05 February 2014 CURIE.1
THE CURIE TEMPERATURE OF GADOLINIUM
The inductance of a coil of copper wire wrapped around a gadolinium sample will be measured as a function of temperature and the Curie temperature of gadolinium will be determined.
Theory:
Ferromagnetic materials (iron, nickel, cobalt, gadolinium, dysprosium) exhibit a long-range ordering phenomenon at the atomic level which causes the unpaired electron spins to line up parallel with each other in a region called a domain.
For a given ferromagnetic material, the long range order abruptly disappears at a certain temperature called the Curie temperature for the material. The Curie temperature gives an indication of the amount of energy needed to break up the long-range ordering in the material.
Above the Curie temperature, ferromagnetic materials become paramagnetic.
Whereas ferromagnetic materials have a very large positive magnetic susceptibility, paramagnetic materials have a much smaller (still positive) susceptibility. In the range of temperatures exceeding the Curie temperature, the magnetic susceptibility depends on temperature according to the Curie-Wiess Law:
   
1

T
C

 
(1) where

is the magnetic susceptibility,

is the magnetic permeability, C

is a materialdependent constant, T is the temperature in Kelvin, and

is the Curie temperature.
The magnetic permeability of a sample can be determined in terms of the inductance of a coil wound around the sample:
  
L
L
0
(2) where

is a geometrical factor dependent on the shape of the coil, L is the inductance of the coil, and L
0
is the inductance of an air-core coil of the same shape.
Substitution into the Curie-Wiess law yields: y




L
L
0

1



1

T
 
C

(3)
Note that y is a linear function of T with slope 1/ C

and y -intercept –

/ C

and that y is equal to zero when T =

. Thus, the intersection of the straight line graph of y versus T with the horizontal (temperature) axis directly determines the value of the Curie temperature.
Apparatus:
The apparatus consists of a tank that will contain water (so that the temperature of the sample can be changed), a mixer/heater, a temperature probe, a multimeter to measure inductance, and an oil-filled jar containing the sample and coil.

05 February 2014 CURIE.2
Figure 1. Equipment Setup
Figure 2. Close-up of jar containing sample

05 February 2014 CURIE.3
Procedure and Experiment:
1. Turn on the cold water tap and let the water run in the sink until it is as cold as possible.
2. Place the stand holding the sample jar in the tank, as shown. Place the heater/mixer unit in the tank, as shown.
3. Using the pitcher, carefully pour cold water into the tank until the water level is above the coil in the sample jar ( but below the label on the jar ).
4. Remove the lid from the sample jar. Using a pair of leads and alligator clips, carefully connect the coil to the multimeter (set to measure inductance in mH). Ensure that the coil wires do not touch each other.
5. Place the temperature probe in the clamp so that the probe is as close as possible to the sample coil.
6. Set the temperature control on the heater/mixer to 30

C. Turn on the mixer (large orange rocker switch) and heater (toggle switch).
7. Measure the inductance of the sample coil at 0.2

C intervals as the temperature increases from 11.0

C to 27.0

C.
Analysis:
Assuming values of L
0
= 1.33 mH and

= 1, plot y versus T (see equation (3) in the theory section). Determine the Curie temperature of gadolinium. Compare your value of the Curie temperature with a referenced comparison value.