1X-ray Diffractionfor powder sample

Rigaku CorporationApplication laboratory

Keigo Nagao

Todays topics (AM)z Features of Rigaku TTRAXz Basics of powder XRD Feature of XRD Evaluation item

z Texture analysis for bulk sampleMeasurement and Process

z SAXS for nano-size sample Principle and Optics Application

2Rigaku TTRAX

Horizontal goniometerHigh power X-ray sourceParallel beam methodIn-Plane axis

X-ray source

Detector

Sample holder

2

2

In-Plane measurement

(2/scan)

Feature of TTRAX

In case the sample isnt set to horizontal.

Hard-to-pack sample

Semi-liquid sample

Thin layer sample

Feature of TTRAX

3In Horizontal goniometer

Independent on sample condition

Hard-to-pack sample

Semi-liquid sample

Thin layer sample

Feature of TTRAX

High power X-ray source

Sealed-off X-ray tube23kW

Rotating anode X-ray tube1018kW

Be window

Target

Coolingwater

Feature of TTRAX

4Geometry for powder samplez Focusing method Parallel Beam

Detector

Sample

DSSS

RSX-ray source

Sample

Detector

X-ray source

Parallel slit analyzerMulti layer

Miller

DS

Parallel beamFocusing method

mediumStrongIntensity

Umbrella effect1. Flat sample2. Umbrella effect3. Adsorption effect4. Eccentric error

Systematic error

Feature of TTRAX

Cross Beam OpticsRigaku patented technology

BB and PB geometries are simultaneously mounted, aligned, and selectable.

X-ray sourceBB selection slit

Multilayer mirror

Sample

Focusing geometry (BB)

Sample

Parallel beam geometry (PB)

PB selection slit

Feature of TTRAX

55 6 7 8 9 10 11 12 13 142(deg)

6 7 8 9 10 11 12 13 142(deg)

Measurement of rough sample surfaceFocusing method Parallel beam

Sample : Zeolite

Hold of peak shape, peak position and FWHM

Rough

Flat

Feature of TTRAX

Free from Eccentric error (Parallel beam)

Datum surfaceEccentric surface

X-ray source

2

2

0 orderdetector

Receiving slit : open

Parallel slit analyzer

2-X

2

Feature of TTRAX

6Braggs condition of diffractionz The conditions for a reflected ( diffracted ) beam are given

by the relation

d

2dsin = n

dInterplanar spacing X-ray wavelengthBragg angle n1,2,3

2dsin =

Braggs equation

Basics of XRD Interaction of substance and X-ray :1

0.1

1

10

100

1000

0 5 10

2 (deg.)

Inte

nsity

( a.

u. )

X-ray diffuse scattering

X-ray SampleScattering angle

( 2 = 0~10 deg. )

Interaction of substance and X-ray :2

Basics of XRD

7Reflection and interferenceTwo beams reflected on the surface and the interface interfere each other.

10-4

10-3

10-2

10-1

100

Refle

ctiv

ity

6543210

2/ (degree)

d

reflection

reflectionrefraction

refraction

Interaction of substance and X-ray :3

X-ray reflectivity profile

Basics of XRD

Integrated Int.of amorphous

Integrated Int.of crystal

: Quantitative analysis

Integrated Int.of amorphous

Integrated Int.of crystal

: Quantitative analysis

Evaluation item in powder sample

Angle2

Inte

nsity

z more than 2=5degPeak positions

d values : Phase IdentificationLattice constant

d shift : Residual stressSolid solution

Peak positionsd values : Phase Identification

Lattice constantd shift : Residual stress

Solid solution

Intensity vs. OrientationPreferred orientationFiber structurePole figure

Intensity vs. OrientationPreferred orientationFiber structurePole figureFWHM

Crystal qualityCrystallite sizeLattice strain

FWHMCrystal qualityCrystallite sizeLattice strain

Crystallinity

Basics of XRD

8Phase Identification in X-ray diffractionz The powder diffraction pattern is characteristic of the substancez The diffraction pattern indicates the state of chemical combination

2 ( deg. )

Inte

nsity

( co

unts

)

Rutile(Cosmetic etc)

Anatase(Photocatalyst etc)

TiO2

Basics of XRD

Quantitative analysis(RIR method)The concentration of each phase is calculated by integrated intensity and RIR value

ResultRutile: 71.6wt%Anatase: 28.4wt%

PreparationRutile:Anatase=3:1

Polymorphs of TiO2Rutile (RIR:3.40)Anatase (RIR:3.30)Brookite

Basics of XRD

9Crystallite size

There is one or multiple crystalline in one particle.

