werner1977, si-o bond lengths, angles

8/13/2019 Werner1977, Si-O Bond Lengths, Angles

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Acta C rys t . ( 1 9 7 7 ) . B 3 3 , 2 6 1 5 - 2 6 1 9

Silicon-Oxy gen Bond Lengths Bridging Ang les Si- O --S i and SyntheticLow TridymiteBY W E RNE R H. BAUR

Dep ar tme n t o f Geo log ica l Sc iences , Un ivers i ty o f I l l ino is , C h icago , I L 6 0 6 8 0 , U S AReceived 19 January 1977; accepted 16 February 1977)

The c rys ta l s t ruc ture of syn the t ic low tr idymite has been re- re fined to an R = 0 .076 for 4117 F (obs) w ithda ta co l lec ted by Kato & Nukui [Acta Cryst. (1976) , B32, 2486-2491] . The s t ruc ture is monoc l in ic , spacegroup Cc, with a = 18.494 (8) , b = 4.991 (2), c = 23 .758 (8) A, f l = 105-79 (2) , Z = 12. The m ean S i- Odis tance measures 1 .597 (10) A and the mean S i- O -S i angle is 150 .0 (7 .4) . The s t ruc ture of th is syn the t icC c low tr idymite and th at of the recently ref ined m eteoritic low tr idymite are identical within the margin o fexperim ental erro r . A regression ana lysis of dat a from tr idym ite, qua rtz , cr is tobalite , coesite , zunyite , hemi-mo rphite , benitoite , beryl, em erald, Sc2Si207, Yb2Si207 and Er2Si207 show s that the correlation coeff icientb e twe e n th e S i - O b o n d l e n g th a n d th e n e g a tiv e s e ca n t o f th e a n gle S i - O - S i i s 0 . 1 9 ; c o n s eq u e n t ly o n ly 4 %o f th e v a r ia t io n in S i - O c a n b e e x p la ine d b y th e d e p e n de n c e o n - s e c ( S i - O - S i ) . T h e r e fo r e the n u llh y p o th e s i s th a t th e S i - O b o n d l e n g th s d o n o t d e p e n d o n - s e c ( S i - O- S i ) c a n b e a c c e p te d a t t h e 2 . 5 % r i s kleve l. For a g iven S i- O bond length the lower limit o f possib le S i- O -S i angles is de te rmined by the shor tes tposs ib le non-bonding Si- Si contac t . There tbre th is lower l imit is a funct ion of the S i -O bond length and notvice versa as required by n-bonding theory .

2 6 1 5

I n tr o d u c t io n

T h e c r y s t a l s t r u c t u r e o f m e t e o r i t i c l o w t r id y m i t e h a sr e c e n t l y b e e n s o l v e d b y D o l l a s e & B a u r ( 1 9 7 6 ) i n s p a c eg r o u p Cc, wi th a = 1 8 . 5 2 4 ( 4 ) , b = 5 . 0 0 3 2 ( 1 5 ) , c =2 3 . 8 1 0 ( 8 ) A , fl = 1 0 5 . 8 2 ( 2 ) , Z = 1 2. T h e r e f in e me n to f 1 2 6 0 M o K c t r e f le c t i o n s g a v e a n R = 0 - 0 6 9 . T h e 4 8i n d i v i d u a l , c r y s t a l l o g r a p h i c a l l y i n d e p e n d e n t S i - O d i s -t a n c e s r a n g e f r o m 1 . 5 5 t o 1 . 6 5 A , w i t h a m e a n v a l u e o f1 . 6 01 A , a n d a s t a n d a r d d e v i a t i o n f r o m t h i s m e a n o f0 . 0 1 7 A . K a t o & N u k u i ( 1 9 7 6 ) d e t e r m i n e d th es t r u c t u r e o f t h e c o r r e s p o n d i n g s y n t h e t i c t r i d y m i t e a n dr e f in e d it f o r 4 1 1 7 M o Kc t r e f l e x io n s to R = 0 . 0 8 5 ICe,a = 1 8 . 4 9 4 ( 8 ) , b = 4 . 9 9 1 ( 2 ) , c = 2 5 . 8 3 2 ( 8 ) A , f l =1 1 7 . 7 5 ( 2 ) , Z = 1 2 ]. T h e 4 8 i n d i v i d u a l S i - Od i s t a n c e s r a n g e f r o m 1 . 5 5 2 t o 1 . 6 3 4 A , w i t h a m e a nv a l u e o f 1 . 5 9 5 ( 2 0 ) A . T h e d a t a u s e d b y D o l l a s e &Ba u r we r e c o l l e c te d in a r a n g e u p to s in 0 /2 = 0 . 7 A - ~ .T h e K a t o & N u k u i d a t a r a n g e u p t o a s in 0 / 2 = 1 . 0A - ~, a n d th e i r r e f in e me n t s h o u ld b e m o r e r e l i a b le .H o w e v e r , t h e s t a n d a r d d e v i a t i o n f r o m K a t o & N u k u i ' sm e a n S i - O v a l u e i s l a r ge r t h a n f o r t h e m e a n v a l u eo b t a i n e d b y D o l l a se & B a u r . B e c a u s e o f c o m p u t e r -m e m o r y l i m i t a t i o n s K a t o & N u k u i ( 1 9 7 6 ) c o u l d n o tr e f i n e a l l p a r a m e t e r s i n t h e s a m e c y c l e . T h i s m i g h t h a v eh i n d e r e d p r o p e r c o n v e r g e n c e .

