Definitions Flashcards
symmetry
If an object has regular arrangement or pattern.
name the different symmetry operations
Identity, inversion, rotation, rotoinvresion , mirror
inversion
taking points (x,y,z) and turning into –> (-x, -y,-z)
rotoinversion
combination of rotation and inversion
property of a symmetry
all symmetries have the property that if you apply them enough times you get back to where you started
The lattice
A lattice is an array of regularly spaced points which represent the translational symmetries of a system. They are defined in terms of basis vectors, for any n-dimensional system we require n non co-planar basis vectors.
unit cell
the unit cell is any region of space which tessellates (fits together) when translated by a lattice vector
primitive cell
primitive unit cell is a cell which contains only 1 lattice point
name a primitive cell
wigner-seitz
how many types of bravais lattice are there
14
packing fractions
calculate the volume fraction of space filled assuming each lattice point is home to a sphere
assumption when calculating packing fraction
- crystal is made up of ideal hard spheres sitting on the lattice points
- each sphere, just touches its neighbour, implying that the radius of the sphere is just half the distance between neightbouring lattice points
vacancy
Vacancy are missing atoms in otherwise perfect structure
substitution
Substitution is when an atom in a otherwise perfect structure is replaced with a different atom.
interstitial
interstitial are atoms which sit between sites in normally unoccupied locations
name different point defects
vacancy, substitution, interstitial
Line defect
linear disruption in the ordering of a material
examples of line defects
edge, screw
why are line defects important
critical to defromation of material. As a material is compressed these defects are able to move.
planar defect
interference between two regions of mismatched perfect crystal
example of planar defect
grain boundary and twin boundary
unit cell of the reciprocal lattice is called
the Brillouin zone
property of Brillouin zones
They all have the same area
reciprocal lattice have vectors…
have vector dimensions of inverse length so can be thought of as a wave vector
each reciprocal lattice vector corresponds …
to a plane in the direct lattice
official definition of X-ray
X-rays are photons which are generated by inner shell transitions within atoms
new definition of x_rays
x-rays can be defined by specifying a wavelength range, typically 10pm -10nm corresponding to photon energies of around 0.1-100Kev
what does the range of photons from x-ray definition do
makes them ideal for scattering from crystals
when an x-ray interacts with an atom, one of two process may occur, what is the one covered in atomic course
The x-ray may be absorbed by the atom, prompting an inner shell electron to the continuum or an unoccupied energy level
when an x-ray interacts with an atom, one of two process may occur, what is the NEW ONE
The photons may scatter from the electrons in the atom, changing its direction, but not in the classical limit, its energy.
diffraction theory
Radiation with wavelength of order the lattice spacing will diffract from a periodic array of scattering
what type of reaction is scattering, give example
elastic
i.e. the radiation wavenumber, K remains unchaged during scatterin
The wigner-seitz cell
is the smallest volue enclosed by the perpendicular bisector of the central point to neighbouring cells
strength of photon scattering
weak, but the atomic density of solids is high enough for results to be appreciable
The Ewald sphere
A sphere intercepting points that fufil the Lave condition
phonos
Phonos are quantised lattice vibrations that have energy and momentum
Neutrons used in elastic scattering for what
to determine points on dispersion curve
Dulong-Petit fails where
For Diamond and Beryllium and all materials at low temperatures
Einsteins model does what
treats each atom as an independent quantum SHO
Debye Model assumption
assumes equally spaced isotropic modes (in reciprocal space) and a linear dispersion
Debye answers what question
The debye temperature is an answer to the question “how quantum is you’r system” and large values correspond to tight bindings
Harmonic potential approximation
- higher temperatures have anharmonic regions
- odd terms in the Taylor expansion are asymmetric
Free electron theory assumption
- Each electron follows a classical trajectory in a uniform potential, set up by ions and other electrinos
- Electrons do not scatter off each other only ions
Scattering FET
Electrons are accelerated by f(t) until they collide and scatter
Collide and scatter (FET)
- time between events is 1/tau
- the proprtion of electrons that scatter is dt/tau so (1-dt/tau) dont scatter
Mathiessen’s rule
phonons and impurities cause electrons to scatter. phono is dependent on temperature
Boin von Karmon boundary condition
The crystal is modelled as a ring so to avoid a difference of pi in phase
pauli exlusion principle
No two fermions can occupy the same quantum state (including spin)
edge defect
and edge dislocation is a line defect formed at the edge of missing or additional half plane of atoms in a structure
A stacking fault
A stacking fault is a disruption to the normally regular arrangement of planes within a material.
Two different types of stacking faults which is which?
intrinsic, missing. Extrinsic additional
