nanoscale investigation-x ray diffraction

8/8/2019 Nanoscale Investigation-x Ray Diffraction

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Investigation in nanoscale

X-RAY DIFFRACTION


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X-ray generation

Wavelength range:0.5-2.5


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Bremsstruhlung radiation-B re m sstra h lu n g p ro d u ce d b y ra p id d e ce le ra tio n o f a h ig h

.e n e rg y e le ctro n in th e e le ctric fie ld o f a n a to m ic n u cle u s

:// . . / /h ttp e n w ikip e d ia o rg w iki B re m sstra hlu n g

impactbeforjustelectronofvelocityv,

masselectronm,volts30,000oforderin theeV,

2

1 2mveVKE ==

T h e d e ce le ra te d e le ctro n e m its e n e rg y

( - ).x ray
http://upload.wikimedia.org/wikipedia/commons/1/1e/Bremsstrahlung.svg


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( , ) W h ite p o ly ch ro m a tic co n tin u o u sra d ia tio n

-C o n tin u o u s X ra yspe ctrum of m olbd en um

( )Mo as of a function of

.a p p lie d v o lta g e


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W h e n a p p lie d v o lta g e e xc e ss a critica l v a lu e C h a ra cte ristic

.R a d ia tio n o ccu rs

C h a ra cte ristic e m issio n s su p e rim p o se o n co n tin u o u s sp e ctru m a n d. -th e y a re n a rro w a n d in te n se T h e y a re u sed fo r x R a y d iffra ctio n

.b eca u se o f th ey are ap p roxim a te m o n och ro m atic

Characteristics radiation


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2p str ns t o n

Characteristic radiation lines, , , .,fall into several sets K L M

in the order of increasing.wavelength Only K line is used

- .in x ray diffraction

3p s1tr ns t on


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K doublet

E le ctro n S p in sta te2 P /3 2

E le ctro n S p in sta te

2 P / 2

K istwice asstrong as K 2

U n re solve d K lineistaken

as w eig h ted av erag e ofw ave len g th of K and K 2


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X-Ray and Braggs law

A crystal is viewed as a planecontaining several lattice point. AtBraggs angle the reflective beamsare in phase and reinforced beamis obtained.
http://upload.wikimedia.org/wikipedia/commons/0/0a/Bragg_diffraction.pnghttp://upload.wikimedia.org/wikipedia/commons/0/0a/Bragg_diffraction.png


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X-RAY spectroscopy

A crystal with planes of known spacing or a grating ofknow spacing can be set at particular angle , thus,the incident wavelength of the radiation can be

determined. Intensity of diffraction at that particular angle is

recorded. Repeat this test for various diffraction angle , a

wavelength-x-ray intensity curve can be plotted.Te st sa m p le -generates xR a y


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X-Ray diffractometerCrystal structure analysis: With known x-Ray irradiation, a crystals

lattice spacing can be determined by thediffraction pattern.

Three methods :

method Laue Variable

(polychromatic)Fixed

Rotating-crystal Fixed

(monochromatic)

Variable in part

powder Fixed(monochromatic)

variable


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Laue method

First x-ray diffraction ever used A white x-ray irradiation falls on a crystal Each set of planes in the crystal, selects and

diffracts a particular wavelength thatsatisfies Braggs law.

S p o ts lyin g o n o n ecu rv e a re tra n sm itte d

d iffra ctio n s fro mp lan es b elon g s to on e

.z o n e


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Rotating crystal method Uses the characteristic x-ray

irradiations The crystal is mounted with one

of its axes or importantcrystallographic direction,

normal to the incident x-ray. The crystal axis or

crystallographic directioncoincides with the axis of the

cylindrical film. The crystal rotates, a particular

set of lattice plane will satisfiesBraggs law at a particularangle and at that instant adiffraction pattern will be


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Powder method

Sample is reduced to very fine powder.Each microscopic grain is a crystal.

Same principle as rotating crystal

method. Only that in powder form,each tiny crystal is orientated atrandom angle with respect to incidentbeam. The mass of powder in fact is

equivalent to a single crystal rotatedat all possible axes. Therefore, alllattice planes are capable ofdiffraction.


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( )a T h e d iffra cte d ra ys fro m a sin g le cry sta l p o in t to d iscre te d ire ctio n s

. ( )e a ch co rre sp o n d in g to a fa m ily o f d iffra ctio n p la n e s S p o t p a tte rn

( ) ( )b The diffractionpattern from a polycrystalline powder sample formsa se rie s d iffra ctio n co n e s if la rg e n u m b e r o f cry sta ls o rie n te d ra n d o m ly in

- .th e spa ce a re cov e re d b y th e in cid e n t x ra y b e a m E a ch d iffra ctio n con eco rre sp o n d s to th e d iffra ctio n fro m th e sa m e fa m ily o f cry sta llin e p la n e s

. ( )in a ll th e p a rticip a tin g g ra in s R in g p a tte rn


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,Jo h n H a rt,n a n o m a n u fa ctu rin g

U n iv e rsity o f M ich ig a n

,T h e co m p o sitio n size a n dd e g re e o f cry sta llin e o f th esam p le m a te ria l ca n b e

e x tra cte d fro m th e rin gp o sitio n s a n d ra d ia l w id th s o f

.th e se rin g s


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S ch e m a ticd ra w in g o f a X