R e r e f i n e m e n t o f s y n t h e t i c t r i d y m i t eT h e t w o d i f f e r e n t u n i t c e l l s u s e d f o r m e t e o r i t i c a n ds y n t h e t i c t r i d y m i t e a r e r e l a te d b y th e t r a n s f o r m a t i o nm a t r ix ( 1 , 0 , 0 / 0 , - 1 , 0 / - 1 , 0 , - 1 ) . S i nc e t h e c h oi c e o for ig in in C e i s a r b i t r a r y f o r x a n d z t h e r e l a t i o n s h i p s f o rt h e p o s i t i o n a l p a r a m e t e r s a r e xo~ = XKN -- ZKN --0 26 06 , YI~B = 0 7 5 - - YKN and ZDB = - -ZKN (wh ere DBa n d K N r e f er t o t h e D o l l a s e & B a u r a n d K a t o & N u k u is e t ti n g s r e s p e c t i v e ly ) . T h e r e - r e f i n e m e n t o f K a t o &N u k u i ' s d a t a w a s p e r f o r m e d i n t h e s e tt i n g o f D o l l a s e &Ba u r . I n th is s e t t in g th e d im e n s i o n s o f th e u n i t c el l o fs y n th e t i c t r id y m i te a r e : a = 1 8 . 4 9 4 ( 8 ) , b = 4 . 9 9 1 ( 2 ) ,c = 2 3 . 7 5 8 ( 8 ) A , / / = 1 0 5 . 7 9 ( 2 ) . T h e s c a t t e r i n gf a c t o r s o f S i 24 a n d O - w e r e t a k e n f r o m I n t e r n a t i o n a lT a b l e s f o r X - r a y C r y s t a l l o g ra p h y ( 1 9 7 4 ) . A s imu l -t a n e o u s , f u l l - m a t r i x , u n i t- w e i g h t r e f i n e m e n t o f al l 32 3a d j u s t a b l e p a r a m e t e r s y i e l d e d in th r e e c y c l e s a n R =0 . 0 7 6 f o r 4 1 1 7 F , , h ~ .

D i s c u s s i o n o f t h e s t ru c t u reT h e n e w p o s i ti o n a l p a r a m e t e r s ( T a b le 1 ) l e a d to S i - Od i s t a n c e s ( T a b l e 2 ) r a n g i n g f r o m 1 . 5 7 6 t o 1 . 6 2 2 A ,w i t h a m e a n o f 1 . 5 9 7 ( 1 0 ) A . T h e r a n g e o f 0 . 0 4 6 A isa p p r e c i a b l y s m a l l e r t h a n f o r e it h e r t h e D o l l a s e & B a u r( 0 . 1 0 A ) o r t he K a t o & N u k u i ( 0 . 0 8 2 A ) r e fi n e m e n t s.I t is o n l y s l ig h t l y l a r g e r t h a n t h e r a n g e o f 0 . 0 3 3 A


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2 6 1 6 S Y N T H E T I C L O W T R I D Y M I T ETable 1. S y n t h e t i c l o w t r i dy m i t e : p o s i ti o n a l a n d t h e r m a l p a r a m e t e r s ( x 10 4)

The temperature factor is exp[ -(fl , th 2 + f l 2 , k 2 + f l 3 ~ l 2 + 2 f l , , h k + 2 f l , ~ h l + 2 f 1 2 . ~ k l) ] . KN indicates the numbers of the atoms used byKato & Nukui (1976). The x and z parameters of Si(11) were not varied, in order to define the origin (*).

