The Structure of Materials
1.2 STRUCTURE OF CERAMICS AND GLASSES
1.2.4 The Structure of Glasses*
b axis c
axis
OH OH
OH OH
O O
O O O
O b = 95½°
~9.94 Å
2 K 6 O
6 O 4 Al 3 Si + Al
3 Si + Al 2 (OH) + 4 O
2 (OH) + 4 O O
O
Figure 1.46 The structure of muscovite (mica), a sheet silicate. Reprinted, by permission, from L. G. Berry, B. Mason, and R. V. Dietrich,Mineralogy: concepts, descriptions, determinations, p. 431, 2nd ed. Copyright1983 by Freeman Publishing, Inc.
1.2.3.3 Silicate Chains and Rings. Sharing two out of the four corners of the SiO4 tetrahedra results in chains. The angle formed between adjacent tetrahedra can vary widely, resulting in unique structures such as rings (see Figure 1.47). In all cases, when only two corners are shared, the repeat unit is (SiO3)2−, and the O/Si is 3.0.
Slight variations in the O/Si ratio can also take place, and result in partially networked structures such as double chains, in which two silicate chains are connected periodically by a bridging oxygen.Asbestos is such a double chain, with O/Si=2.75.
1.2.3.4 Pyrosilicates. One corner of the SiO4 tetrahedron shared results in a (Si2O7)6− repeat unit and a class of compounds called the pyrosilicates. Again, counterions are necessary to maintain charge neutrality. The pyrosilicates are non- networked and have an O/Si of 3.5.
1.2.3.5 Orthosilicates. Finally, no tetrahedral corners shared gives an O/Si of 4.0, and it results in isolated (SiO4)4− tetrahedra. These class of materials are referred to as theorthosilicates.
STRUCTURE OF CERAMICS AND GLASSES 65
Figure 1.47 A silicate ring, beryl, with two corners of the SiO4 tetrahedra shared. From K. M. Ralls, T. H. Courtney, and J. Wulff,Introduction to Materials Science and Engineering.
Copyright 1976 by John Wiley & Sons, Inc. This material is used by permission of John Wiley & Sons, Inc.
Before proceeding further with a description of the structural aspects of glasses, it is advisable to be aware of some pitfalls in nomenclature that abound in the area of glass science. Technically, a glass is a type of noncrystalline solid that is formed from the melt. Thus, a glass need not contain silicon or oxygen at all, but it does need to be obtained by cooling a substance from the molten state. The distinction in processing condition is necessary to distinguish glasses from other types of amorphous materials that also do not contain a regular, repeating structure, but that are formed through other processing routes, such as from the vapor phase, in which case they are calledamorphous solids, or by dehydrating asol to form a gel. These distinctions are summarized in Figure 1.49. We will describe some of these processing techniques in later chapters, but for now we simply note that glasses must technically be formed from the melt and that there are no restrictions on the chemical constituents of a glass.
Additional characteristics of glasses that are sometimes described in the glass litera- ture include a rigid material, a glass transition,Tg, (see Section 1.3.7), and a viscosity greater than about 1015 poise. The viscosity distinction is an important one, since some consider a glass to be a liquid of high viscosity. Finally, the term vitreous is sometimes used in connection with glasses. This term is usually reserved for glassy materials that can be crystallized through proper heat treatment in a process known as devitrification.
The distinction between an amorphous material and a glass is an important one.
For example, an SiO2 glass prepared from the melt has a noticeably different X- ray diffraction pattern than a solid SiO2 gel derived from dehydration of a solution (see Figure 1.50). In both cases, the glass and gel have no long-range order in comparison to cristobalite, which is highly crystalline and exhibits distinct X-ray diffraction lines. The increase in the intensity of the gel pattern at small angles
Si4+ O2− Na+
Figure 1.48 Schematic representation of a random network sodium silicate glass. From W. D. Kingery, H. K. Bowen, and D. R. Uhlmann,Introduction to Ceramics. Copyright1976 by John Wiley & Sons, Inc. This material is used by permission of John Wiley & Sons, Inc.
