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Do Minh Nghiep

Do Minh Nghiep

 Materials Science Center 

 Materials Science Center 

Electron Microscopy

Electron Microscopy

Electron Microscopy

Electron Microscopy

and Diffraction

and Diffraction

and Diffraction

and Diffraction

1. Introduction

1. Introduction

1. Introduction

1. Introduction

(2)

Contact

Contact

Contact

Contact

Lecturer:

Lecturer:

Đỗ

Đỗ

Minh Nghi 

Minh Nghi 

 p

 p

-Tel. 38691332

Tel. 38691332

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Class time: Mon 14:50-17:20

Class time: Mon 14:50-17:20

(3)

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construction

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function

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sample preparation

sample preparation

for 

for 

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elemental 

(4)

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(5)

Lab works

Lab works

Lab works

Lab works

1

1

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(6)

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Textbook:

Textbook:

Handouts

Handouts

References:

References:

1

1

.

.

D

D

.

.

B

B

.

.

W

W

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i

l

l

l

l

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C

.

.

B

B

.

.

C

C

a

a

r

r

t

t

e

e

r

r

,

,

Transmission electron microscopy 

Transmission electron microscopy 

,

,

B

B

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o

o

o

k

k

s

s

1

1

t

t

o

o

4

4

,

,

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n

n

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u

m

m

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s

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,

,

1

1

9

9

9

9

6

6

2

2

.

.

P

P

.

.

H

H

i

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r

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s

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c

c

h

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,

,

e

e

t

t

a

a

l

l

.

.

;

;

Elect

Elect

ron

ron

micro

micro

scopy of

scopy of

thin crystals

thin crystals

;

;

H

H

u

u

n

n

t

t

i

i

n

n

g

g

t

t

o

o

n

n

,

,

N

N

.

.

Y

Y

.

.

,

,

R

R

.

.

.

.

.

.

.

.

,

,

3

3

.

.

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M

M

.

.

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l

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a

y

y

t

t

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e

r

r

,

,

H

H

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n

n

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y

y

S

S

.

.

S

S

l

l

a

a

y

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t

t

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r

r

;

;

Lig

Lig

ht

ht

and

and

ele

ele

ctro

ctro

n

n

mic

mic

rosc

rosc

opy 

opy 

;

;

Ca

Ca

m

m

br

br

id

id

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ge

(E

(E

ng

ng

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an

an

d)

d)

,

,

Ne

Ne

w

w

Y

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or

or

k,

k,

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m

br

br

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ge

Un

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rs

rs

it

it

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Pr

Pr

es

es

s,

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19

19

92

92

.

.

fo

fo

rm

rm

at

at

io

io

n

n

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an

d

d

mi

mi

cr

cr

oa

oa

na

na

ly

ly

si

si

s;

s;

Be

Be

rl

rl

in

in

,

,

Ne

Ne

w

w

Yo

Yo

rk

rk

,

,

Sp

Sp

ri

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ng

ng

er

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-V

-V

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er

la

la

g,

g,

19

19

93

93

(7)

r

r

a

a

n

n

g

g

r

r

a

a

n

n

g

g

The weighting factors used to determine

The weighting factors used to determine

t

t

e

e

n

n

a

a

g

g

r

r

a

a

e

e

:

:

Lab

Lab

work

work

and

and

reports:

reports:

20

20

%

%

(8)

Week

Week

1

1

Why

Why

elect

elect

ron

ron

micros

micros

cope

cope

-

-

a

a

brief

brief

histo

histo

ry

ry

Week

Week

2

2

Electron

Electron

sources,

sources,

Vacuum

Vacuum

Week

Week

3

3

Electron

Electron

optics,

optics,

Electromagnetic

Electromagnetic

lenses,

lenses,

Resolution

Resolution

limits

limits

Week

Week

4

4

Electron

Electron

beam

beam

-specimen

-specimen

interactions

interactions

 Week Week 5 5 Mid-term Mid-term test test 

Week

Week

6

6

SEM:

SEM:

Scanning

Scanning

system,

system,

Detectors,

Detectors,

SE

SE

image,

image,

Backscattered image, Resolution

Backscattered image, Resolution

,

,

-

-

,

,

Diffraction, Phase)

Diffraction, Phase)

