Theoretical assessments of materials
for the radio frequency absorptive coatings
V.M. Lelevkin1 and K.A. Moldosanov2
Kyrgyz-Russian Slavic University, Bishkek 720000, Kyrgyz Republic
ABSTRACT
Theoretical assessments and physical mechanisms of absorptive materials for
screening coatings are presented. These coatings can be applied on walls and/or blinds
to protect rooms against the electromagnetic radiation (EM), to screen the computer
radiation, as well as to absorb EM radiation of the mobile telephony. Here, the
absorber means a material in which the EM wave is faded, and its energy is dissipated
and converted into heat. Dissipation of the EM energy can be provided by means of
increased intensity of electron scattering in metallic nanoparticles. In this approach,
the following physical phenomena are used: (i) increase of the energy distance ΔE
between the electron energy levels when a size of the metallic particle is decreased;
(ii) transparence of the metallic particle with regard to the EM radiation, when the
energy quantum hν of the radiation becomes less than ΔE; (iii) dissipation of the EM
wave energy in the metallic particle due to increased probability of the electron
scattering; (iv) gradual attenuation of the EM wave in a layer of a great number of
metallic particles at the expense of conversion of the EM energy into heat.
Keywords: electromagnetic radiation, absorptive coating, nanoparticle, attenuation,
absorption, Fermi energy
Nowadays, the radio frequency absorptive coatings became actual in connection with
development of the mobile telephony, computer science, and necessity to defend
information against non-sanctioned control and protect rooms and computers from
overhearing. This paper concerns these problems and propounds the nanoparticlebased approach.
Evolution of the electron spectrum of the metallic particle with decreasing its size
When a size of the metallic particle is decreased, a number of metal atoms N in it is
decreased too. Correspondingly, a number of electron energy states in the electron
spectrum is decreased, and the energy distance ΔE ~ EF/N between the electron states
is increased (here, EF is the Fermi energy of the metal of the particle; typical value of
EF ~ 10 eV).
Let the decreasing in size particle is in the field of the EM wave with the energy
quantum of hν . When the number N of atoms is decreased down to the value N0 at
which the energy distance between the electron energy levels exceeds the energy
quantum: ΔE > hν, then the quantum of radiation can not excite the Fermi electron and
transfer it to the next, higher energy level near to the Fermi energy. That means that
the metallic particle becomes transparent for the incident radiation, and the EM wave
goes through the particle without attenuation. In other words, the conductivity
1
2
E-mail: aral@krsu.edu.kg
E-mail: altair1964@yandex.ru
1-176
electrons stop screening of the external EM field and do not oscillate in the field, i.e.,
the reflected wave is absent.
Let us estimate the size of the metallic particle being in the field with the wavelength
of 1 cm (hν = 1.2ּ10–4 eV). We would like to estimate the number N0 of atoms in the
particle which it should consist of in order to become transparent with respect to the 1
cm radiation. From the relationship between ΔE and number N, we find that N0 ~
EF/ΔE ~ 10 eV/1.2ּ10–4 eV ≈ 105 atoms.
Now let us imagine the particle as a cube. Then the maximum size of its edge is N01/3
≈ 105/3 ≈ 46 atoms. To estimate the edge’s size, let us assume for definiteness that the
size of atoms in the particle is 4 Å. Then the edge’s size is about 46ּ4 Å = 184 Å, and
the estimated “diameter” of the particle (i.e., a length of the body diagonal of the
cube) is 184 Åּ31/2 ≈ 320 Å = 32 nm.
Thus, in order the radiation with the wavelength of 1 cm pass through the particles
with no attenuation, their estimated diameter should not exceed 32 nm. Then, creating
