Chapter 3. Crystal Binding

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Terence Payne
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1 Chapter 3. Crystal Binding Energy of a crystal and crystal binding Cohesive energy of Molecular crystals Ionic crystals Metallic crystals Elasticity What causes matter to exist in three different forms? If the intermolecular forces are strong, at relatively higher temperatures a compound could exist as a solid or a liquid. The temperature of matter is directly related to the kinetic energy of the molecules or particles making up the matter. This is given by the kinetic molecular theory (KMT) matter applies to all phases of matter, gas, liquid and solid. Inter-particle forces London Dispersion or Van der Waals Ionic bond Covalent bond Hydrogen Bonding Dipole-dipole Metallic bond

2 London Dispersion-Van der Waals Forces These forces are the weakest of all intermolecular attractions and occur in nonpolar molecules. The London dispersion forces results from instantaneous shifts of electron cloud of non-polar molecules. These shifts in electron cloud create instantaneous dipoles with very short lifetime. A weaker attractive force results because of the short lived dipole attractions between two molecules. Non-polar molecules such as H 2 and N 2 can be cooled to liquids at very low temperature due to the existence of London Dispersion forces. Crystals of inert gases Temporary dipole moments The weakest possible bond is that between non-polar molecules and noble gas atoms (He, Ne, Kr, Ar, Xe, and Ra). These have closed electronic structures - and at first sight should not form bonds. For He this is almost true: the gas condenses at 4.2 K, and the liquid freezes only at 0.95 K at a pressure of 26 atm. The interaction between neutral particles is best described by the van der Waals - London interaction. Cohesive Energies of Elements

3 Van der Waals Interaction In the van der Waals interaction, the long range cohesive potential results from the electrostatic attraction between two mutually induced electric dipoles. Its dependence on the separation r between two molecules has the form and α is the polarizability of the molecule U 12 (r) = - B/ r 6 Repulsive term Repulsive interaction Repulsive Interaction:Pauli Exclusion Principle Two electrons can not have their quantum numbers equal

4 Lennard-Jones potential These two attractive and repulsive terms are combined in the Lennard-Jones potential Ionic Crystals: Ionic Bonding Atoms whose atomic structure only deviates by one or two electrons from a closed outer shell, may easily lose or gain electrons to become a stable charged ion. For example Na: (1s 2 2s 2 2p 6 3p 2 3p 6 ) 4s 1 loses its outer 4s electron to become Na + : (1s 2 2s 2 2p 6 3p 2 3p 6 ) which has the stable Ne electronic structure Similarly F: 1s 2 2s 2 2p 6 3p 2 3p 5 gains an electron to become F - : (1s 2 2s 2 2p 6 3p 2 3p 6 ) Two such ions will be attracted by a Coulomb force, with a binding energy Coulomb s Model where e = charge on an electron = x C ε 0 = permittivity of vacuum = x C 2 J -1 m -1 Z A = charge on ion A Z B = charge on ion B d = separation of ion centers

Ionic Interaction Two such ions will be attracted by a Coulomb force, with a binding energy where r 0 is the equilibrium separation of the ions and q+ and q- are the charges of the positive and

5 Ionic Interaction Two such ions will be attracted by a Coulomb force, with a binding energy where r 0 is the equilibrium separation of the ions and q+ and q- are the charges of the positive and negative ions respectively. The repulsive term U R (r) is a short range interaction Repulsive interaction Pauli exclusion principle Cohesive Energy Coulombic Attractions and Repulsions in the Ionic Crystals A =

6 Madelung Constant Calculation Madelung Constant (A) Lattice Energy The Lattice energy, U, is the amount of energy required to separate a mole of the solid (s) into a gas (g) of its ions.

7 Born_Haber Cycle Energy Considerations in Ionic Structures

Energy and ionic bond formation Na + (s) +Cl(g) Na(g) +Cl(g) +496 kj(i.e.) -349 kj (E.A.) Na + (s) +Cl - (g) Na(g) + 1/2 Cl 2 (g) Na(s) + 1/2 Cl 2 (g) +121 kj(1/2 B.D.E.) +92 kj(s.e.) -771 kj (L.E.) -411 kj( H f ) NaCl(s) Born-Lande Model: This modes include repulsions due to overlap of electron electron clouds of ions.

