Understanding Cell Volume: Why It's Independent of Choice

Click For Summary
SUMMARY

The volume of a primitive cell in crystallography is inherently independent of the choice of the cell due to its definition. A primitive cell contains the minimum number of atoms necessary to construct the entire lattice. Alterations to the cell, such as cutting from one side and adding to another, do not affect its overall volume. This principle is fundamental in understanding the properties of crystalline structures.

PREREQUISITES
  • Understanding of crystallography concepts
  • Familiarity with primitive cells and lattice structures
  • Knowledge of atomic basis in crystal formation
  • Basic principles of volume calculation in geometry
NEXT STEPS
  • Research the concept of lattice types in crystallography
  • Explore the relationship between primitive cells and unit cells
  • Learn about volume calculation methods for different crystal structures
  • Investigate the implications of cell choice on material properties
USEFUL FOR

Students and professionals in materials science, crystallographers, and anyone studying the structural properties of solids will benefit from this discussion.

beman
Messages
16
Reaction score
0
"Volume of a primitive cell is independent of the choice of the cell."
Why?
 
Physics news on Phys.org
Because, by definition, a cell is primitive if it contains exactly the smallest number of atoms possible (the smallest possible basis) from which the entire lattice can be constructed.

Once you have one possible primitive cell you can obtain others by cutting off a bit on one side and adding it on the opposite side. Obviously, this operation does not change the volume of the cell.
 
  • Like
Likes   Reactions: 1 person

Similar threads

Undergrad Why Do Different Primitive Unit Cells for Diamond Look So Different?
  • · Replies 2 ·
Replies
2
Views
7K
Graduate Primitive cell parameter given chemical unit cell info
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Converting Unit Cell Volumes of Minerals to Density
  • · Replies 3 ·
Replies
3
Views
2K
Graduate What is the Wigner–Seitz cell of diamond?
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Trying to understand the inner workings of a solar cell
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Tools to transform primitive cell orientation
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Why is the volume of FCC and BCC different in reciprocal space?
  • · Replies 1 ·
Replies
1
Views
31K
MCNP6.2 - Are results of FMESH tallies already divided by cell volume?
  • · Replies 2 ·
Replies
2
Views
2K
MCNP6: Cell Volume Not Calculated - Assymetrical
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Are solar cells operated under any kind of bias or not?
  • · Replies 3 ·
Replies
3
Views
6K