DETECTION OF EPR USING A PULSED MICROWAVE ACOUSTIC TECHNIQUE

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DETECTION OF EPR USING A PULSED MICROWAVE ACOUSTIC TECHNIQUE

U. Netzelmann, H. Lerchner, J. Pelzl, M. Sigrist

To cite this version:

U. Netzelmann, H. Lerchner, J. Pelzl, M. Sigrist. DETECTION OF EPR USING A PULSED MI-

CROWAVE ACOUSTIC TECHNIQUE. Journal de Physique Colloques, 1983, 44 (C6), pp.C6-221-

C6-226. �10.1051/jphyscol:1983634�. �jpa-00223193�

page C6-

DETECTION OF EPR USING A PULSED MICROWAVE ACOUSTIC TECHNIQUE

U. Netzelmann, H. Lerchner, J. Pelzl and M.W. Sigrist*

AbteiZung far Physik und Astronornie,

UniversitClt BocFurn, 0-4630 Bochm,

*physics Department, ETH, CH-8093 Zurich, Switzerland

Resume - I 1 e s t montre q u ' u n e n o u v e l l e methode p h o t o a c o u s t i q u e dans l e domaine des micro-ondes permet l a d 6 t 6 c t i o n de I'EPR. Les a m p l i t u d e s de p r e s s i o n ob- servees p o u r l e DPPH dans du n-hexane s o n t e n a c c o r d avec l e s p r e v i s i o n s t h e o r i q u e s . Nos c a l c u l s demontrent c l a i r e m e n t que l e s g r a d i e n t s de tempera- t u r e dans 1 ' 6 c h a n t i l l o n s o n t i m p o r t a n t s p o u r o b t e n i r de grandes a m p l i t u d e s de s i g n a l . C e t t e t e c h n i q u e e s t i n t e r e s s a n t e t o u t specialement dans l e cas d 1 6 c h a n t i l l o n s d o n t l a d i s t r i b u t i o n des c e n t r e s paramagn6tiques e s t inhomo- gPne ou dans l e s cas de couches minces.

A b s t r a c t - A new p u l s e d microwave a c o u s t i c method i s shown t o be s u i t e d f o r t h e d e t e c t i o n o f EPR. P r e s s u r e a m p l i t u d e s o b t a i n e d f o r DPPH i n n-hexane agree w i t h t h e o r e t i c a l p r e d i c t i o n s . Our c a l c u l a t i o n s c l e a r l y demonstrate t h a t tem- p e r a t u r e g r a d i e n t s w i t h i n t h e sample a r e i m p o r t a n t f o r g e n e r a t i n g l a r g e s i g n a l amplitudes. Hence t h i s t e c h n i q u e i s o f s p e c i a l i n t e r e s t f o r samples w i t h an inhomogeneous d i s t r i b u t i o n o f paramagnetic c e n t e r s o r f o r t h e s t u d y o f i n t e r - f a c e s .

I - INTRODUCTION

I n t h e l a s t y e a r s a few experiments have been d i s c u s s e d i n l i t e r a t u r e which were concerned w i t h t h e d e t e c t i o n o f EPR i n s o l i d s . The s i g n a l p a t h solid-gas-microphone up t o m o d u l a t i o n f r e q u e n c i e s o f some kHz /1,2/, o r d i r e c t c o n t a c t o f t h e sample t o p i e z o c e r a m i c m a t e r i a l a t low f r e q u e n c i e s / 3 / were used t o p e r f o r m measurements which t o o k p l a c e on a r a t h e r l o n g t i m e s c a l e t o a l l o w t h e h e a t f l u x t o d i s s i p a t e . Here we w i s h t o p r e s e n t t h e f i r s t p u l s e experiment of an EPR s t u d y w i t h t h e s i g n a l p a t h s o l i d - l i q u i d - p i e z o e l e c t r i c t r a n s d u c e r comparable t o t h e o p t o a c o u s t i c t e c h n i q u e /4/, u s i n g microwave p u l s e s w i t h d u r a t i o n s o f microseconds. The e x p e r i m e n t a l r e s u l t s w i l l be v e r i f i e d by a n o n - r i g o r o u s t h e o r e t i c a l model o f t h e s i g n a l g e n e r a t i o n where t h e importance of t e m p e r a t u r e g r a d i e n t s i n t h e system w i l l be p o i n t e d o u t .

