the prediction of bond length variations in … · wnnxnn h. baun, department of geological...
TRANSCRIPT
THE AMERICAN MINERALOGIST, VOI,. 56, SEPTEMBER-OC'I'OBER, 1971
THE PREDICTION OF BOND LENGTH VARIATIONSIN SILICON-OXYGEN BONDS
Wnnxnn H. Baun, Department of Geological Sciences,Unhersity of lllinois at Chicago, Chicago, Il,l,inois 60680.
Assrnecr
Individual silicon-oxygen bond lengths in many accurately determined silicate crystalstructures vary from 1.55 to 1.72 4,. These variations in bond length are strongly correlatedwith the Pauling bond strength, 1o, received by the oxygen atoms. The individual variationsin bond lengths d(Si-O) can be predicted using the expression d(Si-O)",r":(d(Si-O)*-
*0.09141o)4, where d(Si-O)*." is the mean tetrahedral Si-O distance, 0.091 is an empiricalconstant, and A,ps is the difierence in the bond strength received by the individual oxygenatom and the mean bond strength received by the oxygen atoms in the given silicate tetra-hedron. The absolute mean deviation between 148 pairs of d(Si-O).u and d(Si-O)*r" takenfrom a sample of 26 crystal structurescontaining disilicate groups is found to be 0.0104.The correlation coefficient between the bond length variation and the bond strength vari-ation A16 is 0.92, which defines a very strong correlation. The dependence of d(SiO)o6u onthe angle Si-O-Si is found to be a corollary of the more basic correlation between bondlength variation and A2e. In crystal structures in which Ap6:0 for all oxygen atoms, thed(SiO) on {Si-O-Si dependence does not exist. Therefore d-p r-bondng should be ques-tioned as a general bonding theory for the silicates. An influence of the electronegativity ofthe non-tetrahedral cations on d(Si-O)"u" is not found in the case of four pairs of strictlyisostructural pyroxenes. Such efiects have been claimed in previous studies based on acomparison of not isostructural chainsilicates (McDonald and Cruickshank, 1967) and ofnot strictly isostructural clinoamphiboles (Brown and Gibbs, 1970). Ilowever, tle bondlength variations in these two cases, as well as for the pyroxenes, show a good correlationwith tle Aps-values.
The main difference between the extended electrostatic valence rule as applied here,and Cruickshank's (1961) il-p r-bonding theory is that ttre former emphasizes the in-fluence of all the coordinating cations on d(SiO)"1", while the latter stresses the internalelectronic structure within the isolated silicate groups. As this study shows it is not permis-
sible to neglect the influence of the non-tetrahedral cations on the silicon-oxygen bondIength. The silicate group cannot be viewed as an isolated entity within the crystal struc-ture.
InrnooucrroN
Recently, in an extension of earlier ideas on this subject (Baur, 1961),a large number of crystal structure data on borates, silicates, phosphates,sulfates, and titanates was analyzed with a view towards correlating,among other things, the variations of individual bond lengths, d(A-X),with the bond strengtbs, p,, received by the anions (Baur, 1970), One ofthe results of this study was formulated in rule 3, which states that in agiven coordination polyhedron the deviation of an individual bond lengthd(A - X) from the mean (d(A - X) ) is proportional to Ap" and the bondIengths d(A-X) can be predicted from equations of the form
d.(A - x) : (<d(A - x)) I bap,)ir (1)
1573
1574 WItRNIIR II . BALTR
where (d(,4 -X)) and D are empirically derived constants for given pairsof ,4 and X in a given coordination, and where A1" is the difference be-tween the individual P, a.nd the mean p,Ior the c,cordination polyhedron.A and X stand respectively for cations and anions in ionic or partly ioniccrystal structures. The empirical value of the_slope b in the above expres-sion was found for the Si-O bond to be 0.091 Af v.'t., while the <d(A - X)>was obtained from Brown and Gibbs' (1969) expression
(d(s i -o)) : (0.01s cN. + 1.s7e)A t2)which relates the mean Si-O bond length within a sil icate tetrahedron tothe mean coordination number C.N. of the oxygen atoms bonded to sil i-con. This correlation is without doubt valid (see the documentation ofthis point by Shannon and Prewitt,1969), but in many cases the dis-crepancy between observed and calculated mean Si-O distances is ap-preciable: for instance, in topaz it is 0.017 A ltaUte 1, Gibbs and Brown,1969). Predictions of bond lengths based on expression (1) could be af-fected by such inaccurate values chosen flor (d(A-X)).The effect ofAp" on the individual bond lengths could be thus obscured. In order toavoid this complication in this paper the actually obseraed. mean valuesof the Si-O bond lengths wil l be used in expression (1). In this way we wil lnot test the abil ity of rule 3 to predict bond lengths, but instead itspower to predict the deviations of the individual bond distances fromtheir experimentally determined mean for a given silicate tetrahedron.This test of rule 3 is being applied to a clearly defined sample: to allcrystal structures containing the disil icate group SizOz6-, provided: a) thestructure determination is reasonably accurate, b) the error estimates ofthe positional parameters are given in the original papers, and c) thestructure determination came to the attention of the author. Only theSi-O bond distances will be considered in this paper. The bonds from thecxygen atoms to all the other cations in these structures wil l not be dis-cussed here.
Previous references to a possible relationship between bond Iength andbond strength in ionic or partly ionic crystals are scattered throughoutthe l iterature. The earliest discussion seems to be due to Smith (1953).Further l i terature on this subject is quoted in Baur (1970). In none ofthese earlier papers has this relationship been used for the prediction ofbond lengths.
DBnrNrrroNs
y'":sum of bond strengths received by an anion X according tothe electrostatic valence rule (Pauling, 1960; Baur, 1970).
y'o:sum of bond strengths received by an oxvgen atom.
SILICON-OXYGEN BONDS 1575
Ap": bond strength variation: difference between the p, of one in-dividual anion in a coordination pclyhedron around a cationand the mean p, of all ani';ns in this coordination, Ap,:px-pt lmcar l ( ru le 3, Baur, 1970).
v.u.:valence units, measure of p, and Ap,. The bond strengthgiven by a cation to an anion is the formal charge of thecation divided by its coordination number. The sum of thesebond strengths received by an anion is called p". It corre-sponds approximately (with a change in sign) to the formalcharge of that anion (electrostatic valence rule, Pauling,1e60).
d(A-X):interatomic distance from cation ,4 to anion X.(d(A-X)) :mean observed d(A-X) in a g iven coordinat ion poly-
hedron.d(obs) : experimentally observed distance between a cation and an
anion.d(calc) : distance calculated according to rule 3 (Baur, 1970) between
cation and anion.Atl(oc) : difference between the observed and the calculated dis-
tances.Ad(om):bond length variation: difference between d(obs) of one in-
dividual anion in a coordination polyhedron around a cationand the mean d(obs) of all anions in this coordination,Ad(om) : d(obs) - (d(A-X) ).
o:intercept of the l inear regression equation.b:slope of the regression equation.z : correlation coefficient.
e.s.d. : estimated standard deviations of the bond lengths, mostlybased on values supplied by the original authors. In a fewcases these values had to be calculated from the e.s.d.'s ofthe positional parameters of the atoms because of misprintsor mistakes in the original papers.
BoNo SrnrncrH AND BoNn LBNcur rN DrsrLrcATE GRoups
The only structure determinations considered here are those which re-sulted in mean estimated standard deviations of less than 0.03 A for theSi-O bonds. In all these 26 structures the Si-O bonds are the strongestbonds present, because the sil icon atoms have the highest formal chargeof all cations present andfor because they have the smallest coordinationnumber against oxygen. All crystal structures evaluated for this studyare listed in Tables I and 2. The coordination numbers of the cationsused for the calculation of the bond strengths are indicated as super-
WERNER H, BAUR157 6
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1577
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SILICON-OXYGEN BONDS
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d u A o c a o v o v N o !E ^ E ^ r - U O ^
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t \o 0 s 3 p a o oi o . i E i p o
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t578 WERNER II. BAUR
Tab le 3 . Exanp le o f a bond s t r eng th ( p^ ) ca l cu l a t i on :( c a , N a J I e J g n [ + J g g r 6 , ( 1 . , s e e " T a b l e t ) . T h e c o n r r i b u t i o n
f r o m ( C a , N a ) t o e a c h o x y g e n a t o m i s : ( 0 . 5 x 2 . 0 + 0 . 5 x 1 . 0 ) / 8 = 0 . 1 9 '
f r o n A C : 3 . 0 / 4 , f r o m S i : 4 0 / 4 .
C a p . 5 N a 6 . 5 A C
0 ( 1 )
0 ( 2 )
0 ( 5 )
2 x 0 . 1 9 v . u .
5x0 . I 9
2 x 0 . 1 9 0 . 7 5 v . u .
2 x 1 . 0 0 v . u . 2 . 3 8 v . u .
