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The 13^th International Conference on Quasicrystals (ICQ13) was held in Kathmandu, Nepal, from 18^th to 23^rd September 2016. This episode of a series of conferences on quasicrystals followed twelve previous successful meetings. The first event, the "International Workshop on Aperiodic Crystals", was held in Les Houches, France in 1986, which was followed by the "International Workshop on Quasicrystals" in Beijing, China in 1987 and the "International Meeting on Quasicrystals" in Vista-Hermosa, Mexico in 1989. Thereafter, a series of "International Conference on Quasicrystals" took place respectively in St. Louis, Missouri, USA in 1992 (ICQ4), Avignon, France in 1995 (ICQ5), Tokyo, Japan in 1997 (ICQ6), Stuttgart, Germany in 1999 (ICQ7), Bangalore, India in 2002 (ICQ8), Ames, Iowa, USA in 2005 (ICQ9), Zürich, Switzerland in 2008 (ICQ10), Sapporo, Japan in 2011 (ICQ11) and Cracow, Poland in 2013 (ICQ12).

The conference covered a wide range of topics on quasicrystals: formation, growth, and phase stability; structure and modeling; mathematics of quasiperiodic and aperiodic structures; transport, mechanical and magnetic properties; and finally, surfaces and overlayer structures. In addition, other aspects of material science such as metamaterials, polymer science, metallic glasses, and metallic alloys were discussed. The conference also reviewed the state-of -art of quasicrystal research and its future direction.

ICQ13 was attended by 98 researchers from 22 countries, including 26 PhD or master students. There were 13 invited talks (including a public lecture by the 2011 Nobel Laureate in Chemistry, Prof. Dan Shechtman), 3 tutorial lectures, 50 contributed talks and 36 poster presentations. The conference was truly interdisciplinary - comprising of theoretical and experimental physicists, chemists, material scientists, and mathematicians.

The proceedings of the conference are published as open access in the Institute of Physics Conference Series. The papers have been reviewed in the regular refereeing process. Among 35 proceedings received, 30 have been accepted for the publication.

The conference itself was held at the Dhulikhel Lodge Resort. The public lecture was organised at the central campus of Trubhuvan University in Kirtipur, hosted jointly by the Nepal Physical Society and the Central Department of Physics, while the tutorial lectures were held at Kathmandu University. These two events were open to local researchers and students. A special ceremony was organised for the inauguration of ICQ13, which was addressed and attended by the vice-chancellors of Tribhuvan University, Kathmandu University, Nepal Academy of Science and Technology (NAST), and representatives of various professional organisations, including the Nepal Government.

The Jean-Marie Dubois Award for Excellence in Quasicrystals (2016) was presented to Dr. Marek Mihalkovič at ICQ13, for the theoretical work that has enabled and demonstrated the simulation of thermodynamic and dynamic properties of quasicrystals - based on realistic atomic-scale models and energetics. The Jean-Marie Dubois Award was established to recognize important, sustained research on any aspect of quasicrystals in the last 10-year period preceding the award. The prizes for best student presentation were awarded to Ito Natsu from Toyo University of Science, Japan for her paper titled "Synthesis and magnetic properties of the Au-Al-Yb approximant" and Nicolas Macé from Université Paris-Saclay, France for his paper titled "Gap structure and topological indices on the Fibonacci quasicrystal".

We gratefully acknowledge the generous financial support for ICQ13 from the International Union of Crystallography (IUCr), the European Integrated Center for the Development of New Metallic Alloys and Compounds (C-MAC), the International Centre for Diffraction Data (ICDD), Rigaku Oxford Diffraction, Embassy of Israel Kathmandu, Deutsch-Nepalische Gesellschaft, TBI Group, Phul Kumari Mahato Memorial Trust, Nepal Science Foundation Trust, Holy-Cow, officials of Non-Resident Nepali Association (NRNA) and NRNA-Australia.

We would like to express our sincere thanks to the members of the Organising Committee, Program Committee and International Advisory Board, invited speakers, session chairs, editorial board members and reviewers of the conference proceedings and all others for their support and involvement in the conference.

Last, but not least, we would like to thank the Local Organisation Committee of ICQ13 - chaired by Prof. Narayan Prasad Adhikari - for the efforts that made the conference so successful. We would also like to express our gratitude for the support we received from the University of Liverpool, UK, Tohoku University, Japan and Tribhuvan University, Nepal.

We hope that the conference helped to promote the struggling tourism sector of Nepal, after the country was hit by devastating earthquakes in 2015. We thank the Nepal Tourism Board, Atithi Devo Bhava, Chandragiri Cable Car and Cultural Bands to help ICQ13 participants explore the culture, history and natural beauty of the Himalayan country Nepal during their stay.

The 14^th International Conference on Quasicrystals (ICQ14) will be held on 26 - 31 May 2019 in Bled, Slovenia.

