Problem I
Problem 1.3 from text.
Solution:
For Figure (a), the axis intercepts in the [100], [010] and [001] directions are
respectively, 3, 3, and 3.
Taking the reciprocals of the intercepts gives 1/3, 1/3 and
1/3, respectively (corresponding to the equation of the plane,
1
333
x
yz
). Scaling
by 3 to obtain integers then gives the plane, in correct notation, (111).
For Figure (b), the axis intercepts in the [100], [010] and [001] directions are
respectively, 3, 2, and 2.
Taking the reciprocals of the intercepts gives 1/3, 1/2 and
1/2, respectively (corresponding to an equation of the plane,
1
322
xyz
). Scaling
by 6 to obtain integers (multiplying by 6) gives the plane (233).
Problem II
Write out all of the equivalent <110> directions using proper notation. (E.g., [110], [011] etc.)
Solution:
There are twelve equivalent directions:
[110],[110],[110],[110],[101],[101],[101],[101],[011],[011],[011],[011]
Problem III
Calculate the area density of atoms on a (110) plane in Si. (That is if you were to cleave the crystal
along a (110) plane what would be the surface density of atoms. Remember that the “lattice
constant” is the edge length
a