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AP 5301/8301
Instrumental Methods of Analysis
and Laboratory
Zhengkui XU
Office: G6760
Tel: 34429143
Email:[email protected]
Course Objectives
• Basic understanding of materials
characterization techniques
Physical basis – basic components and their functions
Common modes of analysis
Range of information provided by the techniques
Recent development of the techniques
• Emphasis on applications
Typical examples and case studies
How to use different techniques to solve
different problems in manufacturing and
research
Microscopy and Related Techniques
• Light (optical) microscopy (LM) or (OM)
• Scanning electron microscopy (SEM)
Energy dispersive X-ray spectroscopy (EDS)
& Wavelength dispersive X-ray spectroscopy
(WDS)
• X-ray diffraction (XRD)/X-ray fluorescence
(XRF)
• Transmission electron microscopy (TEM)
Surface Characterization Techniques
• Scanning probe microscopy (AFM & STM)
• Secondary ion mass spectroscopy (SIMS)
• Auger electron spectroscopy (AES)
• X-ray photoelectron spectroscopy (XPS)
Non-Destructive Analysis
Processing-structure-property
Processingstructureproperty
Chemical ( Crystal )
composition Structure
Materials
Processing
Microstructure
(Characterization)
(Characterization)
Intrinsic
Materials
Selection
Extrinsic
Properties
Microstructure
Nature, quantity and distribution of phases in the ceramics,
e.g., crystals, glass, porosity, grain boundary and impurity
(secondary) phase.
Secondary (amorphous) phase
impurity
Grain
Boundary
phase
Grain
boundary
Grain
50 m
Grain
boundary
pore
Pore within grain
Phase - A homogeneous portion of a system that has uniform physical
and chemical characteristics.
http://en.wikipedia.org/wiki/Phase_(matter)
Scale and Characterization Techniques
XRD,TEM,STM
SEM
OM
Grain I
Grain II
atomic
1
Valve
Turbo
charge
SiC turbine blades
crack
Grain 1
Intergranular
amorphous phase
Grain 2
2nm
TEM image
Effect of Microstructure on
Mechanical Property
f  d-1/2 d-grain size
10m
50m
a
b
OM images of two polycrystalline samples.
Mechanical test:
Microscopic analysis:
fa > fb Mechanical property
da < db
Microstructure
Identification of Fracture Mode
Cracks
Pores
Grain
boundary
Cracks
4m
20m
Intergranular fracture
Intragranular fracture
OM and SEM
BaTiO3
Growth
step
50m
OM - 2D
5m
SEM – 3D
High Resolution Z-contrast Imaging
Atomic Ordering in Ba(Mg1/3Nb2/3)O3
I a Z2
http://www.youtube.com/watch?v=egPQZw0QkVw
[110]
(STEM)
First Place Winner (TEM category) in the 1998 Ceramographic
Contest at 100th Annual Meeting of Am. Ceram. Soc. Z. Xu et al.
Aberration-corrected high-resolution
transmission electron microscopy
Profile
100%
60%
100%
Sr Ti O
0
20
Simulation
40
60
80
Occupancy (%)
100
SrTiO3
C.L. Jia, M. Lentzen & K. Urban, Science 299, 870 (2003)
STM - Seeing Atoms
STM image showing single-atom
defect in iodine adsorbate lattice
on platinum. 2.5nm scan
Iron on copper (111)
Optical Microscopy
• Introduction
• Lens formula, Image formation and
Magnification
• Resolution and lens defects
• Basic components and their functions
• Common modes of analysis
• Specialized Microscopy Techniques
• Typical examples of applications
http://micro.magnet.fsu.edu/primer
http://www.doitpoms.ac.uk/tlplib/optical-microscopy/index.php
Physics of
http://micro.magnet.fsu.edu/primer
http://www.doitpoms.ac.uk/vidlib/browse.php
How Fine can You See?
• Can you see a sugar cube? The
thickness of a sewing needle? The
thickness of a piece of paper? …
• The resolution of human eyes is of the
order of 0.1 mm.
• However, something vital to human
beings are of sizes smaller than 0.1mm,
e.g. our cells, bacteria, microstructural
details of materials, etc.
Microstructural Features
which Concern Us
• Grain size: from <m to the cm regime
• Grain shapes
• Precipitate size: mostly in the m
regime
• Volume fractions and distributions of
various phases
• Defects such as cracks and voids: <m
to the cm regime
• ……
What is a Microscope?
A microscope is an instrument designed to make
fine details visible. The microscope must accomplish
three tasks:
1. To produce a magnified image of the specimen
(magnification).
2. To separate the details in the image (resolution).
