Burgers vector length

Find the number of supersaturated vacancies that must diffuse to a unit length of climbing screw dislocation to convert it into a helix of radius a. turn spacing 27-p. and Burgers vector length b. 

Note N, number of associated phason halfplanes b. Burgers vector length in terms of the c-lattice constant and actual value in the in sg- and 28-lattice. 

The Burgers vector lengths are related to each other by factors of —x. The negative sign of the factor results from Burgers circuits according to Fig. 22 around the characteristic tiles representing the core this is discussed in Section 4.5.2. 

The sequences of associated phason halfplanes and Burgers vector lengths are opposed with an increasing number of phason halfplanes, the Burgers vector lengths are decreasing. 

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 constructed Burgers vector lengths bp for (,- and E28-Al-Pd-Mn correspond to the experimental values (Table 1). 

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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