Periodic changes in the state of a 4f metal compound under pressure
The statement is proved that in the framework of experimentally achievable pressure the existing compounds containing rare-earths can be characterized as those belonging to one of the three states depending on distance RE-O: an electronic state, a vibronic state, in particular a state of electronic-...
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Донецький фізико-технічний інститут ім. О.О. Галкіна НАН України
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irk-123456789-692662014-10-10T03:01:44Z Periodic changes in the state of a 4f metal compound under pressure Voloshin, V.A. Kuznetsova, V.V. Shevtsova, T.N. The statement is proved that in the framework of experimentally achievable pressure the existing compounds containing rare-earths can be characterized as those belonging to one of the three states depending on distance RE-O: an electronic state, a vibronic state, in particular a state of electronic-vibronic equilibrium, and a semiconductor-metal state. The hypothesis is put forward that the mechanism of realization of superconducting state in PrBa₂Cu₃O₆.₆ can be considere Обосновывается утверждение, что в рамках экспериментально достижимого давления существующие соединения, содержащие редкие земли, могут быть охарактеризованы принадлежностью к одному из трех состояний в зависимости от расстояния RЕ–O: электронному, вибронному (в частности, состоянию электрон-вибронного равновесия) и полупроводниково-металлическому. Выдвигается гипотеза, что механизм реализации сверхпроводящего состояния в PrBa₂Cu₃O₆.₆ можно рассматривать как изменение соотношения полупроводниковой и металлической проводимостей в веществе. Обґрунтовується твердження, що в рамках тиску, який можна експериментально досягти, iснуючі з’єднання, що містять рідкісні землі, можуть бути охарактеризовані належністю до одного з трьох станів залежно від відстані RE–O: електронного, вібронного (зокрема, стан електрон-вібронної рівноваги) та напівпровідниково-металічного. Висувається гіпотеза, що механізм реалізації надпровідного стану в PrBa₂Cu₃O₆.₆ можна розглядати як зміну співвідношення напівпровідникової та металічної провідностей у речовині. 2010 Article Periodic changes in the state of a 4f metal compound under pressure / V.A. Voloshin, V.V. Kuznetsova, T.N. Shevtsova // Физика и техника высоких давлений. — 2010. — Т. 20, № 1. — С. 90-101. — Бібліогр.: 24 назв. — англ. 0868-5924 PACS: 74.25.Fy, 74.20.De, 74.72.Jt http://dspace.nbuv.gov.ua/handle/123456789/69266 en Физика и техника высоких давлений Донецький фізико-технічний інститут ім. О.О. Галкіна НАН України |
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The statement is proved that in the framework of experimentally achievable pressure the existing compounds containing rare-earths can be characterized as those belonging to one of the three states depending on distance RE-O: an electronic state, a vibronic state, in particular a state of electronic-vibronic equilibrium, and a semiconductor-metal state. The hypothesis is put forward that the mechanism of realization of superconducting state in PrBa₂Cu₃O₆.₆ can be considere |
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Voloshin, V.A. Kuznetsova, V.V. Shevtsova, T.N. |
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Voloshin, V.A. Kuznetsova, V.V. Shevtsova, T.N. Periodic changes in the state of a 4f metal compound under pressure Физика и техника высоких давлений |
| author_facet |
Voloshin, V.A. Kuznetsova, V.V. Shevtsova, T.N. |
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Voloshin, V.A. |
| title |
Periodic changes in the state of a 4f metal compound under pressure |
| title_short |
Periodic changes in the state of a 4f metal compound under pressure |
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Periodic changes in the state of a 4f metal compound under pressure |
| title_fullStr |
Periodic changes in the state of a 4f metal compound under pressure |
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Periodic changes in the state of a 4f metal compound under pressure |
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periodic changes in the state of a 4f metal compound under pressure |
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Донецький фізико-технічний інститут ім. О.О. Галкіна НАН України |
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2010 |
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http://dspace.nbuv.gov.ua/handle/123456789/69266 |
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Periodic changes in the state of a 4f metal compound under pressure / V.A. Voloshin, V.V. Kuznetsova, T.N. Shevtsova // Физика и техника высоких давлений. — 2010. — Т. 20, № 1. — С. 90-101. — Бібліогр.: 24 назв. — англ. |
| series |
Физика и техника высоких давлений |
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AT voloshinva periodicchangesinthestateofa4fmetalcompoundunderpressure AT kuznetsovavv periodicchangesinthestateofa4fmetalcompoundunderpressure AT shevtsovatn periodicchangesinthestateofa4fmetalcompoundunderpressure |
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2025-07-05T18:53:51Z |
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Физика и техника высоких давлений 2010, том 20, № 1
© V.A. Voloshin, V.V. Kuznetsova, T.N. Shevtsova, 2010
PACS: 74.25.Fy, 74.20.De, 74.72.Jt
V.A. Voloshin , V.V. Kuznetsova, T.N. Shevtsova
PERIODIC CHANGES IN THE STATE OF A 4f METAL COMPOUND
UNDER PRESSURE
Donetsk Institute for Physics and Engineering, National Academy of Sciences of Ukraine
72 R. Luxemburg St., Donetsk, 83114, Ukraine
E-mail: vika@kiit.net
Received January 5, 2008
The statement is proved that in the framework of experimentally achievable pressure the
existing compounds containing rare-earths can be characterized as those belonging to
one of the three states depending on distance RE-O: an electronic state, a vibronic state,
in particular a state of electronic-vibronic equilibrium, and a semiconductor-metal state.