1 . 0 0 1 . 5 6
1 . 0 0 2 . I 3
scripts in square brackets. Since the Si-atoms are always 4-coordinatedtheir coordination number is omitted from the formulas. An example ofbond strength and bond length calculations, for synthetic soda melilite,is presented in detail in Tables 3 and 4. Both the avera,ges, of the sumof bond strengths (2o) ana of the observed Si-O distances (d(obs)), aretaken for all four oxygen atoms in the silicate group, even when some ofthem are symmetrically equivalent. The values of d(calc) were calculatedusing expression (1) with D:0.091 A/v.u. For further details of the bondstrength calculations, especially concerning the way hydrogen bonds areaccounted for, see Baur (1970). The data derived for the other 25 crystalstructures are presented in Table 5. The values ol Apo, Ad(oc) andAd(om) are not l isted because they can be calculated easily from thedata of Table 5. Furthermore all values ol APo and Ad(om) are displayed
T a b l e 4 . E x a n p l e o f a b o n i l l e n g t h c a l c u l a t i o n : ( C a , N A ) j t l o u t o l t l r o '
see TabLes 3 and 1 , Tab le 1 . ApO i s de f i ned i n t he
t e x t ; d c a l c = ( L . 6 2 2 + 0 . 0 9 l A p 0 ) A w h e r e 1 . 6 2 2 f i s t h e n e a n
obse rved S i -O d i s t ance (nean do6 r ) . Ado . i s t he
d i f f e rence be tween t he obse rved and t he ca l cu l a ted
S i - O d i s t a n c e , w h i l e A d o n i s t h e d i f f e r e n c e b e t w e e n
t h e i n d i v i d u " l d o b , a n d t h e n e a n d o ' r '
po ^Po d . u 1 . d o b , A d o . A d o *
s i - o ( 2 ) 1 . s 6
s i - 0 ( 3 ) 2 . 1 3
s i - 0 ( 3 ) 2 . 1 3
- 0 . 4 9 7 . 5 7 7
0 . 0 8 7 . 6 2 9
0 . 0 8 L . 6 2 9
S i - O ( 1 ) 2 . 3 8 v . u . 0 , 3 3 v . u . 1 ' 6 5 2 i 1 . 6 4 8 ( 3 ) l - 0 . 0 0 4 f r o . o 2 6 l ,
r . s 7 7 ( s ) 0 . 0 0 0 - 0 . 0 4 s
1 . 6 3 1 ( 4 ) 0 . 0 0 2 0 . 0 0 9
1 . 6 3 1 ( 4 ) 0 . 0 0 2 0 . 0 0 9
ne an 2 . 0 5 v . u . r . 6 2 2 0 . 0 0 2
SILICON.OXYGEN BONDS 1579
in Figure 1. Mean Ad(oc) values for each structure are listed in Tables 1and 2.
In order to test the validity of rule 3 more extensively a weighted leastsquares linear regression of Ad(om) on Apo was calculated. The inversesquares of the estimated standard deviations of the individual bondIengths were employed as weights. This decreased the contribution of thevalues with large e.s.d.'s. While most of the crystal structure data used inthis study are fairly precise, the maximum ratio of the estimated standarddeviations nevertheless is iarge: the least precisely determined Si-O bondIength has an e.s.d. of 0.037 A, the most prec ise one oI 0.001 A. Ot te.un-not expect to find meaningful correlations without taking these differ-
Tab le 5 . Bond s t rengths and ca lcu la ted and observed bond lengths fo r a l ld is i l i ca te g roups o f the conpounds l i s ted in Tab les 1 and 2 . Theconpounds are ident i f ied by nunber on ty , the ind iv idua l S ioa groupsd i f fe ren t ia ted by le t te rs , and the br idg ing bonds are a lways l i s tedf i r s t . T h e e . s . d , ' s a r e i n d i c a t e c l h e r e , a s e l s e w h e r e i n t h e p a p e r ,i n u n i t s o f t h e l a s t s i g n i f i c a n t d i g i t s . T h e n u n b e r i n g o f t h eatons use i l in the or ig ina l papers has been re ta ined.
2 . S i - O ( 1 )
s i - o ( 2 )zxs i -O [3 )
3 . s i - 0 ( r )s i - o ( 2 )s i - o ( 3 )s i - o ( 4 )
4 . S i - o ( 1 )3 x s i - 0 ( 4 )
s a . s i ( 1 ) - 0 ( 1 )
s i ( 1 ) - 0 ( 2 )
s i ( 1 ) - 0 ( 3 )s i ( 1 ) - 0 ( 4 )
s b . s i ( 2 ) - o ( 1 )s i ( 2 ) - 0 ( s )s i ( 2 ) - 0 ( 6 )s i ( 2 ) - o ( 7 )
6 . s i - o ( 1 )s i - 0 ( 2 )
2 x s i - o ( 3 )7 a . s i ( 1 ) - o ( a )
s i ( 1 ) - o ( 1 )s i ( 1 ) - o ( 2 )
s i ( 1 ) - o ( 3 )
7 b . s i ( 2 ) - o ( 4 )s i ( 2 ) - o ( s )s i ( 2 ) - o ( 6 )
s i ( 2 ) - o ( 7 )
P 9 d c a l c d o b ,
(v . u , ) (A) (A)
2 . 0 0 r . 6 2 6 1 . 6 2 6 ( 3 )
2 . 0 0 r . 6 2 6 1 . 6 1 4 ( 6 )
2 . 0 0 L . 6 2 6 1 . 6 3 2 ( s )
2 . 0 0 r . 6 2 L 1 . 6 3 2 ( 3 )
2 . 0 0 1 . 6 2 7 1 . 6 3 1 ( s )
2 . 0 0 L . 6 2 r r . 6 1 1 ( s )
2 . 0 0 r . 6 2 1 1 . 6 0 9 ( s )
2 . 0 0 1 . 6 1 2 I . S 9 9 ( 6 )
2 . L 4 r . 6 2 s 7 . 6 2 9 ( 7 )
2 . 0 0 1 . 6 1 4 1 . s 9 9 ( 9 )
2 . 7 3 r . 6 2 6 1 . 6 s 0 ( 9 )
2 . 7 3 7 . 6 2 6 1 . 6 1 8 ( 9 )
1 . 7 5 1 . s 9 1 1 . 5 8 7 ( 9 )
2 . 0 0 1 . 6 1 8 1 . 6 3 8 ( 9 )
2 . 1 3 1 . 6 3 0 r . 6 1 4 ( 9 )
2 . 1 3 1 . 6 3 0 1 . 6 0 7 ( 9 )
t . 7 s 1 . 5 9 s 1 . 6 1 3 ( 9 )
2 . 4 0 1 . 6 7 I 1 . 6 8 8 ( 8 )
1 , 9 0 t . 6 2 s 1 , 6 1 9 ( 1 0 )
1 . 9 s r . 6 2 9 1 . 6 2 s ( 1 0 )
2 . 8 6 1 . 6 9 s 1 . 6 7 2 ( 8 )
1 . 8 6 r . 6 0 4 1 . 6 0 4 ( 1 3 )
r . 8 6 1 . 6 0 4 1 . 6 s 1 ( 1 2 )
1 . 8 6 r . 6 0 4 r . s 8 r ( 9 )
2 . 8 6 1 . 6 9 9 7 . 6 7 3 ( 7 )
1 . 8 6 1 . 6 0 8 1 . s 8 8 ( 1 3 )
1 . 8 6 1 . 6 0 8 1 . 6 4 8 ( 1 4 )
1 . 8 6 1 . 6 0 8 1 . 6 1 4 ( e )
D ^ d - d .' u c a r c o D s( v . u . ) ( A ) ( i )
8 a . s i ( 1 ) - o ( 1 ) 2 . 0 0 7 . 6 2 1 1 . s 9 0 ( 8 )
s i ( 1 ) - o ( 2 ) 2 . 1 3 r . 6 3 2 1 . 6 2 4 ( 1 0 )
s i ( 1 ) - 0 ( 3 ) 2 . 7 3 7 . 6 3 2 1 . 6 3 8 ( 1 1 )
s i ( 1 ) - o ( 4 ) 7 . 7 s 1 . 5 9 8 1 . 6 3 2 ( 1 s )
8 b . s i ( 2 ) - o ( 1 ) 2 . 0 0 1 . 6 3 1 1 . 6 3 6 ( 1 1 )
s i ( 2 ) - o ( s ) 2 . 7 3 r . 6 4 2 1 . 6 6 9 ( 1 0 )
s i ( 2 ) - o ( 6 ) 2 . 7 s L . 6 4 2 1 . 6 1 6 ( 9 )
s i ( 2 ) - o ( 7 ) 1 . 7 s 1 . 6 0 8 1 . 6 0 4 i r 0 )
9 . S i - O ( 2 ) 2 . 3 3 r . 6 6 4 1 . 6 8 3 ( I 4 )
s i - 0 ( 3 ) 2 . 0 0 r . 6 3 4 1 . 6 1 0 ( 1 7 )
2 x S i - O ( 4 ) 2 . 0 0 7 . 6 3 4 1 . 6 3 6 ( 1 0 )
l 0 a . S i ( 1 ) - o ( a ) 2 . 4 3 1 . 6 5 4 1 . 6 3 8 ( 1 4 )
s i ( 1 ) - o ( 1 ) 2 . 1 0 r . 6 2 4 1 . 6 1 s ( 1 4 )
s i ( 1 ) - o ( 2 ) 2 . 2 0 1 . 6 3 3 1 . 6 s 7 ( l s )
s i ( 1 ) - o ( 3 ) 7 . 7 6 1 . s e 3 1 . s e s ( l s )
r 0 b . s i ( 2 ) - o ( 4 ) 2 . 4 3 r . 6 6 7 1 . 6 6 0 ( 1 3 )
s i ( 2 ) - o ( s ) 7 . 6 7 1 , s 9 8 1 . 5 8 0 ( 1 s )
s i ( 2 ) . o ( 6 ) z . r 0 ! . 6 3 7 1 . 6 3 s ( r 4 )
s i ( 2 ) - 0 ( 7 ) 2 . r o 1 . 6 3 7 1 . 6 6 4 ( 1 2 )
l 0 c . s i ( 3 ) - 0 ( 1 r ) 2 . 3 3 1 . 6 4 3 r . 6 2 2 ( r s )
s i ( 3 ) - o ( 8 ) 1 . 7 6 1 . s 9 1 1 . 6 3 0 ( 1 S )
s i ( 3 ) - o ( 9 ) 2 . 2 0 1 . 6 3 1 1 . 6 0 s ( 1 s )
s i ( 3 ) - o ( 1 0 ) 2 . 2 0 1 . 6 3 r 1 . 6 3 7 ( 1 3 )
r 0 d . s i ( 4 ) - o ( 1 r ) 2 . 3 3 1 . 6 s 8 1 . 6 6 s ( 1 s )
s i ( 4 ) - o ( 1 2 ) 1 . 7 6 1 . 6 0 6 1 . s 7 6 ( 1 s l
s i ( 4 ) - o ( 1 3 ) 1 . 6 7 1 . s 9 8 1 . 6 2 4 ( 1 s )
s i ( 4 ) - 0 ( 1 4 ) 1 . 7 6 1 . 6 0 6 1 . 6 0 2 ( 1 S )
1580 WERNER H. BAUR
T a b l e 5 c o n t ' P 9 d c a l c d o b s P g d . . 1 c d o b .
