Effect of phase separation on the properties of simple glasses I. Density and molar volume

JOURNAL OF NON-CRYSTALLINE SOLIDS 1 (1969) 474-498 © North-Holland Publishing Co., Amsterdam

EFFECT OF PHASE SEPARATION ON THE PROPERTIES OF SIMPLE GLASSES I. DENSITY AND MOLAR VOLUME R. R. SHAW* Research Division, American Optical Corporation, Southbridge, Massachusetts 01550, U.S.A. and D. R. UHLMANN Department of Metallurgy & Materials Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, U.S.A. Received 5 May 1969 The variation of bulk density with composition across a miscibility gap is adequately described by a simple model in which volume additivity of the two phases is assumed. The density-weight percent composition function must always have positive (concaveupward) curvature across a two-phase region. The density-mole percent composition function can have either positive or negative curvature, depending upon the location of the miscibility gap in the binary diagram and upon the molecular weights of the endmember oxides. Immiscible composition regions are generally signalled more clearly by simple density-weight percent composition plots than by density-mole percent plots or molar volume or partial molar volume analyses. The model is used to predict possible immiscible regions in the systems KzO-SiO2, PbO-SiOz, B2Oa-GeO2, SiO2-GeO2, PbO-GeOz, and PbO-PzOs. Immiscibility is probably not present on the GeO2-rich side of the alkali germanate series of glasses. The LiF-rich limit of the miscibility gap in the LiF-BeF2 system is estimated.

I. Introduction Once u p o n a time it was assumed that any clear, t r a n s p a r e n t glass, whose composition did not lie in a k n o w n miscibility gap, was a single-phase material. Since then, however, m a n y such glasses have been shown to c o n t a i n two-phase or multi-phase submicrostructures resulting from l i q u i d - l i q u i d immiscibility. Both complex m u l t i c o m p o n e n t technical glasses, a n d simple b i n a r y a n d ternary systems, have shown this phase separation p h e n o m e n o n , and nearly all properties of these materials should be reinterpreted in light of its widespread occurrence. * Based in part on a thesis submitted by R. R. Shaw for the degree of Doctor of Science in ceramics, Massachusetts Institute of Technology, August 1967. 474

EFFECT OF PHASE SEPARATION. I

475

The present paper discusses the changes in density with composition which occur as a miscibility gap is traversed, and describes the compositional variation of the related quantities molar volume and partial molar volume. For simplicity, attention is focused on binary systems - both those where miscibility gaps have been delineated, and those where immiscibility has not yet been reported. It is shown that an accurate knowledge of density variations with composition can indicate those composition regions which are most likely to phase-separate, as well as those which are likely to be homogeneous. The utility of this approach is related to the fact that the scale of phase separation is often so small that detection by ordinary methods, such as optical microscopy or visual examination, is impossible. Electron microscopy, small-angle X-ray scattering, and careful light-scattering techniques are useful in investigating small-scale separation, but are expensive in terms of time and apparatus. Simple density measurements can allow the more refined techniques to be applied with greater confidence and efficiency. Finally, some measurements of density and observations of phase-separation morphologies in a system with a well characterized miscibility gap, viz. PbO-B203, are reported. 2. Effects of two-phase submierostructure on density

Liquid-liquid immiscibility in glass-forming systems leads to multiphase submicrostructures in the resulting glasses. In the binary systems considered here, only two phases can coexist in equilibrium at a given temperature. The simplest possible case to consider is then a system with a steeplyplunging immiscible phase boundary, where the compositions of the individual phases do not vary significantly with temperature. In such a case, the submicrostructure consists of one amorphous phase incorporated within another, with the relative amounts of each phase varying with the location in the appropriate phase diagram. Each phase has, of course, its own characteristic properties, such as density and thermal expansivity. For some properties, the overall properties of the two-phase glass may reasonably be described in terms of the properties and amounts of the end-member components. Such a simple, first-order description should be most satisfactory for those properties, such as density, which are not strongly dependent upon the geometrical distribution of the two phases, and/or the interfacial stresses which develop during the cooling of the phase-separated liquids into the glassy state. Assuming that the volume of the sample is made up of the volumes of its constituent phases, the bulk density p of the sample is related to the volume fraction 1/2 of the second phase by:

476

R.R. SHAW AND D.R. UHLMANN

(1)

P = ,01 + V2(P2 - P l ) ,

where Pl and/9 2 are the densities of the first and second phases, respectively. For the case of a binary system which contains a miscibility gap between compositions xl and x 2 (weight fraction), the Lever Rule can be used to express V2 and p in terms of any composition x (weight fraction between x~ and x2: Pl (x xl) -

-

v~ = (x - x l ) (p, - p~) + (x~ - ~1) p~'

PiP2 ; = [(x - x,)l(x~

x,)]

-

(2)

(3) (p, - p~) +

;~

The first and second derivatives of eq. (3) with respect to x are ~l0

ax

a2p a~ ~

P l P 2 (Pl

-

-

P2)l(x2 - -

Xl)

{[(x - Xl)l(x2 - x,)] (p, -- P2) + P2} 2'

2p,p2 [(Pl - p2)/(x2 {[(x - ~,)I(~

- x,)] ~

- x , ) ] (p, - p2) + p2} 3"

(4)

(5)

