THE EXAFS OF QUASICRYSTALS

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THE EXAFS OF QUASICRYSTALS

A. Sadoc

To cite this version:

A. Sadoc. THE EXAFS OF QUASICRYSTALS. Journal de Physique Colloques, 1986, 47 (C8), pp.C8-1003-C8-1008. �10.1051/jphyscol:19868193�. �jpa-00226100�

Colloque C8, suppl6ment au n o 12, Tome 47, d6cembre 1986

THE EXAFS OF QUASICRYSTALS

A. SADOC

LURE ( C N R S , C E A , M E N ) , B g t . 209 D , U n i v e r s i t e de P a r i s - S u d , F - 9 1 4 0 5 O r s a y C e d e x , F r a n c e

RQsumQ - Une revue des donnges EXAE'S e s t p r Q s e n t Q e pour l e s a l l i a g e s quasi- c r i s t a l l i n s B b a s e d'aluminium. Une Qtude comparative p a r EXAFS d e s phases icosahQdriques A 1 86 MnIhl A l g 5 Mn7 C r e t A 1 C r e s t exposde en d d t a i l s . Pour r e n d r e compte d e s r e s u l t a t s obtenus p a r ' f i ~ ~ ~ 4 , 8 un modOle icosahddrique e s t proposg, dans l e c a d r e de l a s t r u c t u r e a (A1 Mn S i ) e t en r e l a t i o n Q t r o i t e avec l e s t h Q o r i e s r Q c e n t e s de pavages par d e s i c o s a h g d r e s d e Mackay.

A b s t r a c t - EUFS d a t a f o r a number of Al-based q u a s i c r y s t a l l i n e a l l o y s a r e surveyed. A comparative EXAFS s t u d y of i c o s a h e d r a l A 1 Mn A 1 Mn C r and A l g 6 C r 1 4 phases i s p r e s e n t e d i n d e t a i l . To i n t e r g g e t

kk&

I - INTRODUCTION

" I c o s a h e d r a l c r y s t a l s : where a r e t h e atoms ?". T h i s is t h e question asked by Per Bak, a t h e o r e t i c i a n s t u d y i n g of t h e q u a s i c r y s t a l l i n e s t r u c t u r e i n a r e c e n t p u b l i c a t i o n ( 1 ) . S i n c e t h e i r r e c e n t discovery by Shechtman, Blech, G r a t i a s and Cahn ( 2 ) , t h e i c o s a h e d r a l c r y s t a l s have genecated e x t e n s i v e t h e o r e t i c a l and experimental s t u d i e s . A most p u z z l i n g problem is t h e d e t e r m i n a t i o n of t h e a c t u a l atomic p o s i t i o n s of t h e s e phases. S e v e r a l X-ray and n e u t r o n s c a t t e r i n g i n v e s t i g a t i o n s have been performed and t h e i r d i f f r a c t i o n p a t t e r n s indexed using t h e 6 f i v e f o l d symmetry d i r e c t i o n s . However n e i t h e r e l e c t r o n microscopy nor X-ray and neutron d i f f r a c t i o n could answer t h e q u e s t i o n of atomic p o s i t i o n s w i t h i n t h e q u a s i l a t t i c e c e l l . Moreover no simple mathematical model can p o s s i b l y d e s c r i b e t h e s t r u c t u r e . The only models ( 3 , 4 ) based on t h e IY (A1 Mn S i ) s t r u c t u r e , which g i v e r e a s o n a b l e agreement with t h e a c t u a l a v a i l a b l e d a t a f o r both Xrray and neutron s p e c t r a , p r e d i c t t o o low a mass d e n s i t y .

To e l u c i d a t e t h e n a t u r e of t h e l o c a l s t r u c t u r e , EXAFS has t h e g r e a t advantage t o a l l o w , e a s i l y enough, t h e r e c o n s t r u c t i o n of t h e experimental o s c i l l a t i o n s i n t h e k.;reciprocal space using a simple formula c o n t a i n i n g t h e parameters of t h e r e a l space : i . e . t h e type of t h e neighbour atoms around a given c e n t r a l atom, t h e i r d i s t a n c e s and t h e i r numbers. EXAFS can g i v e d i r e c t l y t h i s information and t r y t o determine t h e l o c a l o r d e r .