( v . u . ) ( A ) ( n ) ( v . u . ) ( f r ) ( E )
1 1 . S i - o ( l ) 2 . 2 s
z x S i - 0 ( 2 ) 7 , 9 2
s i - 0 ( 3 1 2 . 2 s
1 2 a . s i ( 1 ) - o ( 5 ) 2 . 2 9
2 x S i ( 1 ) - o ( 2 ) 2 . 0 4
s i ( 1 ) - 0 ( 6 ) 1 . s 0
1 2 b . S i ( 2 ) - O ( s ) 2 . 2 9
s i ( 2 ) - o ( 3 ) 2 . 1 2
2 x s i ( 2 ) - o ( 4 ) 2 . 0 4
1 3 . S i - O ( l ) 2 , s 0
s i - o ( 2 ) 1 . 7 s
z x s i - 0 ( 3 ) 2 . 0 0
1 4 . S i - 0 ( 1 ) 2 . 0 0
s i - o ( 2 ) 2 . 0 0
2 x s i - 0 ( 3 ) 2 . 0 0
1 s a . s i ( I ) - o ( 9 ) 2 . 0 0
2 x s i ( 1 ) - o ( 1 ) 2 . 2 s
s i ( 1 ) - o ( 7 ) 1 . s 4
r s b . s i ( 2 ) - o ( s ) 2 . 0 0
z x s i ( 2 ) - 0 ( 3 ) 2 . 0 4
s i ( 2 ) - 0 ( 8 ) 1 . s 0
1 6 a . S i ( 1 ) - 0 ( 9 ) 2 . 0 0
2 x s i ( 1 ) - O ( 1 ) 2 . 2 9
s i ( 1 ) - o ( 7 ) 1 . s 4
1 6 b . S i ( 2 ) - O ( 9 ) 2 . 0 0
2 x S i ( 2 ) - o ( 3 ) 2 . 0 4
s i ( 2 ) - o ( 8 ) 1 . s 0
I 7 . S i - o ( 4 ) 2 . 0 0
2 x s i - o ( 1 ) 2 . 0 0
s i - o ( 2 ) 2 . 0 0
1 8 a . s i ( 1 ) - o ( 9 ) 2 . 0 0
z x s i ( 1 ) - o ( 1 ) 2 . 2 9
s i ( 1 ) - o ( 7 ) 1 . s 4
r 8 b . s i ( 2 ) - o ( e ) 2 . 0 0
2 x s i ( 2 ) - o ( 3 ) 2 . 0 4
s i ( 2 ) - o ( 8 ) 1 . s 0
1 . 6 4 8 r . 6 5 3 ( 1 ) 1 9 a . S i ( 1 ) - 0 ( 9 ) 2 . 0 0 1 . 6 3 1 1 . 6 4 5 ( 1 1 )1 . 6 1 8 1 . 6 1 5 ( 1 ) 2 x s i ( 1 ) - o ( 1 ) 2 . 2 9 1 . 6 s 8 1 . 6 5 5 ( 1 1 )1 . 6 4 8 1 , 6 4 8 ( 1 ) S i ( 1 ) - O ( 7 ) 1 . s 7 r . 5 9 2 1 . 5 8 s ( 1 2 )
7 , 6 s 7 1 . 6 s 3 ( 4 ) 1 9 b . S i ( Z ) - 0 ( 9 ) 2 . 0 0 1 . 6 1 9 1 . 6 2 0 ( 1 1 )1 . 6 3 4 1 . 6 3 3 ( 3 ) 2 x s i ( 2 ) - 0 ( 3 ) 2 . 0 7 1 . 6 2 6 1 . 6 2 I ( I I )
1 . 5 8 s 1 . s 9 1 ( 4 ) S i ( 2 ) - 0 ( 8 ) 1 . s 0 L . s 7 4 1 . s 8 2 ( 1 3 )
1 . 6 6 0 1 . 6 6 0 ( 4 ) 2 0 a . s i ( I ) - o ( 9 ) 2 . 0 0 7 . 6 2 4 1 . 6 2 s ( l s )
1 . 6 4 s 1 . 6 s 0 ( 4 ) 2 x s i ( 1 ) - 0 ( 1 ) 2 . 2 e 1 . 6 s 1 I . 6 s 2 ( 9 )
1 . 6 3 8 1 . 6 3 4 ( 3 ) S i ( 1 ) - O ( 7 ) 1 , s 4 1 . s 8 2 1 . s 8 0 ( 1 3 )
1 . 6 s 8 1 . 6 4 9 ( 3 1 2 0 b . S i ( 2 ) - O ( 9 ) 2 . 0 0 1 . 6 2 8 1 . 6 2 8 ( 1 s )
1 . s 9 0 1 . s 8 3 ( 6 ) 2 x s i ( 2 ) - 0 ( 3 ) 2 . 0 4 1 , 6 3 2 I . 6 2 7 ( 9 )
1 , 6 1 3 1 . 6 1 9 ( s ) S i ( 2 ) - 0 ( 8 ) 1 . s 0 1 . 5 8 3 1 . 5 9 5 ( 1 s )
1 . 6 2 2 r . 6 0 5 ( 1 ) 2 1 a . s i ( 1 ) - 0 ( 9 ) 2 . 0 0 1 . 6 3 3 1 . 6 s 2 ( r 4 )
1 6 2 2 1 . 6 2 7 ( 2 ) 2 x s i ( 1 ) - o ( 1 ) 2 . 7 s 7 . 6 4 6 1 . 6 4 4 ( 1 4 )
r . 6 2 2 1 . 6 2 8 ( r ) s i ( 1 ) - 0 ( 7 ) 1 . 6 3 1 . s 9 e 1 . s 8 2 ( 1 4 )
r . 6 2 2 1 . 6 2 8 ( 6 ) 2 l b . S i ( 2 ) - o ( e ) 2 . 0 0 1 . 6 3 3 r . 6 2 7 ( r 4 )
1 . 6 4 9 1 , 6 s 2 ( 6 ) z x s i ( 2 ) - o ( 3 ) 2 . 1 3 1 . 6 4 s 1 . 6 3 2 ( 1 4 )
1 . s 8 0 1 . s 6 6 ( 6 ) s i ( 2 ) - 0 ( 8 ) 1 . 3 6 1 . s 7 s 1 . 6 0 3 ( 1 4 )
1 . 6 2 4 r . 6 2 7 ( 6 ) 2 2 . S i - O ( 1 ) 2 . 4 6 1 . 6 6 8 1 . 6 s 4 ( 8 )
1 . 6 2 8 1 . 6 2 0 ( 6 ) S i - O ( 2 ) r . 6 9 1 . s 9 8 1 . s 9 2 ( 1 6 )
1 . s 7 9 1 . 5 9 3 ( 6 ) z x S i - o ( 3 ) 2 . 0 6 I . 6 s 2 I . 6 4 3 ( 1 6 )
r . 6 2 6 1 . 6 3 8 ( 7 ) 2 3 . S i - O ( 4 ) 2 . 3 3 1 , 6 s 2 1 . 6 6 1 ( 1 0 )
1 . 6 5 3 r . 6 s 4 ( 5 ) S i - O ( 1 ) 1 . 8 3 1 . 6 0 ? 1 . 6 2 3 ( 1 4 )
1 , 5 8 4 r . s 6 9 ( 7 ) S i - O ( 2 ) 2 . r 7 1 . 6 3 8 1 . 6 3 s ( 1 6 )1 , 6 2 9 r . 6 3 4 ( 7 ) s i - o ( 3 ) 1 . 8 1 1 . 6 0 7 1 . s 8 6 ( 1 9 )
1 . 6 3 3 I . 6 1 9 ( s ) 2 4 a . S i ( 1 ) - o ( 8 ) 2 . 2 9 I . 6 s 7 1 . 6 8 6 ( 1 9 )
I . s 8 4 1 . 6 0 8 ( 7 ) 2 x s i ( 1 ) - o ( 1 ) 1 . 7 9 1 . 6 1 1 1 . 6 0 4 ( 2 s )
1 . 6 2 8 7 . 6 2 7 ( 4 ) S i ( 1 ) - O ( 4 ) 2 . 2 9 1 . 6 s 7 1 . 6 4 0 ( 2 0 )
r . 6 2 8 7 . 6 2 6 ( 6 ) 2 4 b . S i ( 2 ) O ( 8 ) 2 . 2 e 1 . 6 s 8 r . 6 s 7 ( 1 9 )
1 . 6 2 8 1 . 6 3 r I I 0 ) 2 x s i ( 2 ) - o ( 2 ) 2 . 0 7 1 . 6 3 8 1 . 6 3 4 ( 2 4 )
r . 6 2 6 1 . 6 4 0 ( 7 ) S i ( 2 ) - O ( r 0 ) 2 . r 2 r . 6 4 2 1 . 6 5 0 ( 1 9 )
1 . 6 s 3 1 . 6 4 s ( 7 ) 2 s . S i - 0 ( r ) 2 . 4 0 7 . 6 4 2 1 . 6 2 6 ( 1 6 )
1 . 5 8 4 1 . s 8 6 ( 7 ) S i - 0 ( Z ) 1 . 6 0 1 . 5 6 e 1 . 6 0 7 ( 3 7 )
1 . 6 1 9 7 . 6 2 8 ( 7 ) 2 x S i - 0 ( 3 ) 2 . 2 0 I . 6 2 4 I . 6 7 3 ( z z )
I . 6 2 3 7 . 6 1 2 ( 7 ) 2 6 a . S i ( 1 ) - 0 ( 9 ) 2 . 0 0 I . 6 2 2 r . 6 2 7 ( 2 s )
1 . s 7 4 1 . 5 8 8 ( 7 ) 2 x s i ( 1 ) - 0 ( 1 ) 2 . 2 9 1 . 6 4 9 1 . 6 2 9 ( 2 s )
s i ( l ) - 0 ( 7 ) 1 . s 4 1 . s 8 0 r . 6 r 3 ( 2 s )
2 6 b S i ( 2 ) - O ( 9 ) 2 . 0 0 1 . 6 4 0 1 . 6 0 8 ( 2 s )
2 x s i ( 2 ) - o ( 3 ) 2 . 0 4 1 . 6 4 4 1 . 6 4 s ( 2 s )
s i t 2 ) - o ( 8 ) 1 . s 0 l . s e s r . 6 2 7 ( z s )
ences in precision into account. The correlation coefficient for the re-gression of Ad(om) on Alo for Si-O bonds in disilicates is 0.91 (Table 6,No. 1). This means that 83 percent of the variations of the individualbond lengths from their mean can be interpreted in terms of a depen-dence on Apo (see Fig. 1). In view of the large spread of observed Si-Odistances (1.57 to 1.69 A) the close agreement between Ad(om) and Apois remarkable. The mean deviation (mean Ad(oc)) between d(obs) and
SILICON-OXYGEN BONDS
Ado. vs. Ap.
