Elastic constants and structure of the vitreous system Co3O4P2O5

Journal of Non-Crystalline Solids 72 (1985) 81-108 North-Holland, Amsterdam

81

ELASTIC C O N S T A N T S AND S T R U C T U R E O F T H E VITREOUS S Y S T E M Co304-P205 A.A. H I G A Z Y * and B. B R I D G E Department of Physics, Brunel University, Kingston Lane, Uxbridge, Middlesex, UK Received 26 June 1984

The elastic moduli of the entire vitreous range of the system C o - P - O that can be prepared by melting together C0304 and P205 oxides in open crucibles, have been measured by ultrasonic techniques at 15 MHz. The bulk, shear, longitudinal and Young's moduli and the Poisson ratio are found to be rather sensitive to the glass composition. It is found from this ultrasonic data, that the glass system can be divided into "three compositional regions". This behaviour is qualitatively interpreted in terms of the cobalt co-ordination, crosslink densities, interatomic force constants and atomic ring sizes. Also presented is a full discussion of effects of annealing on elastic properties.

I. Introduction This paper forms part of a programme to explore what information can be obtained about atomic and molecular configurations in glass, from studies of variations in ultrasonic properties with gradual and wide ranging changes in glass composition. Numerous measurements of the elastic moduli of vitreous materials have been made since the advent of the ultrasonic pulse-echo method. However, surprisingly perhaps, most of these ultrasonic data are limited to silicate or borosilicate based oxide glasses and the chalcogenides. Elastic moduli data on interesting glass systems based on the other inorganic oxide glass formers are quite rare. This fact was one of the motivating factors behind our work, since it was felt that an understanding of the processes affecting the systematics of elastic moduli variations in glass would be enhanced by exploring a wider range of glasses than had been done hitherto. The present work concerns the entire range of glasses that can be prepared by melting together C0304 and P205 reagents in open crucibles. The ultrasonic compressional and shear wave velocity measurements made on these glasses at room temperature are discussed; and together with density measurements, the data is used to determine the compositional dependence of the elastic moduli, * On leave from the Physics Department, Faculty of Science, Monofia University, Shebeen EI-Kome, Egypt. 0022-3093/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

82

A.A. Higazy, B. Bridge / Elastic constants and structure of Co~04-P_,Os

and also the Debye temperatures of this glass system (which are to be compared with related parameters obtained from conductivity and infra-red absorption measurements, in a separate publication). It will be shown that from this ultrasonic data, the glass system can be divided into the same composition regimes that could be defined from the chemical analysis and infra-red measurements reported in earlier papers [1,2]. These effects, however, are more clearly displayed in the ultrasonic measurements; and we give a qualitative explanation of the composition dependence of the elastic moduli in terms of changes in the first order stretching force constants, co-ordination numbers, and crosslink densities of network bonds, with all the cobalt cations being regarded as part of the network (this interpretation then paved the way for a more quantitative theoretical model of the elasticity of glasses which is to be presented in a subsequent paper).

2. Crystalline phases of the C o - P - O system In our attempt to interpret the structure of C o - P - O glasses we shall find it necessary also to consider the crystalline phases in the C o - P - O system. This is not to say that we regard the glasses as consisting of micro crystalline phases. However we still need knowledge of the crystalline forms to make certain decisions on likely values of a number of variables (cation cross-linking number, bond length and force constants, etc.) which are the likely determinants of the levels of vitreous elastic moduli. The C o - P - O system exhibits compound formation at ortho-, pyro, and metaphosphate ratios [3]; these crystals are the deep purple ortho-phosphate Co3(PO4)2(3CoO : 1 P205), the blue-purple pyrophosphate Co2P207 (2 CoO : 1 P205) and the lavender metaphosphate Co(PO3) 2 (1 C o O : ] P205). Their melting temperatures are 1160°C, 1240°C and 1105°C respectively. In addition, a number of intermediate compounds consisting of two phase mixtures of the above structures are known (fig. 1). In a crystal of Co3(PO4) 2 [4] one cation shows octahedral co-ordination with an average C o - O bond length of 2.125 ,~; while the other cation is in five-fold co-ordination (as a result of a broken sixth interaction) with an average C o - o bond length of 2.063 .~. The average P - O bond length in this crystal structure is 1.538 .~. This orthophosphate crystal, however, is of no further interest to use since it has no vitreous analogue (the highest cobalt oxide content in our glass range being - 60 mol.%). The structure of the Co2P207 crystal is a nearly eclipsed configuration [5], in which one cation shows octahedral co-ordination with an average C o - O bond length of 2.116 ,~, while the other cobalt cation is five-fold coordinated with an average bond length of 2.049 A. All the terminal oxygen atoms save one are bonded to two Co 2+ and a P ion. The remaining one, bonded to only one Co 2 + and one P ion, shows both the shortest P - O and C o - O bonds in the structure. Solidus temperature, melting points, and X-ray data for the Co(PO3)2

A.A. Higazy, B. Bridge / Elastic constants and structure of '

I

I

1803°

1300

CoO

1100 D

.'~ "~, ,/ "7 I,, Liq-

~

I105"

'

1240' /1~., 1160" // ~I ", B-2'1 ,

~

•

3:1-

~1oc~

83

Liquid

~ \

12.00

I

CO304-P205

Liq

~

\'j

c~ Liq

hi

coO

~- 900

C°3(P04) 2 800 ¸

*

_ C,c2P20

o-4-

Co( P031

;o t ,

70C

MOLE o\* CeO Fig. 1. C r y s t a l l i n e p h a s e s a n d p o l y m o r p h i s m o f t h e C o - P - O

s y s t e m ( a f t e r ref. [3]).

compound have been given [3]. However, C02+-O and P - O bond lengths are not available for this crystal structure. The structure of glassy cobalt metaphosphate has been investigated spectrometrically by Tananaev [6]. The reflectance spectrum of Co(PO3) 2 glass was recorded with an SF-14 spectrophotometer. Tananaev concluded that the form of spectrum was characteristic of tetrahedral cobalt co-ordination (fig. 2). In crystalline Co(PO3) 2 (which is isomorphous with M(PO3) 2 where M = Cd, Fe, Hg, Mg, Mn, Ni, and Zn), the PO 3 groups form tetrametaphosphate rings, and the Co 2÷ ions are octahedrally co-ordinated [7] (fig. 3). However, in glassy Co(PO3) 2 it was argued that [6] tetrahedral co-ordination was attributable to a chain-like structure for the metaphosphate network, with divalent cobalt atoms bonded to the two neighbouring PO 3 groups in the same chain (fig. 2). In a subsequent paper we

\

2+/ /co N 0 ~

\ ~+/ /co N 0

/ P -\

0

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k

2,+

0

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__P--

/ /

0

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Fig. 2. S c h e m a t i c d i a g r a m for t h e s t r u c t u r e o f v i t r e o u s

Co(PO3)

2

( a f t e r ref. [6]).

