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Raman and Raman and
fluorescence fluorescence
Gérard PANCZER,
LPCML, UCBL, Villeurbanne, France
Michael GAFT,
LDS, Petach Tikva, Israel
Georaman international school
“Applications of Raman spectroscopy to Earth
Sciences and Cultural Heritage
14 to 16 th of June 2012, Nancy (France)
Fiat Lux ! Fiat Lux ! (Fluorescence vs Raman) (Fluorescence vs Raman)
Electronicground state
1st ElectronicExcited State
Exc
itatio
n E
nerg
y, σ
(cm
–1)
Vibrationalstates
4,000
25,000
0 IRσ
σ σemit.
2nd ElectronicExcited State
Raman∆σ=σemit.–σ
σ ±∆σ
Stokes
Anti-StokesIntermediate virtual states
Rad
iativ
e el
ectr
onic
tran
sitio
ns
Flu
ores
cenc
e
Abs
orpt
ion
MNHN Grand Sapphire Louis XIV (MNHN)
Mobile mini Raman, 532 nm
Outlines
• Fluorescence vs Raman
• How to get rid of fluorescence (and of thermal
emission) ?
– luminescent centers
– HT Raman
• How to take advantage of fluorescence
(photoluminescence, light emission) ?
• How to play with time ?
– Gated Raman,
– TR PL
• Some various examples
fluorescence
Schematic representation of luminescence
A
BC
D
M0
M
Energie
Etat fondamental
Etat excité
hνννν
A-B : absorption(excitation)
B-C : thermalization 1
hνννν’ < hνννν
C-D : emission(desexcitation)
D-A : thermalization 2
Fluorescence vs Raman
FluorescenceElastic diffusion
(Rayleigh)
Inelastic diffusion (Raman)
Probability (~) 10-4 à 10-2 10-2 à 10-1 10-7 à 10-14
Advice 1: Use safety
goggles (filters)
� For security
� To see the potential
fluorescence
Luminescent centers 1: Intrinsic emissionsLuminescent centers 1: Intrinsic emissions
4 5 6 7
(TiO4)4- (VO
4)3- (CrO
4)2- (MnO
4)-
(ZrO4)4- (NbO
4)3- (MoO
4)2-
(TaO4)3- (WO
4)2-
Opticaly active groups
responsible for intrinsic emissions
and (UO2)2+
Intrinsic emissionsIntrinsic emissions
360 nm
(MoO4)2- in powellite, CaMoO4
360 nm
(WO4)2- in scheellite, CaWO4
Luminescent centers: ions (<%)
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Transitions ions 3dn d10 Heavy ions 4-6s2 4-
6s p
Ti3+ V2+
Cr2+
Cr3+
Cr4+
Cr5+
Mn2+
Mn4+
Mn5+
Fe3+ Co2+ Ni2+ Cu+ As3+
Ag+ In+ Sn2 Sb3+
Tl+ Pb2+ Bi3+
Lanthanides 4fn-4fn-1 5d
La Ce3+ Pr3+ Nd3+ Pm3+ Sm3+
Sm2+
Eu3+
Eu2+ Gd3+ Tb3+ Dy3+
Dy2+
Ho3+
Ho2+
Er3+
Er2+
Tm3+
Tm2+ Yb3+ Lu
Actinides 5fn
Ac Th4+ Pa4+ U6+ Np3+ Pu3+ Am3+ Cm3+ Bk3+ Cf3+ Es3+ Fm3+ Md3+ No3+ Lr
Luminescent ions responsible for
extrinsic emissions
Extrinsic emissionsExtrinsic emissions
Eu3+ and Pr3+ doped powellite Cr3+ doped corundum
Rare earth ions luminescence characteristics
Transitions / shape Decay Time
Rare earth ions 4f – 4f long
Nd3+, Sm3+, Sm3+, Eu3+,
Gd3+, Tb3+, Dy3+, Yb3+Lines ~10 µs - 1 ms
Rare earth ions 5d – 4f short
Ce3+ Bandfully allowed
(~ 10 - 100 ns)
Eu2+ Band ~ 1 µs
Yb2+, Sm2+ Band 100 µs - 1 ms
What is the decay time of Raman scattering ?
