Slides Flashcards
Goal of The class
Gain a fundamental understanding of the structure-composition-property relationship
Types of properties
There are mechanical, electrical, thermal, and optical properties
Mechanical properties
Materials are brittle, ductile, rubbery, or hard
Brittle materials
This includes things like glass that shatter under stress
ductile materials
These are materials that are able to be bent due to dislocations in their atomic lattice. They do not return to their original shape after being bent though.
Rubbery materials
These are materials that elastically deform usually because of long chained polymers that enable these materials to deform and restructure. Polymers have the quality of rectation to act elastically
Hard materials
These are microcrystalline or nanocrystalline materials that are significant because they diffuse crack propagation very rapidly by minimizing intragranular cracking. This is commonly glass-ceramic materials.
Electrical material types
Materials are either conductors, insulators, or semiconductors
Conductive materials
This is a property of materials with loose electrons in the conductance band. They are able to transfer electrons between atoms.
Defects and impurities within the conductor scatters electrons and lower the conductivity of the material. 2D materials and crystals do not have as much deviation in preferred directions of electron transfer which makes them very good conductors.
Electron scattering length
This is a measure of the mobility of electrons in a material. Generally pure and crystalline materials (for semiconductors) have a longer scattering length which correlates to a higher conductivity.
Units are in cm2V-1s-s
Insulators
These are materials with tightly bound electrons and resist current
Semiconductors
These are materials that can elevate electrons into the conductance band under the right conditions of heat or voltage but below this critical value they act as insulators.
Optical properties
Materials are either opaque (absorbs incident light), transparent (one crystal that does not resonate with the oscillations of light or complete disorder), colored (alters the E of light), or translucent
Scattering in a material
Polycrystalline materials cause scattering as the light ray is reflected at each interface which can make them opaque or translucent
Why is glass clear
There are no reflective surfaces on the interior and the resonant frequencies of amorphous SiO2 are above and below most light. Glass is colored by metals that are able to elevate electrons with the general light wavelengths.
Thermal Properties
Materials are either conductors or insulators (dissipate phonons)
Thermal conductivity
Thermal conductivity is given by K = KL + KE
A high K means that heat is well transferred through the material.
KL is the lattice thermal conductivity (phonons) a low value indicates the material scatters phonons (scatter length =nm)
KE is the electronic thermal conductivity (ability to vibrate) a low value would indicate that electrons can flow without causing much oscillations.
A smaller crystal size enables the flow of electrons but the scattering of photons.
Phonons
These are collective vibrations of atoms along a crystalline arrangement. They have wave-particle duality having a frequency of oscillation and speed of propagation but have quantized vibrational mechanical energy and can be scattered. They transfer heat along a crystalline arrangement.
Number of oscillation modes in N atoms
There are 3N phonon modes in a crystal of N atoms based on Einstein’s model
Types of Phonons
There are optical and acoustic phonons
optical phonons move out of phase in opposite directions (like EMR) They are excited by EMR and create heat by coupling with absorbed EMR
Acoustic Phonons: the neighboring atoms move in the same direction as their neighbors (like sound waves)
Phonon Displacement types
Longitudinal displacement is when phonons move parallel to the direction of propagation
Transverse Displacement is when the phonons move in a direction perpendicular to the direction of propagation
Longitudinal Optical Phonon (LO) motion
If there is a row of phonons numerically labelled 1-n then the odd numbered phonons would move to the left when the even photons move to the right and vice versa
In comparison a longitudinal acoustic phonon would have a whole section of the lattice compress as the other section elongates/dilates
Transverse Acoustic Phonon (TA)
Within this mode of oscilation there is wave propogation out of plane (lateral motion) but it is continuous where neighbors have have simlar oscilation paths
Compared to transverse optical phonons (TO) is when neighboring atoms move in transverse directions but when one atom moves down the other moves up and vice versa.
Distinguishing Phonons
Within a crystal lattice there are 3N modes of osculation which are dependent upon the direction of 3-space being considered. Thus, in simple distinguishing you can look down a certain direction of the lattice to identify the mode of oscillation in that given direction.
allotropism
This is a term that defines different structures of the same composition but can only be applied to materials of pure elemental compositions
Thermal: Diamond vs. graphite
Diamond: The very strong, continuous, and rigid lattice network leads to low phonon scattering therefore very high k (~1000 W/mK)
Graphite: Parallel to plane k ~1950 W/mK this is because in plane the bonds are very strong and the hexagons distribute the vibrations well longitudinally
Perpendicular to plane low k (~5.7 W/mK) this is because the van der waals forces do not tightly oscillate along this dimension
Mechanical: Diamond vs graphite
Diamond is the hardest known material with a moh’s hardness of 10 which is why it can be used as an indenter in mechanical tests
Graphite is very rigid within layer but very weak between layers. This is exploited in it being used as a dry lubricant.
