X-Ray Science and Applications

X-Ray Science and Applications

2008 Fall SemesterLecturer; Yang MO KOO

Tuesday and Thursday 14:45~16:00

X-ray & AT Laboratory, GIFT, POSTECH

Contents1. X-ray properties and interactions with matters

1.1 Discovery of x-rays 1.2 Properties of electromagnetic waves1.3 Interactions of X-rays with matters

2. X-ray Sources2.1 Electron-impact x-ray sources2.2 Synchrotron radiation sources

3. X-ray optics3.1 Aberrations3.2 Reflective optics for x-rays3.3 Diffractive x-ray optics

4. X-ray detectors4.1 Characteristics of x-ray detectors4.2 Fluorescence screen4.3 X-ray film 4.4 Channel electron multipliers4.5 Gas detectors4.6 Scintillation Detector4.7 Phosphors4.8 Solid state detector4.9 Electronics of detector


5. X-ray spectrometry5.1 X-ray fluorescence analysis5.2 Total refection x-ray fluorescence analysis5.3 Extended x-ray absorption fine structure5.5 X-ray microprobe analysis

6. Crystal structure and its symmetry6.1 Lattice and crystal6.2 Symmetry operation and point group6.3 Space group of the crystal6.4 Crystal structure of some metals6.5 Stereographic projection6.6 Reciprocal lattice

Textbook; X-ray Science and Applications, Y.M. Koo, and N.S. ShinAjin Pub.(2000)

Evaluation;Home works; 10%Midterm Examination:40%Final Examination: 40%Others; 10%

Contents


Wilhelm Conrad Röntgen(1945-1923)-Nobel Prize in Physics(1901)

Crookes tube Physical Institute of theUniversity of Würzburg

When he shielded the tube with heavy black cardboard, he found that a greenish fluorescent light could be seen from a barium platinocyanidescreen 9 feet away. He concluded that a new type of ray emitted from thetube, passed through the covering, and casted shadows of solid objects. The rays passes through most substances, including the soft tissues of the body, but left the bones and most metals visible. One of his earliest photographic plate from his experiments was a film of his wife, Bertha's hand with a ring, was produced on Friday, November 8, 1895.

1.1 Discovery of x-rays

http://en.wikipedia.org/wiki/Barium

http://en.wiktionary.org/wiki/platinocyanide


• X-radiation (X-ray) to denote its unknown nature • This mysterious radiation had the ability to pass through many materials

that absorb visible light • X-rays also have the ability to knock electrons (photoelectron) loose from

atoms • Over the years these exceptional properties have made x-rays useful

in many fields, such as medicine and research into the nature of the atom.

Crookes tube: a glass bulb with positive and negativeelectrodes, evacuated of air, which displays a fluorescent glow when a high voltage current is passed though it.

Bertha's hand November 8, 1895.



• X-rays were found to be another form of light; Light is the by-product of the constant jiggling, vibrating, hurly-burly of all matter. Like a frisky puppy, matter cannot be still. The chair you are sitting in may look and feel motionless. But if you could see down to the atomic level you would see atoms and molecules vibrating hundreds of trillions of times a second and bumping into each other, while electrons zip around at speeds of 25,000 miles per hour.

• When charged particles collide or undergo sudden changes in their motion they produce bundles of energy called photons that fly away from the scene of the accident at the speed of light. In fact they are light, or electromagnetic radiation, to use the technical term. Since electrons are the lightest known charged particle, they are most fidgety, so they are responsible for most of the photons produced in the universe.

• The energy of the photon tells what kind of light it is. Radio waves are composed of low energy photons. Optical photon, the only photons perceived by the human eye, are a million times more energetic than the typical radio photon. The energies of X-ray photons range from hundreds to thousands of times higher than that of optical photons.



•The speed of the particles when they collide or vibrate sets a limit on the energy of the photon. The speed is also a measure of temperature. (On a hot day, the particles in the air are moving faster than on a cold day.) Very low temperatures (hundreds of degrees below zero Celsius) produce low energy radio and microwave photons, whereas cool bodies like ours (about 30 degrees Celsius) produce infrared radiation. Very high temperatures (millions of degrees Celsius) produce X-rays.

