Atomistic studies of Li+ migration in Y₂O₃ and the structure of related oxides
Atomistic computer simulation techniques based on energy minimization have been employed to predict the equilibrium lattice parameters and volumes of a series of rare-earth sesquioxides and their polymorphs. The results have been found in agreement with experimental data and ab initio studies given...
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Донецький фізико-технічний інститут ім. О.О. Галкіна НАН України
2009
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| Cite this: | Atomistic studies of Li⁺ migration in Y₂O₃ and the structure of related oxides / A.I. Chroneos, G. Busker, I.L. Goulatis, R.V. Vovk, A.A. Zavgorodniy, M.A. Obolenskii, A.G. Petrenko, Pinto Simoes V.M., A.V. Samoilov // Физика и техника высоких давлений. — 2009. — Т. 19, № 4. — С. 18-25. — Бібліогр.: 34 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859915007627624448 |
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| author | Chroneos, A.I. Busker, G. Goulatis, I.L. Vovk, R.V. Zavgorodniy, A.A. Obolenskii, M.A. Petrenko, A.G. Pinto Simoes, V.M. Samoilov, A.V. |
| author_facet | Chroneos, A.I. Busker, G. Goulatis, I.L. Vovk, R.V. Zavgorodniy, A.A. Obolenskii, M.A. Petrenko, A.G. Pinto Simoes, V.M. Samoilov, A.V. |
| citation_txt | Atomistic studies of Li⁺ migration in Y₂O₃ and the structure of related oxides / A.I. Chroneos, G. Busker, I.L. Goulatis, R.V. Vovk, A.A. Zavgorodniy, M.A. Obolenskii, A.G. Petrenko, Pinto Simoes V.M., A.V. Samoilov // Физика и техника высоких давлений. — 2009. — Т. 19, № 4. — С. 18-25. — Бібліогр.: 34 назв. — англ. |
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| container_title | Физика и техника высоких давлений |
| description | Atomistic computer simulation techniques based on energy minimization have been employed to predict the equilibrium lattice parameters and volumes of a series of rare-earth sesquioxides and their polymorphs. The results have been found in agreement with experimental data and ab initio studies given in the literature. To demonstrate the applicability of the computational methodology the migration of lithium ions (Li⁺) in yttria (Y₂O₃) has been considered.
Атомістичні методи комп’ютерного моделювання, основані на принципі мінімізації енергії, використані для прогнозування рівноважних параметрів і об’єма кристалічної гратки ряда рідкоземельних оксидів та їх поліморф. Результати моделювання знаходяться в доброму узгoдженні з експериментальними і літературними даними. Для демонстрації запропонованої обчислювальної методики розглянутo міграцію іонів літія (Li⁺) в оксиді ітрія (Y₂O₃).
Атомистические методы компьютерного моделирования, основанные на принципе минимизации энергии, использованы для предсказания равновесных параметров и объема кристаллической решетки ряда редкоземельных оксидов и их полиморф. Результаты моделирования находятся в хорошем согласии с экспериментальными и литературными данными. Для демонстрации применимости предложенной вычислительной методики рассмотрена миграция ионов лития (Li⁺) в оксиде иттрия (Y₂O₃).
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Физика и техника высоких давлений 2009, том 19, № 4
© A.I. Chroneos, G. Busker, I.L. Goulatis, R.V. Vovk, A.A. Zavgorodniy, M.A. Obolenskii,
A.G. Petrenko, V.M. Pinto Simoes,, A.V. Samoilov, 2009
PACS: 71.20.Ad
A.I. Chroneos1, G. Busker1, I.L. Goulatis2, R.V. Vovk2, A.A. Zavgorodniy2,
M.A. Obolenskii2, A.G. Petrenko3, V.M. Pinto Simoes4,5, A.V. Samoilov2
ATOMISTIC STUDIES OF Li+ MIGRATION IN Y2O3
AND THE STRUCTURE OF RELATED OXIDES
1Department of Materials, Imperial College
London SW7 2BP, United Kingdom
E-mail: chroneos@imel.demokritos.gr
2Kharkov National University
4 Svoboda Sq., 61077 Kharkov, Ukraine
3Donetsk National University
24 University St., 83055 Donetsk, Ukraine
4IPA_ Instituto Superior Autónomo de Estudos Politécnicos
Rua de Xabregas, 20, 1º 1900-440 Lisboa, Portugal
5Instituto Superior Dom Afonso III
Convento Espirito Santo, 8100-641 Loule, Portugal
Received September 2, 2009
Atomistic computer simulation techniques based on energy minimization have been em-
ployed to predict the equilibrium lattice parameters and volumes of a series of rare-earth
sesquioxides and their polymorphs. The results have been found in agreement with ex-
perimental data and ab initio studies given in the literature. To demonstrate the applica-
bility of the computational methodology the migration of lithium ions (Li+) in yttria
(Y2O3) has been considered.
