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THE STRUCTURE OF AMORPHOUS PHOSPHORUS
S. Elliott, J. Dore, E. Marseglia
To cite this version:
T H E STRUCTURE O F AMORPHOUS PHOSPHORUS
++
S.R. E l l i o t t , J.C.
ore'
a n d E. MarsegliaDepartment o f Physical Chemistry, University o f Cambridge, Lensfield Road, Cambridge, U. K .
'~epartrnent of Physics, University o f Kent, Canterbury, U.K.
++Cavendish Laboratory, University o f Cambridge, Madingley Road, Cambuidge, U . K.
Resume
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La s t r u c t u r e du phosphore rouge amorphe a @t@ e t u d i e e en d i f f r a c t i o n neutronique, sur un r e a c t e u r s t a t i q u e e t une source de neutrons pulsee. Les fonc- t i o n s de c o r r e l a t i o n dans l ' e s p a c e r e e l , obtenues par transformee de F o u r i e r des donnees experimentales, o n te t e
cornparees avec l e s r e s u l t a t s de c a l c u l s pour un reseau c o n t i n u a l e a t o i r e t r i p l e m e n t coordonne, r e l a x e dans un mBlange de poten- t i e l s interatomiques l i a n t s e t a n t i l i a n t s . L ' a c c o r d e n t r e l a t h e o r i e e t 1 'expe- r i e n c e e s t assez l i m i t e . Ceci e s t a t r i b u ea
l a presence de d i f f e r e n t s types d ' o r d r e s i n t e r m e d i a i r e s dans l e s o l i d e amorohe, comme par exemple l a formation d'amas de type cage q u i sont c a r a c t e r i s t i q u e s de l a forme monoclinique ( H i t t o r f ) du ohosohore.A b s t r a c t
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The s t r u c t u r e o f amorphous r e d phosphorus has been s t u d i e d by neu- t r o n d i f f r a c t i o n , using both r e a c t o r and pulsed neutron sources. Real-space p a i r c o r r e l a t i o n f u n c t i o n s obtained by F o u r i e r t r a n s f o r m a t i o n o f t h e e x p e r i - mental s c a t t e r i n g data have been compared w i t h those c a l c u l a t e d f o r a three- f o l d coordinated CRN model, which had been energy-relaxed using a combination o f bonding and non-bonding i n t e r a t o m i c p o t e n t i a l s . Only moderate agreement between theory and experiment was found. The discrepancies a r e a s c r i b e d t o t h e presence o f a considerable degree o f intermediate-range o r d e r i n t h e amorphous s o l i d , i n p a r t i c u l a r c o n s i s t i n g o f c a g e - l i k e c l u s t e r s c h a r a c t e r i s t i c o f t h e monoclinic ( H i t t o r f ) form o f phosphorus.I
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INTRODUCTIONThe determination o f t h e s t r u c t u r e o f amorphous s o l i d s using conventional d i f f r a c t i o n experiments alone i s i n general d i f f i c u l t because i n t e r p r e t a t i o n o f t h e s c a t t e r i n g data i s n o t s t r a i g h t f o r w a r d , p a r t i c u l a r l y f o r multicomponent amorphous systems, where t h e measured s c a t t e r i n g i n t e n s i t y i s a s u i t a b l y weighted sum o f c o n t r i b u t i o n s from t h e various types o f i n t e r a t o m i c c o r r e l a t i o n s . Obviously, the problem i s s i m p l e s t f o r an elemental m a t e r i a l where the maximum amount o f s t r u c t u r a l i n f o r m a t i o n can be i n f e r r e d from a s i n g l e s c a t t e r i n g experiment.
This paper r e p o r t s t h e r e s u l t s o f a n e u t r o n - s c a t t e r i n g study o f elemental amor- phous r e d phosphorus, which i s a m a t e r i a l whose s t r u c t u r e i s of i n t e r e s t i n view of t h e wide v a r i e t y o f c r y s t a l l i n e polymorphs which occur. I n p a r t i c u l a r , the question a t i s s u e i s t o what e x t e n t does t h e intermediate-range o r d e r i n t h e amorphous s o l i d
( i f any) r e f l e c t s t r u c t u r a l arrangements c h a r a c t e r i s t i c o f p a r t i c u l a r c r y s t a l 1 in e polymorphs.
C8-350 JOURNAL
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PHYSIQUEthereby forming tubes o f pentagonal cross-section which a r e themselves h e l d t o g e t h e r by Van der Waals' f o r c e s t o form l a y e r s . This s t r u c t u r e has b o t h e c l i p s e d (@ = 0') and semi-staggered ( @ = 70') c o n f i g u r a t i o n s , b u t no staggered bonds.
