Metadislocation series

Experimentally, one finds that the different members of the metadislocation series are not evenly distributed but their number distribution shows a broad maximum. In deformed and undeformed e-Al-Pd-Mn, most metadislocations found have six associated phason halfplanes. Metadislocations with ten halfplanes are observed almost as often, while those with four phason halfplanes are found considerably less frequently. Metadislocations with 16 phason halfplanes are even less frequently found and species with two halfplanes were only observed in very few occasions during an extensive number of experimental investigations. The frequency of occurrence of different metadislocation types considering their energy is discussed in Section 4.5.3. 

Regarding the series of [001] metadislocations, the following facts are noteworthy ... 

We have seen in the previous sections that metadislocations are associated with a certain number of phason halfplanes. The latter are required to accommodate the core into the crystal lattice. In the following, we describe two different ways to construct metadislocations in terms of a tiling representation. This wiU enable the reader to comprehend the relation between the number of associated phason halfplanes and the Burgers vector length, as well as further characteristic properties of the individual metadislocations within the series. 

The other metadislocations of the [0 01] series can be constructed in full analogy. 

In complete analogy with the case of metadislocations in Sg-Al-Pd-Mn (Section 4.4), series of metadislocations with other numbers of associated phason halfplanes can be constructed. Fig. 40 is a transmission electron micrograph showing two metadislocations in a sample region similar to that of Fig. 39(a). The left metadislocation is associated with five phason halfplanes and that on the right with eight phason halfplanes. In the areas directly below both metadislocation cores, regions of -structure are identified. 

Thus, one can construct a sequence of metadislocations with increasing numbers of associated phason halfplanes. As in Ss-Al-Pd-Mn, the Burgers vector lengths of the metadislocations in the sequence are related by factors of —r, and with increasing number of associated phason halfplanes, the Burgers vector length decreases. However, in the -structure, the sequence of associated phason halfplanes is 1, 2, 3, 5, 8,. .. and it follows a Fibonacci sequence, whereas in Se the sequence is 2, 4, 6, 10, 16,. .., which follows a series of twice the Fibonacci numbers. 

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