Quasiquadrupolar echoes in solids containing spins-12 triads undergoing hindered reorientation

Solid State Communications, Vol. 27, pp. 747—748. ©Perganon Press Ltd. 1978. Printed in Great Britain.

O038—lo98/78/0822—0747$02.OO/O

QUASIQUADRIJPOLAR ECHOES IN SOLIDS CONTAINING SPINS— 1/2 TRIADS UNDERGOING HINDERED REORIENTATION

I.C. Baianu~’t, N. Boden, Y.K. Levine**t and D. Lightowlers Dept. of Physical Chemistry, The University, Leeds LS2 9JT, U.K. (Received on 21-6-78 by C.W. McComble 0 The spin echo responses to resonant 9O°—r—8~ rf pulse sequences in solids containing spin—I/2triads undergoing hindered rotations, are shown to be predicted by a model of dipolar coupled quasiparticles of spin—3/2. ‘N

2 that the NMR spin It has been echo responses in suggested” solids containing dipolar— coupled groups of spins—1/2 can be understood in terms of a model of isolated quasiparticles sub— jected to quadrupolar interactions. The dipolar energy levels of an isolated group are, therefore, described in terms of an equivalent quadrupolar Hamiltonian. In this approach, proton pairs in solid H 2 or in H2O in crystalline hydrated are i’,~.Proton e.g. CH considered as triads, isolated quasiparticles of spin 3 and NH3 groups, are described as isolated A—type quasiparticles with spin I • 3/2 and E—type quasiparticles with I 1/22,~.

We have previously shown that the echo reSponses in systems containing proton pairs are more complex than those predicted by such a simple model3’5. Nevertheless, the correct reSponses can be derived by a quasiparticle treat— ment on introducing dipolar interactions be— tween the effective quadrupolar spins3. The isolated quasiparticle model also fails to de— scribe the spin echo responses in solids con—6 taming classically reorienting methyl groups However, the observations can be explained simply by treating the spin system in terms of dipolar interacting quasiparticles of spins— 3/2 and neglecting the contribution of the E—

Powdered CF~COOAg at 293 K I

1•0 08

I

I

I

I

I TI

-

90-t-

-

S

06.

r1~351is

04 02

t2~91 ItS

-

-

-

S

-

-

~ -O•2

-

-

-04

-

-0•6

-

-

-08

-

-

-

.

-1•0-

-

I

0

20

40

60

80

I

I

I

100

120

140

180

160

p/cieg Fig. I.

The dependence of maximum 9F the spins in CF echo amplitude E(t,8) on 8 and t for the ‘ 3COOAg at 293 K. The Continuous lines drawn through the experimental points have been calculated using equation (3) with a/b at

* **

t

t

—

0.38 at r

91 ~s. Theoretically a/b

—

35 ~isand a/b

0.23 as r

0.

Metal Physics Group, Cavendish Laboratory, Madingley Road, Cambridge, U.K. Physics Laboratory, State University of Utrecht, Utrecht, Netherlands. To whom to address correspondence.

747

—

3.78

748

QUASIQUADRUPOLAR ECHOES IN SOLIDS I

900

I

I

I

maximum amplitude at time r following the second 7. The dependence of the maximum echo ampli— pulse tude, Exx(8), following a 9oO_ro~o (xx) pulse

t,r37IAS ~0 ~~gi~s

sequence on the rotation angle B tobe E (B) = ~ (9cos2B — 5cosB) xx 10

08

—

06

04

-j-~ sin2~cos~ G(t

—

has been shown

(1)

t)

and for the 900_r_8~

‘

-

Q2

I

0

I

I

40

I

80

I

I

120

160

B/dee.

Fig. 2.

The dependence of the maximum echo 19F ampli— tude Exy (r,8) on B and r for the spins in CF 3COOAg at 293 K.

The continu—

10

2B

00 (xy) sequence 1) + -~-~ sin28 G(t

— T) (2) E (8) = ~ (3cos where G(t — r) is the echo response function and t is the time following the second pulse. The echo responses are predicted to be independent of the pulse spacing T. The experimental observations for 19p spins in CF 3COOAg 293 K,in undergoing ro8, areat shown figs. I andhindered 2. Similar responses have been obtained for 1H spins in tations H 3OClO1~at 180 K. Clearly these results cannot be described by equations (1) and (2), especially as the angular dependence of the responses change on increasing the pulse spacings. have,expressions therLfore, derived been fitted with The the results theoretical previously6 for the model of interacting quasi—

xy

w

Vol. 27, No. 8

+

particles of spin—3/2. The maximum amplitude of

ous lines drawn through the experimental points have been calculated using equation (4) with values of c = 1.0, d/c = 1.8 and

the echo following an xx pulse sequence 2BcosB is Exx (T,8) = a(r)sin~BcosB— b(r)sin and following an xy sequence

e/c

E

1.4 at

‘t

=

the values are c =

1.1.

d/c

-~‘

27 us. =

For

I

=

0.66, d/c

=

4.1 and e/c

Theoretically for 1.8 and e/c

-~

T

-*

91 us

0, c

=

xy

=

c(r)sin2B —

1,

2.1.

(-r,0)

+

(3)

d(T)sin2Bcos20

e(r)sin’~Bcos2B

(4)

The coefficients a—e are treated as adjustable parameters for a given pulse spacing The values of these coefficients for short values of i are in reasonable agreement with

type States. In this note we show further that the interacting quasiparticle model can be used to account for the spin echo responses in solids containing triads of spins—1/2 undergoing hindered reorientation, When a system of isolated quadrupolar spins— 3/2 is subjected to a resonant 90~—T—B~ rf pulse sequence, a spin echo is predicted with its

those obtained theoretically in the limit r + 0. We, therefore, conclude that the interacting quasiparticle model accounts satisfactorily for the experimental responses. This signifies that as in the cases of proton pairs and classically reorienting triads of spins—l/2, the inter—group dipolar interactions are important in determining the spin echo responses.

REFERENCES I. 2. 3. 4. 5. 6. 7. 8.

T.

METZGER D.S. & GAINES J.R., Phyc. Rev. 147, 644 (1966). ALLEN P.S., HARDING W. & MANSFIELD P., J. Phys. C: Solid State Phys. 5, L89 (1972). BODEN N. & LEVINE Y.K., J. Magnetic Resonance (in press). MOSKVITCH Yu.N., SERGEEV N.A. & DOTSENKO G.I., Soviet Physic8 — Solid State 15, 1912 (1974). BODEN N., LEVINE Y.K., LIGHTOWLERS D. & SQUIRES R.T., Molec. Phys. 29, 1877 (1975). BAIANU I.C., BODEN N., LEVINE Y.K. & ROSS S.M., J. PhyB. C: Solid State Phys. 11, L37 (1978). BONERA, G. & GALIMBERTI M., Solid State Corenun. 4, 589 (1966). GRIFFIN R.G., ELLETT J.D., MEHRING M., BULLIT J.G. & WAUGH J.S., J. Chera. Phys. 57, 2147 (1972).