influence of defects and traps in the scintillation process · influence of defects and traps in...
TRANSCRIPT
-
Influence of defects and traps in the scintillation process
Anna Vedda
University of Milano‐Bicocca, Italy
LUMDETR 2009 – July 15th, 2009
-
Outline•
Trapping processes during ionizing irradiation
•
De‐trapping and e‐h recombinations
•
Thermoluminescence (TSL)
•
Wavelength resolved TSL measurements
•
TSL vs RL spectra
•
Examples of uncommon applications: amorphization, phase transitions
•
TSL equations
•
Data analysis: initial rise, variable heating rate method, curve
fitting
•
Role of traps in scintillation
•
Prediction of RT trap lifetimes
•
Slow tails in scintillation decay, afterglow, permanent trapping
•
Examples: Lead tungstate, perovskites, crystalline silicates
-
Scintillation:Scintillation: Physical processesPhysical processesHi
gh E
nerg
y ph
oton
abs
orpt
ion
h
h hh
eee
e
Conduction Band
Valence Band
Eg
Luminescent Centre
Lexc
Lgnd
Traps
Photon( VIS-UV )
CONVERSION TRANSPORT LUMINESCENCE
-
TRAPPING-DETRAPPING PROCESSES: case of electron traps
Ionizing radiation
(X, γ…)
Valence band
Conduction band
Lground
hνRadioluminescence
A – direct process
T
B – delayed process
ET
Mean time spent in the trap
= τ
= C exp(ET
/kT)According to the ET
value (typically from 10-2
up to 100
eV) a very wide range of τcan be measured (of even less than1 s up to thousands years)
e
h
Lexc
-
TSL-TSC process –
simple scheme (electron traps)
Heating
Valence band
Conduction band
Lground
hνTSL
TET
TSL signal measured by a photomultiplier, no information about the recombination centre
Probability of escape from trap: P = K exp(-ET
/kT)P increases very strongly with temperatureA luminescence peak appears (thermally stimulated luminescence)
TSC
Lexc
0
200
400
0 100 200 300 400 500
Tem
pera
ture
(°C
)
Time (s)
1 104
3 104
5 104
7 104
9 104
50 100 150
TSL
inte
nsity
(arb
. uni
ts)
Temperature (°C)
-
Case of hole traps
Valence band
Conduction band
hνTSL
TET
TSC
1 104
3 104
5 104
7 104
9 104
50 100 150
TSL
inte
nsity
(arb
. uni
ts)
Temperature (°C)
It is not possible to determine from a simple glow curve whether
electron or holes are detrapped during heating
In a TSL process, the name “trap”
is attributed to the defect from which carriers are freed by heating
The name “recombination centre”
is attributed to the defect in which carriers are stably trapped, and in which carriers of opposite sign recombine radiatively
The same defects can act as traps or recombination centres in different temperature intervals
-
V.B.
C.B.
Lg
hνTSL
TETT1.
Classical recombination through conduction band
2.
Thermally assisted tunneling (trap-centre recombination)
TSC
LeETC
T1 2
Different kinds of recombination paths
-
Wavelength resolved TSL measurements
Study of both traps and recombination centers
link to photo-, radio-
luminescence, and scintillation
A wavelength resolved TSL measurement consists in a collection of emission spectra measured at constant temperature intervals (for example 1 K). Usually spectra are measured by a CCD.
