NMR STUDIES OF ADSORBED 3He

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NMR STUDIES OF ADSORBED 3He

M. Richards

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C6, supplkrnent au no 8, Tome 39, aoiit 1978, page C6-1342

NMR

STUDIES O F ADSORBED

3 ~ e M.G. Richards

SchooZ of MathematicaZ and PhysicaZ Sciences, University of Sussex, FaZmer, Brighton, England Rbsum6.- On passe en revue les exp6rience.s de RMN sur 3 ~ e adsorb6 sur le graphite et d'autres subs- trats. On distingue les r6sultats dont lfinterpr6tation est claire des problsmes non r6solus. Abstract.- NMR results for 3 ~ e adsorbed on graphite and other substrates are reviewed. Emphasis is given to results which have a clear interpretation and unsolved problems are highlighted.

This review is designed to discuss what in- reported ; instead emphasis is given to data which formation about adsorbed 3 ~ e one might expect to get can be clearly and unambiguously interpreted. In ad- from NMR experiments and then to see how far these dition, areas where there are gaps in our knowledge expectations have been realised. are indicated.

1 . WHAT TYPE OF INFORMATION MIGHT NMR BE EXPECTED TO GIVE ?.- (i) Structural information about position of adatoms via the second moment of the NMR line, M,. (ii) Whether the adatoms are localised or delocalised via the nuclear susceptibility

X.

(iii) Information about spin-independent adatom- adatom interactions via X. (iv) Information about spin-dependent interactions

(a) Between adatom spins

(b) Between adatom spins and the substrate (v) Informations about the motion of the adatomsfrom

(a) rc, the correlation time for modulation of the local field.

(b) D, the spin diffusion coefficient of the adatoms

.

(vi) Information about the geometry of the substrate, e.g. how are the surfaces oriented with respect to the applied static field Bo ?

2 . WHAT TYPES OF SYSTEM HAVE BEEN INVESTIGATED ?.-

Coverages from a fraction of a monolayer up to seve- ral monolayers of 3 ~ e adsorbed on the following substrates have been studied. (i) Zeolite / I / . (ii) Vycor glass 1 2 1 . (iii) Graphite in the form of

(a) Graphitized carbon black (b) Grafoil / 3 /

(c) UCAR ZYX oriented graphite 1 4 1 .

In addition, there have been a number of studies of bulk 3 ~ e where it is clear that the NMR properties of the system are strongly affected by the properties of the surfaces in contact with the 3 ~ e . No attempt is made here to summarise all the data

3 . WHAT INFORMATION HAS NMR YIELDED TO DATE ?.-

Using the same headings as in I above. (i) The second moment of the NMR line is dependent on the position of the spins and therefore on the structure of the adsorbate. It is most easily measured for a rigid lattice, i.e. when r-' < &: but this situation very rarely obtains in adsorbed 3 ~ e . M2 can also be de- duced from relaxation time data but only within a factor of about 2 due to uncertainties about the geometry of the substrate and this accuracy is in- sufficient to distinguish between different adsorbate lattice forms. (ii) Just as in bulk '~e, the magnetic susceptibility

X is profoundly affected by

whether the atoms are localised on a lattice or not. If they are localised,

x

will follow the Curie Law down to a temperature related to the spin-dependent interactions, i.e. to below 0.1 K. If the atoms are sufficiently mobile, the exclusion principle applies and this leads to a degenerate system with

X falling

below the Curie value.

Three detailed studies have been carried out. Brewer et al. / 5 / showed that as 3 ~ e is added to a Vycor substrate at 0.4 K,

X increases proportionally to

the number of spins adsorbed, at least up to an a- mount corresponding to about two layers. This is

thought to be due to the atoms in the first layer always being localised by the heterogeneous substrate and the more mobile second layer ilways being dense enough to be non-degenerate at 0 . 4 K. Hickernell et al. / 6 / , using a grafoil substrate, found a distinction between films with x, the fraction of a completed monolayer, above and below 0.5.

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The former obey Curie's law down to about 0.1 K suggesting these films are solid while the low coverage films show abrupt deviations of X from thecurie value below about 0.5 K, suggesting these films are

fluid. In a later study, Owers-Bradley et al. 171 also using grafoil, studied the departure from Curie's law down to 0.4 K and found significant de- partures even at I K but the data did not suggest a sharp distinction between solid and liquid films. This study is discussed further below. (iii) Siddon and Schick 181 have shown that the susceptibility of a two dimensional (2D) gas is sensitive to the

spin-

independent interactions between adatoms. This is because of the symmetry requirements connecting spin and orFital states during collisions. They calcula- ted the second virial coefficient for 2D helium using the known froms for the Van der Waals interaction between atoms. They show that the magnetic susceptibility is given by the expression

3

= [n B~(T)

-

B~(T)

]

xc

where AX is the deviation of

x

form the Curie value xC, n is the areal density and BB(T), Ej$T) are the second virial coefficient for, respectively, spinless bo- sons and fermions with the 3 ~ e mass. In figure 1 it is shown that low coverage films of 3 ~ e on graphite obey this law and we can deduce from this that the substrate is not contributing to the lateral adatom- adatom interaction. It would be interesting to see the data of figure 1 extended to observe the cons- tant X expected at sufficiently low T.

