Influence of Structure, Character of Chemical Bonding and Elastic Properties on the Radiation Stability of Silicates, Phosphates and Metal Oxides Deduced by Computer Simulations
The radiation stability of periclase MgO, rutile TiO2, zircon ZrSiO4, xenotime YPO4, quartz SiO2, cristobalite SiO2, gallium phosphate GaPO4 and fluorapatite Ca10(PO4)6F2 has been studied by computer simulations methods. The number of Frenkel pairs after propagation of the primary knock-оn atom of t...
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Інститут геохімії, мінералогії та рудоутворення ім. М.П. Семененка НАН України
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Grechanovsky, A.E. Brik, A.B. Ponomarenko, O.M. 2012-02-17T14:27:46Z 2012-02-17T14:27:46Z 2009 Influence of Structure, Character of Chemical Bonding and Elastic Properties on the Radiation Stability of Silicates, Phosphates and Metal Oxides Deduced by Computer Simulations / А.E. Grechanovsky, A.B. Brik, O.M. Ponomarenko // Мінералогічний журнал. — 2009. — Т. 31, № 4. — С. 30-37. — Бібліогр.: 20 назв. — англ. 0204-3548 https://nasplib.isofts.kiev.ua/handle/123456789/30917 544.163.2 : 544.228 The radiation stability of periclase MgO, rutile TiO2, zircon ZrSiO4, xenotime YPO4, quartz SiO2, cristobalite SiO2, gallium phosphate GaPO4 and fluorapatite Ca10(PO4)6F2 has been studied by computer simulations methods. The number of Frenkel pairs after propagation of the primary knock-оn atom of thorium with a kinetic energy of 10 keV has been characterized by molecular dynamics method. Calculation of chemical bonds covalency degree in studied minerals has been performed using the self-consistent SIESTA method, an implementation of the density functional theory. Calculation of the effective charge of oxygen atoms has been performed using ab initio Hartree-Fock method and B3LYP hybrid functional. It is established that the radiation stability of these minerals depends significantly on the structure topology (the connectivity index, the number of different polyhedra, connected in oxygen positions and the number of nonequivalent positions of oxygen atoms and cations in a structure). Besides, the radiation stability of silicates and metal oxides can be mainly characterized by the effective charge of oxygen atoms. It has been shown, that bulk modulus also influences on radiation stability of silicates with related structures. Радіаційна стійкість мінералів периклазу MgO, рутилу TiO2, циркону ZrSiO4, ксенотиму YPO4, кварцу SiO2, кристобаліту SiO2, фосфату галію GaPO4 та фторапатиту Ca10(PO4)6F2 досліджена за допомогою методів комп’ютерного моделювання. Кількість пар Френкеля, які формуються в структурі мінералу після проходження первинно вибитого атому торію з енергією 10 кеВ, розраховано за допомогою методу молекулярної динаміки. За методом SIESTA (теорія функціонала густини) проведені обчислення ступеня ковалентності хімічних зв’язків для цих мінералів. Обчислення ефективних зарядів атомів кисню проведені з використанням неемпіричного методу Хартрі-Фока та гібридного функціонала B3LYP. Встановлено, що радіаційна стійкість досліджених мінералів значною мірою залежить від топології структури (зв’язність структури, кількість різних поліедрів, що з’єднуються в позиціях атомів кисню, кількість нееквівалентних позицій атомів кисню та катіонів). Окрім того, радіаційна стійкість силікатів та оксидів металів значною мірою залежить від значень ефективних зарядів атомів кисню. Показано, що модуль об’ємної пружності мінералів також є важливим параметром, що впливає на радіаційну стійкість мінералів з однотипними структурами. Радиационная устойчивость таких минералов, как периклаз MgO, рутил TiO2, циркон ZrSiO4, ксенотим YPO4, кварц SiO2, кристобалит SiO2, фосфат галлия GaPO4 и фторапатит Ca10(PO4)6F2 изучена с помощью методов компьютерного моделирования. Количество пар Френкеля, которые формируются в структуре минерала после прохождения первично выбитого атома тория с энергией 10 кэВ, рассчитано с помощью метода молекулярной динамики. По методу SIESTA (теория функционала плотности) проведены вычисления степени ковалентности химических связей для этих веществ. Неэмпирические расчеты методом Хартри-Фока с применением гибридного функционала B3LYP были выполнены для вычисления эффективных зарядов атомов кислорода в минералах. Установлено, что радиационная устойчивость исследованных минералов в значительной степени зависит от топологии структуры (связность структуры, количество различных полиэдров, которые соединяются в позициях атомов кислорода, количество неэквивалентных позиций атомов кислорода и катионов). Кроме того, радиационная устойчивость силикатов и оксидов металлов в значительной степени зависит от значений эффективных зарядов атомов кислорода. Показано, что модуль объемной упругости также служит важным параметром, влияющим на радиационную устойчивость минералов с однотипными структурами. en Інститут геохімії, мінералогії та рудоутворення ім. М.П. Семененка НАН України Мінералогічний журнал Мінералогія Influence of Structure, Character of Chemical Bonding and Elastic Properties on the Radiation Stability of Silicates, Phosphates and Metal Oxides Deduced by Computer Simulations Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Influence of Structure, Character of Chemical Bonding and Elastic Properties on the Radiation Stability of Silicates, Phosphates and Metal Oxides Deduced by Computer Simulations |
