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Papers by Sofia Deloudi

Research paper thumbnail of Crystallography of Quasicrystals. By Walter Steurer and Sofia Deloudi. Springer Series in Materials Sciences No. 126. Springer, 2009. Pp. xiv + 384. Price (hardback) EUR 128.35. ISBN 978-3-642-01898-5, e-ISBN 978-3-642-01899-2, doi 10.1007/978-3-642-01899-2

Acta Crystallographica Section A, 2010

Research paper thumbnail of Structure Analysis

Quantitative structure analysis still means structure analysis based on methods such as X-ray, ne... more Quantitative structure analysis still means structure analysis based on methods such as X-ray, neutron and, to some extent, electron diffraction. Such a structure analysis consists of three main parts, data collection, structure solution, and structure refinement. Features, which peculiar for quasicrystals have to be considered for all three parts. The most important issues are the lack of periodicity and the consequently densely distributed set of Bragg reflections. A general strategy is presented for single-crystal X-ray diffraction-based structure analysis of quasicrystals. The power and limits are discussed of methods such as low-density elimination, charge flipping and entropy maximization. General guidelines are presented for the publication of structural data.

Research paper thumbnail of Structures with 3D Quasiperiodicity

Quasicrystals with icosahedral diffraction symmetry are called icosahedral quasicrystals. Their s... more Quasicrystals with icosahedral diffraction symmetry are called icosahedral quasicrystals. Their structures are quasiperiodic in all three dimensions. There are no 3D quasicrystals known with other than icosahedral noncrystallographic point symmetry. The three different structure types are discussed, i.e., structures based on Mackay-icosahedra, Bergmann clusters, and Tsai-clusters. Examples of the respective approximants are shown in detail. The structure of icosahedral Al–Cu–Fe is treated in physical space as well as its embedding in 6D space.

Research paper thumbnail of Periodic average structures in phononic quasicrystals

Philosophical Magazine, 2007

ABSTRACT Periodic average structures for the pentagonal, heptagonal, octagonal and dodecagonal ti... more ABSTRACT Periodic average structures for the pentagonal, heptagonal, octagonal and dodecagonal tilings were constructed and used for the interpretation of transmission spectra of corresponding two-dimensional phononic quasicrystals (QPNCs). In the hard scattering regime of steel rods in water, the transmission behaviour of QPNCs resembles that of disordered periodic phononic crystals. The average structures allow prediction of position and width of the first bandgap. Additionally, the type of deviation of the quasiperiodic from its periodic average structure is shown to support the understanding of the shape of the transmission spectra and may assist the choice of an optimal structure for specific phononic crystal applications.

Research paper thumbnail of High-resolution scanning tunneling microscopy investigation of the (12110) and (10000) two-fold symmetric d AlNiCo quasicrystalline surfaces

Research paper thumbnail of 5-D modeling of the Co-rich decagonal Al-Co-Ni quasicrystal

Acta Crystallographica Section A, 2005

Research paper thumbnail of Multiple diffraction in an icosahedral Al-Cu-Fe quasicrystal

Philosophical Magazine, 2011

Research paper thumbnail of Higher-Dimensional Approach

The nD approach elegantly restores hidden symmetries and correlations of quasiperiodic structures... more The nD approach elegantly restores hidden symmetries and correlations of quasiperiodic structures. Since it is based on reciprocal space information, it is directly accessible from experimental diffraction data. nD crystallography is an extension of the well-developed 3D crystallography and many well-established powerful 3D methods can be adapted for nD structure analysis. The nD approach is also a prerequisite for understanding phason modes and the structural relationships between quasicrystals and their approximants. In this chapter, the nD embedding will be quantitatively and detailed discussed of 1D, 2D, and 3D quasiperiodic tilings, which have been presented in Chap. 1, on tilings and coverings. In all cases, the direct and reciprocal space symmetry as well as the periodic average structures are treated as well.

