Ellipsometry examination of copper alloys with transitive metals
Electron structure of copper alloys with 3d transition metals (Fe, Co and Cr) have been studied basing on elliposometrical measurement of D and Y in wide spectral range hn = 1.0–4.95 eV. Spectral dependences of Cu-Cr alloys optical conductivity in wide range of chrome concentration (C = 2.5–30 at. %...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2004
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| Цитувати: | Ellipsometry examination of copper alloys with transitive metals / Y.V. Filipov, V.S. Staschuk, L.V. Poperenko, V.V. Vovchenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 3. — С. 287-290. — Бібліогр.: 10 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1191262025-02-23T17:54:18Z Ellipsometry examination of copper alloys with transitive metals Filipov, Y.V. Staschuk, V.S. Poperenko, L.V. Vovchenko, V.V. Electron structure of copper alloys with 3d transition metals (Fe, Co and Cr) have been studied basing on elliposometrical measurement of D and Y in wide spectral range hn = 1.0–4.95 eV. Spectral dependences of Cu-Cr alloys optical conductivity in wide range of chrome concentration (C = 2.5–30 at. %) have been minutely analyzed in this work. Ascertainment that in spectrums of studied alloys (and for copper alloys with other transitive metals) were observed basic band of pure Cu, in addition supplementary band in range 1-2 eV were observed too. Is shown that at small Cr concentrations (C < 5 at. %) alloy is forming a single band similar to copper, with insignificant dependence of Fermi level EF from impurity concentrations. Besides there was founded that in electron structure appear impurity bands situated between Fermi level and d-band of copper. They split on 0.4 eV as a result of spin-orbit interaction. At high impurity concentrations (CCr > 5 at. %) the alloys are heterogeneous mixtures of pure transitive metals and copper based solid solution. 2004 Article Ellipsometry examination of copper alloys with transitive metals / Y.V. Filipov, V.S. Staschuk, L.V. Poperenko, V.V. Vovchenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 3. — С. 287-290. — Бібліогр.: 10 назв. — англ. 1560-8034 PACS: 78.20.-e https://nasplib.isofts.kiev.ua/handle/123456789/119126 en Semiconductor Physics Quantum Electronics & Optoelectronics application/pdf Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Electron structure of copper alloys with 3d transition metals (Fe, Co and Cr) have been studied basing on elliposometrical measurement of D and Y in wide spectral range hn = 1.0–4.95 eV. Spectral dependences of Cu-Cr alloys optical conductivity in wide range of chrome concentration (C = 2.5–30 at. %) have been minutely analyzed in this work. Ascertainment that in spectrums of studied alloys (and for copper alloys with other transitive metals) were observed basic band of pure Cu, in addition supplementary band in range 1-2 eV were observed too. Is shown that at small Cr concentrations (C < 5 at. %) alloy is forming a single band similar to copper, with insignificant dependence of Fermi level EF from impurity concentrations. Besides there was founded that in electron structure appear impurity bands situated between Fermi level and d-band of copper. They split on 0.4 eV as a result of spin-orbit interaction. At high impurity concentrations (CCr > 5 at. %) the alloys are heterogeneous mixtures of pure transitive metals and copper based solid solution. |
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Filipov, Y.V. Staschuk, V.S. Poperenko, L.V. Vovchenko, V.V. |
| spellingShingle |
Filipov, Y.V. Staschuk, V.S. Poperenko, L.V. Vovchenko, V.V. Ellipsometry examination of copper alloys with transitive metals Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Filipov, Y.V. Staschuk, V.S. Poperenko, L.V. Vovchenko, V.V. |
| author_sort |
Filipov, Y.V. |
| title |
Ellipsometry examination of copper alloys with transitive metals |
| title_short |
Ellipsometry examination of copper alloys with transitive metals |
| title_full |
Ellipsometry examination of copper alloys with transitive metals |
| title_fullStr |
Ellipsometry examination of copper alloys with transitive metals |
| title_full_unstemmed |
Ellipsometry examination of copper alloys with transitive metals |
| title_sort |
ellipsometry examination of copper alloys with transitive metals |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2004 |
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https://nasplib.isofts.kiev.ua/handle/123456789/119126 |
| citation_txt |
Ellipsometry examination of copper alloys with transitive metals / Y.V. Filipov, V.S. Staschuk, L.V. Poperenko, V.V. Vovchenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 3. — С. 287-290. — Бібліогр.: 10 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT filipovyv ellipsometryexaminationofcopperalloyswithtransitivemetals AT staschukvs ellipsometryexaminationofcopperalloyswithtransitivemetals AT poperenkolv ellipsometryexaminationofcopperalloyswithtransitivemetals AT vovchenkovv ellipsometryexaminationofcopperalloyswithtransitivemetals |
| first_indexed |
2025-11-24T04:20:31Z |
| last_indexed |
2025-11-24T04:20:31Z |
| _version_ |
1849644056537202688 |
| fulltext |
287© 2004, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Semiconductor Physics, Quantum Electronics & Optoelectronics. 2004. V. 7, N 3. P. 287-290.
