1. The document discusses the structure of materials at different length scales ranging from atomic to macroscopic levels. 2. It introduces various structural descriptors used to quantitatively characterize the arrangements of components in materials. 3. The key atomic bonding mechanisms in materials - metallic, covalent, ionic and van der Waals bonds - are described along with illustrative examples. Bonding determines the crystal structures that form.

1. Department of Materials Science and Engineering
Indian Institute of Technology
Kanpur
Dr. Gouthama
MSE 203 2021 Lecture Slide Set L01
Atomic Bonding and Structure of Materials
Slides prepared based on Illustration and text from:
Science. and Engg of Materials,
By Donald R. Askeland. P P. Fully, W J. Wright , Cenage learning
and
The molecular world
By Lesley Smart and Michael Gagan, Open University publication

2. “…in reality nothing exists but
atoms and the voids…”
- Greek Philosopher Democritus, circa 450 BC

5. Structure and Characterization of Material
• We can examine and describe the structure of materials at five different
levels:
1. Atomic structure;
2. Short- and long-range atomic arrangements;
3. Nanostructure;
4. Microstructure; and
5. Macrostructure.
• The features of the structure at each of these levels may have distinct and
profound influences on a material’s properties and behavior.
• Over the years, materials scientists and engineers have developed a set of
instruments in order to characterize the structure of materials at various
length scales.

6. MSE203: Structure of Materials related topics
• Crystalline state
Crystallography of 2D, plane lattices, plane groups
Symmetry
Crystallography of 3D, Space lattices, Point groups, space groups
Stereographic projection
Important crystal structures
• Non-crystalline state
Generic descriptors
Liquid crystals
• Microstructures
Structural hierarchy
Deformation structure
Transformation structure
Stereology and Quantification of microsctructure

7. MSE203:Characterization related topic
• X- ray Diffraction
Powder, single crystal, macrotexture
• Electron diffraction
SADP, CBED, nanodiffraction
• Optical Microscopy
Typical imaging and special techniques
• Scanning electron microscopy
FESEM, ESEM, LV-SEM, EBSD
• Transmission electron microscopy
CTEM, HRTEM and ACTEM
• Imaging and Spectroscopy for surface analysis
RBS, STM, AFM, XPS, AES
ADDITIONAL: Atom Probe Tomography

8. Meaning of “Structure of Materials”
• Full technical and scientific meaning of this term
“Structure of Materials” we may be able to appreciate
at the end of discussion in the course.
• We can start with its definition: “The structure of materials concerns the
quantitative description of the arrangements of the components that make
up the material on all relevant length scales.”
• We can view these arrangements at different scales, ranging from a few
angstrom units to a millimeter
• For simplicity, we chose to describe a small representative unit of the
structure and then have a repetition scheme.
• We follow certain accepted conventions for doing this. We shall discussion
these aspects fairly comprehensive this this course.

9. Descriptors for Structure
• A “Descriptor” is a conceptual scheme that provides a precise quantitative
characterization of some aspect of structure.
• Examples of Descriptors:
-Specify the types and locations of symmetry elements in a material
-connectivity of phases in a two phase material
• For a given material several quantitative measures may be required to specify its
structure with reasonable completeness.
• In this course we shall be learn the systematic definition and application of
descriptors for the specification of structure for the non-crystalline, liquid
crystalline and crystalline states of matter.
• We start Types of Bonds, the with listing structural descriptors of bonded
materials, viz., (i) Bond length, (ii) Bond angles, and (iii) sizes of atoms and Ions.
• We shall see with examples how different types of bonding leads to different
crystal structure.

10. • Short-range order - The regular and predictable arrangement
of the atoms over a short distance - usually one or two atom spacings.
• Long-range order (LRO) - A regular repetitive arrangement of atoms in a
solid which extends over a very large distance.
• Bose-Einstein condensate (BEC) - A newly experimentally verified state of a
matter in which a group of atoms occupy the same quantum ground state.
Short-Range Order versus Long-Range Order

11. (c) 2003 Brooks/Cole Publishing / Thomson
Learning™
Figure 3.1 Levels of atomic
arrangements in materials: (a)
Inert monoatomic gases have
no regular ordering of atoms:
(b,c) Some materials, including
water vapor, nitrogen gas,
amorphous silicon and silicate
glass have short-range order.
(d) Metals, alloys, many
ceramics and some polymers
have regular ordering of
atoms/ions that extends
through the material.
Courtesey Illustration source:
Science and Engineering of Materials,
Donald R. Askeland – Pradeep P. Phulé
Cenage learning

12. (c) 2003 Brooks/Cole Publishing / Thomson
Learning™
Classification of materials based on the type of atomic order.
Courtesey Illustration source:
Science and Engineering of Materials,
Donald R. Askeland – Pradeep P. Phulé
Cenage learning