Eqs. (4) and (5) indicate that no singular points, maxima, minima, or discontinuities can occur between xi and x2, that the sign of the slope depends on the relative magnitudes of Pl and/)2, and that positive (concave upward) curvature always exists over the immiscible region. This analysis is also valid for ternary and higher-order systems in a twophase region, provided that the composition-density relation is examined in the direction of the tie line connecting the two immiscible phases at a given temperature. The slight rotation of the tie line with changing temperature 1) will introduce a small error, which in most cases would be within the accuracy of the measurement. There are several problems which may arise in the application of these relations to particular systems. First, the complete separation of the liquid into two phases may be prevented by the occurrence of crystallization. Second, the immiscible phase boundary may broaden strongly with decreasing temperature, and a range of compositions may be observed in the final glass as the decreasing molecular mobility prevents the attainment of the equilibrium compositions throughout the volume. To some extent, this can be alleviated by the occurrence of secondary phase separation 2), and in any case it will be minimized by a steep slope of the phase boundary at its outer limits. Third, any compositional variation associated with diffusion fields around the separating phases are neglected. This neglect may be reasonable for well-separated glasses. Fourth, no consideration is given to the effect of

EFFECT OF PHASE SEPARATION. I

477

phase morphology on the properties of the overall glass. That is, no distinction is made between discrete particles in a continuous matrix, expected for compositions near the outer regions of miscibility gaps, and the interconnected phase morphologies frequently observed in the central region. This neglect should be most appropriate for properties, such as density, which are not expected to vary significantly with morphology. Finally, no consideration is given to any differential effect of thermal history on different compositions. Surveying these possible problems, it appears that they should not be important for the present first-order model in most cases, and that the relations of eqs. (3) to (5) can be used with some confidence. 3. Molar volume and partial molar volume

The discussion of the preceding section has shown that compositional regions whose density-weight percent composition plots show smooth, positive curvature, with no extrema or inflections, can be regarded as likely prospects for a more careful search for phase separation. Similarly, compositional regions exhibiting negative curvature, extrema or inflections should be free of phase separation. It is interesting to compare this behavior with that of other quantities derived from the density values, namely the molar volume, V~, and the partial molar volume, J7m. These quantities have been very widely used for structural analysis of many kinds, including possible immiscibility effects 3). The molar volume is defined as the mean molecular weight, M, of the composition divided by its density: Vm = M / p .

(6)

While M varies linearly with composition (in mole percent), the density over a two-phase region does not. This is shown by rewriting eq. (3) in terms of the mole fraction, m2, of the second phase: m 2 P l P 2 ( M 2 --

P = m2Plp2(Vm2 -

M1) + p l P 2 M I Vml) -[- M l p 2

(7)

where M 1 and M 2 refer to the molecular weights of the two phases involved, and Vmi and Vrn 2 a r e their molar volumes. Note that M~ and M E a r e not necessarily the molecular weights of the end-member oxide constituents; indeed, this will rarely be the case. The first and second derivatives of eq. (7) with respect to molar concentration are:

478

R.R. SHAW AND D. R. UHLMANN

Op

p , p ~ M , (3'12 _ M , ) _ plp2M1 2 2 ( V m 2-- V,~I)

~m 2 ~2p

[m2p,P2 (Vm2 - Vmm)+ Map2] 2

~m~

'

2p2p~M, M2 (P2 - Pl) (Vm2 - Vml)

(8) (9)

[rn2P,P2 (Vm2 - V,,,,) + Mlp2] 3

Inspection shows again that no maxima, minima, points of inflection, or discontinuities can occur in the density function over the two-phase region. The sign and magnitude of the slope and curvature are governed by the relative values of the end-member molecular weights and densities, i.e. are dependent on the location of the miscibility gap in the binary system. Table 1 TABLE 1

Curvature of density-molar composition plots and molar volume-molar composition plots over a two-phase region Density-composition curvature positive

positive negative negative zero

Conditions p2 ~ pl, Vm2 ~ Vml p2 ,~/91, Vm2 ~ Vml /98 ~/91, Vm2 ~ Vml p2
trivial case; occurs when /92 --pl, or if ideal solution behavior is followed

Molar volume-composition curvature negative

negative positive positive zero

shows that the curvature in this case can be either positive or negative - in contrast to the results of eq. (5), which show that only positive curvature will be found on a weight percent plot. This last finding can be regarded as a direct result of combining the density-weight percent composition relation with the appropriate weight-to-mole percent conversion, whose curvature depends very strongly on the molecular weights of the binary system components. From eq. (6) and table 1, it is evident that the molar volume will display finite curvature, of opposite sign from that expressed by eq. (9), when plotted over a molar composition region including a miscibility gap. Since the partial molar volumes are obtained from the intersections of the tangents to the molar volume-composition plot with the molar volume scale, their variation is controlled by the curvature of this plot. A small curvature results in little variation in the Vm of either component; it is then difficult to distinguish the immiscible region from ideal solution behavior (which will, of course, result in constant Vn, values).

EFFECT OF PHASE SEPARATION. 1

479

Small curvature in the molar volume-molar composition relation often results from the linear molecular weight-molar composition relation, even over regions where appreciable curvature of the density-molar composition plot exists. The usual molar volume or partial molar volume approaches to glass structure are, then, often not as sensitive an indicator of immiscibility as is a simple density-weight percent composition plot. In addition, it is possible that composition regions which do not include a miscibility gap, and which might clearly indicate this fact on a weight percent plot, will produce a small curvature molar volume plot because of the weight-to-mole percent conversion. Such low curvature could be quite misleading.