I 1 - EXPERIMENTAL

The k l y s t r o n of a commercial EPR-spectrometer was used f o r t h e g e n e r a t i o n o f m i c r o - waves. A f a s t PIN-diode m o d u l a t o r produced microwave p u l s e s w i t h a l e n g t h o f 0.5 us up t o 4 us. The p u l s e s were a m p l i f i e d u s i n g a TWT-amplifier w i t h a maximum o u t p u t power o f 20 W and g u i d e d t h r o u g h waveguides i n t o a s t a n d a r d X-band c a v i t y . The c o n t r o l o f t h e microwave power coupled i n t o t h e c a v i t y was p o s s i b l e by u s i n g a c r o s s c o u p l e r b u i l t i n t o t h e waveguide. The microwave a c o u s t i c c e l l shown i n F i g . 1 c o n s i s t e d o f an NMR sample t u b e made o u t o f q u a r t z and a t e f l o n cup p u t upon t h e upper end o f t h e tube. Both t h e t u b e and t h e cup were f i l l e d w i t h a s a t u r a t e d so- l u t i o n o f t h e paramagnetic sample i n t h e l i q u i d . The cup s e r v e d t o f i x t h e t r a n s - ducer such t h a t i n c i d e n t a c o u s t i c waves f r o m t h e p a r t o f t h e t u b e i n s i d e t h e c a v i t y h i t f r o n t a l o n t o t h e s e n s i t i v e element of t h e t r a n s d u c e r , a p i e z o e l e c t r i c d i s k of z - c u t LiNbO The t r a n s d u c e r has a s e n s i t i v i t y o f 4 uV/Pa and an upper f r e q u e n c y response l i & t o f 15 MHz, i t s d e s i g n i s d e s c r i b e d i n /5/.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983634

JOURNAL DE PHYSIQUE

\solid sample

A f t e r p a s s i n g an impedance matching p r e a m p l i - f i e r , t h e s i g n a l s w i t h amplitudes o f about 1 ~ I V were t o o s m a l l t o be r e c o r d e d i n t h e t i m e do- main. So t h e t r a n s d u c e r o u t p u t was f e d i n t o a

l o c k - i n a m p l i f i e r , where a phase s e n s i t i v e de- t e c t i o n was performed a t a frequency o f 70 kHz.

Our EPR s p e c t r a were o b t a i n e d f r o m a s a t u r a t e d s o l u t i o n o f DPPH ( d i p h e n y l - p i c r y l - h y d r a z y l ) i n t h e s o l v e n t s benzene and n-hexane. There was a s o l i d - l i q u i d boundary i n s i d e t h e c a v i t y ( F i g . 1).

S e l e c t i n g a s u i t a b l e s o l v e n t , we balanced b e t - ween a low d i e l e c t r i c a b s o r p t i o n o f t h e l i q u i d , w i t h advantages f o r n-hexane, and an o p t i m a l t r a n s f e r o f thermal energy i n t o a c o u s t i c energy d u r i n g t h e t h e r m o e l a s t i c process, w i t h advanta- ges f o r benzene. As w i l l be shown l a t e r , a c h a r a c t e r i s t i c e x p r e s s i o n f o r t h i s energy t r a n s f e r i s t h e t e r m yv2/C, where

r e p r e s e n t s t h e t h e r m a l expansion c o e f f i c i e n t , v t h e v e l o - c i t y o f sound and C t h e s p e c i f i c h e a t c a p a c i t y o f t h e specimen.

F i g . 1 - The microwave a c o u s t i c c e l l used i n t h i s experiment.

