"Glass is being used worldwide and has various applications. It is widely used in Buildings and having Industrial applications. The presence of glasses in our everyday environment is so common that we rarely notice their existence. Earlier Egyptians considered glasses as precious materials, as evidenced by the glass beads found in the tombs and holy places. Humans have been producing glasses by melting of raw materials for thousands of years.
The present book covers different important parameters of glass technology. The book is comprehensive guide for researchers, technologists, new entrepreneurs and professionals.
Glass
1. Definition and Historical Summary
Most of us have
stood at one time or another in awe in front of glass-covered
skyscrapers, rose windows of medieval cathedrals, or mosaics in
Byzantine churches, wondering about glass, transparent or opaque,
multicolored or colorless, harder than steel and yet fragile to impact.
The nature of glass, its preparation, and its uses form the subject of
this article.
Many molten
materials do not crystallize to their parent crystalline phases once
the thermodynamic melting temperature Tm is passed on
cooling. Such melts easily supercool to a temperature far below Tm and congeal to
solids without any attendant discontinuous changes in volume or
entropy. These solids, which are isotropic in all their properties, are
known as glass.
A common
misconception is that all glass has the same composition. A variety of
organic and inorganic materials can form glass, and most of those that
do exhibit a moderately sharp transition into the glassy state from the
liquid.
The canonical
definition of the term glass is that by Morey: “Glass is an inorganic
substance in a condition which is continuous with, and analogous to,
the liquid state of that substance but which, as the result of a
reversible change in viscosity during cooling, has attained so high a
degree of viscosity as to be, for all practical purposes, rigid.”
Similarly, the Astm
defines glass as “an inorganic product of fusion that has cooled to a
rigid condition without crystallizing.”
Ease of glass
formation is almost entirely a kinetic question. At no temperature is
glass an equilibrium phase, although glasses
hundreds of millions of years old are not uncommon in
nature. The cooling rate required to form a glass varies with
composition. Some melts (e.g., those of Sio2 or B2O3) can form a
glass at very slow rates of cooling, whereas mixed nitrates of
potassium and calcium or sulfates of potassium and zinc, for instance,
require rapid cooling from their normal melting temperature to form
glass. Glassy metals have become quite common with the advent of rapid
(splat) cooling techniques, the easiest to form having the approximate
formula MxLy, where M is a
transition metal: L is Si, P, C, B, or Ge; x=0.7-0.8; and
y=0.3-0.2. Glasses can even be made from melts of metals such as iron
and cobalt, but still higher quench rates are required than those for
metal-metalloid glasses. Almost any inorganic melt can apparently be
quenched into a glass with a sufficiently fast quenching rate.
Glass is not
merely a supercooled liquid. The distinction between a supercooled
liquid and a glass lies in the ability of structural elements in the
former to rearrange themselves in accordance with the thermodynamic
state of the system, whereas in the latter such rearrangement is not
possible. This inhibition of rearrangement in glass is caused by the
large increase in viscosity on cooling and gives rise to an endothermic
effect on heating, which occurs at the glass transition temperature
(i.e., the temperature above which structural elements in the glass are
sufficiently mobile to rearrange themselves according to their
equilibrium configuration).
The discoverer
of glass manufacture will probably remain unknown. A source of
inspiration may have been the abundant occurrence of glasses in nature.
Obsidian, pumice (a natural foam glass), and tektites (glassy bodies
probably of meteoric origin) are examples of naturally occurring glass.
2. Structure of Glass
Methodology in
condensed-matter physics and chemistry consists of identifying and
relating the physical properties, structure, and constituent elements
of a class of materials. For crystalline solids, the constituents and
structure can be characterized readily. In glass, on the other hand,
understanding of the structure consists almost exclusively of negative
statements: no metric geometry, trivial space group, no Bloch states,
no single ground state, no unique best structure. In addition, the
topology of glass structure is amenable only to indirect experimental
investigation.
It is not
surprising in light of the undetermined nature of the amorphous state
of glass that competing perceptions exist with regard to its character.
The principal difficulty in distinguishing between models has been the
small amount of energy associated with long-range ordering. For
instance, the enthalpy of formation of quartz from silicon and oxygen
at 298 K is -860 Kj/mol: this is only 12 KJ/mol more negative
than that for fused silica (-848kj/mol). Only 1% of the enthalpy of
formation of quartz is therefore associated with long-range ordering.
The two predominant structural models for glass are the
microcrystallite and the random network hypotheses.
Microcrystallite
Hypothesis. The
microcrystallite "cybotactic group" hypothesis was constructed
primarily to account for the discontinuous changes in the properties of
glasses, which can be correlated with similar discontinuities in the
properties of associated crystalline phases. Proponents of this
hypothesis were (with some) rare exceptions such as STEWART and RANDALL
almost exclusively Russian, the first being FRANKENHEIM and
subsequently von
WEIMARN who held that all matter in any state, be that gas, liquid, or
solid is crystalline. This work was followed up by LEBEDEFF who showed
that vitreous amorphous silica varies considerably between 540 and 6000 C in its double
refraction, refractive index, and coefficient of expansion. He inferred
that this variation was due to a polymorphic transformation assumed to
be connected with the low-high temperature transformation of quartz,
which occurs at 5750 C. He
furthermore suggested that vitreous silica consists of an aggregate of
very minute crystals with included quartz crystals that are probably
not in a pure state, but in the form of a solid solution with other
substances, hence accounting for the temperature range over which the
polymorphic transition occurs. Valenkov and Poray-Koshitz analyzed the
X-ray diffraction curves of glasses and concluded that the observed
diffraction patterns were produced by 0.75-2.5-nm crystallites that
were connected to each other by an amorphous layer. These results made
the microcrystallite postulate questionable because 2.5nm crystallites
do not represent long-range ordering in a crystallographic sense.
Refinement of diffraction experiments, particularly at
small angles, has invalidated the original
microcrystallite hypothesis. Recent electron microscopy results, on the
other hand, indicate that multicomponent glasses can be chemically
inhomogeneous, and contain microheterogeneities, which could be taken
to represent microcrystallites.
Random Network
Hypothesis. The
Zernike-Prins-Bernal-Fowler Warren hypothesis considers the liquid a
system of atomic or ionic networks, designated as a random network. For
glasses this implies a rigid system of continuous noncrystalline
networks similar to those assumed to be present in the liquid. It
remains open to debate whether there is one unique random network or
ten thousand or what random really means in the context of liquid
structures. The hypothesis was successful in providing qualitative
explanations for the glass-forming tendency of simple glass-forming
systems as being caused by a rapid increase in viscosity during cooling
of the melt. In addition successful predictions could be made about
potential glass-forming systems as well as rationalizations for most of
property composition relationships. Zachariasen postulated
glass-forming tendencies for simple oxides based on random networks and
the concomitant need for flexibility in linkages. These postulates, in
part already phrased by Gold-Schmidt are the following:
1. Each oxygen atom can be
linked to no more than two cations; the number of oxygen atoms around
any one cation must be small. i.e. three or four; the oxygen polyhedra
must share corners, not edges or faces, to form a three-dimensional
network; at least three corners must be shared.
2. Network formers have a coordination
number of 3 or 4 (Si,B,P,Ge, As, Be, etc.): network modifiers have
coordination numbers greater than or equal to 6 (Na, K, Ca, Ba, etc.).
Intermediate atoms with a variable coordination number between 4 and 6
(Li, Al, Mg, Zn, Pb, Nb, Ta, etc.) can function as network modifiers as
well as network formers; the coordination change is a reflection of
their amphoteric character, i.e., solubility in both inorganic acids
and bases.
Additional
refinements have been made to the random network theory. Dietzel
introduced the concept of cationic
field strength defined as formal cation charge divided by the cation-
anion distance. This concept enables a quantifiable distinction to be
made between the three categories of atoms;
1.
Network formers with a field strength of 1.4-2 N/M.
2. Network modifiers with a field
strength of 0.1- 0.4 N/M and
3. Amphoteric atoms with a field
strength of 0.5-1.0
N/M.
Glass formation
is favored if the difference in field strength between the cations is
larger than 0.3. Smekal expanded on the cationic field strength concept
by taking the bond polarity into account. Glass formation is favored if
mixed bonding with a homopolar and heteropolar component occurs. Weyl
postulated the screening theory used to explain the mechanical
properties of glasses. In this theory the polymerization of polyhedra
to three-dimensional random networks is caused by the polarization and
deformation of residual valence forces. Stevels developed a theory for
invert glasses, which contain polyhedra with less than three connected
corners in contradiction to the Zachariassen postulates. His structural
parameter Y is a measure of the average number of bridging anions. The
properties of the glass are mainly determined by the network modifier
atoms when Y is smaller than 2. This is due to the fact that these
network modifiers compete for the available anions, thus resulting in
an increased degree of disorder.
Among the less
fruitful extensions of the random network theory are those by Huggins
and Tilton. Huggins attempted to explain known discontinuities in
properties by assuming the presence of fixed atom groups, called
structons. A last refinement of the network hypothesis represents the
work by Tilton who postulated the presence of vitrons: aggregates of
silica tetrahedra primarily consisting of five-membered rings, which
combined to form a pentagondodecahedron consisting of 20 tetrahedra.
These vitrons would be connected to one another by less ordered domains.
With the advent
of NMR, laser Raman Spectroscopy, and extended X-ray absorption fine
structure (EXAFS), focus has been directed to dissecting glass
structure in terms of local environments, avoiding any deterministic
statements regarding extended structures. A current area of research
involves determining the extent to which long-range structural elements
can be derived from such local environments.