The hypothesis is put forward that the mechanism of realization of superconducting state
in PrBa2Cu3O6.6 can be considered as a change in the ratio of semiconductor and metal-
lic conductivities in the substance.
Keywords: electronic-vibronic equilibrium, high-temperature superconductivity,
PrBa2Cu3O6.6, conductivity.
1. Introduction
In earlier work [1] the properties of 3d configuration of La0.5Ca0.54MnO3+x
were considered and explained within the framework of a hypothesis of electronic-
vibronic dynamic equilibrium.
In the proposed work the same hypothesis is extended to 4f configuration by
consideration of compounds with Pr. As noticed, the decrease of distance between
rare-earth and oxygen renders very strong influence on properties of a substance,
moving it from an electronic state through a vibronic to a semiconductor-metal
state. Thus, the compound can get in a so-called electronic-vibronic state of dy-
namic equilibrium. When the RЕ–O bond length appears to be less than 2 Å, the
substance begins to show semiconductor properties moving to metallic ones under
pressure. For the compounds in a semicondacting-metal state, for example
PrBa2Cu3O6.6, we shall try to explain the occurrence of high-temperature super-
conductivity, considering only the change of a kind of conductivity in the sub-
stance.
Физика и техника высоких давлений 2010, том 20, № 1
91
2. Three possible states of the electron system of a rare-earth compound
The properties of this system can be described in terms of three possible
states.
2.1. Electronic state
The choice of this term stems from the term vibronic state. The spectra of the
same rare-earth ion entering into the composition of various substances (or the
same substance under different thermodynamic conditions) can differ strongly.
The first group of spectra contains the spectra of rare-earth ethyl sulphates. They
consist of faint narrow lines (Fig. 1,b). Some of the energy levels are degenerate.
What is the cause of these specific features? The narrow lines correspond to the as-
sumption of a near-adiabatic approximation, namely, fast electrons and a slow nu-
cleus. This assumption leads to the only electronic state and, hence, to narrow lines.
Fig. 1. Spectra of the vibronic state of cesium molybdate with praseodymium impurity
(a) (room temperature, the Pr–Ol bond length is 2.38 Å and the Pr–O2 bond length is
2.54 Å) and of the electronic state of lanthanum ethyl sulphates with a praseodymium
impurity (b) (the Pr–Ol bond length is 2.47 Å and the Pr–O2 bond length is 2.65 Å) re-
corded at atmospheric pressure for T = 4.2 K
Физика и техника высоких давлений 2010, том 20, № 1
92
The low intensities of these lines are explained by the fact that the 4f
n configura-
tion is almost isolated [2]. Transitions between the levels of this configuration are
forbidden as rigorously as these electrons are isolated from the environment. Fi-
nally, the degeneracy of the levels is also related to the isolation of this configura-
tion. Jahn and Teller [3] noted that, when considering the Jahn-Teller effect, one
should exclude the orbitally degenerate states where the electrons are not involved
in the formation of a chemical bond in a molecule. Indeed, displacements of the
nuclei in this case do not disturb these states. This is the case for inner electron
shells in the paramagnetic ionic salts of rare-earth elements [3].