Crystallite sizeParticlesize

Polycrystal

Small angle X-ray scattering The width of

diffracted lineScherrer methodHall method

Basics of XRD

x10^3

2.0

4.0

6.0

8.0

10.0

12.0

(CPS

)

Molybdenum - MoI

40 50 60 70 802(deg)

58.0 58.1 58.2 58.3 58.4 58.5 58.6 58.7 58.8 58.9 59.0 59.1 59.2 59.3

900100

Mo

Crystallite size -Mo-

100

900

Debye ring

The width of diffracted line broaden in crystallite size less than 100nm(1000)

Inte

nsity

(cps

)

Basics of XRD

10

Crystallinity

40-1995> (CH2)x - N-ParaffinI

10 15 20 25 30 35 40 452(deg)

Plastic wrap

Crystallinity .

Basics of XRD

23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 402(deg)

0

500

1000

1500

2000

2500

3000

3500

Inte

nsity

(CP

S)

Change of lattice constantMonitoring the change of lattice constant in real time

in situ measurement

Al2O3

2dsin=

25900

25.5825.56

35.1635.12

Basics of XRD

11

d1 d2 d3 d4

Compressive stress d1 > d2 > d3 > d4

d1 d2 d3 d4

Tensile stress d1 < d2

12

Calculation of stress value

(stress value)

Kstress constant)

Material-specific valueEyoungs modulus, poisson ratio,0diffraction angle in stress free condition

sin22

K

21-E cos0

180

Slope of sin2 diagram

sin2

2

sin2

2tension

compresstension

compress

00

N

N

NN

XG

SC

N

N N NXG

SC

plus psiminus psiIso-inclination method(Fixed Psi)

Basics of XRD

Measurement of residual stressz Iron plate

Before rubbing

After rubbing

Basics of XRD

Sample

13

Texture evaluation and pole figure analysis

for bulk sample

Texture and substance

Nonoriented samplebrick, concrete, (powder)

Single crystalsilicon waferdiamondquartz

Oriented samplealuminium foiliron plateplastic bottle

Texture evaluation

14

What is oriented sample?

The condition that a lattice plane faces to the same direction

Approximate equivalent to single crystal

(Epitaxial film)

Uni-axial orientation

fiber orientation

Metal orientation

(rolled sample)

Texture evaluation

2D image and 2-I diffraction pattern

nonoriented oriented

I

2

I

2

2D image

Diffraction pattern

Texture evaluation

15

What is the purpose of texture?Which plane is faced to Rolling direction and Normal direction?

X

YZ

X

Y

Z

a

bc

Texture evaluation

Spherical projection method and Stereographic projection method

3D is described with 2D

Spherical projection method Stereographic projection method

Stereographic projection figure

Texture evaluation

16

Pole figureRDRolling direction

TD

NDNormal direction

Transverse direction

X

YZTD

Texture evaluation

Sample behaviorin Reflection method and Transmission method

Reflection method

Sample is moved centering around purple line

Transmission method

rotation

rotation

Beta rotation at each alpha angleAlpha:5deg step(ex.15208590deg)Beta: 5deg step(ex.05355360deg/ angle)

Texture evaluation

17

Orientation analysis :step1

RD20 90

62

The angle between RD and each pole is estimated with Wulff net.

Pole figure of (111) in rolled Cu-Zn(70-30)

Wulff net.

Texture evaluation

9035

Orientation analysis :step2

The angle between ND and each pole is estimated with Polar net.