Electrical: Diamond vs. Graphite
Diamond has a wide band gap (5.5 eV) which makes it a very poor conductor (σ = 10-16)
Graphite has pi bonds transverse to the hexagonal layers which makes it incredibly conductive (normal to the plane σ = 10 parallel σ = 105)
Optical: Diamond and Graphite
Diamond has a large band gap (5.5 eV) this means that it is transparent until very low wavelengths near UV/ This is the amount of energy needed to cause the “jump” of electrons. Because of the rigidity of the structure IR does not wiggle the carbon atoms either. Also because diamond is isotropic and homogenous there are not any dipoles for incident EMR to couple with.
Graphite has semi-metal conductance bands which leads to free electrons. This means that it is opaque but also shiny.
Pi bonds
Pi bonds are double bonds that align above and below the planes. In graphite they are delocalized which creates a conductance level.
band gap
If Maxwell’s equation is solved for the electron position the electron’s energy can be found as a function of the direction (wavevector). The band gap is the difference in energy between the conductance band and valency bands.
Photon energy (eV’s)
1 photon usuall equates to ~2-3 eV
band gap diagram
This is a chart that is found by solving the wave function for the electrons position in one direction. These directions are then plugged into KE to plot the energy curves of electrons by direction. The upper lines show electrons in the conduction band (exited and transferrable) and the lower lines show electrons in the valence band (shielded)
The area between the two curves is the band gap and is an area of energy that electrons will never enter in terms of energy. The elevate electrons they must receive enough kinetic energy to jump the band gap.
Types of Probing Energies
There is light (IR-Vis-UV), x-rays, electrons and ion
Charge of probing energies
light: 0
x-rays: 0
Electrons: 1.602*10-19 C
Ions: +
Mass of Probing energies
light: 0
x-rays: 0
Electrons: 9.1*10-31 kg
Ions: Varies 6.6*10-26 Ar; 12*10-26 Ga
Energy of Probes
light: .1-6 eV
x-rays: ~10,000 eV
Electrons: 1-50 keV
Ions: 1-50 keV
Wavelength of Probes
light: 12-.2 μm
x-rays: 1-2 angstroms (.1-.2 nm)
electrons: λ = h/(2mE).5 = ~10pm for E~10 keV
Ions: λ = h/(2mE).5 = .1fm for E~10keV
(2mE).5 for electrons and ions is their momentum respectiely
Momentum of Probes and which have the most/least momentum
Light: p=h/λ
This has the least momentum because it has the longest wavelength. Green light has a momentum of 1.3 * 10-27 kg*m/s
x-rays: p=h/λ ~10-27
Electrons: p=[2mE].5 ~10-22
Ions: p=[2mE].5
These have the greatest momentum because they are the most massive and energetic. They have a momentum of 4.4*10-20 kg*m/s
Why to measure the momentum of electrons via energy?
Energy of electrons/ions is easier to determine that their explicit velocities because the kinetic energy can be determined through the process of accelerating the particle in a voltage potential. This also holds true for ions
Focii of Probes
Light: lenses
x-rays: mirrors
Electrons: magnets
Ions: magnets
Determining E for an ion/electron
E = charge*ΔV
Where charge is in coloumbs for the particle (1.602*10-19 C/charge)
ΔV = potential across the gap used to accelerate the charged particle.
eV to J conversion
E = q*V and 1 eV is the energy required by an electron in a electric potential of 1 V
hence, E = qV = 1.6*10-19 * 1
1 eV = 1.6 * 10-19 J
Energy (eV) of a photon at a wavelength in nm
E (eV) = 1242/λ (nm)
Concept of probing
The idea of probing is to cause a destabilization of the material in order to gain information about the material. You increase the entropy (hopefully temporarily) to receive information
What can we probe?
We can probe:
Electronic levels, vibrational levels, rotational levels, and translational energy levels. This fundamentally provides four constraints on our system to derive information
Energy Quantization
This is the idea that when we are probing things we are almost exclusively examining quantized energy levels derived from examining the wavefunction of the thing
When does quantization occur
Whenever a wave is confined (standing wave) the oscillation modes are discretized and can be derived using the schrodinger equation
electronic energy levels change
ΔE ~ 5*10-18 J This is the largest change in energy by level of the differing methods of probing
Vibrational energy level size
ΔE ~ 5*10-20 J
This is the second largest energy level change
Rotational Energy level change
ΔE ~ 5*10-22 J
This is the second smallest change by energy level but it doesn’t really matter because rotation does not readily occur in solids which is our main focus.