4. Experimental In order to test eq. (1), the miscibility gap in the PbO-B203 system was chosen for a density study. This system has one of the best characterized immiscible phase boundaries, which extends from about 1-44 wtg/o PbO (0.4-20 mole~ PbO)4). Granulated B20 3 pellets and powdered Pb30 4 were appropriately combined, fused and stirred in platinum crucibles, and cast into small rectangular blocks in graphite molds. Approximately 50 g fusions were used. Chemical analyses of nine compositions indicated that the batch compositions were accurate to within about +0.5 Wt~o PbO. Densities were determined at 25.4 °C by hydrostatic weighings in kerosene and carbon tetrachloride, whose densities were measured with precision hydrometers. The measurements are considered accurate to within +0.002 g/cm 3. X-ray diffraction studies of a number of specimens indicated that even the glasses which appeared white and opaque were amorphous; in several instances however, a very small amount of crystalline phase could be resolved from the background. It is felt that the very minute volume fraction of crystalline material in these few instances did not seriously affect the density values. Direct transmission electron microscopy and electron diffraction also verified the general amorphous nature of the glasses. All samples were stored under kerosene between casting and measurement.

5. Results The submicrostructures observed at all compositions - even those in the central region of the miscibility gap - consisted of spherical particles of one phase in a continuous matrix of the other phase. An example of this morphology is shown in fig. 1 for the 28 w t ~ PbO ( l l mole~o PbO) composition, which is very near the center of the gap. It is possible that such discrete particle morphologies near the center of the gap may have resulted from the

480

R . R . S H A W A N D D . R. UI-ILMANN

Fig. 1. Fracture surface of 11 PbO. 89 B203 sample, showing B~Oa-rich discrete particles in a PbO-rich matrix. Simultaneous platinum/carbon-shadowed replica. Bar indicates l micron.

coarsening, necking off and spheroidizing of initially-interconnected submicrostructures, similar to the morphological development reported in the system BaO-SiO22). While the large scale of the observed morphologies indicate that this may be a reasonable suggestion~ its confirmation must await further studies of morphological development in the system. The experimental density data for these PbO-B203 glasses, together with molar volumes derived therefrom, are tabulated in table 2. Except where indicated, all reported compositions are nominal compositions calculated from the batch. Fig. 2a compares the observed density-weight percent composition behavior with that predicted by eq. (3), with the end-member

481

EFFECT OF PHASE SEPARATION. I TABLE 2

Density and molar volume data for lead borate glasses (wt ~o)

PbO content (mole ~o)

Density (g/cm3)

Molar volume (cmB/g"m°le)

0 1 * 1.99 4 *5.76 8 * 10.38 12 14 "17.58 18 *20.72 22 24 26 28 30 "31.81 34 *36.40 38 *40.65 42 *44.50 45 50 60

0 0.4 0.6 1.4 1.9 2.6 3.5 4.1 5.0 6.3 6.5 7.6 8.1 9.0 10.0 11.0 11.9 12.8 13.9 15.2 16.2 17.7 18.5 20.1 20.5 23.9 32.0

1.838 ±0.002 1.854 1.870 1.909 1.960 2.000 2.050 2.097 2.136 2.220 2.254 2.315 2.346 2.414 2.460 2.544 2.614 2.670 2.769 2.890 2.995 3.089 3.213 3.346 3.344 3.641 4.300

37.88 37.97 37.75 37.61 37.04 36.85 36.63 36.24 36.19 35.72 35.31 35.16 35.00 34.59 34.55 34.00 33.63 33.4l 32.87 32.15 31.52 31.30 30.47 30.01 30.11 28.43 27.72

* Analyzed value.

values taken as shown. A g r e e m e n t between the simple t h e o r y a n d e x p e r i m e n t is quite good. T h e d e n s i t y - m o l a r c o m p o s i t i o n relation over the same t w o - p h a s e region is presented in fig. 2b, a n d the c o r r e s p o n d i n g m o l a r v o l u m e - m o l a r c o m p o sition relation is shown in fig. 2c. In b o t h figures, the p r e d i c t e d b e h a v i o r is c o m p a r e d with the data. G o o d a g r e e m e n t between the p r e d i c t e d relations and e x p e r i m e n t is again a p p a r e n t . A l s o a p p a r e n t is the fact that the m o l a r v o l u m e plot, fig. 2c, displays very low curvature, and indeed c o u l d be r e a s o n a b l y well fitted with a straight line. This is expected f r o m the low c u r v a t u r e o f the d e n s i t y - m o l a r c o m p o s i t i o n plot, fig. 2b, a n d from the a r g u m e n t s o f the preceding section. The m o r e p r o n o u n c e d curvature o f the d e n s i t y - w e i g h t percent c o m p o s i t i o n plot, fig. 2a, is obvious.

482

R . R . S H A W AND D. R. U H L M A N N

3.40

J

i

[

i

eo

/

X2 = 0.44

3.20

/

3.00

2.80

z

2.60

a 2.40

2.20 .~

Xl = 0.01 p~ = 1.85

2.00

1.80 B20s

I

I

[

I

10

20

30

40

50

PERCENT PbO

WEIGHT

Fig.

2a.