≈ duration of the excitation:
•For CW laser, Raman scattering is not dependant
• For nanosec range pulsed laser, Raman scattering is ≈
10 ns (duration of the laser pulse)
Transition metal luminescence characteristics
Transitions / shape Decay Time
Transition metal ions d - d long
Cr3+ 2E - 4A2 line(s) 1 ms
Cr3+ 4T2 - 4A2 band ~ 10 - 100 µs
Mn2+, Fe3+ 4T1 - 6A1 ; 4T2 - 6A1 band ~ 1 ms
1 2 3 4 GPa
Cr3+ doped corundum (ruby)
widely use as pressure gauge
in DAC
550 600 650 700 750 800 8500
10000
20000
30000
Molecular group luminescence characteristics
Transitions / shape Decay Time
d0 complex ions Charge-transfer
(VO4)3-, (WO4)2-,
(MoO4)2- , (TiO4)4-Band
relatively short
(10 - 100 µs)
(UO2)2+ Band Long (~100 µs - 1 ms)
Glass UO22+ !!
0 500 1000 1500 20000
200000
400000
600000
800000
1000000
1200000
Décroissance des luminescences : Eu3+ (τ
1/2= 300 µs)
MoO4
2- (τ1/2
= 15 µs)
Inte
nsité
Temps (µs)
532 nm exc.
Microluminescence (355 nm)
20 µm
20 µm
500 6000,0
5,0x104
1,0x105
1,5x105
602
573
547
524
502
nm
I (A
.U.)
Uranyl (UO2)2+
in autunite Ca(UO2)2(PO4)2.10H2O
Advice 2: Pay attention:
� Luminescence detection limit
can be in certain case below ppm !
�So be ready to have numerous
luminescent centers even in
synthetic samples (purity 99,99 %
...)
� don’t be frightened; try to
identify them.
Advice 2: Pay attention:
� Luminescence detection limit
can be in certain case below ppm !
�So be ready to have numerous
luminescent centers even in
synthetic samples (purity 99,99 %
...)
� don’t be frightened; try to
identify them.
Gaft, M. et al. (2005) Luminescence Spectroscopy of Minerals and Materials. Springer Verlag, Berlin.
How to get rid of fluorescence ?
Advice 3: Read the Raman
equipment instructions !
�To record (of course) spectra in
relative wavenumber unit (cm-1)
�To record and to explore the
whole spectral range up to 1000 nm
� to identify the nature of the
luminescence.
� to choose the optimum excitation
to avoid luminescence
Advice 3: Read the Raman
equipment instructions !
�To record (of course) spectra in
relative wavenumber unit (cm-1)
�To record and to explore the
whole spectral range up to 1000 nm
� to identify the nature of the
luminescence.
� to choose the optimum excitation
to avoid luminescence
Excitation ≈
absorptionemission
λ (nm)
Black body and thermal emission
T
3
max
10897.2 −×=λ
λmax wavelength (in m)
T (in Kelvin)
Djeva (Montey)
( )1
12,
5
2
−×=
kThce
hcTE λλ
λ
E(l,T) energy intensity emitted at wavelength λ(m)
T (Kelvin)
H Planck constant = 6.625 x 10-34 J.sec;
k Boltzmann cst =1.38 x 10-23 J/K
c speed of light = 3 x 108 m/sec
1000 nm100 nm
HT Raman: get down ! (in wavelength)
UV visible NIR/IR
244 nm (Argon) 458 nm (Ar, blue) 785 nm (diode)
257 nm (diode) 473 nm (diode, blue) 830 nm (diode)
325 nm (He-Cd) 488 nm (Ar, blue)
363.8 nm (Ar) 514 nm (Ar, green) 1064 nm (YAG, IR)
532 nm (YAG, green)
633 nm (HeNe, red)
647 nm (diode, red)
Reynard et al., EMU Notes in Mineralogy, 12 (2012), Chapt. 10, 365–388
HT Raman
200 400 600 800 1000 1200 1400 1600 18000
1x104
2x104
3x104
4x104
325 nm
473 nm633 nm
I
Wavenumber (cm-1)
Heating stages (heating Pt wire and
1500 Linkam)
Lanthanum boro-germanate glass at 1173 K (900 °C) in
which crystallized LaBSiO5 stillwellite for different
excitations (de Ligny, LPCML)
Daniel, I. et al., (1995) Phys Chem Minerals, 22, 74-86.
