Diffraction methods have become standard in the characterisation of stress and strain fields in crystalline materials. To our knowledge, characterisation of strain in amorphous materials by diffraction methods has not been reported. This is remarkable, since their scope within materials science and engineering parallels that of crystalline materials. Most ubiquitously, polymer glasses are used in applications from medicine to transport to space flight. At present localised strain information is only available from surface probes such as optical or electron microscopy. This is unfortunate since surface and bulk characteristics in general differ. Hence, to a large extent, the assessment of strain distributions relies on untested models.

Here we present a universal diffraction method based on hard X-rays for characterising bulk stress and strain fields in amorphous materials. The transmission type set-up involves a focused monochromatic beam, an area detector and acquisition of images while rotating the sample around one axis. Using correlation functions, minute shifts in local maxima are determined in reciprocal space as well as direct space, that is in the S(Q) and g(r) profiles, respectively. The components of the strain tensor are determined with a resolution of 10-4.


Fig. 38: Evolution of the axial (red), transverse (blue) and in-plane shear (green) strain components during compression of a homogeneous bulk metallic glass. The external load is indicated by the line and referring to the scale at the right.


The method was verified by in situ compression experiments on a bulk metallic glass (BMG) performed at beamline ID15B. Shown in Figure 38 are the resulting axial, transverse and shear strains during two consecutive loading cycles, as derived from the first maximum in S(Q). Probing the strain on a length scale of ~10 Å in this way, the axial response for the homogeneous specimen is found to be identical to the macroscopic strain evolution. By comparison, similar plots based on the shifts of the first maxima in g(r) demonstrated that the atomic next-neighbour bonds are 2.7 times stiffer due to structural rearrangements at the 4-10 Å scale. Mapping strain fields is achieved by scanning the specimen, as illustrated in the example of Figure 39. Additional work on partially crystalline BMGs demonstrated that the method is applicable also to composites comprising an amorphous matrix and crystalline inclusions.


Fig. 39: The axial strain field around a circular hole in a 2 mm thick plate of a bulk metallic glass at a compressive stress of 390 MPa acting in the horizontal direction. Shown are the results from the X-ray diffraction experiment (boxes) as well as the result of an analytical model (background) ­ both with reference to the colour code to the right (lattice strain in %).


H.F. Poulsen (a), J.A. Wert (a), J. Neuefeind (b), V. Honkimäki (c) and M.Daymond (d). Nature Materials 4, 33-36 (2005).
(a) Risø National Laboratory, Roskilde (Denmark)
(b) SNS, Oak Ridge National Laboratory (U.S.A.)
(c) ESRF
(d) ISIS, Rutherford Appleton Laboratory (U.K.)