Properties of

Engineering Materials
Atomic Structures &
Interatomic Bonding

Dr. Eng. Yazan Al-Zain

Department of Industrial Engineering
University of Jordan
Fundamental Concepts
 Each atom consists of a very small nucleus composed of protons
and neutrons, which is encircled by moving electrons.

 Both electrons and protons are electrically charged, the charge

magnitude being 1.602 × 10-19 C, which is negative in sign for electrons
and positive for protons; neutrons are electrically neutral.

 Masses for these subatomic particles are infinitesimally small;

protons and neutrons have approximately the same mass, 1.67 ×
10-27 kg, which is significantly larger than that of an electron, 9.11 ×
10-31 kg.

 The atomic number Z (no. of protons) characterizes each element.

 This atomic number ranges in integral units from 1 for hydrogen to 92

for uranium, the highest of the naturally occurring elements.
Fundamental Concepts
 The atomic mass (A) of a specific atom may be expressed as the
sum of the masses of protons and neutrons within the nucleus.

 Atoms of some elements have two or more different atomic masses,

which are called isotopes.

 This is because Although the number of protons is the same for all
atoms of a given element, the number of neutrons (N) may be variable.

 The atomic weight of an element corresponds to the weighted average of

the atomic masses of the atom’s naturally occurring isotopes.
Fundamental Concepts
 The atomic mass unit (amu) may be used to compute atomic
weight.

 A scale has been established whereby 1 amu is defined as of the atomic

mass of the most common isotope of carbon, carbon 12 (12C) (A
12.00000).

 Within this scheme, the masses of protons and neutrons are slightly
greater than unity, and

A Z N
Fundamental Concepts
 The atomic weight of an element or the molecular weight of a
compound may be specified on the basis of amu per atom
(molecule) or mass per mole of material.

 In one mole of a substance there are 6.022 × 10-23 (Avogadro’s

number) atoms or molecules. These two atomic weight schemes are
related through the following equation:

1 amu/atom (or molecule) = 1 g/mol

 For example, the atomic weight of iron is 55.85 amu/atom, or 55.85

g/mol.
Electrons in Atoms
Atomic Models
 Bohr atomic model “an early outgrowth of quantum
mechanics”: is one in which in which electrons are assumed to
revolve around the atomic nucleus in discrete orbitals, and the
position of any particular electron is more or less well defined in
terms of its orbital.

Fig. 1: Schematic representation of the

Bohr atom.
Electrons in Atoms
Atomic Models
 Another important quantum-mechanical principle stipulates that the
energies of electrons are quantized; that is,

 Electrons are permitted to have only specific values of energy.

 An electron may change energy, but in doing so it must make a

quantum jump either to an allowed higher energy (with absorption of
energy) or to a lower energy (with emission of energy).

 Allowed electron energies being associated with energy levels or states.

 Electrons in Atoms
Atomic Models

These energies are taken to

be negative, whereas the
zero reference is the unbound
or free electron.

Fig. 2: (a) The first three

electron energy states for the
Bohr hydrogen atom. (b)
Electron energy states for the
first three shells of the wave-
mechanical hydrogen atom.
Electrons in Atoms
Atomic Models
 Bohr model: imposes limitations as electrons are treated as a particle.

 Resolution: wave-mechanical model, the electron is considered to

exhibit both wavelike and particle-like characteristics.

 With this model, an electron is no longer treated as a particle moving in

a discrete orbital; rather, position is considered to be the probability of an
electron’s being at various locations around the nucleus.
 Electrons in Atoms
Atomic Models

Fig. 3: (a) Comparison of

the (a) Bohr and (b) wave
mechanical atom models in
terms of electron distribution.
Electrons in Atoms
Quantum Numbers
 Using wave mechanics, every electron in an atom is characterized
by four parameters called quantum numbers.

 The size, shape, and spatial orientation of an electron’s probability

density are specified by three of these quantum numbers.

 Bohr energy levels separate into electron subshells, and quantum

numbers dictate the number of states within each subshell.

 Shells are specified by a principal quantum number n, which may

take on integral values beginning with unity; sometimes these shells
are designated by the letters K, L, M, N, O, and so on, which
correspond, respectively, to n = 1, 2, 3, 4, 5, etc.
Electrons in Atoms
Quantum Numbers
Table 1: The Number of Available Electron States in Some of the Electron
Shells and Subshells.

 The second quantum number, l, signifies the subshell, which is

denoted by a lowercase letter—an s, p, d, or f; it is related to the
shape of the electron subshell (the number of these subshells is
restricted by the magnitude of n).
Electrons in Atoms
Quantum Numbers
 The number of energy states for each subshell is determined by the
third quantum number, ml.

