Chapter OutlineUnderstanding of interatomic bonding is the first step towards understanding/explaining materials properties• Review of Atomic Structure: Electrons, Protons, Neutrons, Quantum mechanics of atoms, Electron states, The Periodic Table• Atomic Bonding in Solids: Bonding Energies and Forces• Periodic Table• Primary Interatomic Bonds: Ionic, Covalent, Metallic• Secondary Bonding (Van der Waals): Three types of Dipole Bonds• Molecules and Molecular Solids

Review : Atomic Structure and BondingThe atom consists of neutral neutrons and positively charged protons(which form a dense nucleus) surrounded by negatively charged electrons.

Atoms = nucleus (protons and neutrons) + electronsCharges:Electrons and protons have negative and positive charges of the same magnitude, 1.6 × 10-19 Coulombs.Neutrons are electrically neutral.Masses:Protons and Neutrons have the same mass, 1.67 × 10-27 kg.Mass of an electron is much smaller, 9.11 × 10-31 kg and can be neglected in calculation of atomic mass.# protons gives chemical identification of the element

# protons = atomic number (Z)# neutrons defines isotope number

The atomic mass (A) = mass of protons + mass of neutrons

Atomic mass units. Atomic weight.The atomic mass unit (amu) is often used to express atomic weight. 1 amu is defined as 1/12 of the atomic mass of the most common isotope of carbon atom that has 6 protons (Z=6) and six neutrons(N=6).Mproton ≈ Mneutron = 1.66 x 10-24 g = 1 amu.The atomic mass of the 12C atom is 12 amu.The atomic weight of an element = weighted average of the atomic masses of the atoms naturally occurring isotopes. Atomic weight of carbon is 12.011 amu. The atomic weight is often specified in mass per mole.A mole is the amount of matter that has a mass in grams equal to the atomic mass in amu of the atoms (A mole of carbon has a mass of 12 grams).The number of atoms in a mole is called the Avogadro number,

Nav = 6.023 × 1023. Nav = 1 gram/1 amu.Example: Atomic weight of iron = 55.85 amu/atom = 55.85 g/mol

Some simple calculationsThe number of atoms per cm3, n, for material of density ρ(g/cm3) and atomic mass A(g/mol):

Graphite (carbon): ρ = 2.3 g/cm3, A = 12 g/mol →n = 6×1023 atoms/mol × 2.3 g/cm3 / 12 g/mol = 11.5 × 1022 atoms/cm3

Diamond (carbon): ρ = 3.5 g/cm3, A = 12 g/mol →n = 6×1023 atoms/mol × 3.5 g/cm3 / 12 g/mol = 17.5 × 1022 atoms/cm3

Water (H2O) ρ = 1 g/cm3, A = 18 g/mol →n = 6×1023molecules/mol × 1g/cm3 / 18g/mol = 3.3 × 1022 molecules/cm3

For material with n = 6 × 1022 atoms/cm3 we can calculate the mean distance between atoms L = (1/n)1/3 = 0.25 nm.

! the scale of atomic structures in solids – a fraction of 1 nmor a few Angstroms.

ANn av ρ×

=

electrons

protons & neutrons

Example: Calculate the number of atoms in 100g of silver.

nucleus

Solution:From the periodic table:the atomic mass of Ag = 107.868 g/mol# of 100 g Ag atoms = (100g)×(6.023×1023atom/mol)/(107.868g/mol)= 5.58 ×1023 atoms

Example 1 : The cladding (outside layer–coating) of the U.S. quarter coin consists of an alloy of 75wt%Cu and 25wt%Ni. What are the atomic percent Cu and atomic percent Ni contents of this material? Cu (A = 63.54g/mol) Ni (A = 58.69g/mol)Clad : Composite coinage metal strip composed of a core, usually of a base metal such as copper, and surface layers of more valuable metal, silver (or sometimes copper-nickel). Cladding is a cost-saving measure, making coins cheaper to produce while maintaining a desired appearance. Solution: In 100g of the75wt%Cu-25wt%Ni alloy, there are 75g of Cu and 25g of Ni. Number of gram-mol of Cu = 75g / 63.54g/mol = 1.1803 molNumber of gram-mol of Ni = 25g / 58.69g/mol = 0.4260 mol

----------------Total gram-moles = 1.6063 mol

Cu at% = (1.1803mol / 1.6063mol)(100%) = 73.5at%Ni at% = (0.4260mol / 1.6063mol)(100%) = 26.5at%

Example 2 : An intermetallic compound has the general chemical formula NiXAlY, where X and Y are simple integers, and consists of 42.04wt%Ni and 57.96wt%Al. What is the simplest formula of this nickel aluminide? Ni (A = 58.69g/mol) Al (A = 26.98g/mol)SolutionIn 100g of the 42.04wt%Ni-57.96wt%Al alloy, there are 42.04g Ni and 57.96g Al. Number of gram-mol of Ni = 42.04g / 58.69g/mol = 0.7160 molNumber of gram-mol of Al = 57.96g / 26.98g/mol = 2.1483 mol

----------------Total gram-moles = 2.8643 mol

Ni gram-mol fraction = 0.7160mol / 2.8643mol = 0.25 Al gram-mol fraction = 2.1483mol / 2.8643mol = 0.75

Next, we replace the X and Y in the NiXAlY compound with 0.25 and 0.75 respectively, to give Ni0.25Al0.75 which is the simplest chemical formula. On an integral basis we need to multiply times four to give NiAl3 for the simplest chemical formula of this nickel aluminide.

