2017中秋品牌团购会.ppt

Objectives
By the end of this section you should:
understand the concept of planes in crystals
know that planes are identified by their Miller Index and their separation, d
be able to calculate Miller Indices for planes
know and be able to use the d-spacing equation for orthogonal crystals
understand the concept of diffraction in crystals
be able to derive and use Bragg’s law
Lattice Planes and Miller Indices
Imagine representing a crystal structure on a grid (lattice) which is a 3D array of points (lattice points). Can imagine dividing the grid into sets of “planes” in different orientations
All planes in a set are identical
The planes are “imaginary”
The perpendicular distance between pairs of adjacent planes is the d-spacing
Need to label planes to be able to identify them
Find intercepts on a,b,c: 1/4, 2/3, 1/2
Take reciprocals 4, 3/2, 2
Multiply up to integers: (8 3 4) [if necessary]
Exercise - What is the Miller index of the plane below?
Find intercepts on a,b,c:
Take reciprocals
Multiply up to integers:
Plane perpendicular to y cuts at , 1, 
(0 1 0) plane
General label is (h k l) which intersects at a/h, b/k, c/l
(hkl) is the MILLER INDEX of that plane (round brackets, mas).
This diagonal cuts at 1, 1, 
(1 1 0) plane
NB an index 0 means that the plane is parallel to that axis
Using the same set of axes draw the planes with the following Miller indices:
(0 0 1)
(1 1 1)
Using the same set of axes draw the planes with the following Miller indices:
(0 0 2)
(2 2 2)
NOW THINK!! What does this mean?
Planes - conclusions 1
Miller indices define the orientation of the plane within the unit cell
The Miller Index defines a set of planes parallel to one another (remember the unit cell is a subset of the “infinite” crystal
(002) planes are parallel to (001) planes, and so on
d-spacing formula
For orthogonal crystal systems (. ===90) :-
For cubic crystals (special case of orthogonal) a=b=c :-
. for (1 0 0) d = a
(2 0 0) d = a/2