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 Bonding

The atom consists of neutral neutrons and positively charged protons

(which form a dense nucleus) surrounded by negatively charged

electrons.

Atoms = nucleus (protons and neutrons) + electrons

Charges:

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 calculations

The 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 nm

or a few Angstroms.

A

Nn

avρ×

=

electrons

protons & neutrons

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

the periodic table: the atomic mass of Ag = 107.868 g/mol)

nucleus

Solution:

# 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 mol

Number 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)

Solution

In 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 mol

Number 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 can only say what is the probability of finding it at some distance

from the nucleus. In other words, the exact position of an electron

can not be specified when the energy is known (Heisenberg

Uncertainty Principle)

Only certain “orbits” or shells of

electron probability densities are

allowed. The shells are identified by a

principal quantum number (n)

π4

hpx ≥∆∆

∆∆∆∆x is the uncertainty in the position of the electron, ∆∆∆∆p is the uncertainty in the momentum (mass x velocity)

and h is the Planck’s constant.

The principal quantum number n defines the energy of

the electrons:

Where A is a constant equal to 2.179x10-18J (or 13.6eV)

and Z is the positive charge of the nucleus.

The negative sign of the equation indicates that the

energy of the electron is chosen as zero when n is

infinite (the electron is not longer bound to the nucleus).

2n

AZE

−=

The principal quantum number n is not sufficient to determine the

location of the electron. Two other independent quantum numbers

are needed l and ml

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 sub-shell.

3rd quantum number ml: the number of energy states for each sub-

shell. s - 1 state; p - 3; d - 5; & f - 7.

The above quantum numbers are needed to indicate the orbital of the

electrons. A fourth quantum number (ms) is needed to explain some

chemical and physical properties of the atoms.

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”

Or

“No more than two electrons can occupy a single orbital and when

two electrons occupy a single orbital their spins must be different”

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

1

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

2 2pz2 3s2 3px

1 3py1

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

2 2pz2 3s2

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

2 2pz1

Energy

f

d

s

p

s

s

p

d

s

p

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 Reactivity

The 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 4.1

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. inactive

IA: Alkali metals (Li, Na, K…) have one electron in outermost

occupied s subshell - eager to give up electron – chem. active

VIIA: 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

Bonding Energy and Forces

There 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

bonding

Electron volt – the

energy lost / gained by

an electron when it is

taken through a

potential difference of

one volt.

E = q × V

For q = 1.6 x 10-19

Coulombs

V = 1 volt

1 eV = 1.6 x 10-19 J

Types of Bonding

Primary bonding: e- are transferred or shared

Strong (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)