Masters of Engineering

(Mechanical Engineering)

MME501: Materials for Engineers

Tutorial

Topic 2
Structure and Classification of Materials

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Topics
1. Interatomic bonding
2. Crystalline and non-crystalline materials
3. Crystal structures
4. Crystalline solids and hard sphere models, concept of unit cell
5. Calculation of theoretical density
6. Packing factor, defects in crystalline solids

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 Interatomic Bonding

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Interatomic Bonding
Name the type of atomic bonding in the following materials:
a) Diamond (C)
b) Mercury (Hg)
c) Calcium Flouride (CaF2)
d) Argon (Ar)

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Interatomic Bonding
Name the type of atomic bonding in the following materials:
a) Diamond (C) – Covalent bond
b) Mercury (Hg) - Metallic
c) Calcium Flouride (CaF2) - Ionic
d) Argon (Ar) – Van der Waals

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Crystalline and Non-Crystalline Materials

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Crystalline and Non-Crystalline Materials
Categorise the following materials as single crystal, non-crystalline and
polycrystalline.
1. Glass
2. Calcites
3. Plastic
4. Sand
5. Rock
6. Sugar
7. Salt
8. Quartz solids

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Crystalline and Non-Crystalline Materials
Categorise the following materials as single crystal, non-crystalline and
polycrystalline.
1. Glass – Non-crystalline
2. Calcites – Single crystal
3. Plastic - Non-crystalline
4. Sand - Polycrystalline
5. Rock - Polycrystalline
6. Sugar - Non-crystalline
7. Salts - Polycrystalline
8. Quartz solids – Single crystal

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 Crystal Structures

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Crystal Structures
Which of these statements regarding Body-Centered Cubic (BCC)
Structure is not true?

a) BCC unit cell has atoms at each of the eight corners of a cube
(like the cubic unit cell) plus one atom in the center of the cube.
b) BCC is often the high temperature form of metals that are
closely-packed at lower temperatures.
c) BCC arrangement does not allow the atoms to pack together as
closely as FCC or HCP.
d) Metals with bcc structure are usually softer and more malleable
than close-packed metals such as gold.

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Crystal Structures
Which of these statements regarding Body-Centered Cubic (BCC)
Structure is not true?

a) BCC unit cell has atoms at each of the eight corners of a cube
(like the cubic unit cell) plus one atom in the center of the cube.
b) BCC is often the high temperature form of metals that are
closely-packed at lower temperatures.
c) BCC arrangement does not allow the atoms to pack together as
closely as FCC or HCP.
d) Metals with bcc structure are usually softer and more
malleable than close-packed metals such as gold.

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Crystalline Solids and Hard Sphere Models,
Concept of Unit Cell

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Crystalline Solids and Hard Sphere Models, Concept of Unit Cell
Worked example:
Zinc has HCP structure and the height of the unit cell is 4.935Å.
Determine:
a) The number of atoms in a unit cell
b) Volume of the unit cell.

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Crystalline Solids and Hard Sphere Models, Concept of Unit Cell
Solution:
a) In HCP structure, the number of atoms present in the unit cell is 6.
b) We know that the ratio:
c 8
=
a 3
3
a= c
8

a = 4.935 ×

a = 3.022Å

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Crystalline Solids and Hard Sphere Models, Concept of Unit Cell
Solution cont.
• The volume of the unit cell for HCP structure is given by:
V = Area of the hexagon x height of the prism
V = Area of the hexagon x c
3 3 2x 8 =
= a a 3 2 a3
2 3
V = 3 2× (3.022 × 10 -10 )3
V = 1.17 × 10-28 m3

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Crystalline Solids and Hard Sphere Models, Concept of Unit Cell
Virtual Materials Science and Engineering (VMSE):
• Tool to visualise materials science topics such as crystallography and
polymer structures in three dimensions.

