Reduced Sphere representation of some planes
Planar Density of cfw_111 in FCC
Miller Indices for Directions: Some Examples
Miller Indices for Directions: Some Examples
Miller Indices for
Planes in Cubic
Crystal System
Miller Indices for Planes in Cubic Cr
A Plane
c
B Plane
A Plane
a
3
Hexagonal Array of Circles
BCC: See the stacking of cfw_110 planes and array
of circles forming the planes
A
A
AA
Square Array of Circles
AAA Type of Packing
Packing of cfw_111 in FCC
Notice the Hexagonal array of circles
Pac
One Dimensional Array of Points (Lattice)
a
Smallest Unit: line
Lattice parameter: a (length)
Two Dimensional Array of Points
a
b
Smallest Unit: polygon
Lattice parameter: a, b (length);
and (angle)
Some 2D lattices
Square Lattice
a=b; =90
Rectangular La
Miller indices of Plane: Procedure to determine miller indices of plane: (1) Choose origin in
such a way which lies outside the plane of interest (choice of origin is arbitrary) (2) Find the
intercepts of the plane on the three co ordinate axes (3) Take r
Disadvantages in using Threeaxis coordinate system
Miller Indices of Equivalent Directions in Hexagonal Crystal System
z
<100> in Hexagonal = [100], [010], [110]
Not Permutations
y
[100]
[010]
[11 0]
x
Disadvantages in using Threeaxis coordinate system
a)
b)
c)
The perfect crystal in a) is cut and an extra plane of atoms is inserted
in b). The bottom edge of the extra plane is an edge dislocation in c).
A Burgers vector b is required to close a loop of equal atom spacings
around the edge dislocation.
Ed
Factors that Determine Crystal Structure
1. Relative sizes of ions Formation of stable structures:
maximize the # of oppositely charged ion neighbors.

+



unstable
+


stable
2. Maintenance of
Charge Neutrality :
Net charge in ceramic
should be
Miller Indices For Directions
Determine
the coordinates of the two points (Head and
Tail) in the direction.
Subtract the coordinates: Head Tail
Clear fractions to give lowest integer values for all
coordinates
Indices are written in square brackets wi
CHEMISTRY SECTION I TIME1 hour and 30 minutes NO CALUCLATOR MAY BE USED WITH SECTION I. Note: For all questions, assume that the temperature is 298 K, the pressure 1.00 atmosphere, and solutions are aqueous unless other specified. Throughout the test the
2002 AP Chemistry Exam  KEY
Questions 12 Consider atoms of the following elements. Assume that the atoms are in the ground state. (A) (B) (C) (D) (E) S Ca Ga Sb Br
A 63% C 70%
1. The atom that contains exactly two unpaired electrons
2. The atom that con