Search results
Results from the WOW.Com Content Network
The history of aperiodic crystals can be traced back to the early 20th century, when the science of X-ray crystallography was in its infancy. At that time, it was generally accepted that the ground state of matter was always an ideal crystal with three-dimensional space group symmetry, or lattice periodicity.
The distortion changes the band structure, in part splitting the bands up into smaller bands that can be more completely filled or emptied to lower the energy of the system. This process may not go to completion, however, because the substructure only allows for a certain amount of distortion. Superstructures of this type are often incommensurate.
A crystallographic database is a database specifically designed to store information about the structure of molecules and crystals.Crystals are solids having, in all three dimensions of space, a regularly repeating arrangement of atoms, ions, or molecules.
A set of structure utilities has been included for various applications such as: the transformation of unit cells or complete structures ; strain tensor calculation ; assignment of Wyckoff Positions ; equivalent descriptions of a given structure ; comparison of different structures with support for the affine normalizers of monoclinic space groups.
Commensurability (crystal structure), whether periodic material properties repeat over a distance that is mathematically commensurate with the length of the unit cell. Commensurability (economics), whether economic value can always be measured by money; Commensurability (ethics), the commensurability of values in ethics
If the new periodicity is a rational fraction or multiple of the lattice constant, the density wave is said to be commensurate; otherwise the density wave is termed incommensurate. A sketch in k-space of a (001) section of the Fermi surface of Cr.
The magnetic space group of disordered structure, , transitions to the magnetic space group of the ordered phase, . G 1 {\\displaystyle G_{1}} is a subgroup of G 0 {\\displaystyle G_{0}} , and keeps only the symmetries which have not been broken during the phase transition.
In particular the Aubry–André model has no actual disorder, only incommensurate modulation of onsite energies. This is why the Aubry-André transition happens at a finite value of the pseudo-disorder strength λ {\displaystyle \lambda } , whereas in one dimension the Anderson transition happens at zero disorder strength.