In the case of the electronic state, the spectrum (Fig. 1,b) can be easily inter-
preted (Table 1) [4–7] and the local magnetic moment can be readily calculated [7].
Table 1
Calculated spectrum of the 4f 2 configuration in the electronic state
LSJ ± μ E, cm–1
112 ± 1 22450.7
112 ± 2 22447.5
112 ± 0 22416.8
111 ± 0 21295.4
111 ± 1 21280.2
110 ± 0 20690.5
202 ± 1 16934.4
202 ± 2 16862.9
202 ± 0 16754.9
The energy of electrostatic interaction between two f electrons isolated from
the environment can be described as
( )
1,2
1 , k
k
k
LS LS f ll L F
r
=∑ , k = 0, 2, 4, 6, (1)
where the angular coefficient is
( ) ( ) ( )( )
( ) 22
2, 1 2 1 1
0 0 0
l k
L
k
l k l l l L
f ll L L
l l k
+⎡ ⎤⎛ ⎞ ⎧ ⎫
= − + −⎢ ⎥ ⎨ ⎬⎜ ⎟
⎝ ⎠ ⎩ ⎭⎢ ⎥⎣ ⎦
and F0, F2, F4, and F6 are radial Slater integrals.
In the case of spin-orbit interaction, the matrix element is equal to
( )0 4,S fLSJ H L S J LS L S J′ ′ ′ ′= χ ξ , (2)
where
( ) ( ) ( )( )
1
112, 1 1 2 1
1
L S J L S J
LS L S J l l l LS V L S
S L
′+ + ⎧ ⎫′ ′ ′ ′χ = − + +⎡ ⎤ ⎨ ⎬⎣ ⎦ ′ ′⎩ ⎭
and 4 fξ is a fitting parameter.
The interaction between 4f 2 electrons and the crystal field is described by [5]
Физика и техника высоких давлений 2010, том 20, № 1
93
( )' 1 J Mq
cf k
k q
J k L
SLJM H S L J M B
M q M
− ′⎧ ⎫′ ′ ′ ′ = − ⎨ ⎬′⎩ ⎭
∑∑ ×
× ( ) ( )( )
1 '
21 2 1 2 1S L J k J k JJ J
L S L
′ ′′+ + + ⎧ ⎫′⎪ ⎪′− + +⎡ ⎤ ⎨ ⎬⎣ ⎦ ′⎪ ⎪⎩ ⎭
×
× ( ) ( ) ( ) ( )( ) ( ) ( )
1
21 1 1 2 1 2 1 1 2 1
0 0 0
k L L l
SS
L k L l k l
L L l
l l l
′
′′
′⎧ ⎫ ⎧ ⎫⎡ ⎤ ′− − + − + + − + δ⎡ ⎤ ⎨ ⎬ ⎨ ⎬⎣ ⎦⎣ ⎦ ⎩ ⎭ ⎩ ⎭
.
As follows from the properties of the 3j and 6j symbols,
M + q + M' = 0,
k ≥ 2J, k ≥ 2L and k ≥ 2l.
The crystal-field parameters are
( )
1
2
1
2 1 ,
4
q qi
i ik kk
i
eekB Y
R +
+⎛ ⎞= θ φ⎜ ⎟π⎝ ⎠
∑ ,
where subscripts k and q belong to the Legendry polynomials.
The magnetic moment of an isolated 4f n configuration is calculated and com-
pared with experimental data in [8]:
( )1M g J J= + ,
where
( ) ( ) ( )
( )
1 1 1
1
2 1
J J S S L L
g
J J
+ + + − +
= +
+
.
2.2. Vibronic state
This term was proposed by the authors of the pioneering work [9]. This group of
compounds contains rare-earth molybdates (Fig. 1,a). The spectra of these substances
have strong broad lines, and all degeneracies are removed. The Kramer’s doublets for
odd n in a 4f n configuration are exceptions. In this case, a rare-earth ion is assumed to
be so close to the surrounding ions that the bonds between them are specified not by
the long bond of outer electrons but rather by the short bond determined by the inner
4f n configuration. A mixture of various electron configurations provides a high spec-
tral intensity due to the absence of any forbiddenness. The participation of 4f
n elec-
trons in crystal bonds provides the absence of any degenerate levels. The authors of
[10,11] noted that any symmetrical position of nuclei (except for those located in one
straight line) is unstable for a degenerate electronic state. As a result of this instability,
nuclei shift so that the symmetry of their configuration breaks to an extent that the
degeneracy of the term is completely removed. In particular, the normal electronic
term of a symmetric (nonlinear) molecule is considered to be only a nondegenerate
term [10,11]. In this case, small intervals in an electronic spectrum indicate slow
Физика и техника высоких давлений 2010, том 20, № 1
94
electronic motion with a velocity comparable to the nuclear motion velocity. So, the
nuclear motion cannot be separated from the electronic motion [12].
