1. No category

X-ray Diffraction
for powder sample
Rigaku Corporation
Application laboratory
Keigo Nagao
Today’s topics (AM)
z Features of Rigaku TTRAXⅢ
z Basics of powder XRD
¾ Feature of XRD
¾ Evaluation item
z Texture analysis for bulk sample
¾ Measurement and Process
z SAXS for nano-size sample
¾ Principle and Optics
¾ Application
1
Feature of TTRAXⅢ
Rigaku TTRAXⅢ
2θ
θ
X-ray
source
θ
2θ
Detector
Sample holder
In-Plane measurement
(2θχ/φscan)
・Horizontal goniometer
・High power X-ray source
・Parallel beam method
・In-Plane axis
Feature of TTRAXⅢ
In case the sample isn’t set to horizontal….
Hard-to-pack sample
Thin layer sample
Semi-liquid sample
2
Feature of TTRAXⅢ
In Horizontal goniometer
Hard-to-pack sample
Independent on
sample condition
Thin layer sample
Semi-liquid sample
Feature of TTRAXⅢ
High power X-ray source
Rotating anode X-ray tube
10～18kW
Sealed-off X-ray tube
2～3kW
Cooling
water
Be
window
Target
3
Feature of TTRAXⅢ
Geometry for powder sample
z Focusing method
„
Parallel Beam
Detector
RS
X-ray source
DS
X-ray source
Detector
SS
DS
Multi layer
Miller
Parallel slit analyzer
Sample
Sample
Focusing method
Parallel beam
Systematic error
1. Flat sample
2. Umbrella effect
3. Adsorption effect
4. Eccentric error
Umbrella effect
Intensity
Strong
medium
Feature of TTRAXⅢ
Cross Beam Optics
Rigaku patented technology
BB and PB geometries are simultaneously mounted, aligned, and selectable.
X-ray source
BB selection slit
PB selection slit
Multilayer mirror
Sample
Focusing geometry (BB)
Sample
Parallel beam geometry (PB)
4
Feature of TTRAXⅢ
Measurement of rough sample surface
Focusing method
Parallel beam
Sample : Zeolite
Flat
6
7
8
9
10
11
12
13
14Rough 5
2θ(deg)
6
7
8
9
10
11
12
13
14
2θ(deg)
Hold of peak shape, peak position and FWHM
Feature of TTRAXⅢ
Free from Eccentric error (Parallel beam)
0 order
detector
X-ray source
2θ
Receiving slit : open
Parallel slit analyzer
X
2θ-⊿θ
Datum surface
Eccentric surface
2θ
2θ
5
Basics of XRD
Interaction of substance and X-ray :1
Bragg’s condition of diffraction
z The conditions for a reflected ( diffracted ) beam are given
by the relation
2dsinθ = nλ
θ
Bragg’s equation
θ
2dsinθ = λ
d
λ：X-ray wavelength
n：1,2,3･･･
d：Interplanar spacing
θ：Bragg angle
Basics of XRD
Interaction of substance and X-ray :2
X-ray diffuse scattering
Scattering angle
( 2θ = 0~10 deg. )
Sample
1000
Intensity ( a.u. )
X-ray
100
10
1
0.1
0
5
10
2θ (deg.)
6
Basics of XRD
Interaction of substance and X-ray :3
Reflection and interference
Two beams reflected on the
surface and the interface
interfere each other.
X-ray reflectivity profile
reflection
0
10
θ
refraction
θ’
-1
10
Reflectivity
d
-2
10
-3
10
refraction
reflection
-4
10
0
1
2
3
4
5
6
2θ/θ (degree)
Basics of XRD
Evaluation item in powder sample
z （more than 2θ=5deg）
Peak
Peakpositions
positions
ddvalues
values: : Phase
PhaseIdentification
Identification
Lattice
Latticeconstant
constant
ddshift
shift : : Residual
Residualstress
stress
Solid
Solidsolution
solution
Intensity
Intensityvs.
vs.Orientation
Orientation
Preferred
Preferredorientation
orientation
Fiber
structure
Fiber structure
Pole
Polefigure
figure
FWHM
FWHM
Crystal
Crystalquality
quality
Crystallite
Crystallitesize
size
Lattice
Latticestrain
strain
Integrated
IntegratedInt.
Int.
ofofamorphous
amorphous
Crystallinity
: :Quantitative
Quantitativeanalysis
analysis
Intensity
Integrated
IntegratedInt.