K N # x y z B I I B 2 2 B 3 3 8 1 2 ~ 1 3 ~ 2 3

Si(1) 6 54 77 (2 ) 543 3(7 ) 565 3(2 ) 3(1) 87(7) 4(.3) 0(2) 1(.3) 2 2 )S i ( 2 ) 4 7 0 0 3 ( 2 ) 9 4 5 8 ( 7 ) 7 3 8 1 ( 2 ) 7( 1 ) 7 3 ( 8 ) 4 ( . 3 ) 3 ( 2 ) 2 ( . 3 ) 7 ( 2 )Si(3) 5 4171(2) 5508 (7 ) 6236(2 ) 6(1) 82(7) 4(.3) -1(2) 1(.3) -8(2)S i ( 4 ) 3 5 7 2 4 ( 2 ) 0 4 6 4 ( 7 ) 7 9 7 7 ( 2 ) 8 ( 1 ) 7 4 ( 7 ) 3 ( . 3 ) 5 ( 2 ) i ( . 3 ) - 4 ( 2 )Si(5) 10 92 19 (2 3 55 03 (7 ) 6987(2) 6(1) 79(8) 3(.3) -4(2) 1 (.3) -1(2)Si(6) 12 76 22 (2 ) 94 14 (7 ) 53 93 (2 ) 6(1) 77(8) 4(.3) -1(2) 0(.3) -5(2)Si(7) 9 79 97 (2 ) 4474(7) 7670(2) 7(1) 85(8) 4(.3) 0(2) 3(.3) 7(2)S i ( 8 ) i i 6 4 2 8 ( 2 ) 0 3 9 3 ( 7 ) 6 0 4 2 ( 2 ) 5 ( i ) 7 6 ( 7 ) 3 ( . 3 ) 6 ( 2 ) 1 ( . 3 ) - 1 (2 )S i ( 9 ) 2 8 4 9 3 ( 2 ) 4 6 1 4 ( 7 ) 9 0 3 0 ( 2 ) 5 ( I ) 9 4 ( 8 ) 3 ( . 3 ) - 2 ( 2 ) 0 ( . 3 ) I ( 2 )S i ( I 0 ) 7 9 4 5 4 ( 2 ) 9 6 3 7 ( 7 ) 9 3 7 5 ( 2 ) 6 ( 1 ) 7 2 ( 8 ) 3 ( . 3 ) - 5 ( 2 ) 0 ( . 3 ) 0 ( 2 )S i ( l l ) 1 7 2 1 6 5 6 0 7 ( 7 ) 9 6 1 8 5 ( 1 ) 5 4 ( 8 ) 4 ( . 3 ) 2 ( 2 ) 0 ( . 3 ) 2 ( 2 )Si (12) 8 56 63 (2 ) 54 57 (7 ) 8716(2) 6(1) 88(8) 3(.3) -1(2) 2(.3) -1(2)O ( i ) 5 5 7 2 3 ( 6 ) 3 4 7 1 ( 1 8 ) 8 2 0 4 ( 4 ) 2 0 ( 3 ) 1 3 7 ( 2 9 ) 7 ( 1 ) 3 ( 7 ) 5( i ) - 4 ( 5 )0 ( 2 ) 4 5 6 6 5 ( 5 ) 8 4 5 7 ( 1 5 ) 8 4 9 4 ( 4 ) 1 8 ( 2 ) 4 1 ( 2 0 ) 9 (1 ) 5 ( 5 ) 7 ( I ) 5 ( 4 )0 ( 3 ) 1 7 2 9 7 ( 5 ) 1 3 9 4 ( 1 6 ) 4 8 6 4 ( 3 ) 2 4 ( 3 ) 6 0 ( 2 3 ) 5 ( 1 ) ] ( 6 ) 0 ( I ) 3 ( 4 )0(4) 2 74 88 (5 ) 641 5(1 6) 516 0(4 ) 13(2) 68(23) 9(1) 3(5) -2(1) 0(4)O ( 5 ) 8 4 1 3 3 ( 6 ) 3 5 0 4 ( 1 6 ) 6 7 5 2 ( 4 ) 2 5 ( 3 ) 5 2 ( 2 2 ) 9 (1 ) 1 ( 7 ) 8 ( 2 ) - 4 ( 4 )0 ( 6 ) 7 4 0 9 6 ( 5 ) 8 5 0 5 ( 1 6 ) 6 4 4 4 ( 3 ) 1 6 ( 2 ) 8 3 ( 2 3 ) 6 ( 1 ) - 7 ( I ) 0 ( I ) - 1 2 ( 4 )0 ( 7 ) 1 4 8 7 4 8 ( 4 ) 1 6 2 5 ( 1 6 ) 9 2 2 5 ( 4 ) 6 ( I ) 1 0 8 ( 2 5 ) 9 ( I ) 1 0 ( 5 ) 2 ( I ) 1 0 ( 4 )0(8) 1s 9i30(5) 663 3(1 6) 9375(3) i4(2) 76(23) 7(i ) -i5(S) o(i ) -1(4)0(9) 17 77 14 (5 ) 148 4(1 8) 756 6(4 ) 12(2) 98(26) 14(2) -8(6) 2(2) -4(6)O ( i 0 ) 1 6 7 3 0 2 ( 5 ) 6 4 4 2 ( 1 6 ) 7 4 3 7 ( 4 ) 1 1 ( 2 ) 6 2 ( 2 2 ) 1 2 ( 2 ) - 2 ( 5 ) - I ( I ) - 1 0 ( 5)O ( i i ) 2 0 6 1 7 7 ( 4 ) 3 3 9 1 ( 1 4 ) 5 8 5 6 ( 3 ) 8 ( 2 ) 4 8 ( 2 0 ) 6 ( I) 8 ( 4 ) - l ( 1 ) 3 ( 4 )O ( 1 2 ) 1 9 5 7 8 9 ( 5 ) 8 4 1 0 ( 1 6 ) 5 6 7 0 ( 4 ) 1 4 ( 2 ) 7 7 ( 2 4 ) i 0 ( I ) - 5 ( 6 ) ] ( 1 ) 8 ( 5 )O ( 1 3 ) 1 2 4 9 5 8 ( 4 ) 5 1 0 9 ( 1 8 ) 6 0 8 3 ( 4 ) 6 ( I ) 2 8 0 ( 4 6 ) 8 ( 1 ) 4 ( 6 ) 4 ( 1 ) - 2 ( 5 )O ( 1 4 ) 9 3 5 0 6 ( 4 ) 4 9 2 0 ( 1 7 ) 5 6 5 3 ( 4 ) 5 ( 1 ) 2 5 1 ( 4 4 ) 7 ( 1 ) - ] 0 ( 5 ) 1 ( 1 ) - 2 0 ( 5 )0(15) 18 6524(5) 000 9(2 1) 672 1(4 ) 10(2) 300( 59 ) 6(1) 21(7) 1(1) 16(5)0(16) 11 6490(5) 99 45 (21) 7809(4) 11(2) 348(51) 5(1) 3(7) 4(1) -8(5)0(17) 23 86 07 (6 ) 497 0(2 2) 7324(5 ) 22(3) 311( 50) 12(2) -28(8) 14(2) -11(0)O ( 1 8 ) 1 5 8 3 7 7 ( 6 ) 5 0 0 8 ( 1 9 ) 8 3 4 1 ( 4 ) 2 0 ( 3 ) 2 8 4 ( 5 7 ) 3 ( 1 ) 8 ( 8 ) 2 ( i ) ( I( 5)O ( 1 9 ) 6 5 0 4 0 ( 5 ) 0 0 1 7 ( 2 0 ) 7 4 0 8 ( 4 ) 1 4 ( 2 ) 2 5 0 ( 3 6 ) 8 ( I ) 6 ( 7 ) - 2 ( 1 ) - 9 ( 5 )0 ( 2 0 ) 3 6 3 5 5 ( 4 ) 4 9 7 9 ( 1 8 ) 9 2 7 9 ( 4 ) 4 ( 1 ) 2 4 0 ( 4 5 ) 7 ( 1 ) - 4 ( 5 ) - l ( 1 ) I i ( 5 )O ( 2 1 ) 2 2 9 9 0 0 ( 5 ) 9 8 9 8 ( 2 1 ) 8 8 8 7 ( 4 ) 8 ( 2 ) 3 3 3 ( 5 2 ) 5 ( 1 ) - 1 3 ( 6 ) l ( 1 ) 4 ( 5 )0 ( 2 2 ) 2 1 5 0 0 3 ( 5 ) 4 7 4 1 ( 1 6 ) 4 9 9 9 ( 4 ) 8 ( 2 ) 1 6 8 ( 2 4 ) 4 ( 1 ) 3 ( 6 ) 2 ( I ) - I ( 5 )0 23) 24 72 19 5) 988 2 17) 5902 4) 9 2) 199 37) 7 1) 9 5) 2 1) -6 4)0 24) 10 77 12 5) 8206 20) 916 3 4) 9 2) 256 40) 9 1) 8 0) 6 1) 14 5)

