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15/11/2005 GKMR lecture WS 2005/06 Denninger esr-powder.ppt1
ESR powder spectra
Relevant materials in ESR spectroscopy are available only as powders. Very often solutions are frozen and these frozen solutions behave as powders with respect to the anisotropy of the spectral parameters.
Powders, Powders, Powders …
15/11/2005 GKMR lecture WS 2005/06 Denninger esr-powder.ppt2
B0
Bx
By
Bz
ϕ
θ
x
y
z
The direction cosines cx,cy,cz of the magnetic field B0 with the directions x,y,z are:
x x0 0 sin( ) cos( )B B c B θ ϕ= ⋅ = ⋅ ⋅
0 0y sin( ) sin( )yB B c B θ ϕ= ⋅ = ⋅ ⋅
z z0 0 cos( )B B c B θ= ⋅ = ⋅
For anisotropic interactions described by second rank tensors, one very often needs the direction cosines of a vector with respect to the principal axes x,y,z of the tensor.
An example is the g-tensor and the magnetic field B0:
x,y,z are the directions of the g-tensor’s principal axes.
B0 is the (arbitrary) direction of an external (or internal) magnetic field.
The direction cosines cx, cy , cz are the projections of the vector B0 onto the x,y,z axes.
15/11/2005 GKMR lecture WS 2005/06 Denninger esr-powder.ppt3
0Bˆˆ ( )H B g Sµ= ⋅ ⋅ ⋅Zeeman-Hamiltonian:
The quantity g is the g-tensor. In the majority of cases, this tensor can be diagonalized by a suitable choice of the directions x,y,z along the principal axes of the g-tensor. With the coordinate system aligned along the principal axes:
x yy zz zy zxx x yBˆ ˆ ˆˆ ( + + )H g B S g B S g B Sµ= ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
gxx , gyy , gzz are the principal values of the g-tensor.
(equ. 1)
(equ. 2)
The solutions of equ. 2 can be found by direct diagonalization of the Hamiltonian:
e.g. for S = ½, the two base states are: |+1/2> and |-1/2>.
The operators Sx, Sy, Sz have the following matrix elements:
+1/20<+1/2|
0-1/2<-1/2|
|+1/2>|-1/2>Sz
01/2<+1/2|
1/20<-1/2|
|+1/2>|-1/2>Sx
0-i/2<+1/2|
i/20<-1/2|
|+1/2>|-1/2>Sy
15/11/2005 GKMR lecture WS 2005/06 Denninger esr-powder.ppt4
xx Bzz z B Bx yyy
xx B B zz z Bx yyy
1 122 2
1 12 2 2
-E +
- -E
i
i
g Bg B g B
g B g B g B
µµ µ
µ µ µ
⋅⋅ ⋅
⋅ ⋅ ⋅
⎛ ⎞⋅− ⋅ ⋅⎜ ⎟⎜ ⎟⎜ ⎟⋅ ⋅ + ⋅⎜ ⎟⎝ ⎠
12
−12
+
12
−
12
+
The eigenvalue equation is: H EΨ = Ψ
The characteristic polynomial of this matrix must be zero for a solution:
xx y xx yx xzz z zz z B yy B yyB B B B( 2 ) ( - 2 ) ( ) ( )g B E g B E g B i g B g B i g Bµ µ µ µ µ µ− ⋅ ⋅ + ⋅ ⋅ ⋅ = ⋅ ⋅ + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ − ⋅ ⋅ ⋅
2 2 22 2 22 2 2 2zz xxz yy yxB B B4g B E g B g Bµ µ µ− ⋅ ⋅ + = ⋅ ⋅ + ⋅ ⋅
00⎛ ⎞
= ⎜ ⎟⎝ ⎠
2 2 22 2 22 2 2xx zzyy y zxB B B
12
E g B g B g Bµ µ µ= ± ⋅ ⋅ + ⋅ ⋅ + ⋅ ⋅
15/11/2005 GKMR lecture WS 2005/06 Denninger esr-powder.ppt5
22 22 2 2 zzyyxxx y zB 012E B c g c g c gµ= ± ⋅ ⋅ + ⋅ + ⋅
22 22 22 2 zzyyxxx y zg c g c g c g= ⋅ + ⋅ + ⋅
0B12E g Bµ± = ± ⋅ ⋅
with
B0
E
E+
E-
0BE E E g Bµ−+∆ = − = ⋅ ⋅
The anisotropic g tensor leads to a direction dependent spin-splitting with a g-factor depending on the direction of B0 with respect to the principal axes of the g-tensor.
15/11/2005 GKMR lecture WS 2005/06 Denninger esr-powder.ppt6
x
y
z
x
y
z
gxx gxx
gYY gYY
gZZgZZ
B0B0
In a powder, all orientations of the individual tensor axes with respect to the magnetic field occur.
Averaging the individual ESR-lines with respect to all orientations lead to „Powder-spectra“.