13. (c) 2003 Brooks/Cole Publishing / Thomson
Learning™
Atomic arrangements in crystalline silicon and amorphous silicon. (a) Amorphous
silicon. (b) Crystalline silicon. Note the variation in the inter-atomic distance for
amorphous silicon.
Courtesey Illustration source:
Science and Engineering of Materials,
Donald R. Askeland – Pradeep P. Phulé
Cenage learning
Atomic arrangement: Crystalline Vs Amorphous

14. (c) 2003 Brooks/Cole Publishing / Thomson Learning™
Figure :
(a) Illustration showing sharing of face and
corner atoms.
(b) The models for simple cubic (SC), body
centered cubic (BCC), and face-centered cubic
(FCC) unit cells, assuming only one atom per
lattice point.
Courtesy Illustration source:
Science and Engineering of Materials,
Donald R. Askeland – Pradeep P. Phulé
Cenage learning
Packing of Atoms

15. Relationship between Atomic Radius and Lattice Parameters
(c) 2003 Brooks/Cole Publishing / Thomson Learning™
Courtesy Illustration source:
Science and Engineering of Materials,
Donald R. Askeland – Pradeep P. Phulé
Cenage learning

16. Packing Factor: FCC
74
.
0
18
)
2
/
4
(
)
3
4
(4)(
Factor
Packing
2
4r/
cells,
unit
FCC
for
Since,
)
3
4
)(
atoms/cell
(4
Factor
Packing
3
3
0
3
0
3

=
=
=
=



r
r
r
a
a
Courtesy Illustration source:
Science and Engineering of Materials,
Donald R. Askeland – Pradeep P. Phulé
Cenage learning

17. Courtesy Illustration source:
Science and Engineering of Materials,
Donald R. Askeland – Pradeep P. Phulé
Cenage learning

18. ➢ Interstitial sites - Locations between the ‘‘normal’’ atoms or
ions in a crystal into which another - usually different –
atom or ion is placed. Typically, the size of this interstitial
location is smaller than the atom or ion that is to be introduced.
➢ Cubic site - An interstitial position that has a coordination number
of eight. An atom or ion in the cubic site touches eight other
atoms or ions.
➢ Octahedral site - An interstitial position that has a coordination
number of six. An atom or ion in the octahedral site touches six
other atoms or ions.
➢ Tetrahedral site - An interstitial position that has a coordination
number of four. An atom or ion in the tetrahedral site touches four
other atoms or ions.
Interstitial Sites – Shape of Voids

19. (c) 2003 Brooks/Cole Publishing / Thomson Learning™
The location of the interstitial sites in cubic unit cells.
Courtesy Illustration source:
Science and Engineering of Materials,
Donald R. Askeland – Pradeep P. Phulé
Cenage learning
Interstitial sites in Cubic unit cells

20. Courtesy Illustration source:
Science and Engineering of Materials,
Donald R. Askeland – Pradeep P. Phulé
Cenage learning

21. Factors need to be considered in order to understand crystal
structures of ionically bonded solids:
▪ Ionic Radii
▪ Electrical Neutrality
▪ Connection between Anion Polyhedra
Crystal Structures of Ionic Materials

22. (c) 2003 Brooks/Cole Publishing / Thomson
Learning™
Connection between anion polyhedra. Different possible connections include
sharing of corners, edges, or faces. In this figure, examples of connections between
tetrahedra are shown.
Courtesy Illustration source:
Science and Engineering of Materials,
Donald R. Askeland – Pradeep P. Phulé
Cenage learning

23. (c)
2003
Brooks/Cole
Publishing
/
Thomson
Learning
The perovskite unit cell showing the A and B site cations and oxygen ions occupying the
face-center positions of the unit cell. Note: Ions are not show to scale.
Courtesy Illustration source:
Science and Engineering of Materials,
Donald R. Askeland – Pradeep P. Phulé
Cenage learning

24. (c)
2003
Brooks/Cole
Publishing
/
Thomson
Learning
Corundum structure of alpha-alumina (α-AI203).
Courtesy Illustration source:
Science and Engineering of Materials,
Donald R. Askeland – Pradeep P. Phulé
Cenage learning
Vacancy as structural component in crystal

25. Atomic Bonding
There are four important mechanisms by which
atoms are bonded in engineered materials. These are
• Metallic bonds;
• Covalent bonds;
• Ionic bonds; and
• van der Waals bonds.