obs e rv ed fo r S i - O d i s t anc es in we l l re f ined S iO 4 t e t ra -hedra in which a l l O a toms a re b r idg ing be tween two S ia toms each ( s ee en t r i e s wi th NC = 4 in T ab le 3 ) . T hem e a n c h a n g e i n S i - O b o n d l e n g t h s a c h i e v e d b y th e r e-r e f in e m e n t is 0 . 0 1 2 / k , w h i c h i s m o r e t h a n t h e e s t i m a t e ds t a n d a r d d e v i a t i o n f o r a n i n d i v i d u a l S i - O b o n d o f0 . 0 0 8 / k r e p o r t e d b y K a t o N u k u i ( 1 9 7 6 ) . S i n ce t h es t a n d a r d d e v i a t i o n f r o m t h e m e a n o f t h e s e b o n d l e n g t h si s now ha l f a s l a rge a s i t was be fo re the re - re f inem ent , iti s be l i eved tha t the new re s u l t s a re phys ica l lym e a n i n g f u l . K a t o N u k u i ( 1 9 7 6 ) n o t e d t h e l a r g et h e r m a l a m p l i t u d e s o f t h e i r a t o m s O ( 1 1 ) , O ( 1 2 ) a n dO ( 1 8 ) a n d s u g g e s t e d t h a t t h e s e m i g h t b e d u e t op o s i t io n a l d i s o r d e r . T h e r e - r e fi n e m e n t o f t h e i r d a t a d o e sn o t r e v e a l a n y t h i n g p a r t i c u l a r a b o u t t h e t h e r m a lp a r a m e t e r s o f O ( 1 3 ) , O ( 1 5 ) a n d O ( 1 6 ) ( u s i n g t h en u m b e r i n g s y s t e m o f T a b l e 1 ). I t is r e m a r k a b l e t h a t i nt h e K a t o N u k u i r e f i n e m e n t t h e r a t i o b e t w e e n t h el a r g e st a n d t h e s m a l l e s t f i n p a r a m e t e r o f t h e O a t o m s i s765 , whereas a f t e r re - re f inement th i s ra t io i s reduced to

8 o r b y t w o o r d e r s o f m a g n i t u d e . T h e r e f o r e i t i s n o tn e c e s s a r y t o a s s u m e d i s o r d e r f o r t h e s e a t o m s . A nins pec t ion o f the fl p a r a m e t e r s o f th e O a t o m s r e v e a lst h a t O ( 1 ) t o O ( 1 2 ) h a v e a s m a l l t h e r m a l a m p l i t u d epa ra l l e l to the b ax i s , whe reas the rema in ing O a toms ,O(13) to 0 (24) , have a h igh ampl i tude in th i s d i rec t ion .T h e l a t t e r g r o u p c o r r e s p o n d t o t h e b r i d g i n g O a t o m sin the ch a ins o f S iO 4 t e t rah edra runn ing pa ra l l e l to theps eu doh exag ona l ax i s , [2011 [ s ee F ig . 1 in Dol la s eBaur (1976)1 .W i t h t h r e e e x c e p t i o n s t h e S i - O d i s t a n c e s a n d t h eS i - O - S i a n g l e s i n m e t e o r i t i c l o w t r i d y m i t e ( D o l l a s eBaur , 1976) and in the re - re f ined s yn the t i c lowt r idym i te a re wi th in two poo led e . s . d . ' s o f each o the r .T h e e x c e p t i o n s a r e : S i ( 2 ) - O ( 1 5 ) a n d t h e a n g l e s a r o u n dO(15) and O(18) . T h i s c los e s imi la r i ty be tween there s u l t s o f the re f inements ind ica te s tha t the s t ruc tu re sindeed a re iden t i ca l , even though the i r un i t -ce l l con-s tan t s d i f fe r s l igh t ly : up to s ix t imes the e s t ima teds t a n d a r d d e v i a t io n s .


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W E R N E R H . B A U R 2 6 1 7T able 2 . S y n t h e t i c low t r idymi te , S i - O bond leng ths , S i - O - S i a n g l es a n d S i - S i d is tances(1 ) S i O d i s t a nc e s (A) (me a n e .s .d . 0 -008 A )

S i ( 1 ) - O ( 1 3 ) 1 - 5 89 S i ( 5 ) - O ( 1 7 ) 1 - 5 76 S i ( 9 ) - O ( 2 4 ) 1 . 5 8 8O ( 1 2 ) 1 . 5 9 0 0 ( 5 ) 1 .5 9 1 0 ( 7 ) 1 . 5 9 50 ( 2 2 ) 1 . 6 0 0 O ( 1 9 ) 1 . 5 9 4 0 ( 8 ) 1 . 5 9 6O ( 1 1 ) 1 . 6 15 0 ( 6 ) 1 . 5 9 8 O ( 1 8 ) 1 . 6 0 4m e a n 1 . 5 9 9 m e a n 1 . 5 9 0 m e a n - 5 9 6S i ( 2 ) - O ( i 6 ) 1 . 5 8 6 S i ( 6 ) - O ( 3 ) 1 . 5 8 4 S i ( 1 0 ) - O ( 2 2 ) 1 . 5 8 4O ( 1 0 ) - 5 9 7 0 ( 4 ) 1 . 5 9 2 O ( 2 1 ) 1 . 6 0 0O ( 1 5 ) 1 . 6 0 2 0 ( 2 3 ) 1 . 5 9 9 0 ( 7 ) 1 . 60 1O ( 9 ) 1 . 6 2 2 O ( 1 4 ) 1 . 6 03 O ( 8 ) - 6 1 5m e a n 1 . 6 0 2 m e a n 1 -5 9 5 m e a n 1 . 6 0 0S i ( 3 ) - O ( 6 ) 1 . 5 9 3 S i ( 7 ) - O ( 9 ) 1 . 5 7 8 S i ( 1 1 ) - O ( 3 ) 1 . 5 9 9O ( 5 ) I . 5 9 9 O ( 1 8 ) 1 . 58 1 0 ( 4 ) 1 . 6 0 6O ( 1 3 ) 1 . 6 0 6 O ( 1 7 ) 1 . 5 8 6 0 ( 2 0 ) 1 - 6 08O ( 1 4 ) i . 6 0 8 O ( 1 0 ) I . 5 9 2 0 ( 2 4 ) 1 . 6 0 9m e a n I . 6 0 2 m e a n 1 . 5 8 4 m e a n 1 . 6 0 6S i ( 4 ) - O ( 1 6 ) 1 . 59 4 S i ( 8 ) - O ( 1 5 ) 1 .5 8 5 S i ( 1 2 ) - 0 ( 2 ) 1 . 58 8O ( 1 ) 1 . 5 9 4 O ( 1 1 ) 1 . 5 9 3 0 ( 2 1 ) 1 . 5 9 6O ( 1 9 ) 1 . 5 9 6 O ( 2 3 ) 1 . 6 0 6 0 ( 2 0 ) 1 . 5 9 70 ( 2 ) 1 .6 1 1 O ( 1 2 ) 1 . 6 0 9 O ( I ) 1 . 5 9 8me a n 1 . 599 me a n .598 me a n 1 - 595

