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MME 2001
MATERIALS SCIENCE 1
13.10.2015
outline
● overview of last lecture
periodic table / electronegativity
Classification of elements / interatomic
bonding
● Structure of solids:
crystaline vs noncrystalline
Crystal systems;
BCC, FCC, HCP
atomic packing
crystallographic directions, planes
● QUIZ (will start at 14:50 p.m. !)
The Periodic Law
Mendeleev realized that:
When arranged by increasing atomic
number, the chemical elements display a
regular and repeating pattern of chemical
and physical properties.
what are these properties?
 Metallic vs nonmetallic character
 Atomic radius
 Ionization energies (energy necessary to remove
the outermost electron from the atom)
 Electron affinities (energy change when an
electron is added to a neutral atom)
 Reactivity
 Electronegativity
Organisation of the periodic table
The vertical columns: groups from 1 to 18.
Elements in the same group have similar valence
electron structures
and hence similar
chemical and
physical
properties.
groups
Organisation of the periodic table
elements are situated, with increasing atomic
number, in seven horizontal rows
called periods.
Each contains
elements with
electrons in the
Same outer shell.
periods
Periodic table
nonmetallic character
İonization energy
Negative electron affinity
İonization energy
nonmetallic character
metallic character
Atomic radii
metallic character
Atomic radii
Negative electron affinity
Periodic Table
Ionization Energy
IE = energy required to remove an
electron from an atom in the gas phase.
Mg (g) + 738 kJ ---> Mg+ (g) + e-
Electronegativity
● the tendency of an atom to attract electrons
towards itself.
● Atoms are more likely to accept electrons if their
outer shells are almost full, and if they are less
“shielded” from (i.e., closer to) the nucleus.
electronegativity
increases!
Electronegativity
Electronegativity
Metals, Nonmetals & Metalloids
1
Nonmetals
2
3
4
5
Metals
6
7
Metalloids
Metals
88 elements are metals or metal like element
Physical properties:
 good conductors of heat and electricity
 shiny
 ductile (can be stretched into thin wires)
 malleable (can be pounded into thin sheets)
 High density (heavy for their size)
 High melting point
chemical properties:
 Easily lose electrons
 Form positive (+) ions
 Corrode easily
Non-metals
Their characteristics are opposite to those of metals.
Physical Properties of Nonmetals:
 No luster (dull appearance)
 Poor conductor of heat and electricity
 Brittle (breaks easily)
 Not ductile
 Not malleable
 Low density
 Low melting point
 Many non-metals are gases.
Non-metals
Chemical Properties of Non-metals:
 Tend to gain electrons
 metals that tend to lose electrons but nonmetals
that tend to gain electrons, to form compounds
with each other.
 These compounds are called
ionic compounds.
 When two or more
nonmetals bond with
each other, they form
a covalent compound.
Metalloids
 Metalloids (metal-like) have properties of both
metals and non-metals.
 They are solids
 can be shiny or dull
 They conduct heat
and electricity better
than non-metals but
not as well as metals
 They are ductile and
malleable
interatomic bonding
● the bonding involves the valence electrons
● the nature of the bond depends on the electron
structures of the constituent atoms.
● There are three types of bonding: each bonding
type arises from the tendency of the atoms to
assume stable electron structures.
● Secondary or physical forces and energies are
weaker than the primary ones, but nonetheless
influence the physical properties of some
materials.
interatomic bonding
 Ionic
 Metal (cation) with non-metal (anion)
Transfer of electron(s)
 Strong bond  high melting point
 Covalent
 Non-metal with non-metal
 Sharing of electron(s)
 Non-polar (equal distribution of electrons)
 Polar (uneven electron distribution)
 Weak bonds…low melting points
 Metallic (nuclei in a “sea” of shared electrons)

ionic bonding
● Forms between metallic and nonmetallic
elements; elements at the horizontal extremities
of the periodic table.
● a metallic atom easily gives up its valence
electrons to the nonmetallic atoms.
● In the process all the atoms acquire stable
configurations and become ions.
