NMR STUDIES OF THE STRUCTURE OF GLASS

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NMR STUDIES OF THE STRUCTURE OF GLASS

P. Bray, W. Dell

To cite this version:

P. Bray, W. Dell. NMR STUDIES OF THE STRUCTURE OF GLASS. Journal de Physique Collo-

ques, 1982, 43 (C9), pp.C9-131-C9-142. �10.1051/jphyscol:1982926�. �jpa-00222455�

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JOURNAL DE PHYSIQUE

CoZZoque C9, suppZe'ment au n012, Tome 43, de'cernbre 1982 page c9-131

P.J. Bray and W.J. Dell

Department of Physics, Browz Uniuersitg, Providence, Rh. I . , 02912, U.S.A.

R6sumQ.- Au cours des derniPres 25 annCes les techniques de rCsonance magnQ- tique nuclQaire (RMN) large bande ont QtB utilisdes avec succcs pour Qtudier la structure du verre ii l'Qchelle atomique 111

.

L'analyse de la structure quadrupolaire des spectres RMN des verres de borates a fourni des renseigne- ments quantitatifs sur les coordinences des atomes de bore dans diffQrents entourages dloxygPne

.

AprSs une courte discussion des aspects des theories de RMN on prgsente quelques rQsultats les plus rQcents : Qtude de B~~ dans les verres de borosilicates de Na 2 teneur en soude QlevQs ; B1° dans les verres de borates de lithium et B9 dans les verres de fluoberyllates de Na.

Abstract.- Over the past 25 years, wide-line Nuclear Elagnetic Resonance (NMR) techniques have been used successfully to study the structure of glasses on an atomic scale [l]. Analysis of the quadrupolar structure in NMR spectra of borate glasses has yielded quantitative determinations of the relative numbers of boron atoms in various oxygen environments. After a brief discussion of the relevant as ects of NtfR theory, this paper will present some of the most recent studies:

B1' NMR in sodium borosilicate glasses of high soda content, B" NI4R in lithium borate glasses, and Be9 NMR in sodium fluoride-beryllium fluoride glasses.

1. NMR with Quadrupolar Effects.- Nuclei with spin or greater possess a magnetic

moment given by -f +

11 = y51 (1)

where I is the quantum mechanical spin vector, y is the yromagnetic ratio, and + fi is PlancXts constant. The magnitude of the spin vector,

(q,

is given by

JTrrn;

whqre I can be integer or half integer. If this nucleus is placed in a magnetic fleld H, the Hamiltonian of this familiar Zeeman interaction can be written classically as

-+ +

H = - v ' H

,

and quantum mechanically as

-+ -+

H = - y % I . H

.

For a constant magnetic field -+ H in the z-direction, the eigenvalues are

Eo = -y.hHm (4)

where the magnetic quantum number m can range by integral steps from -I to I. Thus, for a spin 3/2 nucleus such as B", there are four possible energy levels, as shown in Fig. la. At finite temperatures the lower energy levels are more populated than the higher ones according to the Boltzman distribution, but if the sample is bathed with transverse radiation of frequency w (normally in the radio-frequency range) such

that A E = hw=yliH, or w = Y H

,

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then transitions can be induced between levels. This equalizes the populations and results in a net absorption of energy by the sample, leading to a nuclear magnetic resonance spectrum as shown in Fig. lb.

*Research supported by the National Science Foundation under Grant DMR 8004488 and by the Materials Research Laboratory at Brown University.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982926

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JOURNAL DE PHYSIQUE

FIG. 1. Energy l e v e l s and NbfR spectrum FIG. 2. Energy l e v e l s and NMR spectrum f o r a s p i n 3/2 nucleus i n a magnetic f o r a s p i n 3/2 nucleus i n a magnetic f i e l d (Zeeman i n t e r a c t i o n o n l y ) . f i e l d (Zeeman and quadrupolar i n t e r -

a c t i o n s p r e s e n t )

.

Nuclei with s p i n 1 o r g r e a t e r a l s o p o s s e s s a quadrupole moment which w i l l i n t e r - a c t with an e l e c t r i c f i e l d g r a d i e n t p r e s e n t a t t h e n u c l e a r s i t e and p e r t u r b t h e Zeeman energy l e v e l s d i s c u s s e d above. Since t h e e l e c t r i c f i e l d g r a d i e n t depends s t r o n g l y on t h e n a t u r e of t h e immediate chemical bonds, s t r u c t u r a l i n f o r m a t i o n about t h e atomic environment of t h e r e s o n a t i n g nucleus can be e x t r a c t e d from an a n a l y s i s of t h e shape of t h e resonance spectrum. The Hamiltonian of t h i s i n t e r a c t i o n can be w r i t t e n c l a s s i c a l l y a s [ 2 ]

HQ = ~ p ( ; ) v ( Z ) d ~ Z (6)

+ -f

where p(x) i s t h e n u c l e a r charge d e n s i t y , V(x) i s t h e p o t e n t i a l a t t h e nuclear s i t e due t o e x t e r n a l c h a r g e s , and t h e i n s e g r a l i s taken over t h e n u c l e a r volume. Using I,, I y and I, a s t h e components of I i n t h e p r i n c i p a l a x i s system o f t h e e l e c t r i c f i e l d g r a d i e n t t e n s o r , Eq. (6) can b e w r i t t e n quantum-mechanically a s [ 2 ]

where

Qcc = e 2 q Q/h (8)

i s t h e coupling c o n s t a n t , which measures t h e s t r e n g t h of t h e i n t e r a c t i o n , and

r- = (vxx - vyy)/vzz ⁽⁹⁾

i s t h e asymmetry parameter, which measures t h e d e p a r t u r e from c y l i n d r i c a l symmetry of t h e e l e c t r i c f i e l d g r a d i e n t a t t h e n u c l e a r s i t e . I n t h e s e e x p r e s s i o n s

a2v

aE, eq = V,, =

sZ-=

-

i s t h e l a r g e s t component of t h e e l e c t r i c f i e l d g r a d i e n t t e n s o r i n i t s p r i n c i p a l a x i s system, and eQ i s t h e nuclear quadrupole moment, which i s a p r o p e r t y of t h e nucleus and independent of t h e p a r t i c u l a r n u c l e a r environment.