Keywords: atomistic simulation, crystal structure, lithium migration, rare-earth com-
pounds
1. Introduction
The material properties of rare-earth oxides have been studied extensively be-
cause of their wide range of possible applications. For instance, recent experi-
mental studies report the doping of thallium-based cuprate superconductors with
rare-earth oxides [1], the beneficial addition of a mixture of rare-earth oxides into
molybdenum which enhances the emission properties of cathodes [2] and the
unique combination of mechanical, chemical and optical properties of glasses
based on rare-earth oxides and alumina [3]. Notably, rare-earth oxides have been
Физика и техника высоких давлений 2009, том 19, № 4
19
under investigation as potential scintillator materials since they undergo ther-
moluminescence [4]. Many experimental structural determinations of the rare-
earth oxides in the lanthanide series have been carried out for the three distinct
polymorphic forms: A-type hexagonal (space group 3 1P m ) [5–9], B-type mono-
clinic (space group C2/m) [5,10–12] and C-type cubic (space group Ia3) [5,13–17].
Density functional theory calculations have also been employed to determine the
lattice parameters of a number of rare-earth sesquioxides [18]. The hexagonal
A-type rare-earth sesquioxides have been initially studied by Zachariasen [19] but
the space group 3 1P m has been determined by Pauling [20]. The monoclinic
B-type has been presented by Cromer [21] as an intermediate form between the
low-temperature cubic and high-temperature hexagonal phases.
The purpose of this study is to systematically model these materials using a
set of transferable interatomic potentials and compare the resulting structures
to the existing experimental [5–17] and theoretical [18] data. The atomistic
simulation techniques used here have proved to produce reliable results in pre-
vious studies of Y2O3 sesquioxide [22–24] and a range of bixbyite materials
[25] and indeed many other systems (for example hydroxides [26,27]) beyond
the scope of this study. The migration of lithium Li+ ions in yttria (Y2O3) has
been considered to illustrate the applicability of the potential models to prob-
lems of technological interest.
2. Theoretical methodology
2.1. Simulation technique
The atomistic simulation package GULP [28] was used throughout this study.
The simulation technique is based upon a description of the lattice in terms of ef-
fective potentials. The Coulomb forces are summed using Ewald’s method [29],
whereas the short-range forces were modeled using parameterized pair potentials
described later. The simulation commences with a perfect lattice calculation
where the total energy of the lattice is minimized with respect to the unit cell lat-
tice vectors and the positions of the ions within the unit cell.
This study is based on the classical Born model description of the lattice. The
short-range energy terms S(rij) are approximated by a parameterized pair potential
of the Buckingham form
6( ) exp ij ij
ij ij
ij ij
r C
S r A
r
⎛ ⎞
= − −⎜ ⎟⎜ ⎟ρ⎝ ⎠
where rij is the separation between ions i and j, Aij, ρij and Cij are the potential pa-
rameters specific to ions i and j. The parameters used in this study were fitted em-
pirically to the experimental lattice parameters and atomic positions of a range of
oxide compounds. Essential to this atomistic simulation methodology are param-
eterized short-range potentials. The potentials used for this study are presented in
Table 1 and were derived using the multi-structure fitting procedure described
elsewhere [22–25]. The oxygen ions are treated as polarisable by virtue of the
Физика и техника высоких давлений 2009, том 19, № 4
20
Dick and Overhauser shell model [30]. The O2– ions have a shell charge of –2.04 |e|,
a core charge of 0.04 |e| and a force constant 6.3 eV·Å–2.
Table 1
Short-range interatomic potential parameters
Interaction A, eV ρ, Å C, eV·Å6
O2––O2– 9547.96 0.2192 32.0
La3+–O2– 2078.5 0.3467 15.55
Ce3+–O2– 20.15.3 0.3437 15.9
Pr3+–O2– 2004.6 0.3415 14.2
Nd3+–O2– 1975.2 0.3404 13.8
Sm3+–O2– 1941.9 0.34 12.55
Eu3+–O2– 1888.6 0.34 12.2
Gd3+–O2– 1855.9 0.339 11.9
Tb3+–O2– 1838.2 0.3385 14.5
In order to simulate the effect of a defect, the lattice is subsequently partitioned
into concentric spherical regions according to the Mott–Littleton procedure [31].