FOR SFO
IN DISILICATES
A
A
A
.,O(br)
., O(nbr)
", Nd.si.Q a G4si.q
-o.40 -o.20 0 0.20 0.40 0.60 0.80
€APo(v 'u ' )
Iength variation Ad(om) versus Ay'o for silicon-oxygen bond lengths in 26
crystal structures containing disilicate groups.
1581
o.06
o.o2
o
++
{ e
fi)t +
o
os+
' oo
€oo
oA
A
ad-(A)
-o.o2
-o.o4
-o.06-0.60
Fro. 1. Bond
d(calc) for all the data is only 0.011 A and this includes the less accuratelydetermined crystal structures in which the experimental error of the
determination contributes heavily to the Ad(oc) values. The correlationbetween mean Ad(oc) and mean e.s.d. is 0.65 (Table 6, No. 4). This showsthat a considerable part of the value of Ad(oc) is caused by the experi-mental inaccuracy in the original structure determinations.
It is not necessary to explain all the deviations (Ad(oc)) by the imper-fection of the model used. Moreover we can obtain an indication of the
errors inherent in the method by observing the value of the intercept at
e.s.d.:0. It is 0.004 A and can be interpreted to mean that even for the
case of Si-O bond lengths known without any experimental error we
would find values of Ad(oc) of this magnitude. Therefore it is not surpris-ing that the values of the mean Ad(oc)/e.s.d. (Tables 1 and 2) are high
for some of the more precisely determined crystal structures (e.9.,
lawsonite) and Iow for many of the less precise structures (Nos. 9, 10, 19
to 26). However the poor agreement between observed and calculated
WERNER H. BAUR
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SILICON-OXYGEN BONDS 1583
values for the crystal structures of GdrSizOz and NdrSizOT is surprising.Possible explanations for the discrepancy are to assume either that thee.s.d.'s are underestimated or that for these componnds the model is in-sufficient. As discussed at greater length previously (Baur, 1970) thePauling bond strength is used here as an approximate measure of thepotential of the cations on the anion-site in an undistorted coordinationsite. We should therefore expect deviations from rule 3, whenever thisapproximation is insufficient. This could happen when very irregularpolyhedra are present, such as those found in GdzSizOz and NdsSizOzaround the Gd-atoms and the Nd-atoms. The variation in d(Gd-O) isfrom 2.25 to 2.63 A and in d(Nd-O) from 2.24 to 2.95 A. However thereis reason to believe that the first-mentioned explanation applies here'Smolin and Shepelev (1970) have refined NdzSizOz in space groupP2QQL Felsche (1970) contests this assignment and claims that NdzSizOzis pseudo-orthorhombic and belongs to space group P21fn The crystalstructure of GdzSizOz was refined by Smolin and Shepelev both in spacegrotp Pnom, and then in Pna2r The final R-value of 0.073 for 1300 F.r,"in space gtotp Pna21 does not appear to be incontrovertible proof thatthe assignment of an acentric space group is correct (compare Baur andTillmanns, 1970, for the discussion of a similar case). Since there is
sufficient doubt about the correct space groups of both, GdrSizOz andNdzSizOz, only the results of those calculations will be discussed belowwhich exclude data points from these two compounds. Most of the pointsin Figure 1 which are not close to the regression line correspond to bondlengths with large e.s.d.'s, which do not contribute heavily to the cor-relation because they were given small weights. Using unit weights r is
0.80 (Table 6, No. 3) which still defi.nes a strong dependence of Ad(om)on Apo.
The value of the slope , (0.090(3)A/v.u.) is essentially identical withthe value of the slope found previously (b:0.091(3)A/v.u., Baur, 1970).For the calculation of bond lengths (in Tables 4 and 5) the latter valuewas used since it is based on a larger sample. It was derived by a least-squares Iinear regression of 293 observed Si-O distances (obtained from45 silicate crystal structure determinations) on the bond strength, 1o,received by the oxygen atoms (rule 2), according to the expression:
, I (A - X) : (o l bp, \h (3)
Rule 2 is a poorer approximation than rule 3 for the calculation of bondlengths but the slopes in both equations, (1) and (3) obviously have thesame values. Both sets of data, the 45 silicates analyzed. previously(Baur, 1970) and the 26 disilicates studied here, overlap slightly: bondlength data from zoisite, clinozoisite, and piemontite (Dollase, 1968,1969) were used both times.
1584 WERNER H. BAUR
The comparison of d(obs) and d(calc) (Tables 4 and 5), which agree onthe average to within 0.010 A, supports further the validity of rule 3. Itcan be stated confidently that rule 3 rationalizes in considerable detailthe distortions encountered in the bond lengths of disilicate groups.Eighty-five percent of the variation in Ad(om) is explained by the de-pendence on the bond strength variation, Apo (Table 6, No. 2). One canexpress this result differently and say thht all the coordinating cationsof every silicate oxygen atom determine the length of the silicon oxygendistance. Thus this empirical and quantitative approach emphasizes theinfluence of all the ligands on the bond lengths, in contrast to Cruick-shank's (1961) approach which stresses the internal electronic structurewithin the isolated silicate groups.
Bouo LBNcrrr AND rnr ANcrB Snrcow-Oxvcpu-Srr,rcoN
Based on the simple d.-p zr-bonding theory Cruickshank (1961) pre-dicted that in an isolated disil icate group with an dSi-O-Si of 180'thebridging SiO(br) bond should have a length of 1.656 A, while the non-bridging Si-O(nbr) bond Iengths should be t.621 A. tte assumes herethat: a) the Si-O single bond has a length ol1.76 A, b; the Si-O bond is1.63 A long, when it has a zr-bond order of |, and c) the bridging oxygenhas two /-orbitals available for z--bonding with the silicon atoms.As the angle ( Si-O-Si becomes smaller the bridging oxygen atom shouldlose its facility to engage in zr-bonding with the silicon atom and con-sequently the Si-O(br) bonds should become weaker and longer, whilethe Si-O(nbr) bonds should become stronger and shorter. For the caseof a metasil icate chain (SiOr)- with dSi-O-Si of 120", Cruickshankgives an estimate of 1.70 A and 1.56 A for the inner (bridging) and outer(non-bridging) bonds. Presumably this relationship between the Si-O(br)bond length and the angle {Si-O-Si should be most clearly displayed inthe disilicate group itself. In more highly condensed silicates it possiblymight be masked by constraints on the bonding geometry caused bymutual interactions of the tetrahedral groups.
