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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