American Mineralogist, Volume 69, pages 622444, tg\4

Structural studies of silicate glasses and melts-applicationsand limitations of Raman spectroscopy

Peul McMTLLAN

Department of ChemistryArizona State University, Tempe, Arizona 85287

Abstract

Raman spectroscopic studies of alkali and alkaline earth silicate glasses and melts arereviewed, and the major Raman bands observed for these series are summarized. Vitreoussilica shows weak bands near 1200 and 1060 cm-1, a medium intensity band group near 800cm-r , and a strong polarized band near 430 cm-r. Other silicate compositions show strongbands at I 100-1050 cm-r , 1000-950 cm-r , near 900 cm-r and near 850 cm-' , respectivelymaximized in relative intensity near the disilicate, metasilicate, pyrosilicate and orthosili-cate compositions. Glasses more silica-rich than the orthosilicate also show medium tostrong bands in the 700-500 cm-rregion. The variation of these bands with compositionand their polarization character are discussed, and other weak bands observed in variousstudies are noted. There is overall agreement as to the most general interpretation of thesebands in terms of the silicate glass or melt structure. In general, bands in the 1200-800cm-l region have been associated with silicon-oxygen stretching vibrations of tetrahedralsilicate units. The weak high-frequency bands of silica glass have been assigned toasymmetric stretching within a fully-polymerized tetrahedral silicate network, while thestrong polarized bands at l l00-1050 cm I, 1000-950 cm-r. 900 cm-r and 850 cm-r havebeen attributed to symmetric stretching vibrations of silicate tetrahedra with respectivelyone, two, three and four non-bridging oxygens. The bands in the 700-400 cm-r region havebeen associated with the presence of inter-tetrahedral Si-O-Si linkages. A number ofstructural models for silicate melts and glasses have been constructed on the basis of theseor similar band assignments. These are summarized, and discussed in terms of possibleconstraints regarding the vibrational interpretations. It is noted that to realize the fullpotential of Raman spectroscopy in structural studies of silicates in general will require adetailed understanding of their vibrational properties in relation to their structure. Anumber of vibrational calculations have been carried out for various silicate structures toaddress this problem. These are briefly summarized, and some limitations of the methodare noted. Finally, several recent studies have used silicate melt and glass structuralmodels derived from interpretations of Raman spectra to interpret systematic variations inbulk properties of the glasses and melts. Such systematics are examined for the viscosityand the immiscibility behavior of alkali and alkaline earth silicate series, within thelimitations of the Raman spectral interpretations as discussed here.

Introduction

Almost all igneous processes are associated with thepresence of a silicate melt phase, or magma. There hasbeen much interest in relating the physical properties ofsuch liquids to their molecular structure, and a number oftechniques have been used to gain structural informationon molten silicates. One such method has been vibration-al spectroscopy, including Raman scattering. Silicatemelts are high temperature liquids, which poses someexperimental difficulties for Raman spectroscopy. Forthis reason, most studies have been carried out on glassesquenched from their melts, and the results extrapolated to

the liquid structure. Although some authors doubt thegeneral validity of such extrapolations (e.9., Boettcher etal.,1982), they do seem reasonable for vibrational stud-ies. A number of workers have compared the infrared andRaman spectra ofvarious silicate glasses and their corre-sponding melts, and found the glass and melt spectra tobe similar (e.g., Markin and Sobolev, 1960; Sweet andWhite, 1969; Sharma et al., 1978a; Piriou and Arashi,1980; Kashio et al., 1980; Seifert et al., l98l). Thissimilarity was used to suggest that structural interpreta-tions of glass spectra should also be valid for the corre-sponding melts.

Accepting that Raman spectroscopic studies on silicate

0003-004x/84/070E-0622$02. 00 622

McMILLAN: RAMAN SPECTROSCOPY 623

glasses may be used to model the structures of silicatemelts, geochemists have combined their results with thelarge body of data from workers in the glass and solidstate sciences. The first Raman studies of simple silicateglasses were carried out shortly after the discovery oftheRaman effect in the late 1920's, and have continued to thepresent day. From the early 1960's, most ofthese spectrawere obtained using laser sources, but it is of interest tonote that much of the earlier work with arc sources iscomparable in quality to later studies. There are now aconsiderable number of studies which have used Ramanspectroscopy to probe the structures of silicate glassesand melts, which are summarized in Table l. This articleis intended to review these studies for alkati and alkalineearth silicate systems. The initial section discusses indetail the experimental observations for the ensemble ofRaman studies of simple silicate glasses and melts. Thissection is likely to be only of interest to the spectrosco-pist; the major Raman bands observed as a function ofsilica content are shown schematically in Figure 1. Thefollowing section concerns the interpretation of thesespectra in terms of structural models for silicate glassesand melts, beginning with the assignment of observedbands to specific structural features. The most generallyaccepted assignments are summarized, and the resultingstructural models are compared, while the possibility ofvibrational mode localization is discussed along withconstraints it might place on such models. The nextsection considers the relation between vibrational spectraand molecular structure in more detail, and criticallyexamines vibrational calculations which have been car-ried out for silicates. It is noted that until bonding insilicates is better understood, a rigorous correlation be-tween vibrational spectra and structure will not be possi-ble. The final section summarizes the major features ofthe Raman spectroscopic studies, and discusses applica-tions and current limitations of the method in structuralstudies of silicate melts and slasses.

Review of general experimental observations

Most of the experimental studies discussed below haveexamined the Raman spectra of alkali and alkaline earth silicateglasses, although a few have obtained spectra of their melts asnoted above. The glass compositions studied have generallybeen determined by a variety ofexperimental factors. The alkalisilicate systems show no stable liquid immiscibility (Levin et al.,1964; Toropov et al., 1972), and glass series have been preparedcontinuously from silica to near the metasilicate composition.Glasses with higher alkali content have not yet been studied dueto difficulties of preparation and problems of hydrolysis in air.The alkaline earth silicates (except for SiO2-BaO) show largetwoJiquid regions at high silica content and their glass serieshave usually not been studied to as high silica content as thealkali silicate glasses, although McMillan (1981, 1984) examinedCaO-MgO-SiO2 glasses with compositions within the twoJiquidfield. However, alkaline earth silicate glasses have beenprepared and studied to much lower silica content than the alkali

Table I . Previous Raman spectroscopic studies of silicate glassesand melts

P r i n g s h e i n a n d R o s e n ( 1 9 2 8 )

H o l l a e n d e r a n d I i l l i a m s ( 1 9 2 9 )

Gross and Romanovd (1929)

Hol I aender and Hi I I i ams ( 1931 )

Bhagavant i l ( 1931 )

K u j u m z e l i s ( 1 9 3 5 , 1 9 3 6 )

L a n g e n b e r g ( 1 9 3 7 )

v u k s a n d l o f f e ( 1 9 3 8 )

H i b b e n ( 1 9 3 9 , p . 4 0 8 - 4 2 4 )

i l o r r i s ( 1 9 4 1 )

R a n k a n d D o u g l a s ( 1 9 4 8 )

R u e s s ( I 9 4 9 , 1 9 5 0 )

V u k s a n d I o f f e ( 1 9 4 9 a , b )

P r o d ' h m r e ( 1 9 5 1 , 1 9 5 4 )

G r o s s a n d K o l e s o v a ( 1 9 5 2 , 1 9 5 3 )

K r i s h n a n ( 1 9 5 3 )

H i l m o t ( 1 9 5 4 )

H a r r a n d ( 1 9 5 4 )

E o b o v i c h a n d T u l u b ( 1 9 5 6 , 1 9 5 7 ,I 9 5 8 a - d , 1 9 5 9 ) i E o b o v i c he t a l . ( 1 9 5 5 )

F l u b a c h e . e t a l . ( 1 9 5 9 )

S i n o n ( 1 9 6 0 )

S i d o r o v ( 1 9 6 7 )

S i d o r o v a n d P r u d n i k o v a ( 1 9 6 8 )

Tob' in and Baak (1968)

H a s s ( 1 9 6 9 )

E t c h e p a r e ( 1 9 7 0 a , b )

E t c h e p a r e ( 1 9 7 0 c , 1 9 7 2 )

S t o l e n e t a l . ( 1 9 7 0 )

G a s k e l l ( 1 9 7 0 )

H a s s ( 1 9 7 0 )

l { o n g a n d A n g e l l ( 1 9 7 1 ; 1 9 7 6 ,p . 4 3 6 - 4 5 1 ) .

S w e e t e t a l . ( 1 9 7 3 ) ; X h i t e ( 1 9 7 5 )

B a t e s e t a l . ( 1 9 7 4 )

P a r k e ( 1 9 7 4 )

H a g i w a r a a n d o y a n a d a ( 1 9 i 4 a , b )

8.awer (1975)

B r a w e r a n d l h i t e ( 1 9 7 5 )

s m i t h e t a l . ( 1 9 7 5 )

l w a m o t o e t a l . ( 1 9 7 5 )

l . l i n t e r l i n 9 ( 1 9 7 5 )

l jnsuccessful at tenpt to obtain Ranans p e c t r @ o f S i 0 2 9 l a s s .

o b t a i n e d R a n a n s p e c t r m o f h i g h - s i l i c ap l a t e g l a s s .

R a m a n s p e c t r m o f S i 0 2 g l a s s .

S i 0 2 a n d h i g h - s i l j c a o p t i c a l g l a s s e s .

H i g h - s i l i c a o p t i c a l g l a s s e s ,

S i 0 2 a n d h i g h - s i l i c a o p t i c a l g l a s s e s .

s i 0 2 g l a s s ; c m e r c i a l g l a s s e s .

S i 0 2 - N a 0 2 g l a s s s e r i e s .

R e v i e w a r t i c l e .

H i g h - s i ' l i c a o p t i c a l 9 1 a s s e s .

S i 0 z a n d h i g h - s i ' l i c a c m e r c i a lg I asses .

H i g h - s i l i c a c w e r c i a l g l a s s e s ; r e v i e wa r t i c l e .

S i 0 , - N a , 0 g l a s s s e r i e s ; m u l t i c m p o n e n th i g h - s i l i c a q l a s s e s .

S i 0 2 g l a s s ; h i q h - s i l i c a c o m e r c i a lq l a s s e s .

S i 0 ? - K 2 0 , S i 0 2 - N a 2 0 a n d S i 0 2 - 1 i 2 0 g l a s ss e r l e 5 .

S i 0 z 9 l a s s .

S i 0 2 - N a ? 0 9 l a s s s e r i e s .

S i 0 z g l a s s ; p o l a r i z e d .

S i 0 " - K " 0 , S i 0 , - N a , 0 g l a s s s e r i e s ;o t h a r t i g h s i l i c a - g l a s s e s l p o l a r i z e ds p e c t r a ; v j b r a t i o n a l c a l c u l a t i o n s ,

5 i 0 2 g l a s s ; p o l a r l z e d ,

R e v i f l a r t i c l e .

N a r 0 - S i 0 , g l a s s e s d o p e d w i t h v a r i e t y o fcofrponenis; spectra above 700c n - I o n l y .

N a 2 G s i 0 2 g l a s s e s w i t h A s , S b .

s i 0 2 g l a s s ; h i g h - s i l i c a c w e . c i a lg l a s s e s ; p o l a r i z e d s p e c t r a .

S i o , g l a s s ; l d - f r e q u e n c y { < 8 0 0 c m - ! )region only: tmperature dependence,

S i 0 , - N a , 0 , S i 0 , - 8 a 0 , S i 0 , - S r 0 g l a s ss e r i e s ; - v i b r a t i o n a l c a l c i l a t i o n s .

c a t l g s i 2 0 E g l a s s ; p o l a r i z e d .

N e u t r o n - i r . a d i a t e d S i 0 2 g l a s s ( < 8 0 0c m - , o n l y ) .

N a 2 S i 0 3 g l a s s ; v i b r a t i o n a l c a l c u l a t i o n .

S j 0 2 - N a 2 0 g l a s s s e r i e s .

R e v i e w a a t i c l e ,

s i 0 2 , N a z s i 3 0 7 g l a s s e s .

N e u t r o n - i r r a d i a t e d S i 0 2 g l a s s ,

R e v ' i e w a r t i c l e .

Si 02-Pb0 and Si 02-Naz0 91 asses .

K - , N a - a n d L i - n e t a - a n d d i s i l i c a t eg l a s s e s ; v i b r a t i o n a l c a l c u l a t i o n s .

s i 0 r - K r 0 , N a r 0 a n d L i r 0 g l a s s s e r i e s rv i b ; a t i o n a l a a l c u l a t i d n s .

H i g h - s i l i c a o p t i c a l 9 l a s s .

S i 0 2 - K 2 0 g ' l a s s s e r i e s .

S i 0 , g l a s s : b e ] t r 6 0 0 c n - l ; e s P e c l a l l Ylow:faequency region.

624 McMI LLAN : RAMAN SPECTROSCOPY

Table l. (cont.) Table l. (cont.)

l la l rafen and Stone (1975),l ia l rafen ( 1975)

K o n i j n e n d i j k ( 1 9 7 5 )

K o n i j n e n k i j k a n d B u s t e r ( 1 9 7 5 )

Galeener snd Lucovlky (1976.)

