Introduction

Glass is defined by ASTM as “an inorganic product of fusion which has cooled to a rigid condition without crystallizing.” This definition is rather outdated, though, as it excludes all organic glasses (polymers) and implies that glass must be made as a product of cooling a melt or liquid; if such was the case, all optical fibers and many advanced glass applications would have to be excluded, as sol-gel and chemical vapor deposition processes are alternatives to the cooled-from-melt synthesis of glass. However, this discussion will primarily deal with conventional silica-based glasses such as those used in windows, bottles, and tableware.

Soda Lime Silica Glass System

The largest corners of the glass market are in flat glass (windows) and glass containers (beverage bottles); these glasses are primarily soda-lime silicate glasses which contain soda (Na2O), lime (CaO), and silica (SiO2) as their primary constituents in a 16-10-74 ratio:

16 wt% Na2O + 10 wt% CaO + 74 wt% SiO2

Each component in this system has a vital purpose:

Silica (SiO2) is a glass former. At high temperatures, it liquefies into a very viscous melt that general impedes crystallization kinetically when it goes below its melting temperature. However, silica melts at 1713°C, and its viscosity at this point is too high to work with with any reasonable amount of effort. Temperatures in excess of 2000°C must be attained to work pure silica glasses, and these temperatures tend to render such pure silica glasses economically unviable for the majority of glass applications.

Soda (Na2O) is a flux. Its addition reduces the melting temperature of the silica melt dramatically. However, its addition also makes the resulting glass soluble in water.

Lime (CaO) is a stabilizer. Although an excess of calcium oxide to a silica melt will cause devitrification, additions of small amounts of lime stabilize the glass melt with respect to water, fixing the problem of water solubility introduced with the soda component.

Glass Additives

As it turns out, silica is a very good solvent and can dissolve far more oxides than just the above two (soda and lime) in it readily. In fact, many metal oxides can be added to silica melts to contribute different properties to the resulting glass.

  • Alumina (Al2O3) is often added to soda lime glasses at around 1% to provide increased durability
  • Silica (SiO2) not only forms the glass, but its weight percent is an indication of the thermal expansivity of the glass; more silica means lower thermal expansion (and therefore higher resistance to thermal shock)
  • Soda (Na2O) increases the viscosity of the glass melt at a given temperature by is relatively expensive
  • Lime (CaO) contributes to the crystallinity of a glass and is relatively inexpensive as a raw material
  • Boron oxide (B2O3) is a glass former like silica and increases the chemical resistance of the glass
  • Lead oxide (PbO) increases the refractive index of the glass as well as its density; at 24-28% PbO, the glass is considered “crystal,” and in higher amounts creates an x-ray absorptive glass
  • Barium oxide (BaO) is a heavy ion and therefore increases the refractive index and absorptivity of a glass without the harmful effects of lead
  • Conversely, Soda (Na2O) and lithia (Li2O), both light elements, make for good x-ray transmittive glasses for x-ray tubes
  • Cadmium oxide (CdO), a good neutron absorber used in nuclear reactors, can be added as an oxide to glass to make radiation shielding glasses
  • Transition metals’ unfilled d-shells also allow for selective absorptivity when in a glass; for example, chromia (Cr2O3) gives a green tint to glass; neodymium (III) oxide (Nd2O3) colors glass purple, and iron (III) oxide (Fe2O3) lends a green tint
  • Iron (II) oxide (FeO) also couples with infrared, resulting in an IR-absorptive glass

Reducing FeO to Fe2O3 in glasses (using carbon as a reducing agent) can transform a heat-absorptive glass into an IR-transmissive glass. This makes it more suitable for optical fibers, since optical data transmission usually operates in the IR spectrum.

Methodology of Glass Composition Determination

Because the raw materials for glasses are often in carbonate form (for stability reasons) or beneficiated as minerals (compounds containing several oxides), determining the glass composition from raw material batches requires a little mathematics. For the soda-lime silicate (SLS) glass, the raw materials often vary:

  • Sand is “pure” SiO2; its ratio of oxide to total weight is ~100%. Its true purity varies depending on the site from which it was mined.
  • Soda ash is sodium carbonate (Na2CO3); when heated, it transforms into Na2O and CO2. Its oxide to total weight ratio is 0.585 mass units soda per mass unit of soda ash
  • Limestone is calcium carbonate (CaCO3) and releases CO2 on decomposition like soda ash. There are 0.56 units of lime per unit of limestone.
  • Soda feldspar/albite (Na2O-Al2O3-6SiO2) is a mineral which contributes both soda and alumina to glass. It contains 0.118 units soda per unit soda feldspar, 0.194 units alumina per unit soda feldspar, and 0.687 units silica per unit soda feldspar.

Knowing these factors (which are simply / ) allows one to calculate the glass batch composition given a raw material composition. For example, given

  • 2000 lbs sand
  • 800 lbs soda ash
  • 360 lbs limestone

one can calculate the glass batch composition by multiplying the weight of each raw material by its oxide factor:

  • 2000 × 1.0 = 2000 lb SiO2
  • 800 × 0.585 = 468 lb Na2O
  • 360 × 0.560 = 202 lb CaO

This results in a total of 2670 lbs of glass; dividing each oxide mass by this total mass results in the glass batch composition:

  • 20002670 = 74.9% silica
  • 4682670 = 17.5% soda
  • 2022670 = 7.6% lime

This technique can be applied to raw batches containing minerals (such as albite); one must just remember that in such a case, there are multiple sources of each oxide. For example, the addition of albite to the above raw material batch would require one to add the silica, alumina, and soda contributions to the total silica, alumina, and soda masses before summing and dividing to obtain the mass percents of the glass batch.