Thank you.

Conference Chairs,

Dr Hem Raj Sharma (the University of Liverpool, UK)

Prof An Pang Tsai, Tohoku University, Japan

31^st January 2017

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

Where are we now in quasicrystal (QC) research more than three decades after Dan Shechtman's discovery? Do we fully understand the origin of quasiperiodicity, the formation, growth, thermodynamic stability, structure and properties of quasicrystals? First, I will shortly present the status quo, then I will address the still open questions, and identify potential focus areas for future research. Because of the limited space, I will focus on decagonal quasicrystals (DQCs); the status quo for research on icosahedral quasicrystals (IQCs) is comparable.

The shapes of the occupation domains that correspond to the respective local environments of the clusters within a 12-fold packing model of icosahedral quasicrystals (iQCs) have been derived for the first time. The frequencies of appearance of the local environments of the clusters have also been calculated based on the exact volumes. The present results validate the frequencies obtained by a previous study using a statistical approach. Application of the 12-fold packing model to the F-type Al-based iQCs is discussed briefly.

We investigate the origin of the 18-fold symmetry in quasicrystals. We perform Monte Carlo simulations of 2D disks interacting with the hard-core/square-shoulder potential, and we analyze the bond-orientational order and the local vertex configurations. We find that the so-called special clusters of particles play a crucial role in the mixing of the three sets of bond directions 20° apart, producing the 18-fold diffraction pattern.

χ-AlNiRu (H-AlNiRu), as determined by single crystal X-ray diffraction, crystallizes in the trigonal space group, P31c (No.159), with unit cell parameters of a = 1.2095(1) nm, c = 2.6879(1) nm, and V = 3.4056(3) nm³, and atoms/cell = 208.6. The refinement converged with R(F) = 0.087 for 3915 observed reflections measured using Mo Kα radiation (λ = 0.071073 nm). The structure of χ-AlNiRu is similar to that of χ-AlPdRe, wherein pseudo-Mackay type clusters are formed by the disordered distribution of Al in the heavy metal framework.

The short- and medium-range ordering structure in Zr₈₀Pt₂₀ amorphous alloy has been investigated by anomalous X-ray scattering coupled with reverse Monte-Carlo simulation. Pt prefers to construct a Zr-rich icosahedral complex with unique chemical and topological short-range ordering. The present analysis also revealed the medium-range ordering of Pt-Pt pairs corresponding to the pre-peak signal at 17 nm⁻¹ in the diffraction profile. The chemical and topological features around Pt and bonding structure correspond well with those of Mn in the approximant phase of α-AlMnSi.

The statistical approach was in constant development since it was first applied to calculate the structure factor for Fibonacci chain being the model of 1D quasicrystal. Its pertinence was investigated throughout years resulting in fully developed mathematical formalism finally ready to be exploited in its full potential. First serving as an alternative to higher-dimensional description of quasicrystals it proved to be even more general. Structures without nD representation can be investigated within statistical approach as well. Unified description of the variety of structures is possible based on the distribution function constructed upon the reference lattice concept. Furthermore, the distribution is sensitive to disturbances in the structure and reflects them by deformation occurring in the shape of the distribution. Therefore, disorder such as phononic or even phasonic, out of reach for nD approach, can be represented and incorporated in the structural analysis. In the paper we briefly introduce the concept standing behind the statistical approach and discuss the most important achievements of the approach.

The atomic structure of the high-order cubic approximant P₄₀ in the Al-Pd-Ru system is determined by means of single-crystal X-ray diffraction.

The homogeneity range around the Al₃Pd stoichiometry, representing the family of quasicrystalline approximants denoted as _n and/or (Al₃Pd), was involved in the calculated Al-Pd phase diagram. The calculations were performed by means of the CALPHAD method using the Thermo-Calc software. A novel thermodynamic description of the _n/(Al₃Pd) phase was proposed based on the (Al%,Pd)₃(Al,Pd%)₁ two-sublattice model. Existing thermodynamic parameters of stoichiometric phases Al₄Pd and Al₂₁Pd₈ were slightly adjusted. The transition between phases _n/(Al₃Pd) and γ-Al₂₁Pd₈ was predicted thermodynamically at 619°C.

Five (56-60)Zn-(29-35)Mg-(8-13)Y alloys (metal compositions are given in at.%) were investigated after annealing at 400°C for 150h. In the investigation, the scanning electron microscopy equipped with energy dispersive X-ray spectroscopy and the X-ray diffraction were used. The alloys were selected with the intention to collect experimental data about the (I+H) phase equilibrium at 400°C and to show trends applicable in a refinement of the related isothermal section of the Zn-Mg-Y phase diagram. As a result, a specific isothermal section at 400°C of Zn-Mg-Y phase diagram is presented, showing present experimental results and related thermodynamic and experimental data available in literature.