Galeef,er and Lucovsky (1976b)

Stol en ( 1976)

V e r w € i j a n d K o n j j n e n d i j k ( 1 9 7 6 ) iK o n i j n e n d i j k . n d S t e v e l i ( 1 9 7 6 /

Kato ( 1976a ,b)

Stolen and t lalr . fen (1976)

Braf,er and Hhtte ( i977a)

Brawer and mite (1977b)

! r d o . o v e t ! 1 . ( 1 9 7 7 )

Koni jnendi lk and Bu3ter (1977)

Braxer and l iht te {1978)

L a u g h l i n e t a l . ( 1 9 7 8 )

F u r u k a w a e t ! 1 . ( 1 9 i 8 )

} lo116l l and Henshal l (1978)

s h a m a e t a l , ( I 9 7 8 a )

S h a m a 6 t a l . ( 1 9 7 8 b )

S h a r m a € t a l . ( 1 9 7 9 )

S d i s s y e t a l . ( 1 9 7 9 )

l tu.ray aid Greyt.k (1979)

S r i f e r t e t a l . ( 1 9 7 9 )

H e l m a n e t a l . ( 1 9 7 9 )

C h a n d t r s e k h a r e t a l . ( 1 9 t 9 )

Shama (1979) rnd Shama andYoder ( 1979)

P i r l 0 u a n d A l a i n ( 1 9 7 9 )

Furukrra and lhi te (19791

V e r r e t j ( 1 9 7 9 a , b )

I t r s c n e t i l . ( 1 9 8 0 . . b , c , d : l 9 8 l a , b ) ,Vlrgo et al . (1980) ind I tsen andv l r g o 0 9 8 0 r , b , c )

P i r t o u a n d A r s s h i ( 1 9 8 0 )

I t ikkelsen ahd 6aleener (1980)

Furukasa and lhi te (1980)

R a s h i o e t a l , ( 1 9 8 0 )

S h a r m i e t a l . ( 1 9 8 1 )

s h ' l b a t a e t a l . ( 1 9 8 1 )

I t n d i s c h a n d R i s e n ( 1 9 8 1 )

l s u n b w a k i e t a l . ( 1 9 8 r )

Si 02 9l ass.

t l ide rrnge Of alkal i and al tal lne earthglasses, and hor€ c@pler cmposif iOns.

Varlout Si 02- i l2Gt{} 9l asses.

51 0z gl ass; pol ar ized .

Second order spsctrn for 5i02 glass.

S l q g l a s s ( ( 9 0 0 @ - r o n l y ) .

S l 0 2 - K z 0 E l a s s s e r i e s ; o t h e rS i 0 2 - l q 0 t f g l a s s e s .

H i g h - s i l l c a g l a s s e s .

) j ! 2 S l a s : ; h i g h . s l l i c a S t 0 2 - K 2 O g l a s sl n t g n - r a e q u e n c y o n t y ) .

i la-, Ca- and i lg-si l ic6te andl l w i n o B l l i c a t e S l a s s s e t l e s .

i l a 2 s i 3 q 9 l a s s , a n d o t h o r c m t o s i t i o n 3 rdoped r l th chronlw.

v a r l o u s i l a z E T t 0 2 - s i 0 2 g l a s s e s .

5 i 0 2 - l ( 2 0 g l . s s s e . i e s ; o t h e r s ' l l l c a t og l a s s e s ; g l a s l e s c o n t ! i n i n g s u l p h a t e .

L i 2 S l z 0 5 , N a 2 S i 3 q g l a s s e s : p o l a r i z e d idoped rt th Fe20!.

S l 0 2 9 l 6 s s i b o r o s i l i c a t e 9 l a s s iv i b r a t i o n . l c a l c u l a t i o n .

P b G S I 0 , 9 l a s s s e r i e 3 ; d e c o n v o l u t l o n s ;polar lzfo 3pectr8.

P b G S i 0 2 E l a s s s e r i e s ; p o l a r ' l r e d .

S i 0 2 - l l a z 0 g l a s s e s . n d n e l t s .

A l u n i n o s i l i c a t e g l a s s e s ; p o l a r i l e d .

C a i h s i a 0 6 9 l 1 5 s ; p o l a r l z e d :a l m i . o s i l i c a t c a l a s s e s .

S i 0 2 g l a s s f i b e f s i d o p e d w i t h P 2 0 s r n du 2 u 3 .

Sl 02 91 ars; po' l ar i zed .

N a ? S i 0 3 g l a s s ; h i g h - f r e q u e n c y r e g i o no n r y .

S l 0 2 9 l a s 5 ; o p t i c a l g l a s s e s : p o l a r t z e d .

S l 0 z - T 1 0 2 g l r s s s e r l e s ; p o t a r i z e d .

Cat{gsi 2 0€-, . Caz t ts i 207 anda r s t n o s l I t c a t e g t a s t e l .

S i 0 2 - P b 0 g l a s s e s : a l u n i n o s l l l c a t e9 l a s s e s ; p o l a r i : e d ,

L i 2 5 i 2 0 5 g l a s s i p o l a r i z e d .

t ' l 2 s l 0 3 ( X " K , t l . ) . n d t q s i r o q ( i l . K ,N . , L i ) g l a s s e r ; p o l r . t z e d . - -

L i d e r d n g e o f . l k a l i a n d a l t a l t n e e a r t hs i l i c a t e , a l u n i n o s l l i c r t e a n d o t h e rg l a s s e s i b b n d d e c o n v o l u t i O n s .

S l 0 2 - P b o g l a s s a r i p d l a r t z e d ;deconvol ut i ons .

S l 0 z g l a s s ; W p o l a r i z e d o n l y ,

S i 0 , . K , S i 0 , . t { a , S i " Q a n di la25' | Os-gl aises;

'deaoivol ut lon .

5l0z-t{a20 dnd Si02-Cao glass and ne' l ts e r l e t .

S l 0 z g l a s s i p o l a r i z e d .

V a r l o u s h i g h - s l l i c a g l a s s e s .

( i l a , L i ) 2 s i 2 0 s g l a s s e s .

S l 0 2 - C a 0 g l a s s s e r l e r .

t u r u k a | a e t a l . ( 1 9 8 1 )

I t , D i l l a n e t a l . ( r 9 8 r ) , P l r i o u a n di b l i l l a n ( 1 9 8 3 a )

gihuni ik .nd cond. i te (1981)

Sprosdn et al . (1981)

Shama and Simons (1981)

s e i f e r t e t a l . ( 1 9 8 r )

l la lrafen and Krlshnan (1981)

Galeener and l , f i tkel sen (1981)

c i l e e n e r ( 1 9 8 2 a , b )

r,usen et al , (1982a)

f ,usen et al . (1982b)

S e i f e r t e t s l . ( f 9 8 2 )

P h i l I l p s ( 1 9 S 2 )

8 € r t o l u z z a e t a l . ( 1 9 E 2 )

x h i t e ( 1 9 8 2 )

i h i l t l l . n a n d P i . i o ! ( 1 9 8 2 , 1 9 8 3 a ) .I t i t t l l a n e t a l . ( 1 9 8 2 )

I t i l i l l a n a n d P i r i o u ( 1 9 8 3 b )

P i r i o u a n d i t i t i l l a n ( 1 9 8 3 b )

S h . m r e t r l , ( 1 9 8 3 )

t ' tatson et r l . (1983)

f i i l t e r c t . l , ( 1 9 8 3 )

G a l e e n e r e t r l , ( 1 9 8 3 )

Galeener and Getssb€rger (1983)

l t l t l l l a n ( 1 9 8 4 )

S i o , - t { a r 0 g l a s s s e r i e s ; p o l t . i z e d ;d e c 6 n v o T u t l o h s ; v i b . a t i o n r lc a l c u l a t l o n .

C a l h s i 0 q g l a s s ; p o l a r i z e d .

V a r i o u s h i g h - r i l i c a g l a s s e s .

S i 0 2 a n d h i g h - s i l i c a o p t i c l l g l a s sf i b e r s .

A l s i n o s i l l c a t e g l a s s e s ; p o l a . i z c d .

Sior- i lar0 rnd alunlnosl l lcr te glassesard-f lelEsi tmp€rature-reduced spectra.

H i g h - p r e s s u . e S i 0 2 9 l a s s .

S i 0 ? g l d s s i p o l a . l z e d i o r y g e n i s o t o p i cexcnange.

s i 0 r g l a s e ; p o l a r i z e d ; t m p e r a t u r eaeduceo .

S i 0 2 - i l a z 0 , B a o , c i o , ( C a o . s t t e . 5 ) 0 r n dl l90 glass ser i€s; deconvolut ions;f e v i d r a t i c l e .

Si0r-Cao glarses; high-frequency feglono n l i : d e c o n v o l u t l o n s .

Alunlnosi I icate 9l asses ;d@onvol ut i ons.

R e Y i f l a r t i c l e .

R m a n s p e c t f a o f s i l i c a g e l s a n d 9 l a s s .

Heat-treated Ll2Sl20s and sodims t l i c a t e 9 l a l g e s .

Y a . i o u s a l m i n o s l l l c a t e g l a s s s e . i e s ipol ar ' l zedi deconvol ut ion.

S i 0 2 - n a 2 0 a n d ( C 4 0 . s f i g 0 . 5 ) 0 g l a s ss e r i e s l a l u n i n o s l l i c a t e g l a s r e s ; r e v l e in r t l c l e i p o l a r i z e d .

Si0?, CaSt0?, CaltSt0n anda l u i i n o s l l i a a t e g l . s s ; s ; p o l E r i z e d .

V a t i o u i a l m i n o s l l i c l t e g l a s s e s ;pol ! .1 zed .

H t g h - s i l l c a S t o , - t b o ( l " L l , i l a , ( .Rb, Cs) 9l assesl di f fe.ence spectra .

C a O ' A l ? 0 3 - S t 0 2 g l a s s e s .

Si0, and related glasses: r lso neutronscaitBr lng and lnfrared ref lect lond a t r .

S l 0 2 g l a s s r s i l l c o n ' l s o t o p l c e x c h a n g e .

c a o - r u o - s t 0 2 g l r s s e s : p o l a r i z e d :dcconvol ut lons .

series, extending the composition range to near the orthosilicatecomposition.

Previous Raman spectroscopic studies on silicate melts andglasses are summarized in Table l . (For the sake ofcompleteness, this table also includes work on more complexcompositions, such as borosilicate and aluminosilicate systems,but which are not discussed in the text.) Within these studies,spectra for similar glass compositions are generally comparable.Some slight diferences may be ascribed to compositional errors,such as those induced by alkali oxide loss on heating (e.g.,Seifert et al,, 1979), Measured positiorrs of well-resolved bandsgeneral ly agree to within +5 cm-r, which is reasonableconsidering the large band widths involved, while reportedpositions of poorly-resolved bands may vary more than this. Ingeneral, the degree of resolution of irrdividual bands forcomparable experimental conditions decreases in the order Cs >

MCMILLAN : RAMAN SPECTROSCOPY 625

h.bAco'

Poo

Rffi *itl cmr

t@ 8@ 600

l l

fl tr

D Eo!

ntr

s,.q

Fig. l. Schematic of major band groups maximized as afunction of silica content in alkali and alkaline earth glass andmelt scries. The low-frequency (700-400 cm-r) group is shownhere as a single continuously varying band. In fact, discretebands are observed in this region (see text), but their behaviorwith composition is not yet well characterized.

Rb > K > Na > Li > Ca > Mg for systems studied (e.9., Brawerand White, 1975, 19772:' Brawer, 1975; Mysen et al., l9E0a;McMil lan, 1981, 1984; Matson et al. , 1983).

A number of studies have used deconvolution or curve-fittingtechniques to separate such unresolved bands into componentsets (e.9., Furukawa et al., l97E; Piriou and Arashi, 1980;Furukawa and White, 1980; Mysen et al., l9E0a,b,c,d, l9Ela,b,l9E2a,b; Mysen and Virgo, 1980a; McMillan, 1981, 1984; Seifertet al., l9E2; McMillan et al., 1982). When there are sufficientexperimental data and individual band shapes are known,deconvolution methods allow a good solution for componentband number, positions and relative intensities within anunresolved envelope. In general, a single pure vibrationalabsorption band may be approximated by a Lorentzian functioncentered at the resonant frequency (e.g., Carrington andMclachlan, 1979, p.9-ll). In vitreous systems, there is somedistribution of individual geometries which will result in adistribution of vibrational resonant frequencies. At the sametime, there will be vibrational coupling with some degree ofcoherence between vibrating units, which will also affect theobserved band shape. The above efects are not yet wellunderstood, and vibrational band shapes for glassy systems arenot yet known. In most ofthe above work on silicate glasses, thecomponent Raman bands have been approximated by Gaussianfunctions. Although most ofthese studies have given reasonableagreement with the observed spectra, none of the fits reproducethe experimental spectra exactly. This may be due to a variety offactors: noise in the experimental spectra, deviations ofthe truecomponent bands from Gaussian shape; weak true componentbands not considered in the fit, errors in the chosen componentband set, or baseline corrections not accounted for.

In order that the fit be as realistic as possible, a number ofconstraints have been placed on the various fitting models. In allfits, the major component bands must correspond to unresolvedpeak maxima and slope changes in the experimental spectra.This constrains the minimum number of major components andtheir general position, and is more complete when carried out forboth parallel (VV) and perpendicular (VH) polarized spectra.Fitting of weaker bands is generally carried out by ditrerence,using statistical techniques to achieve a best fit, or by makingfurther assumptions as to the behavior ofthe major components.