Week

Week

8

8

Microprobe

Microprobe

analysis:

analysis:

Detection

Detection

systems

systems

(EDS,

(EDS,

WDS),

WDS),

Qualitative

Qualitative

and quantitative analysis

and quantitative analysis

 Week Week 9 9 Practical Practical lab lab for for SEM, SEM, EDS EDS 

Week

(9)

Introduction

Introduction

Introduction

Introduction

a

a

a

a

er

e

e

er a s

r

r a s

a

a

s

s

c

c

c

c

ar

a

ar

a

ra

ra

ac

ac

c

c

e

er

e

er z

r

r za

z

za

a

a

on

on

o

o

n

n

H

Hi

History

History

is

st

to

or

ry

y

W

Wh

Why EM ?

Why EM ?

hy

y

E

EM

M

?

?

(10)

characterization

characterization

characterization

characterization

mean?

mean?

mean?

mean?

 

Character:

Character:

a

a

s

s

u

u

m

m

o

o

f

f

q

q

u

u

a

a

l

l

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t

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i

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s

t

t

h

h

a

a

t

t

m

m

a

a

k

k

e

e

a

a

p

p

e

e

r

r

s

s

o

o

n

n

/

/

t

t

h

h

i

i

n

n

g

g

d

d

i

i

f

f

f

f

e

e

r

r

e

e

n

n

t

t

f

f

r

r

o

o

m

m

others

others

 

Characterize:

Characterize:

t

t

o

o

i

i

n

n

d

d

i

i

c

c

a

a

t

t

e

e

/

/

d

d

e

e

s

s

c

c

r

r

i

i

b

b

e

e

/

/

i

i

n

n

v

v

e

e

s

s

t

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i

i

g

g

a

a

t

t

e

e

/

/

e

e

x

x

p

p

r

r

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e

s

s

s

s

t

t

h

h

e

e

c

c

h

h

a

a

r

r

a

a

c

c

t

t

e

e

o

o

f

f

a

a

p

p

e

e

r

r

s

s

o

o

n

n

/

/

t

t

h

h

i

i

n

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g

g

(

(

a

a

c

c

t

t

i

i

o

o

n

n

)

)

Ma

Ma

ter

ter

ial

ial

s

s

cha

cha

rac

rac

ter

ter

iza

iza

tio

tio

n:

n:

--

i

i

n

n

s

s

p

p

e

e

c

c

i

i

f

f

y

y

i

i

n

n

g

g

t

t

h

h

e

e

inter

inter

nal

nal

micr

micr

ostru

ostru

cture

cture

o

o

f

f

a

a

n

n

e

e

n

n

g

g

i

i

n

n

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r

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a

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s

s

including

including

the chemistry, the crystallography, the structural morphology 

the chemistry, the crystallography, the structural morphology 

(11)

characterization is important?

characterization is important?

characterization is important?

characterization is important?

I

I

t

t

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b

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l

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r

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u

u

g

g

h

h

c

c

o

o

n

n

t

t

r

r

o

o

l

l

o

o

.

.

(12)

structure and properties

structure and properties

structure and properties

structure and properties

-

-•

At

At

om

om

ic

ic

le

le

ve

ve

l:

l:

Ph

Ph

ys

ys

ic

ic

s a

s a

nd C

nd C

he

he

mi

mi

st

st

ry

ry

Mi

Mi

cr

cr

os

os

co

co

pi

pi

c le

c le

ve

ve

l: C

l: C

he

he

mi

mi

st

st

ry a

ry a

nd M

nd M

at

at

er

er

ia

ia

ls S

ls S

ci

ci

.

.

.

.

Ma

Ma

cr

cr

os

os

co

co

pi

pi

c le

c le

ve

ve

l: M

l: M

ec

ec

ha

ha

ni

ni

ca

ca

l an

l an

d Ma

d Ma

te

te

ri

ri

al

al

s En

s En

g.

g.

