EE2317-Course- 02 Atomic Structures and Interatomic bonding.pdf

MATERIAL SCIENCE AND ENGINEERING
Atomic Structures and Interatomic Bonding
Engr. Joseph Benedict N. Prim

Atomic
Structures
and
Interatomic
Bonding

Objectives
• To be able to name two atomic models cited, and note the differences
between them.
• To describe the important quantum-mechanical principle that relates
to electron energies.
• Briefly describe ionic, covalent, metallic, hydrogen and van der Waals
bonds.
• Note which material exhibit each of these bonding types

Outline
• Fundamental Concepts
• Atomic Models
• Quantum Numbers
• Electron Configurations
• Periodic Table
• Atomic Bonding in Solids
• Bonding forces and Energies
• Primary interatomic bonds (ionic, covalent & metallic)
• Secondary bonding

Fundamental Concepts
• Basic Idea:
Properties of materials are a
consequence of
• Identity of the atoms
• Spatial arrangement of the
atoms
• Interaction between the atoms
• Thus, the need to study atomic
structure/bonding.

Atom
• Consists of very small nucleus composed of protons
and neutrons, which is encircles or orbited by
moving electrons.

Atom
Parts Charge Mass
Electrons
1.602 x 10-19
Coulombs
9.11 x 10-31
kilogram (kg)
Protons
1.67 x 10-27
kilogram (kg)
Neutrons Electrically
neutral

Atomic Number (Z)
• For an electrically neutral or complete
atom, the atomic number also equals
the number of electrons.
Example
• Uranium (Z = 92) - The highest of the
naturally occurring elements

Atomic Mass (A)
Sum of the masses of protons
and neutrons; atomic mass
unit = amu = 1/12 mass of 12C

Isotopes
• Atoms that have two or more different atomic masses due to variable
number of neutrons (N)
• A ≈ Z + N

Atomic Weight
• Weighted average of the atomic masses of the atom’s naturally
occurring isotopes.
• It may be expresses in terms of atomic mass units or an atomic basis,
or the mass per mole of atoms.
• Atomic wt = wt of 6.022 x 1023 molecules or atoms
(Unit for atomic weight /mass)
• 1 amu/atom = 1g/mol
• C 12.011
• H 1.008

Atom VS Molecules
Atom
• An atom is smallest particle in an
element that has the properties of
the element.
• It is not possible to breakdown the
atom further retaining the
properties of the element.
• Atoms are not visible to the naked
eye and are the basic building
blocks.
Molecule
• Molecules are formed by the
combination of two or more
atoms.
• Unlike atoms, A molecules can be
subdivided to individual atoms.
• Molecules also are not visible to
the naked eye, while can be seen
through highly magnifying
microscopes and other scientific
devices.
Water is comprised of numerous water molecules. Each water molecule is made up of one oxygen atom and
two hydrogen atoms.

Electrons in Atoms
• The electrons form a cloud around the nucleus,
of radius of around 0.05-2nm.
• Bohr Atomic Model (Quantum theory)
• 1st JJ Thomson
• 2nd Ernest Rutherford
• 3rd Niels Bohr

Electrons
• The Bohr atomic model resembles the planetary system.

Energy Levels
• Energy of electrons is quantized,
meaning that the electrons are
permitted to have only specific values
of energy.
• Energy level or states – an electron may
change energy, 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).

However, quantum mechanics tells us
that this analogy is not correct.

Quantum Mechanics
• A branch of physics that deals with
atomic and subatomic systems; it
allows only discrete values of energy
that are separated from one another.

• Electrons do not revolve around circular orbits, but in odd shaped
orbitals depending on their quantum number.
• Compared with classical mechanics, which allows continuous energy
values.
• Limitations of the Bohr atomic model - Its inability to explain several
phenomena involving electrons.

Quantum
Numbers
• A set of four numbers, the values of which are used to label possible electron states.
• The four parameters that characterized the electron in an atom are:
• size (integer)
• shape (integer)
• spatial orientation (integer)
• energy levels
• Dictates the number of states within each subshell.