● Ionic bonding is non-directional (magnitude of the
bond is equal in all directions around the ion)
● Ceramic materials exhibit ionic bonding
Ionic Bonding
• Occurs between + and - ions.
• Requires electron transfer.
• Large difference in electronegativity required.
Na (metal)
Unstable
11 electrons
electron
Cl (nonmetal)
Unstable
17 electrons
Na (cation) +
Cl (anion)
stable
stable
Coulombic
Attraction
positive and negative ions, by virtue of their net
electrical charge, attract one another
Ionic Bonding - examples
• Predominant bonding in Ceramics
NaCl
MgO
CaF 2
CsCl
Give up electrons
Acquire electrons
Ion Sizes
+
Li,152 pm
3e and 3p
Li + , 78 pm
 e  2e and 3 p
Forming
a cation.
 CATIONS are SMALLER than the atoms from
which they come.
 The electron/proton attraction has gone UP
and so size DECREASES.
Ion Sizes
F, 71 pm
9e and 9p
F- , 133 pm
+ e  10 e and 9 p
Forming
an anion.
 ANIONS are LARGER than the atoms from
which they come.
 The electron/proton attraction has gone DOWN
and so size INCREASES.
 Trends in ion sizes are the same as atom sizes.
ionic bonding
● The predominant bonding in ceramic materials
is ionic.
● Ionic materials are characteristically hard and
brittle and, electrically and thermally
insulative.
● These properties are directly related to
electron configurations and/or the nature of the
ionic bond.
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.
● The covalent bond is directional; it is between
specific atoms and may exist only in the direction
between one atom and another that participates
in the electron sharing.
Covalent Bonding
similar electronegativity  share electrons
bonds are determined by valence –
s & p orbitals dominate bonding
shared electrons
Example: CH4
H
of carbon atom
CH 4
H
C: has 4 valence e-,
∙∙
needs 4 more
H: C : H
H
H
C
∙∙
H: has 1 valence e-,
H
needs 1 more
H
shared electrons
Electronegativities
of hydrogen atom
are comparable.
●
●
●
●
covalent bonding
● Covalent bonds may be very strong, as in
diamond, which is very hard and has a very high
melting temperature, 3550 C, or they may be
very weak, as with bismuth, which melts at about
270 C.
● Polymeric materials typify this bond, the basic
molecular structure often being a long chain of
carbon atoms that are covalently bonded together
with two of their available four bonds per atom.
● The remaining two bonds normally are shared
with other atoms, which also covalently bond.
covalent bonding
● interatomic bonds may be partially ionic and
partially covalent.
● very few compounds exhibit pure ionic or covalent
bonding.
● the degree of either bond type depends on the
relative positions of the components in the periodic
table or the difference in their electronegativities.
● The wider the separation (the greater the difference
in electronegativity), the more ionic the bond.
● the closer they are (the smaller the difference in
electronegativity), the greater the degree of
covalency.
interatomic bonding
No electronegativity difference between two
atoms leads to a purely non-polar covalent bond.
A
B
A small electronegativity difference leads to a
polar covalent bond.
A
B
A large electronegativity difference leads to an
ionic bond.
metallic bonding
● Metallic materials have one, two, or at most,
three valence electrons.
● these valence electrons are more or less free to
drift throughout the entire metal and form a “sea
of electrons”.
● the metallic bond is nondirectional in character.
The free electrons act as a “glue” to hold the ion
cores together.
● Bonding may be weak or strong; bonding energy 68
kJ/mol (0.7 eV/atom) for mercury and 849 kJ/mol
(8.8 eV/atom) for tungsten. Their respective
melting temperatures are 39 and 3410 C.
metallic bonding
Secondary-van der waals-bonding
Secondary, van der Waals, or physical bonds 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.
Secondary bonding is evidenced for the inert gases,
which have stable electron structures, and, in
addition, between molecules in molecular
structures that are covalently bonded.
