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The density of two mixed alkali borate glass systems related to atomic arrangements
Journal of Non-Crystalline Solids 109 (1989) 105-113 North-Holland, Amsterdam
105
THE DENSITY OF TWO MIXED ALKALI BORATE GLASS SYSTEMS ATOMIC ARRANGEMENTS
RELATED TO
B.C.U C H O N G 1, S.H. C H O O 2, S. F E L L E R , B. T E O H , O. M A T H E W S , E.J. K H A W , D. F E I L , K.H. C H O N G 3, M. A F F A T I G A T O , D. B A I N , K. H A Z E N a n d K. F A R O O Q U I Physics Department, Coe College, Cedar Rapids, Iowa 52402, USA
Received 21 October 1988 Revised manuscript received 10 January 1989
Densities of the two mixed alkali borate glass systems, R ( 12Na20 + ~Li 20). B203 and R (12Rb20 + ~2Li 20). B203, have been measured over an extremely wide range of alkali content: from boron oxide through the orthoborate composition. The glasses were prepared with metal carbonate and oxide starting materials. As with the binary alkali borates, a semiempirical model has been applied to the densities in order to determine the volumes of the structural units present. These values, in conjunction with volumes found in the binary borate cases, and with volumes calculated from the ionic radii, were used in a general discussion of the filling of space by the structural units. The results indicate that the size increases of the structural groupings as one goes from small to large alkali are primarily due to the alkali being used.
1. Introduction O v e r the p a s t few years the densities of the b i n a r y alkali b o r a t e glass systems have been syst e m a t i c a l l y m e a s u r e d over very wide ranges of alkali c o n t e n t [1-4]. T h e s e d a t a were a n a l y z e d in terms of a s e m i e m p i r i c a l m o d e l involving q u a n t i tative measures of the b o r a t e structures thought to b e p r e s e n t in the glasses [1-4]. T h e results revealed that the filling of space b y the structural units is essentially i n d e p e n d e n t of the alkali present in all the systems. T h e d e n s i t y trends c o u l d be e x p l a i n e d as a c o m p e t i t i o n b e t w e e n the masses a n d sizes of the various alkali ions p r e s e n t in the glasses within a c o n s t a n t b o r a t e structural b a c k ground. M u c h interest has b e e n g e n e r a t e d in recent y e a r s a b o u t m i x e d alkali b o r a t e glasses. F o r e x a m ple the electrical p r o p e r t i e s of these glasses have Present addresses: 1 Physics Department, Kansas State University, Manhattan, KS. 2 School of Actuarial Science, Temple University, Philadelphia, PA. 3 Computer Science Department, Kansas State University, Manhattan, KS. 0022-3093/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
b e e n e x a m i n e d extensively [5-9]. This p a p e r rep o r t s the densities of two representative m i x e d alkali b o r a t e glass systems, R ( ½ N a 2 0 + ½Li20 ) • B20 3 a n d R ( ½ R b 2 0 + ½Li20 )- B203, where R is the m o l a r r a t i o of a l k a h to b o r o n . T h e m e a s u r e m e n t s were taken over the e x t r e m e l y wide range of values for R f r o m 0 to 3 (0 to 75 mol% alkali). T h e resulting densities were then used in a semiempirical m o d e l d e s c r i b e d in the previous p a p e r s [1-4] in o r d e r to b e t t e r u n d e r s t a n d the a t o m i c a r r a n g e m e n t s present. The s e m i e m p i r i c a l m o d e l y i e l d e d the v a r i o u s volumes associated with the s t r u c t u r a l g r o u p i n g s thought to be in the glass. T h e v o l u m e s of these units were then c o m p a r e d with v o l u m e s c a l c u l a t e d using ionic radii b y f o r m i n g the ratio of the latter to the former. This r a t i o was d e f i n e d as the p a c k ing fraction.
2. Experimental method Samples were p r e p a r e d f r o m two sets of starting materials. F o r the c a r b o n a t e - b a s e d s a m p l e s of l i t h i u m - s o d i u m b o r a t e glasses, the m a t e r i a l s were lithiuim c a r b o n a t e , s o d i u m c a r b o n a t e , a n d b o r i c
B.C.L Chong et aL / Density of two mixed alkali borate glass systems
106
acid. In the lithium-rubidium borate glasses, rubidium carbonate was substituted for sodium carbonate. Using appropriate amounts of these chemicals, 4 g of starting material were thoroughly mixed in a platinum crucible. They were heated for 15 to 25 min at 1000°C under a flowing nitrogen atmosphere. Each sample was weighed 5 min before the end of the heating in order to verify sample composition. It is noted that weighing the sample allows one to determine the onset of carbon dioxide retention by the glass [3]. This is observed when the expected weight loss exceeds the actual weight loss. For the lithium-sodium borate system this occurred between R = 2 and R = 2.5; in the lithium-rubidium system CO 2 retention began between R = 1.4 and R =1.9. Samples also were prepared from the oxides of boron, lithium, sodium, and rubidium. Four-gram samples were mixed under argon and were heated at 1000°C for periods of 5 to 10 min with a weight check as before. The resulting melts were quickly cooled by splat quenching between two brass plates. Glassiness was determined visually and glasses were formed in both systems between R = 0 and R = 3.0. The mixed alkali borate systems displayed a
continuous glass-forming region unlike the binary sodium and rubidium borate systems which have a discontinuity near the metaborate composition (R = 1). All reported compositions are batch. The density was measured by a modified sinkfloat technique [3] using di-iodomethane and acetone. The modification, as described in ref. [3], consisted of bracketing the glass density with the fluid densities in order to avoid problems with the glass reacting with the density fluids. A conservative estimate of the experimental error is + 0.02 g / c m 3 except for high alkali content lithium-rubidium borate glasses (greater than R = 2). These latter glasses have an uncertainty in their density of ___0.03 g / c m 3 due to their reactivity with the density fluids.