Quantum Numbers
• Principal (n) - n = 1, 2, 3, 4, 5….
• Describes the electron shell, or
energy level, of an atom.
• The value of n ranges from 1 to the
shell containing the outermost
electron of that atom
• The distance of an electron from
the nucleus, or its position
Example
• For caesium (Cs), the
outermost valence electron
is in the shell with energy
level 6, so an electron in
caesium can have an n value
from 1 to 6.

Quantum Numbers
• Angular or Azimuthal (L) – L = s, p, d, f
• (also known as the angular quantum number or orbital quantum number)
describes the subshell, and gives the magnitude of the orbital angular
momentum through the relation:
• L2 = ħ2 ℓ (ℓ + 1).
• Gives the shape of the orbital /electron subshell.
• The orbital angular momentum quantum number ℓ (little “el”)
• Planck's constant 6.62607015 × 10−34 joule per second.

Quantum Numbers
• Magnetic (m) – s = 1, p = 3, d = 5, f == 7
• Describes the specific orbital (or "cloud") within that subshell, and yields the
projection of the orbital angular momentum along a specified axis:
• Lz = mℓ ħ.
• Gives the number of energy states for each subshell.
• In the absence of an external magnetic field, the states within each shell are
identical.
• When a magnetic field is applied, these subshell states split, with each state
assuming a slightly different energy.

Quantum Numbers
• Spin moment (s)
• Describes the spin (intrinsic angular momentum) of the electron within that
orbital, and gives the projection of the spin angular momentum S along the
specified axis:
• Sz = ms ħ.

Electron configurations
• Electron state (level)
• One of the set of discrete, quantized
energies that are allowed for electrons.
• In the atomic case each state is specified
by four quantum numbers.

Pauli Exclusion
Principle
• Each electron state can hold no more
than two electrons, which must have
opposite spins.

Relative energies of
Electrons
• Figure 2.4 schematic representation of
the relative energies of the electrons for
the various shells and subshells.
(Introduction to Materials Science and
Engineering, J.M. Ralls, T.H. Courtney and
J. Wulff)

Electrons
From Figure 2.4
• The smaller the principal quantum
number, the lower the energy level.
Example. 1s < 2s < 3s
• Within each shell, the energy of a
subshell level increases with the value
of the l quantum number.
Example. 3s < 3p < 3d

Electrons
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.
Example. 4s < 3d
For most atoms, the electrons fill up the
lowest possible energy states in the
electron shells and subshells, two
electrons with opposite signs per state.

Ground State
• A condition when all the electrons occupy the lowest possible
energies in accord with the foregoing restrictions.
• A normally filled electron energy state form which an electron
excitation may occur.

Ground State
Example
• Figure 2.5 Schematic representation of
the filled and lowest unfilled energy
states for a sodium atom.

Electron Configuration
(structure of an atom)
• For an atom, it is the manner in which possible
electron state are filled with electrons.
• The number of electrons in each subshell is
indicated by a superscript after the shell-subshell
designation.
• Table 2.2 Listing of the expected electron
configuration for some of the common elements.
Callister

Valence electrons
• The electrons in the
outermost occupied
electron shell, which
participates in
interatomic bonding.

Stable Electron
Configurations
• The states within the outermost or valence electrons
shell are completely filled.
Example.
Neon (Ne), Argon (Ar), Krypton (Kr), Helium (He) – these
elements are inert, or noble gases, which are virtually
chemically unreactive.
Some atoms of the elements that have unfilled valence
shells assume stable electron configurations by gaining or
losing electrons to form charged ions, by sharing
electrons with other atoms.

The Periodic Table
• The arrangement of the chemical elements with increasing atomic
number according to the periodic variations in electron structure.
• Nonmetallic elements are positioned at the far right side of the table.

Figure 2.6 the periodic table of the elements. The numbers in parentheses are the atomic weights of the most stable or
common isotopes.

Arrangement:
• Rows or Periods
7 horizontal rows arranged in increasing atomic number.
• Columns or Groups
Have similar valence electron structures, as well as chemical and
physical properties.

Groups in the Periodic Table
• Group IA (alkali metals)
Elements are one electron in excess of stable structures..
• Group IIA (alkaline earth metals)
Elements are two electrons in excess of stable structures.
• Group IIIB through IIB (transition metals)
Have partially filled electron states and in some case, one or two
electrons in the next higher energy shell.
• Group IIIA, IVA, VA
Display characteristics that are intermediate between the metals and
nonmetals by virtue of the valence electron structures.

