key terms Flashcards
(17 cards)
Bravais Lattice
Array of points in space. Each point is equivalent. The lattice looks the same no matter which point it is viewed from. The lattice is invariant under translation.
Basis
Group of atoms placed at each lattice point so that the basis together with the lattice describes the crystal structure.
Wigner-Seitz cell
A primitive unit cell. It is the smallest volume in lattice containing one single lattice point.
Packing Fraction
The volume of a unit cell that is taken up by the atoms contained in the unit cell. It is often assumed that the radius of the atoms is half the nearest neighbour distance.
Primitive unit cell
A choice of unit cell which contains only one lattice point.
Lattice
An infinite set of points where the environment of any point is equivalent to the environment of any given point.
Reciprocal lattice
A set of primitive vectors ππβ such that in relation to the primitive lattice vectors ai of the direct real lattice have the property ππ*ππβ =2ππΏππ
What is the negative term in the Lennard-Jones potential?
An attractive force is necessary for any bonding and this is electrostatic in origin
What is the positive term in the Lennard-Jones potential?
A repulsive force required to keep the atoms from getting too close to each other. The repulsive force acts at very low distances and its origin lies in the Pauli exclusion principle, which forbids two electrons to occupy the same quantum state.
What happens to the electron far from the Brillouin zone boundary?
Not much happens and it still behaves as though it is free with a parabolic dispersion.
What happens as the momentum k value moves to the Brillouin zone boundary?
The electron suffers Bragg reflection
What happens to the elecrtron when k is equal to half the Brillouin zone boundary?
Scattered back
What is created by the electron and the scattered back electron?
The incoming and back reflected wave are out of phase by half a wavelength and set up a standing wave. Consider the initial electron represented as a planewave π(π₯) = π΄ππ₯π(πππ₯). Now the solution is no longer a plane wave but acombination of it to give a standing wave: π(π₯) = π΄ππ₯π(πππ₯) Β± π΄ππ₯π(βπππ₯). There are two independent combinations for the waves going to the right (+) and those reflectedback to the left (-).
Discuss in terms of how the electron charge is distributed with respect to the ion cores.
Charge densities π+π+β has its peaks at x=a, 2a, 3aβ¦..at the positions of the ion cores where the potential is a minimum, while for πβπββ the peaks occur at x=a/2, 3a/2, 5a/2β¦.at positions in between the ion cores, where the potential is a maximum. Thus there is an energy difference between these two solutions and this is the origin of band gaps.
Pauli Exclusion Principle
Two or more identical particles with half-integer spins cannot simultaneously occupy the same quantum state within a system that obeys the laws of quantum mechanics.
Face Centered Cubic (FCC)
A crystal structure where atoms are positioned at each corner of a cube and at the center of each face of the cube. This arrangement results in a highly efficient packing of atoms, with a nearest neighbours of 12 and an atomic packing factor of approximately 0.74.
Body Centered Cubic (BCC)
A type of cubic crystal structure where atoms are located at the corners of a cube and also at the center of that cube. This arrangement results in a total of two atoms within the unit cell, one at the center and one contributed by the corner atoms. It has a nearest neighbours of 8 and a packing fraction of 0.68.