Properties linked with bonding
if the bond energy is higher,
● Melting point is higher
● Thermal expansion
coefficient is smaller
● Elastic modulus is
higher
Energy
ro
r
Primary Bonds
Large bond energy
Ceramics
high Tm
(Ionic & covalent bonding):
high E
small 
Variable bond energy
Metals
moderate Tm
(Metallic bonding):
moderate E
moderate 
Polymers
(Covalent & Secondary):
Directional Properties
Secondary bonding dominates
small Tm
small E
high 
structure of solids
Energy and Packing
Non dense, random packing
Energy
typical neighbour
bond length
typical neighbour
bond energy
Dense, ordered packing
r
Energy
typical neighbour
bond length
typical neighbour
bond energy
Dense, ordered packed
structures tend to have lower energies!
r
Materials and Packing
Crystalline materials:
atoms are situated in a
repeating array over large
atomic distances;
long-range order exists..
each atom is bonded to its
nearest-neighbor atoms.
typical of:
metals
many ceramics
some polymers
crystalline SiO2
Si Oxygen
noncrystalline solids
noncrystalline materials:
no periodic packing of atoms
occurs in the case of
complex structures
rapid solidification
amorphous = noncrystalline
many polymers
some ceramics
? metallic glasses
noncrystalline SiO2
Si Oxygen
Materials and Packing
crystalline SiO2
Si
Oxygen
noncrystalline SiO2
noncrystalline solids
● crystalline vs amorphous solid
depends on the ease with which a random
atomic structure in the liquid can transform to
an ordered state during solidification.
● Therefore, amorphous materials are
characterized by atomic or molecular structures
that are relatively complex and become
ordered only with some difficulty.
noncrystalline solids
● rapid cooling through the freezing temperature
 noncrystalline solid / no time for ordering!
● metals normally form crystalline solids
● some ceramic materials are crystalline, whereas
others, the inorganic glasses, are amorphous.
● polymers may be completely noncrystalline and
semicrystalline consisting of varying degrees of
crystallinity.
noncrystalline solids
T
metals
crystalline
dT/dt 
noncrystalline
t
noncrystalline solids
T
ceramics
crystalline
dT/dt 
noncrystalline
t
Structure of solids
issues of interest
● How do atoms assemble into solid
structures? (we shall focus on metals for
the time being!)
● How does the density of a material depend
on its structure?
● When do material properties vary with the
sample (i.e., part) orientation?
Structures of crystalline solids
● properties of crystalline solids depend on the
crystal structure of the material, the manner in
which atoms are spatially arranged.
● For example, magnesium, having one crystal
structure, is much more brittle (i.e., fracture at
lower degrees of deformation) than aluminium
that has yet another crystal structure.
Structure – mechanical properties
aluminium
magnesium
structure – physical properties
● significant property differences exist between
crystalline and noncrystalline materials having
the same composition.
● For example, noncrystalline ceramics and
polymers normally are optically transparent; the
same materials in crystalline form tend to be
opaque or, at best, translucent.
Alumina
Single crystal
Polycrystal-low porosity
high porosity
structure of crystalline solids
● atomic hard-sphere model: atoms (or ions) are
thought of as being solid spheres having welldefined diameters. These spheres touch one
another.
● the unit cell is the basic structural unit or
building block of the crystal structure and
defines the crystal structure by virtue of its
geometry and the atom positions.
metallic crystal structures
● metallic bonding
● nondirectional: minimal restrictions as to the
number and position of nearest-neighbor atoms
● hence, relatively large numbers of nearest
neighbors
● three relatively simple crystal structures are
found for most of the common metals:
face centered cubic
body-centered cubic
hexagonal close-packed
(FCC)
(BCC)
(HCP)
metallic crystal structures
tend to be densely packed.
Reasons for dense packing:
● Typically, only one element is present, so all
atomic radii are the same.
● bonding is not directional.
● nearest neighbor distances tend to be small in
order to reduce bond energy (energy minimization).
● electron cloud shields cores from each other
● have the simplest crystal structures.
metallic crystal structures
crystal systems
Unit cell: smallest repetitive volume which
contains the complete lattice pattern of a crystal.
