CE 241 – Spring 2015 Problem Set 1

Middle East Technical University
Department of Civil Engineering
CE 241 – Spring 2015
Problem Set 1
1. List the directional and non-directional primary bonds.
Based on this list offer an explanation as to why covalently bonded materials are generally less
dense than ionically or metallically bonded ones.
2. If the atomic radius of a metal that has the face-centered cubic crystal structure is 0.137 nm,
calculate the volume of its unit cell (in nm3).
3. For a metal that has the body-centered cubic crystal structure, calculate the atomic radius (in nm)
if the metal has a density of 7.25 g/cm3 and an atomic weight of 50.99 g/mol.
4. What are the indices for the direction represented by the vector that has been drawn within a
unit cell?
5. What are the Miller indices for the plane shown below?
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6. NaCl has a FCC structure as shown in the unit
cell given. The ionic radii of Na+ and Cl− are 0.97
and 1.81 Å respectively.
Calculate the atomic packing factor of a NaCl
unit cell.
7. Sodium crystallizes in a cubic structure and the
edge of a unit cell is 0.43 nm. The density of
sodium is 0.963 g/cm3 and the atomic unit
weight of sodium is 23 gr/mole.
a)
b)
c)
How many atoms of sodium are contained
in one unit cell?
What type of cubic unit cell does sodium have?
What is the atomic radius of sodium?
8. For a Na+- Cl-ion pair, attractive and repulsive energies UAand UR , respectively, depend on the
distance between the ions r, according to:
−1,436
and
r
UA =
UR =
7,32 𝑥 10 −6
𝑟8
For these expressions, energies are expressed in electron volts per Na+- Cl-ion pair and r is the
distance in nanometers. The net energy UNis the sum of the two expressionsabove.
a)
b)
c)
Superimpose on a single plot UA, UR, and UNversus r up to 1.0 nm.
On the basis of this plot, determine:
i. the equilibrium spacing r0 between the Na and Cl ions
ii. the magnitude of the bonding energy U0 between the two ions.
Mathematically determine the r0 and U0 values and compare them with the resultsobtained
from the graphical solution.
9. For a certain ionic bond, the force-interatomic distance relationship is given by:
5𝐴
8𝐵
F = 𝑟 3 - 𝑟 12
wherer is in nm, A=2.2×10-20 J and B=6.3×10-17 J.
Determine:
a) The attractive energy, repulsive energy and the initial energy (Ui) necessary to from separate
ions if the total energy at the equilibrium distance is -8.76×10-21 J.
b) Find the force necessary to break the bond if the bond becomes unstable for r ≥2.81 nm.
c) Find the modulus of elasticity.
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