EMS 172
Profs. Y. Takamura and A. Moulé, 2009
UNIVERSITY OF CALIFORNIA, DAVIS
Department of Chemical Engineering and Materials Science
EMS 172: Electronic, Magnetic, and Optical Properties of Materials
Homework 3 - Solutions
Due Date: Tuesday, Oct. 20
th
, 2009, in-class
Note: You must show all the steps you used to obtain your answer in order to receive full credit.
1. Conductivity of Metals and Their Alloys
[15 pts]
The experimental data for pure Cu and a Cu-Ni alloy is shown in the figure below.
This system forms a solid
solution across the composition range shown.
(a)
Using the data presented in the graph, determine the linear temperature coefficient of resistivity for pure Cu.
()
[]
1
2
1
2
1
T
T
−
+
=
α
ρ
Hummel Eqn. 7.27
[1 pt for eqn]
The value for
α
depends on the value taken for
ρ
1
, however, here is not a well defined value used.
Some
conventions use the value at
T
1
= 273K, where
ρ
1
= 16 n
Ω
m.
Taking
T
2
=
100K,
ρ
2
= 4 n
Ω
m, then
()
[]
()
1
1
2
1
2
00433
.
0
273
100
1
16
4
1
−
=
−
=
−
⋅
Ω
⋅
Ω
−
=
−
K
K
K
m
n
m
n
T
T
Alternatively, using
T
1
= 100K,
T
2
= 300K,
ρ
1
= 4 n
Ω
m, and
ρ
2
= 18 n
Ω
m
[2 pts for values, does not have to be
same values]
and rearranging the equation above, we get:
()
1
0175
.
0
100
300
1
4
18
−
=
−
=
−
⋅
Ω
⋅
Ω
K
K
K
m
n
m
n
[1 pt for trying, 1 pt for value]
(b)
What is the linear temperature coefficient of resistivity for Cu alloyed with 3.32%?
Repeating the same calculation as above with
T
1
= 273K, where
ρ
1
= 56 n
Ω
m,
T
2
=
100K,
ρ
2
= 42 n
Ω
m,
α
=
0.00145 K
-1
.
[2 pts]
It should be noted, however, that for small alloying concentrations, the slope should remain
unchanged from the case in (a) for the pure metal.
(c)
Briefly explain the trends in the data
a.
the deformed samples have higher resistivity than the annealed sample