As a result, every state of a set of nuclei continuously changing in certain limits
corresponds to all changing electronic states and the spectrum has broad bands.
In [13], we were the first to show that a high pressure can transform the electronic
state of a rare-earth compound into its vibronic state (Fig. 2) [14]. These states
stand rather far from each other, and the boundary between them is controlled by
the bond length between a rare-earth ion and the surrounding ions (Table 2) [15].
Fig. 2. Transformation of the spectrum of praseodymium ethyl sulphate at 78 K from the
electronic type at atmospheric pressure into the vibronic type as the pressure increases to
39 kbar. With temperature gradual increase from 78 to 160 K at a pressure of 39 kbar, the
vibronic state in this compound breaks and transforms into the electronic state [14]
Table 2
Critical distance (Å) for the transition from electronic-vibronic state for various
rare-earth ions and ligands
RE RE–O RE–Cl RE–F
Ce 2.40 2.81 2.33
Pr 2.38 2.79 2.31
Nd 2.36 2.77 2.29
Pm 2.34 2.75 2.27
Sm 2.33 2.74 2.26
Eu 2.32 2.73 2.25
Gd 2.31 2.72 2.24
Tb 2.30 2.71 2.23
Dy 2.29 2.70 2.22
Ho 2.28 2.69 2.21
Er 2.27 2.68 2.20
Tu 2.26 2.67 2.19
Yb 2.25 2.66 2.18
Физика и техника высоких давлений 2010, том 20, № 1
95
State of dynamic electronic-vibronic equilibrium. The hypothesis described
above implies a jump-like transition from the electronic into the vibronic state.
For praseodymium and oxygen, this occurs when the distance between them be-
comes smaller than 2.38Å. However, the authors of [1,16,17] present experimen-
tal data that require a more complex concept. For example, the Pr–0 distances in
PrBa2Cu307 determined by different methods are different. As determined by
neutron diffraction, these distances are approximately 2.45 Å [18], whereas, as
determined from the X-ray absorption fine structure (XAFS), some of these dis-
tances are still equal to 2.45Å and the others are 2.27 Å [19]. The other structural
relations determined by both methods remain the same. In other words, the differ-
ences concern only the position of the oxygen ion. It is important that the distance of
2.45 Å is larger and the distance of 2.27 Å is smaller than the critical distance.
When explaining these different praseodymium-oxygen distances in the YPrBa-
CuO system, one has to take into account that the XAFS method can determine
changes in a structure at a time resolution of 10–16 s, whereas a diffraction method
can do so at a resolution of only 10–13 s. Therefore, the authors of [16,17] assumed
that the praseodymium-oxygen distance changes from 2.27 to 2.63 Å and that the
former method determines two limiting oxygen positions and the latter, the average
position (2.45 Å). In other words, the lifetime of the short-lived state is shorter than
10–13 s (which is the time resolution of neutron diffraction) and is longer than 10–16
s (which is the time resolution of the XAFS method). Thus, there appears an inter-
mediate stage, namely, the stage of dynamic electronic-vibronic equilibrium, where
a substance alternately has the properties of the electronic and vibronic states. For
example, a chemical bond is alternately long and short; the magnetic moment is al-
ternately local or extended over the entire molecular complex; and the sample can
alternately be either an insulator or a conductor. It is clear that this short-lived hard-
to-detect state should substantially affect certain properties. For example, it was un-
clear for a long time why all (R)BaCuO compounds (R is a rare-earth element)
having the same structure exhibit high-temperature superconductivity except for a
praseodymium-containing compound. First, we would like to state that, for super-
conductivity to occur, the lifetime of this state must be longer than the lifetime of a
Cooper pair. As shown in [16], the lifetime of an electronic-vibronic state in this
case is shorter than the lifetime of a Cooper pair. Therefore, for superconductivity
to be detected in such compounds, they must not form this short-lived electronic-
vibronic state irrespective of the contribution (vibronic or electronic) determining
this short time. These compounds should be transformed into the state of electronic-
vibronic equilibrium with a sufficiently long lifetime, which will be possible if the
distance between a rare-earth ion with a degenerate ground state and its neighbors
decreases further. In this case, the lifetime of the vibronic state increases and the
lifetime of the electronic state decreases.