To summarize the results on the alkali and alkaline earth glassseries, it is useful to consider their spectra in three regions: (l)the high-frequency region between 1200 and 800 cm-'; (2) thelow-frequency region between 700 and 400 cm-r, and (3) themid-range region between 800 and 700 cm-'. The band groupsdiscussed below are schematized in Figure l.

The hig h-frequency region

The spectrum of vitreoussilica shows two weak, depolarizedbands (depolarization ratio p - 0.75: Furukawa et al., l98l) near1200 and 1060 cm-t. Seifert et al. (19E2) and Mysen et al. (l9E2a)have suggested that the 1200 cm*r band may be split into twocomponents, at l160 and 1209 cm-t. For compositions betweensilica and the orthosilicate, the high-frequency region of the glassand melt spectra may be expressed in terms offour bands nearl100-1050 cm-', 1000-950 cm-r,900 cm-r, and 850 cm-r (e.g.,Virgo et al., l9E0; Mysen et al., 1980a, 1982a). These bandsappear successively in that order as the silica content isdecreased, with the I100-1050 cm-r band maximized in relativeintensity near the disilicate composition, the 1000-950 cm-lband near the metasilicate composition, and the 900 and 850cm-l bands respectively maximized near the pyrosilicate andorthosilicate compositions (Furukawa et al., l9El ; Mysen et al.,1982a; McMillan, 1981, l9E4).

The 1100-1050 cm-t band. The band appears on initialaddition of MzO to silica in the alkali silicate glass series (e.g.,Hass, 1970; Brawer and White, 1975; Konijnendiik, 1975;Verweij and Konijnendijk, 1976; Konijnendijk and Stevels, 1976;Mysen et al., 1980a, l9E2a; Furukawa et al., l98l; Matson et al.,1983), and is a major component in the spectra of high-silicaalkaline earth glasses (e.g., Etchepare, l970a; Virgo et al., 1980;Mysen et al., 1980a, l9E2a,b; Mysen and Virgo, l9E0; McMillan,l9El, 1984). The band appears near ll00 cm-r for K- and Na-series, near l0E0 cm-r for Li-series and near 1060 cm I for Mg-,Ca-, Sr- and Ba-series, while its width at half height (the "bandwidth") increases from near 50 cm-rfor Na- and K-series tonear 100 cm-rfor Li- and alkaline earth glass series. A fewpolarized (i.e., where parallel (VV) and perpendicular (VH)spectra have been obtained separately) Raman studies have beencarried out for these glasses. The depolarization ratio p is definedas lyg/Iyy (Herzberg, 1945, p. 246-249). Only totally symmetricvibrations of systems with cubic point symmetry are completelypolarized, with p = 0. Antisymmetric vibrations (B, E or Fsymmetry) are fully depolarized, with p = 0.75, while all othervibrations have intermediate depolarization ratios. Thesecorrespond to symmetric modes of non-cubic point groups, andto non-totally symmetric vibrations of cubic groups. Suchvibrations are referred to here as partially polarized. Furukawaand White (1979) suggested that the l0E0 cm-' band for Li2Si2Osglass was completely polarized, while Verweij (1979b) found thesame band to have a depolarization ratio of 0-0.1 for Li2Si2O5,Na2Si2O5 and K2Si2O5 glasses. McMillan (19E4) found the 1056cm-l band for the SiO2-CaMgSiOr glass series to have p - O.2.The l100-1050 cm-r band decreases rapidly in relative intensityfor compositions less silica-rich than the disilicate (Furukawa etal., l98l; McMillan, l9EI, l9E4), although a contribution maystill be present near the orthosilicate composition (McMillan,l9E4; also Mysen et al., l9E2a), and may show a slight frequencydecrease to near 1050 cm-rfor the alkali series between thedisilicate and metasilicate compositions (e.g., Brawer and White,1975; Verweij and Konijnendiik, 1976; Mysen et al., l9E0a,1982a; Furukawa et al., l98l). There is no evidence for such a

I

I

s!%f1

626 McMILLAN: RAMAN SPECTROSCOPY

frequency decrease in the alkaline earth series, but this could beobscured by the poor band resolution.

Some workers have noted additional weak bands near ll00cm ' at high silica content. First, for compositions between silicaand the disilicate in K- and Na-series, the I 100 cm I band has ashoulder near 1120-1180 cm I which appears to have a higherdepolarization ratio than the ll00 cm-r band. (Brawer andWhite, 1975; Iwamoto et al., 1975; Verweij and Konijnendijk,1976; Konijnendilk and Stevels, 1976; Furukawa and White,1980; Mysen et al. , 1980a, 1982a; Furukawa et al. , l98l). Matsonet al. (1983) have obtained difference spectra for high-silicaglasses SiO2-MzO (M : Li, Na, K, Rb, Cs), and observed ashoulder near 1150 cm-r which they found to be polarized.However, this shoulder decreases in relative intensity withdecreasing silica content, unlike the major ll00-1050 cm-r band,and is no longer observed after the disilicate composition. lt ispossible that this weak l120-1180 cm I band is related to the1200 cm-r band described earlier for vitreous silica, or to aspecies similar to that responsible for the major t 100 cm-r band(Matson et al. , 1983).

Verweij (1979b) observed a broad depolarized band (p = 9.6-0.8) near 1080 cm ' for K2Si2O5 and Na2Si2O5 glasses, and near1050 cm I for Li2Si205 glass. Brawer and White (1978) suggestedthat this depolarized band had two components at 1065 and 1045cm-r, although Furukawa and White (1979) found only a singledepolarized band at 1038 cm I for the same glass. Furukawa etal. (1981) observed a depolarized band near 1080 cm ' betweensilica and the disilicate composition for the Na-series, whosedepolarized band maximum decreased sharply to near 1050 cm I

between the disilicate and metasilicate. It is probable that adepolarized band near 1080 cm I is associated with the majorI100 cm ' band for K- and Na-series, while a similar depolarizedband may be present for Li-series. McMillan (1981, 1984)suggested a weak depolarized (p : 0.5-0.8) band at I 154 cm '

for the SiO2-CaMgSiO+ glass series, over a similar compositionrange to the major 1056 cm I band.

The 1000-950 cm I band. In unpolarized spectra of alkalisilicate glass series, a band is first observed near 950 cm-r (forNa- and Li-series; near 930-940 cm I for K-series) near 20moleVo M2O. The band remains at these frequencies andincreases in relative intensity with increasing M2O content untiljust before the metasilicate composition (e.g., Brawer andWhite, 1975; Iwamoto et al., 1975; Verweij and Konijnendijk,1976; Mysen et al., 1980a, 1982a). Between 40 and 50 moleVoM2O, and for unpolarized spectra, it appears that the frequencyof this band increases sharply to near 980 cm | (for Na2SiOlglass;970 cm 'for K2SiO3 glass). Previous descript ions oftheseunpolarized glass spectra have considered that the 950 and 980cm-' bands are the same band, whose frequency increasessharply just before the metasilicate composition, and whoserelative intensity increases smoothly with M:O content tobecome maximized at the metasilicate. However, examination ofpolarized spectra of these glass series shows the interpretation tobe more complex (e.g., Brawer and White, 1978; Furukawa andWhite, 1979; Verweij , l9 ' l9a,b; Furukawa et al. , l98l).Comparison of VV and VH spectra suggests that the 950 cm-lband has a higher depolarization ratio than the major band near970 cm ' which appears later in the composition series, andwhich does not appear in the VH spectra. There are severalpossible explanations for this apparent problem. First, the major970 cm-' band may be unrelated to the depolarized 950 cm I

band, and grows rapidly only on approaching the metasilicate

composition. Second, there could be errors in measuringfrequencies of the weak bands in the VH spectra, and the 950cm I band could in fact correspond to the 970 cm-r VV band.Finally, the 970 and 950 cm I bands could be due to related butdifferent vibrations, the 970 cm-r band only becoming stronglyRaman-active just before the metasilicate composition.

Mysen et al. (1982a) have obtained unpolarized spectra for theseries BaO-SiOu, where the high-frequency bands are well-resolved. As for the alkali series, they find a weak band near 950cm ' at 75 moleVo silica. However, these authors suggest thatthe band decreases in frequency (to near 935 cm-r) until near 60moleVo SiO2, then increases to near 950 cm-r for the metasilicatewhere it forms the major band. The behavior of this band for theCa-, Mg- and (CA + Mg)-series is less clear due to the poor bandresolution in these systems (e.g., Virgo et al., 1980; Mysen andVirgo, 1980a; Mysen et al., 1980a,b, 1982a; Kashio et al., 1980;Tsunawaki et al., l98l; McMillan l98l, 1984). The band appearsnear 980-960 cm ' for all these series. Mysen et al. (1982a)suggest that this band does show a frequency change withcomposition for the Ca-series, while McMillan (1984) found noevidence of significant change for the (Ca + Mg)-series. Thesedifferences are probably partly due to the different deconvolutionprocedures. ln fact, it is likely that small frequency changes dooccur with composition for all these bands, but these may not yetbe well characterized.

McMillan (1981, 1984) found the 972 cm-t band for the (Ca +Mg)-series to be highly polarized (p - 0. l); slightly morepolarized than the 1050 cm ' band (p - 0.2) discussed in theprevrous sectton.

The 900 cm I band. A major band near 900 cm-r has onlybeen explicitly observed for the alkaline earth series (e.g.,Kashio et al. , 1980; Virgo et al. , 1980; Mysen et al. , 1980a,b,d,l98la, l982a,b; Mysen and Virgo, 1980a; McMil lan, l98l, 1984;McMillan and Piriou, 1983b). The band is maximized in relativeintensity near the pyrosilicate composition (Virgo et al., 1980;Mysen et al. , 1980a, 1982a; McMil lan, 1981, 1984), and is onlyresolved for a narrow range of composit ions near thepyrosilicate. lts presence in higher silica glass spectra has beendeduced from band deconvolutions (e.g., Mysen et al., 1980a,l982a,b; McMillan, l98l, 1984), and is first observed in this waybetween the metasilicate and disilicate compositions. lt ispossible that this 900 cm-'band may be present in spectra ofalkali silicate glass series, but unresolved from the major 1000-950 cm-l band (see Mysen et al.,1982a). McMillan (1984) foundthe 906 cm I band for the SiO2-CaMgSiO+ glass series washighly polarized, with a similar depolarization ratio (p - 0.1) tothe 972 cm-' band discussed in the previous sectjon. The bandwidth found for the 906 cm I band (-80 cm-r) was noticeablylower than those for the major 1058 and 972 cm I band (-100cm r; discussed above, but comparable to that of the band near850 cm ' considered below (McMillan, 1984). The major 906cm-' band could be associated with a weak depolarizedcontribution near 1040-1080 cm-' (McMillan, 1984).

The 850 c'm-t band. This band first appears near 40 mole 7oM2O in the alkali silicate glass series, near 860 cm I for Li- andNa-series, and near 830 cm I for K-glasses (e.g., Brawer andWhite, 1975; Verweij and Konijnendijk, 1976; Kashio et al.,1980; Mysen et al., 1980a; Furukawa et al., l98l). The bandincreases in relative intensity with increasing M2O content but isstill weak at the metasilicate, and is highly polarized (Verweij,1979a; Furukawa et al., l98l). In alkaline earth series, the bandis present in the highest silica glasses studied (generally 30-40

mole%6 MO), and is found near 860 cm I for Ca-, (Ca + Mg)- andMg-series (e.g., Kashio et al., 1980; Virgo et al., 1980; Mysen etal. , 1980a,b,d, l98la, l982a,b; Mysen and Virgo, 1980a;McMillan et al., l98l; McMillan and Piriou, 1983b; McMillan,1981, 1984), and near 850 cm-r for Ba-series (Mysen et al.,1982a). McMillan (1984) found the 862 cm t band for the SiO2-CaMgSiOa series to be completely polarized (p < 0.1) withinexperimental error. This 862 cm I band was probably alsoassociated with a weak, depolarized band near 933 cm-r(McMillan et al., l98l; Piriou and McMillan, 1983a).

The low-frequency region

Vitreous silica shows a strong band at 430 cm-'. This band isasymmetric, partly due to weak bands near 270 and 380 cm-rwhich correspond to maxima in the depolarized spectrum(Walrafen and Stone, 1975; McMillan et al., 1982), partly tothermal population efects (e.g., Hass, 1969; Leadbetter andStringfellow, 1974), and, is highly polarized. Two weak, sharppeaks which also appear polarized are observed near 500 and 600cm-r. The origin of these weak peaks is controversial. Theywere originally attributed to structural defects in vitreous silicaassociated with broken Si-O-Si bonds (e.g., Stolen et al., 1970;Bates, 1972; Bates et al., 1974; Stolen and Walrafen, 1976)Galeener and Lucovsky (1976a) suggested that the 500 cm '

peak was due to a longitudinal component associated with themajor 430 cm-r mode (see later), retaining the broken bondmodel for the 600 cm-r peak (Lucovsky, 1979). This model hasbeen criticized by Matson et al. (1983). Mikkelsen and Galeener(1980) and Galeener (1982a) proposed the 600 cm I peak to berelated to a specific vibration of small siloxane rings within theglass, while Sharma et al. (1981) applied this argument to the 500cm I peak, retaining a broken-bond assignment for the 600 cm-rmode. Matson et al. (1983) considered both broken-bond andring defect models possible for this latter peak. Galeener (1982b)suggested that both the 500 and 600 cm -r peaks were due to four-and three-membered siloxane rings. Finally, Phillips (1982) hasrecently proposed a model for defects in vitreous silica involvingdoubly-bonded silicon-oxygen linkages, but this does not seemto be supported by preliminary ab initio molecular calculations(M. O'Keetre and G. V. Gibbs, pers. comm., 1983; in prep.).These peaks are not discussed further here; it is only noted thatthey appear characteristic of the Raman spectrum of vitreoussilica.

