Understanding Atoms in a Simple Cubic Crystal
In a simple cubic crystal structure, atoms are arranged in a cubic lattice with one atom per lattice point. This configuration allows for straightforward calculations regarding the number of atoms per unit area on specific crystal planes.
Determining the (010) Plane
The (010) plane in a simple cubic crystal refers to a plane that intersects the y-axis at 1 and is parallel to the x-z plane. Here’s how to calculate the number of atoms per unit area for this plane:
Unit Cell Description
- A simple cubic unit cell contains:
- 1 atom located at each corner of the cube.
- Each corner atom is shared among 8 adjacent unit cells, contributing 1/8 of an atom per cell.
Atoms on the (010) Plane
- Observing the (010) plane:
- The atoms at coordinates (0,0,0) and (1,0,0) contribute fully to this plane.
- The atoms at (0,1,0) and (1,1,0) are also fully within this plane.
Counting Atoms
- Total atoms in the (010) plane:
- There are 4 atoms at the corners that contribute to this plane.
Area Consideration
- The area of the (010) plane can be considered as:
- The cross-section of the unit cell which is 1 unit by 1 unit (1 square unit).
Final Calculation
- The number of atoms per unit area is calculated as:
- Number of atoms (4) / Area (1) = 4 atoms per unit area.
In summary, the (010) plane of a simple cubic crystal contains 4 atoms per unit area, reflecting the efficient packing of atoms in the crystal structure.