Concepts in Condensed Matter Physics Flashcards
Define ‘equilibrium’.
Substance is in a uniform state.
Define ‘phase’.
Material of specific composition in a specific state.
Define ‘phase transition’.
Phases in equilibrium with each other.
What is the Lennard-Jones potential, V(r)?
V(r) = 4ε [(σ/r)^12 - (σ/r)^6]
Where:
r is the inter-atomic spacing
σ is the separation for V = 0 (~0.3nm)
ε is the minimum potential (at r(m) )
Describe a single crystal.
Single crystal:
* macroscopic specimin with uniform crystal orientation
* crystal growth > nucleation
Define ‘nucleation’.
The process of a substance changing from one state to another.
Describe a polycrystalline material.
Polycrystalline material:
* conglomerate of grains with different orientation
* nucleation > crystal growth
Define ‘conglomerate’.
Gather together into a compact mass.
Describe a ‘grain’.
Grain:
* Uniform composition
* Uniform crystal structure
* Uniform orientation
Describe a ‘grain boundary’.
Grain boundary:
* Interface between grains
* Disrupted long-range order
* Intersecting lattice planes
* Boundary disorder
Define ‘lattice’.
An array of points that represent identical locations in the crystal.
Define ‘unit cell’.
A repeat unit in 2D that generates the crystal.
Define ‘lattice vectors’.
Two vectors in 2D that define all points in the lattice,
r = n(a) 𝐚 + n(b) 𝐛
Define ‘primitive cell’.
A unit cell that contains only one lattice point. The area of the cell,
𝐀 = 𝐚 × 𝐛
Define ‘basis’.
Repeating shape at each lattice point.
Define ‘crystallography’.
Crystallography:
* Primitive lattice preferred
* Atoms (or groups of atoms or molecules) located at lattice points
* Unit cell as compact as possible
Define ‘Bravais Lattice’.
A lattice that fills space without gaps or overlaps.
The number of possible Bravais lattices is ______:
The number of possible Bravais lattices is finite:
* 5 in 2D
* 14 in 3D
What do crystals with the same Bravais lattice have?
- The same symmetry
- Different parameter values
What is a ‘symmetry element’?
An operation that maps each lattice point onto another.
Give the 7 crystal classes (lattice types).
- Cubic
- Tetragonal
- Ortho-rhombic
- Monoclinic
- Hexagonal
- Trigonal
- Triclinic
What is the FCC structure?
Face-Centred Cubic
What is the HCP structure?
Hexagonal Close-Packed
What is the BCC structure?
Body-Centred Cubic
What is a Wigner-Seitz cell?
It is an example of a primitive cell, which is a unit cell containing exactly one lattice point.
What is a phase diagram?
A phase diagram links any two state variables,
e.g. pressure and temperature,
and shows regions in which a substance in equilibrium is in a uniform state.
What is “short range order”?
Short range order refers to the
regular and predictable arrangement of atoms over a short distance,
usually with one or two atom spacings.
What does “amorphous” mean?
“without a clearly defined shape or form.”
“(of a solid) not crystalline, or not apparently crystalline”
What is “long range order”?
Long range order refers to a
regular pattern of arrangement of particles
which repeats itself periodically over the entire crystal.
Which Bravais lattice (in three dimensions) has three different lattice parameters, all angles identical, and four atoms in the unit cell?
Face-centred orthorhombic