84

A.A. Higazy, B. Bridge / Elastic constants and structure of Co~04-P_,Qs

O

P

°o°"

""

P O Fig. 3. Schematic diagram for the structure of crystalline Co(PO3) 2 (after ref. [7]).

use the available knowledge of these crystal structures as discussed above, to develop a quantitative theory of the elastic moduli of glasses belonging to the Co304-P205 system. However the qualitative interpretation presented here will also be found useful since it brings out the essential physics of the problem which is obscured by the rather complex formulae found necessary in the quantitative theory.

3. Summary of previous work on ultrasonically determined vitreous moduli, with critical comments Previous investigations [8] on the elastic moduli of borosilicate glasses (Crown designated as BSC 517/645), have shown that a linear relation was found to exist between elastic moduli and refractive indices, or density, in these glasses. Such empirical relationships can be a substantial practical aid in the production of desired refractive index values, for, arguably, it is easier to measure slight elastic moduli changes over a series of glasses, than to measure the correspondingly small changes in refractive index. Hamilton [9] recently reported that glasses in which nucleation and separation of submicroscopic phases take place (e.g. glasses containing SiO2, B203 and ZnO as major constituents), showed an abnormal change in Young's modulus with refractive index as a result of heat treatment. He observed a decrease in Young's modulus, which was not accompanied by a comparable decrease in refractive index. The structures of binary phosphate glasses have been studied by measurements of the compositional dependence of the refractive index, molar volume and optical dispersion, by Kordes [10]. He divided two component phosphate glasses into normal and anomalous glasses depending upon their properties. In the case of normal glasses, i.e. phosphate glasses containing oxides of Na, Ca,

A.A. Higazy, B. Bridge / Elastic constants and structure of Co304-P,05 O

~o

o~11 o~

j~-,,~ V

o /

it'-o 0

~

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o

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,,.*0/

9

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II o N

o-.+ r~a

0

°

/

,,

O

~o 0

85

,'-o ;l~.~_n 0

°

\

O

I

/

Fig. 4. Schematic two-dimensional representation of the structure of Na-P20 ~ binary phosphate glasses; (a) composed of basic glass former, (b) showing the effect of modifying Na + cation on the glass former.

Ba, Cd and Pb, a number of physical properties (density, molar volume, refractive index, etc.) change continuously as a function of composition over the entire vitreous range. In the anomalous glasses, namely the ZnO-P205, MgO-P205 and BeO2-P205 systems the properties show discontinuities at about 50 tool.% of the metal oxide. According to Tarasov [11], in normal glasses, for example NaO-P205 glasses, the Na ions enter the glass network interstitially, fig. 4. Hence, some network bonds ( P - O - P ) are broken, and replaced by ionic force pairs between the Na ion and singly bonded atoms. The breaking down of the network tends to decrease the elastic moduli, but the simultaneous filling up of the vacancies amidst the network by the interstitial metal ions (i.e. the increased packing density) will tend to increase the moduli, because of the reduced averaged interatomic spacing, which increases the interatomic forces brought into play during elastic deformation. The magnitude of these interatomic forces (called the electrostatic interaction by Tarasov [11]), between the modifying cation and the glass-forming anion must be dependent on the charge as well as the radius of the modifying cation. A more thorough examination of the effects of the electrostatic interaction was made by Lowenstein [12] in a study of silicate-based glasses. It was found that ions are likely to enter glass interstitially, if their radius is too large, or their charge is too small for them to take up network forming positions. Lowenstein proposed a rough proportionality between the Young's modulus of glass, and the logarithm of the field strength of interstitial cations defined as q :/r where q and r are the ionic charge and radius, respectively. The "anomalies" of the ZnO-P205 and MgO-P205 glasses systems have been explained by Tarasov as follows; when the content of ZnO or MgO is lower than 50 mol.%, the Zn 2+ or Mg 2+ cations fill the tetrahedral vacancies of the glass in a fashion relatively close to cubic or hexagonal close packing of oxygen anions. When the modifier content in an anomalous glass is greater than 50 mol.%, the cations of the modifier fill octahedral vacancies, i.e. they co-ordinate with the six oxygen anions (see fig. 5). In Tarasov's discussion no

86

A.A. Higazy, B. Bridge / Elastic constants and structure of Co~04-P20 ~ o

o

o

II

I

II

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II 0

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a

I 0

A 0 0

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I

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I 0 V

I

0

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I

0

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I

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A

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0

0

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p - - o - - P - - O - - X . - - - o - -

I

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I

I

I

x--o--P--O--X--o

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b

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Fig. 5. Schematic two-dimensional representation of the effect of the network modifying XO oxide on the P205 network, where X = Zn 2+, Co 2÷, or Mg 2+ cation; (a) represents the P205 network structure (with PO 4 tetrahedral being the structural unit), (b) represents the structure at 50 mol.% XO oxide (X here is tetrahedrally co-ordinated), and (c) represents the structure of phosphate glasses when XO mol.% > 50 (X here is octahedrally co-ordinated).

clear statement is made as to whether the Zn or Mg atoms reside in network forming, or interstitial positions, or both. However, according to Lowenstein [12] a number of types of ion Be, Mg, Ti, Zn, Fe, and In, occupy both types of position, in silicate bases glasses, and it will be observed that this list includes the cations stated by Kordes to produce anamolous phosphate glasses. Lowenstein also associates the two different types of cation siting with co-ordination changes, thus an atom is assumed generally to possess a higher co-ordination number when sited interstitially, Be being a notable exception in possessing tetrahedral co-ordination in both network forming and network modifying roles. Taking the specific case of zinc, Lowenstein states that in silicates tetrahedral ZnO 4 groups are network forming whilst ZnO 6 groups reside interstitially. If these assumptions were applied to phosphate glasses and Tarasov's description were also accepted, we would conclude that for ZnO contents less than 50 mol.% the Zn atoms reside entirely in network forming positions, whilst for oxide contents exceeding 50 mol.%, Zn atoms also start to enter interstitial positions. A similar conclusion would be reached for Mg. In view of the above reasoning it seems tempting to suggest that the discontinuities in physical properties in phosphate glasses are to be associated with cations which are able to occupy both interstitial and network forming positions. However, the author's own observations of C o - P - O glasses, as well as those made on the M o - P - O vitreous system by a colleague [13], suggests that the situation is not that simple. Both these glass systems exhibit pronounced discontinuities in variation of many properties with oxide content yet we shall argue that both Co and Mo reside in P205 glasses entirely as network formers through the whole vitreous range.

