6) Physical properties of glass:
1. Structural properties of glass:
a) Density and Molar volume:
Density ρ is defined as mass per unit volume. Appropriate units are g/cm 3 (or
g/cc) in the cgs system and kg/m3 in the SI system.
Relative density is defined as density with respect to water at 4°C and is,
hence, unitless. Because the density is inversely proportional to the volume, a
change ΔT in temperature changes the density by –3α ΔT, where α is the
linear thermal expansion coefficient. Molar volume VM is the volume of one
mole formula weight and is computed by:
VM = M/ρ
where M is the mol weight in grams with the formula of glass expressed on a
one-molecule basis (or on a one-atom basis for elemental glasses, such as the
chalcogenides). Thus, a glass of the formula Na2O·Al2O3· 6SiO2 should be
first written as 1/8Na2O · 1/8Al2O3 · 6/8SiO2 to obtain the value of M.
Dependence on Composition:
Density of silica glass is 2.20 g/cm3 at room temperature. There is no
detectable difference observed in density of silica regardless of the different
methods of production. Of the various forms of crystalline silica, the density
of silica glass is closest to that of β-cristobalite (high-temperature form),
which is 2.25 g/cm3. Since the density of α-quartz is 2.65 g/cm3, it is apparent
that large structural changes occur during the melting of sand. Addition of
alkalis to silica increases the density steadily: The alkali ions go inside the
interstices as NWM, taking up holes. Heavier alkali ions generally are more
effective in increasing the density. Likewise, heavy elements such as Ba, Cd,
Pb, and Bi bring large increases in the density.
Because density can be measured readily and accurately to the third decimal
place, and because it is extremely sensitive to composition, density charts are
often used to control the quality of glass production in a commercial
environment.
b) Viscosity:
Viscosity is a property typical of the liquid state describing its flow due to
externally applied stresses. Analogously to Hooke’s law for elasticity, an
externally applied shear stress and the developed shear strain rate are related
through Newton’s law of viscosity:
σxy = η dexy /dt
where η is called the coefficient of viscosity (or simply the viscosity) and has
the units P (poise in the cgs system) and Pa · s (pascal-seconds in the SI
system), where 1 Pa · s = 10 P. Viscosity is the reciprocal of fluidity.
Viscosity-Temperature Dependence:
Viscosity is the single most important physical property that allows
continuous glass forming on an industrial scale. glassmaking involves melting
the glass in a suitable continuous feed container, transporting the molten glass
stream to a forming machine and, after forming a desired product, extracting
heat out of the formed product in a controlled but continuous manner till the
body is rigid. The viscosity-temperature dependence of glass-forming melts is:
η = η0 exp(ΔH/RT)
where R is the gas constant, T the absolute temperature (kelvin scale), ΔH is
the activation energy for viscous flow, and η0 is the preexponential.
However, this equation does not fit well over the entire temperature range of
practical interest. Apparently, a superior empirical fit to inorganic silicate melt
viscosity data is given by the Vogel-Fulcher-Tammann relation (the VFT
relation, also called the Fulcher relation):
log η = − A + B/(T − T0)
where A, B, and T0 are empirically determined constants. This relationship
suggests that the glass viscosity tends to infinity as the temperature
approaches T0 from above. Glass manufacturers often tabulate the values of
A, B, and T0 for their product literature. The various steps of glass forming are
essentially determined by using the η-T curve. Four viscosity reference
temperatures are used as guidelines:
Working point is the temperature at which the viscosity is 10 4 poise. This is
the viscosity at which a machine is able to work on glass without losing
control.
Softening point is the temperature at which the viscosity is 10 7.6 poise. This is
the approximate viscosity at which a glass will deform under its own weight
on the time scale of manufacturing operations. Glass temperature must be
lower than this before the glass leaves the forming machine.
Annealing point is the temperature at which the viscosity is 10 13 poise.
Stresses that form in the glass object are relieved at this viscosity in a matter
of minutes.
Strain point is the temperature at which the viscosity is 10 14.5 poise. Stresses
that form in the glass object are relieved at this viscosity in a matter of hours.
In addition, some industrial consultants use melting point (viscosity = 100
poise) and flow point (viscosity = 105 poise).
Viscosity-temperature dependence of a typical soda-lime-silicate glass is
shown in Fig. 5.1. Glass is melted at around 1450°C, delivered to a forming
machine around 1000°C, placed on a conveyor belt as a formed product at
temperatures lower than about 700°C, and annealed between 530°C and
480°C.
FIGURE 5.1 Viscosity η versus temperature for a typical soda-lime-silicate glass.
c) Surface energy
Surface energy γ: is the reversible work in creating a unit area of the surface.
and has the units of J/m2 in the SI system (or ergs/cm2 in the cgs system).
The surface tension of fluid glass is important in most glass-forming
processes. Particular attention must be paid to surface tension of glass in the
glass-forming processes, for instance, in glass blowing, and drawing processes
also those for tubing, float glass and fiberglass. In addition, the wetting
behavior of molten glass on other substrates such as metals and ceramics is
critically controlled by surface tension.
2. Thermal properties of glass:
a) Thermal expansion
When heat is given to a body, it normally expands. Thermal expansion is the
relative change in a given dimension when the body is heated.