I f t h e Zeeman i n t e r a c t i o n is l a r g e compared with t h e quadrupolar i n t e r a c t i o n , t h e l a t t e r can be t r e a t e d a s a small p e r t u r b a t i o n of t h e former. Using s t a n d a r d p e r - t u r b a t i o n t h e o r y t h e r e q u i r e d m a t r i x elements can be c a l c u l a t e d from Eq. (7) and c o r - r e c t i o n s t o any d e s i r e d o r d e r of t h e eigenvalues Eo can be obtained. The energy l e v e l s c o r r e c t e d t o f i r s t o r d e r a r e shown i n F i g . 2a. Note t h a t t h e frequency of t h e

-%-3

t r a n s i t i o n i s u n a f f e c t e d while t h e f r e q u e n c i e s of t h e o t h e r two s a t e l l i t e t r a n s i t i o n s a r e s h i f t e d , l e a d i n g t o a resonance spectrum a s shown i n F i g . 2b. In a g l a s s o r finely-powdered c r y s t a l , a l l p o s s i b l e o r i e n t a t i o n s of t h e p r i n c i p a l axes of t h e e l e c t r i c f i e l d g r a d i e n t t e n s o r a r e p r e s e n t and t h e s a t e l l i t e t r a n s i t i o n s a r e spread o u t t o form a "powder p a t t e r n " a s shown i n Fig. 3 .

I f Qcc i s l a r g e enough, t h e powder p a t t e r n of Fig. 3 w i l l be s p r e a d over such a wide frequency range a s t o render t h e s a t e l l i t e t r a n s i t i o n s unobservable; i n s t e a d , a narrower sweep range i s used and second-order e f f e c t s on t h e c e n t r a l t r a n s i t i o n s a r e observed. These t h e o r e t i c a l s p e c t r a a r e shown i n Fig. 4 , a g a i n c a l c u l a t e d from

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F I G . 3. F i r s t - o r d e r quadrupolar spectrum f o r an ensemble of random o r i e n t e d s p i n 3/2 n u c l e i . Here

VQ = 3Qcc/21(21

-

1 ) .

frequency Scale In unlfs of

FIG. 4. Seeond-order quadrupolar spectrum f o r an ensemble of randomly o r i e n t e d s p i n 3/2 n u c l e i .

Eq. (7) u s i n g p e r t u r b a t i o n t h e o r y . A r e s o n a t i n g nucleus i n a given atomic environment w i l l y i e l d a spectrum o f given quadrupole parameters Qcc and q . By f i t t i n g com- p u t e r - s i m u l a t e d l i n e s h a p e s t o t h e experimental s p e c t r a , t h e s e parameters can be e x t r a c t e d . Moreover, i f more t h a n one d i s t i n c t " s i t e f 1 e x i s t s i n t h e sample, t h e r e l a t i v e number of n u c l e i i n each s i t e can be e x t r a c t e d by t a k i n g a weighted sum of simulated l i n e s h a p e s , u s i n g quadrupole parameters a p p r o p r i a t e t o each s i t e . S p e c i f i c examples of t h i s technique w i l l be p r e s e n t e d below.

2. B" NMR i n Na20-B203-Si02 Glasses o f High Soda Content.- E a r l i e r NMR s t u d i e s of t h i s system from t h i s l a b o r a t o r y [ 3 , 4 ] c o n c e n t r a t e d on t h e glass-forming r e g i o n s of r e l a t i v e l y low sodium oxide c o n t e n t . A s t r u c t u r a l model was p u t forward which was c o n s i s t e n t with a l l t h e d a t a , but i t has been suggested i n t h e l i t e r a t u r e L 5 1 and by p r i v a t e communication from S. 2 . Xiao t h a t t h e model breaks down f o r samples of h i g h e r soda c o n t e n t . Xiao h a s a l s o p u t forward a s t r u c t u r a l model whlch d e v i a t e s s h a r p l y from t h a t p r e s e n t e d i n Refs. 3 and 4.

In t h e p r e s e n t work, new NMR s t u d i e s were c a r r i e d o u t on 35 samples of h i g h e r soda c o n t e n t . Figure 5 summarizes t h e b a t c h compositions of t h e samples; n o t e t h a t t h e p r e v i o u s work has been extended i n R and two new K f a m i l i e s have been added.

(Here, R=mol%Na20/mol%B~0~ and K=mo1%SiO2/mol%B~O3). The samples were p r e p a r e d by m e l t i n g a p p r o p r i a t e amounts of Na2C03, H3B03, and SiOn a t approximately 1300°C f o r 3/4 hour. (About 0 . 3 mol%Fea03 was added t o each b a t c h t o h e l p reduce t h e s p i n - l a t t i c e r e l a x a t i o n time TI and avoid s a t u r a t i o n e f f e c t s [ 7 ] . ) The m e l t s were r a p i d l y quenched by pouring onto a metal p l a t e and covering q u i c k l y with a b r a s s block. B"

NMR s p e c t r a a t 16 MHz were o b t a i n e d a t room temperature f o r each sample u s i n g a Varian A s s o c i a t e s c u r r e n t - r e g u l a t e d electromagnet, a Varian Associates r a d i o - f r e - quency ( r f ) u n i t ( o r i n some c a s e s a Mid-Continent Instruments Model 5005 r f u n i t i n c o n j u n c t i o n w i t h a Matec Model 110 o s c i l l a t o r ) , a PAR Model HR-8 l o c k - i n , and a Nicolet Model 1174 s i g n a l averager.

One r e p r e s e n t a t i v e spectrum i s shown i n F i g . 6. The s p e c t r a l f e a t u r e s a r e smoothed due t o t h e e f f e c t s of d i p o l a r broadening[7] i n t h e sample, and due t o t h e d e t e c t i o n scheme used, t h i s i s t h e f i r s t d e r i v a t i v e of t h e t h e o r e t i c a l a b s o r p t i o n spectrum shown i n Fig. 4. This spectrum e x h i b i t s c l e a r l y r e s o l v e d f e a t u r e s i n d i - c a t i n g t h e presence of borons i n t h r e e d i s t i n c t environments:

1 ) The narrow, o f f - s c a l e response l a b e l e d (a) i n Fig. 6 a r i s e s from borons i n a s i t e c h a r a c t e r i z e d by a very small (<400 kHz) coupling constant ^Qcc. This i s a t t r i b - u t e d t o borons t e t r a h e d r a l l y coordinated by oxygens. (Neglecting e x t e r n a l charges, a p e r f e c t t e t r a h e d r o n would l e a d t o a coupling c o n s t a n t o f z e r o ) .

