lattice

Examples of lattice in the following topics:

• Lattice Energy

  • Lattice energy is a measure of the bond strength in an ionic compound.
  • Lattice energy is an estimate of the bond strength in ionic compounds.
  • as the charge of the ions increases, the lattice energy increases
  • as the size of the ions increases, the lattice energy decreases
  • This tutorial covers lattice energy and how to compare the relative lattice energies of different ionic compounds.

• Crystal Structure: Packing Spheres

  • Consider the arrangement of spheres within a lattice to form a view of the structure and complexity of crystalline materials.
  • Crystalline materials are so highly ordered that a crystal lattice arises from repetitions along all three spatial dimensions of the same pattern.
  • The crystal lattice represents the three-dimensional structure of the crystal's atomic/molecular components.
  • The structure seen within the crystalline lattice of a material can be described in a number of ways.
  • In principle, one can reconstruct the structure of an entire crystal by repeating the unit cell so as to create a three-dimensional lattice.

• Solutions and Heats of Hydration

  • The attractive interactions between ionic molecules are called the lattice energy, and they must be overcome for a solution to form.
  • The greater the value of a compound's lattice energy, the greater the force required to overcome coulombic attraction.
  • In fact, some compounds are strictly insoluble due to their high lattice energies that cannot be overcome to form a solution.
  • A hot solution results when the heat of hydration is much greater than the lattice energy of the solute.
  • Predict whether a given ionic solid will dissolve in water given the lattice energy and heat of hydration

• Ionic Crystals

  • The arrangement of ions in a regular, geometric structure is called a crystal lattice.
  • The exact arrangement of ions in a lattice varies according to the size of the ions in the crystal.
  • The resulting crystal lattice is of a type known as "simple cubic," meaning that the lattice points are equally spaced in all three dimensions and all cell angles are 90°.
  • The CsCl lattice therefore assumes a different arrangement.
  • In CsCl, metal ions are shifted into the center of each cubic element of the Cl–-ion lattice.

• Bonding in Metals: The Electron Sea Model

  • Metallic bonding may be described as the sharing of free electrons among a lattice of positively charged metal ions.
  • Metallic bonding may be described as the sharing of free electrons among a lattice of positively charged metal ions.

• More on coupled spring/mass lattices

  • On the web page you will find a Mathematica notebook that solves the eigenvalue/eigenvector problem for a lattice of many coupled masses (you can select the number yourself).
  • A plot of some of these modes for a homogeneous (i.e., all the spring constants and masses are the same) lattice of 50 mass points is given in Figure 1.12.
  • In each column you see the time evolution of an initial displacement imposed on the lattice; on the left side the initial disturbance is smooth (a Gaussian in fact) on the right the initial disturbance is sharp (corresponding to displacing one mass point and letting it go).
  • Figure 1.13: Waves on a lattice (discrete string).
  • Figure 1.12: A sample of the normal modes (free oscillations) of a homogeneous 50 point lattice with fixed ends.

• Metallic Crystals

  • Understood as the sharing of "free" electrons among a lattice of positively charged ions (cations), metallic bonding is sometimes compared to the bonding of molten salts; however, this simplistic view holds true for very few metals.
  • The strength of a metal derives from the electrostatic attraction between the lattice of positive ions and the "sea" of valence electrons in which they are immersed.
  • The high density of most metals is due to the tightly packed crystal lattice of the metallic structure.
  • In metals, the charge carriers are the electrons, and because they move freely through the lattice, metals are highly conductive.
  • Electrical conductivity, as well as the electrons' contribution to the heat capacity and heat conductivity of metals, can be calculated from the free electron model, which does not take the detailed structure of the ion lattice into account.

• X-Ray Diffraction

  • William Lawrence Bragg formulated the equation for Bragg's law, which relates wavelength to the angle of incidence and lattice spacing.
  • This depends on the wavelength and the lattice spacing.

• X-Ray Spectra: Origins, Diffraction by Crystals, and Importance

  • Shown below, Bragg's Law gives the angles for coherent and incoherent scattering of light from a crystal lattice, which happens during x-ray diffraction.
  • For example, current research in high-temperature superconductors involves complex materials whose lattice arrangements are crucial to obtaining a superconducting material.
  • Bragg's Law of diffraction: illustration of how x-rays interact with crystal lattice.

• Formulas of Ionic Compounds

  • On a macroscopic scale, ionic compounds, such as sodium chloride (NaCl), form a crystalline lattice and are solids at normal temperatures and pressures.