Pentagonal–decagonal twins

Hahn, Th.; Klapper, H.

doi:10.1107/97809553602060000644

International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

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International Tables for Crystallography (2006). Vol. D. ch. 3.3, p. 408

Section 3.3.6.8. Pentagonal–decagonal twins

Th. Hahn^a ^* and H. Klapper^b

^a Institut für Kristallographie, Rheinisch–Westfälische Technische Hochschule, D-52056 Aachen, Germany, and ^bMineralogisch-Petrologisches Institut, Universität Bonn, D-53113 Bonn, Germany
Correspondence e-mail: hahn@xtal.rwth-aachen.de

3.3.6.8. Pentagonal–decagonal twins

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As was pointed out in Note (8) of Section 3.3.2.4 and in part (iii) of Section 3.3.4.4, there exist twin axes with noncrystallographic multiplicities [n = 5, 7, 8] etc. Twins with five- or tenfold rotations are frequent in intermetallic compounds. As an example, FeAl₄ is treated here (Ellner & Burkhardt, 1993; Ellner, 1995). This compound is orthorhombic, $[2/m\,2/m\,2/m]$ , with an axial ratio close to $[ c/a = \tan 72^\circ]$ , corresponding to a pseudo-fivefold axis along [[010]] and equivalent twin mirror planes [(101)] and $[({\bar 1}01)]$ , which are about 36° apart. In an ideal intergrowth, this leads to a cyclic pseudo-pentagonal or pseudo-decagonal sector twin (Fig. 3.3.6.8). All features of this twinning are analogous to those of pseudo-hexagonal aragonite, treated in Section 3.3.2.3.2, and of K₂SO₄, described above as Example 3.3.6.7.

Figure 3.3.6.8 | top | pdf |

Pentagonal–decagonal twins. (a) Decagonal twins in the shape of tenfold stars on the surface of a bulk alloy, formed during the solidification of a melt of composition Ru₈Ni₁₅Al₇₇. Scanning electron microscopy picture. Typical diameter of stars ca. 200 µm. The arms of the stars show parallel intergrowth. (b) Pentagonal twin aggregate of Fe₄Al₁₃ with morphology as grown in the orthorhombic high-temperature phase, showing several typical 72° angles between neighbouring twin partners (diameter of aggregate ca. 200 µm). Orthorhombic lattice parameters [a = 7.7510] , [b = 4.0336] , [c = 23.771] Å, space group [Bmmm] . The parameters c and a approximate the relation $[c/a = \tan 72^\circ]$ ; the pseudo-pentagonal twin axis is [010]. On cooling, the monoclinic low-temperature phase is obtained. The twin reflection planes in the orthorhombic unit cell are (101) and $[(10{\bar 1})]$ , in the monoclinic unit cell (100) and $[({\bar 2}01)]$ ; cf. Ellner & Burkhardt (1993, Fig. 10), Ellner (1995). Both parts courtesy of M. Ellner, Stuttgart.

The intersection symmetry of all twin partners is $[{\cal H}^\ast = 12/m1]$ ; the reduced composite symmetry $[{\cal K}^\ast]$ of a domain pair in contact is $[ 2'/m\,2/m\,2'/m]$ . The extended composite symmetry of the ideal pentagonal sector twin is $[{\cal K}(10)={\cal K}(5) = 10(2)/m\,2/m\,2/m]$ .

References

Ellner, M. (1995). Polymorphic phase transformation of Fe₄Al₁₃ causing multiple twinning with decagonal pseudo-symmetry. Acta Cryst. B51, 31–36.Google Scholar

Ellner, M. & Burkhardt, U. (1993). Zur Bildung von Drehmehrlingen mit pentagonaler Pseudosymmetrie beim Erstarrungsvorgang des Fe₄Al₁₃. J. Alloy. Compd. 198, 91–100.Google Scholar

International Tables for Crystallography (2006). Vol. D. ch. 3.3, p. 408