2 ) F e a t u r e s (b) a r i s e from borons i n a s i t e c h a r a c t e r i z e d by a much l a r g e r coupling c o n s t a n t and a r e a t t r i b u t e d t o symmetric t h r e e - c o o r d i n a t e d borons--that i s , borons surrounded by e i t h e r t h r e e b r i d g i n g o r t h r e e non-bridging oxygens.

3) F e a t u r e s (c) a r i s e from borons i n a s i t e c h a r a c t e r i z e d by a r e l a t i v e l y l a r g e asymmetry parameter r) and a r e a t t r i b u t e d t o asymmetric three-coordinated_ bqrons-- t h a t i s , b o r o n s % y t h e i t h e r o n e o r t w o non-bridging oxygens.

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JOURNAL DE PHYSIQUE

&k

^/ ^I^I

^L'

^/

^::

^I

1 1 (C)

Ib,c)

' . .

^(a

8,4 K

-

^{0 5} ^{1 0} ^{2 0}³⁰⁴⁰⁶⁰ _S102 ^lk920 L ~ S U O 15960

k;F

^lb000 ^.6020 ^160UO LLOBD

FIG. 5 . Batch compositions of samples FIG. 6 . Experimental NF4R spectrum f o r used i n t h i s s t u d y . Dots a r e from Ref. 3 t h e K = 3 , R = 2 . 5 sample. Dashed l i n e and c r o s s e s a r e from t h e p r e s e n t work. i s t h e computer-simulated lineshape The "no g l a s s " r e g i o n i s f o r bulk samples discussed i n t h e t e x t .

onlvr61. .L +

The dashed l i n e i s a computer sirnufation o f t h e lineshape due t o t h e t h r e e - coordinated s i t e s [ 8 ] , c a l c u l a t e d u s i n g Qcc = 2.51 MHz,

n

⁼0.59 f o r t h e asymmetric s i t e and Qcc = 2.64 ? 8 z , q = 0.13 f o r t h e symmetric s i t e , and weighting them i n t h e r a t i o I = 78:22. The f r a c t i o n o f borons i n f o u r c o o r d i n a t i o n , N + , i s found by i n - t e g r a t i n g t h e spectrum and comparing t h e a r e a of t h e i n t e g r a l due t o f e a t u r e (a) w i t h t h e t o t a l a r e a . The f r a c t i o n of borons i n symmetric t h r e e - c o o r d i n a t i o n , N a A , a r e t h e n c a l c u l a t e d e a s i l y from

and

N3s=

N ~ A = (1

-

N4)

i-y-iq

¹^-^NL,

-

^{N 3 ~}

.

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A composite o f t h e r e s u l t s from t h i s work and from Ref. 3 i s shown i n F i g s . 7 and 8. The new d a t a f o r high-R a r e n o t q u a n t i t a t i v e l y c o n s i s t e n t w i t h models p r e - s e n t e d i n e i t h e r Refs. 3 , 4 o r 5 . Using i d e a s from Yun and Bray[3] and from t h e p r e s e n t work, t h e following s t r u c t u r a l model i s suggested f o r sodium b o r o s i l i c a t e g l a s s e s :

1 ) R ( 0 . 5 -- A s p o i n t e d o u t byYun and Bray[3], i n t h i s r e g i o n t h e t e r n a r y system behaves j u s t l i k e t h e b i n a r y a l k a l i b o r a t e system i n t h a t NI, = R[9,10]. This shows t h a t a l l t h e sodium oxide goes t o forming four-coordinated borons, r e g a r d l e s s o f t h e amount of s i l i c a p r e s e n t . The equal numbers of t h r e e - c o o r d i n a t e d and f o u r - c o o r d i n a t e d borons a t R = 0.5 may, i n f a c t , be arranged i n d i b o r a t e groups,but t h i s i s not a r e q u i s i t e f o r t h e arguments o f t h e p r e s e n t work. Nevertheless, f o r conve- n i e n c e , t h e combination o f two t h r e e - c o o r d i n a t e d and two f o u r - c o o r d i n a t e d borons w i l l be r e f e r r e d t o a s a "diborate" u n i t ( s e e F i g . 10d).

2) 0.5

5

R

5 RmX

= 1/2 + 1/16 K

--

In t h i s r e g i o n , a l l t h e a d d i t i o n a l sodium oxide combines with some of t h e d i b o r a t e u n i t s t o form reedmergnerite u n i t s , whose presence i n b o r o s i l i c a t e g l a s s e s was f i r s t p o s t u l a t e d by Yun and Bray[3]. (A reedmergnerite u n i t i s a boron t e t r a h e d r o n with each oxygen bridged t o a s i l i c a t e t s a - hedron; i t s chemical formula i s k(Na20-B203-SSiOz).) I f m moles of Na20 a r e added t o t h e R = 0 . 5 composition, based on on mole of B2O3 t h i s conversion p r o c e s s can t h e n be w r i t t e n a s

k(Na20-2B20~)+K(SiO2)+m(Na2O) + (k-m) (NazO-2B203)+2m(Na20-B2O3-8Si02)+ (K-16m)SiOz 0 2 ) where m = R - 0.5. The endpoint of t h i s p r o c e s s occurs when a l l t h e SiOz i s used up;

t h a t i s , when K

-

16m = 0. A t t h i s p o i n t m = 1/16K and R = R ~ = x1/2 ⁺1/16K.

Using N b = % f o r t h e d i b o r a t e u n i t and N q = 1 f o r t h e reedmergnerite u n i t , t h e p r e - d i c t e d v a l u e of N b a s a f u n c t i o n of R can e a s i l y be found from t h e RHS of Eq. 12.