The addition of thermal energy causes a pair of atoms to acquire a larger mean
interatomic separation (based on residence time) because of the asymmetric
potential well about each atom.
The linear thermal expansion coefficient (often called as TEC or TCE in
industry) α is obtained by dividing thermal expansion by the change in
temperature; i.e.,
α = ΔL/L0 ΔT
Because thermal expansion coefficient usually varies with temperature, an
average thermal expansion coefficient αm over the temperature range T1 to T2
is obtained as
αm = (L2 − L1)/L0(T2 − T1)
and the true expansion coefficient αT at temperature T as
αT = dL/L dT
Appropriate units for thermal expansion coefficient are /°C or cm/cm/°C. (The
reader is cautioned about the use of /°F as is common in U.S. industry. Also,
thermal expansion coefficient of glasses is often written in terms of × 10−7/°C,
as opposed to × 10−6/°C or ppm/°C for metals. The corresponding volume
expansion coefficients β are obtained by substituting V for L in the
expressions. For most solids with small expansion coefficients, β = 3α.
Temperature and composition dependence of thermal expansion
coefficient:
Fused silica and some other single-component glasses such as Zn(PO3)2, BeF2,
and GeO2 display anomalous negative thermal expansion coefficient in the
vicinity of absolute zero temperature. The exact cause of this behavior is not
clearly understood.
Between 20°C and 1000°C, a value of 5.5×10–7/°C is often quoted as the
linear thermal expansion coefficient for fused silica, making it one of the
lowest for silicate glasses and enables silica glass products to be extremely
resistant to thermal shock. Addition of alkali and alkaline earths, which act to
convert bridging oxygens to nonbridging, resulting in a decreased
connectivity, causes a steady increase in α. In general, the larger the NWM
ion concentration the larger the α (see Fig 5.2). On the other hand, the addition
of alkali to B2O3 glass increases the connectivity by converting triangularly
coordinated boron atoms to tetrahedral coordination. This increased
connectivity results in a decrease in α down to 13 to 17 mol% added alkali and
increasing subsequently because of steric influences.
The variation of α with the added alkali is shown in Fig 5.3.
FIGURE 5.2 Thermal expansion of R2O-SiO2 glasses.
The addition of TiO2 lowers the expansion coefficient of silica glass. A
7.5TiO2- 92.5SiO2 (wt%) glass, made by a vapor-phase process, has an α of
0 ± 0.3 × 10−7/°C over the 5 to 35°C range, and is sold under the trade name
ULE (ultralow expansion) glass.
The ultralow expansion is very desirable for earth-based and deep-spacebased telescope mirror applications.
The soda-lime glasses generally have α in the range of 85 to 95×10–7/°C,
which is “high” for a glass, making it quite susceptible to thermal shock. The
soft potash-soda-lead glasses also have similar values of α, making them and
soda-lime glasses a near-ideal pair to produce several glass products having
complex-shaped parts at an optimized lower total cost. (As an example, a
common household incandescent lamp shell is made out of soda-lime glass to
which the filament assembly is fused via a potash-soda-lead glass mount
structure).
Between the large-expansion soda-lime glasses or the lead glasses and the
low-expansion silica glasses are the borosilicates (α values in the range of 33
to 55 × 10−7/°C) and the alkaline earth aluminosilicates (α values in the range
of 40 to 60 × 10−7/°C).
FIGURE 5.3 Thermal expansion of R2O-B2O3 glasses.
b) Thermal Shock Resistance
When a glass plate has a temperature gradient that is a function of the
thickness direction z only, then it may be shown that planar stresses σ x or σy
are given by:
where Ta is the average temperature across the thickness. This implies that a
biaxial tensile stress develops wherever the temperature is less than the
average and a compressive stress develops where the temperature is higher
than the average. In either case, the magnitude of the stress is directly
proportional to the thermal expansion coefficient. The biaxial stress has the
same mathematical form as the temperature distribution.
FIGURE 5.4 Development of stresses across a wall due to thermal shock.
Hence, when the plate has a parabolic temperature distribution with center
temperature Tc and surface temperature Ts (such as that obtained in normal
cooling from both sides) a parabolic stress distribution is expected, with
outside surface having a tensile stress of the magnitude
and the center having a compressive stress of the magnitude
Because of a high probability of flaws on the surface, glass fracture may
result. The term (Tc − Ts) clearly depends on several parameters such as the
thermal diffusivity and the thickness in the direction of the heat flow.
c) Heat Capacity
The amount of thermal energy needed to raise the temperature of a unit
mass of the substance is called its heat capacity, denoted generally by Cp
when the measurement is made at constant pressure (for instance, under
laboratory atmosphere) or by Cv when the measurement is made at constant
volume. Appropriate units are cal/(g·°C) in conventional cgs units or J/(kg·K)
in SI units. Heat capacity is conveniently measured by using a differential
scanning
calorimeter (DSC), in which the rate of heat input to raise the temperature of a
small known mass of the substance, say 50 mg, at a specified rate is measured
and compared to that of the empty pan. A typical heat capacity versus
temperature curve for a soda lime silicate glass is shown in Fig. 5.5.
FIGURE 5.5 Thermal history dependence of heat capacity of glass showing steep rise in the
transition range.
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