3. To render the details visible to the eye, camera,
or other imaging device (contrast).
Introduction- Optical Microscopy
• Use visible light as illumination source
• Has a resolution of ~o.2m
• Range of samples characterized - almost
unlimited for solids and liquid crystals
• Usually nondestructive; sample preparation
may involve material removal
•Main use – direct visual observation;
preliminary observation for final characterization with applications in geology, medicine,
materials research and engineering, industries,
and etc.
• Cost - $15,000-$390,000 or more
http://www.youtube.com/watch?v=bGBgABLEV4g&feature=endscreen&NR=1
http://www.youtube.com/watch?v=sCYX_XQgnSA&feature=related
<2min
Old and Modern
Light Microscopes
http://www.youtube.com/watch?annotation_id=annotation_100990&f
eature=iv&src_vid=L6d3zD2LtSI&v=ntPjuUMdXbg
http://www.youtube.com/watch?v=X-w98KA8UqU&feature=related
Simple Microscope
Low-power magnifying glasses
and hand lenses
2x
4x
10x
A microscope is an instrument used to see objects that are
too small for the naked eye. The science of investigating small
objects using such an instrument is called microscopy.
Refraction of Light
Light path bends at interface between two transparent
media of different indices of refraction (densities)
q1
Refracted angle q2
Incident angle
Normal
air
Sinq1
Sinq2
=
V1
V2
=
N2
N1
Snell’s Law
Materials
N - Refractive index of material
- Speed of light in vacuum
N 1
- Velocity of light
in material
Air
Water
Lucite
Immersion oil
Glass
Zircon
Diamond
N
1.0003
1.33
1.47
1.515
1.52
1.92
2.42
http://micro.magnet.fsu.edu/primer/java/refraction/refractionangles/index.html
Focusing Property of A Curved Surface
In entering an optically more dense medium (N2>N1), rays
are bent toward the normal to the interface at the point of
incidence.
Curved (converging) glass surface
normal
Air
N1
N2
F
f
F - focal point
Focal plane
f – focal length
Curvature of Lens and Focal Length
Normal
N1 N2
Bi-Convex Lens
The larger curvature angle q
The shorter focal length f
q1
F
Optical axis
f1
q2
q1 > q2
F
N1 N2
f2
Centerline of the lens
f1 < f2
Converging (Convex) Lens
f
f
F
Focal plane
The simplest magnifying lens
f  curvature angle and lens materials (N)
the larger N, the shorter f
N:
lucite
1.47
glass
1.51
diamond
2.42
http://www.youtube.com/watch?v=hDRb9HAK5s4
http://www.youtube.com/watch?v=K5LeAV0Ztkg
Image Formation by a Converging Lens
Two fundamental properties of lenses:
1. Deviating a light beam parallel to its own axis, then making
it to pass through the focus;
2. Leaving unaltered the path of the rays which pass through
the lens center.
The A ray (principal ray) passes through the lens center and is not
deflected.
The B ray comes to the lens moving parallel to the axis and passes
through F1.
The C ray which in a similar way passes through F2 and leaves the
lens parallel to the optical axis.
Any two of these three characteristic rays can be utilized to
determine the size and placement of the image formed by the
lens.
http://www.youtube.com/watch?v=-k1NNIOzjFo&feature=related
http://www.youtube.com/watch?v=lBKGP6Fh9vs
Magnifier – A Converging Lens
If o’-o’ is ~0.07mm, qo=0.016o
NDDV-ability to distinguish as separate
points which are
~0.07mm apart.
retina
I’
I’
qo - visual angle
nearest distance of distinct vision (NDDV)
subtended at the eye
by two points o’-o’ at o”
NDDV.
o-object distance
Magnification
I-I o”-o”
m=
=
I’-I’ o’-o’
m = q/qo
o” h
Virtual
image
A
qo
q
-i
cornea
B
o
f
25cm
Ray diagram to show the principle of a single lens
http://www.youtube.com/watch?v=_5dEO-LRV-g
Real
inverted
image
Lens formula and magnification
Objective lens
ho
f
f
O
Lens Formula
hi
i
1
_
f
=
1
_
O
+
1_
i
I1 -Inverted
image
f-focal length (distance)
O-distance of object from
lens
Magnification m = hi = i i-distance of image from
o ho O
by objective
lens
http://micro.magnet.fsu.edu/primer/java/lenses/converginglenses/index.html
Maximum Magnification of a Lens
1/f = 1/O + 1/i
• Angular magnification is maximum when
virtual image is at “near point” of the eye,
i.e. 25 cm (i = -25 cm)
• Using the lens formula, o = 25f/(25+f )
• q0  h/25
and
q  h/o
q
h o 25 25  f
25
m