As a result, the faint weak line spectrum should change into a strong broadband
spectrum. As an example, we consider praseodymium ethyl sulphate. Its structure
was studied comprehensively in [20] and is often used as a model for comparison.
Физика и техника высоких давлений 2010, том 20, № 1
96
Praseodymium is surrounded by nine neutral water molecules, which is one of the
causes of a weak external influence on the state of the 4f configuration. Each three
molecules lie in one plane and form equilateral triangles. In two small triangles the
Pr–O distance is 2.47 Å and in the medium triangle and the large triangle the Pr–O
distance is 2.65 Å. At 25 kbar, these distances decrease to 2.38 and 2.56 Å, respec-
tively [14]. Fig. 2 shows the transformation of the narrow-band «electronic» spectrum
of praseodymium ethyl sulphate 77 K into a broadband «vibronic» spectrum as the
pressure increases from atmospheric to 39 kbar. These pressure-induced changes are
removed upon heating to 160 K. At this temperature, an increase in the praseodym-
ium-oxygen distance breaks the vibronic state and the spectrum recorded at a pressure
of 39 kbar returns almost exactly to its shape recorded for 77 K at 32 kbar.
As noted, superconductivity in the PrBaCuO system is suppressed because of
the formation of a short-lived electronic-vibronic state. This state appears upon a
fluctuation-assisted transition from the electronic into the vibronic state, while the
predominant long-lived state is the electronic state. In other words, the short life-
time of the electronic-vibronic state is specified by the lifetime of the vibronic
contribution. Therefore, if this time increases (it should increase as the Pr-0 dis-
tance decreases as compared to the critical distance), the lifetime of the elec-
tronic-vibronic state becomes longer than the lifetime of the Cooper pair at a
certain time; as a result, a superconducting state appears. These considerations
are supported by the experimental data from [21,22]. Let us analyze the lattice pa-
rameters c of the RBa2Cu3O7 (R is a rare-earth ion) superconducting compounds
fabricated by a traditional method [18,23] (Fig. 3). The lattice parameters с of all
compounds, except for a praseodymium-containing compound, are seen to lie in
one curve, and the lattice parameter of the latter is well below them. This suggests
that an increase in the lattice parameter
с of the latter compound makes this
compound superconducting. This result
was achieved in [21,22], where this com-
pound was synthesized by a new
method: the parameter с increased, and
the compound transformed into a super-
conducting state. The superconducting
transition temperature Tc is 56 K, and the
lattice parameter с is very large [23] and
lies above its expected value in the gen-
eral curve. It is reasonable to apply a
high pressure to decrease this parameter,
and the authors of [21,22] realized this
idea. As the pressure grows to 93 kbar, Tc
increases to 105 K. At a higher pressure, с
is likely to become smaller than the opti-
mum value and Tc begins to decrease.
Fig. 3. Dependence of the lattice pa-
rameter c on the number of electrons n in
f-shell for RBa2Cu3O6 (○, ●; R is a rare-
earth ion) and RBa2Cu3O7 (□, ■). ●, ■ –
the data for traditionally grown crystals
[18]; ○, □ – the data for radiation-assisted
growth of crystals with R = Pr [21,22]
Физика и техника высоких давлений 2010, том 20, № 1
97
Here, we do not consider any mechanism. Therefore, we return to the hypothesis of
electronic-vibronic equilibrium, whose lifetime is shorter than the lifetime of the
Cooper pair because of the short lifetime of the vibronic state. As the pressure in-
creases, the life-time of the electronic state will decrease and the lifetime of the vi-
bronic state will increase; so the lifetimes of both states will be longer than the Coo-
per-pair lifetime. Thus, the compound will transform into a superconducting state. As
the pressure increases, the relation between the lifetimes continuously approaches an
optimum relation. In this case, Tc will increase. However, there should be a time
when this temperature begins to decrease due to a decrease in the electronic-state
lifetime. As the pressure increases further, superconductivity should disappear.