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 Crystalline Solids and Hard Sphere Models, Concept of Unit Cell

Examples of actual VMSE screenshots

FCC Structure HCP Structure

https://drbuc2jl8158i.cloudfront.net/VMSE/index.html
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Calculation of Theoretical Density

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Calculation of Theoretical Density
Worked example:
Copper has an atomic radius of 0.128 nm, an FCC crystal structure, and
an atomic weight of 63.5 g/mol.
Compute its theoretical density and compare the answer with its
measured density.

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Calculation of Theoretical Density
Solution:
Because the crystal structure is FCC, n, the number of atoms per unit cell, is 4.
Furthermore, the atomic weight ACu is given as 63.5 g/mol.
The unit cell volume VC for FCC as determined earlier is given by 16R3 2, where
R, the atomic radius, is 0.128 nm.

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Calculation of Theoretical Density
Solution cont.
• Substituting in the equation for theoretical density:

• The literature value for the density of copper is 8.94 g/cm3, which is
in very close to the above value.

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Packing Factor, Defects in Crystalline Solids

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Packing Factor, Defects in Crystalline Solids
Identify the incorrect statement:

a) A dislocation may be defined as a disturbed region between two

substantially perfect parts of a crystal.
b) A Frenkel imperfection changes the overall electrical neutrality of
the crystal.
c) An interstitial defect arises when an atom occupies a definite
position in the lattice that is not normally occupied in the perfect
crystal.
d) Grain boundary is a two-dimensional imperfection.

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Packing Factor, Defects in Crystalline Solids
Identify the incorrect statement:

a) A dislocation may be defined as a disturbed region between two

substantially perfect parts of a crystal.
b) A Frenkel imperfection changes the overall electrical neutrality
of the crystal.
c) An interstitial defect arises when an atom occupies a definite
position in the lattice that is not normally occupied in the perfect
crystal.
d) Grain boundary is a two-dimensional imperfection.

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Packing Factor, Defects in Crystalline Solids

TEM micrograph of dislocations in Ti3Al

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Packing Factor, Defects in Crystalline Solids

A transmission electron micrograph of a titanium

alloy in which the dark lines are dislocations. 51,000X

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Packing Factor, Defects in Crystalline Solids

Bulk volume defects

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 Packing Factor, Defects in Crystalline Solids
• A transmission electron micrograph of a titanium alloy in which the
dark lines are dislocations, 50,000.

(Courtesy of M. R. Plichta, Michigan Technological University.)

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Packing Factor, Defects in Crystalline Solids
• Schematic representations of surface
defects that are potential adsorption
sites for catalysis.
• Individual atom sites are represented as
cubes.

• High-resolution transmission electron

micrograph that shows single crystals of
(Ce0.5Zr0.5)O2;this material is used in
catalytic converters for automobiles.
• Surface defects represented schematically
are noted on the crystals.

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Packing Factor, Defects in Crystalline Solids
• Cross-section of a cylindrical copper ingot.
• The small, needle-shape grains may be observed, which extend
from the center radially outward.

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Packing Factor, Defects in Crystalline Solids
a) Polished and etched grains as they might appear when viewed with an
optical microscope.
b) Section taken through these grains showing how the etching characteristics
and resulting surface texture vary from grain to grain because of
differences in crystallographic orientation.
c) Photomicrograph of a polycrystalline brass specimen, 60.

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 Packing Factor, Defects in Crystalline Solids
a) Section of a grain boundary and its surface groove produced by
etching; the light reflection characteristics in the vicinity of the groove
are also shown.
b) Photomicrograph of the surface of a polished and etched
polycrystalline specimen of an iron–chromium alloy in which the grain
boundaries appear dark, 100.

[Photomicrograph courtesy of L. C. Smith and C. Brady, the National Bureau of Standards, Washington, DC
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References
• W. D. Callister, D. G. Rethwisch, Materials Science and Engineering
• https://www.mse.berkeley.edu
• www.srmuniv.ac.in
• https://www.engr.mun.ca
• web.deu.edu.tr/metalurjimalzeme/pdf

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 End of Topic 2
Any questions or comments?

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