Structure of Special Melts and Glasses
Almost all
industrially manufactured glasses are silicate glasses. As a
consequence, these system are emphasized in the following discussion,
the goal being to provide a terminus a quo rather than a terminus ad
quem for the study of amorphous materials. The viscosity of various
silica-containing melts is used as a reference against which structural
concepts can be matched. The use of viscosity is somewhat ironic,
however; although viscosity illustrates nicely the role of
network-forming atoms in comparison with network-modifying atoms, it is
the least understood property of melts or glasses. The structural
description of glasses and melts is based on Q (quartz) distribution
theory and Q designation. The use of this model enables description of
silica species in both solids and aqueous solution in terms of the
distribution of local silicon environments, which are amenable to
investigation by NMR. These designations are as follows:
1. Each silicon atom is
coordinated tetrahedrally to four oxygen atoms.
2. If all oxygen atoms in a
tetrahedron are connected to two silicon atoms, the local environment
around the silicon atom is designated Q4. All four Si-O bonds of the
tetrahedron are, therefore, bridging bonds, designated Si-O (br).
3. The local silicon
environments are designated Q3, Q2, Q1, and Q0 if three, two, one, or zero oxygen
atoms are connected to two silicon atoms. In Q3, three Si-O (br) bonds and one
Si-O nonbridging bond, designated Si-O (nbr) exists. For Q0, all Si-O bonds are Si-0 (nbr).
4. Designations Q4 to Q0 of local environments coincide
with connectivity 4 to connectivity 0 of the extended environment.
Four reactions
suffice to describe all possible rearrangements in local environments
in those alkali oxide (R20) silicate
glasses in which all oxygen atoms are connected to silicon atoms.
1. 2Q4 +
R20 2Q3 (depolymerization)
2.
2Q3 Q2 + Q4
3. Q2
+
Q3 Q1 + Q4 (stepwise condensation)
4. Q1
+
Q3Q0 + Q4
The Q
distribution can in principle be determined experimentally by
high-resolution solidstate NMR. This distribution does not, however,
necessarily relate glass structure to glass properties. Examination of
Figure 2 makes this clear. Two hypothetical two-dimensional networks,
each containing 45 open tetrahedra and 11 black tetrahedra, are shown.
The open tetrahedra represent silicon; the black tetrahedra, lithium in
fourfold oxygen coordination. The difference in Q distribution between
the two networks is small. Nevertheless, measurement of the transport
properties of the two networks would give wildly different results; the
arrangement in figure 2B has very high electrical conductivity and
diffusivity (and possibly low viscosity) because of a continuous
pathway through the solid in contrast to that in Figure 2A. Clearly the
Q distribution does not correlate glass structure with glass properties
and additional information is required to make such a connection. This
additional information is obtained from Monte Carlo type computer
calculations.
KEEFER
recognized that the question of the structure of a silica-rich
alkali-metal silicate glass is analogous to that of electron spin
correlation in a two-dimensional Ising Model. This Model attempts to
explain magnetic properties of materials by constructing a lattice with
two possible electron spin states, up or down, which allows the problem
to be considered in terms of a statistical distribution. Alkali
silicate and spin glasses share two characteristics: (1) slow
relaxation and (2) a tendency to settle into any one of a large number
of atomic configurations. In silica-rich alkali-metal silicate glasses,
the two possible spin states correspond to bridging and non-bridging
oxygen atoms; silica-rich glass is required because photoelectron
spectroscopy has demonstrated that only in such systems are nonbonding
oxygen atoms not present. In the absence of non-bonding oxygen, the
ratio between bridging and non-bridging oxygen atoms is fixed by the
stoichiometry of the sample.
As stated
before, connecting Q distribution with physical properties of a glass
or melt requires Monte Carlo type calculations. The computational
problem involves assignment of the enthalpies of formation of the four
principal reactions between Q species; calculation of network patterns;
derivation of the thermodynamic properties of the system from these
patterns; and use of percolation theory to compute the rheological and
transport properties of melts, A rule of thumb is given by Ziman with
respect to site percolation site percolation occurs in a regular
three-dimensional assembly when favorable regions occupy ca. 15% (in
the two-dimensional case 45%) of the total volume.
Local silicon
environments can be measured by 29Si magic angle
spinning (mas)
NMR. Two problems arise in using this technique: variations in chemical
shift for a specific silicon species and, partly as a result of this,
limited spectral resolution. The first problem is illustrated in Figure
3, which shows the 29Si MAS NMR
spectrum of Na24Y8 (Si24O72] which is a
single-chain silicate with 24 silica tetrahedra per unit cell (a 24er
chain in the Liebau classification) and local environment Q2. The 29Si MAS NMR
spectrum of this compound shows 12 peaks with a chemical shift range of
5.12 ppm. Thus, small perturbations in the local environment around one
Q2 species can
cause a substantial chemical shift. In this case, the variations are
due to chain twisting. Such variations in chemical shift of a single
silica species, combined with the large number of species possible
present (ten Q2 species are
possible) and the limited NMR spectral resolution in glass, render
determination of the silica species distribution in glass tentative at
best. Despite this, some assessment of the degree of intermediate-range
order in lithium silicate glasses has been obtained by combining NMR
and ESCA (electron spin chemical analysis) results together with the
application of proper stoichiometric constraints on the system. Doing
this shows clearly that the 29Si NMR spectra
of such glasses indicate the presence of only a small number of local
environments, in contrast to the total possible number enumerated in
Figure 1.
Composition of Glass
Multicomponent
glass-forming systems contain, according to Zachariasen, appreciable
amounts of elements that form vitreous oxides or other elements that
can replace the former isomorphously. Ternary glasses can consist of
one network former and two modifiers, or three network formers. Most
ternary oxide systems have been sampled, and investigation has been
extended to quaternary and quinary systems.
The properties
of complex industrial glasses tend to be rationalized in terms of
simple systems. The following discussion, therefore, begins with
vitreous silica as the cannonical single-component glass, followed by
simple two-component systems: the alkali-metal and alkaline-earth
silicate, borate, phosphate, and germinate glasses. Boro-,alumino-, and
lead silicate glass is then discussed, followed by two nonoxide
systems, the chalcogenide and halide glasses. Finally, the chemical
composition of industrially important glasses is tabulated.
1. Single-Component Glass
The most
important single-component glass is vitreous silica. The structure
consists of corner-sharing siO4 tetrahedra. Each oxygen atom is shared
by two silicon atoms, forming Q4 local silicon
environments. Long-range order is, of course, absent. Vitreous silica
is an excellent dielectric with a very low equilibrium solubility (on
the order of 100ppm at room temperature) in all acids except
hydrofluoric. A synopsis of the properties of Corning 7940 fused silica
and other amorphous silicas is given in Table 1.
The difference
in structure between vitreous silica and two crystalline silicas is
shown in Figure 4. Here the Frequency of occurrence of average Si-0-Si
angles is illustrated by using the 29Si MAS NMR
spectrum of vitreous silica and the formula of Thomas and coworkers,
which relates chemical shift to the Si-0-Si angle. Average Si-0-Si
angles vary between 1220 and 1700 in vitreous
silica, the most common value being 147 (or 151 if the spectrum of
Gladden and coworkers is used). On the other hand, quartz and
cristobalite each have one single Si-0-Si angle, with values of 1430 and 1460, respectively.
Superimposed on
the plot of Si-0-Si angle versus frequency in Figure 4 is the
two-center energy, taken to reflect the bond energy, for a
silicon-oxygen bridging bond as a function of Si-0-Si angle, calculated
by using semiempirical molecular orbital calculations. Inspection of
this curve shows that a Si-0- bond with a Si-O-Si angle of 1800 is stronger
(i.e. has a more negative two-center energy. ca. -1760kj) than that at
a Si-0-Si angle of 120º (two-center energy. ca.-1530kj). Examination of
figure 4 suggests that although glasses are intrinsically less stable
than their crystalline counterparts, a vitreous silica more stable than
quartz or cristobalite is conceivable; the challenge is to make a glass
with a larger percentage of Si-0-Si angles >150º. Only this
angle must be considered because the energy barrier to rotation between
connected silica tetrahedra is negligibly small.
Fused silica
transmits light of wavelengths into the UV region and is the oxide
glass most resistant to damage caused by radiation. It finds use in
windows for space vehicles and wind tunnels, ultrasonic delay lines,
crucibles for growing ultrapure silicon or germanium crystals, and
optical systems in spectrophotometric equipment.
Vitreous silica
can be produced by several methods. These processes and the impurities
associated with them are listed in table 2.
Fused quartz
made by electrically fusing quartz crystals has very low moisture
content and, hence, good IR Transmission. The disadvantage of quartz as
a raw material is that even highgrade pure quartz crystals contain 1-2
ppm of aluminum, alkali, manganese, and titanium. The presence of these
elements increases the number of Si-O (nbr) bonds, which thereby
reduces UV transmission. Flame fusion of quartz or flame hydrolysis of
SiCl4, on the other
hand, gives glasses of very high purity except for large amounts of
water, which decrease IR transmission. For some applications,
impurities as low as 1 part in 1012 become
important. An example is uranium; this problem is best solved by
ensuring that the silica source is biogenic rather than associated with
granitic rocks or pegmatites.
2. Silicate Glasses with Two components
Two-component
silicate glasses are of particular interest in studying glass
formation. Addition of alkali-metal or alkaline-earth oxides breaks
Si-O-si linkages, the alkali-metal
or alkaline-earth nestling at non-bridging oxygen sites in the network,
hence, the description net-work modifiers. This decrease in
connectivity of the silica network manifests itself in a very large
decrease in viscosity, melting point, and UV transmission. Modifiers
also cause a decrease in resistivity, an increase in thermal expansion,
and generally lower chemical durability.
Different
alkali-metal atoms have different effects on the properties of silicate
glasses. Thus, lithium silicate glasses are nonhygroscopic, whereas
sodium, potassium, rubidium, or cesium silicate glasses show
increasingly higher hygroscopicity. Another example is the volume
contraction of the silicate network in the presence of lithium and its
expansion in the presence of potassium. The almost monotonic variation
in cation-oxygen distance, as measured by X-ray diffraction, has led to
a variety of schemes for the comprehensive compilation of the
properties of alkali metal or alkaline-earth silicate crystals or
glasses. Among these are the cation field energy and field strength,
which are the formal cation charge divided by the cation-anion distance
and the square of the cation-anion distance, respectively.