in such nanoparticles a mechanism of dissipation of the EM wave energy, and
preparing a layer-matrix of a great number of non-agglomerated nanoparticles of sizes
less than 32 nm, it is possible to provide a gradual attenuation (absorption) of the
radiation in such the layer-matrix.
Now, let the metallic nanoparticle is radiated with the EM wave of the frequency
typical for mobile communucation, for example, 800 MHz. For this radiation, the
energy quantum hν = 3.3ּ10–6 eV, the number of atoms N0 ≈ 3ּ106, the edge’s size of the
cube: 144 atoms, or 576 Å, and the estimated “diameter” of the particle is 576 Åּ31/2 ≈
1000 Å = 100 nm. Thus, in order the nanoparticles let pass the 800 MHz wave without
attenuation, their estimated diameter should not exceed 100 nm.
Dissipation of the EM energy in the nanoparticle with the electron energy states
density (EESD) peak at its Fermi energy
Let we have transparent nanoparticles. Now, if we cause in them an insignificant
dissipation of the EM energy, then, making a layer-matrix of these nanoparticles, we
could provide: first, passing of the EM wave inside the layer-matrix; and second, a
gradual attenuation of the EM wave. And at sufficient thickness of the layer-matrix,
the wave would entirely fade. Attenuation of the wave in nanoparticles through
dissipation of the wave energy can be provided at the expense of electron scattering.
For that, let us artificially create some number of energy states close by the Fermi
energy EF of the metal of nanoparticle. These energy states should have the value of
the energy distance ΔE' less than that in the transparent metallic nanoparticles, i.e., for
these states ΔE' < hν. Under these conditions, the energy dissipation would be
provided at the expense of scattering of electrons of the artificial energy states located
close by EF. This physical mechanism could be realized if we introduce the impurity
atoms into the nanoparticle, with the following requirements to energy states of
impurity atoms: (a) they should get into the vicinity of the Fermi energy of the metal
of nanoparticles; and (b) they should be arranged more often than those of the metal
of nanoparticles. It turned out that suitable pairs of metals for nanoparticles and
impurity atoms exist.
1-177
For example, aluminium can be chosen as the metal for nanoparticles, and the 3dmetals, vanadium, chromium, and manganese, can be chosen as the suitable impurity
atoms. In systems with 3d-metal ions dissolved in Al, the electrons of the d-bands of
V, Cr, and Mn get close by the Fermi energy of Al, which causes an increased
probability of scattering of electrons which have been excited by the wave to the
states near to EF . Data of the Table 1 show that the electron energy states density
(EESD) peaks in intermetallic compounds of Al and V, Cr, or Mn are closer by the
Fermi energy of Al than those in other compounds of Al and 3d-metals.
As a distance between the electron energy states within the d-band, ΔEd , is less than
that in s- and p-bands, ΔEs,p , of the metal of nanoparticle (Al), then in nanoparticles of
the intermetallide a situation may take place, when ΔEs,p > hν, but ΔEd < hν. In this
case, the EM wave would excite the Fermi electrons into the d-band, and they would
be scattered by electrons of the d-band and by lattice ions. Intensity of scattering
would be rised, as the number of empty electron states in vicinity of the Fermi energy
of the proper intermetallic compound is large. In this way, the EM wave energy would
be converted into heat, and the EM wave would fade. To absorb apprecially the
incident radiation, one should use a great number of considered here almost
transparent nanoparticles by putting them into paint, varnish or other matrix (plastic,
cloth, rubber, ceramics, etc.).
Table 1. Parameters of the EESD peaks created by impurity 3d-atoms in Al [1]
Impurity atoms
Reference Parameters
V
Cr
Mn
Fe
Co
Ni
Cu
Ed – EF
—
—
– 0.72 – 0.93 – 1.53 – 2.42 – 4.52
[2]
—
—
1.44
1.54
1.64
1.22
1.12

