Chapter 2: Atomic bonding

Reading assignment Ch. 2 and 3 of textbook

Homework No. 1 Problems 2-8, 2-9, 2-13.

Homework No. 2 Problems 3-13, 3-15, 3-17, 3-19, 3-20, 3-21, 3-27.

Effect of atomic bonding Example: carbon exists as graphite (soft with greasy feeling) or diamond (hardest known material) Atomic & electronic configuration Bonding BOND STRENGTH Mechanical & Physical Properties graphite diamond

Primary and secondary bonding primary bonds: strong atom-to-atom attractions produced by changes in electron position of the valence e– . Example : covalent atom between two hydrogen atoms secondary bonds: much weaker. It is the attraction due to overall “electric fields”, often resulting from electron transfer in primary bonds. Example: intramolecular bond between H2 molecules  gas

Electronic configurations

Valence electrons They represent the ability of an element to enter into chemical combination with others. Valence es− participate in the bonding between atoms. Valence = # of electrons in outermost combined sp level. Examples of the valence are: Mg: 1s22s22p63s2 valence = 2 Al: 1s22s22p63s23p1 valence = 3 Ge: 1s22s22p63s23p63d104s24p2 valence = 4

Primary bonding types Ionic bonding Covalent bonding Metallic bonding

Ionic bonding

Ionic bonding in NaCl 3s1 3p6 Chlorine Sodium Atom Atom Cl Na Chlorine Ion Cl - Sodium Ion Na+ 2-15

Ionic bonding Ionic Bond: The attractive bonding forces are coulombic (different polarities):

Interionic force Force of attraction between Na+ and Cl- ions Z1 = +1 for Na+, Z2 = -1 for Cl- e = 1.60 x 10-19 C , ε0 = 8.85 x 10-12 C2/Nm2 a0 = Sum of Radii of Na+ and Cl- ions = 0.095 nm + 0.181 nm = 2.76 x 10-10 m 2-18

Interatomic spacing The equilibrium distance between atoms is caused by a balance between repulsive and attractive forces. Equilibrium separation occurs when no net force acts to either attract or separate the atoms or the total energy of the pair of atoms is at a minimum. For a solid metal the interatomic spacing is equal to the atomic diameter or 2r. For ionically bonded materials, the spacing is the sum of the two different ionic radii.

Bond energy Bonding force and Energy curves for a Na+ & Cl- pair. Since F = dE/da, the equilibrium bond length (ao) occurs @ F=0 and E is a minimum.

Coordination Coordination number (C.N.) = No. of nearest neighbors (radius R) around (touching) a particular atom/ion (radius r). C.N. depends on r/R ratio.

C.N. = 4 (in 2 dimensions) Unstable Stable Stable (critical case) r/R > min r/R = min r/R < min

C.N. = 2 Schematic drawing with nearest neighbors not in contact

C.N. = 3 Schematic drawing with nearest neighbors not in contact

C.N.= 4 3 dimensions

C.N. = 4 (3 dimensions)

C.N. = 8 (3 dimensions)

C.N. = 12 (3 dimensions)

C.N. = 6 3 dimensions

C.N. = 6 (3 dimensions)

C.N. = 4 (in 2 dimensions) C.N. = 6 (in 3 dimensions) Unstable Stable (critical case) r/R > min r/R = min r/R < min

C.N. = 3

C.N. = 8 (3 dimensions)

C.N. = 4

Criteria of packing ions in a solid Positive charge = negative charge Nearest neighbors of a cation are anions; nearest neighbors of an anion are cations. (Nearest neighbors touch one another.) The coordination number (CN) is determined by r/R, where r = radius of smaller ion (usually the cation), and R=radius of larger ion (usually the anion). The greater is r/R, the higher is CN. The largest allowable CN is most favorable.

Summary on ionic bonding The attractive force (energy) for two isolated ions is a function of distance. Bonding is nondirectional. This is the predominant bonding type in ceramics. 600-1500 kJ/mol (3-8 eV/atom) bonding energies are large  high Tm.

Directional bond due to the sharing of electrons between atoms Covalent bonding Directional bond due to the sharing of electrons between atoms

Cl2 molecule Planetary model Actual electron density Electron dot schematic Bond line schematic

Example 1. Br2 (a bromine molecule) Br has an outermost electronic configuration of 4s24p5, i.e.,

A single bond A -bond End-to-end overlap

Example 2. O2 (an oxygen molecule) O has an outermost electron configuration of 2s22p4, i.e.,

A double bond A σ-bond (end-to-end overlap) together with a π-bond (side-to-side overlap).

Double bond Single bonds

Every carbon atom along the chain is four-fold coordinated.

The electronic configuration of carbon is 1s22s22p2, i.e.

An excited state of carbon with electronic configuration

Mixing of an s electron cloud with three p electron clouds sp3 hybridization Mixing of an s electron cloud with three p electron clouds

Methane molecule

Methane molecule

Four sp3 orbitals are directed symmetrically toward corners of regular tetrahedron. This structure gives high hardness, high bonding strength (711KJ/mol) and high melting temperature (3550oC). Carbon atom Tetrahedral arrangement in diamond 2-25

SiO4 tetrahedron in silicate glass

Silicon dioxide (SiO2)

Covalent network solids Network of covalent bonds Examples: diamond, silicon, etc.

