MAUD School 2015 Structural Analysis of Nanomaterials using Electron Diffraction
Philippe BOULLAY Cristallographie et Sciences des Matériaux – CRISMAT UMR 6508 CNRS – Caen, France
0. Structural and microstructural analyses : why using electrons?
1. Precession Electron Diffraction Tomography : from structure solution to structure refinement
2. Electron Powder Diffraction : Rietveld analyses using MAUD
[001] fit E-WIMV 82 Å data
38 Å MAUD School 2015 Structural Analysis of Nanomaterials using Electron Diffraction
Philippe BOULLAY Cristallographie et Sciences des Matériaux – CRISMAT UMR 6508 CNRS – Caen, France
0. Structural and microstructural analyses : why using electrons?
XRD single-crystal ◄ tens of micrometer ► powder cell, symmetry and structure
Mo K =0,7107Å phase S/M, structure and microstructure (size, shape, texture) Structural Analysis of Nanomaterials using Electron Diffraction
XRD single-crystal ◄ tens of micrometer ► powder cell, symmetry and structure
Mo K =0,7107Å phase S/M, structure and microstructure (size, shape, texture)
PEDT ◄ tens of nanometer ►
Nanoparticles (NP)
200kV =0,0251Å
Precession Electron Diffraction Tomography (PEDT) Electron Powder Diffraction (EDP) patterns Structural Analysis of Nanomaterials using Electron Diffraction
Amplitude scattered by a crystalline lattice
in “ 3D ” transmission function
atoms in the elementary unit cell crystal form factor atomic form factors structure factor
TF atomic positions ‐1 2 TF measure Ig=||Ag|| the phase is lost Motif de diffraction Fraunhofer Diffraction = FT of the transmission function of the object Structural Analysis of Nanomaterials using Electron Diffraction
Electron beam / matter interactions charged particules e‐ strong ► interact with the electrostatic potential coulomb of the crystal (electrons + nucleus) interactions
is the atomic diffusion factor or atomic form factor is related to the differential elastic scattering
cross‐section :
electron density X‐ray of atom (ion) n
electrons electrostatic potential of atom (ion) n elastic e- / e- repulsion low scattering angles e- / nucleus attraction higher scattering angles backscattering Structural Analysis of Nanomaterials using Electron Diffraction
Electron beam / matter interactions
‐ interact with the electrostatic potential of the crystal (electrons + nucleus) ‐ strong coulomb interactions
kinematicaldiffraction approximation iscoherent generally elastic not scattering valid in sample preparation no energyelectron or wavelength diffraction change multipleof the incident scattering wave events
kinematical approximation interactions of very weak magnitude incident wave: hardly modified scattered wave: small perturbation Structural Analysis of Nanomaterials using Electron Diffraction
Multiple scattering A diffracted beam acts as a secondary incident beam : visible effect translation of the whole diffraction patterns
k0 k1
0 0 0 0 0 0* h k l h 0 0 : h = 2n extra spots observed due to multiple scattering
not visible effect affect the diffracted intensities biased intensities = problem for structure refinement Structural Analysis of Nanomaterials using Electron Diffraction
Crystallography : determine the arrangement of atoms in a crystalline solid
Crystal structure : structure solution and structure refinement
mostly rely on the analysis of diffraction patterns (X-ray, neutrons and electrons)
Cs corrected HREM imaging e‐ / matter : strong interactions ED atomic positions, strain analysis Cs corrected STEM imaging small diffracting volume dynamical scattering Z-contrast (HAADF and BF) EDX thin films, nanosized particle / area CBED chemical mapping STEM-EELS TODAY ! chemical and valence mapping
You can do a lot more than just diffraction Imaging and spectroscopy experiments in a modern TEM or STEM ! at atomic resolution Structural Analysis of Nanomaterials using Electron Diffraction
incident parallel e‐beam
O
G I
a* b* 000
10 Bragg’s law 2dsin =n Structural Analysis of Nanomaterials using Electron Diffraction zone axis [uvw] Several (hi ki li) planes intersect along the direction incident e‐beam [uvw] (zone axis) of the crystal.