| spellingShingle |
Influence of Structure, Character of Chemical Bonding and Elastic Properties on the Radiation Stability of Silicates, Phosphates and Metal Oxides Deduced by Computer Simulations Grechanovsky, A.E. Brik, A.B. Ponomarenko, O.M. Мінералогія |
| title_short |
Influence of Structure, Character of Chemical Bonding and Elastic Properties on the Radiation Stability of Silicates, Phosphates and Metal Oxides Deduced by Computer Simulations |
| title_full |
Influence of Structure, Character of Chemical Bonding and Elastic Properties on the Radiation Stability of Silicates, Phosphates and Metal Oxides Deduced by Computer Simulations |
| title_fullStr |
Influence of Structure, Character of Chemical Bonding and Elastic Properties on the Radiation Stability of Silicates, Phosphates and Metal Oxides Deduced by Computer Simulations |
| title_full_unstemmed |
Influence of Structure, Character of Chemical Bonding and Elastic Properties on the Radiation Stability of Silicates, Phosphates and Metal Oxides Deduced by Computer Simulations |
| title_sort |
influence of structure, character of chemical bonding and elastic properties on the radiation stability of silicates, phosphates and metal oxides deduced by computer simulations |
| author |
Grechanovsky, A.E. Brik, A.B. Ponomarenko, O.M. |
| author_facet |
Grechanovsky, A.E. Brik, A.B. Ponomarenko, O.M. |
| topic |
Мінералогія |
| topic_facet |
Мінералогія |
| publishDate |
2009 |
| language |
English |
| container_title |
Мінералогічний журнал |
| publisher |
Інститут геохімії, мінералогії та рудоутворення ім. М.П. Семененка НАН України |
| format |
Article |
| description |
The radiation stability of periclase MgO, rutile TiO2, zircon ZrSiO4, xenotime YPO4, quartz SiO2, cristobalite SiO2, gallium phosphate GaPO4 and fluorapatite Ca10(PO4)6F2 has been studied by computer simulations methods. The number of Frenkel pairs after propagation of the primary knock-оn atom of thorium with a kinetic energy of 10 keV has been characterized by molecular dynamics method. Calculation of chemical bonds covalency degree in studied minerals has been performed using the self-consistent SIESTA method, an implementation of the density functional theory. Calculation of the effective charge of oxygen atoms has been performed using ab initio Hartree-Fock method and B3LYP hybrid functional. It is established that the radiation stability of these minerals depends significantly on the structure topology (the connectivity index, the number of different polyhedra, connected in oxygen positions and the number of nonequivalent positions of oxygen atoms and cations in a structure). Besides, the radiation stability of silicates and metal oxides can be mainly characterized by the effective charge of oxygen atoms. It has been shown, that bulk modulus also influences on radiation stability of silicates with related structures.
Радіаційна стійкість мінералів периклазу MgO, рутилу TiO2, циркону ZrSiO4, ксенотиму YPO4, кварцу SiO2, кристобаліту SiO2, фосфату галію GaPO4 та фторапатиту Ca10(PO4)6F2 досліджена за допомогою методів комп’ютерного моделювання. Кількість пар Френкеля, які формуються в структурі мінералу після проходження первинно вибитого атому торію з енергією 10 кеВ, розраховано за допомогою методу молекулярної динаміки. За методом SIESTA (теорія функціонала густини) проведені обчислення ступеня ковалентності хімічних зв’язків для цих мінералів. Обчислення ефективних зарядів атомів кисню проведені з використанням неемпіричного методу Хартрі-Фока та гібридного функціонала B3LYP. Встановлено, що радіаційна стійкість досліджених мінералів значною мірою залежить від топології структури (зв’язність структури, кількість різних поліедрів, що з’єднуються в позиціях атомів кисню, кількість нееквівалентних позицій атомів кисню та катіонів). Окрім того, радіаційна стійкість силікатів та оксидів металів значною мірою залежить від значень ефективних зарядів атомів кисню. Показано, що модуль об’ємної пружності мінералів також є важливим параметром, що впливає на радіаційну стійкість мінералів з однотипними структурами.
Радиационная устойчивость таких минералов, как периклаз MgO, рутил TiO2, циркон ZrSiO4, ксенотим YPO4, кварц SiO2, кристобалит SiO2, фосфат галлия GaPO4 и фторапатит Ca10(PO4)6F2 изучена с помощью методов компьютерного моделирования. Количество пар Френкеля, которые формируются в структуре минерала после прохождения первично выбитого атома тория с энергией 10 кэВ, рассчитано с помощью метода молекулярной динамики. По методу SIESTA (теория функционала плотности) проведены вычисления степени ковалентности химических связей для этих веществ. Неэмпирические расчеты методом Хартри-Фока с применением гибридного функционала B3LYP были выполнены для вычисления эффективных зарядов атомов кислорода в минералах. Установлено, что радиационная устойчивость исследованных минералов в значительной степени зависит от топологии структуры (связность структуры, количество различных полиэдров, которые соединяются в позициях атомов кислорода, количество неэквивалентных позиций атомов кислорода и катионов). Кроме того, радиационная устойчивость силикатов и оксидов металлов в значительной степени зависит от значений эффективных зарядов атомов кислорода. Показано, что модуль объемной упругости также служит важным параметром, влияющим на радиационную устойчивость минералов с однотипными структурами.