A.A. Higazy, B. Bridge / Elastic constants and structure of Co~04-P205

87

This is the appropriate stage to mention that in any event the categorisation of cations (which do not form oxide glasses by themselves) in glasses, into occupiers of interstitial sites or network sites, is essentially an arbitrary one, based on bond type, for unlike the case of regular crystal lattices, the term "interstitial" cannot have a precise "geometrical" meaning. Cations forming strongly covalent and therefore directional bonds with oxygen we describe as part of the network, whilst cations which are linked to oxygen atoms in glass via predominantly ionic (and therefore non-directional bonds) we describe as residing interstitially. Now many formulae have been proposed to express the fractional ionic character (FIC) of chemical bonds. Two representative examples are Pauling's equation [14] FIC = 1 - e - ',(X.~ -

(1)

Xb) 2

and that of Hannay and Smyth [15] given by FIG = 0.16(X b - Xa) + 0.035(X b - Xa) 2

(2)

where X~ and X b are the electronegativities of the anion and cation respectively (i.e. X~ < Xb). For any bond Pauling's formula tends to yield rather high values, and the second formula tends to yield rather low values but all formulae proposed agree in that FIC always increases as I Xa--Xbl increases, and so any one formula is useful for the purposes of semi-quantitative comparison. Thus, using the following values of electronegativities [16] 0.90, 1.88, 3.5, 2.16, 1.65, 1.50, 1.80, 2.10, for Na, Co, O, Mo, Zn, Be, Si and P respectively and eqs. (1) and (2), we find the following set of FIC's (table 1) for each of the cations referred to in the preceding discussion, when bonded to oxygen. From this data we reach some interesting conclusions in relation to our work: (i) We find that the C o - O bonds are slightly less ionic, i.e. are slightly more covalent in character than the Si-O bond, which is undisputedly always a network forming bond in glass. Again the C o - O bond is also more covalent than the B e - O bond and Z n - O bonds which are said to be able to occupy network forming sites as well as interstitial positions in glasses. Precisely the same arguments also apply to the M o - O bond. It is clear from this discussion that both Co and Mo appear to belong to the category of ions which can occupy network forming positions.

Table 1

Na-O Co-O Mo-O Zn-O Be-O Si-O P-O

Pauling

Hannay and Smyth

0.82 0.48 0.36 0.57 0.63 0.51 0.39

0.65 0.35 0.28 0.42 0.46 0.37 0.29

88

A.A. Higazy, B. Bridge / Elastic constants and structure of Co304-P_,05

(ii) Eqs. (1) and (2) have only been thoroughly tested (i.e. by comparison with experimental dipole moments) for simple bonds in simple diatomic compounds, and they take no account of changes in co-ordination number, such as may occur in glasses. However, if we assume that FIC's are not changed grossly by co-ordination number changes * the distinction between interstitial sitings and network former position for cations like Be, Zn, Mo, Co seems rather artificial. Only in the case of ions with obviously high FIC's like Na does a clear distinction seem to emerge. For these reasons in the interpretation of our own work on C o - P - O glasses we assume that the Co occupies network sites throughout the whole entire vitreous range of the C o - P - O system. Our assumption is supported by our infra red spectra [2] which displayed no evidence of ionic groups being present over any of the vitreous range. We also adopt a similar approach in our discussion of detailed data on M o - P - O glasses reported previously [13]. In any event our interpretation of elastic data cannot be affected by the use or non-use of terms like "interstitial" or "network former", since we base our theory, developed subsequently, solely on precisely quantifiable physical quantities, i.e. bond lengths, stretching force constants and co-ordination numbers. Many empirical and semi-empirical models, attempting to explain the order of magnitude variation of elastic moduli of glasses with gross changes in the glass composition, have been given, for example by Soga and Anderson [17], Philips [18,19], Williams and Scott [20], Makishima and Mackenzie [21], and Bridge et al. [22]. However, these empirical formulae are strictly valid only for the glass compositions used to compile the theory and need to be used with caution in any extrapolation or interpolation exercise. With this proviso they may be suitable for estimating the rough effect on the elastic moduli, of a gross change in the composition of "normal glasses"; however they cannot be used for the prediction of the discontinuities in compositional gradients of elastic properties in anomalous glasses, nor are they suitable for predicting changes in moduli with gradual changes in glass composition, whether or not anomalies are present. Concerning the latter statement, prior to the author's work and that of Patel and Bridge [23], and Patel et al. [24], only Gladkov and Tarasov [25] have attempted to use elastic data to identify structural changes resulting from gradual changes in composition. Their approach was essentially qualitative and did not involve any proposed empirical formula. The dependence of elastic moduli on glass composition of a number of phosphate glasses has been studied by Farley and Saunders [26], Field [27], Bridge and Moridi [28], Patel and Bridge [23], and Patel et al. [24]. The amount of data is very limited compared to that available for borate and silicate

* The small change in interatomic spacings (and small corresponding changes in bond strength associated with changes in Co-O and Mo-O co-ordination numbers) support this assumption.

A.A. Higazy, B. Bridge / Elastic constants and structure of CojO4-P20~

89

glasses, and to date no formulae to predict overall compositional trends of the elastic moduli of phosphate glasses, have been proposed. 4. Experimental The compositions of the specimens studied are listed in table 1. Details of the techniques for the preparation and chemical analysis of these glasses are to be presented elsewhere [1]. Specimens used for ultrasonic measurements were in the form of cylindrical rods of 1.6 cm diameter and 0.5 cm thickness with end faces optically polished to a parallelism of 1-2 s of arc, using a polishing machine (Metal Research, Multipol 2), with a special jig (MR, Mk 2) holding the specimen. The procedures used to prepare the glasses with the roughly parallel faces required to use this preparation technique have been fully described elsewhere by Bridge and Moridi [28]. The ultrasonic compressional and shear wave velocity measurements were made by the pulse echo technique, at a frequency of 15 MHz. X cut and Y cut quartz transducers coupled to the glass rods by " N o n a q stopcock grease" or "Krautkramer ZYG shear wave paste" were used to generate longitudinal and transverse waves respectively. A block diagram of the pulse echo instrumentation, which allowed rapid yet accurate measurements using combined broad and narrow bond techniques, is shown in fig. 6. In each measurement the transducers are first shock-excited using the thyratron transmitter pulse from a commercial ultrasonic flaw detector. This produces pulse echo rise times rapid enough for corresponding cycles in different echoes to be readily identified. At the same time, because the broad band amplifier employed has a low frequency cut-off at 5 MHz (which meant that pulse lengths were quite long, - 1 0 cycles), the frequency spectrum of the echoes laid mostly outside the region in which significant geometrical dispersion might be expected. A digital delay generator (Berkeley Nucleonics Type 7030) allowed the time delays between corresponding individually displayed cycles of RF in successive pulses to be measured to + 0.2 ns absolutely, whilst relative measurements could be made to + 200 ps (twice the maximum time jitter of the digital delay pulses). The second stage of the measurement is to switch to RF (resonant) excitation of the transducers and narrow-band amplification. Transit times were then remeasured using the broad band data to match up corresponding cycles of RF in the narrowband (slow rise time) echo display. Broad band and narrow band time measurements rarely differed by more than 1-2 ns. Since all glass samples had identical geometry, measurement errors caused by diffraction and geometrical dispersion effects tend to cancel when data on different glasses are compared. Having carried out all the other usual error analysing procedures, our transit time measurements are considered to be accurate to + 1 ns-1 (0.05%), for the purposes of comparing different glasses. Since thicknesses were measured to ___0.02 %, the velocities are defined to + 0.03% ( + 1 m/s). The densities were measured by Archimedes' method, using toluene as an immersion liquid, and for the comparison of different glasses only are accurate to + 0.001 g cm- 3.

