow curve

1 INTRODUCTION

energy, E, attempt to escape frequency, s, trapped charge concentrauon, n, lmttal trapped charge concentration, no, etc Thus, one knows m advance the parameter value(s), e g the activation energy, that should be reproduced by the repeated lnmal rise simulation It is reasonable to conelude that the repeated m m a l rise method would apply to single peak glow curves, but it ts not apparent that It applies to TL systems containing overlapping glow peaks and/or those where retrappmg is non-neghglble As will be demonstrated, m some T L systems the repeated mltml rise method supplies erroneous conclus~ons In others, a m~xture of correct and erroneous results is obtained The validity of the repeated mltml method was tested for T L systems described by first order, second order, general one trap (GOT), and interactive T L kinetics

ThE INITIAL rise and the repeated imtml rise methods for determining the acuvatlon energies assocmted with thermolumlnescence (TL) have been evaluated by smmulatlng these techmques on a computer The inltml rise method is based on the fact (for a system with one glow p e a k ) that the initial T L from a sample is well approximated by the equation I ( T ) = c o n s t a n t [ e x p ( - E / k T ) ] Thzs ts based on the assumption that the change In trapped charge concentratwn during heating is small enough to legltzmately assume that the trapped charge concentration ts constant during the temperature excursion (Garhck and Gibson, 1948) The data from an initial rise measurement are usually used to obtain an activation energy by constructing an Arrhenlus plot Furthermore, the approximation described above applies to all of the commonly used kmetmcs that describe TL emission A repeated lmtml rise measurement, sometimes called a fractional glow measurement (Gobrecht and Hofmann, 1966), is the luminescence measured during repeated heating and coohng of a sample, with the maximum temperature increasing by some fixed amount (e g 5 or l0 K) for each successive cycle To s~mulate a repeated initial rise measurement, the TL emission from specified kinetic equations is computed using selected values for the activation

2. T H E R M O L U M I N E S C E N T

KINETICS

All the computations in this paper utlhze the dlfferenual equation forms of the first order, second order, G O T , and interacUve T L kmeUc equations These are equations (1)-(4), respectively dn ---=ns dt

*Supported by the U S Dept of Energy, Contract No De-ACO2-76CH0001 19

e -~kT

(!)

20

J A K I E R S T E A D and P W L E V Y dn

.... dt

n"s'e -Ekr

where

s'=s/N

a,(N-n) 1 - - -dn = ns e E , ~ 1 dt arn + a,(N - n)

(2)

stant, and time, t. is measured from the onset of coohng The value of C chosen was based on the coohng rate observed m typical thermolummescent measurements

(3) 3 SIMULATION PROCEDURE

dn,

dt - n,s,e EkT-__

njsje-E, ~-

(4) I=l

and

n,=~nj )=1

where E is a c t w a u o n energy, s is the attempt to escape frequency, n is the trapped charge 0 e electron) concentration at time t, n o Is m m a l trap charge (1 e electron) concentratmn, k is Boltzmann's constant, T is absolute temperature (K), N is trap concentration, a, is the cross-section for charge trapping or re-trapping, a, is the cross-section for radmtlve (hght emxttmg) electron hole r e c o m b m a t m n at r e c o m b m a t m n centers, and rn Is the number of different types of electron traps The interactive kinetics case used for all examples apphes to a system whxch contains one type of recombination center (l e hole trap) and more than one type of charge trap (x e electron trap) which " c o m p e t e " for thermally released electrons Each electron hole recombination at recombination centers creates one photon If an electron is retrapped at an electron trap light is not emitted but the electron may again be thermally released An electron may be thermally released and retrapped many times before r e c o m b m m g with a hole at a recombination center The parameters N,, n,, a,, s, and E, are those described above but for the ~th type of electron trap Also, n, Is the trapped-hole concentration (and equals the recombination center concentratmn in this model) The c o n d m o n that n, equals the sum of the trapped electron concentratmns of each type of trap results from the requirement that the material be electrically neutral (l e the total number of trapped holes equals the total number of trapped electrons) A more detailed &scussion of these equations and further references may be found m Levy (1984a, b) Furthermore, to simulate the normally used hnear temperature dependence, a linear relation between time and temperature is used Specifically, T = To + fit, where To is the initial temperature and fl is the heating rate (1 e a constant) During each cycle the hnear temperature increase is followed by radmtwe coohng approximated by a decreasing exponential In other words, durmg coohng, T = T O+ ( T , ~ - To)exp[-Ct], where T,. is the highest temperature reached m each cycle, C is a con-