3 ) RmX ( R

5

RD1 = 1/2 + 1/4K

- -

I n t h i s r e g i o n a l l t h e a d d i t i o n a l sodium oxide i s absorbed by t h e reedmergnerite u n i t s t o form non-bridging oxygens on t h e s i l i c a t e t r a h e d r a . C l e a r l y , t h e v a l u e of N b w i l l n o t change i n t h i s r e g i o n . The b e s t f i t t o t h e d a t a occurs when it i s assumed t h a t t h i s process ends when each p a i r of reedmegnerite u n i t s has absorbed 1 . 5 a d d i t i o n a l molecules of Na20. A t t h e end- p o i n t o f t h i s p r o c e s s ,

RD1(Na20).B203.K(sio2) = (1/2-1/16K) ( N ~ Z O - ~ B Z O ~ ) + ~ / ~ K ( ~ . ~ N ~ ~ O . B ~ O ~ S ) (13) from which it i s e a s i l y seen t h a t R D 1 = 1 / 2 + 1/4K.

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4 ) R D I ( R

2

R D i 2 + K

--

I n t h i s r e g l o n t h e f r a c t i o n (2 - K/4)/(2+KJ of t h e a d d i t i o n a l sodlum oxide combines w i t h t h e remaining d i b o r a t e u n i t s t o form borons with two non-bridging oxygens (pyroborate u n i t s ) , and t h e f r a c t i o n (K+K/4)/(2+K) of t h e a d d i t i o n a l sodium oxide combines with t h e reedmergnerite u n i t s t o form pyro- b o r a t e u n i t s and s i l i c a t e t r a h e d r a with two non-bridging oxygens p e r S i atom. This s h a r i n g r e l a t i o n s h i p was a r r i v e d a t by assuming t h a t t h e NazO d i v i d e d i t s e l f pro- p o r t i o n a t e l y between t h e d i b o r a t e u n i t s and reedmergnerite u n i t s according t o t h e t o t a l number of B and S i atoms i n each; from Eq. (13) it i s e a s i l y seen t h a t t h i s number i s (1/2-1/16K) (4) = (2-K/4) f o r t h e d i b o r a t e u n i t s and (1/8K) (2+8) = (K+K/4) f o r t h e reedmergnerite u n i t s . I f m l moles of Na20 go t o t h e d i b o r a t e u n i t s and m2

moles of Na20 go t o t h e reedmergnerite u n i t s , t h e s e p r o c e s s e s can b e l ~ r i t t e n a s

and (14)

1/8X(2. 5Na20-B2O3.8Si02)+m2 (Na20) +

(1/8K-2/15m2)2. 5Na20.B203-8Si02)+2/15m2 [ ( ~ N ~ O B O + ( S Z + Na20) 1 ⁽¹⁵⁾ where (ml +m2) = R-R,, and m l / m 2 = (2-K/4)/ (_K+K/4). The endpoints of t h e s e p r o c e s s e s occur simultaneously: t h e d i b o r a t e u n i t s a r e f u l l y converted when (1/2-1/16~-1/3ml)

= 0, o r ml = 3(1/2-K/16), and t h e reedmergnerite u n i t s a r e f u l l y converted when (1/8K-2/15m2) = 0, o r m 2 = 15/16K. This occurs a t RDg = (ml+ mn)+RDl = 2+K, and a t t h i s p o i n t N U = 0 and N3* = 1.

FIG. 7. Composite Gf N 4 d a t a from Ref. FIG. 8. Composite a f NsA d a t a from Ref.

3 and t h e p r e s e n t work. Dashed l i n e s 3 and t h e p r e s e n t work. Dashed l i n e s a r e p r e d i c t i o n s based on t h e model p r e - a r e p r e d i c t i o n s based on t h e model p r e - s e n t e d i n t h e t e x t . s e n t e d i n t h e t e x t .

The conversion of d i b o r a t e u n i t s i n t o pyroborate u n i t s a s expressed by Eq.(14) need n o t proceed d i r e c t l y , however. For example, a d i b o r a t e u n i t might f i r s t com- b i n e with one molecule o f Na20 t o form two borons each with one non-bridging oxygen, and t h e n t h i s "metaborate" u n i t would combine with two more molecules of Na20 t o form t h e p y r o b o r a t e u n i t . This a l t e r n a t i v e p r o c e s s would n o t a f f e c t any of t h e c a l - c u l a t i o n s p r e s e n t e d so f a r . The b e s t f i t t o t h e N,, N3A, and N 3 ~ d a t a o c c u r s i f it i s assumed t h a t t h e d i b o r a t e u n i t s a r e f i r s t destroyed t o form equal numbers of Na20-B2O3 u n i t s and 2Na20.B203 u n i t s , w i t h t h e Na20-B2O3 u n i t s themselves d i v i d e d up i n t o metaborate u n i t s and l o o s e boron t e t r a h e d r a i n t h e r a t i o 2 : l . I t can b e shown under t h e s e assumptions t h a t R = RD2 = 3/2+3/4K i s t h e p o i n t a t which a l l t h e d i b o r a t e u n i t s a r e destroyed, and f o r RD2

5

R < R D ~ t h e model assumes t h a t t h e meta- b o r a t e u n i t s and boron t e t r a h e d r a a r e t h e n destroyed t o form t h e pyroborate u n i t s .

The dashed l i n e s i n Figs. 7 and 8 a r e t h e model p r e d i c t i o n s f o r N 4 and N3A c a l - c u l a t e d from t h e above a l g e b r a i c e x p r e s s i o n s , and i t i s seen t h a t t h e agreement between model and experiment i s q u i t e good over t h e e n t i r e range of e x i s t i n g d a t a f o r t h e system. The d e c r e a s e i n N3,4 and t h e i n c r e a s e i n

N3s

f o r R > RD3 i s a t t r i b - u t e d t o t h e d e s t r u c t i o n of t h e pyroborate u n i t s and t h e formation o f borons with t h r e e non-bridging oxygens ( o r t h o b o r a t e u n i t s ) . Since only a few samples belong t o t h i s r e g i o n , no attempt h a s been made t o model t h e g l a s s i n t h i s r e g i o n i n any f u r t h e r d e t a i l .

