FULL PAPER DOI:10.1002/ejic.201200780 Structure Determination of γ-Brass-Related Composite Structures in the Ni–Zn System: A Guided Tour by a (3+1)-Dimensional Space Description Partha Pratim Jana* [a] and Sven Lidin [a] Keywords: Intermetallic phases / Incommensurate phase / Zinc / Nickel / Structure elucidation / X-ray diffraction Three incommensurately modulated γ-brass-related compos- ite structures in the Ni–Zn system have been solved from X- ray single crystal diffraction data using a 3+1 dimensional super space description. The compounds at the end points of the compositional domain NiZn 3–δ (–0.09  δ  0.34) and NiZn 3.30 crystallize in the orthorhombic superspace group Introduction While formerly mostly considered for their mechanical properties, in recent years intermetallic compounds have been identified as a possible source for new electronic and catalytic materials. Intermetallic compounds now have broad industrial applications and a richly varied structural chemistry, electronic structure and physical properties. [1–6] The present work in the Ni–Zn system deserves chemical interest because of its catalytic selectivity and reactivity pro- file. Ni–Zn alloys have also been identified as the most via- ble nonprecious-metal catalysts. [7] Moreover zinc-rich alloys have been the topic of interest because of their complex phase relationship and intricacies of structures. The formation and stability of a large group of intermet- allic phases is controlled by the Hume-Rothery rule. [8–10] Hume-Rothery pointed out the importance of the e/a ratio in controlling the phase stability and the phase boundaries in brass-like alloys. According to Hume-Rothery, brass-like alloys occur at a certain ratio between the number of val- ence electrons and the total number of atoms (e/a). Alloys that obey such electron counting rules are known as Hume- Rothery alloys or electron compounds. This particular type of intermetallics is formed by noble metals and group 2, 12–15 elements. The γ phases that occur at valence-electron concentration (vec = e/a) values close to 21/13 presently at- tract attention because of their structural complexity and the understanding of the stabilization mechanism. [11,12] The γ-phase consists of a 26-atom γ cluster. The γ cluster is built up of four atomic shells: an inner tetrahedron (IT), an outer tetrahedron (OT), an octahedron (OH) and a distorted cu- [a] CAS Chemical Centre, Lund University, Getingevägen 60, Box 124, 22100 Lund, Sweden Fax: +46-46-222-40-12 E-mail: Partha.Jana@polymat.lth.se Homepage: http://www.polymat.lth.se/index.html Eur. J. Inorg. Chem. 2013, 91–98 © 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 91 Fmmm(α00)0s0 {F = [(1/2, 1/2, 0, 0); (1/2, 0, 1/2, 0); (0, 1/2, 1/2, 0)]} with the following fundamental cell dimensions a = 4.165(1) Å, b = 8.883(2) Å, c = 12.545(3) Å, q ≈ 0.6311a*; a = 4.161(2) Å, b = 8.876(3) Å, c = 12.535(4) Å, q ≈ 0.6314a* and a = 4.177(2) Å, b = 8.899(1) Å, c = 12.570(2) Å, q ≈ 0.6378a*. boctahedron (CO). It is also equivalently describable by dis- crete quadruples of distorted icosahedra about the IT atoms enclosing a common IT, also called a Pierce clus- ter. [13] A similar, yet expanded cluster, consisting of 34 atoms forms a quadruple of icosahedra about the OT atoms. Each of the four icosahedra shares one of its faces with an enclosed IT. Clusters of this size partially interpen- etrate. [14,15] Several variations of γ and γ-related structures have been reported to date. Among them, significantly more complex, modulated structures of some Cd-, [16] and Zn-rich phases [17] have recently been reported. Their lattice param- eters are metrically related according to a o = a c , b o = √2a c , co = 1/3na c with n = 5, 8, 13, 18, 21, 31 bearing a close resemblance to the respective cubic γ-brass-type phase with lattice parameter a c . [18,19] Morton was the first to find that the γ-brass regions of Ni–Zn, [20] Cu–Zn [21] and Pd–Zn [22] not only accommodate the γ-brass phase but are also structurally related, complex phase bundles with lower symmetry. The cubic Ni 4 Zn 22 [23] phase adopts the Hume-Rothery γ-brass structure with the lattice parameter, a ≈ 9.00 Å in the body centred cubic space group I4 ¯ 3m. Nover et al. found a superstructure in the Ni– Zn system i.e. NiZn 3 . The structure of NiZn 3 is closely re- lated to the γ-brass with a long axis along [110] with refer- ence to cubic Ni 4 Zn 22 and the long axis increases as the mol fraction of zinc approaches the value of the cubic γ- phase structure. [24] This finding has been corroborated by Morton (Figure 1). A single crystal structure of the NiZn 3 phase was first reported by Nover et al. [24] and re-examined by Thimmaiah and Harbrecht et al. [25] According to Nover et al., the structure crystallizes in the orthorhombic space group Abm2 with cell parameters: a1 = 33.326 Å, a2= 8.869 Å and a3 = 12.499 Å. A redetermination of the phase by Thimmaiah, Harbrecht et al. revealed that the γ-brass region in fact consists of three phases. These are given in