HISTORICAL HIGHLIGHT Some historians credit the added illumina-
tion made possible by glass with heightening interest in cleanliness and hygiene. Windows made dirt more visible. And thanks to supe- rior mirrors — made with transparent glass that reflected properly from the thin men- tal foil on one side— people could see and understand themselves and their conditions more accurately than ever before; glass, a miraculous substance that is at once as solid
as a rock and as invisible as air, shed as much light on people’s minds as on their surround- ings. Moreover, the magnifying powers of glass eventually enlightened scientist as well, enabling them to understand what it is inside of materials that makes the stuff of the world the way it is.
Source: Reprinted, by permission, from I. Am- ato,Stuff, p. 32. Copyright1997 by Harper Collins Publishers, Inc.
is due to microporous structures that result from the removal of water during dry- ing—inhomogeneities that are not present in the silica glass. Both the glass and the gel do possessshort-range order, however, as indicated by the broad peak centered at ad-spacing of about 0.12 nm. This short-range order is attributed chiefly to the SiO4
tetrahedral structural unit present in all silicates.
STRUCTURE OF CERAMICS AND GLASSES 67
Amorphous precipitation
Amorphous solid Disturbed short-range order
Amorphous powder
Glass
Crystal
Dehydrated
gel Amorphous
Glassy
Crystalline Large surface
EvaporationEvaporation Shearing
Energy Radiation Pulverizing
Melt Solution
Figure 1.49 Comparison of preparation procedures of noncrystalline solids illustrating the difference between glassy and amorphous solids. Reprinted, by permission, from H. Scholze, Glass, p. 123. Copyright1991 by Springer-Verlag.
Intensity
SiO2 glass
SiO2 gel Cristobalite
0 0.04 0.08 0.12 0.16 0.20 0.24 0.28 sin q/l
Figure 1.50 X-ray diffraction patterns of vitreous silicon, crystalline silica (cristobalite), and sol – gel-derived silica. Reprinted, by permission from H. Scholze, Glass, p. 97. Copyright 1991 by Springer-Verlag.
Though it may seem nonsensical to obtain X-ray diffraction patterns from mate- rials that have no long-range structure (i.e., crystallinity) since there is no spacing between crystal planes, the X-ray pattern provides additional information that is useful in analyzing the structure of glasses. Even though the peaks in an amorphous pattern are broad, we can extract additional information using something called the radial distribution function (rdf):
rdf=4π r2n0g(r) (1.38) whereg(r)is thepair distribution functionbetween adjacent atoms—that is, the proba- bility of finding another atom a distancerfrom the reference atom located atr =0. The pair distribution function is determined from various diffraction experiments (electron, neutron, X ray). The quantityn0 in Eq. (1.38) is the average number density=N /V. If we plot rdf versus r, we obtain a curve similar to the one shown in Figure 1.51.
The dotted line represents the parabola 4π r2, and deviations from the dotted line indi- cate regions of greater probability for finding an atom. The “peaks,” then, correspond to likely bond distances as indicated: Si–O, O–O, and Si–Si. The radial distribution function is useful for characterizing not only glasses, but liquids and polymers as well.
So, we have seen that glasses have short-range structure, but no long-range structure, at least relative to the wavelength of the probing X rays. But can we predict, or at least rationalize, which compounds will form glasses readily, and which ones will not? The answer is, “Yes.” Once again, there are several sets of “rules,” or guidelines, for describing the ability of certain cation/anion pairs to form glassy compounds. We will look at three such sets of guidelines, and you should recognize some of their components from earlier guidelines, such as Pauling’s rules and the Hume–Rothery rules. Although we know that glasses by definition may consist of any types of cations and anions, oxide glasses are by far the most common and industrially most important.
We will limit our discussion to oxide glasses for the moment.
Radial electron density
nm r
0 0.2 0.4 0.6
Si – O O – O Si – Si
Figure 1.51 Radial distribution of electron densities of vitreous silica from X-ray exposures (Scholze). Reprinted, by permission, from Scholze, H., Glass, p. 98. Copyright 1991 by Springer-Verlag.
STRUCTURE OF CERAMICS AND GLASSES 69
1.2.4.1 Zachariasen Rules. In 1932, W. H. Zachariasen considered the conditions for constructing a random network like the one shown in Figure 1.48 and proposed four rules for the formation of oxide glasses:
ž An anion (oxygen atom) is linked to not more than two glass-forming cations (metal atoms).