On addition of alkali or alkaline earth oxide, the 430 cm I bandof vitreous silica decreases in relative intensity, disappearing atbetween 25 mole 7o (for K-series) and 50 mole Vo (for Mg-series)metal oxide. This band is replaced by a system of bands atprogressively higher frequency with decreasing silica content.These bands are poorly-resolved for all but the series SiO2-K2O(e.g., Iwamoto et al. , 1975; Brawer and White, 1975;Konijnendijk and Stevels, 1976; Verweij and Konijnendijk,1976), which is described first. On initial addition of K2O to silica(10 mole Vo KzO), the sharp 500 cm-t peak of vitreous silicaappears to increase in intensity. At 20 mole Vo K2O, this banddominates the low-frequency region, and has moved to 520cm t. At the same time, a band near 590 cm I has increased inintensity. By the disilicate composition, these bands are nearlyequal in intensity, and the lower frequency band has increased infrequency to near 560 cm-r. On continued addition of K2O, the560 cm-r band shows no further frequency change, butdecreases in relative intensity and is only a weak shoulder at themetasilicate composition. The 590 cm I band shows no

McMILLAN : RAMAN SPECTROSCOPY 627

frequency change with composition, and is the dominant low-liequency band for K2SiO3 glass.

Similar changes with decreasing silica content are observed forthe Na- and Li-glass series (e.g., Hass, 1970; Brawer and White,1975; Konijnendrjk, 1975; Mysen et al., 1980a, 1982a. Furukawaet al., 1981). The initial bands in these series also appear near 520cm-r, but rapidly become unresolved from the increasing bandat higher frequency, near 590 cm-t. The 520 cm I band appearsto show a similar frequency increase with M2O content as for theK-series, but this is partly obscured by the poor band resolution.

Similar bands are observed with increasing MO content in thealkaline earth series (e.g., Etchepare,1970b; Virgo et al., 1980;Kashio et al. , 1980; Mysen et al. , 1980a,b, 1982a; Mysen andVirgo, 1980a; Tsunawaki et al. , l98l; McMil lan, 1981, 1984;McMillan and Piriou, 1983). For the Ba-series near the disilicate,two bands are just resolved near 540 and 600 cm ' (Etchepare,1970b; Mysen et al., 1982a). As the BaO content is increased, theband system changes to give an unresolved asymmetric bandwhose frequency maximum increases to near 600 cm I near themetasilicate composition. The band asymmetry suggests at leastone other band at higher frequency. Ca-, Mg- and (Ca + Mg)-series have been prepared to near the orthosilicate composition(e.9., Virgo et al. , 1980; Mysen et al. , 1980a, 1982a; McMil lan etal. , 1981 ; McMil lan, 1981, 1984). For higher MO content than themetasilicate, the low-frequency band continues to increase rnfrequency to near 700 cm-' for the pyrosilicate, and becomesmore symmetric. Between the pyrosilicate and the orthosilicate,this band remains near 700 cm-r but decreases in relativeintensity.

The polarized Raman studies of Brawer and White (1977b,1978), Verweii (1979a,b), Furukawa and White (1979) andFurukawa et al. (1981) suggest that the 520-560 cm-r and 590cm ' bands for the alkali series are always highly polarized,although the weak 560 cm-r band near the metasi l icatecomposition in the SiO2-K2O series shows a significant peak inthe VH spectrum (Verweii, 1979a). McMillan (1984) found theasymmetric band near 600 cm-r and the band at 700 cm I for the(Ca + Mg)-series to be highly polarized.

It was suggested above that the bands near 500 and 600 cm I

observed on initial addition of M2O to vitreous silica might berelated to the sharp bands in the silica spectrum at thesefrequencies; however, this is considered unlikely. For very smalladditions of Na2O (Mysen et al., 1982a) or CaO (McMillan, 1984)to silica, the 500 and 600 cm t bands of silica glass are observedto decrease in intensity along with the silica glass spectrum. Thebands which develop on further addition of Na2O or CaO arethen new bands. Also, high-silica SiOz-CaO and SiOr-MgOglasses show a new band growing near 610 cm-r, as a shoulderon the 600 cm I peak of vitreous silica, with addition of MO(McMillan, 1981, 1984). The 520-560 and 590-610 cm I bandsobserved in the SiOz-M2O and SiO2-MO glass series are thennot simply derived from the 500 and 600 cm ' bands of vitreoussilica, but are new bands introduced with addition of metaloxide. However, their frequencies are similar to those of thesilica bands, which may suggest that they are due to similarvibrations in both silica and the other silicate slasses.

The mid-range region

The spectrum of silica glass shows an asymmetric band near800 cm r, with probable components near 790 and 830 cm I

(e.g., Mysen el al., 1982a). Comparison of VV and VH spectrashows that the lower frequency component has a higher

62E MCMILLAN: RAMAN SPECTROSCOPY

depolarization ratio than the other, although neither are highlypolarized (e.g., McMil lan, 1984; McMil lan et al. , 1982). Onaddition of alkali or alkaline earth oxide, this band moves tolower frequency (to near 770 cm-' at the metasi l icatecomposition), and shows diferent asymmetry. The band is nolonger clearly observed after the metasilicate composition (e.9.,Virgo et al. , 1980; Mysen et al. , 1980a, 1982a; McMil lan, l9El,1984).

Interpretation of spectra

Assignment of observed Raman bands

Most of the Raman spectroscopic studies discussed inthe preceding section have assigned the Raman bandssummarized above to specific types of vibration of vari-ous structural units, and hence developed models for theglass or melt structure. The arguments used in suchassignments have mainly been based on observed bandpositions and symmetry character, examination of sys-tematic changes in spectra with composition, and com-parison of corresponding glass and crystal spectra. Theassignments discussed below are the most generally ac-cepted in the current literature. Many of the basic con-cepts were developed early in the history of Ramanstudies of silicate glasses (e.g., Gross and Kolesova,1952, 1953; Bobovich and Tulub, 1958a-d. 1959). butmost have been modified over the past decade. Most ofthe Raman studies have primarily considered band as-signments related to vibrations of the silicate units, whichare generally described in terms of tetrahedral SiO4groups in various states of polymerization by corner-sharing of oxygen between tetrahedra (e.g., Liebau,1980). This is consistent with the results of diffraction andother spectroscopic experiments on vitreous and moltensilicates (e.g., Urnes, 1960, 1969; Mozzi and Warren,1969; Domenici and Pozza, 1970; Narten, 1972; Konnertand Karle, 1973; Wright and Leadbetter, 1976; Wasedaand Toguri, 1977; Nukui et al., 1978; Okazaki, 1979;Taylor and Brown, 1979; Misawa et al., 1980: Waseda.1980, p. 133-158; Greaves et al., 1982), and with thestructures of corresponding crystalline phases.

The high-frequency region It was concluded in theprevious section that the high-frequency spectra of alkaliand alkaline earth silicate glasses or melts could bedescribed in terms of combinations of four major polar-ized Raman bands; at I100-1050 cm-', 1000-950 cm-r,near 900 cm-1, and near 850 cm-1, each dominant at thedisilicate, metasilicate, pyrosilicate and orthosilicatecompositions respectively (see Fig. l). These bands havegenerally been assigned to symmetric silicon-oxygenstretching motions of silicate units containing SiOa tetra-hedra with respectively one, two, three and four non-bridging oxygens, denoted here as the groups = SiO,: SiO2, - SiO3 and SiOa (Fig. 2). This was suggestedindependently by a number of workers, beginning in themid- 1950's, and has been accepted by most other workers

sioII

sio - l i i - os i

IIo

Sl

r2oq|060= S i =

(c) S-ioII

s i o - s i _ o -

oJ I

i loo-o50

=s io

oII

sio- si _o-

II

900-si03

Fig. 2. Silicate structural units. (a) Schematic indicating thenature of bridging and non-bridging oxygen in the presentcontext. M* may also refer to 0.5 M2+, as in the alkaline earthseries; (b) The weak, depolarized bands at 1200 and 1060 cm-lare thought to correspond to asymmetric silicon-oxygenstretching vibrations within a fully-polymerized tetrahedralnetwork = Si =; (c) The four major polarized high-frequencybands are generally assigned to symmetric stretching vibrationsof tetrahedral silicate units with one. two. three and four non-bridging oxygens.

in the field (see references in Table | ). These assignments

have been rationalized by the following arguments.

The 1200-800 cm-r region contains the highest fre-quency first-order Raman bands of silicate melts and

sio

I5 i g - S i - 6 -

IIo -

tooo- 950

=s ioz

o-II-O -S i - o -

I

850

si04

MCMILLAN: RAMAN SPECTROSCOPY 629

glasses, consistent with silicon-oxygen stretching vibra-tions of tetrahedral silicate groups (see e.g., Lazarev,1972, p. 37-72; p. 163-164). The four dominant bandsnoted above are highly polarized, and that near 850 cm-rmay be completely polarized within experimental error.This would be consistent with a symmetric vibration withcubic point symmetry for the 850 cm-r band, and sym-metric vibrations of non-cubic symmetry for the 1100-1050 cm-r, 1000-950 cm-r and 900 cm-r band (e.g.,Herzberg, 1945, p. 271). Finally, there is considerablesimilarity between the spectra of glass or melt andcorresponding crystals at the disilicate, metasilicate, pyr-osilicate and orthosilicate compositions (e.g., Gaskell,1970; Etchepare, 1970c, 1972; Brawer, 1975; Brawer andWhite, 1975; Konijnendijk and Stevels, 1976; Verweij andKonijnendijk, 1976; Verweij, l979a,b; Furukawa andWhite, 1979; Sharma and Yoder, 1979; McMillan et al.,l98l; Piriou and McMillan, 1983a). Crystalline disilicatesshow major Raman bands near llfi) cm-r which havebeen compared with the 1100-1050 cm-r glass bandmaximized near the disilicate composition. Crystallinemetasilicates show strong bands near 1000 cm-i, compa-rable to the 1000-950 cm-r glass band maximized nearthe metasilicate composition. Crystalline pyrosilicatesand orthosilicates have their major high-frequency bandsnear 900 cm-l and 850 cm-l respectively, compared withthe major g lass bands near 900 cm-rand 850 cmlmaximized near the pyrosilicate and orthosilicate compo-sitions.

Alkali disilicate crystals have structures based on infi-nite sheets of silicate tetrahedra. Each tetrahedron hasthree oxygens corner-shared with other silicate tetrahe-dra, known as bridging oxygens. One oxygen per tetrahe-dron is non-bridging, and is coordinated directly to metalcations (Fig. 2). Alkali and alkaline earth metasilicates arebased on a variety ofchain or ring structures, where eachsilicate tetrahedron has two bridging and two non-bridg-ing oxygens. Pyrosilicates have structures in which twotetrahedra share an apex to give silicate dimer units, withone bridging and three non-bridging oxygens per tetrahe-dron. Finally, orthosilicates have silicate tetrahedra withonly non-bridging oxygens (e.9., Wyckoff, 1963, 1968;Bragg et al., 1965; Deer et al., l97l). The similarities inthe vibrational spectra of corresponding crystals andglasses were used here to suggest similar features in theirmolecular structures. (The term "molecular structure" isused to describe static structures within the glass, definedby relative atomic positions. This is distinguished fromthe "vibrational structure", which refers to atomic dis-placements during vibrational modes.) Combination ofthe preceding arguments has led to the band assignmentssummarized above, on which there is general agreement.However, there remains some uncertainty as to theextent of a structural unit characterized by these vibra-tional bands. For instance, is the l100-1050 cm-r bandcharacteristic of an "infinite" sheet of = SiO units, as indisilicate crystals, or may it indicate the presence of

discrete = SiO groups, perhaps isolated from each otherby other structural units? This important point is ad-dressed in a later section.

It was noted in the previous section that there are anumber of weak, depolarized high-frequency bandswhich seem associated with the major bands describedabove. It is likely that these are due to asymmetricstretching vibrations associated with the various silicategroups, although some second-order contribution fromcombinations of lower frequency bands is possible in thisregion. It was also noted previously that a band appearednear 940 cm-r for glasses with 30-40 mole Vo SiO2, whichincreased in intensity with decreasing silica content, toapparently become the dominant 1000-950 cm-r bandnear the metasilicate composition. Current band assign-ments do not yet provide any satisfactory interpretationofthe detailed behavior ofthis band (see earlier, and e.g.,Furukawa et al., l98l; p.3228-3229).

