Physics 440 Condensed Matter Physics a k a

Physics 440 Condensed Matter Physics a. k. a. Materials Physics Solid-State Physics

I. Introduction A. The Domain of Study B. Materials We Will Study C. Phenomena and Properties of Interest D. Types of Interactions that Bind CM E. Potential Energy Functions & Diagrams

A. Domain of Study Any physical system in which the particle separation is small enough so particles have significant interactions can be regarded as “condensed”. • crystalline solids (the basic paradigm for CM) • amorphous solids • liquids • soft matter (foams, gels, biological systems) • atomic clusters/nanoparticles (< 1000 atoms) • white dwarf & neutron stars • nuclear matter domain of astrophysics and nuclear physics

In this course we will focus mainly on perfect crystalline solids because their periodic structure allows for simple mathematical models to predict their properties

B. Materials We Will Study Elemental solids in the periodic table arranged in families or groups, including: alkali metals (Li, Na, K, Rb, Cs) alkaline earth metals (Be, Mg, Ca, Sr, Ba) transition metals (Fe, Ni, Co, …) coinage metals (Cu, Ag, Au) semiconductors (Si, Ge, Sn) noble gas solids (He, Ne, Ar, Kr, Xe, Rn) We will study mainly the metals and semiconductors, which make up the majority of the periodic table

C. Phenomena and Properties of Interest • structural • mechanical • thermal • electrical • magnetic • optical • superconducting We will concentrate on these

Experimental Techniques Most CMP experiments use a probe (electrons, photons, neutrons) and measure the scattering or absorption of such particles or the response of the sample in order to deduce properties of the sample and details of the interactions inside: Ex. Photoemission experiment ejected electron photons sample

D. Types of Interactions that Bind CM 1. van der Waals (noble gas liquids and solids) Neutral atoms with closed electronic shells have no timeaverage dipole moment but have “fluctuating dipole moments” that can be correlated with the fluctuating dipoles of nearby atoms to produce a weak attraction: + snapshot at one instant in time - +

2. Hydrogen bonding (molecular liquids and solids—H 2 O) Molecules with permanent dipole moments align in such a way that causes a fairly weak ionic attraction: H+ O- these are small fractional charges due to unequal sharing of electrons H+ H+ OH+

3. Ionic bonding (atoms with very different electronegativities) e. Na Cl Na+ Cl- Transfer of electron allows each ion to attain a stable closed electronic shell. The molecule or compound formed has a strong Coulomb attraction.

4. Covalent bonding (atoms with very similar electronegativities; semiconductors, diamond) Tetrahedral coordination of atoms (sp 3 bonding) Valence electrons are “shared” between atoms, so the negative electron clouds localized along the interatomic axes attract the ion cores. These produce strong, directional bonds.

5. Metallic bonding (most metals) One or more valence electrons leaves its parent atoms and is “free” to move throughout the solid. The negative electrons in the “free electron gas” attract the ion cores and keep them together. Bonding here is non-directional. + + + + positive ion cores “free electron gas”

E. Potential Energy Functions and Diagrams All of these interactions have potential energy curves that look something like this, where U = 0 means there is no interaction: U 0 short-range repulsion (Pauli exclusion) R 0 Long-range attraction (Coulomb or van der Waals)

Approximate Potential Energy Functions vd. W systems: Lennard-Jones potential ionic systems: Born-Mayer potential These and other approximate potential energy functions are chosen in order to best fit experimental measurements.

Remember: Problems worthy of attack Prove their worth by hitting back --Piet Hein