Neuville D. R. et al., (2007) X-Ray Absorption Fine Structure - XAFS13, 882, 413-415
Raman shift = relative wavenumber (cm-1)
100 200 300 400 500 600 700 800 900 1000
780 nm
532 nm
633 nm
325 nm
Eu3+
Eu3+
Eu3+
Nd3+
Nor
mal
ized
Inte
nsity
Raman Shift (cm-1)
Eu, Nd, Na:Powellite
Nd3+
x
x
νλ
λ−
∗
=−7
0
7
10
110
• wavelength λx
(nm)
• excitation λ0
(nm)
• relative
wavenumber (cm-1)
xν
328 330 332 334
0,0
0,5
1,0
782 nm633 nm
532 nmN
orm
aliz
ed In
tens
ity
Wavelength (nm)
325 nm
535 540 545 550 555 560
0,0
0,5
1,0
Eu3+
Nd3+
Nd3+
Eu3+
Nor
mal
ized
Inte
nsity
Wavelength (nm)
Eu3+
635 640 645 650 655 660 665 670
0,0
0,5
1,0
Nor
mal
ized
Inte
nsity
Wavelength (nm)
790 800 810 820 830 840
0,0
0,5
1,0
Nor
mal
ized
Inte
nsity
Wavelength (nm)
Wavelength (nm) or absolute wavenumber (cm-1)
13
mm
ν1(Ag)
ν3(Eg, Bg)
ν4(Bg)
ν2(Ag+Bg)R
T
Conversion
• From relative vawenumbers to wavelength:
• The intensity of the Raman signal is inversely proportional to the
fourth power of the laser wavelength λ0:
I1/I2 = (λ2/ λ1)4
I248 = 21× I532 = 100×I785
x
x
νλ
λ−
∗
=−7
0
7
10
110
• wavelength λx (nm)
• excitation λ0 (nm)
• relative wavenumber (cm-1)
4)1
( −≈λRI
Polarized Raman and fluorescence
200 400 600 800 1000 1200 1400
Z(XR)Z
X(YR)X
X(ZR)X
Raman shift (cm-1)
I
Z(XR)Z
X(YR)X
X(ZR)X
964
581
550 600 650 700 750 800 850 900Wavelength (nm)
I
579
870
Ramanrange
E
Z
X
E
X’
X
E
X
Z
Mn2+
Nd3+
ν1 streching (PO4)
ν4
bending
ν2 bending
ν3
streching
Fiesch apatite (Alpes)
Porto notation
Ex: Tetragonal (a = b ≠ c ; α = β = γ =
90°
Z(XR)ZX(ZR)XX(YR)X =
X(X’R)X
E
E
E
Porto, S.P.S. & Scott, J.F. (1967) Physical Review, 157, 716-719.
Advice 4: Turn you sample !
(if anisotropic)
The luminescence can be as
well polarized.
Advice 4: Turn you sample !
(if anisotropic)
The luminescence can be as
well polarized.
Gated Raman
M. Gaft & L. Nagli, Opt. Mat. 30 (2008) 1739–1746
UV gated Raman spectroscopy
for standoff detection of
explosives (organic matters)
Needed:
• pulsed laser
• delay and temporal gate
generator
• time resolved detection
(ICCD)…
Time-resolved photoluminescence
Delay generator
Sample
Cryostat
Spectrometer(gratting400 or 1200 l/mm
Opticalfiber
Dye
(>= 4 ns)
ICCD
ext. trig.
fire
To
trig
LASER
cd
GPIB
EximerYAG
Cooler
ICCD
delay
generator
microscope
Pulsed
laser
Time resolved photoluminescence equipment
100 200 300 400 5000
3
6
9
12
temps, µµµµs450 500 550 600 650 700 750
0,0
5,0x104
1,0x105
1,5x105
2,0x105
2,5x105
Eu3+
Sm3+
Eu3+
Sm3+Dy3+
Dy3+
rela
tive
inte
nsity
(A
.U.)
wavelength (nm)
Delay 200 µs Gate 1 ms
Delay 1 µs Gate 1 ms
450 500 550 600 650 700 750
5,0x104
1,0x105
1,5x105
2,0x105
Dy3+
Dy3+
Eu2+
rela
tive
inte
nsity
(A
.U.)
