Discontinuous alignments

Figure 5.98 Schematic illustration of discontinuous, aligned fiber-reinforced composite.

Discontinuous aligmnents must be represented as sets of alignments, each of which is a single list of coordinates. The regions between discontinuous alignments are not represented at all in the data, and, to display these regions, the missing pieces... 

Figure 5.94 Schematic illustration of aligned discontinuous fibers in polymer matrix. Reprinted, by permission, from N. G. McCrum, C. P. Buckley, and C. B. Bucknall, Principles of Polymer Engineering, 2nd ed., p. 111. Copyright 1997 by Oxford University Press.

The shift factors to align the plots at different temperatures with the plot for the chosen reference temperature are determined and then these are fitted to the WLF equation to find the constants. The equation can then be used to predict the response at service temperatures. The principle of constructing a master curve is illustrated ion Figure 15.8 and the plot of log aT against temperature in Figure 15.9. More details of fitting the WLF equation and possible problems with a discontinuity in the relation are considered in reference 49. 

Fig. 8. Generation of the form of the helical diffraction pattern. (A) shows that a continuous helical wire can be considered as a convolution of one turn of the helix and a set of points (actually three-dimensional delta-functions) aligned along the helix axis and separated axially by the pitch P. (B) shows that a discontinuous helix (i.e., a helical array of subunits) can be thought of as a product of the continuous helix in (A) and a set of horizontal density planes spaced h apart, where h is the subunit axial translation as in Fig. 7. This discontinuous set of points can then be convoluted with an atom (or a more complicated motif) to give a helical polymer. (C)-(F) represent helical objects and their computed diffraction patterns. (C) is half a turn of a helical wire. Its transform is a cross of intensity (high intensity is shown as white). (D) A full turn gives a similar cross with some substructure. A continuous helical wire has the transform of a complete helical turn, multiplied by the transform of the array of points in the middle of (A), namely, a set of planes of intensity a distance n/P apart (see Fig. 7). This means that in the transform in (E) the helix cross in (D) is only seen on the intensity planes, which are n/P apart. (F) shows the effect of making the helix in (E) discontinuous. The broken helix cross in (E) is now convoluted with the transform of the set of planes in (B), which are h apart. This transform is a set of points along the meridian of the diffraction pattern and separated by m/h. The resulting transform in (F) is therefore a series of helix crosses as in (E) but placed with their centers at the positions m/h from the pattern center. (Transforms calculated using MusLabel or FIELIX.)...

R. M. McMeeking, Power Law Creep of a Composite Material Containing Discontinuous Rigid Aligned Fibers, International Journal of Solids and Structures, 30, 1807-1823 (1993). 

To investigate this possible hep arrangement of atoms, HRTEM studies of vertically oriented silver nanoprisms were conducted. For a defect in the <111> direction to be observed in the TEM, it is necessary that the nanoprism is oriented such that a 110 plane is in the plane of the image. In this orientation, two 111 planes and a 100 plane are aligned vertically with respect to the electron beam. The defects can then be detected as discontinuities in either the 100 or 111 planes that propagate away from the flat face of the nanoprism. This is illustrated schematically in Figure 11.51. 

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