I 1 3 WHAT ARE THE QUASICRYSTALS ? s THE FORBIDDEN SYMMETRY

The q u a s i c r y s t a l l i n e a l l o y s a r e g e n e r a l l y prepared by m e l t r s p i n n i n g , s o they a r e o b t a i n e d i n t h e form of r i b b o n s . The m i c r o s t r u c t u r e of t h e A 1 based q u a s i c r y s t a l s examined by t r a n s m i s s i o n e l e c t r o n microscopy show q u a s i c r y s t a l l i n e g r a i n s of flower shape, embedded i n a f c c aluminium matrix. T h e i r d i f f r a c t i o n p a t t e r n s show Bragg peaks a s s h a r p a s t h o s e of s i n g l e c r y s t a l s but they p r e s e n t

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19868193

C8-1004 JOURNAL DE PHYSIQUE

icosahedral symmetry, including f i v e f o l d symmetry axes. This is a t variance with a well-known theorem i n c r y s t a l l o g r a p h y which s t a t e s t h a t f i v e f o l d symmetry axes can never appear i n a t r u l y longsrange p e r i o d i c c r y s t a l . Therefore, t h e new s t r u c t u r e is l i k e a c r y s t a l i n t h a t it h a s long range t r a n s l a t i o n a l o r d e r and long range o r i e n t a t i o n a l order. However t h e t r a n s l a t i o n a l o r d e r i s not p e r i o d i c . I n s t e a d , t h e new s t r u c t u r e i s quasiperiodic. There e x i s t s a space f i l l i n g arrangement of a small number of d i f f e r e n t building blocks (Penrose t i l e s ) with icosahedral d i f f r a c t i o n p a t t e r n s . How a r e these t i l i n g s r e l a t e d t o t h e a c t u a l s t r u c t u r e is t h e c e n t r a l question.

I11 EXAFS REVIEW n STATE OF ART

To answer t h i s question, s e v e r a l EXAFS s t u d i e s have been undertaken on A 1 Mn and A 1 Mn S i a l l o y s . A pionnering work was published i n November 1985 by S t e r n , Ma and Bouldin ( 5 ) . They r e p o r t e d a comparative study of q u a s i c r y s t a l l i n e and c r y s t a l l i n e A l , Mn powders. They remarked f i r s t t h a t t h e a m p l i t u d e o f f b spectrum of t h e q u a s i c r y s t a l is s m a l l e r than those of t h e c r y s t a l by a f a c t o r ( r is t h e golden mean). A f t e r a n a l y s i s , using t h e A l , Mn c r y s t a l a s a s t a n d a r d , they found two types of Mn s i t e s , t h e average MnmA1 bond being c l o s e l y t h e same a t t h e two s i t e s , with no d r a s t i c change of t h e coordination number b u t one of t h e s i t e s having a l a r g e r d i s o r d e r . They a l s o noted some change beyond R = 5 A between t h e q u a s i c r y s t a l and t h e c r y s t a l which t h e y i n t e r p r e t e d by d i s t o r s i o n of t h e bonds i n t h e q u a s i c r y s t a l . They concluded t h a t t h e i r r e s u l t s showed t h a t t h e icosahedral phase was not r e l a t e d t o t h e c r y s t a l l i n e a (A1 Mn S i ) phase.