(13)

of materials

of materials

of materials

of materials

Mechanical properties

Mechanical properties

e

e

m

m

c

c

a

a

p

p

r

r

o

o

p

p

e

e

r

r

e

e

s

s

Physical properties

Physical properties

--

Th

Th

er

er

ma

ma

l pr

l pr

op

op

er

er

ty

ty

--

Op

Op

ti

ti

ca

ca

l pr

l pr

op

op

er

er

ty

ty

--

El

El

ec

ec

tr

tr

ic

ic

al

al

pr

pr

op

op

er

er

ty

ty

--

Ma

Ma

gn

gn

et

et

ic

ic

pr

pr

op

op

er

er

ty

ty

(14)

Equipments

Equipments

Equipments

Equipments

analysis

analysis

analysis

analysis

molecular levels)

molecular levels)

molecular levels)

molecular levels)

(15)

Equipments

Equipments

Equipments

Equipments

analysis

analysis

analysis

analysis

levels)

levels)

levels)

levels)

(16)

Histor

Histor

Histor

(17)

Op

Op

ti

ti

ca

ca

l

l

/l

/l

i

i

gh

gh

t

t

m

m

i

i

cr

cr

os

os

co

co

pe

pe

(

(

O

O

M)

M)

:

:

v

v

i

i

s

s

i

i

b

b

l

l

e

e

l

l

i

i

g

g

h

h

t

t

l

l

i

i

m

m

i

i

t

t

s

s

m

m

a

a

g

g

n

n

i

i

f

f

i

i

c

c

a

a

t

t

i

i

o

o

n

n

o

o

f

f

m

m

a

a

x

x

1

1

0

0

0

0

0

0

-

-

2

2

0

0

0

0

0

0

X

X

a

a

n

n

d

d

r

r

e

e

s

s

o

o

l

l

u

u

t

t

i

i

o

o

n

n

o

o

f

f

0

0

,

,

2

2

m

m

m

m

.

.

E

E

l

l

e

e

c

c

t

t

r

r

o

o

n

n

m

m

i

i

c

c

r

r

o

o

s

s

c

c

o

o

p

p

e

e

(

(

E

E

M

M

)

)

is

is

de

de

ve

ve

lo

lo

pe

pe

d

d

fo

fo

r

r

ov

ov

er

er

co

co

mi

mi

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ng

th

th

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es

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li

li

mi

mi

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on

s.

s.

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1

1

9

9

3

3

2

2

-

-

1

1

9

9

3

3

8

8

:

:

--

T

T

h

h

e

e

f

f

i

i

r

r

s

s

t

t

T

T

E

E

M

M

(

(

1

1

9

9

3

3

2

2

,

,

i

i

d

d

e

e

a

a

o

o

f

f

E

E

M

M

,

,

M

M

a

a

x

x

K

K

n

n

o

o

l

l

l

l

a

a

n

n

d

d

E

E

r

r

n

n

s

s

t

t

R

R

u

u

s

s

k

k

a

a

,

,

Germany)

Germany)

--

T

T

h

h

e

e

f

f

i

i

r

r

s

s

t

t

S

S

E

E

M

M

(1

(1

93

93

8,

8,

la

la

te

te

STEM

STEM

-

-

T

T

E

E

M

M

w

w

i

i

t

t

h

h

s

s

c

c

a

a

n

n

n

n

i

i

n

n

g

g

c

c

o

o

i

i

l

l

,

,

K

K

n

n

o

o

l

l

l

l

a

a

n

n

d

d

,

,

 

19

19

40

40

-1

-1

95

95

2

2

:

:

--

T

T

h

h

e

e

f

f

i

i

r

r

s

s

t

t

S

S

E

E

M

M

f

f

o

o

r

r

t

t

h

h

i

i

c

c

k

k

s

s

a

a

m

m

p

p

l

l

e

e

(

(

1

1

9

9

4

4

2

2

,

,

Z

Z

w

w

o

o

r

r

y

y

k

k

i

i

n

n

e

e

t

t

a

a

l

l

.

.

,

,

R

R

C

C

A

A

a

a

o

o

r

r

a o

a o

r

r

e

e

s

s

.

.

.

.

, r

, r

e

e

s

s

o

o

u

u

o

o

n

n

m

m

m

m

.

.