PACS: 78.20.-e
Ellipsometry examination of copper alloys
with transitive metals
Y.V. Filipov, V.S. Staschuk, L.V. Poperenko, V.V. Vovchenko
Department of Physics, Kyiv National Taras Shevchenko University, 6, prospect Glushkova, 03127 Kyiv, Ukraine
E-mail: filipov@univ.kiev.ua
Abstract. Electron structure of copper alloys with 3d transition metals (Fe, Co and Cr) have
been studied basing on elliposometrical measurement of ∆ and Ψ in wide spectral range hν =
1.0�4.95 eV. Spectral dependences of Cu-Cr alloys optical conductivity in wide range of chrome
concentration (C = 2.5�30 at. %) have been minutely analyzed in this work. Ascertainment
that in spectrums of studied alloys (and for copper alloys with other transitive metals) were
observed basic band of pure Cu, in addition supplementary band in range 1-2 eV were ob-
served too. Is shown that at small Cr concentrations (C < 5 at. %) alloy is forming a single
band similar to copper, with insignificant dependence of Fermi level EF from impurity con-
centrations. Besides there was founded that in electron structure appear impurity bands situ-
ated between Fermi level and d-band of copper. They split on 0.4 eV as a result of spin-orbit
interaction. At high impurity concentrations (CCr > 5 at. %) the alloys are heterogeneous
mixtures of pure transitive metals and copper based solid solution.
Keywords: Spectroellipsometry, refractive index, absorption index, optical conductivity, cop-
per, alloy, transitive metals, energy structure, density of electron states, impurity bands.
Paper received 14.04.04; revised version 07.09.04; accepted for publication 21.10.04.
1. Introduction
Among all 3d transition metals, only Ni is well soluble in
copper under formation of continuous series of solid so-
lutions with fee lattice [1]. Other transition metals, e.g.,
Fe, are low soluble, while Co and Cr, according to litera-
ture, are almost copper-insoluble [1]. In this case, optical
characteristics, such as refraction n and absorption ae
indices, the dielectric permeability ε and optical conduc-
tivity σ must be described by linear functions of impurity
concentration. This is due to that, according to [1, 2], the
alloys are heterogeneous mixtures of almost pure copper
and impurity, thus, the experimental spectra of the men-
tioned quantities must be formed by superposition of spec-
tra of the mentioned components with the corresponding
weight coefficients.
In this work, the optical properties of binary copper
alloys with low content of Fe, Co and Cr have been stu-
died within the spectral range where the interband elec-
tron transitions play the main part. The results obtained
evidence that the limiting solubility of Fe, Co and Cr in
copper is substantially higher than it was believed be-
fore.
In the case of Cu-Ni solid solutions, a narrow d-band
in electron spectrum has been revealed which is associa-
ted with Ni and is situated between the top of d-band and
the Fermi level [2, 3]. Since other transition metals, espe-
cially Co, are closely similar to Ni in their physical pro-
perties, the formation of the impurity band in alloys is to
be expected if those are single-phase. Before, a compre-
hensive research of impurity bands by optical method was
carried out for a series of 3d transition metal alloys. In
parallel, the electronic structure of disordered alloys was
studied rather intensely using theoretic methods promoted
by optical researches of the precious metal alloys [4, 5].