-
TSL
NO
RM
ALI
ZE
0
ENERGY (eV)
1.5 2.0 2.5 3.0 3.5 4.0 4.50
4
8
12
16
20
24
(A)
(B)
(C)
(D)
TEMPERATURE (K)
25 50 75 100TS
L N
OR
MAL
IZE
D IN
TEN
SIT
Y0
20
40
60
80
100(C)
(B)(A)
An example: low T Thermally Stimulated Luminescence (TSL) of PbWO4
3D TSL measurement after x-ray irradiation at 10 K
After temperature integration
TSL emission spectra
After wavelength integration
TSL glow curves
10 K40 K
60 K
90 K
RT decay times in the micro-milli second time scale
-
Comparison between TSL and radio-luminescence (RL) spectraOne would expect that they are the same…
but the nature of traps as well as specific trap-centre spatial correlations makes them often different
Case of Lu2
SiO5 :RE
Significant differences between RL and TSL:
RL spectra are governed by the emissions of principal dopant ions
TSL spectra display main
ly emissions from RE which capture holes during irradiation (Ce3+,Tb3+___ Ce4+,Tb4+)
even if they are present as trace impurities
Evidence of the electronic nature of traps0
1
2
3
4
5
6
1.5 2 2.5 3 3.5 4 4.5 5
Nor
mal
ized
TSL
and
RL
ampl
itude
Energy (eV)
undoped
Ce
Tb
Tm
Sm
4G5/2
- 6Hx
3P0 - 3H
4
1D2 - 3H
6
3P0 - 3H
5
3 P0 -
3 H6
5D3 - 7F
x5D
4 - 7F
x
5d1 - 4f
620 413 310 248
Wavelength (nm)
RL TSL
-
Spatial correlation between Gd3+ and traps in silica
0
2
4
6
8
10
2 2.5 3 3.5 4
RL
inte
nsity
(arb
.uni
ts)
0.1 mol% Ce,3 mol% Gd
Energy (eV)
3 mol% Gd0.1 mol% Ce RL
TSL
Gd3+
emission
The difference between RL (where both Ce3+
and Gd3+emissions are observed) and TSL spectra (featuring only Gd3+
emission line) is due to the spatial correlation between Gd3+
and oxygen-related electron traps.
0.1 mol% Ce,3 mol% Gd
5d-4f Ce3+
6P7/2
-
8S7/2 Gd3+
-
TSL glow curves are sensitive to material amorphization
Crystalline quartz
Amorphous silica
The amorphous structure o f a m a t e r i a l o f t e n
induces broadening of
T S L g l o w p e a k sdue to the presence of
continuous distributions o f t r a p l e v e l s
1.0
1.2
1.4
1.6
1.8
50 100 150 200 250 300 350 400TR
AP
ENER
GY
(eV)
Partial cleaning Temperature (°C)
SiO2
:500 ppmCe
0
2 105
4 105
6 105
8 105
1 106
0 50 100 150 200 250 300 350
TSL
INTE
NSI
TY (
Arb
. Un.
)
T (°C)
-
TSL glow curves can also be sensitive to phase transitions
P.D. Townsend et al., Rad. Meas. 27, 31 (1997)
Example of Ammonium Bromide (NH4
Br)
Modifications of trap depths
Increased effects in case of localized trap-centre recombinations
Possibility to monitor temperature lags between heater and sample, which are a common error
source in TSL measurements
-
T
TdTkTTE
skTTEsnTI
0
''/expexp)/exp(0)(
TSL equations
1/
0
''/exp/''11/)/exp(0'')(
bbT
TdTkTTEsbkTTEnsTI
First order recombination: no retrapping
General order recombination: non negligible probability of retrapping
-
0.001
0.01
0.1
1
5 10 15 20 25
Nor
mal
ized
TSL
Am
plitu
de
1000/T (1/K)
0.09
eV
0.15
eV
0.23
eV
0.26
eV
0.40
eV
0.53
eV
0.62
eV
AG F E D C B
kTEsnTI o exp)(
Data analysis:
partial cleaning and initial rise method
This procedure allows to evaluate the trap depth independently upon the kinetic order
Case of YALO3
RT X-RAY IRRADIATION
PRE-HEATING T=TSTOP
TSL GLOW CURVE
RAPID COOLINGTO RT
-
100
1000
104
105
106
50 100 150 200 250 300 350 400
TSL
inte
nsity
(arb
. uni
ts)
T (°C)
55
6575
250260
270
340
350
10
100
1000
104105106
1.8 2 2.2 2.41000/T (1/K)
Tstop
=260 °C
E = 1.60 eV
EVALUATION OF TRAP DEPTHSpartial cleaning of glow curves and initial rise
(104
ppm
Ce, 50 ppm
Zr)-doped LuAG
I=c·exp(-E/kb
T)
E1
=1.05 eVτRT
≈5.5 h
E2
=1.60 eVτRT
≈106
yE3
=1.92 eVτRT
≈1011
y
-
102
104
50 150 250 350
LYSO:Ce dose dependence
TSL
inte
nsity
(arb
. uni
ts)
Temperature (oC)
1
300
60
The presence of first order kinetics can be tested by verifying if TSL peak maxima do not vary with increasing dose. In this case,
mkTEs
mkT
E exp2
Evaluation of the frequency factor (s).
