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Compositional and Annealing Dependence of some Mechanical and Acoustical Properties for V<sub>2</sub>O<sub>5</sub>/P<sub>2</sub>O<sub>5</sub> Glasses

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Compositional and annealing dependence of some mechanical and acoustical properties for V

2

O

5

/P

2

O

5

glasses

A H K h a f a g y , M A E w a id a , M M S G h o n e im , A A H ig a z y a n d I Z H a g e r

D e p a r tm e n i o f P h y s ic s , F a c u lty o f S c ie n c e . M e n o u fia U n iv e rs ity , S h e b in F L -K o o m , F g y p i

Received 16 October 1990, accepted 11 April 1991

A b s t r a c t : T h e g la s s d e n s ity , in te r n a l fric tio n , a n d u ltra s o n ic a tte n u a tio n in so m e V2O5 / P2O5 g la s s e s w e r e m e a s u re d b y d i f fe r e n t te c h n iq u e s . D e p e n d e n c e o f th e s e p ro p e rtie s o n c o m p o s iu o n sh o w e d “ th r c e -c o m p o s itio n -r e g io n s ” . T h is re v e a le d th e a n o m a lo u s c h a ra c te r w h ic h is a ttrib u te d to s o m e s tru c tu ra l c h a n g e s in te s te d g la s se s . A lso , d e p e n d e n c e o f th e a b o v e p ro p e rtie s a s w e ll as th e e la s tic m o d u lu s a n d u ltra s o n ic v e lo c ity o n a n n e a b n g o f s p e c im e n s w e re in v csL ig atcd . A ll re su lts o b ta in e d f o r aU p a ra m e te rs m e a s u re d sh o w e d in c re a s e w ith a n n e a lin g te m p e ra tu re . In te rp re ta tio n o f b e h a v io u r s o b ta in e d f o r th e p r o p e r u e s in v e s tig a te d h a s b e e n g iv e n a c c o r d m g to th e c u r re n t c o n c e p ts w h ic h p u t fo re w o re d to e x p la in su c h th e s e d a u .

K e y w o r d s : V a n a d a te p h o s p h a te g la s s e s , in te rn a l fric tio n , u ltra s o n ic a tte n u a tio n , a n o m a lo u s g la s s a n d c ro s s h n k in g .

P A C S N o s . : 6 2 .4 0 , +1. 6 2 .6 5 . -fh. 8 1 .2 0 . P e . 8 1 .4 0 . F.f

1

. In tro d u c tio n

A m ong th e e a r l i e r in f o r m a t io n s a b o u t th e p r o d u c t io n o f V2O5/ P2 0 5 g la s s e s a r e th o s e reported b y R a w s o n ( 1 9 6 7 ) a n d R o s c o e ( 1 9 6 8 ) , w h ic h s h o w th a t it is p o s s ib le to p r e p a r e glasses c o n ta i n in g m o r e th a n 9 5 w t% V2O5. T h e g la s s - f o r m i n g r e g i o n s in a n u m b e r o f binary v a n a d a te g la s s e s in c lu d in g V2O5/ P2O5 s y s te m w e r e d e te r m in e d (D e n to n

et al

1 9 5 4 ) and it w a s s h o w n t h a t th e s e g la s s e s a r e s e m ic o n d u c t o r s . T h e e le c tr i c a l c o n d u c ti v it y in se m ic o n d u c tin g v a n a d a te g la s s e s w a s s tu d ie d (H ir a s h im a

et al

1 9 8 2 ,1 9 8 3 a n d Y o s h id a

ei al

1985), a n d w a s s h o w n to b e c o m p a r a b le to th o s e o f s u p e r io n ic c o n d u c tin g o x id e g la s s e s . The c o n d u c tio n m e c h a n is m in V2O5/ P2O5 g la s s e s w a s a ttr ib u te d to th e e le c tr o n h o p p in g o rig in a tin g f r o m e i t h e r V'** io n s p r o d u c e d d u r i n g th e s a m p le p r e p a r a ti o n b y th e r m a l d e c o m p o s itio n , o r V** io n s o rig in a lly in c o r p o r a te d in to th e m a trix fr o m V2O5 ( D e B o e r a n d V erw ey 1 9 3 7 , S e w e ll 1963 a n d A lle r s m a

et al

1 9 6 7 ).