Many physical
properties of alkali metal or alkaline earth silicate glasses change
almost monotonically as a function of cationic field strength or
energy. For example, the critical liquid immiscibility temperature
decreases linearly as a function of cationic field strength from
magnesium to barium silicates, and from lithium to cesium silicates.
Similarly, the freezing point depression increases more or less
monotonically from lithium to cesium silicates whereas the surface
tension decreases. Viscosity, refractive index, and density show a
minimum for sodium silicate melts.
Even the few 29Si MAS NMR
chemical shift data on crystalline alkali-metal silicates suggest a
relation between chemical shift and cationic field strength, less
negative (downfield) chemical shifts being associated with greater
cationic field strength. More sophisticated analysis of a variety of
silica-containing systems has been carried out. In alkali-metal or
alkaline-earth silicate glasses, most physical properties vary more or
less linearly with cationic field strength, with the exception of
viscosity, refractive index, and density, Although it is useful as a
mnemonic device, no true cause and effect relations are associated with
cationic field strength or energy.
3. Borate, Phosphate, and Germanate Glasses
Borate glasses
contain planar BO3 groups as
structural units, rather than tetrahedral SiO4 groups. The
oxygen atoms are, as in silica, again connected to two network-forming
atoms, in this case boron. Radial distribution analysis describes the B2O3 glass structure
as consisting of boroxyl rings, i.e., planar rings containing three
boron atoms and three oxygen atoms. Recent results on molecular
dynamics have shown that the radial distribution pattern is consistent
with structures having a low concentration of such rings.
Although borate
glass forms a three-dimensional network, its viscosity is substantially
lower than that of silicate glass, as shown in table 4. Again, addition
of alkali lowers the viscosity of the melt, but the effect is by no
means as dramatic as for silicate glass.
Introduction of
alkali or moisture to alkali-metal borate glasses causes some of the
three-co-ordinate boron atoms to become four-coordinate, as shown
by the pioneering NMR work of Bray and O KEEFE. The ratio of three to
four-coordinate boron in alkali-metal borate glasses has an upper limit
of about 1.2.
Phosphate
glasses contain tetrahedrally coordinated PO4 building
blocks; however, they do not show the same type of connectivity as
silicate glasses. Oxygen 1s photoelectron
spectroscopy suggests that in phosphate glasses, three types of oxygen
atoms occur: those bonded to two phosphorus atoms, the bridging oxygens
O(br): those bonded to one phosphorus atom and one alkali metal atom,
the non-bridging oxygens O (nbr); and those bonded only to phosphorus,
the doubly bonded oxygens O (d). A characteristic oxygen 1s
photoelectron spectrum of a phosphate glass is shown in figure 9. In
contrast, silicate glasses never contain double-bonded oxygen atoms and
only rarely non-bonded oxygen, i.e. oxygen atoms not connected to at
least one silicon atom. An example of the latter is glassy Pb2SiO4.
Oxygen 1s
photoelectron spectroscopy indicates both the concentration of
different oxygen atoms in a material and the actual charges on these
atoms. The relation between energy shift of the oxygen 1s
photoelectron spectral line and charge is shown in Figure 10. According
to this method, quartz, cristobalite, and vitreous silica have an
oxygen charge of -0.74. Oxygen atoms with higher negative charge are
encountered, for example, in lead silicate glasses, which show oxygen
charge variations comparable to those found for super conducting
materials. Some oxygen 1s derived charges for
various compounds are compiled in table 5. Assignment of charges is a
partitioning problem without a unique solution.
Some special
phosphate glasses show a connectivity of four, identical to that found
in vitreous silica. Examples are ZnP2O6 and AIPO4 glasses.
The structure of
alkali phosphate glasses is well known because these glasses, in
contrast to alkali silicate glasses, either do not, or only at very
small rates, repolymerize on dissolution in aqueous solution. As a
result, the length of the phosphate chains remains unchanged. The
relative proportions of different chains in solution, analyzed
chromatographically, give a true measure of the distribution of
extended environments in phosphate glasses. The most common chain
length is three to four phosphorus atoms, with a maximum chain length
of seven. No analogies between the distribution of structural elements
in phosphate and silicate glasses exist. This is due to the limited
cross-linking and branching that occur in phosphate glasses in
comparison to silicate glasses due to the presence of P=O bonds.
Phosphate
glasses tend to have low durability. Despite this, important commercial
applications exist. One of these is associated with the sharper
absorption bands of iron oxide in the ultraviolet and infrared in
phosphate glasses compared with silicate glasses. Iron-containing
phosphate glasses are, therefore, nearly transparent to visible light,
enabling the manufacture of virtually clear heat absorbing glasses
containing several percent iron oxide.
Phosphate-based
glasses are more resistant than silicate glasses to hydrofluoric acid.
Some optical glasses produced by Schott, Hoya, Owens-Illinois, and
Corning France use phosphate as the primary glass former.
Fluorophosphate glasses, designated FK-5 and FK-50 by Schott, have very
low optical dispersion, with Abbe numbers of 70.4 and 81.5,
respectively.
Optical Properties
Introduction
Glasses are
among the few solids, which transmit light in the visible region of the
spectrum. Glasses provide light in our homes through windows and
electric lamps. They provide the basic elements of virtually
all-optical instruments. The worldwide telecommunication system is
based on the transmission of light via optical
wave guides. The esthetic appeal of fine glassware and crystal
chandeliers stems from the high refractive index and birefringence
provided by lead oxide, while the magnificent windows of many
cathedrals exist only because of the brilliant colors which can be
obtained in glasses.
The optical
properties of glasses can be subdivided into three categories. First,
many applications of glasses are based on the bulk optical properties
such as refractive index and optical dispersion. Other properties,
including colour, are based on optical effects, which are strong
functions of wavelength. Finally, modern glass technology increasingly
relies on the application of non-traditional optical effects such as
photosensitivity, photochromism, light scattering, Faraday rotation,
and a host of others.
Bulk Optical Properties
The history of
optical science closely parallels the history of the development of
optical glasses. Development of early telescopes and microscopes
immediately forced a search for new optical glasses with appropriate refractive
index and optical dispersion characteristics.
It can be argued that the development of modern astronomy, biology, and
medical science were controlled by the ability of glass makers to
develop glasses with the appropriate optical properties.
Refractive
Index
The refractive
index remains the most measured optical property of glasses as well as
the most basic optical property for determination of the appropriate
glass for many applications. The refractive index of any material is
defined as the ratio of the velocity of light in a vacuum to the
velocity of light in a medium. This ratio can be measured by
application of Snell's law, which states that the refractive index, n,
is given by the expression.
Where qi is the angle of
incidence and qr is the angle of
refraction for a beam of light striking the surface of a material. The
refractive index can also be measured using methods based on the
reflectivity of a surface, measurement of the critical angle for total
reflection or Brewster's angle, or the Becke line technique. Further
discussion of these methods can be found in many texts on optical
properties.
The refractive
index is not actually a constant, but varies with the wavelength of the
incident light. The most commonly quoted index is usually designated as
nD and represents
the index at the yellow emission line of sodium (589.3 nm). The index
at the yellow emission line of helium (587.6 nm), designated nD, is also
commonly used. Since these wavelengths are nearly identical, there is
very little difference between these indices.
The refractive
index of glasses is determined by the interaction of light with the
electrons of the constituent atoms of the glass. Increases in either electron
density or polarizability of the ions
increases the refractive index. As a result, low indices are found for
glasses containing only low atomic number ions, which have both low
electron densities and low polarizabilities. Glass based on BeF2 has refractive
indices in the range of 1.27, while vitreous silica and vitreous boric
oxide have refractive indices of about 1.458. At the other extreme,
glasses with high lead, bismuth, or thallium contents may have
refractive indices ranging from 2.0 to 2.5.
Since a majority
of the ions in any glass are usually anions, the contribution to the
refractive index from the anions is very important. Replacement of
fluorine by more polarizable oxygen ions, or by other halides,
increases the refractive index. Conversely, partial replacement of
oxygen in oxide glasses by fluorine to form fluoroborate glasses, for
example, reduces the refractive index. Since non-bridging oxygens are
more polarizable than bridging oxygens, compositional changes which
result in the formation of non-bridging oxygens increase the refractive
index of glasses, while changes in composition which reduce the
non-bridging oxygen concentration can reduce the refractive index. The
refractive indices of alkali silicate glasses thus increase with
increasing alkali oxide concentration, while replacement of alkali
oxides by alumina, which reduces the non-bridging oxygen concentration,
can cause a reduction in the refractive index.
The
polarizability of the cation present increases as the field strength of
the ion decreases, so that glasses containing cesium have a higher
refractive index than those containing sodium. The most polarizable
ions have very large electronic clouds and small oxidation numbers e.g.
TI+ and Pb2+, which are used
to produce very high refractive index glasses. Glasses which contain
very high PbO concentrations, such as those found in unusual systems
such as the PbO – Ga2O3 binary and the
PbO-Ga2O3-Bi2O3 ternary, have
refractive indices in excess of 2.5.
The density of a
glass also plays a role in controlling the refractive index. Decreases
in fictive temperature, which increase the density of most glasses,
increase the refractive index. Since the fictive temperature is
determined by the cooling rate through the glass transformation region,
the refractive index is found to increase with decreasing cooling rate.
This effect can be very important for optical applications, where fine
annealing is essential to minimize local index variations. The
refractive index also increases when glasses are eight reversibly or
irreversibly compacted by pressure or by exposure to high-energy
radiation.
Thermal
expansion of glasses can result in either an increase or a decrease in
the refractive index. The density of a glass will decrease if it
expands upon heating, which should decrease the refractive index. The
polarizability of the ions, however, increases with temperature, which
increases the refractive index and may therefore offset the effect of
the decreasing density. Glasses with high thermal expansion
coefficients and low temperature variations in polarizability are
usually found in systems containing fluorine, such as the fluoride,
fluorophosphate, or fluorosilicate systems. These glasses have negative
coefficients for the variation of refractive index with temperature, dn/dT.