90

A.A. Higazy, B. Bridge / Elastic constants and structure of

Ultrasonoscope Type B I ~

Co304-P205

Transducer

1

Specimen

IIB

2'

Sl

$2

Pulsed power oscillator

~

Arenberg tuned pre-amplifier (PA-620)

Arenberg (PG-650G) 93 ohms Attenuator Sr.No. 719

S3

]Arenberg broadband amplifier Type WA60E [ (5-60 MHz)

I

Delay generator BNC Type 7030

Y! Y2

High frequency CRO Tetronix

S 4

Trig.

Type 581 A

Fig. 6. Instrumentation for rapid, accurate ultrasound velocit measurements. (1) Switches S 1, S 2 and S 3 in position 1 for velocity measurements using fast rise time pulses. (2) Switches S 1, S z and S 3 in position 2 for velocity measurements using pulses of narrower frequency bandwidth, i.e. pulses of slow rise time. (3) Switch S4 in position 2 for visual location of delay pulse in the vicinity of the echo of interest: in position 1, for display of first quarter cycle of selected echo on fastest time base setting.

The elastic constants of the glasses were calculated at r o o m temperature from the measured densities and the velocities of longitudinal 1,1L and ~ of ultrasound waves by using the following expressions: Longitudinal m o d u l u s L = p V L, (3) Shear m o d u l u s

S = PVs 2,

(4)

Bulk m o d u l u s

K = L -(4/3)G,

(5)

Poisson's ratio

a = ( V 2 - 2V~2 ) / ( VL2 -- V~2),

(6)

Young's modulus

E = (1 + a ) 2 G .

(7)

M o d u l u s differences between different glasses are accurate to + 0.07%.

30

40

410

200 + Co203 (mole~)

I 20 6*0

Fig. 7. Dependence of molar volume (i.e. the volume containing x ;ram molecules of Co203, y gram molecules of CoO and (1 - x - y ) ,ram molecules of P205) on the composition.

0

5O

~0

2.8

3.0

Co 0 tco203{

I ~,0

mole

I 40 °JD) Fig. 8. Variation of density with composition (mol.%).

A

1.2

I 60

9

t~

t~

t~

9

3. £

A-12 C-1 C-2 C-3 C-4 C-5 C-6 C-7 C-8 C-9 C-10 C-11 C-12 C-13 C-14 C-15 C-16 C-17 C-18 C-19 C-20 C-21

Glass

300 300 300 300 300 300 300 300 300 300 300 400 400 400 400 400 400 400 400 400 400 400

temp. (C ° )

temp. (C ° )

580 850 850 850 850 850 950 950 950 950 950 950 980 980 980 980 980 980 1100 1150 1150 1150

Annealing

Melting

2.520 2.522 2.540 2.556 2.572 2.585 2.600 2.619 2.650 2.685 2.701 2.741 2.773 2.788 2.804 2.824 2.833 2.844 2.855 2.857 2.859 2.862

( g / c m 3)

Density

4.05 5.02 5.26 5.58 6.02 6.16 6.70 6.86 7.14 7.63 8.91 10.62 11.89 12.09 15.61 16.40 17.85 21.08 24.39 28.55 32.56

mol.%

Co203)

(CoO +

56.3 55.9 55.3 54.9 54.5 54.1 53.8 53.2 52.6 51.9 51.5 50.4 49.4 48.8 48.5 47.2 46.8 46.3 45.3 44.4 43.4 42.4

ume (cm3)

Molar vol-

4055 4088 4300 4315 4450 4470 4590 4636 4700 4780 4850 4913 4913 4905 4900 4870 4865 4861 4852 4850 4838 4831

Long 2190 2198 2350 2452 2505 2585 2620 2680 2750 2790 2825 2853 2850 2846 2844 2830 2825 2821 2815 2815 2795 2785

Shear

Ultrasonic wave velocity m / s

414 421 470 476 509 516 548 563 585 613 635 662 669 671 673 670 671 672 672 672 669 668

Long 121 121 140 154 161 173 179 188 200 209 216 223 225 226 227 226 226 225 226 226 223 222

Shear

Elastic moduli (K bar)

253 260 283 271 294 286 310 312 318 335 348 364 369 370 371 368 369 372 371 370 371 372

Bulk 313 314 361 387 409 431 449 470 497 519 536 556 561 563 565 563 563 561 564 564 558 556

Young's 0.290 0.289 0.287 0.262 0.268 0.249 0.258 0.249 0.240 0.242 0.243 0.246 0.246 0.246 0.246 0.245 0.246 0.249 0.246 0.246 0.250 0.251

Poisson's ratio

307 305 328 342 350 361 367 375 386 394 399 405 405 405 405 403 403 401 400 399 395 392

(K)

Debye temp.

Table 2 Melting and annealing temperatures, density, composition, molar volume, longitudinal and shear ultrasound velocities (broad-band technique) and the elastic moduli of C o - P - O glasses at room temperature

e~

3"

C-22 C-23 C-24 C-25 C-26 C-27 C-28 C-29 C-30 C-31 C-32 C-33 C-34 C-35 C-36 C-37 C-38 C-39 C-40 C-41 C-42 C-43 C-44 C-45

1150 1150 1200 1200 1200 1200 1200 1200 1200 1200 1250 1250 1250 1250 1250 1250 1250 1250 1250 1250 1250 1250 1250 1250

400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400

2.865 2.870 2.884 2.902 2.914 2.921 2.930 2.946 2.950 2.966 2.975 3.990 3.013 3.052 3.075 3.094 3.133 3.154 3.172 3.189 3.201 3.230 3.243 3.256

37.63 38.70 40.17 42.29 42.67 43.68 44.60 44.90 45.15 46.72 47.20 47.48 49.46 50.78 51.74 52.72 54.64 55.36 56.25 57.14 57.78 58.8 59.05 59.21