The Electromagnetic Spectrum. The wavelength of radiation produced byan object is usually related to its temperature.



Important Events in the History of X-ray Science

• 1895 Discovery of x-rays (Röntgen)• 1896 First medical uses of x-rays• 1899 Find evidence for diffraction of x-rays (Haga and Wind)• 1905 X-ray is a form of electromagnetic radiation (Barkla)• 1907 Discovery of characteristic radiation by atom (Barkla)• 1912 Discovered crystal diffraction (Laue, Bragg etc.)

- Construction of the first x-ray spectrometer• 1913 The vacuum x-ray tube (Coolidge)• 1914 Mosley’s Law; the square root of frequency of a given characteristic

x-ray is approximately proportional to atomic number.• 1914 Find temperature effect for Bragg diffraction (Debye)• 1916 Observed x-ray refraction (Barkla etc.)• 1917 Powder diffraction developed (Debye and Scherrer)• 1922 Observed Compton effect (Compton)• 1922 Measured refractive index of x-ray (Compton)• 1924 Diffraction grating for x-rays (Carrara)• 1940 First successful x-ray reflection from a multilayer mirror• 1946 First observations of synchrotron radiation• 1948 Birth of x-ray astronomy• 1948 Kirkpatrick-Baez mirror systems developed• 1951 First experiments with insertion devices for synchrotron radiation



•1952 Development Wolter optics• 1960 Construction of the first 2-gerneration synchrotron radiation sources;

(Aladdin, Wisconsin USA (see ref.))• 1961 First plasma x-ray sources• 1965 First high resolution zone plate• 1984 First demonstration of XUV lasing• 1993 Construction of the first 3-gerneration synchrotron radiation sources; Advanced

Light Source(1.5~1.9 GeV) (ALS) , Berkeley, California, USA• 1994 Construction of the first 3-gerneration synchrotron radiation sources; Pohang Light

Source (2.4 GeV) (PLS), Pohang, South Korea• 1994 Construction of high energy synchrotron radiation source; European

Synchrotron Radiation Facility (6GeV) (ESRF)•1996 Construction of high energy synchrotron radiation source; Advanced Photon

Source (7 GeV) (APS) , Argonne, USA•1997 Construction of high energy synchrotron radiation source;

Super Photon Ring (8 GeV), (Spring-8), Harima Science Garden City, Hyogo, Japan


http://www.esrf.fr/


1.2 Properties of electromagnetic waves

( )( )

πωνωω

πλ

ωω

/2 , :Energy frequency :

2 , :Momentum

vector wave: where

:Direction

Equations Wave

2

2

=

=

×−⋅=−⋅=

=⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

−∇

=⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

−∇

h

hk

k

k

BErkBrkE

H

E

tiexpB tiexpE

tc

tc

0

0

2

2

2

2

2

2

01

01

( )

( )00

0

8

000

1

1099821

εμμεn

nc c

.c c

===

×===

where,medium a in

vacuum in

npropagatio of Speed

με

εμ


Reflection (Critical angle) Scattering (Scattering factor)

Diffraction (collectiveeffect of scattering: Interferencefunction)

Refraction (Refractive index)




http://upload.wikimedia.org/wikipedia/commons/9/99/EM_Spectrum3-new.jpg


currentelectric netdensity current

surface overflux magnetic surface overflux electric

surfaceby closed chargeelectric density chargeelectric

ty)permittivi relative s(material' constantdielctric medium the ofindex refractive

medium the inty permittivielectric medium the inty permeabilimagnetic

vacuum inty permittivielectric vacuum inty permeabilimagnetic

I: J:

S: S:

S: Q:

:/n: :

: μ: :μ

B,S

S,E

S

r

Φ

Φ

=ρ

εεε

ε

ε

0

0

0



Name Differential form Integral form

Gauss's law:

Gauss' law for magnetism(absence of magnetic monopoles):Faraday's law of induction:

Ampere's Circuital Law(with Maxwell's correction):