0.02 0.04 0.06 0.08 0.10 0.11 I I I I I ' A T=O.BK

-

0 T = I . O K

-

A A 0 A

-

0 0 A 0 I I 0.0 0.2 0.4 0.6 0.8 1.0 Fractional Coverage X

Fig. 1 : The fractional departure of the magnetic susceptibility from the Curie value at two different temperatures against areal density for 3 ~ e adsorbed on grafoil

(iv) N M R relaxation times T2 and TI give information

about the time dependence of the local magnetic field. In the case of bulk 3 ~ e the only field pre-

sent is that due to the dipolar coupling of each spin to its neighbours and the large amount of NMR

data on liquid and solid 3 ~ e have been successfully interpreted 191 in terms of this coupling. However, with adsorbed 3 ~ e , other local fields may be present due to paramagnetic impurities, "dangling" bonds and bulk magnetic properties of substrate including the presence of conduction electrons. For instance, Husa et al. /I01 were able to show clearly by studying the NMR spin echo damping from ethanol in grafoil that an important damping mechanism is the diffusion of spins in the spatially varying magnetic field created by the anisotropic demagnetisation of graphite. The field could be characterised by two pa- rameters : a correlation length for the spatially varying field which was found to be about 1 vm and an rms strength for the local field which is propor- tional to the applied field B and led to a contri- bution to l/T2 a B:. Howeyer, it has not been possi- ble to retain this model for 3 ~ e atoms in grafoil, possibly because of the much shorter length of about 100

fi

over which solid monolayers in grafoil are found by neutron scattering to be ordered /11/.

A number of studies have been carried out which strongly suggest that in some ranges of temperature and coverage dipole-dipole coupling does pre- dominate. Using Vycor as a substrate, TI minima were found by Thomson et al. 1121 by varying the temperature. The minimum TI values were approximately pro- portional to mo, the Larmor frequency, and a value of 20 msec was found for w / 2 ~ = 1 MHz. Working at

0

the same frequency, Cowan et al. 1131 found minima of about 30 ms with a grafoil substrate both when T was varied at x = 1 and as x was varied with T z IK. As reported in this conference 1141, a group from

the University of Tokyo working at 10 MHz, again with grafoil, found minim between 300 msec and

500 msec, depending on T and x. All these results are consistent with the BPP 1151 expression

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C6- 1 344 JOURNAL DE PHYSIQUE

(1) These expressions are only applicable to an isotro- pic three dimensional system and modifications are required for motion in a plane inclined at an angle

6 to the applied field Bo. However, for Vycor and for grafoil Ill/ where the exposed basal planes are far from parallel, these expressions may be used to give order of magnitude estimates of M2 and T ~ .

The temperature dependence of the relaxation times T 1 and T2 for a completed monolayer of 3 ~ e on grafoil is shown in figure 2. The data show many of the features produced by equation (I). Below 3 K, T2 is independent of temperature suggesting quantum

interparticle spacing (i.e. from different x runs, assuming a triangular solid lattice) in figure 3.

30, d a t a ( R e f 17)

1

Fig. 3 : The activation temperature W/k for creation bf thermal excitations in monolayers of 3 ~ e adsorbed on grafoil as a function of the interparticle spacing in the two dimensional solid lattice

The similarity to the results 1171 for bulk solid hcp 3~ suggest that as in that case, the excitations are vacancies. Above 5 K, T1 and T2 change their temperature dependence and become field dependent, This is probably due to the solid films melting and by using the onset of field dependence in T2 and an observed abrupt change of slope in T 1 we may follow the melting curve for different values of x. The results of this are plotted in figure 4 where the position of the specific heat peaks associated with melting /I81 are also shown.

