We now understand crystal structure and how to measure it

1. We now understand crystal structure and how to measure it We now move into bigger condensed matter questions. First up: What holds a crystal together? (A hot topic in early CMP) Generalization to nonzero temps (Helmholtz free en(V,T)) gives eq. thermodynamics Mostly electrostatics of the outer electrons, which can describe the form of materials.

2. By the end of this section you should be able to: Use a simple harmonic oscillator model to understand attractive forces in noble gases Apply a van der Waals-London interaction Use the Lennard-Jones potential to understand equilibrium lattice parameters (noble gases) Simply by looking at the periodic table, begin to explain why other types of bonding might exist (will develop more next time) Today’s Objectives Heads up: Notes on the board won’t be available online (lots today)

3. Models of Atoms K shell L shell M shell

4. Understanding Elemental Properties by the filling of the orbitals 1s2 1s2 2s2 2p6 1s2 2s2 2p6 3s2 3p6 Closed-shell elements: noble gases What would you say about the properties of noble gases? What causes these elements to stick together?

5. van der Waals Bond • Arise from charge fluctuations in atoms due to zero-point motion (due to Heisenberg uncertainty principle); these create dipole moments that are attractive • Depends on p2/r6, short ranged • Typical strength of 0.2 eV/atom ~1% of other bonds • Always present, but significant only when other types of bonding not possible (closed electron shells, saturated molecules) • What do weak bonds mean in terms of properties? graphite

6. Repulsive force: What works against bringing atoms closer? The exact dependence with R is found experimentally. For inert gases ~B/R12 where the power of 12 and B found by experiment As atoms are brought close, the Pauli exclusion principle will prevent two electrons from having the same quantum numbers. Overlap increases the total energy and causes repulsive term.

7. Lennard-Jones Potential: joining attractive and repulsive energies Parameter definitions

8. What about the properties of non-noble gases? Closed-shell elements: noble gases

9. Consider the case of sodium (atomic # 11) • On your own write down the electronic configuration: 1s2… Why 4s before 3d?

10. Other Properties Closed-shell elements: noble gases Closed-shell –plus one (alkali) elements: reactive due to loosely-bound outer electron in s-shell

11. Why mobile electrons appear in some solids and not others? • According to the very simple Drude model, the valance electrons are responsible for the conduction of electricity, thus termed conduction electrons. • Na11 ￫ 1s2 2s2 2p6 3s1 • This valance electron, which occupies the third atomic shell, is the electron which is responsible chemical properties of Na. Valance electron (loosely bound) Metallic 11Na, 12Mg and 13Al are assumed to have 1, 2 and 3 mobile electrons per atom respectively. Core electrons

12. What would a group I element most easily bind with? Closed-shell elements: noble gases Does this group have a valence of 7? Closed-shell–minus-one elements (halogens): elements with high electron affinity A (energy gained when an additional electron is added to a neutral atom); will easily form negative ions (take additional electron) in remaining p-shell state; very reactive Closed-shell –plus one (alkali) elements: reactive due to loosely-bound outer electron in s-shell

13. Warning: Confusing Terminology There exist many forms of valence! • By valence electrons here we mean outer electrons...the ones that could easily be pulled from the core to form an electron gas (In chemistry) Valence = Maximum number of bonds formed by atom Where would these definitions differ? Sometimes even the experts mix up this terminology even in papers

14. Dmitri Mandeleev Organization of Periodic Table Columns: groups with similar shells, similar properties Rows: periods with elements with increasingly-full shells Metallic/insulating properties can be understood by how loose (i.e. low ionization energy) outer electrons are. So, on which side of the table are the metals?

15. How the mobile electrons become mobile • When we bring Na atoms together to form a Na metal, the orbitals overlap slightly and the valance electrons become no longer attached to a particular ion, but belong to both. This is another type of bonding called metallic bonding, stronger than van der Waals but weaker than ionic/covalent. + + + + + + Na metal

16. METALLIC PROPERTIES • All conduction e-s in a metal combine to form a sea of electrons that move freely between cores  high electrical and thermal conductivity. • More electrons=stronger attraction. Means melting and boiling points are higher, and metal is stronger and harder.  • The free electrons act as the bond (or a “glue”) between the positive ions. • This type of bonding is nondirectional and rather insensitive to structure. • As a result we have a high ductility of metals: the “bonds” do not “break” when atoms are rearranged – metals can experience a significant degree of plastic deformation. + + + + + + + + +

17. Combining alkalis and halogens Closed-shell elements: noble gases Closed-shell–minus-one elements (halogens): elements with high electron affinity A (energy gained when an additional electron is added to a neutral atom); will easily form negative ions (take additional electron) in remaining p-shell state; very reactive Closed-shell –plus one (alkali) elements: reactive due to loosely-bound outer electron in s-shell

18. Electronegative and Electropositive An atom is electronegative if it gains energy by gaining an extra electron. What group of elements are very electronegative? Why are the Group I elements electronegative? What if you join Na and Cl together?

19. Bonding • Elemental Na would be metallic, but you can change that if brought in contact with a more electronegative element (e.g. Cl)

20. NaCl (salt) Ions and Cations and Anions, Oh My! Draw the K, L & M shells of Na and Cl before and after bringing in contact. Anion = Negative ion (atom with extra electrons) Cation = Positive ion (atom missing electrons) Which is the anion? Which is the cation? Which is/are electronegative?