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Journal ArticleDOI

Permittivity and permeability of epoxy–magnetite powder composites at microwave frequencies

22 Jan 2020-Journal of Applied Physics (AIP Publishing)-Vol. 127, Iss: 4, pp 045102
TL;DR: In this paper, the authors fabricated and characterized two samples using different ratios of two easily commercially available materials: epoxy (Stycast 2850FT) and magnetite (F e 3 O 4) powder.
Abstract: Radio, millimeter, and sub-millimeter astronomy experiments as well as remote sensing applications often require castable absorbers with well known electromagnetic properties to design and realize calibration targets. In this context, we fabricated and characterized two samples using different ratios of two easily commercially available materials: epoxy (Stycast 2850FT) and magnetite ( F e 3 O 4) powder. We performed transmission and reflection measurements from 7 GHz up to 170 GHz with a vector network analyzer equipped with a series of standard horn antennas. Using an empirical model, we analyzed the data to extract complex permittivity and permeability from transmission data; then, we used reflection data to validate the results. In this paper, we present the sample fabrication procedure, analysis method, parameter extraction pipeline, and results for two samples with different epoxy-powder mass ratios.

Summary (2 min read)

Introduction

  • Radio, millimeter, and sub-millimeter astronomy experiments as well as remote sensing applications often require castable absorbers with well known electromagnetic properties to design and realize calibration targets.
  • The authors fabricated and characterized two samples using different ratios of two easily commercially available materials: epoxy (Stycast 2850FT) and magnetite (Fe3O4) powder.
  • 2–6 Examples of instruments with custom designed loads include the Atacama Large Millimeter Array7–9 (ALMA), the Planck Low Frequency Instrument10,11 (LFI), and the proposed Primordial Inflation Explorer12 as examples concerning astrophysical experiments, or the European Space Agency (ESA) MetOp13–15 satellite project for what concerns remote sensing applications.
  • The authors measured transmittance and reflectance through a thin ( 2 mm) slab of material, and they used an empirical model to extract information about the electromagnetic properties of their samples through transmission data.

II. CHARACTERIZATION OF AN ABSORBER

  • In general, the authors describe the behavior of matter in the presence of an electromagnetic field through the complex relative dielectric permittivity and magnetic permeability.
  • But this approximation is not always valid when the authors extend the analysis to a broader frequency range.

B. SAMPLE FABRICATION

  • To fabricate the samples, the authors built a mold consisting of a flat 10-mm aluminum baseplate covered with a 1-mm polytetrafluoroethylene (PTFE) sheet to facilitate the release of the finished sample.
  • Once the epoxy-powder mixture is poured into the mold and the lid is inserted, the exceeding material can flow out through four holes at the corners of the lid.
  • Both samples were prepared by mixing the components (epoxy, catalyst, and magnetite powder), outgassing the mixture to ensure a uniform sample, and curing the sample in a oven at 65 C.
  • From now on, the authors will refer to the first material as Mag27 and the second as Mag60.

C. MEASUREMENT SETUP

  • To reduce the number of parameters to be determined through the fitting routine of the transmission data, and therefore reduce the degeneracy, the authors measure the static permittivity of the TABLE I. Summary of the samples analyzed in this study.
  • In Table I, a summary of the results for the static relative permittivity and thickness of the two samples is given.

D. PARAMETERS VALIDATION

  • After extracting all the parameters of their model using transmission data, the authors calculate reflection from a slab of material with the same thickness of their sample, and they compare the computed response to S11,cal data to validate their results.
  • This is likely due to an imperfect calibration in this band; however, the authors highlight here that this mismatch does not have an impact on the result of the fit because they do not use reflection data to constrain the parameters of the model, but purely to cross-check the results.
  • The results, for the materials analyzed in this work, are shown in Fig. 6 for Mag27 and in Fig. 7 for Mag60; from these, it can be seen that both values of the real and the imaginary parts of both permittivity and permeability increase with the relative amount of magnetite powder in the composite material.
  • As it appears clear from these data, the loss tangent is dominated by magnetic losses at low frequency.

III. CONCLUSIONS

  • The authors fabricated and tested the electromagnetic properties of two samples made with Stycast 2850FT and Fe3O4 powder .
  • While Stycast 2850FT has already been used extensively for similar applications, most applications use CIP (carbonyl iron powder)24 as the filler.
  • The authors presented here the analysis procedure and results for the measurement of dielectric permittivity and magnetic permeability of the two samples they made with magnetite powder and Stycast 2850FT.
  • The ability to tune the complex permeability at low frequencies is in good agreement with results in the literature; however, some applications might require knowledge of the complex permittivity and permeability on a broader frequency range for design purposes.