R a yD iffra cto m e te r

: -S X R a y so u rce:H ro ta tio n ta b le, : -A B X R a y o p tics:F re ce iv in g slit o f

the detector

,D iffra ctio n p a tte r a b o u t-on e h alf of th e e n tire ran g e

.o f 21


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O n ly cry sta llin em a te ria l g iv e s

.na rrow pe aksFro m th e

lo ca tio n s o f th e se

( ),p ea ks rin g sla ttice sp a cin gca n b e

.ca lcu la te d


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Calculation of DiffractionIntensity

Lattice is considered as gratings for thedetermination of diffraction direction(Braggs law)

In real X-Ray irradiation, lattice cannotbe considered a not a grating. For thecalculation of diffraction intensity, X-ray is considered as photons of highenergies and the intensity is the result

of photon-electron, photon-nucleusinteraction. The emission of diffractedbeams is a result of interference ofscattered X-Rays, but not the incidentX-Ray,

Eff t d d b th


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Effects produced by thepassage of X-ray through

matter

C on trib u te to

ba ckgrou n dn o ise

Form s

D iffractio np a tte rn


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Factors of intensitycalculation

Structure factor Multiplicity factor

Absorption factor Temperature

factor

D ete rm in e dby the

stru ctu re o fthe crystal

A ccou n t for sam p le-a b sorp tio n o f x ra ya n d th e re su lta n t

.te m p e ra tu re rise

( ) MeApFI 22

2

2

cossin

2cos1

+=

Me

2( )A

F

p

,I relative integrated

intensity


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Example of intensitycalculation

, -C op p er face cen tered cub e

T h e in te n sity a n a lysisg iv e s m o re d e ta ils o n

the a tom arran ge m e nt.o f th e u n it ce ll

To g e th e r w ith th e

la ttice sp a cin ge x tra cte d fro m th e

,d iffra ctio n a n g le th estru ctu re o f th e cry sta l

.ca n b e p re d icte d


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Intensity in x-ray scattering Scattering factors is proportional to the atomic number. The

scattering factor of atoms of similar atomic numbers areclose, therefore it is difficult to identify similar atoms.

Problem materials: compound containing N andO(polymers) aluminosilicates, Al, Si.

the peak of maximum is taken as 100 and all the otherpeaks are scaled accordingly. A set of peaks and theirheights are adequate for phase identification. Sometimesaccurate measurement of peak positions is required.

If preferred orientation exist for a material, it is likely thatonly those orientations will be manifested.

Sample preparation affects the scattering intensity. It is


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Broadening of diffractionpeak

, -B fu ll p e a k w id th a t h a lfm ax im u m

21=B


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http://prism.mit.edu/xray

Particle size and Peakwidth

P. Scherrer, Bestimmung der Grsse und der inneren Struktur vonKolloidteilchen mittels Rntgenstrahlen, Nachr. Ges. Wiss.Gttingen26 (1918) pp 98-100.

J.I. Langford and A.J.C. Wilson, Scherrer after Sixty Years: A Survey

and Some New Results in the Determination of Crystallite Size,J.Appl. Cryst.11 (1978) pp 102-113.

BB

t

cos9.0=

( )eak width B is inversely ( )roportional to crystallite size t


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Particle size is not the onlyattribution to peak boardening

66 67 68 69 70 7 72 73 742 ( .)eg These diffraction patterns were produced from the xact same sample , ,Two different diffractometers with different optical configurations were use h e a p p a r e n t p e a k b r o a d e n i n g i s du e s o l el y t o t h e i n s t ru m e n t at i o n


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The Laue Equations describe the intensity of adiffracted peak from a single parallelopipeden

crystal

N1, N2, and N3 are the number of unit cells along the a1, a2, and a3directions

When N is small, the diffraction peaks become broader

The peak area remains constant independent of N

( ) ( )( ) ( )

( ) ( )( ) ( )

( )( )( ) ( ) 3

2

33

2

2

2

22

2

1

2

11

2

2

/sin/sin

/sin/sin

/sin/sin

assaNss

assaNss

assaNssFII

O

O

O

O

O

O

e

=

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

2.4 2.9 3.4

N=99

N=20

N=10

N=5

N=2

0

50

100

150

200

250

300

350

400

2.4 2.9 3.4

N=20

N=10

N=5

N=2


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Stress measurement

U n ifo rm e d stra inre su lt in sh ift in 1 B ,

w ith n o a ffe ct on

.p ro file o f th e p e a kU sed fo r

m ea surem en t of.m a cro stre ss

-N o n u n ifo rm e dm icro stra in d istu rb s

th e g rain sha p e b u t

n o d isto rtio n to th ee n tire v o lu m e o f th e.sam p le T h e re sults

is n o t sh ift in 1B ,b u t th e p ro file o f th e

p e a k w ill b e a lte re d


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XRD Strain measurement

( )

2

22

2

11

2211

2

sincosstressbiaxial

sin1

+=

++

=

EEd

dd

o

o

,In re a lte st w illb e ch a n g e d sev e ra ltim e sa n d d11 .recorded


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Definition of


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Stress measurementExample

C o m p re sse d th in g o ld film

nanoscale investigation-x ray diffraction

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