Related papers: Slip and twinning in Bravais lattices

We investigate lattice energies for radially symmetric, spatially extended particles interacting via a radial potential and arranged on the sites of a two-dimensional Bravais lattice. We show the global minimality of the triangular lattice…

Bravais lattices are the most fundamental building blocks of crystallography. They are classified into groups according to their translational, rotational, and inversion symmetries. In computational analysis of Bravais lattices, fulfilment…

We consider the symmetries of coincidence site lattices of 3-dimensional cubic lattices. This includes the discussion of the symmetry groups and the Bravais classes of the CSLs. We derive various criteria and necessary conditions for…

Band engineering in twisted bilayers of the five generic two-dimensional Bravais networks is demonstrated. We first derive symmetry-based constraints on the interlayer coupling, which helps us to predict and understand the shape of the…

We study the local optimality of Simple Cubic, Body-Centred-Cubic and Face-Centred-Cubic lattices among Bravais lattices of fixed density for some finite energy per point. Following the work of Ennola [Math. Proc. Cambridge, 60:855--875,…

In this paper we construct and analyze a two-well Hamiltonian on a 2D atomic lattice. The two wells of the Hamiltonian are prescribed by two rank-one connected martensitic twins, respectively. By constraining the deformed configurations to…

In this paper, we focus on finite Bravais lattice energies per point in two dimensions. We compute the first and second derivatives of these energies. We prove that the Hessian at the square and the triangular lattice are diagonal and we…

An implementation of BFACF-style algorithms on knotted polygons in the simple cubic, face centered cubic and body centered cubic lattice is used to estimate the statistics and writhe of minimal length knotted polygons in each of the…

This article investigates the properties of a few interacting particles trapped in a few wells and how these properties change under adiabatic tuning of interaction strength and inter-well tunneling. While some system properties are…

We consider pairwise interaction energies and we investigate their minimizers among lattices with prescribed minimal vectors (length and coordination number), i.e. the one corresponding to the crystal's bonds. In particular, we show the…

We propose a method of free energy calculation for a system of interacting particles arranged in a Bravais lattice. It will be shown how to treat divergences for infinite unbounded systems with "catastrophic" potetntials like Coulomb and…

We study the problem for the optimal charge distribution on the sites of a fixed Bravais lattice. In particular, we prove Born's conjecture about the optimality of the rock-salt alternate distribution of charges on a cubic lattice (and more…

We demonstrate from a fundamental perspective the physical and mathematical origins of band warping and band non-parabolicity in electronic and vibrational structures. Remarkably, we find a robust presence and connection with pairs of…

Griffith thermodynamic energy balance is employed to analyze cleavage phenomenon from atomic level. Results show that the cleavage toughness, the strain energy release rate, and the surface energy can be defined by the bond strength (the…

We consider a classical, two-dimensional system of identical particles which interact via a finite-ranged, repulsive pair potential. We assume that the system is in a crystalline phase. We calculate the normal vibrational modes of a…

As noticed in 2006 by the author of the present article, the hypothetical crystal---described by crystallographer F. Laves (1932) for the first time and designated ``Laves' graph of girth ten" by geometer H. S. M. Coxeter (1955)---is a…

We present a continuum model for symmetry-breaking phase transformations in intercalation compounds, based on Ericksen's multi-well energy formulation. The model predicts the nucleation and growth of crystallographic microstructures in…

We construct and study Sarkisov links obtained by blowing up smooth space curves lying on smooth cubic surfaces. We restrict our attention to the case where the blowup is not weak Fano. Together with the results of arXiv:1106.3716 which…

Correct identification of the Bravais lattice of a crystal is an important step in structure solution. Niggli reduction is a commonly used technique. We investigate the boundary polytopes of the Niggli-reduced cone in the six-dimensional…

We describe how the usual supercharges of extended supersymmetry may be {\it twisted} to produce a BRST-like supercharge $Q$. The usual supersymmetry algebra is then replaced by a twisted algebra and the action of the twisted theory is…