Unit Cell Chemistry Simple Cubic, Body Centered Cubic, Face Centered Cubic Crystal Lattice Structu
Introduction to Unit Cells
Overview of Unit Cell Structures
- The video introduces three types of unit cell structures: simple cubic, body-centered cubic, and face-centered cubic.
- Each structure contains a different number of atoms per unit cell:
- Simple cubic: 1 atom
- Body-centered cubic: 2 atoms
- Face-centered cubic: 4 atoms
Coordination Numbers
- The coordination number indicates how many atoms are adjacent to a single atom:
- Simple cubic: Coordination number is 6.
- Body-centered cubic: Coordination number is 8.
- Face-centered cubic: Coordination number is 12.
Volume Efficiency of Structures
- Volume efficiency varies among the structures:
- Simple cubic occupies 52% of its volume with atoms (48% empty space).
- Body-centered cubic has an efficiency of 68%, leaving 32% as empty space.
- Face-centered cubic is the most efficient at 74%, with only 26% empty space.
Edge Length and Atomic Radius Relationships
Definitions and Relationships
- Edge length (denoted as x) refers to the side length of the cube, while r represents the atomic radius.
Formulas for Different Structures
- For each structure, there are specific formulas relating edge length to atomic radius:
- Simple Cubic: x = 2r
- Body-Centered Cubic: x = 4/sqrt3 r
- Face-Centered Cubic: x = sqrt8 r
Detailed Analysis of Simple Cubic Structure
Atoms in Unit Cell
- In a simple cubic structure, there are eight corner atoms contributing one-eighth each, totaling one full atom per unit cell.
Coordination Number Explanation
- Each atom in this structure is surrounded by six others—above, below, left, right, front, and back—leading to a coordination number of six.
Volume Calculation Methodology
- The volume formula for a cube is x^3 . Given that x = 2r , substituting gives:
[
V_cube = (2r)^3 = 8r^3
]
Volume Ratio Calculation
- To find the ratio of atomic volume to cube volume:
[
V_atoms = 4/3pi r^3
]
Resulting in approximately 52.36% occupancy when calculated against total cube volume.
Body-Centered Cubic Structure Insights
Atom Count Per Unit Cell
- This structure contains two atoms per unit cell; eight corner atoms contribute one-eighth each plus one whole atom at the center.
Coordination Number Clarification
- The central atom connects with eight corner atoms leading to a coordination number of eight.
Edge Length Derivation Process
- The edge length relates to atomic radius through diagonal calculations involving right triangles within the cube.
Volume Occupancy Confirmation
- Calculating relative volumes shows that body-centered cubics occupy about 68% of their total volume with matter.
This structured approach provides clarity on key concepts related to unit cells while allowing easy navigation through timestamps for further exploration.