I 1 - EXPERIMENTAL
Samples o f b u l k r e d a-P, made by thermal conversion from w h i t e P /2/, were used i n t h i s study. Measurements were taken u s i n g b o t h r e a c t o r and pulsed neutron sources. The form r u t i l i z e d t h e D4 d i f f r a c t o m e t e r a t t h e ILL, u s i n g neutrons w i t h wavelength h = 0.59i, and a l s o t h e Curran d i f f r a c t o m e t e r on the Dido r e a c t o r a t AERE, Harwell using A = 1.378 neutrons. The pulsed neutron measurements, made using t h e TSS Mk. I 1 spectrometer a t t h e H e l i o s e l e c t r o n l i n a c , A RE, Harwell, enabled the s c a t t e r i n g data t o be extended t o h i g h values o f
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( = 3 0 k 1 ) ; a l l the data s e t s were combined t o g i v e t h e t o t a l s c a t t e r i n g i n t e n s i t y , I ( Q ) , shown i n Fig. 1. F u r t h e r d e t a i l s o f data c o l l e c t i o n and a n a l y s i s are given elsewhere (Dore, S t e y t l e r , Marseglia and E l l i o t t , t o be published).Fig. 1
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S c a t t e r i n g i n t e n s i t y o f a-P measured u s i n g b o t h r e a c t o r and pulsed neutron sources.I 1 1
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EXPERIMENTAL RESULTSF o u r i e r t r a n s f o r m a t i o n o f t h e f u n c t i o n Q I ( Q ) y i e l d e d t e reduced RDF, G(r), shown i n
B
Fig. 2. Two sharp peaks a r e e v i d e n t a t 2.224 and 3.49,
f o l l o w e d by a s e r i e s of - s u b s i d i a r y peaks a t h i g h e r values o f r. The f i r s t two c o o r d i n a t i o n s h e l l s l y i n g a tRDF o b t a i n e d from t h e X-ray d i f f r a c t i o n s t u d y /4/ i s a l s o shown i n F i g . 3.
Fig.2. Reduced RDF o b t a i n e d f r o m t h e n e u t r o n s c a t t e r i n g i n t e n s i t y o f F i g . 1 compared w i t h t h a t c a l c u l a t e d f o r a CRN model (see t e x t f o r d e t a i l s ) .
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Model
- - - -
This
work
.----.--
Krebs & Grijber
(1967)
40 - 30 - 20 - - 10 --
0-
-10" " " " " " " " " ' " " ' " " " " ' " " ' " ' " ' " " I
b l 2 3 4 5 6 78 P ( A )
F i g . 3. RDF o b t a i n e d f r o m t h e p r e s e n t n e u t r o n s c a t t e r i n g d a t a compared w i t h e a r l i e r X-ray d a t a /4/ and t h e RDF c a l c u l a t e d f o r a CRN model.D e t a i l e d e x a m i n a t i o n o f t h e shape o f t h e second peak i n t h e RDF shows i t t o be d i f f e r e n t f r o m t h a t o f t h e f i r s t and a c o n s i d e r a b l e d i s t o r t i o n f r o m a gaussian l i n e - shape i s found; i t i s b r o a d e r a t t h e base, p a r t i c u l a r l y on t h e l o w - r s i d e . Such a shape c o u l d r e s u l t f r o m an asymmetric bond-angle d i s t r i b u t i o n , P(O), o r even a b i - modal P(O) w i t h t h e main c o n t r i b u t i o n l y i n g a t t h e average bond angle, 0 = 103', w i t h a l e s s e r c o n t r i b u t i o n a t a s m a l l e r angle, O
=
95'. T h i s p o i n t , and a c o n s i d e r a t i o n of t h e peaks i n t h e RDF l y i n g beyond t h e second s h e l l , w i l l b e d i s c u s s e d l a t e r . I V-
MODELLING STUDIESC8-352 JOURNAL
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PHYSIQUEo f a-P was constructed. A 3 - f o l d coordinated " b a l l - a n d - s t i c k " continuous random network (CRN) model, o r i g i n a l l y constructed t o simulate t h e s t r u c t u r e o f a-As /5,6/, was used as a s t a r t i n g p o i n t , and the model was m o d i f i e d by computer means t o a l t e r the average bond angle t o the value c h a r a c t e r i s t i c o f a-P, w h i l s t l e a v i n g the topo- l o g y ( r i n g s t a t i s t i c s etc.) unchanged. The m o d i f i c a t i o n was e f f e c t e d by s u b j e c t i n g the "atoms" i n t h e model t o an energy r e l a x a t i o n procedure i n which b o t h bonding i n t e r a c t i o n s (Keating p o t e n t i a l f o r bond s t r e t c h i n g and bending / 7 / ) and non-bonding i n t e r a c t i o n s (Buckingham o r exp-6 p o t e n t i a l /8/) were used; d e t a i l s o f t h e r e l a x a t i o n procedure are given e l sewhere ( E l 1 io t t , Carter, Marsegl i a and Dore, t o be pub1 ished)
.
