Vibrational Motion of Molecules
Atoms are bonded by “effective springs”
Molecule can be modelled as a quantum simple harmonic oscillator
In quantum mechanics, the energy of SHM is quantised
Solid State Physics
The Crystal Structure and Bonding in Solids
Condensed matter includes liquids and solids;
The distance between atoms is of the order of the atom size (~ 0.1 – 0.5 nm);
X-ray, electron and neutron diffraction are used to determine the inner structure of solids.
Solids
Solids have a rigid structure. In this structure, atoms or molecules are held in fixed positions relative to each other.
There are two main types:
Crystalline Solids – Long-Range Order of Atoms
Amorphous Solids – Short-Range Order of Atoms
Crystals
Have ‘long range order’ i.e. repeated structure (lattice).
Diamond is monocrystalline because unit cells are arranged regularly over large distances.
Metals, e.g. copper, are usually polycrystalline. Atoms with a particular alignment form grains (~0.01mm across). Between these grains are boundaries. Presence and size of boundaries affects mechanical properties of metals.
A crystal lattice is a repeating pattern of (mathematical) points called lattice points;
Each atom (or group of atoms) is associated with a lattice point;
Depending on size of atoms and their interactions, solid crystals have different crystallographic structures.
Crystalline: Repeating or periodic array over large atomic distances. 3-D pattern in which each atom is bonded to its nearest neighbors;
Crystal structure: the manner in which atoms, ions, or molecules are spatially arranged.
Unit cell: small, repeating, entity of the atomic structure. The basic building block of the crystal structure. It defines the entire crystal structure with the atoms positions within.
Crystals are generally strong due to covalent or ionic bonds;
Regular atomic structures are studied using X-ray diffraction;
X-rays have a wavelength of about 10-10 m, comparable to interatomic spacing;
The principles are similar to spectroscopy using a diffraction grating.
Energy Band Theory
Consider two identical atoms far apart, i.e. non interacting, as r >> d;
Electrons occupy discrete energy levels;
Both atoms have the same set of energy levels;
The Pauli exclusion principle does not apply to non-interacting electrons.
Pauli exclusion principle
T
he
state of an electron, in any atom, is specified by a unique set of
quantum numbers: n, ℓ, mℓ, and ms, the principal, orbital,
orbital magnetic, and spin magnetic quantum number, respectively;There cannot be another electron with the same set of values for these quantum numbers in a particular atom.
C
rystals
usually have many allowed energy bands;Some energy bands overlap;
White areas indicate energy band gaps or “forbidden” energy states;
Blue: filled energy states
Gold: vacant energy states.
Electrical Conduction
Electrical conduction: the property of a material to conduct electricity;
The electric current is produced by the movement of electric charges in response to an applied electric field;
→ Free charge carriers are needed
When an external electric field is applied to a conductor, an amount of Kinetic Energy is transferred to charge carriers;
These charge carriers could then jump to Higher energy states if these are available;
The energy band model could be used to explain and estimate the charge carrier density.
Conductors - Energy Bands
Fermi level: marks the maximum allowed energy of electrons in a solid;
→ It depends on material type and temperature;
Conductors: the Fermi level is within an energy band;
Conduction band: the highest energy band available;
Valence band: the energy band just below the conduction band.