AP 5301/8301Instrumental Methods of Analysis

and Laboratory

Zhengkui XUOffice: G6760Tel: 27889143Email: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

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