3.40

3.20

3.00

2.8(

2.6( Z 2.40

2.20

2,00

1.80 B2C

I

I

I

I

5

10

15

20

MOLE PERCENT Pbo

Fig. 2b.

25

EFFECT

OF PHASE

.

i•

36

.?

34

~

32

O >

3O

~

2s

~

26

SEPARATION.

I

483

..

24 I

I

I

I

I

MOLE PERCENT PbO

Fig. 2c. Fig. 2. (a). Variation of density with composition' in wt ~. over the miscibility gap in the system PbO-B~Oa. Solid curve represents eq. (3). (b). Variation of density with composition in m o l e ~ over the miscibility gap in the system PbO-B2Oa. Solid curve represents eq. (7). (c). Variation of molar volume with composition in m o l e ~ over the miscibility gap in the system PbO-B~Oa. Solid line represents expected behavior from arguments of this paper.

• 6. D i s c u s s i o n

Examination of fig. 2 shows that, in the case of the PbO-B20 a system, the variation of density with weight percent composition is a fairly sensitive indicator that immiscibility is present. The molar volume-molar composition data is much less informative, and does not clearly show the curvature demanded by the curvature of the density-molar composition plot; the reasons for this have been discussed above. The density-weight percent composition plot appears superior in its ability to indicate the presence of a two-phase region. This is not to say that molar volume-composition plots are always insensitive. They are indeed quite sensitive at times, but unfortunately sometimes to the wrong thing. An example is provided by the work of Klemm and BergerS), whose density measurements in the PbO-B203 system agree well with the present results on the PbO-rich side of the miscibility gap. On the BzO3-rich side, however, their reported densities become consistently higher than the present results, and are clearly in error as shown by their result of 2.00 g/cm 3 for B203 ; this is much higher than reported by any other worker. It appears that some systematic error was involved in their measurements. Fig. 3a shows that their density-weight percent composition relation, although inaccurate, still has strong positive curvature, i.e. is still qualitatively

484

R.R.

SHAW

AND

D.R.

UFILMANN

MOLE PERCENT PbO B2 O;

10

20

30

40

1

I

l

I

8.00

60 I

80 IO0

I

J

I B

e'.

!.

7.00 ÷

6.00

5.00

2t,J O

4.00

e

3.00

%o

o

o

2.00

o.Oo

1.00

,' _ - -

I

B20 10 20

r

t

30

40

j

50

_

I

I

60

70

1 ,,

r

80

90

100

WEIGHT PERCENT PbO

Fig. 3a. 3B ~ i

i

--

r

-r

I

- ~

36

~v

34

u~ IE

32

~

3o

~

2e

~

26 24

B20

20

40

60

80

100

MOLE PERCENT PbO

Fig. 3b. F(g. 3. (a). Variation of density with composition in wt % of glasses in the system PbO-BzO3. (Q) ref. 5; (A) ref. 6; (A) ref. 7; (÷) ref. 8; ( I ) ref. 9; (©) this study. (b). Molar volume-molar composition plot in the system PbO-B20~, calculated from the density data of ref. 5.

EFFECT OF PHASE SEPARATION. I

485

capable of indicating the presence of a second phase. The data of other workers are also included. Fig. 3b indicates, however, that the molar volume plot derived from these same data shows a strong maximum at about 5 mole% PbO. This maximum is spurious, and results from the density errors in the high-B203 compositions discussed above. The partial molar volumes gyrate wildly because of this spurious peak; but obviously no significance can be attached either to the behavior of the molar volumes or the partial molar volumes. It is apparent, then, that the molar volume approach in this system is insensitive in providing information on the presence of immiscibility, but is quite sensitive to measurement errors. In contrast, the density-weight percent relation is relatively insensitive to such measurement errors, and is a more reliable indicator of the two-phase region. Similar remarks apply to the partial molar volume analyses of glasses in the Na20-SiO2 and the K20-SiO2 systems made by CallowlO). This investigator found sharp minima for the partial molar volumes of N a 2 0 and K 2 0 in composition regions now known (at least in the case of the Na20-SiO2 system) to include immiscible regions. These minima were produced by inflections of the molar volume-molar composition plots, similarly located within the gaps, and which themselves arose because of apparent inflections of the density-composition curves at the same points. It will be seen below that these inflection points were initially poorly chosen, and the elaborate structural explanations built around the locations of the sharp partial volume minima are invalid. This represents another example of the marked susceptibility to error of molar volume approaches. It is of interest to check eq. (3) further by examining the variation of density with composition in other phase-separated systems. Unfortunately, density data are seldom presented across the many miscibility gaps in the literature, especially when turbidity or opacity is present, in several systems, however, considerable data do exist, most of which were taken before the presence of immiscibility was well established. These will be examined in some detail in the following section, as will the application of the simple model to systems whose immiscibility behavior has not yet been characterized.

7. Application of simple model to other systems The collected density data for glasses in the Li20-SiO 2 system are compared with eq. (3) in fig. 4. Although the data are somewhat scattered, a reasonable fit of eq. (3) can be made between pure SiO 2 and 20 wt% Li20 (33.5 mole% Li20 ). This agrees well with the known location of the immiscible phase boundary 18-2°) for this system.

486

R.R.

