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Temperature Dependence of Magnetostriction
in Alloys of FeCo and FeGaZn
Jeremy Hyde
Sophomore
Physics Department
Carnegie Mellon University
August 8, 2013
Mentors:
Dr. Nicholas Jones, Dr. James Restorff,
and Mrs. Marilyn Wun-Fogle
Metallurgy and Fasteners Branch, Code 612
Naval Surface Warfare Center
Carderock Division

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Abstract
In this paper we investigated the temperature dependence of the
magnetostriction of a series of FeCo alloys in the [100] and [111]
directions with varying compositions of cobalt and a series of FeGaZn in
the [100] direction with varying composition of zinc. In both the [100]
and [111] directions, the addition of cobalt to Fe led to a positive increase
in magnetostriction. The FeCo in the [100] direction was temperature
independent and had a positive magnetostriction with a maximum room
temperature magnetostriction of 80 ppm in the 6% cobalt sample. The
FeCo in the [111] direction had a positive slope and a negative
magnetostriction with the smallest room temperature magnetostriction of
-8 ppm in the 6% cobalt sample. The FeGaZn in the [100] direction
showed a peak in magnetostriction when the % composition zinc was
between 2.3% and 2.4%. The FeGaZn alloy with 4.1% zinc also showed
an unusual drop off in magnetostriction compared to the others as it
approached room temperature, the cause of which requires further
investigation.
Background
Magnetostriction is the dimensional change of a material when it has
been exposed to a magnetic field. In 1842 the French physicist James
Joule discovered this effect when he observed the change in length of an
iron rod when magnetized. Magnetostriction () is the strain the magnetic
field produces and is found by dividing the change in length over the
initial length of the material. However, magnetostriction is not limited to
a change in length and can produce changes in both torsion and
bending.
When a substance is demagnetized its magnetic domains are oriented
such that the net magnetism of the sample is zero. When a large enough
magnetic field is applied to the material, the domain walls begin to shift
and, when they reach the lowest energy state, their magnetic moments
will begin to rotate in the direction of the magnetic field. It is this new
alignment which leads to magnetostriction and the change in length in
the direction of the magnetic field. Hence, if the stress (T) on a material
was zero but a magnetic field (H) was applied the material would strain
(ε) proportional to the strength of the magnetic field as seen in equation 1
where the piezomagnetic constants are d and d* and the compliance is
denoted by s.
ε = sT + dH Equation 1

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Similarly when a compressive stress is applied to a material it will cause
the material to become slightly magnetized (B) as can be seen in equation
2. This is caused by the forced rotation and shifting of magnetic
moments so they are oriented perpendicular to the compressive force if
the magnetostriction is positive and parallel if it is negative. For our
purposes the piezomagnetic constants, d and d*, are equal as is shown
in the piezomagnetic constants relationship.
B = μH +d*T Equation 2
d = d* (piezomagnetic constants relationship)
In order to get the largest change in length the material is first put under
a compressive stress in order to orient the magnetic moment
perpendicular to the compressive force (this is assuming positive
magnetostriction). A magnetic field is then applied to the material
parallel to the compressive force, which (if strong enough) forces the
material’s magnetic moments to rotate out of plane, parallel to the
compressive stress, producing the largest elongation possible.
Although discovered in 1842, it had not been put to any practical
purpose until the late 20th century. All magnetic materials have a certain
amount of magnetostrictive properties to them (measured in parts per
million, ppm), however, most don’t have enough to make them useful in
any practical application. It was only after the discovery of giant
magnetostrictive properties in rare earth elements that alloys such as
Terfenol – D and Galfenol were created. These have magnetostrictive
properties ranging from several hundred to several thousand parts per
million (several hundred times that of normal materials) at room
temperature. People have begun to explore various applications for them
such as shaking oil out of rocks, a hearing aid that works through the
teeth, and energy harvesting.
Procedure
The goal is to measure the magnetostrictive properties of
various materials and alloys with respect to temperature
and crystallographic orientation, which is done by
measuring the strain of the material in an applied
magnetic field. Therefore a strain gauge is attached to the
sample and the sample is lowered into an electromagnet which produces
a magnetic field.

