Brittle fracture studied by ultra-high-speed synchrotron X-ray diffraction imaging

Abstract

In situ investigations of cracks propagating at up to 2.5 km s−1 along an (001) plane of a silicon single crystal are reported, using X-ray diffraction megahertz imaging with intense and time-structured synchrotron radiation. The studied system is based on the Smart Cut process, where a buried layer in a material (typically Si) is weakened by microcracks and then used to drive a macroscopic crack (10−1 m) in a plane parallel to the surface with minimal deviation (10−9 m). A direct confirmation that the shape of the crack front is not affected by the distribution of the microcracks is provided. Instantaneous crack velocities over the centimetre-wide field of view were measured and showed an effect of local heating by the X-ray beam. The post-crack movements of the separated wafer parts could also be observed and explained using pneumatics and elasticity. A comprehensive view of controlled fracture propagation in a crystalline material is provided, paving the way for the in situ measurement of ultra-fast strain field propagation.

X-ray Diffraction Topography (Imaging) of Crystals Grown from Solution: A Short Review

“…Contrast corresponding to the traces of slip planes was observed following compression and subsequent annealing . From these beginnings, the techniques have developed to a point where cracks propagating at up to 2.5 km s –1 can now be imaged directly on the microsecond time scale …”

“…1 From these beginnings, the techniques have developed to a point where cracks propagating at up to 2.5 km s −1 can now be imaged directly on the microsecond time scale. 2 While Berg's and subsequently Barrett's 1945 methods exploited the characteristic lines, 3 in 1954 Schulz used the continuous part of the X-ray spectrum, observing diffraction contrast across crystals in the Laue technique. 4 It was this white beam method that Turkka Tuomi and colleagues used to take transmission X-ray topographs with exposure times of the order of seconds using the newly available sources of synchrotron radiation 5 in 1974.…”

“…26 The elastic self-energy per unit length of a dislocation E(b,l,c ij ) may be written as (1) where b is the Burgers vector, l is a unit vector in the direction of the dislocation line, and c ij are the elastic constants. The elastic energy per unit length normal to the growth face of the crystal W(b,l,n,c ij ) is then (2) where n is a unit vector normal to the growth face and α(n,l) is the angle between the dislocation line direction and the normal to the growth face. As the variation in the logarithmic term of eq 1 is always small, the optimum direction for the dislocation line is determined by the minimization of K(b,l,c ij )/cos α.…”