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HW#1 IET 307: Materials Science
1) What is metallic bonding? How is it formed? What are its characteristics?
Metallic bonding is a primary interatomic bond involving nondirectional sharing of nonlocalized
valence electrons that are mutually shared by all the atoms in a metallic solid.
Metals are bonded by using moderate melting temperature (Tm), moderate energy (E), and
moderate unit cell length (α).
Metals are good conductors of both electricity and heat, and they are ductile in nature.
2) What is ionic bonding? How is it formed? What are its characteristics?
Ionic bonding is always found in compounds that are composed of both metallic and nonmetallic
elements.
Atoms of the metallic element give up their valence electrons to the atoms of the nonmetallic
element, thus creating a bond.
These materials are normally hard and brittle. They are poor conductors of heat and electricity,
insulators if you will.
3) What is covalent bonding? How is it formed? What are its characteristics?
Covalent bonding is when electrons are shared between adjacent atoms. Each atom contributes
at least one electron. These electrons belong to both atoms even though they are shared.
These materials are bonded by using large melting temperature (Tm), large energy (E), and small
unit cell length (α).
Their characteristics are varied; they can be very hard or very weak. They are all however
directional.
4) What is Van der Waals Bonding? How is it formed? What are its characteristics?
These are secondary bonds, and are very weak compared to primary bonds.
Virtually all atoms have this type of bonding. It exists when the positive end of on atoms dipole
is attracted to the negative end of another atoms dipole.
5) What are unit cell, lattice constant and number of atoms per unit? What is the number of atoms
of BCC, FCC and HCP?
Unit cell – this is the basic structural unit of a crystal structure, it is generally defined in terms of
atom (or ion) positions within a parallelepiped volume.
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Lattice constant – this is the height, width and depth of a crystal structure.
Number of atoms per unit cell – Varies depending on cell structure.
BCC = 2 atoms per unit cell
FCC = 4 atoms per unit cell
HCP = 6 atoms per unit cell
6) What is the atomic packing factor? What are the atomic packing factors for BCC, FCC and HCP?
Does the volume increase or decrease when FCC ion changes to BCC ion? Why?
The atomic packing factor is the volume of atoms in unit cell divided by the volume of the unit
cell.
APF for BCC = 0.68
APF for FCC = 0.74
APF for HCP = 0.74
When an FCC ion changes to a BCC ion the volume decreases due to the APF.
7) What are the families of crystal directions and planes?
Equivalent directions are grouped into a family. A family of planes contains all planes that are
crystallographically equivalent.
8) What are the closest packed crystalline direction and plane of BCC and FCC?
The closest packed crystalline direction and plane would be FCC.
9) What are the similarity and difference between FCC and HCP crystalline structures?
The APF is the same for both FCC and HCP, however the stacking sequence is different.
10) What is the Miller index of the crystal plane in the following figure?
(311)
11) If the atomic radius of aluminum is 0.143 nm, calculate the volume of its unit cell in cubic
meters.
0.187149248 x 10-9
12) Calculate the radius of an iridium atom given that iridium has a FCC crystal structure, a density
of 22.4 g/cm3, and an atomic weight of 192.2 g/mol.
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0.3432nm
13) Rhenium has an HCP crystal structure, an atomic radius of 0.137 nm and a c/a ratio of 1.615.
Compute the volume of the unit cell.
Vc = 8.63 x 10-2nm3
14) Explain why the properties of polycrystalline materials are most often isotropic.
This is caused by the random orientation of the grains as the grow and join together.
15) Why are covalently bonded materials generally less dense than ionically or metallically bonded
ones?
They are less dense because these bonds are between nonmetallic materials, Ionically and
metallically bonded materials have at least one metallic element.