Glasses with low thermal expansion coefficients and higher temperature
variation of polarizability, as is the case for most silicate and
borate glasses, have positive temperature coefficients of refractive
index. These variations in refractive index are reversible so long as
no relaxation of the density occurs during the temperature excursion.
Molar and Ionic Refractivities
The molar
refractivity is directly proportional to the
polarizabilities of the constituent ions of a glass. It can be shown
that the molar refractivity, Rm, is given by
the expression
Where Vm is the molar
volume of the glass and n is the
refractive index at the wavelength of measurement. The molar volume is
equal to the molecular weight of the glass divided by its density.
The molar
refractivity of a compound can be calculated from the contributions of
each of the constituent ions. The molar refractivity for the compound AxBy for example, is
given by the sum of the ionic refractivities of the
constituent ions, Rn, times their
concentration in the compound, or, in this case
Since the ionic
refractivity depends on the polarizability of the ion, large values are
found for the large, low field strength ions such as TI+ and Pb2+. Variations in
the ionic refractivity explain many of the major trends in the
refractive index of glasses.
Although this
method of estimating the molar refractivity works well for many
inorganic compounds, it is difficult to apply to oxide glasses. The
ionic refractivity of oxygen depends upon its role in the glass
structure, so that the values for bridging and non-bridging oxygens are
structure, so that the values for bridging and non-bridging oxygens are
not identical. Furthermore, the ionic refractivity of oxygen ions
depends on the nature of the associated cations. As a result, one can
only use ionic refractivities as a guideline to the choice of ions for
altering the refractive index of oxide glasses and not for quantitative
calculations.
Since a typical
glass contains from 50 to 80 atomic percent of anions, the ionic
refractivities of the anions are very important in controlling the
molar refractivity. The polarizabilities of the common anions increase
in the order F– < OH– < Cl– <O2 – <S2 –Se2- <Te2– . This trend in
ionic refractivities explains why replacement of oxygen by fluorine in
fluoroborate, fluorsilicate, or fluorogermanate glasses decreases the
refractive index of glasses, even though two fluorine ions are required
to replace a single oxygen ion. The high refractive indices of
chalcogenide glasses stem directly from the high ionic refractivities
of sulfur, selenium, and tellurium ions.
The use of the
molar refractivity stresses the role of ionic packing in controlling
the refractive index of a glass. Since the refractive index is
proportional to the molar refractivity divided by the molar volume, it
is obvious that a small molar volume will yield a larger refractive
index for a glass consisting of ions of similar polarizabilities. An
example of this effect can be found in the refractive indices of many
glasses containing lithium compared to similar glasses containing
sodium or potassium. Since lithium actually causes a contraction of the
vitreous network in many glasses, the molar volume is reduced by
addition of lithium ions. This reduction in molar volume more than
offsets the lower ionic refractivity of the lithium ion relative to
that of sodium or potassium ions and results in a glass with a higher
refractive index. In many cases, apparently anomalous trends in
refractive index are resolved when the data are converted to molar
refractivities.
Tables of
optical data for glasses often include values for the specific
refractivity, which is given by the expression
Where r
is the density of the glass. The specific refractivity is primarily
used for designing optical systems, where the mass of glass used may be
important.
Dispersion
The variation in
index with wavelength, known as optical dispersion or
simply as dispersion, is critical in the control of
chromatic aberration of optical lenses. Ideally, dispersion is
described by the entire curve of refractive index versus wavelength
over the desired wavelength range. In general, however, it is more
convenient to measure the refractive index at a few specified
wavelengths and use these measurements as the basis for terms, which
can be used to compare the dispersion of different glasses.
These values are
nearly identical.
More detailed
information regarding the dispersion curve as a function of wavelength
is often provided in the form of an expression of the form.
Ultraviolet
Absorption
Even
transparent, colorless glasses cannot transmit radiation at wavelengths
beyond their inherent ultraviolet edge. This
frequency is believed to be due to the transition of a valence electron
of a network anion to an excited state. Conversion of a network anion
from the bridging state to a non-bridging state will lower the energy
required for the electronic excitation and shift the ultraviolet edge
to lower frequencies. The addition of alkali oxides to silica,
therefore, results in a shift of the ultraviolet edge toward the
visible region of the spectrum. Since initial additions of alkali
oxides to boric oxide result in conversion of boron from three-to
four-fold coordination, thus strengthening the network bonds, the
ultraviolet edge does not shift toward the visible. Once the
concentration of alkali oxide becomes sufficient to produce
non-bridging oxygens, the expected shift of the edge toward the visible
with increasing alkali oxide content is observed.
The ultraviolet
edge of vitreous germania is closer to the edge of the visible spectral
region than that of the other common oxide glassformers. Addition of
large concentrations of alkali oxides shifts this edge to a frequency
very near the visible. If these glasses are heated, they gradually
become yellow with an increase in the intensity of the color with
increasing temperature. The glasses return to the colorless state on
cooling. This effect, known as reversible thermochromism,
is due to the shift of the ultraviolet edge into the visible region at
elevated temperatures.
In reality, the
inherent ultraviolet edge of a glass is rarely observed. Very small
concentrations of iron and other impurities result in very intense
absorption bands. Since the absorption of energy is due to the transfer
of an electron from the cation to a neighboring anion, these
absorptions are said to be due to a charge transfer transition
and the absorption band is called a charge transfer band.
These bands are so intense that only their tail can be detected, so
that the appearance of the spectrum is identical to that due to the
inherent ultraviolet absorption. The impurity iron content of most
silica used in glassmaking is so great that the inherent ultraviolet
edge of silicate glasses is usually undetectable.
Visible
Absorption
Absorption in
the visible is perceived as color. A number of mechanisms exist for the
creation of color in glasses. The most important commercial colored
glasses contain either 3d transition metal ions or 4f rare earth
(lanthanide), ions, where the coloration arises from the so-called
ligand field effect. Other sources of color include the formation of
metal or semi-conductor colloidal particles; optical defects induced by
solarization or radiation, and charge transfer bands in the visible
region of the spectrum.
Ligand
Field Coloration of Glasses
Coloration of
glasses by 3d transition metals ions is due to electronic transitions
between normally degenerate energy levels of d-electrons. Since a
detailed description of the mechanism leading of these electronic
transitions (called ligand field or crystal
field theory) can be found in many places, only a brief
qualitative discussion will be provide here.
The 3d
electronic levels are identical in energy for free ions. However, when
a transition metal ion is surrounded by a few anions, called ligands,
as in a crystal of glass, the interaction of the electric fields causes
a small splitting of the energy levels. The magnitude of this splitting
is a function of the field strength, number, and geometric arrangement
of the neighboring anions. The number of different levels formed is a
function of the electronic configuration and coordination number of the
cation. Since the energy differences which commonly result for 3d
transition metal ions from ligand fields are in the range of 1-3 eV,
the absorption of photons by electronic transitions between split 3d
levels results in visible coloration.
Similar
arguments apply to the 4f electronic levels of the rare earth ions,
where splitting of the 4f levels also produces absorption bands in the
visible. Differences in the nature of the 3d and 4f ions result in less
intense absorptions for the rare earth ions, as well as more complex
spectra, which are due to the greater number of possible configurations
of the seven 4f levels compared to the five 3d levels of the transition
metal ions.
All of these
electronic transitions are technically forbidden by Laporte’s rule,
which states that electronic transitions can only occur if the orbital
angular momentum changes by ± 1 during the transitions. Since this does
not occur for transitions from one d state to another d state, or from
one f state to another f state, no absorption should occur for these
ions. Fortunately, Laporte’s rule is relaxed in solids due to the lack
of perfect spherical symmetry which results from the presence of a
limited number of point sources, so that electronic transitions can
occur with a low probability between 3d or 4f levels which are split by
the fields of the neighbouring ligands. The low probability of these
transitions, however, does reduce the intensity of the absorption. As a
result, ligand field induced transitions are much weaker than the
charge transfer effects, which occur in the ultraviolet.
Since the
coloration of glasses by transition metal and rare earth ions results
from ligand field effects, several general trends can be predicted.
First, a change in oxidation state results in a change in the number of
3d or 4f electrons, resulting in a different number of possible
electronic transitions for otherwise identical conditions. Since each
possible electronic transition represents absorption with a different
energy, a difference in oxidation state will result in a different
absorption spectrum.
Most 3d
transition metal ions are found in either octahedral or tetrahedral
coordination in oxide glasses. A change in coordination number will
result in a difference in splitting energy and, depending upon the
number of 3d electrons present, possibly a change in the number and
relative positions of the potential electronic transitions.
Changes in the
identity of the anions results in a change in their ligand field
strength and thus a shift in the positions of the absorption bands with
no change in their number or relative positions. The ligand field
strength of the common anions decreases in the order O2– > F–> Cl– > Br– > I–. In many cases,
the transition metals appear to prefer to be associated with halide
ions instead of oxygen ions in nominally oxide glasses. For example,
the substitution of a small amount of NaCl of Na2O in a sodium
borate glass containing cobalt oxide can cause the color due to CO2+ ions to change
from a dark blue-purple to lighter blue-green due to a small shift in
the absorption band positions to longer wavelengths. Addition of a
small amount of NaBr can result in a green glass, while additions of
Nal can yield a red-brown glass. The CO2+ ions must
preferentially associate with the small number of halide ions, since
the color of the glass is actually due to a very small concentration of
the transition metal ions.
The color is
also altered by changes in concentration of the coloring cation, in the
identity of the network former, and in the identity and concentration
of the modifiers present. The effect of the concentration of the
coloring ion is obvious: more chromophores, or
coloring species, result in more absorption. The effects of changes in
the network former and the modifier ions present are due to alterations
in bond distance and bond strength between the coloring ions and the
surrounding ligands. Replacement of a small diameter modifier ion by a
larger one can also occasionally cause a change in the most favorable
coordination number for the coloring ion.