ž The coordination numbers of the glass-forming atoms (cations) is small, four or less.
ž The oxygen polyhedra (structural units) share corners with each other, not edges or faces.
ž The polyhedra are linked in a 3-D network (at least three corners of each polyhedra should be shared).
The “structural polyhedra” are those that we have already been using: triangles, tetrahedra, and octahedra. Zachariasen’s rules, as supported and modified by Warren, came to be known as the random network theory and, despite its limitations, is still widely used.
1.2.4.2 Stanworth Rules. In the late 1940s and early 1950s, Stanworth proposed a set of much simpler guidelines that did not rely on the formation of polyhedra. He suggested that the primary criteria for glass formation in metal oxide glasses were
ž A cation valence≥3
ž An increasing tendency for glass formation with decreasing cation size
ž A cation electronegativity between 1.5 and 2.1
Based on what we already know, there is circumstantial evidence to support these guidelines. For example, using the electronegativity values in Table 1.4, we see that two well-known glass-forming metal oxides B2O3and SiO2meet the electronegativity criterion (χB=2.04, χSi=1.90), whereas Na2O does not (χNa=0.93). Similarly, both B3+ and Si4+ have valencies greater than or equal to three, and they have relatively small cation sizes (0.2 and 0.39 ˚A, respectively) in comparison to other 3+valence, non-network-forming cations like Co and Fe (0.65 and 0.67 ˚A, respectively).
1.2.4.3 Oxide Glass Cations. Perhaps the single most useful guideline is a table (Table 1.18) that classifies cations into three categories: glass formers, intermediates, and modifiers. These classifications are actually an extension of the random network model, but also include some of Stanworth’s guidelines. Glass formers are cations with a valence greater than or equal to three (this is a Stanworth rule) and a coordination number less than four (a Zachariasen rule). Note that there are many more glass- forming cations than just silicon. Intermediates are cations of lower valence and higher coordination number that can sometimes act as glass formers (such as aluminum), but can also act as network modifiers. A network modifier is a cation that serves to interrupt the random, glass network, partly by being of high enough valence to provide additional oxygen to the network, thereby increasing the oxygen-to-metal atom ratio and destroying the network (see Table 1.17). Note that some cations can be in several categories, such as Pb, which can have multiple oxidation states. We know that leaded- glass exists for such important applications as television screens, but the role of lead can be that of either an intermediate or a network modifier. Sodium is a well-known
Table 1.18 Coordination Number and Bond Strength of Oxides
M in
MOx Valence
Dissociation Energy per MOx
(kcal/g-atom)∗
Coordination Number
Single-Bond Strength (kcal/g-atom)∗
Glass formers B 3 356 3 119
Si 4 424 4 106
Ge 4 431 4 108
Al 3 402–317 4 101–79
B 3 356 4 89
P 5 442 4 111–88
V 5 449 4 112–90
As 5 349 4 87–70
Sb 5 339 4 85–68
Zr 4 485 6 81
Intermediates Ti 4 435 6 73
Zn 2 144 2 72
Pb 2 145 2 73
Al 3 317–402 6 53–67
Th 4 516 8 64
Be 2 250 4 63
Zr 4 485 8 61
Cd 2 119 2 60
Modifiers Sc 3 362 6 60
La 3 406 7 58
Y 3 399 8 50
Sn 4 278 6 46
Ga 3 267 6 45
In 3 259 6 43
Th 4 516 12 43
Pb 4 232 6 39
Mg 2 222 6 37
Li 1 144 4 36
Pb 2 145 4 36
Zn 2 144 4 36
Ba 2 260 8 33
Ca 2 257 8 32
Sr 2 256 8 32
Cd 2 119 4 30
Na 1 120 6 20
Cd 2 119 6 20
K 1 115 9 13
Rb 1 115 10 12
Hg 2 68 6 11
Cs 1 114 12 10
∗Multiply by 4.184 to obtain units of kJ/mol.
Source: W. D. Kingery, H. K. Bowen, and D. R. Uhlmann;Introduction to Ceramics. Copyright1976 by John Wiley
& Sons, Inc.
network modifier and is added to sand (quartz) in the form of Na2O to form sodium silicates, which constitute a large class of glasses and, in the aqueous solution form, a large class of adhesives.