The lattice is relaxed around the defect as energy minimization proceeds. It is im-
portant to select large enough region sizes so as no significant change in defect
formation energy occurs if the region sizes are increased further. In these calcula-
tions region I had a radius of 10 Å (456 species) and region IIa extends the radius
to 31 Å (13000 species).
2.2. Migration Enthalpy Calculation
The static atomistic simulation code was applied to predict defect enthalpies of
intermediate steps in migration mechanisms. In Y2O3 activated migration mecha-
nisms consist of sequential jumps of the migrating ions between interstitial sites.
Y2O3 exhibits the cubic C-type rare-earth sesquioxides (bixbyite structure, space
group Ia3) with a lattice parameter of 10.604 Å [32]. The bixbyite structure can
accommodate interstitial ions at three distinct sites: the 8b position, the 16c (x = 1/8)
position and the 24d (x = –1/4) position. The activation enthalpy for migration is
the difference between the enthalpy of the system when the migrating ion is at the
saddle point and the enthalpy of the ion at equilibrium. The saddle point enthalpy
is calculated by introducing a fixed lithium ion at the saddle point location and
then relaxing the surrounding lattice. The evaluation of the potential energy sur-
face both parallel and perpendicular to the diffusion path is necessary to identify
the configuration of the diffusion path.
3. Results and Discussion
3.1. Basic Lattice Properties
Before simulating the effect of defects in the rare-earth oxides it is necessary to
simulate the structural properties and compare them to the corresponding experi-
Физика и техника высоких давлений 2009, том 19, № 4
21
mental data. The experimental [10–12] structural parameters of the B-type rare-
earth sesquioxides are presented in Table 2 and compared with the atomistic
simulation data shown in Table 3. The energy minimized volumes of B-type
monoclinic Sm2O3, Eu2O3 and Tb2O3 are overestimated by less than 1.4%. To
elucidate trends, the volume per molecule (stoichiometric formula unit) of A-type
and C-type rare-earth sesquioxides were compared in Fig. 1 and Fig. 2, respec-
tively. The atomic scale simulations results for the A-type rare-earth sesquioxides
are significantly closer to the experimental results than the ab initio data, apart
from the case of La2O3, which is overestimated by 1.4%.
56 58 60 62 64 66 68 70 72
70
75
80
85
90
V
ol
um
e
pe
r m
ol
ec
ul
e,
Å
3
Atomic number
Fig. 1. Volume per molecule as a function of atomic number for A-type rare-earth sesqui-
oxides calculated from atomic scale models: –□– – this study, –○– – experiment [5–9],
–Δ– – ab initio [18]
Fig. 2. Volume per molecule as a function of atomic number for C-type rare-earth sesqui-
oxides calculated from atomic scale models: –□– – this study, –○– – experiment [5,13–
17], – Δ– – ab initio [18]
Table 2
Experimental data [10–12] for volumes, lattice parameters and angles of the B-type
rare-earth sesquioxides
Parameters Sm2O3 Eu2O3 Tb2O3
V, Å3 149.722 146.945 141.917
a, Å 14.198 14.110 14.030
b, Å 3.627 3.602 3.536
c, Å 8.856 8.808 8.717
β, grad 99.986 100.037 100.100
For the C-type rare-earth sesquioxides there is complete agreement between the
results of this study and the DFT and the experimental data. It is evident from Fig. 2
and Table 3 that the potential model reproduces accurately the crystal structure of
both the B-type and C-type polymorphs, thus indicating the transferability of the
model. For several C-type sesquioxides the DFT method employed by Hirosaki et
al. [18] did not converge or was not feasible due to the absence of suitable pseu-
dopotentials. Energy minimization techniques can bridge this gap by providing
Физика и техника высоких давлений 2009, том 19, № 4
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Table 3
Atomistic computer simulation data for volumes, lattice parameters and angles
of the B-type rare-earth sesquioxides
Parameters Sm2O3 Eu2O3 Tb2O3
V, Å3 151.520 149.066 143.557
a, Å 14.383 14.311 14.143
b, Å 3.613 3.593 3.547
c, Å 8.898 8.848 8.737
β, grad 100.587 100.647 100.720
crystal structure data comparable to the experimental studies. It is evident from
the results that the volume per molecule of the rare-earth oxides decreases with
increasing atomic number regardless of their crystal structure. This is explained
by the reduction of the rare-earth ionic radius with respect to the increase in
atomic number (lanthanide contraction [33]).
