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Computational Materials Science 153 (2018) 176–182
Contents lists available at ScienceDirect
Computational Materials Science
journal homepage: www.elsevier.com/locate/commatsci
Core electron level shifts in zirconium induced by vacancy, helium and
hydrogen
T
⁎
L.A. Svyatkina, , O.V. Lopatinaa, I.P. Chernova, Yu. M. Koroteevb
a
Department of General Physics, School of Nuclear Science and Engineering, National Research Tomsk Polytechnic University, 30 Lenin Avenue, Tomsk 634050, Russian
Federation
b
Institute of Strength Physics and Materials Science of Siberian Branch, Russian Academy of Sciences, 2/4 pr. Akademicheskii, Tomsk 634055, Russian Federation
A R T I C LE I N FO
A B S T R A C T
Keywords:
Binding energy
Core-level shift
Charge transfer
Hydrogen
Helium
Vacancy
The paper presents a first-principle calculation of the influence of lattice defects (a hydrogen atom, a vacancy
and a helium-in-vacancy complex) and their concentration on the core electron binding energies in zirconium
atoms. It is shown that the formation of a vacancy or a helium-in-vacancy complex causes core-level shifts of Zr
atoms to lower binding energies. Hydrogen dissolution leads to core-level shifts to both lower and higher binding
energies. Besides, the effects of electron density redistribution in zirconium (due to the appearance of the defect
and, as a consequence, the change of the crystal volume and the lattice relaxation around the defect) on the core
electron binding energies are studied.
1. Introduction
Zirconium based alloys are widely used as structural materials for
active zones of light water reactors. Water radiolysis under influence of
radiation during the operation of these reactors leads to the release of
atomic hydrogen, which is actively accumulated in the materials.
Moreover, hydrogen, as well as helium is accumulated in structural
materials due to (n, p) and (n, α) nuclear reactions. In addition, as a
result of a long-term operation of the reactor, an appreciable number of
vacancies are formed due to elastic collisions of neutrons with zirconium atoms. Accumulating in the zirconium alloys, these defects impair
operational properties of the materials, reducing their plasticity and
increasing brittleness [1–3]. The influence of hydrogen, helium and
vacancies on the mechanical properties of zirconium and its alloys was
investigated from the first principles in [4–8]. However, these studies
did not investigate the influence of the defects on the distribution of the
electron density of the metal, which is necessary to understand the
degradation processes at the microscopic level.
Important information on the influence of impurities on the electron
density distribution in a crystal can be obtained from core-level
binding-energy shifts [9–11]. Experimentally, these shifts were measured by X-ray photoelectron spectroscopy (XPS) and other spectroscopic methods [12–15]. The most complete information on the corelevel shifts (CLSs) can be obtained within the framework of all-electron
first-principles full-potential calculations. In the present work, the formation process of the core electron level shifts and the electron density
⁎
Corresponding author at: 43 Lenin Avenue, Tomsk 634050, Russian Federation.
E-mail address: svyatkin@tpu.ru (L.A. Svyatkin).
https://doi.org/10.1016/j.commatsci.2018.06.034
Received 23 January 2018; Received in revised form 21 June 2018; Accepted 23 June 2018
Available online 30 June 2018
0927-0256/ © 2018 Elsevier B.V. All rights reserved.
redistribution in zirconium caused by the formation of vacancies and
the presence of H and He atoms is theoretically studied.
2. Theoretical approach and computational details
Self-consistent calculations of core electron energy and electron
density distribution of pure Zr and Zr-vacancy (Zr-vac), Zr-H, Zr-He-vac
systems were performed using the density functional theory [16,17]. To
describe the exchange and correlation effects, the generalized gradient
approximation in the form of Perdew-Burke-Ernzerhof (PBE) [18] was
used. The Kohn-Sham equations are solved using the all-electron fullpotential linearized augmented plane wave (FP-LAPW) method
[19,20], as implemented in the FLEUR code [21]. This implementation
includes calculations of total energy and atomic forces, which allows
carrying out a structural optimization.
The core states were described fully relativistically, while the semicore (4s and 4p states of Zr) and valence states were treated by the
scalar relativistic approximation. Inside the muffin-tin spheres, the
wave functions were expanded in spherical harmonics with an angular
momentum of up to l = 8 for zirconium and 4 for hydrogen and helium.
