ABSTRACT
The quantities
A
/
a
,
B
/
b
, and
C
/
c
can be fractional or integer (
a
,
b
, and
c
are
lattice constants
), but they must be converted into a set of the smallest integers:
u
,
v
, and
w
. In a three-number
notation, indices of the lattice direction, as well as those of all the directions parallel to it, are the smallest integers in square brackets: [
uvw
]. For instance, [100] denotes the
x
-axis in its positive direction, and [ ] denotes the same axis in the negative direction. There can be several lattice directions with the same indices arranged differently and having different signs (see
form
). In a fournumber
notation for
hexagonal systems
, the indices of [
UVTW
] lattice direction can be found from Miller indices [
uvw
] as follows:
U = 2u – v
,
V = 2v – u
,
T =
–(
u + v
), and
W = 3w
. The obtained numbers
U
,
V
,
T
,
and
W
are to be reduced to the smallest integers.