Related Experiment Video
Updated: Jun 12, 2026

Fabrication of Three-Dimensional Graphene-Based Polyhedrons via Origami-Like Self-Folding
Published on: September 23, 2018
Crumpling transition of the triangular lattice without open edges: effect of a modified folding rule
1Department of Physics, Faculty of Science, Okayama University, Okayama 700-8530, Japan.
Abstract:
Folding of the triangular lattice in a discrete three-dimensional space is investigated by means of the transfer-matrix method. This model was introduced by Bowick and co-workers as a discretized version of the polymerized membrane in thermal equilibrium. The folding rule (constraint) is incompatible with the periodic-boundary condition, and the simulation has been made under the open-boundary condition. In this paper, we propose a modified constraint, which is compatible with the periodic-boundary condition; technically, the restoration of translational invariance leads to a substantial reduction in the transfer-matrix size. Treating the cluster sizes L
Related Concept Videos
Structures of Solids
Lattice Centering and Coordination Number
Types of Unit Cells
Imagine taking a large number of identical...
X-ray Crystallography
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
Imperfections in Crystal Structure: Point, Line and Plane Defects
Crystal Field Theory - Octahedral Complexes
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
Lattice Energies of Ionic Crystals