The Electronic Structure of AtomsElectrons move not in circular orbits, but in 'fuzzy‘ orbits. Actually, we cannot tell how it moves, but only can say what is the probability of finding it at some distance from the nucleus.The electrons form a cloud around the nucleus, of radius of 0.05 – 2 nm. This picture looks like a mini planetary system. But quantum mechanics tells us that this analogy is not correct:Only certain “orbits” or shells of electron probability densities are allowed. The shells are identified by a principal quantum number n, which can be related to the size of the shell, n = 1, 2, 3 .. are larger. The second quantum number l,defines subshells within each shell. Two more quantum numbers characterize states within the subshells.

These "orbitals" may be of different shapes, orientations and energies. The "behavior" and "character" of the electrons within these orbitals are described by four quantum numbers:Principal quantum number n: shell - 1,2,3,…

shells can also be designated by the letters K, L, M, N,O,…2nd quantum number l: subshell - denoted by s, p, d or f.

It is related to the shape of the electron subshell. 3rd quantum number ml: the number of energy states for each subshell. s - 1 state; p - 3; d - 5; & f - 7.4th quantum number ms: the spin moment (+1/2 or -1/2) one for each of the spin orientation.

•The quantum numbers arise from solution of Schrodinger’s equation•Pauli Exclusion Principle: only one electron can have a given set of the four quantum numbers.

C (Z= 6) 1s2 2s2 2px1 2py

1

Si (Z = 14) 1s2 2s2 2px2 2py

2 2pz2 3s2 3px

2 3py1

Mg (Z = 12) 1s2 2s2 2px2 2py

2 2pz2 3s2

F (Z = 9) 1s2 2s2 2px2 2py

2 2pz1

Ene

rgy

f

d

sp

s

sp

d

sp

Principle Quantum Number, n

Electrons that occupy the outermost filled shell – the valence electrons – they are responsible for bonding.Electrons fill quantum levels in order of increasing energy (only n, l make a significant difference). Example: Iron, Z = 26: 1s22s22p63s23p63d64s2

Electronic Structure and Chemical ReactivityThe chemical properties of the atoms of the elements depend principally on the reactivity of the outer electrons.Noble gases Most stable (He – 1s2 , all others s2p6 configuration)Valence electrons: occupy the outermost filled shell. [Valence of an atom = No. of electrons that the atom loses, gains or shares to attain an octet]

Example: Sodium atom: Na: 1s22s22p63s1

Na+

+11e

Only 1 electron in the 3rd shell, it is readily released.Once this electron is released, it becomes Sodium ion (Na+).Cation: positive charge (usually a small atom)Anion: negative charge (usually a large atom)

Electronic Configuration Valence(a) C 1s2 2s2 2p2 4(b) Li 1s2 2s1 1(c) Be 1s2 2s2 2(d) Mg 1s2 2s2 2p6 3s2 2(e) P 1s2 2s2 2p6 3s2 3p3 3(f) S 1s2 2s2 2p6 3s2 3p4 2

Electronegativity: Electronegativity is defined as the degree to which an atom attracts electrons to itself. Electronegativity is measured in a scale from 0 to 4.1Ionization Potential: The energy (in eV) required to cause any atom to lose an electron and thus become a cation.Atomic Size: Each atom can be considered as a sphere with a definite radius. The radius of the atomic sphere is not constant but depend on its environment.

The Periodic Table

Elements in the same column (Elemental Group) share similar properties.Group number indicates the number of electrons available for bonding.

0: Inert gases (He, Ne, Ar...) have filled subshells: chem. inactiveIA: Alkali metals (Li, Na, K…) have one electron in outermost occupied s subshell - eager to give up electron – chem. activeVIIA: Halogens (F, Br, Cl...) missing one electron in outermost occupied p shell - want to gain electron - chem. active

In general: within a horizontal row in the periodic table, the more electropositive elements are those farthest left, and the more electronegative elements are those farthest right. within a vertical column in the periodic table, the more electropositive elements are those towards the bottom, and the more electronegative elements are those towards the top.

Different types of atomic radii(!! atoms can be treated as hard spheres !!)

element or compounds

elements or compounds(„alloys“)

compounds only

Variation of atomic radii through the Periodic table

Other quantities that show a systematic variation through the Periodic System: Electronegativity, Ionisation Potential ...

Bonding Energy and ForcesThere is a potential well for two interacting atoms The repulsion between atoms, when they are brought close to each other, is related to the Pauli principle: when the electronic clouds surrounding the atoms starts to overlap, the energy of the system increases abruptly.

The origin of the attractive part, dominating at large distances, depends on the particular type of bonding.

The electron volt (eV)– energy unit convenient for description of atomic bondingElectron volt – the energy lost / gained by an electron when it is taken through a potential difference of one volt.E = q × VFor q = 1.6 x 10-19

CoulombsV = 1 volt

1 eV = 1.6 x 10-19 J

Types of BondingPrimary bonding: e- are transferred or sharedStrong (100-1000 KJ/mol or 1-10 eV/atom)Ionic: Strong Coulomb interaction among negative atoms (have an extra electron each) and positive atoms (lost an electron). Example -Na+Cl-

Covalent: electrons are shared between the molecules, to saturate the valency. Example - H2

Metallic: the atoms are ionized, loosing some electrons from the valence band. Those electrons form a electron sea, which binds the charged nuclei in place.

Secondary Bonding: no e- transferred or shared. Interaction of atomic/molecular dipoles Weak (< 100 KJ/mol or < 1 eV/atom)•Fluctuating Induced Dipole (inert gases, H2, Cl2…)•Permanent dipole bonds (polar molecules - H2O, HCl...)•Polar molecule-induced dipole bonds (a polar molecule like induce a dipole in a nearby nonpolar atom/molecule)