Studying the absorption spectra of Cu-Fe and Cu-Cr,
it was determined that small impurities of Fe, Cr and Ni
do not influence essentially the position of sp- and d-bands
connected genetically with Cu. Changes in electron spec-
tra of all the alloys, like the Cu-Ni ones, occur mainly
between the top of Cu d-bands and the Fermi level EF due
to formation of the impurity band (with position depend-
ing on impurity type), in spite of different solubility of
the mentioned metals in copper. Optical methods allow
getting a series of parameters characterizing the impu-
rity band, for example, its half-width ∆, its center posi-
tion with respect to the Fermi level Ed � EF, and a series
of other electron parameters can be calculated proceed-
ing from the above ones.
2. Experimental details
The optical properties of Cu-Fe, Cu-Co and Cu-Cr alloys
have been studied basing on the constants n and ae meas-
288
SQO, 7(3), 2004
Y.V. Filipov et al.: Ellipsometry examination of copper alloys with transitive metals ...
ured at ambient temperature within the wavelength range
λ = 0.25�1.24 µm (or photon energy range hν = 1.0�
4.95 eV) by ellipsometric method. The samples of alloys
with impurity content from 2.5 to 40 at. % are prepared
by vacuum arc melting in argon atmosphere using sev-
eral consecutive melting's. The samples were annealed
for 24 hours in the same atmosphere at 900°C to provide
the most possible homogeneity. The mirror surfaces of
samples were prepared by mechanical grinding and pol-
ishing by diamond powders and pastes of different abra-
sive grain sizes. The recrystalisations anneal in vacuum
at 450°C during 3 hours and electric polishing was car-
ried out to remove surface strains.
3. Experimental results and discussion
The curves of the optical conductivity dispersion σ(hν)
are of the most interest in studying optical properties of
the alloys. Using these curves, the data can be obtained
on the changes in electron spectrum of copper doped with
3d transition metals, because σ is connected directly with
interband density of electron states [6]. The experimen-
tal curves σ(hν) for Cu-Fe, Cu-Co and Cu-Cr alloys are
shown in Figs l�3, respectively. In these Figures, the
curves for pure components are presented, too.
It is seen that within the photon energy region hν <
< 1.5 eV the optical conductivity σ of copper monoto-
nously increases as hν decreases. This means that it is
just free electrons that contribute mainly to absorption
due to transitions within each band crossing the Fermi
level. In Cu-Co alloys, as well as in Cu-Cr ones, the con-
tribution of free carriers are almost unobservable within
spectral range under study. From our own data that the
characteristic peculiarities of the copper optical spectrum
are sharp edge of the interband absorption at the photon
energy hν = 2.1�2.3 eV as well as very intense absorption
band with a maximum at photon energy about 4.62 eV.
These peculiarities of the copper optical spectrum are
manifested, to a higher or lower extent, for all alloy sam-
ples. The experimental data allow evaluating the thresh-
old of the optical interband absorption as the half-sum of
the energy values corresponding to maximum and mini-
mum σ near the absorption edge. This value is equal to
2.2 eV for pure copper but in alloys it is within limits of
2.21�2.24 eV, i.e. remains essentially unchanged upon
Co and Cr addition to the alloy. In all alloys studied, there
is also the main band with a maximum at 4.58�4.65 eV,
i.e. the band is shifted along the energy scale by 0.3�0.4
eV only with respect to the maximum for copper. Except
for these two features, a weak maximum is revealed for
alloys at photon energy 3.5�3.6 eV that is more pro-
nounced for alloys with high Cr content. We cannot find
experimentally that maximum for the pure copper al-
though it is very pronounced in the theoretical σ(hν) curve
constructed using the calculated electron spectrum data
for this metal.
