Extra oxygen and carrier distribution in CuO₂ layers in HgBa₂Can₋₁CunO₂n₊₂₊δ compounds (n=1,2,4)
It is proposed to determine the equilibrium state of the crystal lattice by minimizing the total energy in order to elucidate the role of electrostatic interactions as well as to determine the nonstoichiometry in Hg-contained high temperature superconductors (HTSC). The approximation of non-inter...
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Інститут фізики конденсованих систем НАН України
1999
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| Назва видання: | Condensed Matter Physics |
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| Цитувати: | Extra oxygen and carrier distribution in CuO₂ layers in HgBa₂Can₋₁CunO₂n₊₂₊δ compounds (n=1,2,4) / R.V. Lutciv, Ya.V. Boyko // Condensed Matter Physics. — 1999. — Т. 2, № 3(19). — С. 481-486. — Бібліогр.: 4 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1205412017-06-13T03:05:54Z Extra oxygen and carrier distribution in CuO₂ layers in HgBa₂Can₋₁CunO₂n₊₂₊δ compounds (n=1,2,4) Lutciv, R.V. Boyko, Ya.V. It is proposed to determine the equilibrium state of the crystal lattice by minimizing the total energy in order to elucidate the role of electrostatic interactions as well as to determine the nonstoichiometry in Hg-contained high temperature superconductors (HTSC). The approximation of non-interacting holes is used to evaluate the band energy. Such an approach enables us to satisfactorily describe the changes of oxygen nonstoichiometry and to indicate the preferred localization of the carriers on oxygen sites in CuO₂ layers. Для з’ясування ролі електростатичних взаємодій і визначення нестехіометрії у Hg-вмісних високотемпературних надпровідниках (ВТ- НП) пропонується визначати рівноважний стан кристалічної гратки шляхом мінімізації загальної енергії. Для обчислення зонної енергії використовується наближення повністю невзаємодіючих дірок. Такий підхід дає змогу добре описати зміни нестехіометрії за киснем і показує переважнe розміщення носіїв на позиціях кисню у площинах CuO₂. 1999 Article Extra oxygen and carrier distribution in CuO₂ layers in HgBa₂Can₋₁CunO₂n₊₂₊δ compounds (n=1,2,4) / R.V. Lutciv, Ya.V. Boyko // Condensed Matter Physics. — 1999. — Т. 2, № 3(19). — С. 481-486. — Бібліогр.: 4 назв. — англ. 1607-324X DOI:10.5488/CMP.2.3.481 PACS: 74.25.Fy, 74.62.Dh, 74.72.Jt http://dspace.nbuv.gov.ua/handle/123456789/120541 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
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English |
| description |
It is proposed to determine the equilibrium state of the crystal lattice by
minimizing the total energy in order to elucidate the role of electrostatic
interactions as well as to determine the nonstoichiometry in Hg-contained
high temperature superconductors (HTSC). The approximation of non-interacting holes is used to evaluate the band energy. Such an approach
enables us to satisfactorily describe the changes of oxygen nonstoichiometry and to indicate the preferred localization of the carriers on oxygen sites
in CuO₂ layers. |
| format |
Article |
| author |
Lutciv, R.V. Boyko, Ya.V. |
| spellingShingle |
Lutciv, R.V. Boyko, Ya.V. Extra oxygen and carrier distribution in CuO₂ layers in HgBa₂Can₋₁CunO₂n₊₂₊δ compounds (n=1,2,4) Condensed Matter Physics |
| author_facet |
Lutciv, R.V. Boyko, Ya.V. |
| author_sort |
Lutciv, R.V. |
