crystal lattice

Examples of crystal lattice in the following topics:

• Crystal Structure: Packing Spheres

  • 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.
  • For a sphere in the interior of a crystal lattice, the number of spheres contacting the sphere that is being evaluated is known as the bulk coordination number.

• Crystal Structure: Closest Packing

  • These cells are periodically arranged to give rise to a crystal's lattice structure.
  • This section considers how the packing of atoms within unit cells contributes to a crystalline solid's lattice structure.
  • The packing efficiency is the fraction of volume in a crystal structure that is occupied by constituent particles, rather than empty space.
  • An understanding of atomic packing in a unit cell and crystal lattice can give insight to the physical, chemical, electrical, and mechanical properties of a given crystalline material.
  • Discuss the two ways in which atoms/molecules pack in the most efficient way in crystals.

• Lattice Energy

  • Lattice energy is a measure of the bond strength in an ionic compound.
  • As an example, the lattice energy of sodium chloride, NaCl, is the energy released when gaseous Na+ and Cl- ions come together to form a lattice of alternating ions in the NaCl crystal.
  • The energy value can be estimated using the Born-Haber cycle, or it can be calculated theoretically with an electrostatic examination of the crystal structure.
  • Sodium ions (Na+) and chloride(Cl-) ions, depicted in purple and green respectively, alternate in the crystal lattice of solid NaCl.
  • This tutorial covers lattice energy and how to compare the relative lattice energies of different ionic compounds.

• 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.
  • This process is known as x-ray crystallography because of the information it can yield about crystal structure.
  • For example, current research in high-temperature superconductors involves complex materials whose lattice arrangements are crucial to obtaining a superconducting material.
  • X-ray diffraction from the crystal of a protein, hen egg lysozyme, produced this interference pattern.
  • Bragg's Law of diffraction: illustration of how x-rays interact with crystal lattice.

• 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°.
  • Lattice energy, while due mainly to coulombic attraction between each ion and its nearest neighbors (six in the case of NaCl) is really the sum of all the interactions within the crystal.
  • Halite forms cubic crystals.

• The Third Law

  • According to the third law of thermodynamics, the entropy of a perfect crystal at absolute zero is exactly equal to zero.
  • The third law of thermodynamics is sometimes stated as follows: The entropy of a perfect crystal at absolute zero is exactly equal to zero.
  • At zero kelvin the system must be in a state with the minimum possible energy, thus this statement of the third law holds true if the perfect crystal has only one minimum energy state.
  • In simple terms, the third law states that the entropy of a perfect crystal approaches zero as the absolute temperature approaches zero.
  • Provided that the ground state is unique (or W=1), the entropy of a perfect crystal lattice as defined by Nernst's theorem is zero provided that its ground state is unique, because log(1) = 0.

• Solutions and Heats of Hydration

  • The first reaction (ionization) is always endothermic; it takes a lot of work to break up an ionic crystal lattice into its component ions.
  • 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

• Metallic Crystals

  • Metallic crystals are held together by metallic bonds, electrostatic interactions between cations and delocalized electrons.
  • 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.

• Crystalline Solids

  • The existence of more than one crystal form for a given compound is called polymorphism.
  • Polymorphs of a compound are different crystal forms in which the lattice arrangement of molecules are dissimilar.
  • Many polymorphic compounds have flexible molecules that may assume different conformations, and X-ray examination of these solids shows that their crystal lattices impose certain conformational constraints.
  • The crystal colors range from bright red to violet.
  • It displayed six polymorphic crystal forms, pictures of which are shown below.

• Covalent Crystals

  • Covalent solids are a class of extended-lattice compounds in which each atom is covalently bonded to its nearest neighbors.
  • This means that the entire crystal is, in effect, one giant molecule.
  • Similarly, a covalent solid cannot "melt" in the usual sense, since the entire crystal is one giant molecule.
  • It is also quite hard because of the strong covalent bonding throughout the lattice.
  • Cubic boron nitride adopts a crystal structure, which can be constructed by replacing every two carbon atoms in diamond with one boron atom and one nitrogen atom.