Int.
ofofcrystal
crystal
Angle（2θ）
7
Basics of XRD
Phase Identification in X-ray diffraction
Intensity ( counts )
z The powder diffraction pattern is characteristic of the substance
z The diffraction pattern indicates the state of chemical combination
Anatase
(Photocatalyst etc)
TiO2
2θ ( deg. )
Rutile
(Cosmetic etc)
Basics of XRD
Quantitative analysis(RIR method)
The concentration of each phase is calculated by
integrated intensity and RIR value
Polymorphs of TiO2
Rutile (RIR:3.40)
Anatase (RIR:3.30)
Brookite
Preparation
Rutile:Anatase=3:1
Result
Rutile: 71.6wt%
Anatase: 28.4wt%
8
Basics of XRD
Crystallite size
Polycrystal
There is one or multiple crystalline in one particle.
Small angle
X-ray scattering
Crystallite size
Particle
size
The width of
diffracted line
・Scherrer method
・Hall method
Basics of XRD
Crystallite size -MoThe width of diffracted line broaden in crystallite size
less than 100nm(1000Å)
Debye ring
12.0
Mo
強度(CPS)
Intensity(cps)
10.0
900Å
900Å
100Å
8.0
6.0
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
100Å
4.0
2.0
x10^3
√I
40
Molybdenum - Mo
50
60
70
80
2θ(deg)
9
Basics of XRD
Crystallinity
Plastic wrap
非晶質
結晶質
Crystallinity ６６.１５％
√I
10
40-1995> (CH2)x - N-Paraffin
15
20
25
30
2θ(deg)
35
40
45
Basics of XRD
Change of lattice constant
Monitoring the change of lattice constant in real time
→in situ measurement
3500
Intensity(CPS)
3000
2dsinθ= λ
35.12° 35.16°
Al2O3
25.56° 25.58°
2500
2000
1500
900℃
25℃
1000
500
0
23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
2θ(deg)
10
Basics of XRD
Stress and interplanar spacing
Compressive stress
d’1
d’1 > d’2 > d’3 > d’4
d’2
d’3
Tensile stress
d’1
d’4
d’1 < d’2 <d’3 < d’4
d’2
d’3
d’4
Bragg’s condition of diffraction
2d sinθ = nλ
Basics of XRD
Peak shift and sin2ψdiagram
N(N’)
N
N’
N
N’
ψ
ψ
Normal line of sample surface :N
N
ψ
ψ
ψ=0°
ψ =0 °
N’
:N’
Intensity(counts)
Normal line of lattice plane
N
2θ
2θ(deg)
sin2ψ
11
Basics of XRD
Calculation of stress value
σ(stress value)＝ K・
Δ2θ
Δsin2ψ Slope of sin2ψ diagram
π
-E
・cosθ0･
K（stress constant)＝
180
2（1＋ν）
Material-specific value
｛E：young’s modulus, ν：poisson ratio,
θ0：diffraction angle in stress free condition｝
N’
SC
N
N
N
ψ
N’
ψ
XG
ψ
ψ
N’
tension
SC
XG
minus psi
plus psi
2θ
compress
2θ
compress
tension
Iso-inclination method(Fixed Psi)
ｰsin2ψ 0
0
sin2ψ
Basics of XRD
Measurement of residual stress
z Iron plate
Before rubbing
Sample
After rubbing
12
Texture evaluation and
pole figure analysis
for bulk sample
Texture evaluation
Texture and substance
Nonoriented sample：brick, concrete, (powder)
Oriented sample：aluminium foil，
iron plate
plastic bottle
Single crystal：silicon wafer，diamond，quartz
13
Texture evaluation
What is oriented sample?
The condition that a lattice plane faces to the same direction
Metal orientation
(rolled sample)
Approximate equivalent
to single crystal
Uni-axial
orientation
(Epitaxial film)
（fiber orientation）
Texture evaluation
2D image and 2θ-I diffraction pattern
oriented
nonoriented
2D image
I
I
Diffraction
pattern
2θ
2θ
14
Texture evaluation
What is the purpose of texture?
Which plane is faced to Rolling direction and Normal direction?
X
Z
Y
a
X
b
c
Y
Z
Texture evaluation
Spherical projection method and
Stereographic projection method
3D is described with 2D
Stereographic
projection figure
Spherical projection method
Stereographic projection method
15
Texture evaluation
Pole figure
RD（Rolling direction）
X
TD
（Transverse
direction ）
Y
Z
TD
ND（Normal direction）
Texture evaluation
Sample behavior
in Reflection method and Transmission method
α
Reflection
method
Beta rotation at each alpha angle
Alpha:5deg step
(ex.15→20・・・85→90deg)
Beta: 5deg step
(ex.0→5・・・355→360deg/α angle)
βrotation
βrotation
α
Transmission
method
Sample is moved centering around purple line
16
Texture evaluation
Orientation analysis :step1
Pole figure of (111) in rolled Cu-Zn(70-30)
20 RD
°
90°
Wulff net.