Details of the
coloration of glasses due to ligand field effects are further
complicated by the possibility of redox interactions between two or
more different transition metal ions. Other elements such as arsenic
and antimony, which do not directly affect color, may alter the
oxidation state of a coloring ion and alter the color of the glass.
Changes in furnace atmosphere can also inadvertently alter the
oxidation state of coloring ions due to changes in the concentrations
of O2, CO, CO2, and H2O vapor.
Amber
Glass
Many glass
containers have a brownish color popularly called ‘beer-bottle brown’.
This particular color occurs in glasses containing both iron and
sulfur. Carbon is usually added to the batch to provide a reducing
agent to insure the presence of sulfide ions. One model suggests that
the coloration is due to an iron (iii) ion in tetrahedral coordination
with three O2– and one S2– ions. The
actual absorption is due to a charge transfer process.
Control of amber
browns in commercial glasses in quite difficult. The coloring agent, or
chromophore, contains both an oxidized form of iron and a reduced form
of sulpur. These forms can only co-exist in a melt in a narrow range of
oxygen partial pressures. Since the intensity of the color will vary
with oxygen partial pressure, reproducibility of the color is
difficult. The oxygen partial pressure is usually controlled by varying
the amount of carbon added to the melt or by controlling the redox of
the combustion process. Replacement of sulfur by selenium changes the
color from brown to black.
Colloidal
Metal Colors
The red color
produced in many glasses containing gold, known as gold-ruby glasses,
is due to the presence of very fine colloidal gold particles. The color
is not due to light scattering, but rather to absorption by the
particles, which cause an intense optical absorption band at about 530
nm. Doremus has calculated the shape and position of this band by
assuming that the particles are spherical and using the optical
properties of gold. He suggests that this band can be considered as a plasma
resonance band, where the free electrons in the particles
are treated as bounded plasma. A similar absorption band, attributed to
an identical mechanism, at 410 nm is obtained for glasses containing
colloidal silver. The shift in band position results in a strong yellow
coloration, which is called silver-yellow or silver
stain.
A somewhat less
esthetically pleasing red color can be produced in glasses containing
copper. The absorption band due to copper occurs at 565 nm for these
glasses and is similar in shape to those for gold and silver. While the
red color of these glasses is usually attributed to copper colloids,
others have proposed that the color is due to colloidal crystals of Cu2O. Since both
metallic copper and Cu2O are often
found in copper-ruby glasses, it is possible that
the color arises from a combination of these species. Although the
solubility of both gold and silver in silicate glasses limits the
concentration of colloids which can be formed, the much higher
solubility of copper permits the formation of a very large number of
colloids. If the density of colloids is sufficiently high, the glass
will be opaque rather than transparent.
A number of
other colloidal species, including, but not limited to, Pb, As, Sb, Bi,
Sn, and Ge, can be formed in glasses. The properties of the metals are
such that these colloids result in brown, black, or gray colorations.
Colloids are
usually formed by producing the glass with the metal in the ionic form
and subsequently reducing the ions to form atoms. These atoms diffuse
through the glass until they encounter other such atoms. The atoms then
agglometrate to form nuclei, which grow to form the final colloids.
Reduction can result from a redox reaction with other components of the
glass or by reaction with an external reducing agent such as H2. Many ruby
glasses contain SnO2, which provides
an internal reducing agent. At the high temperatures used in melting,
the oxidation equilibrium favors the production of Au+ and Sn2+ ions.
This reaction,
which is called, striking, occurs spontaneously
upon reheating an originally colorless glass to the correct
temperature. As similar process can be used to produce glasses colored
by silver or copper. The color is distributed uniformly throughout the
glass.
Reduction by an
external agent will occur if glasses containing gold, silver, or copper
ions are exposed to H2 gas at
temperatures near the glass transformation range. Since reduction will
occur in the near-surface region and grow into the glass, the color
will occur in a layer at the glass surface. The thickness of this layer
increases with the square root of time, indicating that hydrogen
diffusion is important in controlling the coloration process. Although
formation of colloids of other metals is difficult by use of an
internal reducing agent, formation of a surface layer containing Pb,
As, Sb, and Bi colloids is quite easy using an external reducing agent
such as hydrogen gas.
Silver colloids
can also be formed in the surface region of a glass by interdiffusion
of silver from an external source with sodium or other alkali ions in
the glass. The silver can be supplied from either metallic silver films
or from molten silver salts. Since the exchange process requires that
the silver be present as ions, metallic films must be heated in air or
other sources of oxygen to temperatures above 150ºC to form Ag2O. Use of
metallic films allows the production of complex images in the surface
of the glass by sputtering the film through a mask. After ion exchange
is completed, the glass is exposed to hydrogen to reduce the silver and
create the colloids.
Silver colloids
will form spontaneously if silver films on float glass are heated in
air to temperatures above 300ºC. The process involves ion exchange
between the silver ions and sodium ions from the glass, followed
immediately by reduction of the silver by tin (II) ions in the glass
surface. The tin (II) ions are present due to diffusion into the glass
from the molten tin bath used in producing float glass. This reaction
is highly specific to the ‘tin-surface’ of float glass and only occurs
within the outer few micrometers of the glass surface.
Colloidal
Semiconductor Colors
A number of
glasses ranging in color continuously from yellow to orange to red to
black can be produced by doping the melt with various combinations of
CdS, CdSe, and/or CdTe. Similar glasses are produced using a mixture of
CdS and ZnS. The as-cast glasses are colorless and must be heat-treated
at »550-700ºC to ‘strike’ the color. The optical spectra of these
glasses differ from those of the colloidal metal colored glasses, with
a sharp cutoff of transmission in the visible or near infrared, instead
of the absorption bands observed for glasses colored by gold, silver,
or copper colloids. This cutoff in transmission is due to the formation
of very small semi conducting crystals of various cadmium
chalcogenides. The absorption of higher frequency light is due to
absorption of all photons having energies greater than the band gap of
the semiconductor. Since continuous solid solutions form, it is
possible to the semiconductor. Since continuous solid solutions form,
it is possible to adjust this band gap over a wide range of energies,
giving rise to a variety of colors. It has also been shown that the
color is dependent upon crystallite size, with a shift toward the red
with increasing crystal radius.
Radiation-induced
Colors
An extremely
large number of optical defects can be formed in glass by exposure to
high-energy radiation. These defects consist of trapped electrons or
holes either at pre-existing sites in the glass or at sites created by
the bond-breaking action of the radiation. Most of these defects give
rise to absorption bands in the ultraviolet region of the spectrum and
hence do not cause visible coloration of the glass. In general, the
optical absorption results from electronic states in the gap between
the valence and conduction bands. Photons induce transitions between
the valence band and the defect levels or from the defect levels to the
conduction band. Since a number of defects are often simultaneously
produced by the radiation, multiple, overlapping absorption bands
usually occur, producing complex optical absorption spectra.
Although
vitreous silica usually remains colorless following irradiation to very
high doses, doped silicas can become colored through the formation of
defects associated with impurities. Purple samples, for example are
formed if the glass contains a small amount of aluminum, due to the
formation of aluminum-oxygen hole centers (AlOHC).
Other impurities, such as germanium or titanium, can also produce
colored vitreous silica by formation of defect centers.
Most common
silicate glasses become after irradiation. The color is due to
formation of many defects, especially hole centers associated with the
non-bridging oxygens present in glasses containing alkali or alkaline
earth oxides.
These optical
absorptions can be bleached, or thermally annealed, by heating to
sufficiently high temperatures. The thermal stability of the defects
differs widely, so that the elimination of one defect may occur at room
temperature, while the elimination of another requires heating to near
the glass transformation temperature of the glass.
Solarization
Coloration of
glasses by exposure to sunlight is known as solarization.
Although some of the defects produced by higher energy radiation can
also be produced by ultraviolet radiation, the classic solarization of
glasses is due to a radiation-induced change in the valence of
manganese.
Many years ago,
manganese was frequently added to glasses to serve as a ‘decolorizer’
for iron-induced optical absorption. Since this practice is no longer
common, modern glasses do not produce the deep purple color
characteristic of Mn3+ ions after
long-term exposure to sunlight. While less common, other pairs of ions,
including Mn-As, Fe-As, and several couples involving cerium, can also
produce optical absorption changes due to solarization. Solarization of
modern glasses usually produces brown shades similar to those produced
by higher energy irradiation.
Infrared
Absorption
Absorption of
light in the ultraviolet and visible regions of the spectrum is due to
electronic transitions. While there are some lower energy electronic
transitions in the infrared region of the spectrum, most optical
absorption in this region in glasses are due to vibrational
transitions. This absorption can be divided into three categories:
impurity absorption due to gases or bound hydrogen isotopes, the infrared
cutoff, or multiphonon edge, and the
fundamental structural vibrations.
Infrared
Absorption by Bound Hydrogen Species
Virtually all
oxide glasses contain hydroxyl in various forms,
while other molecular species may or may not be present. The primary
absorption band due to Si-OH bonds occurs at 2730 µm for vitreous
silica. Since this is a vibrational absorption, overtones occur
at v/2, v/3, etc. Other bands due to hydroxyl arise from the
combination of the Si-OH frequencies with fundamental Si-O vibrations.
These overtone and combination bands are relatively weak and are not of
much importance for thin samples. However, when one forms an extremely
long (km) optical fiber from vitreous silica, these bands become
significant and must be eliminated to reduce optical losses to levels
acceptable for telecommunication systems. Many millions of dollars have
been invested in the research leading to the effective elimination of
these very weak infrared absorption bands.
Replacement of
hydrogen by deuterium of tritium causes all of these bands to shift
toward the infrared, as predicted by Equation 11. Replacement of Si4+ by B3+, Ge4+, Al3+, or other ions
also results in shifts of the band positions, with a larger shift due
to germanium than due to the other elements.
