Question

The electrical conductivity of titanium is approximately 2500 times greater than that of silicon. Titanium has a hexagonal close-packed structure, and silicon has the diamond structure. Explain how the structures relate to the relative electrical conductivities of the elements.

Short answer

The hexagonal close-packed (hcp) structure of titanium allows for free-electron gas, enabling high electrical conductivity. In contrast, the diamond structure of silicon has covalently bonded atoms in a tetrahedral arrangement, making electrons less free to move, resulting in lower electrical conductivity. Thus, titanium's hcp structure leads to a conductivity approximately 2500 times greater than silicon's diamond structure.

Step-by-step solution

1. Hexagonal Close-Packed Crystal Structure

The hexagonal close-packed (hcp) crystal structure is one of the most common and most efficient ways to pack spheres in three-dimensional space, with each sphere being surrounded by 12 other spheres. In an hcp structure, the atoms are arranged in a hexagonal lattice, where each row of atoms is shifted with respect to the previous, which ultimately results in a three-dimensional packing of atoms. This structure is prevalent in many metals, including titanium.

2. Diamond Crystal Structure

The diamond crystal structure is a tetrahedral crystal structure that is found in elements such as silicon, germanium, and carbon in the form of diamond. In this structure, each atom is bonded covalently to four other atoms in a tetrahedral arrangement. These covalent bonds create a strong, rigid structure in which electrons are not free to move throughout the material.

3. Electrical Conductivity

Electrical conductivity is the measure of a material's ability to conduct an electric current. In metals, the conductivity is usually high because they possess a 'free-electron gas' in their crystal structure. In such arrangements, the electrons are available for conduction and can move freely throughout the material. However, in materials like silicon, the electrons are bound in covalent bonds and are thus not free to move about and contribute to the electrical conductivity.

4. Explaining the Relative Electrical Conductivities of Titanium and Silicon

The hcp structure of titanium allows for free-electron gas, resulting in a higher electrical conductivity. In contrast, the diamond structure of silicon consists of covalently bonded atoms in a tetrahedral arrangement. These covalent bonds hold the electrons tightly and do not allow them to move freely, resulting in the lower electrical conductivity of silicon. Therefore, the crystal structures of titanium and silicon are directly related to their electrical conductivities, with the hcp structure of titanium resulting in a conductivity approximately 2500 times greater than that of the diamond structure of silicon.