TEST 2 Flashcards
What are the four main point defects?
Vacancy
Interstitial
Interstitial foreign atom
Substitutional foreign atom
What is a vacancy
when an atom is missing so adjacent atoms try to compensate
What is an interstitial defect?
When a foreign atom that is smaller than lattice atoms is present in lattice
How does Nv/N correlate with Gibbs Free Energy?
There should be some point where at a certain Nv/N, G is at a minimum
formula for vacancy concentration?
Nv/N= exp(-delta(Hv)/RT)= exp(-Q/kT)
What criteria is used for metal alloys?
Hume Rothery Rules
What are the Hume Rothery Rules?
1) Atomic Radii should be within 15% of each other
2) Crystal structure should be the same
3) Electronegativity of solute and solvent should be similar
4) Valence of solute and solvent should be the same
What are the point defects in ceramics?
Cation interstitial
Cation Vacancy
Anion Vacancy
What is Cation Interstitial?
Extra cation in lattice
What is cation vacancy?
Cation absence
What is anion vacancy?
Anion absence
If an Na+ is missing in an NaCl ceramic lattice, what kind of particle must replace an Na+?
at least one particle with +2 charge.
If three Fe2+ are missing from an iron oxide consisting of Fe2+ and O2-, how many Fe3+ particles should be presdnt
two +3 particles
Why? there will be a net charge of 6- so there must be two Fe3+ particles to make up the difference
Formula for point defect probability
Ndef/N= exp[-Qdef/(2kT)]
What is a burgers vector
Vector that describes the magnitude and direction of the lattice distortion associated with a dislocation
What are the three types of linear dislocation
edge dislocation
screw dislocation
mixed dislocation
What is edge dislocation
Linear defect that centers around and perpendicular to the plane of the page
Imagine a line of particles perpendicular to page is removed
does a burgers vector tend to be large or small
Dislocations will always tend towards the smallest possible burgers vector
What takes more energy, larger or smaller burgers vector?
larger
What is a screw dislocation?
When the lattice planes trace a helical path around the dislocation line
What are the types of 2D imperfections?
Grain boundaries
What is a grain boundary
lattice pattern is constant but at an angle making a boundary
Why do things diffuse?
to reach an optimum energy state (a lower energy state usually)
How do atoms diffuse?
Atoms will fill neighboring vacancies
What does diffusion rate depend on?
Diffusion rate depends on
#vacancies
activation energy for atom jumps
Does it take energy to diffuse>
Yes, there is a certain E that acts as a kinetic barrier for atoms jumping vacancies
What is interstitial diffusion?
Diffusion with an atom that is much smaller so they can diffuse between atoms
What is faster, interstitial or vacancy diffusion>
Interstitial; energy it takes to move is much lower because of smaller size
what is this equation:
D= Do * exp[-Qd/RT]
Function of diffusion constant in regards to time
What happens when temperature increases in terms of diffusion?
High temperature leads to increase in energy, therefore movement of molecules
This increases the rate of diffusion
What are the units for this equation D= Do * exp[-Qd/RT]
D:
Do:
Qd:
R:
T:
D: Diffusion coefficient m^2/s
Do: pre-exponential constant m^2/s
Qd: activation energy J/mol
R: gas constant J/K*mol
T:temp K
What is this formula and what is z, λ, and v
(1/6)zλ^2v
Pre-exponential constant formula for diffusion (Do)
z: number of potential sites for jumps
λ: distance of diffusive jumps
v: atomic vibration frequency
What 5 factors influence diffusion?
- Interstitial vs vacancy
- The interacting substances (Do and Qd is different for every particle)
- Temperature
- Crystal Phase
- Microstructure; diffusion is faster in polycrystalline materials
What can Fick’s first Law tell us
J= -D (dC/dx)
D: diffusion constant
J: Flux across plate
C: concentration
Substances will diffuse from areas of high concentration to lower concentration
J=Mass/(area*time)
What can Fick’s 2nd law tell us
dC/dt = D (d^2C/dx^2)
+ : concentration will increase
-: concentration will decrease
What does this proportion mean?
x proportional to sqrt(Dt)
t increases –> depth of penetration increases
penetration depth of diffusion formula for 1D, 2D, 3D?
sqrt(2Dt)
sqrt(4Dt)
sqrt(6Dt)
What is required to diffract light for a lattice?
