1.2 Crystals I Flashcards
Define a Crystal
A solid whose atoms are arranged in a regular repeating pattern that extends over a large distance
Define a crystal lattice
An infinite set of points defined by integer sums of a set of linearly independent primitive lattice vectors (PLVs)
What are the two 2D lattice types?
Square and Triangular (hexagonal)
What is meant by the choice of PLVs not being unique?
They can be anything as long as you can reach every point with them
Give an alternative definition for a crystal lattice which includes the environment
A lattice is a set of points where the environment of any given point is the same as that for any other point
How can we describe a crystal structure using a basis?
Represent the periodic structure as a lattice of repeating patterns. Basis = repeated object
lattice + basis = crystal structure
Define the unit cell
A region of space such that when identical units are stacked, it completely fills space
OR a PLV contains exactly 1 lattice point
State the three types of cubic lattices
Simple cubic, FCC, BCC
Describe the properties of a cubic lattice
All sides are equal, all angles are equal (90 deg)
How many types of 3D lattices are there that satisfy all symmetry operations and periodic conditions, and what are they called?
Bravais lattices - 14
Describe some symmetry operations
Translation, rotation, reflection
Describe the atomic packing factor
- Place an atom on each lattice point
- Assume sphericicity, radius R
- Calculate the percentage of space filled
What is the only element that has a simple cubic structure?
Po
Describe the structure of a of a BCC
A simple cubic with an extra lattice point in the centre a/2
Describe the structure of a of a FCC
Simple cubic with an extra lattice point at the centre of each face
State how many lattice points are contained in a simple cubic, BCC, FCC
Simple cubic = 1
BCC = 2
FCC = 4
What cubic structure are most elements found in and why?
FCC - densest possible packing method
How do we describe directions when navigating a cubic and define a negative?
uvw. Use a bar for negative numbers (like a vector)
Describe the movement for <100>
Along a unit cell axis
Describe the movement for <110>
Along a face diagonal
Describe how to treat <2 4bar 6>
Reduce to simplest form:
<1 2bar 3>
Define a plane
A plane intercepts the axis at u’ w’ v’ or a/h b/k c/l for side lengths abc
What is the traditional notation used in relation to planes and what must we note when writing them down?
The Miller indices hkl. They must all be integers
State the 4 point defects which can arise during the formation of a crystal
Schottky defect, colour centre, frenkel defect, impurities
Describe the Schottky defect
There is a vacancy - one atom is missing in the lattice which distorts it. no expected for N atoms at an energy Ev to remove a lattice:
n = N * exp(-Ev / kt) vacancies
Describe the colour centre defect
The colour changing of a crystal due to lattice damage
- caused when crystal is irradiated by x-rays, gamma rays, electrons etc
Describe the frenkel defect
When there is a vacancy and interstitial atom
- distorts atom
- needs 5-10x more energy than a normal vacancy
Describe the impurity defect
When there is a different material on a lattice point
State the two dislocations
Stacking faults/edge dislocations
Screw dislocations
Define grain boundaries
Most materials are not single crystals, but many small crystallites orientated wrt to each other
