J. Appl. Cryst. (1999). 32, 417±420 The structure of approximant l-Al 4 Mn interpreted as a modulated crystal Masaya Uchida a,b * and Shigeo Horiuchi a a National Institute for Research in Inorganic Materials, Tsukuba, Ibaraki 305-0044, Japan, and b High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan (Received 20 May 1998; accepted 24 November 1998 ) Abstract The structure of the -Al 4 Mn phase, which is an approximant of icosahedral and decagonal quasicrystals, is interpreted as a modulated crystal structure. It basically comprises modulated layers, in which the ordering of atomic vacancies takes place in the close- packed layers. The modulation is considered to be due to the rearrangement of atomic vacancies as a response to the occurrence of charge-density waves. 1. Introduction Since the discovery of icosahedral Al±Mn quasicrystals in 1984 (Shechtman et al., 1984), much attention has been focused on approximants related to icosahedral or decagonal quasicrystals (Bendersky, 1987; Shoemaker et al., 1989; Le Lann & Shoemaker, 1993; Kreiner & Franzen, 1995). Their structures are periodic and locally similar to those of quasicrystals. Their electron diffrac- tion patterns (EDPs) are very similar to those of quasicrystals. The approximants have played important roles in understanding the atomic arrangements in quasicrystals. The -Al 4 Mn phase is one of the approximants in the Al±Mn system and has a composition close to those of icosahedral and decagonal quasicrystals (Bendersky, 1987; Shoemaker et al., 1989; Le Lann & Shoemaker, 1993). It gives EDPs similar to those of icosahedral and decagonal quasicrystals (Bendersky, 1987), and its structure with a large hexagonal unit cell (P6 3 /mmc, a = 19.98, c = 24.673 A Ê ) has been determined by Shoe- maker et al. (1989); they used it to deduce structure models of the icosahedral quasicrystal in the Al±Mn system (Le Lann & Shoemaker, 1993). Kreiner & Franzen (1995) have described the structure of the -Al 4 Mn phase based on the cluster concept. In the present paper we try to describe the structure of the -Al 4 Mn phase in a way similar to that used in our previous study (Uchida & Horiuchi, 1998) in which we analysed a dodecagonal quasicrystal as a modulated crystal. That is to say, we interpret it from the viewpoint of the modulated crystal. 2. Description of the layer structure The structure of the -Al 4 Mn phase is formed by hexagonal layers stacked perpendicularly to the c axis (Shoemaker et al., 1989; Kreiner & Franzen, 1995). The a and b axes are nearly parallel to the pseudo-®vefold axes (Bendersky, 1987). Fig. 1 shows the projection of the structure along the pseudo-®vefold [100] axis. The unit cell contains 12 layers of two different kinds, i.e. ¯at layers (F layers) and puckered layers (P layers), which are stacked in the order PFPPFPPFPPFP. The F layers are located on the mirror plane at z = 1/4 and 3/4, and on the pseudo-mirror plane at z = 0 and 1/2, while the P layers are located above and below the F layers. By stacking three layers (PFP), a periodic arrangement of deformed decagons of atoms is formed, as indicated by circles in Fig. 1, where solid circles represent atoms in the F layers, and open and grey circles represent atoms in the P layers, respectively. This means that the stacking arrangements of F and P layers are important in 417 # 1999 International Union of Crystallography Journal of Applied Crystallography Printed in Great Britain ± all rights reserved ISSN 0021-8898 # 1999 Fig. 1. Projection of the structure of -Al 4 Mn along the pseudo- ®vefold [100] axis. There are 12 layers of F and P type along the [001] direction. The solid circles represent atoms in the F layers. The open and grey circles represent atoms in the puckered A and B layers, respectively.