Introduction of carbon into a metallic lattice generally results in a harder, less ductile substance with lower electrical and thermal conductivities. Explain why this might be so.

A metallic lattice consists of positively charged metal ions surrounded by a sea of delocalized electrons, also known as free electrons. These free electrons are responsible for the electrical and thermal conductivity in metals and also contribute to the ductility of the material, as they allow the ions to slide past each other when a force is applied.

When carbon atoms are introduced into the metallic lattice, they generally occupy the interstitial sites (spaces between the metal ions). Carbon atoms have a different size and charge compared to the metal ions, causing a distortion in the overall lattice structure. This distortion restricts the movement of the free electrons and the metal ions in the lattice.

- Hardness: The presence of carbon atoms increases the hardness of the alloy because the distortion in the lattice structure causes an increase in the resistance to dislocation movement. Dislocations are defects in the lattice that enable the metal ions to slide past each other when a force is applied. The restricted movement due to carbon atoms makes it harder for dislocations to move, increasing the material's resistance to deformation, and thus increasing the hardness. - Ductility: Considering the increased hardness, the ductility of the material (its ability to be drawn out into a thin wire or bend without breaking) is reduced. The carbon atoms in the lattice restrict the movement of metal ions and dislocations when deforming the material, making it more likely to crack or break instead of bending or stretching. - Electrical conductivity: The presence of carbon atoms also affects the movement of free electrons in the lattice by distorting the lattice structure. The restricted movement of the free electrons results in reduced electrical conductivity, as fewer electrons are available to flow through the material under an external electric field. - Thermal conductivity: Similar to the case of electrical conductivity, the lattice distortion due to the presence of carbon atoms also hinders the movement of free electrons responsible for thermal conduction. As a result, the thermal conductivity is reduced in a material with carbon atoms in its lattice structure.

In conclusion, the introduction of carbon atoms into a metallic lattice results in a harder, less ductile substance, with lower electrical and thermal conductivities. This is because the carbon atoms distort the lattice structure, restricting the movement of free electrons and dislocations, which affects the various properties of the material.