SHAW

AND

D. R. UHLMANN

MOLE PERCENT Li20 SiO2 2.40

10

,

i

2.35

o) >_" 2.30 e~

2.25

2.20 q SiO

20 I

t

30 I

40 I

///

. s ~ J :~ '~"

,

i

I0

,

I

20

, 30

WEIGHT PERCENT Li20

Fig. 4. Variationof density with compositionin wt ~ in the systemLieO-SiOe.(O) ref. 11 ; (A) ref. 12; (A) ref. 13; (÷) ref. 14; (D) ref. 15; ( I ) ref. 16; (0) ref. 17; solid curve represents eq. (3). Fig. 5 presents a similar comparison for glasses in the system Na20-SiO2. As shown in the figure, eq. (3) provides an adequate fit of the data between pure SiO 2 and 25 wt% Na20 (24.5 mole% NaeO). This agrees fairly well with the extent of the immiscible phase boundaryl~,27), which extends to about 20mole% Na20 at 550°C, and is still broadening with decreasing temperature. Data are also available in the alkali borate glass systems across the immiscible regions zs), but the greater sensitivity of the alkali borate densities to water content, preparation technique, annealing schedules, etc. tends to scatter the data of different investigators more than in the alkali silicate glass systems. Fig. 6 presents collected density data for glasses in the system Li20-B203, together with the predicted relation of eq. (3) over the known miscibility gapeS). As shown in the figure, reasonable agreement is found. Fig. 7 similarly indicates fairly good agreement between experimental data and the simple theory for glasses in the system Na20-B203. Fig. 8, however, shows poor agreement for glasses in the KeO-BzO3 system. This suggests either that the extent of the miscibility gap of ref. 28 is in error, or that the density values are erroneous. Consistent with the latter suggestion, this system has larger discrepancies among the results of different investigators

487

EFFECT OF PHASE SEPARATION. 1

MOLE PERCENT Na=O

10

2.60

20

30

50

40

o,~,* *°o °-6

2.50 ,l~i °

a ),-

2.40

a

2.30

/

2.21 SiO2

I

10

2tO

30

n

t

40

50

WEIGHT PERCENT Na=O Fig. 5. Variation of density with composition in w t ~ in the system Na20-SiO2. (&) ref. 21; (+) ref. 13; (A) ref. 14; (open hexagon) ref. 12; (O) ref. 11; (IS]) ref. 22; (It) ref. 23; (T) ref. 24; (©) ref. 25; ( 0 ) ref. 16; (solid diamond) ref. 26; solid curve represents eq. (3).

than does any other. Fig. 9 indicates reasonable agreement for glasses in the Rb20-B203 and C S z O - B 2 0 3 systems, although additional data would obviously be useful. In summary, it appears that the simple density model expressed by eq. (3) does in fact realistically describe the variation of density with composition in phase-separated glass systems. This does not mean that every composition region exhibiting positive curvature of the density-weight percent composition plot will be a two-phase region. However, such regions will certainly be the most promising ones to examine for immiscible behavior, and regions with strong negative curvature, or which contain maxima, minima, inflections, or discontinuities, can be eliminated as potential candidates for such behavior. A few examples of how this approach can provide information in binary glasses are discussed below.

488

R . R . SHAW AND D. R. UHLMANN

MOLE PERCENTLi20 2.4oS~

K) I

20

30

I

I

2.30

io

2.20 o

e

i

2.10

•

o

O

2.00 1.90 1.82

B203

I

I

I

5

I0

15

20

WEIGHT PERCENTLi20 Fig. 6. Variation of density with composition in wt% in the system Li20-B2Oa. ( 0 ) ref. 29; (©) ref. 30; (A) ref. 31 ; (&) ref. 32; solid curve represents eq. (3).

7.1. POTASSIUM SILICATE GLASSES Immiscibility has never been clearly demonstrated in glasses in the K20-SiO 2 system, although the possibility of its occurrence has been the subject of much discussion. The principal difficulties in elucidating this question are associated with the expected 37) low temperatures of the metastable miscibility gap relative to the glass transition region, and the consequent exceedingly small submicrostructure which would result. Fig. l0 shows the density-weight percent composition relation for K20-SiO 2 glasses. A good fit of eq. (3) to these data can be made between pure SiO2 and 22 wt% K20 (18 mole% K20), suggesting that a two-phase structure may indeed be present between these composition limits, or at least that this would be the appropriate composition range to look for phase separation.

489

EFFECT OF PHASE SEPARATION. I

MOLE PERCENT No2O

B203

4O

20

2.40

I

I

o

I

o,1~.

li,"

2.30

/

2.20

&

,

,Y, m

>: 2.10 Lu

t-,

2.00

1.90

! .

1.82 S:03

I

I

I

20

40

WEIGHT PERCENT No,C)

Fig. 7. Variation of density with composition in w t ~ in the system Na~O-B2Oo. ( 0 ) ref. 29; (A) ref. 32; (A) ref. 12; (-b) ref. 6; (©) ref. 33; (V) ref. 34; (V) ref. 24;

([]) ref. 31 ; ( I ) ref. 35; solid curve represents eq. (3).