Simple case of first order kinetics
If E is already known, s can be evaluated (often only its order of magnitude due to s e v e r a l e r r o r s o u r c e s )
0
5 104
1 105
1,5 105
2 105
2,5 105
200 300 400 500 600 700 800
Lu3Ga(x)Al(1-x)
5O
12:Ce
15s 20cm 10mA
150s 20cm10mA
300s 20cm 20mA
300s 10cm 20mA
TSL
inte
nsit
y (a
rb. u
n.)
Temperature (K)
-
Variable heating rate method
0
2 104
4 104
6 104
8 104
1 105
1,2 105
300 350 400 450
LuGaG
1°C/s1,5°C/s2°C/s2,5°C/s3°C/s
TSL
int
ensi
ty (a
rb.u
n.)
Temperature (K)
mkTEs
mkT
E exp2
From:
Plotting lnTm2/β
vs 1/Tm
10,6
10,8
11
11,2
11,4
11,6
11,8
2,68 10-3 2,7 10-3 2,72 10-3 2,74 10-3 2,76 10-3 2,78 10-3 2,8 10-3
ln(T
m2 /
ß)
1/Tm
(1/K)
Slope = E/k
Intercept = ln (E/sk)
E = 0.92 eVs = 3x1010 s-1
Possibility to extend to general order kineticsNeed of good separation between different peaks
-
Glow Curve Fit
50 100 150 200 250 300
TSL
Ampl
itude
T (K)
x 100 x 3
TSL glow curve of YAP:0.1%Eu (full circles). The continuous red line represents the numerical fit of the glow curve in the framework of first order kinetics.
Made in the framework of first or general order kinetics
Difficult: E,s, and b (order of kinetic) are implicit parameters
If several overlapping peaks are present, the number of parameters can be very high
Need of preliminary information by other methods
-
Role of traps in scintillation If the RT decay time
is of the order of micro-
or milli-
seconds
Slow tails in the scintillation decay
Traps can be studied by heating at a constant rate after irradiation (slow scintillation tails correspond to TSL peaks at cryogenic temperatures, while afterglow and permanent trapping are related to peaks above RT)
The determination of trap parameters by some method of analysis alows the
evaluation of the order of magnitude
of the RT lifetime
(higher precision is
commonly prevented by several error sources and by the temperature dependence of the frequency factor, which is hardly predictable)
Longer
(minutes, hours)
AfterglowVery long
(days, years)
Permanent trapping
-
The investigation of the role of traps in scint i l lat ion involves the fol lowing steps:
Evidence of slow scintillation tails or afterglow
Need to understand the nature of responsible defects
Study of defects by an independent technique giving information about thermal stability of defects and their r a d i a t i v e r e c o m b i n a t i o n p r o p e r t i e s ( T S L )
Correlation of TSL data with other techniques which allow structural information about traps (e.g. EPR)
Tuning of material synthesis to reduce the investigated defects
-
100
101
102
103
104
50 100 150 200 250 300
YALO3:Ce
Lu2-x
YxSiO
5:Ce
Lu3Al
5O
12:Ce
TSL
Inte
nsity
(arb
. uni
ts)
Temperature (K)
Role of traps in scintillation time decayComparison between silicates, garnets, and perovskites
The presence of fewer shallow traps in silicates with respect to other scintillators
(very low TSL intensity below RT) is in agreement with th
e absence of slower
components in th
e scintillation decay.