1.0 - 0 9 - 0.8 - ₀ X 0.7

-

0 TZ frcq. dependence 0.6 - 8 T, change o f slope Spec. heat(ref. 181 0.5 - Ordered

-

Fig. 4 : Part of the phase diagram fir ':~e

1

adsorbed

1

10

0.1 5 0.20 0.25 on grafoil

I/T(K-')

Fig. 2 : The spin-lattice (TL) and spin-spin (T2) We may also look at the coverage dependence relaxation times for a completed monolayer of 3 ~ e

adsorbed on grafoil as a function of temperature at of T and T2 at one temperature and this is shown in three different Larmor frequencies figure 5. The general shape is very similar to fi-

gure 2. This data is discussed in a contributed pa- tunnelling (see further discussion below in connec- per /20/ in this conference and three points only. tion with figure 5). The increase in T2 between 4 K will he mentioned here. Using equation (I), the T I and 6 K is due to some thermally activated process minima allow one to say unambiguously that

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FractionaI Coverage x

Fig. 5 : T, and T, for monolayers of 3 ~ e adsorbed on grafoil at 1 K as a function of the fraction of a completed monolayer at three different Larmor frequencies. x = 1 is defined from a 4.2 K isotherm using the point B criterion (see reference 1181)

in this conference show that T~ s

lo-'

s at x = 0.63 and are again consistent with dipolar coupling pre- dominating in the region. The sharp T2 minimum close to x = 1 is unique in the field because it is the only sign of an abrupt change signifying layer completion. The failure of T, to equal T and the Ere- quency dependence of T, and T on the low x (i.e. short Tc) side of the T, minima are in conflict with equation (I) and indicate the need either for ano- ther field to be contributing beside the dipole field and perhaps also a range of correlation times that has the effect of increasing the Tl/T, rate /lo/ when w T < 1. The dramatic reduction in T, as

0 C

monolayer completion proceeds on graphite is in mar- ked contrast to the situation 1211 in Vycor where TZ increases as more atoms are adsorbed, presumably caused by t@e very low mobility of low coverages due to adsorption energy heterogeneity.

Similar failures in the simple BPP model of equation (1) are found in the temperature dependence 1121 of T, and T p with Vycor as the substrate and

the assumption of a wide range of T ' s in the system has been partially successful in explaining the data. This extension of BPP theory has helped explain 1221 one puzzling feature of the data which has frequen- tly recurred /22-23/ namely the linear dependence of T on w

0'

Lattice Spacing (A)

Fig. 6 : Tunnellingfrequencies in two and three dimensional 3 ~ e

The data described so far all relate to sys- tems where is believed that the 3 ~ e adatoms are localised, i.e. high coverages on graphite and all coverages up to x = 1 on Vycor, Zeolite and other heterogeneous substrates. However we know from specific heat 1191 and susceptibility 171 data that low coverage films (x < 0.7) on graphite are highly mobile, behaving like a 2D fluid. The effect on rvrlR

relaxation times should be very strong since for dipolar coupling -rc will now be %I fl'2s instead of %10-~s for solid films. However, dramatic changes in T I and T, are not seen. This is probably because there are either local fields that vary slowly throughout the sample or small regions of the surface with ano- malous properties. Such regions could be so-called

"deep sites" where the adsorption energy is anoma- lously high and adatoms would tend to get trapped, or regions near a paramagnetic impurity.

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C6- 1346 JOURNAL D E PHYSIQUE

Fig. 7 : T1 and T ₂ f o r a low coverage monolayers of

3 ~ e adsorbed on g r a f o i l a s a f u n c t i o n of temperature

0A.O

0;

012

0 ;

016

04

oI6

0.;

Fractional Coverage X

Pig. 8 : T1 and T2 f o r low coverage monolayers of

3 ~ e adsorbed on g r a f o i l a t 1 K

l a y e r s adsorbed on g r a f o i l . No model has been pro- posed t o e x p l a i n t h i s d a t a b.;t t h e f o l l o w i n g f e a t u - r e s should p r o v i d e u s e f u l c l u e s t o f u r t h e r under- s t a n d i n g .

(a)The fidependence of T1 and T2 s u g g e s t s c o r r e l a - t i o n times determined by thermal v e l o c i t i e s . (b) That T i n c r e a s e s a s T i n c r e a s e s s u g g e s t s t h a t

1

w T < I f o r t h e f i e l d f l u c t u a t i o n s t h a t c o n t r o l TI. 0 C

(c) The p r o p o r t i o n a l i t y of TI and T2 t o x a t low x i s c o n s i s t e n t 1241 w i t h r e l a x a t i o n o c c u r r i n g i n r e s t r i c t e d r e g i o n s of t h e s u b s t r a t e which a r e v i s i - t e d by a l l s p i n s d u r i n g r e l a x a t i o n . (d) S p i n - l a t t i c e r e l a x a t i o n a t x ?. 0.3 i s probably l a r g e l y c o n t r o l l e d by deep s i t e s s i n c e t h e presence of 10 % 4 ~ e g r e a t l y i n c r e a s e s T1, presumably b y p r e - f e r e n t i a l l y occupying t h e s e s i t e s . T i s not simi-

2

l a r l y a f f e c t e d .

(e) The f i e l d dependence of T s u g g e s t s a l o c a l 2

f i e l d c o n t r i b u t i o n from t h e s u s c e p t i b i l i t y of t h e s u b s t r a t e .

