Structure of thin films by electron diffraction

János L. Lábár

Usage of diffraction data in structure determination

• Identifying known structures

• Solving unknown structures– Structure determination

• Unit cell dimensions• Space group symmetry• Unit cell content (atoms and their appr. coordinates)

– Structure refinement• More accurate atomic coordinates• Validation of the structure (attainable match)

Structure determination• Periodic functions Fourier coefficients

– Amplitude : diffraction the phase problem

– Phase : real space (HRTEM, fragment)

reciprocal space (Direct methods)

• Single crystal diffraction– X-rays, neutrons electrons

• Powder diffraction– X-rays, neutrons electrons

Single crystal diffraction

• Tilting experiments

• Identification of reflections: indexing– Unit cell dimensions– Space group symmetry (XRD, SAED, CBED)

• Integration of individual intensities– Background

• Phases (real reciprocal space)– Dynamic intensities in SAED

Single crystal diffraction• XRD:

– Up to 2000 atoms in the asymmetric unit– Up to 100 atoms: guaranteed success– Rule of thumb: # refl > 10 * # atoms

• SAED:– CRISP, ELD Direct methods (EDM)– Dynamic intensities in SIR97– Up to 30 atoms in the asymmetric unit– Size, image

Powder diffraction

• Collapse of 3D into 1D– Types:

• Equivalent reflections, multiplicity• Exact overlap: e.g. (43l) (50l) in tetragonal• Accidental: within instrumental resolution

– Indexing programs– Peak decomposition

• La Bail• Pawley

Powder diffraction• Degree of overlap: Resolution

• Background

• Instability: negative peaks / oscillating int.

• XRD (+ refinement from neutrons) :– Synchrotron: 60 atoms in asymmetric unit– Laboratory: 30 atoms in asymmetric unit

• Neutron: better for refinement

• SAED: instrumental resolution limit, BKG

Powder diffraction: SAED resolution (peak width)

• Beam convergence

• Elliptical distortion

• OL spherical aberration size of selected area

Powder diffraction: SAED elliptical distortion

Powder diffraction: SAED spherical aberration

Powder diffraction: Pattern decomposition with ProcessDiffraction• Background

– Normal, log-Normal– Polynomial, Spline

• Peak shapes– Gaussian,

Lorentzian– Pseudo-Voigt

• Global minimum– Downhill SIMPLEX– Manual control

• Example: Al + Ge: SAED on film– Large crystal Al:

Gaussian– Small crystal Ge:

Lorentzian

Pattern decomposition with ProcessDiffraction

Structure refinement: The Rietveld method

• Start from assumed structure• Least-square fitting of whole-pattern• Fitting parameters:

– Scale-factor– Atomic positions– Temperature factors– Cell parameters– Peak shape parameters (instrumenal sample)– Background– Additional peaks (phase)

The Rietveld method

• Most known structures from Rietveld refinement• Scaling factors Quantitative phase analysis

(volume fractions)• Neutrons: no angle dependence best for

refinement• Resolution (peak width) is less important

SAED can also be used efficiently for refinement• SAED: Cell parameters camera length

Quantitative phase analysis for nanocrystalline thin films from SAED

• Example:

100 Å Al + 100 Å NiO

• Measured volume fraction by ProcessDiffraction: 51% Al + 49% NiO

• Fitted parameters: peak parameters, L, scaling factors, DW

Structure refinement from SAED

• Integrated intensities:– ELD– ProcessDiffraction

• Refinement:– FullProf– ProcessDiffraction

• Simple example: TiO2 – Anatase– Selection of origin transform „z” before compare

Structure refinement with ProcessDiffraction

• Structure definition modul– Checks: coordinates site symmetry

• Options modul checks – if selected site is „refinable” (variation of coordinate

value does not change site symmetry)– If selected options are reasonable

• Cross-checking for nanocrystalline samples– Pair correlation function (different models

measured)

ProcessDiffraction: Options for refinement

Structure refinement with ProcessDiffraction

• Example: Anatase 4 nm powder

• Acceptable match• Refined position of

oxygen: z=0.217• Compare to

z=0.2064 (Pearson’s)z=0.2094 (Weirich transformed)

Is the example result acceptable?Independent test

• Pair correlation function– Measured– Calculated for

both structures

• Refined result is in agreement with g(r)

Remarks to refinement

• Nanocrystalline films are strained

• Exact shape and size of the background is ambiguous in electron diffraction

• Refined position is also a function of refined cell dimensions (accurate calibration of camera length)

Conclusions: structure of thin films by electron diffraction

• Phase identification from both single crystal and powder patterns

• Quantitative phase analysis from nanocrystalline powder patterns

• Structure determination from single crystal patterns (SAED, CBED)

• Structure refinement from nanocrystalline powder patterns

• Limits are still to be examined