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Related Concept Videos

The Seven Crystal Systems: Overview01:24

The Seven Crystal Systems: Overview

Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific requirements are not imposed on the...
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Classical mechanics provides a mathematical description of the motion of bodies under the influence of forces. A key principle within this field is the work-energy theorem, which establishes a bridge between the net work done on an object and its kinetic energy.The work-energy theorem states that the net work done on a particle by all the forces acting on it equals the change in its kinetic energy.In simple terms, the work-energy theorem is a method to analyze the effects of forces on an...
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Crystal Field Theory
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...
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Crystal symmetry operations are isometric transformations that map objects onto indistinguishable copies while preserving distances, angles, and volumes. The simplest symmetry operation is translation, which shifts the entire infinite crystal lattice parallelly by a translation vector.Crystallographic rotations involve rotations by an angle of 2π/n around an axis without changing the positions of points on the axis. It is called the rotational axis of the symmetry, denoted by n. The combination...
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Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
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Crystallographic point groups represent the various symmetry operations that can occur within crystals. They are unique in that at least one point will always remain unchanged during these actions. For instance, consider the triclinic system. This system, devoid of any axis or plane of symmetry, aligns with the C1 and Ci point groups.where Cᵢ is characterized solely by a center of inversion.Contrastingly, the monoclinic system introduces an element of symmetry. This system with one plane and...

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Novel Techniques for Observing Structural Dynamics of Photoresponsive Liquid Crystals
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Classical time crystals.

Alfred Shapere1, Frank Wilczek

  • 1Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40502, USA.

Physical Review Letters
|December 11, 2012
PubMed
Summary
This summary is machine-generated.

Researchers explore classical dynamical systems for time crystals, analogous to spatial crystals. They demonstrate how broken symmetry in lowest-energy states can lead to time crystal formation, even with traveling waves.

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Area of Science:

  • Physics
  • Classical Mechanics
  • Condensed Matter Physics

Background:

  • Classical dynamical systems typically settle into a lowest-energy static state.
  • The concept of time crystals, exhibiting periodic behavior in time analogous to spatial crystals, is an emerging area of physics.

Purpose of the Study:

  • To investigate the possibility of time crystal formation in classical dynamical systems.
  • To identify and overcome challenges associated with realizing time crystals in classical mechanics.

Main Methods:

  • Analyzing nonsingular Lagrangian systems.
  • Demonstrating arbitrary orbits of angular variables as lowest-energy trajectories.
  • Exploring dynamics within broken symmetry states.

Main Results:

  • Arbitrary orbits can be lowest-energy trajectories in specific classical systems.
  • Broken symmetry dynamics provide a viable mechanism for time crystal formation.
  • Models exhibiting time crystals, including those with traveling density waves, were successfully constructed.

Conclusions:

  • Classical dynamical systems can exhibit time crystal behavior.
  • Broken symmetry is a key ingredient for creating time crystals in classical mechanics.
  • The proposed models offer a pathway to experimentally realizing classical time crystals.