8 Energy and ionic bond formation Na + (s) +Cl(g) Na(g) +Cl(g) +496 kj(i.e.) -349 kj (E.A.) Na + (s) +Cl - (g) Na(g) + 1/2 Cl 2 (g) Na(s) + 1/2 Cl 2 (g) +121 kj(1/2 B.D.E.) +92 kj(s.e.) -771 kj (L.E.) -411 kj( H f ) NaCl(s) Born-Lande Model: This modes include repulsions due to overlap of electron electron clouds of ions. εo = permitivity of free space A = Madelung Constant r o = sum of the ionic radii n = average born exponet depend on the electron configuration

9 Lattice energy The higher the lattice energy, the stronger the attraction between ions. Lattice energy Compound kj/mol LiCl 834 NaCl 769 KCl 701 NaBr 732 Na 2 O Na 2 S MgCl MgO 3795 Lattice Energy Degree of Covalent Character Fajan's Rules (Polarization)Polarization will be increased by: 1. High charge and small size of the cation 2. High charge and large size of the anion 3. An incomplete valence shell electron configuration

10 Trends in Melting Points Silver Halides Compound M.P. o C AgF 435 AgCl 455 AgBr 430 AgI 553 Dipole-Dipole Intermolecular Forces. This include the attraction between all polar molecules through the dipoles (except F-H, O-H and N-H dipoles) dipolar covalent bond formed by unequal sharing of electrons of bonds in a molecule. A molecule can be non-polar even though it may have polar covalent bond because of the symmetry of the molecular structure canceling the dipoles. Therefore, there are no dipole-dipole interactions in non-polar molecules. Molecular Structure and Bonding Bonding Theories 1. Lewis Theory 2. VSEPR Theory 3. Valence Bond theory (with hybridization) 4. Molecular Orbital Theory (molecular orbitals)

11 Bonding in Covalent (net-work) Crystals Si, Ge, C Share electrons, overlap of electrons Directionality Tetrahedral bond 1S 2 2S 1 2P 3 hybridization exchange interaction spin dependent Coulomb energy

12 Hydrogen Bonding Three special cases of stronger dipole-dipole interactions resulting from F-H, O-H and N-H dipolar covalent bond are called hydrogen bonding. This is because F, O and N have the largest electronegativities among other elements. Hydrogen bonding (between O-H and O-H dipoles) in water allows water to exist as a liquid at room temperature. N-H dipole in proteins allows the formation of doubles helix structure in DNA and other complex structures found in living cells. Hydrogen bonding in HF 2 - F - F - H + Bonding Models for Metals Bonding Models for Metals Molecular orbital bands Band Theory of Bonding in Solids

13 Metallic Bonding Metals are held together by delocalized bonds formed from the atomic orbitals of all the atoms in the lattice. The idea that the molecular orbitals of the band of energy levels are spread or delocalized over the atoms of the piece of metal accounts for bonding in metallic solids. Bonding Models for Metals Band Theory of Bonding in Solids Bonding in solids such as metals, insulators and semiconductors may be understood most effectively by an expansion of simple MO theory to assemblages of scores of atoms Linear Combination of Atomic Orbitals

14 Linear Combination of Atomic Orbitals Types of Materials A conductor (which is usually a metal) is a solid with a partially full band An insulator is a solid with a full band and a large band gap A semiconductor is a solid with a full band and a small band gap Element Band Gap C 5.47 ev Si 1.12 ev Ge 0.66 ev Sn 0 ev

15 Different Types of Atomic Radii In the way they are measured: 1 Covalent Radii: Radii based on covalently liked atoms in covalently bonded molecules. 2 van der Waals Radii: Radii based on non bonded atoms in solids. 3 Metallic Radii (12-coordinate):Radii based on metallic solids. 4 Ionic Radii: Radii basesd on bond distances in ionic solids.

Bonding. Honors Chemistry 412 Chapter 6

Bonding. Honors Chemistry 412 Chapter 6 Bonding Honors Chemistry 412 Chapter 6 Chemical Bond Mutual attraction between the nuclei and valence electrons of different atoms that binds them together. Types of Bonds Ionic Bonds Force of attraction