Iridium crystallizes in a face-centered cubic unit cell that...

Iridium crystallizes in a face-centered cubic unit cell that has an edge length of $3.833 \AA$. The atom in the center of the face is in contact with the corneratoms, as shown in the drawing. (a) Calculate the atomic radius of an iridium atom. (b) Calculate the density of iridium metal.

Key Concepts

Density Calculation of Crystalline Materials

The density of a crystalline solid can be determined by relating the mass contained in a unit cell to the volume of that unit cell. This is typically done by calculating the number of atoms per unit cell, multiplying by the atomic weight (or mass), and then dividing by the cell volume while also considering Avogadro’s number for conversion from microscopic to macroscopic scales. This concept is vital in material science as it connects the microscopic atomic arrangement with bulk material properties such as density.

Face?Centered Cubic (FCC) Crystal Structure

The FCC structure is one of the most common and efficient packing arrangements in crystalline materials. In this structure, atoms are arranged at each of the corners and the centers of all the faces of the cube. This high degree of symmetry leads to specific relationships between the atomic radius and the cell parameter, and it determines the number of atoms per unit cell. Understanding the FCC structure is essential when analyzing how atoms are situated in a crystal and how they contribute to the material's properties.

Relationship Between Atomic Radius and Unit Cell Edge Length in FCC

In an FCC crystal, the atoms are in contact along the face diagonals of the cube. This results in a direct mathematical relationship between the atomic radius and the cell edge length. Specifically, the face diagonal is equal to four times the atomic radius, while the edge length relates to the face diagonal by a factor of ?2. Recognizing and applying this relationship allows one to compute the atomic radius from the known dimensions of the crystal lattice, a key step in understanding the structure of the material.

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