Quasicrystals and their approximants

Sven Hovmöller and Xiaodong Zou and Linus Hovmöller Zou

The Nobel Prize in chemistry 2011 was awarded to Daniel Shechtman for his discovery of quasicrystals; an AlMn alloy having 5-fold symmetry.

Quasicrystals (QC) containing the "forbidden" 5-, 8-, 10- and 12-fold symmetries present a great challenge to the structural chemist. Different approaches may be used to solve such structures. We have used X-ray crystallography, electron microscopy and electron diffraction data combined with crystallographic image processing for solving approximants to 10- and 12-fold QC. We have also constructed a model for an 8-fold quasi-crystal.
Approximants are chemically and structurally closely related to quasicrystals. They are very complicated but have true classical crystal structures.
    This work started as a collaboration with Prof. Kehsin Kuo’s group in the Beijing Laboratory of Electron Microscopy (BLEM), Chinese Academy of Sciences.


Hovmöller, Sven, Zou,Xiaodong, Hovmöller Zou, Linus, Grushko, Benjamin,m Structures of pseudo decagonal approximants in Al-Co-Ni. Phil Trans Roy Soc A 28 (2012) 2949-2958.

This paper has my and Xiaodong Zou's son Linus Hovmöller Zou as a co-author. Linus was only 10 years old when he helped to solve four quasicrystal approximant structures in June 2011. This became a great event in media. Perhaps Linus is the youngest ever to co-author a scientific paper, at least in this journal, which is the oldest scientific journal in the world (founded 1660). Linus was interviewed by BBC, The Times, New Scientist and was quoted in hundreds of newspapers in Sweden and around the world.

Li,M.R., Sun,J.L., Hovmöller,S., Zou,X.D., Oleynikov, P. and Grushko,B. A complicated quasicrystal approximant epsilon16 solved by the strong reflections approach. Acta Cryst. B66 (2010) 17-26.

Li,M.R., Hovmöller,S., Sun,J.L. and Kuo,K.H. Crystal structure of the 2/1 cubic approximant Ag42In42Yb16. Journal of Alloys and Compounds 465 (2008) 132-138.

Zhang,H., Wang,S.J., Wang,S.C., Li,Z.C., Hovmöller,S. and Zou,X.D. “A Structure Model for tau2-Al13Co4 deduced by the strong reflections approach” J. Computational and Theoretical Nanoscience, 5 (2008) 1735-1737.

Zhang,H., He,Z.B.,Oleynikov,P., Zou,X.D.,Hovmöller,S. and Kuo,K.H. Structure model for the tau(mu) phase in Al-Cr-Si alloys deduced from the lambda phase by the strong-reflections approach. Acta Cryst. B62 (2006) 16-25.

Oleynikov,P., Demchenko,L., Christensen,J.,Hovmöller,S., Yokosawa,T., Döblinger,M., Gruschko,B. and Zou,X.D., Structures of the pseudodecagonal Al-Co-Ni approximant PD4. Philosophical Magazine 86 (2006) 457-462.

Zhang,H., Zou,X.D., Oleynikov,P. and Hovmöller,S. Structures relations in real and reciprocal space of hexagonal phases related to i-ZnMgRE quasicrystals. Philosophical Magazine 86 (2005) 543-548.

Christensen,J., Oleynikov,P., Hovmöller,S. and Zou,X.D. Solving Approximant Structures Using a "Strong Reflection" Approach. Ferroelectrics 305 (2004) 273-277.

Zou,X.D, Mo,Z.M., Hovmöller,S., Li, X.Z. and Kuo,K. Three dimensional reconstruction of the v-AlCrFe phase by electron crystallography. Acta Cryst.A59 (2003) 526-539.

Boström,M and Hovmöller,S. Preparation and Crystal Structure of the Novel Decagonal Approximant Mn127Ga133 J. Alloys and Compounds. 314 (2001) 154-159.

Boström,M and Hovmöller,S.A pentagonal cluster in certain approximants to decagonal quasicrystals Acta Cryst B57 (2001) 646-651.

Boström,M. and Hovmöller,S. Preparation and Crystal Structure of the Pseudo Decagonal Approximant Ga5Mn3 J. Solid State Chem. 153 (2000) 398-403.

Sui,H.X., Liao,X.Z., Kuo,K.H. Zou,X.D. and Hovmöller,S. Structural model of the non-Fibonacci approximant in the Al12Fe2Cr alloy. Acta Cryst. B53 (1997) 587-595.

Jiang,J.C., Hovmöller,S. and Zou,X.D. A three-dimensional structure model of eight-fold quasicrystals obtained by high-resolution electron microscopy Phil.Mag.Lett. 71 (1995) 123-129.

Wang,D.N., Ishimasa,T., Nissen,H.U., Hovmöller ,S. and Rhyner,J. Dislocations, Domains and Quenched Phonon and Phason Strains in Al-Mn Quasicrystals Observed by Electon Microcsopy. Philosophical Magazine (1988) 58, 737-752.