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J. Appl. Phys. 127, 045102 (2020); https://doi.org/10.1063/1.5128519 127, 045102
© 2020 Author(s).
Permittivity and permeability of epoxy–
magnetite powder composites at microwave
frequencies
Cite as: J. Appl. Phys. 127, 045102 (2020); https://doi.org/10.1063/1.5128519
Submitted: 19 September 2019 . Accepted: 05 January 2020 . Published Online: 22 January 2020
T. Ghigna , M. Zannoni , M. E. Jones, and A. Simonetto

Permittivity and permeability of epoxymagnetite
powder composites at microwave frequencies
Cite as: J. Appl. Phys. 127, 045102 (2020); doi: 10.1063/1.5128519
View Online
Export Citation
CrossMar
k
Submitted: 19 September 2019 · Accepted: 5 January 2020 ·
Published Online: 22 January 2020
T. Ghigna,
1,2,a)
M. Zannoni,
3,4
M. E. Jones,
1
and A. Simonetto
5
AFFILIATIONS
1
Sub-Department of Astrophysics, University of Oxford, Keble Rd., Oxford OX1 3RH, United Kingdom
2
Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
3
Dipartimento di Fisica, Universitá di Milano-Bicocca, P.za della Scienza 3, 20126 Milano, Italy
4
INFN, Sez. di Milano-Bicocca, P.za della Scienza 3, 20126 Milano, Italy
5
CNRIstituto per la Scienza e la Tecnologia dei Plasmi (ISTP-MI), via R. Cozzi 53, 20125 Milano, Italy
a)
Author to whom correspondence should be addressed: tommaso.ghigna@physics.ox.ac.uk
ABSTRACT
Radio, millimeter, and sub-millimeter astronomy experiments as well as remote sensing applications often require castable absorbers with
well known electromagnetic properties to design and realize calibration targets. In this context, we fabricated and characterized two samples
using different ratios of two easily commercially available materials: epoxy (Stycast 2850FT) and magnetite (Fe
3
O
4
) powder. We performed
transmission and reflection measurements from 7 GHz up to 170 GHz with a vector network analyzer equipped with a series of standard
horn antennas. Using an empirical model, we analyzed the data to extract complex permittivity and permeability from transmission data;
then, we used reflection data to validate the results. In this paper, we present the sample fabrication procedure, analysis method, parameter
extraction pipeline, and results for two samples with different epoxy-powder mass ratios.
Published under license by AIP Publishing. https://doi.org/10.1063/1.5128519
I. INTRODUCTION
Castable electromagnetic wave absorbers are us ually compos-
ite materials made with a polymer encapsulant matrix and a
dielectric or magnetic filler. There are examples of this type of
material commercially available. The ven dors provide electromag -
netic properties (dielectric permittivity, magnetic p ermeability, or
loss tangents) up to 1820 GHz;
1
however, for many applica-
tio ns, values at higher frequencies are requi red to help instrument
designs.
26
Example s of instruments with custom designed loads
include the Atacama Large Millimeter Ar ray
79
(ALMA), the
Planck Low Frequency Instrument
10,11
(LFI), and the proposed
Primordial Inflation Explorer
12
(PIXIE) as examples concerning
astrophysical experim ents, or the European Space Agency (ESA)
MetOp
1315
satellite project for what conce rns remote sensing
applications.
In this paper, we explore the possibility of fabricating a cast-
able absorber using cheap commercially available materials: Stycast
2850 FT
16
as the dielectric encapsulant and magnetite powder
17
(chemical composition Fe
3
O
4
) as the magnetic filler, and we
measure the properties up to 170 GHz with a vector network
analyzer (VNA).
W e made two sam ples with d iffer ent encapsulant-filler mass
ra tio, in order to show the possibility of tuning the pr operties depend-
ing on specific experiment needs. The maximum magnetite particle
size is 45 μm, and the typical size is 200 nm. W e do not e xpect the par-
ticle size to make a significant difference as it is very small compared
to the wavelen gth. W e measured transmission and reflection from the
samples below 170 GHz, corresponding to wav elengths * 1:7mm.We
measured transmit tance and reflectance through a thin (2 mm) slab
of material, and we used an empirical model to extr a ct informa tion
about the electromagnetic properties of our samples thr ough transmis-
sion data.
1820
Themeasurementsetupandoneofthemeasured
samplesasshowninFig. 1. To validate our results, we use the extrac ted
parameter s to calculate, by means of an empirical model, reflection
data, and w e compare them with measurement s.
In Sec. II, we present the model and the method for the elec-
tromagnetic parameters retrieval, and in Sec. III, we present and
discuss the results obtained for the samples under study.
Journal of
Applied Physics
ARTICLE scitation.org/journal/jap
J. Appl. Phys. 127, 045102 (2020); doi: 10.1063/1.5128519 127, 045102-1
Publ ished under license by AIP Pub lishing.