41.1 40.8 40.2 39.5 39.2 38.8 38.4 38.7 38.0 37.4 37.2 36.9 36.2 35.4 35.0 34.5 33.7 33.3 32.9 32.5 32.3 31.8 31.6 31.4

4839 4841 4844 4844 4845 4847 4852 4853 4855 4860 4865 4879 4894 4920 4947 4970 5015 5020 5042 5080 5121 51.60 5200 5220

2777 2775 2776 2775 2776 2776 2775 2773 2772 2765 2761 2760 2763 2768 2770 2775 2784 2787 2794 2805 2822 2835 2850 2874

671 673 677 681 684 686 690 690 694 695 701 709 722 738 753 764 788 795 8O6 823 840 860 877 887

221 221 222 224 225 225 226 227 227 227 227 228 230 234 236 238 243 245 248 251 255 260 263 269

376 378 381 383 385 386 389 392 393 398 402 406 415 427 438 447 464 468 476 488 5O0 514 526 529

554 555 558 561 564 565 567 570 570 572 573 576 582 593 6OO 607 620 626 633 643 654 667 677 690

0.255 0.255 0.256 0.256 0.256 0.256 0.257 0.258 0.258 0.261 0.262 0.263 0.266 0.268 0.271 0.274 0.277 0.277 0.278 0.281 0.282 0.284 0.285 0.283

388 387 388 387 388 387 387 388 387 386 386 386 387 388 389 390 392 393 394 396 398 4O0 403 4O7

9

i

e~

e~

4.

::z:

94

A.A. Higazy, B. Bridge / Elastic constants and structure of Co304-P_,0~

5. Molar volume and density

Table 2 contains the molar volumes and the densities of all cobalt-phosphate glasses examined in this work. The molar volumes were calculated from the following expression: V = M/0

(8)

where p is the density of the glasses (g cm 3) and M its molecular weight (g atom) calculated from the relation M = x M c o o + yMco2o~ + (1 - x - y ) Mv2o,,

(9)

where x, y and ( 1 - x - y ) are the mole fractions of the constituents, and Mcoo, Mco2% and Mp2o, are the molecular weights of the constituents. Fig. 7 shows the plot of molar volume versus mol.% of cobalt oxides, The variation of the molar volume with tool.% of cobalt oxides is seen to display a decrease up to about 40 mol.% cobalt oxides, whence a point of inflexion occurred. The plot of density versus mol.% (see fig. 8) showed an increase with increase in mol.%, with points of inflexion at about 15 and 40 tool.%. The inflexion at 15 mol.% coincides with the boundary between two composition regions defined by chemical analysis [1], which showed that at compositions < 15 mol.% the ratio of Co 3+ to Co 2+ content varies from very high to very low, whereas at compositions > 15 mol.% probably all the cobalt ion is in the reduced Co 2+ form. However the definite change at 40 mol.% is probably attributable to a change in co-ordination numbers of Co z+ ion (from 4 to 6). Using Korde's classification of glasses (see section 3) our glasses may be termed "anomalous", for smooth curves or linear variation should have resulted if only " n o r m a l " glasses are involved [10]. However our interpretation of the discontinuities in vitreous properties with composition is quite different from that of Kordes, i.e. we do not attempt to explain them in terms of different proportions of Co cations entering the glass interstitially rather than via the network. On the contrary our model assumes that these cations enter the network throughout the entire vitreous range of the Co304-P205 systems for the reason already discussed earlier in section 3.

6. Elastic moduli and Poisson's ratios

Also collected in table 2 are the longitudinal and shear velocities, and the elastic moduli, Poisson's ratios and Debye temperatures for the cobalt-phosphate glasses examined at room temperature. The addition of Co304 to the vitreous P205 structure increases both the longitudinal and the shear wave velocities up to about 15 mol.% cobalt oxides (figs. 9 and 10). Then beyond 15 mol.% there is an almost constant variation in both the sound velocities with further addition of Co304 oxide, until about 40 tool.% cobalt oxide content. Beyond 40 tool.% there was a clear increase in the

A.et, Higazy, B. Bridge / Elastic" constants and structure of Co304-P205

--q I

I

I

r

i

1

I

95

[ Q

o +

I

I

I

I

J

I

I~

0

I r

(Is l u g )

X&IDO'liHA H A V t A " ~ I V H H S

0

I

I

I

%

I

I

I

!

+

~

D

>© F

~._~ I

I

I

I

I

I

•

J

500

CoO +Co203

I 40

I

I

20

I

( m o l e °/o )

60

I

I

Fig. 11. Compositional dependence of longitudinal and Young's moduli in C o - P - O glasses.

300'

400

I11

0

~ 600

700

800 ,.~

9OO

J 40 CoO ÷ Co203(mole

2JO

i

o/o )

K

60

f

Fig. 12. Variation of the bulk and shear moduli with composition for the C o - P - O glass system.

200

30(

5O(

i

I

r~

A.A. Higazy, B. Bridge / Elastic constants and structure of Co30~-P20s

97

wave velocities with increase in composition. All the elastic moduli, viz longitudinal, shear, bulk and Young's modulus show the same trend as the acoustic wave velocities (figs. 11 and 12), i.e. they exhibit the same "3-composition-regions" behaviour that we identified in the density, infra red absorption [2] and chemical analysis data [1] for our Co304-P205 glass system. In the following discussion we give a qualitative interpretation of how the elastic constants vary with the glass structure. Our method is to interpret the Bulk modulus data and the Poisson's ratio data. Then by definition the explanation of the other constants G, L and E follows automatically. 6.1. Bulk modulus

The interpretation is based on a simple idea put forward by Bridge et al. [23] (which is summarized here and described in more detail in a future paper). They supposed that the Bulk modulus of a structure consisting of a 3-dimensional network of A - O bonds (A = cation, O = oxygen atom) can be expressed in the form: K = Constant. F b / ( t )n

(10)

where F b is the A - O bond bending force constant which to a first approximation may be taken as proportional to the bond stretching force constant F; and is the diameter of the atomic rings; i.e. the smallest closed circuit of A - O bonds; the rings being assumed to take the form of planar circles, for simplicity, so that t = no. of A - O bonds in ring X length of A - O bond/~r. The constant is determined empirically and so is the power n, which is typically high - say 4. The model was originally proposed to account for the Bulk modulus of the pure vitreous oxides whose ring sizes were assumed to be similar to the ring sizes occurring in the analogous crystal structures and which were known from X-ray crystallography. The model is readily adapted in principle to mixed oxide glasses; one simply performs an averaging procedure for F and ~ over all the different types of network bond. However quantitatively it is difficult to see how the model could be successfully applied to predict moduli, since the ring sizes in mixed oxides are not generally known. However the model can be very useful qualitatively if one assumes that with gradual changes in glass composition, as the cross-linking density tends to increase the atomic ring sizes tend to decrease, it is relatively easy to decide qualitatively how a crosslink density changes with glass composition. So, with this reasoning, we attempt a qualitative interpretation of moduli changes in our glass system on the assumption that the moduli tend to increase with both crosslink density and average first order stretching force constants. It is generally considered that pure vitreous P205 is built up of an infinite 3D network of PO 4 tetrahedra with each tetrahedron being joined at three corners to other tetrahedra and the remaining unshared oxygen atoms being linked to the phosphorus atoms by a double bond. If one assumed that the only effect of adding cobalt cations was to rupture P - O bonds and produce

