mse 4003 exam 1

Auger electron spectroscopy

Atomic force microscopy

Differential thermal analysis

Differential scanning calorimetry

Electron back-scatter diffraction

Focused ion beam

Fourier transform infrared spectroscopy

Numerical aperture

Scanning electron microscopy

Scanning probe microscopy

Transmission electron microscopy

Visible light microscopy

X-ray Fluorescence

X-ray photoelectron spectroscopy

X-ray diffraction

Confocal laser scanning microscopy

Auger electron spectroscopy

Electric discharge machine (cutting electrically conductive samples without mechanical stresses)

High-density polyethylene

Low-density polyethylene

Powder diffraction file

Polyolefin elastomer

Photomultiplier tube (converts light into electrical signals)

Short wavelength limit

Charge-coupled device

International Center of Diffraction Data

Field Emission Gun

Full-width half-maximum

High-resolution X-ray diffraction

Poly(ether-ether-ketone)

Ultra-high molecular weight polyethylene

Small-angle X-ray scattering

Wide-angle X-ray diffraction

Bright-field

Dark-field

Dicalcium phosphate dihydrate

Fast Fourier transform

High-resolution transmission electron microscopy

Octacalcium phosphate

Polycarbonate

Polybutylene Terephthalate

Selected Area Diffraction

2D spatial map of signal or intensity, as a function of position

Optical (uses lenses: VLM, TEM)
Scanned (using detectors: SEM, AFM)

Intensity due to interference as a function of angle
Uses COHERENT ELASTIC SCATTERING to reveal crystal structure

Spectral sensitivity, signal sensitivity, and resolution

intensity as a function of "interaction"
Uses INCOHERENT, INELASTIC SCATTERING

minimum distance of eye to focus
virtual images placed here via eyepieces

the ability to distinguish closely-spaced features - controlled by diffraction effects (Rayleigh criterion)

Equation: 0.61(lambda)/NA, NA = n sin(alpha)

Lambda limited to 400 nm minimum
NA upper limit = 1.6 with oil immersion lenses
Best R = 150 nm

0.2 mm
Ideal magnification in VLM = 1000x

Higher mag simply makes an image bigger, but at a certain point, it does not add any more visual information

intensity of light
depends on (NA)^2 and M^2 in TRANSMISSION
depends on (NA)^2 and M^4 in REFLECTION

Very important for detection (resolution isn't enough)
( I_obj - I_background ) / I_background
Visibility threshold varies with brightness

ability to distinguish an object present in an image; depends on CONTRAST

Range of OBJECT heights over which the object APPEARS to be in focus (only one true focal point)

Small alpha = Large depth of field
Large alpha = Small Resolution
(Compromise between R and Df)

In VLM, Df ~= R (< 1 µm) - samples must be quite flat

Range of IMAGE plane positions over which the image APPEARS to be in focus, for a fixed object position

D_focus >> D_field usually

D_focus = (M^2)D_field

Chromatic Aberration
Spherical Aberration
Astigmatism
Curvature of Field

Focal length varies with lambda; shorter lambda focused more strongly

Disk of confusion results

Focal length varies with off-axis distance; off-axis rays focused more strongly

Disk of confusion results

Focal length varies with polarization
Leads to elliptical disks of confusion
Hard to correct in VLM

Focal plane of the image is not truly flat
Most noticeable at high-magnification, short focal length lenses

1) Operate at disk of least confusion focal plane
2) Lower alpha and combine different lens types (to reduce CA and SA)
3) Use monochromatic light (to reduce CA)
4) No easy fix for astigmatism

Köhler system:
- Two illuminating lenses: collector and condenser
- Two imaging lenses: objective and eyepiece

Collector lens + field diaphragm = alters illuminated spot size on specimen, blocks stray reflections

Aperture diaphragm + condenser lens = controls alpha and NA, thus controls Df and R

Info on them: magnification, IOR, NA, application, lens-image distance, WD

Achromat = corrects SA for green light and CA for green and red light

Semiachromat (Fluorite) = expensive! corrects CA better

Apochromate = eliminates CA and corrects SA for red and green; highest NA

Simply to magnify the primary image from the objective (usually 4x or 10x)

1) Close aperture diaphragm or use different lens so as to reduce NA
2) Lower magnification for a given NA
3) Use high-power eyepiece with low-power, high NA objective
4) Use longest lambda possible