Fig. 1. Optical conductivity of pure Cu (1) and for Cu�Fe alloys
with Fe content (at. %): 7.5 (2), 15 (3) and 30 (4).
1 2 3 4
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
h , n eV
s´1 0 , s–1 5 – 1
1
2
3
4
0 1 2 3 4
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
h n, eV
s´1 0 , s–1 5 –1
1
2
3
4
5
6
7
8
Fig. 2. Optical conductivity dispersion of Cu-Co alloys with Co
content (at. %): 2.5 (2), 5 (3), 10 (4), 17.5 (5), 30 (6) and 50 (7) as
well as for pure Cu (1) and Co (8). Curves 3 and 7 are lifted up by
5⋅103 s�1 and 4�6, by 104 s�1.
1 2 3 4
0.0
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
h n, eV
s´1 0 , s–1 5 – 1
1
6
2
3
4
5
7
Fig. 3. Optical conductivity of Cu�Cr alloys with Co content (at. %):
2.5 (1), 5 (2), 10 (3), 17.5 (4) and 30 (5) as well as for pure Cu (6)
and Cr (7). Curve 4 is lifted up by 0.3⋅103 s�1 and 7 by 3.6⋅104 s�1.
Y.V. Filipov et al.: Ellipsometry examination of copper alloys with transitive metals ...
289SQO, 7(3), 2004
Alloying of Cu with Co and Cu with Cr is found to
cause a strong effect, namely, appearance of a very in-
tense band in σ(hν) curves in the near IR region of the
absorption spectrum at the photon energy hv from 0.8 to
1.8 eV. Its intensity increases monotonously with increas-
ing impurity content. For Cu-Cr alloys, this band has
composite structure and consists of a several components.
For the alloys containing 2.5 at. % Cr, these maximums
correspond to the photon energy 1.34 and 1.70 eV (Fig. 3).
At Cr concentration 5 at. %, the long-wave band inten-
sity increases sharply but its maximum becomes shifted
towards lower energy values by about 0.26 eV. At a fur-
ther increasing of Cr concentration, the long-wave band
intensity increases but not so sharply. The maximum of
this band for alloys with Cr content 10 and 17.5 at. % is
at photon energy 1.10 and 1.24 eV, respectively. In the
alloy with 30 % Cr, only one absorption band with a maxi-
mum at 1.50 eV is observed. It should be noted that there
are no peculiarities in the energy range 1.10�1.34 eV
where the maximum of the long-wave band is situated in
σ(hν) spectra of pure Cu, Co, and Cr. For copper, a slight
increase in o as the photon energy decreases is characteris-
tic in the mentioned range, which is connected with free
carrier absorption. In addition, the fact is worth to note
that for the alloys, the intensity of high-energy maximum
at 4.65�4.75 eV associated with Cu depends very weakly
on the impurity concentration. The mentioned facts evi-
dence that the σ(hν) spectra of the alloys cannot be ob-
tained by simple superposition of Cu and Cr as well as of
Cu and Cr ones with corresponding weight coefficients,
as could be expected according the data of the well-known
reference book [1] where the solubility of Co and Cr in
copper is said to be not more than 0.8 at. %.
In other words, in accordance with [1], e.g., Cu�Cr
alloys comprise two phases: almost pure Cr and Cu�Cr
solid solution (the concentration NCr < 0.04�0.8 at. %).
The results of the computer simulation have shown that
the optical conductivity spectra of alloys cannot be ob-
tained by simple summation of those for pure Cu and Cr
with weight coefficients determined by the lever rule [1].
Moreover, the experimental spectra cannot be get also
under suggestion that the alloy components are pure Cr
and solid solution Cu�Cr at Cr concentration of 2 at. %.
The experimental spectrum agrees well with the calcu-
lated one in the case when Cr solubility in Cu is sug-
gested to be not less than 5 at. % and increases further as
the Cr concentration rises. Almost the same situation
takes place in Cu�Co alloys.