In Figure 2 the Ad,(om) for the Si-O(br) bonds are plotted versus
d Si-O-Si. The Ad(om) rather than the d(Si-O) are plotted in order tofacilitate comparison with Figure 1. The correlation coefficient is -0.72
(Table 6, No.6), which means that slightly more than half of the vari-ation in the bridging bond lengths can be explained by the dependenceon dSi-O-Si. While it is obvious that a correlation between Ad(om) andthe angle does exist, it is a) distinctly poorer than the correlation betweenAd(om) and Apo and b) it applies only to the bridging bonds, thereforeit cannot be used to calculate the non-bridging silicon oxygen bonds, andis therefore of less practical value than the Ad(om) versus A1o correla-tion. These two correlations seem to be related to each other. Whenever
SILICON-OXYGEN BONDS 1585
O:O4O
d*(A)
Ado, vs. * Si-O-Si lN 9lgLlCATE,S+ A l G d . S i . O r ' a I* A
lruo.si.o,'^ |A
t o.o20
-o.o20
-o.o40t60
+* si-o-si ( ')Frc. 2. Bond length variation Ad(om) versus {Si-O-Si
for disilicate groups.
the O(br) atom is involved in a straight or large {Si-O-Si it cannot becoordinated (because of steric reasons) to any additional cations an<i con-sequently receives a bond strength of 2.0 v.u., and therefore will form
Si-O bonds of average length. However if the bridging oxygen atom is in-volved in a smaller {Si-O-Si, it is more likely to engage in additionalcontacts to other cations, thus increasing the bond strength it receives,and therefore form bonds of more than average length. This is borne outby the data in Tables I and 2. The average {Si-O-Si for all bridgingO-atoms in 3- or 4-coordination is 134o, for all those in 2-coordination it is
154" (this excludes the cases with angles of 180'). However this does not
mean that the bridging oxygen atom is 3- or -coordinated because the
<Si-O-Si is small or vice versa that the dSi-O-Si is small because the
oxygen atom is 3- or 4-coordinated. It is sufficient to say that both condi-
tions do occur together and it is the higher coordination (which means
larger po-values) which causes the longer Si-O distance and it is not
necessarily the small { Si-O-Si, which is responsible for the bond length-
ening.If this interpretation is corregt and the Ad(om) on {Si-O-Si correla-
tion is only a corollary of the more basic Ad(om) on Apo correlation then
we sht-ruld expect no correlation between Si-O(br) bond length (or
Ad(om)) and d Si-O-Si in cases were all silicate oxygen atoms receive the
1586 WERNER TT. BAUR
T a b l e 7 . A n g l e s s i - 0 - s i , d i s t a n c e s s i - o a n d a d o , f o r c r y s t a l s t r u c t u r e s w i t hA p O = 0 f o r a l l s i l i c a t e o x y g e n a t o n s .
l o w c r i s t o b a l i t e
1 o w c r i s t o b a l i t e
c o e S l t e
c o e s i t e
c o e s l t e
c o e s i . t e
c o e s i t e
c o e s i t e
c o e s l t e
c o e s l t e
q u a f t z
q u a r t z
k e a t i t e
k e a t i t e
k e a t i t e
k e a t i t e
k e a t i t e
k e a t i t e
h i g h t r i d y n i t e
h i g h t r i d y n i t e
h i g h t r i d y n i t e
h i d h + r i i . , - i + -
Y b z S i z O z
E 1 2 S i 2 O ?
h F h i n ^ r h h i i a
t h o r t v e i t i t e
i S i - O - S i d ( S i - o ) A d o ^ r e f e r e n c e
1 4 6 . 8 0 1 . 6 0 1 ( 4 ) E - 0 , 0 0 4 4 D o l 1 a s e , 1 9 6 5
1 4 6 . 8 1 . 6 0 8 ( 4 ) 0 . 0 0 j D o L l a s e . t 9 6 5
1 8 0 . 0 1 . 6 0 0 ( 3 ) - 0 . 0 0 9 A r a k i G Z o I t a i , 1 9 6 9
1 4 3 . 8 1 . 6 0 8 ( 3 ) - 0 . 0 0 9 A r a k i G Z o 1 t a i , 1 9 6 9
1 4 5 . 0 1 . 6 0 7 ( 5 ) - 0 . 0 0 2 A r a k i E Z o l t a i , 1 9 6 9
1 4 5 . 0 1 . 6 1 9 ( 6 ) 0 . 0 0 2 A r a k i q Z o l t a i , 1 9 6 9
1 5 0 . 4 1 . 5 9 8 ( 5 ) - 0 . 0 1 1 A r a k i G Z o 1 t a i , 1 9 6 9
1 5 0 . 4 1 . 6 2 5 ( 5 ) 0 . 0 0 8 A r a k i E Z o l t a i , 1 9 6 9
1 3 6 . 1 1 . 6 3 1 ( 5 ) 0 . 0 2 2 A r a k i 6 Z o l t a i , t 9 6 9
1 3 6 . 1 1 . 6 1 i ( 5 ) 0 . 0 0 0 A r a k i 6 Z o l t a i , 1 9 6 9
1 4 3 . 5 1 . 6 0 3 ( 2 ) - 0 . 0 0 7 Z a c h a r i a s e n E p l e t t i n g e r ,1 9 6 5
1 4 3 . 5 1 . 6 1 6 ( 2 ) 0 . 0 0 6 Z a c h a r i a s e n q p l e t t i n g e r ,1 9 6 5
1 5 5 . 8 1 . 5 8 ( 2 ) - 0 . 0 2 S h r o p s h i r e e t a l . , 1 9 5 9
1 5 5 . 8 1 , 5 9 ( 2 ) - 0 . 0 1 S h r o p s h i r e e t a t . , t 9 S 9
1 4 9 . 4 1 . 6 1 ( 2 ) 0 . 0 1 S h r o p s h i r e e t a 1 . , l 9 S 9
1 4 9 . 4 1 . 6 r ( 2 ) 0 . 0 2 S h r o p s h i r e e t a I . , 1 9 5 9
1 5 5 . 3 I . 6 I ( 2 ) 0 . 0 1 S h r o p s h i r e e t a 1 . , 1 9 5 9
1 5 5 . 3 I . 5 7 ( 2 ) - 0 . 0 2 S h r o p s h i r e e t a t . , t 9 S 9
1 4 9 . 1 1 . 6 2 f ( 1 0 ) 0 . 0 0 8 D o 1 l a s e , 1 9 6 7
1 4 6 . 2 1 . 6 2 5 ( 1 0 ) 0 . 0 I 2 D o l l a s e , 1 9 6 7
1 5 0 . 0 1 . 6 0 8 ( 2 0 ) - 0 . 0 0 5 D o 1 1 a s e , t 9 6 7
1 5 0 0 1 . 5 9 7 ( 2 0 ) - 0 . 0 1 6 D o 1 1 a s e , 1 9 6 7
1 8 0 . 0 1 . 6 1 5 ( 3 ) 0 . 0 0 0 S n o l i . n G S h e p e l e v , 1 9 7 0
1 8 0 . 0 1 . 6 2 1 ( 3 ) 0 . 0 1 1 S m o l i n € S h e p e l e v , I 9 7 0
1 5 0 . 3 1 , 6 1 6 ( 4 ) - 0 . 0 0 1 M c D o n a l d q C r u i c k s h a n k ,7967 a
1 8 0 . 0 I . 5 9 3 ( 5 ) - 0 . 0 1 7 P r e w i t t , 1 9 7 0 , p e r s . c o n m .
same bond strength and therefor e Apo for all oxygen atoms is zero. Casesamong the disil icates lr/ ith Alo:0 are: Nos. 2, 3, 14, and 17. Since this isnot sumcient for establishing the presence or absence of a correlation, thedata from the SiOz polymorphs have to be included (Table 7). The aver-age coordination number of the oxygen atoms in a silicate group is 2 inSiOr, in the four disil icates it is 2.75. In order to make the two sets ofbond lengths comparable, the values of the Si-O distances for the disili-cates have been reduced by 0.75X0.015:0.011 A lsee expression 2) . Thebond length values of the Si-O bonds in tridymite are those corrected by
S I LI CO){ -OX YC T:,N BOA' D.S
Dollase (1967) for the effects of thermal motion (riding model). This cor-rection amounts to about 0.06 A because the thermal movement of theseoxygen atoms is extremely large and highly anisotropic. The values ofthe {Si-O-Si had to be corrected acccrdingly. For all other bond lengthsthe thermally uncorrected values are being used, since the possible cor.rections are estimated to be smaller than 0.01 A. The bond lengths inkeatite (Shropshire et al.,1959) were assigned e.s.d.'s which are reasonableguesses, because no errors have been stated in the original paper. Like'wise the errors of t}i'e corrected, bond lengths in tridvmite are estimated.Both estimates are probably too low. Correlations have been calculatedfor both: d(Si-O) versus {Si-O-Si, and Ad(om) versus {Si-O-Si. Inneither case can a correlation between bond length variation and
{ Si-O-Si be proved (Table 6, Nos. 10 and 11). This result is at variancewith the finding of Brown et al. (1969) who claim to have established ad(Si-O) versus dSi-O-Si correlation for the SiOz polymorphs (Table 6,Nos. 8 and 9). This discrepancy has two reasons: a) Brown et al. usedunit weights for their least squares fit, thus giving undue weight to thedemonstrably poor keatite data and to two of the tridymite points,and b) they used the uncorrected bond length values for tridymite, be-cause they apparently overlooked the Iarge and anisotropic thermal mo-tion of the oxygen atoms in this compound.
In this context Brown and Gibbs' (1970) proposal regarding the order-ing of tetrahedral cations in sil icates sh,culd be discussed. They state that"Si should prefer those tetrahedral sites involved in the widest averageT-O-T angles, and Al, B, Be, or Mg those involved in the narrowestaverage T-O-T angles." It is thus argued by these authors that the di- andtri-valent tetrahedral cations 'pref er' tetrahedral sites with smallerT-O-T angles. If one turns the reasoning around it makes sense as a con-sequence of Pauling's electrostatic valence rule. Since oxygen atomsbonded tc AI, B, Be, or Mg wil l generally have relatively small contribu-ticns to their po from the tetrahedral cations, the angle T-O-T must besmall, so that additional contacts to non-tetrahedral cations can bemade, thus increasing the po-values of these oxygen atoms. This pro-posal is therefore a corollary of the electrostatic valence rule.
BoNo LBNcTHS AND ErpcrnoNpcATrvrry
The difficulty of reconciling the observed bond distances in certainsilicates with the tl-p r-bonding theory has led McDonald and Cruick-shank (1967a,b) to make additional assumptions. In hemimorphite(1967a) they had to assume the formation cf covalent bonds betweenzinc and oxygen atoms. They pointed out that the bond angles aroundthe oxygen atoms O(1) and O(2) (both non-bridging) are close to 120".
