gisaxs data analysis with bornagain

MLZ is a cooperation between:

GISAXS data analysis with BornAgain

Céline Durniak*, Jonathan Fisher, Marina Ganeva, Gennady Pospelov, Walter Van Herck, Joachim Wuttke

Jülich Centre for Neutron Science (JCNS) at Heinz Maier-Leibnitz Zentrum (MLZ), Forschungszentrum Jülich GmbH, Garching, Germany

*Now at: DMSC filial of European Spallation Source ESS AB, Copenhagen, Denmark

Outline

l  Theoretical background

l  Introduction to BornAgain

l  Working with BornAgain I: Graphical User Interface

l  Working with BornAgain II: Python API

l  Fitting

15/06/16 M. Ganeva, GISAXS Tutorial, ALBA SR-ALD workshop 2

Theoretical background


Born Approximation DWBA

•  considers only incident and outgoing wave

•  multiple scattering is ignored

•  the differential cross section

J  accounts for reflection-refraction effects close to the critical angle

J  equations for the layer structure solved exactly

J  surface structure is treated as a small perturbation

The form factor


Born DWBA The Born form factor is the Fourier transform of the shape of the particle

Example: spherical particle of radius R

DWBA: interference between particles


The expectation value of the differential cross section is

where

Cylinder form factor Interference function Cylinder form factor with interference function

Approximations for polydisperse structures


Decoupling approximation (DA) è No correlation between type and interparticle distances

Local Monodisperse Approximation (LMA) è Incoherent superposition of different domains, each with their own type and interference function

dσdΩ

q( ) = Id q( )+ S q( ) ⋅ Fα q( )α

2

dσdΩ

q( ) = Sα q( ) ⋅ Fα q( )2

α

Size-Space Correlation Approximation (SSCA) è Interparticle distance depends on sizes of the two particles considered

Interface roughness: parameters


Roughness of the interface is described by: •  RMS roughness σ •  Hurst parameter H •  Lateral correlation length Lc

Additionally for multilayer: •  Cross-correlation length Lh

uncorrelated correlated

Lh = 0 Lh >> h

DWBA limitations: gratings


V. Soltwisch et. al., arXiv:1509.02003v2

V. Soltwisch et. al., GISAS 2015 abstract booklet

References


Theoretical background

l  BornAgain User Manual, 2016, http://bornagainproject.org/documentation

l  Gilles Renaud et. al., Surf. Sci. Rep. 64, 255 (2009)

l  Rémi Lazzari, J. Appl. Cryst. 35, 406-421 (2002)

Interface roughness

l  V. Holý and T. Baumbach, Phys. Rev. B 49, 10668 (1994)

l  Sinha, et al., Phys. Rev. B 38, 2297 (1988)

Books

l  Jens Als-Nielsen and Des McMorrow “Elements of modern x-ray physics”

l  Martin Schmidbauer “Diffuse Scattering from Self-Organized Mesoscopic Semiconductor Structures”

l  Ezquerra, T.A., et al. (Eds.), “Applications of Synchrotron Light to Scattering and Diffraction in Materials and Life Sciences”

BornAgain framework l  Open-source multi-platform software project developed by scientific computing

group of MLZ (Garching, Germany) l  Simulation of grazing-incidence small-angle scattering for X-rays and neutrons l  Physics model is based on the Distorted Wave Born Approximation (DWBA) l  Development started in April, 2012. l  Project website http://bornagainproject.org


Functionality overview


l  Fit of the experimental data l  Graphical user interface l  Different shapes of nanoparticles l  Size distributions (polydispersity) l  Nanoparticle assemblies l  Multilayer systems l  Different interference functions

l  Polarized neutrons l  2 types of detectors l  Detector resolution l  Beam divergence

BornAgain: how to start


Introduction bornagainproject.org

Demo: BornAgain GUI define a sample


Available form factors


Complex shapes


Core shell particles Particles with size distribution With possibility to link parameters