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0204-3548 |
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https://nasplib.isofts.kiev.ua/handle/123456789/30917 |
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Influence of Structure, Character of Chemical Bonding and Elastic Properties on the Radiation Stability of Silicates, Phosphates and Metal Oxides Deduced by Computer Simulations / А.E. Grechanovsky, A.B. Brik, O.M. Ponomarenko // Мінералогічний журнал. — 2009. — Т. 31, № 4. — С. 30-37. — Бібліогр.: 20 назв. — англ. |
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30 ISSN 0204�3548. Mineral. Journ. (Ukraine). 2009. 31, No 4
UDК 544.163.2 : 544.228
А.E. Grechanovsky, A.B. Brik, O.M. Ponomarenko
INFLUENCE OF STRUCTURE, CHARACTER OF CHEMICAL
BONDING AND ELASTIC PROPERTIES ON THE RADIATION
STABILITY OF SILICATES, PHOSPHATES AND METAL
OXIDES DEDUCED BY COMPUTER SIMULATIONS
The radiation stability of periclase MgO, rutile TiO2, zircon ZrSiO4, xenotime YPO4, quartz SiO2, cristobalite SiO2, galli;
um phosphate GaPO4 and fluorapatite Ca10(PO4)6F2 has been studied by computer simulations methods. The number of
Frenkel pairs after propagation of the primary knock;оn atom of thorium with a kinetic energy of 10 keV has been cha;
racterized by molecular dynamics method. Calculation of chemical bonds covalency degree in studied minerals has been
performed using the self;consistent SIESTA method, an implementation of the density functional theory. Calculation of
the effective charge of oxygen atoms has been performed using ab initio Hartree;Fock method and B3LYP hybrid functio;
nal. It is established that the radiation stability of these minerals depends significantly on the structure topology (the
connectivity index, the number of different polyhedra, connected in oxygen positions and the number of nonequivalent
positions of oxygen atoms and cations in a structure). Besides, the radiation stability of silicates and metal oxides can be
mainly characterized by the effective charge of oxygen atoms. It has been shown, that bulk modulus also influences on
radiation stability of silicates with related structures.
E;mail: grechanovsky@igmof.gov.ua
МІНЕРАЛОГІЧНИЙ ЖУРНАЛ
MINERALOGICAL JOURNAL
(UKRAINE)
Introduction. Nuclear power production was
increased in some countries (including Ukraine)
in the last decades. The "Strategy of the nuclear
power industry development" [20] assumes that the
nuclear power plant share in the total national
power generation reached in 2005 will be main;
tained on the same level during the period of 2006
to 2030 (this is about a half of the total annual
electric power generation in Ukraine). On the
basis of the preliminary estimation of electric
power generation increasing in 2.2 times during
this period it has been offered both extension of the
service life of existing and construction of new
facilities at the nuclear power plants. Therefore for
stable and progressively development of the
nuclear power engineering a decision of some
problems, related to long;term storage of high
level wastes (HLW) is needed.
So, the future of nuclear power engineering is
linked to our ability to effectively handle a nuclear
waste. Vitrification, or immobilization of the
nuclear waste in glass, has been and remains to be
a popular way of its handling. But the operating
period of glass matrices is about 40—50 years only.
The effective alternative to vitrification has been
immobilization of HLW in ceramic matrices and
minerals. The central question is how effective a
matrix will remain as a barrier over the required
period of time, which for various isotopes varies
from tens to tens of thousands years.
For explaining different radiation stability of
different minerals and technical materials some
criteria have been offered in literature, one of
which relates radiation stability to the ability to
form glass by liquid quenching [19], second crite;
© А.E. Grechanovsky, A.B. Brik,
O.M. Ponomarenko, 2009
INFLUENCE OF STRUCTURE, CHARACTER OF CHEMICAL BONDING AND ELASTIC PROPERTIES
ISSN 0204�3548. Мінерал. журн. 2009. 31, № 4 31
rion relates radiation stability to the "structure
topology" [5], third — with degree of chemical
bonds covalency in studied minerals [3, 4, 13, 17],
fourth — with certain physical properties, such as
a polymerization degree of mineral structures and
bulk modulus of minerals [2]. In spite of conside;
rable successes, many questions are not studied
enough in this area of knowledge. It belongs, in
particular, to finding out principles which deter;
mine radiation stability of minerals.
The purpose of this research is an attempt to find
relation between the radiation stability of phos;
phates, silicates and metal oxides and characteris;
tics of its crystalline structures.
