Scherrer grain-size analysis adapted to grazing-incidence scattering with area detectors.

Ever since its formulation, the Scherrer formula has been the workhorse for quantifying finite size effects in X-ray scattering. Various aspects of Scherrer-type grain-size analysis are discussed with regard to the characterization of thin films with grazing-incidence scattering methods utilizing area detectors. After a brief review of the basic features of Scherrer analysis, a description of resolution-limiting factors in grazing-incidence scattering geometry is provided. As an application, the CHESS D1 beamline is characterized for typical scattering modes covering length scales from the molecular scale to the nanoscale.

[1]  Detlef-M. Smilgies,et al.  Grazing‐incidence small‐angle X‐ray scattering from thin polymer films with lamellar structures – the scattering cross section in the distorted‐wave Born approximation , 2006 .

[2]  Jerome B. Cohen,et al.  Grazing-incidence small-angle X-ray scattering: new tool for studying thin film growth , 1989 .

[3]  D. Smilgies,et al.  Characterization of polymer thin films with small‐angle X‐ray scattering under grazing incidence (GISAXS) , 2002 .

[4]  K. Lonsdale.  X-Ray Diffraction , 1971, Nature.

[5]  T. Matsushita,et al.  A systematic method of estimating the performance of X-ray optical systems for synchrotron radiation. I. Description of various optical elements in position–angle space for ideally monochromatic X-rays , 1980 .

[6]  B. Warren,et al.  X-Ray Diffraction , 2014 .

[7]  S. Hotta,et al.  Reciprocal space mapping and single-crystal scattering rods. , 2005, Journal of synchrotron radiation.

[8]  E. W. Meijer,et al.  Two-dimensional charge transport in self-organized, high-mobility conjugated polymers , 1999, Nature.

[9]  P. Scardi,et al.  Diffraction line profiles from polydisperse crystalline systems. , 2001, Acta crystallographica. Section A, Foundations of crystallography.

[10]  Dorthe Posselt,et al.  Structural instabilities in lamellar diblock copolymer thin films during solvent vapor uptake. , 2008, Langmuir : the ACS journal of surfaces and colloids.

[11]  R. Lazzari,et al.  IsGISAXS: a program for grazing‐incidence small‐angle X‐ray scattering analysis of supported islands , 2002 .

[12]  Jacques Jupille,et al.  Real-Time Monitoring of Growing Nanoparticles , 2003, Science.

[13]  Jan Skov Pedersen,et al.  Analysis of small-angle scattering data from colloids and polymer solutions: modeling and least-squares fitting , 1997 .

[14]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[15]  Kwang-Woo Kim,et al.  Structural Analysis of Block Copolymer Thin Films with Grazing Incidence Small-Angle X-ray Scattering , 2005 .

[16]  J. Langford,et al.  Scherrer after sixty years: a survey and some new results in the determination of crystallite size , 1978 .

[17]  R. Hosemann,et al.  Direct analysis of diffraction by matter , 1962 .

[18]  O. Robach,et al.  Corrections for surface X-ray diffraction measurements using the Z-axis geometry: finite size effects in direct and reciprocal space , 2000 .

[19]  N. Jedrecy.  Coupling between spatial and angular variables in surface X-ray diffraction: effects on the line shapes and integrated intensities , 2000 .

[20]  T. Matsushita,et al.  A systematic method of estimating the performance of X‐ray optical systems for synchrotron radiation. II. Treatment in position‐angle–wavelength space , 1980 .

[21]  O. Bunk,et al.  Simulating X-ray diffraction of textured films , 2008 .

[22]  Qun Shen,et al.  Multilayer X-ray optics at CHESS. , 2006, Journal of synchrotron radiation.

[23]  Masao Kakudo,et al.  Small Angle Scattering of X-Rays , 1968 .