Lattice spacing must be comparable to the wavelength of the incident wavelength
What is this equation and what are its variables?
nλ= 2dhkl *sin theta
Bragg’s diffraction law
n: wavelength number (take it as 1 usually)
λ: wavelength
dhkl: spacing between planes
What does Bragg’s diffraction law tell us?
Constructive interference (max diffraction) will occur if path difference between rays is equal to nλ
formula for dhkl?
d= λ/(2sintheta)
theta: critical scattering angle
Formula for dhkl without theta?
dhkl = a/sqrt(h^2 + k^2 + l^2)
how does h, k, and l relate to interplanar spacing?
hkl increases —> interplanar spacing decreases
How are the incident and reflection angle related to each other in an x ray diffractometer
reflection angel should be twice the incident angle therefore if theta is the incident angle, 2theta is the diffraction angle
What kind of intensity vs diffraction angle will a crystal have?
approximately at a constant low level with distinct jumps in intensity at certain angles
What kind of intensity vs diffraction angle will a liquid/amorphous substance have?
one absolute maximum with the change being fairly gradual
What kind of intensity vs diffraction angle will a semi-crystalline solid have?
it will look like an amorphous graph with peaks like a crystal;
will have spikes in intensity but will not be at a constant low intensity usually
when will SCC not have diffraction?
none; all hkl will diffract
when will FCC not diffract?
when hkl is either all even or all odd
when will BCC not diffract?
When the sum of hkl is even
What can x ray diffraction determine?
can determine crystal structure and interplanar spacing (lattice constant)
What is electric conductivity range of metals?
σ> 10^5 (Ohm*m)^-1
What is electric conductivity range of semiconductors?
10^-6 <σ< 10^5 (Ohm*m)^-1
What is electric conductivity range of insulators?
σ<10^-6 (Ohm*m)^-1
Do electrons have a net force?
No; electrostatic force is canceled out by force that results from bumping into obstacles
what does σ=neu mean>
σ: conductivity
n: number density of carriers
e: carrier charge
u: carrier mobility
what is the trend for neu of metals compared to semiconductors
n: (lots of carriers)
e: same
carreir mobility: lower
trend for neu of semiconductors:
n: low amt of carriers
e: same
u: high
5 Factors that affect resistivity?
grain boundaries
dislocations
impurities
vacancies
lattice vibrations
Resistivity increases with:
temp
% impurity
% cold work
p=?
p= pthermal+ pimpurity + pdeformation
What would a graph of % impurity vs resistivity look like between two metals\
would look like an upside down parabola
resistivity increases until the “impurity” becomes the majority which is when resistivity begins to decrease again
Compare conductivity of metals and semiconductors
σmetal» σsemiconductor
Metals have a lot of carriers but are limited by their mobility
Semiconductors have lots of mobility but are limited by lack of carriers
What is an electron energy band structure
band shows allowed energies for electrons from each atoms when interacting with each other
What will a band structure look like for metals
The highest occupied band will be partially filled or bands will overlap
What does it mean when two bands overlap?
electrons in the overlapped band mean they are in different states but have the same energy, meaning that they can switch bands
What is Fermi Energy
Highest filled state when at 0 K
Every energy state below Ef will be filled and all above will be empty
What is a filled band? Can the electrons in a filled band conduct?
a filled band is an energy state where all allowed energies are taken up. Electrons in a filled band cannot conduct because there is no energy level they can jump to
Why can’t electrons below fermi energy conduct?
in order to conduct, electrons must use energy from the electric field to jump to a higher energy state. However, since all the energies below Ef are occupied, there are no energy states to jump to.