 1
q 0 h 25 o
f
f
f
in cm
Magnification when the Eyes
are Relaxed
1/f = 1/O + 1/i
• The eyes can focus at points from infinity to
the “near point” but is most relaxed while
focus at infinity.
• When o = f, i = 
• For this case, q0  h/25 and q  h/f
q 25
m

q0
f
Limitations of a Single Lens
• From the formula, larger magnification
requires smaller focal length
• The focal length of a lens with
magnification 10 is approximately
2.5cm while that of a 100 lens is
2.5mm.
• Lens with such a short focal length
(~2.5mm) is very difficult to make
• Must combine lenses to achieve high
magnifications
Image Formation in Compound Microscope
Compound microscope consists of two converging lenses,
the objective and the eyepiece (ocular).
25cm
• Object (O) placed just outside focal point of objective lens
• A real inverted (intermediate) image (I1) forms at or close to
focal point of eyepiece.
• The eyepiece produces a further magnified virtual inverted
image (I2).
• L – Optical tube length http://www.youtube.com/watch?v=RKA8_mif6-E
•
•
•
•
Magnification of Compound
Microscope
Magnification by the objective m0 = s’1/s1
Since s’1  L and s1  f0, therefore
magnification of objective mo  L/fo
Magnification of eyepiece me = 25/fe
(assuming the final image forms at )
Overall magnification M = mome
 L   25 
M =    
 f o  f e 
How Fine can You See with an
Optical Microscope?
 Magnification


M = 25L/fofe
If we can make lenses with extremely
short focal length, can we design an
optical microscope for seeing atoms?
Can you tell the difference between
magnification and resolution?
Imagine printing a JPEG file of
resolution 320240 to a A4 size print!!
Empty Magnification
Higher resolution
Lower resolution
Diffraction of Light
Light waves interfere constructively
and destructively.
Sinq=/d
Distribution
1st
2nd 3rd
film
http://micro.magnet.fsu.edu/primer/java/diffraction/basicdiffraction/index.html



Resolution of an Optical Microscope –
Physical Limit
Owing to diffraction, the
image of a point is no
longer a point but an
airy disc after passing
through a lens with
finite aperture!
The disc images
(diffraction patterns) of
two adjacent points may
overlap if the two points
are close together.
The two points can no
longer be distinguished
if the discs overlap too
much
Resolution of Microscope –
Rayleigh Criteria
Rayleigh Criteria: Angular separation
 of the two points is such that the
central maximum of one image falls
on the first diffraction minimum of
the other
 =qm  1.22/d
Resolution of Microscope –
Rayleigh Criteria
Image 1
Image 2
http://micro.magnet.fsu.edu/primer/java/imageformation/rayleighdisks/index.html
Resolution of Microscope – in
terms of Linear separation



To express the resolution in
terms of a linear separation r,
have to consider the Abbe’s
theory
Path difference between the
two beams passing the two
slits is d sin i  d sin a  
Assuming that the two beams
are just collected by the
objective, then i = a and
I
II
I
II
dmin = /2sina
Resolution of Microscope –
Numerical Aperture



If the space between the specimen and the
objective is filled with a medium of refractive index
n, then wavelength in medium n = /n
The dmin = /2n sina = /2(N.A.)
For circular aperture
dmin= 1.22/2(N.A.)=0.61/(N.A.)
where N.A. = n sina is called numerical aperture
Immersion oil n=1.515
http://micro.magnet.fsu.edu/primer/java/imageformation/rayleighdisks/index.html
Numerical Aperture (NA)
NA=1 -
theoretical
maximum numerical
aperture of a lens
operating with air as
the imaging medium
a
Angular aperture
(72 degrees)
One half of A-A
NA of an objective is a measure of its ability to
gather light and resolve fine specimen detail at
a fixed object distance. NA = n(sin a)
n: refractive index of the imaging medium between
the front lens of objective and specimen cover glass
http://micro.magnet.fsu.edu/primer/java/microscopy/immersion/index.html
Factors Affecting Resolution



Resolution = dmin = 0.61/(N.A.)
Resolution improves (smaller dmin) if  or n or a
Assuming that sina = 0.95 (a = 71.8°)
Wavelength