The unit cell geometry is completely defined in
terms of six lattice parameters
edge lengths: a, b, and c
(lattice constants)
interaxial angles:
, , and  (lattice angles)
There are seven different
possible combinations of
a, b, and c, and ,  and 
crystal systems
7 distinct crystal systems
cubic
tetragonal
hexagonal
orthorhombic
rhombohedral
monoclinic
triclinic
14 crystal lattices
crystal systems
cubic: a=b=c, ===90
simple
cubic
body-centered
cubic (BCC)
face-centered
cubic (FCC)
tetragonal: a=bc, ===90
simple
tetragonal
body-centered
tetragonal (BCT)
crystal systems
orthorombic: abc, ===90
simple
body-centered base-centered face-centered
monoclinic: abc, ==90
simple
monoclinic
base-centered
monoclinic
crystal systems
rhombohedral
a=b=c,
==90
hexagonal
a=bc,
==90 =120
Total of 14 Bravais lattices!
triclinic
abc,
90
crystal systems
cubic
a=b=c
===90
triclinic
abc
90
maximum symmetry
minimum symmetry
metallic crystal structures
How can we stack metal atoms to minimize
empty space?
2-dimensions
vs
cube
6 faces
8 corners
12 edges
metallic crystal structures
F.C.C. Crystal structure:
hard-sphere unit cell
reduced-sphere unit cell
aggregate of many atoms
simple cubic structure (SC)
• Rare due to low packing density
(only Po has this structure)
• Close-packed directions are cube edges.
• Coordination # = 6
(# nearest neighbors)
simple cubic (SC) structure
● Atoms touch each other along cube edges.
● each of 8 corner atoms is shared by eight unit
cells:
8 x (1/8) = 1 atom/unit cell
R
a = 2R
unit cell
volume = a3 = 8R3
BCC crystal structure
● unit cell has cubic geometry
● atoms are located at the corners of the cube.
● Some of the materials that have a bcc structure
include lithium, sodium, potassium, chromium,
barium, vanadium, alpha-iron and tungsten.
● Metals which have a BCC structure are usually
harder and less malleable than close-packed
metals such as copper and gold.
● When the metal is deformed, the planes of
atoms must slip over each other, and this is more
difficult in the bcc structure.
Body Centered Cubic Structure (BCC)
8
5
6
4
1
2
7
3
Coordination # = 8
Atomic packing of
an BCC (110)
plane.
body centred cubic (BCC) structure
● Atoms touch each other along cube diagonals.
● each of 8 corner atoms is shared by eight unit
cells; single center atom is wholly owned:
8 x (1/8) + 1 = 1 + 1 = 2 atoms/unit cell
● each center atom touches eight corner atoms:
8 nearest neighbors
a
2.a
3.a = 4R
FCC crystal structure
● unit cell has cubic geometry
● atoms are located at the corners and the
centers of all the cube faces.
● familiar metals with FCC crystal structure
copper
aluminium
silver
gold
Atomic arrangements - FCC
Reduced sphere FCC unit cell with the (110) plane.
Atomic packing of an FCC (110) plane.
Atoms touch each other along face diagonals.
Face Centered Cubic Structure (FCC)
The face-centered atom in the front face is in contact
with four corner atoms and four other face-centered
atoms behind it (two sides, top and bottom) and is
also touching four face-centered atoms of the unit
cell in front of it.
Coordination # = 12
FCC crystal structure
atoms touch one another across
a face diagonal; cube edge length
a and the atomic radius R
a2 + a2 = (R+2R+R)2
2a2 = (4R)2 = 16R2
a2 = 8R2
a = 2R2
R = a /(22)
a
2R
R
R
FCC crystal structure
each of 8 corner atoms is shared by eight unit cells;
each of 6 face-centered atoms belongs to only two.
8 x (1/8) + 6 x (1/2) = 1 + 3 = 4 atoms/unit cell
The volume of the unit cell,
a3 = (2R2)3 = 16R32
4R=2.a
(a = 2R2)
cubic crystal structures
X’tal structure Coordination # Atoms/unit cell
simple cubic
6
1
body centred
8
2
face centred
12
4
atomic packing factor (APF)
APF is the sum of the sphere volumes of all
atoms within a unit cell divided by the unit
cell volume:
the maximum packing possible for spheres
all having the same diameter.