1) Use highest NA possible in objective
2) Use high magnification
3) Use shortest lambda possible
4) Keep illumination centered
5) Adjust field and aperture diaphragms, adjust brightness

Purpose = to control lambda and intensity

Neutral density (ND) = regulates intensity w/o changing lambda

Colored and interference filters = isolate specific colors or bands of wavelength

Heat filters = absorb IR radiation that causes specimen heating

Sectioning
Mounting
Grinding
Polishing
Etching

Abrasive cutting = common approach, with SiC, alumina, or diamond wheels/disks

EDM = electric discharge machine = cutting via spark erosion (good for electrically conductive materials; avoids mechanical stresses)

Microtomy = shaving thin slices using sharp glass or diamond knife (good for biological/polymer microscopy)

Hot mounts = thermosetting plastics at high T and P
Cold mounts = epoxy or acrylic mixed with hardener (versatile!)

removes sectioning damage
SiC papers with particles of different sizes
Grind from low to high grit, wash in between

Artifacts = scratches, structural disorder

Coarse polishing = abrasives down to 3 µm
Fine polishing = abrasives down to 1 µm or even 0.25 µm (diamond); alumina slurries can get down to 0.05 µm

Artifacts = "hard" particle pull-out due to excessive pressure during polishing (comet-tail effect)

Selective chemical dissolution to reveal microstructure; yields topographical differences in reflectivity or brightness

Total # of citations to published articles in past 2 years / total # of published articles in past 2 years

digital object identifier = digital handle used to identify and find objects/papers online

Rods = function at lower ambient intensity; no color sensitivity
Cones = detect colors red, green, and blue in good illumination
ONLY SENSITIVE TO AMPLITUDE AND WAVELENGTH, NOT PHASE

BF = object evenly illuminated via annulus
DF = illumination by oblique light via central stop (enhances contrast in VLM)

Phase changes are converted into amplitude changes via interference of beams

- Uses a phase plate after objective to advance different parts of direct beam by fractions of a wavelength
- In conjunction with any sample phase interactions, constructive/destructive interference can occur and give contrast

Optically anisotropic materials = have different IORs in different directions

O-wave = ordinary wave (along direction with high n)
E-wave = extraordinary wave (along direction with low n)

Plane-polarized light in -> phase difference -> elliptically polarized light out

A linear polarizer (crossed from the first) allows elliptically polarized light of different phase differences to form an analog range of amplitudes once filtered. The eye can detect these as usual

Uses an optically anisotropic prism (Wollaston prism), for samples that are not birefringent themselves

Strong contrast from subtle features

**Prism splits the beam in two based on birefringence
**Difference in phase between the two beams after interacting with the specimen yields interference, elliptical polarization, and conversion into amplitude contrast upon detection

Can sometimes show twinning/dislocations too!

Fluorescence = when objects emit light of longer wavelength after being excited by shorter wavelengths

Dyes = fluorochromes needed usually
UV or blue monochromatic light source
**Dichroic mirror = reflects short wavelengths and transmits longer ones
*Exciter filter = selectively transmits a band of short wavelength (initial filter of system)
*Barrier filter = transmits fluorescent light only (final filter prior to imaging)

- Laser beam focused as spot on specimen
- Scanning device moves beam in XY
- Pinhole aperture blocks stray reflected light
- 3D image obtained by stacks of 2D images
*Gives much better resolution in 3D than most techniques (0.2 µm)

Approach 1 = specimen scanning = best for lower resolution; stage moves

Approach 2 = laser scanning = mirrors rotate; MUCH harder to align

Bremsstrahlung and Characteristic

Braking radiation:
- electrons decelerating give a range of X-ray photons emitted
- short wavelength limit (SWL) = due to an electron giving up all of its energy as one, high-E photon

- electron transitions into core shell vacancies yield characteristic wavelengths (sharp peaks in X-ray spectrum)

K, L, M, ... = termination level
alpha, beta, gamma, ... = # of levels dropped
1, 2, ... = in order of decreasing drop height within a degenerate state transition

Cr, Fe, Mo, Cu (Cu Kalpha x-rays are most common)

Selectively absorb certain X-ray wavelength ranges, to acquire a primarily monochromatic beam for XRD

