Intermolecular Forces Part 2 The Solid State: Crystals 1 Prof. Zvi C. Koren 20.07.2010
Calculation of Lattice Energy, U, from a Thermodynamic Cycle What are the energies, virtual and real, involved in uniting oppositely charged ions together in an ionic bond? What are the driving forces that stabilize an ionic bond? Recall Coulomb s Law: But Coulomb doesn t tell the whole story! 2 (continued) Prof. Zvi C. Koren 20.07.2010 U q 1 q r 2
Born-Haber Cycle for the Calculation of the Lattice Energy, U, from the Heat of Formation, DH f of an Ionic Compound Goal: To Describe the Heat (or Enthalpy ) of Formation in terms of the Lattice Energy Recall the meaning of a Formation reaction. For example, the formation of NaCl is: Na(s) + ½ Cl 2 (g) NaCl(s), The Born-Haber Cycle is an application of Hess s Law, which states: The energy (or heat) of an overall process is the sum of the heats of all the steps in that process: DH total = DH 1 + DH 2 + = ΣDH i For example: Calculate the lattice energy, U, for NaCl from its heat of formation, DH f, and other energy properties. 3 Prof. Zvi C. Koren 20.07.2010
Energy Born-Haber Cycle for NaCl Na + (g) + e + Cl(g) ΔH E.A. = 349 kj Electron Affinity ΔH I.E. = 496 kj Ionization Na + (g) + Cl (g) Na(g) + Cl(g) ΔH diss = ½D Cl-Cl = 121.68 kj Bond Dissociation Na(g) + ½Cl U = 786 kj 2 (g) Lattice Energy ΔH atom, ΔH sub = 107.32 kj Atomization, Sublimation Na(s) + ½ Cl 2 (g) ΔH f = 410 kj Formation 4 Prof. Zvi C. Koren 20.07.2010 NaCl(s)
Determining the Structures of Crystals X-Ray Diffraction A beam of x-rays is directed at a crystalline solid The photons of the x-ray beam are scattered by the atoms of the solid. The angle of scattering depends on the locations of the atoms in the crystal. The scattered x-rays are detected by a photographic film or an electronic detector. 5 Prof. Zvi C. Koren 20.07.2010
The Unit Cell Properties of the Unit Cell: Smallest repeating unit Has all the symmetry characteristics of the crystal Every unit cell is a parallelepiped Points that define the unit cell are lattice points and are all equivalent 6 Prof. Zvi C. Koren 20.07.2010
The 3 Cubic Unit Cells Simple Cubic sc (Primitive) Body-Centered Cubic bcc Face-Centered Cubic fcc 7 Prof. Zvi C. Koren 20.07.2010
(sc) (bcc) (fcc) 7 Crystal Classes 14 Bravais Lattices (Rhombohedral) 4 Types of Unit Cells: P = Primitive I = Body-Centered F = Face-Centered C = Side-Centered 8 Prof. Zvi C. Koren 20.07.2010
The NaCl ( Rock Salt ) Structure Questions: Recall: Lattice Points are all equivalent and define the Unit Cell. Where are the lattice points here? Note the unit cell is face-centered cubic (fcc). Consider all the atoms (lattice and non-lattice) on the: Corners Faces Edges What is the net formula of this unit cell? Many salts and oxides have this structure: KCl, LiF, AgBr, KBr, PbS,..., MgO, FeO,... (except for CsCl, CsBr, CsI) 9 Prof. Zvi C. Koren 20.07.2010
The CsCl Structure cubic primitive or simple cubic (sc) Intermetallic compounds (not necessarily ionic crystals), but also common salts assume this structure; e.g. CsCl, TlI,..., AlNi, CuZn,... 10 Prof. Zvi C. Koren 20.07.2010
Perovskite Structure The lattice is essentially cubic primitive, but may be distorted to some extent and then becomes orthorhombic or worse. It is also known as the BaTiO 3 or CaTiO 3 lattice A particular interesting perovskite (at high pressures) is MgSiO 3. It is assumed to form the bulk of the mantle of the earth, so it is the most abundant stuff on this planet, neglecting its Fe/Ni core. The mechanical properties (including the movement of dislocations) of this (and related) minerals are essential for geotectonics - forming the continents, making and quenching volcanoes, earthquakes - quite interesting stuff! 11 Prof. Zvi C. Koren 20.07.2010
The ZnS ( Zinc Blende ) or Diamond Structure The CaF 2 (fluorite) or ZrO 2 Structure These two are different face-centered cubic (fcc) the typical lattice of covalently bonded group IV semiconductors [C (diamond form), Si, Ge] or III-V compounds semiconductors [GaAs, GaP, InSb, InP,..] face-centered cubic (fcc) 12 Prof. Zvi C. Koren 20.07.2010
Closest Packing in Crystal Lattices In most crystal lattices, atoms or ions fill space as efficiently as possible: Square Hexagonal (more efficient) 13 Prof. Zvi C. Koren 20.07.2010
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hcp = hexagonal closest packed In both cases, the spheres fill the maximum posssible space, 74.04% of the cell. ccp = cubic closest packed fcc 15 Prof. Zvi C. Koren 20.07.2010
Holes in Crystal Lattices 16 Prof. Zvi C. Koren 20.07.2010
Ion Size, Crystal Volume & Density Volume of a Unit Cell (e.g., NaCl): For cubic: V = a 3 = (5.52 Å) 3 = 168 Å 3 8 10 cm = 168 Å 3 o 1A 3 1.68x10 22 cm Density of a Unit Cell (e.g., NaCl): d = m/v MW NaCl = 58.5 g/mol(1 mol/6.02x10 23 molecules) 9.72x10-23 g/molecule 4 NaCl molecules in the cell: m of NaCl unit cell = 4 molecules(9.72x10-23 g/molecule) = 3.89x10-22 g d = m/v = (3.89x10-22 g)/1.68x10-22 cm 3 = 2.31 g/cm 3 Experimentally: 2.164 g/cm 3 3 2r 2r Na Cl (assume all oppositely charged ions touch each other) r Na r Cl 0.95 o A o - 1.81 A 17 Prof. Zvi C. Koren 20.07.2010