HOLZ lines splitting on SiGe/Si relaxed samples: analytical solutions for the kinematical equation
Related Experiment Video
Updated: Jun 16, 2026

A Millimeter Scale Flexural Testing System for Measuring the Mechanical Properties of Marine Sponge Spicules
Published on: October 11, 2017
C Alfonso1, L Alexandre, Ch Leroux
1CNRS, IM2NP (UMR 6242), Faculté des Sciences et Techniques, Campus de Saint-Jérôme, Avenue Escadrille Normandie Niemen-Case 262, F-13397 Marseille Cedex, France. claude.alfonso@univ-cezanne.fr
Abstract:
Sample thinning for TEM observation introduces large changes with respect to the initial strain state of the bulk sample and particularly relaxation via the free surfaces which leads to HOLZ lines splitting in the CBED pattern. This phenomenon has been simulated owing to extensive calculations either in the kinematical or the dynamical framework of electron diffraction mainly using displacement fields resulting from finite element modelling of the sample relaxation. HOLZ line splitting is well reproduced and numerical fits can be used to compare experimental and calculated curves. This paper proposes new analytical solutions for the kinematical equation of electron diffraction. Simple mathematical functions are used to approximate the deformation profiles. We showed that, under certain conditions, the rocking curve profile can be analytically calculated, thus providing some clue to separate different contributions to the rocking curves against deformation profile. These simplified analytical expressions are used to extract the maximum amplitude displacement within the sample with about 10% accuracy. This accuracy can even be improved to 1% with a short adjustment routine. The influence of the shape of the displacement profile on the rocking curves is demonstrated.
Related Concept Videos
¹H NMR: Complex Splitting
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied first.
Kinematic Equations: Problem Solving
Boundary Conditions: Lossless Lines
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...
Kinematic Equations - III
Using the kinematic equations,...
Kinematic Equations - II
Suppose a car merges into freeway traffic on a 200 m long ramp. If its initial velocity is 10 m/s and it accelerates at 2 m/s2, then the...
Relative Velocity in Two Dimensions