Three EXAFS s t u d i e s ( 6 , 7 , 8 ) have r e c e n t l y been reported f o r icosahedral A 1 Mn and A 1 Mn S i a l l o y s and comparison made with a ( A 1 Mn S i ) and t o t h e orthorhombic A l , Mn phase. A l l t h e s e papers r e p o r t e d r a t h e r small i n t e n s i t i e s of t h e s p e c t r a of t h e icosahedral phases s i n c e a s t r a i g h t f o r w a r d a n a l y s i s of t h e d a t a gave about 6 A 1 neighbours i n s t e a d of 10 i n A l , Mn (Ref. 9 ) and gel 2 i n a ( A 1 Mn S i ) (Ref. 1 0 ) . So, a s remarked by Boyce e t a l . ( 7 ) t h i s r u l e s out t h e Mn being t h e c e n t e r of a n icosahedron. The apparent l o s s of c o o r d i n a t i o n was i n t e r p r e t e d a s t h e s i g n a t u r e of a broad asymmetric d i s t r i b u t i o n s i m i l a r t o m e t a l l i c amorphous a l l o y s (11). D i f f e r e n t t y p e s of two s u b s h e l l f i t s (two gaussian o r two asymmetric s u b s h e l l s ) gave approximately same r e s u l t s . I n an attempt t o quantify t h e d i s t a n c e s and coordination numbers, we obtained 2.55 and 2.78 + 0.05 A f o r t h e f i r s t Mn-A1 d i s t a n c e s . A l l t h e s e models supposed A 1 f i r s t neighb&iurs. We have a l s o considered t h e p o s s i b i l i t y of t h e neighbourhood of a Mn atom t o c o n s i s t of A 1 and Mn atoms ( 8 ) . This y i e l d e d f i t s of e q u i v a l e n t q u a l i t y a s two A 1 s u b s h e l l s although no Mn?Mn c o n t a c t e x i s t s i n c r y s t a l l i n e A1-Mn coumpounds with up t o 33 $ Mn. The r e s u l t i n g r a d i a l d i s t r i b u t i o n P(R) based on A 1 f i r s t neighbours showed c l o s e resemblance t o those i n a ( A 1 Mn S i ) . On t h e o t h e r hand, n e i t h e r i c o s a h e d r a l phase showed much resemblance t o t h e orthorhombic phase. F i n a l l y , Marcus e t a l . ( 6 ) concluded t h a t t h e icosahedral A 1 Mn S i resembles a d i s t o r t e d a-phase and may be b u i l t of icosahedra glued t o g e t h e r with A 1 atoms a s i n t h e a s t r u c t u r e . They suggested a l s o t h a t inAl Mn is perhaps a more disordered v e r s i o n of i - A 1 Mn S i .

More r e c e n t l y , Maurer (12) has compared iaAl Mn t o t h e hexagonal A l , Mn phase. A s a matter of f a c t , t h e A l , , Mn,, samples c o n s i s t of icosahedral g r a i n s p l u s some A 1 matrix. Therefore, t h e composition of t h e q u a s i c r y s t a l s is near those of A l , Mn. Unfortunately, although t h e c r y s t a l s t r u c t u r e of h*Al, Mn is well e s t a b l i s h e d , t h e p o s i t i o n s of t h e atoms w i t h i n t h e u n i t c e l l a r e not y e t resolved.

Nevertheless, from t h a t EXAFS s t u d y , t h e icosahedral A 1 Mn s t r u c t u r e could appear a s a smeared version of t h e hexagonal phase.

While a l l t h e s e papers mostly concern t h e f i r s t neighbourhood of a Mn atom, Ma e t a l . (13) have s t u d i e d i n d e t a i l t h e more d i s t a n t s h e l l s i n connection with t h e a (A1 Mn S i ) s t r u c t u r e (10) and r e l a t e d models ( 3 , 1 4 ) . To i n t e r p r e t t h e peaks a t l a r g e R d i s t a n c e i n t h e Fourier transforms of i - A 1 Mn and i * A l Mn S i , they proposed a model based on s t r u c t u r a l u n i t s i n t h e form of Mn icosahedron, with d i f f e r e n t connections of t h e Mnricosahedra i n t h e two icosahedral phases and i n t h e a (A1 Mn S i ) phase.

discussed i n t h e hypothesis t h a t t h e Ru atoms s t a b i l i z e the icosahedral phase.

I V ⁷ i - A 1 (Mn, C r ) SYSTEMS

I V 7 1 7 Data c o l l e c t i o n and a n a l y s i s

To get new i n s i g h t s i n t o t h e l o c a l s t r u c t u r e of icosahedral phases, t h e EXAFS above t h e Mn and/or C r Knabsorption edges of icosahedral A l , , Mn,, , ^{A l , ,} Mn, C r , (Fig. 1 ) and A l , , C r , , a l l o y s have been recorded. This study was done i n connection with neutron s c a t t e r i n g experiments , ( 1 6 ) using isomorphic s u b s t i t u t i o n . The negative coherent l e n g t h of Mn f o r thermal neutrons provided a v a r i a b l e c o n t r a s t between t h e a l l o y s .