Vitreous silica itself shows two weak, depolarized high-frequency bands at 1200 and 1060 cm-r (or three, at 1060,ll57 and 1209 cm-t; Mysen et al., 1982a). Raman spectraof crystalline tetrahedral silica polymorphs show twogroups of bands centered near 1050 and 1200 cm-'(Bates, 1972; Etchepare, 1972; McMillan et al., 1982).Diffraction studies on silica glass and melt suggest thattheir structures are based on some fully-polymerizedthree-dimensional network of corner-sharing SiOa tetra-hedra, similar to those of its tetrahedral crystalline poly-morphs such as quartz or cristobalite (e.g., Wyckoff,1963, p. 312-322). The above observations have led mostworkers to assign the high-frequency bands to non-symmetric silicon-oxygen stretching vibrations withinthe framework structure. Galeener and Lucovsky (1976a)and Galeener (1982b) suggested that the two sets ofhigh-frequency modes for vitreous silica were due to trans-verse and longitudinal vibrational components, separatedin frequency by the electrostatic field in the glass (seee.g., Sherwood, 1972, p.3-4, p.20-22, p. 85-9a). Mysenet al. (1980a, l98lb, 1982a) considered instead that themodes indicated the presence of two structural units,differing in average Si-O-Si angle, within the glass.McMillan et al. (1982) discussed these interpretations,and suggested that the two or more high-frequency bandsof silica glass could be more simply be assigned todifferent vibrational modes associated with silicon-oxy-gen stretching within a single structure. However, arecent hyper-Raman scattering study by Denisov et al.(1978, 1980) seems to support the interpretation of the1200 and 1060 cm-r bands as a longitudinal-transversepair (also Matson et al., 1983). The best interpretation ofthese bands is not yet clear, and must await a betterunderstanding of the dynamics of vitreous silica.

The low-frequency region. All of the classes of crystal-line silicates described above, except for the orthosili-cates, show major Raman bands in the 700-400 cm-lregion. This observation has been used to suggest thatbands in this region are associated with the presence of

630 MCMILLAN : RAMAN SPECTROSCOPY

bridging oxygens, or Si-O-Si linkages, in the structure(e.g.,Lazarev,1972, p. 64-66). The appearance ofthesebands in the silicate glass spectra has been generallytaken as diagnostic of Si-O-Si linkages within the glassstructure, or silicate units more polymerized than theorthosilicate.

In the present silicate glass series, the frequency ofthe700-400 cm-r band changes systematically with composi-tion; this could be related to the degree of silicatepolymerization. The band occurs at 430 cm-' for silicawith only bridging oxygens between : Si : units,through 520-600 cm-r then 590-650 cm-r for linkagesbetween = SiO and : SiOz units respectively, to near 700cm-r for - SiO3 groups (see Fig. l). A number of studieshave shown that the frequencies of bands in this regionare sensitive to the Si-O-Si bond angle (e.g., Etchepare,1970a; Lazarev, 1972, p. 63-72; Scheetz, 1972;' Brawer,1975; Furukawa et al., l98l). If the nature of the vibrationresponsible for the 700-400 cm-r band remains similarwith changing silicate polymerization, it is possible thatthe systematic decrease in the frequency of this band withincreasing silica content may be due to an increase inaverage Si-O-Si angle with polymerization.

The detailed nature of the vibrations responsible for the700-400 cm-r bands is not yet well understood. Thesebands are always highly polarized, suggesting symmetricmotions. Lazarev (1972, p.63-72) used group theory todescribe the transition from orthosil icate to pyrosil icate,and concluded that the 700 cm-r band of the pyrosil icate(Si2O7) unit was due to a symmetric stretching of theterminal - SiO3 groups about the bridging oxygen. This isconsistent with the 28Si/30Si substitution experiment ofTarte et al. (19'13) for K2Pb2Si2O7, which has a linear Si-O-Si linkage. The large observed isotope shift for the 669cm I Raman band suggests a major component of Simotion in this vibration. However, the isotopic study ofGaleener and Mikkelsen ( l98l) for vitreous sil ica showedthat its 430 cm I band involves a large displacement ofthe bridging oxygen. Some workers have suggested thatthe 700-400 cm I band group is due to symmetric motionof the bridging oxygen in the plane bisecting the Si-O-Sil inkages (e.g., Bates, 1972; McMillan et al., 1982), whileother but similar interpretations involving oxygen motionhave been suggested (e.g., Bell and Dean, 1970). It isprobable that the true nature of these vibrations liesbetween these two extremes of silicon and oxygen dis-placement, and that their character changes with chang-ing polymerization of the silicate unit.

The mid-range bands. These bands near 800 cm-lappear weak in the room-temperature spectrum of silicaglass, but have a reasonable Raman intensity when thetemperature-normalized spectrum is considered (e.g.,Leadbetter and Stringfellow, 1974;McMillan et al., 1982).This, coupled with their low infrared activity (e.g., Miler1968), has been used to suggest a fairly symmetric originfor these bands (Piriou and McMillan. 1983b). The bandshave a high depolarization ratio which could be consistent

with symmetric vibrations of a point group with symme-try far from cubic within the isotropic glass. McMillan etal. (1982) have suggested that the bands near 800 cm-r forvitreous SiO2 are mainly associated with motions ofsilicon against its tetrahedral oxygen cage, with littleassociated oxygen displacement, which may involve asilicon motion symmetric about the bridging oxygen(Laughlin and Joannopoutos, 1977; Piriou and McMillan,1983b). This would be consistent with the small observedisotope shift in the 160/160 substitution experiment ofGaleener and Mikkelsen (1981), and the large associatedzt57:051 shift of Galeener and Geissberger (1983).

The Raman intensity ofthe band group decreases as theband becomes more asymmetric and moves to lowerfrequency (to near 770 cm-r) with decreasing silicacontent and is no longer visible below around ffi mole %osil ica (e.g., Furukawa et al., l98l; Mysen et al., 1982a).Weak Raman bands are observed in the 700-800 cm-lregion for crystalline disilicates and the tetrahedral silicapolymorphs, but generally not for less-polymerized sili-cates (e.g., Etchepare, 1972; Brawer and White, 1975;Verweij and Konijnendijk, 1976; Verweij, l979a,b;Sharma and Yoder, 1979; Piriou and McMillan, 1983a;McMillan, 1984). If these modes are associated mainlywith motion of silicon against its oxygen "cage", it ispossible that such vibrations may only be present forhighly-polymerized, semi-rigid networks. For less-poly-merized silicate units, such modes might transform to orcouple with other vibrations of the system with a greaterdegree of associated oxygen motion.

Many of the above band assignments to detailed vibra-tional motions are at present highly speculative. Firmerassignments will require further isotopic substitution ex-periments, and calculation of vibrational properties fromthe structure and bonding in the glass. A number of suchcalculations have been carried out for silicate glasses, andgive results in general agreement with the major bandassignments discussed above. However, such calcula-tions have a number of inherent limitations, and may notyet be used to resolve the true vibrational nature ofsilicate systems.

Band assignments and structural models for sili-cate glasses and melts

The vibrational band assignments discussed abovehave been used to construct a number of structuralmodels for silicate glasses and melts. These models showa number of common features, which are summarizedbelow.

The major high-frequency bands at l100-1050 cm-r,1000-950 cm-r, 900 cm-r and 850 cm-l are associatedwith the presence of = SiO, : SiOz, - SiO3 and SiOagroups following the notation described in McMillan(1984) (see Fig. 2), and may be used as indicative of thepresence of these structural units. The low-frequencybands (700-500 cm-r) are associated with the presence ofSi-O-Si linkages in groups more polymerized than SiOa:

MCMILLAN : RAMAN SPECTROSCOPY 631

The fully-polymerized silica network (= Si =) has onlyweak high frequency bands, but may be characterizedbyits strong asymmetric band in the 500-400 cm-r region.The groups = SiO, : SiO2, -SiO3 and SiOa are respec-tively dominant near the disilicate, metasilicate, pyrosili-cate and orthosilicate compositions, consistent with pro-gressive depolymerization of the silicate unit as the silicacontent is decreased. At compositions other than puresilica, there is coexistence ofthree or more bands charac-teristic of diferent silicate units, consistent with a distri-bution of polymer species. Mysen et al. (1982a) haveattempted to quantify this for a number of silicate sys-tems. Up to this level of structural modelling, there isreasonable agreement between interpretations. The gen-erally-accepted view is that of a fully-polymerized tetra-hedral silica network becoming gradually depolymerizedon addition of alkali or alkaline earth oxide. At anycomposition there is some distribution of silicate poly-meric species, whose average polymerization decreaseswith increasing metal oxide content. The character of thisdistribution is presumably a function of the system andthe experimental conditions.

Most of the Raman studies on silicate glasses andmelts, especially the earlier work, have not attempted tofurther specify the nature of these molecular groups.Etchepare (1970c, 1972) compared the spectra of crystal-line and glassy diopside (CaMgSizO6), and suggested thatthe : SiOz units in the glass structure were linked to form"infinite" chains as in the crystal. Brawer and White(1975) discussed alkali disilicate and metasilicate glassesin terms of sheet and chain structures by analogy withtheir corresponding crystals. These authors envisaged agradual change in structure with silica content for inter-mediate compositions via "concentration fluctuations,"where adjacent silicate tetrahedra may have differentdegrees of polymerization. This allows for a continuousoverall depolymerization of the glass structure by ran-domly breaking Si-O-Si linkages with decreasing silicacontent. This schema may be contrasted with the struc-tural model of Mysen, Virgo and coworkers (e.g., Mysenet al., 1980a, 1982a; Virgo et al., 1980), which alsoconsiders the melt structure to consist predominantly ofsheet units at the disilicate composition, and chains at themetasilicate. However, these authors considered that theRaman data and other observations were inconsistentwith the presence of structures intermediate betweensheet and chain in the glass or melt. They suggestedinstead that, for compositions between the disilicate andmetasilicate, sheets and chains coexisted as discretestructural units in mutually varying proportions. Theseworkers also proposed three other silicate structuralunits; a three-dimensional network unit, and dimer(Si2O9-) and monomer (SiOX-) units. Mysen et al. (1980a)considered that there was no spectroscopic evidence forstructures intermediate between the dimer unit and the"infinite" chain, Si2O{-.

The major diference between the above models arises

from the interpretation of linkages between silicate tetra-hedral units in the glass and melt structure. Since all ofthese models are based on Raman spectroscopic observa-tions, it is important to assess whether Raman spectros-copy of silicate glasses is in fact sensitive to thesedifferences, and whether limiting constraints may beplaced on such structural models from Raman data. Forthis, it is necessary to consider the spatial extent andcoherence of the vibrational modes responsible for themajor characteristic bands of structural units in thesilicate melt and glass.

Vibrational mode localization

A number of observations have led several authors tosuggest that certain vibrational modes of silicate glassesand melts are highly localized. The first and most obviousis that, although silicate melts and glasses are known tobe macroscopically disordered, they generally have majorRaman bands which are well-defined and are often highlypolarized. These suggest vibrating units with high sym-metry within the glass structure. Extended motions with-in the disordered network might be expected to giveweak, broad and depolarized bands in the Raman spec-trum, suggesting that the major polarized bands observedare localized within groups with at least a pseudo- pointsymmetry. This has been discussed by Brawer (1975),Furukawa and White (1980), and Furukawa et al. (1981)(see also White, 1982).

It was noted earlier that the major Raman band groupsof silicate melts and glasses correspond to those ofanalogue crystalline silicates. The major classes of sili-cate crystal structures may be distinguished on the basisof the degree of polymerization of their constituent SiOatetrahedral units (e.g., Liebau, 1980). Within any onegroup of silicates, the major features of their vibrationalspectra are remarkably similar; independent of the metalcation, crystal symmetry, unit cell size, or relative ar-rangement of the silicate tetrahedra. For example, Mc-Millan and Piriou (1983b) compared the Raman spectra ofcalcium magnesium metasilicates, (Ca,Mg)SiO3. In thesecompounds, the metal cation is varied between Ca2* andMg2*, the unit cells have orthorhombic, monoclinic ortriclinic symmetry and contain 10, 20 or 30 atoms in thespectroscopic unit cell, and the silicate units are presentas pyroxene or pyroxenoid chains or Si3O$- rings (e.g.,Wyckofl 1968, p. 294-296,301-303, 314-316 and 342-343; Deer et al., 1971, p. 99-l 19, 140-143). The Ramanspectra of all these compounds are similar, with onestrong band near 1000 cm-r and a second in the region650-550 cm-r, similar to the major bands of metasilicateglasses (e.g., McMillan and Piriou, 1983a). This could beinterpreted as due to localization of the modes responsi-ble for these major Raman bands within vibrating unitscommon to all these crystal structures. The commonfeatures in this case are the presence of SiOa tetrahedrawith two non-bridging oxygens (: SiOz units), and Si-O-Si linkages between such units, suggesting that the modes

632 MCMILLAN: RAMAN SPECTROSCOPY

may be localized within these groups. Since the spectra of(Ca,Mg)-metasilicate glasses may be equally well com-pared with any of the above crystal spectra, the glassRaman bands may not be used to distinguish betweenchain and ring structures in the glasses. In fact, if theinterpretation of major band localization is accepted forthe crystal spectra, this must also apply to those of theglasses.