Addition of
alkali oxide to silica results in the formation of new bands due to
hydroxyl as well as a shift in the position of the fundamental band
toward the infrared. Hydroxyl bands are found at 2.75-2.95, 3.35-3.85,
and 4.25 µm for common sodium silicate and soda-lime-silica glasses.
The two bands at longer wavelengths are attributed to hydroxyl groups,
which are hydrogen bonded to neighbouring non-bridging oxygens at two
different distances. Replacement of alkali oxides by alumina, which
eliminates the non-bridging oxygens from the structure, results in the
elimination of the two bands attributed to hydrogen-bonded hydroxyls.
The hydroxyl spectra of alkali borosilicate glasses, which are often
phase separated, with silica-rich and alkali borate-rich regions, are
also very different from those of glasses containing large quantities
of non-bridging oxygens.
Glasses can also
contain bound hydrogen in the form of Si-H, B-H, and similar units. The
fundamental vibration for Si-H occurs at 4.44 µm for vitreous silica.
The absorption band is much sharper than those due to hydroxyl. These
groups are usually found in glasses which have been melted under a
hydrogen atmosphere, or which have been irradiated in the presence of H2 gas. In both
cases, the hydride groups can be removed by thermal treatment in air or
vacuum at temperatures below the glass transformation range.
Hydroxyl can be
formed in glasses by many methods. The most common form of hydroxyl, of
course, stems from melting in the presence of water vapor and thus
occurs for most commercial and laboratory melts. Formation of hydroxyl
by reaction with water vapour can be described by the reaction.
The hydroxyl and
hydride groups formed by these reactions are less stable than those
formed by reaction with water molecules and can usually be removed at
lower temperatures. The reaction described by Equation 14 can be driven
either thermally during melting, or by irradiation at room temperature
of glasses containing dissolved hydrogen. The thermal stability of the
species formed is quite different, with a much lower temperature
required for removal of the hydroxyl and hydride formed during
irradiation.
Exposure of
irradiated glasses of hydrogen gas after irradiation can also result in
hydroxyl and hydride formation by reaction of H2 molecules
diffusing into the glass with radiation-induced defects. As a result,
the defects are eliminated, the glass becomes colorless, and the
infrared transmission is reduced. If the glass contains dissolved
hydrogen during irradiation, no defects will be found after
irradiation. This process, known as chemical annealing,
can be used to eliminate optical defects in the ultraviolet and visible
region for many glasses. Replacement of hydrogen with deuterium results
in the formation of deuteroxyl instead of hydroxyl. In addition, the
pre-existing hydroxyls in the glass will isotope exchange with the
deuterium and become deuteroxyls.
Infrared
Absorption by Dissolved Gases
Diatomic
molecules containing only one element (H2, O2, N2, etc.) do not
absorb infrared radiation in the free gaseous state. It has been found,
however, that hydrogen molecules dissolved in glasses cause a very weak
infrared absorption band in silicate glasses in the region of 2.41 µm.
This band, which is relatively symmetric and narrow for an infrared
band of glasses, varies only slightly in position with glass
composition for silicate glasses.
Dissolved carbon
dioxide also causes an infrared absorption band in glasses. A narrow
absorption band due to dissolved CO2 molecules is
found at 4.26 µm in sodium aluminosilicate and heavy metal fluoride
glasses. Bands due to carbonate species formed by reaction of carbon
dioxide with oxide melts have also been reported.
Infrared
Cutoffs or the Multiphonon Edge
The infrared
cutoff, or multiphonon edge, of glasses, is caused by the combinations
and overtones of the fundamental infrared vibrations between the
cations and anions, which make up the glass structure. These extremely
intense absorption bands prevent the practical application of glasses
for transformation of light at longer wavelengths. The position of this
edge is controlled by the strength of the bond between the atoms in the
glass and the mass of those atoms. The edge wavelength shifts toward
the infrared in the order B2O3 < SiO2 < GeO2 for the simple
glassforming oxides. Traditional oxide glasses for infrared
transmission are based on either germanate or calcium aluminate
compositions, which transmit to »6 µm. Recently, the discovery of lead
gallate and lead bismuth gallate glasses has extended the edge position
for the best oxide glasses to »8 µm.
The elimination
of oxygen, as in the heavy metal fluoride and chalcogenide glasses,
permits the formation of glasses, which transmit further into the
infrared. Fluoride glasses typically have cutoff wavelengths in the
range of 6-8 µm. Replacement of fluorine by chlorine, with both weakens
the bonds and increases the average mass, extends this cutoff to 12-14
µm, while replacement by Br or I can shift the edge to >20
and >30 µm, respectively. Unfortunately, the
glasses based on Br and I have such weak bonding that their physical
and chemical properties are quite poor, preventing widespread
application to date.
Chalcogenide
glasses are frequently semiconductors, which means that they have a
smaller band gap than those found for oxide glasses. In most cases,
these glasses are actually opaque in the visible, with transmission
only becoming measurable at >1 µm. The fundamental vibration
frequencies for the network bonds are much lower than those found in
oxide glasses, so the infrared cutoffs occur at much longer
wavelengths. The cutoff wavelength increases in the order S < Se
< Te. Practical infrared windows, which transmit to around 16
µm, have been made from these glasses. Since all oxygen must be
excluded during melting to form high quality materials, processing
problems continue to limit the application of these glasses. The
toxicities of Se and Te also increase the difficulty in processing
commercial quantities of these glasses.
Mechanical Properties
Introduction
Glasses are
brittle materials. As a result, their fracture behavior is usually
determined by environmental factors and not by the inherent strength of
the bonds forming the vitreous network. The fracture strength of
glasses varies with prior surface treatment, chemical environment, and
the method used to measure the strength. As brittle materials, glasses
are also quite susceptible to failure due to thermal shock.
Other mechanical
properties of glasses are inherent to
the material. The elastic modulus, E, is determined
by the individual bonds in the material and by the structure of the
network. The hardness of glasses is a function of the strength of
individual bonds and the density of packing of the atoms in the
structure.
Elastic
Modulus
As classic
brittle materials, glasses exhibit nearly perfect Hookian behavior on
application of a stress. The ratio of the strain, e, resulting from
application of a stress, s, is a constant which is known as the elastic
modulus, or young’s modulus, E, which is defined by the
expression.
If a tensile
stress is applied to a specimen in the direction of the x-axis, the
specimen will elongate in that direction. This elongation will be
accompanied by contraction in the y and z directions. The ratio of the
transverse strain to the axial strain is called Poisson’s
ratio. Poisson’s ratio for oxide glasses generally lies
between 0.2 and 0.3, although the value for vitreous silica is only
0.17. The shear modulus, G, which relates shear
strain, g, to shear stress, t, is given by the expression.
Young’s modulus,
the shear modulus, and Poisson’s ratio are related by the expression.
The elastic
modulus of a material arises from the relation between an applied force
and the resultant change in the average separation distance of the
atoms, which form the structure of that material. If we consider the
Condon-Morse curve for force, F, as a function of
atomic separation distance, r, we can write an expression of the form.
The simple model
based on the Condon-Morse curve applies quite well to highly ionic,
close packed structures. If we consider the structure of glasses, we
find that the modulus is also influenced by the dimensionality and
connectivity of the structure, with a trend toward increasing elastic
moduli as the structure changes from a chain structure to a layered
structure to a fully connected three-dimensional network. Weak bonds
between chains or layers effectively offset the influence of the strong
bonds between atoms within the building blocks of the structure and
allow easier distortion of the structure. The presence of breaks in the
linkage within a structure, e.g. non-bridging oxygens, also allows
easier displacement of atoms and reduces the elastic modulus.
Replacement of modifier ions by aluminum ions, which reduce the
non-bridging oxygen concentration and increases the connectivity of the
network, also increases the elastic modulus of silicate glasses. The
highest elastic moduli for oxide glasses are found in glasses such as
the rare earth or yttrium aluminosilicates, which feature strong bonds
and high packing densities. Nitriding of these glasses, which provides
three-coordinated nitrogen linkages between tetrahedra, further
increases the elastic modulus, with very high values found for glasses
in SIALON (silicon aluminum oxynitride) systems. Values for the elastic
modulus of inorganic glasses typically range for 10 to 200 Gpa.
Since the
elastic modulus of glasses is related to bond strength, it is not
surprising to find that glasses with high glass transformation
temperatures usually also have high moduli. Furthermore where it was
shown that the thermal expansion coefficient is also explained using a
Condon-Morse diagram, it should not be too surprising to learn that low
expansion glasses often have high elastic moduli.
Hardness
The hardness of
glasses is usually defined in terms of either the scratch hardness
using the Moh’s scale or indentation
hardness using a Vickers indenter.
Oxide glasses lie in the range of 5-7 on Moh’s scale, i.e.,
they will scratch apatite (hardness of 5) but will not scratch
crystalline quartz (hardness of 7). The Vickers hardness of oxide
glasses ranges from 2 to 8 GPA, with values of over 11 Gpa for nitrided
glasses. These values are much lower than the Vickers hardness of
diamond, which is »100 Gpa. Borate, germanate, and phosphate glasses
are typically softer than silicate glasses. Chalcogenide glasses are
much softer, with Vickers hardness values in the range of 0.3 Gpa for
vitreous selenium to just over 2.0 Gpa for the three-dimensional
structures found for Ge-As-S glasses. In general, the effects of glass
composition on hardness parallel those found for elastic modulus.
Fracture
Strength
The fracture
strengths of glasses are usually far less than their theoretical
strengths. Fracture strength can only be described in terms of a
distribution function and does not exhibit a single value
characteristic of a given glass composition. The reduction is strength
is attributed to surface flaws, which severely weaken the glass.
Theoretical
Strength of Glasses
The theoretical
strength of a material is given by the force, which must be applied to
overcome the maximum restorative force predicted by equation 4. Once
the interatomic separation distance exceeds the distance corresponding
to the maximum restorative force, continued application of force will
extend the bond distance until the bond is broken and a crack can
propagate through the material. Orowan proposed that the stress
necessary to break a bond is determined by the energy necessary to
create two new surfaces due to the fracture. The Orowan stress, sm is given by the
expression.
