Mechanisms of self-screening in pure ice
Possible approaches to a correct account of the Coulomb interaction in system of proton-hydroxyl pairs in
 pure ice (a proton version of intrinsic semiconductor) are discussed for a possibility to evaluate correlation properties
 of semiconducting media.
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| Date: | 2015 |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2015
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| Cite this: | Mechanisms of self-screening in pure ice / I. Chikina, V. Shikin // Физика низких температур. — 2015. — Т. 41, № 6. — С. 588-589. — Бібліогр.: 4 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860247781816401920 |
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| author | Chikina, I. Shikin, V. |
| author_facet | Chikina, I. Shikin, V. |
| citation_txt | Mechanisms of self-screening in pure ice / I. Chikina, V. Shikin // Физика низких температур. — 2015. — Т. 41, № 6. — С. 588-589. — Бібліогр.: 4 назв. — англ. |
| collection | DSpace DC |
| container_title | Физика низких температур |
| description | Possible approaches to a correct account of the Coulomb interaction in system of proton-hydroxyl pairs in
pure ice (a proton version of intrinsic semiconductor) are discussed for a possibility to evaluate correlation properties
of semiconducting media.
|
| first_indexed | 2025-12-07T18:38:59Z |
| format | Article |
| fulltext |
Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 6, pp. 588–589
Mechanisms of self-screening in pure ice
I. Chikina1 and V. Shikin2
1CEA Saclay, CEA CNRS, LIONS DSM IRAMIS NIMBE, UMR 3299, F-91191 Gif Sur Yvette, France
2Institute of Solid State Physics of RAS, 142432, Chernogolovka, Russia
E-mail: shikinv@yandex.ru
Received November 24, 2014, published online April 23, 2015
Possible approaches to a correct account of the Coulomb interaction in system of proton-hydroxyl pairs in
pure ice (a proton version of intrinsic semiconductor) are discussed for a possibility to evaluate correlation pro-
perties of semiconducting media.
PACS: 61.20.Qg Structure of associated liquids: electrolytes, molten salts, etc.
Keywords: charges, screening, dissociation.
From the viewpoint of its conduction properties, pure
ice possesses all properties of a classical wide gap se-
miconductor [1]. Its conductivity demonstrates a clear ac-
tivation-type behavior with the activation energy T∆ >>
(∆ coincides with the intrinsic gap in the energy spectrum
of pure ice, T is the temperature measured in energy units).
Proton-hydroxyl pairs, which exist in pure ice due to
the activation decay of H2O molecules, interact among
themselves in a nontrivial way, necessitating an accurate
account of screening effects. Charged systems of low den-
sities 3
icen b± −<< (b is the lattice spacing), in which carrier
are characterized by a relatively large (compared to elec-
trons) effective masses, support a typical self-screening of
the long-range Coulomb interaction. The problems involv-
ing evaluation of the dissociation degree, mobility, and
collective phenomena (Wigner crystallization) need either
a proper accounting of the self-screening or a justification
for its neglect. In this paper we discuss possible mecha-
nisms for classical self-screening.
The self-screening effect is well known (e.g., see Ref. 2).
The relevant energy is
coul
1= , = 0.
2 a a a a a
a a
E V ez n z nϕ∑ ∑ (1)
Here az is the charge of ions of type a, an is their concen-
tration, aϕ is the potential of the field acting upon the ion
of type a due to the presence of all other charges.
Expression (1) contains divergent contributions of
charged ions of different signs, each of them compensating
to a large extent the divergency arising due to the opposite-
ly charged ions. For brevity, this mutual compensation
effect is referred to as “self-screening”.
The existence of energy (1) is important for various as-
pects of the theory of many-particle systems with Coulomb
interaction. The relevant areas involve properties of ion
lattices [3], correlation phenomena in classical plasma,
semiconductors, and electrolytes [2], Coulomb (Wigner)
crystallization [4], etc. Not all applications of the general
formalism have been developed in sufficient detail. The re-
sults in this paper are relevant to the dissociation problem
and correlation phenomena in pure ice. Here the available
literature [1] completely ignores the energy given by Eq. (1).
1. One of the scenarios of self-screening is as follows
(the Debye–Hückel scheme, see Ref. 2). We place one of
the ions at the origin and allow the other ions to screen it:
4= ( ), ( ) = | |[ ( ) ( )],r r e n r n r+ −
π
∆ϕ σ σ −
ε
(2)
0( ) = exp[ ( )/ ].n r n e r T± ±ϕ (3)
By expanding Eq. (2) in the small parameter ( ) < ,e r Tϕ the
set (2), (3) transforms into an equation linear in ( ):rϕ
2
2 2 2 2
0
8= / , = , = .D D D D
e n
T
− π
∆ϕ ϕ λ λ κ κ
ε
(4)
The solution to Eq. (4), which satisfies the boundary
conditions
| 0 |( ) , ( ) 0,r rr r Z r→ →∞ϕ → ϕ → (5)
is
2
2
0
8( ) = exp( )/ , = .D D
er e r r n
T
π
ϕ −κ κ
ε
In the expansion of ( )rϕ (6) for small r
2
2( ) ...D
ee r e
r
ϕ − κ + (7)
© I. Chikina and V. Shikin, 2015
Mechanisms of self-screening in pure ice
the first term is the self-energy of the central ion. The se-
cond term represents [2] the required correlation correction
to the energy of the interaction between the charges in the
ionized state:
2
corr .DU e κ (8)
Equations (2)–(8) form the basis for all correlation phe-
nomena in classical systems with Coulomb interaction. It is
easy to show that Eq. (8) also provides a real value of the
energy (1) per pair of ions.