100 200 300 400 500 600 700 800
lum
. int
ensi
ty [a
rb.u
nits
]
time [ns]
Photoluminescencedecay time = 54 ns
Lu3Al
5O
12:Ce (0.12%)
a - scintillationb - PL
60 ns
600-1000 ns
Ifast
= 40%
1000
100
10 10
100
1000
100 200 300 400 500 600 700 800
YAlO3:Ce
Lum
. Int
ensi
ty [a
rb. u
nits
]
time [ns]
I(t) = 954exp(-t/24ns) + 110exp(-t/60ns) + 17exp(-t/329ns)+7.89
Ifast
= 65%
10
100
1000
100 200 300 400 500 600 700 800
Lu2-x
YxSiO
5:Ce
Lum
. Int
ensi
ty [a
rb. u
nits
]time [ns]
I(t)=459exp(-t/45ns) + 4.1exp(-t/714ns)+ 14.2
Ifast
= 88%
-
10-9
10-7
10-5
10-3
10-1
101
103
0 50 100 150 200 250 300 350
293
K tim
e de
cay
(s)
Tmax (K)
Pb+ - V0
WO4
3 - - La3+
WO4
3 -
WO3
- - APb
MO4
3-
Present only in Mo-doped samples
Example of lead tungstate (PbWO4
– PWO)
Suppressed by trivalent ion doping
Room temperature time decays
a 460 ppm Lab 80 ppm Lac undoped
Doping with La3+
reduces slow components in the scintillation decay, as well as TSL glow
peaks at cryogenic temperatures
La3+
favours the reduction of intrinsic lattice defects
TSL of undoped PWO
Scintillation time decay
Defect structures determined by EPR measurements
Intrinsic RT scintillation decay time
-
S c i n t i l l a t i o n decays o f a )undopedPWO and b)PWO(2750Mo,500Nb,50Y) at RT.
TSL glow curves of differently doped PWO samples
Effect of different ion dopings in very slow decay components in
PWO
Alpha coefficient: normalized difference between the signal level before the excitation pulse and the true background (It measures the level of very slow components)
Good correlation between alpha coefficients of differently doped
samples and TSL integral intensities below RT
-
YAlO3
undoped crystals
Wavelength (nm)
Tem
pera
ture
(K)
1 2 3 4 5 60
0.2
0.4
0.6
0.8
1
Nor
mal
ized
TS
L A
mpl
itude
Energy (eV)
10-50 K
130-260 K
50-130 K
5d1-4f Ce3+
defects
intrinsic emissions
50 100 150 200 250 300
TSL
Am
plitu
de
Temperature (K)
154
K
190
K
232
K
66 K
89 K
110
K
30 K
Wavelength integration
Temperature integration
Several emission centres for each glow peak
Recombinations involving valence/conduction bands
-
50 75 100 125 150 175 200 225 250 275 3000.0
0.5
1.0
1.5
2.0
2.5
3.0 50 ppm Ce 5000 ppm Ce
EPR
, TSL
inte
nsity
(arb
. uni
ts)
T (K)
OI
OII
OIII
OIVTSL
Structural nature of trapsCorrelation with EPR signals
The TSL peaks at 154 K, 190 K, and 232 K are due to the de-trapping of holes from O-
centres followed by recombination with electrons stored in oxygen vacancies
-
50 100 150 200 250 300
Nor
mal
ized
TS
L A
mpl
itude
Temperature (K)
2% Yb
Undoped
0.1% Eu
x 10
x 100 x 2
Doping of YAlO3
with Yb3+, Eu3+, and Tm3+Trapping of electrons during irradiation
0.1% Tm
1 2 3 4 5 6
TSL
Am
plitu
de
Energy (eV)
2% Yb
Undoped
0.1% Eu
x 1025-100 K
140-160 K260-290 K
10-310 K
10-50 K
130-260 K
50-130 K
2F5/2
- 2F7/2
CT emissions
5D0-7F
x
defects
5d1-4f Ce3+
intrinsicemissions
0.1% Tm10-310 K
1D2 - 3H
6
3P0 - 3H
5
3P0 - 3H
6
3P0 - 3H
4
Hole traps are similar to those observed in undoped crystals. Rare earth ions compete with oxygen vacancies in electron trapping (becoming temporarily Yb2+, Eu2+, Tm2+) and act as recombination centres in the TSL process
TSL emissions
-
TSL peak E (eV) ν
(1/s)
at RT (s)
45 K 0.09 107 10-7
66 K 0.15 1010 10-8
89 K 0.23 1011 10-8
110 K 0.26 1010 10-6
154 K (O-) 0.40 1011 10-5
190 K (O-) 0.53 1012 10-3
232 K (O-) 0.62 1011 10-1
Detrapping and recombination: Case of YAlO3
:Yb
232
K
154
K
190
K
Due to their long RT decay times, traps responsible for the TSL peaks above 100 K (mostly O-
centres) cause slow tails in the scintillation time decay
-
Doping with Ce3+, Pr3+, and Tb3+Trapping of holes during irradiation –
a TSL pattern different from that occurring with Yb3+, Eu3+, Tm3+
doping is expected
50 100 150 200 250 3000
1
2
3
4
Nor
ma
lized
TSL
Inte
nsity
Temperature (K)
0.1% Tb
0.1% Pr
Undoped
0.5% Ce
Tunneling emissionTunneling emission
Evidence of one or two dominant Evidence of one or two dominant TSL peaks, similar to those TSL peaks, similar to those observed in the cases of undoped, observed in the cases of undoped, Yb, Eu, and Tm doped crystalsYb, Eu, and Tm doped crystals
TSL spectral emissions of rareTSL spectral emissions of rare-- earth ions trapping holesearth ions trapping holes
O-O- O-
CeCe3+ 3+ emissionemission
TbTb3+ 3+ emissionemission
PrPr3+ 3+ emissionemission
-
1 2 3 4 5 6
TSL
Ampl
itude
Energy (eV)
0.1% Tm
Undoped
0.1% Tb
defectsintrinsicemissions
5D4 - 7F
x
5D3 - 7F
x
5d1-4f
Ce traces
3P0 - 3H
4
1D2 - 3H
6
3P0 - 3H
5
3P0 - 3H
6
RE-doped YAPTSL spectra Example: 190 K peak
Emissions from electron and hole trapping RE ions observed in the same TSL peaks.