3. Results
The density data for the lithium-sodium and lithium-rubidium borates are shown in figs. 1 and 2. The error limits shown are the values given above. In both cases, the densities of the mixed systems fall somewhat closer to the larger alkali borate system although they generally follow an
2.4-
t
+
+
2.3
+t -F
+
+~+~+
t+
+or
++~
++~R+,
2.2
E O~ v
2.1
1.9
1.~
I
0
I
I
0.4
[3
Metol Oxides
I
0.8
I
I
1.2
I
I
1.6 +
I
I
I"
2
I
2,4
I
I
2.8
I
3.2
R Metal Carbonotes
Fig. 1. The density of l i t h i u m - s o d i u m borate glasses as a function o f R (in all figures, R is defined as the ratio of alkali to boron).
B.C.L Chang et aL / Density of two mixed alkali borate glass systems
107
3.2 3.1
o
3
+ 4-
2.9
+
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+
+
+ +
4=1= +
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E 2.5
b
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2 1.9 1.8
i
i
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i
1.2
i
i
1.6
i
2
F
i
2.4
2.8
R (3
Metal Oxides
+
Metal Carbonates
Fig. 2. The density of lithium-rubidium borate glasses as a function of R.
2.4
0 0 0 ~ o ~ ÷+
T 0
O
O
O
0
I
+
<>
+$+¢+
+++
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o+0 [] ¢ 1.9 o
1.8
0
1
2
3
R
0
Lithium
+
Ltth|um-~d|um
¢
Sodium
Fig. 3. The density of mixed lithium-sodium borate glasses compared with binary systems [1,2].
108
B . C . L Chong et al. / Density of two mixed alkali borate glass systems 3.2 +
3.1 Rubidium
0
3 +
¢
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l 0.4
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+
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i 2
R Lithium-Rubidium
Fig. 4. T h e d e n s i t y o f m i x e d l i t h i u m - r u b i d i u m
average functional behavior. This is shown explicitly in fig. 3 for the lithium-sodium borates and in fig. 4 for the lithium-rubidium borates. As can be seen in fig. 1 the densities of lithium-sodium borate glasses are not a function of starting material even when carbon dioxide is retained in the glass. However, lithium-rubidium borates show some deviation outside of the experimental error for values of R > 2.5 (see fig. 2). This region of composition has a value of R greater than that of the onset of carbon dioxide retention. Thus, carbonated glasses in this latter system show a small but real difference in density when compared with measurements of the glasses prepared from the oxides. These oxide glasses absorb some platinum from the crucible but not enough to account for the observed difference.
A model for the density of alkali borate glasses based on atomic arrangements has been used suc-
i 2.8
Rubidium
borate glasses compared with binary systems [1-3].
cessfully [1-4]. This representation is based on the ideas of Krogh-Moe and others in which the glass is viewed as a random assembly of certain fundamental structural groupings derived from crystalline configurations [10-12]. Nuclear magnetic resonance studies of Bray and O'Keefe [13], Jellison and Bray [14], Jellison [15], Bray et al. [16] among others have shown a
Table 1 T h e f r a c t i o n s o f b o r o n units [1] u s e d in a m o d e l for d e n s i t y in w h i c h f r a c t i o n s are i n d e p e n d e n t o f alkali t y p e 0.0 ~ R ~ 0.4
0.4 ~< R ~< 0.7
0.7 ~< R ~<1.0 1-R
fl
1-R
1-R
f2 f3 f4 f5
R 0 0 0
g/6+~ 5R/60 0
1.0 ~< R ~< 2.14
2.14 ~< R ~< 2.5
2.5 ~< R ~< 3.0
0 - R/4+5/8 - 0 . 5 5 R + 1.175 0.6(R --1) 0.2(R - 1 )
0 - R/4+5/8 0 - R/2+7/4 3R/4-11/8
0 0 0 3- R R -2
4. Discussion of the results 4.1. Models for the density data
0
i
fl fz f3 f4 f5
3I
-R4+ 5R/40 0
~ 58
B.C.L. Chong et al. / Density of two mixed alkali borate glass systems
close similarity in the structural arrangements present in the alkali borate glasses independent of the type of alkali. However, recent work by Bray et al. [17] indicates that the fractions of borons in various structural units depend on which alkali is present. Therefore, model calculations in this paper
109
Table 3 Associated volumes of structural groupings found in lithiumsodium and lithium-rubidium borate glasses compared with lithium, sodium, and rubidium borates Fractional Symbol
Relative volume of unit compared with boron with 3 bridging oxygens (at R = 0) Li-Rb
Li-Na
Rb
Na
Li
0.99 1.89 2.30 a) a~
0.96 1.19 1.65 2.15 2.80
0.98 0.91 1.32 1.69 1.95
0.98 1.76 2.29
0.95 1.17 1.62
0.98 0.91 1.32
(a) Using the fractions from table 1 Table 2 The fractions of the boron units [17] used in a model for density in which the fractions are a function of the alkali L i - N a borate system
fl f2 f3 f4 f5
0.0 ~< R ~< 0.28
0.28 ~< R ~<0.61
0.61 ~< R ~<1.0
1-R 0.853 R 0.147 R 0 0
1-R 0.342 R +0.197 0.658 R -0.197 0 0
1-R -0.439 R +0.625 1.439 R -0.625 0 0
0.0 ~< R ~<0.33
0.33 ~
0.50 ~< R ~<1.0
fl
1-R
f2
2 R/3 R/3
1-R 0.42 R +0.08 0.58 R - 0 . 0 8 0 0
1-R - 0 . 1 6 R +0.37 1.16 R - 0 . 3 7 0 0
0.0 ~< R ~<0.4
0.4 ~
0.7~< R ~<1.0
1-R R 0 0 0
1-R 0.167R +0.333 0.833 R -0.333 0 0
1-R - 0 . 2 5 R +0.625 1.25R -0.625 0 0
0.0 ~< R ~< 0.335
0.335 ~< R ~< 0.75
0.75 ~< R ~<1.0
1-R 0.862 R 0.138 R 0 0
1-R 0.173 R +0.288 0.827R -0.288 0 0
1-R -0.362 R +0.664 1.362 R -0.664 0 0
0.0~
0.348~
0.716~
1-R 0.685 R 0.315 R 0 0
1-R 0.16 R +0.227 0.84 R -0.227 0 0
1-R -0.243 R +0.478 1.243 R -0.478 0 0
0 0
Li borate system
fl f2 f3 f4 f5
N a borate system
fl f2 f3 f4 f5
Rb borate system
fl f2 f3 f4 f5
0.98 1.42 1.86 2.53 3.28
0.98 1.03 1.49 1.87 2.35
(b) Using the fractions from table 2 fl f2 f3
0.98 1.24 1.81
0.97 1.02 1.38
f4
a)
a)
a)
a)
a)
f5
a)
a)
a)
a~
a)
a) No data.