Practical
Strengths of Glasses
The strengths
calculated using Equation 6 are orders of magnitude greater than those
found in practical applications of bulk glasses. This reduction of
strength is attributed to the presence of flaws in the surface of the
glass. These flaws act as stress concentrators, increasing the local
stresses to levels exceeding the theoretical strength and causing
fracture of the glass. Griffith treated this problem in detail and
derived the expression.
Where sf is the failure
stress and c is the critical crack length for crack growth. Attainment
of the critical crack length is only a necessary condition for crack
growth. It is also necessary for the stress at the crack tip of exceed
the theoretical strength of the material before the crack will grow
spontaneously. Since Griffith flaws typically have curvatures
approaching atomic dimensions at their tips, Orowan argues that any
applied stress sufficient to exceed the Griffith criterion will also
exceed the theoretical strength of the material and that the Griffith
criterion is usually sufficient to cause fracture. We have already
argued that the elastic modulus and the fracture surface energy are
relatively small functions of glass composition. Flaws, which are
introduced by external factors, are not intrinsic to the material. Flaw
lengths are determined by prior treatment of the surface and can vary
over several orders of magnitude. It follows that the inherent strength
of a glass is usually of little importance in determining the practical
strength. The hardness of a glass can influence the practical strength
through its influence on the resistance to flaw formation, i.e.
scratch resistance.
Flaw
Sources and Removal
How are the
critical, or Griffith, flaws introduced into glasses? Obviously,
contact with any material, which is harder than the glass, can cause a
flaw. Abrasion with hard material thus degrades the strength of a
glass. Actually, contact with another piece to the same glass or with
metal objects used to handle the glass is sufficient to generate flaws.
Chemical attack can also generate flaws. Touching a glass with a
fingertip will generate flaws through the attack on the surface due to
the NaCI deposited from the skin. Thermal stresses induced during rapid
cooling of a glass introduce flaws though thermal shock. Heating
glasses for prolonged times has also been shown to reduce their
strength by formation of a small number of surface crystals or by
bonding of dust particles to the glass surface. In either case, a
thermal expansion mismatch creates local flaws during cooling.
Protection of
glass surfaces against flaw formation is very difficult. The surface of
a freshly produced glass has a very high coefficient of friction for
contact against other materials. Flaw generation can be reduced if a
lubricant is applied to the fresh glass surface before any flaws are
formed. Lubricating coatings are often applied to the surfaces of glass
containers just after they exit from the annealing lehr. This coating
must be resistant to wear, since any contact, which penetrates the
coating, will result in flaw formation on the underlying glass.
Flaws can be
removed by removing the outer surface of the material by chemical
etching or mechanical polishing. Etching blunts the flaw tip and
reduces the flaw length, while polishing simply reduces the length of
the flaw to below the Griffith criterion. Flame polishing removes flaws
through viscous flow in the near-surface region.
Strengthening
of Glass
The strength of
glasses can be increased by two methods. First, we can prevent the
formation of flaws and remove those, which do form. Removal of flaws is
only effective for short times since new flaws are readily formed,
while preventing their formation by use of coatings has proven to be of
limited value. If we accept the fact that flaws will be present, we
must concentrate on the prevention of crack growth. Since crack growth
requires the presence of a tensile stress at the flaw tip, creation of
a near-surface compression region should prevent crack growth. No
growth will occur until the applied stress is large enough to overcome
the residual compressive stress and produces a tensile stress at the
crack tip.
Compressive
surfaces can be produced by ion exchange, thermal tempering, or
by application or formation of a compressive coating. Thermal tempering
involves the formation of a compressive layer by rapidly cooling a
glass from at or above the upper limit of the glass transformation
range. Since the interior of the glass will cool more slowly than the
surface, the fictive temperature of the interior will be lower than
that of the surface and the equilibrium density will be greater than
that of the surface region. Since the interior and surface regions are
bonded together, elastic strains must arise to counter the difference
in equilibrium densities. The surface region is placed in compression,
while the interior is placed in tension. The difference in fictive
temperature is a function of the difference in cooling rate between the
interior and surfaces of the glass, so that the magnitude of the
compressive stress increases with increasing cooling rate and glass
thickness. Consideration of the volume/temperature diagram for glasses
reveals that the compressive stress also increases with the thermal
expansion coefficient of the glass and with the difference between the
thermal expansion coefficients of the glass and the super cooled
liquid. It follows that thermal tempering is not very efficient for
very thin wall containers or fibers because only a small difference in
cooling rate occurs, or for low expansion glasses such as vitreous
silica or many commercial borosilicate glasses, where the volume
difference as a function of fictive temperature difference is small.
A compressive
surface layer can be formed if a thin layer of material having a lower
thermal expansion coefficient than the bulk glass can be created.
Cooling the composite will create a compressive surface layer with a
balancing tension region in the bulk glass. Application of a glaze can
be carried out by fusing a thin sheet of a glass with a lower glass
transformation temperature to the surface of a bulk glass or by more
traditional glazing methods involving application of a low melting
glass frit.
A variation of
the ion exchange method using an ion, which is smaller than that
initially present in the glass, can also produce a surface region of
lower thermal expansion coefficient. If, for example, exchange of
sodium from the glass with lithium from a bath occurs at temperatures
above the Tg of the glass,
relaxation will occur and chemical stuffing stresses will not exist.
Since the surface region now consists of a glass containing lithium
rather than sodium, the thermal expansion coefficient will usually be
reduced in this region. Cooling the glass will force the lower
expansion glass into compression, while the bulk glass is placed in
tension.
The exchange of
lithium for sodium offers another route to strengthening of glasses by
formation of a surface crystallized region. If the glass is an alkali
aluminosilicate, it may be possible to crystallize only the exchanged
region, forming a very low thermal expansion coefficient phase such as
virgilite or spodumene. Cooling the material will place the
crystallized region in compression and the substrate glass in tension.
Formation of a region which can be crystallized may also be possible
after ion implantation of magnesium ions or by exchange of silver for
sodium to form a region with a high nucleation density where
crystallization will occur more readily than in the bulk glass.
Low expansion
surface regions can be obtained by removal of alkali ions from the
surface region of alkali-alkaline earth-silicate glasses. Exposure to SO2 vapor, which is
often carried out to improve chemical durability, leaches alkali ions
from the surface, producing a silica-rich near-surface region. The
reduction in alkali concentration reduces the thermal expansion
coefficient and produces a compressive layer after cooling the glass.
Many other
methods of strengthening are based on formation of composites by
inclusion of fibers or whiskers or by crystallization to form
glass-ceramics. Phase separation may also affect the strength by
altering crack propagation mechanisms. Transformation toughening has
also been attained by formation of a small concentration of zirconia
crystals in glasses.
Statistical
Nature of Fracture of Glass
Since the
fracture strength of glass is usually controlled by the nature and
concentration of the flaws present in the surface, it is not surprising
to find a wide variation in measured strengths for a set of supposedly
identical samples. Furthermore, since the propagation of a crack
depends upon the simultaneous occurrence of a crack of sufficient
length and a stress of sufficient magnitude, the experimental method
used to measure strength affects the outcome of the measurement. Use of
a three-point bend test, for example, yields more scatter in fracture
strength data than does use of a four point bend test. Consideration of
the stress distribution in a rod used in these tests reveals that the
maximum stress in a three-point bend test occurs at the point directly
opposite the load point, while the maximum stress in a four-point bend
test occurs over the region between the two load points. Since the area
subjected to the maximum stress is much greater in the latter case, the
probability of a critical flaw for a given stress occurring within the
region of maximum stress is much greater.
Experimental
results of failure stress studies can often be represented by a Gaussian
distribution. According to Doremus, the probability, P,
of finding a sample with a failure stress, S, is given by the
expression.
A second
distribution function, called the Weibull distribution, is
often used to describe fracture strengths. In this case, the fraction,
F, of samples, which fail at stresses below S, is given by the
expression.
For convenience
is plotting data, the Weibull distribution expression given by equation
9 is often converted to the form.
The data are
then plotted as log [-1n [1-f] versus the load
required for failure and the values of m and So determined from
a least-squares fit of the data. A plot of data in this form is called
a Weibull plot.)
Fatigue
of Glasses
The strength of
glasses usually decreases with time under normal ambient conditions.
This effect, known as static fatigue, is due to
interaction of the glass with the surrounding atmosphere, resulting in
crack growth under constant load. One also finds that higher failure
strength is observed when the load is increased rapidly than when it is
increased slowly. Since this effect is observed under conditions of
changing load, it is often called dynamic fatigue.
Both static and
dynamic fatigue disappears for samples tested at liquid nitrogen
temperatures. Since fatigue effectively disappears below –100ºC, the
use of liquid nitrogen simply provides a convenient method for
obtaining very low temperatures and is not of particular relevance in
fatigue studies. At higher temperatures, the time to failure for a
given set of conditions decreases as the temperature increases. When
tests are carried out at normal room temperatures, the rate of fatigue
increases with increasing humidity.
Fatigue of
silicate glasses is generally attributed to the stress-enhanced
reaction of water with the silicate lattice at the crack tip,
as expressed by the reaction.
This reaction
between the silicate network and water molecules results in sharpening
of the crack tip instead of lengthening of the crack. Since the
reaction rate is essentially zero at very low temperatures, no fatigue
occurs for testing at liquid nitrogen temperature (-196ºC). The
increase in fatigue rate at higher temperatures is consistent with the
increase in reaction rate expected with increasing temperature.
Increases in humidity increase the fatigue rate by providing a higher
concentration of reactant. Dynamic fatigue results reflect the
requirement of sufficient time for the chemical reaction. If the load
rate is increased rapidly, a higher stress will be reached before
sufficient chemical reaction occurs to cause failure.