Maxwell Equations

Maxwell's equations are a set of four equations that can all be found at various places (8 equations) in Maxwell's 1861 papers. Apart from Maxwell's amendment to Ampare'scircuital law, none of these equations are original. In the year 1884 Oliver Heaviside selected these four equations, he put them into modern vector notation. This gives rise to the claim by some scientists that Maxwell's equationsare in actual fact Heaviside's equations.


http://en.wikipedia.org/wiki/Amp%C3%A8re%27s_Circuital_law

http://en.wikipedia.org/wiki/Faraday%27s_law_of_induction

http://en.wikipedia.org/wiki/Magnetic_monopole

http://en.wikipedia.org/wiki/Magnetic_monopole

http://en.wikipedia.org/wiki/Gauss%27s_law

http://en.wikipedia.org/wiki/Integral

http://en.wikipedia.org/wiki/Partial_differential_equation

http://en.wikipedia.org/wiki/Differential_form


In order to connect the theory of classical electrodynamics to mechanicswe need to add another equation to the four Maxwell's Equations. The forceexerted upon a charged particle by the electric field and magnetic field is given by the Lorentz force equation:

where q is the charge on the particle and v is the particle velocity.

Maxwell's equations are generally applied to macroscopic averages of the fields, which vary wildly on a microscopic scale in the vicinity of individual atoms (where they undergoquantum mechanical effects as well). It is only in this averaged sense that one can define quantities such as the permittivity and permeability of a material. Below themicroscopic, Maxwell's equations, ignoring quantum effects, are simply those of a vacuum — but one must include all atomic charges and so on, which is generally an intractable problem


( )BvEF ×+= q

http://en.wikipedia.org/wiki/Electric_field

http://en.wikipedia.org/wiki/Magnetic_field

http://en.wikipedia.org/wiki/Lorentz_force

http://en.wikipedia.org/wiki/Quantum_mechanics


Linear materials


t

t

χ χ

) )()

χ εχ

m

e

rm

re

me

∂∂

+=×∇

∂∂

−=×∇

=⋅∇=⋅∇

==+=+==+=+=

==

EJH

HE

BE

HHHMHB EEPED

HEB DHMEP

MP

ε

μ

μρε

με

μμμμχμεεεχε

strength.) field the upon depend and makingby well,as materials nonlinear handle to extended beactually can (This

material, the oflity susceptibimagnetic the is material, the oflity susceptibi electrical the is

where(1

(1 :by and to related are fields and the and

and :by given are

density ionmagnetizat and density onpolarizati the materials, linear In

0

000

000

0


In vacuum, without charges or currents


t

t

∂∂

−=×∇

∂∂

=×∇

=⋅∇=⋅∇

==

HE

EH

BE

HBED

:space free in equations Maxwell the obtain we vacuum, the in present chargeelectric or current no is there Since

. and by denoted are vacuum the in constantsality proportion the and medium, lessdispersion isotropic, s,homogeneou linear, a is vacuum The

00

0

0

00

00

εμ

εε

με


Propagation of waves in 3D


zz

yy

xx

tv

∂∂

+∂∂

+∂∂

=∇

=∂∂

−∇

=•

•

•

ordinates,-co Cartesian in where

equation wavethe satisfies it that such z and y x,on depends also) field-E of amplitude be (could edisturbanc of amplitude Let

shomogeneou is medium the if forward straight is dimensions-3 to equation wavethe of tiongeneraliza The

etc.. medium dielectric a in source light water,or air in source wavesound E.g. directions allinequally gpropagatinwavesinresultsthatedisturbanc a Imagine

012

2

22 ψψ

ψψ


Plane waves


( ) ( ) .EEEE

tan

.,cosE,sinE

)tkxcos(H)tkxcos(H

)tkxcos(H

)tkxcos(H)t,r(

)tkxcos(E)tkxcos(E

)tkxcos(E

)tkxcos(E)t,r(

zyz

y

zyzy

zzyy

zz

yy

zzyy

zz

yy

202020

01

00

00

0

0

00

0

0

0

0

+=⎟⎟⎠

⎞⎜⎜⎝

⎛=

==

+−++−=⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

+−

+−=

+−++−=⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

+−

+−=

− E

EE

zyH

zyE

and where

and phases, and amplitudes theby zedparameteri is waveplane The

and fieldelectric the for

is direction x the in traveling netic waveelectromag an for solution sinusoidal plane The