A further observation consistent with localization ofthe vibrations associated with their major bands is provid-ed by the Raman spectra of phase-separated silicateglasses. Furukawa et al. (1981) obtained the spectra ofheat-treated Na2O-SiO2 glasses with 20 and 15 mole %oNa2O. They found that the ll00 cm-r band and itsassociated shoulder near 1165 cm-' did not change onannealing, which they attributed to a high localization ofthe vibrations responsible for these modes (see alsoWhite, 1982). For the 20 mole VoNa2O sample, rhe low-frequency band group near 500 cm-l resolved into bandsat 495 and 450 cm-l characteristic of vitreous silica andanother component at 530 cm-t, which Matson et al.(1983) used to suggest a relative delocalization for modesnear 500 cm-t. McMillan (1981, 1984) prepared sampleswith bulk compositions within the CaO-MgO-SiO2 two-liquid field. Normally quenched glasses were opaque andmacroscopically unmixed, while fast-quenched sampleswere transparent and homogeneous on the micron scale.The spectra of both sets were identical, and were simplesuperpositions of the bands of the limiting unmixedcompositions, which McMillan (1981, 1984) discussed asconsistent with a high degree of vibrational localization.On the basis of optical transparency, this localization wasproposed to be on at least the hundred Angstrom level.Brawer (1975) and White (1982) have come to similarconclusions. It is also noted that a high degree of localiza-tion of the vibrations responsible for these major Ramanbands would rationalize the observed correspondence ofsilicate glass and melt spectra, noted in the Introduction.The localized vibrating units are mainly associated withtetrahedral silicate units, which seem from diffractionstudies to be largely unchanged between glass and melt(e.g., Waseda and Toguri, 1977; Nukui et al., 1978).

Finally, the results of several vibrational calculationsfor silicate glasses imply a certain localization for thesemajor bands. A number of such calculations have onlyconsidered small silicate clusters (one or two linked SiOatetrahedra), and successfully reproduced the 1200-800cm-r and 700-400 cm-r bands (e.g., Etchepare, 1970a;Brawer, 1975; Brawer and White, 1975; Furukawa et al.,l98l). This suggests that the vibrations responsible forthe major bands may be localized within these vibratingunits. In addition, Bell and co-workers (e.g., Bell, et al.,1968; Bell and Dean, 1970; Bell, 1976) constructed arandom network model for vitreous silica and calculatedits vibrational properties. These workers defined a partic-ipation ratio which gave information on the localization ofselected modes, and found that silicon-oxygen stretching

motions associated with non-bridging surface oxygenswere highly localized (Bell et al., 1970).

The above arguments place some limitations on thetypes of structural model for silicate glasses and meltswhich may be derived from interpretation of their Ramanspectra. The major polarized bands at l100-1050 cm-'and 1000-950 cm-' have been associated with symmetricsilicon-oxygen stretching vibrations of groups containing= SiO and : SiO2 units. It was argued above formetasilicates with : SiO2 groups (McMillan and Piriou,1983b) that this vibration is probably highly localizedwithin individual : SiOz units. Similar arguments may bemade for the symmetric silicon-oxygen stretching vibra-tion of = SiO groups in disilicates. If this is so, then the1100-1050 cm-r and 1000-950 cm I Raman bands givelittle or no information as to how individual = SiO and :

SiO2 units are linked to neighboring silicate tetrahedralgroups.

The weak, depolarized high-frequency bands of thevitreous silica network (: Si :) have been assigned toantisymmetric silicon-oxygen stretching motions, andmust be less localized than the vibrations discussedabove. In principle, the behavior of these bands withaddition of metal oxide should give information on thedepolymerization mechanism of the silica framework.However, these bands are weak, and are usually ob-scured by the dominant stretching bands of less-polymer-ized species. Little can be said as yet regarding the-SiO3 stretching vibrations near 900 cm-I, since thereare insufficient Raman studies on crystalline pyrosilicates(with Si2O7 dimer groups) and silicates with - SiO3 unitsbound to other groups for comparison. These might helpdecide whether the symmetric - SiOr stretching motionsare mainly localized within individual - SiO3 units, or arecharacteristic of SizOr dimers.

Information on the coupling of adjacent silicate tetrahe-dral groups is probably contained in the low-frequency(700-400 cm-r) band group associated with vibrations ofthe Si-O-Si linkages. Different bands do appear in thisregion as a function of silicate polymerization, but thefrequencies of individual bands also vary with silicacontent (see previous discussion for the observed low-frequency region of the SiO2-K2O glass series). Untilthese vibrations are better understood in relation to themolecular structures of silicates, it does not seem reason-able to relate specific bands in the 700-400 cm

-r region to

Si-O-Si linkages between particular silicate tetrahedralunits. It is concluded here that the characteristic high-frequency Raman bands of the = SiO, : SiOz, SiOa andperhaps - SiO3 units, are to a first approximation,independent ofthe nature ofadjacent silicate groups. Thenecessary information is presumably present in, but notyet easily extracted from, the bands in the 700-400 cm-'region. This suggests that models based on Raman studiesin terms of extended structural units, such as sheets,chains, rings etc. (e.g., Virgo et al., 1980; Mysen et al.,1980a, 1982a), are only speculative at present. This does

MC'MILLAN: RAMAN SPECTROSCOPY 633

not imply that such models are incorrect, only that ourcurrent understanding of the Raman spectra of silicateglasses and melts is not sufficient to firmly establish thelong-range structures present in these latter.

Detailed vibrational assignments

The correlation of vibrational with molecular structure

In the studies considered above, Raman spectroscopy hasbeen used to gain information on the structures of silicate glassesand melts. This has been carried out by the assignment ofvibrational bands to specific structural features, which have thenbeen used to formulate models for the glass or melt structure.Such an assignment requires an understanding of the atomicdisplacements involved in each vibrational mode, in order toldentify the vibrating unit and relate it to a feature of thestructure. The assignments in the previous section were mainlybased on the energies ("frequencies") and symmetries of theobserved vibrational transitions, and do not give a detaileddescription ofthe nature and spatial extent ofeach mode. This isonly possible from a dynamical analysis of the system.

The molecular structure of a system defines the relativepositions of its constitutent atoms and the interactions betweenthem. If one or more atoms are moved from their equilibriumposition, the interatomic forces tend to restore the system to itsequilibrium configuration. The atomic displacements executedduring this process are described by the equations of motion ofthe system, whose solutions are its normal modes of vibration(e.g., Nakamoto, 1970, p. f-75; Lazarev, 1972, p. l-7; Berry etal., 1980, p. 343-355). The mathematical formulation for thedynamics of discrete molecules and of crystalline lattices arewell establ ished (e.g., Herzberg, 1945; Vol 'kenshtein et al. ,1949; Born and Huang, 1954; Wilson et al., 1955) In general inthese treatments, the potential energy ofthe system is expandedin a Taylor series of the small atomic displacements from theirequilibrium positions during vibrational motion. The forceconstants for the system described the curvature of the potentialenergy surface near the equilibrium geometry. For certain smallmolecules, completely general, self-consistent force fields havebeen obtained from extensive vibrational and rotationalanalyses. However, for most molecules, including the silicates,the assumed force constants are a function of the particularmodel used to describe both the interatomic interactions and thevibrational motions. Solution of the equations of motion for thesystem using appropriate force constants gives the energies ofv ib ra t iona l t rans i t ions . and the i r assoc ia ted a tomicdisplacements (e.g., Nakamoto, 1970, p.3-15; Berry et al. , 1980,p. 343-355). Treatment of the dynamics of condensedamorphous systems remains a current research problem (e.g ,Shuker and Gammon, 1970; Brawer, 1975; Barker and Sievers,1975; Bell, 1976; Laughlin and Joannopoulos, 1977; Galeener andSen,1978; Thorpe and Ga leener , l980a,b) . V ib ra t iona lcalculations have been carried out for silicate glasses and meltsusing similar methods to those above by considering theamorphous network either as a single large molecule, or byconsidering small representative units (see references in thefollowing section).

The validity of such vibrational calculations is criticallydependent on the force constant model used, and its relevance tothe true interatomic potential surface. Realistic force constantsmay be evaluated if this surface is known analytically; however,

this is not yet the case for silicates (see discussions in O'Keeffeand Navrotsky, l98l; Gibbs, 1982). A number of methods areavailable to construct sets offorce constants designed to modelinteratomic interactions within complex systems (see e.g.,Nakamoto, 1970, p. 55-57), a variety of which have been used inthe vibrational calculations for silicates discussed below. It iscommon to compare vibrational spectra calculated using a givenforce constant set with observed spectra, as a criterion for theapplicability of that force constant set. However, it is known thata given observed spectrum may be reproduced using a widevariety offorce fields (e.g., Cochran, 1969,p. 10-13; Leigh et al.,l97l; Szigeti , l97l; Sherwood, 1972, p. 38). I f the chosen forcefield does not approximate the true potential surface, thencalculated atomic displacements may not resemble the motionsassociated with the true vibrational modes, although the infraredand Raman spectra may bave been calculated to withinexperimental error.

From these considerations, a rigorous correlation of thevibrational properties of silicates with their structures must awaita better understanding of their interatomic bonding. A number ofthe vibrational calculations discussed below have calculatedatomic displacements associated with given vibrational modes.These are subject to the limitations noted above, and assignmentof vibrational bands to structural features may not safely betaken much further than the general assignments discussed in theprevious section. However, examination ofa range ofvibrationalcalculations reveals a number of consistent features, which maybe used to gain further insight into the vibrational properties ofsilicates.

Vibrational calculations for silicates

Some of the earlier work was carried out by Saksena (1940,1942, 1945) for a-quartz, assuming force constants for Si-Ostretching and Si-O-Si and O-Si-O bending. Barriol (1946)performed a similar calculation for B-quartz using two forceconstants; for Si-O and O-O stretching. Matossi (1949)computed the vibrational spectra for a number of silicatefragments, including the Si2O7 unit, the SijOe ring, isolated SiO4,a linear Si2O6 chain with translational symmetry, and the SiO2network as linked SiOa units. For all except Si2O7, only Si-O andO-O stretching force constants were considered, while for Si2O7,O-Si-O bending was taken into account. Matossi alsodistinguished between SiO6 and Si-On5 stretching constants (O6is a bridging and On6 a non-bridging oxygen: see earlier). Aroundthis time were developed much more efficient techniques forca lcu la t ing the v ib ra t iona l spec t ra o f mo lecu les (e .g . ,Vol'kenshtein et al., 1949; Wilson et al., 1955). Stepanov andPrima (1958a, b) and Prima (1960) used these methods tocalculate infrared band positions and intensities for a number ofsilicate fragments representative of chain, sheet, ring andnetwork silicates. Similar calculations were carried out byBobovich et al. (1955) and Bobovich and Tulub (1956, 1957).These authors assumed relatively complex force constant setswith Si-O stretching and Si-GSi and O-Si-O bending, andterms for interaction between these. Further calculations werecarried out by Saksena (1961) and Saksena et al. (1963), but withmuch simpler force constant sets: Si-O stretching (withseparated Si-O6 and Si-O"b), and O-Si-O and Si-O-Si bending.Su et al. (1962) applied the method to calculate the vibrationalspectra of silicate glasses, based on the vibrations of SiOa units.They assumed a complex force field, with Si-O stretching andSi-O-Si and O-Si-O bending terms, inter-term interactions, and

634 MCMILLAN: RAMAN SPECTROSCOPY

torsional contributions. Wadia and Balloomal (1968) and Bockand Su (1970) performed similar calculations for silica glass, withrespectively four (Si-O, O-O, O-Si-O, and Si-O-Si) and three(Si-O, O-Si-O and Si-O-Si) force constants. Gaskell (1967,1970) and Etchepare (1970a) also carried out a number ofcalculations for various silicate fragments; Gaskell with simpleSi-O, O-Si-O and Si-O-Si force constants, and Etchepare usingSi-O, O-O and cross-term interactions. In an extensive series ofarticles beginning in the 1960's, Bell, Dean and co-workerscalculated the vibrational modes for a many-atom randomnetwork of vitreous silica (e.g., Bell et al., 196E, 1980; Bell andDean, 1970; Bell, 1976), using only two (Si-O and O-Si-O) forceconstants. A large number of calculations have since beencarried out for crystalline silicates, using methods similar tothose developed by Born and Huang (1954). The largest group isfor the crystalline silica polymorphs, especially a-quartz (e.g.,Kleinman and Spitzer, 1962; Elcombe, 1967; Mirgorodskii et al.,1970; Bates, 1972; Etchepare et al., 1974; 1978; Striefler andBarsch, 1975; Iishi and Yamaguchi, 1975,1976; Barron et al.,1976; Iishi, 1978a), while a smaller number have been carried outfor other silicates (e.g., Oehler and Gunthard, 1969; Omori, 197 | ;Lazarev, 1972, p. 240-253; Pavinich et al., 197 6; Zulumyan etal., 1976; von Stengel, 1977; Iishi, 1978b; Tomisaka and lishi,1980). All of these calculations assumed rather complex forcefields, with various two-, three- and higher-body interactions andoften inter-term contributions.