Calculating the mass of raw materials needed to obtain a given glass batch composition is a more practical exercise and is equally as simple. If one was to create a 16-10-74 batch of soda lime silica glass (mass percents identified respectively), one would just assume 16 units of soda, 10 units of lime, and 74 units of silica would be needed. Dividing these required amounts by the mass factors of the raw materials would produce masses of each raw material needed:

  • 16 units soda / 0.575 units soda per unit soda ash = 27.35 units soda ash needed
  • 10 units lime / 0.580 units lime per unit limestone = 17.86 units limestone needed
  • 74 units sand / 1.0 units silica per unit sand = 74 units sand needed

By convention, these masses of raw material are then normalized around an English ton of sand. Thus, for each mass of raw material needed, divide by 74 (the quantity of sand needed for the desired batch) and multiply by 2000 (pounds of sand around which the rest of the raw materials are normalized).

Empirical Determination of Glass Density

Because silica is a “universal solvent,” glass compositions are continuously variable; thus, their properties (such as refractive indices, densities, resistance to chemical/thermal shock, et cetera) are also continuously variable and not constrained by the stoichiometric boundaries which fix chemical compounds’ properties. Measuring all of these properties on an industrial scale is often impractical; for example, having fluoresence instrumentation at a glass manufacturing plant is not economically feasible. It follows that density is used as a surrogate property of composition (and therefore refractive index, shock resistances, and so on). There are several ways to measure glass density easily.

The sink/float method of density measure is unique to the glass industry and capitalizes on the linear relationship between the composition of a mixture of organic liquids and the density of the mixture. It involves filling a container with a liquid of density slightly higher than the glass sample to be measured; this causes the glass sample to float on its surface. The liquid is then heated precisely, causing the liquid to expand and therefore decrease in density. The temperature at which the glass begins to sink is recorded.

By using 20°C as a reference temperature and knowing that the organic liquids most often used for these analyses expand at roughly 0.0018 grams per cc per degree C, one can reason that every for every 10°C the liquid temperature is raised, the liquid density decreases by about 0.02 g/cc. Thus, if a piece of glass sinks into the liquid at 35°C, it can be estimated that that piece of glass’ density is 0.03 g/cc lower than the organic liquid’s density at 20°C.

It is also of notable importance to measure the density distribution of a region of glass; regions of different composition from the bulk (such as those due to surface volatization of sodium atop the melt) that get folded back into the glass melt create string-like regions of the bulk glass liquid that are depleted or enriched with a certain element called cord. When the glass melt is poured and cooled, it may have regions of inhomogeneity (which can be detected as variations in density) due to this cord.

By means of pouring two organic liquids of very different density into a column at varying rates, it is possible to set up a column of liquid with a linear density gradient, or a situation where a higher concentration of the denser liquid at the bottom and a higher concentration of the lighter liquid at the top. Pulverizing a glass sample that contains a piece of cord and pouring it into this density gradient results in the pieces of glass reaching neutral buoyancy at different distances down the column. Effectively, this easily sorts the glass powder according to density on a continuous scale.

It is also important to know that, according to convention in the glass industry, such density distributions are expressed in the somewhat cryptic unit “degrees C” - this means that, knowing that every 10°C is equivalent to a 0.02 g/cc change in density of the organic liquids, all of the glass particles sink over the stated temperature range. Thus, a density distribution of 10°C means that all of the glass particles are within 0.02 g/cc of each other.

Theoretical Determination of Glass Density

Glass density is often a parameter in glass composition determination, and calculating the density of a hypothetical batch is of great interest. Physical theory implies that the molar volume of a mixture should be additive; that is, the molar volume of a material should be the mass-weighted sum of its constituents. Of course, the inverse of the molar volume is the molar density, and from this the mass density can be calculated.

In terms of glasses, knowing the molar volumes of crystalline and glassy phases of glass-forming materials allows one to extrapolate the glass-phase molar volume of oxides which in fact do not even form glasses.

Why is knowing the molar volume of a non-existant glassy oxide of any use? As it turns out, because the inverse of molar volume is molar density (and specific volume’s inverse is specific mass, or density) and molar volumes are additive in mixtures, the density of a glass can be roughly calculated by knowing these hypothetical and real glassy-phase molar volumes. For example, the 16-10-74 soda-lime silica glass’ constituents have specific volumes of…

  • SiO2 - 0.454 cc/gram
  • Na2O - 0.288 cc/gram (this is a hypothetical specific volume)
  • CaO - 0.303 cc/gram (another hypothetical specific volume)

Adding these specific volumes together on a mass-weighted basis yields

0.16 Na2O × 0.288 + 0.10 CaO × 0.303 + 0.74 × 0.454 = 0.412 cc/gram

Inverting this specific volume yields the theoretical density of a 16-10-74 soda lime silica, which comes out to be 2.425 g/cc. The real density of 16-10-74 SLS is actually 2.5 g/cc; thus, this method (called the English-Turner method) of density estimation is roughly accurate on an absolute basis.

However, it is considerably more precise in predicting the effect on density caused by slight variations in composition (such as those caused by surface volatization of sodium). These changes in density due to compositional variation are expressed in the same was a density distributions as stated in the previous section - in degrees C.