The samples were prepared by G. Regazzoni and R. Rey-Flandrin (Aluminium Pechiney, Voreppe, FRANCE). They were obtained by r a p i d quenching on a r o t a t i n g copper wheel using a melt-spinning method and t h e i r m i c r o s t r u c t u r e checked by transmission e l e c t r o n microscopy. S i m i l a r e l e c t r o n d i f f r a c t i o n p a t t e r n s were obtained f o r t h e t h r e e a l l o y s ( 1 7 ) . I n t h e same way, t h e x ( k ) EXAFS s p e c t r a (Fig. 2) show a s t r i k i n g resemblance s o t h a t some s i m i l a r l o c a l o r d e r i n g has t o be p r e s e n t i n t h e d i f f e r e n t i c o s a h e d r a l a l l o y s .

The Fourier transforms (FT) of k 3 x ( k ) e x h i b i t , f o r a l l t h e a l l o y s , a main peak a t about 2 A (uncorrected f o r phase s h i f t ) . However, i n t h e case of i = A l C r , a n o t i c e a b l e peak a t 4.2 A i s a l s o observed (Fig. 3). These r e s u l t s have t o be compared with t h e neutron data (16) obtained on t h e same samples. Strong d i f f e r e n c e s e x i s t between t h e d i f f r a c t i o n p a t t e r n s which cannot be simply explained by t h e d i f f e r e n t s c a t t e r i n g l e n g h t s of Mn and C r . They could be due t o somewhat d i f f e r e n t mean or long range order o r even t o small d i f f e r e n c e s i n t h e l o c a l order ( f o r example AR changes 4 0.02 A ) .

The peak a t 4.2 A h a s i t s e x a c t c o u t e r p a r t i n t h e FT obtained f o r a pure chromium f o i l (Fig. 3 ) . Moreover, t h e i n v e r s e FT of these two corresponding peaks a r e i n phase through a l l t h e energy range. I n pure C r , t h i s peak is due p r i n c i p a l l y t o t h e 24 f o u r t h neighbours a t 4.78 A. Some c o n t r i b u t i o n comes, however, from t h e f i f t h s h e l l of 8 C r at 5.00 A s o t h a t , when e x t r a c t i n g experimental amplitudes and phase s h i f t s , it was analysed a s being due t o 32 atoms a t a n average d i s t a n c e 4.835 A. Then, t h e corresponding peak i n i ~ A l C r was found t o be due t o 5-7 C r a t about 4.85 + ^0.05 A.

For t h e t h r e e a l l o y s , s i m i l a r inverse FT of t h e f i r s t peak (2 A) were obtained s o t h a t t h e same f i t t i n g could be found with small changes of t h e parameters N , R and o (AN = + 0.5, AR = + ^{0.05 A, A} a = + ^0.02 A ) . Therefore, only t h e i;. A 1 C r r e s u l t s ( 1 8 7 w i l l be discussed i n tti& following. T h e o r e t i c a l amplitudes and phase s h i f t s ( 1 9 ) were used and d i f f e r e n t types of Gaussian s u b s h e l l s f i t s were t r i e d . For example, a s i n g l e A 1 gaussian s h e l l gave a coordination of only 6 A 1 atoms a t 2--55 + 0.03 A. Then t h e f i t t i n g was performed using the a (A1 Mn S i ) s t r u c t u r e a s a model'.

I V -. 2 * w(A1 Mn S i )

Using c r y s t a l l o g r a p h i c d a t a (10) t h e cubic a ( A 1 Mn S i ) phase has r e c e n t l y ( 3 , 14) been described a s a bcc packing of Mackay icosahedra ( 2 0 ) . I n t h e b a s i c u n i t , the Mn atoms a r e l o c a t e d a t t h e v e r t i c e s of an icosahedron, t h e c e n t r e of which is unoccupied (Fig. 4 ) . ; 12 A 1 atoms a r e l o c a t e d a t half t h e d i s t a n c e d of t h e v e c t o r s pointing t o t h e Mn v e r t i c e s , thereby forming themselves a half-sized p a r a l l e l icosahedron. Moreover, 30 A 1 atoms occupy t h e midpoints of t h e edges of t h e l a r g e r Mn icosahedron. I f a l a b e l s t h e edge of t h e Mn icosahedron, t h e atoms surrounding a Mn atom a r e 1 A 1 a t d/2, 5 A 1 a t a / 2 and 5 Mn a t a. I n t h i s d e s c r i p t i o n , t h e r e a r e only 6 A 1 neighbours. Icosahedra of t h e same o r i e n t a t i o n a r e packed with t h e i r f a c e s d i r e c t e d towards one a n o t h e r forming a c o n t r a c t e d octahedron. The connect ion occurs along t h r e e f o l d axes.