Translational change in energy
ΔE ~ 5*10-60 J These are so small that they are often considered to be continuous
ΔE hierarchy for probing (Least to greatest)
Translational Energy, rotational, vibrational, electronic
Bohr Model: Energy of an Electron
En = -13.6 Z2/n2 (eV)
where Z = atomic number and n = energy level
Electron E quantization: why?
If you find the wavefunction representing a certain set of orbitals there will be zero points where P(electron) = 0. These act as control points where oscillations cannot occur and we can consider them to be standing waves.
Energy of vibrations
Atomic oscillators can be described using a wavefunction that resembles a spring or a pendulum where their point where V=0 are control points for the standing wave.
Ev = (v+.5)(h/2pi)[k/m*].5
where: v = vibrational quantum number
k = “spring constant” related to the bonding energy = restoring force constant
m*= reduced mass = (1/m1) + (1/m2) where m1 and m2 are from the oscilating atoms or particles
Rotational Energy
The rotation of a periodically rotating molecule is confined by the moment I of the molecule.
Erot = J(J+1) ℏ2/2I
where J = rotational quantum number
ℏ = h/2pi
I = moment of inertia of the rotating particle
ℏ = ?
ℏ = h/2pi = reduced Planck’s constant
Translational Energy
En = (h2/8mL2)n2
n>0
L = Boundary x
m = mass
Particle in a box
This is a concept that is used to derive the translational energy levels of a particle. It postulates that if we have a particle that can move from 0 to L along x that is confined by a box that there are defined energies of the particle defined by different oscillation modes
Maxwell’s equation for E
E(x,t) = Asin(kx-ωt)
where: k2 = wave number = (ω/c)2
ω = angular frequency = 2pi c/λ
Schrodinger’s time independent function
This is the part of the equation with eiωt
ℏ2/2m + d2 ψ(x)/dx2 =Eψ(x)
How do we derive translational energy?
With schrodingers equation we can guess Asinkx + Bcossinkx where we are limited by ∫01 ψ(x)2 dx =1 and ψ(0)=0 ; ψ(L)=0
We can then solve for the unknowns and plug into schrodingers equation.
Solving for E we get that E= (ℏk)2/2m and k = wavenumber so k*L=npi because the wave must be equal to zero at x=L which only occurs in intervals of pi
Plug k in terms of npi/L and that is the energy equation
UPS
UV photoelectron Spectroscopy
UV light to KE of e
A beam of UV light extracts electrons from samples. The KE is measured to provide information on the binding energy in the valence region that the electron once occupied. It is measured by count/binding energy (eV)
FTIR
Fourier Transform InfraRed
IR to IR
incident IR light is absorbed by vibrational levels. The IR not absorbed is transmitted. Transmittance vs. wavenumber is characteristic of certain materials.
XRF
X-Ray Fluorescence
x-ray to x-ray
X-rays eject core electrons and when the outer ring electrons lower their energy level they emit characteristic x-rays. This is measured in counts/energy. Every atom has many responses that help to constrain the system or make it more complicated.
XPS/ESCA
X-Ray Photoelectron Spectroscopy/ Electron Spectroscopy for Chemical analysis
x-ray to KE of e
Beam of x-rays extracts e from samples the KE is proportional to the binding energies and intensity vs. eV reveals binding energies within certain orbitals
EDS
Energy Dispersive Spectroscopy
electrons to x-rays
Bean of electrons ejects core electrons and when outer electrons relax into vacancy they release characteristic x-rays and we measure count/energy
AES
Auger electron spectroscopy
electron to KE of e
A beam of electrons ejects core electron. An outer electron fills the vacancy and releases energy which ejects another outer electron. This electron is analyzed for KE
RBS
Rutherford Backscattering spectroscopy
ions to KE of ions
Ion beam collides with a sample. E of backscattered ions is measured and the change in energy of the ions is characteristic of atoms in the sample. This is given in energy vs count
SIMS
Secondary Ions Mass Spectroscopy
Ions to charge and mass of ions
Ion beam breaks a sample into ionic fragments. The mass and charge of fragments are measured by MS. Results are MS results; m/z vs intensity
Types of Imaging Techniques
SEM, TEM, AFM
SEM
Scanning Electron Microscopy
Electron source
Backscattered e from scanning beam are collected to image the surface topology and compositional variations
TEM
Transmission Electron Microscopy
Electron source
Electrons are transmitted through a thin sample to produce an image. This is also a diffraction technique that can indicate crystallograhy
AFM
Atomic Force Microscopy
This uses an atomically sharp tip to raster scan a material and produce its topology
Diffraction Techniques
TEM, XRD, ND
ND
Nuetron Diffraction
Neutron Source
Neutron beam diffracted through a sample and generates a diffraction pattern characteristic of crystallagrophy
XRD
X-Ray Diffraction
X-Ray beam is diffracted off of the sample surface to generate a diffraction pattern characteristic of crystallography
What does infrared light represent
This is the radiation of heat. All things radiating heat radiate IR.
