Chapter 13: Structures, Properties, and Applications of Solids

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Chapter 13 Structures, Properties, and
Applications of Solids

• When substances freeze, or separate as a solid
  from solution, they tend to form crystals
• Crystals have highly regular features and are
  said to possess symmetry or be symmetrical

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• The symmetry, or repetitive pattern, in
  crystalline solids is called a lattice
• The particles that make up the lattice are called
  lattice points
• The basic repeating unit in a lattice is called
  the unit cell
• Starting from a unit cell, the entire lattice can
  be generated by repeating the unit cell in all
  directions
• The same unit cell can describe many different
  structures

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• The simplest and most symmetrical three-
  dimensional lattice is called a simple cubic or
  primitive cubic lattice

(a) A simple cubic unit cell showing the lattice
points. (b) A portion of a simple cubic lattice.
(c) Only a portion of each atom of a substance
that forms a simple cubic lattice lies within a
particular unit cell.
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• Only 1/8 of each atom lies in a particular simple
  cubic unit cell
• Each simple cubic unit cell contains
• Two additional cubic lattices are possible
  face-centered cubic (fcc) and body-centered cubic
  (bcc)

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Lattice points in a fcc unit cell are found at
each of the eight corners and in the center of
each face. A fcc unit cell contains 1 atom from
the eight corners plus 61/23 atoms from each
face for a total of 4 atoms. Lattice points in
a bcc unit cell are located at each of the eight
corners and in the center of the unit cell. A bcc
unit cell contains 2 atoms.

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• A number of metals and compounds have cubic
  lattices

Copper and gold both crystallize in a fcc
structure. The unit cell in gold is larger
because copper atoms are smaller than gold atoms.
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Chloride ions in NaCl are associated with the
lattice points of a fcc unit cell. The sodium
ions are placed between the chloride ions.
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• The stoichiometry of the unit cell must match the
  stoichiometry of the compound

Both ZnS and CaF2 have fcc unit cells. Particles
must be weighted correctly to recover the
stoichiometry of the compound.
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A unit cell of NaCl shows how to weight lattice
points corners have a weight of 1/8, faces a
weight of 1/2, and edges a weight of 1/4. This
unit cell contains four sodium and four chloride
ions.
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• The packing of particles is also important
• Structures that achieve the maximum packing
  density are called closest-packed structures
• Different ions usually have different sizes
• Using spheres of the same size helps visualize
  the different way layers can pack
• In closest-packed structures

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(a) One layer of closely packed spheres. (b) The
second layer is started by placing a sphere
(colored red) in the depression formed between
three spheres in the first layer. (c) Completed
second layer showing how the atoms are stacked
over the first layer.
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Two options exist for starting the third layer.
(a) The first atom (colored green) is placed over
a hole in both the first (colored blue) and
second layer (colored red). (b) The first atom is
placed over a hole in the second layer that is
directly over an atom in the first layer.
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As more atoms are added to the third layer, two
different structures result. (a) Cubic closest
packed (ccp) spheres. (b) Hexagonal closest
packed (hcp) spheres. In an hcp structure the
layers alternate in an A-B-A-B pattern, where A
stands for the orientation in the odd layers and
B the orientation of the even layers. In a ccp
structure, the layers alternate in an
A-B-C-A-B-C pattern. The first layer is oriented
like the fourth, the second like the fifth, and
the third like the sixth.
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• Not all solids are crystalline
• Glass is a general term used to refer to a
  noncrystalline or amorphous solid
• Amorphous solids lack the long-range repetitive
  internal structure found in crystals
• For this reason they are sometimes called
  supercooled liquids, a term suggesting the kind
  structural disorder found in liquids
• Crystalline structure can be determined using the
  technique of X-ray diffraction

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X-rays emitted from atoms are in phase in some
directions and out of phase in others. This gives
rise to a diffraction pattern that can be used to
determine the structure of the crystalline solid
that contains the atoms.
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(a) The production of an X-ray diffraction
pattern. (b) An X-ray diffraction pattern
produced by sodium chloride recorded on a
photographic plate.
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• Crystals can be divided into four types ionic,
  molecular, covalent, and metallic
• Ionic crystals have cations and anions at the
  lattice sites
• Tend to be brittle, have high melting points, and
  are nonconducting in the solid phase and
  conducting in the liquid phase.
• Molecular crystals have neutral molecules at the
  lattice sites
• Due to the relatively weak intermolecular
  attractions, solids made from small molecules
  tend to be soft with low melting points. They are
  nonconducting in both the liquid and solid phase.

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• Covalent crystals have atoms at the lattice sites
  covalently bonded to other atoms
• These are also called network solids and the
  crystal is essentially one large molecule. A
  typical example is diamond which is very hard,
  has a very high melting point, and is a
  nonconductor of electricity.

Each carbon atom in diamond is covalently bonded
to four others at the corners of a tetrahedron.
The structure extends throughout the entire
crystal.
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• Metallic crystals have cations at the lattice
  sites surrounded by mobile electrons
• Metallic crystals conduct heat and electricity
  well, have metallic luster, and tend to have high
  melting points.

A highly simplified view of a metallic solid.
Metal atoms lose valence electrons to the solids
as a whole and exist as positive ions surrounded
by a mobile sea of electrons.