Figure 1 Absorption bands of Fe2+, Fe3+, and Cr3+ in a glass melt, and radiation intensity in the combustion space of a furnace illustrated in a simplified way by black‐body radiation emitted at 1600 °C from the upper lining (the crown) of the furnace; relative intensities.
3.2 Calculation of Batch Composition
An accurate chemical analysis of every raw material is a prerequisite for batch preparation (Chapter 1.2). On this basis, one swiftly determines the batch composition by solving a system of linear equations where data are arranged in a specific way (Table 2). First, the total number of different oxides in the raw material basis is determined (6 in the example shown). The target glass composition is entered as an oxide column vector YTARGET. The large matrix shaded in gray contains the results of raw‐material analyses. It is arranged in the order of carriers of the respective glass oxides. For each oxide that is not represented by a specific raw material, the entry 1 is filled in the matrix. If an oxide has more than one carrier raw material (in the example, Al2O3 has two carriers, namely feldspar and Calumite®), then their ratio has to be specified, and the respective column entries are merged to a single column in proportion of this ratio. Through these operations, the gray area takes the form of a square matrix M. Next, a preliminary vector RPRE of the batch composition is obtained from the product RPRE = M −1·YTARGET. It may contain negative figures since it is impossible to make for example an iron‐free glass from iron‐containing raw materials. To derive the actual batch‐composition vector R, these negative figures are thus set to zero. The real glass composition is then given by the product YREAL = M·R before YREAL is normalized to 100 wt % and R to 1000 kg of resulting glass, or 2000 kg of sand (see following paragraph), or to any other convenient reference mass.
Table 2 Batch calculation scheme.
| The glass | The raw material basis | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Raw material | Sand | None | Feldspar | Calumite® | None | Dolomite | Limestone | Soda ash | None | |||
| For oxide | SiO2 | TiO2 | Al2O3 | Al2O3 | Fe2O3 | MgO | CaO | Na2O | K2O | |||
| Ratio | 0.5 | 0.5 | ||||||||||
| Y TARGET | Y REAL | |||||||||||
| Oxide | wt % | wt % | Oxide | kg/kg | kg/kg | kg/kg | kg/kg | kg/kg | kg/kg | kg/kg | kg/kg | kg/kg |
| SiO2 | 72.00 | 71.80 | SiO2 | 0.9960 | 0.6920 | 0.3550 | 0.0002 | 0.0040 | ||||
| TiO2 | 0.00 | 0.04 | TiO2 | 0.0001 | 1.0000 | 0.0080 | ||||||
| Al2O3 | 1.50 | 1.50 | Al2O3 | 0.0009 | 0.2010 | 0.1250 | ||||||
| Fe2O3 | 0.00 | 0.03 | Fe2O3 | 0.0002 |