C8-1006 JOURNAL DE PHYSIQUE

Figure 2 : Experimental EXAFS spectra for icosahedral alloys.

Ale, Mn,, (a), Al,, Mn, Cr, (b) Mn edge, (c) Cr edge and Al,, Cr

(d)

.

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: ^{1 . 0} 2

R. 0

l . O

b C

5. 0

5

0 I Figure 3 : Fourier transforms of

k 3 ~ ( k ) data for (a) pure chromium ( b ) icosahedral Al,, Cr,, (multiplied by 10). The FT were obtained with the same k;.window

(10 3 300 eV).

1 0 (b)

I I I I I . . . , n1mu , I , -

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. :J%,

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9Y0 8 . 0 0 0 8 . 1 0 0 8.200 B.%O 6 . 400 0 . 5 0 0 6 eO0 8 700 8.800

Figure 1 : Cr and Mn K-edge absorption curves of icosahedral Al,, Mn, Cr, alloy

With t h e Mackay icosahedron d e s c r i p t i o n of t h e a phase, t h e main c o n t r i b u t i o n of neighbours around a Mn/Cr atom a r i s e s from t h e 5 A 1 atoms a t a / 2 and does correspond t o t h e EXAFS d i s t a n c e of about 2.55 A. T h i s y i e l d s a = 5.10 A , which is t h e edge l e n g t h of t h e Mn/Cr icosahedron i n t h e Audier and Guyot model

( 3 ) .

To determine t h e missing A 1 atoms, we have f i r s t looked f o r 1 A 1 a t about 2-40 ⁷ 2.45 A by using a f i t t i n g program. The b e s t f i t was obtained f o r 5 A 1 a t 2.60 A ( a = 0.12 A ) and 1 A 1 a t 2.425 A (o = 0.114 A ) . This l a s t d i s t a n c e corresponds e x a c t l y t o d/2 = 2.425 A , t h e d i s t a n c e between t h e A 1 and Mn icosahedra i n t h e Audier and Guyot model. But t h e r e a r e s t i l l only 6 A 1 neighbours, s o we have t r i e d t o f i n d another s u b s h e l l c o n s i s t e n t with t h e EXAFS spectrum. This can be done with A 1 atoms a t 2.75 + 0.05 A. A t t h i s d i s t a n c e 1 t o 5 A 1 atoms can be found according t o t h e a parameter value (o = 0.13 ¹ 0.17 A ) . The r e s u l t i n g r a d i a l d i s t r i b u t i o n of t h e A 1 atoms is asymmetric (18) and compares well with t h e histogram of t h e Mn7A1 d i s t a n c e s i n a (A1 Mn S i ) . We have a l s o considered t h e p o s s i b i l i t y of A 1 and C r f i r s t neighbours. This f i t of the inverse FT of t h e f i r s t peak y i e l d e d a C r - C r d i s t a n c e equal t o 2.59 ; 0.05 A. The e x t r a Cr/Mn s u b s h e l l (Mn-Mn = 2.61 A ) could explain t h e d i f f e r e n c e s obtained i n t h e neutron d i f f r a c t i o n p a t t e r n s ( 1 6 ) .

Figure 4 : Schematic r e p r e s e n t a t i o n of t h e a ( A 1 Mn S i ) s t r u c t u r e constructed with Mackay icosahedra. I t i s a l s o a p o s s i b l e model of t h e icosahedral A 1 (Mn, C r ) a l l o y s . The small c i r c l e s r e p r e s e n t Cr/Mn atoms and t h e big ones t h e A 1 atoms.