Groups in the Periodic Table
• Group VIA
Elements are two electrons deficient from having stable
structures.
• Group VIIA (halogens)
Elements are one electron deficient from having stable
structures.
• Group O (inert gases)
Elements have filled electron shells and stable electron
configurations.
Inert – lacking the ability to move
– chemically inactive

Electro-positive
• They are capable of giving up their few valence electrons to become
positively charged ions.
Electro-negative
• They readily accept electrons to become negatively charged ions, or
sometimes share electrons with other forms.

Figure 2.7 the electronegativity values for the elements. (The nature of the Chemical Bond, 3rd ed. Linus Pauling)

Electro-negative
Elements
• Conversely, the closer the atoms are
together (i.e. the smaller the difference
in electronegativity), the greater the
degree of co-valency.
• Atoms are more likely to accept
electrons if their outer shells are almost
full, and if they are less “Shielded” from
or closer to the nucleus.

Atomic Bonding in
Solids
• The principles of atomic bonding are best
illustrated by considering how tow isolated
atoms interact as they are brought close
together from an infinite separation.
• Large distances
• Interactions are negligible.
• The atoms are too far apart to have an
influence on each other.
• Small distances
• Each atom exerts forces on each other.
• The magnitude of each depends on the
separation or interatomic distance, r.
• Equilibrium Spacing (r0)
• The centers of two atoms will remain
separated even at equilibrium.

Bonding energy (E0)
• The minimum net energy that corresponds to the equilibrium
spacing.
• The energy that would be required to separate two atoms to an
infinite separation.

Bonding energy (E0)
• Figure 2.8 (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.

Electron Volt
• An energy unit that is convenient for describing atomic bonding.
• It is the energy gained or lost by an electron

Primary Bonding Types
• Primary or Chemical Bonds
• Ionic
• Covalent
• Metallic

Bonds found in solids.
• The bonding that involves the valence electrons.
• The nature of the bond depends on the electron structure of the
constituent atoms.
• Each of the three types of primary bonding arises from the tendency
of the atoms to assume stable electron structures, like those of the
inert gases, by completely filling the outermost electron shell.
• Why Atoms bond? - to lower their energy

Ionic Bonding
• Type of bonding between metals and non-metals.
• Elements that are suited for this type of bonding are located at the
horizontal extremities of the periodic table.
• Atoms of metals easily give up their valence electrons to their non-
metallic counterpart, thus we have a transfer of electrons
• In the process, all the atoms acquire stable or inert gas
configurations; also, they acquire an electrical charge, thus becoming
ions.

Ionic Bonding
• Let’s take the prevalent example of the
Sodium Chloride (NaCl), where the
outermost orbit of the sodium has one
electron, while chlorine has seven
electrons in the outermost shell.
• So, Chlorine needs only one electron to
complete its octet. When the two atoms
(Na and Cl) are put close to each other,
the sodium donates its electron to
chlorine. Thus by losing one electron
sodium becomes positively charged and
by accepting one electron chlorine
becomes negatively charged and becomes
chloride ion.

Ionic Bonding
• A sodium atom can assume the
electron configuration of neon
(with a net single + charge) by
the transfer of its one valence 3s
electron to the chlorine atom.
Aster the transfer, the chlorine
now has a net negative charge
with an electron configuration of
argon

Ionic Bonding
• Attractive forces are coulombic, meaning due to the positive and
negative ions, they attract one another.
• Large differences in electronegativity
• Non-directional type – the magnitude of the bond is equal in all
directions around the ion.
• Bonded atoms preferred specific orientations, have definite shape.
• For ionic materials to be stable, all positive ions mush have as nearest
neighbors negatively charged ions in a three dimensional scheme and
vice-versa.

Covalent Bonding
• Stable electron configurations are achieved by sharing of electrons
between adjacent atoms.
• The two atoms involved will each contribute at least one electron to
the bond.
• Comparable electronegativity
• Directional type

Covalent
Bonding
• Covalent bonds involve the sharing of the
electrons between the atoms. The pairing
of the shared electron, produce a new
orbit around the nuclei of both the atoms
referred to as molecule.
• For example, water having the formula as
H2O, in this the covalent bond is between
each hydrogen and oxygen molecules,
where two electrons are shared between
hydrogen and oxygen, one from each.
• As a hydrogen molecule, H2 contains two
hydrogen atom which is linked by the
covalent bond with oxygen. These are the
attractive forces between the atoms
occurring in the outer most orbit of the
electrons.