Methods. The radiation stability of minerals was
studied by molecular dynamics simulation method
(MD simulation method). This method consists in
calculation of atoms trajectories in a simulation
box, using Newton's second law of motion. Initial
coordinates and velocities of the atoms, and also
interatomic potentials are set as initial data. We
have used the following interatomic potentials for
studied minerals:
a) Buckingham potential in the form
V(r) = A · exp(–r/ρ) – C · r –6, (1)
with the parameters r — the distance between two
atoms (°А), A — the pre;exponential factor for the
repulsive part of the potential (eV), ρ — the hard;
ness parameter (°А), C — the force parameter for
Van der Waals interaction (eV · °А6);
b) Potential of Morse in the form
V(r) = D · [exp(–2α(r — r0)) —
— 2exp(–α(r — r0))], (2)
with the parameters r — the distance between two
atoms (°А), D — the dissociation energy of the
bonding atoms (eV), α — the softness parameter
(°А–1), r0 — the bond distance between the atoms
(°А). The parameters, appearing in (1) and (2) were
taken from the works [3, 15, 17]. To establish these
parameters optimization of the structures was per;
formed using the experimental values of unit;cell
parameters, bond lengths, bond angles, elastic
constants and bulk modulus of studied minerals.
As a recoil atom for the nanofragments of simu;
lated minerals, containing about 2 ·105 atoms we
have used the primary knock;оn atom (PKA) of
thorium with energy of 10 keV. At such energies
the number of Frenkel pairs increases in propor;
tion to the PKA energy [1]. Therefore from
methodological and practical points of view (li;
mited computational power) using the PKA with
energy of 10 keV is rational, in spite of the fact that
the real energy of a thorium recoil atoms is about
to 70 keV. For interatomic distances smaller than
1 °А, the pair potentials were fitted to the strong
repulsive ZBL potentials [17]. On the preliminary
stage of the simulations all structures were brought
to the state of thermal equilibrium during 10 ps at
300 K using the NPT ensemble (constant pressure,
temperature and number of atoms). The main
stage of the simulations is performed using the
NVE microcanonical ensemble (constant volume,
energy and number of atoms). All MD simulations
were performed using the DL_POLY molecular
simulation package [17], designed to facilitate the
molecular dynamics simulations of macromole;
cules, polymers, ionic systems and minerals.
For the calculation of the degree of chemical
bonds covalency in studied minerals we have used
the self;consistent SIESTA method [11], an
implementation of the density functional theory
(DFT) [6]. The electronic density was obtained
using the exchange;correlation potential of
Perdew in the Perdew;Burke;Ernzerhof parame;
trization [12], and normconserving pseudopoten;
tials in the Kleinman;Bylander form [8], to
remove the core electrons from the calculations.
The Kohn;Sham eigenstates were expanded in a
localized basis set of numerical orbitals, calculated
by the Numerov numerical method [7]. We have
used a split;valence basis sets [11] during these
quantum;chemical calculations.
For the calculation of the effective charge of
oxygen atoms in the minerals we have performed
ab initio calculations by the Hartree;Fock method
[14] using the B3LYP hybrid functional [3, 13]
(density functional theory). We have used the PC
GAMESS code [10] for this purpose. The para;
meters of atoms basis sets are shown in Table 1: 1 —
the atom type, 2 — the number and the types of
Atom type Gaussian primitives Shells
Mg
O
Ti
Si
P
Ga
Ca
Zr
Y
15s, 7p
14s, 6p, 2d
20s, 12p, 3d
15s, 9p, 1d
16s, 8p, 1d
21s, 13p, 5d
21s, 13p, 3d
26s, 17p, 9d
26s, 17p, 10d
1s, 3sp
1s, 3sp, 2d
1s, 3sp, 1d
1s, 3sp, 1d
1s, 3sp, 1d
1s, 5sp, 2d
1s, 4sp, 1d
1s, 4sp, 3d
1s, 4sp, 3d
Table 1. Parameters of basis sets,
used in Hartree�Fock calculations
32 ISSN 0204�3548. Mineral. Journ. (Ukraine). 2009. 31, No 4
gaussian primitives, 3 — the number and the types
of shells, corresponding to these primitives (for
example record "2d" indicates that some GTOs
combines in two d;shells).
We have used the connectivity index as a para;
meter, which characterizes influence of mineral
structure topology on its radiation stability. This
parameter is determined as the number of polyhed;
rons, connected in oxygen atoms positions.
Results and discussion. The results of performed
MD; and DFT simulations are given in Table 2.