( 2) S i - O - S i a n g le s (o )S i ( 4 ) - - O ( l ) - S i ( l 2 ) 1 4 8 .0 3 . 0 6 9 S i ( 1 ) - O ( 1 3 ) - S i ( 3 )S i (l 2 ) - O ( 2 ) - S i ( 4 ) 1 4 7 .8 3 . 0 7 4 S i ( 6 ) - O ( 1 4 ) - S i ( 3 )S i ( 6 ) - - O ( 3 ) - S i ( 1 1 ) 1 4 8 .5 3 . 0 6 3 S i ( 8 ) - O ( 1 5 ) - S i ( 2 )S i ( 6 ) - O ( 4 ) - S i ( l 1 ) 1 4 8 .9 3 . 0 8 0 S i ( 2 ) - O ( 1 6 ) - S i ( 4 )S i ( 5 ) - O ( 5 ) - S i ( 3 ) 1 4 6 .9 3 . 0 5 8 S i ( 5 ) - O ( 1 7 ) - S i ( 7 )S i ( 3 ) - O ( 6 ) - S i( 5) 1 46 -3 3 . 0 5 4 S i ( 7 ) - O ( 1 8 ) - S i ( 9 )S i ( 9 ) -O ( 7 ) - - S i (1 0 ) 1 4 3- 4 3 . 0 3 4 S i ( 5 ) - O ( 1 9 ) - S i ( 4 )S i ( 9 ) - O ( 8 ) - S i ( 1 0 ) 1 4 3- 9 3 - 0 53 S i ( 1 2 ) - O ( 2 0 ) - S i ( l 1 )S i ( 7 ) - O ( 9 ) - S i ( 2 ) 1 4 7. 3 3 - 0 7 0 S i ( 1 2 ) - O ( 2 1 ) - S i ( 1 0 )S i ( 7 ) - O ( 1 0 ) - S i ( 2 ) 1 4 7 .0 3 - 0 5 8 S i ( 1 0 ) - O ( 2 2 ) - S i ( l )S i ( 8 ) - O ( l 1 ) - S i ( l ) 1 4 5 .6 3 . 0 6 4 S i ( 6 ) - O ( 2 3 ) - S i ( 8 )S i ( l ) - O ( 1 2 ) - S i ( 8 ) 1 4 2 .7 3 . 03 1 S i ( 9 ) - O ( 2 4 ) - S i ( 1 1 )m e a n s

( m e a n e . s .d . 0 . 6 ) a n d c o r r e s p o n d i n g S i - S i d i s t an c e s ( A ) ( m e a n e . s .d . 0 . 0 0 4 A )5 1 . 2 3 . 0 9 54 5 . 2 3 . 0 6 45 3 . 7 3 . 1 0 35 5 . 9 3 . 1 1 07 9 . 1 3 . 1 6 255 .3 3 .1115 5 . 5 3 . 1 1 748 .1 3 -0814 9 . 8 3 . 0 8 55 5 . 4 3 . 1 1 04 4 . 8 3 - 0 5 65 0 . 8 3 - 0 9 35 0 . 0 3 . 0 7 9

A n g le S i O S i v r s u s distance S i OI n n u m e r o u s c r y s t a l s t r u c t u r e s i n d i v i d u a l b o n d l e n g t h sS i - O d e p e n d o n th e b o n d - st r e n g th v a r i a ti o n A p O )of the O a tom s (Bau r , 1970 , 1976) . In ca s es whereA p O ) = 0 . 0 t h e b o n d - l e n g t h v a r i a ti o n o b v i o u s l y c a n n o tdepend on Ap(O) ; s uch ins tances a re us e fu l fo rs tudy ing o the r bond ing e f fec t s (Baur , 1971) . Int r i d y m i t e t h e r e a r e 1 2 c r y s t a l l o g r a p h i c a l l y in d e p e n d e n tf o u r - c o n n e c t e d S i O 4 t e t r a h e d r a i n w h i c h a l l O a t o m sa re va lence -ba lanced ; tha t i s the i r A p O ) i s ze ro . T hes e12 t e t rahedra can be added to the f ive s uch t e t rahedraprev ious ly known in the l i t e ra tu re ( s ee T ab le 3 ) in o rde rt o t es t th e d e p e n d e n c e o f in d i v i d u al S i - O b o n d l e n g t h so n t h e n e g a ti v e s e c a n t o f t h e b r i d g i n g a n g l e S i - O - S i ,a s d i s cus s ed by Gibbs , Hami l , L ou i s na than , Ba r te ;1 &Yow (1972) . In add i t ion th i s co r re la t ion was t e s t ed fo ra d a t a s e t w h i c h i n c l u d e d n o t o n l y t h e t e t r a h e d r a f r o mt r idymi te , low qua r tz , low c r i s toba l i t e , coes i t e andz u n y i t e , b u t a l s o S i - O b o n d s t o c h a r g e - b a l a n c e d Oa toms in s eve ra l d i s i l i ca te s , r ing s i l i ca te s and ther e m a i n i n g S i - O b o n d i n z u n y i t e ( T a b l e 3 ) . I n e i t h e rcas e the cor re la t ion coe f f i c i en t s a re sma l l (13 and 19 )