S tr u c tu r e s o f s o m e b in a r y p h o s p h a t e g la s s e s c o n ta i n in g o x id e s o f N a , C a , B a , C d , Pb, Z n , M g a n d B o w e r e s tu d ie d ( K o r d e s

et al

1 9 5 3 ). B y i n v e s ti g a ti n g th e c o m p o s it io n a l d e p e n d e n c e o f th e d e n s i ty , m o l a r v o lu m e a n d r e f r a c tiv e in d e x . T h e s e a u th o r s c la s s if ie d th e tested g la s s e s in t o n o r m a l a n d a n o m a l o u s a c c o r d in g to th e v a r ia tio n o f th e a b o v e p h y s ic a l

© 1 9 9 2 lA C S

(2)

2 9 0

A I I Khafagy, M A Ewaida, M M S Ghoneim, A A Higazy and I Z Hager property with the content of the added cation i.e., the glass is termed normal, if Uie measured property changes continuously as a function of composition over the entire vitreous range, but it is called anomalous when the properties show some discontinuities at a certain composition, as observed by the same authors, only in the PaOs/ZnO, PiOs/MgO.

P

2 0 5

/Ba

0 2

systems at about 50 mol.% of metal oxide while other investigated glasses showed normal behaviours. However, the plot of density versus composition of P

2

O

5

/C

03

O

4

system (Higazy and Bridge 1985a, 1985b) showed two points of inflexion at about 15 and 40 mol.% of cobalt oxide.

The dependence of elastic moduli on glass composition of number of phosphate glasses has been investigated by several authors (Farly and Saunders 1975, Field 1969, Bridge and Moridi 1977, Patel and Bridge 1983, Patel el al 1983, Bridge and Higazy 1985).

However, the results reported (Higazy and Bridge 1985a, 1985b) exhibit existence of 3- composition regions in the

P2O5/C03O4

glasses. These regions have been identified by

the

density, infrared absorption and chemical analysis data.

The effect of annealing temperature on the elasticity and electrical conductivity of some oxide glasses has been investigated by several authors (Makenzie 1960, Bridge and Moridi 1977, Patel 1982 and Patel el al 1983). All results reported in these works showed increase in elasitc moduli with increasing temperature, but the conductivity showed decrease under the same conditions. In this paper, we throw some light upon the compositional dependence and annealing effect of V

2

O

5

/P

2

O

5

glasses on some physical properties; i.e.

glass density, internal friction, ultrasonic attenuation, clastic modulus and wave velocity through the use of different techniques of measurement.

2 . E x p e rim e n ta l 2.1. Glass preparation :

Vanadium phosphate glasses of starting compositions expressed in mol.%, were prepared

from laboratory reagent grades of Analar P

2

O

5

and Analar V

2 0

j. Amounts of these materials

are weighed and mixed in an alumina crucible which is then inserted in an electric furance

held at 250°C for one hour. After this treatment, each mixture Was transferred to another

electric furnace open to the atmosphere with its temperature pre-adjusted to that of melt. It

has been observed that, different temperatures were required to suit different preparations and

the melting temperature was in the range from 700-950®C with the highest one applied to

the mixture rich in P

2

OS. The molten mixture was then occasionally stirred with an alumina

rod to ensure its homogeinity and maintained in the furnace for about 20 minutes. Then the

melt was poured into a mild-steel mould, at room temporature to form glass rods of circular

cross-section with diameter 1.2 cm. After casting each glass, it was immediately transferred

to an electric furnace held at 250®C fw one hour. Thereafter, the fimiace is switched off with

specimens inside it to be annealed and cooled slowly to room temperature. The amorphous

nature of the samples prepared here was identified by X-ray diffraction. Also, these

(3)

specimens were chemically analysed as has been described previously (Khafagy et al 1992).

Glass rods (each 1.5 cm long and 1.2 cm in diameter) were cut with their opposite faces optically polished for obtaining good parallelism to suite the required ultrasonic measurements of this work.

2.2. Techniques of measurements:

(i) Density measurements :

Densities of prepared glasses in this work, p, were measured by the Archimedes method using toluene as an immersion liquid-with an accuracy of ±

0.001

gm. cm”

F ig u re 1. The transmission-receiving technique used for measunng the ultrasonic attenuauon.