wavelength (nm)
450 500 550 600 650 700 750
5,0x104
1,0x105
1,5x105
2,0x105
2,5x105
Eu2+
Ce3+
rela
tive
inte
nsity
(A
.U.)
wavelength (nm)
Delay 0 Gate 1 ms
Laser pulse
450 500 550 600 650 700 750
5,0x104
1,0x105
1,5x105
2,0x105
2,5x105
Dy3+
Dy3+
rela
tive
inte
nsity
(A
.U.)
wavelength (nm)
Delay 50 µs Gate 1 ms
Gated spectroscopies and time-resolved luminescence
τ = 4 µs
τ = 40 µs
τ = 900 µs
τ/0
tt eII −=
Gated Raman
1000 1500 2000 25000,0
5,0x105
1,0x106
1,5x106
2,0x106
2,5x106
3,0x106 λλλλex
=532 nm cw
I
cm-1500 1000 1500 2000 2500
0,0
5,0x105
1,0x106
1089
Mn2+
ττττ=11 ms
I
Raman shift (cm-1)
500 1000 1500 2000 2500
6,0x104
8,0x104
1,0x105
G=10 ns
I
Raman shift (cm-1)
λex=532 nm pulsed
Delay=0
Gate=10 ns
λex=532 nm pulsed
Delay=0
Gate=15 ms
λex=532 nm
CW continueous
Advice 5:
To conduct good gated
Raman,
shut it as much as you can !
(the gate).
Advice 5:
To conduct good gated
Raman,
shut it as much as you can !
(the gate).
Gaft M. & Nagli L., Eur. J. Mineral. 2009, 21, 33–
42
UV gated Raman (266 nm)
1000 2000 3000 4000
5
10
1000 2000 3000 4000
5
10
1000 2000 3000 4000
500
1000
1500
1000 2000 3000 40000
200
400
1000 2000 3000 40000
500
1000
1500
1000 2000 3000 40000
100
200
300
3426.4869 3152.303357
0.25
796
827.
7907
1038
.795
9
2244
.405
5
3028
.735
1
3544
.419
680.
345
975.
476
1085
.43
1189
.59
3770
.54
917.
607
1160
.66
3944
.15
625.
4613
6
1009
.954
311
33.1
28
1626
.401
3410
.646
3488
.450
7
Inte
nsity
(a.
u.)
Inte
nsity
(a.
u.)
Inte
nsity
(a.
u.)
Water
Ice
Apophyllite
Raman Shift, cm -1
KCa4Si
8O
20(F,OH)x8H
2O
PyromorphitePb
5(PO
4)3Cl
TopazAl
2SiO
4(F,OH)
2
Gypsum
Raman Shift, cm -1
CaSO4x2H
2O
M. Gaft, L. Nagli. European Mineral. J, 2009, 21, 33–42.
λex=266 nm
Raman cross-section of
H2O at 248 nm is
• 120 times larger than
at 532 nm and
• 120 times larger than
at 785 nm
because of pre-
resonance
enhancement.
Why and how to get advantage from fluorescence?
• Raman probes medium to short range order,
while
• Fluorescence probes short range order
(sensitivity to local environment around the
luminescent ion)
• Luminescents trace elements (REE) are often
tracers of genetic conditions
Materials FOR optics
Optical materials Synthetic Natural analogues
Phosphors (Ce3+, Tb3+) : LaPO4Pr3+: CaWO4(Cu+, Al3+): ZnS; Mn2+: ZnSCe3+:Y5(SiO4)3FTb3+: LaSiO 2F(Ce3+, Tb3+):Gd4(Si2O7)F2Tb3+ : CaYSi3O3F4
MonaziteScheeliteSphaleriteBritholite
WollastoniteCuspidine
Melilite
Scintillators Ce3+ : CaWO4Ce3+ : PbWO4Ce3+ : YbPO4Pr3+ : CaTiO3
ScheeliteStolzite
XenotimePerovskite
Dosimeters U6+ : CaF2 ; REE3+ : CaF2(Dy3+, Tb3+) : CaSO4(Cr3+, Ti3+) : Al 2O3
FluoriteAnhydriteCorundum