I 40 (mole

I 20

Co 0 + C o 2 0 3

7o)

D/

D

I 60

I

Fig. 13. Schematic diagram representing the variation of the elastic moduli with composition in the vitreous system Co304-P205, for various assumed co-ordinations of the Co atom as discussed in the text.

t~

D 0 0

3

I

2.4

~

I

2.7

I

2.6

DENSITY

2.8

I

~ I

I

3.0

(9.cm -3)

2.9

~ I

3.1

3.2

I

Coz 08

CoO

Fig. 14. Variation of mole percentage of C0203 (i.e. Co 3+ ions) and CoO (i.e. Co 2+ ions) oxides content as obtained from chemical analysis data [1], with density (g cm-3).

I

0.4 I-

~to.8

8,

N

r~ ~L2

o11.6 0

0

~2.0

Z

~2.6

3.2

3.6[

40 0

30

I

A.A. Higazy, B. Bridge / Elastic constants and structure of Co304-P_,0~

99

extra P - O - C o crosslinks and that the co-ordination number and valency of the cobalt did not change, then a smooth increase in bulk moduli with oxide content would be expected. Thus, suppose that the cobalt stayed entirely in the form of Co 3+ with octahedral co-ordination (as in Co304) and a crosslink density of 4, then a relatively steep but smooth increase of moduli with oxide content could be expected (curve A D fig. 13). Alternatively if the cobalt resided in the glass entirely in the tetrahedral Co 2+ form with its crosslink density of 2 (figs 2 and 5), the increase of moduli with oxide content would be more gentle but still smooth (curve A D fig. 13). However the composition dependence of the Bulk modulus displayed the same "3-regions" behaviour that we found in the chemical analysis and infra red measurements [1,2], which we interpret as follows, with reference to fig. 14. In the region 0-15 mol.% cobalt oxides the Bulk modulus increases sharply as P - O bonds are replaced by P - O - C o crosslinking involving both Co 3 + and Co 2 + ions. The increase is sharpest following the curve A D, at the lowest oxide contents because the ratio of octahedral Co 3+ (with its greater crosslink density) to the tetrahedral Co 2+ is at its highest. Then for oxide contents > 15 mol.% (i.e. beyond the point B on the curve A D) the rate of increase in bulk modulus with oxide content slows down because all the added cobalt goes in the form of tetrahedral Co 2+ with its lower crosslink density. However, if we inspect our experimental curves we find that in the second composition region the bulk modulus actually starts to decrease with increasing Co content. This can be understood in terms of the fact that as the Co content is increased, not only does the Co 2+ content increase but the Co 3* content progressively disappears (the latter is a maximum at the boundary of the 1st and 2nd composition regions) so that the average crosslink density might actually decrease. So the curve of increase of bulk modulus with oxide content tends more and more towards curve A D which it meets at the point C, i.e. at about 40 mol.% cobalt oxide content. It has been claimed [6] that at about 50 mol.% cobalt oxides (cobalt metaphosphate glasses) the P=O double bonds are completely transformed into the bridging bonds. However in our present investigations it was deduced from infra-red measurements that P=O double bonds disappeared completely at about 40 mol.%, i.e. the boundary between the "2nd and 3rd" composition region. This supports the above model: that the sole effect of the entry of cobalt into the glass in the 1st and 2nd composition regions was to replace the P=O bonds by P - O - C o bridging bonds. As the cobalt oxide increases beyond 40 mol.%, i.e. as the 3rd composition region is entered, sudden and substantial increases in bulk modulus comparable with the rate of increase in the first composition region, occur. Now Tananaev et al. [6] claimed that at about 50 mol.% cobalt oxide content (metaphosphate composition) Co 2+ ions are totally tetrahedrally coordinated; whereas at oxide contents of - 66 mol.% the Co 2+ is said to go into octahedral co-ordination, by analogy with crystalline cobalt-pyrophosphate (Co 2 P207) [5]. In octahedral co-ordination the crosslink density of Co 2 ÷ is increased to 4. So

100

A.A. Higazy, B. Bridge / Elastic constants and structure of Co304-PeOs

we interpret the sharp increase in bulk modulus with oxide content, for compositions > 40 mol.% (curve C D) cobalt oxide, as due to a gradual transition of tetrahedral Co 2+ (crosslink density = 2) to octahedral Co 2 + (crosslink density = 4). Finally, in this qualitative discussion we have got to discuss the effect of the stretching force constants on the bulk modulus. The stretching force constants for the Co ions vary in the order F(Co 3+ octahedral, as occurring in C0304 oxide)> F(Co 2+ octahedral, as occurring in C02P207)> F(Co 2+ tetrahedral, as occurring in vitreous C o ( P O 3 ) 2 ).

This sequence would tend to cause the bulk modulus to increase with increasing cobalt oxide content in compositional region 1, to increase with Co content in region 3, and to exhibit a minimum or an inflexion in compositional region 2. Thus the force constant sequence will strengthen the effects of crosslink density variations discussed previously. 6. 2. Poisson's ratio

To interpret our data on the compositional dependence of Poisson's ratio we first give a general qualitative model of the variation of a with vitreous composition developed from an ideal first expressed by Bridge et al. [22]. Consider the three hypothetical chain networks of fig. 15, identical except for having crosslink densities (defined as the number of bridging bonds per cation less 2) of 0, 1 and 2 respectively. Now Poisson's ratio is formally defined for any structure as the ratio of lateral to longitudinal strain produced when tensile forces are applied. For tensile stresses applied parallel to the chains the longitudinal strain produced will be the same for all three networks (i.e. it is unaffected by the crosslinks), neglecting inconsequential differences in interchain Van der Waal's type forces. However, the lateral strain, i.e. strain perpendicular to the chain, is clearly greatest for the pure chain network as only the weak interchain Van der Waal's forces are available to resist the forces urging contraction. The lateral strain is greatly decreased for the second network with a unit crosslink density, as these crosslinks will generate strong covalent forces to resist lateral contraction, and for the third network with double the crosslink density of the second, the lateral strain will be only one half of the value for the second network. Thus the ratio of lateral to longitudinal strain, i.e. a, decreases with increasing crosslink density, for stresses applied parallel to the chains. Now looking along any direction in an (isotropic) vitreous network one can still identify chains and crosslinks, although there will now be a distribution in bond angles along both chains and crosslinks, rather than the fixed 90 ° and 180 ° angles assumed in fig. 15. Such differences do not in essence change the preceding arguments and so we can understand why network forming groups, having a connectivity of 2 (zero crosslink density) have Poisson's ratios - 0.4 (for example chain structures like