7.2. LEAD SILICATEGLASSES

Fig. 11 indicates that the density-weight percent composition relation for PbO-SiO2 glasses displays positive curvature over a wide composition range. Eq. (3) fits the data well from pure SiO 2 to about 79 wt~o PbO (50 mole~o PbO), indicating that this is the most probable composition range in which to observe immiscibility. 7.3. BOROSIL1CATEGLASSES

Charles and Wagstaff 42) have shown that immiscibility exists in the B 2 0 3SiO 2 glass system, and have calculated a metastable phase boundary extending completely across the binary system. Fig. 12 shows that the available

R.R. SHAWAND D. R. UHLMANN

490

MOLE PERCENTK20 IO 20

B20.~

30 I

2.40t 2.30 u

2.20

>-

E

2.10 2.00 1.90

I

1.82 B20 ~

10

I

2JO

30

410

WEIGHTPERCENTK20 Fig. 8.

Variation of density with composition in wt ~ in the system KzO-BzO3. (O) ref. 29; (&) ref. 32; (A) ref. 12; solid curve represents eq. (3).

I

I

I

'I

f

I

I

3.20 Z

3.00

q

S

2.60

Cs=O Gla°

m

U )-

3.60

2.20

i

,

t~~R°b20

~o

2.80

0

2.40

~

i m

ilaHes a2

1.80; B203

2.00 I

I

20

I

I

40

I

I

60

I

80

WEIGHTPERCENTMaO Fig. 9. Variation of density with composition in wt ~ in the systems Rb20-B~O3 and Cs20-B2Oa, (A) and (Q) ref. 32; (©) ref. 36; solid curves represent eq. (3).

EFFECT

OF PHASE SEPARATION.

491

1

MOLE PERCENT KaO SiO2 2.50

.

20

.

.

.

40

.

o

o~o

/

2.40 >:

X 2.30

2"2Oio 2

1

I

I

30

I

I

50

WEIGHT PERCENT K20

Fig. 10. Variation of density with composition in wt~o in the system K20-SiO2. (©) ref. 25; (A) ref. 14; (0) ref. 16; (÷) ref. 13); (V) ref. 12; (O) ref. 11; solid curve represents eq. (3).

density data for this system consistently lie below the expected curve, indicating that the high silica limit of the miscibility gap is perhaps not at the pure SiO 2 limit. 7.4. GERMANATEGLASSES Glasses in the systems B203-GeO 2 and SiO2-GeO 2 obey eq. (3) well over the entire binary composition range, as shown in fig. 13. From these data it appears that very wide miscibility gaps may exist in these systems. Positive curvature also exists in the density-weight percent composition relation for PbO-GeO2 glasses, as shown in fig. 13. A rough fit of eq. (3) is possible over the range 0-35 Wt~o PbO (0-20 mole~o PbO), indicating a promising range for investigation. Immiscibility might be expected in alkali germanate glasses because of the distorted liquidus lines found at high GeO2 concentrations in the LiEO_GeO248) and Kz~O-GeO 249) equilibrium diagrams. Such distortion of liquidus lines often signifies subliquidus immiscibility. However, the density data which exist over the appropriate concentration ranges for L i 2 0 - G e O 2

492

R . R . S H A W A N D D . R. U H L M A N N

MOLE PERCENT PbO 20

SiO 9~)0

40

I

I

I

60 I

I

7.00

80 PbO I

¢

g

Z

$.00

3.00

SiO

I

I

I

l

20

40

60

80

PbO

WEIGHT PERCENT PbO

Fig. 11. Variation of density with composition in wt% in the system PbO-SiO2. (A) ref. 38; (0) ref. 39; (O) ref. 40; (&) ref. 9; ([~) ref. 41 ; solid curve represents eq. (3).

and N a 2 0 - G e O 2 glasses, fig. 14, indicate only negative curvature. Maxima occur at slightly higher alkali concentrations, and, at least in the N a 2 0 - G e O 2 system, negative curvature occurs at still higher N a 2 0 concentrations. The wrong curvature, as well as the presence of maxima, indicate that immiscibility is not to be expected in these composition regions. Similar remarks apply to glasses in the system K 2 0 - G e O 2 in the high-GeO2 composition range, as shown in fig. 15. As indicated there, both negative curvature and a maximum are present in the density-weight percent composition relation. Positive curvature appears to exist above about 25 wt% K20, however, and immiscibility may possibly occur in this region. Insufficient data is available to make any predictions in the R b 2 0 - G e O 2 and Cs20-GeO2 systems52).

493

EFFECT OF PHASE SEPARATION. I MOLE PERCENT SiO2 B203 2.30

I0 I

20 i

30 I

40 I

50 I

60 I

70 I

80 [

90 I

SiOa

2.20

2.1o

2.00

1.90

1.80 BaOa

I 20

I 40

I 60

WEIGHT PERCENT

I 80

SiO

Si02

Fig. 12. Variation of density with composition in wt~ in the system B203-SIO2. (©) ref. 43; (0) ref. 44; solid curve represents eq. (3). 7.5. ALKALI BERYLLIUMFLUORIDEGLASSES Vogel and Gerth ~3) have made extensive investigations into immiscibility in alkali fluoride-beryllium fluoride glass systems, and have presented numerous electron micrographs of the two-phase submicrostructures in these systems. In the case of the LiF-BeF 2 system, it is possible to estimate the volume fraction of the second phase (LiF-rich) for several compositions, and obtain the LiF-rich limit of the miscibility gap through eqs. (1)-(3). Assuming that the high-BeF2 immiscible phase boundary extends to pure BeF2, and measuring the second-phase volume fractions from figs. 12 and 13 of ref. 53, the following results are obtained: Composition (mole % LiF)

Composition (wt % LiF)

p (g/cms)

p2

X2

I/2

(g/cms)

(wt ~ LiF)

39.1 44.0

26 30

2.167 2.190

0.857 0.988

2.197 2.193

29.9 30.3

494

R.R.SHAW AND D.R.UHLMANN 7.00

I

I

I

I 0

0

6.00

U

O0 O

5D0 bO-GeOa

al >~ Z

4.00

3.00

B203- G e O 2 ~ 2.00 GeO2

I

20

[

40

I

60

I

80

100

WEIGHT PERCENT MxO,

Fig. 13.