--

T

T

h

h

e

e

f

f

i

i

r

r

s

s

t

t

F

F

ie

ie

l

l

d

d

Em

Em

i

i

ss

ss

io

io

n

n

el

el

ec

ec

tr

tr

on

on

so

so

ur

ur

ce

ce

(

(

1

1

9

9

4

4

2

2

,

,

F

F

E

E

G

G

u

u

n

n

)

)

--

The

The

S

S

E

E

M

M

w

w

i

i

t

t

h

h

r

r

e

e

s

s

o

o

l

l

u

u

t

t

i

i

o

o

n

n

o

o

f

f

5

5

0

0

n

n

m

m

(

(

1

1

9

9

5

5

2

2

,

,

O

O

a

a

t

t

l

l

e

e

y

y

a

a

n

n

d

d

M

M

c

c

M

M

u

u

l

l

l

l

a

a

n

n

,

,

n

n

g

g

a

a

n

n

(18)

1959-1967:

1959-1967:

--

S

S

E

E

M

M

w

w

i

i

t

t

h

h

stereoscan

stereoscan

(Wells)

(Wells)

--

P

P

e

e

r

r

f

f

o

o

r

r

m

m

a

a

n

n

c

c

e

e

o

o

S

S

E

E

d

d

e

e

t

t

e

e

c

c

t

t

o

o

(

(

1

1

9

9

6

6

0

0

,

,

E

E

v

v

e

e

r

r

h

h

a

a

r

r

t

t

a

a

n

n

d

d

Thornley)

Thornley)

--

T

T

h

h

e

e

f

f

i

i

r

r

s

s

t

t

co

co

mm

mm

er

er

ci

ci

al

al

EM

EM

(1965)

(1965)

--

E

E

l

l

e

e

c

c

t

t

r

r

o

o

n

n

-

-

c

c

h

h

a

a

n

n

n

n

e

e

l

l

i

i

n

n

g

g

c

c

o

o

n

n

t

t

r

r

a

a

s

s

t

t

f

f

o

o

r

r

c

c

r

r

y

y

s

s

t

t

a

a

l

l

o

o

r

r

i

i

e

e

n

n

t

t

a

a

ti

ti

o

o

n

n

s

s

(1967)

(1967)

[

[

O

O

a

a

t

t

l

l

e

e

y

y

(

(

1

1

9

9

8

8

2

2

)

)

,

,

J

J

.

.

A

A

p

p

p

p

l

l

.

.

P

P

h

h

y

y

s

s

.

.

5

5

3

3

,

,

R

R

1

1

]

]

(19)

1932 theory of EM

1932 theory of EM

thth

Antonie van Leeuwenhoek,

Antonie van Leeuwenhoek,

1986 Nobel Prize winners

(20)

James Hillier 

(21)

EM

EM

1940

1940

1938

(22)

The prototype of the

The prototype of the

first Stereoscan

first Stereoscan

supplied by the

supplied by the

Company to the

Company to the

duPo

duPo

nt

nt

Com

Com

pany

pany

,

,

U.S.A. (Stewart and

U.S.A. (Stewart and

McMullan’s original

(23)

W

W

h

h

E

E

M

M

?

?

W

(24)

e

e

n

n

o

o

n

n

e

e

n

n

o

o

n

n

Microscope

Microscope

-

-

A

A

device

device

w

w

i

i

t

t

h

h

a

a

l

l

e

e

n

n

s

s

o

o

r

r

s

s

e

e

r

r

i

i

e

e

s

s

o

o

f

f

l

l

e

e

n

n

s

s

e

e

s

s

t

t

h

h

a

a

t

t

e

e

n

n

l

l

a

a

r

r

g

g

e

e

(

(

m

m

a

a

g

g

n

n

i

i

f

f

y

y

)

)

t

t

h

h

e

e

a

a

p

p

p

p

e

e

a

a

r

r

a

a

n

n

c

c

e

e

o

o

f

f

a

a

n

n

o

o

b

b

j

j

e

e

c

c

t

t

.

.

Image

Image

-

-

P

P

e

e

r

r

c

c

e

e

p

p

t

t

i

i

o

o

n

n

o

o

f

f

a

a

n

n

o

o

b

b

j

j

e

e

c

c

t

t

u

u

s

s

i

i

n

n

g

g

y

y

o

o

u

u

r

r

e

e

y

y

e

e

s

s

(

(

vision

vision

).

).

