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Small-angle scattering: Principles, data analysis and advanced modeling 2025 - 2.5 ECTS
Provider: Faculty of Science

Activity no.: 5335-25-04-31There are 33 available seats 
Enrollment deadline: 01/07/2025
Date and time24.08.2025, at: 09:00 - 29.08.2025, at: 16:00
Regular seats35
ECTS credits2.50
Contact personHenriette Hansen    E-mail address: henha@food.ku.dk
Enrolment Handling/Course OrganiserJacob Judas Kain Kirkensgaard    E-mail address: jjkk@food.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockSummer
Exam formCourse Participation; Written Assignment
Exam detailsActive participation and submission of a final report outlining the application of minimum one of the tools taught on real data
Grading scalePassed / Not passed
Course workload
Course workload categoryHours
Preparation20.00
Practical exercises8.00
Lectures20.00
Theoretical exercises20.00
Sum68.00
Aim and content
Description and aim
This 2.5 ECTS course introduces small-angle scattering using X-rays (SAXS) and neutrons (SANS) for structural investigations. The course will have a strong hands-on approach, combining lectures, simulations, walked-through analysis examples and actual experiments. For the latter, we will use one of the three SAXS machines at University of Copenhagen. Passing the course requires active participation and submission of a final report. The course is relevant for all fields of material science where structure on the nanoscale is important and for students aiming to use SAS in their project, for example polymer science, food science, plant science, nanoparticle research, soft matter physics, structural biology, drug-delivery etc.
There are no specific requirements to attend the course but we assume you are a PhD student in the natural sciences with a general background from chemistry, biology, physics, mathematics, food & pharma, material science etc. We welcome theoretical and experimental backgrounds alike.

A tentative program / list of modules:
Preparations before the course (*to be finalized*)
• Book chapters/review paper
• Video lecture(s)
• Prepare a slide about your own project (upload to Absalon course site)
• Quiz

Introduction to the principles of x-ray and neutron scattering
• Properties of x-rays and neutrons
• Form factors, structure factors, polydispersity, contrast and variation thereof

Experimental principles
• Lab source vs synchrotron radiation setups
• Sample preparation
• Advanced sample environments
• In situ and time-resolved measurements
• USAXS/USANS setups

Experiments
• Experiments at one of UCPH’s three SAXS instruments
• Calibration samples for SAXS/WAXS
• Absolute intensity calibration
• Prepare and measure student's own samples

Primary data reduction and analysis
• Data reduction and background subtraction
• Data quality assessment
• Primary data analysis, including Guinier analysis, Porod and Kratky plots, and indirect Fourier transformation (IFT).

Basic modeling and analysis of scattering data
• Monte Carlo simulation of scattering patterns
• Model fitting in SasView,

Advanced modelling (vary from year to year and will depend on the availability of relevant Guest lectures)
• Reparametrization and molecular constraints
• Anisotropic data analysis
• Integrating SAS with molecular dynamics simulations
• Ab-initio 3D shape reconstruction

Specialized applications (vary from year to year and will depend on the availability of relevant Guest lectures)
• Possible topics include ASAXS, SE-SANS or time-resolved SAXS using microfluidics.
• In the August 2024 edition, we had a module on GISAXS in this category.

Formal requirements
PhD students in natural sciences.

Learning outcome
Knowledge:
Through lectures and theoretical exercises, the students will:
• Understand the principles of how structural information can be obtained from X-ray or neutron scattering. This including knowledge of central concepts such as form factors and structure factors.
• Be able to explain the experimental setup for a SAXS/SANS experiment, including important corrections.
• Be aware of possibilities and limitations of different strategies for analysing the data.

Skills:
Through hands-on exercises and tutorials, the students will be able to:
• Reduce and quality check their data, including error analysis and aggregation state.
• Perform primary data analysis, including Guinier analysis and indirect Fourier Transformation.
• Analyse their data with relevant software, including software packages SasView, McSAS and ATSAS.

Competences:
Through reflection and discussions of practical and theoretical aspects, the students can:
• Design and prepare a relevant SAXS or SANS experiment to answer a given scientific question.
• Decide on a relevant analysis strategy and do the analysis.

Literature
To be decided. We might include book chapters, or recorded lectures for flipped classroom (replacing/complementing the devolution phase of some of the models).

Also, we might include a quiz.

Target group
Students working with small-angle scattering across disciplines, but mainly within soft matter and biology.

Teaching and learning methods
The course will encompass three key elements:
1) Experimental exercises. We plan a full day for measurements. This will include discussion of sample requirements, experimental setup and corrections.
2) Lectures. We will have lectures covering basic scattering theory, data reduction, primary data analysis and modelling.
3) Exercises. We believe hands-on exercises are critical for deeper learning, and have developed a series of tutorials (SAStutorials.org) guiding the students in analysis of SAXS of SANS data.

We will use a modular strategy, where lectures and exercise are integrated. Our goal is that each module roughly follows the TDS model:
• Introductory lecture (devolution)
• Hands-on exercises (activation)
• Presentation/discussion of results between students and in plenum (formulation)
• The teacher discusses the results of the exercises and potential pitfalls (validation)
• The teacher discusses relevant research using the learned concepts, including their own research, and may discuss present challenges (institutionalization)

Lecturers
Brian Pauw, BAM, Germany: teaching monte carlo analysis and basics of SAXS experiments.

Andreas Haahr Larsen, University of Copenhagen, Denmark

Martin Cramer Pedersen, University of Copenhagen, Denmark

Jacob Kirkensgaard, University of Copenhagen, Denmark

More lecturers will be announced...

Remarks
The course is the second edition of a course we (Jacob Kirkensgaard, Andreas Haahr Larsen, Martin Cramer Pedersen) intend to run for many years. Optimally in a joint effort with ESS/DMSC/MAXIV/LINXS but taking advantage of our combined in-house X-ray scattering infrastructures at UCPH.

We expect the course to be free of charge.

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