Pure iron crystallizes in a body-centered cubic structure, shown in the figure. but small amounts of impurities can stabilize a facecentered cubic structure. Which form of iron has a higher density?

Verified step by step guidance

1. Identify the two types of crystal structures mentioned: body-centered cubic (BCC) and face-centered cubic (FCC).
2. Recall the formula for density: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \).
3. Determine the number of atoms per unit cell for each structure: BCC has 2 atoms per unit cell, and FCC has 4 atoms per unit cell.
4. Calculate the volume of the unit cell for each structure using the lattice parameter \( a \): For BCC, \( a = \frac{4r}{\sqrt{3}} \), and for FCC, \( a = \frac{4r}{\sqrt{2}} \), where \( r \) is the atomic radius.
5. Compare the densities by considering the mass of the atoms in the unit cell and the calculated volume for each structure.

Key Concepts

Crystal Structure

Crystal structure refers to the orderly arrangement of atoms in a crystalline material. In body-centered cubic (BCC) structures, atoms are located at the corners of a cube with one atom at the center, while in face-centered cubic (FCC) structures, atoms are at the corners and the centers of each face of the cube. The arrangement affects properties like density and packing efficiency.

Density Calculation

Density is defined as mass per unit volume (density = mass/volume). The density of a crystalline material can be influenced by its atomic arrangement and the mass of the atoms involved. In general, FCC structures tend to have higher packing efficiency than BCC structures, which can lead to differences in density between the two forms of iron.

Effect of Impurities

Impurities in a material can alter its crystal structure and properties. In the case of iron, small amounts of certain impurities can stabilize the FCC structure, which typically has a higher density than the BCC structure. Understanding how impurities affect the arrangement of atoms is crucial for predicting changes in physical properties like density.