- uses the concept of absorption edge in a materials absorption coefficient

e.g. Ni edge just so that Cu Kbeta rays absorbed and Cu Kalpha transmitted

Bragg's law: n(lambda) = 2d_hkl*sin(theta)
(When constructive interference occurs)

Final X-ray amplitude depends on:
1) Angle = atomic scattering factor; large angles from beam axis give smaller amplitudes overall
2) Atomic scattering function = depends on electron wavefunction arrangement within atoms, and total X-ray ∆phase based on X-ray-electron diffraction
3) Unit-cell-wide diffraction = STRUCTURE FACTOR = sum of diffraction and ∆phase due to all atoms in unit cell
4) Bragg diffraction = constructive interference among all unit cells

G-vectors for which R*G=2(pi)n
- R = lattice vectors between unit cells
- G = recip lattice vectors = ∆k for a given diffraction scenario

* In real space, G vectors plotted = the normal vector of the Bragg plane under discussion

A crystallographic axis for which many planes intersect (usually a low-index direction i.e. 100)

- Diffraction pattern seen down zone-axis contains recip lattice points whose hkl values make G-vectors that are perpendicular to the zone axis direction

- Imaginary sphere with radius (1/lambda)
- Center located at crystal being examined
- Incident beam = line through sphere center targeting the origin of k-space, located on the sphere surface
- Diffraction beam = line at angle 2(theta) from beam axis
** If diffraction beam/Ewald sphere hits a recip lattice point, Bragg conditions are satisfied for those hkl planes

Recip lattice moves with crystal rotation
Sphere moves with beam rotation

Flat Ewald sphere; many k-space lattice points intersected/visible on diffraction pattern

No preferred orientation of grains = Debye ring-type diffraction pattern, where Ewald sphere points are smeared out in rings

Radii of rings + known lattice parameter = indexing of diffraction rings

** Equivalent to rotating the k-space lattice around its origin about the beam axis

Total atomic scattering intensity < sum of electron XRD intensities (due to some destructive interference between electrons once in an atom)

Special hkl values that make the structure factor = 0, even when Bragg conditions would support the observation of a diffraction peak

Fixed incident beam, stage and detector rotate (2x speed for detector) on goniometer = physical circular track

Focusing circle = imaginary circle containing the source, specimen, and detector on the circumference

Soller slits = prevent beam divergence

NOT suitable for thin-film XRD; requires a parallel, monochromatic beam

1) Axial divergence error - beam divergence when it hits specimen (irradiated parts of specimen not on focusing circle)
2) Flat specimen error - specimens are often rough (certain atomic planes not on focusing circle)
3) Specimen transparency - X-rays giving info about diffraction deeper in sample

Specimen must remain tangentially tilted to the focusing circle

Powder Diffractometry used for polycrystalline samples = allows for sampling of many grains

Problems that could arise:
1) Grinding = can cause strain, decomposition, contamination, amorphization, etc.
2) Irradiation = polymerization, decomposition, amorphization can result
3) Thermal issues = water loss, high T decomposition

Peak positions = given by 2(theta)
Peak intensities = given by relative diffraction strengths
Variation in intensity with 2(theta)

2(theta) = usually 5-65˚

lambda = usually Cu K(alpha) since it can probe a wide range of typical interplanar spacings

Scan step = 0.02˚ per step (10-20 bins at FWHM of a peak)
- Too large = smooth weak peaks
- Too small = inaccurate peak shifts

Preferential orientation = relative changes in intensity; may make certain peaks invisible

Crystallite size = small grains can cause peak broadening; calculated via Scherrer equation
(due to incomplete destructive interference in non-Bragg planes for small grains)

Residual stress:
*Tension = lowers 2(theta)
*Compression = raises 2(theta)
- uniform strain = peak shifts
- non-uniform strain = peak broadening

Crystal Phase Identification
- search and match XRD patterns in database against PDFs (powder diffraction files)

Lattice Parameter Determination
- small errors in sin(theta) give large errors in a
- Calculate a for several peaks, then extrapolate using various functions to cos^2(theta)=0 to find a0

Systematic = misalignment of instrument, beam divergence, absorption

Random = stochastic errors involved in peak observation

- Intensity of peaks from a phase is proportional to the volume fraction of that phase (assumption)
- compared against external standard (pure component), internal standard (known phase mixtures)

- Powders not required since you use a single peak

Traditional approach for single crystals
For a film/detector at D from sample, a diffraction spot at a radial distance Ri corresponds to Bragg angle:

(theta)_i = 1/2*arctan(Ri/D)

Modern approach with very sensitive detectors
- small angles correspond to large periodicities - used in polymers, proteins, etc.