(U) Ultrasonic attenuation measurements :

A technique based on the idea of the transmission receiving system is used to calculate the attenuation of the ultrasonic waves propagating in tested glasses. Figure 1 shows a schematic diagram for the system employed. Two identical quartz crystals, silver-coated at their opposite faces (each of 0.3S cm thickness and 2.5 cm diameter) were^ used as piezoelectric transducers, transmitter and receiver, respectively. They were bonded to the specimen by silicon grease as an acoustic couplant. The transmitter was driven by a B-K pi^ision 3010 function generator at its resonance frequency (800 KHz). Amplitude of both the transmitted and received wave displayed on the screen of a CRO (Mode COS 5020) were measured. The ultrasonic attenuation, a, is calculated according t o ;

20 , ^

o . - l o g -

(I)

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292

A H Khafagy, M A Ewaida, M M S Ghoneim, A A Higazy and I Z Hager Where 1 is the length of the tested sample, A^ and A, are the amplitudes of the transmitted and received waves, respectively. However the ultrasonic attenuation was calculated with accuracy ±0.015 dB. cm"

(Hi) Internal friction technique :

A magnetostrictive delay-line system described previously in detail (Bell and Pelmore 1977) is used here to calculate the internal friction, Q~ \ longitudinal wave velocity, v, and longitudinal clastic modulus, E. In this technique, a generated burst o f mechanical o.scillations is used to excite each tested specimen at either the natural frequency or one of the harmonic frequencies of the specimen. This system is characterized by a resultant echo signal which recorded by the system and illustrated schematically in Figure

2

. The parameters shown in this figure arc used to calculate, absolutely, the internal friction (Bell and Pelmore 1977) as follows :

Qn,

On + a .

= X (

2

)

nN ^ In ( 2 / ( 1 - x ) )

Qc 1 + jc

(3)

where Qc and arc the coupling and material g-factors, respectively, a^, and N are indicated in Figure 2, the initial amplitude, the steady state amplitude, and the number of oscillations to the observed cross-over which results due to the sup>erposition of the two anti-phased signals; one reflected from the junction of the specimen with the wire-line of the system and the other reflected from the back of the specimen. The standard deviation for the calculated values of internal friction was ±0.0019.

Figure 2. Schematic diagram of the resultant echo-pattern displayed in the magnetostrictive delay-line system.

In practice, each specimen was cemented at the centre of its faces, by Araldite, to the

remote end of the transmission line wire and excited axially at its fundamental resonance

frequency.

(5)

T h e r e s o n a n c e f r e q u e n c y ,

F,

i s r e l a te d to th e lo n g itu d in a l w a v e v e lo c ity ,

V,

b y th e equation

V = 2LF

(4 )

L,

le n g th o f te s te d s p e c im e n . A c c o r d in g ly , th e lo n g itu d in a l e la s tic m o d u lu s ,

E,

is c a lc u la te d as f o l l o w s :

E = pV^

(5)

w h ere p is th e d e n s ity o f th e s p e c im e n .

T h e e f f e c t o f a n n e a l i n g w a s d e t e r m i n e d b y s u b j e c t i n g g l a s s e s o f d i f f e r e n t c o m p o s itio n s o f d i f f e r e n t a n n e a l in g te m p e r a tu r e s : 5 2 3 , 5 7 3 , 6 2 3 , 6 7 3 a n d 7 2 3

K.

E a c h tested s p e c i m e n is m a i n ta i n e d f o r 2 h o u r s a t th e s e le c te d a n n e a l te m p e r a tu r e a n d th e n th e fu rn a c e is s w itc h e d o f f to b e c o o le d s lo w ly to r o o m te m p e r a tu r e , a n d m e a s u r e m e n ts o f p ,

Q

V a n d £ a r e s u c c e s s iv e ly fo llo w e d .

3. R e s u l t s a n d d i s c u s s i o n

3.1. Dependence o f glass-density, internal friction and ultrasonic attenuation on composition fo r V

2

OSIP

2

OS glasses :