| title |
Extra oxygen and carrier distribution in CuO₂ layers in HgBa₂Can₋₁CunO₂n₊₂₊δ compounds (n=1,2,4) |
| title_short |
Extra oxygen and carrier distribution in CuO₂ layers in HgBa₂Can₋₁CunO₂n₊₂₊δ compounds (n=1,2,4) |
| title_full |
Extra oxygen and carrier distribution in CuO₂ layers in HgBa₂Can₋₁CunO₂n₊₂₊δ compounds (n=1,2,4) |
| title_fullStr |
Extra oxygen and carrier distribution in CuO₂ layers in HgBa₂Can₋₁CunO₂n₊₂₊δ compounds (n=1,2,4) |
| title_full_unstemmed |
Extra oxygen and carrier distribution in CuO₂ layers in HgBa₂Can₋₁CunO₂n₊₂₊δ compounds (n=1,2,4) |
| title_sort |
extra oxygen and carrier distribution in cuo₂ layers in hgba₂can₋₁cuno₂n₊₂₊δ compounds (n=1,2,4) |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
1999 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120541 |
| citation_txt |
Extra oxygen and carrier distribution in CuO₂ layers in HgBa₂Can₋₁CunO₂n₊₂₊δ compounds (n=1,2,4) / R.V. Lutciv, Ya.V. Boyko // Condensed Matter Physics. — 1999. — Т. 2, № 3(19). — С. 481-486. — Бібліогр.: 4 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT lutcivrv extraoxygenandcarrierdistributionincuo2layersinhgba2can1cuno2n2dcompoundsn124 AT boykoyav extraoxygenandcarrierdistributionincuo2layersinhgba2can1cuno2n2dcompoundsn124 |
| first_indexed |
2025-07-08T18:06:11Z |
| last_indexed |
2025-07-08T18:06:11Z |
| _version_ |
1837103029277425664 |
| fulltext |
Condensed Matter Physics, 1999, Vol. 2, No. 3(19), pp. 481–486
Extra oxygen and carrier distribution in
CuO2 layers in HgBa2Can−1CunO2n+2+δ
compounds (n=1,2,4)
R.V.Lutciv, Ya.V.Boyko
Chair of Radio-electronic Material Sciences, Physics Department, Ivan
Franko State University of Lviv, 50 Dragomanov Str., 290005 Lviv, Ukraine
Received July 1, 1998
It is proposed to determine the equilibrium state of the crystal lattice by
minimizing the total energy in order to elucidate the role of electrostatic
interactions as well as to determine the nonstoichiometry in Hg-contained
high temperature superconductors (HTSC). The approximation of non-in-
teracting holes is used to evaluate the band energy. Such an approach
enables us to satisfactorily describe the changes of oxygen nonstoichiom-
etry and to indicate the preferred localization of the carriers on oxygen sites
in CuO2 layers.
Key words: HTSC, carrier distribution, nonstoichiometry
PACS: 74.25.Fy, 74.62.Dh, 74.72.Jt
While investigating the high-temperature superconductors (HTSC) there is still
an important problem to elucidate the role of different interactions in the forma-
tion of their physical characteristics. Superconducting properties of all HTSC types
are determined by the concentration of carriers and their distribution in the lattice
cell. In many works which are dedicated to the investigation of LSCO, YBCO, BiSr-
CaCuO and TlBaCaCuO systems it is pointed out that the electrostatic (Madelung)
energy is the most important factor which determines the distribution of carriers.
Other factors, such as the ionization potentials of metallic ions and the electron
affinity of the oxygen, are not essential or remain stable with changes of doping
levels [1].
In this work it is proposed to study the distribution of the carriers in Hg-HTSC
among atomic positions determining an equilibrium state of the crystal lattice by
minimizing the total energy, the latter including EM (electrostatic energy) and Eb
– band energy:
Etot = EM + Eb.