3. B~~ NMR i n Li20-B203 Glasses ^{- -}The use of B ' O NMR spectroscopy f o r t h e i n v e s - t i g a t i o n of g l a s s s t r u c t u r e was r e c e n t l y i n t r o d u c e d i n t h i s laboratory[lO-151 and

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C9-136 JOURNAL DE PHYSIQUE

a p p l i e d t o s o d i m b o r a t e g l a s s e s of low a l k a l i oxide c o n t e n t . The r e s u l t s were found t o be c o n s i s t e n t with t h e Krogh-Moe s t r u c t u r a l model of g l a s s e s [ l 6 ] . In t h e p r e s e n t work, B 1 ° NMR spectroscopy i s a p p l i e d t o l i t h i u m b o r a t e g l a s s e s ; samples spanning t h e glass-forming r e i o n of t h e system (up t o 65 mol%LizO) were prepared and s t u d i e d . m e t h e o r y of BkO NNR i s discussed e x t e n s i v e l y elseuhere[lO-151, but f o r convenience w i l l be b r i e f l y summarized h e r e . Like t h e B" nucleus, which has been used e x t e n s i v e l y f o r NElR s t u d i e s of g l a s s [ l l , t h e B ' O nucleus has an e l e c t r i c quadrupole moment which i n t e r a c t s with e l e c t r i c f i e l d g r a d i e n t s p r e s e n t a t t h e nu- c l e a r s i t e . I n a g l a s s o r p o l y c r y s t a l l i n e powder, t h i s i n t e r a c t i o n r e s u l t s i n a d i s - t r i b u t i o n of resonance f r e q u e n c i e s y i e l d i n g a powder p a t t e r n . Since B ' O has s p i n 3 t h e powder p a t t e r n has a q u a l i t a t i v e l y d i f f e r e n t s h a p e [ l l ] t h a n Fig. 3 o r 4 , but s t r u c t u r a l information i s s t i l l o b t a i n e d by f i t t i n g computer-simulated l i n e s h a p e s t o t h e experimental s p e c t r a . Unlike t h e c a s e f o r ^B" s p e c t r a , t h e e f f e c t s of d i p o l a r broadening a r e small compared t o distribution e f f e c t s f o r t h e B ' O s p e c t r a ; t h i s means t h a t u s i n g B" NMR, one can a l s o gain i n f o r m a t i o n about d i s t r i b u t i o n s of t h e quadrupole parameters i n t h e g l a s s .

A s e t o f 12 l i t h i u m b o r a t e g l a s s e s of varying composition was used i n t h i s s t u d y . Appropriate amounts of Li2C03 and N 3 B O 3 (enriched t o 92% B1°[17])were mixed t o g e t h e r and heated t o 1 0 0 0 ~ ~ u n t l l a l l bubbles d i s a ~ p e a r e d . Glasses with low c o n c e n t r a t i o n s

(< 30 mol%) of L i 2 0 were poured d i r e c t l y from t h e melt i n t o carbon molds and allowed t o cool t o room temperature. Glasses with h i g h e r c o n c e n t r a t i o n s of L i n O were quenched between two metal p l a t e s i n o r d e r t o e f f e c t r a p i d c o o l i n g o f t h e samples.

A l l g l a s s e s were doped w i t h M n C 1 2 ( 1 mol% o r l e s s ) i n o r d e r t o d e c r e a s e t h e s p i n - l a t t i c e r e l a x a t i o n time T I and avoid s a t u r a t i o n e f f e c t s . [ 7 ]

F i g u r e s 9a and 9b p r e s e n t t h e B ' O NMR experimental r e s u l t s f o r g l a s s e s of v a r i - ous compositions. In t h e s e f i g u r e s , R i s defined by mol%Li20/mol%B2O3 which e q u a l s x / ( l - x ) , where t h e composition of t h e g l a s s e s can be w r i t t e n i n t h e form

xLizO(1-x)B203. The smooth l i n e s superimposed on t h e experimental s p e c t r a a r e t h e computer-simulated l i n e s h a p e s , which w i l l be d i s c u s s e d a t l e n g t h below.

The Krogh-hfoe s t r u c t u r a l model1161 s t a t e s t h a t t h e g l a s s e s of a system a r e , i n g e n e r a l , c o n s t r u c t e d from t h e s t r u c t u r a l groupings p r e s e n t i n t h e c r y s t a l l i n e compounds of t h e system, but randomly o r i e n t e d w i t h r e s p e c t t o each o t h e r . The computer-generated l i n e s h a p e s shown i n Figs. 9a and 9b were c a l c u l a t e d by t a k i n g a weighted sum of s p e c t r a t h a t a r e each a s s o c i a t e d with a p a r t i c u l a r s t r u c t u r a l grouping and c h a r a c t e r i z e d by a s e t of quadrupole parameters. Figure 10 shows t h e s t r u c t u r a l groupings t h a t a r e expected i n t h e l i t h i u m b o r a t e system, and Table 1 summarizes some of t h e i r p r o p e r t i e s , i n c l u d i n g t h e quadrupole parameters used i n t h i s s t u d y . P e n t a b o r a t e and t r i b o r a t e u n i t s a r e assumed t o occur i n p a i r s and form t e t r a b o r a t e u n l t s [ l 6 ] . The metaborate is drawn a s a chain, but i t may be a r i n g ( o r a combination of b o t h ) . The l o o s e BOI, u n i t i s a boron atom with f o u r bridging oxygens, b u t it i s not p a r t of any l a r g e r s t r u c t u r a l g r o u p i n g [ l 8 , 1 9 ] . C l e a r l y , some of t h e u n i t s c o n t a i n s i t e s of b o t h t h r e e - c o o r d i n a t e d and four-coordinated boron atoms, s o t h e r e a r e two s e t s of quadrupole parameters a s s o c i a t e d w i t h t h e s e u n i t s . I t should be noted t h a t t h e quadrupole parameters given i n Table 1 a r e i n a l l c a s e s q u a l i t a t i v e l y c o n s i s t e n t with t h e atomic environments shown i n F i g . 10; f o r example, t h e asymmetry parameter

n

f o r t h e metaborate u n i t i s r e l a t i v e l y l a r g e , r e f l e c t i n g t h e asymmetric f l e l d g r a d i e n t caused by t h e non-bridging oxygens. Gaussian d i s t r i - b u t i o n s of both Qcc and q were used f o r each s i t e , and t h e widths o f t h e s e d i s t r i b u - t i o n s a r e given by t h e parameters OQcc and