Microwave radiation: oscillations
This is the effect of the electric fields of EMR being long enough to couple with molecules to cause oscillations. By coincidence microwaves can couple with water easily to create oscillations. These induce heat and are used to warm things via a microwave oven.
How is frequency related to light energy
An increase in frequency is equivalent to more oscilations/time which is related to increased energy within the wave.
How do x-rays interact with matter
x-rays have significant energy and can couple with larger atoms like calcium and phosphorous in our bones. This is why x-rays show our bones because they are the parts of us that absorb the rays. Smaller atoms (C, O, N) do not couple.
light properties as a wave
As a wave light has wavelength, amplitude, velocity, and time dependent vector quantity (phase dependent).
Amplitude is proportional to intensity
phase can be measured through interference
velocity is proportional to density and crystallographic interactions
and wavelength is proportional to the induced oscillations
Light as a particle
Planck postulated that light as a particle is the photon which are “energy packets” with E = hν
Under this impression light has a momentum given by h/λ and transfers energy through collisions with materials
Force on a charge in a field
F = q X E where q = 1.69 * 10-19 (C) for an electron
Polarization
This is the measure of how distorted the electron field becomes when interacting with an external electric field.
P = εo Χ E
Χ = dielectric susceptibility = f(material) = how electrons do not transfer but shift relative position
εo = permittivity of a vacuum = C1
What is the dielectric susceptibility a function of?
Χ is a material property that varies with the magnitude of a dipole (either induced or natural) and the wavelength of the electric field
Dipole Moment
μ = q X d where d and μ are vectors and points in the direction of the negative charge. Thus μ is in the direction opposite to E.
Charge sign within an E field
An electric field attracts a positive charge.
Three kinds of electric field-matter interactions
- Reorientation: This is the slowest oscillations of materials that is common within radio and microwaves.
- vibrations: These are between pairs of charged atoms and induce phonons in the IR and micro area
- electronic oscillations (Lorentz oscillators): This is the idea of electrons being semi-bound to the nucleas and influenced by high frequency oscillations in the vis or UV range.
Resonant frequency of vibrational oscillators
νo = (1/2pi) (k*μ).5 where k = “spring constant” = f(bonding)
μ = reduced mass = (1/m1+1/m2)
This is used to describe ionic and some covalent bonds that have rather rigid bonds
What determines coupling of vibrational oscillators
A larger mass of the atoms translates to greater time needed to change acceleration. Additionally, a higher spring constant (bond strength) means a higher resonant frequency because there is a greater restoring force.
Resonant frequency of electronic oscillators
ωo is proportional to μ.5 where μ = 1/me because m/n is much larger than the mass of an electron it is the dominant part of the atom that is being polarized by an interactiving light wave.
Is polarization a vector?
P can be described in 3 space by the dielectric susceptibility in each direction. If a material is isotropic or a glass then there is little to no difference between the x, y, and z directions.
P is a function of the wavelength of the light and can interact with multiple E-fields at one point in space/time.
Potential results of light proceeding into a solid
Transmission
Reflection: any change in refractive index causes some light to not enter the material.
absorption: dissipation and coupling which transfers energy to the material
scattering: The change of light direction. There is not energy transfer only energy redirection.
Reflection
R = Ir/Io = (n-1/n+1)2 when the material is transparent and the light incidence is normal to the surface.
This means that with an increase in n there is an increase in R
n proportional to e
the magnitude of n is defined by how strongly electrons couple with the incident light aka the polarizability of the material
n = [1-P/εoE].5 = (εr).5= 1- χ
Three ways to measure the coupling capacity of materials
P, χ, ε, and n are all related and can indicate how strongly light and matter couple. Generally large atoms that have a less dense electronic cloud are more polarizable, have a higher chi, P, epsilon, and n
What material character does n not determine
n cannot give indication to some structural features. For example a single quartz crystal and glass will have the same n. Diffraction bust be used to determine crystallography.