When the incident e‐beam goes through the crystal along [uvw], these planes are close to Bragg’s condition diffraction.
Direct Lattice these planes obey the relation: planes in zone hu + kv + lw=0 (uvw)* [uvw]
The Ewald sphere is tangent to the reciprocal Reciprocal Lattice lattice plane passing by the origin and
containing all hikili spots (RL nodes) forming the zero order Laue zone (ZOLZ). 11 Zero order Laue zone diffraction patterns Structural Analysis of Nanomaterials using Electron Diffraction
Ewald sphere :: X-ray versus electrons V=200kV =2,508 10‐12m zero order Laue zone (ZOLZ)
The Ewald sphere radius (1/ ) is large in electron diffraction: ‐ Ewald sphere can be assimilated to a plane ‐ diffraction condition verified for several reciprocal nodes
Electron Diffraction allows direct observation of reciprocal planes (zone axis patterns) Structural Analysis of Nanomaterials using Electron Diffraction
Amplitude scattered by a crystal (finite size effects) crystal form factor
Structural Analysis of Nanomaterials using Electron Diffraction
Higher order Laue zones (HOLZ)
level 1 level 0
zone axis [uvw] incident e‐beam sample Laue zone 0 (ZOLZ) Laue zone 1 (FOLZ) Laue zone 2 (SOLZ)
Ewald sphere
2D 3D screen or detector Structural Analysis of Nanomaterials using Electron Diffraction
Can be used for symmetry determination from zone-axis pattern
“This atlas contains all the useful theoretical zone-axis electron diffraction patterns drawn for each of the 187 extinction symbols. Comparison of these theoretical patterns with experimental PED and CBED patterns allows, through a systematic method, an easy unambiguous identification of the space group of a crystal.” MAUD School 2015 Structural Analysis of Nanomaterials using Electron Diffraction
Philippe BOULLAY Cristallographie et Sciences des Matériaux – CRISMAT UMR 6508 CNRS – Caen, France
1. Precession Electron Diffraction Tomography : from structure solution to structure refinement
a. Electron Diffraction Tomography (EDT)
b. Precession Electron Diffraction Tomography (PEDT)
c. PEDT and structure solution (kinematical approximation)
d. PEDT and structure refinement (dynamical approach) Structural Analysis of Nanomaterials using Electron Diffraction
Electron Diffraction Tomography (EDT) = gain 3D info + high data completeness
“phi-scan” data collection U. Kolb et al., Ultramicroscopy 107 (2007) 507 collection of a series of randomly oriented ED patterns at a fixed angular interval Structural Analysis of Nanomaterials using Electron Diffraction
Electron Diffraction Tomography (EDT) = gain 3D info + high data completeness
“phi-scan” data collection PETS (L. Palatinus) 1 > peak search U. Kolb et al., Ultramicroscopy 107 (2007) 507 transmitted beam position, collection of a series of randomly oriented goniometer tilt, calibration, ED patterns at a fixed angular interval reflections size, … n frames ► peaks list “2D” + center position
2 > peaks analysis same reflection in several frames
peaks list “3D” (x,y,z) + clusters analysis
3 > JANA2006 (V. Petricek)
indexing + orientation matrix + RS sections
4 > data extraction
hklm I (I) file Structural Analysis of Nanomaterials using Electron Diffraction
Electron Diffraction Tomography (EDT) = gain 3D info + high data completeness ► EDT datasets : go further and use intensities for structure solution ?
