Small-angle scattering: Principles, data analysis and advanced modeling
PhD School at the Faculty of SCIENCE at University of Copenhagen
This is a specialised course where 50% of the seats are reserved for PhD students enrolled at the Faculty of SCIENCE at UCPH and 50% of the seats are reserved for PhD students at other faculties and universities. Seats will be allocated on a first-come, first-served basis and according to the applicable rules.
Anyone can apply for the course, but if you are not a PhD student, you will be placed on the waiting list until enrollment deadline. After the enrollment deadline, available seats will be allocated to applicants on the waiting list.
Aim and Content
This 2.5 ECTS course introduces small-angle scattering using X-rays (SAXS) and neutrons (SANS) for structural and dynamic 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 the three SAXS machines at University of Copenhagen. Passing the course requires active participation, presentations during the course 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.
Tentative program / list of modules:
Preparations before the course (to be finalized)
• Book chapters/review papers (will be announced on the Absalon course site)
• Prepare a slide about your own project (upload to Absalon course site)
• Quiz/online tutorial (will be announced on the Absalon course site)
Introduction to the principles of x-ray and neutron scattering (Monday)
• Properties of x-rays and neutrons
• Form factors, structure factors, polydispersity, scattering contrast and variation thereof
Experimental principles (Monday)
• Lab source vs synchrotron radiation setups
• Sample preparation
• Advanced sample environments
• In situ and time-resolved measurements
• USAXS/USANS setups
Experiments (Monday)
• Experiments at (one of) UCPH’s three SAXS instruments
• Calibration samples for SAXS/WAXS
• Absolute intensity calibration
• Prepare and measure student's own samples
Basic modeling and analysis of scattering data (Tuesday)
• Monte Carlo simulation of scattering patterns
• Model fitting in SasView,
Primary data reduction and analysis (Tuesday)
• Data reduction and background subtraction
• Data quality assessment
• Primary data analysis, including Guinier analysis, Porod and Kratky plots, and indirect Fourier transformation (IFT).
Analysis of data from hierarchical structures (Wednesday)
• The relation between slopes on log-log plots and dimensionality and surface roughness
• Fitting using generic hierarchical models and physical models with several structural levels.
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
• Integration of Alpha-fold into modelling of SAS data
Specialized applications (vary from year to year and will depend on the availability of relevant Guest lectures)
• In the August 2024 edition, we had a module on GISAXS in this category, and in the 2025 edition we had a module on SESANS. Possible topics for the 2026 course: USAXS/USANS, or time-resolved SAXS, or SAXS at XFEL
Learning outcomes
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 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.
Target Group
PhD students and postdocs working with soft matter.
This spans colloids or exotic lipid phases in food science, drug delivery particles and protein/nucleotide complexes in pharmacy, and new polymer-based materials in organic chemistry.
Recommended Academic Qualifications
A MSc from science or health. We have students from a broad background of natural sciences and health. Therefore, we aim to design the course to make it accessible with all these backgrounds. To achieve this, we have much emphasis of hands-on-work and work on individual projects.
Research Area
Food science, pharmacy, material science.
Teaching and Learning Methods
We apply a modular concept, with modules of 1.5-2 hours. Each module should contain an introduction to the subject, hands on exercises, and be followed up by institutionalization. We follow this structure ourselves, and also help our guest lectures to use this format. To support a hands-on teaching, we have developed an online learning platform sastutorials.org. Our teaching philosophy has been described more thoroughly in Larsen et al 2025, J. Appl. Cryst 58: 603-608 (https://doi.org/10.1107/S1600576725001062)
Type of Assessment
We require the students to participate actively, and to present their project work orally on the last day of the course and in a written report just after the course. This is required to pass the course, but we do not provide any grading. These presentations receive feedback from us.
Literature
To be announced
Course coordinator
Jacob Kirkensgaard
Guest Lecturers
Annette Langkilde, University of Copenhagen, Department of Drug design and Pharmacology
Jan Skov Pedersen, Aarhus University
Wim Bouwmann, Delft University of Technology
More international guest lecturers - To be confirmed
Dates
24-28 August 2026
Expected frequency
Annually in mid to late August
Course location
To be announced
Course fee
• Participant fee: 0 DKK
• PhD student enrolled at SCIENCE: 0 DKK
• PhD student from Danish PhD school Open market: 0 DKK
• PhD student from Danish PhD school not Open market: 3.000 DKK
• PhD student from foreign university: 3.000 DKK
• Master's student from Danish university: 0 DKK
• Master's student from foreign university: 3.000 DKK
• Non-PhD student employed at a university (e.g., postdocs): 3.000 DKK
• Non-PhD student not employed at a university (e.g., from a private company): 8.400 DKK
Cancellation policy
• Cancellations made up to two weeks before the course starts are free of charge.
• Cancellations made less than two weeks before the course starts will be charged a fee of DKK 3.000
• Participants with less than 80% attendance cannot pass the course and will be charged a fee of DKK 5.000
• No-show will result in a fee of DKK 5.000
• Participants who fail to hand in any mandatory exams or assignments cannot pass the course and will be charged a fee of DKK 5.000
Course fee and participant fee
PhD courses offered at the Faculty of SCIENCE have course fees corresponding to different participant types.
In addition to the course fee, there might also be a participant fee.
If the course has a participant fee, this will apply to all participants regardless of participant
type - and in addition to the course fee.