Covalent Bonding
• for a molecule of methane (CH4). The carbon
atom has four valence electrons, whereas each
of the four hydrogen atoms has a single
valence electron. Each hydrogen atom can
acquire a helium electron configuration (two 1s
valence electrons) when the carbon atom
shares with it one electron.
• The carbon now has four additional shared
electrons, one from each hydrogen, for a total
of eight valence electrons, and the electron
structure of neon. The covalent bond is
directional; that is, it is between specific atoms
and may exist only in the direction between
one atom and another that participates in the
electron sharing.

% Ionic Character
• It is possible to have interatomic bonds that are partially ionic and
partially covalent, and, in fact, very few compounds exhibit pure ionic
or covalent bonding. For a compound, the degree of either bond type
depends on the relative positions of the constituent atoms in the
periodic table or the difference in their electronegativities.
• The wider the separation (both horizontally—relative to Group IVA—
and vertically) from the lower left to the upper right-hand corner (i.e.,
the greater the difference in electronegativity), the more ionic the
bond.
• Conversely, the closer the atoms are together (i.e., the smaller the
difference in electronegativity), the greater the degree of covalency.

% Ionic Character
• The percent ionic character (%IC) of a bond between elements A and
B (A being the most electronegative) may be approximated by the
expression
where
Xa, Xb - electronegativity
- from Pauling’s table of electronegativities
= [1 – e ] x 100%
-0.25(Xa – Xb) 2

% Ionic Character
• Example
Given: XCl = 3.0, XH = 2.1, XNa = 0.9
Find:
(1) Determine the % ionic character of HCL, NaCl and Cl2;
(2) rank the bonds in HCL, NaCl and Cl2 from most covalent to most ionic
Ans.
(1)Cl2 – 0 difference
HCL = {1 –exp[-0.25 (2.1 – 3.0)2]} x 100%
= 18% ionic
NaCl= {1 –exp[-0.25 (0.9 – 3.0)2]} x 100%
= 67% ionic
(2) Cl2 > HCl > NaCl - differences in electronegativities

Metallic bonding
• Valence e- drifting through the entire metal to form a sea (cloud) of
electrons
• Sharing of electrons
• Comparable electronegativity
• Non-directional type

Metallic bonding
• Due to the presence of the delocalized or free-electrons of the
valence electrons, Paul Drude came up with the name “sea of
electrons” in 1900. The various characteristics properties of the
metals are; they have high melting and boiling points, they are
malleable and ductile, good conductors of the electricity, strong
metallic bonds, and low volatility.
• In this type, the valence electrons continuously move from one atom
to other as the outermost shell of electrons of each metal atoms
overlaps the neighboring atoms. So we can say that the in metal the
valence electrons continuously moves independently from one place
to another throughout the entire space.

Metallic bonding
• A. Outermost electrons wander freely
through metal. Metal consists of cations
held together by negatively-charged
electron "glue."

Metallic bonding
• B. Free electrons can move rapidly in
response to electric fields, hence metals
are a good conductor of electricity.

Metallic bonding
• C. Free electrons can transmit kinetic
energy rapidly, hence metals are good
conductors of heat.

Metallic bonding
• D. The layers of atoms in metal are hard
to pull apart because of the electrons
holding them together, hence metals
are tough. But individual atoms are not
held to any other specific atoms, hence
atoms slip easily past one another. Thus
metals are ductile. Metallic Bonding is
the basis of our industrial civilization.

Comparison Chart
BASIS FOR COMPARISON COVALENT BOND METALLIC BOND IONIC BOND
Meaning When there is a strong
electrostatic force of
attractions between two
positively charged nuclei
and the shared pair of
electrons is called the
covalent bond.
When there is the strong
attractions between the
cation or atoms and the
delocalized electrons in
the geometrical
arrangement of the two
metals, is called a metallic
bond.
When there is a strong
attraction between a
cation and an anion (two
oppositely charged ions)
of elements is called the
ionic bond. This bond is
formed between a metal
and a non-metal.
Existence Exist as solids, liquids and
gasses.
Exist in the solid state
only.
They also exist in the solid
state only.
Occurs between Between two non-metals. Between two metals. Non-metal and metal.