 For an s subshell, there is a single energy state, whereas for p, d, and f

subshells, three, five, and seven states exist, respectively.

 Related to this spin moment is the fourth quantum number, ms, for
which two values are possible (+1/2 1nd -1/2) one for each of the
spin orientations.

 Thus, the Bohr model was further refined by wave mechanics, in

which the introduction of three new quantum numbers gives rise to
electron subshells within each shell (See Fig. 2).
 Electrons in Atoms
3 important notes
Quantum Numbers
1. The smaller the principal quantum
number, the lower the energy level; for
example, the energy of a 1s state is
less than that of a 2s state.

2. Within each shell, the energy of a

subshell level increases with the value
of the l quantum number. For
example, the energy of a 3d state is
greater than a 3p.

3. There may be overlap in energy of

a state in one shell with states in an
adjacent shell, which is especially true
of d and f states; for example, the
energy of a 3d state is generally
Fig. 4: Schematic representation of the relative greater than that for a 4s.
energies of the electrons for the various shells
and subshells.
Electrons in Atoms
Quantum Numbers
Table 2: A Listing of the Expected Electron Configurations for Some of the
Common Elements.
Element Atomic # Electron configuration
Hydrogen 1 1s 1
Helium 2 1s 2 (stable)
Lithium 3 1s 2 2s 1
Beryllium 4 1s 2 2s 2
Boron 5 1s 2 2s 2 2p 1
Carbon 6 1s 2 2s 2 2p 2
... ...
Neon 10 1s 2 2s 2 2p 6 (stable)
Sodium 11 1s 2 2s 2 2p 6 3s 1
Magnesium 12 1s 2 2s 2 2p 6 3s 2
Aluminum 13 1s 2 2s 2 2p 6 3s 2 3p 1
... ...
Argon 18 1s 2 2s 2 2p 6 3s 2 3p 6 (stable)
... ... ...
Krypton 36 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable)
Electrons in Atoms
Electron Configurations
 Pauli exclusion principle: used to determine the manner in which
electron states are filled with electrons.

 This principle stipulates that each electron state can hold no more
than two electrons, which must have opposite spins.

 Thus, s, p, d, and f subshells may each accommodate, respectively, a

total of 2, 6, 10, and 14 electrons.
Electrons in Atoms
Electron Configurations
 For most atoms, the electrons fill up the lowest possible energy
states in the electron shells and subshells, two electrons (having
opposite spins) per state.

 The energy structure for a sodium atom is represented schematically

in Figure 5.

 When all the electrons occupy the lowest possible energies, an atom
is said to be in its ground state.
Electrons in Atoms
Electron Configurations

Fig. 5 Schematic representation of

the filled and lowest unfilled energy
states for a sodium atom
Electrons in Atoms
Electron Configurations
 comments regarding these electron configurations are necessary.

 First, the valence electrons are those that occupy the outermost shell.
These electrons are extremely important; they participate in the bonding
between atoms to form atomic and molecular aggregates. Furthermore,
many of the physical and chemical properties of solids are based on
these valence electrons.
 Second, inert atoms have what are termed stable electron
configurations; that is, the states within the outermost or valence
electron shell are completely filled. (Ne, Ar, Kr, and He).
 Some atoms of the elements that have unfilled valence shells assume
stable electron configurations by gaining or losing electrons to form
charged ions, or by sharing electrons with other atoms. This is the basis
for some chemical reactions, and also for atomic bonding in solids.
Electrons in Atoms
Electron Configurations
ex: Fe - atomic # = 26 1s2 2s2 2p6 3s2 3p6 3d 6 4s2

4d
4p N-shell n = 4 valence
electrons
3d
4s

Energy 3p M-shell n = 3
3s

2p L-shell n = 2
2s

1s K-shell n = 1
The Periodic Table
 In the periodic table, the elements are situated, with increasing
atomic number, in seven horizontal rows called periods.

 The arrangement is such that all elements arrayed in a given column or

group have similar valence electron structures, as well as chemical and
physical properties.
 These properties change gradually, moving horizontally across each
period and vertically down each column.
The Periodic Table Fig. 6: Periodic Table

inert gases
give up 1e-
give up 2e-

accept 2e-
accept 1e-
give up 3e-

H He
Li Be O F Ne
Na Mg S Cl Ar
K Ca Sc Se Br Kr
Rb Sr Y Te I Xe
Cs Ba Po At Rn
Fr Ra

Electropositive elements: Electronegative elements:

Readily give up electrons Readily acquire electrons
to become + ions. to become - ions.
The Periodic Table
Electronegativity Fig. 7: The electronegativity
values for the elements
• Ranges from 0.7 to 4.0,
• Large values: tendency to acquire electrons.

