Strain mapping technique

Enabled by the high resolution of spectra, which is enhanced by the use of spatial filter assembly having a small (200 pm) pin hole, the principle of the strain-induced band shift in Raman spectra has been further extended to the measurement of residual thermal shrinkage stresses in model composites (Young et al., 1989 Filiou et al., 1992). The strain mapping technique within the fibers is employed to study the... 

The return mapping techniques in inelastic solutions are a natural consequence of splitting the total strain into elastic and inelastic strains. Let tensor uy, an incremental field to describe the deformation, and its gradient, Vt/,y, show the deformation rate. The solution is implemented by the following steps. Step 1 introduces a loading condition such as F = (/, 4- V ,t)Fj." where ly is the unity second-rank tensor and the superscripts n and n 4-1 represent, respectively, the previous and current load steps. In step 2 the material is elastically stretched... 

In this chapter we show how restricting the angular acceptance of the detector adds another dimension to the information available from high resolution diffraction techniques, enabling strains and tilts in a sample to be identified separately. We explain the reciprocal space representation of triple-axis diffraction maps, and give several examples of its application to materials characterisation. 

X-ray topography is the X-ray analogue of transmission election microscopy and as such provides a map of the strain distribution in a crystal. The theory of image formation is well established and image simulation is thus a powerful means of defect identification. Despite a reputation for being a slow and exacting technique, with modem detector technology and care to match spatial resolution of detector and experiment, it can be a powerful and economical quality-control tool for the semiconductor industry. 

In general, unlike for the perfect epitaxial structures of fully strained materials, for nitride heteroepitaxial layers it is essential to perform not a single scan for a symmetrical reflection, but a set of two- or even three-dimensional maps of symmetrical and asymmetrical reflections. Additionally, for some applications, an intense beam is needed and therefore low-resolution X-ray diffractometry can be sometimes a preferable technique to the commonly used high-resolution XRD. For example, if we examine a heterostructural nitride superlattice, low resolution diffractometry will give us a broader zeroth-order peak (information on the whole layer) but more satellite peaks (information on the sublayers). Therefore, multipurpose diffractometers with variable configurations are the most desirable in nitride research. 

As experimental techniques for measuring displacement and strain become increasingly accurate at micro- and nano- length scales, experiments must be performed to verify the accuracy of predictions of models of material behavior at these scales. In particular, the use of diffraction techniques for measurements of lattice distortion [20] combined with surface measurement techniques such as micro-Moire [21], speckle interferometry [22] and displacement mapping [23] promise to provide essential information on the local deformation behavior of metals and alloys in the vicinity of grain boundaries, voids and second phase particles. These techniques must be further developed and applied to the analysis of real materials to increase our knowledge of material behavior at these length scales. 

The main outputs of flow modeling are flow visualizations, to illustrate the process mechanism and to compare with experimental marker techniques (section 10.3.7, Experimental Row Validation ). These include streamlines, particle tracks, velocity maps, and strain-rate contour plots. Elow models can also be validated... 

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