%;

t h e y a r e a d j u s t a b l e from s i t e t o s i t e but a r e n o t observed t o vary s i g n i f i c a n t l y . The c e n t r a l v a l u e s of Qcc and

n

a r e known approximately from B" work[20] and a r e a d j u s t a b l e i n t h i s s t u d y only w i t h i n t h e e r r o r l i m i t s of t h e B" work. (Note t h a t t h e r a t i o o f coupling c o n s t a n t s f o r t h e B 1 ° and B" n u c l e i i s t h e same a s t h e r a t i o o f t h e i r quadrupole moments, 2.084).

To g e n e r a t e t h e computer s i m u l a t i o n s shown I n F i g s . 9a and Yo, it i s n e c e s s a r y t o determine t h e r e l a t i v e weightings of each of t h e s i t e s given i n Table 1. These weightings a r e not a l l independent but a r e s u b j e c t t o t h e following c o n s t r a i n t s :

(here, a t y p i c a l symbol denotes t h e f r a c t i o n o f a l l t h e boron atoms i n t h e g l a s s t h a t a r e found i n t h e given s i t e ; e . g . , D~ i n d i c a t e s t h e f r a c t i o n of borons t h a t a r e four-coordinated

and

found i n d i b o r a t e u n i t s , e t c . See Table 1 ) .

a ) S i t e C o n s t r a i n t s :

T3 = 3T4

,

^D3= D 4 (16.1)

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-

^U

FIG. 9a. B~~ experimental s p e c t r a and computer-simulated l i n e s h a p e s f o r l i t h i u m b o r a t e g l a s s e s with R 1 0 . 4 .

FIG. 9b. B" experimgntal s p e c t r a and computer-simulated l i n e s h a p e s f o r l i t h i u m b o r a t e g l a s s e s with R 2 0.5.

b) Charge Conservation:

The sum o f p o s i t i v e charges on a l l t h e a l k a l i ions i n t h e g l a s s must equal t h e sum of a l l t h e n e g a t i v e charges on t h e s t r u c t u r a l u n i t s :

c ) Boron Conservation:

1 = B 3 + T3 + T4 + D 3

+

iI4 + L * + M~ + p 3 +

o 3

(16.3) d) N 4 C o n s t r a i n t :

The f r a c t i o n of four-coordinated boron atoms must equal t h e e x p e r i m e n t a l l y determined v a l u e [ 9 ] :

N,+ = T' + D~ + L4 (16.4)

In a d d i t i o n , t h e glass-forming range i s d i v i d e d up (somewhat a r b i t r a r i l y ) i n t o t h r e e convenient r e g i o n s , and s t r u c t u r a l groupings whose composition i s f a r removed from a given r e g i o n a r e assumed n o t t o e x i s t i n t h a t r e g i o n . In r e g i o n I (0 ( R < 0 . 4 ) , only b o r o x o 1 , - t e t r a b o r a t e , and d i b o r a t e u n i t s a r e assumed t o e x i s t ; i n r e g i o n I1

(0.4

2

^R^<1 . 0 ) , only d i b o r a t e , t e t r a b o r a t e , metaborate, and loose B04 u n i t s a r e assumed t o e x i s t ; and i n r e g i o n 111 (1.0 ( R ( 1 . 8 6 ) , only metaborate, l o o s e BOI,, p y r o b o r a t e , and o r t h o b o r a t e u n i t s a r e assumed t o e x i s t . F i n a l l y , i f we impose t h e e x p e r i m e n t a l l y known NI, v a l u e s from p r e v i o u s B" work[9] (see Fig. l l ) , t h e n only one f r e e parameter remains i n Eqs. 16.1-16.4, and t h e weighting o f any s i t e can be o b t a i n e d once t h e weighting of any o t h e r s i t e i s known. D 3 o r

o3

was v a r i e d f o r t h e computer-generated l i n e s h a p e s u n t i l a v i s u a l b e s t f i t with t h e experimental s p e c t r a was o b t a i n e d . O v e r a l l , t h e f i t s achieved i n Fig. 1 a r e q u i t e good, e s p e c i - a l l y c o n s i d e r i n g t h a t t h e r e is only one f r e e parameter t h a t v a r i e s from g l a s s t o g l a s s .

The r e l a t i v e abundances o f each of t h e boron s i t e s a s determined by t h e simula- t i o n procedure d i s c u s s e d above a r e d i s p l a y e d i n F i g . 12. S t r u c t u r a l models f o r each of t h e t h r e e r e g i o n s w i l l now be d i s c u s s e d s e p a r a t e l y ; t h e s e models were chosen s o a s t o be c o n s i s t e n t with t h e d a t a p r e s e n t e d i n F i g . 12.

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CHMICAL FORMILA COMPOSITION (R) STRUCTURAL GROUPING

LABEL (MHz) (MHz)

Reglon I (0 ( R < 0.4) - - The solid lines in Fig. 12 for region I represent mixing of the structural units according to simple lever rules. The data follow these simple predictions only qualitatively, revealing an overabundance of boroxol and diborate units and a consequent shortage of tetraborate units. These results are very similar to those obtained by Jellison and Bray[l3] for the sodium borate system in this compositional region.

