Metals: Bonding, Conductivity, and Magnetism (Ch. 6)
Big-picture perspective:
Metals and alloys are essential to modern technologies, especially as electrical conductors,
structural materials, and magnets. We will find that these unique properties arise from the
atomic and electronic structures of metals. Most metalsand alloys have relatively simple crystal
structures based on sphere packings, although others can be very complex.
Learning goals:
• Identify and assign unit cells, coordination numbers, asymmetric units, numbers of atoms
contained within a unit cell, and the fraction of space filled in a given structure.
• Relate molecular orbital theory to the delocalization of valence electrons in metals.
• Understand the concepts of electron wavelength and density of states.
• Understand the consequences of the nearly free electron model for the band structure of
metals and their conductivity.
• Explain why some metals are magnetic and others are diamagnetic, and how these
phenomena relate to bonding and orbital overlap.
• Use the Curie-Weiss law to explain the temperature dependence of magnetic ordering.
• Acquire a physical picture of different kinds of magnetic ordering and the magnetic hysteresis
loops of ferro- and ferrimagnets.
2/3 of the elements are metals
Unit cells
Parallelepiped from which the entire crystal can be built up by purely
translational displacements
Unit cells
Unit cells
Unit cells
Unit cells
Unit cells and lattices
Unit cells and lattices
We can generate the “2D” NaCl structure by placing the “NaCl” asymmetric
unit (basis) on each lattice point of a cubic lattice
14 Bravais lattices
lattice points onto which asymmetric units are placed
Body centered cubic (bcc) structure
How many complete atoms in the unit cell? Coordination number?
Close-packed structures
Simple cubic and body centered cubic do not maximize the filling of space.
Think about the best way to fill space with hard spheres…
Hexagonal vs. cubic close packed
hcp
ccp (= fcc)
Cubic close packed (ccp) is face centered cubic (fcc)
Face centered cubic (fcc) structure
How many complete atoms in the unit cell? Coordination number?
Work on this
together in groups
Crystal structures of the elements
Bonding and Conductivity
What are the periodic trends?
Molecular Orbitals in Metals
1-D Chain of Na atoms
What is the wavelength of an electron in these MO's?
Molecular Orbitals in Metals
Infinite chain of Na atoms
What are the energies of the MO's in metals?
Molecular Orbitals in Metals
What are the energies of the MO's in metals?
Nearly free electron model:
KE = ½ mv2 = p2/2m = h2/2mλ2
k = π/a
h2k2
E = 8π2m
…
2D
3D
…
Energy
…
1D
EF
…
k (= 2π/λ)
Density of States
(Number of orbitals per unit energy)
Band Diagrams
Metals vs. Insulators (or Semiconductors)
Conduction in Metals
Metals vs. Insulators (or Semiconductors)
"Nearly free" electrons
conduct electricity and heat
Conduction in Metals
• Electrons in metals are accelerated by an electric field, but they scatter by
interacting with the lattice (lattice vibrations, defects, impurities)
• The mean free path is long (~40 nm) compared to the atomic spacing (0.2 nm)
(football field vs. football). Thus we have an electron "gas"
• Scattering gives rise to resistance (Ohm's law, V = iR)
Bonding, Energetics, and Magnetism
Why is Mg (=[Ne]3s2) a metal?
The promotion energy (3s2
3s13p1) is less than the bonding energy
Bonding, Energetics, and Magnetism
• How many bonding electrons does each atom have?
• Why does W have such strong bonding?
• Why are the 3d elements different from 4d & 5d?
Bonding, Energetics, and Magnetism
Which transition metals are magnetic?
Four kinds of magnetic behavior
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Other kinds of spin ordering:
Antiferromagnetic
Ferrimagnetic
No unpaired spins
Spin alignment in a magnetic field
Paramagnets follow Curie Law behavior
c=
low T
C
T
high T
Spins align in a magnetic field at low T
No ordering in the absence of an applied field
Ferro-, ferri-, and antiferromagnets
Above Tc, ferro/ferrimagnets follow the Curie-Weiss Law
c=
C
T - TC
Spins spontaneously order below TC
Paramagnetic behavior above TC
Antiferromagnets resist parallel alignment of spins
=> negative TC
C
c=
T +q
Also paramagnetic above TC
Ferro-/ferrimagnets below TC
What competing energies cause
magnets to have micron-size domains?
How do domain walls move in an
applied magnetic field?
Magnetic hysteresis loops
What are hard vs. soft magnets?
When would you want a soft magnet?