ENS 205 Materials Science I Chapter 2: Atomic Bonding

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ENS 205Materials Science IChapter 2 Atomic
Bonding
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Objectives

• At the end of this chapter
• Know the quantum number of elements and apply
  them.
• Know the periodic table of elements
• Know the 4 methods by which atoms bond to each
  other
• Understand the energy/force relationship between
  atoms making atomic bonds.

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Material Infrastructure

• What makes their materials behavior, mechanical
  for instance, different?
• Microstructure- major properties result from
  mechanisms occurring at either atomic or the
  microscopic level
• Chemical or Atomic Bonding
• Strong bonding of ceramics high strength and
  stiffness, and resistance to temperature and
  corrosion, but brittle
• Weakly bonding of chain molecules in polymers
  low strength and stiffness, creep deformation

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Atom

• Atoms nucleus (protons and neutrons)
  electrons
• Protons and Neutrons have the same mass, and
  determines the weight of the atom
• Mass of an electron is much smaller than mass of
  proton/neutron, and can be neglected in
  calculation of atomic mass.

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Atom
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Atom Definitions

• Consider the number of protons and neutrons in
  the nucleus as the basis of the chemical
  identification ? periodic table (placed by the
  number of protons)
• Atomic Mass Unit (amu) mass of proton or neutron
  1.66x10-24 gr

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Atom Definitions

• Atomic number the number of protons in the
  nucleus
• Avogadros number, Nav 6.023x1023 ? of
  protons or neutrons necessary to produce a mass
  of 1 gr. ? Avogadros number (Nav )of atoms of a
  given element termed as gram-atom
• amu1/ Nav
• 1.66x10-24 1/6.023x1023

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Atom definitions

• 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).
• Example C12 carbon isotope
• 1 C12 atom? 6 protons6 neutrons ?12 amu
• Nav many C12 atom?1 mole C12 atom ?12 gr
• Mole of a compound contains Avogadros number of
  each constituent atom
• E.g. 1 mole of NaCl, 6.023x1023 of Na atoms
  6.023x1023 Cl atoms

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Atomic number
Atomic mass (in amu)
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Quantum Numbers

• Electronic energy levels in atoms are specified
  by using quantum numbers
• The principal quantum is n.
• n indicates the primary electron shell in an atom
  where the shells are represented by K1, L2,
  M3, etc.

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Planetary atomic model
The atomic structure of sodium, atomic number 11,
showing the electrons in the K, L, and M quantum
shells.
the most inner K-shell can accommodate only two
electrons, called s-electrons the next L-shell
two s-electrons and six p-electrons the M-shell
can host two s-electrons, six p-electrons, and
ten d-electrons and so on.
The electronic configuration of the different
energy levels fill in a relatively straight
forward pattern in a shorthand notation. 1s2 2s2
2p6 3s2 3p6 3d10 4s2 4p6 4d10 5s2 . eg., for
Carbon, which has an atomic number of 6, it has 6
protons and 6 electrons. Its electronic
configuration in shorthand notation is 1s2 2s2
2p2 .
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Electron (Atomic) Orbitals
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Electron (Atomic) Orbitals

• The electron volt (eV) energy unit convenient
  for description of atomic bonding
• Electron volt - the energy lost / gained by an
  electron after it has moved through a potential
  difference of 1 volt .
• E q V
• For q 1.6 x 10-19 Coulombs V 1 volt
• 1 eV 1.6 x 10-19 J

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Identification of the Elements
We can identify the elements using their
florescence energy when a material is irradiated
by an x-ray, electron or gamma ray.
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Identification of the Elements
The energy of an x-ray emitted from a K, L or M
shell electron can be used to identify the atomic
number of the element present in a material.
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Atomic Bonding

• Classification of engineering materials may be
  based on the nature of atomic bonding.
  Understanding the atomic bonding requires the
  understanding of the structure of the individual
  atoms
• Chemical bonds hold atoms and molecules together
  in solids.
• Most of the materials not composed of just a
  single specie of atoms. They are compounds,
  composed of molecules made up of atoms from two
  or more elements.
• When two or more atoms combine to form molecules
  of a compound, they form atomic bonds between
  them through chemical bonding.
• Chemical bonding is essentially the interaction
  of electrons from one atom with the electrons of
  another atom. The bonding of adjacent atoms is
  essentially an electronic process
• Primary Bonding
• Secondary Bonding

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Atomic Bonding

• When atoms are combined into solids, there are
  several bonding mechanisms that can occur, which
  result in properties that may differ
  substantially from those of the atom alone.
  Hence, it is necessary to understand the types of
  bonding that can occur In the Solid Sphere Model,
  there are three primary or strong bonds and one
  weaker or secondary (but important!) type of bond
  between atoms or ions.
• 1) Ionic bonds
• 2) Covalent bonds
• 3) Metallic bonds
• 4) Van der Waals bonds

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Atomic or ionic radius

• An atomic or ionic radius refers to the radius
  corresponding to the average electron density

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Valence Electrons

• Valence electrons are those electrons in the
  outer shells that are easily removed or added to
  form either a positive or negative charge for the
  purpose of combinations with other atoms.
• These then form ions, which we shall see, are
  important for ceramics and semiconductors.
• Valence electrons are the single most important
  structure of an atom or ion as they determine the
  physical (mechanical), electrical, photonic and
  magnetic properties of materials.