Using this method it is possible to determine the contents of the excessive oxygen
which can be compared to the experimental data. The inter-ion Coulomb energy
c© R.V.Lutciv, Ya.V.Boyko 481
R.V.Lutciv, Ya.V.Boyko
was calculated using Evald’s method which was generalized for a random number
of ions in the lattice cell:
EM =
e2
2
4π
V0
[
∑
~K 6=0
|S( ~K)|2
exp(−K2/4η2)
K2
−
π
V0K2
(
∑
n
qn)
2 +
∑
~R
∑
n,n′
qnqn′erfcc(ηRnn′)
Rnn′
−
2η
π
∑
n
q2n
]
, (1)
where S( ~K) =
∑
n qne
i ~K~r, η is the width of Gauss distribution; ~R, ~K are vectors
of the direct and reciprocal lattice, respectively; V0 is the volume of the lattice
cell. Environment screening effects were accounted for by introducing a dielectric
constant [2]. The following approach is suggested to estimate the band energy. Let
ph be the number of holes per one CuO2 plane. The hole energy in the system L x
L which is formed by a number of planes can be presented as
εk =
h̄2k2
2m∗
, (2)
where m∗ is a hole effective mass in the parabolic band. Then ph = a2
2π
k2
F (a is
the lattice parameter) or kF =
√
(2π/a2)ph (Fermi wave vector) and Fermi energy
εF = πh̄2
m∗a2
ph.
Thus, the densities of states will be presented as
D(ε) =
m∗a2
πh̄2
.
A band energy per one CuO2 plane is expressed as:
Ebi =
∫ εF
0
D(ε)εdε =
πh̄2
2m∗a2
p2h.
Then we shall consider a band energy per one lattice cell as a sum over planes [2]:
Eb =
πh̄2
2m∗a2
∑
i
p2hi.
A one-electron band energy (2) can also be considered as an a eigenvalue of Hub-
bard hamiltonian in the approximation of completely non-interacting holes U=0,
where U is a parameter of Coulomb repulsion at one site. Then the effective mass
is connected with intra-plane transfer integral t||: m
∗ = h̄2/(2t||a
2). According to
Cyrot’s model [3] there is a connection between the temperature of the supercon-
ducting transition and the parameters of the Hubbard hamiltonian which for U=0
is expressed as Tc = tnh, where nh is the total number of holes in the lattice cell.
Finally, a band energy is expressed as:
Eb =
πTc
nh
∑
i
p2hi. (3)
482
Extra oxygen and carrier distribution
Table 1. Ionic charge in HgBa2CuO4+δ
Atom x/a y/b z/c q
Hg 0 0 0 2
Ba 1/2 1/2 0.298 2
Cu 0 0 1/2 2 + 2yδ
O(1) 1/2 1/2 0 −2 + δ(1− y)
O(2) 0 0 0.2076 −2
O(3) 1/2 1/2 0 −2δ
Table 2. Ionic charge in HgBa2Ca3Cu4O10+δ
Atom x/a y/b z/c q
Hg 0 0 0 2
Ba 1/2 1/2 0.142 2
Ca(1) 1/2 1/2 0.324 2
Ca(2) 1/2 1/2 1/2 2
Cu(1) 0 0 0.2502 2+δxy
Cu(2) 0 0 0.4160 2+δ(1− x)y
O(1) 1/2 0 0.248 −2 + (δ/2)x(1− y)
O(2) 1/2 0 0.4174 −2 + (δ/2)(1− x)(1− y)
O(3) 0 0 0.102 −2
O(4) 1/2 1/2 0 −2δ
In order to make the analysis according to the above scheme the authors used
structural data and properties of the sample series from [4]. In the structure with
four CuO2 planes the nonequivalence of external and internal planes was taken into
account [2] by introducing x-parts of the holes which go into internal planes. Tables
1, 2 show the examples of choice distribution of ionic charges between atoms for
determining the Madelung energy.
The total energy minimization was effected relating to the excessive oxygen con-
tents (figure 1).