what is a band gap
band gaps are electron energy states that can NOT be filled
What will a band diagram for a insulator look like
The valence band will be completely filled with a large band gap. There will be no states that electrons can jump to because the gap is too big (the gap will be greater than 2 eV
What will band diagram for semiconductor look llike
valence band will be completely filled but the band gap energy will be very small (Eg<2 eV
What are the types of charge carriers in semiconductors
electrons: negatively charged particle
holes: positively charged vacant state from an electron
What is an intrinsic semiconductor?
conductor without any dopant
relationship between holes and electrons?
amt of electrons and holes will be equal;
what does n=p=ni= n0 * exp[-Eg/(2kT)]
n= no density of free electrons
p= no density of free holes
the expression shows how n and p change with T
how does T and conductivity relate
T increases –> conductivity decreases
relationship between lattice spacing and band gap?
lattice spacing decreases –> band gap increases
What is an extrinsic Semiconductor
doped semiconductor
What is a p type semiconductor
semiconductor doped to increase amount of holes
p»n
what is an n type semiconductor
semiconductor doped to increase amount of mobile e-
n»p
relationship between carrier mobility and impurity concentraiton
impurity concentration increases –> mobility decreases
Carrier mobility vs temp
temp increases –> mobility can decrease or have a maximum depending on concentration
how to find threshold condition for absorption of light by semiconductors?
Egap<_ hc/λ —–> λ<_ hc/Egap
c/λ= frequency
What are three types of semiconductor devices?
solar cell
MOSFET
LED
What is a p-n junction
boundary between two semiconductor material types; usually a p type and n type
What is a diode
device that acts as a one way switch for current. It allows current to flow freely in one direction but severely restricts the opposite direction
What is forward bias flow diode
charge carriers will flow through both p and n regions; holes and electrons recombine at junction
thus CURRENT FLOWS
what is reverse bias flow diode
charge carriers will flow away from junction; junction region depleted of carriers
little current flows
What is Moore’s Law
the amt of transistors in a CPU will double every two years
therefore amt of computing power will double every two years
What is an LED
light emmiting diode
is an LED in forward or reverse bias
emits light when forward biasedd
How does LED emit light
when recombining, the electron and hole are eliminated and a photon is emitted
How do solar cells work
pn junction in reverse bias;
holes and electrons flow away from junction as more energy is introduced from incident light
Band gap vs intrinsic semiconductor lattice constant
decrease lattice constant –> increase in band gap
Band gap vs difference in electronegativity
large difference in EN –> larger Eg
What is a dielectric material
-An insulator that contains electric dipole; positive and negative charges are separated at an atomic level
-An electric field will cause dipoles to align which will affect the material properties
What is capacitance
ability to store charge across a potential difference
What does a capacitor do
One plate will have an excess of charge causing a net charge on both plates.
The charge will remain even if the battery in the circuit is removed.
If a resistor is added charge will flow again until there is no net charge on plates (kinda like a battery)
what is this formula
ℨo(A/l)
capacitance formula
ℨ: dielectric constant for a vacuum between two plates
A: area of plate
l: distance between plates
what is this formula ℨr= ℨ/ℨo
formula for dielectric constant if there is no vacuum
What is polarization
When internal charges are moved from their equilibrium positions by a strong electric field
What is electronic polarization
displacement of electron clouds from the positive nucleus.
Occurs in all materials
requires electric fields
Ionic polarization
occurs in ionic materials
applied electric field displaces cations and anions in opposite directions
orientation polarization
alignment of permanent dipoles from random directions
What is a ferroelectric material
materials where polarization remains permanently, even after removing electric field
What is a piezoelectric material
Material where polarization can be varied by mechanical force
What is M=Xm H
Formula for magnetization field of material
M: Internal magnetiation field of material
Xm: Magnetic susceptibility
H: applied (external) magnetic field
What does Xm depend on?
Depends on magnetic force per atom
alignment of magnetic force among atoms
As you increase the frequency of an applied alternating electric field to a dielectric material, its
dielectric constant begins to decrease as different polarization mechanisms become non-responsive to the
alternating field. The order in which these mechanisms freeze out from low to high frequency is
orientation ionic electronic
OIE