Scattering
this is the phenomenon where light is redirected but energy is not transferred. It occurs when light couples with the natural frequency of electrons and then is remitted radially. It is generally inefficient has a small influence on our observed optical phenomena.
Is = Io (a/λ4) This says that light scattering efficiency is very sensitive to changes in wavelength.
Why is the sky blue?
Scattering efficiency is a function of wavelength and blue light has a lower wavelength than red light meaning that it is more likely to be scattered. Because scattering is a redirection of light path, this means that the blue light is scattered down where we see it. This is why sunsets are red too because the blue light has been scattered since we are directly looking towards the sun through a thick atmosphere.
Absorption
This is the process of light transferring energy to the substance via photons. It occurs when light resonates with electron dipole and atom dipole oscillations. A materials transparency domain is determined by alpha where if light is not absorbed then it is transmitted.
Ia/Io = e -α(λ)*l This says that α(λ) the absorption coefficient causes an exponential increase in absorbed light with thickness of the material, l.
Transmission
This is the proportion of light that passes through the material. Generally, transmission is maximized between the resonant frequency for electronic and dipole-dipole oscillators. It is also less for materials with larger atoms (higher n) because of reflection. The size of the atoms is also proportional to the upper and lower bounds of the optical window where larger atoms tend to have an optical window at larger wavelengths.
Conservation of E in light
Io = It + 2nIr + Ia + Is where n = number of panes or interfaces the light is travelling through
Transmission equation
T= (1-R)2 e-α(λ)*z
Parts of an optical window graph
The optical window is a plateau of high transmittance for some materials. The lower and upper bounds are defined by the electronic and vibrational oscillators coupling with the incident light. A more energetic (lower wavelength higher frequency) upper bound indicates a higher band gap and/or a smaller electron cloud. a less energetic lower energy bound indicates larger atoms which need longer wavelengths to oscilate and/or weaker bonds.
The degree to which T approaches 1 is a function of n where the larger the atoms the more light will be lost to reflection.
Coupling
This is the idea that within a classic mechanical model of the world that when the EMR E-fields oscillate at ωo and the EMR transfers energy to the particle or electron to cause an increase in amplitude. When this occurs the iωγ term of n2 dominates γ is the dampening term so T goes to zero
Why is there an optical window and not an absorbance band?
This is because at energies above the band gap there are many different electronic configurations which create incremental jumps with delta E approaching zero. On the other side, although quantized, the jumps in vibrational energies are also very small which make absorption outside the bandgap nearly continuous although with some materials there will be a small hop from the state change
Lorentzian Oscillator: Quantum vs. Classical model
In classical mechanics the system acts like electrons are attached on several springs with some amplitude at a frequency defined by ωo and absorption occurs when light oscillates at ωo
In quantum mechanics there is some ΔE between orbitals proportional to h*ωo and E can be derived from ψ(x). Light is observed when h*ωo =E
Lorentzian oscillator for an isotropic, pure solid like C4
ψ(r) α eikr U(r) where U(r) is the bloch function, a periodic oscillating function that repeats throughout the lattice
What is the value of ψ(r)2 within the band gap?
It is ~0 which indicates that the probability of finding an electron in the bandgap is ~0
critical wavelength
This is the wavelength that the light has enough energy to promote electrons across the bandgap which is synonymous to resonating with the electrons and in both energy is transferred from the light to the electrons.
λc = h*c/eg
Glasses filter out light at wavelengths longer than their critical wavelength.
Which has a larger bandgap, blue or red glass?
Blue glass has a larger bandgap because this indicates that the glass transmits higher energy (shorter wavelength) blue light and not the longer wavelength lower energy red light. Hence black materials (Si) have a bandgap just less than that of visible light ~1.1 eV. If it were zero then it would appear metallic though because all incident electrons would cause transitions.
Why does Si become more conductive when incident light increases?
eg (si) ~1.1 eV ; visible light is in the 2-3 eV range. Thus with an increase of incident electrons there is an increase in the conductivity because more electrons are elevated into the bandgap.
How does ΔE differ between crystals and glass?
Crystals have well defined PE wells. Between atoms the PE increases significantly and near the atom the PE is at a minimum. This means that electrons have well defined bounds and PE states. There is a significantly higher proportion of predefined states where electrons may exist.
Glasses are amorphous by character thus they do not have PE wells within the band gap due to oddities in the configuration of atoms. This means that the potential wells of glass vary and the distribution of electrons at any PE is wide.
Multiphonon cutoff
This is the low energy version of the critical wavelength. It represents the wavelength where at wavelengths less than the multiphonon cutoff, atomic vibrations become the sites of transferring the EMR energy and absorption increases. This decreases with atomic mass.
