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Miller indices for planes
Miller indices and plane spacing
Two-dimensional lattice showing
that lines of lowest indices have the
greatest spacing and greatest
density of lattice points
Indices of directions
Indexing the hexagonal
system
Indexing the hexagonal system
• (hkl)
[UVW]
(hkil) h+k+i=0
[uvtw]
All shaded planes in the cubic lattice
shown are planes of the zone {001}
Zone axis [uvw]
plane (hkl)//[uvw]
then hu+kv+wl=0
Two non-parallel planes (h1k1l1) and
(h2k2l2) then zone axis [uvw]=
Two non-parallel planes to find
zone axis
h1
k1
l1
h1
k1
l1
h2
k2
l2
h2
k2
l2
Two zone planes to find zone axis
A face parallel to two given lines
u1
v1
w1
u1
v1
w1
u2
v2
w2
u2
v2
w2
Test of tautozonality
h1
h2
h3
k1
k2
k3
l1
l2  0
l3
Test of coplanarity
u1
u2
u3
v1
v2
v3
w1
w2  0
w3
Zone condition
uh+vk+wl=0
Addition and subtraction rule
If (h1 k1 l1) and (h2 k2 l2) belong to
the same zone then (mh1±nh2
mk1±nk2 ml1±nl2) also belong to the
same zone, where m, nєI