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Valence Electrons

• What is the valence of an atom?
• The valence is the ability of the atom to enter
  into chemical combination with other elements and
  is often determined by the number of outermost
  combined s, p, and /or d levels.
• Examples are
• Mg 1s2 2s2 2p6 3s2 valence 2
• Al 1s2 2s2 2p6 3s2 3p1 valence
  3
• Ge 1s2 2s2 2p6 3s2 3p1 3d10 4s2 4p2 valence
  4
• Valence electrons determine all of the properties
  of the material!

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Valence Electrons(contd)

• There are exceptions to the filling order of the
  electronic shells
• e.g., Iron, Fe atomic no. 26 1s2 2s2 2p6 3s2
  3p6 3d8 3d6 4s2 instead of completely filling
  the 3d orbital with 8 electrons, Fe first fills
  the 4s orbital.

Electron Configuration of Nickel
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xt/Fe/econ.html
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Exceptions in 3d, 4d, 5d

• A d subshell that is half-filled or full (ie 5 or
  10 electrons) is more stable than the s subshell
  of the next shell. This is the case because it
  takes less energy to maintain an electron in a
  half-filled d subshell than a filled s subshell.
• For instance, copper (atomic number 29) has a
  configuration of Ar4s1 3d10, not Ar4s2 3d9
• Likewise, chromium (atomic number 24) has a
  configuration of Ar4s1 3d5, not Ar4s2 3d4
  where Ar represents the configuration for argon.

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Valence Electrons
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Atomic Structure

• Filled outermost shells are the most stable
  (non-reactive) configurations. The atoms with
  unfilled valence shells strive to reach the
  stable configuration by gaining or loosing
  electrons or sharing electrons with other atoms.
  This transference/sharing of electrons result in
  a strong bonding among atoms,

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Electronegativity

• Some properties of elements include
• Electronegativity is the tendency of an atom to
  gain an electron. High electronegativity atoms
  tend to be on the right side of the Periodic
  Table and low electronegativity atoms are on the
  left side. What is the most electronegative
  element?
• Electropositivity is the tendency of an atom to
  loss electrons.
• High electronegative atoms tend to react with
  high electropositive atoms to form ionic
  molecules and ceramic materials.
• The sharing of electrons tends to make very
  strong atomic bonds. In the case of ceramics
  these bonds may break abruptly making the ceramic
  brittle.

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The electronegativities of selected elements
relative to the position of the elements in the
periodic table.
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Periodic Table
The atomic number, atomic mass, density and
crystal structure are given.
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Atomic Bonding

• Primary Bonds are formed when outer orbital
  electrons are transferred or shared between
  atoms. strong and stiff, hard to melt, metals and
  ceramics,
• Ionic
• Covalent
• Metalic

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Secondary bonds

• Secondary bonds relatively weak, behavior of
  liquids, bonds between carbon-chain molecules in
  polymers, due to subtle attraction between
  positive and negative charges (no transfer or
  sharing)
• Van der Waals
• Hydrogen

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Primary Chemical Bonds Ionic Bonding

• An ionic bond is created between two unlike
  atoms with different electronegativities. When
  sodium donates its valence electron to chlorine,
  each becomes an ion attraction occurs due to
  their opposite electrostatic charges, and the
  ionic bond is formed.
• The size of the Cl ion is big compared to its
  elemental size whereas the size of Na ion is
  small compared to its elemental size.
• eg. Na and Cl form NaCl where the properties of
  the resultant material (salt) is very different
  from either of the atoms. Cl and Na are both
  highly corrosive where Cl is associated with
  acids and Na is associated with bases.