The following quantities are indicated in this table:
1 — the mineral and its chemical formula; 2 — the
space group of mineral; 3 — the connectivity of
mineral structure, which characterizes the number
and the types of polyhedrons, connected in oxygen
atoms positions; 4 — the bulk modulus G, which
characterize the pressure ∆P needed for the rela;
tive compression of a mineral on a value of ∆ε =
= ∆V/V (G = ∆P/∆ε); 5 — the value of the elec;
trons charge, localized between X and O atoms,
which characterizes the degree of chemical X—O
bond covalency; 6 — the number of Frenkel pairs
NF and the linear size of a displacements cascade
DF after defects annealing; 7 — the maximum
number of Frenkel pairs Nmax and the linear size of
a displacements cascade Dmax before defects
annealing; 8 — the critical temperature of amor;
phisation Tc (if T > Tc, then a mineral cannot be
amorphized). Quantities from cl. 3 are given from
the structural data, cl. 4 — from the experimental
data [3, 15, 17], cl. 5—7 — from the results of
this study (MD; and DFT simulations), cl. 8 —
from the ion;beam irradiation experiments with
800 keV÷1.5 MeV Kr+ ions [9, 17].
The results of performed Hartree;Fock study of
the minerals (the effective charge of oxygen atoms
Q(O)) are given in Table 3. The ionic nature of the
periclase structure implies that the Madelung
potential must be included in the quantum;che;
mical calculations. Indeed, several properties of
MgO are incorrectly described if the long;range
Mineral and its
chemical formula
Parameters, which characterize
the mineral structures
Results of MD; and DFT simulations
Tc, K
Space group Connectivity G, GPa Q(X–O), |e|
Periclase MgO
Rutile TiO2
Zircon ZrSiO4
Xenotime YPO4
Quartz SiO2
Cristobalite SiO2
Gallium phosphate
GaPO4
Fluorapatite
Ca10(PO4)6F2
Fm3m
P42/mnm
I41/amd
I41/amd
P3221
P41212
P3221
P63/m
O—6Mg
O—3Ti
O—2Zr, Si
O—2Y, P
O—2Si
O—2Si
O1—Al, P
O2—Al, P
O1—2Ca1, P, Ca2
O2—2Ca1, P, Ca2
O3—Ca1, P, 2Ca2
240
237
222
147
33
16
40
99
–0.11 (X = Mg)
–0.35 (X = Ti)
–0.6 (X = Si)
–0.29 (X = Zr)
–0.61 (X = P)
–0.25 (X = Y)
–0.61 (X = Si)
–0.62 (X = Si)
–0.59 (X = P)
–0.57 (X = Ga)
–0.64 (X = P)
–0.08 (X = Ca)
30
–
5
490
–
54
820
–
28
790
–
67
2220
–
128
3240
–
114
3240
–
143
1690
–
131
1280
–
71
6230
–
90
6600
–
62
7220
–
99
4430
–
136
6510
–
120
5650
–
143
15260
–
132
20
205
1000
428
1400
—
650
475
Table 2. Characteristics of studied minerals and results of MD simulations and DFT simulations of the minerals
А.E. GRECHANOVSKY, A.B. BRIK, O.M. PONOMARENKO
Nmax
Dmin( °А)
NF
DF( °А)
Mineral and its
chemical formula
Methodology Q(O), |e|
Q(O), |e|
[18]
Periclase MgO
Rutile TiO2
Zircon ZrSiO4
Xenotime YPO4
Quartz SiO2
Cristobalite SiO2
Gallium phos;
phate GaPO4
Fluorapatite
Ca10(PO4)6F2
Embedded cluster
[Ti3O14]–16 cluster
[Zr5Si6O44]–44 cluster
[Y5P6O44]–43 cluster
[Si5O16H12] cluster
[Si6O18H12] cluster
[Ga3P3O18H12] cluster
[Ca9P6O27]–6 cluster
–1.96
–1.29
–1.06
–0.96
–0.79
–0.78
–0.92
–1.18
–1.86
–1.26
—
—
–0.78
—
—
—
Table 3. Results of Hartree�Fock
calculations of studied minerals
Coulomb interactions are not taken into account.
To provide a simple representation of these inte;
ractions we have used [Mg7O6]2+ fragment,
embedded in large arrays of ±2 |e| point charges.
For rutile, zircon, xenotime and fluorapatite struc;
tures we have used respectively [Ti3O14]–16,
[Zr5Si6O44]–44, [Y5P6O44]–43 and [Ca9P6O27]–6
clusters. Using of larger clusters was restricted due
to limited computational power. In quartz, cristo;
balite and gallium phosphate clusters (respectively
[Si5O16H12], [Si6O18H12] and [Ga3P3O18H12])
dangling bonds have been saturated by H atoms,
common procedure to terminate clusters of cova;
lent materials [16]. The positions of H atoms were
fixed at a distance of 0.96 °А from the respective
O atoms along the O–Si and O–Ga directions.
The position of all Si, Ga and O atoms of the clus;
ter has been reoptimised. Electrostatic energy was
taken into account for all quantum;chemical cal;
culations. Urusov et al. data [18], obtained by
means of the minimization of cohesive energy
as the function of the oxygen atoms charge for
three minerals (periclase, rutile, quartz), are also
given in Table 3 for comparison of our results with
other data.