4 > data extraction structure ? hklm I (I) file
► Electron crystallography : more complicated than XRD due to dynamical conditions
limit the dynamical effects PED thin samples, light atoms, oblique texture ED, …
-limit the interactions between the diffracted beams
-lesssensitive to thicknessvariation
-increase the resolution limit
-integrated intensities
R. Vincent and P.A. Midgley, Ultramicroscopy 53 (1994) 271 Structural Analysis of Nanomaterials using Electron Diffraction
Precession Electron Diffraction Tomography (PED + EDT)
“phi-scan” data collection z U. Kolb et al., Ultramicroscopy 107 (2007) 507 s collection of a series of randomly oriented g Ewald sphere in PED ED patterns at a fixed angular interval ▼ x relrods intensity integration g PED angle = 1.2° step 1°
data collection time ~ 1h Structural Analysis of Nanomaterials using Electron Diffraction
Precession Electron Diffraction Tomography (PED + EDT)
limit the dynamical effects PED NdGaO3 Pnma ap√2 x 2ap x ap√2
Data Analysis ►1 hkl I (I) file
-limit the interactions between the diffracted beams -less sensitive to thickness variation -increase the resolution limit ~0,8° -integrated intensities ~1,75° zone‐axis PED
increase the data completeness EDT Ewald sphere in PED PEDT z Precession Electron Diffraction Tomography sg
structure solution structure refinement g kinematical approximation Structural Analysis of Nanomaterials using Electron Diffraction
PrVO3: a representative example of tilted perovskite
PETS (L. Palatinus) Pnma (SG n°62) 1> "peak search" a= 5.44 Å transmitted beam position, b=7.76 Å goniometer tilt, calibration, c=5.40 Å reflections size, … n frames ► peaks list “2D” + center position data collection using tilt x 2> "peaks analysis" same reflection in several frames
peaks list “3D” (x,y,z) + clusters analysis 3> JANA2006 (V. Petricek)
indexation + orientation matrix
4> "data extraction"
55° to -55° step 1°/ precession angle 2° hklm I (I) file + RS sections Structural Analysis of Nanomaterials using Electron Diffraction Data Analysis > like single crystal XRD Phi scan
-55° to +55°, step 1° *.xyz
c*
PED angle: 2.0° a*
Lattice indexation 111 unoriented patterns nb. Of reflections : ~ 1050 [I> 3σ(I)] Parameters: a ≈ 5,471 Å; b ≈ 7,698 Å; c ≈ 5,356 Å; _Acquisition time ≈ 20 min α ≈ β≈ γ ≈ 90° coverage 1Å shell ~98% Structural Analysis of Nanomaterials using Electron Diffraction
Check symmetry using reciprocal space sections PETS
(0kl)c* (1kl) c* (h0l) c*
b* b* a*
(hk0) (hk1) b* b* ►
► a* a* ►
Orthorhombic Pnma a = 5,47 Å; b = 7,69 Å; c = 5,36 Å Structural Analysis of Nanomaterials using Electron Diffraction
PrVO3: a representative example of tilted perovskite structure solution refinement ▼ check SUPERFLIP consistency ▼ with X-ray density map powder + ► interpretation diffraction
b
a Electronsolution density map refinement V Pr O kinematical approximation Pnma (SG n°62) a= 5.44 Å, b=7.76 Å and c=5.40 Å independent Ref. obs/all = 197/369 R(obs)≈ 25 % !! Structural Analysis of Nanomaterials using Electron Diffraction
PrVO3: a representative example of tilted perovskite
Pnma (SG n°62) a= 5.44 Å, b=7.76 Å and c=5.40 Å Residual dynamic effects ! reliability factors calculated based on kinematical approximation are biased
► does it means that this structure is wrong Kinematical? dist. restric.
PrVO3
confidence ? ADRA= Average Distance of Reference Atoms (comparison with the NPD reference*)
* M.J. Martinez-Lope et al., Inorg. Chem. 47 (2008) 2634-2640 Structural Analysis of Nanomaterials using Electron Diffraction
Use dynamical scattering theory Dyngo Structure refinement (MSLS J. Jansen,ASTRA AP. Dudka et al.,…) JANA
Intensity calculation: Bloch waves formalism (Bethe (1928) & Humphreys (1979)).
JANA/PETS workshop http://jana.fzu.cz/w027.html
# 2015 International Union of Crystallography Experimental parameters & Selection/Computation parameters
Crystal thickness,
Orientation of the incident beam
Orientation of the surface normal with respect of the crystal lattice. see L. Palatinus et al., Acta Cryst. A 71 (2015) 235 for further informations on DynGo implementation in JANA2006 Structural Analysis of Nanomaterials using Electron Diffraction
► Dedicated integration procedure of intensities PETS for each frame : list of reflections, hkl , intensity, scale and estimated standard deviation σ(I) ►n hkl I (I) files !
