AP 5301/8301
Instrumental Methods of Analysis
and Laboratory
Zhengkui XU
Office: G6760
Tel: 27889143
Email:apzkx@cityu.edu.hk
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)
•
•
•
•
Auger electron spectroscopy (AES)
X-ray photoelectron spectroscopy (XPS)
Secondary ion mass spectroscopy (SIMS)
Rutherford backscattering spectroscopy (RBS)
Processing-structure-property
Processingstructureproperty
Chemical
Crystal
(
composition Structure)
Ceramic
Fabrication
Microstructure
(Characterization)
Intrinsic
Materials
Selection
Properties
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
Scale and Characterization Techniques
XRD,TEM,STM
SEM
OM
Grain I
Valve
Turbo
charge
Grain II
atomic
1
Microstructure ranging from crystal structure to
Engine components (SiC)
SiC turbine blades
crack
Grain 1
Intergranular
amorphous phase
Grain 2
2nm
TEM image
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
[110]
(STEM)
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
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
• ……
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
Old and Modern
Light Microscopes
Simple Microscope
Low-power magnifying glasses
and hand lenses
2x
4x
10x
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
Snell’s Law
Sinq1
Sinq2
=
V1
V2
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
=
N2
N1
N
1.0003
1.33
1.47
1.515
1.52
1.92
2.42
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
The larger curvature angle
The shorter focal length
q1
F
Optical axis
f
q2
F
N1 N2
f
Centerline of the lens
q1 > q2
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
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
qo
A
q
Virtual
image
B
o
25cm
Ray diagram to show the principle of a single lens
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
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
•
•
•
•
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
1st
2nd 3rd
film



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
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
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
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
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.
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.
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
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
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
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.
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.
Do review problems on OM
Read “dispersion and refraction of
light and lens”
Please visit the following site and have some fun
www.funsci.com/fun3_en/lens
/lens.htm
Derivation of Snell’s Law
AB – Common
wavefront of two
parallel rays A’A
and B’B
q1
q2
Normal
Incident angle
q1
interface
q2
Refracted angle
t-time for the wavefront to travel from AB to CD
BD=ct=ADsinq1 c-velocity of light in vacuum
AC=vt=ADsinq2 v-velocity of light in medium
sinq1
sinq2
=
c
v
=N
c/v1=N1
c/v2=N2
sinq1
sinq2
=
v1
v2
=
N1
N2