Laser Materials REE3+: CaWO4REE3+: CaMoO4(Cr3+, Cr4+): Y3Al 5O12(Cr3+, Ti3+): BeAl 2O4REE3+: ZrSiO 4Cr4+: Mg2SiO4Mn5+: Sr5(PO4)3(Cl, F)Yb3+: Sr5(PO4)3(Cl, F)Mn2+: (Ca, Sr, Ba)2(PO4, VO4)ClCr3+: (Ca, Sr)(Y, Gd) 4Si3O13(Nd3+, Ho3+): Ca5(PO4)3F
ScheeliteMolybdenite
GarnetAlexandrite
ZirconForsterite (olivine)
F, Cl ApatiteApatite
Spodiosite (Apatite)Apatite
Fluorapatite
phosphors
400 500 600 7000
1x105
2x105
nm
I
Luminophores RVB (exc. 365 nm)
5 µm
100 µm
Spectre d’émission globale
5 µm
400 500 600 7000
1x106
2x106 Eu2+
nm
I
BAM (BaAl 10MgO17:Eu2+)
400 500 600 7000,0
5,0x105
1,0x106
1,5x106
Mn2+
nm
I
Zn2SiO4:Mn 2+
400 500 600 7000,0
5,0x105
1,0x106 Eu3+
nm
I
Y2O3:Eu3+
Microphotoluminescence of RGB phosphors
Panczer G. etal. (2003) J. Optical Material, 24, 1-2, 253-257
Raman and fluorescence: some examples
• Self irradiation in minerals
– U bearing powellite CaMoO4
– monazites (La,Ce)PO4
• Cultural heritage (on site analyses)
– Chauvet cave (30 000 yrs)
– Grand sapphire of Louis XIV
Raman and fluorescence of Mo rich glass ceramic
νννν1
νννν2
νννν4 νννν3
Mo-O
575 600 625 800 825
0
15000
30000
45000
Glassy matrix
Crystalline phase
Eu3+
Nd3+
4F5/2
+2Η9/2
→4I9/2
5D0→7F
2
5D0→7F
1
Inte
nsity
Wavelengh (nm)
5D0→7F
0
Ceramic
Raman fluorescence
BSE
Ex.1: U bearing powellite CaMoO4 (Kazakhstan)
PL Pr3+
9,0 cm-1
12,1 cm-1
20 µm
BSE878 cm-1 Raman
FWHM
0 50 100 150 200 250
9
10
11
12
FW
HM
(cm
-1)
Distance (µm)
Mapping desorder (chemical and radiation induced)
Luminescence mapping of incorporated REE (exc. 532 nm)
600 700 800 900
[UO2]2+
Er3+
Nd3+
Nd3+
Inte
nsité
Longueur d'onde (nm)
Pr3+
Pr3+ Er3+ Nd3+Type
[UO2]2+
)
� Uranium and REE are concentrated during the crystal growth history as
in the synthetic glass ceramic
Mendoza, C. et al., (2012) Am. Min. (submitted)
Ex.2: Self irradiations in monazites (La,Ce)PO4
Trimouns YS35 Moacir DIG19 Manangotry
Locality France China Brazil Canada Madagascar
ThO2
(wt %)nd
5.74–
15.606.92 9.03–10.33 13.25
UO2
(wt %)nd
0.29–
0.940.13 0.14–0.46 0.20
Age
(My)99 24 474 1928 545
Ref.
Schärer
et al.
(1999)
Schärer
et al.
(1994)
Seydoux-
Guillaume et al.
(2002b)
Schärer &
Deutsch
(1990)
Paquette et
al. (1994)
Natural monazites from various localities, age and Th and U content
Raman and disorder in monazites (La,Ce)PO4
Ruschel K. et al. (2012) Miner Petrol , 105, 41–55
Substitution induced disorder Annealing of radiation induced disorder
Nd3+ luminescence and disorder in natural monazites
800 825 850 875 900 925
0,0
0,5
1,0
4F3/2
→4I9/2
4F5/2
+2H9/2
→ 4I9/2
TRIM
DIG
MADA
MOAC
Nor
mal
ized
I (A
U)
Wavelength (nm)
YS
Manangotry
(Madagascar),
DIG19 (Canada),
Moacir (Brazil),
YS35 (China),
Trimouns (France)
Note the broadening of the 4F3/2 �4I9/2 Stark
sublevels.
Panczer G. et al. (2012) EMU Notes Book in Mineralogy Series, (J. Dubessy & F. Rull, editors). 12, 1–22.