2. It is worthwhile to consider an alternative estimate for
corrU borrowed from the theory of ion lattices [3]. If an
ensemble of dissociation-related charges is arranged in a
regular lattice suitable to be treated using the Ewald rules,
then the energy corrU per ion pair can be represented as
2 1/3
corr ice ice 0/ , ( ) ,U e R R n −γ (9)
where γ is a Madelung constant which depends on the
lattice type and 0n is the ionized fraction density from (3).
The expressions (8) and (9) for the correlation energy
corrU have different structures and are differently substan-
tiated. Equation (8) is commonly accepted and regularly
manifests itself in numerous correlation effects typical of
cold plasma and electrolytes (e.g., Coulomb corrections to
osmotic pressure [2]). However, derivation of Eq. (8) in-
volves a violation of the translational symmetry in the ge-
nerally homogeneous system. In addition, the simplifica-
tions made to obtain Eq. (4) from Eqs. (2) and (3) also do
not add convincing arguments.
Equation (9) actually also relies on model considera-
tions (arrangement of ions into a lattice is equivalent to
substitution of a disordered and on the whole neutral sys-
tem of ions by a fictitious crystal structure). However, this
procedure does not violate the homogeneity on the whole.
In addition, derivation of Eq. (9) does not require the ine-
quality ( ) < ,e r Tϕ which is certainly violated in real sys-
tems. Most likely, the difference between Eqs. (8) and (9)
can be discovered in a properly designed experiment.
3. Summary. The present report considers the estimate
for the correlation energy corrU in a classical system of
interacting ions. In addition to expression (8) for corr ,U
available in the literature, an alternative estimate (9) is
suggested, based on rather general arguments. The differ-
ence between (8) and (9) can be detected by accurate
measurements of the dissociation degree of donors in pure
ice or other intrinsic semiconductors. To the best of our
knowledge, no such data are currently available.
This work was partly supported by the RFBR Grant
N 15-02-04706 and the Program of the Presidium of RAS.
1. N. Fletcher, The Chemical Physics of Ice, Cambridge,
University Press (1970).
2. L. Landau and E. Lifshits, Statistical Physics, Nauka,
Moscow (1995) (in Russian).
3. M. Born and Kun Huang, Dynamical Theory of Crystal
Lattices, Oxford, Clarendon Press (1954).
4. P.M. Chaikin and T.C. Lubensky, Principles of Condensed
Matter Physics, Cambridge, University Press (1997).
Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 6 589
|
| id | nasplib_isofts_kiev_ua-123456789-127932 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0132-6414 |
| language | English |
| last_indexed | 2025-12-07T18:38:59Z |
| publishDate | 2015 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Chikina, I. Shikin, V. 2017-12-31T13:50:40Z 2017-12-31T13:50:40Z 2015 Mechanisms of self-screening in pure ice / I. Chikina, V. Shikin // Физика низких температур. — 2015. — Т. 41, № 6. — С. 588-589. — Бібліогр.: 4 назв. — англ. 0132-6414 PACS: 61.20.Qg https://nasplib.isofts.kiev.ua/handle/123456789/127932 Possible approaches to a correct account of the Coulomb interaction in system of proton-hydroxyl pairs in
 pure ice (a proton version of intrinsic semiconductor) are discussed for a possibility to evaluate correlation properties
 of semiconducting media. This work was partly supported by the RFBR Grant
 N 15-02-04706 and the Program of the Presidium of RAS. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур 10th International Conference on Cryocrystals and Quantum Crystals Mechanisms of self-screening in pure ice Article published earlier |
| spellingShingle | Mechanisms of self-screening in pure ice Chikina, I. Shikin, V. 10th International Conference on Cryocrystals and Quantum Crystals |
| title | Mechanisms of self-screening in pure ice |
| title_full | Mechanisms of self-screening in pure ice |
| title_fullStr | Mechanisms of self-screening in pure ice |
| title_full_unstemmed | Mechanisms of self-screening in pure ice |
| title_short | Mechanisms of self-screening in pure ice |
| title_sort | mechanisms of self-screening in pure ice |
| topic | 10th International Conference on Cryocrystals and Quantum Crystals |
| topic_facet | 10th International Conference on Cryocrystals and Quantum Crystals |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/127932 |
| work_keys_str_mv | AT chikinai mechanismsofselfscreeninginpureice AT shikinv mechanismsofselfscreeninginpureice |