Presentation on theme: "Big-picture perspective: Metals and alloys are essential to modern technologies, especially as electrical conductors, structural materials, and magnets."— Presentation transcript:
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. Metals: Bonding, Conductivity, and Magnetism (Ch. 6)
2/3 of the elements are metals
Parallelepiped from which the entire crystal can be built up by purely translational displacements Unit cells
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 Unit cells and lattices
14 Bravais lattices lattice points onto which asymmetric units are placed
How many complete atoms in the unit cell? Coordination number? Body centered cubic (bcc) structure
Simple cubic and body centered cubic do not maximize the filling of space. Think about the best way to fill space with hard spheres… Close-packed structures
Hexagonal vs. cubic close packed hcpccp (= fcc)
Cubic close packed (ccp) is face centered cubic (fcc)
How many complete atoms in the unit cell? Coordination number? Face centered cubic (fcc) structure 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 mv 2 = p 2 /2m = h 2 /2mλ 2 Energy k (= 2π/λ) k = π/a E = h2k2h2k2 8π 2 m 1D 2D 3D Density of States EFEF … … … … (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]3s 2 ) a metal? The promotion energy (3s 2 3s 1 3p 1 ) 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 } } } No unpaired spins Other kinds of spin ordering: Antiferromagnetic Ferrimagnetic
Spin alignment in a magnetic field Paramagnets follow Curie Law behavior Spins align in a magnetic field at low T No ordering in the absence of an applied field low T high T
Ferro-, ferri-, and antiferromagnets Above Tc, ferro/ferrimagnets follow the Curie-Weiss Law Spins spontaneously order below T C Paramagnetic behavior above T C Antiferromagnets resist parallel alignment of spins => negative T C Also paramagnetic above T C
Ferro-/ferrimagnets below T C 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?