θ

ααθθ

αωαω

αω

αω

αωαω

αω

αω



( ) ( )

( )[ ]

,

equations th-4 and rd-3 theapply and

of form the is equations above the of solution a If

and

equations wavethe recover wespace, of function vectorany is where

identity vector the note weIf

z

/

r

ryy

/

r

rz

zrr

zyrr

y

zrr

zyrr

y

rrrr

EHEH

-ωωiexpA

tH

xH,

tH

xH

tE

xE,

tE

xE

t,

t

21

0

0

21

0

0

2

2

002

2

2

2

002

2

2

2

002

2

2

2

002

2

2

2

002

2

2

002

2

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛=

⋅

∂∂

=∂∂

∂

∂=

∂

∂∂∂

=∂∂

∂

∂=

∂

∂

∂∂

=∇∂∂

=∇

∇−⋅∇∇=×∇×∇

μμεε

μμεε

μμεεμμεε

μμεεμμεε

μμεεμμεε

xk

HHEE

VVVV



( )

( )

( )

( )

index. absorption is and decrementindex refractive the called is where

rewrite can we1, than less little a but 1 to closevery is rray - xFor

numbercomplex becomeindex refractive Then

be would wavesofvelocity The matter. the in absorbed are snetic waveelectromag zero, not is tyconductivielectric the if However,

.velocity of ratio the is material a ofindex refractive the and is vacuum the in light ofvelocity the Since

βδβδ

ωσμμ

μμεε

σ

μεεμμε

με

in

iγrccn

i*c

n

/c c nc

*

**

rrr

/rr

/

/

−−=

+=⎟⎠⎞

⎜⎝⎛=

+=

=⎟⎟⎠

⎞⎜⎜⎝

⎛=

== −

1

1

0

002

2121

00

0

21000

0


Spherical waves

θθ

φφxx

yy

zz

rr


012

011

111

2

2

22

2

2

2

22

2

2

2

2222

22

=∂∂

−∂∂

+∂∂

=∂∂

−⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

=∇

tvrrr

or

,tvr

rrr

sinrsin

sinrrr

rr

ψψψ

ψψ

θφψ

ϕθθθ

θθ

written,be can equation wavethe ly,Consequent. or not r, ononly depends symmetry, spherical Given

ordinates-co polar spherical In



( )

( )

( ) ( )

( ) ( )

( )

spheres are fronts Wave !! r1/ as decreases amplitude i.e.

is, solution whoseequation, wavethe just is

But

that, noteNow

tkrfr

tkrgtkrfr

tr

vrr

tr

v

tvr

rrrr

rr

rrr

rrr

ωψ

ωωψ

ψψ

ψ

ψψψψψψψψ

−=

++−=

=∂

∂−

∂∂

∂∂

=

∂∂

=⎥⎦

⎤⎢⎣

⎡∂∂

+∂∂

=∂∂

+∂∂

=⎥⎦⎤

⎢⎣⎡

∂∂

+∂∂

=∂

∂

1

01

1

22

2

2

22

2

2

2

2

2

2

22

2

2

2

2

2


Energy in Electromagnetic Waves


221

0

0

221

0

0

y

/

r

rz

y

/

r

rz

ES

ES

⎟⎟⎠

⎞⎜⎜⎝

⎛=

⎟⎟⎠

⎞⎜⎜⎝

⎛=

=

μμεε

μμεε

wavesspherical the for And

writtenbe can waveplane a forintensity average The

x vector, Poynting theBy described is area unit per transportenergy of rate The fields.

magnetic andelectric the both withassociated an is There space.empty through travelthey asenergy carry snetic waveElectromag

HΕS

density energy


λ

eψψ oi

π20

0

=

= ⋅

K

rK

where

Plane wave•wavelength: l

MaxMin

Travelling wavesnapshot

Drawing of the time independent plane waves



Spherical wavesnapshot

MaxMin

λπ2

0

=

=⋅

K

rK

r

where

reψΨ

i

Drawing of the time independent spherical waves


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