Air (n= 1)
Oil (n = 1.515)
Red
650 nm
0.42 m
0.28 m
Yellow
600 nm
0.39 m
0.25 m
Green
550 nm
0.35 m
0.23 m
Blue
475 nm
0.31 m
0.20 m
Violet
400 nm
0.27 m
0.17 m
(The eye is more sensitive to blue than violet)
Resolution of a Microscope (lateral)
The smallest distance between two specimen points
that can still be distinguished as two separate entities
dmin = 0.61/NA
NA=nsin(a)
 – illumination wavelength (light)
NA – numerical aperture
a-one half of the objective angular aperture
n-imaging medium refractive index
dmin ~ 0.3m for a midspectrum  of 0.55m
Optical Aberrations
Reduce the resolution of microscope
Aberration in optical systems (lenses intended to produce a
sharp image) generally leads to blurring of the image. It
occurs when light from one point of an object after transmission
through the system does not converge into a single point.
Two primary causes of non-ideal lens action:
• Spherical (geometrical) aberration – related to the
spherical nature of the lens
• Chromatic aberration – arise from variations in the
refractive indices of the wide range of frequencies in
visible light
Astigmatism, field curvature and comatic aberrations
are easily corrected with proper lens fabrication.
http://www.youtube.com/watch?v=XGjg64rayfM
Aberration of microscope
Defects in Lens



Spherical Aberration –
Peripheral rays and axial
rays have different focal
points (caused by spherical
shape of the lens surfaces).
causes the image to appear
hazy or blurred and slightly
out of focus.
very important in terms of
the resolution of the lens
because it affects the
coincident imaging of points
along the optical axis and
degrade the performance of
the lens.
http://micro.magnet.fsu.edu/primer/java/aberrations/spherical/index.html
Defects in Lens
 Chromatic Aberration


Axial - Blue light is refracted to
the greatest extent followed by
green and red light, a
phenomenon commonly referred
to as dispersion
Lateral - chromatic difference of
magnification: the blue image of a
detail was slightly larger than the
green image or the red image in
white light, thus causing color
ringing of specimen details at the
outer regions of the field of view
A converging lens can be combined
with a weaker diverging lens, so that
the chromatic aberrations cancel for
certain wavelengths:
The combination – achromatic doublet
weaker diverging lens
http://micro.magnet.fsu.edu/primer/java/aberrations/chromatic/index.html
Defects in Lens


Astigmatism - The
off-axis image of a
specimen point
appears as a disc or
blurred lines instead
of a point.
Depending on the
angle of the off-axis
rays entering the o
lens, the line image
may be oriented
either tangentially
or radially
http://micro.magnet.fsu.edu/primer/java/aberrations/astigmatism/index.html
http://www.youtube.com/watch?NR=1&v=6YxffFmi4Eo&feature=endscreen
A
Defects in Lens


Curvature of Field
- When visible light
is focused through a
curved lens, the
image plane
produced by the lens
will be curved
The image appears
sharp and crisp
either in the center
or on the edges of
the viewfield but not
both
http://micro.magnet.fsu.edu/primer/java/aberrations/curvatureoffield/index.html
Defects in Lens

Coma - Comatic
aberrations are
similar to spherical
aberrations, but they
are mainly
encountered with offaxis objects and are
most severe when the
microscope is out of
alignment.
Coma causes the image of a non-axial point to be reproduced
as an elongated comet shape, lying in a direction
perpendicular to the optical axis.
http://micro.magnet.fsu.edu/primer/java/aberrations/coma/index.html
Axial resolution – Depth of Field
Depth of Field Ranges
m)
(F (F
m)
Depth of focus (f mm)
NA
f
F
0.1 0.13 15.5
0.4 3.8 5.8
.95 80.0 0.19
The distance above and below The axial range through which
geometric image plane within an object can be focused without
which the image is in focus
any appreciable change in image
sharpness
M
M
NA
NA
f
f
F
F
F is determined by NA.
http://micro.magnet.fsu.edu/primer/anatomy/objectives.html
Optical Microscopy
 Introduction
 Lens formula, Image formation and
Magnification
 Resolution and lens defects
 Basic components and their
functions
 Common modes of analysis
 Specialized Microscopy Techniques
 Typical examples of applications
Scanning Electron Microscopy
Do review problems (1-9) on OM
Read “dispersion and refraction of
light and lens”
http://www.doitpoms.ac.uk/tlplib/optical-microscopy/questions.php