Research paper thumbnail of Ab initio structure solution by iterative phase-retrieval methods: performance tests on charge flipping and low-density elimination

Journal of Applied Crystallography, 2010

Research paper thumbnail of Reciprocal-space imaging of a real quasicrystal. A feasibility study with PILATUS 6M

Journal of Applied Crystallography, 2008

Research paper thumbnail of Colloidal quasicrystals with 12-fold and 18-fold diffraction symmetry

Proceedings of The National Academy of Sciences, 2011

Research paper thumbnail of Bulk and surface structure of the clean and adsorbate-covered decagonal Al Co Ni quasicrystal

Journal of Physics-condensed Matter, 2008

Research paper thumbnail of Tilings and Coverings

Tilings fill space without gaps and overlaps, they can be periodic, quasiperiodic or nonperiodic.... more Tilings fill space without gaps and overlaps, they can be periodic, quasiperiodic or nonperiodic. If decorated with atoms or larger atomic arrangements, tilings can serve as models for quasiperiodic structures. One-, two-, and three-dimensional examples will be discussed in detail. Beside substitutional sequences such as the Fibonacci and Octonacci sequences, also sequences with almost continuous and singular continuous spectra will be discussed. The tilings underlying really existing quasicrystals with 5-, 8-, 10-, 12-, and 14-fold symmetry or their approximants are treated in detail. Finally, the three-dimensional Penrose tiling is dealt with as example for the quasilattice of icosahedral quasicrystals. Furthermore, coverings will be discussed, which are important for understanding the geometry of cluster structures. Contrary to packings and tilings, coverings fill the space without gaps but with partial overlaps. There is always a one-to-one correspondence between coverings and tilings.

Research paper thumbnail of Generalized Quasiperiodic Structures

This chapter is dedicated to the discussion of soft polymeric quasicrystals, which show dodecagon... more This chapter is dedicated to the discussion of soft polymeric quasicrystals, which show dodecagonal symmetry, as well as photonic and phononic quasicrystals. On the example of transmission spectra, the characteristic features of one-, two- and three-dimensional phononic quasicrystals are illustrated. The high-symmetry of particular quasicrystals makes omnidirectional band-gaps possible even in low-contrast materials. The structures used for that purpose are the Fibonacci sequence, the octagonal tiling and the Ammann tiling. The consequences of soft and hard contrast as well as the role of resonant and Bragg scattering are discussed.

Research paper thumbnail of 5D Modelling of decagonal Al--Co--Ni based on the W-approximant

Philosophical Magazine, 2006

ABSTRACT A structure model for decagonal Al–Co–Ni with 8 Å periodicity along the decagonal axis i... more ABSTRACT A structure model for decagonal Al–Co–Ni with 8 Å periodicity along the decagonal axis is proposed. The model agrees well with available experimental information, such as electron microscopic images and three-dimensional (3D) Patterson maps calculated from X-ray-diffraction data. The model is based on a novel columnar cluster with 20 Å diameter and symmetry 5/mm building the W-approximant, Al72.5Co20Ni7.5. The proposed cluster also allows modelling of the various types of disorder and superstructures found in decagonal Al–Co–Ni.

Research paper thumbnail of Phase Formation and Stability

Locally similar icosahedral structural ordering between parent phase and nucleating phase is beli... more Locally similar icosahedral structural ordering between parent phase and nucleating phase is believed to be responsible for the frequently occurring formation of icosahedral quasicrystals from undercooled liquid alloys or during devitrification of metallic glasses. Microscopic mechanisms for the formation and stabilization of quasicrystals are discussed, with emphasis on the role of clusters. The different types of experimentally observed phase transitions will be discussed, from amorphous to quasicrystalline, quasicrystalline to ordered/disordered quasicrystalline, and quasicrystalline to crystalline as a function of temperature, pressure, irradiation, and high-energy ball milling, respectively.