II. CHARACTERIZATION OF AN ABSORBER
In general, we describe the behavior of matter in the pr esence of
an electromagnetic field through the complex relativ e dielectric per-
mittivity and magnetic permeability . Often, w e can assume these
quantities to be cons tant, especially if w e limit our analysis to a narrow
frequency band. But this approxima tion is not always valid when we
extend the analysis to a br oader fr equency range. In this case, we ha v e
to take into account a dir ect dependence from the frequency
ϵ(ν) ¼ ϵ
r
(ν) þ iϵ
i
(ν), (1)
μ(ν) ¼ μ
r
(ν) þ iμ
i
(ν): (2)
A. PARAMETERS EXTRACTION
Using Eq. (1) and (2), we can write the complex frequency-
dependent refractive index
^
n(ν) ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ϵ(ν)μ(ν)
p
¼ n(ν) þ ik(ν): (3)
From Eq. (3), it is easy to find the key parameters to compute
reflection and transmission through the medium,
21,22
the reflection
parameter [Eq. (4)], and δ, which combine the phase shift and
damping factor [Eq. (5)],
R ¼
^
n(ν) 1
^
n(ν) þ 1
2
, (4)
δ / exp
i2π
^
n(ν)νΔx
c

: (5)
Using a Debye relaxation model
23
for the relative permittivity of
the medium
ϵ(ν) ¼ ϵ
1
þ
ϵ
dc
ϵ
1
1 i
ν
ν
ϵ
, (6)
and a Lorentzian resonant model for the relative permeability
μ(ν) ¼ 1 þ
μ
dc
1
1 i
ν
ν
μ

2
, (7)
we can describe the transmission and reflection from a slab of
material with known thickness Δx with five free parameters: ϵ
1
(relative permittivity at high frequency), ϵ
dc
(static relative permit-
tivity), ν
ϵ
(relaxation frequency), μ
dc
(static relative permeability),
and ν
μ
(resonant frequency).
B. SAMPLE FABRICATION
To perform the analysis, we fabricate thin (Δx 2mm)
square samples (200 200 mm). To fabricate the samples, we
built a mold consisting of a fl at 10-mm al uminum baseplate
covered with a 1-mm polytetrafluoroethylene (PTF E) sheet to
facilitate the release of the finished sample. This PTFE sheet is
kept in place by a second 10-mm aluminum plate with a square
aperture (200 200 mm), which can be screwed to the baseplate
to form the molding structure. To obtai n the required thickness,
we made a PTFE lid, to be inserted into the mold aperture, of
proper dimensions to obtai n the 2 mm thick sample. Once
the epox y-powder mixture is poured into the mold and the lid
is inserted, the exceeding material can flow out through four
holes at the corners of the lid. We used a release agent to
prevent the sample from stic king to the aluminum walls of
the mold.
In this paper, we present the results of two samples made
using Stycast 2850FT (ideal for cryogenic applications), catalyst 24
LV (7% mass ratio), and Fe
3
O
4
-powder. Both samples were pre-
pared by mixing the components (epoxy, catalyst, and magnetite
powder), outgassing the mixture to ensure a uniform sample, and
curing the sample in a oven at 65
C.
The two samples differ in mass ratio between the magnetic
powder and the epoxy encapsulant: 27% and 60%. From now on,
we will refer to the first material as Mag27 and the second as
Mag60.
C. MEASUREMENT SETUP
As explained in Sec. II A, our parametric model has five free
parameters. To reduce the number of parameters to be determined
through the fitting routine of the transmission data, and therefore
reduce the degeneracy, we measure the static permittivity of the
FIG. 1. (a) Measurement setup. Two horns antenna are facing each other with
the thin flat sample on the aperture of one of the antennas. Transmission and
reflection data are measured using a VNA. (b) One of the measured samples
with a 1 euro coin for size reference.
TABLE I. Summary of the samples analyzed in this study. Powder-to-epoxy mass
ratio, thickness, and permittivity measured with the capacitor are shown for each
sample.
Sample Mass ratio Δx ϵ
dc
Mag27 27% 2.38 mm 7.57
Mag60 60% 2.31 mm 17.79
Journal of
Applied Physics
ARTICLE scitation.org/journal/jap
J. Appl. Phys. 127, 045102 (2020); doi: 10.1063/1.5128519 127, 045102-2
Publ ished under license by AIP Pub lishing.