TEM = optical image
SEM = scanned image

Electron gun
2 condenser lenses
Specimen
Objective, intermediate, and projector lenses
Fluorescent screen/camera

Thermionic guns = high temp allows electrons to escape work function
- Tungsten (short lasting)
- LaB6 (longer lasting, requires better vacuum and gentle handling)

Field Emission = electrons tunnel through work function barrier via electric field
- Thermal field emission (heat assists)
- Cold FE (at room temp)
* Needs very high vacuum, but very bright

Pre-thinning:
- slice down to 1 mm thickness
- Hand or dimple grinding

Final thinning:
- reducing thickness to electron transparency

1) Electropolishing = for metals
- make the sample the anode in electrolytic cell
- depends on many environmental factors

2) Ion milling = for metals and ceramics
- sputtering atoms away via ion beam
- cooling with liquid N necessary

3) Ultramicrotomy = for polymers
- shave electron transparent slices with a diamondlass blade
- often use cryo-ultramicrotomy to help with rigidity issues
- transfer to 3 mm grid
*Main issues: tearing, wrinkling

4) Nanoparticulate specimens
- use support grids/films to image directly

5) Surface and Extraction Replication
- grind and polish bulk material to expose precipitates
- add coating material to which precipitates adhere
- bulk material removed; particulates isolated on film

Mass-Density Contrast
Diffraction Contrast
Phase Contrast

For biology/polymer specimens
- INELASTIC scattering of electrons by atoms in specimen
- scattering amount proportional to mass-density in local region
* Depends on atomic #, thickness, density, aperture size, electron energy

Main image formation method
*Based on Bragg diffraction = COHERENT scattering
BF contrast generated when objective aperture excludes Bragg-diffracted electron beams
**Very sensitive to specimen tilting

- Focusing aperture on a diffraction spot other than main beam = DF imaging (only grains with that orientation/Bragg diffraction condition light up)

Diffraction pattern from TEM obtained from a single crystal region
- BF imaging = aperture allows main beam
- DF imaging = aperture allows an off-axis diffracted beam only

*** Centered DF (tilt beam, don't translate aperture) is best because it prevents severe image distortions = SA, CA, astigmatism

**Allowing two or more Bragg-diffracted beams through objective aperture
- Interference AFTER the specimen creates contrast, as a result of the specimen interaction with the electrons
- interpretable structures from 2-beam phase contrast

Many-beam phase contrast:
- enhances resolution
- fringes and dots can correspond to planar/atomic spacings!

From small angle approx of Bragg's law:

lambda*L=R*d
R = on-screen, off-axis distance of spot
L = specimen-to-screen distance

Low precision
Small angles only (<2˚)
Good at orientation measurement, NOT at lattice parameter determination

Inelastic + elastic scattering of electrons in thicker TEM samples
- Inelastic scattering due to interactions with sample electrons; creates secondary source in all directions of electrons (further from beam axis, lower intensity though)
- Elastic scattering due to SOME of these electrons satisfying Bragg conditions and creating diffraction cones
- Kikuchi lines are planar slices of the larger diffraction cone edges

Closer line = darker = deficit
Further line = brighter = excess
**Come in parallel pairs

Used as a road map for tilting the specimen until a zone axis is found

1) Diffraction mode
- SAD aperture above the intermediate lens at the "real space" IMAGING PLANE of the specimen rays

2) Imaging mode
- Objective aperture above the intermediate lens at the "k-space" BACK FOCAL PLANE of the specimen rays

1) Thickness fringes = sample thickness changing continuously, causing wedge fringes

2) Bend contours = diffuse curved bands in TEM; due to physical bending in specimen causing some rotated planes to satisfy Bragg conditions (MOVE QUICKLY UPON TILTING)

3) Defects/dislocations - local distortions of planes near defects in TEM samples
- appear as short line segments (advantage of TEM is observing these!)

