Phason defects

Fig. 44(a) shows a HAADF micrograph of a metadislocation in T-Al-Mn-Pd. The planar defect at the right-hand side, that is the slab of R-phase, is visible between the dashed lines. The metadislocation core is indicated by a polygon, which directly corresponds to the predicted polygon representing a metadislocation core [cf. Fig. 42(d)]. In addition three phason defects are visible at the left-hand side of the metadislocation core. Fig. 44(b) shows a full tiling representation of the defect. 

A pecuhar sohd phase, which has been discovered not too long ago [172], is the quasi-crystalline phase. Quasi-crystals are characterized by a fivefold or icosahedral symmetry which is not of crystallographic type and therefore was assumed to be forbidden. In addition to dislocations which also exist in normal crystals, quasi-crystals show new types of defects called phasons. Computer simulations of the growth of quasicrystals [173] are still somewhat scarce, but an increasing number of quasi-crystalline details are studied by simulations, including dislocations and phasons, anomalous self-diffusion, and crack propagation [174,175]. 

Fig. 9 Calculated variation in the potential energy surface as a function of different defect types for a tip-induced transition from the c(4 x 2) structure shown in (i) to the two-phason state shown in (iii), via the three-in-a-row configuration shown in (ii). From Ref 44.

Phason lines and phason planes can assume a dual function in s-type phases. On the one hand, they are structural defects, for instance in the phases Sg-Al-Pd-Mn and -Al-Pd-Mn. On the other hand, phason lines and phason planes can arrange regularly, forming a related e-type phase with larger c-lattice constant, and hence become elements of a new ideal structure. Phason lines and phason planes are pivotally connected to metadislocation formation and movement, as well as in phase transitions and formation of e-phases. 

Note that phason lines, even though they are linear defects, are not dislocations. Analyzing them in terms of ideal tile edges ( modified Burgers circuit, see Section 4.3) reveals that they do not possess a Burgers vector. 

Phason lines are linear defects with a [010] line direction, which can move along the [0 01] direction. It is unlikely, however, that phason lines move as a whole, that is, that the complete line performs a vertex jump in one single step. Although this has not been investigated in detail, it is a plausible assumption that phason lines move by a mechanism involving sequential jumps of small portions of the line, that is, by the formation of kinks and their subsequent movement along the line. This is in full analogy to the Peierls model, which describes dislocation motion by a kink-pair mechanism [36]. 

Related phases and phase transitions in terms of phason planes In Section 2.2, we have introduced the fact that the ss-phase is the basic structure of a family of related phases, the s-phase family. Fig. 4 shows examples of corresponding hexagon tilings. The S28-phase [Fig. 4(a)] is represented by a tiling which consists of hexagons and banana pentagons. The latter are thus structural elements of the S28-phase, while they are defects in the ss-phase. 

The overall appearance of the metadislocation resembles a dislocation in a simple metal but the differences are obvious the apparent extension of the strain field of the metadislocation is larger by more than one order of magnitude, and the associated phasons are not inserted hal lanes like those of an edge dislocation in a simple metal, but consist of a locally transformed area. Historically, the first observed metadislocations in E2s-Al-Pd-Mn were interpreted as defects in a structure of defects (Section 3.2) and were, therefore, termed metadislocations [1]. 

Engel and Trebin demonstrated [30] that all s-phases (referred to as H-phases in their paper) can be constructed by means of a projection formalism on the basis of a three-dimensional hyperspace. The result of the projection is a two-dimensional tiling in the (010) plane. These authors were able to reproduce the lattices of all E-phases and their structural defects of phasonic type, that is, phason lines and phason planes. 

In the following section, it is shown that metadislocations exist is a wide range of CMAs other than s-phases. To start with, we discuss metadislocations in monoclinic -phases. These are closely related to the orthorhombic s-phases, and so are their metadislocations. In Sections 6.2 and 6.3, we proceed to structures more distantly related, for which the existence of metadislocations was theoretically predicted [46]. We show that metadislocations indeed exist in these systems, albeit in a different form than expected. In particular, the associated defects are not phason planes but different types of planar fault, which leads to a more general view of the characteristic features of metadislocations. 

It is obvious that the core structure of the experimental [Figs 44(a) and 44(b)] and predicted [Fig. 42(d)] metadislocation are represented by the same tile. Hence they both have the same Burgers vector. However, they are connected to different types of planar defects. While the metadislocation in Fig. 42(d) is associated with six phason planes, the metadislocation in Fig. 44(b) is associated with a slab of R-phase. The phason elements on the left-hand side of the metadislocation core change the stacking sequence of the ideal T-phase structure A,B,A,B,A to a sequence A,A,A,B,B. These additional defects are required to accommodate the symmetrical metadislocation core into the structure and have to move along with the latter. In other words, the three phason lines act as escort defects to the metadislocation core, which move ahead and clear the way for the latter. Upon movement, the metadislocation locally transforms the T-phase structure, leaving a slab of modified R-phase in its wake. Different types of metadislocations in T- and R-phase structures and their modes of motion are discussed in Section 6.4. 

Fig. 44. Metadislocation in T-Al-Mn-Pd. (a) High-resolution HAADF micrograph. Dashed lines indicate the location of the slab of R-phase. The metadislocation core and three phason lines are highlighted, (b) Tiling representation of the defect...

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