samples independently using a capacitor made with two planar
copper plates of area A,
C ¼ ϵ
0
ϵ
dc
A
Δx
, (8)
where C is the capacitance, ϵ
0
is the absolute vacuum permittivity,
and Δx is the distance between the plates, corresponding to the
thickness of the sample. By measuring the capacitance, knowing A,
Δx, and ϵ
0
, it is possible to obtain the static relativ e permittivity of
the sample. With this preliminary step, we reduce the free parameters
from five to four. In Table I, a summary of the results for the static
relative permittivity and thickness of the two samples is given.
Transmission and reflection measurement are carried out
using six different pairs of standard rectangular horn antennas,
FIG. 2. Transmission data and fit for Mag27. Data and the result of the analysis
are split in three sub-plots for clarity: (a) X, Ku, K, Ka, and Q bands; (b) V and
W bands; and (c) D band.
FIG. 3. Transmission data and fit for Mag60. Data and the result of the analysis
are split in three sub-plots for clarity: (a) X, Ku, K, Ka, and Q bands; (b) V and
W bands; (c) D band.
Journal of
Applied Physics
ARTICLE scitation.org/journal/jap
J. Appl. Phys. 127, 045102 (2020); doi: 10.1063/1.5128519 127, 045102-3
Publ ished under license by AIP Pub lishing.

between 7 and 75 GHz, and two pairs of circular corrugated
horn antennas, from 75 up t o 170 GHz. In total, we use eight
pairs of antennas to cover the whole frequenc y range with a
vector network analyzer (Agilent PNA-X N5245A with
N5261A mm- wave test se t an d related OML extensions). We
place the sa mple under test on the aperture of the tra nsmitting
antenna to carry out both transmission (S
21
) and reflection
(S
11
) measurements at the same time. To calibrate the data, we
measure S
21
without the sample (free-space) and S
11
for a per-
fectly reflective surface (mirror) and for a perfectly absorptive
surface (pyramidal foam with S
11
, 50 dB). The calibrated
FIG. 4. Reflection data and simulated data based on the extracted permittivity
and permeability for Mag27. Data and the result of the analysis are split in three
sub-plots for clarity: (a) X, Ku, K, Ka, and Q bands; (b) V and W bands;
(c) D band.
FIG. 5. Reflection data and simulated data based on the extracted permittivity
and permeability for Mag60. Data and the result of the analysis are split in three
sub-plots for clarity: (a) X, Ku, K, Ka, and Q bands; (b) V and W bands;
(c) D band.
Journal of
Applied Physics
ARTICLE scitation.org/journal/jap
J. Appl. Phys. 127, 045102 (2020); doi: 10.1063/1.5128519 127, 045102-4
Publ ished under license by AIP Pub lishing.

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171 citations

Journal ArticleDOI
Shibing Ni, Shumei Lin, Qingtao Pan, Feng Yang1, Kai Huang, Deyan He 
TL;DR: In this paper, a simple hydrothermal method was used to synthesize well-dispersed Fe3O4 nanocrystals, which were characterized by field emission scanning electron microscopy, transmission electron microscope, selected area electron diffraction, x-ray diffraction and vibrating sample magnetometer.
Abstract: Well-dispersed Fe3O4 nanocrystals were synthesized by a simple hydrothermal method. The as-synthesized products were characterized by field emission scanning electron microscopy, transmission electron microscopy, selected area electron diffraction, x-ray diffraction, vibrating sample magnetometer and vector network analysis. The complex permittivity and permeability of paraffin wax and Fe3O4 with different Fe3O4 volume fractions were measured to increase linearly with the increase in the volume fraction of Fe3O4. The magnetic loss was caused mainly by natural resonance, which is in good agreement with the Kittel equation results. When the matching thickness is 3 mm, the calculated reflection loss reaches a maximum value of −21.2 dB at 8.16 GHz with 30% volume fraction of Fe3O4.

145 citations

Frequently Asked Questions (2)
Q1. What are the contributions mentioned in the paper "Permittivity and permeability of epoxy–magnetite powder composites at microwave frequencies" ?

The authors performed transmission and reflection measurements from 7 GHz up to 170 GHz with a vector network analyzer equipped with a series of standard horn antennas. Using an empirical model, the authors analyzed the data to extract complex permittivity and permeability from transmission data ; then, they used reflection data to validate the results. In this paper, the authors present the sample fabrication procedure, analysis method, parameter extraction pipeline, and results for two samples with different epoxy-powder mass ratios. 

These works showed already the possibility to tune the electromagnetic properties ( specifically complex permeability and therefore the magnetic loss tangent ) by changing the ratio of Fe3O4 at low frequency ( 20 GHz ). For the future work, the authors can imagine a setup to measure this parameter independently similarly to what they have done with the capacitance measurements to obtain a better constraint of this parameter and reduce even further the number of free parameters to be fitted. In conclusion, this work shows the possibility of using Stycast 2850FT in combination with magnetite powder to fabricate an RF-absorbing material, and it describes a method to measure complex permittivity and permeability on a broad frequency range with transmission and reflection measurements. This work shows that the material can be customized for the specific application to achieve the required permittivity and permeability values by changing the Fe3O4-Stycast 2850FT mass ratio.