Properties of covalent network solids Materials have poor ductility. Poor electrical conductivity. Many ceramic, semiconductor and polymer materials are fully or partly covalent.

Mixed bonding (ionic + covalent) Few compounds exhibit pure ionic or pure covalent bonding.  the bond type degree depends on their position in the Periodic Table. The greater the difference in electronegativity, the more ionic is the bond. Conversely, the smaller the difference, the larger is the degree of covalency.

There is one unpaired electron. Example of mixed ionic-covalent bonding: HF (a hydrogen fluoride molecule) The electronic configuration of H is 1s1, i.e., There is one unpaired electron.

The electronic configuration of F is 1s22s22p5, i.e. There is also one unpaired electron.

Metallic Bonding Found in metallic elements (low electronegativities). Give up their valence electrons to form a “sea or cloud” of electrons. The valence electrons move freely within the electron sea and become associated with the ion cores.  The free electrons shield the (+) charged ion cores from repulsion.

Atoms in metals are closely packed in crystal structure. Loosely bounded valence electrons are attracted towards nucleus of other atoms. Electrons spread out among atoms forming electron clouds. These free electrons are reason for electric conductivity and ductility Since outer electrons are shared by many atoms, metallic bonds are Non-directional Positive Ion Valence electron charge cloud 2-28

Metallic Bonding Good thermal & electrical conductors The free electrons in the “cloud” move freely under an applied voltage. Good thermal & electrical conductors

Bond energy It is the energy required to create or break the bond. Materials with high bond energy  high strength and high melting point. Ionic materials have a large bond energy due to the large difference in electronegativities between the ions. Metals have lower bond energies, because the electronegativities of the atoms are similar.

Bond energy and melting temperature

Secondary bonding Van der Waals bonding Secondary bonding exists between virtually all molecules, but its presence is diminished if any primary bond is present.

Dipoles are created when positive and negative charge centers exist. Dipole moment=μ =q.d q= Electric charge d = separation distance +q -q d Skewed electron cloud 2-30

Secondary bonds are due to attractions of electric dipoles in atoms or molecules.

Electric dipole types Permanent dipoles Induced dipoles

Dipoles that do not fluctuate with time Permanent dipoles Dipoles that do not fluctuate with time

Example of a permanent dipole Hydrogen fluoride HF

Permanent dipoles in water

Water Attraction between positive oxygen pole and negative hydrogen pole.

Dipole-dipole interaction Dipole-dipole interaction in water H O 105 0 Dipole-dipole interaction H 2-33

Methane Vector sum of four C-H dipoles is zero.

Methane Methyl chloride CH4 CH3Cl Symmetrical arrangement of 4 C-H bonds No dipole moment CH4 Methyl chloride Asymmetrical tetrahedral arrangement Creates dipole CH3Cl 2-32

Cl- ions in green

Hydrogen bonding Hydrogen bonds are dipole-dipole interaction between polar bonds containing hydrogen atoms. It is a particularly strong type of secondary bonding, due to the almost bare proton. Examples: water, HF, etc.

Induced dipoles No permanent dipole moment Statistical fluctuation in electron density distribution London dispersion forces (weak) Examples: argon (an inert gas), methane (CH4 - a symmetric molecule)

Weak secondary bonds in noble gasses. Dipoles are created due to asymmetrical distribution of electron charges. Electron cloud charge changes with time. Symmetrical distribution of electron charge Asymmetrical distribution (Changes with time) 2-31

London forces between methane molecules

Another example of mixed bonding types in a material Graphite

Crystal forms of carbon Graphite Diamond Fullerene

Fullerene (a molecule)

Diamond

Graphite

The electronic configuration of carbon is 1s22s22p2, i.e.

An excited state of carbon with electronic configuration

Mixing of an s electron cloud with two p electron clouds sp2 hybridization Mixing of an s electron cloud with two p electron clouds

Bonding in graphite In-plane bonding: covalent + metallic Out-of-plane bonding: van der Waal’s bonding

Consequent properties of graphite Van der Waal’s bonding between layers - ease of sliding between layers (application as lubricant) Metallic bonding within a layer – high in-plane thermal and electrical conductivity

Bonding in benzene molecule sp2 hybridization of the carbon atoms

C C C C C C Chemical composition of benzene is C6H6. The carbon atoms are arranged in hexagonal ring. Single and double bonds alternate between the atoms. H C H H C C C C H H C H Structure of benzene Simplified notations 2-27

Effect of atomic bonding on material properties

Modulus of elasticity Related to the material stiffness. Defined as the amount that a material will stretch when a force is applied. It is related to the slope of the force-distance curve.

A steep dF/da slope gives a high modulus.

Coefficient of thermal expansion Describes how much a material expands or contracts when its temperature changes.

Asymmetric energy trough resulting in thermal expansion phenomenon