In the case of periclase (Fm3m space group) the
connectivity index of the structure (Fig. 1) is equal
to C = 6. Such high value of the connectivity index
agreed with a low degree of Mg–O bond covalen;
cy (Q(Mg–O) = –0.11 |e|), with a high value of
oxygen charge (Q(O) = –1.96 |e|), and also with
considerable radiation stability of this mineral (the
number of Frenkel pair at the end of simulation
NF = 30 and the critical temperature of amor;
phization Tc = 20 K). The periclase structure is
characterized by a high value of the bulk modulus
(G = 240 GPa), however the size of displace;
ments cascade before defects annealing Dmax =
= 71 °А due to the presence of nanochanels in
the structure.
Rutile (P42/mnm space group) is characterized
by the connectivity index C = 3 (Fig. 2). From
other hand, the degree of chemical bonds covalen;
cy is higher (Q(Ti–O) = –0.35 |e|) and the oxygen
charge is less (Q(O) = –1.29 |e|) in compare with
periclase structure. So, the radiation stability of
rutile structure is less in compare with periclase
structure both from the experimental data (Tc =
= 205 K for rutile and Tc = 20 K for periclase) and
from the MD simulations data (NF = 490 for rutile
and NF = 30 for periclase). In spite of identical
values of the bulk modulus of two minerals (G ≈
≈ 240 GPa) rutile is characterized by a larger li;
INFLUENCE OF STRUCTURE, CHARACTER OF CHEMICAL BONDING AND ELASTIC PROPERTIES
ISSN 0204�3548. Мінерал. журн. 2009. 31, № 4 33
Fig. 1. Periclase structure
Fig. 3. Zircon structure
Fig. 2. Rutile structure
near size of displacements cascade (Dmax = 90 °А)
in compare with periclase.
Zircon and xenotime structures (Fig. 3) with
I41/amd space group are determined by the alter;
nating edge;sharing [AO8] dodecahedrons (A =
= Zr, Y) and [BO4] tetrahedrons (B = Si, P) for;
ming chains parallel to the (001) axis. The connec;
tivity index of these structures is C = 3, however
unlike previous structures two AO8 polyhedrons
and one BO4 tetrahedron are combine in every
oxygen atom positions. From other hand, these
structures are characterized by a large degree of
chemical bonds covalency (Q(Si–O) = –0.6 |e| for
zircon and Q(P–O) = –0.61 |e| for xenotime), and
a small value of the oxygen charge (–1.06 |e| for
zircon and –0.96 |e| for xenotime). These results
agree with the radiation stability of zircon and
xenotime, obtained from the MD simulation data
(NF = 820 for zircon and NF = 790 for xenotime).
In spite of this, the radiation stability from the MD
simulation data for xenotime does not agree with
the experimental data (Tc = 1000 K for zircon and
Tc = 428 K for xenotime). This disagreement will
be discussed below.
A less value of the oxygen charge in xenotime
than one in zircon correlates with a higher value of
the maximum number of Frenkel pairs in xeno;
time in compare with zircon (Nmax = 7220 for
xenotime and Nmax = 6600 for zircon). Besides,
for higher values of the PKA energy (the PKA
energy is more than 10 keV) it can result in a hig;
her value of the number of Frenkel pairs in xeno;
time in compare with zircon after defects annea;
ling. It should be also note that displacements cas;
cade in xenotime has a larger sizes in compare with
zircon (DF = 28 °А for zircon and DF = 67 °А for
xenotime) due to a less bulk modulus in xenotime
than one in zircon.
Next two minerals (quartz and cristobalite) have
a low radiation stability. In the case of quartz struc;
ture (Fig. 4, a) with P3221 space group and cristo;
balite structure (Fig. 5) with P41212 space group
the connectivity index is equal C = 2. In addition,
the degree of Si–O bond covalency is Q(Si–O) ≈
≈ –0.6 |e| and the oxygen charge is Q(O) ≈
≈–0.8 |e| for both structures. However, the radia;
tion stability of cristobalite less than one of quartz
because the bulk modulus in cristobalite less (G =
= 16 GPa) in compare with quartz (G = 33 GPa).
Gallium phosphate structure (Fig. 4, b) with
P3221 space group is determined by the alternating
PO4 and GaO4 tetrahedrons, spiraling along the
three;two screw c;axis. PO4 and GaO4 tetrahed;
rons are characterized by approximately equal
covalency degree of P–O and Ga–O chemical
bonds (Q(P–O) = –0.59 |e| and Q(Ga–O) =
= –0.57 |e|), and the GaPO4 oxygen charge has
even a higher value in compare with quartz. But,
for the gallium phosphate structure a different
tetrahedrons (PO4 and GaO4) are combined in
every oxygen position. Consequently this material
has a less radiation stability than quartz from the
MD simulation data (NF = 3240 for GaPO4 and
NF = 2220 for quartz), in spite of the fact that the
bulk modulus in GaPO4 even more, than in quartz.
However, as well as in the case of xenotime, the
radiation stability of gallium phosphate from the
MD simulation data does not agree with the expe;
rimental data (Tc = 650 K for GaPO4 and Tc =
= 1400 K for quartz).