Smaller electronegativity Larger electronegativity

Bonding Forces & Energies
- Attractive force depends on type of
bonding.
- Repulsive force arises from the
negatively charged electron cloud
for the 2 atoms.

- Equilibrium spacing: r0.

- Minimum energy to separate
atoms (bonding energy): E0.

Fig. 8: (a) The dependence of repulsive,

attractive, and net forces on interatomic
separation for two isolated atoms. (b) The
dependence of repulsive, attractive, and net
potential energies on interatomic separation
for two isolated atoms.
Primary Interatomic Bonds
Ionic Bonding
 It is always found in compounds that are composed of both metallic
and nonmetallic elements.

 Atoms of a metallic element easily give up their valence electrons to

the nonmetallic atoms.

 In the process all the atoms acquire stable or inert gas configurations
and, in addition, an electrical charge; that is, they become ions.
Primary Interatomic Bonds
Ionic Bonding
 Sodium chloride (NaCl) is the classic ionic material.

Na (metal) Cl (nonmetal)
unstable unstable
electron

Na (cation) + - Cl (anion)
stable Coulombic stable
Attraction

Fig. 9: Ionic bonding in NaCl

Primary Interatomic Bonds
Ionic Bonding
 Energy – minimum energy most stable
 Energy balance of attractive and repulsive terms


A 
B
EN = EA + ER =
r rn
Repulsive energy ER

Interatomic separation r

Net energy EN

Attractive energy EA
27
 Primary Interatomic Bonds
Covalent Bonding
 stable electron configurations are assumed by the sharing of
electrons between adjacent atoms.

 Two atoms that are covalently bonded will each contribute at least one
electron to the bond, and the shared electrons may be considered to
belong to both atoms.
shared electrons
C: has 4 valence e-, H
from carbon atom
needs 4 more CH 4
H: has 1 valence e-,
needs 1 more H C H

Electronegativities shared electrons

are comparable. from hydrogen
H
Fig. 10: Schematic representation of covalent atoms
bonding in a molecule of methane (CH4).
Primary Interatomic Bonds
Ionic- Covalent Mixed Bonding
 It is possible to have interatomic bonds that are partially ionic and
partially covalent.

 In fact, very few compounds exhibit pure ionic or covalent bonding.

 For a compound, the degree of either bond type depends on the

difference in their electronegativities.

 The greater the difference in electronegativity, the more ionic the

bond, and the smaller the difference the greater the degree of
covalency.
Primary Interatomic Bonds
Ionic- Covalent Mixed Bonding
Primary Interatomic Bonds
Metallic Bonding
 Found in metals and their alloys.

 Metallic materials have one, two, or at most, three valence electrons.

 In a proposed model, these valence electrons are not bound to any

particular atom in the solid and are more or less free to drift
throughout the entire metal.

 They may be thought of as belonging to the metal as a whole, or forming

a “sea of electrons” or an “electron cloud.”

 The remaining non-valence electrons and atomic nuclei form what

are called ion cores, which possess a net positive charge equal in
magnitude to the total valence electron charge per atom.
 Primary Interatomic Bonds
Metallic Bonding

The free electrons shield the positively

charged ion cores from mutually repulsive
electrostatic forces.

In addition, these free electrons act as

a “glue” to hold the ion cores together.

Fig. 11: Schematic illustration of metallic

bonding.
SECONDARY BONDING OR
VANDER WAALS BONDING
 They are weak in comparison to the primary or chemical ones.

 Bonding energies are typically on the order of only 10 kJ/mol (0.1

eV/atom).

 Secondary bonding exists between virtually all atoms or molecules,

but its presence may be obscured if any of the three primary bonding
types is present.

 Evidenced for the inert gases and between molecules in molecular

structures that are covalently bonded.
SECONDARY BONDING OR
VANDER WAALS BONDING
 Secondary bonding forces arise from atomic or molecular dipoles.

 An electric dipole exists whenever there is some separation of

positive and negative portions of an atom or molecule.

 The bonding results from the coulombic attraction between the positive
end of one dipole and the negative region of an adjacent one.

 Hydrogen bonding, a special type of secondary bonding, is found to

exist between some molecules that have hydrogen as one of the
constituents.
Fig. 12 Schematic illustration
of van der Waals bonding
between two dipoles.
SECONDARY BONDING
• Fluctuating dipoles
asymmetric electron ex: liquid H 2
clouds H2 H2

+ - + - H H H H
secondary secondary
bonding bonding

• Permanent dipoles-molecule induced

secondary
-general case: + - bonding
+ -

secondary
-ex: liquid HCl H Cl bonding H Cl

se con
-ex: polymer dary
bondi secondary bonding
ng

35
Primary Interatomic Bonds
Bonding Energy
Table 3: Bonding Energies and Melting Temperatures for Various
Substances.