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The first step is to prepare the sample by
attaching a small disk of the material to a copper
block and adding a strain gauge to it. The sample
is attached to the copper block for additional
support. This attachment is done by the use of GE
7031 glue to a piece of paper that will allow the
sample to expand and contract freely without any
additional stress from the aforementioned copper
block during magnetostriction. The strain gauge
must be attached in the desired crystallographic
direction.
While measuring the magnetostriction of a
sample, it is important to place it in a strong magnetic field such that the
saturation strain is reached. It is then rotated at least 90 degrees around
the sample’s axis in order to measure the maximum magnetostriction
from a compressed state to a fully elongated state A full 360 degree
rotation is used in order to verify sample alignment and to have a better
sinusoidal fit. The uniform magnetic field is created by a large
electromagnet capable of producing fields exceeding 20 kOe. The sample
is attached to a long non-magnetic metal rod with a gear on the top,
which allows the sample to be lowered into the center of the
electromagnet and rotated to the desired angle.
However, taking measurements at temperatures below room temperature
requires a series of insulated jackets and liquid nitrogen to keep the
sample at the desired temperature. The largest jacket is the vacuum
jacket, which surrounds the other two. It is used
to prevent the liquid nitrogen from heating up
too fast through conduction and convection. The
outer-liquid nitrogen jacket is used for much the
same purposes as it is used to keep the liquid
nitrogen in the inner jacket cool by preventing
heat transfer to the outside so the liquid
nitrogen doesn’t boil away during an experiment.
The inner liquid nitrogen jacket is the most
important as it provides a controlled flow of
liquid nitrogen to the sample via a throttle valve
in order to regulate the temperature. It is important to vacuum the inner
jacket and the sample chamber and then fill them with Helium before
performing a cryogenic temperature run in order to make sure no foreign
objects or water will be frozen by the liquid nitrogen and either block the
supply of liquid nitrogen or disrupt the sample (the boiling point of
helium is below that of nitrogen so it will be unaffected and slowly
escape).

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Once the sample rod has been placed into the jackets, liquid nitrogen
cools it down, and a heater is used to regulate the sample temperature.
The electromagnet is turned on producing the desired magnetic field and
the sample is rotated while strain measurements are taken.
Data Analysis
The magnetostriction of single crystal samples of pure iron in the [111]
direction, FeCo in both the [100] and [111] directions, and FeGaZn in the
[100] direction were tested for their temperature dependence. The FeCo
[100] and FeCo [111] samples included compositions with 3% and 6%
cobalt. These were then compared with the previously mentioned pure
iron sample in the [111] direction as well as a room temperature
measurement of a pure iron sample in the [100] direction. The FeGaZn
included samples with 0.5%, 3.5%, 4.1% and 4.6% Zn (Fe83.2Ga16.3Zn0.5,
Fe81.2Ga15.3Zn3.5, Fe81.5Ga14.4Zn4.1, and Fe82.6Ga12.8Zn4.6). It should be
noted that these FeGaZn samples may vary as much as 0.5% in their
zinc composition. All of these samples were measured in the
electromagnet described above at temperatures starting at 77.9 K (LN2)
and from 100K to 300 K in 50 degree increments.
In figure 1 we observe the temperature dependence of the
magnetostriction of various single crystal alloys of FeCo oriented in the
[100] direction. A single crystal sample is a sample in which there is
minimal atomic misorientation such that the sample can be oriented
precisely. The average magnetostriction of magnetic materials is around
15 ppm so it is easy to see that pure iron has unusually strong
magnetostriction of about 50 ppm and that cobalt only heightens this
effect by further increasing the magnetostriction to 63 ppm at 3% and
then to 80 ppm at 6 %.

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Figure 1 – Temperature dependence of the magnetostriction of various single crystal alloys of FeCo oriented in
the [100] direction
The most interesting thing to note about this graph is the slope of the
curves. This slope suggests that these alloys are more or less
temperature independent. These curves show that even large
temperature differences only produces a small change in the
magnetostriction of iron alloys with traces of cobalt in them. Little to no
temperature dependent magnetostriction can be a useful property in
sensitive equipment that requires any change in its dimensions, like
those caused by magnetostriction, to be constant at all temperature as to
not mess up any readings.
The change in magnetostriction from pure iron to Fe97Co3 and from
Fe97Co3 to Fe94Co6 were identical within the confines of experimental
error, and since both of these changes were over a 3% increase in cobalt
composition it suggests a constant increase in magnetostriction of about
5.2 ppm per % cobalt. However, this must be confirmed by further
testing on other FeCo samples (possibly 9%).
Similarly to figure 1, figure 2 describes the temperature dependence of
the magnetostriction of various alloys of single crystal FeCo, however,
this time in the [111] direction. The magnetostriction in the [111]
direction is negative, signifying that the magnetic field causes the alloys
to contract in the [111] direction. The cobalt seems to lessen this
contraction however, as the magnetostriction of pure iron at room
temperature is -32 ppm while the magnetostriction of the 3% and 6%