T h e c o m p o s itio n a l d e p e n d e n c e o f g la s s - d e n s ity , in te rn a l fr ic tio n a n d u ltr a s o n ic a tte n u a tio n for s o m e p r e p a r e d V2O5/ P2O5 g la s s e s o f th is w o rk , is s h o w n in F ig u r e s 3 (a ) , (b ) a n d (c ) re s p e c tiv e ly . T h e s e f ig u r e s in d ic a te th r e e - c o m p o s itio n - r e g io n s . H o w e v e r , s i m i la r p lo ts a r e o b s e r v e d f o r b o th t h e in t e r n a l f r ic ti o n a n d u lt r a s o n i c a tt e n u a ti o n w h ic h a r e in c o n v e r s e b e h a v io u r to th a t o f d e n s ity . T h e f ir s t r e g io n s h o w s th a t a r a p id in c r e a s e in th e g la s s d e n s ity (F ig u re 3 (a ) ) c o r r e s p o n d s to a r a p i d d e c r e a s e in th e in te r n a l fr ic tio n a n d th e a tt e n u a ti o n (F ig u re 3 ( b ) a n d ( c ) ) a s th e V2O5 c o n te n t i n c r e a s e s fr o m 0 u p to 2 2 m o l .% , w h ile , th e s e c o n d o n e ( 2 2 - 5 3 ) V2O5 m o l.% , s h o w s th a t a ll p a r a m e te r s in v e s tig a te d in th is f ig u r e a r e a lm o s t s ta b le . B e y o n d 5 3 V2O5 m o l .% , th e d e n s ity s h o w s c o n s i d e r a b l e i n c r e a s e b u t th e in te rn a l fr ic tio n a n d u ltra s o n ic a tte n u a tio n s h o w s c o n s id e ra b le d e c r e a s e w ith in c r e a s in g V2O J c o n te n t.

T h e o b s e r v a tio n o f th e a b o v e th r e e c o m p o s itio n a l r e g io n s a n d th e o c c u r r e n c e o f th e in f le x io n p o in ts a t a b o u t 2 2 a n d 5 3 V2O5 m o l.% in d ic a te th a t o u r V2O5/ P2O5 s y s te m m a y be c o n s id e r e d a s a n a n o m a lo u s g la s s (K o r d e s

et al

1 9 5 3 ). H o w e v e r a n o m a l o u s b e h a v io u r s w e re a ls o o b s e r v e d p r e v i o u s ly (H ig a z y a n d B r id g e 1 9 8 5 a , 1 9 8 5 b , J a n a k i r a m a R a o 1 9 6 5 , C a lv o a n d J o r d a n 1 9 7 6 , D r a k e

et al

1 9 7 8 a n d K h a n

et al

1 9 7 5 ) f o r d i f f e r e n t p h o s p h a t e g la s s e s a n d th e y a r e c o n f i r m e d h e r e b y o u r in te r n a l f r ic tio n a n d u lt r a s o n i c a tt e n u a ti o n in v e s tig a tio n , b e s id e s th e d e n s ity d a ta .

A n o m a lo u s b e h a v io u r s w h ic h h a v e b e e n o b s e r v e d in a ll b in a r y g la s s e s in v e s tig a te d in p r e v io u s w o r k s w e re a ttr ib u te d to th e o c c u r r e n c e o f s o m e s tr u c tu r a l c h a n g e s w h ic h r e s u lt fro m th e d if f e r e n t p r o p e r tie s o f th e a d d e d c a tio n s to th e p h o s p h a t e m a tr ix , i.e . th e w a y b y w h ic h , th e a d d e d c a tio n c a n e n te r th e g la s s n e tw o r k e it h e r in t e r s t it ia l ly o r s u b s titu tio n a lly

(6)

294

A H Khafagy, M A Ewaida, M M S Ghoneim, A A Higazy and

/ Z

Hager

(K o r d e s

et al

1 9 5 3 , T a n a n a e v

ei al

1 9 6 9 a n d H ig a z y a n d B r id g e 1 9 8 5 a , 1 9 8 5 b ). T h is , of c o u rs e , le a d s to s o m e c h a n g e s in b o th th e c r o s s lin k in g d e n s i ty a n d c o o r d i n a ti o n n u m b e r o f

'Eu

f t

>- ie

M '

Figure 3. Dependence of the density, internal friction and ultrasonic attenuation on the composition of V2O5/P2O5 glasses.

th e g la s s stru c tu re . T h e re fo r e , th e c o m p o s itio n a l d e p e n d e n c e o f th e d e n s i ty , in te r n a l fric tio n a n d u ltra s o n ic a tte n u a tio n f o r th e V2O5/P2O5 g la s s e s in v e s tig a te d h e r e c a n b e in te r p r e te d as f o l l o w s :