a n d t h e s l o p e o f t h e S i - O b o n d l e n g t h w i t h th e n e g a t i v es e c a n t ( s e e T a b l e 4 ) i s m u c h s m a l l e r t h a n f o u n d b yG i b b s et al. ( 1 9 7 2 ) . T h e n u l l h y p o t h e s i s ( t h a t t h ecor re la t ion coe f f i c i en t and the s lope equa l ze ro ) can beaccep ted a t the 0 . 025 r i s k l eve l becaus e ne i the r va lue o fI tl exceeds t (77 , 0 . 0 5) ,-~ t (6 6 , 0 . 02 5) ~ 1 . 99 (one - ta i l edte s t) . F or the l a rge r s amp le , I l l ba re ly reachest (7 7 , 0 . 05 ) ~ 1 . 67 . T h i s i s a s ma l l cons o la t ion s ince l e s st h a n 4 o f t h e v a r i a t i o n s i n S i - O a r e e x p l a i n e d b y t h ed e p e n d e n c e o n s e c ( S i - O - S i ) . T h e d i f f e r e n c e b e t w e e nthe two re s u l t s i s pa r t ly due to the inc lus ion o f thez u n y i t e d a t a ( L o u i s n a t h a n & G i b b s , 1 9 7 2 ), w h i c h w e r en o t p r e s e n t i n t h e d a t a s e t a n a l y z e d b y G i b b s et a l .A c t u a l l y t h e c o r r e l a t i o n w o u l d b e f a i r if t h e d a t a f o rzuny i t e , E r2S i20 v and Yb2S i20 v were no t inc luded (F ig .1 ) . Cons ide r ing the p re s en t ly ava i l ab le empi r i ca le v i d e n c e , h o w e v e r , t h e S i - O vs s e c ( S i - O - S i ) c o r -r e l a t i o n c a n n o t b e v i e w e d a s a g e n e r a l p r o p e r t y o fcha rge -ba lanced b r idg ing O a toms in s i l i ca te s .

O ' K e e f f e & H y d e ( 1 9 7 6 ) h a v e r e c e n t l y p o i n t e d o u tt h a t b r i d g i n g a n g l e s b e tw e e n t e t r a h e d r a l g r o u p s o f Siand o th e r f i r s t, s econd and th i rd ro w e leme nts ins t r u c t u r e s o f c r i s t o b a l i t e t y p e d e p e n d m o s t l y o n t h e


4/5

2 6 8 S Y N T H E T I C L O W T R I D Y M I T E

T a b l e 3 . I n d i v i d u a l d i s t a n c e s S i - O a n d S i - S i ( / k ) a n d a n g l e s S i - O - S i ( ) in co , s ta l s t ruc tures in which a l l 0a t o m s a r e c h a r g e - b a la n c e d l A p ( O ) = 0 . 0 ]T h e c o n n e c t i v i t y o f t h e S i O 4 t e t r a h e d r a , N C , i s t h e n u m b e r o f b r id g i n g ( S i - O - S i ) O a t o m s p e r t e t r a h e d r o n . T h e e s t i m a t e d s t a n d a r dd ev ia t io n s o f al l S i - O b o n d s a r e 0 . 0 1 0 /k o r s ma l l e r . A ll d i s t an ces an d an g le s h av e b een r eca lcu la t ed f r o m th e p o s i t io n a l p a r am e te r se t c . i n th e o r ig in a l p ap e r s .

C o m p o u n d S i - O1.601C r i s to b a l i t e ' 1 .608Lo w q u a r t z 2 1 . 6 0 31.6151 . 5 9 81 . 6 0 81.6071.619C o es i t e 3 1 .5981.6251.6311 . 6 1 7

S i - O - S i S i - S i N C C o m p o u n d S i - O S i- O - - Si S i - S i N C1 4 6 . 8 3 . 0 7 6 4 / 1 . 6 2 8 1 8 0 . 0 3 . 2 5 8 41 4 6 . 8 3 . 0 7 6 4 Zu n y i t e4 / 1 . 6 3 0 1 8 0 . 0 3 - 2 5 8 1143.6 3 .05 7 4 Yb2Si2075 1 .626 180.0 3 .252 1143.6 3-05 7 4 Er2Si2075 1 .632 180.0 3 .265 1180.0 3 .196 4 Sc2Si2Ov6 1 . 6 0 4 1 8 0 - 0 3 . 2 0 8 11 4 3 . 8 3 . 0 5 6 4 H em imo r p h i t e 7 1 . 6 2 7 1 5 0 . 4 3 - 1 4 5 1145-0 3-077 4 Benito i te8 / 1 .630 132.9 3 .005 21 4 5 . 0 3 . 0 7 7 4 / 1 . 6 4 8 1 3 2 . 9 3 . 0 0 5 21 5 0 . 5 3 . 1 1 6 4 / 1 . 5 9 4 1 6 8 . 8 3 . 1 7 4 2150.5 3 .11 6 4 Beryl9 / 1 .595 168.8 3 .17 4 21 3 6 . 1 3 . 0 1 2 4 Emer a ld 9 [ 1 . 5 8 5 1 6 9 . 3 3 - 1 7 6 2136.1 3 .01 2 4 [ 1 .604 169.3 3 .17 6 2

R ef e r en ces : ( 1 ) D o l l a s e ( 1 9 6 5 ) . ( 2 ) Zach a r i a s en & P le t t in g e r ( 1 9 6 5 ) . ( 3 ) A r ak i & Zo l t a i ( 1 9 6 9 ) . ( 4 ) Lo u i s n a th an & G ib b s ( 1 9 7 2 ) .( 5 ) S mo l in & S h ep e lev ( 1 9 7 0 ) . ( 6 ) S mo l in , S h ep e lev & T i to v ( 1 9 7 3 ) . ( 7 ) M cD o n a ld & C r u ick s h an k ( 1 9 6 7 ) . ( 8 ) F i s ch e r ( 1 9 6 9 ) . ( 9 ) G ib b s ,B r e c k & M e a g h e r ( 1 9 68 ) .