L i - R b borate system
f3 f4 f5
fl f2 f3 f4 f5
were done using both hypotheses regarding the dependence of the borate units on the alkali ions. In either case, the following configurations were used in the density models (notations for the fractions of borons in each structural unit are given in parentheses): (1) boron with three bridging oxygens (f~); (2) boron with four bridging oxygens and one alkali ion ( f 2 ) ; (3) boron with two bridging and one non-bridging oxygen and one alkali ion (f3); (4) boron with one bridging and two non-bridging oxygens and two alkali ions (f4); (5) boron with three non-bridging oxygens and three alkali ions (fs)Table 1 lists the fractions used for the case where the equations were assumed to be independent of the alkali present [1-4]. Table 2 gives the fractions for the case where the equations were a function of alkali [17]. The following equation is used for the glass density [2], p: p=
faMl + f2M2 + f 3 M 3 + f4M4 + fsM5 flV1 + f2V2 + f3V3 -4- f4V4 + fsV~
(1)
where M, is the mass of the ith structural group-
110
B.C.L. Chong et aL / Density of two mixed alkali borate glass systems 2.4
2.3
2.2 E OI
2.1
v
c
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1,8
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f
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1.6
Metal Oxides
I
2
I
t
2.¢
I
I
2.8
3.2
R Metal Carbonates
+
Fig. 5. Density model which assumes fractions of borate units are independent of the alkali present overlaid onto the lithium-sodium density data.
3.2 []
3,1 3 2.9 2.8 2.7 E
2.6 2.5
c
2.4 2.3 2.2 2.1 2 1.9 1.8
I
0
I
I
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[]
Metal Oxides
I
0.8
I
I
I
I
1.2
I
1.6 +
I
2
I
I
2.4
I
I
2.8
R Metal Carbonates
Fig. 6. Density model which assumes fractions of borate units are independent of the alkali present overlaid onto the lithium-rubidium density data,
B.C.L. Chang et al. / Density of two mixed alkali borate glass systems
111
2.4
+;t+~;+
2.3
+++
+Dr
,+~
+4-
+
+
2.2 E
#.
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I
1.6
Metal Oxides
I
2
I
I
2,4
I
I
2.8
3.2
R Metal Carbonates
+
Fig. 7. Density model which assumes fractions of borate units are dependent on the alkali present overlaid onto the lithium-sodium density data.
3.2 FI
r7
3.1 3
+
2.9 # 2.8
+
+
+
4-
+
2.7 E v
t~
2.6 2.5 2.4 2.3 2.2 2.1 2 1.9 1.8
I
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I
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0.4D
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I
0.8
I
I
I
I
1.2
I
1.6 +
I
2
I
J
2.4
I
I
2.8
R Metal Carbonates
Fig. 8. Density model which assumes fractions of borate units are dependent on the alkali present overlaid onto the lithium-rubidium density data.
112
B.C.L. Chong et al. / Density of two mixed alkali borate glass systems
Table 4 The packing fractions for the mixed alkali borates and relevant binary borates systems Borate system
Packingfractions for fl f2 f3
f4
f5
(a) Using the fractions frorn table 1 Li-Na 0.34 0.62 0.35 Li-Rb 0.34 0.55 0.36 Li 0.34 0.65 0.37 Na 0.35 0.57 0.34 Rb 0.34 0.52 0.38
0.38 0.40 0.38 0.37 a)
0.39 0.41 0.41 0.37 ~)
(b) Using the fractions of table 2 Li-Na 0.34 0.62 Li-Rb 0.34 0.63 Li 0.34 0.66 Na 0.35 0.58 Rb 0.34 0.55
a) a) ~) a) ")
a) a) a) a) a)
0.38 0.37 0.37 0.35 0.38
~) No data. ing and V, its associated volume. In eq. (1) the masses and fractions are known, leaving the volumes as unknowns. A least-squares analysis employing the density data (not including lithium-rubidium borate results from carbonate starting materials for R >/2.5) was performed [18] using eq. (1). The ratios of the volumes with respect to the V1 unit in boron oxide glass (R = 0) were obtained from this calculation. This analysis allowed all of the volume terms to vary throughout the glass forming range [18,19]. For the fractions given in table 1 the analysis was able to yield the volumes of all of the structural groupings. For the fractions given in table 2 only V1, V2 and V3 could be obtained since spectroscopic data terminate near R = 1. The resulting volumes from both analyses are reported in table 3. It is interesting to note that the volumes are not a strong function of the model used. Figures 5-8 depict the model calculations overlaid onto the data. In both mixed alkali borate systems the density trends and the fractions of the units change at very similar values of R. This is used as supporting evidence for the assumption of a simple relationship between structure and density. Thus, in both systems near R = 0.4 the density levels off signalling the growth of borate units containing non-bridging oxygens. Near R = 1 another change can be clearly seen; in the lithium-sodium case the density ends a decline and levels off whereas
in the lithium-rubidium system the density trend goes through a point of inflection. This is related to the growth of the f4 and f5 units (see figs. 5 and 7). It is important to note that in figs. 5 and 7 the corresponding changes in the model densities are caused by changes in the fractions and that these equations are inputs into the model and are not derived from the density data. 4.2. Volumes f r o m density model compared with volumes calculated f r o m ionic radii
