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Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

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The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
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Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
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Ionic Crystal Structures

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Ionic crystals consist of two or more different kinds of ions that usually have different sizes. The packing of these ions into a crystal structure is more complex than the packing of metal atoms that are the same size.
Most monatomic ions behave as charged spheres, and their attraction for ions of opposite charge is the same in every direction. Consequently, stable structures for ionic compounds result (1) when ions of one charge are surrounded by as many ions as possible of the opposite...
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The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed 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...
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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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An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
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Related Experiment Video

Updated: Sep 10, 2025

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Lattice-dependent orientational order in active crystals.

Till Welker1,2, Ricard Alert2,3,4

  • 1School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom. t.a.welker@sms.ed.ac.uk.

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|August 26, 2025
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Summary
This summary is machine-generated.

Active crystals exhibit coupled positional and orientational order. Researchers explored how particle interactions influence alignment, revealing strategies to control orientational order by engineering crystalline lattices.

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Area of Science:

  • Physics
  • Soft Matter Physics
  • Active Matter

Background:

  • Self-propelled particles can form ordered phases like crystals and flocks through non-equilibrium mechanisms.
  • The interplay between positional order (crystallinity) and orientational order in active systems is not well understood.

Purpose of the Study:

  • To investigate the coupling between positional and orientational order in crystals of active particles.
  • To explore how interparticle interactions influence the alignment of active particles within a crystalline structure.

Main Methods:

  • Studied crystals of active particles with interactions causing them to turn towards or away from each other.
  • Mapped the orientational dynamics to a spin lattice model with ferromagnetic/antiferromagnetic and nematic interactions.

Main Results:

  • Active particles align along directions dictated by the underlying crystalline lattice.
  • The degree of alignment depends on how interparticle interactions vary with distance.

Conclusions:

  • Positional and orientational order are strongly coupled in active crystals.
  • Engineering the crystalline lattice offers a method to control the orientational order of active particles.