MSE 227 Homework Assignment #1 – Ch.2
Bond Energy
1.
Given the following data, carefully make a bond-energy versus separation
distance graph for the following materials. Label the portion of each curve that represents
the melting temperature, elastic modulus and thermal expansion.
Property
Melting Temperature
Elastic Modulus
Thermal Expansion
Coefficient
Nickel
1455 oC
204 GPa
13.3 x 10-6 /oC
Lead-Tin solder
183 oC
30 GPa
24 x 10-6 /oC
2.
For a K+- Cl- ion pair, attractive and repulsive energies EA and ER depend on the
distance between the ions r, according to:
1.436
5.86  10 6
EA  
ER 
r
r9
For these expressions, energies are expressed in electron volts per K+- Cl- pair, and r is
the distance in nanometers. The net energy EN is just the sum of the preceding two
expressions.
(a)
Superimpose on a single plot EN, EA and ER vs. r up to 1 nm. (use a spreadsheet)
(b)
On the basis of this plot, determine (i) the equilibrium spacing ro between K+ and
Cl ions, and (ii) the magnitude of the bonding energy Eo between the two ions.
(c)
Mathematically determine the ro , Eo and E values and compare these with the
graphical results from (b).
HINT: Differentiate EN with respect to r, and then set the resulting expression equal to
zero, because the curve EN vs. r is minimum at ro. Solve for ro, which is the equilibrium
interionic spacing. Differentiate EN again to determine the elastic modulus, E.
3.
What type(s) of bonding would be expected for each of the following materials:
brass (a copper-zinc alloy), LiF, MgO, boron nitride (BN) and pure Si? For
those that are not purely metallic or covalent, calculate the percent ionic character.