(i) In th e f ir s t r e g io n ; a s th e V2O5 c o n te n t is in c r e a s e d f r o m 0 to 2 2 m o l.% P - 0 b o n d s w h ic h e x is t in th e v itre o u s P2O5 m a trix a re ru p tu re d a n d re p la c e d b y P -O -V c ro s s lin k s a s b rid g in g b o n d s in v o lv in g v a n a d iu m io n s w ith d i f f e r e n t v a le n c e s . T h u s , th e d e n s ity in c re a s e s (F ig u re 3 (a )) a n d c o n s e q u e n tly b o th th e in te rn a l fr ic tio n a n d u ltr a s o n ic a tte n u a tio n a rc d e c re a s e d a s o b se rv e d in F ig u re 3 (b ) a n d (c ), re s p e c tiv e ly .

(ii) In th e s e c o n d re g io n o f c o m p o s itio n ( 2 2 - 5 3 m o l .% ) , th e d e n s i ty te n d s to b e c o n s ta n t a s a r e s u lt o f th e v a n a d iu m v a le n c y c h a n g e s , w h e n th e v a n a d iu m io n s o f te tra h e d ra l c o o r d in a tio n (L o w e r c ro s s lin k in g d e n s ity ) is in c r e a s e d in th e s t r u c tu r e b y th e e n d o f th e

(7)

first re g io n . S o , n e a r l y c o n s t a n t v a lu e s f o r b o th th e in t e r n a l f r ic ti o n a n d u lt r a s o n i c attenuation a r e o b s e r v e d a s w o u ld b e e x p e c te d , a n d sh o w n in F ig u r e 3.

(iii) F o r g la s s e s o f V2O5 c o n te n t m o r e th a n 5 3 m o l.% v a n a d iu m io n s o f v a le n c e s with h ig h e r c r o s s li n k d e n s ity ( o c ta h e d ra l c o o r d in a tio n ) a re in c r e a s e d in th e m a trix w ith th e in crease o f v a n a d iu m o x id e c o n te n t . C o n s e q u e n tly , a s h a r p in c r e a s e in th e g la s s - d e n s ity (F ig u re 3 ) a n d c o r r e s p o n d i n g d e c r e a s e s in b o th t h e in t e r n a l f r ic ti o n a n d u lt r a s o n i c attenuation a r e o b ta in e d in F ig u r e 3 (b ) a n d (c ) re s p e c tiv e ly .

3,2. Effect o f annealing :

V ariatio n s o f th e g la s s d e n s i ty , lo n g itu d in a l w a v e v e lo c ity , lo n g itu d in a l c la s tic m o d u lu s , internal fr ic tio n a n d u ltr a s o n ic a tte n u a tio n w ith a n n e a lin g te m p e ra tu re w e re in v e s tig a te d fo r som e V2O5/ P2O5 g la s s e s w ith d if f e r e n t c o m p o s itio n s . T h e r e s u lts o b ta in e d fro m th e s e in v e s tig a tio n s a r e s h o w n in F ig u r e s 4 , 5 , 6. 7 a n d 8(a ) , (b ) a n d (c). I t c a n b e o b s e r v e d th a t all p a r a m e te r s in v e s t i g a t e d h e r e in g e n e r a l , in c r e a s e d w ith th e in c r e a s e o f a n n e a l in g te m p e ra tu re a n d th e r e s u lts o b ta in e d im p ly th a t s tru c tu r a l fe a tu re s c a n c o n tin u e to c h a n g e w ith h e a t tr e a tm e n t f o r in c r e a s in g a n n e a lin g te m p e ra tu re s .

Figure 4. The effect of annealing

temperature on the density. Figure 5. The effect of annealing temperature on

the ultrasonic velocity.

I n t e r p r e t a t i o n s f o r i n c r e a s e in th e e l a s t i c i t y o f o x id e g l a s s e s w ith i n c r e a s i n g a n n e a lin g te m p e r a t u r e w e re g iv e n e a r l ie r ( G la d k o v e a n d T a r a s o v e 1 9 6 0 a n d H ig a z y a n d B rid g e 1 9 8 5 a , 1 9 8 5 b ). G la d k o v e

et al

in th e ir s tu d ie s o f s o d iu m s ilic a te g la s s e s c o n s id e r e d

3A(9)