1 587
1588 WERNER H. BAUR
Ado" vs. { Si-O-Si
IN SiO. POLYMORPHS
AND 4 DISILICATES (Ap=O)
Ao*(A)
-o.020
-o.o40t40 t60
--+ + si-o-si (.)Frc. 3. Bond length variation Ad(om) versus {SiO-Si for silicates
in which Apo equals zero for all oxygen atoms.
thus indicating sp2 hybridization. This reasoning cannot be easily ex-tended to include the bridging oxygen atoms in the disilicates, becausethe average angle Si-O-Si (Tables I and. 2) for three-coordinated O(br)is 131.5" (mean of 6) and for four-coordinated O(br) it is 136.6o (meanof 6). It is of interest that these numbers are very close to those for three-and four-coordinated oxygen atoms in anorthite, (132.0' and 136.9",averages of 19 and of 4 values, Megaw et al., 1962). This means that onecannot generally assume spz and sp3 hybridization in these cases, sincethe values of the angles should then be close to 120o and 109.5'.
In their discussion of chain-silicates McDonald and Cruickshank(1967) went one step further and suggested that the different electro-positive character of the cations in the series of structures listed in Table8 could be related to the formation of partially covalent bonds of differ-ent strengths between these cations and the oxygen atoms of the silicategroup. Because of these covalent bonds the silicate 'ions' would lose partof their r-bonding potential. The more the silicate groups would thus'shed' their negative charge the smaller would the difierences (Ad(obs))between the Si-O(br) and the Si-O(nbr) bond distances become. Accord-ing to McDonald and Cruickshank (1967b) the decreasing values ofAd(obs) in Table 8 should therefore be caused by 'the Iower electroposi-
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C)bo^F.ax t <
b 0 0
ou),i 'o
F r+r' o
oo E
{J
o5 - C
qt
b o o
, d 7b 0 9.o c)k
uP O
k
o qU q
d €. d
o o
oh q
o <
P F6
d €o ( d
' i! do . dP od
U d
d o
o€ >( ! q
o . d
l r o
o o
o
(BF.
1590 WERNER II . BAUR
tive character of calcium, manganese and tin compared with sodium.'Ilowever it seems that this decrease in Ad(obs) can just as well be corre-lated with decreasing Apo-values of the bridging and non-bridging oxygenatoms in this series of chain-silicates. The main results of detailed calcu-lations of the same type as presented earlier for the disilicates are shownin Table 8 for the five chain silicates. The values of ArC(calc) closelyparallel those of Ad(obs). Since the full details of the calculations are notpresented here, at least the range of the Afo(br) is given in Table 8. It isobvious that the diminishing differences between Si-O(br) and Si-O(nbr)are related to the diminishing Apo values. While it cannot be ruled outcompletely that the electropositive character of the cations is also some-how connected with these differences, this series of compounds is a poorsample for testing this hypothesis, because the compounds are not iso-structural and the different oxygen atoms receive widely different bondstrengths.
The four pairs of strictly isostructural pyroxenes listed in Table 9 pro-vides the basis for a better comparison. The pyroxenes used representfour different structural types of pyroxene:
M2(2a1tat y 1(2+) I6r SirO6, diopside-type,
M 2(2 +)t6t M 1 (2 + ) tGr SirO6' orthoenstatite-type,
M 2(l +)tgt M 1 (3 +) t6r Si:Ou, j adeite-tvpe, and
M 2 (l + ) t6t M 1 (3 + ) I 61 S i r O o, sp o d u m e ne - t-v-pe.
Even the three clinopyroxenes are not strictly isostructural, because theycontain cations of different valence states in the ,44-sites, and have dif-ferent coordination numbers for the cations in the M2-site. As a conse-quence of this, the coordination numbers of the individual oxygen atomsand their Apo-values vary appreciably. Therefore a test for the influenceof the electronegativity can only be made within each given pair. Theelectronegativity-values in question are: Li, 1.0; Na, 0.9; Mg, 1.2; Ll, l.5;Ca, 1.0; Mn, 1.5, and Fe, 1.8 (Pauling, 1960). In Table 9 the pyroxeneswith the more electronegative Ml-cations (Mn, Fe) are listed on theright side, those with the less electronegative Ml-cations (Mg, Al) on theIeft side. The oxygen atoms O(1) are coordinated twice to MI, the O(2)-atoms only once. In orthoenstatite and orthoferrosilite the M2-site isoccupied by Mg and Fe respectively; each oxygen atom has one contactto the M2-site. No unambiguous trend attributable to electronegativitiesis apparent between the bond lengths of the pyroxenes on going from theleft to the right side of Table 9. The mean tetrahedral distances Si-O in-crease (Nos. 1 and 3), decrease (No. 2), or do not change (No. a). The Si-O(1) distances decrease (Nos. 2a, 3 and 4) or do not change (Nos. 1 and
SILICON-AXYGEN BONDS 1591
t * t " ' ' : l : " i ; io" i3or i ' i l l l i , i l ro i l i ;?)^: lo i l i . rd i f , rerent pyroxene structure types rhe po
2 a )
s i A - o 1 A
s i A - 0 2 A
s i A - 0 3 A
S i A - O 3 A
n e a n :
2 b )
t) po Apo
s i - o ( r ) r . 9 2 - n 2 r
s i - o ( 2 ) 1 . s 8 - o . s s
s i - 0 ( 3 ) 2 . 5 0 O . 3 7
s i - 0 ( 3 ) 2 . 5 0 0 3 7
n e a n : 2 . 1 3
o l o P s l d e , L a f f g s r 2 oC l a r k e t a 1 . . 1 9 6 9
d c " l c d o b s o d o . o d o u ,
1 . 6 1 6 1 . 6 0 2 ( 2 ) - 0 . 0 1 4 _ 0 . 0 3 3
1 . 5 8 5 1 . s 8 5 ( r ) 0 . 0 0 0 _ 0 . 0 s 0
r . 6 6 9 1 . 6 6 4 ( 2 ) - 0 . 0 0 5 0 . 0 2 91 . 6 6 9 1 . 6 8 7 ( 2 ) 0 . 0 1 8 0 . 0 5 2
1 . 6 3 5 0 . 0 0 9
o r t h o e n s t a t i t e , M g 2 S i 2 O 5M o r i n o t o 6 K o t o , 1 9 6 9
dcalc t lobs ado. Adont
I . 6 2 3 1 . 6 1 4 ( 8 ) - 0 . 0 0 9 _ 0 0 1 61 . 5 9 2 1 . 5 9 8 ( 8 ) 0 0 0 6 - 0 . 0 3 2
1 6 S 3 1 . 6 7 3 ( 1 0 ) 0 . 0 2 0 0 . 0 4 31 , 6 5 3 1 . 6 3 s ( 1 0 ) - 0 . 0 1 8 0 . 0 0 5
1 . 6 3 0 0 . 0 1 3
1 . 6 5 4 1 . 6 1 9 ( 8 ) - 0 . 0 1 5 _ 0 . 0 2 2
1 . 6 0 3 1 . 5 9 6 ( 9 ) - 0 , 0 0 7 - 0 . 0 4 s
1 . 6 6 4 1 . 6 6 3 ( 1 0 ) - 0 0 0 r o o 2 2I 6 6 4 1 . 6 8 7 ( 9 ) 0 . 0 2 3 0 . 0 4 6
1 . 6 4 1 0 0 1 2
j a d e i t e , N a A l S i r O 6P r e v i t t I B u r n h a n , 1 9 6 6
d - d A d A d
1 . 6 2 9 t - 6 3 7 ( 2 ) 0 0 0 8 0 . 0 1 4
1 . s 8 4 1 . s 9 0 ( 2 ) 0 0 0 6 - 0 0 5 3
1 . 0 4 0 1 . 6 2 8 ( 2 ) , 0 , 0 1 2 0 0 0 5
1 . 6 4 0 1 . 6 3 6 ( 2 ) 0 . 0 0 4 0 , 0 1 3
r - 6 2 3 0 - 0 0 8
d c a l c d o b s o d o . o d o ,
r , 6 2 5 r . 6 0 4 ( 6 ) - 0 . 0 2 1 - 0 . 0 4 0
1 . 5 9 4 r . s 9 4 ( 6 ) 0 . 0 0 0 - 0 . 0 5 0
1 . 6 7 8 1 , 6 8 3 ( 7 ) 0 0 0 5 0 , 0 3 9
1 . 6 7 8 t . 6 9 3 ( 7 ) 0 0 1 5 0 . 0 4 9
r . 6 4 4 0 . 0 1 0
o r t h o f e r r o s i l i t e , F e 2 S i 2 O 6B u r n h a n , 1 9 6 7
d c a l c d o b s a d o . o d o *
1 . 6 0 ? 1 . 5 8 1 ( 9 ) - 0 . 0 2 6 - 0 . 0 3 3
1 5 7 6 1 . 5 9 4 ( 1 0 ) 0 . 0 1 8 - 0 . 0 2 0
r . 6 3 7 1 , 6 4 4 ( 9 ) 0 . 0 0 7 0 . 0 3 0
1 . 6 3 7 1 . 6 3 8 ( 9 ) 0 . 0 0 1 0 0 2 4
1 , 6 1 4 0 , 0 1 3
1 . 6 1 7 1 . 6 1 r ( 8 ) - 0 . 0 0 6 - 0 . 0 1 3
1 . 5 8 6 1 . 5 7 3 ( 9 ) - 0 , 0 1 3 - 0 . 0 5 1
1 . 6 4 7 1 . 6 6 4 [ I 0 ) 0 . 0 1 7 0 , 0 4 0
I . 6 4 7 1 . 6 4 7 ( 9 ) 0 . 0 0 0 0 . 0 2 3
I 6 2 4 0 . 0 0 9
a c n i t e , N a F e S i r O .c l a r k e t a 1 . , 1 9 6 9
d - d ^ d A J
| 6 3 4 1 6 2 9 ( 2 1 - o o o 5 o o o r
1 , s 8 9 r 5 9 8 ( 2 ) o o o 9 - o . o 3 o
1 . 6 4 s 1 . 6 3 7 ( 2 ) - 0 0 0 8 0 - 0 0 9
I 6 4 s r , 6 4 6 ( 2 ) 0 . 0 0 r 0 0 1 8
t 6 2 8 ( 2 ) o 0 0 6
L i F e S i z O ec l a r k e t a l . , 1 9 6 9
d c u l c d o b s d d o .