► Parameters optimization JANA2006
d* limit
Thickness optimization
R-factor
~280 nm orientation optimization thickness Structural Analysis of Nanomaterials using Electron Diffraction
► Dynamical refinement results (no distance constraints and no data selection: 111 PED patterns)
Dynamical Dynamical ref. ref. + ADP + aniso. ADP PrVO3 dynamical refinement
better ▼
accuracy
confidence
►111 frames
Towards accurate structure refinement with an accuracy comparable to XRD and NPD
L. Palatinus et al., submitted Structure refinement using precession electron diffraction tomography and dynamical diffraction Structural Analysis of Nanomaterials using Electron Diffraction
limit the dynamical effects PED use dynamical scattering theory JANA
Data Analysis ►1 hkl I (I) file Frame by frame fit ►n hkl I (I) files
-limit the interactions between the diffracted beams -Bloch-waveformalism -lesssensitive to thicknessvariation -models for thickness variation -increase the resolution limit -orientation optimizationfor eachframe 0 -integrated intensities -max. deviation from exact Bragg condition (S g ) min max min/max 0 -PED: S g and S g where S g = S g ± | g | φ increase the data completeness EDT -… see L. Palatinus et al., Acta Cryst. A 71 (2015) 235
Precession Electron Diffraction Tomography
structure solution structure refinement kinematical approximation dynamical approach
works fine even for complex structures case of Bi5Nb3O15 incommensurate modulated structure ► P. Boullay et al. Inorg. Chem., 2013, 52 (10), 6127 Structural Analysis of Nanomaterials using Electron Diffraction
…
single crystal
1 2x 4x More crystals more reflections, resulting in concentric rings with a central beam in the middle
PEDT ◄ tens of nanometer ►
Nanoparticles (NP)
single crystal Electron Powder Diffraction (EDP) patterns MAUD School 2015 Structural Analysis of Nanomaterials using Electron Diffraction
Philippe BOULLAY Cristallographie et Sciences des Matériaux – CRISMAT UMR 6508 CNRS – Caen, France
2. Electron Powder Diffraction : Rietveld analyses using MAUD
a. phase search and indexing
b. sizes, shapes and textures
c. structure refinements
P. Boullay, L. Lutterotti, D. chateigner and L. Sicard, Acta Cryst. A 70 (2014) 448-456
Fast Microstructure and Phase Analyses of Nanopowdersusing Combined Analysis of TEM scattering patterns Structural Analysis of Nanomaterials using Electron Diffraction
Quantitative and statistically representative analysis of crystallite sizes and shapes, structure and crystallographic texture of nanoparticles in the form of powders and thin films?
Extraction of intensities from electron diffraction “ring patterns” for quantitative or semi-quantitative analysis …
Vainshtein (1964), …
PCED 2.0 : X.Z. Li, Ultramicroscopy 110 (2010) 297-304 ProcessDiffraction : J.L. Labar, Microsc. Microanal. 15 (2009) 20-29 TextPat : P. Oleynikov, S. Hovmoller and X.D. Zou in Electron Crystallography
The MAUD program : L. Lutterotti Nuclear Inst. and Methods in Physics Res. B268 (2010) 334-340. Structural Analysis of Nanomaterials using Electron Diffraction
MAUD Rietveld pattern fitting Delft size-strain (PV) Popa anisotropic Evolutionary Size/Strain distributions Simulated Annealing Planar faulting (Warren) Marquardt (Least squares) Turbostratic (Ufer) Metadynamics optimization Indexing Simplex (Nelder-Mead) Size-Strain (COD phase search procedure) Genetic
March-Dollase Peak location X-ray Harmonic Neutron Texture (E)WIMV Electron Standard Functions Peak fitting Residual stresses Geometric Structure refinement Voigt, Reuss, Hill Triaxial Stress Structural Analysis of Nanomaterials using Electron Diffraction
Incident e‐beam
Ewald sphere
direction of the diffracted beam for (hkl) planes direct beam camera length calibration camera length L dhklRhkl = L= K (Å.mm)
screen or detector
Rhkl
The relation with the diffraction angle is tg(2 hkl) = Rhkl/L (for small angles, ~ sin ~ tg )
inter‐planar distances Bragg’s law : dhklRhkl = L (=cste) Structural Analysis of Nanomaterials using Electron Diffraction
Intensity extraction along the rings by segments using an ImageJ plugin
pixel size
only dependent of the specification of your CCD camera► pixel to mm Structural Analysis of Nanomaterials using Electron Diffraction
Intensity extraction along the rings by segments using an ImageJ plugin
120 patterns
3° CAKING
chi=phi=0° / omega=90° / eta: 0° to 360° Transmission geometry for TEM scattering experiments with the nomenclature used in MAUD Structural Analysis of Nanomaterials using Electron Diffraction
Intensity extraction along the rings by segments using an ImageJ plugin
72 patterns
estimation of the center position using a reference circle 5° on the screen CAKING
chi=phi=0° / omega=90° / eta: 0° to 360° Structural Analysis of Nanomaterials using Electron Diffraction
Corrections for center position and elliptical distortion ?