The wave functions in the interstitial region were expanded into augmented plane waves with a cutoff of kmax = 4.0 (a.u.)−1, corresponding
to the 178 basis LAPW functions per atom. The muffin-tin radii were
chosen as 2.5, 1.0 and 1.0 a.u. for Zr, He and H, respectively. Selfconsistency was considered to be achieved when the total energy variation from iteration to iteration did not exceed 0.02 meV. For the self-
Computational Materials Science 153 (2018) 176–182
L.A. Svyatkin et al.
opt
δErelax = ΔEZr − X −ΔEZr
−X .
0
ΔEZr
−X
(5)
opt
ΔEZr
−X
and
are the binding energies of Zr core electrons
where
of the Zr–X system with lattice parameters of pure zirconium and with
optimized ideal lattice parameters, correspondingly.
The defect formation in a crystal causes the redistribution of its
valence electron density (valence charge transfer δQ to or from Zr
atoms) which in turn leads to the change in the binding energy of core
electrons [9,23]. Therefore, to study in detail the nature of the CLS, we
calculated the change of the electron charge δQ in the Zr MT-sphere due
to the defect formation, as well as its partial components δQdef, δQvol
and δQrelax arising at the above-mentioned stages
δQ = QZr − X −QZr ,
(6)
0
δQdef = QZr
− X −QZr.
(7)
0
δQ vol = Q optZr − X −QZr
−X ,
(8)
δQrelax =
opt
QZr − X −QZr
−X .
(9)
where Q is the valence charge in the MT-spheres of the pure Zr (QZr)
and the Zr–X system with lattice parameters of pure Zr (Q0Zr–X) and with
optimized lattice parameters for ideal (Qopt
Zr–X) and relaxed (QZr–X)
atomic configurations in the supercell.
Fig. 1. The calculated supercell of Zr-vac, Zr-He-vac and Zr-H systems with the
defect concentration of ∼6 at.%. a and c are the supercell parameters.
3. Results and discussion
3.1. Vacancy
consistent calculations, the Brillouin zone was sampled at 108 k points.
The considered systems were relaxed and the atoms were assumed to be
in the equilibrium configuration when the force on each atom was
below 0.025 eV/Å.
In our calculations a supercell consisting of a 2 × 2 × 2 block of hcp
zirconium unit cells was used (Fig. 1) to study the defect concentration
of ∼6 at.% in zirconium. For convenience of discussion, all the Zr
atoms in Fig. 1 are numbered. The supercell of the Zr-H system contained sixteen Zr atoms and one H atom in a tetrahedral (T) or octahedral (O) site. To simulate the Zr-vac system one Zr atom (at number
twelve) was removed from the supercell. In the case of the Zr-He-vac
system one He atom was placed in the vacancy (instead of the twelfth Zr
atom in the supercell). As it was shown in [6,22], this configuration is
most energetically favorable. To study the defect concentration of
∼3 at.% the lateral supercell parameter a for all the considered systems
was 1.5 times greater than at the concentration of ∼6 at.%. Thus, a
supercell consisting of a 3 × 3 × 2 block of hcp zirconium unit cells
was used.
The binding energy of Zr core electrons in the considered systems
was calculated as
ΔEZr − X = EF−Ecore,
The first coordination sphere of a vacancy includes nine Zr atoms
(Fig. 1): atoms 9, 10 and 11 are located in the same basal plane as the
vacancy; atoms 5, 7, 8 and 13, 15, 16 lie in the neighboring basal planes
above and below the vacancy, respectively. Atoms 6 and 14 belong to
the second coordination sphere. The third and fourth coordination
spheres contain, correspondingly, atom 4 and atoms 1, 2, and 3. The
CLSs δE calculated for the Zr atoms of the above-mentioned coordination spheres from Eq. (2) are presented in Fig. 2. It is seen that the
vacancy formation leads to a shift of the core electron levels to lower
binding energies by 0.06–0.26 eV depending on the coordination sphere
number. The value of the CLS depends weakly on the quantum numbers
of the electron states. Therefore, only the 3d3/2 state of Zr is considered
further below.
Fig. 3a shows the contributions of the vacancy occurrence (δEdef),
decrease in the crystal volume (δEvol) and atom displacements from the
(1)
where EF is the Fermi energy of the Zr–X system (X is the vacancy,
hydrogen or helium) and Ecore is the energy of Zr core electron. The CLS
δE was obtained as
δE = ΔEZr − X −ΔEZr ,
(2)
where ΔEZr is the core electron binding energy of pure Zr.