We investigate the superstructure of binary Al_2.75Ir and Al_2.63Rh 1/0 approximants by X-ray diffraction method and transmission electron microscopy. Al_2.75Ir possesses a 2a × 2a × 2a C-centred monoclinic lattice with space group C2 or Cm or C2/m. Al_2.63Rh possesses a 2a × 2a × 2a face centred lattice with space group F23 or Fm3.

The present study describes the synthesis characterization and hydrogen storage behavior of Ti_41.5+XZr_41.5-XNi₁₇ (x=0, 3.5, 11.5 and 13.5) nano quasicrystalline ribbons synthesized through rapid solidification technique. The nano quasicrystalline ribbons of alloys have been synthesized at Cu-wheel speed of 45 m/sec. The investigation also describes the effect of different compositions of Ti and Zr on the structure, microstructure and their correlation with hydrogen storage characteristics of as quenched nano quasicrystalline ribbons. It has been found that the hydrogen storage capacity of these ribbons increases with increasing the content of Ti in i-phase ribbons.

The analysis of low-temperature specific heat of rare-earth (RE)-containing quasicrystals and periodic approximants and consequent interpretation of their electronic properties in the T → 0 limit is frequently hampered by the Schottky effect, where crystalline electric fields lift degeneracy of the RE-ion Hund's rule ground state and introduce additional contribution to the specific heat. When the low-temperature specific heat C is analyzed in the C/T versus T² scale, the Schottky effect (a single-ion property in a system of non-interacting electrons) and the electron-electron interactions both yield a very similar upturn in the T → 0 limit. The origin of the upturn can be unraveled from the magnetic-field dependence of the low-temperature specific heat.

We report on ac magnetic susceptibility measurements of the Au-Al-Yb approximant under pressure. It is known that the approximant shows unconventional quantum criticality at the critical pressure P_c ∼ 2 GPa, and further that the magnetic ordered state emerges at a low temperature (T_g ∼ 100 mK) for P > P_c. We nd that the nonlinear susceptibility shows a peak around the temperature T_g at which the linear susceptibility peaks. We also nd that T_g increases with frequency of the modulation eld. From these results, we suggest that the magnetic ordered state of the approximant below T_g is a spin-glass-like short-range ordered state.

Formation of the valence bands in AlIr, RuAl₂ and RuGa₃ was analysed on the basis of Wannier functions. It was sufficient to consider nine (s-, p- and d-like) Wannier functions per cluster centred on each transition metal for describing the valence bands. As in the case of Al-Cu-Ir quasicrystalline approximant, which we reported previously [Kitahara K, Takagiwa Y and Kimura K 2015 J. Phys. Soc. Jpn.84 014703-1-8], covalent bonds between clusters form where the distance between neighbouring clusters is about 0.3 nm, making conduction states as antibonding functions. sp³d²-, sp³- and p_y-like Wannier functions are used for the covalent bonds in AlIr, RuAl₂ and RuGa₃, respectively.

The formation of Mn-Cr-Ni-Si dodecagonal quasicrystal has been studied at 600 and 700 °C. The growth process of the quasicrystal from as-cast β-Mn phase was explained by Johnson-Mehl-Avrami equation. In order to evaluate structural quality of the quasicrystal, distortion in the diffraction pattern observed along the 12-fold axis was analyzed. This analysis indicated that the aging at 600 °C for 100 h is the best condition to synthesize the quasicrystal.

The dependence of surface structure formation on preparation conditions of NiAl(100) has been investigated by Scanning Tunnelling Microscopy (STM), Low Energy Electron Diffraction (LEED) and Density Functional Theory (DFT). STM and LEED have been used to study the surface after sputtering, low temperature annealing (T<500K) and high temperature annealing (500K<T<1000K). A (1×1) phase is observed both after sputtering and low T annealing, with STM images indicating the formation of row structures - the density of which appears dependent on annealing time. ${\rm{A c(}}\sqrt 2 \times 3\sqrt 2 ){\rm{R}}45^\circ$ regime is detected upon higher T annealing - forming two, orthogonal, row-based domains. STM simulation produced using DFT explains the origin of one of the domains - a defect based structure with a dominant Ni density of states contribution.

Medium energy ion scattering (MEIS) is employed to characterize the composition and structure of the five-fold surface of the icosahedral Ag₄₂In₄₂Yb₁₆ quasicrystal. The composition of the surface after sputtering is dominated by Ag and In, and when the surface is annealed at temperatures approaching 430°C, Yb is restored at the surface. The composition is that expected from the bulk structure if the surface is formed at bulk planes involving the centre of rhombic triacontahedral clusters, the building blocks of the system. Structural analysis of MEIS results are also consistent with a surface after annealing that is in close agreement with bulk truncation intersecting the cluster centre.