Mag up to 1 million
R down to 10 nm
Df up to 1 mm at low mag

Electron gun
2 condenser lenses and a spray aperture
Scan coils and magnification control
3rd condenser lens to demagnify beam
*Final aperture
Specimen, detector

By the ratio between scan size and on-screen pixel size!

BSEs:
- relatively elastic scattering of electrons at high angles off sample atoms
- best for elemental composition contrast
*Can escape from deeper
*Poorer resolution due to deeper, wider interaction volume

SEs:
- inelastic interactions with sample electrons, causing them to be ejected
- low energy electrons ejected (3-5 eV)
- main signal in SEM; topological contrast
*Only escape from near surface
*resolution close to probe diameter

Everhardt-Thornley:

- Faraday cage with scintillator inside = can be biased +250V to attract all electrons (majority are SEs) = SE mode
- Or, biased to -50V to repeal low energy SEs (BSE mode)
- Scintillator at high +voltage
- Light guide and photomultiplier tube
- Amplification up to 1 million times before screen display

- determined by final aperture diameter and working distance

- Increase brightness
- Optimize alpha_final (too large of alpha can cause SA)
- Increase accelerating voltage to decrease lambda

** Part of how to obtain high-resolution in SEM

Minimal spot size AND good contrast (high probe current)

∆signal must be ≥ 5 times the noise level; ∆S/S = desired contrast

time to scan a frame / pixels per frame

larger dwell time = smaller MINIMUM probe current for a desired contrast (better conditions)

Regions of sample pointing towards detector will give larger (brighter) SE signals

Looks like surface with inclined optical illumination
(Can be misleading though)

Electron probe hits an edge or protrusion and some of interaction volume escapes to give brighter signal

**Probability of BSE escape increases with increasing atomic #
- due to ∆work function between materials & large nuclei back-scattering electrons

eta = backscattering coefficient = n_BSEs / n_incident electrons

BRIGHTER AREAS = HIGHER ATOMIC #

Working Distance - Dw
Final Aperture Size - Rfap
Accelerating Voltage - V

Larger with:
- Long Dw
- Small Rfap - reduces probe current and S/N ratio

!! Gives poorer resolution though

High V:
- lower lambda of electrons
- improves resolution via smaller probe size

Low V:
- decreases excitation volume
- improves resolution via less secondary excitations
- less beam/charging damage

Hydrocarbons decomposed under beam and leave carbon deposits (formed more quickly at high mag)

causes image distortions and streaking

Thin metal or carbon application via sputter coating or evaporation

- use metals when care only about surface topology since they're more conductive

Chemical fixation
Cryogenic fixation

Solvent, freeze, or critical point dehydration

Probability of BSE escape changes with orientation

*** At Bragg angles, fewer BSEs escape (dip in eta)

Kikuchi band formation from Bragg-scattered BSEs

- Much wider range of angles than TEM kikuchi formation (easier to find zone axes in field of view)
- Indexing done with Hough transform; via relative widths and orientations of the Kikuchi lines

Much higher pressures
Multiple pressure-limiting apertures; can be larger
Smaller Beam-gas path length
Can operate at higher pressures without as much scattering

Cheaper (only two vacuum pumps)
One pressure-limiting aperture
- must be small to avoid gas flow in high pressure differential
- limits rastering ability
Longer beam-gas path lengths (more chance of scattering)

GDD = Gas detection device
- electrons escaping from specimen collide with gas molecules, as they're attracted to a (+) biased beam-column exit cup
- cascade of electrons; SE signal amplified
- positive gas ions drift away from cup towards specimen; PREVENTS CHARGING

Non-conductive and hydrated samples
Dirty/contaminated samples
Phase transformations and environmental changes

Milling = high ion current = sputtering away atoms
Deposition = low ion current = laying down metal atoms from a precursor gas (via gas injection system needle)
Imaging = very low current; ionization of sample leads to huge SE signal
- Strong orientation contrast, beam damage possible

Ion beam for milling/deposition
SEM for imaging/spectroscopy

- 2-in-1 instrument
- excellent for cutting/imaging cross-sections
- Great for site-specific TEM prep
- Serial-sectioning tomography

Beam-gas path length

Back-scattered electron detector

Conventional scanning electron microscopy

Gas field ion source

Liquid metal ion source

Low vacuum scanning electron microscopy

Micro-channel plate

Pressure-limiting aperture