The TL kmeucs for first order second order. G O T and lnteracuve kinetics were simulated on a Vax 11/785 computer using a Fortran program and the &fferenual equation solving routine, D I V P A G . from the I M S L Library ( I M S L User's Manual. 1987) The TL emission curves were then computed using specified (1 e known) parameter values In all computations, only E (the activation energy) was vaned Other parameters had the following fixed values s = 101°s -1, N = 1016cm -3, no= 1015cm -3 for each trap, o , / o ~ = a = 0 1, fl = l ° C s -~, a startmg temperature, To of 300 K, and a coohng ume constant C of 0 2 Also, an integration time of 1 s polnt-~ was used In each successwe cycle the final temperature (Tin) was increased by a fixed increment, T,.¢, which was set at 5 K The &fferenual equation solving routine D I V P A G as equipped with an internal test of the "accuracy" of the c o m p u t a u o n This Is a user-selectable parameter called the "tolerance" For all computations reported, the tolerance was set at 10 -~° It was demonstrated that this Is adequate for the computatxons described here A typical set of repeated m m a l rise measurements is generated m the following manner The desired kinetics, number of traps, and a c t w a u o n energy0es) for the trap(s) are selected To sxmulate a signal just large enough to emerge " o u t of the noise", the hght output is numerically computed and retamed m the calculation at all temperatures but is not included m the (simulated) data unless one part m a million of the total mmal trapped charge is released m the time/temperature interval producing one data point [1 s(°C) -~] This c o n d m o n was apphed to all computed emissions, l e the simulated TL It emulates the response from a detector (l e a phototube) during an actual measurement During the first cycle the hght emission (l e the change m trapped charge concentration) is computed from 300 K until 0 1% of the trapped charge m the lowest temperature trap is released The next higher temperature (m K) evenly &vlslble by T,.¢ (1 e 5 K) IS defined as T~o, the maximum temperature of the first heating cycle The portion of the computation. for the first heating cycle, that is used as simulated data on an Arrhenms plot lies between the temperature of the first point m which one part m a mllhon of the total initial trapped is released and T,.o After reaching T.,0 the temperature is assumed to decrease exponentially toward room temperature The maximum temperature m each cycle. T,., is gwen by T,. = T.,o + T,.¢ (n - 1). where T.,0 and T,. c are defined above and n is the heating cycle number (e g where T,nc=5, n = 1 imphes Tin= T,.0, n = 2 lmphes

VALIDITY OF TL KINETIC PARAMETER DETERMINATIONS 7". = T ~ + 5, etc, ) The emmmon d u n n g coohng ~s computed, retained m the calculation, but not included m the "results" The enussmn d u n n g coolmg m the range T = To to To + 5 was assumed to be neghgtble and was not computed These steps describe the first heaung cycle The cychng procedure is continued until less than 0 5% of the total mlttal trapped charge remains trapped Arrhenms plots (Fig 1) were constructed for each heating cycle The act~vatton energy, E r, was calculated from a portion o f t h e data curve that is midway between the m m t m u m and maxtmum of the mtenmty values (m the usual log plot) and usually includes a one order of magmtude part of the data The ternperature assigned to the computed Er value ts the temperature at the midway pomt This choice, for the temperature assigned to each heating cycle, appears to correspond to that used m some pubhshed m m a l rise measurements, e g Stnckertsson (1985) It could be argued that the temperature assigned to each cycle should be the mmal temperature If the temperature change m each cycle is small, it would neither change the pubhshed results nor those gwen below m any tmportant way A hst of the cases investigated and a summary of the results is contained in Table 1 4. R E S U L T S AND D I S C U S S I O N Typical results for single trap, ~e single peak glow curves for first order, second order and G O T kinetics (curves) are shown in Figs 2, 3, and 4 In all three cases the computed E r values appear as a plateau and agree with the value used to compute the TL emlss~on However, the temperature for each computed series for first order and G O T kmettcs is shifted to the lower temperature side of the corresponding normal glow curve This was observed by

21

Table 1 Cases investigated and results No Oi peaks (energy, eV)

Kinettcs

Results

1 First order (1 0) 1 Second order (1 0) I GOT (1 0) 3 First order (1 0, 1 25, 1 5) 3 Second order (1 0, 1 25, 1 5) 3 Interactive (1 0, 1 25, 1 5)

Good E value agreement* Good E value agreement Good E value agreement* Good E value agreement* Good E value agreementt Good E value agreement for first and third peaks, but not for second peak

