X-ray Diffraction for powder sample Rigaku Corporation Application laboratory Keigo Nagao Today s topics (AM) Features of Rigaku TTRAXⅢ Basics of powder XRD Feature of XRD Evaluation item Texture analysis for bulk sample Measurement and Process SAXS for nano-size sample Principle and Optics Application 1
Feature of TTRAXⅢ Rigaku TTRAXⅢ X-ray source θ θ 2θ 2θ Detector Sample holder In-Plane measurement Horizontal goniometer High power X-ray source Parallel beam method In-Plane axis (2θχ/φscan) 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 Sealed-off X-ray tube 2~3kW Cooling water Rotating anode X-ray tube 10~18kW Be window Target 3
Feature of TTRAXⅢ Geometry for powder sample Focusing method Parallel Beam Detector X-ray source RS X-ray source DS SS Detector DS Multi layer Miller Parallel slit analyzer Sample Systematic error Intensity Focusing method 1. Flat sample 2. Umbrella effect 3. Adsorption effect 4. Eccentric error Strong Sample Parallel beam Umbrella effect 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 Sample Focusing geometry (BB) 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 14 2θ(deg) Rough 5 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) X-ray source 2θ 0 order detector Receiving slit : open Parallel slit analyzer Datum surface Eccentric surface 2θ 2θ X 2θ- θ 5
Basics of XRD Interaction of substance and X-ray :1 Bragg s condition of diffraction The conditions for a reflected ( diffracted ) beam are given by the relation 2dsinθ = nλ Bragg s equation d θ θ 2dsinθ = λ d:interplanar spacing λ:x-ray wavelength θ:bragg angle n:1,2,3 Basics of XRD Interaction of substance and X-ray :2 X-ray diffuse scattering X-ray Sample Scattering angle ( 2θ = 0~10 deg. ) 1000 Intensity ( a.u. ) 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. reflection 10 0 X-ray reflectivity profile θ θ d refraction Reflectivity 10-1 10-2 10-3 refraction reflection 10-4 0 1 2 3 4 5 6 2θ/θ (degree) Basics of XRD Evaluation item in powder sample (more than 2θ=5deg) Peak Peak positions positions d d values values : : Phase Phase Identification Identification Lattice Lattice constant constant d d shift shift : : Residual Residual stress stress Solid Solid solution solution Intensity FWHM FWHM Crystal Crystal quality quality Crystallite Crystallite size size Lattice Lattice strain strain Intensity Intensity vs. vs. Orientation Orientation Preferred Preferred orientation orientation Fiber Fiber structure structure Pole Pole figure figure Integrated Integrated Int. Int. of of amorphous amorphous Crystallinity Integrated Integrated Int. Int. of of crystal crystal : : Quantitative Quantitative analysis analysis Angle(2θ) 7
Basics of XRD Phase Identification in X-ray diffraction The powder diffraction pattern is characteristic of the substance The diffraction pattern indicates the state of chemical combination Intensity ( counts ) 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 TiO 2 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 Particle size Crystallite size The width of diffracted line Scherrer method Hall method Basics of XRD Intensity(cps) 強度 (CPS) 12.0 10.0 8.0 6.0 4.0 Crystallite size Mo -Mo- The width of diffracted line broaden in crystallite size less than 100nm(1000A ) Debye ring 900A 100A 900A 100A 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 2.0 x10^3 I Molybdenum - Mo 40 50 60 70 80 2θ(deg) 9
Basics of XRD Crystallinity Plastic wrap 非晶質結晶質 Crystallinity 66.15% I 40-1995> (CH2)x - N-Paraffin 10 15 20 25 30 35 40 45 2θ(deg) Basics of XRD Change of lattice constant Monitoring the change of lattice constant in real time in situ measurement Intensity(CPS) 3500 3000 2500 2000 1500 1000 Al 2 O 3 25.56 25.58 900 2dsinθ= λ 35.12 35.16 25 500 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 2 > d 3 > d 4 d 1 d 2 d 3 d 4 Tensile stress d 1 < d 2 <d 3 < d 4 d 1 d 2 d 3 d 4 Bragg s condition of diffraction 2d sinθ = nλ Basics of XRD Peak shift and sin 2 ψdiagram Normal line of sample surface :N Normal line of lattice plane :N N(N ) ψ=0 ψ N N ψ N N ψ N Intensity(counts) 2θ 2θ(deg) sin 2 ψ 11