( f ) The s h a r p dip i n TI a t a coverage corresponding t o one 3 ~ e atom on every t h i r d g r a p h i t e hexagon ap- p e a r s t o show how narrow a r e g i o n of t h e phase diagram i s occupied by t h e s o c a l l e d 1191 r e g i s t r y pha- s e of helium on g r a p h i t e . What happens t o t h e mobi- l i t y of t h e a d s o r b a t e a t r e g i s t r y cannot unfortuna- t e l y b e deduced s i n c e t h e r e l a x a t i o n mechanisms f o r t h e s e coverages a r e n o t understood.

( v i ) The NMR r e l a x a t i o n times f o r atoms moving i n a p l a n e depend s t r o n g l y 1161 on t h e o r i e n t a t i o n o f t h e p l a n e t o t h e s t a t i c f i e l d B

.

Such a n i s o t r o p y i n T and T would n o t a f f e c t d a t a on Vycor o r Z e o l i t e

1 2

w i t h t h e i r convoluted pore s t r u c t u r e s b u t g r a f o i l and UCAR ZYX o r i e n t e d g r a p h i t e do have p r e f e r e n t i a l alignment of t h e c r y s t a l l i t e s u r f a c e s . L i t t l e a n i s c r t r o p y is seen i n g r a £ o i l / 131 presumably because of t h e

v e r y poor o r i e n t a t i o n I l l / . More s i g n i f i c a n t r e s u l t s a r e o b t a i n e d w i t h t h e UCAR s u b s t r a t e a s shown i n a c o n t r i b u t e d paper 1201.

4. SUMMARY.- ( i ) Monolayer f i l m s on heterogeneous

s u b s t r a t e s such a s Z e o l i t e and Vycor have s o l i d li-

ke NMR p r o p e r t i e s below about 4 K. A t low coverages t h e p a r t i c l e s a r e l o c a l i s e d on a d s o r p t i o n s i t e s and a t h i g h coverage p a i r quantum t u n n e l l i n g becomes

important. There i s evidence f o r a wide range of

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predominates a t h i g h c o v e r a g e s w h i l e a t low covera- g e s t h e l o c a l f i e l d s c o n t r i b u t i n g t o r e l a x a t i o n a r e n o t known. There i s no a b r u p t change i n m o b i l i t y ac- companying m e l t i n g . ( i i i ) F u r t h e r work i s needed p a r t i c u l a r l y i n two d i r e c t i o n s . An i d e a l s u b s t r a t e i s needed which would c o n t r i b u t e no l o c a l magnetic f i e l d s and would b e of e f f e c t i v e l y i n f i n i t e e x t e n t . G r a p h i t e would be i d e a l i f i t c o u l d be o b t a i n e d i n t h e form of p a r a l l e l s u r f a c e s of c r y s t a l l i t e s a t l e a s t 10 um l o n g and o f f e r i n g a n a r e a f o r a d s o r p t i o n o f a t l e a s t l o 4 t o l o 5 cm2 p e r cm3 o f sample. S u r f a c e d i f f u s i o n c o u l d t h e n b e s t u d i e d by NMR. Secondly more work i s

needed i n t h e m i l l i d e g r e e r e g i o n t o s t u d y t h e dege- n e r a c y e f f e c t s of 2D mobile f i l m s on g r a p h i t e and t o make c o n t a c t w i t h t h e i n t e r e s t i n g r e l a t e d work /25/ on b u l k l i q u i d 3 ~ e i n c o n t a c t w i t h g r a p h i t e a n d o t h e r s u r f a c e s .

ACKNOWLEDGEMENT.- The work described h e r e from t h e U n i v e r s i t y of S u s s e x h a s been c a r r i e d o u t i n co-ope- r a t i o n w i t h D r . B.P. Cowan, M r . J.R. Owers-Bradley and D r . A.L. Thomson, w i t h whom i t h a s been a p l e a - s u r e t o c o l l a b o r a t e . F i n a n c i a l s u p p o r t from t h e S c i e n c e R e s e a r c h C o u n c i l i s a l s o acknowledged. R e f e r e n c e s / I / Z e o l i t e i s t h e name g i v e n t o a s e r i e s o f molecu- l a r s i e v e s whose p o r e d i a m e t e r s r a n g e from 3 A t o 1 3A

/ 2 / Porous Vycor 7930 g l a s s manufactured by Corning G l a s s Works, New York. The a v e r a g e p o r e s i z e i n a b o u t 70A

/ 3 / G r a f o i l i s t h e trademark of a g a s k e t p r o d u c t ma- n u f a c t u r e d by Union C a r b i d e , New York

/ 4 / UCAR o r i e n t e d g r a p h i t e g r a d e ZYX i s a n o t h e r Union C a r b i d e p r o d u c t e x f o l i a t e d from s i n g l e c r y s t a l s of g r a p h i t e

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