0.5% Ce5d
1-4f
1 2 3 4 5 6TS
L Am
plitu
deEnergy (eV)
2% Yb
Undoped
0.1% Eu
x 10
2F5/2
- 2F7/2
CT emissions
defectsintrinsicemissions
5d1-4f
Ce traces
5D0-7F
x
0.1% Pr 5d1-3H
4,5
3P0-3H
4,51D2-3H
4
-
In RE-doped YAP, traps and recombination centres do not act like separate entities, but rather as parts of defect complexes in which carriers can be transferred from intrinsic levels (O-
centres and oxygen vacancies) to the rare earth ion levels.
The observation of a nearly temperature independent TSL emission
suggests that tunnelling driven recombination processes occur in addition
to the
temperature driven recombination, supporting the existence of such complexes w i t h c l o s e s p a t i a l c o r r e l a t i o n b e t w e e n t r a p s a n d c e n t r e s .
Due to the formation of defect complexes, the kind of recombination centre (capturing holes or electrons, e.g. Ce
or Yb) is not always a proof of the nature
(electron-
or hole-kind) of a trap
The comparison of the TSL patterns of crystals doped with a variety of rare earth ions
proved to be essential in order to highlight this phenomenology,
which nevertheless could be more common in TSL experiments than expected.
-
50 100 150 200 250 3000.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Nor
mal
ized
TS
L A
mpl
itude
Temperature [K]
Undopedx 10
Pr-0.1%
Ce-0.1%
(RT) ~ 10-3s
(RT) ~ 10-4s
Sample Concentr.Melt (%)
Growth method
&Crucible
Nphels /MeV(phels per
MeV)
FWHM (%) at
662 keV
Nphels% of
standard
RL_intens.% of
standardYAP:Ce Ce-0.05 CZ - Ir 1978 7.3 71 81YAP:CeCzech
Ce-0.5 CZ –
Mostandard
2803 4.8 100 100
YAP:Pr Pr - 0.05 CZ - Ir 2280 7.1 81 147YAP:Pr Pr – 1.0 CZ - Ir 1026 8.9 37 113YAP:PrCzech
Pr – 0.5 CZ - Mo 975 10.3 35 130
YAP:PrCzech
Pr – 1.1 CZ - Mo 1127 9.1 40 n.m.
Consequences of trap levels RT decay times on scintillation efficiency
Ligh
t yie
ld (
1 μs
)
Stea
dy s
tate
RL
As the glow curve peak occurs at a much higher temperature in the case of Pr doping, the RT
lifetime of it main trap is a b o u t o n e o r d e r o f
magnitude larger with
respect to that of Ce-
d o p e d Y A P .
This can be one of the reasons why delayed radiative recombination processes in YAP:Pr are more pronounced and its photoelectron yield is lower with respect to that of YAP:Ce in spite of its higher steady state RL efficiency.
