On the calibration of high‐energy X‐ray diffraction setups. II. Assessing the rotation axis and residual strains

The calibration of high-energy X-ray diffraction setups using an area detector and a rotation axis is discussed. The characterization of the tilt and spatial distortions of an area detector was discussed in part one of this series [Borbely, Renversade, Kenesei & Wright (2014). J. Appl. Cryst. 47, 1042–1053]. Part II links the detector frame to the laboratory frame comprising an additional rotation axis and introduces a general diffractometer equation accounting for all sources of misalignment. Additionally, an independent high-accuracy method for the evaluation of the crystallographic orientation and cell parameters of the undeformed reference crystal is presented. Setup misalignments are mainly described in terms of a residual strain tensor, considered as a quality label of the diffractometer. The method is exemplified using data sets acquired at beamlines ID11 (European Synchrotron Radiation Facility) and 1-ID (Advanced Photon Source) on Al and W single crystals, respectively. The results show that the residual strain tensor is mainly determined by the detector spatial distortion, and values as small as 1–2 × 10−4 can be practically achieved.

[1]  Jonathan P. Wright,et al.  On the calibration of high-energy X-ray diffraction setups. I. Assessing tilt and spatial distortion of the area detector , 2014 .

[2]  S. Schmidt.  GrainSpotter: a fast and robust polycrystalline indexing algorithm , 2014 .

[3]  W. J. Palenstijn,et al.  Advances in X-ray diffraction contrast tomography: Flexibility in the setup geometry and application to multiphase materials , 2013 .

[4]  J. Härtwig,et al.  A tunable multicolour 'rainbow' filter for improved stress and dislocation density field mapping in polycrystals using X-ray Laue microdiffraction. , 2013, Acta crystallographica. Section A, Foundations of crystallography.

[5]  S. E. Offerman,et al.  A fast methodology to determine the characteristics of thousands of grains using three‐dimensional X‐ray diffraction. II. Volume, centre‐of‐mass position, crystallographic orientation and strain state of grains , 2012 .

[6]  S. E. Offerman,et al.  A fast methodology to determine the characteristics of thousands of grains using three-dimensional X-ray diffraction. I. Overlapping diffraction peaks and parameters of the experimental setup , 2012 .

[7]  Lars Pilgaard Mikkelsen,et al.  Measuring the stress field around an evolving crack in tensile deformed Mg AZ31 using three-dimensional X-ray diffraction , 2012 .

[8]  G. Johnson,et al.  Lattice refinement strategies. , 2012, Acta crystallographica. Section A, Foundations of crystallography.

[9]  J. Schuren,et al.  Quantifying the uncertainty of synchrotron-based lattice strain measurements , 2011 .

[10]  M. Miller,et al.  Far-field high-energy diffraction microscopy: a tool for intergranular orientation and strain analysis , 2011 .

[11]  Jonathan P. Wright,et al.  Grain-resolved elastic strains in deformed copper measured by three-dimensional X-ray diffraction , 2011 .

[12]  Nathan R. Barton,et al.  Precision of lattice strain and orientation measurements using high-energy monochromatic X-ray diffraction , 2011 .

[13]  P. Dawson,et al.  A method for measuring single-crystal elastic moduli using high-energy X-ray diffraction and a crystal-based finite element model , 2010 .

[14]  Jonathan P. Wright,et al.  Determining grain resolved stresses in polycrystalline materials using three-dimensional X-ray diffraction , 2010 .

[15]  M. Miller,et al.  In situ single-grain peak profile measurements on Ti–7Al during tensile deformation , 2009 .

[16]  Jonathan P. Wright,et al.  Friedel-pair based indexing method for characterization of single grains with hard X-rays , 2009 .

[17]  Bjørn Clausen,et al.  Evolution of stress in individual grains and twins in a magnesium alloy aggregate. , 2009 .

[18]  U. Lienert,et al.  Synchrotron applications of an amorphous silicon flat-panel detector. , 2008, Journal of synchrotron radiation.

[19]  G. Vaughan,et al.  Invited article: the fast readout low noise camera as a versatile x-ray detector for time resolved dispersive extended x-ray absorption fine structure and diffraction studies of dynamic problems in materials science, chemistry, and catalysis. , 2007, The Review of scientific instruments.

[20]  P. Withers,et al.  Evolution of intergranular stresses during in situ straining of IF steel with different grain sizes , 2006 .

[21]  H. Poulsen,et al.  Measuring strain distributions in amorphous materials , 2004 .

[22]  S. Schmidt,et al.  Simultaneous measurement of the strain tensor of 10 individual grains embedded in an Al tensile sample , 2004 .

[23]  S. Schmidt,et al.  Watching the Growth of Bulk Grains During Recrystallization of Deformed Metals , 2004, Science.

[24]  S. Schmidt,et al.  Lattice rotations of individual bulk grains Part II: correlation with initial orientation and model comparison , 2004 .

[25]  Henning Friis Poulsen,et al.  Lattice rotations of individual bulk grains. Part I: 3D X-ray characterization , 2003 .

[26]  S. Zwaag,et al.  Grain Nucleation and Growth During Phase Transformations , 2002, Science.

[27]  H. Poulsen,et al.  Strain tensor development in a single grain in the bulk of a polycrystal under loading , 2002 .

[28]  Henning Friis Poulsen,et al.  Tracking: a method for structural characterization of grains in powders or polycrystals , 2001 .

[29]  H. Poulsen,et al.  In Situ Measurement of Grain Rotation During Deformation of Polycrystals , 2001, Science.

[30]  Paul R. Dawson,et al.  Effects of grain interaction on deformation in polycrystals , 1998 .

[31]  H. Graafsma.  Accurate determination of strain tensors from small shifts of reflections measured on a four circle diffractometer , 1992 .

[32]  C. Wilkinson.  Linear least-squares adjustment of UB matrix elements and the prediction of reflection positions , 1990 .

[33]  Donald E. Sands,et al.  Vectors and Tensors in Crystallography , 1982 .

[34]  H. A. Levy,et al.  ANGLE CALCULATIONS FOR 3- AND 4-CIRCLE X-RAY AND NEUTRON DIFFRACTOMETERS. , 1967 .

[35]  W. L. Bond,et al.  Precision lattice constant determination , 1960 .

[36]  E. Schmid,et al.  Über die Temperaturabhängigkeit der Kristallplastizität , 1931 .

[37]  S. Koch.  The Fundamentals of Crystallography , 2016 .

[38]  T. Han,et al.  Load partitioning between single bulk grains in a two-phase duplex stainless steel during tensile loading , 2010 .

[39]  J. E. Glynn,et al.  Numerical Recipes: The Art of Scientific Computing , 1989 .

[40]  J. L. Schlenker,et al.  Strain-Tensor Components Expressed in Terms of Lattice Parameters , 1978 .