Pawley fitting refining centrecenter andbut nottilting tilting x-center error = -0.00755(4)-0.00717(5) mm y-center error = -0.01093(4)-0.01278(5) mm Pawley fitting without refining center or tilting tiltingRwp = error 2.32 x % (sin(error)) = -0.0048(3) Centre defined graphically on the image tilting error y (sin(error)) = 0.1211(3) Rwp = 2.83 % Rwp = 1.56 % Structural Analysis of Nanomaterials using Electron Diffraction
Intensity extraction along the rings by segments using an ImageJ plugin
? not important here BUT
72 patterns
estimation of the center position using a reference circle 5° on the screen CAKING
chi=phi=0° / omega=90° / eta: 0° to 360° we have to calibrate the distance specimen/detector ► mm to 2 Structural Analysis of Nanomaterials using Electron Diffraction
Intensity extraction along the rings by segments using an ImageJ plugin calibrate the distance specimen/detector using a « reference material »
► an assembly of nanoparticles with known SG and lattice parameters ► best if microstructural features (size, shape, ….) are known (from XRPD)
Camera length read on the TEM (mm) Apparent spec/detc distance (mm) 600 109.9 800 145.3 1000 180.6 1200 229.4 1500 271.2 2000 375.1
▼
▼
▼ ▼ Structural Analysis of Nanomaterials using Electron Diffraction
Intensity extraction along the rings by segments using an ImageJ plugin
120 patterns 2D plot estimation of the center position using a reference circle 3° on the screen CAKING
chi=phi=0° / omega=90° / eta: 0° to 360° Structural Analysis of Nanomaterials using Electron Diffraction
1D XRPD-like pattern (360° summed intensity)
peak location and intensities
b(x): background => pic at 0° + polynomial function
2 (°) => Q (Å-1) measured profile h(x) = f(x) g(x) + b(x) Structural Analysis of Nanomaterials using Electron Diffraction The whole pattern representing the summed intensity along the rings can be used for an automatic phase search procedure in the Crystallography Open Database* using the program S_FPM (L. Lutterotti).
Database Pattern
Rietveld fit (for each phase in the database)
Add new Ranking ‐ 1D XRPD‐like experimental profile phases ‐ list of elements (synthesis condition, EDX, EELS, …) Best phase End: Y N ‐ instrumental parameters (pixels to scattering angle, peak shape> threshold function, …) Rietveld
* S. Grazulis, D. Chateigner, R.T. Downs, A.F.T. Yokochi, M. Quirós, L. Lutterotti, E. Manakova, J. Butkus, P. Moeck and A. Le Bail, J. Appl. Crystallogr. 42, 726-729, 2009. Structural Analysis of Nanomaterials using Electron Diffraction The pattern representing the summed intensity along the rings can be used for an automatic phase search procedure in the Crystallographic Open Database using the program S_FPM (L. Lutterotti).
