Rutile is a mineral composed of Ti and O. Its unit cell, shown in the drawing, contains T atoms

step 1 Rutile is a mineral composed of titanium and oxygen. Its unit cell contains titanium atoms at ea

Rutile is a mineral composed of Ti and O. Its unit cell,...

Rutile is a mineral composed of $\mathrm{Ti}$ and $\mathrm{O}$. Its unit cell, shown in the drawing, contains $T$ atoms at each corner and a Ti atom at the center of the cell. Four $\mathrm{O}$ atoms are on the opposite faces of the cell, and two are entirely within the cell. (a) What is the chemical formula of this mineral? (b) What is the nature of the bonding that holds the solid together? (c) What is the coordination number of each atom?

Key Concepts

Unit Cell Structure

This concept describes the smallest repeating arrangement of atoms in a crystal lattice. It involves analyzing the positions of atoms within the cell, including those at the corners, faces, edges, and interior. Understanding this structure is vital for determining how many atoms actually belong to a single cell through the use of fractional contributions from atoms on shared positions.

Fractional Atomic Counting and Stoichiometry

In crystallography, atoms located on the edges, faces, or corners of a unit cell contribute only a fraction of an atom to that specific cell. By summing these fractional contributions along with any atoms that lie entirely within the cell, one can determine the empirical chemical formula of a compound. This process is essential for converting geometric arrangements into chemical formulas.

Bonding in Solids

This key concept encompasses the different types of bonds that hold a solid together, such as ionic, covalent, and metallic bonds. Understanding the nature of the bonding involves looking at the differences in electronegativity, electron sharing, and electron transfer, which help explain the unique physical and chemical properties of the material. In many compounds derived from metal and non-metal elements, the bonding often shows a combination of ionic and covalent characters.

Coordination Number and Local Geometry

The coordination number refers to the number of nearest neighboring atoms or ions surrounding a central atom within a crystal lattice. This number elucidates the local geometry around an atom, which is important for understanding the structural, mechanical, and electronic properties of the material. It is foundational in solid-state chemistry and crystallography for determining how atoms interact within a lattice.

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