Engineering Materials Science

CHAPTER 3 : Materials Structure

Materials Structure Categories

Three Materials Structure Categories

Macrographic Structure Amorphous, Crystalline and

or Macrostructure Poly-Crystalline Structure

Micrographic Structure
or Microstructure
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Macrographic Structure or Macrostructure

Macrography or Macrostructure Examination is a method of examination of large regions

of the specimen surface or fractured section with the naked eye or under low
magnification .

Damascus Steels
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Micrographic Structure or Microstructure

We can define four types of atomic or ionic arrangements:
 No Order In monoatomic gases, such as argon (Ar), atoms or ions have no orderly
arrangement. These materials randomly fill up whatever space is available to them.

 Short-Range Order (SRO) if the special arrangement of the atoms extends only to the
atom’s nearest neighbors. Each water molecule in steam has a short-range order due
to the covalent bonds between the O and the 2 H
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 Long-Range Order (LRO) Most metals and alloys, semiconductors, ceramics, and some
polymers have a crystalline structure in which the atoms or ions display long-range order;
the special atomic arrangement extends over much larger length scales ≥ 100 nm. The
atoms or ions in these materials form a regular repetitive, grid-like pattern, in three
dimensions.

 Liquid crystals (LC) are polymeric materials that have a special type of order. Liquid
crystal polymers behave as amorphous materials (liquid-like) in one state
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Amorphous and Crystalline Materials

 Amorphous Material Any material that exhibits only a short-range order of atoms or
ions is an amorphous material; that is, a non-crystalline one.

 Crystalline Material is one in which the atoms are situated in a repeating or periodic
array over large atomic distances; that is, long-range order exists, such that upon
solidification, the atoms will position themselves in a repetitive three-dimensional
pattern, in which each atom is bonded to its nearest-neighbor atoms.
All metals, many ceramic materials, and certain polymers form crystalline structures
under normal solidification conditions.

Amorphous Silicon Crystalline Silicon

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Polymorphism and Allotropy

Some metals, as well as nonmetals, may have more than one crystal structure, a
phenomenon known as polymorphism (ex: Fe2O3 Ferric Oxide, TiO2 Titanium Dioxide).
When found in elemental solids, the condition is often termed allotropy (ex: Coal,
Graphite, Diamond).

Unit Cells
 In crystal structures, it is often convenient to subdivide the structure into small repeat
entities called unit cells.
 Unit cells for most crystal structures are parallelepipeds or prisms having three sets of
parallel faces.
 A unit cell contains a full description because the structure is a generation of
repeating stacking of adjacent unit cells.

Hard-sphere unit cell Reduced-sphere unit

representation cell representation
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Lattice Parameters

The unit cell geometry is completely defined in terms of six parameters (called lattice
parameters) : the three edge lengths a, b, and c, and the three interaxial angles a, b,
and g.

x, y, and z : coordinate axes

a, b, and c : edge lengths
a, b, and g : interaxial angles
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Crystal Systems
There are seven different possible combinations of a, b, and c, and a, b, and g, each of
which represents a distinct crystal system. These seven crystal systems are: cubic,
tetragonal, hexagonal, orthorhombic, rhombohedral, monoclinic, and triclinic.

 Cubic unit cell

 Tetragonal

 Hexagonal
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 Orthorhombic

 Rhombohedral

 Monoclinic

 Triclinic
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Bravais lattices
How atoms (hard spheres) stacked together within a given unit cell.
There are 14 Bravais lattices for the 7 Crystal systems.
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Metal Structures

Metals

Pure metals Metal alloys

Pure metals have the following physical properties : The aim of making alloy is :
 High density  To increase the strength and hardness of a
 High melting and boiling points pure metal
 Good conductors of heat and electricity  To increase the resistance to corrosion of a
 Malleable pure metal
 Easily oxidized  To improve the appearance of a pure metal
 Ductile
 Lustrous Most alloys are mixtures of metals. For example,
 Impurity (0.1 to 0.5%) bronze is an alloy of copper and tin.

To improve the properties of a pure metal, it is Some alloys may contain mixtures of a metal and
made into an alloy a non-metal (or metalloids) such as carbon. For
example, steel is an alloy of iron and carbon.
Alloys: 2 elements (Binary), 3 elements (Ternary),
4 elements (Quaternary).
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Metal Structures
 In metals, 3 types of crystalline structures (Bravais Lattice) can be found

• Body-centered cubic : BCC

• Face-centered cubic : FCC

• Hexagonal close-packed : HCP

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 In metal crystalline structure, an important factor can be defined, the atomic packing
factor (APF) :

volume of atoms in a unit cell

APF =
total unit cell volume

 The cube edge length a and the atomic radius R are related :

a = fct (R)

 Density computation of metal :

n A

VC  N A

Where : n = number of atoms associated with each unit cell

A = atomic weight
Vc = Volume of the unit cell
NA = Avogadro’s number ( 6.022  10 23 atoms / mol )
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Metal Structure (BCC)

APF = 0.68

Body-centered cubic (BCC) structure for metals showing (a) the arrangement of lattice points for a unit
cell, (b) the actual packing of atoms (represented as hard spheres) within the unit cell, and (c) the
repeating bcc structure, equivalent to many adjacent unit cells.
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Metal Structure (FCC)

APF = 0.74

Face-centered cubic (FCC) structure for metals showing (a) the arrangement of lattice points for a unit
cell, (b) the actual packing of atoms within the unit cell, and (c) the repeating fcc structure, equivalent
to many adjacent unit cells.
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Metal Structure (HCP)