15/11/2005 GKMR lecture WS 2005/06 Denninger esr-powder.ppt7
High Field (High Frequency) ESR
3.275 3.300 3.325 3.350 3.375 3.400 3.425 3.450 3.475
-4000
-2000
0
2000
4000
6000
8000
10000
12000
W-band spectrumT = 240 K
(Cr-bis-Toluol)2+ C602-
chrombistoluol_wband_240k.opj
ES
R-s
igna
l (1s
t. de
rivat
ive)
Magnetic Field (T)
0.31 0.32 0.33 0.34 0.35 0.36
-300
-200
-100
0
100
200
300X-bandT = 240K
(Cr-bis-toluol)2+C602-
chrombistoluol_xband_240k.opj
ES
R-s
igna
l (1st
der
ivat
ive)
Magnetic Field (T)
X-band: fµw = 9.371 GHz
W-band: fµw = 94.2 GHz
15/11/2005 GKMR lecture WS 2005/06 Denninger esr-powder.ppt8
0.31 0.32 0.33 0.34 0.35 0.36
-300
-200
-100
0
100
200
300X-bandT = 240K
(Cr-bis-toluol)2+C602-
chrombistoluol_xband_240k.opj
ES
R-s
igna
l (1st
der
ivat
ive)
Magnetic Field (T)
X-band result: single line, line width 2.8 mT, g ≈ 1.99
Hardly any indication of a g-resolved powder spectrum.
15/11/2005 GKMR lecture WS 2005/06 Denninger esr-powder.ppt9
3.275 3.300 3.325 3.350 3.375 3.400 3.425 3.450 3.475
-4000
-2000
0
2000
4000
6000
8000
10000
12000
W-band spectrumT = 240 K
(Cr-bis-Toluol)2+ C602-
chrombistoluol_wband_240k.opj
ES
R-s
igna
l (1s
t. de
rivat
ive)
Magnetic Field (T)
measurement
Fit to powder distribution
W-band result: clearly resolved powder pattern, line width 7.6 mT
gxx = 1.9793 gyy = 1.9907 gzz = 1.9911gxx = -11496 ppm gyy = -5803 ppm gzz = -5603 ppm
gxx
gyy
gzz
15/11/2005 GKMR lecture WS 2005/06 Denninger esr-powder.ppt10
The spin-system: Cr(C7H8)2C60 Chromium-bis-toluene C60
At lower temperature (e.g. 240K), the crystal structure is triclinic, the C60
2- are dimerized, and one measures the spin on the Cr(C7H8)2
2+
Cr(C7H8)22+ Only the W-band analysis yields the g-
tensor principal values from the powder pattern:
gxx = 1.9793 = -11496 ppm
gyy = 1.9907 = -5803 ppm
gzz = 1.9911 = -5603 ppm
The g-tensor is nearly axial.
Measurements and analysis: Jürgen Rahmer, Dissertation, University of Stuttgart.
High field ESR: Necessary to determine g-tensors (especially from powders).
15/11/2005 GKMR lecture WS 2005/06 Denninger esr-powder.ppt11
Radicals in red wine: enclosed in tartrates.
3410 3420 3430 3440 3450 3460-600
-400
-200
0
200
400
600
esr_10db.opj
Mittenfeld [ G]: 3435.000Sweepweite [ G]: 50.000Sweepzeit [ s]: 50Verst„rkung [a.u.]: 1.000E+0006Zeitkonst. [s]: 8.000E-0002Offset : 0Modulation [G]: 1.000Modul.Frq. [kHz]: 100.000Phase [ø]:0Leistung [dB]: 0Frequenz [GHz]: 9.62571000Temperatur [K]: 0.00Datenpunkte : 1024Durchl„ufe : 10
3430.84
3436.48
ES
R-A
mpl
itude
Magnetic Field (Gauss)
Radical signal
Background signal glass tube
Typical signal from the deposited tartrates in a red wine from spain.
15/11/2005 GKMR lecture WS 2005/06 Denninger esr-powder.ppt12
3475 3480 3485 3490 34950
50000
100000
150000
200000
250000
300000
350000
400000+1000 ppm
+500 ppm-2000 ppm0 ppm
ESR
-Sig
nal
Magnetic Field (Gauss)
15/11/2005 GKMR lecture WS 2005/06 Denninger esr-powder.ppt13
3475 3480 3485 3490 3495-2000000
-1000000
0
1000000
2000000
3000000+1000 ppm
+500 ppm
-2000 ppm0 ppmE
SR
-Sig
nal,
1st d
eriv
ativ
e
Magnetic Field (Gauss)
15/11/2005 GKMR lecture WS 2005/06 Denninger esr-powder.ppt14
33460 33480 33500 33520 33540 33560
2000
3000
4000
5000
6000
7000
8000
9000
10000Formel1= extern(8)+p6+p7*(x-33515)+lor(x,p8,p9,p10)Formel2=Formel3=
P0= -730.062 R0= 0.001P1= 300.222 R1= 0.001P2= 299.871 R2= 0.001P3= 1.18612 R3= 0.0001P4= 0.589942 R4= 0.001P5= 0.583681 R5= 0.001P6= 2458.2 R6= 0.0001P7= 0 R7= 0P8= 36800 R8= 0P9= 14.4 R9= 0P10= 33518.8 R10= 0.0001
+300ppm -730 ppm0 ppm
w297_004.opj
ESR
-ech
o-Si
gnal
Field (Gauss)Field swept echo spectrum, sample w297.