-
0
1
2
0 100 200 300 400
TSL
inte
nsity
(arb
. uni
ts)
Temperature (oC)
x 20 LSO:Ce
LYSO:Ce
Lu2
SiO5
:Ce and Lu1.96
Y0.04
SiO5
:Ce –
identification of the nature of traps thanks to their localized recombination mechanism
LSO:Ce
Recombination mechanism:Ce4+
+ e (freed from the electron trap) →
Ce3+*
(excited state) →
Ce3+
+ hν
(TSL emitted light)Evidence of the electronic nature of TSL traps
0.5
1.0
1.5
50 100 150 200 250 300 350
LSO:CeLYSO:Ce
Trap
dep
th (e
V)
Tstop (oC)
78 °C 300 °C236 °C181°C135 °C
Constant trap depth for all glow peaks except the 300 °C one
-
No dependence of maximum
temperatures from dose
No retrapping
rs expIn the case of a thermally assisted tunneling processWhere “s”
is the frequency factor and “r”
is the distance between the trap and the recombination centre
mm kTEs
kTE exp2
106107108109
1010101110121013
2 2.5 3 3.5 4
LSO
LYSO
Freq
uenc
y fa
ctor
(1/s
)
O-Lu distance (Angstrom)
2.0
3.0
4.0
0 2 4 6 8
Lu1-
O d
ista
nce
(A)
oxygen site no.
LSO structure
78 °
C
236
°C
181
°C
135
°C
Exponential dependence of the frequency factors from Lu1(Ce)-Oxygen distances
Oxygen vacancies act as electron traps responsible for TSL peaks
-
Conclusions
TSL is a powerful technique for the study of luminescent materials; especially when performed in wavelength resolved mode, it can really provide a deep insight in the t r a p p i n g - r e c o m b i n a t i o n p r o c e s s e s o c c u r r i n g i n a s c i n t i l l a t o r .
Several types of recombination mechanisms between traps and luminescent centres exist. Their comprehension needs very often the possibility to vary sample parameters like kind of doping, dopant concentration, synthesis and annealing conditions, and to probe their influence on TSL features. Anyway, in some cases only qualitative descriptions of the recombination processes remain possible.
Data analyses are delicate; the handling of trap parameters needs a clear consciousness of the error sources linked to experimental data and numerical methods. This is important especially if a comparison with similar parameters obtained by other techniques has to be performed. Such consciousness of the limits of the technique doesn’t lower, but increases its potential allowing to handle data in a critical and therefore constructive way.
-
References1.
M. Martini, F. Meinardi, G. Spinolo, A. Vedda, M. Nikl, Y. Usuki, “Shallow traps in PbWO4 by wavelength resolved thermally stimulated luminescence”, Phys. Rev. B 60, 4653 (1999).
2.
Vedda, M. Nikl, M. Fasoli, E. Mihokova, J. Pejchal, M. Dusek, G.
Ren, C.R. Stanek, K. J. McClellan, D.D. Byler, “Thermally stimulated tunneling in rare-earth doped Lu-Y oxyorthosilicates”, Phys. Rev. B 78, 195123 (2008).
3.
A. Vedda, N. Chiodini, D. Di Martino, M. Fasoli, L. Griguta, F. Moretti, E. Rosetta, “Thermally stimulated luminescence of Ce and Tb doped SiO2 sol-gel glasses” , Journal of Non-Cryst. Solids 351, 3699 (2005).
4.
Vedda, D. Di Martino, M. Martini, V.V. Laguta, M. Nikl, E. Mihokova, J. Rosa, K. Nejechleb, K. Blazek, “Thermoluminescence of Lu3 Al5 O12 :Ce crystals”, Physica Status Solidi A 195, R1 (2003).
5.
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Influence of defects and traps in the scintillation processOutlineSlajd numer 3Slajd numer 4Slajd numer 5Slajd numer 6Slajd numer 7Slajd numer 8Slajd numer 9Slajd numer 10Spatial correlation between Gd3+ and traps in silicaSlajd numer 12Slajd numer 13TSL equationsSlajd numer 15Slajd numer 16Slajd numer 17Variable heating rate methodGlow Curve FitSlajd numer 20Slajd numer 21Slajd numer 22Slajd numer 23Slajd numer 24Slajd numer 25Slajd numer 26Slajd numer 27Slajd numer 28Slajd numer 29Slajd numer 30Slajd numer 31Slajd numer 32Slajd numer 33Slajd numer 34Slajd numer 35Slajd numer 36