Variation of density with composition in w t ~ in the systems B203-GeO2, SiO2-GeO2, and PbO-GeO2. ( 0 ) ref. 45; (A) ref. 46; (O) ref. 47; solid curves represent eq. (3).

These calculations indicate that the LiF-rich limit of the miscibility gap occurs at about 30 wt~ LiF, and the end-member density there should be about 2.195 g/cm a. Fig. 16 indicates that eq. (3) describes the density variation reasonably well, using the density and composition calculated above. 7.6. LEAD PHOSPHATE GLASSES

Fig. 17 shows that eq. (3) provides a good fit of the density data in the system PbO-P205 over the composition region 0-76 wtg/oPbO (0-67 mole~ PbO). This region would then appear to be the most promising one in which to observe a two-phase structure. 8. Conclusions

1) A plot of density against weight percent composition must always have positive (concave-upward) curvature across a two-phase region. This is a more reliable indicator of immiscibility in binary glasses than a density-mole percent composition plot, whose curvature may be either positive or negative depending upon the molecular weights of the end-member oxides.

495

EFFECTOF PHASESEPARATION.I

2) Molar volume and partial molar volume approaches to structural analysis are very often less sensitive to the presence of immiscibility than is the simple density-weight percent composition plot. 3) Good agreement between the predictions of a simple two-phase model and experimental densities has been obtained. The relations which were developed are useful both in detecting those composition regions most likely to phase separate, and in determining those regions which are not immiscible.

4.201

I

t

l

I

I

I

I

I

I

I

5

10

15

20

25

oofL 3.60 ~

3.40 GeO

A\

WEIGHT PERCENT M20 Fig. 14.

Variation of density with composition in wt ~o in the systems Li~O-GeO~ and NazO-GeO~. (A) ref. 48; (O) ref. 50; (O) ref. 47; (A) ref. 51.

4) It is predicted that immiscibility may exist in particular regions of the systems K20-SiO2, PbO-SiO2, B203-GeO2, SiO2-GeO2, PbO-GeO2, and PbO-P2Os. The miscibility gap may extend completely across the binary systems B2Oa-GeO 2 and SiO2-GeO2, but probably does not in the B203SiO2 system. Immiscibility is probably not present on the GeO2-rich side of the alkali germanate series of glasses. The LiF-rich side of the LiF-BeF2 miscibility gap extends to about 30 wt~ LiF (44 mole~ LiF).

496

R.R. SHAW AND D.R. UHLMANN

MOLE PERCENT K~,O Ge 02 4.00

10

20

30

40

I

I

1

I

3.80

o~

>.-

3.60

D-

3.40 t

3.20 V GeO2

5

15

25

45

35

WEIGHT PERCENT K20

Fig. 15. Variation of density with composition in WtToo in the system K20-GeO2. (O) ref. 49; (©) ref. 47.

MOLE PERCENT LiF

2.30

BeF

10

20

30

40

50

I

J

I

I

I

60

G

6

2.20 u u

z

2.10

2.00

1.90 fief

I

I

I

I

10

20

30

40

WEIGHT PERCENT LIF

Fig. 16. Variation of density with composition in wt ~ in the system LiF-BeF2. (A) ref. 53 ; density of pure BeFz glass from ref. 54; solid curve represents eq. (3).

EFFECT

OF

PHASE

SEPARATION.

497

1

MOLE PERCENT PbO P20s

20 i

40

i

i

i

60 i

i

80 i

i

7.~

6.00

5.00

r, 4.00

3.00

2.20

I

P20s

I

I

20

I

I

40

I

60

I

I 80

WEIGHT PERCENT PbO

Fig. 17. Variation of density with composition in wt% in the system PbO-P2Os. ( 0 ) ref. 55; (©) ref. 56; solid curve represents eq. (3).

Acknowledgments The M.I.T. part of this work was supported by the U.S. A t o m i c Energy C o m m i s s i o n u n d e r C o n t r a c t AT(30-1)2574. R. G r a f p r e p a r e d the lead borate glasses used in this work. J. F. Breedis a n d D. G u e r n s e y o f M.I.T. provided electron microscopy a n d chemical analyses, respectively.

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10)

G. Masing, Ternary Systems (Reinhold, New York, 1944) ch. 7. T. P. Seward, D. R. Uhlmann and D. Turnbull, J. Am. Ceram. Soc. 51 (1968) 278. J. O. Bockris, J. W. Tomlinson and J. L. White, Trans. Faraday Soc. 52 (1956) 299. J. Zarzycki and F. Naudin, Phys. Chem. Glasses 8 (1967) 11. A. Klemm and E. Berger, Glastechn. Ber. 5 (1927) 405. J. M. Stevels, Physical Properties of Glass (Elsevier, New York, 1948) p. 96. S. M. Brekhovskich, Glastechn. Ber. 32 (1959) 437. S. M. Brekhovskich, Glass Ceram. (USSR) 14 (1957) 264. E. Kordes, Glastechn. Ber. 17 (1939) 65. R.J. Callow, J. Soc. Glass Technol. 36 (1952) 137.