Atomic Packing Factor (APF)-SC
Volume of atoms in unit cell
APF =
Volume of unit cell
atoms
unit cell
a
R=0.5a
APF =
volume
atom
4
 (0.5a) 3
1
3
a3
close-packed directions
volume
unit cell
1
contains
8 x 1/8 = 1 atom/unit cell
APF for a simple cubic structure = 0.52
Atomic Packing Factor: BCC
4R
3a
a
2a
R
a
2a
Close-packed directions:
length = 4R = 3 a
atoms
volume
4
3
unit cell 2  ( 3a/4)
atom
3
APF =
APF(BCC)= 0.68
volume
a3
unit cell
Atomic Packing Factor: FCC
Close-packed directions:
length = 4R = 2 a
2a
a
Unit cell contains:
6 x 1/2 + 8 x 1/8
= 4 atoms/unit cell
volume
atoms
4
3
atom
)
p
(
2
a/4
4
unit cell
3
maximum
APF =
= 0.74 achievable APF
a3
volume
unit cell
Closed packed crystal structures
A portion of
a close-packed
plane of
atoms; A, B, and
C positions
are indicated.
The AB
stacking
sequence for
close packed
atomic planes.
Hexagonal close packed (HCP)
crystal structure
Not all metals have unit cells with cubic symmetry;
some common metals have a hexagonal structure
Closed packed crystal structures
The real distinction
between FCC and HCP
lies in where
the third close-packed
layer is positioned.
For HCP, the centers
of this layer are
aligned directly above
the original A
positions.
stacking sequence,
ABABAB ...,
Atomic alignment repeats every other plane!
Closed packed crystal structures
These planes are of the (111) type
For FCC
structure,
the centers
of the third
plane are
situated
over the C
sites of the
first plane.
This yields an ABCABCABC . . . stacking sequence;
the atomic alignment repeats every third plane.
FCC Stacking Sequence
• ABCABC... Stacking Sequence
• 2D Projection
B
A sites
B sites
C sites
A
B
C
B
C
B
B
C
B
B
A
B
C
FCC Unit Cell
Hexagonal close packed (HCP)
crystal structure
● The HCP metals: Cd, Mg, Ti, and Zn.
● top and bottom faces consist of six atoms that
form regular hexagons and surround a single atom
in the center.
● Another plane that provides three additional
atoms to the unit cell is situated between the top
and bottom planes. The atoms in this mid-plane
have as nearest neighbors atoms in both of the
adjacent two planes.
Hexagonal close packed (HCP)
crystal structure
● The equivalent of six atoms is contained in
each unit cell
● one-sixth of each of the 12 top and bottom
face corner atoms, one-half of each of the
2 center face atoms, and all 3 midplane
interior atoms.:
12 x 1/6 + 2 x ½ + 3 = 2 +1 + 3 = 6
corner
face midplane
Closed packed crystal structures
● both FCC and HCP crystal structures have
atomic packing factors of 0.74, which is
the most efficient packing of equal-sized
spheres or atoms.
● these two crystal structures may be
described in terms of close-packed planes
of atoms (i.e., planes having a maximum
atom or sphere packing density)
Hexagonal Close-Packed Structure (HCP)
• ABAB... Stacking Sequence
• 3D Projection
c
a
• 2D Projection
A sites
Top layer
B sites
Middle layer
A sites
• Coordination # = 12
• APF = 0.74
• c/a = 1.633
Bottom layer
6 atoms/unit cell
ex: Cd, Mg, Ti, Zn
Unit cell volume
Sin 60 = h /a h = a sin 60
Atomic packing factor
2R=a; R=a/2
ideal c/a ratio in HCP
a/2
h2= a2+(a/2)2
x=(2/3)h
x2 + (c/2)2 = a2
see you next week!