The packing fraction p, is defined as P
volume of unit determined from ionic radii volumeof unit determined from density model "
(2)
The ionic radii used in the calculation were [3,4,20-22]: radius of boron = 0.19 ,~, radius of bridging or non-bridging oxygen bonded to three-coordinated boron = 1.19 A, radius of bridging oxygen bonded to four-coordinated boron = 1.28 A, radius of Li ion = 0.68 ,~, radius of Na ion = 0.97 A, radius of Rb ion = 1.47 ,~. The boron volume is negligible and was ignored in the calculation of the packing fractions. The calculation assumed hard spheres and ignored the empty space between the spheres for the volumes determined by ionic radii. However, the associated volumes determined from the density include empty space; hence the concept of a packing fraction is appropriate. The resulting packing fractions are given in table 4. It can be seen that the filling of space for a particular unit (characterized by fraction fi) is quite uniform and thus the variable which affects the absolute size of a given unit is the size of the alkali ion present. It seems clear that the mixed alkali borate glasses have structures which are quite similar to the binary cases. It is worthy of note that the packing fractions are not strongly influenced by the particular model used for the fractions of the borate units present in the glasses. The planar trigonal structures (ft, f3, f4, and fs) all have very similar packing fractions. This
B.C.L. Chong et al. / Density of two mixed alkali borate glass systems
indicates that such units fill space with equal efficiency independent of both the numbers of non-bridging oxygens in the unit and the type of alkali. The results given in table 4 indicate that the four-coordinated boron units use space in a more efficient way than the planar units. These remarks also applied to the binary borates [3,4].
5. Conclusions The densities of glasses in the lithium-sodium and lithium-rubidium borate systems have been measured over an extremely wide range of compositions. Lithium-sodium borate densities were found to be independent of carbon dioxide retention. However, some differences were found in the lithium-rubidium system at high alkali content. These density data were modelled semiempirically to relate the measurements to the atomic arrangement present in the glass. The densities are consistent with a view of the structure in which a constant b o r o n - o x y g e n framework is present independent of the alkali. Differences in density occur through a competition between the masses and volumes of the alkali ions. This result is similar to that found for the binary borate systems studied earlier [3,4]. This material is based upon work supported by the National Science Foundation under Grant No. DMR-8722901. Coe College is thanked for providing housing and other support to students working on this project. Ms. Peggy Knott is acknowledged for help in preparing the manuscript. H. Zhong and S. Koritalc are thanked for help with some of the measurements.
113
References [1] M. Shibata, C. Sanchez, H. PateL S. Feller, J. Stark, G. Sumcad and J. Kasper, J. Non-Cryst. Solids 85 (1986) 29. [2] A. Karki, S. Feller, H.P. Lim, J. Stark, C. Sanchez and M. Shibata, J. Non-Cryst. Solids. 92 (1987) 11. [3] H.P. kim, A. Karki, S. Feller, J. Kasper and G. Sumcad, J. Non-Cryst. Solids 91 (1987) 324. [4] H.C. Lim and S. Feller, J. Non-Cryst. Solids 94 (1987) 36. [5] J.O. lsard, J. Non-Cryst. Solids 1 (1969) 235. [6] D.E. I)ay, J. Non-Cryst. Solids 21 (1976) 343. [7] J.R. Hendrickson and P.J. Bray, Phys. Chem. Glasses 13 (1972) 43. [8] J.R. Hendrickson and P.J. Bray, Phys. Chem. Glasses 13 (1972) 107. [9] H. Jain, H.L. Downing and N.L. Peterson, J. Non-Cryst. Solids 64 (1984) 335. [10] J. Krogh-Moe, Phys. Chem. Glasses 3 (4) (1962) 101. [11] J. Krogh-Moe, Phys. Chem. Glasses 6 (2) (1965) 46. [12] D.L. Griscom, in: Materials Science Research, Vol. 12, eds. L.D. Pye, V.D. Frechette and N.J. Kreidl (Plenum, New York, 1978). [13] P.J. Bray and J.G. O'Keefe, Phys. Chem. Glasses 4 (1963) 37. [14] G.E. Jellison, Jr. and P.J. Bray, J. Non-Cryst. Solids 29 (1978) 187. [15] G.E. Jellison, Jr. PhD Thesis, Brown University (1977). [16] P.J. Bray, S.A. Feller, G.E. Jellison, Jr. and Y.H. Yun, J. Non-Cryst. Solids. 38 & 39 (1980) 93. [17] P.J. Bray, E.J. Holupka, J. Zhong, and R.V. Mulkern, private communication (1987). [18] B. Teoh, independent work at Coe College (1987). [19] O. Mathews, Honor's Project, Coe College (1988). [20] R.L. Mozzi and B.E. Warren, J. Appl. Cryst. 3 (1970) 251. [21] W.H. Zachariasen, Acta Cryst. 16 (1963) 385. [22] R. Weast, M. Astle and W. Beyer, Eds., Handbook of Chemistry and Physics, Vol. 66 (CRC, Boca Raton, Florida, 1985-1986) B-2. [23] E.J. Khaw, B.C.L Chong and K.H. Chong, independent work at Coe College (1987-1988).