Mac-OS interface dedicated to this task …
TiO2 rutile nanoparticules … see M. Reddy et al., ElectroChem. Com. 8 (2006) 1299‐1303 for details Electron atomic scattering factors from the tables of L.M. Peng et al Structural Analysis of Nanomaterials using Electron Diffraction
automatic phase search procedure is possible (COD database, multi-phases)
a web site dedicated to this task is available
Test on nanopowders (TiO2 rutile, Mn3O4 hausmannite,kinematic CoFe2O4 spinel) and textured approximation is used to thin films (MgO on Pt) calculate the whole pattern profile • low texture : one single ED‐RP is sufficient •strongtexture : more tricky …need more than one ED‐RP
http://nanoair.dii.unitn.it:8080/sfpm and http://cod.iutcaen.unicaen.fr Structural Analysis of Nanomaterials using Electron Diffraction
1D XRPD-like pattern (360° summed intensity)
peak location and intensities
peak broadening vs. dhkl
b(x): background => pic at 0° + polynomial function
2 (°) => Q (Å-1) measured profile h(x) = f(x) g(x) + b(x) Structural Analysis of Nanomaterials using Electron Diffraction
Line broadening causes h(x) = f(x) g(x) + b(x) sample contribution instrumental broadening •instrumental broadening •finite size of the crystals (acts like a Fourier truncation: size broadening)
•imperfection of the periodicity (due to dh variations inside crystals: microstrain effect) • generally: 0D, 1D, 2D, 3D defects
All quantities are average values over the probed volume ► electrons, x-rays, neutrons: complementary ► distributions: mean values depend on distributions’ shapes
Extraction of f(x) can be obtained by a whole-pattern (Rietveld) analysis Need to know g(x) the instrumental broadening !
L. LutterottiThe and instrumental P. Scardi, J. of Appl. Peak Crystallogr. Shape 23,Function 246-252 is(1990) obtained by analysing nanoparticules of known sizes and shapes as obtained from X-ray analyses Structural Analysis of Nanomaterials using Electron Diffraction
Mn3O4 hausmanite (L. Sicard - ITODYS - UMR 7086 CNRS / Univ. Paris 7)
Reflection mode Bruker D8 / Lynx Eye 1D TOPCON 2B / CCD ORIUS acq. time:3h30 =1.54056 Å (Cu K 1) > 100mg powder =0.0251Å
SG: I 41/a m d a=5.764(2)Å and c=9.448(4)Å
TransmissionTransmission mode mode acq.acq. time:6h time: few seconds! powdervery small in a amount capillary of powder Structural Analysis of Nanomaterials using Electron Diffraction
Mn3O4 hausmannite g(x) ► f(x) structure Bruker D8 / Lynx Eye 1D
=1.54056 Å (Cu K 1)
SG: I 41/a m d a=5.764(2)Å and c=9.448(4)Å
64 Å POPA anisotropic
53 Å shape f(x) ► g(x) pattern matching background substracted TOPCON 2B / CCD ORIUS =0.0251Å
a=5.7757(2)Å and c=9.4425(4)Å
Cagliotti function U=3.32 10-4 V=-2.5 10-2 TEM : poor resolution ! ►not for particles larger than 20 nm W=3.2 Structural Analysis of Nanomaterials using Electron Diffraction
Mn3O4 hausmannite
64 Å POPA anisotropic
53 Å shape
TOPCON 2B / CCD ORIUS =0.0251Å
a=5.7757(2)Å and c=9.4425(4)Å f(x) ► g(x) Structural Analysis of Nanomaterials using Electron Diffraction
(1) Microstructure of nanocrystalline materials: TiO2 rutile
from phase search: TiO2 rutile P42/mnm a= 4.592Å a=2.957Å (COD database ID n°9001681)
72 patterns
5°
20nm FEI Tecnai / CCD USC1000 / =0.0197Å
(1) M. Reddy et al., ElectroChem. Com. 8 (2006) 1299-1303 Structural Analysis of Nanomaterials using Electron Diffraction
4-circles diffract. / INEL CPS structure XRPD = CuK
average anisotropic crystallite size
POPA (up to R4)
pattern matching EPD Structural Analysis of Nanomaterials using Electron Diffraction
► Electron crystallography: more complicated than XRD due to dynamical conditions
pattern matching
structure factors kinematical approx.
