Materials Science and Engineering 294–296 (2000) 361–365 Structural modelling of the Ti–Zr–Ni quasicrystal R.G. Hennig a,∗ , E.H. Majzoub a , A.E. Carlsson a , K.F. Kelton a , C.L. Henley b , W.B. Yelon c , S. Misture d a Physics Department, Washington University, St. Louis, MO, USA b Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY, USA c Research Reactor, University of Missouri, Columbia, MO, USA d New York State College of Ceramics, Alfred, NY, USA Received 30 August 1999; accepted 11 November 1999 Abstract The atomic structure of the icosahedral Ti–Zr–Ni quasicrystal is studied using a canonical cell tiling approach. An investigation of the previously proposed structure for W-Ti–Zr–Ni, the 1/1 crystal approximant to the Ti–Zr–Ni icosahedral quasicrystal, has revealed improbable occupation of sites in the region between the Bergman clusters and at the cluster centre. The 1/1 structure is refined for a better-ordered sample of the approximant, using X-ray and neutron diffraction measurements and ab initio relaxation studies. Based on this refined structure, an atomic decoration model for large canonical cell tilings is developed. Calculated diffraction patterns from the generated structures are in reasonable agreement with those measured for the icosahedral quasicrystal. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Icosahedral quasicrystals; Atomic structure; Decoration model; Ab initio calculations; Ti–Zr–Ni alloys 1. Introduction Since the discovery of quasicrystals by Shechtman et al. [1], much effort has been spent in investigating their physical properties, and in particular, exploring the conditions under which nature prefers quasiperiodic to periodic order. Most work has concentrated on aluminium-based quasicrystals. Here, we consider Ti–Zr-based quasicrystals. As early as 1990, Molokanov and Chebotnikov [2] discovered a metastable icosahedral phase in Ti–Zr–Ni. In the following years further icosahedral phases in the alloys Ti–Zr–Fe [3] and Ti–Zr–Co [4] were found. In the Ti–Zr–Ni system, a thermodynamically stable phase has been discovered [5]. The icosahedral phases in these alloys are disordered with coherence lengths of less than 200 Å. Furthermore, the Ti–Zr-based quasicrystals are formed by rapid quenching or solid state reactions at temperatures of ≈ 600 ◦ C, gen- erally leading to a fine microstructure of quasicrystal and crystal phases. Therefore, an atomic structure determination by diffraction experiments is hardly possible. Consequently little is known about their atomic structure. There is a hope of obtaining information on the atomic arrangement in Ti–Zr-based quasicrystals by studying the ∗ Corresponding author. Tel.: +1-314-935-6379; fax: +1-314-935-6219. E-mail address: rhennig@hbar.wustl.edu (R.G. Hennig). structure of related periodic approximants. In the approxi- mants one is also confronted with the problem of random site occupation, but in these systems the distribution prob- abilities for the different atoms on the various sites may be determined by diffraction experiments. In this investigation, we consider the experimentally well-studied Ti–Zr–Ni system. There are several competing periodic phases known in the Ti–Zr–Ni phase diagram. Be- sides the binary phases -Ti–Zr, Ti 2 Ni and Zr 2 Ni, there are two ternary phases; a cubic Frank–Kasper type structure (W-phase) and a hexagonal Laves type phase. The addition of very small amounts of Pd to the W-phase and of Pb to the quasicrystal stabilises these structures [6]. Kim et al. [7] used X-ray and neutron powder diffractions to deter- mine the structure of the W-Ti–Zr–Ni phase, which can be interpreted as a Fibonacci 1/1 approximant of i-Ti–Zr–Ni. The chemical occupation of several sites of the determined structure seems problematic. The cluster centre is only partially occupied and Ni and Ti, despite their chemical differences, share sites. The experimental investigations raise three questions which will be considered in this work: (a) What is the atomic structure of the 1/1 approximant Ti–Zr–Ni? (b) How does Pd stabilise the 1/1 structure? (c) What are the struc- tural details of the quasicrystal? In this paper, we present a new structural analysis of the 1/1 approximant phase in 0921-5093/00/$ – see front matter © 2000 Elsevier Science B.V. All rights reserved. PII:S0921-5093(00)01084-4