O

O

n

n

e

e

c

c

a

a

n

n

s

s

e

e

n

n

s

s

e

e

a

a

n

n

o

o

b

b

j

j

e

e

c

c

t

t

w

w

i

i

t

t

h

h

o

o

u

u

t

t

v

v

i

i

s

s

i

i

o

o

n

n

(

(

t

t

o

o

u

u

c

c

h

h

,

,

e

e

t

t

c

c

.

.

.

.

)

)

.

.

Re

Re

qu

qu

ir

ir

es

es

vi

vi

si

si

bl

bl

e

e

li

li

gh

gh

t.

t.

Lens

Lens

-

-

A

A

l

l

e

e

n

n

s

s

i

i

s

s

a

a

n

n

optical component 

optical component 

w

w

h

h

i

i

c

c

h

h

i

i

s

s

u

u

s

s

e

e

d

d

t

t

o

o

.

.

m

(25)

M

M

a

a

n

n

i

i

f

f

i

i

c

c

a

a

t

t

i

i

o

o

n

n

-

-

T

T

h

h

e

e

ratio

ratio

between

between

ima e size

ima e size

t

t

o

o

t

t

h

h

e

e

ob

ob

je

je

ct

ct

si

si

ze

ze

.

.

C

C

a

a

n

n

b

b

e

e

v

v

a

a

r

r

i

i

e

e

d

d

b

b

y

y

c

c

h

h

a

a

n

n

g

g

i

i

n

n

g

g

t

t

h

h

e

e

d

d

i

i

s

s

t

t

a

a

n

n

c

c

e

e

b

b

e

e

t

t

w

w

e

e

e

e

n

n

t

t

h

h

e

e

o

o

b

b

j

j

e

e

c

c

t

t

a

a

n

n

d

d

t

t

h

h

e

e

f

f

i

i

n

n

a

a

l

l

l

l

e

e

n

n

s

s

(

(

o

o

f

f

t

t

h

h

e

e

e

e

y

y

e

e

)

)

o

o

r

r

b

b

y

y

.

.

(26)

Resolution

Resolution

--

RP

RP

is t

is t

he

he

sma

sma

lle

lle

st

st

points at which two or more

points at which two or more

objects can be

objects can be

dis

dis

tin

tin

uis

uis

hed

hed

as

as

se

se

ara

ara

te

te.

.

--

Res

Res

olu

olu

tio

tio

n i

n i

s

s

the

the

ability 

ability 

of 

of 

a lens

a lens

to distinguish

to distinguish

at infinity, when they are

(27)

 

I

I

n

n

1

1

8

8

7

7

0

0

,

,

E

E

r

r

n

n

s

s

t

t

A

A

b

b

b

b

e

e

(

(

1

1

8

8

4

4

0

0

-

-

1

1

9

9

0

0

5

5

)

)

de

de

ri

ri

ve

ve

d

d

ma

ma

th

th

em

em

at

at

ic

ic

al

al

RP  RP ≈≈ (1/2)(1/2)λ λ 

e

e

x

x

p

p

r

r

e

e

s

s

s

s

i

i

o

o

n

n

f

f

o

o

r

r

r

r

e

e

s

s

o

o

l

l

u

u

t

t

i

i

o

o

n

n

o

o

f

f

m

m

i

i

c

c

r

r

o

o

s

s

c

c

o

o

p

p

e

e

:

:

Res

Res

olu

olu

tio

tio

n

n

is

is

limited to

limited to

≈ ≈ 

0.5 the wavelength of illuminating source.

0.5 the wavelength of illuminating source.

,

,

RP 

RP 

= ---

=

---NA

NA

=

=

n.sin 

n.sin 

--

..

-

-n

n

-

-

ind

ind

ex of r

ex of r

efr

efr

act

act

ion

ion

α α 

-

-

half

half

angl

angl

e of

e of

illum

illum

inati

inati

on

on

i

i

n

n

c

c

r

r

e

e

a

a

s

s

i

i

n

n

g

g

t

t

h

h

e

e

h

h

a

a

l

l

f

f

a

a

n

n

g

g

l

l

e

e

o

o

f

f

i

i

l

l

l

l

u

u

m

m

i

i

n

n

a

a

t

t

i

i

o

o

n

n

,

,

b)

b)

in

in

cr

cr

e

e

as

as

in

in

g

g

th

th

e

e

re

re

f

f

ra

ra

ct

ct

iv

iv

e

e

i

i

n

n

d

d

e

e

x

x

o

o

f

f

t

t

h

h

e

e

l

l

e

e

n

n

s

s

b

b

y

y

u

u

s

s

i

i

n

n

g

g

C

C

r

r

o

o

w

w

n

n

g

g

l

l

a

a

s

s

s

s

,

,

a

a

n

n

d

d

c)

c)

d

d

e

e

c

c

r

r

e

e

a

a

s

s

i

i

n

n

g

g

t

t

h

h

e

e

.