The RDF o f t h e energy-relaxed model was c a l c u l a t e d from the atomic coordinates. c o r r e c t e d f o r t h e f i n i t e s i z e o f t h e model, and the r e s u l t i n g RDF i n histogram form was then convoluted w i t h a gaussian t o simulate both thermal and instrumental broad- ening e f f e c t s . Although such a broadening procedure i s i n s u f f i c i e n t t o p e r m i t a d e t a i l e d study o f t h e peak shapes, o n l y a q u a l i t a t i v e comparison o f t h e c a l c u l a t e d curves i s attempted here, and so such a l i m i t a t i o n i s o f l i t t l e account.
The c a l c u l a t e d reduced RDF, G ( r ) , f o r t h e model i s compared w i t h t h e experimen- t a l neutron data i n Fig. 2, and t h e c a l c u l a t e d RDF, J ( r ) , i s compared w i t h b o t h the present neutron and e a r l i e r X-ray /4/ r e s u l t s i n Fig. 3. I t can be seen t h a t t h e r e i s good agreement between t h e model and experimental curves f o r t h e f i r s t two peaks. This, however, i s n o t t o o s u r p r i s i n g , s i n c e the model has 3 - f o l d nearest-neighbour c o o r d i n a t i o n and t h e bond l e n g t h i s scaled t o the experimental value. Furthermore, the average bond angle i s s e t t o the experimental value i n t h e energy r e l a x a t i o n program, and so t h e p o s i t i o n o f t h e second peak i s expected t o match experiment.
V
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DISCUSSIONConsiderable discrepancies between the model and experiment occur, however, a t l a r g e r distances. The most obvious d i f f e r e n c e i s i n t h e average d e n s i t y ; as can be seen from F i g . 3, t h e model has a d e n s i t y 15-20% h i g h e r than e x p e r i m e n t a l l y observed values. Varying the parameters i n the i n t e r a t o m i c p o t e n t i a l s , i n p a r t i c u l a r t h e r e l a t i v e s t r e n g t h o f bonding and non-bonding i n t e r a c t i o n s , gave a t most o n l y a 1% change i n density. The discrepancy must t h e r e f o r e be a s c r i b e d t o a f a i l i n g o f t h e model. The CRN model, as b u i l t , contains o b l a t e voids which a r e a consequence o f the 2D geometry c h a r a c t e r i s t i c of p 3 bonding /6/. Red a-P prepared from w h i t e P /2/ has a s p h e r u l i t e growth morphology /3/, and as a consequence would have a h i g h e r v o i d concentration, and t h e r e f o r e lower density, than an otherwise homogeneous m a t e r i a l . Although t h i s may be one reason f o r the discrepancy i n density, another reason may have t o do w i t h intermediate-range o r d e r (IRO). The CRN model contains no intent-ional IRO, i . e . p a r t i c u l a r r i n g s i z e s o r c l u s t e r s etc.; i f such forms o f I R O were a c t u a l l y present i n the r e a l m a t e r i a l , packing c o n s t r a i n t s would probably ensure a lower o v e r a l l d e n s i t y than f o r an amorphous s t r u c t u r e n o t c o n t a i n i n g such large, we1 1 -d e f i n e d s t r u c t u r a l arrangements.
A f u r t h e r s t r i k i n g d i f f e r e n c e between the model RDF and experiment i s i n t h e r e l a t i v e s i z e and p o s i t i o n o f t h e t h i r d peak; t h e model peak i s much l a r g e r i n height, and l i e s a t a l a r g e r distance, than i s found exp r i m e n t a l l y (see Fig. 2).