T a b l e 4 . R e g r e s s i o n e q u a t i o n s f o r S i - O on- s e c ( S i - O - S i ) : source o f da ta , sam ple s i z e , in te rcep ta) , s lope b) , corre lat ion coef f ic ien t r ) , per cen tv a r i a t i o n e x p l a i n e d ( ) , I lD ata J Tab le s 2 an d 3 G ib b s e t a l . ( 1 9 7 2 )s ou rc e I N C = 4 N C = l , 2 a n d 4 N C = 4 N C = l , 2 a n d 4Sam ple s ize 68 79 12 27a 1 .578 (23) 1 .573 (19) 1 .539 1 .545b 0 - 0 2 0 ( 1 9 ) 0 . 0 2 7 ( 1 6 ) 0 - 0 6 ( 2 ) 0 . 0 6 ( 2 )r 0 - 1 2 6 0 . 1 8 7 0 . 5 7 0 . 5 81.6 3 .5 32 34I t l 1 .03 1 .67 2 .3 3 .6

n o n - b o n d e d c a t i o n - c a t i o n c o n t a c t s [b a s e d o nG l i d e w e l l ' s ( 1 9 7 5 ) r a d i i ] . I n o r d e r t o t e s t t h i sh y p o t h e s i s t h e s h o r t e s t p o s s i b l e S i - S i d i s t a n c e b e t w e e nn e i g h b o r i n g t e t r a h e d r a m u s t b e d e t e r m i n e d . I t o c c u r s i nb e n i t o i t e , w h i c h i s n o t s u r p r i s i n g s i n c e , i n t h e t i g h tc u r v a t u r e o f th e S i 3 0 9 r i n g s , t h e S i a t o m s a r e f o r c e dt o g e t h e r m o r e c l o s e l y t h a n i n m o s t o t h e r s i l i c a t eg e o m e t r i e s . T h e r e f o r e , i f w e a s s u m e ( a ) t h a t S i a t o m s i ns i li c a te s w i t h c h a r g e - b a l a n c e d O a t o m s c a n n o ta p p r o a c h e a c h o t h e r c l o s e r t h a n 3 . 0 /k a n d ( b ) t h a tb o t h S i - O b o n d s in t h e S i - O - S i b r id g e a r e o ft h e s a m e l e n g t h , t h e n n o d a t a p o i n t s s h o u l d o c c u r

s ~ - o ~ )

I . s 5 S i - 0 v s . - s e c S i - O - S i ) ~ . e 4 . . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . .1 . 6 3 + ++ + . .

11 . 6 2 ++ : 1 : ~+ . . . . . . . . . . . . . . .1 . 6 1 + + * , __ .._ .~+ +.+._ +__ . . . . . . - - - , - = '- ~ . . . . .

+ 'l + . . . . . . . ~ +

+ + . f t . + + +1 . 5 9 + + ++ + +5 8 1 4 + + + 'I + '4 . .+ . -

1 . 5 7 I I . ' ', o o , o ~ 6 0 , , ~ , 2 o , 2 5 , 3 o , 13 5 , ~ o , , 5 5 0 - s e c S i - O - S i )

F i g . 1. S i - O b o n d l e n g t h s v e r s u s - s e c ( S i - O - S i ) f o r 1 7 f o u r - c o n n e c t e d t e t r a h e d r a a n d 1 1 S i - O b o n d s o f o t h e r b r i d g in g O a to m s . T h ed a ta a r e f r o m Tab le s 2 an d 3 . Th e d as h ed l in e co r r e s p o n d s to th e r eg r es s io n eq u a t io n f o r th e s amp le co n s i s t in g o f 7 9 v a lu es ( s ee Tab le 4 ) .F o r th e ex p lan a t io n o f th e d o t t ed l in es s ee t ex t .