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Primary Chemical Bonds Ionic Bonding

• A collection of such charged ions, form and
  electrically neutral solid by arranging
  themselves into regular crystalline array
• Makes material hard and brittle
• Non-directional A cation (Na) will attract any
  adjacent anion (Cl-) equally in all directions

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When a voltage is applied to an ionic material,
entire ions must move to cause a current to flow.
Ion movement is slow and the electrical
conductivity is poor. Thus ionic materials like
SiO2 and Al2O3 make good insulators of
electricity.
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Primary Chemical Bonds Ionic Bonding
Nature of the bonding force for the ionic bond ?
coulombic attractions force Fc With small a, Fc
gets large, then a ideally be equal to zero?
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Primary Chemical Bonds Ionic Bonding

• With small a, FC gets large, then a ideally be
  equal to zero?
• Oppositely charged ions gets closer, leads to
  increase in FC, but it is counteracted by an
  opposing repulsive force FR due to
• overlapping of the similarly charged electric
  fields from each ions
• the attempt to bring the two positively charged
  nuclei closer together
• where ? and ? are experimentally determined
  constants for a given ion pair

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Primary Chemical Bonds Ionic Bonding
Interatomic spacing The equilibrium distance
between atoms is caused by a balance between
repulsive and attractive forces. Equilibrium
separation occurs where the total-atomic energy
of the pair of atoms is at a minimum, or when no
net force is acting to either attract or repel
the atoms. The interatomic spacing is
approximately equal to the atomic diameter or,
for ionic materials, the sum of the two different
ionic radii.
Bonding Force, Net force FFRFC Equilibrium
bond length where F0
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Primary Chemical Bonds Ionic Bonding

• Bonding energy, E is related to bonding force
  through the differential expression
• Equilibrium bond length a0 corresponds to
• F 0 and
• A minimum in the energy curve ? stable ions
  positions

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Primary Chemical Bonds Ionic Bonding
A material that has a high binding energy will
also have a high strength and high melting
temperature.
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Bonding Energy

• How does bonding energy relate to melting point?
• Modulus of Elasticity?
• Coefficient of Thermal Expansion?
• Hint The higher the bonding energy the more
  tightly the atoms are held together.

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Primary Chemical Bonds Ionic Bonding
Coordination number

• Coordination number is the number of adjacent
  ions (or atoms) surrounding a reference ion (or
  atom)
• Depends directly on the relative sizes of the
  oppositely charged ions
• Radius ratio r/R (smaller ion to the larger ion)

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Coordination number
Larger ions overlap instability because of high
repulsive forces
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Coordination number
MORE TO COME IN Ch 3
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Coordination Number
As r/R?1, a coordination number as high as 12 is
possible
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Questions to think on ?

• Why dont we have a coordination number greater
  than unity.
• Why coordination numbers of 5, 7, 10, 11 are
  absent?

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Covalent Bonds

• Materials with covalent bonds tend to occur among
  atoms with small differences in electronegativity
  and therefore the elements are close to one
  another in the periodic table.
• Two or more atoms share two or more electrons.
• The atoms most commonly share their outer s and p
  electrons so that each atom can tend to approach
  an inert gas structure.
• Example, Si Z 14 1s2 2s2 2p6 3s2 3p2 or 1s2
  2s2 2p6 3s1 3p3 are possible with the second
  configuration being more stable.

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Electron orbitals are represented as particles
orbiting at a fixed radius. In reality, electrons
charge is found in a range of radii.
Representation of the actual electron
density Highly directional due to sharing of
electrons with specific neighboring atoms
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Primary Chemical Bonds Covalent Bonding

• While ionic bonds are non-directional, covalent
  bonds are very directional so atoms can best
  share their electrons.

• Covalent bonds are very strong.
• They tend to be brittle with poor electrical
  conductivity. Why then is Silicon and other like
  materials used in the electronics industry?
• Many hydrocarbons, eg., C2 H4 , are covalently
  bonded. Many polymeric materials such as
  polyvinyl chloride (PVC), used as molded plastic
  on cars, have primarily covalent bonds.

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Primary Chemical Bonds Covalent Bonding

• A continuous covalent bond arrangement to form a
  3D network of a solid
• Diamond is a cubic crystal structure of carbon
  (formed at a temperature of 1325C, a pressure of
  50000 kg/cm2 is required to grow diamond)
• Highest melting temperature
• Highest hardness
• Highest elastic modulus

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Carbonss electronic configuration in shorthand
notation is 1s2 2s2 2p2 Double bond ? covalent
sharing of two pairs of valence electrons When
energy provided Bonding of adjacent molecules,
double bond?single bond between each adjacent
molecule pair
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Spaghetti-like structure of solid polyethylene
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Primary Chemical Bonds Covalent Bonding

• The bonding force and energy curves are similar
  to ionic bonding
• But the nature of the bonding is different
  leading to different force equations

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Primary Chemical Bonds Covalent Bonding

• Bond Angle
• An important characteristic as the bonding is of
  directional nature of valence electron sharing

Carbon atom tends to form four equally spaced
bonds, resulting tetrahedral configuration.
tetragonal having four corners or angles
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Ionic-Covalent Bonds

• Many materials have properties, which can best be
  described as a mixture of ionic and covalent
  bonding.
• Example 1, Silica (SiO2), a group IV-VI compound
  from the periodic table. Each Si atom bonds with
  4 O atoms and each O atom binds with 2 Si atoms
  to give 8 electrons to each (see next slide).
• Oxygen s electronic configuration
  (8 electrons) 1s2 2s2 2p4
• Silicons electronic configuration (14
  electrons) 1s2 2s2 2p6 3s2 3p2
• Example 2, Gallium Arsenide (GaAs), a group
  III-V compound from the periodic table, used for
  lasers.
• Example 3, Indium Phosphide (InP), a group II-VI
  compound from the periodic table, used for Light
  Emitting Diodes (LEDs).
• These materials are are very important as
  electronic and photonic materials.