I n F i g . 2 we show an EPR spectrum o f DPPH t a k e n w i t h t h e e x p e r i m e n t a l s e t u p des- c r i b e d above. Both t h e l i n e w i d t h and t h e g - f a c t o r a r e t h e same as f o r s o l i d DPPH i n c o n d e n t i o n a l EPR. The underground a b s o r p t i o n i s due t o d i e l e c t r i c a b s o r p t i o n i n t h e l i q u i d .

DPPH in hexane

2

F i g . 2 - Microwave a c o u s t i c EPR spectrum o f s o l i d OPPH i n n-hexane. Accumulation o f f i v e s ~ e c t r a .

>

a

t

a#

0 3

C

d

E

I

0.322 0.326. 0.330 0.334

m a g n e t ~ c field B,T

fl ^pulse repetition r a t e ^{width l p s} 7 0 k k -20W. 9.3GHz

I 1 1 - THEORETICAL CONSIDERATIONS

-

C m

.-

I n o r d e r t o o b t a i n a q u a n t i t a t i v e e s t i m a t e o f t h e s i g n a l a m p l i t u d e we d e f i n e a one-

dimensional model system c o n s i s t i n g o f two h a l f s p a c e s w i t h t h e a b s o r b i n g s o l i d

sample a t x

0 ( i n d e x s ) and t h e t r a n s f e r l i q u i d a t x < 0 ( i n d e x

The b a s i c

e q u a t i o n s f o r t h e microwave a c o u s t i c e f f e c t i n t h e l i q u i d and i n t h e s o l i d body i n -

c l u d e t h e c o n s e r v a t i o n o f energy and o f momentum as w e l l as t h e c o r r e s p o n d i n g

e q u a t i o n s o f s t a t e /6,7/. The r e l a t i o n s become v e r y s i m p l e i f one assumes t h a t t h e

s o l i d behaves i s o t r o p i c a l l y and i f one c o n s i d e r s o n l y l o n g i t u d i n a l e l a s t i c waves. If

i n a d d i t i o n c o n v e c t i v e and d i s s i p a t i v e terms a r e n e g l e c t e d , t h e b a s i c e q u a t i o n s can

where p: density, u(x,t): displacement, B : bulk modulus, u : thermal expansion coef- ficient, 8(x,t): temperature distribution, a: thermal diffusivity, Q(x,t): heat source distribution and C: specific heat capacity.

Equation (1) follows from a combination of the Navier-Stokes equation in its Euler form and the volume dilatation. It relates the displacement field u(x,t) with the temperature distribution 8(x,t). It is noted that the driving term responsible for the thermoelastic generation of acoustic waves is proportional to the spatial temperature gradient. The temperature field 8(x,t) itself is determined by the equation of heat conduction (2) where Q(x,t) represents the heat source due to the absorbed microwave radiation. Only the time-dependent portions are taken into account. Since deformation effects on the temperature field 8(x,t) are neglected

/6/, O(x,t) is independent on the pressure amplitudes and can thus be calculated

by solving Eq. (2) for the solid and the liquid halfspace respectively. The deter- mination of 0(x,t) in the defined one-dimensional model is closely related to the way described in the Rosencwaig-Gersho (RG) theory of the photoacoustic effect in

solids /8/ and will not be described in detail here. Differences are due to the energy impact caused by microwaves of an intensity I . and an absorption coefficient for microwaves Bs and the simplification of having only a boundary between liquid and sample material. The microwave is supposed to be modulated sinusoidally with the frequency

Since microwave radiation experiences only a very slight attenuation in paramagnetic samples, we are treating the "optical" transparent case in the sense of RG. As a result of this deduction we get the following expressions for the temperature components periodic with

in the model system:

:, (x,t)

8 .(I- P

P l+g for x 0

S

ukX iwMt

8L(x,t)=0.-.e _{P l+g} - ^{e for x}

⁰

with 0

Bslo P 2as"s7

where Bp: complex temperature amplitude inside the sample, A: thermal conductivity, cr=(l+i) .a where a= w: thermal diffusion coefficient, g=i, ak/Asas: parameter of the boundary. The temperature variation at the boundary takes place within the thermal diffusion length ~l=l/a, which in our system is of the order of some 10-7 m at the modulation frequency of 70 kHz.

