AP 5301/8301Instrumental Methods of Analysis
and Laboratory
Zhengkui XUOffice: G6760Tel: 27889143Email:[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)• Auger electron spectroscopy (AES)• X-ray photoelectron spectroscopy (XPS)• Secondary ion mass spectroscopy (SIMS)• Rutherford backscattering spectroscopy (RBS)
Processing-structure-property
Chemical composition
Microstructure
Processingstructureproperty
Properties
IntrinsicMaterials Selection
CeramicFabrication
Crystal Structure( )
(Characterization)
Effect of Microstructure on Mechanical Property
f d-1/2 d-grain size
50m10m
a b
Mechanical test: fa > fb Mechanical property
Microscopic analysis: da < db Microstructure
OM images of two polycrystalline samples.
Scale and Characterization Techniques
Microstructure ranging from crystal structure to Engine components (SiC)
XRD,TEM,STM SEM OM
Grain I
Grain II
atomic
ValveTurbocharge
1
SiC turbine blades
TEM image
Grain 1
Grain 2
2nm
Intergranular amorphous phase
crack
Identification of Fracture Mode
4m
Intergranular fracture
20m
Intragranular fracture
Cracks CracksPores
Grain boundary
OM and SEM
50m
5m
Growthstep
OM - 2D
SEM – 3D
BaTiO3
High Resolution Z-contrast Imaging
Atomic Ordering in Ba(Mg1/3Nb2/3)O3
(STEM)
[110]
I Z2
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.2m• 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 charac-terization 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
Incident angle 1
Refracted angle 2
Normal
N - Refractive index of material
- Speed of light in vacuum
- Velocity of light in material
Materials N Air 1.0003 Water 1.33 Lucite 1.47Immersion oil 1.515 Glass 1.52 Zircon 1.92Diamond 2.42
Sin1 V1 N2= =Sin2 V2 N1
Snell’s Law
N 1
Light path bends at interface between two transparent media ofDifferent indices of refraction (densities)
air
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.
normalCurved (converging) glass surface
F
f
N2N1
F - focal point f – focal length
Focal plane
Air
Curvature of Lens and Focal Length
N2N1
Normal
N1 N2
F
F
f
f
The larger curvature angleThe shorter focal length
1
2
1 > 2
Centerline of the lens
Optical axis
Converging (Convex) Lens
f
The simplest magnifying lens
f curvature angle and lens materials (N) the larger N, the shorter f lucite glass diamondN: 1.47 1.51 2.42
Focal plane
F
f
Magnifier – A Converging Lens
nearest distance of distinct vision (NDDV)
retinaI’I’
If o’-o’ is ~0.07mm, o=0.016o
Ray diagram to show the principle of a single lens
NDDV-ability to distin-guish as separate points which are ~0.07mm apart.
o - visual angle subtended at the eye by two points o’-o’ at NDDV.
Magnification
m= =I-I o”-o”
I’-I’ o’-o’
m = /o
o”
o”
o
o25cm
h
o-object distance
Virtual image
Real inverted image
AB
1 1 1_ = _ + _f O i
Lens Formula f-focal length (distance)O-distance of object from lens
i-distance of image from lens
I1
O i
iO
= =moMagnificationby objective
Lens formula and magnificationObjective lens
-Inverted image
ff
ho
hi
hiho
Maximum Magnification of a Lens
• 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 )0 h/25 and h/o
ff
f
oh
ohm
251
2525
250
1/f = 1/O + 1/i
f in cm
Magnification when the Eyes are Relaxed
• 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, 0 h/25 and h/f
fm
25
0
1/f = 1/O + 1/i
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
• 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
25cm
Compound microscope consists of two converging lenses, the objective and the eyepiece (ocular).
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
eo ff
LM
25 =
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 320240 to a A4 size print!!
Empty Magnification
Higher resolution Lower resolution
Diffraction of Light
Sin=/d
film
1st 2nd 3rd
Light waves interfere constructively and destructively.
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 thecentral maximum of one image falls on the first diffraction minimum of the other
=m 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
Assuming that the two beams are just collected by the objective, then i = and
dmin = /2sin
sinsin did
I II
I II
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 sin = /2(N.A.) For circular aperture
dmin= 1.22/2(N.A.)=0.61/(N.A.)
where N.A. = n sin is called numerical aperture
Immersion oil n=1.515
NA of an objective is a measure of its ability togather light and resolve fine specimen detail at a fixed object distance. NA = n(sin )n: refractive index of the imaging medium betweenthe front lens of objective and specimen cover glass
Numerical Aperture (NA)
Angular aperture
One half of A-A
NA=1 - theoretical maximum numerical aperture of a lens operating with air as the imaging medium
(72 degrees)
Factors Affecting Resolution Resolution = dmin = 0.61/(N.A.)
Resolution improves (smaller dmin) if or n or Assuming that sin = 0.95 ( = 71.8°)
(The eye is more sensitive to blue than violet)
Wavelength
Red
Yellow
Green
Blue
Violet
A ir (n= 1) O il (n = 1.515)
0.42 m
0.39 m
0.35 m
0.31 m
0.27 m
0.28 m
0.17 m
0.20 m
0.23 m
0.25 m
650 nm
600 nm
550 nm
475 nm
400 nm
The smallest distance between two specimen points that can still be distinguished as two separate entities
dmin = 0.61/NA NA=nsin
– illumination wavelength (light)NA – numerical aperture -one half of the objective angular aperture n-imaging medium refractive index
dmin ~ 0.3m for a midspectrum of 0.55m
Resolution of a Microscope (lateral)
Optical Aberrations
• 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
Two primary causes of non-ideal lens action:
Astigmatism, field curvature and comatic aberrationsare easily corrected with proper lens fabrication.
Reduce the resolution 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.
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
Defects in Lens
A converging lens can be combined with a weaker diverging lens, so that the chromatic aberrations cancel for certain wavelengths: The combination – achromatic doublet
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 lens, the line image may be oriented either tangentially or radially
Defects in Lens
o
A
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 off-axis objects and are most severe when the microscope is out of alignment.
Defects in Lens
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.
Depth of focus (f mm)
The distance above and belowgeometric image plane withinwhich the image is in focus
The axial range through whichan object can be focused withoutany appreciable change in imagesharpness
(F m)
M NA f FM NA f F
Axial resolution – Depth of FieldDepth of Field Ranges (F m)
F is determined by NA.
NA f F0.1 0.13 15.50.4 3.8 5.8.95 80.0 0.19
www.funsci.com/fun3_en/lens/lens.htm
Please visit the following site and have some fun
Do review problems on OMRead “dispersion and refraction of light and lens”
Derivation of Snell’s Law
Normal
1
1
2
2
Incident angle
Refracted angle
AB – Common wavefront of two parallel rays A’A and B’B
interface
t-time for the wavefront to travel from AB to CDBD=ct=ADsin1 c-velocity of light in vacuumAC=vt=ADsin2 v-velocity of light in medium
sin1
sin2
= = Nc
vc/v1=N1
c/v2=N2
sin1
sin2
=v1
v2
=N1
N2