Mass transfer and reactions at high temperature
Atoms in a solid are not still. They vibrate around their places. The hotter it is, the bigger the vibration. Sometimes an atom gets enough energy to jump into a gap or a missing place (a vacancy). This hopping from place to place is diffusion, one kind of mass transfer.
Diffusion in a solid is very slow when it is cold and speeds up very fast when it is hot. The rule is D = D₀ × e−Q/RT: D is the diffusion rate, Q the energy an atom needs to jump (activation energy), R the gas constant and T the temperature in kelvin. A small rise in T gives a big rise in D.
Two solid powders can react without melting: this is a solid-state reaction. For example, MgO + Al₂O₃ make spinel MgAl₂O₄ at about 1400 °C. The reaction starts only where grains touch. A product layer forms there, and now the atoms must diffuse through that layer to meet. So the layer grows slower and slower. Its thickness follows x² = k × t: four times as long gives only twice the thickness.
Fine powder, pressing the grains together and higher temperature all speed up the reaction. The same hopping also joins grains in sintering, which makes a fired pot hard.
Melting and crystallisation
When a crystal is heated to its melting point, the vibration becomes so big that the ordered rows fall apart and the solid becomes a liquid. It takes energy (latent heat) to do this, so the temperature stays flat while it melts.
Crystallisation is the reverse. When the liquid cools, a few atoms group together in the right pattern. This tiny seed is a nucleus (nucleation). More atoms then stick to it in the same pattern: crystal growth. Many nuclei give many small crystals (fine grain); few nuclei give a few large crystals.
A liquid can stay liquid a little below its melting point. This is supercooling. If the liquid is cooled so fast that the atoms never find their places, we get glass instead of a crystal.
A mixture often melts lower than either pure part. Potters and glass makers add a flux, such as soda or lime, to melt silica at a lower temperature and save fuel.
Oxidation and reduction at high temperature
Oxidation is a substance gaining oxygen or losing electrons. Reduction is losing oxygen or gaining electrons. They always happen together (a redox reaction).
Example of reduction: metal oxide + carbon at high temperature. MO + C → M + CO. The carbon takes the oxygen away, so the metal oxide is reduced and carbon is oxidised. This is how iron, zinc and many metals are got from ores. High temperature is needed because the bond between metal and oxygen is strong.
Whether carbon can do this job depends on temperature. Carbon's ability to take oxygen grows with temperature, so a hot enough furnace can reduce oxides that carbon cannot reduce when cool. (A chart called the Ellingham diagram shows this for each metal.)
Furnace atmosphere matters. In an oxidising kiln (plenty of air) iron in clay stays Fe₂O₃ and the pot turns red. In a reducing kiln (little air, smoke) iron becomes FeO or Fe₃O₄ and the pot turns grey or black. Some non-oxides, like silicon carbide, form a thin protective SiO₂ skin when heated in air, and that skin saves the rest from burning.
Key formulas and definitions
- D = D₀ × e^(−Q/RT) (T in kelvin)
- x² = k × t (product layer thickness x after time t)
- T(K) = T(°C) + 273
- Reduction by carbon: MO + C → M + CO
- Key terms: diffusion, vacancy, sintering, nucleation, supercooling, flux, redox
Worked examples
1. Convert the firing temperature 1400 °C to kelvin.
T = 1400 + 273 = 1673 K.
2. A product layer is 2 µm thick after 1 hour, and it follows x² = kt. How thick is it after 4 hours?
x² = k t, so x ∝ √t. x₂ = 2 µm × √4 = 4 µm. Four times the time gives twice the thickness.
3. In the reaction ZnO + C → Zn + CO, which is oxidised and which is reduced?
ZnO loses oxygen, so it is reduced to Zn. Carbon gains oxygen to make CO, so carbon is oxidised.
4. Why does a fine powder react faster than a lump of the same solid at the same temperature?
A fine powder has many more grain contacts, so the reaction starts in many places and atoms have shorter distances to travel.
Common mistakes
- Thinking solids must melt to react. Many ceramic reactions happen with all solids, by diffusion.
- Using °C in the exponent e^(−Q/RT). Always use kelvin.
- Assuming the product layer grows at a steady rate. It slows down because atoms must cross a thicker layer.
- Mixing up oxidation and reduction: in MO + C → M + CO the oxide is the one reduced, even though it was "oxygen" that moved.