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)