514 nm
y = 0,0637x + 2,8383
R2 = 0,9474
1,0
2,0
3,0
4,0
5,0
6,0
7,0
8,0
9,0
0 5 10 15 20 25 30
ThO2 (wt%)
FW
HM
line
1 ~
863
nm
Gd
Ce
Nd
La,Nd
McG
osr
eE
mb
ala
an
Moa
cir
Are
nd
al
Dig
19Y
S3
5
Mad
agas
car
500°C
700°C
800°C900°C
1000°C500°C
700°C800°C900°C
1000°C
500°C
700°C
800°C
900°C
1000°C
FWHM Nd3+ 573 nm line vs annealing
ThO2 (wt %)
Maximum natural
irradiation level
Synthetic monazites
Natural monazites
annealing
Zero irradiation level
Ex.3: On site analyses Chauvet cave (Ardèche, France)
Upper Paleolitic
30 000 years old
Phosphates (bones, tooth,
phosphatic concretions)
Fluorescence
in Chauvet cave
450 500 550 600 650 7000
50
100
150
200
250
300
350
400
Inm
Raman and fluorescence on Chauvet site
400 600 800 1000 1200 1400 1600 18000
500
1000
1500
2000
2500
3000
713,78
1088,36
283
raman stalactite calcite 1 532 nm(début solarisation)
I
cm-1
500 1000 1500 20000
500
1000
950 Raman 785 nmvertebre 2
I
cm-1
calcite
apatite
Raman
Luminescence
490 nm Irradiation induced
defect (Rn*) in calcite
or
fulvique acid
fluorescence ???
Gaft M. et al. Am. Min., 93 (2008) 158–167
Perrette Y. et al. Chemical Geology 214 (2005) 193– 208
Ex.4: On site analyses of the Grand sapphire (Louis XIV)
600 700 800 900 1000
0
500
1000
1500
2000
2500
3000
3500
4000 Grand saphir luminescence 532 nm
Inte
nsity
(A
U)
wavelength (nm)
500 1000 1500
5,0x102
1,0x103
Inte
nsity
(A
U)
Raman shift (cm-1)
Grand sapphire 785 nm 532 nm
Luminescence Cr3+
in SCF
Raman 780 nm
MNHNMNHN
� Historical context and
fluorescence characteristics
lead to a probable Ceylan
(Sri Lanka) origine
SOPRANO team SOPRANO team
Aknowledgments to
• Dominique DE LIGNY and Xiaochun WANG, LPCML, UCBL, Villeurbanne,France
• Clément MENDOZA, LPCML & LMPA, CEA Valhro-Marcoule, France
• Anne-Magali SEYDOUX-GUILLAUME, GET, UPS, Toulouse, France
• François FARGES, MNHN, Paris
Thanks for your attention !
Philosophy (…) established
as principle of things :
Water or abyss, dry
substance or atoms or
earth,
spirit or air, and in the
fourth place, light ;
Because these elements
distinguished each
other in the fact that
they cannot exchange
their nature but that
all – here more, there
less, here some of them
only – meet and
combine in a pleasant
manner.
La philosophie (…) a posé comme
principes des choses :
l’eau, ou abysse ; la substance
sèche, ou atomes, ou terre ;
l’esprit, ou air ; et, en quatrième
lieu, la lumière ;
car ces éléments se distinguent
en ce qu’ils ne peuvent
échanger leurs natures mais
que tous – ici davantage, là
moins, ici tous, là quelques-
uns seulement – se
rencontrent et s’associent de
manière heureuse.
De magia naturali,
Giordano Bruno,
1548-1600
philosopher, disciple of
Copernic, precursor of
modern science, burned
in Rome in 1600
2E
2T1
4A2
2T2
2A1
4T2
4T1
50
40
30
10
10 20 30
E/B
∆/BIntensité du champs crystallin
Energie
Cr3+
4A2
4T2
4T1
champ fort
2E
absorption
ra ie d’ém ission
bande de conduction
b ande de valence
Cr3+ in strong crystal field
2E
2T1
4A2
2T2
2A1
4T2
4T1
50
40
30
10
10 20 30
E/B
∆/BIntensité du champs crystallin
Energie
Cr3+
bande de conduction
b ande de valence
4A2
4T2
4T1
champ faible
2E
ba nde d’ém ission
absorption
Cr3+ in weak crystal field