2.3. Semiconductor-metal state
Received in 1998 experimental data on the temperature dependence of electri-
cal resistivity [21,22] show that under pressure the properties of PrBa2Cu3O6.6
vary from semiconductor to metallic.
Let's assume that the compound, in which the R–O bond length (R is a rare-
earth ion) is less than 2 Å, is in a specific semiconductor-metallic state. We intro-
duce the concept of semiconducting and metal conductivities:
1
0
2
0
1( ) ,
( ) ,
( ) exp
2
nT
T
nT
ET
kT
−
σ =
ρ +α
σ =
Δ⎛ ⎞ρ +α ⎜ ⎟
⎝ ⎠
(3)
here the parameter n is the portion of semiconductor conductivity in the material, ρ0
is the residual resistivity, α is a temperature coefficient, and EΔ is the width of the
energy gap. The parameter n can vary from 0 to 1. For n = 0, σ2(T) = 0, and the mate-
rial possesses only metallic conductivity; when n = 1, σ1(T) = 0, and the material has
only semiconductor conductivity. The metallic contribution is predominant at a high
temperature, and the semiconducting contribution – at a low temperature.
From the analysis of the metallic and semiconductor properties of the com-
pounds containing rare-earth ions, a fundamental trait of high-temperature super-
conductors is revealed: at a certain temperature T, the values of σ1(T) and σ2(T)
are equal, i.e., their curves cross [23]. Semiconductor conductivity dominates at
high temperatures, while metallic conductivity dominates at low ones. A special
resonant interaction of these conductivities occurs in this case, with which the
material’s conductivity can be formally represented as the sum of these values.
In view of this, the experimental temperature dependence of the resistance,
ρexp(T), can be described by the expression:
( ) ( )
0
1 2
1( )
(1 ) exp
2
TT
ET T n n
kT
ρ +α
ρ = =
−Δσ +σ ⎛ ⎞− + ⎜ ⎟
⎝ ⎠
. (4)
Физика и техника высоких давлений 2010, том 20, № 1
98
The values of the adjustable coefficients ρ0, ρ, n, and ΔE/2k were calculated by trial
and error with a software program, on the assumption that with a specific set of these
coefficients, the value provided by equation (4) coincides, to an accuracy, with the
experimental value of ρexp(T) [21] at the corresponding temperature.
After analyzing the data obtained, we selected the coefficients with which
equation (4) fairly accurately describes the experimental curve at P = 0 as far as
Tc: n = 0.942, ρ0 = 0.0078 mΩ⋅cm, α = 0.00057 mΩ⋅cm/K, and EΔ /2k = 270 K
[23]. However, below Tc the theoretical curve drops smoothly to 0 without dis-
playing a transition to a superconducting state (Fig. 4).
If graphs of σ1(T) and σ2(T) (Fig. 5,a), calculated using the already selected
coefficients, are constructed according to (3), we find that they intersect at T
which does not coincide with Tc in the experiment. However, if σ2(T) is multi-
plied and σ1(T) is divided by the same factor, so that n remains in the region of
the change, then the point of their intersection shifts. Thus, at P = 0 with
0.364σ1(T) and 2.75σ2(T) we get an intersection of the curves at Tc = 56 K (Fig.
5,b), that corresponds to the experimental results. The amendments for σ1(T) and
σ2(T) are calculated similarly, they correspond to experimental curve under pres-
sure [21,22]. The calculation has shown that these amendments decrease with in-
crease of pressure and at about 9 GPa become equal to unity (Table 3).
a b
Fig. 5. Temperature dependences of metallic σ1(T) (–■–) and semiconductor σ2(T) (⎯)
conductivities for P = 0 without correction (a) and with correction 0.364σ1(T) for metal-
lic and 2.75σ2(T) for semiconductor conductivities (b)
Fig. 4. Temperature dependences of the
electrical resistivity of РrBa2Cu306,6 at
various pressures (1 – P = 0, 2 – 1.2, 3 –
2.0, 4 – 3.0, 5 – 4.0, 6 – 6.0, 7 – 9.3 GPa).
