chapter  L
8 Pages

L

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.