sem1 Flashcards
What is pauli’s exclusion principle and what does it mean
two or more electrons may not occupy the same quantum state.
overlap of electron clouds from
two atoms is only possible by promoting some of the electrons to higher quantum states, which requires a large amount
of energy
What is Van Der Waals Interactios
a neutral atom w 0 point motion has a rapidly fluctuatng dipole moment.
Causing instantaneous dipole in first atim which induces dipole in the next atom causing pot. energy of pair to be lowered
What is Lennard-Jones potential?
The total energy for the interaction of two inert gas atoms is therefore given by the sum of the attractive and
repulsive potentials a
Lennard Jones Potential equation
U(R) = -(A/R^6)+(B/R^12)
What is the cohesive energy of inert gas crystals at absolute zero and zero pressure ?
Utot(R0) = -8.5Ne
What is principle quantum number, n?
determines the energy of an electron in hydrogenic atoms and can take integer
values starting from 1. Atomic orbitals with the same value of n are said to be in the same shell and we label
the orbitals, starting with this principle quantum number.
What is angular momentum quantum number,l ?
Angular momentum from spatial wave function of electron specifies shape of orbital so s = 1, p=2 etc.
What is magnetic quantum number, m
Orientation in space of given energy and shape -
What is spin quantum number
orinetation of spin axis of electron
Whats Ionic bonding
Electrostatic interaction of oppositely charged ions
Large ion seperation - ionic equsation
Uattract =+-((q^2)/4piE0R)
Small ion seperation - ionic equsation
U(R) =+((B/R^12)+-((q^2)/4piE0R)
What is covalent bonding
Sharing of electrons between atoms
Explain Diamond
Sp3 molecular orbit
tetrahedral orbit
no unpaird electron - insulator
Expalin Graphite
Sp2 molecular orbit
sheets of carbon atoms
hexagonal arangement
bound by wan de vaals
Metallic bonfing
Valence electrons removed from ion core
Electrins free to move in crystal - conductive
What is crystal structure
Lattice X Basis
What is simple cubic
Atoms on each vertices of cube
What is Body Centered cubic
Atom of each vertices + one 2
opposite faces
WHAT IS FACECENTERED CUBIC?
Atom on each verticy + middle of each face
What is Hexagonal
Atom on every verticy of hexagonal prism base and one on both hexagonal face
What is packing fraction
Measure of volume taken by actual atoms
Vol of atoms/ vol of unit ce;;
what is packing fraction of fcc
0.74
What is Braggs law, when does braggs law occur
2dsintheta = n lamda
Occurs at wavelengths smaller than 2d
What causes efficency of scattering to decrease rapidly
as 2theta increases
What is atomic form factor
Measure of how effciently an atom scatters Xrays under specific conditions
What are Laue conditions for diffraction?
A large scattering amplitude is obtained only when the contributions from all the lattice points are in phase, and
this is achieved when,
K.a = 2πh, K.b = 2πk, K.c = 2πl
What is the relationship between the reciprocal lattice vector Ghkl and the (hkl) Miller index plane in real space?
dhkl =2π/|Ghkl|
What is the Ewald sphere?
-Plot recipocal lattice of crystal
-Draw wavevectors of incident beam k which terminated at reciprocal lattice point
-Draw sohere of radius k=2pi/lamda
Diffracted beam will be formed if Ewald sphere intercepts any point in the reciprocal lattice
The Ewald sphere is a sphere of the radius defined as the reciprocal of the wavelength of the incident wave 1/λ,
What is reciprocal space
mathematical space which corresponds to FT of real space
What is the Brillouin zones?
region closest to center of recipocal space which contains all possible wavevectors which can be diffracted by crystal lattice
What are wavevectors in recipocal soace?
momentum of wave, e.g xrays or electrons if waves diffracted
Relationship between real and reciprocal vectors in SC lattice
a∗ =2π/a,i
b∗ =2π/a,j
c∗ =2π/a,k
Relationship between real and reciprocal vectors in BCC lattice
a∗ = (2π/a)(j + k),
b∗ = (2π/a)(i + k),
c∗ = (2π/a)(i + j)
Relationship between real and reciprocal vectors in FCC lattice
a = (1/2)a(j + k),
b = (1/2)a(i + k),
c = (1/2)a(i + j)
From miller indicies what diffraction conditon for BCC
h+k+l must be even
From miller indicies what diffraction conditon for FCC
h, k and l must be either all odd or all even
What can the free electron model be deduced to ?
Particle in the box problem
−((hbar^2)/2m)(∇^2)ψ = epsilonψ
epsilon = energies of electrons
Density of states ewuation
g(epsilon) = V/(2(π^2)(hbar^3))(Epsilon^1/2)
What is Fermi Energy?
Highest energy state occupied by electron at absolute zero temperature
What is Fermi-Dirac distribution function?
f(ε,T)=1/
exp((ε-εf)/kbt))+1
Number of electrons per unit energy range?
n = density of states x occupation of states at temp
g(ε) x f(ε,T)
What happens if Fermi Sphere completely fits inside Brillioun zone
No electrons satisfy diffraction conditions
Electron current density equation
j = nqv = [(n tau e^2)/m(e)] = sigma E
Ohms law where conductivity; j=sigma E
sigma = [(n tau e^2)/m(e)] =n e mew
What are phonons
Lattice Vibrations
What is Matthiessen Rule
Resistivity = temperature-independent resistivity (ideal resistivity) and its temperature-dependent resistivity (residual resistivity).
What is the implications of Mattiessen Rule
The implication of Matthiessen’s rule is that two different samples of the same metal, one pure (with minimal defects) and the other impure or alloyed, should exhibit similar resistivity vs temperature curves. However, the impure sample will have a higher overall resistivity due to the presence of additional defects, leading to an offset in the curves corresponding to the residual resistivity.
Hall Energy equation
EH = RHB × j
What is Band Theory
Why causes materials behavoiur when conductinf electricity
1- Peroidocity and Bloch Equations
2- Free Electrons and not so free electrons
3- Brillouin Zones
4- Occupying energy bands
-
What is the nearly free electron model
Periodic potential of ion cores as weak perturbation on band electrons
Energy Gaps and the Bragg Condition
Standing Waves and Energy Gaps
Band Structure Calculation:
The tight binding approximation
The opposite approach to the nearly free electron model, the tight binding approximation considers the electrons
to be tightly bound to the atoms that make up the crystal. When the atoms are widely separated the wavefunctions
of the valence electrons will be those of the isolated atoms. As the distance between them decreases we might expect
that the electrons will begin to move from one atom to the next. We can consider this motion as the transfer of an
electron from one state on the atom to the same state on a neighbouring atom.
1- find suitable wavefunction
2- Calculate E(k)
3- Consider tight binding in sc lattice
Fermi surfaces
Isolated atoms to free electron limit
Effective mass and positive holes