r 6 3 2 1 . 6 2 9 ( 2 ) - 0 . 0 0 3
1 . s 8 6 r . 5 9 6 ( 3 ) o . o 1 0
1 . 6 3 2 1 . 6 2 6 [ 2 ) - 0 . 0 0 6
1 . 6 3 2 r 6 2 7 ( 2 ) - O . O O 5
1 . 6 2 0 0 0 0 6
Po APo
2 0 0 , 0 . 0 8
1 - 6 7 - 0 , 4 2
2 - 3 3 0 , 2 5
z - 3 3 0 2 5
2 . 0 8
s i B - o l B 2 f r o - 0 . 0 8
s i B - o 2 B 1 . 6 7 - 0 . 4 2
s i B - o 3 B 2 . s 3 0 2 5
s i B - o 3 B 2 . 3 3 0 , 2 5
n e a n : 2 . 0 8
3 ) p o ^ p o
s i o ( r ) 2 \ 3 0 . 0 7
s i - o ( Z ) 1 . 6 3 - 0 4 3
s i - o ( 3 ) 2 . 2 5 0 , 1 9
s i - o ( 3 ) 2 . 2 s 0 . 1 9
n e a n : 2 . 0 6
4 l p o
s i . - o ( r ] 2 1 7
s i o ( z ) 1 . 6 7
s i - o ( 5 ) 2 . 1 7
s i - o ( 3 ) 2 1 7
2 . 0 4
s p o d u n e n e , L i A l S i r , , 6C l a r k e t a l , 1 9 6 9
a P o d c a r c d o t r A d o . a d n .
0 1 3 I 6 3 0 1 6 5 8 ( 2 ) 0 0 0 8 O 0 2 O
0 3 7 I s 8 4 1 . s 8 6 ( 2 ) 0 0 0 2 - 0 . 0 3 2
0 1 3 I 6 3 0 1 . 6 2 2 ( 2 ) - 0 0 0 8 0 0 0 4
0 1 3 1 . 6 3 0 r . 6 2 6 ( 2 ) - 0 0 0 4 0 0 0 8
t . 0 1 8 0 , 0 0 6
a d o t
0 0 0 9- 0 . 0 2 4
0 . 0 0 6
0 . 0 0 7
2b). The Si-O(2) distances increase (Nos. 1, 3, and 4), decrease (No. 2b) ordo not change (No. 2a). Likewise there is no clearcut correlation betweenthe Ad(om) and the electronegativities of the cations in the Mt- and M2-sites. On the other hand the correlation between Ad(om) and A2o isexcellent and offers a reasonable interpretation for the differences in thebond lengths of the four different types of pyroxenes (see also the dis-cussion of clinopyroxenes by Clark et al., (1969). Brown and Gibbs (1969,1970) and Mitchell et al. (197O) attempted to correlate the Si-O bondIength differences in four clinoamphiboles with the electronegativities ofthe non-tetrahedral cations and with {Si-O-Si. The four amphiboles inquestion with their type formulas are:
1592 WERNER H. BAUR
tremolite, Ca2Mg5SisOrr(OH)r, Papike el al,. (1969):
M (2+) r r8t M (2+) 3t6t M (2*) r r6rSiaOr: (OH) z
Mn-cummingtoni te, (Mg, Mn, l -e)TSisOzz(OH)2, Papike et a l . (1969):
M (2+)r t4+2tM (2! ) . , rs t 17 (2+) , I6rSi80r , , (OH) '
g laucophane, Na2(Mg, Fe, Al ) rSiaOzz(OH)r , Papike & Clark (1968):
M (l +) rl8t M (2 +).\t6t M (3* ) zr61 SisO,,(OH) r
and gruner i te , FezSirO:z(OH)2, F inger (1969) :
M (.2.11 "t
t+ <z)t M (2 + ) 3t 6t M ( 2 + ):) r 6r Si8O r' (OH)'
Similarly to the case of the pyroxenes, no two of these four amphibolesa,re strictly isostructural. Cationic valences and coordination numbersvary distinctly. The greatest similarity is between Mn-cummingtoniteand grunerite, but the latter has a rather odd four plus two coordinationof ox1'gen atoms around the Fe2+-atoms which is essentially a one-sidedfour coordinat ion (Fe-O :2XI .99,2X2.14, and 2 X 2.76 A) . Consequent lythe number and valence state of the l igands of the sil icate oxygen atomsvary so much between these four amphiboles that it is impossible toascribe the silicon-oxygen bond length variations to the electronegativitydifferences of the non-tetrahedral cations. However the Ad(om) correlatewell with the Apo (see Table VI, in Baur, 1970, where the results of thebond lengths calculations for three of these amphiboles are shown).Since Brown and Gibbs (1969, 1970) and Mitchell et al. (1970) do notmake the comparisons between strictly isostructural amphiboles, theirdiscussion of SiO bond lengths versus electronegativity (and {Si-O-Si)is not convincing.
The experience with the strictly isostructural pairs of pyroxenes indi-cates that the search for a dependence of Si-O bond lengths on the electro-negativit l. of the other cations might be futi le. In principle, and apartfrom the Si-O case, one would think that such a dependence would bemost pronounced whenever an oxygen atom is involved in two bonds o-very unequal strength: the weaker bond should be affected by the electrofnegativitv of the cation forming the strong bond to the oxygen atom.For instance in cases l ike: X-O---H-O or X-O-H---O, where X is P, V, orAs the hydrogen bond distance should be influenced by the substitutionsin isostructural compounds. Three such cases have been investigatedlately: a) Naz(OHz)z(POBOH) and Naz(OHz)z(AsOrOH) (Baur andKhan, 1970), b) NaoF(OHz)rs(NaHzO) (AsOr)z and NasF(OH)16(NaHzO)(POr), (Til lmanns and Baur, 1970, and unpublished results) and c)
[Nau-u(OH)0-r(OH)481(XOa)r with X:P, V, or As (Til lmanns and
SILICON-AXYGEN BONDS 1593
Baur, 197 1). However the substitutions of As or V flor P did. not show amgefect on the average hydrogen bond lengths.
Appr,rcarroNs
The prediction of individual bond lengths has, apart from its intrinsicinterest, practical applications. It allows us to compare actually observedbond distances with the calculated ones so that we:
a) have an additional criterion for the correctness or accuracy ofcrystal structure determinations. Such was the case in Znz(BOz)zwhere the Zn-O distances varied from 1.86 to 2.13 A and the B-Odistances varied irom 1.22 to 1.544 when the structure was re-fined in the acentric space group Ic by Garcia-Blanco and Faycs(1968). Since the Apo were zero for all oxygen atoms such rangewas unusnal. Refinement of the structure in space grottp I2f c re-duced the bond length spread to 1.91 to 2.02 A f.or Zn-O, 1.33 to1.404 for B-O (Baur and Til lmanns, 1970).In this case the use ofthe Pauling-Zachariasen method of balancing valences (Zachari-asen, 1963) would not have shown that this structure was refinedin the wrong space group, because this method has no predictivevalue. It deduces bond strengths from the observed bond lengths,and therefore one cannot use it for the prediction of bond lengthsunless one wishes to reason in a circle.
b) can detect more complicated and interesting bonding phenomenaafter we are certain to have taken into account the simple effects ofApo on the bond lengths. While it is unlikely after the foregoing dis-cussions, that the {Si-O-Si or the electronegativit ies of certainligands have pronounced effects on Si-O bond lengths, it is never-theless certain that many other factors influence bond lengths (e.9.,
Jahn-Teller effect, lone pairs of electrons on certain cations, subtleasymmetries in the d-electron configuration as in the ruti le-typephases, Baur and Khan, 1971).
c) can predict bond lengths in pcorly known crystal structures, pro-vided we know the coordinalions of anions and cations around eachother. Actually it seems reasonable to assume that the d(calc) inTable 5 for Nos. 7 to 10, and 21 to 26 are closer to the true bondIengths Si-O in these compounds than the d(obs) are. A similarprediction made for i lvaite (Baur, 1970) has been verif ied recentlyas can be seen in Table 10 (Til lmanns and Baur, 1970, unpublisheddata). The predicted values in column 2 were based on equation (1)with the (d(Si-O)) taken from equation (2). Since this underesti-mated the (d(SiO)) for the Si(2)-tetrahedron the deviations be-
1594 WERNER H. BAUI\
tween columns 2 and 3 are for this tetrahedron all in one direction.This detailed prediction of individual bond Iengths approaches inits accuracy (mean Ad(oc):0.01 A) the precision of modern crystalstructure determinations.
d) can get additional information on the crystal chemistry of certaincompounds. An example is pumpellyite (No. 24, Table 2) thechemical formula of which is traditionally written in such a wayas to indicate the presence of water molecules in this mineral:
CarAl2(Mg, Fe, AI) (SiOr)Si rO?(OH)r(HrO, OH).