Polar net

Texture evaluation

18

Orientation analysis :step3

(h2k2l2)(h1k1l1)

24.143.156.8

036.953.1

210

033.648.2

211

39.275.0

18.450.871.5

26.663.490

210

19.561.990

3054.773.290

35.365.9

211

35.390

06090

110

070.5109.5

54.7111

4590

110

090

100111100

Angle between plane in (h1k1l1) and (h2k2l2) of cubic crystal

ND

RD

Texture evaluation

Rotate standard (110) projection of cubic crystal 35degree clockwise.RD is [112]This texture is (110)[112]. (hkl)[uvw]=h*u+k*v+l*w=0

Angle between plane of cubic

111110=35.590

111211=19.561.990

ND

RD

Orientation analysis :step4

ND RD

Texture evaluation

19

Rotate 35degree

Process by stereographic objection figure

Standard (110)objection of cubic crystal

RD[112]

[112]

Texture evaluation

Small angle X-ray scatteringfor nano-size sample

20

Purpose of SAXS

z Particle size estimation (X-ray scattering)

z Phase identification (X-ray diffraction)

Small Angle X-ray Scattering

Particle sizethe distribution

molecularstructure

Small angle X-ray scattering

0.1

1

10

100

1000

0 1 2 3 4 5

2 (deg.)

Inte

nsity

( a.

u. )

0.1

1

10

100

1000

0 5 10

2 (deg.)

Inte

nsity

( a.

u. )

Principle of SAXS

X-ray SampleScattering angle

( 2 = 0~10 deg. )

Scattering Diffraction 2dsin=n

Small angle X-ray scattering

21

0.1

1

10

100

1000

0 2 4 6 8 10

2 (deg.)

Inte

nsity

( a.

u. )

Particle informationz Particle size and particle distribution

Slope of SAXS profile : Average size

Shape of SAXS profile: Breadth of distribution

Small angle X-ray scattering

Phase informationz Long-period structure

0.1

1

10

100

1000

0 1 2 3 4 5

2 (deg.)

Inte

nsity

( a.

u. )

1

1/31/2

Peak position of SAXS: Structure and Interval

Small angle X-ray scattering

22

Instrument for SAXS

NANO-Viewer

TTRAX III

Ultima

Small angle X-ray scattering

Point focus opticsz NANO-Viewer ( 2D-SAXS System )

2D image

3slits optics

X-ray source

1st slit 2nd slit 3rd slit

Sample

2D detector

Semiconductor 2D detector Pilatus100k

Small angle X-ray scattering

23

NANO-Solverz Automatic particle size & distribution estimation !

0 2 4 6 8 102 (deg.)

Inte

nsity

( a.

u. )

SAXS profile

sizedistribution

Dis

tribu

tion

( a.u

. )

Particle / Pore size ( nm )0 5 10

Closely particle sphere cylinder Core/shell

Small angle X-ray scattering

Relations of size and profilesz Size : 3nm z Size : 60nm

0 2 4 6 8 102 (deg.)

Inte

nsity

(a.u

.)

0 2 4 6 8 102 (deg.)

Inte

nsity

(a.u

.)

Normalized dispersion : 10 %

Small angle X-ray scattering

24

Relations of dispersion and profiles

z Dispersion : 10 % z Dispersion : 90 %

0 2 4 6 8 102 (deg.)

Inte

nsity

(a.u

.)

0 2 4 6 8 102 (deg.)

Inte

nsity

(a.u

.)

Average diameter : 3 nm

Small angle X-ray scattering

Applications of SAXS

Particle size estimation( transmission mode )

Small angle X-ray scattering

25

SAXS profiles and size distribution

z Au nanoparticles

Inte

nsity

(CPS

)

No.1No.2No.3

0 2 4 6 82 (deg.)

101

102

103

104

105

1000 2 4 6 8 10

No.1No.2No.3

Particle size ( nm )

Dis

tribu

tion(

a.u

.)

Small angle X-ray scattering

Comparison of TEM image

Particle size ( nm )0 2 4 6 8 10

No.1No.2No.3

Dis

tribu

tion(

a.u

.)

No.1 No.2 No.3TEM image

SAXS

Small angle X-ray scattering

26

Nano size of porous silicazMesoporous silica

0 1 2 3 4 52 (deg.)

Inte

nsity

(a.u

.)

0 1 2 3 4 52 (deg.)

Inte

nsity

(a.u

.)

Small angle X-ray scattering