FALLSEM2018-19_MEE1005_ETH_MB309_VL2018191003386_Reference Material III_Linear and Planar densities1

Linear and Planar Atomic Densities
Linear Density:
Directional equivalency is related to the atomic linear density in the
sense that equivalent directions have identical linear densities.
The direction vector is positioned so as to pass through atom centers.
The fraction of line length intersected by these atoms is equal to the
linear density.
Planar Density:
Crystallographic planes that are equivalent have the same atomic planar
density. The plane of interest is positioned so as to pass through atom
centers.
Planar density is the fraction of total crystallographic plane area that is
occupied by atoms.
Linear and planar densities are one- and two-dimensional
analogs of the atomic packing factor.

2
ex: linear density of Al in [110]
direction
a = 0.405 nm
FCC: Linear Density
• Linear Density of Atoms  LD =
a
[110]
Unit length of direction vector
Number of atoms
# atoms
length
1
3.5 nm
a 2
2
LD
-
= =
Adapted from
Fig. 3.1(a),
Callister &
Rethwisch 8e.

Linear Density for BCC
Calculate the linear density for the
following directions in terms of R:
a. [100]
b. [110]
c. [111]

4
Planar Density of (100) Iron