Research paper thumbnail of A high-pressure study of Co-rich decagonal Al-Co-Ni and its approximant, the W phase

Philosophical Magazine, 2007

The stability of Co-rich decagonal Al–Co–Ni and its closely related approximant phase, W-Al–Co–Ni... more The stability of Co-rich decagonal Al–Co–Ni and its closely related approximant phase, W-Al–Co–Ni, was studied in situ using powder diffraction and synchrotron radiation at high pressures up to 61.4(1) GPa (d-Al–Co–Ni) and 50.6(2) GPa (W-Al–Co–Ni), respectively. Within the experimental errors, both compounds show comparable values of the bulk modulus, i.e. K0=120(11) GPa for the quasicrystal and K0=138(11) GPa for its approximant phase, respectively. Both phases were found to be stable within the framework of the experiment. The results indicate that the local structure dominates the bulk property and the type of long-range order has only a minor influence.

Research paper thumbnail of Twofold surface of the decagonal Al-Cu-Co quasicrystal

Research paper thumbnail of Fascinating quasicrystals

Acta Crystallographica Section A, 2008

Research paper thumbnail of Structures with 2D Quasiperiodicity

Axial quasicrystals have just one special axis N with multiplicity n larger than two. Along this ... more Axial quasicrystals have just one special axis N with multiplicity n larger than two. Along this axis they show a periodic sequence of atomic layers, which are ordered quasiperiodically in two dimensions. Theoretically, n could be any integer number, there are no principal geometrical restrictions. However, all stable axial quasicrystals known so far show 5- or 10-fold symmetry only. This is not too surprising since icosahedral coordination is the most frequent atomic environment type (AET) in intermetallic phases. However, since icosahedra cannot be packed without gaps, they are distorted and/or mixed with other AET. There are a few reports on quasicrystals with 8- or 12-fold symmetry. However, these quasiperiodic phases are either metastable or of poor quality. Not a single quasicrystal with any other noncrystallographic symmetry has ever been reported. We present a general overview of the axial quasicrystals found so far and discuss the structures of d-Al–Co–Cu and d-Al–Co–Ni in detail.

Research paper thumbnail of Crystallography of Quasicrystals. By Walter Steurer and Sofia Deloudi. Springer Series in Materials Sciences No. 126. Springer, 2009. Pp. xiv + 384. Price (hardback) EUR 128.35. ISBN 978-3-642-01898-5, e-ISBN 978-3-642-01899-2, doi 10.1007/978-3-642-01899-2

Acta Crystallographica Section A, 2010

Research paper thumbnail of Structure Analysis

Quantitative structure analysis still means structure analysis based on methods such as X-ray, ne... more Quantitative structure analysis still means structure analysis based on methods such as X-ray, neutron and, to some extent, electron diffraction. Such a structure analysis consists of three main parts, data collection, structure solution, and structure refinement. Features, which peculiar for quasicrystals have to be considered for all three parts. The most important issues are the lack of periodicity and the consequently densely distributed set of Bragg reflections. A general strategy is presented for single-crystal X-ray diffraction-based structure analysis of quasicrystals. The power and limits are discussed of methods such as low-density elimination, charge flipping and entropy maximization. General guidelines are presented for the publication of structural data.

Research paper thumbnail of Structures with 3D Quasiperiodicity

Quasicrystals with icosahedral diffraction symmetry are called icosahedral quasicrystals. Their s... more Quasicrystals with icosahedral diffraction symmetry are called icosahedral quasicrystals. Their structures are quasiperiodic in all three dimensions. There are no 3D quasicrystals known with other than icosahedral noncrystallographic point symmetry. The three different structure types are discussed, i.e., structures based on Mackay-icosahedra, Bergmann clusters, and Tsai-clusters. Examples of the respective approximants are shown in detail. The structure of icosahedral Al–Cu–Fe is treated in physical space as well as its embedding in 6D space.