In a second step we introduce eqs. (3) to (5) into ( 1 ) and obtain the following ansatz for the displacements us(x,t) and uL(x,t) for the regions (s) and (k) res- pectively

iw (t

- ^>)

^{x ioMt}

uS(x,t)

U l e S + u - e ₂ . e for x > ⁰

iwM(t

L )

i w t

uL(x,t)

U3e v ~ + u ~ . e ' . ^{e for x}

o ( 7 )

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where v . = v m , i

s,L denote t h e sound speeds. The f i r s t t e r m r e p r e s e n t s a wave t r a v e l l i n g away f r o m t h e boundary o f l i q u i d and s o l i d whereas t h e second t e r m d e s c r i b e s m o d i f i c a t i o n s of phase and a m p l i t u d e near t h e boundary. V e r i f i c a t i o n o f ( 6 ) and ( 7 ) i m m e d i a t e l y y i e l d s t h e c o e f f i c i e n t s U2 and U4, so f o r example:

where 6

w /v i s t h e a c o u s t i c wave number.

M

The r e m a i n i n g c o e f f i c i e n t s U1 and U3 a r e o b t a i n e d by u s i n g t h e f o l l o w i n g boundary c o n d i t i o n s :

a) The displacement u ( x , t ) a t t h e boundary x=O i s t h e same f o r b o t h t h e l i q u i d and t h e s o l i d , t h u s

b ) The p r e s s u r e a m p l i t u d e a t t h e boundary p (x=O,t) i s t h e same i n t h e l i q u i d and t h e s o l i d :

Some a l g e b r a i c t r a n s f o r m a t i o n s y i e l d a r a t h e r l e n g t h y e x p r e s s i o n f o r U3 which can t h e n be i n s e r t e d i n t o t h e f o l l o w i n g e q u a t i o n ( 1 1 ) f o r t h e p r e s s u r e pL i n t h e l i q u i d which i s e x t r a c t e d f r o m t h e e q u a t i o n o f t h e volume d i l a t a t i o n :

( 1 1 ) Since we a r e i n t e r e s t e d i n t h e p r e s s u r e a t t h e t r a n s d u c e r , we c a l c u l a t e pL f a r away f r o m t h e boundary, where I x 1 ^>> 1 ¹ /uR l , ^x<O:

The complex p r e s s u r e a m p l i t u d e pR a t t h e t r a n s d u c e r i s g i v e n by:

The a c o u s t i c wavelengths i n t h e m a t e r i a l s used i n t h i s experiment a r e XaC=v/v - 2 * 1 0 - ~ m a t v = 70 kHz, which i s much g r e a t e r t h a n t h e t h e r m a l d i f f u s i o n l e n g t h u

c a l c u l a t e d above. We can approximate l a L ( > > 6 L and I B Q ~ ~ ( > > ] B ~ S ~ / i n ( 1 3 ) and g e t

t h e f i n a l r e s u l t :

T h i s r e s u l t i s s i m i l a r t o one o b t a i n e d b y Pate1 i n / 4 / f o r t h e t h i c k i l l u m i n a t e d c y l i n d e r . To compare t h i s t h e o r e t i c a l r e s u l t w i t h t h e e x p e r i m e n t a l v a l u e , we t a k e t h e absorbed power d e n s i t y 3 S I o and t h e measured s i g n a l a m p l i t u d e f r o m t h e e x p e r i - ment. W i t h t h e known Q - v a l u e o f t h e microwave c a v i t y , t h e microwave power and t h e microwave a b s o r p t i o n o f DPPH a power d e n s i t y o f 1 . 6 - 1 0 - 7 i s c a l c u l a t e d . I n s e r - t i n g t h i s y a l u e and t h e m a t e r i a l c o n s t a n t s o f n-hexane and DPPH i n t o ( 1 5 ) we g e t