3.2. Li+ Migration in Y2O3
The interstitial sites in the bixbyite structure form two paths. The 8b to 16c
path was found to be more energetically favourable than the 16c to 24d path
for the migration of lithium ions in Y2O3. To verify that the lithium ion fol-
lows a straight-line path from 8b to 16c a contour plot was generated repre-
senting the plane passing through the saddle point, perpendicular to the migra-
tion vector (Fig. 3.). Fig. 3 is based on
25 calculations as the Li+ was posi-
tioned in an equidistant 5 × 5 grid in
Y2O3. The lowest enthalpy point lies in
the middle of the contour plot indicat-
ing that the lithium ion followed a
straight-line path from interstitial site
8b to 16c.
Fig. 4 is a contour plot of the migra-
tion of Li+ interstitial in Y2O3, parallel to
the migration vector containing the 16c–
8b–16c interstitial site sequence. In this
contour plot the Li+ was placed in a 21 ×
× 21 grid and the 16c–8b–16c interstitial
sites lie in the diagonal of the plot. The
VI coordinate Li+ ion has an ionic radius
of 0.76 Å whereas Y3+ has an ionic ra-
dius of 0.9 Å [34]. The lowest enthalpy
sites are the interstitial sites and the low-
est enthalpy path is the straight line con-
necting the 16c–8b–16c interstitial sites.
Fig. 3. Contour plot of the energy surface
for a plane passing through the saddle
point perpendicular to the migration
vector containing the 16c–8b interstitial
sites in Y2O3. The contour plot was ob-
tained from positioning the lithium inter-
stitial in 25 mesh points. The contour
interval is 0.05 eV
Физика и техника высоких давлений 2009, том 19, № 4
23
As a fully ionic model was used and the
calculations correspond to the dilute
limit, the defect enthalpies will be over-
estimated. Nevertheless, relative enthal-
pies are very reliable.
4. Conclusion
Atomic scale simulations adequately
reproduce the 17 rare-earth oxides con-
sidered. This study provides a frame-
work for further computational and
structural studies. The derived short-
range interatomic potential parameters
can be used to systematically investigate
the complex behaviour and defect
chemistry of these materials at the
atomic level. As such, we hope that the
data presented here will encourage oth-
ers to apply this model and develop new
trends for rare-earth oxides and related
compounds.
The authors gratefully acknowledge Prof. Robin Grimes and Dr Mark Levy of
Imperial College London for useful conversations and Prof. Julian Gale of Curtin
University for providing the GULP code.
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contour interval is 0.5 eV
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А.І. Хронеос, Г. Баскер, І.Л. Гулатіс, Р.В. Вовк, A.A. Завгородній, M.О. Oболенський,
О.Г. Петренко, В.М. Пінто Сімоес, О.В. Самойлов
АТОМІСТИЧНЕ МОДЕЛЮВАННЯ МІГРАЦІЇ Li+ В Y2O3 І СТРУКТУРА
СУПУТНІХ ОКСИДІВ
Атомістичні методи комп’ютерного моделювання, основані на принципі мінімізації
енергії, використані для прогнозування рівноважних параметрів і об’єма кри-
сталічної гратки ряда рідкоземельних оксидів та їх поліморф. Результати моделю-
вання знаходяться в доброму узгoдженні з експериментальними і літературними
даними. Для демонстрації запропонованої обчислювальної методики розглянутo
міграцію іонів літія (Li+) в оксиді ітрія (Y2O3).
Ключові слова: атомістичне моделювання, кристалічна структура, міграція літія,
рідкоземельні сполуки
Физика и техника высоких давлений 2009, том 19, № 4
25
А.И. Хронеос, Г. Баскер, И.Л. Гулатис, Р.В. Вовк, A.A. Завгородний,
M.A. Oболенский, A.Г. Петренко, В.М. Пинто Симоэс, A.В. Самойлов
АТОМИСТИЧЕСКОЕ МОДЕЛИРОВАНИЕ МИГРАЦИИ Li+ В Y2O3
И СТРУКТУРА СОПУТСТВУЮЩИХ ОКСИДОВ
Атомистические методы компьютерного моделирования, основанные на принципе
минимизации энергии, использованы для предсказания равновесных параметров и
объема кристаллической решетки ряда редкоземельных оксидов и их полиморф.