Research paper thumbnail of Periodic average structures in phononic quasicrystals

Philosophical Magazine, 2007

ABSTRACT Periodic average structures for the pentagonal, heptagonal, octagonal and dodecagonal ti... more ABSTRACT Periodic average structures for the pentagonal, heptagonal, octagonal and dodecagonal tilings were constructed and used for the interpretation of transmission spectra of corresponding two-dimensional phononic quasicrystals (QPNCs). In the hard scattering regime of steel rods in water, the transmission behaviour of QPNCs resembles that of disordered periodic phononic crystals. The average structures allow prediction of position and width of the first bandgap. Additionally, the type of deviation of the quasiperiodic from its periodic average structure is shown to support the understanding of the shape of the transmission spectra and may assist the choice of an optimal structure for specific phononic crystal applications.

Research paper thumbnail of High-resolution scanning tunneling microscopy investigation of the (12110) and (10000) two-fold symmetric d AlNiCo quasicrystalline surfaces

Research paper thumbnail of 5-D modeling of the Co-rich decagonal Al-Co-Ni quasicrystal

Acta Crystallographica Section A, 2005

Research paper thumbnail of Multiple diffraction in an icosahedral Al-Cu-Fe quasicrystal

Philosophical Magazine, 2011

Research paper thumbnail of Higher-Dimensional Approach

The nD approach elegantly restores hidden symmetries and correlations of quasiperiodic structures... more The nD approach elegantly restores hidden symmetries and correlations of quasiperiodic structures. Since it is based on reciprocal space information, it is directly accessible from experimental diffraction data. nD crystallography is an extension of the well-developed 3D crystallography and many well-established powerful 3D methods can be adapted for nD structure analysis. The nD approach is also a prerequisite for understanding phason modes and the structural relationships between quasicrystals and their approximants. In this chapter, the nD embedding will be quantitatively and detailed discussed of 1D, 2D, and 3D quasiperiodic tilings, which have been presented in Chap. 1, on tilings and coverings. In all cases, the direct and reciprocal space symmetry as well as the periodic average structures are treated as well.

Research paper thumbnail of Ab initio structure solution by iterative phase-retrieval methods: performance tests on charge flipping and low-density elimination

Journal of Applied Crystallography, 2010

Research paper thumbnail of Reciprocal-space imaging of a real quasicrystal. A feasibility study with PILATUS 6M

Journal of Applied Crystallography, 2008

Research paper thumbnail of Colloidal quasicrystals with 12-fold and 18-fold diffraction symmetry

Proceedings of The National Academy of Sciences, 2011

Research paper thumbnail of Bulk and surface structure of the clean and adsorbate-covered decagonal Al Co Ni quasicrystal

Journal of Physics-condensed Matter, 2008

Research paper thumbnail of Tilings and Coverings

Tilings fill space without gaps and overlaps, they can be periodic, quasiperiodic or nonperiodic.... more Tilings fill space without gaps and overlaps, they can be periodic, quasiperiodic or nonperiodic. If decorated with atoms or larger atomic arrangements, tilings can serve as models for quasiperiodic structures. One-, two-, and three-dimensional examples will be discussed in detail. Beside substitutional sequences such as the Fibonacci and Octonacci sequences, also sequences with almost continuous and singular continuous spectra will be discussed. The tilings underlying really existing quasicrystals with 5-, 8-, 10-, 12-, and 14-fold symmetry or their approximants are treated in detail. Finally, the three-dimensional Penrose tiling is dealt with as example for the quasilattice of icosahedral quasicrystals. Furthermore, coverings will be discussed, which are important for understanding the geometry of cluster structures. Contrary to packings and tilings, coverings fill the space without gaps but with partial overlaps. There is always a one-to-one correspondence between coverings and tilings.