Here after, let Cu�Cr alloys be considered in more
detail. Taking into account the results of electron struc-
ture research of pure copper and it optical spectrum, a
model of electron structure for the Cu-Cr solid solution
can be proposed basing on the data obtained. In accor-
dance with [7], the absorption edge for pure copper at
photon energy 2.1�2.2 eV is associated with the electron
transition from the top of d-bands near the L3 point of the
Brillouin band to unoccupied states of L2′ type sp-bands
in the vicinity of the Fermi level EF. The energy band
structure of copper is shown in Fig. 4 where the possible
transitions forming the optical conductivity spectrum
σ(hν) are shown by the arrows. From the experimental
data on the optical properties of Cu-Cr alloys and the
interpretation of the absorption edge, a conclusion can
be drawn that for the Cu-Cr solid solution, not only the
distance between the d-band top and the Fermi level re-
mains unchanged but the whole structure of bands shifted
from Fermi level by 2.2�2.3 eV does not change.
The intense absorption above the absorption edge is
connected with electron transitions in a large volume of
the Brillouin band [8] in directions L�W and X�F (the
possible transition are shown on Fig.4 by arrows). The
optical spectrum (hv) in the photon energy range 2.5�
4.0 eV results from the superposition of different bands
associated with these transitions. Since the σ(hν) spec-
trum character of Cu-Cr solid solutions remains almost
unchanged in the mentioned range, the structure of bands
shifted from the Fermi level by 2.5�4.0 eV in photon en-
ergy remains the same as for the pure Cu. At last, the
absorption spectrum character in the photon energy range
4.0�5.0 eV where the main absorption band of pure cop-
per connected with transitions from L3 d-states to free
levels of L1′ (see Fig. 4) does not change essentially in the
alloys. Thus, the structure of s, p, d-bands shifted up to
5 eV from the Fermi level is the same as in pure copper.
Thus, the study of optical properties of Cu�Cr alloys
with low Cr content (where it is well soluble in Cu) show
that the s, p, d-bands of copper remote at least 5 eV from
the Fermi level remain unchanged in their structure and
energy spectral position. An impurity band is formed due
to Cr situated under the Fermi level. Supposing that the
new absorption band in the σ(hν) optical spectra of Cu�
Cr alloys in the photon energy range 0.8�1.6 eV is re-
lated to electron transitions from the impurity d-under-
band to free electron states near the Fermi level, the posi-
tion of impurity band center with respect to the Fermi
level, Ed � EF, and its half-width can be found basing on
the experimental data.
The above facts indicate that Cu d-bands can be
smoothed out without any essential shift along the en-
ergy scale due to Cu and Cr d-states hybridizing occur-
ring when Cr concentration in the alloy increases. Moreo-
ver, an impurity band is formed situated under Fermi
0
1
2
3
4
�4
�1
�2
�3
�5
W
W
W
W
W '
W '
W '
W '
E , eV
q
p
p
p
p d,
p d,
p d,
d p,
d d
5
4
f
2
3
1
d
d
d
d
d d
s d,
s d,
s
s p,
s p,
L
L '
L
K
K
K
K
KL
W L '
L '
1
1
1
3
2
1
1
2 1
1
1
2
3
43
3
3
2
12
25
l G
G
G'
D
X
E
X
X
X '
X
X KW
Fig. 4. Energy bands for Cu-Cr alloys. Region of possible dipole
transitions of electron shown by arrows. The impurity band of Cu
and Cr solution is shadowed.
290
SQO, 7(3), 2004
Y.V. Filipov et al.: Ellipsometry examination of copper alloys with transitive metals ...
level EF with E(hν) increasing slightly with Cr concentra-
tion in the solution. If Cr would be well soluble in Cu, a
single band of the alloy should arise at high Cr concen-
tration in the alloy, similar to the case of Cu�Ni [3, 9].
However, according to our data, the maximum Cr solu-
bility in Cu is not high (although being substantially
higher than it was believed before) and it exceeds slightly
5 at. %.