The initial stage of the growth of a Bi overlayer on the fivefold surface of icosahedral Ag-In-Yb quasicrystal is studied using the first-principles density functional calculation. Comparing to the previous study about Pb adsorption on the same surface, it turns out that Bi is bound stronger than Pb on the surface, and small differences are found in the relative magnitude of the adsorption energy of some stable sites. Those may lead some differences in the sequence of the growth in the initial stage, it is concluded that the under- and first-layers observed in the growth of Pb are formed also in the Bi case.

In a spectacular experiment of the year 2000 Edagawa et al. observed white spots in HRTEM images of d-Al-Cu-Co, which formed the vertices of a tiling. On a time scale of seconds to minutes the spots changed positions corresponding to phason flips. To illuminate the origin of the spots, their jump mechanism and frequencies we employ a structure model of Zeger and Trebin of 1996. It consists of quasiperiodic double layers stacked periodically by 4.18 Å. Each double layer contains rings of ten atoms whose centers form the vertices of a Tübingen triangle tiling. Correlated jumps of two atoms in each sublayer cause a simpleton phason flip of the entire ten ring. The stacking of the double layers leads to columns of the ten rings which might be interrupted due to the flips. Columns which contain a critical minimum number of complete ten rings are considered visible as white spots. Simultaneous appearences of vertices and their flipped positions give rise to the pentagonal Penrose pattern as observed by Edagawa et al. and also in other experiments. Postulating microscopic flip rates for the correlated jumps of pairs of atoms in the sublayers we calculate the probabilities for the numbers of complete ten rings in a column and confirm the mesoscopic time scales for the jumps of the white spots.

We study the quantum diffusion of charge carriers in octagonal tilings. Our numerical results show a power law decay of the wave-packet spreading, L(t) ∝ t^β, characteristic of critical states in quasicrystals at large time t. For many energies states are sub-diffusive, i.e. β < 0.5, and thus conductivity increases when the amount of defects (static defects and/or temperature) increases.

The problem of screening of local moments in a metallic environment is revisited, in the context of quasiperiodic solids. The motivation for this study comes from experimental studies showing that low temperature thermodynamic properties are strongly anomalous in the quasicrystalline phase, but less or not anomalous in the related approximant phase. A model for a magnetic impurity in a quasiperiodic environment is introduced and solved numerically. Arguments are given for the existence of a singular distribution of Kondo temperatures in the quasicrystal, thereby providing a possible explanation for the experimental observations.

We study the extended Anderson model on a two-dimensional Penrose lattice to discuss how the electronic reconstruction in the valence is realized at low temperatures. Making use of the real-space dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method, we find that inhomogeneous electronic distribution appears at low temperatures. The system size dependence is also addressed.

We study the gap properties of nearest neighbors tight binding models on quasiperiodic chains. We argue that two kind of gaps should be distinguished: stable and transient. We show that stable gaps have a well defined quasiperiodic limit. We also show that there is a direct relation between the gap size and the gap label.

We propose a generalization of the well-known two-dimensional table tiling to three dimensions – the brick tiling. We develop a color/digit code for this tiling. We also discuss possible implications for higher dimensions.

We construct a lattice substitution tiling associated with and coding for the three-dimensional brick tiling. Its prototiles are 48 unit cubes labeled by digits nicknamed "colors".

A one-parameter family of binary inflation rules in one dimension is considered. Apart from the first member, which is the well-known Fibonacci rule, no inflation factor is a unit. We identify all cases with pure point spectrum, and discuss the diffraction spectra of other members of the family. Apart from the trivial Bragg peaks at the origin, they have purely singular continuous diffraction.

Modifying Rudin's original construction of the Rudin-Shapiro sequence, we derive a new substitution-based sequence with purely absolutely continuous diffraction spectrum.

The discovery of complex dodecagonal patterns in historical Islamic architecture is generating a renewed interest into understanding the mathematical principles of traditional Islamic geometry. By employing a compass and a straightedge, ancient craftsmen utilized consistent design principles that allowed for diverse geometric expressions to be realized throughout the ancient world. Derived from these principles, a global multi-level structural model is proposed that provides a general guiding principle for constructing a wide variety of infinite dodecagon-based quasiperiodic patterns.

A submodule of a -module determines a coloring of the module where each coset of the submodule is associated to a unique color. Given a submodule coloring of a -module, the group formed by the symmetries of the module that induces a permutation of colors is referred to as the color group of the coloring. In this contribution, a method to solve for the color groups of colorings of N-planar modules where N = 4 and N = 6 are given. Examples of colorings of rectangular lattices and of the vertices of the Ammann-Beenker tiling are given to exhibit how these methods may be extended to the general case.

We have argued the temperature dependence of conductivities of the icosahedral Al-Pd-Ru quasicrystals from the standpoint of the quasicrystal-like system with sp-d hybridization, using the thermal Green's function technique.