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cobalt at similar temperatures is -23 ppm and -8 ppm respectively. It
would be beneficial to have a sample at 9% cobalt in order to see whether
its magnetostriction is positive or zero.
Figure 2 – Temperature dependence of the magnetostriction of alloys of FeCo oriented in the [111] direction
The slopes of the curves show a distinct upward trend which signifies a
positive temperature dependence of the magnetostriction of FeCo alloys.
This positive temperature dependence means that the magnetic and
elastic properties of the alloys are less coupled than they were at lower
temperatures. The decoupling of the magnetic and elastic properties
lessens any elongation or contraction that would have occurred due to a
magnetic field at lower temperatures. These slopes are linear within
experimental error and parallel to one another indicating that the
temperature dependence is uniform despite changes in composition
causing the magnetostriction to increase at a rate of about 0.07 ppm per
degree Kelvin.
By using both the data from the [100] and [111] direction samples, an
estimate of the temperature dependence of the magnetostriction of a
polycrystalline FeCo sample can be determined via equation 3. The room
temperature polycrystalline FeCo alloys have a calculated
magnetostriction of 11 ppm and 27 ppm at 3% and 6% cobalt
respectively. In contrast polycrystalline pure iron has a magnetostriction
of 0.4 ppm.

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λpoly = 0.6λ111 + 0.4λ100 Equation 3
As can be seen in figure 3 by combining the data from the [100] and
[111] FeCo alloys, the temperature dependence of the polycrystalline
alloys can be calculated. Figure 3 shows that the polycrystalline FeCo
samples have a low but positive magnetostriction and are temperature
dependent at a rate of about 0.05 ppm per degree Kelvin.
Figure 3 – Temperature dependence of the calculated magnetostriction of polycrystalline FeCo alloys
Several samples of FeGaZn in the [100] direction were also analyzed in
the electromagnet for the temperature dependence of their
magnetostrictive properties. In figure 4 we see that all of these alloys
have a relatively high magnetostriction (around 20x more than the
average for a magnetic material).

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Figure 4 – Temperature dependence of the magnetostriction of alloys of FeGaZn oriented in the [100] direction
As the temperature increases the amount of energy in the alloys
increases; this causes more misalignment of the magnetic moments and
softening of the elastic constants that in turn decreases the saturation
strain of the alloy. As the temperature increase various things could
happen.
The magnetostriction may continue downwards and at a certain
temperature known as the Curie Temperature, the alloy will be
demagnetized due to a net magnetic moment of zero yielding a minimum
in magnetostriction.
Another possibility is that the magnetostriction might go past zero and
become negative. In this case the same magnetic field would contract the
alloy instead of elongating it as before. Nevertheless at the alloy’s Curie
Temperature the alloy will be demagnetized and the magnetostriction is
minimized.
The only way the magnetostriction can become zero, however, is when
there is decoupling of the magnetoelastic properties of the material. If
this does not occur there is the possibility of magnetostriction occurring
at temperatures above the Curie Temperature given a strong enough
magnetic field.

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The [100] curves are parallel except for the sample which contains 4.1%
Zn. The unusually large drop off in magnetostriction between 250 K and
300K of this sample required a second set of measurements at 10 degree
increments between 250 K and 300 K in order to better understand this
irregularity. The new points showed a decrease in magnetostriction
which got faster and faster. However, the new data did little more than
confirm the irregularity. In order to better understand this drop off more
testing should be done at higher temperatures and possibly send the
sample to have its composition retested as both the 3.5% and 4.6% zinc
samples behave “normally”.
Figure 5 – Magnetostriction at 300 K of various FeGaZn alloys showing a polynomial trend line
One of the most useful pieces of information we got from the FeGaZn
data was the peak in magnetostriction versus % composition of zinc. In
figure 3 the 3.5% zinc sample has the greatest magnetostriction of the
samples tested. Figure 5 shows the graph of the 300 K measurements
made on each sample. By using a simple polynomial fit it can be initially
estimated that the magnetostriction of FeGaZn alloys peaks between
2.3% or 2.4% zinc at around 340 ppm. It may be useful then to try other
compositions with FeGa if magnetostriction above 340 ppm is required.

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Figure 6 – Magnetostriction of laminated stress annealed rods of Galfenol under various compressive stresses
in magnetic fields ranging from 0 kOe to 1 kOe
Several samples were also placed in the MTS Jr., a machine which
provides a controlled compressive force and measures the strain of the
material under compression and in a magnetic field.