Brawer (1975) developed a formalism for calculation ofvibrational modes in amorphous systems. A similar approachwas suggested by Galeener and Sen (1978). This has been used tocalculate the vibrational spectra of a number of alkali silicateglasses (e.g., Brawer, 1975; Brawer and White, 1975; Furukawaet al., l98l), assuming a simple force constant set with Si-Ostretching (separated Si-O6 and Si-O"b), and O-Si-O and Si-O-Si bending. Laughlin and Joannopoulos (1977) have used a Bethecluster approach to calculate the spectrum of vitreous silica,using only Si-O and O-Si-O force constants. Sen and Thorpe(1977) derived a method of calculating the vibrations ofdisordered networks, which has been further developed byGaleener (1979) and Thorpe and Galeener (1980a,b). Thesecalculations assumed only as a first approximation one centralstretching force constant: in the case of vitreous silica, Si-Ostretching.

All of the above calculations have included a term for Si-Ostretching, with magnitude ranging from around 300 to 700Nm t. Gibbs et al. (l9El) carried out an ab initio molecularorbital calculation for the Si(OH)o molecule, for which theyderived an Si-O stretching force constant of 665 Nm-r. This is ofthe same order of magnitude as those used in the vibrationalcalculations, suggesting that the values used for Si-O stretchingmay be generally realistic. This is consistent with the fact thatmost of the calculations have reproduced the high-frequencyregion of the vibrational spectrum, usually associated with Si-Ostretching motions.

O'Keetre et al. (1980) have pointed out that this Si-Ostretching force constant also includes a component fromnearest-neighborO . . . Ointeractions, since O .' . Odistancesare changed during Si-O stretching. These interactions havebeen ignored in a number of the above calculations, and inothers, have been estimated to be of the order of 10-80 Nm I(e.g., Matossi, 1949; Zulumyan et al., 1976; Iishi, 1978a, b;O'Keeffe et al., 1980). Those calculations which explicitlyconsidered O . . .O interactions tend to be associated with

lower Si-O stretching force constants, suggesting that neglect ofO ' ' ' O interactions in the calculation results in over-estimationof the Si-O force constant to compensate.

Most calculations have separated the Si-O stretching forceconstant into two populations: one associated with Si-O"u andone for Si-O5, with the Si-0.6 force constant some 50-100 Nm-'larger than the Si-Ob. This separation of the Si-O term hasusually been justified by the observed Si-O.6 and Si-O6distances in silicates, with Si-O"6 generally (but not always)shorter than Si-Ou (e.g., Ramberg, 1952; Brown et al. 1969;Furukawa et al., l98l). Meagher et al. (1980) calculated Si-O6stretching force constants of 732 to 878 Nm-r (as a function ofthe Si-O-Si angle) for the HuSi2OT molecule; larger than thevalue calculated by Gibbs et al. (1981) for Si(OH)+ (665 Nm r).

This would appear consistent with the assumed relativemagnitudes of Si-Ou and Si-On6 stretching force constants.However, O'Keeffe et al. (1980) calculated the Si-O stretchingforce constant (combined with O ' . .O interactions) forH6Si2O7 at 540 Nm r, less than that for S(OH)4.

A number of vibrational calculations for silicates have ignoredthe terms for M-O stretching (M is the alkali or alkaline earthcation) on the assumption that metal cations do not participate inor affect the vibrations of the silicate unit (e.g., Saksena, l96l;Gaskell, 1970; Etchepare, 1970a; Brawer and White, 1975;Furukawa et al., l98l). This approximation may be valid forcertain modes under given circumstances, which will bediscussed later. Those calculations which have included M-Ointeractions have estimated the following stretching forceconstants: Mg-O 30-90 Mn-r, Ca-O 5-50 Nm-r, K-O 10-14Nm-r, Na-O l8 Nm-t and Li-O 40 Nm t (Oehler andGunthard, 1969; Zulumyan et al., 1976; Pavinich et al., 1976; vonStengel, 1977; Iishi, 1978b; Tomisaka and lishi, 1980). Somecalculations have included terms for nearest neighbour non-bonded M . ' 'M interactions (where M is Si, or an alkal i oralkaline earth cation). The Mg . . . Si interaction in forsterite hasbeen estimated at 4-30 Nm ' (Oehler and Gunthard. 1969: Iishi.1978b) , w i th Mg. . .Mg a t 194 Nm-r (Oeh ler and Gunthard ,1969). The latter authors also estimated Ca. . . Si andCa. . .Ca in 'pCa2SiOa a t 178 and 6 l Nm-r respec t ive ly .Si ' ' ' Si non-bonded interactions in quartz have been estimatedto contribute 40-120 Nm-t to the force field (see O'Keeffe et al.,1980), while O'Keeffe et al. (1980) calculated the force constantfor Si . . . Si repulsion at near 100 Nm ' for the H6Si2Ozmolecule. with an Si . . . Si separation near 34.

Most calculations have also considered O-Si-O, and forpolymerized silicates Si-O-Si, angle bending forces. Theestimated value for O-Si-O bending has ranged from 20-70Nm-r (expressed as (l/r2)(a2Eldr2), where r is the Si-O bondlength) while the force constant for Si-O-Si bending has beenestimated at 2-20 Nm-r. Gibbs et al. (1981) have calculated anO-Si-O bending force constant for the Si(OH)a molecule of 100Nm-r, while O'Keetre et al. (1980) calculated 8-18 Nm-r (as afunction of the Si-O-Si angle) for the Si-O-Si bending forceconstant of HuSi2O7. These values calculated from molecularorbital studies are of comparable magnitude to those estimatedfor the lattice dynamical studies.

A number of general conclusions may be drawn from theabove discussion. For studies with similar force constant sets,there is at least an order of magnitude agreement for preferredvalues of individual force constants. If the force fields derivedfrom molecular orbital calculations on small silicon-oxygenclusters are realistic and transferable to condensed silicate

MCMILLAN: RAMAN SPECTROSCOPY 635

systems (see O'Keeffe et al., 1980; Gibbs et al., 1980; Gibbs,1982), then the sllicate bending and stretching force constantsused in the vibrational calculations appear reasonable. However,most of the calculations neglect one or more of the interactionterms described above (which are already far from a completelist of possible interactions in complex silicates). This must becompensated by an over- or underestimate of those forceconstants used, or the inclusion of additional interaction termswhich are not necessarily real. Individual force constantscalculated from molecular orbital studies of small clusters maylikewise be poorly estimated, since a detailed analysis of the datais required to separate individual contributing interactions, whenthis is in fact possible (see O'Keefe et al., 1980).

In the silicates described here, the short-range interactionsseem to be dominated by the Si-O stretching force constant.Although the estimates for this force constant range from 300 to700 Nm-t, the actual contribution from pure Si-O stretching isprobably at the low end of this range when other contributinginteractions are identified and subtracted.

The vibrational spectra of silicates in general may be describedin terms of the major band groups discussed in the previoussection: for all, a high-frequency group from 1200-800 cm-r; forsilicates more polymerized than the orthosilicate, a group from700-400 cm-t ; and for the disilicate and silica, a mid-range groupin the 800-700 cm-r region.

Sen and Thorpe (1977) calculated the vibrational spectrum ofSiO2 considering only the central Si-O stretching force constant,and reproduced both the high- and low-frequency band sets. Allof the other vibrational calculations considered above, withdominant Si-O stretching force constants but often considerabledifferences in other assumed interactions, have also consistentlyreproduced these regions of silicate spectra in general. Theseobservations seem to suggest that both the 1200-800 cm-r andthe 700-400 cm-t bands of silicate vibrational spectra are due tomodes dominated by Si-O stretching.

O'Keeffe et al. (1980) have suggested that the force constantfor Si ' ' ' Si non-bonded interaction may be rather large, and ofthe order of the Si-O stretching force constant. Such interactionshave been neglected explicitly or assumed small in most silicatecalculations; although they may be largely subsummed into anSi-O-Si bending force constant. The effect ofignoring this termmay become important for more polymerized silicates, where thenumber of Si ' . . Si interactions becomes comparable to thenumber of Si-O stretching forces to be considered. This neglectwill only be impoftant for modes in which the Si . . . Si distanceis varied, but may result in considerable overestimation of otherinteractions considered, for example, Si-O-Si bending forces.

Motions derived from Si-? stretching

The isolated SiOo tetrahedron. The vibrat ions of ahypothetical isolated tetrahedral SiOa group may be described interms of the totally symmetric stretching mode (zr) and thetriply-degenerate asymmetric stretch (23) (e.g., Herzberg, 1945,p. 100). These are shown schematically in Figure 3(a). Anydeviation from tetrahedral symmetry will result in a mixing orvibrational coupling of z1- and (4-type modes (see Piriou andMcMillan, 1983a).

The fully-polymerized SiO2 network. This may be consideredas a network of SiO4 tetrahedra polymerized by corner-sharingeach oxygen between two SiOa units. The vibrations derivedfrom Si-O stretching may be simply understood following themodel of Sen and Thorpe (1977). These authors developed a

I

oII

s lt ^ t - / l \

l 6 l

tY

t "3

\ -/"4 ./>s t

_ . , {

( b )o u t - o t - P h a 3 o

h l g h f r e q u c n c Y

)" , /o\ . ,a. / \

I n - p h a a a

l o w t r a q u e n c y

" 'Po-S5,-- l8\ . '2-o

( c ) , '

t r

/o t o

s i l l c o n ' c a g e "

m o t l o n

Fig. 3. Schematic of possible types of normal mode insilicates. (a) z1- and ,/3-type stretching vibrations of the isolatedSiOa tetrahedron. (b) The in-phase (low-frequency) and out-of-phase (high-frequency) resultant vibrations of two coupled Si-Ostretching motions (only Si-O stretching is considered). (c) Thetype of motion suggested by various vibrational calculations forsilica polymorphs to be associated with the Raman bands near800 cm-r (drawing after Laughlin and Joannopoulos, 1977). Nosuch vibration is calculated when only central Si-O stretching isconsidered, as in (b).

vibrational model for condensed AX2 systems where A istetrahedrally coordinated by X, and X two-fold coordinated byA. They considered only the A-X stretching force, and followedthe character of vibrational modes as the X-A-X angle (0) wasvaried. Sen and Thorpe found that for d smaller than somecritical angle, the vibrations were best described in terms of z1-and 4-type motions of the isolated AXa tetrahedra. For 0largerthan the critical angle, the stretching modes of adjacenttetrahedra became strongly coupled. This critical angle for SiO2was found to be near ll2'. Since the average Si-O-Si angle insilica glass is larger than this, the coupled mode description mustbe used. The resulting vibrations may be described in terms ofstretching motions of adjacent Si-O bonds linked at oxygen: ahigh-frequency band of modes where the coupled Si-O stretchesare out ofphase, giving a resultant oxygen motion sub-parallel tothe Si . ' . Si line, and a low-frequency set of modes whereadjacent Si-O sFetching is in phase to give a resultant oxygenmotion in the plane bisecting the Si-O-Si bond (Sen and Thorpe,1977). These are shown schematically in Figure 3(b). lt is of

636 Mt'MILLAN : RAMAN SPECTROSCOPY

interest to compare these simplified vibrations with thosecalculated using more sophisticated force models for vitreousand crystalline silica polymorphs (e.9., Mirgorodskii et al., 1970;Bates, 1972; Etchepare et al., 1974, 1978; Lucovsky, 1919;Furukawa et al., l98l). In all cases, the atomic displacementscalculated for the strong Raman-active modes in the 400-500cm-rregion are similar to those described above for the low-frequency band set, with mainly oxygen displacement in theplane bisecting Si-O-Si, and those for the 1000-1200 cm I

region similar to the above high-frequency bands with oxygenvibrating between silicons in the Si-O-Si bond. This lartermotion is generally calculated to involve a larger component ofassociated silicon displacement.

The central force model of Sen and Thorpe does not predictthe silica bands near 800 cm-r, which must require considerationof some other interaction. The models of Bell and co-workers(e.g., Bel l et al. , 1968, 1980; Bel l and Dean, 1970; Bel l , 1976) andLaughlin and Joannopoulos (1977), both of which consider onlySi-O stretching and O-Si-O bending interactions, do reproducea band near 800 cm '. The frequency spectrum from a moleculardynamics calculation with Si-O, O-O and Si-Si interactions alsoshowed a peak near 800 cm t (Garofalini, 1982). All of thesecalculations suggested that the 800 cm-r modes involvedpredominantly silicon motion, consistent with the isotopicsubstitution experiments of Galeener and Mikkelsen (1981) andGaleener and Geissberger (1983). The calculated atomicdisplacements for this mode after Laughlin and Joannopoulos(1977) are shown in Figure 3(c). More complex calculations forSi02 polymorphs have reproduced similar atomic displacementswithin Si-O-Si units.

Other silicate compositions. The Sen and Thorpe central forcemodel has since been extended to other cation and anioncoordinations (e.g., Galeener and Sen, 1978; Thorpe andGaleener, 1980a, b), while Seifert et al. (1982) and Mysen er al.(1982a) have applied the model to aluminosilicate systems withSi-O-Al linkages. It is possible that the model may be extendedto simple silicate systems with both Si-O-Si and Si-O-Mlinkages, where M is some cation other than silicon, and theoxygen and M coordination may vary.