A.A. Higazy, B. Bridge / Elastic constants and structure of Co304-P,05 v

v

1O1

v

Tensile s%ress

"

-0

e

0

~

0

:

O

e u)

-0 (a) Crosslink

~

0

=

0

=

0

densitj = 0

e

~q c+ F-

g b-J

b

o co

(b') Crosslink

density = I

5. © m

--c

(c) Crosslink O-

0

density = 2

anions

e - cations

Fig. 15. Illustrating the variation of Poisson's ratio (lateral strain/longitudinal strain) with crosslink density for tensile stresses applied parallel to oriented chains. The forces resisting lateral contraction increase with crosslink density.

rubber and polystyrene); networks having a connectivity of 3 (crosslink density of 1) have Poisson's ratio - 0.3 (for example As203, B203 and P205 glasses); whilst networks with a connectivity of 4 (crosslink density of 2) have Poisson's ratios of - 0.15 (for example diamond, SiO 2 and G e O 2 glasses). To isolate another possible variable affecting the Poisson's ratio of glass we next consider the relationship o = (E/2G)

- 1,

(11)

102

A.A. Higazy, B. Bridge / Elastic constan ° and structure of Co~04-P2Qs

applied to the 3 chain networks of fig. 15. There we note that as the crosslink density is increased (figs. 15a to fig. 15c) the value of E for tensile stresses applied in the chain direction will remain constant whilst the value of G for shearing forces applied parallel to the chains will increase with the crosslink density. Thus we reach the same conclusion as previously, i.e. o decreases (as the ratio E/G decreases) with increasing crosslink density and as before the argument can be extended to isotropic crosslinked structures. However the use of eq. (11) identifies another possible way in which o might change with crosslink structure; for we note that for stresses parallel to the chain structures of fig. 15 and constant crosslink density, E will increase with bond stretching force constants, whilst G will increase with the bond bending force constant. Thus as the ratio of bond bending force constant to stretching force constant increases E/G decreases and so Poisson's ratio decreases. Such a model explains why generally covalent lattices with their directional bonds have low Poisson's ratios compared with, for example, metallic lattices whose bonds are only weakly directional. Now in binary glasses where both the degree of crosslinking and the relative proportions of different types of bonds may be changed with composition, it is clear that both types of mechanism will be present, i.e. to summarise, we propose to interpret our glass elastic data on the model: (i) o decreases with crosslink density (for constant ratio of bond bending to stretching force constant), (ii) o decreases with increasing ratio of bond bending to stretching force constant Fb/F (at constant crosslink density). The expected variations in crosslink density are easily verifiable by independent means already described (i.e. from assumed models of coordination numbers and numbers of each bond type as determined by chemical analysis and knowledge of analogous crystal structures). However we have no such independent confirmation of ratios of Fb/F. For this reason we attempt to interpret our data as far as possible by invoking mechanism (i), keeping mechanism (ii) as a last resort. If then we apply mechanism (i), we find that the variation of Poisson's ratio with composition ought to be exactly the reverse of the bulk modulus variations described earlier, i.e. o would fall steeply in region 1 (fig. 16) where the rate of increase of crosslink density with Co content is high, as most of the cobalt is in the Co 3+ (octahedral) form with its high crosslink density. Then in the second region, the rate of change of o would level off (or even reverse) as the rate of increase of crosslink density with Co content decreases (or even reverses), due to most of the cobalt residing in the form of Co 2+ (tetrahedral) with its lower crosslink density. Finally, in region 3, o ought to decrease again with increasing Co content, since the latter enters the glass increasingly in the form of Co 2+ (octahedral) with its higher crosslink density. Experimentally, although the Poisson's ratio behaves roughly as just proposed in regions 1 and 2, in region 3 exactly the reverse occurs, i.e. o increases

A.A. Higazy, B. Bridge / Elastic constants and structure of C0304-P205

103

0.30

0,29 0 ~" 0 . 2 8

0.27 ~D

"z

0 0.26 rD ~ 0.25

L 10

I 20

t 30

Co0+Co203

I 40 { mole

I 50 °/o

6~0

)

Fig. 16. Variation of Poisson's ratio with composition for the C o - P - O glass system. In the range 0 - 4 0 mol.% of CoO the Poisson's ratio behaviour is explained in terms of crosslink density. However in the range of 40-60 mol.% of CoO, the Poisson's ratio of the glass is governed mainly by the weak directionality of the Co 2+ (octahedral) ion.

remarkably rapidly with increasing cobalt content. The explanation of this is clearly beyond qualitative interpretation in terms of crosslink densities as just presented. It seems that instead we have to invoke mechanism (ii), i.e. the experimental data might indicate that the Co 2÷ ion in octahedral co-ordination is unusually weakly directional-producing a low ratio of FJF and correspondingly a high Poisson's ratio. Unfortunately as stated at the beginning of this discussion, we have no independent proof of this notion.

7. Annealing effects in cobalt-phosphate glasses The effect of annealing temperature on the elasticity and the electrical properties of some oxide glasses has been reported previously [13,24,28,29]. All the glasses studied showed increases in elastic moduli with increasing annealing temperature, but the conductivity showed decreases under the same conditions. For studying the effect of annealing temperature on the elasticity of cobalt-phosphate glasses, four different glasses of different compositions were subjected to different annealing temperatures (see table 3). It was observed

CoO + Co203 mol.~b

7.14

42.67

46.72

54.64

Glass no.

C-9

C-25

C-31

C-38

423 473 523 573 623 473 573 623 673 723 773 473 523 573 623 673 723 473 573 620 670 725

Annealing temp. K

Table 3 Data for annealing effect on C o - P - O glasses

2.705 2.725 2.715 2.735 2.769 2.925 2.949 2.955 2.966 2.984 2.992 2.978 2.995 3.015 3.032 3.034 3.052 3.142 3.175 3.181 3.210 3.22

Density g cm -3

51.5 51.1 51.3 50.9 50.3 39.1 38.7 38.6 38.5 38.28 28.18 37.6 37.4 37.2 37.0 36.9 36.7 33.5 33.1 33.0 32.7 32.6

Molar volume cm 3 652 658 657 670 681 687 696 699 703 709 713 706 712 718 724 730 737 801 814 818 828 844

211 213 213 217 220 225 228 230 231 233 235 231 233 235 237 239 241 249 253 255 261 264

Shear

Long

2795 2797 2801 2815 2818 2776 2783 2788 2792 2797 2800 2786 2791 2794 2797 2808 2812 2816 2824 2832 2850 2862

Shear

Long 4910 4915 4919 4948 4960 4847 4858 4863 4870 4875 4882 4869 4876 4880 4885 4965 4915 5050 5065 5072 5080 5120

Elastic moduli (kbar)

Ultrasonic wave wave velocity ( m / s ) Bulk 371 374 373 381 388 387 392 392 395 398 400 398 401 405 408 411 416 469 477 478 480 492

533 537 537 548 555 565 573 577 580 584 590 581 585 591 596 600 606 635 645 650 663 672

Young's

i~

'~

~.