It represents the point where low wavelength light can cause multiphonon vibrational states so ΔE ~0.
What are the basic components of a Spectrometer?
There is a light source (aim for broad wavelengths), monochromator (grating), and a detector
UV-Vis double bean spectrometer.
This uses a deuterium lamp for λ ~200-300 nm and a tungsten/halogen lamp for λ ~300-2500 nm. It typically employs the use of a rotating mirror to minimize the influence changes in intensity of the source across the source’s wavelength.
They typically use gratings as a monochromator and a Photomultiplier tube or photodiode as a detector. They will have a rotating mirror that continuously shifts between a reference and the transmitted sample light.
Monochromators
These are tools that are used to divide light into its constituent wavelengths to analyze individual parts of a spectrum
Grating equation
nλ = d(sin i - sin r)
n = m = order
d = spacing
i = angle of incidence
r = angle of reflection (angle from normal)
Gratings when n = 0
When n = 0 the resultant light in not a function of incidence. It is specular reflection
Photomultiplier tube
These are more complex light detection devices that have a photosensitive material which interacts with the incident monochromatic light to create a free electron. This electron is accelerated and interacts with various dynodes/anodes to be amplified and the resultant voltage is measured. At every collision the electron is accelerated to produce more electrons from the collision following. Ultimately it creates a measurable current near 100 e-
It is best for low light intensity but is more costly.
Photodiode
This uses a doped semiconductor (PN junction) attached to a voltage to cause a current as a function of incident light. They are cheaper, less accurate, and do not work at wavelengths less than 100 nm (1 micron) where Si is absorbent. They can also lead to false signals due to heat related pyroelectricity.
Why are glasses useful?
Generally we have three options for our optical materials. Monocrystalline material (good optics but hard to synthesize). Polycrystalline materials (bad optics easy synthesis). Glass materials (good optics and easy to synthesize)
Transparency of solids based on band gap
Generally PURE insulators (ionic materials like salt) have Eg = ~8.5 eV which is far beyond the energy of visible light and therefore are transparent
Semiconductors have a mid range Eg = ~1 eV which means that visible light is just over the amount of energy to excite electrons over the bandgap and thus the light is absorbed.
Ruled gratings
Reflective materials that have periodic notches on their surface separated by some distance, d. Incident light reflects differently dependent upon wavelength.
Vibrations: classical vs. quantum
In classical mechanics vibrations are a defined by radians from r=0 and there is a parabolic continuum of energetic states about r=o.
In quantum mechanics there are a series of probabilistic bands at discrete energy levels (n) who are defined by ΔE= h*νo
FTIR wavelength separation
FTIR’s used a michelson interferometer to separate wavelengths for absorption analysis. It is much faster and more accurate than a grating. The reason these are not used within UV-Vis is because they rely upon mechanical positioning which can be accurately done for longer wavelengths but not the short UV-vis wavelengths
Michelson Interferometer
This is a tool for FTIR spectroscopy wavelength-dependent absorption.
First a light source (blackbody radiation) hits a collineating mirror.
This then goes through a beam splitter (50% reflected 50% transmitted)
These beams reflect off mirrors, recombine, go through the sample and are focused on the detector.
Interferometer mechanism
When the beam of light is split it interacts with two mirrors.
One is fixed. The other moves a distance +- h
This change in distance causes retardation of half of the light. This causes constructive/destructive interference which produces different wavelengths because the blackbody is emmitting a broad band of wavelengths so at a certain position only one wavelength is constructive while the others are destructive.
interferogram
This is a graph of intensity vs. mirror displacement.
If we had a single wavelength of light then this would be a simply sinusoidal curve oscillating between 0 and 1 with 0 intensity when the mirror is at one half of the wavelength.
Interferogram for more than one wavelength
When you add more wavelengths to the interferometer, certain areas constructively interfere and other areas destructively interfere.
For example, if you have 2 wavelengths there is a boudin shaped sinusoid which can be ~broken into two superimposed sinusoids.
Fourier Transform
This is a mathematical tool that leverages the fact that sin/cos waves are easy to differentiate. Because of this, it is convenient to write oscillating functions in terms of superimposed sin/cos waves.
Incidentally, these sin/cos waves, for the use of interferometers, are the original oscillating waves of light that interfere to produce the resultant pattern. This means that the fourier transform “decomposes” the superimposed functions into discrete inputs.
It is like a taylor/mcclaurin series for oscillating functions.
Frequency domain
The frequency domain is the hypothetical space that the results from a fourier transform.