15/11/2005 GKMR lecture WS 2005/06 Denninger esr-powder.ppt15
33460 33480 33500 33520 33540 33560
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
unknown signal
Mn-line
powder
fit
measurement
Formel1= extern(8)+p6+p7*(x-33515)+lor(x,p8,p9,p10)Formel2=Formel3=
P0= -730.109 R0= 1P1= 300.099 R1= 1P2= 300.526 R2= 1P3= 1.14581 R3= 1P4= 0.594174 R4= 1P5= 0.586747 R5= 1P6= 2426.87 R6= 1P7= -1.19332 R7= 0.1P8= 38257.3 R8= 0.1P9= 12.1353 R9= 0.1P10= 33512.9 R10= 0.1P11= 9603.44 R11= 1P12= 5.49747 R12= 1P13= 33531 R13= 0.1
extern()=gmm.exe
Fehlerquadratsumme= 2.33122e+007
+300ppm -730 ppm0 ppm
w297_004_a.opj
ESR
-ech
o-Si
gnal
Field (Gauss)Field swept echo spectrum, sample w297. Decomposition into components.
15/11/2005 GKMR lecture WS 2005/06 Denninger esr-powder.ppt16
3460 3465 3470 3475 3480 3485 3490 3495 3500 3505 3510-300
-250
-200
-150
-100
-50
0
50
100
150
200
250
powder simulationES
R-S
igna
l (AD
C-u
nits
)
Magnetic Field (Gauß) R118_014.opj
difference *5
R118_014.asc
X-band, 1st derivative spectrum , sample R118.
15/11/2005 GKMR lecture WS 2005/06 Denninger esr-powder.ppt17
3480 3481 3482 3483 3484 3485 3486 3487 3488 3489 3490-20000
-15000
-10000
-5000
0
5000
10000
15000
20000
+338 ppm -598 ppmE
SR
-Sig
nal 1
st d
eriv
.
Magnetic Field (Gauß)
0 ppm
powder_simul_01.opj
Linewidths:Lorentz 0.236 GaußGauß 0.095 Gauß
g-tensor is axial: gxx = gyy = +338 ppm gzz = -598 ppm
15/11/2005 GKMR lecture WS 2005/06 Denninger esr-powder.ppt18
3480 3481 3482 3483 3484 3485 3486 3487 3488 3489 3490
-2000
0
2000
4000
6000
powder_simul_01.opj
ESR
-Sig
nal 1
st d
eriv
.
Magnetic Field (Gauß)
0.236 Gauß0.473 Gauß1.182 Gauß2.365 Gauß
The appearance of the powder pattern depends on the linewidth.
15/11/2005 GKMR lecture WS 2005/06 Denninger esr-powder.ppt19
3475 3480 3485 3490 3495
-400
-200
0
200
400
600
800
powder_simul_01.opj
+338 ppm
-598 ppm0 ppm
ES
R-S
igna
l 1st
der
iv.
Magnetic Field (Gauß)
1.182 Gauß2.365 Gauß
15/11/2005 GKMR lecture WS 2005/06 Denninger esr-powder.ppt20
3475 3480 3485 3490 3495-300
-200
-100
0
100
200
300
powder_simul_01.opj
+338 ppm
-598 ppm0 ppm
ES
R-S
igna
l 1st
der
iv.
Magnetic Field (Gauß)
2.365 Gauß
fmw = 9.7667 GHz
15/11/2005 GKMR lecture WS 2005/06 Denninger esr-powder.ppt21
3460 3465 3470 3475 3480 3485 3490 3495 3500 3505 3510-300
-250
-200
-150
-100
-50
0
50
100
150
200
250
powder simulationES
R-S
igna
l (AD
C-u
nits
)
Magnetic Field (Gauß) R118_014.opj
difference *5
R118_014.asc
15/11/2005 GKMR lecture WS 2005/06 Denninger esr-powder.ppt22
34750 34800 34850 34900 34950-4000
-2000
0
2000
4000
6000
8000+338 ppm
0 ppm
-598 ppm
fmw = 97.667 GHz
powder_simul_01.opj
ESR
-Sig
nal 1
st d
eriv
.
Magnetic Field (Gauß)
W-band (94 GHz)