Ed – EF
0.17 – 0.25 – 0.60 – 1.03 – 1.84 – 3.43 – 6.57
[3]
3.26
2.56
2.06
1.64
1.26
0.80
0.30

Ed – EF
0.13 – 0.40 – 0.60 – 0.82 – 1.20 – 1.82 – 3.40
[4]
2.90
2.10
1.80
1.50
1.20
0.92
0.64

Ed – EF
0.0
– 0.3
– 0.6
– 0.8
– 1.1
– 1.8
– 3.1
[5]
6.8
5.8
4.6
4.0
3.0
1.2
1.4

Ed – EF
—
—
– 0.48 – 0.82
—
—
—
[6]
—
—
2.72
1.52
—
—
—

Notes: (Ed – EF) is a position of the EESD peak’s center relatively to EF, eV;
 is a width of the EESD peak at half of its maximum, eV.
Another example. As the metal for nanoparticles, there could be chosen copper, and
as the metal providing the EESD peak at the Fermi energy of the copper, – nickel.
Nickel has the d-band at its Fermi energy. Being dissolved in the Cu lattice, Ni ions
provide the d-band at the Fermi energy of the Cu-Ni alloy [7].
At last, let us consider a special case of so called system with heavy fermions. There
are the compounds of simple metals and the rare-earth elements, which at low
temperatures possess anomalously high values of the specific heat, magnetic
susceptibility, specific resistance (~ 10–4 Ohmּcm), and effective electron mass as large
as 102-103 free electron masses. Such systems have very high, narrow and partly filled
1-178
the EESD peak of f-electrons (f-band) at the Fermi energy, which just causes the
anomalous properties of these compounds. When using nanoparticles of the heavy
fermions systems, the EM wave would be attenuating fast due to high intensity of
electron scattering. Hence, a thickness of the absorptive layer would be small.
In large crystals of the heavy fermions systems, at room temperatures (T ≈ 300 K), a
very narrow EESD peak of the f-band is “washed away” by phonons (kT ≈ 2.6ּ10–2 eV)
and disappeared, i.e., the f-electrons would be “shaked out” into the s-p-d-states above
EF. But the narrow EESD peak of the f-band can be kept if the compound with heavy
fermions is prepared as sufficiently small particle, with a size providing a distance
between the f-band and the nearest unfilled energy state of the s-p-d-band (above the
f-peak) more than the energy of 2.6ּ10–2 eV. In this case, phonons could not excite the
electrons of the f-band to the states of the s-p-d-band above it, and the f-peak would be
kept. But the quantum of the radio frequency EM radiation could excite the electron
of the f-band and transfer it from its initial state near to EF to the state above it within
the f-band. There, the excited electron would be subjected to intensive scattering and,
having no time to emit the secondary radio frequency quantum, would be shaked off
to the state near to the EF.
Let us now briefly evaluate what should be the number of atoms N0 in the particle of
the heavy fermions compound in order the electron energy states be separated from
each other by the energy exceeding the thermal smearing kT ≈ 2.6ּ10–2 eV. Again as
before, N0 ≤ EF/kT ~ 10 eV/2.6ּ10–2 eV ≈ 385 atoms. Then the edge of the estimated
cube should consist of 3851/3 ≈ 7 atoms, and the estimated “diameter” of the particle is
7ּ31/2 ≈ 12 atoms. Let again for definiteness, the size of atoms is 4 Å. Then the
estimated “diameter” of the nanoparticle is 12ּ4 Å = 48 Å ≈ 5 nm.
Conclusion
Correctness of the approach considered here is confirmed by results of the
paper [8]. The authors discovered that the impurity nanoparticles of Ni and Fe in the
matrix of nanodiamonds were able essentially enhance attenuation of the microwave
EM radiation. Meanwhile, just Ni and Fe have maximum electron energy states
densities at their Fermi energies [9]. This fact allows us to think that the considered
approach, i.e., the use of metallic nanoparticles with the EESD peak at the Fermi
energy, is acceptable for producing the radio frequency absorptive coatings.
References
1. V.I. Anisimov, V.P. Antropov, V.A. Gubanov et al., “Electron structure of
admixtures and defects in transition metals, their alloys and compounds”,
Nauka Publishers, Moscow, 1989 (in Russian).
2. P. Steiner, H. Höchst, W. Steffen, and S. Hüfner, “XPS study of 3d-metal ions
dissolved in aluminium“, Z. für Physik B, vol. 38, pp. 191-199, 1980.
3. E. Mrosan and G. Lehmann, “Electronic states of 3d-transition metal
impurities in aluminium“, Phys. Stat. Sol. B, vol. 87, pp. K21-K24, 1978.
4. R.M. Nieminen and M. Puska, “3d-impurities in Al density functional results“,
J. of Phys. F: Metal Phys., vol. 10, pp. L123-L127, 1980.
5. J. Deutz, P.H. Dederichs, and R. Zeller, “Local density of states of impurities
in Al“, J. of Phys. F: Metal Phys., vol. 11, pp. 1787-1800, 1981.
1-179
6. V.A. Gubanov, A.I. Liechtenstein, and A.V. Postnikov, “Magnetism and
chemical bonds in crystals”, Nauka Publishers, Moscow, 1985 (in Russian).
7. S. Hüfner, G.K. Wertheim, and J.H. Wernick, “X-Ray photoelectron spectra of
the valence bands of some transition metals and alloys”, Phys. Rev. B, vol. 8,
pp. 4511-4524, 1973.
8. S.A. Maksimenko, V.N. Rodionova, G.Ya. Slepyan et al, “Attenuation of
electromagnetic waves in onion-like carbon composites”, Diamond & Related
Materials, vol. 16, pp.1231-1235, 2007.
9. P. Ziesche, G. Lehmann, “Ergebnisse in der Elektronentheorie der Metalle”,
Akademie-Verlag, Berlin, 1983.
1-180