CHM 511 chapter 3 page 1 of 25 Chapter 3 The Structures of Simple Solids Types of bonding in solids ● Covalent Significant sharing of electrons between atoms. Can form vast arrays (e.g. C—diamond, graphite; SiO2—quartz, cristobalite) or molecular solids (e.g. CO2, SO2, H2O) ● Ionic ● Metallic Classifications to describe crystalline solids Lattice: three dimensional infinite array of points (atoms) where each atom is surrounded in an identical way by neighboring points Unit cell: the simplest set of lattice points from which the entire crystal structure can be built by purely translational displacements The seven crystal systems:
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CHM 511 chapter 3 page 1 of 25
Chapter 3
The Structures of Simple Solids Types of bonding in solids
● Covalent
Significant sharing of electrons between atoms. Can form vast arrays (e.g. C—diamond, graphite;
SiO2—quartz, cristobalite) or molecular solids (e.g. CO2, SO2, H2O)
● Ionic
● Metallic
Classifications to describe crystalline solids Lattice: three dimensional infinite array of points (atoms) where each atom is surrounded in an
identical way by neighboring points
Unit cell: the simplest set of lattice points from which the entire crystal structure can be built by
purely translational displacements
The seven crystal systems:
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1. Primitive unit cell (P): has an atom at each vertex and nowhere else.
2. Body-centered unit cell (I or bcc (body-centered cubic)): has an atom at each vertex and in the
center.
3. Close packed unit cell (cp):
less wasted space
each atom will have 12 nearest neighbors
two types (hcp & fcc)
Hexagaonally close packed (hcp)
Two differently positioned layers
-layer A is set down
-layer B is in the “dimples” of layer A
-3rd layer is exactly the same as A
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Cubic close packed (ccp) aka, face centered cubic (fcc)
Three differently positioned layers
-set down layer A
-layer B is placed in “dimples” of layer A
-layer C is placed in “dimples” of layer B, but not directly above
atoms in the A layer
Often, atoms can be squeezed in the empty spaces between atoms (holes).
How much space is between atoms in a ccp structure????
Translational symmetry coordinates
Consider a primitive cubic cell, starting with one atom as the “origin” (location is such that
numbers are positive).
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Fractional atomic coordinates and projections To draw 2-D representations of where atoms are, use a coordinate system.
Holes in close packed structures
Octahedral hole (Oh holes):
lies between 2 planar triangles
For hcp lattice, see hexagons below:
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For ccp, Oh holes are located at midpoints of each edge of the cube AND in the center
Tetrahedral hole (Td holes): lies between a planar triangle capped with a single atom
For hcp lattices:
For ccp lattices:
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The structures of metals and alloys
Many metals adopt close packed structures—but which? hcp or ccp? Actually, there are many
polytypes.
Polytypes: structural forms in which two dimensions are the same, but the 3rd dimension aligns
the atoms differently.
See periodic table in figure 3.21, page 73, many are hcp or fcc, but not all
Body centered cubic (bcc or cubic-I)—common among metals of groups 1, 5, 6
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Primitive cubic (cubic-P)—uncommon among metals (only Po adopts this under standard
conditions)
Polymorphism: the ability to adopt different crystalline
forms at various temperatures and pressures.
Figure to the right is showing iron at various temperatures
and pressures.
Atomic radii of metals
rmetal: one half the distance between the nearest-neighbor atoms in a solid state metallic lattice
This value is dependent on the coordination number (i.e., the nearest neighbor atoms)
Atoms appear larger if there are more neighbors. This data applies the Goldschmidt correction.
Coordination Number 12 8 6 4
Relative Ratio 1.00 0.97 0.96 0.88
If the 12-coordinate Fe radius is 126 pm, what is the expected size of Fe at 1 bar and 298 K?
Alloys and interstitials Alloy: a blend of metallic elements prepared by mixing the molten components and then cooling
the mixture to produce a metallic solid.
● can be homogeneous
● can be made of definite compounds (definite composition and internal (crystalline) structure)
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Classification of alloys
Substitutional alloy
● atomic radii must be within 15% of size
● crystal structures of the elements must be the same