Section 3.3.10.6.5. Fivefold cyclic twins in nanocrystalline materials

Multiply twinned particles occur frequently in nanocrystalline (sphere-like or rod-shaped) particles and amorphous thin films (deposited on crystalline substrates) of cubic face-centred metals, diamond-type semiconductors (C, Si, Ge) and alloys. Hofmeister & Junghans (1993) and Hofmeister (1998) have carried out extensive HRTEM investigations of nanocrystalline Ge particles in amorphous Ge films. The particles reveal, among others, fivefold cyclic twins with coinciding (111) twin reflection planes and twin boundaries (spinel type). A typical example of a fivefold twin is presented in Fig. 3.3.10.11: The five different {111} twin boundaries are perpendicular to the image plane () and should theoretically form dihedral angles of 70.5° (supplement to the tetrahedral angle 109.5°), which would lead to an angular gap of about 7.5°. In reality, the five twin sectors are more or less distorted with angles ranging up to 76°. The stress due to the angular mismatch is often relaxed by defects such as stacking faults (marked by arrows in Fig. 3.3.10.11). The junction line of the five sectors can be considered as a pseudo-fivefold twin axis (similar to the pseudo-trigonal twin axis of aragonite, cf. Fig. 3.3.2.4; see also the fivefold twins in the alloy FeAl₄, described in Example 3.3.6.8 and Fig. 3.3.6.8).

Figure 3.3.10.11 | top | pdf | HRTEM micrograph of a fivefold-twinned Ge nanocrystal (right) in an amorphous Ge film formed by vapour deposition on an NaCl cleavage plane. Projection along a [] lattice row that is the junction of the five twin sectors; plane of the image: . The coinciding {111} twin reflection and composition planes (spinel law) are clearly visible. In one twin sector, two pairs of stacking faults (indicated by arrows) occur. They reduce the stress introduced by the angular misfit of the twin sectors. The atomic model (left) shows the structural details of the bulk and of one pair of stacking faults. Courtesy of H. Hofmeister, Halle; cf. Hofmeister & Junghans (1993); Hofmeister (1998).

For the formation of fivefold twins, different mechanisms have been suggested by Hofmeister (1998): nucleation of noncrystallographic clusters, which during subsequent growth collapse into cyclic twins; successive growth twinning on alternate cozonal (111) twin planes; and deformation twinning (cf. Section 3.3.7).

The fivefold multiple twins provide an instructive example of a twin texture, a subject which is treated in the following section.