3 First order (1 0, 1 1, 1 2, 1 3, 1 4) 5 Second order l', ~: (1 0, 1 1, 12, 1 3, 1 4) InteracUve t, :~ 5 (1 0, 1 1, 1 2, l 3, 1 4) *The computed series of vahd Er values hes to the low temperature slde of the normal glow peak tThe transmon of E T values from one plateau to the next

is not sharp ~The computed Er values agree only for the lowest temperature peak

,60 80

20 O0

10m

:TL" T ET

2°t L5

't 00

f

15o

17o

,~.o

2~.o

2~o

~o

FIG I Arrhemus plot for a typical lmtlal rise measurement The section between the arrows is used to determine the mmal rise actwatlon energy (Er) where the temperature (T) assigned to the Er value is the midpoint of the selected range

o

~

~o

~

,

~

TerrT:~-okre (C)

&

~o

FIG 2 Glow curve computed wRh first order kinetics and speofied acuvaUon energy, E, of 1 0 eV Also shown are the computed mmal rise measurements and Er values The glow curve shown on the actlvauon energy plot is for dlustrauon purposes only It is not on the same intensity scale as the computed mmal rise curves Both plots have the same temperature scale The computed Er value agrees well with the specified (i e known) E value In this case the

computed ET values overlap the lmUal part of the normal glow peak

J A K I E R S T E A D and P W L E V Y

22

8o~

°°t

'°t 20

O0

i

i

T '~¸

i

i

2.0-

t51.0-

/

05-

\, ,\

j

O0

~o

i 4O0

~

--7 50(3

Temperature (C) FIG 3 Glow curve computed with second order kinetics and specified actwatlon energy, E, of I 0 eV Also shown are the computed mmal rise measurements and E r values The glow curve shown on the acuvauon energy plot ,s for dlustratlon purposes only It ~s not on the same mtensny scale as the computed mmal nse curves The temperature scale *s the same on both plots Both the computed act,vatlon energy values, tl-e ErS, and the corresponding temperatures agree well with the known E value and the temperature range of the normal glow curve S t n c k e r t s s o n (1985), who attributed the shift to an effective l o w e n n g o f the heatmg rate due to the repetmve heating by the repeated m m a l rise techtuque However, it is a p p a r e n t that this shift is a property o f the m e t h o d and is not an artifact Also,

the shift might be shghtly exaggerated by the m e t h o d used to asstgn temperatures to each cycle The agreement between the selected (t e known) E value and the c o m p u t e d E r values Is very g o o d This can be regarded as a venficauon o f the c o m p u t e r model Also, the extstence o f a well-defined plateau s u p p o r t s the use o f the repeated initial rise techmque but, as explained later, onl) f o r single peak glon curves The results obtained by simulating a first order system with three types o f traps, with activation energies o f 1 0, 1 25, and 1 5 eV, are s h o w n m Fig 5 The c o m p u t e d E r values agree with the k n o w n starting values and appear m the stmulauons as well-defined plateaux with sharp transitions between plateaux However, the plateaux occur at temperatures that are distinctly lower than the c o r r e s p o n d i n g glow peaks for first order and G O T kinetics In the second order case (Fig 6), the mlual rise a c u v a u o n energms are in g o o d agreement in value and occur at temperatures c o r r e s p o n d i n g to the peak o f the normal glow curve However, the t r a n s m o n from one plateau, wtth one activation energy, to the next, is not sharply dehneated In the mteractwe case (Fig 7) the c o m p u t e d ET values agree with the k n o w n values for the l 0 and l 5 e V peaks This is not true for the 1 25 eV peak (Fig 7) F u r t h e r m o r e , the simulation contains two plateaux which do not c o r r e s p o n d to

2004

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o°"r~ °°

............

15 050

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~ ~ Temperature (C)

,o0

Too

FIG 4 Glow curve computed w~th general one trap (GOT) kmencs with specified actlvanon energy, E, of 1 0 eV Also shown are the computed initial nse measurements and E r values The glow curve shown on the acuvatlon energy plot ts for illustration purposes only It ~s not on the same intensity scale as the computed lmUal rise curves Both plots have the same temperature scale There ,s good agreement between the specified 0 e known) E value and the computed E r values However, the computed E r series hes on the low temperature side of the normal glow peak

DO

200

300

400

50O

T~(C) FtG 5 Computed glow curve described by first order kinetics with specified actwauon energies of 1 0, 1 25 and 1 5 eV Also shown are the computed mmal rise measurements, the computed mmal rtse E r values and the individual glow peaks The glow curve shown on the activation energy plot ~s for illustration purposes only It ~s not on the same mtenslty scale as the computed mmal rise curves All plots have the same temperature scale The computed E r values agree with the specified values and occur m well-defined plateaux separated by sharp transmons However, the plateaux occur on the low temperature s~de of the corresponding glow peak