Comparison Chart
Involves Sharing of electrons in the
valence shell.
The attraction between
the delocalized electrons
present in the lattice of
the metals.
Transfer and accepting of
electrons from the
valence shell.
Conductivity Very low conductivity. High thermal and
electrical conductivity.
Low conductivity.
Hardness These are not very hard,
though exceptions are
silicon, diamond and
carbon.
These are not hard. These are hard, because
of the crystalline nature.

Comparison Chart
Melting and Boiling Points Low. High. Higher.
Malleability and Ductility These are non-malleable
and non-ductile.
Metallic bonds are
malleable and ductile.
Ionic bonds are also non-
malleable and non-
ductile.
Bond They are the directional
bond.
The bond is non-
directional.
The bond is non-
directional.

Comparison Chart
Bond energy Higher than the metallic
bond.
Lower than the other two
bond.
Higher than the metallic
bond.
Electronegativity Polar covalent: 0.5-1.7;
Non-polar<0.5.
Not available.
>1.7.
Examples Diamond, carbon, silica,
hydrogen gas, water,
nitrogen gas, etc.
Silver, gold, nickel, copper,
iron, etc.
NaCl, BeO, LiF, etc.

Secondary, van der Waals, or physical bonds
• Interatomic and intermolecular bonds that is relatively weak in
comparison to primary or chemical bonds.
• Bonding energies are relatively small on the order of only 10kJ/mol or
0.1 eV/atom.
• Exists between virtually all atoms or molecules, but its presence may
be obscured if any of the three primary bonding types are present.

Secondary, van der Waals, or physical bonds
• Evidenced for the inert gases, which have stable electron structures,
and between molecules that are covalently bonded.
• Normally atomic or molecular dipoles are involved. Dipoles exist
whenever there is some separation of positive and negative portion
of an atom or molecule.

Secondary,
van der
Waals, or
physical
bonds
• Bonding results from the coulombic attraction
between the positive end of one dipole and the
negative region of an adjacent one.
• Occur between induced dipoles and polar
molecules (which have permanent dipoles), and
between polar molecules.

Hydrogen Bonding
• A special type of secondary bonding.
• A strong secondary interatomic bond that exists between a bound
hydrogen atom (the unscreened proton) and the electrons of
adjacent atoms.

Dipoles
• An electric dipole is a separation of positive and negative charges.
• The simplest example of this is a pair of electric charges of equal
magnitude but opposite sign, separated by some (usually small)
distance

Fluctuating Induced Dipole Bonds
• A dipole may be created or induced in an atom or molecule that is
normally electrically symmetric.

Dipoles
• Fluctuating Symmetric refers to the overall spatial distribution of the
electrons in symmetry with respect to the positively charged nucleus.
Dipole Bonds
• All atoms are experiencing constant vibration that can cause
instantaneous and short lived distortions of electrical symmetry and
can create small electric dipoles.
• These attractive forces may exist between large number of atoms or
molecules, which forces are temporary and fluctuate with time.

Polar Molecule-Induced Dipole Bonds
• Polar molecule
• Are molecules in which there exist a permanent electric dipole moment by
virtue of the asymmetrical distribution of positively and negatively charged
regions.
Figure 2.14. Schematic representation of a
polar hydrogen chloride (Hcl) molecule.

Permanent Dipole Bonds
• The associated bonding energies are significantly greater than for
bonds involving induced dipoles.
• Also called as electret.
• A special case of polar molecule bonding is the Hydrogen bond.
• Hydrogen bond
• Strongest secondary bonding type
• Examples are HF, H2O and NH3.
• Hydrogen is covalently bonded with fluorine, oxygen and nitrogen.