The last investigated mineral is fluorapatite with
P63/m space group. In this mineral (Fig. 6) the
connectivity index is equal C = 4. However, the
process of defects annealing in a displacements
cascade is complicated due to a difficult structure
of fluorapatite (presence of three nonequivalent
oxygen positions (O1, O2, O3) and two nonequi;
А.E. GRECHANOVSKY, A.B. BRIK, O.M. PONOMARENKO
34 ISSN 0204�3548. Mineral. Journ. (Ukraine). 2009. 31, No 4
Fig. 4. Quartz (a) and gallium phosphate (b) structures
Fig. 5. Cristobalite structure
valent calcium positions (Ca1, Ca2)), large degree
of P–O bond covalency (Q(P–O) = –0.64 |e|) and
significant mobility of fluorine atoms. So, NF =
= 1690 from the MD simulation data. However, as
well as for others phosphate minerals, the radiation
stability of fluorapatite from the MD simulation
data does not agree with the experimental data
(Tc = 475 K). It should be also noted, that a low
value of the bulk modulus for fluorapatite (G =
= 99 GPa) agrees with significant size of a dis;
placements cascade (DF = 131 °А).
We paid attention in this article that the radia;
tion stability of phosphate minerals, obtained from
the MD simulation data does not agree with the
experimental data. This disagreement connected
with the fact, that MD simulations have nanose;
conds time;limit even for modern supercomputers.
Defects annealing in a displacements cascade
takes place during nanoseconds. However, after
this time the radiation;enhanced recrystallization
of amorphous zones takes place during significant;
ly longer time scale.
In the case of silicates the activation energy of
the radiation;enhanced recrystallization of amor;
phous zones has a large value Ea ≈ 3 eV [9] and the
recrystallization does not take place at the mode;
rate temperatures (T ≈ 500 K) even during the
geological time. Therefore the radiation stability of
silicates obtained from the MD simulation data
agrees with the experimental data. For phosphates
this energy is Ea ≈ 1÷1.5 eV [9] and even at the
moderate temperatures (T ≈ 500 K) the recrystal;
lization takes place very rapidly (in some cases
during a seconds). In this case the MD simulation
data reflect the number of Frenkel pairs, rema;
ining in a structure after defects annealing in a dis;
placements cascade. However, in the case of con;
sideration of phosphates separately from silicates
and metal oxides its radiation stability, obtained
from the MD simulation data correlates with the
experimental data — the critical temperature of
amorphization decreases with decreasing the
number of Frenkel pairs in phosphates.
Our methods and approaches can be used for
the decision of practical tasks. So, zircon;bearing
rare;earth garnetiferous matrix (Ca3–xAx)×
×(Zr2–yFey) Fe3O12 (A = Ce, Th, La, Gd, Sr) was
successfully synthesized in the Institute of envi;
ronmental geochemistry of the National Academy
of Sciences and Ministry of Emergencies of
Ukraine. Gamma;irradiation of matrices samples
was performed up to doses 2.3 ·107 Gy for the ve;
rification of its radiation stability. The matrices
samples remain in the crystalline state at such
doses. From other hand, it is also important to
investigate the matrices response on α;recoil
atoms motion for the estimation of its radiation
stability. Performing of heavy ion;beam irradia;
tions of matrices needed for these investigations
is impossible for our researchers at present.
However such tasks can be decided by our com;
puter simulations.
Conclusions. The results of researches show that
the radiation stability of minerals caused by vari;
ous factors. In the case of metal oxides (periclase,
rutile) two main factors are following: the connec;
tivity index and the degree of chemical bonds
covalency of the structures (or effective charge of
oxygen atoms). In the case of silicates (zircon,
quartz, cristobalite) one more factor which influ;
ences on its radiation stability is the value of bulk
modulus. Displacements cascades in minerals with
a higher values of the bulk modulus are characte;
rized by a less value of longitudinal dimensional
and respectively these minerals are characterized
by more radiation stability than minerals with a
less value of the bulk modulus (these minerals
must have related structures and close degrees of
chemical bonds covalency).
It should be noted that for metal oxides and si;
licates the connectivity index and the effective
charge of oxygen atoms are interconnected.
Structures with a large connectivity index (peri;
clase, rutile) are characterized by large values of
both the effective charge of oxygen atoms and the
radiation stability. Structures with a small connec;
tivity index (quartz, cristobalite) are characterized
by small values of both the effective charge of oxy;
INFLUENCE OF STRUCTURE, CHARACTER OF CHEMICAL BONDING AND ELASTIC PROPERTIES
ISSN 0204�3548. Мінерал. журн. 2009. 31, № 4 35
Fig. 6. Fluorapatite structure: 1 — Ca on 1/4 c; 2 — Ca on
3/4 c; 3 — Ca on 0, 1/2 c; 4 — O on 3/4 c; 5 — O on 1/4 c; 6 —
O on 1/20, 3/20 c etc.; 7 — F on 1/4, 3/4 c.
gen atoms and the radiation stability. In simple
terms, the relevance of the type of interatomic
forces for resistance to amorphization can be dis;
cussed as follows. After the displacement of atoms
by propagating heavy ion, the rearrangement of
atoms needed to regain coherence with the crys;
talline lattice involves significant atomic motion.