~

~"

A.A. Higazy, B. Bridge / Elastic constants and structure of Co:04-PeO: 1

!

105

I

3.3

3.2

~

e

%

C

o

O

3.1 A

3.0

~

0 42.7 mole°,/oCoO

2.9

2,8 mole%CoO

2.7

2.6 I

300 ANNEALING

I

I

500 700 T E M P E R A TURE

(K}

Fig. 17. The effect of annealing temperature on the density.

that the density, the ultrasonic wave velocities and the elastic moduli increased with annealing temperature (see figs. 17 to 19). In this study of sodium silicate glasses, Gladkov [22] considered that increases in the elastic moduli of sodium silicate glasses after annealing were due to increases in the number of crosslinks. He argued that in glass melts which have been cooled rapidly, the framework is not crosslinked 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 he claimed that annealing causes broken bonds to take part in crosslinking. However, in our view, annealing would be expected to increase the elastic moduli on density considerations alone, i.e. it is not necessary to invoke changes in crosslinking. It is well known that the annealing process leads to

106

A.A. Higazy, B. Bridge / Elastic constants and structure of I

!

Co304-P205

I

J

5.1

~ . ~ - - ' ~ " ' - " ~ q 4 . 6 mole % CoO 5.0

4.9

CoO

mol % CoC 4.8

54.6 mole~, C o ~ ~

2.85

~

2,80

CoO. 42.7 mole~', CoO

2.75

I 300

ANNEALING

I 500

i 700

TEMPERATURE

{K)

Fig. 18. The effect of annealing temperature on the ultrasound velocities. density increases, i.e. the average interatomic spacing decreases, and, assuming a standard form of interatomic central force potential, this decrease alone would be sufficient to increase the elastic moduli even if no changes in number of type of network bonds per mole occurred. The mechanism by which annealing always increases the density can be understood as follows. In the casting process residual stresses are frozen into the glass. Tensile stresses caused by those interatomic spacings which are greater than the normal crystalline values will, on macroscopic balance, cancel out compressive stresses due to interatomic spacings smaller than the crystalline value. From the form

A.A. Higazy, B. Bridge / Elastic constants and structure of Co~04-P_,Q~

107

A

mole°/oCoO 800

L.

750

_~ 0

700

0 Z 0

650

e~

260

°le°z°C°O °/oc od

~ ~

ole % CoO

6

mole% CoO-

240

~ ~ 4 6 , 7 mole°/oCoO"

O 220 ,

le% CoO

I

I

I

300

500

700

ANNEALING

TEMPERATURE

( K )

Fig. 19. The effectof annealingtemperatureon the longitudinaland shear modulus. of interatomic force potentials it is obvious that for a given level of tensile/compressive stress, average interatomic 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 atom. For the same reason the release of stress on annealing will cause a reduction in the average atomic spacing, and a corresponding increase in density. Again, from the form of interatomic force potentials increased elastic moduli go hand in hand with the reduced spacings.

108

A.A. Higazy, B. Bridge / Elastic constants and structure of Co304-P205

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]

A.A. Higazy and B. Bridge, Phys. Chem. Glasses 26 (1985) 82. A.A. Higazy and B. Bridge, J. Mat. Sci. (1985) in press. J.F. Sarver, Trans. Brit. Ceram. Soc. 65 (1966) 191. C. Calvo, J. Phys. Chem. Solids 24 (1963) 1411. N. Krishnamachari and C. Calvo, Acta. Cryst. B28 (1972) 2883. L.V. Tananaev and B.F. Dzhurinskii, Daki. Chem. 187 (4-6) (1969) 615. D.E. Corbridge, The Structural Chemistry of Phosphorus (Elsevier, Amsterdam, 1974) p. 156 and refs. 227, 228, 2039. S. Spinner and A. Napolitano, J. Amer. Ceram. Soc. 39 (1965) 11; 390. E.H. Hamilton, J. Amer. Ceram. Soc. 47 (1964) 4; 167. E. Kordes, W. Vogel and R. Feterowsky, Z. Elektrochem. 57 (1953) 5; 282. V.V. Tarasov, New Problems in the Physics of Glass (Israel Progr. Sci. Transl., Jerusalem, 1963) Ch. 5. K.L. Lowenstein, Phys. Chem. Glasses 2 (1961) 69. N.D. Patel, PhD Thesis, Brunel University (1982). L. Pauling, in: The Nature of the Chemical Bond (Comell University Press, 1960) p. 98. R. McWeeny, Coulson's Valence, Third Edition (Oxford University Press, 1979) p. 164. F. Cotton and G. Wilkinson, Advanced Inorganic Chemistry (Wiley-lnter-Science, New York-London-Sydney-Toronto, 1972) p. 115. N. Soga and O.L. Anderson, 7th Int. Conf. on Glass, Brussels, 1965 (Inst. Nat. du Verre, Charleroi, Belgium, 1966) paper no. 37. C.J. Phillips, ibid., paper no. 95. C.J. Phillips, Glass Technol. 5 (1964) 216. M.L. Williams and G.E. Scott, Glass Tech. 11, No. 3 (1970) 76. A. Makishima and J.D. Mackenzie, J. Non-Crystalline Solids 17 (1975) 147; 12 (1973) 35. B. Bridge, N.D. Patel and D.N. Waters, Phys. Stat. Sol. (a)77 (1983) 655. N.D. Patel and B. Bridge, Phys. Chem. Glasses 24, No. 5 (1983) 130. N.D. Patel, B. Bridge and D.N. Waters, Phys. Chem. Glasses, 24.N5 (1983) 122. A.V. Gladkov and V.V. Tarasov, Structure of Glass 2 (1960) 277. J.M. Farley and C.A. Saunders, Phys. Stat. Sol. (a)28 (1975) 199. M.B. Field, J. Appl. Phys. 40, No. 6 (1969) 2628. B. Bridge and G.R. Moridi, Institute of Acoustics, Spring Conf. and Exhibition (1977) p. 6. J.D. Mackenzie, Modem Aspects of the Vitreous State (Butterworths, London, 1960) (a) p. 189; (b) p. 101; (c) p. 191; (d) p. 190.