.

(28)

Increase sin

Increase sin

α 

α 

d

d

e

e

cr

cr

. w

. w

o

o

rk

rk

in

in

d

d

i

i

s

s

ta

ta

n

n

c

c

e

e

i

i

n

n

cr

cr

. s

. s

i

i

z

z

e o

e o

f t

f t

h

h

e l

e l

e

e

n

n

s

s

:

:

(29)

Replacing visible light

Replacing visible light

Replacing visible light

Replacing visible light

by electron beam

by electron beam

by electron beam

(30)
(31)

e

e

s

s

m

m

a

a

e

e

s

s

t

t

s

s

t

t

a

a

n

n

c

c

e

e

e

e

tw

tw

e

e

e

e

n

n

t

t

w

w

o

o

p

p

o

o

n

n

t

t

s

s

t

t

a

a

t

t

c

c

a

a

n

n

e

e

resolved by

resolved by

 

u

u

m

m

a

a

n

n

e

e

y

y

e

e

:

:

.

.

-

-

.

.

m

m

m

m

Light

Light

microscope:

microscope:

0.2

0.2

μ

μ

m

m

SEM:

SEM:

1-2

1-2

nm

nm

TEM:

TEM:

2

2

Å

Å

This high resolution is achieved by TEM thanks to the

This high resolution is achieved by TEM thanks to the

use of a high energy electron beam (small wavelength).

(32)

e

e

w

w

n

n

g

g

o

o

p

p

o

o

n

n

s

s

e

e

w

w

n

n

g

g

o

o

p

p

o

o

n

n

s

s

Sample

Sample

thickness

thickness

Sample

Sample

environment

environment

Resolution

Resolution

[µm]

[µm]

Magnification

Magnification

Instrument

Instrument

c

c

ye

ye

Thick

Thick

Air 

Air 

15-100

15-100

2-10

2-10

Magnifying

Magnifying

glass

glass

Thick

Thick

Air or Oil

Air or Oil

0.2

0.2

200-1300

200-1300

Optical

Optical

microscope

microscope

c

c

acuum

acuum

.

.

(33)

-Electron

Electron

Electron-Electron-

-

-

dual (wave-

d

d

dual (wave-

u

u

a

a

l (

l (

w

w

a

a

v

v

e

e

-particle) character:

-particle) character:

particle) character:

particle) character:

Light particles

Light particles

Light particles

-Light particles -

-

-

Matter waves

Matter waves

M

M

a

a

t

t

t

t

e

e

r w

r w

a

a

v

v

e

e

s

s

Hermann Busch (1924):

Hermann Busch (1924):

Axial magnetic fields refract electrons

Axial magnetic fields refract electrons

h

h

-

-

Planc

Planc

k cons

k cons

tant

tant

(6.624

(6.624

X 10-27

X 10-27

erg/s

erg/s

)

)

-

-

ele

ele

ctr

ctr

on

on

vel

vel

oci

oci

ty

ty

(

(

 p

 p

=

=

mv 

mv 

: momentum)

: momentum)

-

-

acc

acc

ele

ele

rat

rat

ing

ing

vol

vol

tag

tag

e

e

m

m

oo

-

-

res

res

t e

t e

lec

lec

tro

tro

n m

n m

ass

ass

(34)

1/2

1/2

e

e

r

r

o

o

g

g

e

e

r

r

e

e

a

a

t

t

o

o

n

n

s

s

p

p

e

e

r

r

o

o

g

g

e

e

r

r

e

e

a

a

t

t

o

o

n

n

s

s

p

p

Resolution limit of light microscope:

Resolution limit of light microscope:

--

c

c

a

a

n e

n e

c

c

r

r

e

e

a

a

s

s

e

e

o

o

nm

nm

--

n

n

.sin

.sin

α 

α 

is limited to

is limited to

1.6

1.6

--

Thu

Thu

s t

s t

he

he

ma

ma

xim

xim

um

um

res

res

ol

ol

uti

uti

on

on

is

is

abo

abo

ut

ut

200 nm

200 nm

(35)

e

e

s

s

o

o

u

u

o

o

n

n

o

o

m

m

c

c

r

r

o

o

s

s

c

c

o

o

p

p

e

e

s

s

e

e

s

s

o

o

u

u

o

o

n

n

o

o

m

m

c

c

r

r

o

o

s

s

c

c

o

o

p

p

e

e

s

s

Resolution of electron microscope:

Resolution of electron microscope:

--

λ

λ

can decrease to

can decrease to

10

10

-3

-3

nm

nm

--

n

n

.sin

.sin

α 

α 

is very small, because

is very small, because

n

n

1 and

1 and

α 

α 

0.1 radians

0.1 radians

--

,

,

of 0.0389

of 0.0389

Å

Å

and a

and a

theoretical resolution

theoretical resolution

of 0.0195

of 0.0195

Å

Å

!

!

--

But

But

in

in

pra

pra

cti

cti

ce m

ce m

ost

ost

TEM

TEM

s w

s w

ill

ill

on

on

ly h

ly h

av

av

e an

e an

actual 

actual 

resolution

(36)

refraction/bending

refraction/bending

refraction/bending

refraction/bending

m

o

m

o

n

n

e

e

d

d

a

a

i

i

u

u

r

r

m

m

a

a

y

y

o

o

f

f

o

o

f

f

d

d

i

i

i

i

f

f

l

l

f

f

l

l

e

e

u

u

r

r

m

m

i

i

n

n

i

i

g

g

n

n

a

a

d

d

t

t

i

i

e

e

o

o

n

n

n

n

s

s

i

i

e

e

t

t

y

y

n

n

t

t

c

c

e

e

a

a

r

r

u

u

i

i

n

n

s

s

g

g

i

i

n

n

a

a

g

g

.

.

 

I

I

n

n

t

t

h

h

e

e

v

v

a

a

c

c

u

u

u

u

m

m

e

e

n

n

v

v

i

i

r

r

o

o

n

n

m

m

e

e

n

n

t

t

o

o

a

a

n

n

e

e

l

l

e

e

c

c

t

t

r

r

o

o

n

n

m

m

i

i

c

c

r

r

o

o

s

s

c

c

o

o

e

e

t

t

h

h

e

e

i

i

n

n

d

d

e

e

x

x

o

o

f

f

r

r

e

e

f

f

r

r

a

a

c

c

t

t

i

i

o

o

n

n

i

i

s

s

1

1

.

.

0

0

a

a

n

n

d

d

t

t

h

h

e

e

r

r

e

e

f

f

o

o

r

r

e

e

NA

NA

d

d

e

e

p

p

e

e

n

n

d

d

s

s

s

s

o

o

l

l

e

e

l

l

y

y

o

o

n

n

t

t

h

h

e

e

h

h

a

a

l

l

f  

f  

angle

angle

α α 

of

of

il

il

lu

lu

mi

mi

na

na

ti

ti

on

on

.

.

 

I

I

n

n

e

e

l

l

e

e

c

c

t

t

r

r

o

o

n

n

m

m

i

i

c

c

r

r

o

o

s

s

c

c

o

o

p

p

y

y

t

t

h

h

e

e

r

r

e

e

f

f

r

r

a

a

c

c

t

t

i

i

v

v

e

e

i

i

n

n

d

d

e

e

x

x

c

c

a

a

n

n

n

n

o

o

t

t

e

e

x

x

c

c

e

e

e

e

d

d

Refractive index:

Refractive index:

.

.

,

,

e

e

a

a

a

a

n

n

g

g

e

e

s

s

v

v

e

e

r

r

y

y

s

s

m

m

a

a

,

,

a

a

n

n

d

d

t

t

h

h

u

u

s

s

t

t

h

h

e

e

o

o

n

n

l

l

y

y

t

t

h

h

i

i

n

n

g

g

t

t

h

h

a

a

t

t

c

c

a

a

n

n

b

b

e

e

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