Transcript Slide 1

DESCRIBING CRYSTALS MATHEMATICALLY
Three directional vectors
Three distances: a, b, c
Three angles: a, b, g
All points can be described
using coordinate system in
terms of the three vectors
qa, rb, sc
In cubic systems, symmetry
makes a = b = c and
a= b = g = 90o
Describe points using
(q, r, s)
CRYSTAL DIRECTIONS
Directions are represented by
arrows
Labeled as [hkl] where h,k,l
represent the coordinates of the
point they pass through, when they
originate from the origin
Directions in crystals are like
compass points; they don’t depend
on where they start from
All directions parallel to [111] are
all [111], similar to north being
north regardless of where you are
standing.
CRYSTAL PLANES
Planes are described using
Miller Indices
They are the reciprocals of
the intercepts on the major
axes, reduced to the lowest
possible integers
Represented by (hkl)
In (001) the intercepts are
∞ for the x and y axes as they
are parallel; and 1 for the z
axis
All parallel planes have the
same Miller Indices
CRYSTAL PLANES
In (110)
There are intercepts on the
x and y axes
The plane is parallel to the
z axis
Intercepts are
for h
for k
for l
CRYSTAL PLANES
For (111)
There are three
intercepts
All at one unit vector
FOR FCC
THIS IS THE
HEXAGONAL
PLANE
IT IS THE CLOSEST
PACKED PLANE
SUMMARY OF MEANINGS OF PARENTHESES
(q,r,s) represents a point – note the exclusive use of commas
[hkl] represents a direction
<hkl> represents a family of directions
(hkl) represents a plane
{hkl} represents a family of planes