Research paper thumbnail of Generalized Quasiperiodic Structures

This chapter is dedicated to the discussion of soft polymeric quasicrystals, which show dodecagon... more This chapter is dedicated to the discussion of soft polymeric quasicrystals, which show dodecagonal symmetry, as well as photonic and phononic quasicrystals. On the example of transmission spectra, the characteristic features of one-, two- and three-dimensional phononic quasicrystals are illustrated. The high-symmetry of particular quasicrystals makes omnidirectional band-gaps possible even in low-contrast materials. The structures used for that purpose are the Fibonacci sequence, the octagonal tiling and the Ammann tiling. The consequences of soft and hard contrast as well as the role of resonant and Bragg scattering are discussed.

Research paper thumbnail of 5D Modelling of decagonal Al--Co--Ni based on the W-approximant

Philosophical Magazine, 2006

ABSTRACT A structure model for decagonal Al–Co–Ni with 8 Å periodicity along the decagonal axis i... more ABSTRACT A structure model for decagonal Al–Co–Ni with 8 Å periodicity along the decagonal axis is proposed. The model agrees well with available experimental information, such as electron microscopic images and three-dimensional (3D) Patterson maps calculated from X-ray-diffraction data. The model is based on a novel columnar cluster with 20 Å diameter and symmetry 5/mm building the W-approximant, Al72.5Co20Ni7.5. The proposed cluster also allows modelling of the various types of disorder and superstructures found in decagonal Al–Co–Ni.

Research paper thumbnail of Phase Formation and Stability

Locally similar icosahedral structural ordering between parent phase and nucleating phase is beli... more Locally similar icosahedral structural ordering between parent phase and nucleating phase is believed to be responsible for the frequently occurring formation of icosahedral quasicrystals from undercooled liquid alloys or during devitrification of metallic glasses. Microscopic mechanisms for the formation and stabilization of quasicrystals are discussed, with emphasis on the role of clusters. The different types of experimentally observed phase transitions will be discussed, from amorphous to quasicrystalline, quasicrystalline to ordered/disordered quasicrystalline, and quasicrystalline to crystalline as a function of temperature, pressure, irradiation, and high-energy ball milling, respectively.

Research paper thumbnail of A high-pressure study of Co-rich decagonal Al-Co-Ni and its approximant, the W phase

Philosophical Magazine, 2007

The stability of Co-rich decagonal Al–Co–Ni and its closely related approximant phase, W-Al–Co–Ni... more The stability of Co-rich decagonal Al–Co–Ni and its closely related approximant phase, W-Al–Co–Ni, was studied in situ using powder diffraction and synchrotron radiation at high pressures up to 61.4(1) GPa (d-Al–Co–Ni) and 50.6(2) GPa (W-Al–Co–Ni), respectively. Within the experimental errors, both compounds show comparable values of the bulk modulus, i.e. K0=120(11) GPa for the quasicrystal and K0=138(11) GPa for its approximant phase, respectively. Both phases were found to be stable within the framework of the experiment. The results indicate that the local structure dominates the bulk property and the type of long-range order has only a minor influence.

Research paper thumbnail of Twofold surface of the decagonal Al-Cu-Co quasicrystal

Research paper thumbnail of Fascinating quasicrystals

Acta Crystallographica Section A, 2008

Research paper thumbnail of Structures with 2D Quasiperiodicity

Axial quasicrystals have just one special axis N with multiplicity n larger than two. Along this ... more Axial quasicrystals have just one special axis N with multiplicity n larger than two. Along this axis they show a periodic sequence of atomic layers, which are ordered quasiperiodically in two dimensions. Theoretically, n could be any integer number, there are no principal geometrical restrictions. However, all stable axial quasicrystals known so far show 5- or 10-fold symmetry only. This is not too surprising since icosahedral coordination is the most frequent atomic environment type (AET) in intermetallic phases. However, since icosahedra cannot be packed without gaps, they are distorted and/or mixed with other AET. There are a few reports on quasicrystals with 8- or 12-fold symmetry. However, these quasiperiodic phases are either metastable or of poor quality. Not a single quasicrystal with any other noncrystallographic symmetry has ever been reported. We present a general overview of the axial quasicrystals found so far and discuss the structures of d-Al–Co–Cu and d-Al–Co–Ni in detail.