To study the mechanism of the origin of the CLS in the considered
systems, we divided the system formation process into three stages: (1)
the appearance of the defect in the ideal metal lattice and (2) the
subsequent change of the crystal volume (lattice parameters optimization) with (3) the relaxation of atomic positions in the lattice. The CLSs
caused by the defect occurrence (δEdef), the change of the lattice
parameters (δEvol) and the lattice relaxation (δErelax) were calculated as
0
δEdef = ΔEZr
− X −ΔEZr.
(3)
opt
0
δE vol = ΔEZr
− X −ΔEZr − X ,
(4)
Fig. 2. The CLS δE of Zr atoms in the Zr-vac system. Numbers indicate the
vacancy coordination spheres. Letters a and b denote the atoms of the first
coordination sphere lying in the same basal plane with the vacancy and in the
neighboring basal planes, respectively.
177
Computational Materials Science 153 (2018) 176–182
L.A. Svyatkin et al.
Fig. 3. (a) Shifts of the core 3d3/2 level of zirconium atoms δE, δEdef, δEvol, δErelax in the Zr-vac system and (b) charge transfer δQ, δQdef, δQvol, δQrelax to/from Zr
atoms depending on the distance between the metal atoms and the vacancy.
sites of an ideal lattice (δErelax) into the total CLS (δE) of the 3d3/2 state
as a function of the distance r between the Zr atoms and the vacancy. It
is seen that the function δE(r) has a nonmonotonic character which is
formed at the stages of the vacancy occurrence and the lattice relaxation, and all the considered stages give a significant contribution to the
magnitude of the total shifts δE. So, the fact of the vacancy occurrence
causes the CLS δEdef in the range from −0.01 to −0.14 eV depending
on the coordination sphere number. The crystal volume decrease due to
the vacancy occurrence leads to the CLS δEvol ∼ 0.09 eV, which depends weakly on the coordination sphere number. The zirconium lattice
relaxation leads to the CLS δErelax to both higher (up to 0.06 eV) and
lower (up to −0.07 eV) binding energies.
The values of the total charge transfer δQ to/from the Zr atoms and
its partial components δQdef, δQvol, δQrelax are presented in Fig. 3b as a
function of the distance r between the Zr atoms and the vacancy. The
analysis of Fig. 3a and b shows that an increase of the valence electron
charge in the zirconium MT-spheres leads to a decrease of the core
electron binding energy. The clearest correlation between the CLS and
the charge transfer to/from the Zr atoms is observed in the stages of the
crystal volume decrease (δEvol(r) and δQvol(r) curves) and the lattice
relaxation (δErelax(r) and δQrelax(r) curves): these functions are almost
identical in their character and opposite in sign.
At the stage of the vacancy occurrence, there is no explicit correlation between the CLS δEdef and the charge transfer δQdef. This is due
to the fact that the binding energy of the core electrons ΔE is calculated
relative to the Fermi level (see Eq. (1)), which is significantly displaced
as a result of the vacancy occurrence (i.e. the decrease in the number of
atoms and electrons in the crystal). This displacement can be estimated
from the density of electron states as the change of the Fermi level
position (due to the vacancy occurrence) relative to the bottom of the Zr
conduction band. According to our estimations, it equals ∼0.18 eV.
Taking into account this Fermi level displacement, the δEdef(r) curve is
completely shifted to the region of positive energy values; as a result,
the correlation between the CLS δEdef(r) and the charge transfer δQdef(r)
becomes apparent.
Fig. 4. CLS δE of Zr atoms in the Zr-He-vac system. Notations are the same as in
Fig. 2.
which is 1.1–1.8 times less than the CLS caused by the single vacancy.
The CLS values in the Zr-He-vac system weakly depend on the quantum
numbers of the electron states. Therefore, as in the previous case, only
the 3d3/2 state will be considered. Fig. 5a shows the total CLS δE and
contributions δEdef, δEvol and δErelax as the functions of the distance r
between Zr and He atoms. It is seen that the placement of helium into
the vacancy does not change the behavior of these functions. In contrast
to the previous case, the main contribution to the total CLS δE is provided by the stage of the He-vac defect occurrence (δEdef varies from
−0.03 to −0.15 eV), whereas the sum of the contributions of the
second and third stages (δEvol + δErelax) does not exceed 0.06 eV in
absolute value.