Within the Si-O-Si linkages of silicates in general, the Si-O-Siangle is larger than the Sen and Thorpe critical angle (see above),hence modes associated with Si-O stretching about an Si-O-Silinkage must be considered in terms of coupled Si-O stretchvibrations as discussed above for silica. For Si-O-M linkages(where M is an alkali or alkaline earth cation, and the oxygen isthat usually referred to as "non-bridging"), the character of themode may be assessed in terms of the relative contributions fromM-O and Si-O stretching to the total stretching force on theoxygen along the line of the Si-O bond. It can be shown simplythat if Si-O contributes ksi6 (the Si-O stretching force constant),each M-O stretch contributes kye cos2 d, where kro is the M-Oforce constant and 0 is the complement of the Si-O-M angle (M.O 'Keef fe , pers . comm. , 1982) . As an example , thesecontributions may be evaluated for forsterite, MgzSiOa.

The Si-O-Mg angles in forsterite range from 90' to lZ4"(Brown, 1980, p. 364). Each oxygen is coordinated to silicon andthree magnesium atoms. For 0 : 90", the Mg-O stretchingcontribution is zero (cos2 90'). The maximum contribution fromeach Mg-O would be 0.31 kMeo at 124", which for threemagnesium atoms coordinated to oxygen is 0.93 k1,a"o, to give aresultant Si-O stretching force constant of k5;o + 0.93 kMso.However, ksi6 is probably almost an order of magnitude larger

than ky"a (see previous section), so there should be little or noparticipation of Mg-O stretching in these predominantly Si-Ostretching modes. The vibrational calculation oflishi (1978b) forforsterite supports this prediction, with no contribution fromMg-O stretching appearing in the potential energy changeassociated with Si-O stretching. It is of interest that this alsosupports the usual description of the Si-O stretching modes inforsterite in terms of the z,- and z.-motions of isolated SiOatetrahedra, as described above.

In the alkali and alkaline earth silicates, oxygen is generallycoordinated by two to four cations (including Si) in Si-O-Mlinkages, with Si-O-M angles ranging from 90'to around 140"(MlSi). In most cases, k5;6 is probably larger than kr6 (seeprevious section). Following similar arguments to that forforsterite, Si-O stretching motions in Si-O-M linkages should belargely decoupled from M-O stretching. This was found to be thecase for Si-O-Mg and Si-O-Ca in diopside, CaMgSi2O6(Tomisaka and Iishi, 1980). This would be a partialjustificationfor the common neglect of M-O interactions in simplified silicatevibrat ional calculat ions, although M-O stretching maycontribute significantly to other vibrations of the silicate unit.The "internal mode approximation" is commonly used tointerpret the vibrational spectra of silicates in terms of thevibrations of their constituent silicate units (e.g., Lazarev , 1972,p. 7-26, 46-48; Tarte l963a,b). The above discussion alsojustifies this approximation, at least for vibrations derived fromSi-O stretching.

ln si l icate systems with polymerization between theorthosilicate and silica, a given silicate unit may have both Si-O-M and Si-O-Si linkages to a given silicon. As discussed above,silicon-oxygen stretching should result in high- and low-frequency bands from coupled stretching within each Si-O-Siunit, and a high-frequency band from Si-O stretching uncoupledfrom M-O in each Si-O-M linkage. The degree of couplingbetween these sets of modes will be a function of the system andthe particular vibration. Furukawa et al. (1981) have calculatedthat the major high-frequency Raman band for an Si2O6("chain" ; : SiOr) unit involves mainly stretching motion of non-bridging oxygens against silicon with little participation ofbridging oxygens, suggesting decoupling of the Si-O-Si and Si-O-(M) (the M cation is in parentheses, since it was notconsidered explicitly by Furukawa et al., l98l) contributions.The same was true for the calculated major modes of an Si2O5("sheet"; = SiO) unit. However. Tomisaka and lishi (1980) havecarried out a more complete calculation of diopside, CaMgSi2O6,with pyroxene chains of :SiOz units. One high-frequency modeis similar of that of Furukawa et al. (1981), with decoupled Si-O-Si and Si-O-M stretching, but another shows large componentsof both the high-frequency resultant Si-O-Si and the Si-O-Mstretching vibrations.

A number of workers have observed that the frequency of theband near 700-600 cm-r for crystalline pyrosilicates (SirO,groups) increases with decreasing Si-O-Si angle (e.g., Lazarev,1972, p. 66-72; Scheerz, 1972, p.75-81). Lazarev (1972) alsonoted a corresponding decrease in the high-frequency bandderived from asymmetric stretching of Si-O-Si. This may berationalized in terms of the Sen and Thorpe model for thestretching vibrations ofthe Si-O-Si linkage discussed above. Asthe Si-O-Si angle becomes narrower, the individual Si-O6stretching vibrations become less coupled. This will decrease thehigh-frequency asymmetric and increase the low-frequencysymmetric components of coupled Si-O-Si stretching, to

McMILLAN: RAMAN SPECTROSCOPY 637

approach the z1 and z3 frequencies of isolated SiOo units (Senand Thorpe, 1977).

In silicate crystals and glasses in general, the frequency of the700-400 cm-1 band increased with decreasing silica content, ordecreasing polymerization of the silicate unit (Fig. l). Theaverage Si-O-Si angles do seem to show a general increase frompyrosilicates to the silica polymorphs, which may partiallyrationalize the behavior of the 700-400 cm I band following asimilar argument to that above for pyrosilicates.

The frequency of the major Raman band in the 1200-800 cm-'region shows a general decrease from silica to the orthosilicate.However, except for the case of silica, this band is probablymostly associated with motions of "non-bridging" oxygens inSi-O-M linkages, not with the high-frequency component of Si-O-Si. It is difficult to relate the lowering of frequency of thisband with decreasing polymerization to any specific structuralchange, since the particular vibrating unit giving rise to the majorhigh-frequency band changes with polymerization ofthe silicateunit. Then the pseudo-symmetry of the vibrating unit, and thenature and Raman activity of particular vibrational modes, arenot the same for silicate tetrahedra in diferent polymerizationstates.

Summary

A large body of Raman spectral data has been assem-bled for alkali and alkaline earth glasses and liquids.Many attempts have been made to relate these spectra tothe glass and liquid structure at various levels of model-Iing. Part ofthe purpose ofthe present article has been tocritically examine these, and assess the potential applica-tions and limitations of Raman spectroscopy for suchstructural studies.

First, there is general agreement as to the majorobserved bands as a function of composition. However,many details of the experimental spectra remain unclear,especially for weaker bands. More work is needed onsystems with well-resolved Raman bands, e.g., SiO2-K2O and SiO2-BaO, to define the frequency behaviorwith composition and the polarization characteristics ofall the bands. These results would be helpful in constrain-ing realistic deconvolutions for systems with less well-resolved bands. For these systems, careful polarizedstudies noting slope changes on unresolved bands andsystematic statistical fitting experiments would be useful.

As noted in the text, there is also agreement as to thegeneral assignment of major band groups to types ofstructural unit. This is extremely useful, as these bandsare then diagnostic of particular units, and this has beenused to construct various structural models for the glass-es and melts. However, such assignments have beenlargely phenomenological, and give little indication as tothe detailed nature of the vibrational modes. In manycases, this information is necessary to differentiate be-tween possible alternative models. Isotopic substitutionexperiments on silicate glasses and crystals would helpgive more detailed vibrational interpretations, but suchdata are rare at present. In theory, dynamical calculationson silicate structures should directly give the nature of

vibrational modes. However, such calculations rely onmodels of interatomic interactions in silicate systemswhich may not yet be assessed, due to our currentunderstanding of chemical bonding. Systematic series ofcalculations would be useful at the present time, forinstance to assess the effect of inclusion or neglect ofparticular interaction terms on the form of the calculatednormal modes for a particular cluster. Until the vibration-al properties of silicates are better understood in terms oftheir structure and bonding, vibrational spectroscopycannot be rigorously used as a tool for investigating theirdetailed molecular structure.

The major interest in structural studies of silicateglasses and melts for geological applications has been therationalization and eventual prediction of properties suchas viscosity, density or heat content of a magma as afunction of temperature, pressure and composition. Inview of the preceding discussion, it remains only specula-tive to correlate detailed melt and glass structural modelsderived from Raman spectroscopic studies with varia-tions in bulk properties. However, some general system-atic correlations may be made, as discussed below.

It has been noted by many workers that the isothermalviscosity (a) of silicate liquids and glasses decreases byseveral orders of magnitude as alkali or alkaline earthoxides are added to pure silica (e.g., Heidtkamp andEndell. 1936: Shartsis et al.. 1952t Bockris and Lowe,1954; Bockris et al., 1955; Mackenzie, 1960; Urbain et al.,1982). This decrease has been interpreted in terms ofdepolymerization of the silica melt or glass network onaddition of metal oxide, consistent with the interpretationof Raman spectra of silicate glasses and melts. Urbain etal. (1982) found discontinuities in their curves of ln 4versus mole fraction SiO2 for their NazO-SiO2 liquidsnear 0.8 and 0.6 Xsio., with a smaller rate of change inviscosity with silica content between 60 and 80 mole Vosilica. The systems SiO2-K2O and SiOz-LizO show simi-lar inflections in their ln ? - X5is" curves at slightlydifferent silica contents (Bockris et al., 1955; Mackenzie,1960). It is ofinterest that these compositions, near 80-90mole Vo and 60 mole Vo silica, are respectively wherefully-polymerized silica network units =Si: seem todisappear and where orthosilicate groups SiOa first ap-pear, from Raman spectroscopic studies. The viscositychanges could then be interpreted as a large initial changeon initial depolymerization of the :Si= network, fol-lowed by a region of gently decreasing viscosity between80-90 and 60 mole Vo silica as units of intermediate butdecreasing polymerization are formed, then sharply de-creasing viscosity as discrete orthosilicate groups beginto appear in the melt structure. Unfortunately for theabove hypothesis, the alkaline earth systems do not showany inflection near 60 mole %o silica (Bockris and Lowe,1954; Bockris et al., 1955; Mackenzie, 1960). At present,more data are needed on the viscosities of simple silicatesystems (see Urbain et al., 1982) before realistic structur-al models may be attempted. Raman spectroscopy may

638 McMILLAN: RAMAN SPECTROSCOPY

play an important part in the elaboration of such models.Although the details offlow processes in such associatedIiquids do not yet seem to be well understood, it is likelythat the flow units involved are somewhat larger than thestructural groups sampled by our present interpretation ofthe Raman spectra. It is concluded that both the measure-ment and interpretation of silicate liquid viscosities, andtheir correlation with Raman spectroscopic and otherstructural studies, should remain an active research prob-lem.

Roedder (1979) has recently discussed the currentstatus of liquid immiscibility as a petrological process. Ithas long been known that liquids in the systems SiO2-MgO, CaO and SrO show large miscibility gaps at highsilica content (e.g., Greig, 1927), while SiO2-BaO andSiOrLi2O, Na2O and perhaps K2O show metastableimmiscibility in high silica glasses (e.g., Charles, 1966,1967, 1969; Galakhov and Varshal, 1973; Haller et al.,1974; Hess, 1977). ln all cases, the silica-rich liquid isnear pure silica (90-100 mole Vo SiO2), while the composi-tion of the metal oxide-rich liquid or glass becomesprogressively richer in metal oxide in the order Ba < Sr <Ca < Mg for alkaline earth oxides, and for the alkalies, K< Na < Li; with Li between Mg and Ca, Na between Srand Ba, and K lower than Ba (e.g., Kracek, 1939;Charles, 1967; Galakhov and Varshal, 1973; Hess, 1977).McMillan (1981, 1984) and Marson er al. (1983) haverecently derived similar but independent models fromRaman spectroscopic studies which rationalize this be-havior. This model has been extended to aluminosilicatesystems by McMillan et al. (1982), and was used tosuccessfully rationalize and predict systematics in theenthalpies of mixing along the joins SiO2-NaAlO2, SiO2-CaAl2Oa (Navrotsky et al., 1982) and SiO2-MgAl2Oa (Per-audeau and Navrotsky, in prep.; Navrotsky and Roy, inprep.).

It is concluded that Raman spectroscopy does provideuseful information as to the structures of silicate meltsand glasses, and if used carefully in conjunction withother techniques, can help us better understand theirstatic and dynamic properties. It is suggested that consid-erable further work is necessary to fully realize itspotential, and to define its useful limits in this type ofstudy.

Acknowledgments

This work was begun as part ofresearch for a doctoral degreein geochemistry at Arizona State University, and has beensupported by NSF grants EAR-7809954, INT-7926523, INT-8006965 and EAR-S108748,the French CNRS, and the ptRpSEVprogram. The author would like to thank all those in Scotland,France and the United States who advised, encouraged andsupported him during this time, including his three principaladvisors John Holloway, Alex Navrotsky, and Bernard piriou;also Bill Brown, Georges Calas, Paul Caro, Jean-Pierre Cou-tures, Roger Dron, Jean Etchepare, Colin Graham, and GeorgesUrbain, and finally Mike O'Keeffe for recent discussions onstructure and bonding in silicates. The author also thanks the

following institutions for their hospitality; CNRS Bellevue (El6-ments de transition dans les solides) and CNRS Odeillo (Ultra-r6fractaires), ENSTA Palaiseau (Optique appliqu6e), I'Univer-sitd de Nancy I and I'Universitd de Paris VI. The manuscript wasread by John Clemens, Chris Capobianco, Mike O'Keeffe andNancy Ross and reviewed by Ed Stolper and Shiv Sharma, all ofwhose helpful comments were appreciated, and was typed byNita Dagon and Mike Palitz.

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