5/5

W E R N E R H . B A U R 2 61 9b e lo w th e d o t t e d d i a g o n a l c u rv e i n F ig . 1 . A n u p p e rl im i t fo r p o ss ib le d a t a p o in t s i s g iv e n b y t h e d o t t e dh o r i z o n t a l l in e in F ig . 1 a t S i -O = 1 .6 4 ,~ , b e c a u seS i - O d i s t a n ce s i n v o lv i n g c h a r g e - b a l a n c e d O a t o m sra re ly e x c e e d t h i s v a lu e . Th e o n ly d a t a o u t s id e t h e sel imi ts a re the beni to i te poin ts and one coesi te poin t ,w h ic h d o n o t c o n fo rm to a ssu m p t io n (b ) . Th e a v e r -a g e s o f t h e t w o S i - O b r i d g in g b o n d s in b o th c a s e sfa l l w i th in t h e b o u n d s . I t i s p a r t i c u l a r ly im p re ss iv e t h a tt h e l o n g e s t S i - O d i s t a n c e s o f a p p r o x i m a t e l y 1 . 63 / ko c c u r o v e r t h e w h o le r a n g e o f b r id g in g a n g le s fro m 1 8 0to 133 wi th ess ent ia l ly co nst an t va lues. I t i s equa l lyi n t er e s ti n g t o s e e t h a t s t r a ig h t S i - O - S i b o n d s c a no c c u r fo r S i - O b o n d s r a n g i n g f r o m 1 . 5 7 6 t o 1 . 6 3 2 / k .T h i s c o v e r s a l m o s t t h e w h o l e ra n g e o f S i - O b o n dle n g th s , si n c e o n ly o n e S i - O b o n d in t h e w h o le sa m p lei s o u t s id e t h e se l im i t s . Th e 7 9 d a t a p o in t s a red i s t r i b u t e d o v e r a l l t h e a l l o w e d sp a c e ; h o w e v e r , t h e ya re n o t u n i fo rm ly d i s t r i b u t e d . Th e re fo re , r e g re ss io nc a l c u l a t i o n s , e sp e c i a l l y w h e n th e y i g n o re p o in t s i n t h eu p p e r l e ft o f t h e d i a g ra m , t e n d t o g iv e p o s i t i v ec o rr el at io n s be tw e en S i - O a nd - s e c ( S i - O - S i ) . T h ed ia g o n a l d o t t e d c u rv e i n F ig . 1 i s c a l c u l a t e d f ro m th eg e n e ra l e x p re ss io n r e l a t i n g o n e a n g le t o t h e t h re e s id e so f a t r i a n g l e . S in c e t h i s e x p re ss io n i s , w i th in t h e l im i t s o fin t e re s t, n o t f a r f ro m b e in g l i n e a r w i th t h e se c a n t o f th eS i - O - S i a n g le , it i s n o t s u r p ri s i n g th a t G i b b s et al .( 1 9 7 2 ) f o u n d a l i n e a r r e l a t i o n s h i p b e t w e e n S i - O a n dt h e s ec a n t o f S i - O - S i . A n a l y s is o f sm a ll s a m p le sw h ic h h a v e n o o r fe w v a lu e s w i th lo n g S i -O d i s t a n -c e s a t s t r a i g h t o r n e a r l y s t r a i g h t S i - O - S i a n g l esy i el d s s i g n if i c an t c o r r e la t i o n s b e t w e e n S i - O a n d- s e c ( S i - O - S i ) ( P r ew i t t, B a l dw i n G i b b s , 1 97 4) .Su c h c o r re l a t i o n s d i s a p p e a r w h e n l a rg e r , l e ss b i a se ds a m p l e s a r e s t u d ie d . F o r c a s e s w h e r e th e S i - S i d i s t a n c ei s c l os e t o th e n o n b o n d i n g c o n t a c t l e n g th o f 3 . 0 / k t h ec o r re l at io n b e t w ee n S i - O d i s ta n c es a n d S i - O - S ia n g le s d o e s e x i s t b e c a u se o f t h e d e p e n d e n c e o f t h ea n gl e S i - O - S i o n t h e S i - O d i s ta n c e s a n d n o t v i cev e r s a a s r e q u i re d b y r r -b o n d in g t h e o ry (G l id e w e l l ,1 9 7 5 ) . Th e re fo re i t a p p e a r s t h a t t h e a p p ro a c h o fO 'K e e f fe H y d e (1 9 7 6 ) i s u se fu l t o o b t a in a l o w e rl im i t o f po s s i bl e S i - O - S i a n g l es , e v en t h o u g h i t c a n n o tg i v e u s a n u p p e r l i m i t . F o r S i - O b o n d s r a n g i n g i nl e n g th f ro m 1 .5 7 6 to 1 .6 3 2 /k t h e u p p e r l im i t o fS i - O - S i i s e m p i r i c a l ly f o u n d t o b e 1 8 0 . A n g l e s l a r g e rt h a n t h e l o w e r l i m i t m a y b e i m p o s e d b y p a c k i n gc o n s t r a in t s o f t h e c ry s t a l s t ru c tu re s (B a u r , 1 9 7 2 ).

I t h a n k t h e C o m p u t e r C e n t e r o f t h e U n i v e r s i ty o fI l l i n o i s , Ch ic a g o , fo r c o m p u te r t im e .N o t e a d d e d i n p r o o f : - - A f t e r t h i s p a p e r w a s s u b m i t t e dfo r p u b l i c a t i o n a sh o r t c o m m u n ic a t i o n b y G l id e w e l l( 1 9 7 7 ) w a s p u b l i sh e d . T h e n o n - b o n d e d a t o m i c r a d i u so f S i h a s b e e n u s e d t h e r e t o r a t io n a l i ze t h e S i - O - S ia n g le s i n t h e s i l i c a p o ly m o rp h s .

ARAKI, T.387.BAUR, W.155.BAUR, W.BAUR, W.BAUR, W.60.DOLLASE,

Ref erence sZOLTAI, T. (1969). Z. Kris tal logr . 1 2 9 , 3 8 1 -

H. ( i970) . Trans . Ame r . Co s t . Assoc. 6, 129-H (1971). Amer. Min. 56, 1573-1599.H. (1972). Amer. Min. 57, 709-731.H. (1976). Ame r. C o s t . Assoc. Program Abs . 4 ,W. A. (1965). Z. Kris tal logr . 1 2 1 ,3 6 9 -3 7 7 .DOLLASE W. A. BAUR W. H. (1976). Amer. Min. 61,9 7 1 -9 7 8 .FISCHER, K. (1969). Z. Kris tal logr . 129, 222-243.GIBBS, G. V., BRECK, D. W. MEAG HER, E. P. (1968).Li thos , I , 275-285.GIBBS, G. V., HAMIL, M. M., LOUISNATHA N, S. J ., BARTELL,L. S. Yow , H. (1972). Amer. Min. 57, 1578-1613.GLIDEWELt,, C. (1975). lnorg. Chim. Acta, 12, 219-22 7.GLIDEWELL, C. (1977). Inorg. Nucl . Chem. Let t . 13,6 5 -6 8 .Internat ional Tables for X-ray Cm s tal lography (1974). Vol.IV. Birmingham: Kynoch Press.KATO, K. NUKU I, A. (1976). Aeta Co,s t . B32, 2486-2491.LOUISNATHAN, S. J. GIBBS G. V. (1972). A m er . Mi n . 57,1089-1108.MCDONALD, W. S. CRUICKSHANK, D. W. J. (1967). Z.Kristal logr. 124, 180-191.O'KEEFFE, M. HYDE, B. G. (1976). A c t a C o s t . B32,2923-2936.PREWITT, C. T. , BALDWIN, K. J. GIBB S, G. V. (1974) .Geol. So. Amer . Abs . Program s, 6 , 917.SMOLIN, YU. I. SHEPELF,V, YU. F. (1970). Acta Crys t . B26,4 8 4 -4 9 2 .SMOLI.IN, Yu. I., SttEPELEV, Yu. F. TITOV A. P. (1973).Soy. Phys . Crvs tal logr . 17, 749-750.ZACHARIASEN, W. H. PLFTTINGER, H. A. (1965). A c t aCo s t . 18, 710-714.

werner1977, si-o bond lengths, angles

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