(8)

that increases in the elastic moduli of the tested glasses, on annealing were due to increase in the number of crosslinks. The authors argued that in glass melts which have been cooled rapidly, the framework is not cross-linked to the full extent of the chemical crosslinking which the original composition allows. Therefore, any heat treatment involves changes of the crosslinking density of the structure. So, they claimed that annealing causes broken bonds to take part in crosslinking. On the other hand, Higazy and Bridge (1985a, 1985b) cobalt-phosphate glasses and reported that, observed increase in die elastic moduli of their tested glasses upon annealing was based on density consideration alone. They explained the mechanism by which annealing always increases the density as follows: in the casting process residual stfesses are frozen into the glass. Tensile stresses caused by those interatomic spacing which are greater than the normal crystalline values will on macroscopic balance, cancel out compressive stresses due to interatomic spacing smaller

296

A H Khctfagy, M A Ewaida, M M S Ghoneim, A A Higary and I Z Hager

Figure 6. 'Hie effect of annealing lempcralure on the longitudinal modulus.

6a 0^

w 6 •

4 -

2 l -

64.67mot%V^05

60 molV.

Figure 7. The effect of annealing temperature on the internal friction.

than the crystalline value. From the form of interatomic force potentials it is obvious that for a given level of tensil^compressive stress, average interatcanic spacings are greater than the crystalline value and correspondingly, the glass density is smaller than what

would

occur for a crystalline arrangement of the same atoms. Therefore the release of stress on

annealing will cause a reduction in the average aumiic q>acing with a corre^tonding decrease

in the glass density and so increase in elastic moduli.

(9)

In a crosslinked glass aetwork which has a high molecular weight the average interatomic spacings could be decreased from further crosslinking. Both the molecular weight and the interatomic spacings are considered as efficient factors for changing the glass density. Therefore, a combined effect due to density and crosslinking changes is responsible for increasing the elastic modulus and ultrasonic wave velocity on annealing the V

2

O

5

/P

2

O

5

glasses of the present work (Figures

6

and 5).

Figure 8(a). The effect of annealing temperature on the ultrasonic attenuation.

It is well known that annealing or the removal of internal stress leads to glass crystallization by introducing some amount of intermediate range order. The degree of ordering and molecular orientation are affected by heat treatment. These structural changes have profound effects, not only on the elastic modulus and wave velocity but also on the internal friction and ultrasonic attenuation as shown in Figures 7 and

8

.

The increase in both the internal friction and the ultrasonic attenuation on V

2

O

5

/P

2

OS

glasses may be u n d ^ to o d acctx’ding to the interpretation reported earlier (lllers and Breuer

1963) for the effect of crystal size on the amorphous regions as follows : at low to medium

crystallinities there would be many small ordered regions which would act like crosslinks

(10)

and inhibit the segmental motion in the amorphous regions, while at high crystallinities the ordered regions would be larger and fewer and thwefcMe would allow the segments in the amorphous regions more freedom. Thus, at the start with low annealing temperature

298

A H Khafagy, M A Ewaida, M M S Ghoneim, A A Higazy and I

Z

Hager

Fig ure 8(b). The effect of annealing temperature on the ultrasonic attenuation.

molecular motion inhibited by restraints which are imposed by the small ordered regions in the glassy matrix. This leads to lower damping (i,c., small values of both the internal friction and ultrasonic attenuation, Figures 7 and

8

). As the annealing temperature is increased the molecular motion is enhanced and contributes to the increased damping (i.e.

the internal friction and attenuation).

(11)

F igure 8(c). The effect of annealing temperature on the ultrasonic attenuation.

R eferences

AUersma T, Hakim R, Kennedy T N and Makenzie I D 1967 /. Chem, Phys. 46 154 BeU J F W and Pclmorc J M 1977 J. Phys. ElO 1145

Bridge B and Moridi G R 1977 InslUuie o f Acoustics Spring Conf. and Exhibition p 6 Bndge B and Higazy A A 1985 J. Mater. Sci. 20 4484

a iv o C and Jordan B D 1976 Phys. Chem. Glasses 17 220

Dc Boer J H and Verwey E J W 1937 Proc. Phys. Soc. (London) Suppl. 49 59 Denton E P. Rawson H and Stanwoith J E 1954 Nature 173 1030

Drake C F, Stephan T A and Yates B 1978 J. Non-Cryst. Solids 28 61 Farley J M and Saunders C A 1975 Phys. Stat. S d . (a) 28 199 Field M B 1969 J. Appl. Phys. 40 2628

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