Результаты моделирования находятся в хорошем согласии с экспериментальными и
литературными данными. Для демонстрации применимости предложенной вычис-
лительной методики рассмотрена миграция ионов лития (Li+) в оксиде иттрия
(Y2O3).
Ключевые слова: атомистическое моделирование, кристаллическая структура, ми-
грация лития, редкоземельные соединения
|
| id | nasplib_isofts_kiev_ua-123456789-69237 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0868-5924 |
| language | English |
| last_indexed | 2025-12-07T16:04:49Z |
| publishDate | 2009 |
| publisher | Донецький фізико-технічний інститут ім. О.О. Галкіна НАН України |
| record_format | dspace |
| spelling | Chroneos, A.I. Busker, G. Goulatis, I.L. Vovk, R.V. Zavgorodniy, A.A. Obolenskii, M.A. Petrenko, A.G. Pinto Simoes, V.M. Samoilov, A.V. 2014-10-09T14:32:50Z 2014-10-09T14:32:50Z 2009 Atomistic studies of Li⁺ migration in Y₂O₃ and the structure of related oxides / A.I. Chroneos, G. Busker, I.L. Goulatis, R.V. Vovk, A.A. Zavgorodniy, M.A. Obolenskii, A.G. Petrenko, Pinto Simoes V.M., A.V. Samoilov // Физика и техника высоких давлений. — 2009. — Т. 19, № 4. — С. 18-25. — Бібліогр.: 34 назв. — англ. 0868-5924 PACS: 71.20.Ad https://nasplib.isofts.kiev.ua/handle/123456789/69237 Atomistic computer simulation techniques based on energy minimization have been employed to predict the equilibrium lattice parameters and volumes of a series of rare-earth sesquioxides and their polymorphs. The results have been found in agreement with experimental data and ab initio studies given in the literature. To demonstrate the applicability of the computational methodology the migration of lithium ions (Li⁺) in yttria (Y₂O₃) has been considered. Атомістичні методи комп’ютерного моделювання, основані на принципі мінімізації енергії, використані для прогнозування рівноважних параметрів і об’єма кристалічної гратки ряда рідкоземельних оксидів та їх поліморф. Результати моделювання знаходяться в доброму узгoдженні з експериментальними і літературними даними. Для демонстрації запропонованої обчислювальної методики розглянутo міграцію іонів літія (Li⁺) в оксиді ітрія (Y₂O₃). Атомистические методы компьютерного моделирования, основанные на принципе минимизации энергии, использованы для предсказания равновесных параметров и объема кристаллической решетки ряда редкоземельных оксидов и их полиморф. Результаты моделирования находятся в хорошем согласии с экспериментальными и литературными данными. Для демонстрации применимости предложенной вычислительной методики рассмотрена миграция ионов лития (Li⁺) в оксиде иттрия (Y₂O₃). The authors gratefully acknowledge Prof. Robin Grimes and Dr Mark Levy of Imperial College London for useful conversations and Prof. Julian Gale of Curtin University for providing the GULP code. en Донецький фізико-технічний інститут ім. О.О. Галкіна НАН України Физика и техника высоких давлений Atomistic studies of Li+ migration in Y₂O₃ and the structure of related oxides Атомістичне моделювання міграції Li⁺ в Y₂O₃ і структура супутніх оксидів Атомистическое моделирование миграции Li⁺ в Y₂O₃ и структура сопутствующих оксидов Article published earlier |
| spellingShingle | Atomistic studies of Li+ migration in Y₂O₃ and the structure of related oxides Chroneos, A.I. Busker, G. Goulatis, I.L. Vovk, R.V. Zavgorodniy, A.A. Obolenskii, M.A. Petrenko, A.G. Pinto Simoes, V.M. Samoilov, A.V. |
| title | Atomistic studies of Li+ migration in Y₂O₃ and the structure of related oxides |
| title_alt | Атомістичне моделювання міграції Li⁺ в Y₂O₃ і структура супутніх оксидів Атомистическое моделирование миграции Li⁺ в Y₂O₃ и структура сопутствующих оксидов |
| title_full | Atomistic studies of Li+ migration in Y₂O₃ and the structure of related oxides |
| title_fullStr | Atomistic studies of Li+ migration in Y₂O₃ and the structure of related oxides |
| title_full_unstemmed | Atomistic studies of Li+ migration in Y₂O₃ and the structure of related oxides |
| title_short | Atomistic studies of Li+ migration in Y₂O₃ and the structure of related oxides |
| title_sort | atomistic studies of li+ migration in y₂o₃ and the structure of related oxides |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/69237 |
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