Chapter Outline
Understanding 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):
N av × ρ
n=
A
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.
nucleus
protons & neutrons
electrons
Example: Calculate the number of atoms in 100g of silver.
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 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 Atoms
Electrons 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 2py1
Si (Z = 14)
1s2 2s2 2px2 2py2 2pz2 3s2 3px2 3py1
Mg (Z = 12)
1s2 2s2 2px2 2py2 2pz2 3s2
F (Z = 9)
1s2 2s2 2px2 2py2 2pz1
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
f
d
Energy
d
p
s
p
s
p
s
s
Principle Quantum Number, n
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
(a) C
1s2 2s2 2p2
(b) Li 1s2 2s1
(c) Be 1s2 2s2
(d) Mg 1s2 2s2 2p6 3s2
(e) P
1s2 2s2 2p6 3s2 3p3
(f) S
1s2 2s2 2p6 3s2 3p4
Valence
4
1
2
2
3
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
Ionization 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. 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
compounds
only
elements or
compounds
(„alloys“)
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 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+ClCovalent: 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)