Region I1 (0.4

5

R < 1.0) - - In this region the data deviate significantly from simple lever rule predications. A structural model is here proposed, in which diborate and tetraborate units are, upon addition of LizO, proportionately destroyed to form metaborate units and loose BO4 units. Using the fact that the lever rules predict that at R = 0.4 the ratio of the number of diborate units to tetraborate units equals three, and using chemical formulas for the structural units as given in Table 1, this process can be written as

Here R = mol%Li20/mol%B~03= (a+0.4)/1.0, or a = R-0.4. Balancing the equation gives

The relation N 4 = T 4 + D~ + L4 = R/6 + 1/3 for 0.4 ( R < 0.7 leads to

Similarly, the relation N 4 = 5/8 - R/4 for 0.7

5

R < 1.0 leads to and

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FIG. 10 ( l e f t ) . S t r u c t u r a l groupings i n l i t h i u m b o r a t e g l a s s e s . S o l i d c i r c l e s r e p r e s e n t boron atoms, open c i r c l e s oxygen atoms. An open c i r c l e with a n e g a t i v e s i g n i n d i c a t e s a non-bridging oxygen. ( a ) boroxol, (b) p e n t a b o r a t e , (c) t r i b o r a t e , (d) d i b o r a t e , (e) meta- b o r a t e , ( f ) pyroborate, (g) o r t h o b o r a t e ,

0.5- 0.4

-

0.3- 0.2-

0.

I -

0.0

0.4

0.8 1.2

1.6

2.0 R

FIG. 11. ^N4d a t a f o r l i t h i u m b o r a t e g l a s s e s a s determined by B" NMR (taken from Ref. 9 ) . The d a t a have been f i t by t h r e e s t r a i g h t - l i n e segments given by:

NI+ = R f o r 0 < R < 0.4;

N 4 = 1 / 3 +

R/K

f o r 0.4 < R < 0.7;

NI, = 5/23 - R/4 f o r 0 . 7 x R 2 1 . 8 6 . Note t h a t Eqs. (23) and (25) f o r M 3 f o l l o w d i r e c t l y from t h e experimental NI, r e l a - t i o n s and t h e c o n s t r a i n t Eqs. (16.1-16.4); t h e y a r e n o t dependent on t h e model expressed by Eq. (17). The s o l i d l i n e s i n r e g i o n I 1 of Fig. 12 r e p r e s e n t t h e s e e q u a t i o n s ; a l l t h e d a t a a r e c o n s i s t e n t with model p r e d i c t i o n s .

Region I 1 1 (1.0 < R < 1.86)

- -

In t h i s region t h e d a t a a r e i n agreement with a model proposed by ~ < n agd Bray (on t h e b a s i s of B" NPIR s t u d i e s [ 2 0 ] ) which s t a t e s t h a t metaborate and l o o s e BOI, u n i t s a r e destroyed l i n e a r l y (but not p r o p o r t i o n a t e l y ) t o form p y r o b o r a t e and o r t h o b o r a t e u n i t s . The s o l i d l i n e s i n F i g . 12 f o r t h i s r e g i o n r e p r e s e n t Eqs. (12) of Ref. 20, which were d e r i v e d assuming t h i s model. Data from Ref. 20 a r e a l s o included i n Fig. 12 f o r t h i s r e g i o n ; t h e d a t a from both s t u d i e s a g r e e w i t h each o t h e r and g e n e r a l l t f i t q u i t e well with model p r e d i c t i o n s .

4 . ~ e ' NMR i n NaF-BeF2 Glasses.

-

Because of t h e i r p o t e n t i a l u l t r a - h i g h t r a n s - parency, g l a s s e s based on beryllium f l u o r i d e a r e c u r r e n t l y of g r e a t t e c h n o l o g i c a l i n t e r e s t f o r use a s l a s e r g l a s s e s and o p t i c a l waveguides[21-231. I n t h e p r e s e n t work, Be9 N?4R s t u d i e s have been c a r r i e d o u t t o y i e l d i n f o r m a t i o n about t h e atomic environment of t h e beryllium nucleus i n t h e s e m a t e r i a l s . Two samples were prepared f o r s t u d y by D r . Marvin J . Weber and D . D . Kingman a t t h e Lawrence Livermore Labora- t o r y . The b a t c h compositions o f t h e samples were zero w t . % NaF and 33 w t . % NaF, w i t h 0.2 w t . % MnFz added t o h e l p reduce t h e s p i n - l a t t i c e r e l a x a t i o n time T I and avoid s a t u r a t i o n e f f e c t s [ 7 ] . The b a t c h e s were melted i n Np i n carbon c r u c i b l e s , and t h e g l a s s e s were c a s t d i r e c t l y i n t o Vycor t u b e s and s e a l e d with epoxy.

Figures 13 and 14 show t h e Be9 NMR s p e c t r a a t 8.362 MHz f o r t h e nominally p u r e and b i n a r y samples r e s p e c t i v e l y . Since t h e Be9 nucleus has s p i n 3 / 2 , quadrupolar e f f e c t s ( i f t h e y a r e observable) should manifest themselves a c c o r d i n g t o F i g s . 3 and 4. Figure 13 shows c l e a r l y t h e s u p e r p o s i t i o n of two symmetric responses of d i f f e r i n g l i n e w i d t h W: W(narrow) = 2.3 kHz and W(broad) = 8 . 5 kHz. Assuming Gaussian l i n e s h a p e s , t h e corresponding r a t i o o f i n t e n s i t i e s i s (2.3/8. 512 = 7.3%.

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FIG. 12. Weightings of t h e s t r u c t u r a l groupings used t o c a l c u l a t e t h e computer- simulated l i n e s h a p e s i n Fig. 9. The s t r a i g h t - l i n e segments r e p r e s e n t t h e s t r u c - t u r a l models d i s c u s s e d i n t h e t e x t . Open symbols r e p r e s e n t d a t a taken from Ref. 2.

But t h i s s p e c t r a l s t r u c t u r e i s n o t t y p i c a l of quadrupolar e f f e c t s ; t h e spectrum i s not t h a t expected from n u c l e i s i t e s having r e l a t i v e l y small (but non-zero) quadru- p o l a r e f f e c t s , because t h e r a t i o of i n t e n s i t i e s i n t h e " c e n t r a l " (narrow l i n e ) and

" s a t e l l i t e " (broad l i n e ) p o r t i o n s i s n o t c o r r e c t f o r t h a t c a s e . The s p e c t r a l s t r u c t u r e i s n o t due t o second-order quadrupolar e f f e c t s e i t h e r , because t h e spectrum d i d n o t spread o u t when recorded a t 4 MHz. This would be expected s i n c e t h e second-order quadrupolar s p l i t t i n g b u t n o t t h e d i p o l a r broadening i s i n v e r s e l y p r o p o r t i o n a l t o t h e o p e r a t i n g f r e q u e n c y [ 2 , 7 ] . Moreover, t h e s t r u c t u r e i s n o t due t o t h e r m a l l y a c t i v a t e d motional narrowing e f f e c t s [ 2 4 ] because t h e r e l a t i v e i n t e n s i - t i e s d i d not change when t h e spectrum was recorded a t -70°c and 160°C. We conclude t h a t t h e narrow response i s due t o Be0 impurity; t h e NMR spectrum o b t a i n e d from commercial p o l y c r y s t a l l i n e Be0 was found t o match c l o s e l y t h e narrow l i n e of Fig. 13. Raman s t u d i e s [ 2 5 ] have a l s o r e v e a l e d t h e p r e s e n c e of Be0 i m p u r i t y i n v i t r e o u s BeF,.