In a covalent structure, the interactions can be
thought of as short;range directional constraints,
due to the substantial electronic charge being
localized between the neighbouring atoms.
Therefore cooperative atomic motion is "hooked"
by the electrons between neighbouring atoms, and
requires breaking directional covalent bonds with
associated energy cost. On the other hand, highly
ionic structure can be viewed as a collection of
charged ions. The cooperative rolling of spheres
which are only electrostatically charged, does not
require additional activation energy, giving da;
maged ionic structure better chances to re;establish
coherence with crystalline lattice.
Unlike silicates which are characterized by
almost full absence of the radiation;enhanced
recrystallization of amorphous zones at the mo;
derate temperatures (T ≈ 500 K), this process
takes place very rapidly in phosphates for these
temperatures (in some cases during a seconds).
However, in spite of peculiarities of phosphate
structures, the radiation stability of phosphate
minerals is influenced mainly by the connectivity
index, the effective charge of oxygen atoms and
"structure complication" (the number of different
polyhedra, connected in oxygen positions, and the
number of nonequivalent positions of oxygen
atoms and cations in the structure).
So, fluorapatite structure is characterized by a
higher connectivity index (C = 4) as compared
to xenotime structure (C = 3). However, fluor;
apatite structure is more complicated, than xe;
notime structure. So, the radiation stability of
fluorapatite structure is a less in compare with
xenotime structure (Tc = 428 K for xenotime and
Tc = 475 K for fluorapatite). In the case of gallium
phosphate GaPO4 the connectivity index is equal
C = 2. So, the radiation stability of this material
is a less (Tc = = 650 K) in compare with fluor;
apatite or xenotime.
Results of this study can be used for solving fun;
damental and practice tasks connected with
immobilization and disposal of a high;level waste.
In particular, these results can be used for the
assessment of radiation stability of matrices, pro;
posed for immobilization of the high;level waste.
Our computer simulations permit to analyze and
predicted matrices reliability under radiation da;
mage. Using computer simulation methods can
save timing and money budgets and promotes to
choice of the appropriated matrix.
А.E. GRECHANOVSKY, A.B. BRIK, O.M. PONOMARENKO
36 ISSN 0204�3548. Mineral. Journ. (Ukraine). 2009. 31, No 4
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M.P. Semenenko Inst. of Geochemistry, Mineralogy Received 14.09.2009
and Ore Formation of the NAS of Ukraine, Kyiv
РЕЗЮМЕ. Радіаційна стійкість мінералів периклазу MgO, рутилу TiO2, циркону ZrSiO4, ксенотиму YPO4, квар;
цу SiO2, кристобаліту SiO2, фосфату галію GaPO4 та фторапатиту Ca10(PO4)6F2 досліджена за допомогою методів
комп’ютерного моделювання. Кількість пар Френкеля, які формуються в структурі мінералу після проходження
первинно вибитого атому торію з енергією 10 кеВ, розраховано за допомогою методу молекулярної динаміки. За
методом SIESTA (теорія функціонала густини) проведені обчислення ступеня ковалентності хімічних зв’язків
для цих мінералів. Обчислення ефективних зарядів атомів кисню проведені з використанням неемпіричного
методу Хартрі;Фока та гібридного функціонала B3LYP. Встановлено, що радіаційна стійкість досліджених
мінералів значною мірою залежить від топології структури (зв’язність структури, кількість різних поліедрів, що
з’єднуються в позиціях атомів кисню, кількість нееквівалентних позицій атомів кисню та катіонів). Окрім того,
радіаційна стійкість силікатів та оксидів металів значною мірою залежить від значень ефективних зарядів атомів
кисню. Показано, що модуль об’ємної пружності мінералів також є важливим параметром, що впливає на
радіаційну стійкість мінералів з однотипними структурами.
РЕЗЮМЕ. Радиационная устойчивость таких минералов, как периклаз MgO, рутил TiO2, циркон ZrSiO4, ксе;
нотим YPO4, кварц SiO2, кристобалит SiO2, фосфат галлия GaPO4 и фторапатит Ca10(PO4)6F2 изучена с помощью
методов компьютерного моделирования. Количество пар Френкеля, которые формируются в структуре мине;
рала после прохождения первично выбитого атома тория с энергией 10 кэВ, рассчитано с помощью метода
молекулярной динамики. По методу SIESTA (теория функционала плотности) проведены вычисления степени
ковалентности химических связей для этих веществ. Неэмпирические расчеты методом Хартри;Фока с при;
менением гибридного функционала B3LYP были выполнены для вычисления эффективных зарядов атомов
кислорода в минералах. Установлено, что радиационная устойчивость исследованных минералов в значительной
степени зависит от топологии структуры (связность структуры, количество различных полиэдров, которые
соединяются в позициях атомов кислорода, количество неэквивалентных позиций атомов кислорода и катио;
нов). Кроме того, радиационная устойчивость силикатов и оксидов металлов в значительной степени зависит от
значений эффективных зарядов атомов кислорода. Показано, что модуль объемной упругости также служит
важным параметром, влияющим на радиационную устойчивость минералов с однотипными структурами.
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