2. Crystal structure Flashcards
What is the crystal lattice?
An origin and all other equivalent sites in a crystal where the arrangement of atoms around these points is identical to the arrangement of atoms around the origin point.
What are lattice vectors?
The two shortest vectors from the origin to the nearest neighbours for a crystal lattice, usually named a and b.
What is a lattice translation vector?
A vector that can be used to map out the entire crystal lattice using two lattice vectors (i.e. any point in the lattice can be reached by a lattice translation vector, T).
Give the equation for a lattice translation vector
T = lattice translation vector
u, v = integers
a, b = lattice vectors
What is the basis of a crystal?
The position of the atoms relative to each lattice point.
Give the equation for the basis vector
r = basis vector
x, y = integers
a, b = lattice vectors
What two components make up the crystal structure
Lattice & Basis
Give the equation for the translation vector of a 3D crystal
T = lattice translation vector
u, v, w = integers
a, b, c = lattice vectors
What is a unit cell?
An arrangement of points in space, such that the arrangement of points about a given point is exactly the same as the arrangement of points about any other point.
What is a primitive unit cell?
A unit cell that only has one lattice point in the crystal.
What are the 4 types of Bravais lattice covered in this course?
- Simple cubic (sc)
- Body-centred cubic (bcc)
- Face-centred cubic (fcc)
- Hexagonal (hex)
Describe the shape of a simple cubic Bravais lattice
Describe the shape of a body-centred cubic Bravais lattice
Describe the shape of a face-centred cubic Bravais lattice
Describe the shape of a hexagonal Bravais lattice
Which type of Bravais lattice is primitive?
Simple cubic (sc)
What lattice structure does NaCl have?
Rocksalt structure: fcc with a basis of Na atoms and a basis of Cl atoms
What lattice structure does silicon have?
Two interpenetrating fcc lattices
What lattice structure does GaAs have?
Zinc blende structure: fcc with a two-atom basis (interpenetrating)
What lattice structure does gold have?
fcc: single atom basis
What lattice structure does titanium have?
hcp (hexagonal close-packed): two-atom basis
What is the packing fraction?
A measure of how much volume is taken up by actual atoms within a crystal, also known as the packing efficiency.
Give the equation for the packing fraction
Volume occupied by atoms (in the unit cell) / Total volume (of the unit cell)
How is the plane through a crystal determined?
Find the intercepts of the a, b, and c vectors.
How is the Miller index of a crystal plane determined?
- Find the intercepts of the a, b, and c vectors.
- Take the reciprocals of each intercept.
- Reduce the values to the smallest integers with the same ratio.
- This is the Miller index (hkl).
Give examples of the Miller Indices of cubic crystals
The hat over an index represents a negative plane.
How does the Miller-Bravais system work for hexagonal crystals?
a1 is associated with h
a2 is associated with k
a3 is associated with i (and is redundant)
c is associated with l
How can planes within crystals become surfaces?
By cleaving the crystal to expose the surface.
Cubic crystals have a ______ indices while hexagonal crystals have a ______-_______ indices.
Miller
Miller-Bravais
