Kittel Problem 1.3
p
Show that the c/a ratio for an ideal hexagonal close-packed structure is 8/3 =
1.633. If c/a is significantly larger than this value, the crystal structure may be
thought of as composed of planes of closely packed atoms, the planes being loosely
packed.
h. . .height of the equilateral triangle
a. . .lattice constant
r
h=
p
1
1− ∗a=
4
a2 − (a/2)2 =
r
3
∗a
4
Distance x from an atom to the middle of the triangle:
r
2
2
3
x= ∗h= ∗
∗a
3
3
4
1
x= √ ∗a
3
r
r
c √ 2
1
2
= a − x 2 = a2 − a2 =
∗a
2
3
3
r
c
8
=
a
3
1