62°
The angle between RD and each pole is
estimated with Wulff net.
Texture evaluation
Orientation analysis :step2
Polar net
90°
35
°
The angle between ND and each pole is
estimated with Polar net.
17
Texture evaluation
Orientation analysis :step3
Angle between plane in (h1k1l1) and (h2k2l2) of cubic crystal
(h1k1l1)
100
110
100
0
90
45
90
111
54.7
210
26.6
63.4
90
35.3
65.9
211
(h2k2l2)
ND
RD
110
0
60
90
35.3
90
18.4
50.8
71.5
30
54.7
73.2
90
111
0
70.5
109.5
39.2
75.0
19.5
61.9
90
210
211
0
36.9
53.1
24.1
43.1
56.8
0
33.6
48.2
Texture evaluation
Orientation analysis :step4
Angle between plane of cubic
（111）（110）=35.5，90°
ND
（111）（211）=19.5，61.9，90°
RD
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
ND
RD
18
Texture evaluation
Process by stereographic objection figure
Rotate 35degree
[112]
RD
[112]
Standard (110)objection of cubic crystal
Small angle X-ray scattering
for nano-size sample
19
Small angle X-ray scattering
Purpose of SAXS
Small Angle X-ray Scattering
z Particle size estimation (X-ray scattering)
z Phase identification (X-ray diffraction)
・Particle size
・the distribution
・molecular
structure
Small angle X-ray scattering
Principle of SAXS
X-ray
Scattering angle
( 2θ = 0~10 deg. )
Sample
Scattering
Diffraction 2dsinθ=nλ
1000
Intensity ( a.u. )
Intensity ( a.u. )
1000
100
10
1
0.1
100
10
1
0.1
0
5
2θ (deg.)
10
0
1
2
3
4
5
2θ (deg.)
20
Small angle X-ray scattering
Particle information
z Particle size and particle distribution
Intensity ( a.u. )
1000
Shape of SAXS profile
: Breadth of distribution
100
10
1
Slope of SAXS profile : Average size
0.1
0
2
4
6
8
10
2θ (deg.)
Small angle X-ray scattering
Phase information
z Long-period structure
1000
Intensity ( a.u. )
1
Peak position of SAXS
: Structure and Interval
100
1/√3
1/2
10
1
0.1
0
1
2
3
4
5
2θ (deg.)
21
Small angle X-ray scattering
Instrument for SAXS
UltimaⅣ
TTRAX III
NANO-Viewer
Small angle X-ray scattering
Point focus optics
z NANO-Viewer ( 2D-SAXS System )
Semiconductor
2D detector Pilatus100k
2D image
X-ray
source
1st slit
2nd slit
2D detector
3rd slit
Sample
3slits optics
22
Small angle X-ray scattering
NANO-Solver
Intensity ( a.u. )
Distribution ( a.u. )
z Automatic particle size & distribution estimation !
0
2
4 6 8
2θ (deg.)
0
5
10
Particle / Pore size ( nm )
10
™size
™distribution
SAXS
profile
Closely particle
sphere
cylinder
Core/shell
Small angle X-ray scattering
Relations of size and profiles
Intensity (a.u.)
z Size : 60nm
Intensity (a.u.)
z Size : 3nm
0
2
4
6
2θ (deg.)
8
10
0
2
4
6
2θ (deg.)
8
10
Normalized dispersion : 10 %
23
Small angle X-ray scattering
Relations of dispersion and profiles
z Dispersion : 90 %
Intensity (a.u.)
Intensity (a.u.)
z Dispersion : 10 %
0
2
4
6
2θ (deg.)
8
10
0
2
4
6
2θ (deg.)
8
10
Average diameter : 3 nm
Small angle X-ray scattering
Applications of SAXS
Particle size estimation
( transmission mode )
24
Small angle X-ray scattering
SAXS profiles and size distribution
z Au nanoparticles
No.1
No.2
No.3
104
103
102
101
100
0
2
4
6
2θ (deg.)
No.1
No.2
No.3
Distribution( a.u.)
Intensity (CPS)
105
8
0
2
4
6
8
Particle size ( nm )
10
Small angle X-ray scattering
Comparison of TEM image
TEM image
SAXS
No.2
No.3
Distribution( a.u.)
No.1
No.1
No.2
No.3
0
2
4
6
8
Particle size ( nm )
10
25
Small angle X-ray scattering
Nano size of porous silica
Intensity (a.u.)
Intensity (a.u.)
z Mesoporous silica
0
1
2
3
2θ (deg.)
4
5
0
1
2
3
2θ (deg.)
4
5
26