In Fig. 5b the total charge transfer δQ to the Zr atoms and its partial
components δQdef, δQvol and δQrelax are presented as functions of the
distance r between Zr and He atoms. These functions are similar in
shape to those observed for the Zr-vac system. However, the values of
the charge transfer δQ in the Zr-He-vac system are lower than those in
the Zr-vac system. Since we had already known the influence of a vacancy on the charge transfer and CLS, we tried to specify the contribution to these values made by the helium atom as a result of its
placement in vacancies. Comparing Fig. 3a and Fig. 5a, it can be seen
that the insertion of helium into a vacancy (the first stage) increases the
3.2. Helium-in-vacancy complex
In the considered system the Zr atom distribution over the coordination spheres of the helium-in-vacancy (He-vac) complex remains
the same as in the previous case. The zirconium CLS calculated from Eq.
(2) for these coordination spheres are shown in Fig. 4. It can be seen
that the presence of the He-vac complex in zirconium causes a shift of
the core electron levels to lower binding energies by 0.03–0.21 eV,
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L.A. Svyatkin et al.
Fig. 5. (a) Shifts of the core 3d3/2 level of zirconium atoms δE, δEdef, δEvol, δErelax in the Zr-He-vac system and (b) charge transfer δQ, δQdef, δQvol, δQrelax to/from Zr
atoms depending on the distance between the metal atoms and the He-vac complex.
displacement of the Zr core electron levels in the first coordination
sphere to lower binding energies and has practically no effect on the
more distant coordination spheres. This is due to ousting the valence
charge density from the vacancy to the surrounding region (i.e. to the
first coordination sphere) by the helium atom [24], whereas in the MTspheres of more distant atoms the valence charge practically does not
change (see Fig. 3b and Fig. 5b). In the second stage, the presence of the
He atom in the vacancy reduces the contributions δEvol and δQvol by
2.7–3.4 times. This is due to the fact that, getting into the vacancy,
helium reduces (in absolute value) the negative excess volume introduced by the vacancy into the crystal. In the third stage, as can be
seen from Fig. 2b and Fig. 3b, as well as Fig. 2c and Fig. 3c, helium
reduces the contributions δErelax and δQrelax. This is apparently connected with the fact that the displacement of metal atoms from the ideal
lattice sites is less near the He-vac complex than that near a single vacancy.
lower binding energies (by an amount not exceeding 0.07 eV), depending on the coordination sphere number. In the case of tetrahedral
coordination, the core electron levels are shifted mainly to higher
binding energies. The dependences of the total CLS δE and contributions δEdef, δEvol and δErelax for the 3d3/2 state on the distance r between
the metal and hydrogen atoms are shown in Fig. 7a and Fig. 8a for the
tetrahedral and octahedral coordination, respectively. It is clear that the
function δE(r) has an oscillating character formed at the stages of hydrogen dissolution (δEdef) and the relaxation of atomic positions
(δErelax). In general, all considered stages make a significant contribution to the formation of the total CLS δE.
Fig. 7b and Fig. 8b show the total charge transfer δQ to/from the Zr
atoms and its partial components δQdef, δQvol, δQrelax as a function of
the distance r. From Fig. 7a and b, Fig. 8a and b it can be seen that, as in
the case of a vacancy, the correlation between the CLS and the charge
transfer to/from the Zr atoms is most clearly observed at the stages of
crystal volume increase (functions δEvol(r) and δQvol(r)) and lattice relaxation (the curves δErel(r) and δQrel(r)). The dependence of the CLS
δEvol and δErelax on the charge transfer δQvol and δQrelax to/from the Zr
atoms for all the considered defects is shown in Fig. 9. It can be seen
that this dependence is practically linear and does not depend on the
defect type. The linear approximation by the least-squares method gives
the line with a slope coefficient of (−2.71 ± 0.07) eV/electron passing
through the origin. This latter circumstance indicates that the CLS at the
second and third stages are caused only by the charge transfer to/from
Zr atoms, i.e. in the absence of charge transfer the CLS are not observed.
At the stage of the defect formation, the correlation between the CLS
δEdef and the charge transfer δQdef is not traced. It can be seen from
Fig. 7b and Fig. 8b that the charge transfer δQdef to/from the Zr atoms
decreases sharply with increasing distance r, and the value of δQdef is
already close to zero for the atoms of the third coordination sphere. At
the same time, the functions δEdef(r) in Fig. 7a and Fig. 8a have an
oscillating character and weakly damp with increasing distance r. This
is due to the fact that the dissolution of hydrogen in zirconium leads to
the formation of Zr-H chemical bonds, which manifests itself in the
anisotropic electron density redistribution [24,26]. As a result, the
screening of the potentials (those produced by the hydrogen and the
nearest Zr atoms) by the electronic density of the metal depends on the
crystallographic direction in the crystal. This, in turn, leads to Zr CLS
varying in the magnitude and sign depending on the coordination
sphere number.