The p r i n c i p a l c o n t r i b u t i o n t o t h e t h i r d peak a t r s = 5.3
!i
comes from 3-bondc o r r e l a t i o n s i n semi-staggered o r staggered conformations ( w i t h a r e l a t i v e frequency of ccurrence o f 1:2); e c l i p s e d c o n f i g u r a t i o n s g i v e 3-bond c o r r e l a t i o n s a t 2.85 and 4.41. The CRN model used i n t h i s study does n o t have a random dihedral-angle d i s t r i - bution, b u t staggered c o n f i g u r a t i o n s are approximately t w i c e as probable as e c l i p s e d c o n f i g u r a t i o n s /6/. From t h i s , we may i n f e r t h a t a-P contains a much h i g h e r pro- p o r t i o n o f non-staggered, probably eclipsed, c o n f i g u r a t i o n s than i s present i n the CRN model.
a s c r i b e d e i t h e r t o e c l i p s e d c o n f i g u r a t i o n s w i t h s m a l l e r ( 0 96') bond angles, o r t o semi-staggered c o n f i g u r a t i o n s c o n t a i n i n g a m i x t u r e o f l a r g e and small bond angles i n which
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i s determined by t h e s m a l l e r bond angle.Thus, i t appears t h a t t h e f e a t u r e s i n the RDF o f a-P l y i n g i n t h e range 4-68 a r i s e from a preponderence o f e c l i p s e d and/or semi-staggered c o n f i g u r a t i o n s . I t should be noted t h a t eclipsed c o n f i g u r a t i o n s do not occur i n the orthorhombic b l a c k P s t r u c t u r e , and so the suggestion /4,9/ t h a t t h e IRO i n a-P i s c h a r a c t e r i s t i c o f t h i s polymorph i s t h e r e f o r e u n l i k e l y t o be t r u e . I t i s i n t e r e s t i n g t o note, however, t h a t both e c l i p s e d and semi-staggered ( b u t n o t staggered) c o n f i g u r a t i o n s occur i n the H i t t o r f monoclinic form, which c o n s i s t s o f Pg and Pg c l u s t e r s . We suggest t h a t , on t h e basis o f t h e d i f f r a c t i o n evidence, the IRO i n a-P i s c h a r a c t e r i s t i c o f H i t t o r f ' s P, namely t h a t Ps (and perhaps P9) c l u s t e r s e x i s t i n t h e s t r u c t u r e . P8 u n i t s , i n p a r t i c u l a r , can r e a d i l y form by p o l y m e r i z a t i o n o f two Pb molecules i n t h e w h i t e P precursor, w i t h minimal atomic movement, Confirmatory evidence f o r the presence of Pe o r Pg c l u s t e r s comes a l s o from an a n a l y s i s o f t h e Raman spectrum o f a-P
/ l o / .
V I
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CONCLUSIONSA h i g h - r e s o l u t i o n neutron s c a t t e r i n g study o f r e d a-P has been performed. Compari- son o f the experimental RDF w i t h t h a t o f a CRN model having minimal intermediate- range order (IRO) r e v e a l s s u b s t a n t i a l discrepancies i n t h e r e g i o n o f t h e t h i r d and f o u r t h peaks. It i s suggested t h a t the IRO i n a-P i s s i m i l a r t o t h a t found i n the H i t t o r f , monoclinic form o f P, namely Pa ( o r Ps) c l u s t e r s a r e present.
ACKNOWLEDGEMENTS.
We a r e g r a t e f u l t o Drs. D.C. S t e y t l e r , P. Chieux and E.K. Osae f o r assistance w i t h the d i f f r a c t i o n experiments and t o M r . R.D. C a r t e r f o r assistance w i t h t h e s t r u c t u r a l model 1 ing.
REFERENCES
/1/ Corbridge, D.E.C., "The S t r u c t u r a l Chemistry o f Phosphorus" ( E l s e v i e r : 1974). /2/ a-P samples obtained from Mining and Chemical Products Ltd, Alperton, brembley, U. K.
/3/ Extance, P.and E l l i o t t , S.R., P h i l . Mag. 843 (1981) 469. /4/ Krebs, H. and GrGber, H.U., Z. N a t u r f o r s c K 22(a) (1967) 96. /5/ Greaves, G.N. and Davis, E.A., P h i l . Mag. 29 (1974) 1201.
/6/ Greaves, G.N., E l l i o t t , S.R. and Davis, E . r , Adv. Phys.
8
(1979) 149. /7/ Keating, P.N., Phys. Rev. 145 (1966) 637./8/ Maitland, G.C., Rigby, M.,-Srfiith, E.B. and Wakeham, W.A. " I n t e r m o l e c u l a r Forces" (Clarendon Press : 1981).
/9/ Beyeler, H-U and Veprek, S., P h i l . Mag. 841 (1980) 327.