The simple model
offered here explains the gross fatigue behavior of glasses, but does
not explain some of the details of the process. Several other, more
complex models have been offered to explain fatigue of glasses. A model
proposed by Michalske and Freiman addresses the actual mechanism of the
chemical reaction. Their model successfully predicts static fatigue in
the presence of other molecules such as ammonia, while simultaneously
explaining why fatigue does not occur in the presence of N2 or CO. Another
proposed mechanism known as the chemical wedge suggests
that the reacting molecules do not actually reach the crack tip.
Molecules entering the crack are drawn toward the tip by capillary
action. The wedging action of these molecules increases the stress at
the crack tip, causing rupture of the Si-O-Si bonds.
Thermal
Shock
Thermal shock is a serious
problem wherever glasses are rapidly cooled over extended temperature
ranges. A cooling rate gradient can lead to thermal tempering of
glasses by producing different fictive temperatures in the surface and
bulk of the glass. Unfortunately, cooling with a temperature gradient
in a glass also produces temporary stresses, which counter the
permanent stresses due to differences in fictive temperature. If we
consider a glass plate held at the glass transformation temperature, no
stress will exist after some finite relaxation time and the fictive
temperature will be Tg. If we were able
to cool the surface of this plate instantaneously to room temperature,
the volume in the surface region should shrink due to thermal
contraction (the negative of thermal expansion during heating) to the
room temperature value appropriate for a fictive temperature of Tg. If the center
of the plate is still at the glass transformation temperature, however,
the local volume will be considerably greater than that of the surface.
After thermal equilibration at room temperature, the volumes of the
surface and bulk should be approximately equal since their fictive
temperatures are nearly equal because little change in fictive
temperature will occur for a moderately slow cooling from Tg. (Remember, in
tempering, we cool from a temperature well above Tg so that regions
of different fictive temperatures can be formed.) The sample should now
be relatively free of stress, i.e., any stresses
occurring during cooling are temporary.
Although the
stresses formed during cooling are temporary, failure can occurs due to
the high stress which occurs when the surface and bulk temperatures
differ. The maximum possible stress will be generated if the surface is
instantaneously cooled, while the bulk is still at the original
temperature.
In practical
situations, one is usually more interested in the maximum possible DT,
which can exist without failure of the glass. By rearranging
Equation 13, we can write the expression.
Examination of
Equation 13 reveals that the temporary stress which occurs during rapid
cooling for a given temperature differential increases with increasing
thermal expansion coefficient and elastic modulus. The best thermal
shock resistance is thus found for low-expansion, low modulus glasses.
The maximum temperature differential, which can be used without sample
failure, will be very high for a very low thermal expansion glass such
as vitreous silica. On the other hand, even high thermal expansion
glasses such as vitreous boric oxide may not be susceptible to thermal
shock failure if their glass transformation temperatures are very low.
(As a first approximation, we can assume that no stress will occur
above Tg since the
relaxation time will be very short at higher temperatures. This
assumption becomes less valid as the cooling rate increases.)
In reality, an
instantaneous cooling rate cannot be obtained for a sample of finite
size. If we consider the case of a plate cooled at a constant rate, f,
in k sec-1, we will still
generate a parabolic thermal gradient through the thickness of the
plate. If the material has a thermal diffusivity given by k/rCp, where k is the
thermal conductivity of the material, r is the density, and Cp is the heat
capacity at constant pressure, the stress at the surface is given by
the expression.
Viscosity of Glassforming Melts
Introduction
The kinetic
model of glass formation indicates that the temperature dependence of
the viscosity plays a major role in determining the ease of glass
formation for any melt. Glasses are most easily formed if either (a)
the viscosity is very high at the melting temperature of the
crystalline phase, which would form from the melt, or (b) the viscosity
increases very rapidly with decreasing temperature. In either case,
crystallization is impeded by the kinetic barrier to atomic
rearrangement, which results from a high viscosity.
In addition to
controlling the ease of glass formation, viscosity is also very
important in determining the melting conditions necessary to form a
bubble-free, homogeneous melt, the temperature of annealing to remove
internal stresses, and the temperature range used to form commercial
products. The viscosity also determines the upper use temperature of
any glass object and the conditions under which devitrification
(crystallization) may occur. The very high viscosity
encountered in the glass transformation range leads to viscoelastic
behavior, and to time dependence in many of the properties of the melt.
Viscosity Definitions and Terminology
Viscosity is a
measure of the resistance of a liquid to shear deformation, i.e., a
measure of the ratio between the applied shearing force and the rate of
flow of the liquid. If a tangential force difference, F, is
applied to two parallel planes of area, A, which is
separated by a distance, d, the viscosity, h, is
given by the expression.
The original
unit for viscosity was based on the cgs system, where the viscosity is
given in dyne s cm-2. This unit,
which is termed poise and given the symbol P, is used in virtually all
literature prior to 1970 and is still used extensively throughout the
glass industry. In SI units, which have replaced cgs units in much of
the recent literature, viscosity is given in N s m-2, or, since a
pascal is a N m-2, the viscosity
is reported in Pa s. Since 1 Pa s = 10 P, the conversion of viscosity
data from one unit to the other is very straightforward. The viscosity
of water at room temperature is 0.01 P, or 0.001 Pa s.
Fluidity is the
reciprocal of the viscosity. A melt with a large fluidity will flow
readily, whereas a melt with a large viscosity has a large resistance
to flow. While fluidity is often used in dealing with ordinary liquids,
virtually all literature dealing with glass forming melts discusses
flow behavior in terms of the viscosity.
A number of
specific viscosities have been designated as reference points on the
viscosity/temperature curve for melts. These particular viscosities
have been chosen because of their importance in various aspects of
commercial or laboratory processing of glass forming melts. Several
other reference temperatures, which occur at approximate viscosities,
are also routinely used by glass technologists.
The viscosity of
a typical melt under conditions where fining and homogeneity can be
obtained in a reasonable time is termed the melting
temperature. Melting usually occurs at a viscosity of <
10 Pa s for commercial glasses, but can occur at lower
viscosities for non-silicate and, particularly, non-oxide glasses.
Since this temperature is not truly a melting point in the classic
sense, but rather simply a processing temperature, the term practical
melting temperature should be used to distinguish between
the true melting points of crystals and a reference viscosity, which is
based entirely on pragmatic considerations.
Formation of
glass object from a melt requires shaping a viscous mass of liquid,
termed a gob, by some process involving deformation
of the material. The melt must be fluid enough to allow flow under
reasonable stresses, but viscous enough to retain its shape after
forming. Commercial forming methods require very precise control of the
viscosity throughout the forming process in order to achieve high
throughput and high yield of acceptable products. Melt is typically
delivered to a processing device at a viscosity of 103 Pa s, which is
known as the working point. Once formed, an object
must be supported until the viscosity reaches a value sufficiently high
to prevent deformation under its own weight, which ceases at a
viscosity of 10 Pa s, which is termed the softening point. The
temperature range between the working and softening points is known as
the working range. Melts, which have a large
working range, are often referred to as long glasses,
while those with a small working range are called short
glasses. If the working range occurs at high temperatures
relative to the working range of typical soda-lime-silica melts, the
composition is termed a hard glass. On the other
hand, if the working range is below that of soda-lime-silica melts; the
composition is termed a soft glass. This
particular terminology is often confusing since the terms hard and soft
in this context do not refer to the resistance to scratching usually
designated by these same terms.
The softening
point is more properly termed the Littleton softening point, after
the specific test used to define this reference point. The viscosity of
10 Pa s does not represent the deformation temperature for all objects.
This particular reference point is defined in terms of a well-specified
test involving a fiber »0.7 mm in diameter, with a length of 24 cm. The
softening point is defined as the temperature at which this fiber
elongates at a rate of 1 mm min-1 when the top 10
cm of the fiber is heated at a rate of 5 K min-1. In fact, if
the density of the fiber is significantly different from that of a
typical soda-lime-silica composition, the viscosity will not be exactly
10 Pa s at this temperature.
Once an object
is formed, the internal stresses, which result from cooling, are
usually reduced by annealing. The annealing
point (cited in various sources as either 1012 or 1012.4 Pa s), which is
also determined using a fiber elongation test, is defined as the
temperature where the stress is substantially relieved in a few
minutes. The strain point (1013.5 Pa s) is
defined as the temperature where stress is substantially relieved in
several hours. The strain point is determined by extrapolation of data
from annealing point studies. Other tests are also used for these two
reference points, with slightly different results.
Two other
reference temperatures are often quoted for glass forming melts. While
neither of these temperatures represent exact viscosities, they are
convenient for relative comparison of the viscosity of different
compositions. The glass transformation temperature, Tg, can be
determined from measurements of the temperature dependence of either
the heat capacity or the thermal expansion coefficient during reheating
of a glass. This temperature is somewhat dependent upon the property
measured and on the heating rate and sample size used in the
measurement. As a result, different studies will report slightly
different values for Tg for supposedly
identical glasses. Moynihan has shown that the viscosity corresponding
to Tg for common
glasses has an average value of 1011.3 Pa s. This value
appears to decrease for glasses with very low glass transformation
temperatures.
Another
viscosity point can be obtained from thermal expansion curves. The dilatometric
softening temperature, Td, is usually
defined as the temperature where the sample reaches a maximum length in
a length versus temperature curve during heating
of a glass. Varies slightly with the load applied to the sample by the
dilatometer mechanism and the sample size. The viscosity corresponding
to Td lies in the
range 108-109 Pa s.
Viscoelasticity
At low
viscosities, glass forming melts usually behave as Newtonian liquids,
which immediately relax to relieve an applied stress. At extremely high
viscosities, however, these liquids respond to the rapid application of
a stress as if they were actually elastic materials. It follows that
there must exist an intermediate range of viscosities where the
response of these melts to application of a stress is intermediate
between the behavior of a pure liquid and that of an elastic solid.
Since this behavior has aspects of both viscous flow and elastic
response, it is known as viscoelasticity, or
viscoelastic behavior.
Since the
response of a liquid to the application of an external stress is
dependent upon the rate of application of that stress, viscoelasticity
can occur over a wide range of viscosities.