► microstructural features can be obtained in the pattern-matching mode ► not convincing using structure factors from kinematical approximation …
Take into account dynamical conditions ? Structural Analysis of Nanomaterials using Electron Diffraction
► Electron crystallography: more complicated than XRD due to dynamical conditions
2-beams or Blackman correction
ratio between the dynamical and kinematical intensity of a hkl reflection
H in MAUD H can be: - a refineable thickness parameter -the anisotropiccrystallitesize usedfor line broadening
( ) J0 is the zero order Bessel function, Fhklis the kinematical structure factor* , H is the thickness in Angstrom of the crystallite, Vc the cell volume, m and e are respectively the mass and charge of the electron, h the Planck constant and E the acceleration voltage of the microscope in Volts
(*) electron atomic scattering factors from the tables of L.M. Peng et al., Acta Cryst. A52 (1996) 257. Structural Analysis of Nanomaterials using Electron Diffraction
► Electron crystallography: more complicated than XRD due to dynamical conditions
pattern matching
structure factors kinematical approx.
Blackman correction (2-beams interactions) Structural Analysis of Nanomaterials using Electron Diffraction
a=4.5875(2)Å c=2.9475(2)Å XRPD a=4.584(1)Å c=2.949(1)Å
x(O1)=y(O1)=0.3062(5) pattern matching POPA R0 + R1
a=4.5853(3)Å c=2.9448(3)Å
x(O1)=y(O1)=0.3006(2) 2-beams more reliable Blackman 2-beams correction results for structure x(O1)=y(O1)=0.3064(2) structure refinement refinement Structural Analysis of Nanomaterials using Electron Diffraction
6μm 0.5μm
decreasing the selected area
intensity variation along the rings
fit fit no texture E-WIMV local texture analysis data data
Q (Å-1) Q (Å-1) Structural Analysis of Nanomaterials using Electron Diffraction
QTA analysis of Pt thin film deposited on Si (11 EPD patterns from +25° to -25° step 5°)
coverage
Tested using both Pawley structure factors extraction or Blackman structure factors calculation considering E-WIMV ODF refinement and one fiber texture component {111} pole figure from ODF refinement
The features available in MAUD allow a full quantitative texture analysis for general cases (not only fiber textures) from EPD patterns with the obtention of accurate pole figures Structural Analysis of Nanomaterials using Electron Diffraction
PDF analyses on EPD ?
see A.M.M. Abeykoon, C.D. Malliakas, P. Juhás, E.S. Božin, M.G. Kanatzidis, S.J.L. Billinge, Z. Kristallogr. 227 (2012) 248 T.E. Gorelik, M.U. Schmidt; U. Kolb, S.J.L. Billinge, Microscopy and Microanalysis 21 (2015) 459
TEM =0.0251Å CuK (150o 2 )
√I*Q=f(Q)I=f(Q)
NP TiO2 rutile synchrotron =0.486Å What can we do in MAUD ? ▼ Rietveld “PDF-like” Structural Analysis of Nanomaterials using Electron Diffraction
Rietveld analyses on high-Q range data : BaTiO3 (PDF2GET3 example) normal refinement, sqrt statistic, anisotropic B factors : Rw=1.81%
synchrotron XRD data (?)
badly fitted ▼ give more weight to high-Q Structural Analysis of Nanomaterials using Electron Diffraction
Rietveld analyses on high-Q range data : BaTiO3 (PDF2GET3 example) PDF-like refinement, Rw(sqrt*Q-bkg)=0,942%, anisotropic B factors
synchrotron XRD data (?)
first step towards PDF analyses in MAUD ▼ «PDF-like» Rietveldrefinement Structural Analysis of Nanomaterials using Electron Diffraction
Rietveld “PDF-like” analyses on EPD in MAUD
Rietveld refinement :: combined analysis
√I*Q=f(Q)
NP TiO2 rutile 5.0 10.0
a=4.588(1)Å c=2.945(1)Å
x(O1)=y(O1)=0.3059(2) Biso Ti = 2,2 Biso O = 1,5
Radial Distribution Function and Direct Space analysis … in progress!