The state density N(E) within the impurity band can
be calculated basing on experimental data [8], process-
ing from models of that band. On Fig. 5, the state density
curves for the impurity band of Cu�Cr solid solutions
with 5 at. % Cr is presented. Roughly speaking, the state
density N(E) for each mentioned solid solution is equal to
the sum of state density within limits of the impurity band
and that for pure copper.
4. Conclusions
It follows from the studies that the energy bands of alloys
are similar to Cu at low Cr concentration when it is solu-
ble well in Cu and Cr forms the impurity band situated
nearly in the middle between the Cu d-band top and the
Fermi level EF. Another variant is also possible which
explains the nature of the low-intensity absorption band
of the alloys in the range 1.6�1.7 eV. If it is assumed that
incomplete solubility takes place even at small Cr amounts
in copper, so that Cr clusters are formed, then the absorp-
tion band similar to Cr one is formed due the absorption
by the clusters. The second Cr absorption peak at 1.95 eV
in the spectra may not appear because it is in the range of
absorption minimum of pure copper. With increasing Cr
concentration, it is possible that the size of clusters and
their number increase only insignificantly, because Cr
solubility in copper is increased. As Cr content increases,
the structure of Cu d-bands becomes slightly smoothed
out without any essential shift along the energy scale.
With increasing Cr concentration, the impurity band is
widened and at high Cr concentrations, a single band of
alloy can be formed at last. This cannot be realized to
the full measure in the alloys under study, because the Cr
solubility in Cu is limited, as is shown by the results of
optical properties study on the alloy containing 30 at. %
Cr. It follows from the data presented that the electron
spectrum of Cu�Cr alloys is rather complicated. At low
Cr concentrations (where it is well soluble in Cu), the
energy bands of the alloys are similar to those of copper
while the Cr impurity forms an additional band situated
between the top of Cu d-band and Fermi level. The ap-
pearing of the impurity band in Cu�Cr alloys is indisput-
able and it results in change of other physical properties
of the alloys. At high Cr concentrations, clusters of this
metal are formed, and the experimental spectra of the
alloys are resulted from the superposition of spectrum of
Cu�Cr solution containing not less 5 at. % Cr and that of
pure Cr.
The determination of the limiting Cr solubility in Cu
is the most important result of Cu�Cr alloy optical prop-
erties study; it exceeds slightly 5 at. %. The optical method
turned out to be extremely sensitive in determining the
limiting Cr solubility in Cu as well as that of Co and Fe
[10].
By studying the optical properties, it is found that at
impurity concentrations C < 10 at. %, optical character-
istics, such as refraction and absorption indices, dielec-
tric constant , optical conductivity and the reflection
coefficient under the normal incidence R = ((n�1)2+ae2)/
(n+1)2+ae2), depend non-linearly on the impurity con-
centration. This is due to a complicated transformation
of the copper electron spectrum in the presence of Fe,
Co, or Cr additives. At high impurity concentrations
(C > 10 at. %), the alloys contain two phases and are het-
erogeneous mixtures of the almost pure Fe, Co or Cr and
a copper-based solid solution containing about 95 % Cu.
Experimental dependences of the mentioned optical char-
acteristics on the wavelength result from superposition of
Fe, Co or Cr spectra and that of the mentioned solid solu-
tion with according weight coefficients
References
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4. V.S. Staschuk, A.E. Doroshenko, S.N. Tkachenko // Fiz.
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8. V.L. Moruzzi, J.F. Janak, A.R. Williams, Calculated Elec-
tronic Properties of Metal, Pergamon Press Inc., NY, 1985.
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(2001).
10. L.V. Poperenko, V.S. Staschuk, V.V. Vovchenko // Functional
Mater., 7(3), p. 482 (2000).
�10 �8 �6 �4 �2 0
0
1
2
3
4
5
6
7
D
e
n
si
ty
o
f
st
a
te
s
(s
ta
te
s/
e
V
)
Energy relative to Fermi level (eV)
2
Fig. 5. Calculated state densities N(E) for Cu-Cr alloy with Cr
content 5 at. %. The portion formed by impurity states, pointed
by arrow.
|