The calculations were carried out as follows. At different values of y those values
of x were determined for which at the given magnitude of an index δ the energy
had the minimum value. Then using the received values x(δ) dependencies E tot(δ)
for one of the samples of a series were determined. At the δ minimizing energy co-
inciding with that experimentally determined (such δ are marked in the table 3 by
asterisks) an appropriate value of y was used for minimizing the E tot in relation to δ
on structural data of the other examples of a series. It means that relative changes
of nonstoichiometry were determined. It should be noted, that experimental mea-
surements of δ also determined only relative changes of nonstoichiometry because δ
values which were determined by different methods do not coincide. As it is shown
483
R.V.Lutciv, Ya.V.Boyko
���� ���� ���� ��������
����
����
����
���
δ
( �WR
W����
�� �H
9
Figure 1. The total energy Etot as a function of the nonstoichiometry δ for Hg-
1201 compound (the sample with Tc=53 K)
Table 3. Results of calculations
Compounds y δxp δcalc Tc, K
0.18∗ 0.18∗ 95
0.08 0.09 53
Hg-1201 0.16 0.04 0.11 0
0.23 0.29 30
0.21 0.22 80
0.18 0.16 94
0.14 0.08∗ 0.08∗ 92
0.22 0.23 126
0.17 0.22∗ 0.22∗ 112
Hg-1212 0.38 0.36 120
0.21 0.35∗ 0.35∗ 104
0.28 0.32 123
0.21 0.33∗ 0.33∗ 122
0.21 0.29 126
Hg-1234 0.25 0.4∗ 0.4∗ 125
0.47 0.56 120
* – values through which y were chosen.
484
Extra oxygen and carrier distribution
in table 3, the calculated values give a very good description of δ changes. δcalc
are always present in the same doping area (insufficient or excessive doping) with
experimentally determined values.
In addition, the calculations show a predominant localization of the holes at the
oxygen position which matches experimental data for other HTSC types.
Thus, it is possible to make a conclusion on the similarity of
HgBa2Can−1CunO2n+2+δ homological series and other HTSC families by the type of
the chemical link and by the characteristics of the charge carrier distribution among
the structural elements (nonequivalence of internal and external CuO2 planes, a
preferred localization on the O2p orbitals).
References
1. Feiner L.F., de Leeuw D.M. Hole distribution and Madelung energy in the high-Tc
oxide superconductors. // Sol. Stat. Commun., 1989, vol. 70, No. 12, p. 1165–1169.
2. Tristan Jover D., Wijngaarden R.J., Wilhelm H., Griessen R., Loureiro S.M., Cap-
poni J.-J., Schilling A., Ott H.R. Pressure dependence of the superconducting critical
temperature of HgBa2Ca2Cu3O8+y and HgBa2Ca3Cu4O10+y up to 30 GPa. // Phys.
Rev. B, 1996, vol. 54, No. 6, p. 4265–4275.
3. Cyrot M. On High-Tc Superconductivity in La2CuO4 Type Compounds.//Sol. Stat.
Commun., 1987, vol. 62, No. 12, p. 821–823.
4. Loureiro S.M., Capponi J.-J., Antipov E. V., Marezio M. On the Synthesis and Struc-
ture HgBa2Can−1CunO2n+2+δ Superconductors. – In: Studies of High Temperature
Superconductors. vol. 25, New York, Nova Science Publisher, 1998.
485
R.V.Lutciv, Ya.V.Boyko
Надлишковий кисень і розподіл носіїв у площинах
CuO2 у сполуках HgBa2Can−1CunO2n+2+δ (n=1,2,4)
Р.В.Луців, Я.В.Бойко
Львівський державний університет, фізичний факультет,
кафедра радіоелектронного матеріалознавства,
290005 Львів, вул. Драгоманова, 50
Отримано 1 липня 1998 р.
Для з’ясування ролі електростатичних взаємодій і визначення не-
стехіометрії у Hg-вмісних високотемпературних надпровідниках (ВТ-
НП) пропонується визначати рівноважний стан кристалічної гратки
шляхом мінімізації загальної енергії. Для обчислення зонної енергії
використовується наближення повністю невзаємодіючих дірок. Та-
кий підхід дає змогу добре описати зміни нестехіометрії за киснем і
показує переважнe розміщення носіїв на позиціях кисню у площинах
CuO2.
Ключові слова: ВТНП, розподіл зарядів, нестехіометрія
PACS: 74.25.Fy, 74.62.Dh, 74.72.Jt
486
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