105
THE DENSITY OF TWO MIXED ALKALI BORATE GLASS SYSTEMS ATOMIC ARRANGEMENTS
RELATED TO
B.C.U C H O N G 1, S.H. C H O O 2, S. F E L L E R , B. T E O H , O. M A T H E W S , E.J. K H A W , D. F E I L , K.H. C H O N G 3, M. A F F A T I G A T O , D. B A I N , K. H A Z E N a n d K. F A R O O Q U I Physics Department, Coe College, Cedar Rapids, Iowa 52402, USA
Received 21 October 1988 Revised manuscript received 10 January 1989
Densities of the two mixed alkali borate glass systems, R ( 12Na20 + ~Li 20). B203 and R (12Rb20 + ~2Li 20). B203, have been measured over an extremely wide range of alkali content: from boron oxide through the orthoborate composition. The glasses were prepared with metal carbonate and oxide starting materials. As with the binary alkali borates, a semiempirical model has been applied to the densities in order to determine the volumes of the structural units present. These values, in conjunction with volumes found in the binary borate cases, and with volumes calculated from the ionic radii, were used in a general discussion of the filling of space by the structural units. The results indicate that the size increases of the structural groupings as one goes from small to large alkali are primarily due to the alkali being used.
1. Introduction O v e r the p a s t few years the densities of the b i n a r y alkali b o r a t e glass systems have been syst e m a t i c a l l y m e a s u r e d over very wide ranges of alkali c o n t e n t [1-4]. T h e s e d a t a were a n a l y z e d in terms of a s e m i e m p i r i c a l m o d e l involving q u a n t i tative measures of the b o r a t e structures thought to b e p r e s e n t in the glasses [1-4]. T h e results revealed that the filling of space b y the structural units is essentially i n d e p e n d e n t of the alkali present in all the systems. T h e d e n s i t y trends c o u l d be e x p l a i n e d as a c o m p e t i t i o n b e t w e e n the masses a n d sizes of the various alkali ions p r e s e n t in the glasses within a c o n s t a n t b o r a t e structural b a c k ground. M u c h interest has b e e n g e n e r a t e d in recent y e a r s a b o u t m i x e d alkali b o r a t e glasses. F o r e x a m ple the electrical p r o p e r t i e s of these glasses have Present addresses: 1 Physics Department, Kansas State University, Manhattan, KS. 2 School of Actuarial Science, Temple University, Philadelphia, PA. 3 Computer Science Department, Kansas State University, Manhattan, KS. 0022-3093/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
b e e n e x a m i n e d extensively [5-9]. This p a p e r rep o r t s the densities of two representative m i x e d alkali b o r a t e glass systems, R ( ½ N a 2 0 + ½Li20 ) • B20 3 a n d R ( ½ R b 2 0 + ½Li20 )- B203, where R is the m o l a r r a t i o of a l k a h to b o r o n . T h e m e a s u r e m e n t s were taken over the e x t r e m e l y wide range of values for R f r o m 0 to 3 (0 to 75 mol% alkali). T h e resulting densities were then used in a semiempirical m o d e l d e s c r i b e d in the previous p a p e r s [1-4] in o r d e r to b e t t e r u n d e r s t a n d the a t o m i c a r r a n g e m e n t s present. The s e m i e m p i r i c a l m o d e l y i e l d e d the v a r i o u s volumes associated with the s t r u c t u r a l g r o u p i n g s thought to be in the glass. T h e v o l u m e s of these units were then c o m p a r e d with v o l u m e s c a l c u l a t e d using ionic radii b y f o r m i n g the ratio of the latter to the former. This r a t i o was d e f i n e d as the p a c k ing fraction.
2. Experimental method Samples were p r e p a r e d f r o m two sets of starting materials. F o r the c a r b o n a t e - b a s e d s a m p l e s of l i t h i u m - s o d i u m b o r a t e glasses, the m a t e r i a l s were lithiuim c a r b o n a t e , s o d i u m c a r b o n a t e , a n d b o r i c
B.C.L Chong et aL / Density of two mixed alkali borate glass systems
106
acid. In the lithium-rubidium borate glasses, rubidium carbonate was substituted for sodium carbonate. Using appropriate amounts of these chemicals, 4 g of starting material were thoroughly mixed in a platinum crucible. They were heated for 15 to 25 min at 1000°C under a flowing nitrogen atmosphere. Each sample was weighed 5 min before the end of the heating in order to verify sample composition. It is noted that weighing the sample allows one to determine the onset of carbon dioxide retention by the glass [3]. This is observed when the expected weight loss exceeds the actual weight loss. For the lithium-sodium borate system this occurred between R = 2 and R = 2.5; in the lithium-rubidium system CO 2 retention began between R = 1.4 and R =1.9. Samples also were prepared from the oxides of boron, lithium, sodium, and rubidium. Four-gram samples were mixed under argon and were heated at 1000°C for periods of 5 to 10 min with a weight check as before. The resulting melts were quickly cooled by splat quenching between two brass plates. Glassiness was determined visually and glasses were formed in both systems between R = 0 and R = 3.0. The mixed alkali borate systems displayed a
continuous glass-forming region unlike the binary sodium and rubidium borate systems which have a discontinuity near the metaborate composition (R = 1). All reported compositions are batch. The density was measured by a modified sinkfloat technique [3] using di-iodomethane and acetone. The modification, as described in ref. [3], consisted of bracketing the glass density with the fluid densities in order to avoid problems with the glass reacting with the density fluids. A conservative estimate of the experimental error is + 0.02 g / c m 3 except for high alkali content lithium-rubidium borate glasses (greater than R = 2). These latter glasses have an uncertainty in their density of ___0.03 g / c m 3 due to their reactivity with the density fluids.