After completing the transform there will be a long summation with a bunch of sins and cosines. Each of these will have a unique wavelength and intensity but in order to understand what each means in terms of absorbance, we convert the unique wavelength to frequency.
Interferogram: Raw data
This will be a plot of intensity vs. displacement. There will be a maximum at displacement=0 because of constructive interference.
It quickly goes to a constant with some bumps at displacement not equal to zero. This can be transformed into wavelength vs intensity.
Processing FTIR data
- collect broadband source interferogram
- collect several interferograms (each takes seconds) to minimize signal to noise ratio
- Fourier transform and convert to I vs wavelength
- subtract out the intensity of the source
- analyze
FTIR light source
Most commonly a silicon carbide coil is resistively heated (pass a current through it) to emit the whole IR range.
Pyroelectric detectors
These are FTIR detectors for high intensity. They are basically solar panels with an IR absorbent material on the surface that heats up the semiconductor and causes a change in potential across the pn boundary. It is an improved thermocouple.
One complication with pyroelectrics is that you end up with a plot of V vs. t that must be aligned to the Fourier transformed interferogram.
MCT
These are low intensity IR sensors used in FTIR. They are made of HgCdTe which are all large, electronically saturated atoms. The photon hits the semi-conductor which excites an electron into conductance. The corresponding change in voltage is measured.
MCT detector needs
An MCT detector requires being constantly cooled (usually with liquid nitrogen) because of the highly sensitive semiconductor used within.
This is because E (temperature) > Eg and is given by E = kbT
What does FTIR measure?
FTIR measures vibrational states of molecules. Different energies cause vibrations which absorb incident IR light. This means that when you subtract the light transmitted vs broadband source you can see where certain sinusoidal functions were absorbed within the sample.
FTIR sample prep
IF IR transparent/translucent
Simply insert into the spectrometer
IF IR absorbent
For an insoluble solid it is ground with IR transparent KBr pellets then pressed into a pellet to be observed.
For soluble solids they are dissolved into an IR transparent solvent and dried onto an IR transparent substrate
Impurity impacts
Impurities within materials can generate additional electronic and vibrational transitions that shift how light interacts with your material.
Why do transition metals color things?
Characteristic d orbital subsplitting creates different energy states that correspond to the energy of visible light. This causes different absorbance as a function of crystal field theory.
Crystal field theory
This is a theory describing why/how materials are colored. For metals within glasses or crystals, they are cations in interstitial tetrahedral/octahedral positions. The complex orbital structure of the d orbitals creates a higher electron density near the anions which means a higher PE state. This causes splitting where certain orbitals are at a higher PE. The difference between these orbitals is given by delta and measured in Dq (difference in quanta)
Optical losses
I/Io = e-αl This says that as light moves through a substance of l thickness there is an exponential decrease in intensity derived from α which is the degree to which the EMR wave is attenuated.
α = f(c[metal+]) as an impurity in the substance. Therefore, a larger concentration of impurity causes more loss.
How does impurity mass impact absorbance
Low mass impurities (ex O or H) generate higher wavelength absorbance because νo = (1/2pi) (k*μ).5
where k = “spring constant” = f(bonding) μ = reduced mass = (1/m1+ 1/m2)
Reflection Spectroscopy
This principally investigates how light interacts with a solid through reflection.
Specular reflection stage
This is a stage that has three mirrors and a sample holder. Incident light hits one mirror reflects off the sample and other mirrors to be routed to the measuring device.
It is an “add-on” component for UV-vis double beam spectrometers and/or FTIR spectrometers.
It is important for the window industry that needs to accurately asses how light is absorbed throughout different light orientations. Additionally it is used for solar cells that need to reflect everything less than 1.1 eV
Diffuse reflection integrating sphere
This is a sphere used to determine diffuse reflection which is most helpful when the surface roughness is ~the same as the incident wavelength.
It has a portal that enables incident light to enter. It then reflects on an angled sample so that most of the incident light enters a light trap.
The remaining diffusely reflected light reflects on the highly reflective sphere interior (Au or Ag) until it hits a detector which measures the diffuse reflection.
Total reflectance
This has a sphere with incident light and a sample but the whole interior is mirrored so the detector reads all of the reflected light.
It is used in combination with data from diffuse reflectance and specular reflectance. total = specular + diffuse
Scattering measurements
This uses a diffuse reflectance sphere where the sample is placed in the center and there is a light trap behind the sample. This means that the only light that exits the sample is scattered light.
This is also used to measure the diffuse transmittance of a sample.
These samples require high surface polishing but the measurements help to determine if the nanocrystalline structure is of approximately the same size as the incident wavelength.