~ 0 . 7 Nm- f o r t h e p r e s s u r e a t t h e t r a n s d u c e r , a f t e r a c o r r e c t i o n w i t h r e s p e c t t o t h e a c t u a l l y r e c t a n g u l a r i n s t e a d o f a s i n u s o i d a l m o d u l a t i o n as assumed i n t h e a

e s t i m a t i o n . T h i s v a l u e i s o f t h e same o r d e r as t h e measured v a l u e o f 0.3 ~ m - 2 and, a c c o r d i n g t o t h e a p p r o x i m a t i o n s made i n t h e t h e o r y and t h e u n c e r t a i n t i e s i n t h e e s t i m a t i o n o f t h e absorbed power, a r a t h e r good agreement.

E q u a t i o n ( 1 4 ) i n d i c a t e s t h a t f o r Xa,>>u t h e p r e s s u r e a m p l i t u d e i s p r o p o r t i o n a l t o t h e t e m p e r a t u r e v a r i a t i o n O p . w i t h i n t h e sample b u t n o t p r o p o r t i o n a l t o t h e t o - t a l l y absorbed microwave power i n t h e specimen, i . e . i n c r e a s i n g t h e amount o f s o l i d DPPH does n o t a u t o m a t i c a l l y i n c r e a s e t h e a c o u s t i c a m p l i t u d e . The d e t e c t e d s i g n a l r a t h e r o r i g i n a t e s f r o m t h e t e m p e r a t u r e jump a t t h e boundary s o l i d - l i q u i d w i t h i n t h e v e r y s m a l l t h e r m a l d i f f u s i o n l e n g t h s us and ua r e s p e c t i v e l y .

I V - CONCLUDING REMARKS

The p r e s e n t measurements o b t a i n e d f o r DPPH d e m o n s t r a t e t h e f e a s i b i l i t y o f p u l s e d microwave a c o u s t i c EPR s p e c t r o s c o p y . I n comparison t o c o n v e n t i o n a l p u l s e d EPR t h i s t e c h n i q u e o f f e r s t h e g r e a t advantage o f t h e d e c o u p l i n g o f t h e e x c i t a t i o n channel from t h e d e t e c t i o n c h a n n e l . The microwave a c o u s t i c s i g n a l i s p r o p o r t i o n a l t o t h e s p a t i a l t e m p e r a t u r e v a r i a t i o n i n s i d e t h e specimen. The a c o u s t i c s i g n a l g e n e r a t i o n i s t h u s dominated by t e m p e r a t u r e g r a d i e n t s . The a b s o r p t i o n o f t h e microwave r a d i a - t i o n induces such g r a d i e n t s o n l y a t r e g i o n s w i t h an inhomogeneous d i s t r i b u t i o n of p a r a m a g n e t i c c e n t e r s and a t i n t e r f a c e s . I n t h e p r e s e n t e x p e r i m e n t t h e dominant c o n t r i b u t i o n t o t h e microwave a c o u s t i c s i g n a l o r i g i n a t e s f r o m t h e boundary between t h e s o l i d DPPH and t h e l i q u i d . A l t h o u g h t h e a c t i v e s u r f a c e i s r a t h e r s m a l l , a mea- s u r a b l e s i g n a l c o u l d be observed. I t s a m p l i t u d e agrees r e a s o n a b l y w e l l w i t h t h e t h e o r e t i c a l p r e d i c t i o n . T h i s r e s u l t d e m o n s t r a t e s t h a t t h e microwave a c o u s t i c s p e c t r o s c o p y may be s u c c e s s f u l l y a p p l i e d t o t h e s t u d y o f boundary l a y e r s o r sand- w i c h s t r u c t u r e s due t o t h e h i g h t e m p e r a t u r e g r a d i e n t s caused i n such systems when a b s o r b i n g microwave r a d i a t i o n .

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(1982) 32.

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