An Introduction to Small-Angle X-ray (and Some Neutron) Scattering:

This course is being prepared as of 041211 but may have some useful information.

Please e-mail Greg Beaucage if you are interested in contributing to this page or in adding public access links.

(content will be free public access via multiple sites when completed)

Purpose:  This web course will provide the essential tools needed to understand and apply scattering to a variety of technical and scientific problems from an introductory level and is aimed at first or second year graduate students and researchers new to the the field.  The course will be based on a web text which will be updated as the course is taught at the University of Vermont and at the University of Cincinnati.  The course text is intended as a web reference on small-angle scattering and covers more material than can be taught in a traditional quarter or semester course.  This web text is an on-going effort and will be frequently updated and modified.  Please feel free to submit a contribution to the text, comments, corrections and questions.  The outline below is intended to frame the subject of small angle x-ray scattering.  It contains some entries but is far from complete.

Glatter/Kratky Book (1982) 46Mb

1)  Physics of Scattering Event (This could be an appendix)

            Texts:  Warren/Guinier etc. Better copy of Guinier

                 Special emphasis on differences between synchrotron and tube sources, definition of all types of insertion devices and comparative flux for difference sources.  Links to user facilities and discussion of proposal process for beamtime at international facilities.  Probability of success for first time applications and hints at successful proposal writing.

                 List of world class SAXS facilities with some kind of ranking would be good also with the odds of a first time user gaining access.

            Links:  XRD Chapter (UC); Imaginary Numbers and Scattering; Cambridge University Imaginary Numbers; LANL Neutron Diffraction (moderately slow load), Svergun Book Article

2)  Classification of scattering.  Correlation versus structure.  Similarity and differences in scattering features from regular structure and periodicity.  
(philosophy of scattering.)

            Links: Chapter from XRD Course (UC); (Older Version);  SAXS Laboratory Experiment (UC); Glatter on SAXS (moderately slow load); Rod scattering; SAXS Page Drexel; SANS ISIS; SAXS OklU; UNICAT Chicago; UNICAT Chicago

3)  Disordered structural scattering (globally dilute systems)::

            Guinier

            Porod

            Schmidt (surface scattering)

            Hurd/Martin/Schaefer (Mass-fractal Scattering)

            Unified Function

4)  Concentration effects in disordered systems

            f (1-f)

            correlation: Born-Green Function

            Mass-fractal scaling

            Micellar Correlations

5)  Polydispersity

            Sphere function dispersions etc.

            Maximum Entropy and other methods

            Unified approach

            Moments available from scattering

            Comparison with other techniques particularly microscopy

6)  Scattering from idealized regular structure

            Polymer lamellar scattering

            BCP

            Colloids

            Complex biological systems:  Svergun

7)  Scattering from highly correlated systems

            Correlation function approach

            Catagorization of disorder in order

8)  Techniques to study Orientation

            Legendre polynomials

            Uniaxial orientation and the Hermans Orientation Function

            Biaxial orientation

            General orientation in 3D

            Application to polymer lamellae

            Application to other systems

            Wilchinsky triangle and Stein Approach

            Empirical and semi-empirical approaches.

9)  Thermodynamics from Scattering (single phase scattering)

            Compressibility

            Zimm (dilute)

            RPA/deGennes (concentrated)

            BCP and micellar thermodynamics

10)  Contrast enhancement and matching/Phase contrast and absolute intensity

11)  Multiple scattering (NIST)

12)  Synchrotron facilities/application of tunable wavelength techniques

13)  Scattering Contrast Imaging (Such as at UNICAT)

14)  Survey of scattering instrumentation

            Pinhole

            Bonse-Hart

            Kratky

            Other Cameras

15)  Desmearing (Code and links to shareware code such as UNICAT code.)

            Schmidt

            Austrians/Gratz

            Lake (UNICAT)

16)  Data reduction Shareware

            NIST

            UNICAT

            etc.

17)  Links to scattering sites around the world (in order of entry not ranking Please email to be added beaucag@uc.edu):

            1)  UNICAT/APS

            2)  ID02/ESRF

            3)  IPNS/Argonne

            4)  NIST

            5)  ILL

18)  TOPICAL SECTION (Contributors needed)

            1)  Scattering in Biology/ACA workshop

            2)  Scattering in Semi-crystalline polymers

            3)  Scattering in Solutions and Polymer/Polymer blends

            4)  Scattering from Disordered Materials

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