Attenuated total Internal Reflectance
This is a tool used for when materials are either too small to use within a typical FTIR or are highly absorbent. It uses an IR transparent crystal with incident IR internally reflected to increase the number of interactions with the sample which increases accuracy.
Evanescent field
This is a tiny E-field (usually <5 microns) that extends beyond the interface during reflection. This means that if you have a sample in this 5 micron interface that it will absorb some of the wavelengths in the evanescent field causing losses in the final reading.
Infrared fibers
These are optical fibers, most often made from chalcogenide glass designed for total internal reflectance of IR light. They are important for evanescent wave spectroscopy because they can be “dipped” into a sample for FTIR analyses.
Number of Reflections for evanescent wave spectroscopy
N(θ, d, L) = L* [tan(90-θ)/d]
where: N = number of reflections
θ = angle from horizontal
d = diameter
This says that as diameter decreases, length increases, and the angle from horizontal increases that the number of reflections increases. This is a design problem though because the smaller the diameter, the weaker the material.
Where is evanescent spectroscopy used?
It is commonly used in biology to measure cells and other membrane-like materials.
Optical losses in fibers
Because l is very large α needs to be minimized. α = f(c[impurity]) so the fiber needs to be very pure.
Measuring α in fibers
The most common method is the “cut back method” where you measure the intensity of light exiting an optic fiber at two different lengths where L1 > L2 and α = [1/(L2-L1)] *ln (I2/I1)
Usually this is done at several different wavelengths because scattering and absorbance is dependent on wavelength
Optical Loss Units
These are reported in dB/length where dB=decibels = 10*log10 (I/Io) where I = output power and Io = input power
This can be used to characterize materials.
1 dB of loss is ~ x% transmission?
1 dB ~ 80% transmission
Losses in Si fiber optics are below 1dB/km
Attenuation in silica fibers
Prior to today, Si fibers only had transmission windows at 1.3 and 1.55 microns because of OH vibrations in water and the general constraints that any solid has for coupling with EMR. CVD has helped minimize the presence of OH impuritites.
Wavelength-division multiplexing (WDM)
This is the idea of using different wavelengths of lasers to transmit different information. They take advantage of low-OH silica fibers to have an optical window from 1.1-1.7 microns which can transmit 100 channels only .2 nm apart (25 Ghz)
Erbium doped fiber amplifiers
EDFAs are fibers that are used to amplify signals in fiber optic cables. Right now the C band amplifies signals between 1525-1565 nm (1.525-1.565 microns) and the L band between 1570-1610 nm (1.57-1.61 microns)
Optical telecommunication networks
These are telecom systems that use a binary format where a laser pulse = 0 or 1. This can be tracked at 100 Gb/sec in a single channel and there are about 100 channels in one fiber using WDM. 100 Gb/sec*channel * 100 channels = 10 Tb/sec
This means that we can transfer information faster than electrons in computers move to process the information. This is why quantum computing would be game-changing.
Dispersion in optical fibers
even with very precise lasers they still have pulses that are not perfectly quantized at one wavelength (usually ~.02 nm in width). Because n = f(λ) and n=c/v this means that at the long path length of an optical fiber that there is a change in velocity between the front and end of the pulse which can cause overlapping.
Point Group Theory
This is the theory that is used to determine the symmetry of molecules and crystals. It is synonymous to crystallography bet with different notation. σ is used for denoting mirror planes where σh is the mirror plane perpendicular to the maximum rotational symmetry (main symmetry axis). σv denotes mirror planes that are parallel with the main rotational axis. Cn is rotational symmetry where n is the number of rotations. The groups are denoted by Dn .
Why does NSOM operate at a constant height?
This is because light diffracts, and the exiting ray increases exponentially with distance beyond the minimum aperture (d α r4) . Thus the probe operates at a constant height so that the optical observations can be as precise as possible. This also influences the van-der-walls forces acting on the tip so maintaining a constant height also ensures accurate topology.
Detecting diffraction cones
In power XRD, you create cones that represent the d-spacings present in your sample. By scanning in a semi-circle collinear to the incident beam you intersect all of these diffraction cones and hence can have I vs. 2θ in one sweep.
How does a HREM image work in principle?
Upon exiting the sample, the transmitted waves exit in the same trajectory that they entered whereas the diffracted waves exit at an angle. Where these interfere constructively (where the lines cross) can help to indicate the structure of the material being inspected. The crystalline specimen can then be reoriented to gather all of the rays that satisfy bragg’s equation.
It produces a pattern very similar to the Laue Method