VALIDITY OF TL KINETIC PARAMETER DETERMINATIONS

0~|

,

,

tO 0.~

"~

tO0.5-

O0

Flo 6 Computed glow curve descnbed by second order IaneUcs voth speofled activation cnergpes of 1 0. 1 25, and 1 5 eV Also shown are the computed mmal nse measurements, the computed mmal rise E r values and the individual glow peaks The glow curve shown on the acuvaUon energy plot is for dlustraUon purposes only It ss n o t on the same intensity scale as the computed mmal nse curves All plots have the same temperature scale The computed E r values are m good agreement w~th the known E values However, the transsUous from one plateau to the next are not sharply defined

23

any trap m the system In general, m the mteracuve kinetic case, both the computed E r values and plateau positions are inconsistent with known E values and the temperature pos~tlons of the normal glow peaks, except for the lowest temperature peak of the system Thus, the electron retrappmg l~neUcs plays a c r u o a l role m the apphcauon o f the repeated mlUal nse method In an actual measurement, the kinetics would have to be known to use th~s techmque rehably Slmulatmns for first order, second order, and mteracUve kinetics for a system of five traps with a c u v a u o n energies of I 0, I 1, 1 2, I 3, and 1 4 e V are shown m Ftgs 8-10 The first order and interactive systems gwe nse to mflectmn pumts 0 e changes m the rate of change of slope) m the plots of activation energy vs temperature, but well-defined plateaux 0 e constant E r values) are not obtained The dominant pattern of the curves ts a gradual increase m acuvaUon energy w~th temperature In the second order kmeucs case, the E r values change smoothly from the lowest value (Le 1 0 eV) to the highest 0 e 1 4 eV) value The existence of the intermediate traps is not apparent m the simulated mlUal nse analysis Th~s model ~s identical, at least m p n n o p l e , w~th one of the methods used by Stnckertsson (1985) m which the sample is heated and allowed to cool to r o o m temperature vothout controlhng the

70-

15.0-

6.05.0-

~.0 2.0tOO0

i

i

i

i

tOI

0.5O0

toJ 0

i Flo 7 Computed glow curve described by interactive kinetics with speofied activation energpes of 1 0, 1 25. and I 5 eV Also shown are the computed mmal nse measuremerits, the computed mmal nse E r values and the mdlwdual glow peaks The glow curve shown on the acuvauon energy plot ts for fllustraUon purposes only It ~s n o t on the same intensity scale as the computed mmal nse curves All plots have the same temperature scale The computed Er values agree with the known E values for the 1 0 and I 5 eV peaks but do not agree for the 1 25 eV peak Note parucular]y that there are two plateaux which do not correspond to any speofied E values Furthermore. the plateaux are shifted to the low temperature side of the corresponding glow peak

05oo

~ , ~

(c)

Flo 8 Computed glow curve described by first order kmeucs vath speofied acUvatson euerg~es of I 0. 1 1. i 2, 1 3, and l 4eV Also shown are the computed initial nse measurement, the computed mmal nse Er values and the individual glow peaks The glow curve shown on the acUvauon energy plot is for dlustrat~on purposes only It ss n o t on the same mtenuty scale as the computed mmal nse curves All plots have the same temperature scale The Er values do not cluster m meaningful plateaux, t e only poorly defined reflect.on points are observed

24

J A K I E R S T E A D and P W L E V Y

tOO

>'°1 O0

3O

"°l tO

O0

J

i

Z0-

1.5-

/ "~>

0.500-; 0

temperature d u n n g coohng An ~mportant variation on th~s techmque ~s obtamed when the temperature ~s controlled d u n n g coolmg (e g decreasing the temperature hnearly) If a hnear temperature decrease ts employed and ff the trapped charge concentrauon &d not change slgmficantly the curves for heating and coolmg should be nearly ldenUcal It has been stated that this ~s a necessary condition for the repeated m m a l rise method to apply (Gobrecht and Hofmann, 1966) However, it should be emphasized that even ff this c o n d m o n ~s sausfied, ff there are different types of electron traps w~th &fferent actlvat~on energies (and/or s values) that release electrons at the same temperature then the actlvauon energy obtained would be an (unspecified) average value weighted by the relatwe c o n t n b u u o n from each type of trap A study, szmflar to that reported here, m which the hnear temperature rise is followed by a hnear temperature decrease, ~s underway