3. Results
The density data for the lithium-sodium and lithium-rubidium borates are shown in figs. 1 and 2. The error limits shown are the values given above. In both cases, the densities of the mixed systems fall somewhat closer to the larger alkali borate system although they generally follow an
2.4-
t
+
+
2.3
+t -F
+
+~+~+
t+
+or
++~
++~R+,
2.2
E O~ v
2.1
1.9
1.~
I
0
I
I
0.4
[3
Metol Oxides
I
0.8
I
I
1.2
I
I
1.6 +
I
I
I"
2
I
2,4
I
I
2.8
I
3.2
R Metal Carbonotes
Fig. 1. The density of l i t h i u m - s o d i u m borate glasses as a function o f R (in all figures, R is defined as the ratio of alkali to boron).
B.C.L Chang et aL / Density of two mixed alkali borate glass systems
107
3.2 3.1
o
3
+ 4-
2.9
+
t;;;i + +
+
+
+ +
4=1= +
2.8
4+
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4-
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E 2.5
b
2.4 2.3
+
2.2 2.1
4-
2 1.9 1.8
i
i
i
i
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i
i
0.8
i
i
1.2
i
i
1.6
i
2
F
i
2.4
2.8
R (3
Metal Oxides
+
Metal Carbonates
Fig. 2. The density of lithium-rubidium borate glasses as a function of R.
2.4
0 0 0 ~ o ~ ÷+
T 0
O
O
O
0
I
+
<>
+$+¢+
+++
++~
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0
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2.2
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o%
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o+0 [] ¢ 1.9 o
1.8
0
1
2
3
R
0
Lithium
+
Ltth|um-~d|um
¢
Sodium
Fig. 3. The density of mixed lithium-sodium borate glasses compared with binary systems [1,2].
108
B . C . L Chong et al. / Density of two mixed alkali borate glass systems 3.2 +
3.1 Rubidium
0
3 +
¢
2.9
+ 2.8
+~:,
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l 0.4
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i
+
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i
i 1.6
i 2
R Lithium-Rubidium
Fig. 4. T h e d e n s i t y o f m i x e d l i t h i u m - r u b i d i u m
average functional behavior. This is shown explicitly in fig. 3 for the lithium-sodium borates and in fig. 4 for the lithium-rubidium borates. As can be seen in fig. 1 the densities of lithium-sodium borate glasses are not a function of starting material even when carbon dioxide is retained in the glass. However, lithium-rubidium borates show some deviation outside of the experimental error for values of R > 2.5 (see fig. 2). This region of composition has a value of R greater than that of the onset of carbon dioxide retention. Thus, carbonated glasses in this latter system show a small but real difference in density when compared with measurements of the glasses prepared from the oxides. These oxide glasses absorb some platinum from the crucible but not enough to account for the observed difference.
A model for the density of alkali borate glasses based on atomic arrangements has been used suc-
i 2.8
Rubidium
borate glasses compared with binary systems [1-3].
cessfully [1-4]. This representation is based on the ideas of Krogh-Moe and others in which the glass is viewed as a random assembly of certain fundamental structural groupings derived from crystalline configurations [10-12]. Nuclear magnetic resonance studies of Bray and O'Keefe [13], Jellison and Bray [14], Jellison [15], Bray et al. [16] among others have shown a
Table 1 T h e f r a c t i o n s o f b o r o n units [1] u s e d in a m o d e l for d e n s i t y in w h i c h f r a c t i o n s are i n d e p e n d e n t o f alkali t y p e 0.0 ~ R ~ 0.4
0.4 ~< R ~< 0.7
0.7 ~< R ~<1.0 1-R
fl
1-R
1-R
f2 f3 f4 f5
R 0 0 0
g/6+~ 5R/60 0
1.0 ~< R ~< 2.14
2.14 ~< R ~< 2.5
2.5 ~< R ~< 3.0
0 - R/4+5/8 - 0 . 5 5 R + 1.175 0.6(R --1) 0.2(R - 1 )
0 - R/4+5/8 0 - R/2+7/4 3R/4-11/8
0 0 0 3- R R -2
4. Discussion of the results 4.1. Models for the density data
0
i
fl fz f3 f4 f5
3I
-R4+ 5R/40 0
~ 58
B.C.L. Chong et al. / Density of two mixed alkali borate glass systems
close similarity in the structural arrangements present in the alkali borate glasses independent of the type of alkali. However, recent work by Bray et al. [17] indicates that the fractions of borons in various structural units depend on which alkali is present. Therefore, model calculations in this paper
109
Table 3 Associated volumes of structural groupings found in lithiumsodium and lithium-rubidium borate glasses compared with lithium, sodium, and rubidium borates Fractional Symbol
Relative volume of unit compared with boron with 3 bridging oxygens (at R = 0) Li-Rb
Li-Na
Rb
Na
Li
0.99 1.89 2.30 a) a~
0.96 1.19 1.65 2.15 2.80
0.98 0.91 1.32 1.69 1.95
0.98 1.76 2.29
0.95 1.17 1.62
0.98 0.91 1.32
(a) Using the fractions from table 1 Table 2 The fractions of the boron units [17] used in a model for density in which the fractions are a function of the alkali L i - N a borate system
fl f2 f3 f4 f5
0.0 ~< R ~< 0.28
0.28 ~< R ~<0.61
0.61 ~< R ~<1.0
1-R 0.853 R 0.147 R 0 0
1-R 0.342 R +0.197 0.658 R -0.197 0 0
1-R -0.439 R +0.625 1.439 R -0.625 0 0
0.0 ~< R ~<0.33
0.33 ~
0.50 ~< R ~<1.0
fl
1-R
f2
2 R/3 R/3
1-R 0.42 R +0.08 0.58 R - 0 . 0 8 0 0
1-R - 0 . 1 6 R +0.37 1.16 R - 0 . 3 7 0 0
0.0 ~< R ~<0.4
0.4 ~
0.7~< R ~<1.0
1-R R 0 0 0
1-R 0.167R +0.333 0.833 R -0.333 0 0
1-R - 0 . 2 5 R +0.625 1.25R -0.625 0 0
0.0 ~< R ~< 0.335
0.335 ~< R ~< 0.75
0.75 ~< R ~<1.0
1-R 0.862 R 0.138 R 0 0
1-R 0.173 R +0.288 0.827R -0.288 0 0
1-R -0.362 R +0.664 1.362 R -0.664 0 0
0.0~
0.348~
0.716~
1-R 0.685 R 0.315 R 0 0
1-R 0.16 R +0.227 0.84 R -0.227 0 0
1-R -0.243 R +0.478 1.243 R -0.478 0 0
0 0
Li borate system
fl f2 f3 f4 f5
N a borate system
fl f2 f3 f4 f5
Rb borate system
fl f2 f3 f4 f5
0.98 1.42 1.86 2.53 3.28
0.98 1.03 1.49 1.87 2.35
(b) Using the fractions from table 2 fl f2 f3
0.98 1.24 1.81
0.97 1.02 1.38
f4
a)
a)
a)
a)
a)
f5
a)
a)
a)
a~
a)
a) No data.