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Atomic Bonding of Silicon Dioxide
Each Si atom bonds with 4 O atoms and each O atom
binds with 2 Si atoms to give 8 electrons to each
Both the outer shells of Si and O are filled with
electrons making SiO2 a very stable material.
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Ionic-Covalent Bonds

• As the electronegativity difference between the
  atoms increases, the bonding becomes more ionic.
• The fraction of bonding that is covalent can be
  estimated from the following equation

where DE is the difference in electronegativities.
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Metallic Bonds

• Metallic bonds occurs in Metallic elements, which
  tend to have a low electronegativity.
• A metallic bond is non-directional
• The outer (valence) electrons are given up to
  form a sea of mobile electrons, which are
  attracted by a set of fixed positive ion cores.
• These mobile electrons are called conduction
  electrons and they form the glue to bond the
  metal atoms together.
• The sharing of electrons produces a lower energy
  state than when the individual atoms are
  collected separately

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Metallic Bonding

• Less than half full shell of electrons, each atom
  donates its outer shell electrons to a cloud of
  electrons
• Shared by all the (metal) atoms
• Atoms to become positively charged ions as they
  all give up electrons to for the cloud
• Ions are attracted by the electron cloud and held
  together
• Nondirectional
• The mobility of the electrons ? electrical
  conductivity

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When voltage is applied to a metal, the electrons
in the electron sea can easily move and carry a
current.
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Secondary bonding

• Atomic bonding without electron transfer or
  sharing ? much less bonding energy
• Attraction of opposite charges (somewhat similar
  to ionic bonding) that are asymmetrically
  distributed-dipoles-within each atom or molecular
  unit being bonded

A dipole (Greek dyo two and polos pivot) is
a pair of electric charges, separated by some
(usually small) distance. Dipoles can be
characterized by their dipole moment, a vector
quantity with a magnitude equal to the product of
the charge and the distance separating the two
poles
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Secondary bonding Van der Waals Bonding

• These bonds are much weaker than the three
  primary bonds but are very prevalent in
  materials, and thus very important.
• These bonds are formed by electrostatic
  attraction between groups of atoms or molecules
  that are either permanently polarized or
  dynamically polarized (i.e., changing as in a
  chemical process).
• They possess an electric dipole moment
• eg., H2O where the oxygen is more strongly
  electronegative than H so O shares H2s electrons
  giving oxygen a negative potential and H a
  positive potential.
• Many organic molecules, polymers, and ceramics
  exhibit this type of bonding, often referred to
  as hydrogen bonding with permanent
  polarization on an atomic level.
• These weak bonds enable lifes processes to occur
  such as photosynthesis and the Hydrogen Cycle.

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Secondary bonding
When two neutral argon atoms (perfectly
symmetric) brought nearby, slight shift from
symmetry (induced dipole) ?weak attraction force
between the two Ar. Argon (a noble gas) does not
tend to form a primary bond because it has
stable, filled outer orbital shell
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Secondary bonding

• Externally electrically neutral chemical
  molecules can have a dipole inside.
• water is a triangular molecule, H2O
• The internal charge distribution is such that the
  hydrogen side has a slight excess of positive
  charge and the oxygen end is correspondingly
  negative.

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Van der Waals Bonding

• Van der Waals bonding can change the properties
  of a material substantially.
• eg., for long chained carbon molecules, polymers
  are covalently bonded and hence might be expected
  to be brittle. The long chain molecules are
  bonded together between the chains by Van der
  Waals bonds so ductility is obtained by the
  distortion of the weak bonds rather than between
  the strong covalent bonds along the chain itself.

In Polyvinyl Chloride (PVC), the chloride atoms
attached to the polymer chain have a negative
charge and the hydrogen atoms are positively
charged enabling van der Waals bonding.
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Chemical Bonding
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Sample Problems

• The number of atoms per cm3, n, for material of
  density d (g/cm3) and atomic mass M (g/mol)
• n Nav d / M
• Diamond (carbon) d 3.5 g/cm3, M 12 g/mol
• n 61023 atoms/mol 3.5 g/cm3 / 12 g/mol
  17.5 1022 atoms/cm3