APF = 0.74

Hexagonal close-packed (HCP) structure for metals showing (a) the arrangement of atom centers
relative to lattice points for a unit cell. There are two atoms per lattice point (note the outlined
example). (b) The actual packing of atoms within the unit cell. Note that the atom in the midplane
extends beyond the unit-cell boundaries. (c) The repeating hcp structure, equivalent to many adjacent
unit cells.
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The relationship between the unit-cell size (edge length) and the atomic radius is given in the table
below :
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Metal Structures (Stacking of close-packed planes )

Comparison of the fcc and hcp structures. They are each efficient stackings of close-packed planes.
The difference between the two structures is the different stacking sequences. The fcc stacking is
reffered to as an ABCABC… sequence, the hcp stacking is reffered to as an ABAB… sequence.
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Ceramic Structures

 Due to the wide variety of chemical compositions of ceramics, we give a systematic list of some of
the most important and representative ones (MX, MX2, M2X3)
 In ceramic crystalline structure, we define the ionic packing factor (IPF) : represents the fraction
of the unit cell volume occupied by the various cations and anions.
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Ceramic Structure (MX)
M : metallic element
X : non-metallic element
CsCl

Cesium chloride (CsCl) unit cell showing (a) ion positions and the two ions per lattice point and (b) full
size ions.
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Ceramic Structure (MX)
NaCl

Sodium chloride (NaCl) structure showing (a)

ion positions in a unit cell, (b) full-size ions,
and (c) many adjacent unit cells.
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Ceramic Structure (MX2)
Examples : CaF2, UO2, ThO2, TeO2

CaF2 (Fluorite)
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Ceramic Structure (MX2)

SiO2 (Silica)

 Widely available in raw materials in the earth’s crust

 Represents a large fraction of the ceramic materials available to engineers
 Different structure under different temperature and pressure
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Ceramic Structures (Other structures)

Graphite

(a) An exploded view of the graphite (C) unit cell (b) A schematic of the nature of graphite’s layered
structure.
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Ceramic Structures (Other structures)

Buckyball and Buckytube

 Buckyball: uniform distribution of 12 pentagons among 20 hexagons (soccer ball) (ex.: Fullerence)
Superconductors: by capturing metal ions within carbon cages (Cn)

 Buckytube: array of hexagonal rings of carbon atoms

Highly strength fibers in composites
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Polymeric Structures
 Polymers : chain of long polymeric molecules
 The arrangement of these long molecules into a regular and repeating patterns is difficult
 Most commercial plastics are noncrystalline
 Crystalline structure : Structure tends to be quite complex

Polyethylene (PE)

Orthorhombic unit cell

 Single crystal of PE is difficult to grow. Produced by

cooling of a dilute solution, they tend to be thin
platelets (10 nm thick)
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Crystallographic Points, Directions and Planes
Crystallographic Points (Lattice Positions)

xyz
Point Coordinates, or Position :
abc
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Lattice Translations

Lattice translations connect structurally equivalent positions (e.g., the body center) in various unit
cells
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Crystallographic Directions (Lattice Directions)
 A crystallographic direction is defined as a line between two points, or a vector
 A vector is positioned such that it passes through the origin of the coordinate system
 The length of the vector projection are measured in terms of the unit cell dimensions a, b, and c.
 These three numbers are multiplied or divided by a common factor to reduce them to the smallest
integer values
 The three indices, not separated by commas, are enclosed in square brackets, thus: [uvw]
 Negative indices are represented by a bar over the appropriate index. For example, the 11 1

Family of direction : 111  111 ,  111 , 111 , 111  ,  111  , 111  ,  111  ,  111
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Angles between directions, Linear density and Planar density
Angles between directions
 Directions [u v w] and [u’ v’ w’]
 Vectors directions :
D = ua + vb + wc , D’ = u’a + v’b + w’c
 The angle between directions :

D .D' uu'  vv'  ww'

cos   
D  D' u2  v 2  w 2  (u')2  (v')2  (w')2
Linear density

Number of atoms centered on direction vector

Linear density =
Length of direction vector

Planar density

Number of atoms centered on a plane

Planar density =
Area of the plane
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Crystallographic Directions for an Hexagonal Crystal

Conversion from the three-index system to the four-index system:

 u  a1
v  a

x y z   u v t w   2

 t  a3
 w  z
1
u ( 2x  y )
3
1
v  (2y x)
3
t  ( u  v )
wz
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Crystallographic Planes (Lattice planes)
 If the plane passes through the selected origin, another parallel plane must be constructed within
the unit cell by a translation.
 At this point the crystallographic plane intersects or parallels each of the three axes.
 The reciprocals of these numbers are taken.
 If necessary, these three numbers are changed to the set of smallest integers by multiplication or
division by a common factor
 Finally, the integer indices, not separated by commas, are enclosed within parentheses, thus: (hkl).

crystal planes labeling system

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Crystallographic Planes (Hexagonal Crystal)

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Polycrystalline Materials
Most crystalline solids are composed of a collection of many small crystals or grains; such materials are
termed polycrystalline.
Various stages in the solidification of a polycrystalline material (square = unit cell):
1. Small crystallite nuclei
2. Growth of the crystallites; the obstruction of some grains that are adjacent to one another is also shown
3. Upon completion of solidification, grains having irregular shapes have formed
4. The grain structure as it would appear under the microscope; dark lines are the grain boundaries.

Garnet single crystal (China)

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Isotropy and Anisotropy

 This directionality of properties is termed anisotropy, and it is associated with the variance of
atomic or ionic spacing with crystallographic direction.

 Example: the elastic modulus, the electrical conductivity, and the index of refraction may have
different values in the [100] and [111] directions.

 Substances in which measured properties are independent of the direction of measurement

are isotropic.