L i - R b borate system
f3 f4 f5
fl f2 f3 f4 f5
were done using both hypotheses regarding the dependence of the borate units on the alkali ions. In either case, the following configurations were used in the density models (notations for the fractions of borons in each structural unit are given in parentheses): (1) boron with three bridging oxygens (f~); (2) boron with four bridging oxygens and one alkali ion ( f 2 ) ; (3) boron with two bridging and one non-bridging oxygen and one alkali ion (f3); (4) boron with one bridging and two non-bridging oxygens and two alkali ions (f4); (5) boron with three non-bridging oxygens and three alkali ions (fs)Table 1 lists the fractions used for the case where the equations were assumed to be independent of the alkali present [1-4]. Table 2 gives the fractions for the case where the equations were a function of alkali [17]. The following equation is used for the glass density [2], p: p=
faMl + f2M2 + f 3 M 3 + f4M4 + fsM5 flV1 + f2V2 + f3V3 -4- f4V4 + fsV~
(1)
where M, is the mass of the ith structural group-
110
B.C.L. Chong et aL / Density of two mixed alkali borate glass systems 2.4
2.3
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2.1
v
c
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I
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f
0,¢ []
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I
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Metal Oxides
I
2
I
t
2.¢
I
I
2.8
3.2
R Metal Carbonates
+
Fig. 5. Density model which assumes fractions of borate units are independent of the alkali present overlaid onto the lithium-sodium density data.
3.2 []
3,1 3 2.9 2.8 2.7 E
2.6 2.5
c
2.4 2.3 2.2 2.1 2 1.9 1.8
I
0
I
I
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[]
Metal Oxides
I
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I
I
I
I
1.2
I
1.6 +
I
2
I
I
2.4
I
I
2.8
R Metal Carbonates
Fig. 6. Density model which assumes fractions of borate units are independent of the alkali present overlaid onto the lithium-rubidium density data,
B.C.L. Chang et al. / Density of two mixed alkali borate glass systems
111
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+;t+~;+
2.3
+++
+Dr
,+~
+4-
+
+
2.2 E
#.
07
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I
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Metal Oxides
I
2
I
I
2,4
I
I
2.8
3.2
R Metal Carbonates
+
Fig. 7. Density model which assumes fractions of borate units are dependent on the alkali present overlaid onto the lithium-sodium density data.
3.2 FI
r7
3.1 3
+
2.9 # 2.8
+
+
+
4-
+
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t~
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0.4D
Metal Oxides
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I
I
I
I
1.2
I
1.6 +
I
2
I
J
2.4
I
I
2.8
R Metal Carbonates
Fig. 8. Density model which assumes fractions of borate units are dependent on the alkali present overlaid onto the lithium-rubidium density data.
112
B.C.L. Chong et al. / Density of two mixed alkali borate glass systems
Table 4 The packing fractions for the mixed alkali borates and relevant binary borates systems Borate system
Packingfractions for fl f2 f3
f4
f5
(a) Using the fractions frorn table 1 Li-Na 0.34 0.62 0.35 Li-Rb 0.34 0.55 0.36 Li 0.34 0.65 0.37 Na 0.35 0.57 0.34 Rb 0.34 0.52 0.38
0.38 0.40 0.38 0.37 a)
0.39 0.41 0.41 0.37 ~)
(b) Using the fractions of table 2 Li-Na 0.34 0.62 Li-Rb 0.34 0.63 Li 0.34 0.66 Na 0.35 0.58 Rb 0.34 0.55
a) a) ~) a) ")
a) a) a) a) a)
0.38 0.37 0.37 0.35 0.38
~) No data. ing and V, its associated volume. In eq. (1) the masses and fractions are known, leaving the volumes as unknowns. A least-squares analysis employing the density data (not including lithium-rubidium borate results from carbonate starting materials for R >/2.5) was performed [18] using eq. (1). The ratios of the volumes with respect to the V1 unit in boron oxide glass (R = 0) were obtained from this calculation. This analysis allowed all of the volume terms to vary throughout the glass forming range [18,19]. For the fractions given in table 1 the analysis was able to yield the volumes of all of the structural groupings. For the fractions given in table 2 only V1, V2 and V3 could be obtained since spectroscopic data terminate near R = 1. The resulting volumes from both analyses are reported in table 3. It is interesting to note that the volumes are not a strong function of the model used. Figures 5-8 depict the model calculations overlaid onto the data. In both mixed alkali borate systems the density trends and the fractions of the units change at very similar values of R. This is used as supporting evidence for the assumption of a simple relationship between structure and density. Thus, in both systems near R = 0.4 the density levels off signalling the growth of borate units containing non-bridging oxygens. Near R = 1 another change can be clearly seen; in the lithium-sodium case the density ends a decline and levels off whereas