Solid lines were calculated under the as-
sumption of suppressed superconductivity
[23], and points demonstrate the experi-
mental results [21,22]
Физика и техника высоких давлений 2010, том 20, № 1
99
Table 3
The amendments for σ1(T) and σ2(T), that shift the point of intersection of these
conductivities, under pressure [21,22]
P, GPa Amendment ofσ1(T) Amendment of σ2(T)
1.0 2.75 0.364
1.2 2.12 0.472
2.0 1.82 0.550
3.0 1.55 0.645
4.0 1.39 0.719
6.0 1.16 0.867
9.3 1.08 0.926
At the intersection, σ1(T) and σ2(T) are equal. This means that, at this point,
the PrBa2Cu3O6.6 crystal displays properties of both a semiconductor and a metal.
The transition to a superconducting state occurs when the metallic conductivity
σ1(T) suppresses the semiconductor conductivity σ2(T). Then, taking into account
the conditions for transition to a superconducting state, equation (4) with the cor-
rection for the conductivities can be written as follows:
1 2 1 2
1 1( )
0.364 2.75 0.364 2.75
Tρ = −
σ + σ σ − σ
. (5)
Fig. 6 shows a graph of ρ(T) obtained using equation (5), which agrees with the
experimental curve at P = 0 [21,22].
For ρ(T) under pressure we have also a good agreement with the experiment
[21,22].
3. Conclusion
We have shown that, as the pressure increases, a rare-earth compound trans-
forms from the electronic into an electronic-vibronic state and undergoes substan-
tial changes. For example, its spectrum changes from a faint narrow-line spectrum
into a strong broadband spectrum. At the further decrease of the R–O bond length
the substance is in a semiconductor-metallic state. Therefore, for PrBa2Cu3O6.6 the
Fig. 6. Temperature dependence of elec-
trical resistance with the transition to a
superconducting state for P = 0: ⎯ –
ρtheor(T) (Eq. (5), –○– – ρexp(T)
Физика и техника высоких давлений 2010, том 20, № 1
100
result of this study is a combination of values for the conductivities 0.364σ1(T)
and 2.75σ2(T) (and only these conductivities), that describes the whole set of ex-
perimental values obtained, including the superconducting transition. Conse-
quently, the material’s transition to a superconducting state can be associated with
a change in the ratio of conductivities in the crystal, which can be considered
analogous to the occurrence of Cooper pairs in a low-temperature superconductor.
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Физика и техника высоких давлений 2010, том 20, № 1
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В.А. Волошин , В.В. Кузнецова, Т.М. Шевцова
ПЕРІОДИЧНІ ЗМІНЕННЯ В СТАНІ 4f-МЕТАЛІЧНОЇ СПОЛУКИ
ПІД ТИСКОМ
Обґрунтовується твердження, що в рамках тиску, який можна експериментально
досягти, iснуючі з’єднання, що містять рідкісні землі, можуть бути охарактеризо-
вані належністю до одного з трьох станів залежно від відстані RE–O: електронного,
вібронного (зокрема, стан електрон-вібронної рівноваги) та напівпровідниково-
металічного. Висувається гіпотеза, що механізм реалізації надпровідного стану в
PrBa2Cu3O6.6 можна розглядати як зміну співвідношення напівпровідникової та ме-
талічної провідностей у речовині.
Ключові слова: електрон-вібронна рівновага, високотемпературна надпровідність,
PrBa2Cu3O6.6, провідність
В.А. Волошин , В.В. Кузнецова, Т.Н. Шевцова
ПЕРИОДИЧЕСКИЕ ИЗМЕНЕНИЯ В СОСТОЯНИИ
4f-МЕТАЛЛИЧЕСКОГО СОЕДИНЕНИЯ ПОД ДАВЛЕНИЕМ
Обосновывается утверждение, что в рамках экспериментально достижимого давле-
ния существующие соединения, содержащие редкие земли, могут быть охарактери-
зованы принадлежностью к одному из трех состояний в зависимости от расстояния
RЕ–O: электронному, вибронному (в частности, состоянию электрон-вибронного
равновесия) и полупроводниково-металлическому. Выдвигается гипотеза, что ме-
ханизм реализации сверхпроводящего состояния в PrBa2Cu3O6.6 можно рассматри-
вать как изменение соотношения полупроводниковой и металлической проводимо-
стей в веществе.
Ключевые слова: электрон-вибронное равновесие, высокотемпературная сверх-
проводимость, PrBa2Cu3O6.6, проводимость
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