Particle compositions collection of particles with fixed inter-particle distance coherent interference

All can be rotated

Very large particles


Large particles gives rise to a problem, known in communication theory as aliasing: Rapidly oscillating signal measured at fixed points shows up as slow sinusoid

In GISAS simulation Rapidly oscillating form factor of large particles leads to a significant variation of intensity over the detector bin. dx

dy

Very large particles


analytical calculations Monte-Carlo integration

Small cylinders height = 10 nm radius = 20 nm

Large cylinders height = 1000 nm radius = 2000 nm

Interference functions


o  1D lattice o  Radial paracrystal

a b

o  2D lattice o  2D paracrystal

Demo: BornAgain GUI set up the instrument


GISAXS Instrument: Beam Parameters


l  beam is defined via wavelength and incidence angles

l  it is possible to define beam divergence

beam divergence OFF beam divergence ON

GISAXS Instrument: Detector


BornAgain supports two kinds of detectors: Spherical detector Rectangular detector

Detectors are defined by the number of bins and the accessible range

Specular and Off-specular geometry


specular geometry

off-specular geometry

Demo: BornAgain Python API


Software validation


l  Validation against IsGISAXS

l  Self validation

In process

l  Validation against experimental data

Planned

l  We agreed with HipGisaxs team upon cross-validation of our packages (& possibly others)

Validation against IsGISAXS


BornAgain results mostly coincide with IsGisaxs on numerical level

Self Validation


Part of new BornAgain’s functionality can be validated via BornAgain itself o  Rotation machinery example o  Particle compositions example

o  Create box (30,20,6) o  RotateY by 90 degrees o  Compare with non-rotated box

(6,20,30) o  Scattering intensities should be

identical

o  Create particle composition from two hemi spheres

o  Assign same material to them o  Compare with normal full sphere, same

material, same radius o  Scattering intensities should be identical

Demo: Fitting of experimental data


Fitting in BornAgain


BornAgain

Fitting in BornAgain: main features (1)


o  Variety of minimization algorithms

o  Possibility to fit every sample parameter or their combination

o  Various fit strategies (e.g. fix/release

parameters)

FitParameter(“par1”, 8.0*nm, limited(5.0, 15.0))

radius = fun1(par1); lattice_length = fun2(par1)

Fitting in BornAgain: main features (2)


o  Organizing different minimization algorithms into the chain o  Genetic minimizer explores large parameter space, Levenberg-Marquardt finalize location of

minima o  Simultaneous fit of multiple datasets

o  Two or more experimental images obtained for different incident angles can be fitted with one sample model

o  Fitting along slices, masking certain areas of the detector image

o  Fitting along slices

Fitting problems


Why?

1e+05 CPU seconds later … Minimizer: “J”

fitting

Fitting problems


Possible reasons

l  An unreliable sample model

l  Large correlations between parameters

l  Very different scales of parameters involved in the calculation

l  Too many fit parameters

l  Multiple local minima

Fitting problems: multiple local minima


Fitting problems: multiple local minima


There you are!

Fitting problems


Possible reasons

l  An unreliable sample model

l  Large correlations between parameters

l  Very different scales of parameters involved in the calculation

l  Too many fit parameters

l  Multiple local minima

Troubleshooting

l  Choose a small number of free fitting parameters

l  Eliminate redundant parameters

l  Provide a good initial guess for the fit parameters

Announcement


1st BornAgain School and User Meeting

(a satellite of the GISAXS2016 workshop)

which will take place on 21-22 November 2016 at Heinz Maier-Leibnitz-Zentrum in Garching (near Munich), Germany.

Registration at https://webapps.frm2.tum.de/indico/event/34/ More information at http://bornagainproject.org

Thank you for your attention!


Contact:

http://bornagainproject.org

[email protected]

[email protected]

gisaxs data analysis with bornagain

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