in the lithium-rubidium system the density trend goes through a point of inflection. This is related to the growth of the f4 and f5 units (see figs. 5 and 7). It is important to note that in figs. 5 and 7 the corresponding changes in the model densities are caused by changes in the fractions and that these equations are inputs into the model and are not derived from the density data. 4.2. Volumes f r o m density model compared with volumes calculated f r o m ionic radii
The packing fraction p, is defined as P
volume of unit determined from ionic radii volumeof unit determined from density model "
(2)
The ionic radii used in the calculation were [3,4,20-22]: radius of boron = 0.19 ,~, radius of bridging or non-bridging oxygen bonded to three-coordinated boron = 1.19 A, radius of bridging oxygen bonded to four-coordinated boron = 1.28 A, radius of Li ion = 0.68 ,~, radius of Na ion = 0.97 A, radius of Rb ion = 1.47 ,~. The boron volume is negligible and was ignored in the calculation of the packing fractions. The calculation assumed hard spheres and ignored the empty space between the spheres for the volumes determined by ionic radii. However, the associated volumes determined from the density include empty space; hence the concept of a packing fraction is appropriate. The resulting packing fractions are given in table 4. It can be seen that the filling of space for a particular unit (characterized by fraction fi) is quite uniform and thus the variable which affects the absolute size of a given unit is the size of the alkali ion present. It seems clear that the mixed alkali borate glasses have structures which are quite similar to the binary cases. It is worthy of note that the packing fractions are not strongly influenced by the particular model used for the fractions of the borate units present in the glasses. The planar trigonal structures (ft, f3, f4, and fs) all have very similar packing fractions. This
B.C.L. Chong et al. / Density of two mixed alkali borate glass systems
indicates that such units fill space with equal efficiency independent of both the numbers of non-bridging oxygens in the unit and the type of alkali. The results given in table 4 indicate that the four-coordinated boron units use space in a more efficient way than the planar units. These remarks also applied to the binary borates [3,4].
5. Conclusions The densities of glasses in the lithium-sodium and lithium-rubidium borate systems have been measured over an extremely wide range of compositions. Lithium-sodium borate densities were found to be independent of carbon dioxide retention. However, some differences were found in the lithium-rubidium system at high alkali content. These density data were modelled semiempirically to relate the measurements to the atomic arrangement present in the glass. The densities are consistent with a view of the structure in which a constant b o r o n - o x y g e n framework is present independent of the alkali. Differences in density occur through a competition between the masses and volumes of the alkali ions. This result is similar to that found for the binary borate systems studied earlier [3,4]. This material is based upon work supported by the National Science Foundation under Grant No. DMR-8722901. Coe College is thanked for providing housing and other support to students working on this project. Ms. Peggy Knott is acknowledged for help in preparing the manuscript. H. Zhong and S. Koritalc are thanked for help with some of the measurements.
113
References [1] M. Shibata, C. Sanchez, H. PateL S. Feller, J. Stark, G. Sumcad and J. Kasper, J. Non-Cryst. Solids 85 (1986) 29. [2] A. Karki, S. Feller, H.P. Lim, J. Stark, C. Sanchez and M. Shibata, J. Non-Cryst. Solids. 92 (1987) 11. [3] H.P. kim, A. Karki, S. Feller, J. Kasper and G. Sumcad, J. Non-Cryst. Solids 91 (1987) 324. [4] H.C. Lim and S. Feller, J. Non-Cryst. Solids 94 (1987) 36. [5] J.O. lsard, J. Non-Cryst. Solids 1 (1969) 235. [6] D.E. I)ay, J. Non-Cryst. Solids 21 (1976) 343. [7] J.R. Hendrickson and P.J. Bray, Phys. Chem. Glasses 13 (1972) 43. [8] J.R. Hendrickson and P.J. Bray, Phys. Chem. Glasses 13 (1972) 107. [9] H. Jain, H.L. Downing and N.L. Peterson, J. Non-Cryst. Solids 64 (1984) 335. [10] J. Krogh-Moe, Phys. Chem. Glasses 3 (4) (1962) 101. [11] J. Krogh-Moe, Phys. Chem. Glasses 6 (2) (1965) 46. [12] D.L. Griscom, in: Materials Science Research, Vol. 12, eds. L.D. Pye, V.D. Frechette and N.J. Kreidl (Plenum, New York, 1978). [13] P.J. Bray and J.G. O'Keefe, Phys. Chem. Glasses 4 (1963) 37. [14] G.E. Jellison, Jr. and P.J. Bray, J. Non-Cryst. Solids 29 (1978) 187. [15] G.E. Jellison, Jr. PhD Thesis, Brown University (1977). [16] P.J. Bray, S.A. Feller, G.E. Jellison, Jr. and Y.H. Yun, J. Non-Cryst. Solids. 38 & 39 (1980) 93. [17] P.J. Bray, E.J. Holupka, J. Zhong, and R.V. Mulkern, private communication (1987). [18] B. Teoh, independent work at Coe College (1987). [19] O. Mathews, Honor's Project, Coe College (1988). [20] R.L. Mozzi and B.E. Warren, J. Appl. Cryst. 3 (1970) 251. [21] W.H. Zachariasen, Acta Cryst. 16 (1963) 385. [22] R. Weast, M. Astle and W. Beyer, Eds., Handbook of Chemistry and Physics, Vol. 66 (CRC, Boca Raton, Florida, 1985-1986) B-2. [23] E.J. Khaw, B.C.L Chong and K.H. Chong, independent work at Coe College (1987-1988).