DISCUSSION

I t is c l e a r t h a t t h e r e i s not a unique f i t of t h e EXAFS due t o s t r o n g c o r r e l a t i o n s between parameters. Nevertheless, a number of important f e a t u r e s can be e x t r a c t e d from t h e systematic comparison between t h e d i f f e r e n t EXAFS s t u d i e s . F i r s t t h e environment around t h e average Mn/Cr s i t e c o n t a i n s a t l e a s t two s h e l l s , t h e f i r s t d i s t a n c e being 2.55 A. Secondly, t h e second s u b s h e l l ( A 1 o r Mn/Cr) is g e n e r a l l y not taken i n t o account i n t h e t h e o r e t i c a l works ( 3 , 4 ) . This could explain t h e t o o small value found f o r t h e c a l c u l a t e d density.

C8-1008 JOURNAL DE PHYSIQUE

The f a r t h e r neighbourhood a p p e a r s d i f f e r e n t i n t h e s e v e r a l Al-based q u a s i c r y s t a l s and d i f f e r e n t from t h o s e i n a (A1 Mn Si). T h i s c o u l d b e due t o more o r less d i s o r d e r e d b o n d i n g s i n s i d e t h e i c o s a h e d r o n o r t o d i f f e r e n t c o n n e c t i o n s between t h e i c o s a h e d r a .

ACKNOWLEDGMENTS

I t is a p l e a s u r e t o acknowledge P. S a i n f o r t (Aluminium n P e c h i n e y ) , A.M.

F l a n k a n d P . L a g a r d e (LURE) f o r h e l p f u l a n d f r u i t f u l d i s c u s s i o n s .

REFERENCES

1 c BAK, P . , Phys. Rev. L e t t . 56 ( 1 9 8 1 ) 861

2 a SHECHTMAN, D . , BLECH, I . , GRATIAS, D . , C A H N , J . W . , Phys. Rev. L e t t . 5 3 (1984) 1951

3 c AUDIER, M., GUYOT,P., P h i l . Mag. B 3 (1986) L 43

4

-

5 ;:STERN, E.A., MA, Y . , BOULDIN, C.E., PhyS. Rev. L e t t . 55 (1985) 2172 6 ⁿ MARCUS, M.A., CHEN, H.S.. ESPINOZA, G.P., TSAI, C.L.,

S o l i d S t . Commun. 2 ( 1 9 8 6 ) 227

7 * BOYCE, J.B., MIKKELSEN, J.C. J r , BRIDGES, F., EGAMI, T., Phys. Rev. B 3 (1986) 7314

8 ^a SADOC, A . , FLANK, A.M., LAGARDE, P., SAINFORT, P., BELLISSENT, R . , J . P h y s i q u e 3 (1986) 8 7 3

9

-

1 0 ^s; COOPER, M . , ROBINSON, K . , ~ ; t a C r y s t . 20 (1966) 614

11 -; SADOC, A . , EXAFS i n v e s t i g a t i o n of a n amorphous N i , , Zr,, a l l o y . Comparison w i t h n e u t r o n d i f f r a c t i o n i n f o r m a t i o n s . EXAFS and Near Edge S t r u c t u r e I V , F o n t e v r a u d ( 1 9 8 6 ) , t h e s e p r o c e e d i n g s .

1 2 1 MAURER, M . , t o a p p e a r i n J. Phys. F ( L e t t e r ) 1 3 r MA, Y . , STERN, E.A., BOULDIN, C.E., P r e p r i n t 1986 14 ;:ELSER, V . , HENLEY, C.L., Phys. Rev. L e t t . 55 (1985) 2883 1 5

*

p r e p r i n t ( J u n e 1 9 8 6 )

16 ⁷ BELLISSENT, R . , BOUREErVIGNERON, F., SAINFORT, P., I n t e r n a t i o n a l Workshop o n A p e r i o d i c C r y s t a l s , L e s Houches (19861, t o b e p u b l i s h e d i n J. de P h y s i q u e C o l l o q u e s ( J u l y 1986)

17 n SAINFORT, P . , P r i v a t e communication

1 8 n SADOC, A . , LAGARDE, P., SAINFORT, P., s u b m i t t e d t o J . P h y s i q u e ( ~ u n e 1986) 19 * LEE, P .A., BENI, G., PhyS. Rev. B 15 (1 9 7 7 ) 2868 and

TEO, B.K., LEE, P.A., J . Am. Chem. SOC. 101 (1979) 2815 20 ^e MACKAY, A.L., Acta C r y s t . 15 ( 1 9 6 2 ) 916