26. Courtesy Illustration source:
Solid state physics,
James D. Patterson & Bernard C. Bailey
Springers, 2007

27. 27
©
2003
Brooks/Cole
Publishing
/
Thomson
Learning™
The metallic bond forms when atoms give up their valence electrons,
which then form an electron sea. The positively charged atom cores are
bonded by mutual attraction to the negatively charged electrons
Courtesy Illustration source:
Science and Engineering of Materials,
Donald R. Askeland – Pradeep P. Phulé
Cenage learning
Metallic bonds

28. 28
©
2003
Brooks/Cole
Publishing
/
Thomson
Learning™
Covalent bonding requires that electrons be shared
between atoms in such a way that each atom has its
outer sp orbital filled.
In silicon, with a valence of four, four covalent bonds
must be formed
Courtesy Illustration source:
Science and Engineering of Materials,
Donald R. Askeland – Pradeep P. Phulé
Cenage learning
Covalent bonds
©
2003
Brooks/Cole
Publishing
/
Thomson
Learning™
Covalent bonds are directional.
In silicon, a tetrahedral
structure is formed, with angles
of 109.5° required between
each covalent bond

29. 29
©
2003
Brooks/Cole
Publishing
/
Thomson
Learning™
Silicon has a valence of four and shares electrons with four oxygen atoms, thus giving a total
of eight electrons for each silicon atom. However, oxygen has a valence of six and shares
electrons with two silicon atoms, giving oxygen a total of eight electrons. Figure illustrates
one of the possible structures.
Courtesy Illustration source:
Science and Engineering of Materials,
Donald R. Askeland – Pradeep P. Phulé
Cenage learning

30. ➢ Covalently bonded materials frequently have complex
structures in order to satisfy the directional restraints
imposed by the bonding.
Covalent Structures
Courtesy Illustration source:
Science and Engineering of Materials,
Donald R. Askeland – Pradeep P. Phulé
Cenage learning
(c)
2003
Brooks/Cole
Publishing
/
Thomson
Learning
Diamond cubic (DC)
A special type of face-centered cubic
crystal structure found in carbon,
silicon, and other covalently bonded
materials.
(a) Tetrahedron and (b) the diamond cubic (DC) unit cell. This open structure is
produced because of the requirements of covalent bonding.

31. (c) 2003 Brooks/Cole Publishing / Thomson Learning™
Figure 3.3 Tetrahedral
arrangement of C-H bonds in
polyethylene.

32. (c) 2003 Brooks/Cole Publishing / Thomson Learning™
Figure 3.2 Basic Si-0
tetrahedron in silicate glass.

33. (c)
2003
Brooks/Cole
Publishing
/
Thomson
Learning
Figure 3.40 The silicon-oxygen tetrahedron and the resultant β-cristobalite
form of silica.
Courtesy Illustration source:
Science and Engineering of Materials,
Donald R. Askeland – Pradeep P. Phulé
Cenage learning
Covalent structure: Packing of tetrahedra

34. 34
© 2003 Brooks/Cole Publishing / Thomson Learning™
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, and the ionic bond is formed
Ionic bonds
Courtesy Illustration source:
Science and Engineering of Materials,
Donald R. Askeland – Pradeep P. Phulé
Cenage learning

35. 35
© 2003 Brooks/Cole Publishing / Thomson Learning™
Illustration of London forces, a type of a van der Waals force, between
atoms
van der Waals bonds.
Courtesy Illustration source:
Science and Engineering of Materials,
Donald R. Askeland – Pradeep P. Phulé
Cenage learning

36. 36
© 2003 Brooks/Cole Publishing /
Thomson Learning™
The Keesom interactions are formed as a result of polarization of
molecules or groups of atoms.
In water, electrons in the oxygen tend to concentrate away from the
hydrogen. The resulting charge difference permits the molecule to be
weakly bonded to other water molecules
Hydrogen bonds
Courtesy Illustration source:
Science and Engineering of Materials,
Donald R. Askeland – Pradeep P. Phulé
Cenage learning

37. 37
Interatomic spacing is the equilibrium spacing between the centers of two atoms.
Binding energy is the energy required to separate two atoms from their
equilibrium spacing to an infinite distance apart.
Binding Energy and Interatomic Spacing
Courtesy Illustration source:
Science and Engineering of Materials,
Donald R. Askeland – Pradeep P. Phulé
Cenage learning
© 2003 Brooks/Cole Publishing / Thomson Learning™
Atoms or ions are separated by and equilibrium spacing that corresponds to the minimum inter-atomic
energy for a pair of atoms or ions (or when zero force is acting to repel or attract the atoms or ions)

38. © 2003 Brooks/Cole Publishing / Thomson
Learning™
The force-distance curve for two materials, showing the relationship between atomic
bonding and the modulus of elasticity, a steep dFlda slope gives a high modulus
Courtesy Illustration source:
Science and Engineering of Materials,
Donald R. Askeland – Pradeep P. Phulé
Cenage learning
Structure and Property relationship: Elastic Modulus

39. 39
© 2003 Brooks/Cole Publishing / Thomson
Learning™
The inter-atomic energy (IAE)-separation curve for two atoms. Materials that display a
steep curve with a deep trough have low linear coefficients of thermal expansion
Courtesy Illustration source:
Science and Engineering of Materials,
Donald R. Askeland – Pradeep P. Phulé
Cenage learning
Structure and Property relationship: Thermal Expansion

40. Illustration source:
The molecular world By
Lesley Smart and Michael Gagan,
Open University publication

42. Illustration source:
The molecular world By
Lesley Smart and Michael Gagan,
Open University publication

43. Coming up Next………..
Crystallography of 2D:
Translation, Reflection and Glide