I t i s not y e t c l e a r why t h e i m p u r i t y i s n o t apparent i n t h e b i n a r y sample (Fig.

1 4 ) . A simple d i p o l a r l i n e w i d t h c a l c u l a t i o n shows t h a t t h e Be n u c l e i which g i v e r i s e t o t h e narrow l i n e i n Fig. 13 cannot be immediately bonded t o even a s i n g l e f l u o r i n e atom o r t h e r a t i o of l i n e w i d t h s would be much c l o s e r t o u n i t y . The oxygen i s not i n OH groups e i t h e r , because an NMR s e a r c h f o r p r o t o n s a t 60 MHz y i e l d e d a n u l l r e s u l t . While it i s n o t c l e a r a t what s t a g e o f t h e sample-making p r o c e s s t h e oxygen e n t e r e d , it i s c l e a r t h a t g r e a t c a r e must be taken t o avoid t h i s problem i f high t r a n s p a r e n c y m a t e r i a l i s d e s i r e d ; i n f a c t , D r . P e t e r S c h u l t z and co-workers a t Corning Glass have abandoned t h e m e l t i n g technique a l t o g e t h e r and a r e concen- t r a t i n g on vapor d e p o s i t i o n techniques t o achieve t h e d e s i r e d p u r i t y [ 2 6 ] .

The spectrum of t h e nominally pure sample shown i n F i g . 15 was taken with t h e same experimental parameters a s f o r Fig. 13 but over a much wider f i e l d sweep. The spectrum shows a very broad, low amplitude, symmetric response; t h i s i s due t o t h e f i r s t - o r d e r s a t e l l i t e t r a n s i t i o n s , but t h e i n d i v i d u a l s h o u l d e r s and divergences a r e n o t r e s o l v e d due t o a l a r g e d i s t r i b u t i o n i n quadrupole parameters ( s e e F i g . 3 ) .

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I n t e g r a t i o n of t h e spectrum r e v e a l s t h a t 59% of t h e t o t a l i n t e n s i t y i s i n t h e s a t e l l i t e s , i n good agreement with t h e t h e o r e t i c a l v a l u e of 60%. Computer simula- t i o n o f t h e l i n e s h a p e r e v e a l s t h a t t h e average coupling c o n s t a n t i s about 100 kHz,

k z d

FIG. 13. ~ e ' NMR spectrum o f t h e nomi- n a l l y p u r e sample taken a t 8.362 MHz.

FIG. 14. ~ e ' NMR spectrum of t h e b i n a r y sample taken a t 8.362 MHz.

with a d i s t r i b u t i o n of about 40 kHz around t h i s v a l u e . A s i m i l a r wide-sweep spectrum taken of t h e b i n a r y sample did not r e v e a l t h e s a t e l l i t e t r a n s i t i o n s , p r e - sumably because t h e average coupling c o n s t a n t i s much b i g g e r i n t h i s sample. (This conclusion i s f u r t h e r supported below.)

Figure 16 shows t h e spectrum of t h e b i n a r y sample recorded a t 1.129 MHz. Note t h a t t h e spectrum has become asymmetric and a l s o has broadened d r a m a t i c a l l y from t h e c a s e a t 8 MHz (Fig. 1 4 ) ; a s d i s c u s s e d above, t h e s e f e a t u r e s a r e t y p i c a l o f second-order quadrupole e f f e c t s . A s i m i l a r run performed a t 1.129 MHz on t h e nomi- n a l l y pure sample d i d not r e s u l t i n any broadening. (This i s c o n s i s t e n t with t h e v a l u e Qcc = 100 kHz concluded above.) I t i s c l e a r t h a t t h e average coupling con- s t a n t i s much l a r g e r i n t h e binary sample than i n t h e nominally pure sample.

Computer s i m u l a t i o n r e v e a l s t h a t f o r t h e b i n a r y sample Qcc = 300 kHz with a spread of about 100 kHz about t h i s value.

Brawer and Weber have performed e x t e n s i v e molecular dynamics c a l c u l a t i o n s f o r t h i s system[27] and have concluded t h a t a s NaF i s added t o BeF, g l a s s , BeF, t e t r a - hedra t a k e on an e x t r a F atom and become f i v e c o o r d i n a t e d with f l u o r i n e . This would d e s t r o y t h e t e t r a h e d r a l symmetry of t h e b e r y l l i u m s i t e and l e a d t o a l a r g e r coupling c o n s t a n t . The p r e s e n t work shows e x a c t l y t h i s e f f e c t and i s c o n s i s t e n t w i t h t h e e x i s t e n c e of f i v e - c o o r d i n a t e d b e r y l l i u m i n NaF-BeFs g l a s s e s .

FIG. 15. Be NMR spectrum of t h e FIG. 16. Be NMR spectrum of t h e b i n a r y nominally p u r e sample t a k e n a t 8.362 sample taken a t 1.129 MHz.

MHz over a much wider f i e l d sweep.

Acknowledgments. - The a u t h o r s wish t o g r a t e f u l l y acknowledge D r . S. A. F e l l e r f o r c a r r y i n g o u t much of t h e B' work p r e s e n t e d h e r e , and D r . S. G. Greenbaum of t h e Naval Research Laboratory, D r . P. C. S c h u l t z , D r . M. J . Weber and S. Z . Xiao f o r very h e l p f u l d i s c u s s i o n s and communications.

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