Temperafure (C)

FIG 9 Computed glow curve described by second order klneUcs with specified activation energies of I 0, 1 1, 1 2, 1 3 and 1 4eV Also shown are the computed lnmal rise measurement, the computed inmal rise E r values and the indlwdual glow peaks The glow curve shown on the activation energy plot is for illustration purposes only It is not on the same intensity scale as the computed Initial rise curves All plots have the same temperature scale The Er values gradually increase with temperature from 1 0 to 1 4eV, l e meaningful actlvatmn energies are not observed

n~

100-

80-

-~

6o-

"~

40-

:/'"-'~

20 q

O0 0

~ 100

--

- 200 Temperature

300

' ~ 400

500

(C)

FIG 10 Computed glov, curve described by interactive kinetics with specified activation energies of I 0, 1 1, 1 2, I 3 and 1 4eV Also shown are the computed mmal rise measurement, the computed initial nse E r values and the Individual glow peaks The glow curve shown on the actwatlon energy plot is for Illustration purposes only It Is not on the same intensity scale as the computed initial rise curves All plots have the same temperature scale The Er values gradually increase with temperature and plateaux associated w~th meaningful actwatlon energies are suggested by inflection points

5 SUMMARY The repeated mmal rise 0mttal slope) techmque for determining the activation energy0es) associated with TL emission has been stu&ed by slmulatmg this process on a computer The TL emission that would normally gwe rise to both single and muluple peak glow curves determined by first, second, G O T and interactive kmeucs were mvesUgated For each case stu&ed Arrhemus plots were constructed for each temperature cycle An activation energy, E r, was computed from the central porUon of each Arrhemus plot curve and assigned the temperature, T, of the m~dpolnt of the curve In turn the actlvauon energy values, Er, were superimposed on normal (continuous) glow curves, for the same system, computed with the same heating rate Thus the a c u v a u o n energy, Er, vs temperature plots and the normal glow curves have the same temperature axis The principle results include the following (1) The acuvaUon energies, E r values, obtained from all single peak glow curves are m good agreement w~th the known values However, on the superposmon plots the rehable acUvatlon energies (as m&cated by plateaux of constant value) usually occur only on the low temperature side of the normal glow peak Occasionally, the signal has &sappeared-the trap ~s e m p t y - - a t temperatures below the peak of the normal glow curve (2) Mulupeak systems (a) the "correct" acUvatlon energy was always obtained for the lowest temperature peak, provided that tt was sufticlently separated from the other peaks, (b) m some systems reasonable energies were obtained for the lowest and h~ghest temperature peaks but not the mtermedmte temperature peak(s),

VALIDITY O F TL KINETIC P A R A M E T E R D E T E R M I N A T I O N S (c) occasionally there are mchcauons of acUvaUon energies, e.g a plateau of c o ~ t a n t activatiOtl energies, that do not correspond to any of the energies inserted into the s,mulauons In other words, enUrely nusleadmg values can be obtained from repeated ~mttal slope measurements, (d) m cases where the glow peaks are widely separated, reasonable values can be obtained from mulupeak curves, (e) systems v~th overlapping glow peaks are not hkely to be analysable by the repeated tmual nse method For example, systems vnth overlapping peaks m normal glow curves may yteld a curve of acuvauon energy vs temperature that suggests there ~s a continuous dlstnbuuon of energies If the system contains a "plateau" of acttvat~on energies, they may not correspond to any actual energy and/or occur at temperatures other than those corresponding to peak temperatures m normal glow curves

25

REFERENCES Garhck G F J and Cnbson A F (1948) The electron trap mechamsm of luminescence m sulplude and sthcate phosphors Proc Phys Soc 60, 574-590 Gobrecht H and Hofmann D (1966) Spectroscopy oftral~ by fracaonal 8low techmque J Phys Chem SohdJ 27, 509-522 IMSL User's Manual, Math 1.2brary--Fortran Subroutines for Mathematws Apphcatwas (1987) IMSL, lnc, Houston, TX, pp 640-652 Levy P W (1984a) Thermohnmnescance systems with two or more glow peaks described by anomalous kmet~ parameters Nucl m.vtrum Tech Phys Res BI, 436--444 Levy P W (1984b) Thermolununescent kmetms m systems more general than the usual 1st and 2nd order kinetics J Luminescence 31/32, 133-135 Stnckertsson K (1985) Thermolmmnescence of potamum feldspars---glow curve charactensucs and mtttal rise measurements Nucl Tracks Radtat Meas 10, 613-617