King Fahd University of Petroleum & Minerals
MECHANICAL ENGINEERING DEPARTMENT
ME 215 : MATERIALS SCIENCE FOR ME
Fall Semester 2006-2007 (061)
Quiz # (SOLUTION)
Name
___________________________
Mr. B. J. Abdul Aleem
Student # _________________________
Saturday: November 11, 2006
Section: ME 215.01
Time Allowed: 25 minutes
Problem 1
Calculate the energy for vacancy formation in silver, given that the equilibrium number of
vacancy at 800°C is 3.6 × 1023 m−3. The atomic weight and density at 800°C for silver are
107.87 g/mole and 10.49 g/cm3, respectively.
This problem calls for the computation of the energy for vacancy formation in silver. Upon
examination of Equation (4.1), all parameters besides Q are given except N, the total number of
v
atomic sites. However, N is related to the density, (), Avogadro's number (N ), and the atomic
A
weight (A) according to Equation (4.2) as
N =
=
6.023
= 5.86 x 10
NA  Ag
AAg

x 10 23 atoms / mol 10.49 g / cm 3

107.87 g / mol
22
3
28
3
atoms/cm = 5.86 x 10 atoms/m
Now, taking natural logarithms of both sides of Equation (4.1), and, after some algebraic
manipulation
N 
QV =  RT ln  V 
 N 
3.60 x 10 23 m3 
=  8.62 x 10 -5 eV/atom - K (1073 K) ln 

28 m 3 

5.86 x 10



= 1.11 eV/atom
ME 215 – Quiz # 3 (061)
Mr. Abdul Aleem
2
Problem 2
Carbon is allowed to diffuse through a steel plate 10 mm thick. The concentration of carbon
at the two faces are 0.85 and 0.40 kg C/cm3 Fe, which are maintained constant. If the preexponential and activation energy are 6.2 × 10−7 m2/s and 800,000 J/mole, respectively,
compute the temperature at which the diffusion flux is 6.3 × 10−10 kg/m2−s.
This problem asks that we compute the temperature at which the diffusion flux is 6.3 x 10
-10
2
kg/m -s.
Combining Equations (5.3) and (5.8) yields
 Q 
C
J =  Do
exp  d 
x
 RT 
Solving for T from this expression leads to
Qd 
1
T =  
R

D
 
o C 
ln 

 Jx 
1
80, 000 J / mol 
= 

8.31 J / mol- K  
7
2
3
6.2 x 10
m / s 0.45 kg / m

ln 
6.3 x 10 10 kg / m 2 - s 10 2 m








= 900 K = 627C
2 (b) - List four important parameters that determine the degree to which the solute atoms
replace or substitute the host atoms in forming a substitutional solid solution.
(1) Atomic Size Factor
(2) Crystal Structure
(3) Electro negativity
(4) Valences