Basics of XRD Calculation of stress value Δ2θ σ(stress value)= K Δsin 2 ψ K(stress constant)= -E cosθ 2(1+ν) 0 π 180 Material-specific value {E:young s modulus, ν:poisson ratio, θ 0 :diffraction angle in stress free condition} Slope of sin 2 ψ diagram SC N XG N ψ N N N ψ XG N SC minus psi plus psi Iso-inclination method(fixed Psi) 2θ tension compress 2θ ー sin 2 ψ 0 0 sin 2 ψ compress tension Basics of XRD Measurement of residual stress 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 (Epitaxial film) Uni-axial orientation (fiber orientation) Texture evaluation 2D image and 2θ-I diffraction pattern nonoriented oriented 2D image Diffraction pattern I I 2θ 2θ 14
Texture evaluation What is the purpose of texture? Which plane is faced to Rolling direction and Normal direction? X Z X Y a c b 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 ) Z TD Y ND(Normal direction) Texture evaluation Reflection method Sample behavior in Reflection method and Transmission method α βrotation 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 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 62 Wulff net. 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 (h 1 k 1 l 1 ) and (h 2 k 2 l 2 ) of cubic crystal (h 1 k 1 l 1 ) 100 110 111 210 211 RD 100 0 90 45 90 54.7 26.6 63.4 90 35.3 65.9 ND 110 0 60 90 35.3 90 18.4 50.8 71.5 30 54.7 73.2 90 (h 2 k 2 l 2 ) 111 0 70.5 109.5 39.2 75.0 19.5 61.9 90 210 0 36.9 53.1 24.1 43.1 56.8 211 0 33.6 48.2 Texture evaluation Orientation analysis :step4 Angle between plane of cubic (111)(110)=35.5,90 (111)(211)=19.5,61.9,90 ND 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 [112] Rotate 35degree [112] RD 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 Particle size estimation (X-ray scattering) Phase identification (X-ray diffraction) Particle size the distribution molecular structure Small angle X-ray scattering Principle of SAXS X-ray Sample Scattering angle ( 2θ = 0~10 deg. ) 1000 Scattering Diffraction 2dsinθ=nλ 1000 Intensity ( a.u. ) 100 10 1 Intensity ( a.u. ) 100 10 1 0.1 0 5 10 0.1 0 1 2 3 4 5 2θ (deg.) 2θ (deg.) 20
Small angle X-ray scattering Particle information Particle size and particle distribution Intensity ( a.u. ) 1000 100 10 1 0.1 Shape of SAXS profile : Breadth of distribution Slope of SAXS profile : Average size 0 2 4 6 8 10 2θ (deg.) Small angle X-ray scattering Long-period structure Phase information Intensity ( a.u. ) 1000 100 10 1 1 1/ 3 1/2 Peak position of SAXS : Structure and Interval 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 NANO-Viewer ( 2D-SAXS System ) Semiconductor 2D detector Pilatus100k 2D image X-ray source 1st slit 2nd slit 3rd slit 2D detector Sample 3slits optics 22
Small angle X-ray scattering NANO-Solver Automatic particle size & distribution estimation! Intensity ( a.u. ) 0 2 4 6 8 10 2θ (deg.) SAXS profile Distribution ( a.u. ) 0 5 10 Particle / Pore size ( nm ) size distribution Closely particle sphere cylinder Core/shell Small angle X-ray scattering Relations of size and profiles Size : 3nm Size : 60nm Intensity (a.u.) Intensity (a.u.) 0 2 4 6 8 10 2θ (deg.) 0 2 4 6 8 10 2θ (deg.) Normalized dispersion : 10 % 23
Small angle X-ray scattering Relations of dispersion and profiles Dispersion : 10 % Dispersion : 90 % Intensity (a.u.) Intensity (a.u.) 0 2 4 6 8 10 2θ (deg.) 0 2 4 6 8 10 2θ (deg.) 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 Au nanoparticles Intensity (CPS) 10 5 10 4 10 3 10 2 10 1 No.1 No.2 No.3 Distribution( a.u.) No.1 No.2 No.3 10 0 0 2 4 6 8 0 2 4 6 8 10 2θ (deg.) Particle size ( nm ) Small angle X-ray scattering Comparison of TEM image TEM image No.1 No.2 No.3 SAXS Distribution( a.u.) No.1 No.2 No.3 0 2 4 6 8 10 Particle size ( nm ) 25
Small angle X-ray scattering Nano size of porous silica Mesoporous silica Intensity (a.u.) Intensity (a.u.) 0 1 2 3 4 5 2θ (deg.) 0 1 2 3 4 5 2θ (deg.) 26