Section 8. Surfaces and thin films Experimental evidence of the stability of net planes in decagonal quasicrystals Cynthia J. Jenks a, * , Jennifer Bjergaard a , Paul Canfield b , Amy R. Ross c , Walter Steurer d , Patricia A. Thiel a a Department of Chemistry, Ames Laboratory, Iowa State University, Ames, IA 50011-3020, USA b Department of Physics and Astronomy, Ames Laboratory, Iowa State University, Ames, IA 50011-3020, USA c Department of Materials Science and Engineering, Ames Laboratory, Iowa State University, Ames, IA 50011-3020, USA d Laboratory of Crystallography, ETH-Z€ urich, CH-8006 Z€ urich, Switzerland Abstract Because of the aperiodic nature of quasicrystals, lattice planes, in the traditional sense, do not exist for quasicrystals. For decagonal quasicrystals, it has been proposed, however, that one can link the aperiodic and periodic directions using what are termed net planes [Acta Crystallogr. A 57 (2001) 333]. These net planes are thought to play a critical role in the stability and growth of decagonal quasicrystals. To explore their potential role during growth and to shed light on their structural stability, we have studied single-grain surfaces of decagonal Al–Ni–Co by low energy electron diffraction and scanning tunneling microscopy. Our results suggest that these planes do indeed have special stability. Published by Elsevier B.V. PACS: 61.14.Hg; 61.44.Br; 68.37.Ef; 81.05.Bx 1. Introduction Quasicrystals may be structurally divided into three classifications: three-dimensional (aperiodic in three dimensions), two-dimensional (aperiodic in two dimen- sions and periodic in the third), or one-dimensional (aperiodic in one dimension and periodic in the other two). The focus of this paper is on two-dimensional quasicrystals, in particular, decagonal Al–Ni–Co. The structure of decagonal quasicrystals is often thought of as a periodic stacking of aperiodic planes. Quite com- monly, these planes are considered decoupled. However, Steurer and Cervellino recently introduced the notion that these planes may in fact be coupled [1]. They pro- posed that the aperiodic planes are coupled to the periodic axis via net planes [2]. Conceptually, net planes can be thought of as analogous to lattice planes for periodic crystals. Both types of planes, as will be dis- cussed, can be stacked such that they are inclusive of all atoms in the structure. Initial evidence for the existence of net planes came from examination of the growth morphology of Al–Ni– Co quasicrystals. As shown elsewhere, the ends of the needle-like crystals typically exhibit facets inclined to- wards the 10-fold axis [1]. That they are inclined towards the 10-fold axis suggests that the aperiodic planes and periodic planes must be linked. The facets, by the nature of their existence, must be formed by dense atomic layers. Examination of bulk structures of these materials shows identifiable planes with a high density of atoms; these planes are spaced aperiodically [3]. These planes themselves are not net planes, because aperiodically spaced planes cannot cut through the 10-fold axis peri- odically to ensure that, like lattice planes, all atoms in the structure are included. Net planes must be spaced periodically for decagonal quasicrystals to ensure that all atoms are incorporated. To overcome the dilemma of needing the planes to be periodically spaced, Steurer and coworkers, detail in previous work the concept of * Corresponding author. Tel.: +1-515 294 8486; fax: +1-515 294 4709. E-mail address: cjenks@iastate.edu (C.J. Jenks). 0022-3093/$ - see front matter Published by Elsevier B.V. doi:10.1016/j.jnoncrysol.2003.12.028 Journal of Non-Crystalline Solids 334&335 (2004) 486–490 www.elsevier.com/locate/jnoncrysol