Related papers: What is a crystal?
Constructing a quantum description of crystals from scattering experiments is of paramount importance to explain their macroscopic properties and to evaluate the pertinence of theoretical ab-initio models. While reconstruction methods of…
The robust and automated determination of crystal symmetry is of utmost importance in material characterization and analysis. Recent studies have shown that deep learning (DL) methods can effectively reveal the correlations between X-ray or…
We develop a general framework to study hyperuniformity of various mathematical models of quasicrystals. Using this framework we provide examples of non-hyperuniform quasicrystals which unlike previous examples are not limit-quasiperiodic.…
An increasing variety of crystal structures has been observed in soft condensed matter over the past two decades, surpassing most expectations for the diversity of arrangements accessible through classical driving forces. Here, we survey…
Electronic states in quasiperiodic crystals generally preclude a Bloch description, rendering them simultaneously fascinating and enigmatic. Owing to their complexity and relative scarcity, quasiperiodic crystals are underexplored relative…
In this article we describe the crystallization conjecture. It states that, in appropriate physical conditions, interacting particles always place themselves into periodic configurations, breaking thereby the natural translation-invariance…
A two-dimensional system of soft particles interacting via a two-length-scale potential is studied. Density functional theory and Brownian dynamics simulations reveal a fluid phase and two crystalline phases with different lattice spacing.…
Quasicrystals are nonperiodic structures having no translational symmetry but nonetheless possessing long-range order. The material properties of quasicrystals, particularly their low-temperature behavior, defy easy description. We present…
The paper presents a teaching module about liquid crystals. Since liquid crystals are linked to everyday student experiences and are also a topic of a current scientific research, they are an excellent candidate of a modern topic to be…
Crystallographic tilings of the Euclidean space $\mathbb{E}^n$ are defined as simple tilings whose group of isometric automorphisms is crystallographic. To classify crystallographic tilings by their automorphism groups it is necessary to…
This paper continues our study of quasicrystals initiated in Part I. We propose a general mechanism for constructing quasicrystals, existing globally in time, in spatially-extended systems (partial differential equations with Euclidean…
Due to their aperiodic nature, quasicrystals are one of the least understood phases in statistical physics. One significant complication they present in comparison to their periodic counterparts is the fact that any quasicrystal can be…
Hyperuniform systems, which include crystals, quasicrystals and special disordered systems, have attracted considerable recent attention, but rigorous analyses of the hyperuniformity of quasicrystals have been lacking because the support of…
Generating novel crystalline materials has the potential to lead to advancements in fields such as electronics, energy storage, and catalysis. The defining characteristic of crystals is their symmetry, which plays a central role in…
Quasicrystals remain among the most intriguing materials in physics and chemistry. Their structure results in many unusual properties including anomalously low friction as well as poor electrical and thermal conductivity but it also…
We describe here in detail the recently introduced methodology for simulation of structural transitions in crystals. The applications of the new scheme are illustrated on various kinds of crystals and the advantages with respect to previous…
The discovery of quasicrystals 30 years ago challenged our understanding of order at the atomic scale. While quasicrystals possess long-range orientational order they lack translation periodicity. Structurally complex, yet crystalline…
Ideal symmetry is known to break down under almost any noise. One measure of asymmetry in a periodic crystal is the relative multiplicity Z' of geometrically non-equivalent units. However, Z' discontinuously changes under almost any…
Atomic structure analysis of crystalline materials is a paramount endeavor in both chemical and material sciences. This sophisticated technique necessitates not only a solid foundation in crystallography but also a profound comprehension of…
Non-periodic systems have become more important in recent years, both theoretically and practically. Their description via Delone sets requires the extension of many standard concepts of crystallography. Here, we summarise some useful…