Upon calculation of the bond strengths for this mineral it is im-mediately obvious that no oxygen atoms in this structure receives abond strength of less than 1.00 v.u., when the contributions of thehydrogen atoms are disregarded. This excludes the possibility thatany one of these oxygen atoms represents a water molecule.Secondly the oxygen atom O(10) receives from Si(2) and one Ca-atom a bond strength of only 1.29 v.u., while the Si(2)-O(10) dis-tance is 1.650(18) A. Assuming O(10) not to be a hydroxyl group,the bond length calculation for the Si(2) tetrahedron would be aspresented in Table 11. Very obviously the d(calc) computed thisway disagree completely with the d(obs) (mean Ad(oc):0.032 A).When the calculations are based on the assumption that O(10) is ahydroxvl group, the mean Ad(oc) equals 0.006 A (Table 5, No. 24b).Therefore it has to be concluded that pumpellyite actually con-tains SizOo(OH) groups and not SizOz-grouPs, and that the chem-ical formula should be written as
CazAh(Al, Mg, Fe)(O, OH)(OH), (SiOu)SizOoOH,
where the nonsilicate oxygen atoms are most likely disordered withOH-groups in the sites O(7) and O(11), and are replaced by OH tothe same degree as divalent cations are replacing aluminum atoms.
CorqcLusroNs
1. The extended electrostatic valence rule (rule 3, Baur, 1970), hasbeen found to give a reasonable interpretation of the bond length vari-ations in the disilicates, the pyroxenes and other silicate structures.
2. The dependence of d(Si-O) (and Ad(om)) on {Si-O-Si has beenfound to be a secondary consequence of the extended electrostatic valencerule. In crystal structures where Apo equals zero lor all silicate oxygenatoms, this dependence does not seem to exist. Therefore the simple d-2zr-bonding approach as discussed by Cruickshank (1961) andBrown et al.(1969) should be discarded as a general bonding theory for silicates.
1595
N N N @
N N N @
@ Q Q h
=
N N O OO O N N
^ ^ ^ o
do
N N N N E
< n a o q
?
o
o
€o
o
x
o
o
d
o
v o
@ @
P X
H d
€ o
o o
O ^. i o
d vi o
i d
U P
F
SILICAN-AXYGEN BONDS
trd
o s i o o + Fh 0 o @ h sa 9 h 9 @ @
i - d i d i
o i o i i N d
o o o o o o
d o N - n i r a- d o o o H o o
@ 0 @ q o n
: : i : : :d d i i i d
s d o o a aN @ 9 N @ @
i i i d d d
h !
6 !
oC od i
O
o ^
O N
I P
d . i
a
> oo d
o
atsrd
!
d
o
d
Q N
"d
o d
q a
9 Ep 6o
'd
0 0> 3
o o
O qo
a
o oo ( H
l . do !
( J p
o
dF.
X XN N
4 N O 4 n +
i d i N N N
. d . i . H . i . i . i
a o o @ o o
1596 WERNER H. BAAR
3. Brown and Gibb's (1970) proposal regarding the ordering of tetra-hedral Al, B, Be, and Mg in sil icates as a function ol T-O-T angle is acorollary of the electrostatic valence rule.
4. The dependence of d(SiO) (and Ad(om)) on the electronegativityof other cations bonded to the silicate oxygen atoms (McDonald andCruickshank, 1967b; Brown and Gibbs, 1969;1970) has not been proved.The previous workers overlooked that one would have to compare strictlyisostructural compounds in order to establish such a relationship. Effectsattributed by them to the dependence on electronegativity have beeninterpreted here as the consequence of Apo-variations.
5. The extended electrostatic valence rule, while it is useful as a tool forpredicting individual bond lengths in many crystalline compounds ofcourse cannot replace a detailed bonding theory based on the electronicstructure of the atoms. Attempts to establish such a theory should startpreferably where the extended electrostatic valence rule fails: in caseswhere all the oxygen atoms have Apq:O. Since in these cases no bondlength variations can be attributed to Apo-variations, rule 3 cannot beused to predict bond lengths, and therefore other effects can be studied indetail without the interference from Apo-effects. Among silicon con-taining compounds not only the SiOz-polymorphs, but also olivine,kyanite, and many other minerals, usually with simple crystal structures,fall into this group. A future detailed bonding theory of the sil icates andof other oxy-compounds, wil l have to take into account not only theelectronic structure within certain groups of atoms, such as the silicate-or phosphate-tetrahedra but also their relationships to all neighboringcations. Meanwhile we can use the extended electrostatic valence ruleand simple geometrical considerations for a semiquantitative predictionof bond lengths.
Acrc.low r-tocnllrlts
I thank Drs. W. C. Forbes, A. A. Khan, and R. B. McCammon for fruitful discussionsand the critical reading of the manuscript. I am grateful to Drs. W. A Dollase, J. H. Fang,
J. Felsche, and C. T. Prewitt for suppiying me with crystal structure data previous to theirpublication. The computing facilities used in this study were supported partly by NSF,Grant No. GP-7275.I thank Drs. J. R. Clark, R. D. Shannon, C. T. Prewitt and G. V.Gibbs for constructive criticism of the manuscript. The Computer Center and the ResearchBoard of the University of Illinois, Chicago, provided the computer time.
RrrnraNcps
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- (1970) Bond length variation and distorted coordination polyhedra in inorganiccrystals. Trans. Amer. Crystollogr. Ass.6, 129-155.
aro A. A. Knew (1970) On the crystal chemistry of salt hydrates. VI The crystal
SILICON-OXYGEN BONDS 1597
structures of disodium hydrogen orthoarsenate heptahydrate and of disodium hydro-gen orthophosphate hep tahydr ate. A c I, a C r y s t al,l o gr . 826, 1 584-1 596.
--, AND A. A. Kner (1971) On rutile-tlpe compounds. IV. SiOz, GeOr and a compari-
son with other rutile-type structures. Acta Crystol,Iogr. 827, in press.--, AND E. Trr.r.uaNNs (1970) The space group and crystal structure of trizinc di-
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1[o2ft, S.S.SR. 81, 581-584Bnowx, G. E., eNn Grrss, G. V. (1969) Oxygen coordination and the Si-O bond. Amer.
Mineral. 54. 1528-1539AND - (1970) Stereochemistry and ordering in the tetrahedral portion of
silicates. Amer. Mi.neral 55, 1587-1607.---t-t aNo P. H. Rrrrr (1969) The nature and the variation in length of the
Si-O and Al-O bonds in framework silicates. Amer. Mi,neral'.54, 104+-1061.BunNn,ur, C. W. (1967) Ferrosilite. Carnegie Insl. Wash. Year Booh. 65,285-290.C,lNnrto, E , A Der, Nncno, AND G. Rossr (1969) On the crystal structure of barylite.
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S teinbach meteorite. A c La Cr y s t al,l o gr. 23, 6t7 -623.-- (1968) Refinement and comparison of the structures of zoisite and clinozoisite.
Amer. Minerol 53, 1882-1898.- (1969) Crystal structure and cation ordering of piemontite. Amer. Mineral..54,
710-717.-- (1971) Refinement of the crystal structures of epidote, allanite and hancockite.
Amer. Mineratr. 56, M7464.Fnr,scnr,J (1970) Thecrystalstructureof o-PrzSizOz. Noturwi.ssmschaJten'57r452.ffrxcrn, L. W. (1969) The crystal structure and cation distribution of a grunerite. Mineral'.
Soc. Amer. Spec. Pap.2,95-100.Irnrno, R. L., axo D. R. Pnacon (1967) Refinement of the crystal structure of johannsen-
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1598 WERNER II. BAUR
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Ba:TiOSi:O;. z. Kristallogr. 130, 438-4148.Monnroro, N. aNo K. Koro (1969) The crystal structure of orthoenstatite. Z. Krislallogr
129, 65-83.
S. Arruoto, K. Koro, ,txn M. ToroNnur (1970) Crystal structures of high pres-
sure modifications of Mn2GeOa and CozSiOr. Phys. Earth Ptranel'. Interiors, 3' 161-165.
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Manwcript receireil, February 23, 1971; aceepteil Jor publ,ieation, March 26, 1971'
slLrcoN_oxYGEN BONDS 1.59S
lYote addedin prooJ.In my literature survey, I had overlooked the crystalstructure of kornerupine (Moore and Bennett, 1968), which also con-tains SirOz groups. The agreement between-observed and calculated bondlengths Si-O is in this case Ad(oc):0.004 A, using 1o-values of 1.83 v.u.for O(3) and O(4), and 2.17 v.u. for O(9). The bond strength valuesstated by Moore and Bennett in lheir Table 3 are partly in error.
An application of the extended electrostatic valence rule to kinoite(Laughon, 1971) shows that this new mineral should not be formulatedas CuzCarSisOro'2HzO as proposed by Laughon. If Laughon's formulais accepted, the water molecule oxygen, O(7), would be accepting a bondstrength oI 2.90 v.u. (from two Cu-ions, one Ca-ion, and two hydrogenatoms), while O(6) would receive 1.33 v.u. from one Si- and one Ca-atom,and the calculated Si-O bond lengths would completely disagree with thed(Si-O)"r". These inconsistencies can be removed by assuming that 0(6)and O(7) are both hydroxide groups. Therefore the correct formulationshould be
CuzCaz(OH)zSLOa(OH) z,
with discrete SLOs(OH), groups in the structure.
RrrnnrNcns
Mooto, P. B., eNo J. M. BnNNam (1968) Kornerupine: its crystal stntchte. Science
tsg,524-526.LeuGuoN, R. B. (1971) The crystal structure of kinoite. Amer. MineraL 56, 193-200.