498

R.R.SHAWANDD.R.UHLMANN

11) J. C. Young, F. W. Glaze, C. A. Faick and A. N. Finn, J. Res. Natl. Bur. Std. 22 (1939) 453. 12) C. E. Weir and L. Shartsis, J. Am. Ceram. Soc. 38 (1955) 299. 13) D. Hubbard, J. Res. Nat. Bur. Std. 36 (1946) 365. 14) A. Dietzel and H. A. Sheybany, Verres Refractaires 2 (1948) 63. 15) F. P. Glasser, Phys. Chem. Glasses 8 (1967) 224. 16) R. J. Charles, J. Am. Ceram. Soc. 49 (1966) 55. 17) N. E. Kind, Inorg. Mater. 2 (1966) 1411. 18) Y. Moriya, D. H. Warrington and R. W. Douglas, Phys. Chem. Glasses 8 (1967) 19. 19) N. S. Andreev, D. A. Goganov, E. A. Porai-Koshits and Yu. G. Sokolov, in: Structure of Glass, Vol. 3, Translation from Russian by E. B. Uvarow, (Consultants Bureau, New York, 1964) pp. 47-52. 20) W. Haller, National Bureau of Standards, Washington, D.C., private communication. 21) F. W. Winks and W. E. S. Turner, J. Soc. Glass Tech. 15 (1931) 185. 22) D. E. Day and G. E. Rindone, J. Am. Ceram. Soc. 45 (1962) 489. 23) A. Winter, "Remarks on General Ideas Applied to Glass", Verres Refractaires 20 (1966) 448. 24) J. H. Strimple and E. A. Giess, J. Am. Ceram. Soc. 41 (1958) 231. 25) G. W. Morey and H. E. Merwin, J. Opt. Soc. Am. 22 (1932) 632. 26) V. V. Akimov, in: Structure of Glass, Vol. 2 (1960) pp. 440-44. 27) J. J. Hammel, in: Proc. VII Intern. Congr. on Glass, Brussels, 1965, Vol. I, (Institut National de Verre, Charleroi, and Federation de l'Industrie du Verre, Brussels, Belgium, 1966) paper 36. 28) R. R. Shaw and D. R. Uhlmann, J. Am. Ceram. Soc. 51 (1968) 377. 29) R. I. Bresker and K. S. Evstropiev, J. Appl. Chem. USSR 25 (1952) 981. 30) B. S. R. Sastry and F. A. Hummel, J. Am. Ceram. Soc. 41 (1958) 7. 31) L. Shartsis, W. Capps and S. Spinner, J. Am. Ceram. Soc. 36 (1953) 35. 32) M. Coenen, Glastech. Bet. 35 (1962) 14. 33) M. Foex, Compt, Rend. (Paris) 208 (1939) 278. 34) F. C. Eversteijn, J. M. Stevels and H. I. Waterman, Phys. Chem. Glasses I (1960) 123. 35) D. R. Stewart, G. E. Rindone and F. Dachille, J. Am. Ceram. Soc. 50 (1967) 467. 36) J. Krogh-Moe, Arkiv Kemi 12 (1958) 247. 37) R.J. Charles, J. Am. Ceram. Soc. 50 (1967) 631. 38) A. A. E1-Azm and A. L. Hussein, J. Chem. U.A.R. 5 (1962) 1. 39) V. I. Minenko, S. M. Petrov and N. S. Ivanova, Glass Ceram. (USSR) 17 (1961) 318. 40) G. W. Morey, Properties of Glass (Reinhold, New York, 1938) p. 239. 41) P. D. Calvert and R. R. Shaw, to be published. 42) R. J. Charles and F. E. Wagstaff, J. Am. Ceram. Soc. 51 (1968) 16. 43) A. Cousen and W. E. S. Turner, J. Soc. Glass Tech. 12 (1928) 169. 44) R. Bruckner and J. Navarro, Glastechn. Ber. 39 (1966) 283. 45) M. K. Murthy and B. Seroggie, Phys. Chem. Glasses 7 (1966) 68. 46) E. F. Riebling, J. Am. Ceram. Soc. 51"(1968) 406. 47) K. S. Evstropiev and A. O. Ivanov, in" Advances In Glass Technology, Vol. 2 (Plenum Press, New York, 1962) pp. 79-85. 48) M. K. Murthy and J. Ip, J. Am. Ceram. Soc. 47 (1964) 328. 49) M. K. Murthy, L. Long and J. Ip, J. Am. Ceram. Soc. 51 (1968) 661. 50) M. K. Murthy and J. Aguayo, J. Am. Ceram. Soc. 47 (1964) 444. 51) C. R. Kurkjian, private communication. 52) M. K. Murthy and J. Ip, Nature 201 (1964) 285. 53) W. Vogel and K. Garth, Glasteehn. Ber. 31 (1957) 15. 54) A. G. Pincus, J. Opt. Soc. Am. 35 (1954) 92. 55) E. Kordes, Z. Physik. Chem. B43 (1939) 119. 56) C. A. Elyard, P. L. Baynton, and H. Rawson, Glastechn. Ber. (1959) 36.