Hydrogen bond
Figure 2.15. schematic representation of hydrogen bonding in hydrogen fluoride (HF)

Hydrogen bond
• The single hydrogen electron is shared with the other atom.
• The hydrogen end of the bond is basically a positively charge bare
proton because it is unscreened by any electron.
• This highly positive end is capable of strong attractive force with the
negative end of an adjacent molecule.
• Magnitude is generally greater than that of the other types of
secondary bonds and may be as high as 51kJ/ mol (0.52 eV/molecule)
• Melting and boiling temperatures for hydrogen fluoride and water are
abnormally high in light of their low molecular weights, as a
consequence of hydrogen bonding.

Molecules
• Many are composed of groups of atoms that are bound together by
strong covalent bonds.
Examples.
• Elemental diatomic molecules (F2, O2, H2 etc)
• Compounds (H2O, CO2, HNO3, C6H6, CH4 etc)
• Bonds between molecules are weak secondary ones

Molecules
• Molecular materials have relatively low melting and boiling
temperatures.
• Small molecules – gases at ordinary, or ambient, temperatures and
pressures
• Large molecules – modern polymers exist as solids, some of the
properties are strongly dependent on the presence of van der waals
and hydrogen secondary bonds.

Summary
• Electrons in Atoms
• The two atomic models are Bohr and wave-mechanical. Whereas the Bohr model
assumes electrons to be particles orbiting the nucleus in discrete paths, in wave
mechanics we consider them to be wavelike and treat electron position in terms
of a probability distribution.
• The energies of electrons are quantized—that is, only specific values of energy
are allowed.
• The four electron quantum numbers are n, l, ml, and ms. Each of these specifies a
distinct electron characteristic.
• According to the Pauli exclusion principle, each electron state can accommodate
no more than two electrons, which must have opposite spins.

Summary
• The Periodic Table
• Elements in each of the columns (or groups) of the periodic table have distinctive
electron configurations. For example,
• Group 0 elements (the inert gases) have filled electron shells, and Group IA
elements (the alkali metals) have one electron greater than a filled electron
shell.

Summary
• Bonding Forces and Energies
• Bonding force and bonding energy are related to one another according to
Equation 2.4.
• Attractive, repulsive, and net energies for two atoms or ions depend on
interatomic separation per the schematic plot.
• From a plot of interatomic separation versus force for two atoms/ions, the
equilibrium separation corresponds to the value at zero force.
• From a plot of interatomic separation versus potential energy for two atoms/ions,
the bonding energy corresponds to the energy value at the minimum of the curve

Summary
• Primary Interatomic Bonds
• For ionic bonds, electrically charged ions are formed by the transference of
valence electrons from one atom type to another. This type of bonding is found in
ceramic materials.
• There is a sharing of valence electrons between adjacent atoms when bonding is
covalent. Polymers and some ceramic materials covalently bond.
• The percent ionic character (%IC) of a bond between two elements (A and B)
depends on their electronegativities (X’s).
• With metallic bonding, the valence electrons form a “sea of electrons” that is
uniformly dispersed around the metal ion cores and acts as a form of glue for
them.
• Metallic materials exhibit this type of bonding.

Summary
Important Terms and
Concepts
atomic mass unit (amu)
atomic number (Z)
atomic weight (A)
Bohr atomic model
bonding energy
coulombic force
covalent bond
dipole (electric)
electron configuration
electronegative
electron state
electropositive
ground state
hydrogen bond
ionic bond
isotope
metallic bond
mole
Pauli exclusion principle
periodic table
polar molecule
primary bond
quantum mechanics
quantum number
secondary bond
valence electron
van der Waals bond
wave-mechanical model

References
Materials Science and Engineering – an Introduction
William D. Callister, Jr. and David G. Rethwisch
• https://depositphotos.com/64489357/stock-illustration-black-and-white-gecko-lizard.html
• https://study.com/academy/lesson/what-is-a-wave-mechanical-model.html
• https://surfguppy.com/ionic-and-covalent-bonding/electronegativity-bond-scale/
• https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplement
al_Modules_(Physical_and_Theoretical_Chemistry)/Physical_Properties_of_Matter/Atomic_and_Molecular_
Properties/Intermolecular_Forces/Specific_Interactions/Lennard-Jones_Potential
• https://biodifferences.com/difference-between-covalent-metallic-and-ionic-bonds.html

EE2317-Course- 02 Atomic Structures and Interatomic bonding.pdf

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