3.3. Hydrogen
As reported in [4,25,26], the tetrahedral interstitial sites are most
energetically favorable for hydrogen atoms. However, for the concentration considered in the present work the binding energies of hydrogen in the octahedral and tetrahedral interstitial sites differ by
30–100 meV. This means that at the temperatures of the nuclear reactor
operation, hydrogen atoms will occupy both interstitial sites with almost equal probability. Therefore, we calculated the Zr CLS, both for
the tetrahedral and octahedral coordination of hydrogen atoms. In the
case of the tetrahedral coordination the nearest neighbors of hydrogen
are atom 12 (at the vertex of the tetrahedron) and atoms 5, 7 and 8 (at
the tetrahedron base) (Fig. 1). The second coordination sphere contains
atom 4. Atom 6 and atoms 9, 10 and 11 belong to the third coordination
sphere. Atoms 1, 2 and 3 and atoms 13, 15 and 16 lie in the fourth and
fifth coordination spheres, respectively. The most remote sixth coordination sphere contains atom 14. In the case of the octahedral coordination, the zirconium atoms denoted by numbers 5, 6, 8, 10, 11 and
12 are the nearest neighbors of hydrogen. The second coordination
sphere contains atoms 7 and 9. Atoms 2, 3, 4, 13, 14 and 16 and atoms 1
and 15 belong to the third and fourth coordination spheres, respectively.
The CLSs δE of Zr atoms, caused by the presence of hydrogen in
tetrahedral and octahedral interstitial sites, are presented in Fig. 6a and
b, respectively. It can be seen that the dissolution of hydrogen in zirconium leads to the shift of the core electron levels both to higher and
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Computational Materials Science 153 (2018) 176–182
L.A. Svyatkin et al.
Fig. 6. The CLS δE of Zr atoms in the Zr-H system with tetrahedral (a) and octahedral (b) coordination of hydrogen. Numbers denote the hydrogen coordination
sphere number. 1a are the atoms of the first coordination sphere lying at the vertex of the tetrahedron, 1b is at its base. 3a and 3b are the atoms of the third
coordination sphere lying in one basal plane with the vertex of the tetrahedron and its base, respectively.
the case of the tetrahedral hydrogen coordination, the difference in the
CLSs for both considered concentrations reach 40 meV, while at the
octahedral coordination it does not exceed 11 meV. Fig. 11 shows that
the decrease of the hydrogen concentration in tetrahedral interstitial
sites leads to the increase of the charge transfer to/from the Zr atoms of
the first two coordination spheres and, as a consequence, to the increase
in the CLSs of these atoms. At the same time, in the Zr atoms of the
farther coordination spheres the decrease in the absolute value of the
charge transfer and the CLS is observed. It indicates that the Zr-H interaction become more local with the decrease in the hydrogen concentration. In the case of the octahedral coordination, the concentration
lowering leads to the same effect. However, in this case the difference in
the charge transfer (less than 0.0015e) and, as a consequence, the CLS is
insignificant. This is due to the fact that the charge transfer is caused
mainly by the zirconium lattice relaxation and the formation of the Zr-H
chemical bond. Since the volume of the octahedral site is four times
larger than the volume of the tetrahedral site, at the octahedral coordination these factors are less dependent on the hydrogen concentration than in the case of the tetrahedral coordination.
3.4. Influence of defect concentration
To study the influence of the defect concentration on the core-level
binding-energy shifts of Zr atoms, we calculated the CLSs at a concentration of ∼3 at.%. The dependences of the CLS δE for the 3d3/2
state and the charge transfer δQ to/from the Zr atoms on the distance r
between the metal atom and defect are shown in Figs. 10 and 11. In
addition, the corresponding dependences δE(r) and δQ(r) at the defect
concentration of ∼6 at.% are presented in Figs. 10 and 11.
It can be seen from Fig. 10 that a decrease in the concentration of
vacancies and He-vac complexes from ∼6 at.% to ∼3 at.% leads to a
decrease in the absolute value of the CLS and charge transfer to/from
the Zr atoms practically for all the considered coordination spheres. So,
the vacancy (He-vac complex) formation at the concentration of 3 at.%
causes the CLSs in the range from −0.09 to 0.01 eV (−0.08 to 0.03 eV)
depending on the coordination sphere number. At the same time, the
oscillating character of the dependence δE(r) and its correlation with δQ
(r) is kept.
The lowering of the hydrogen concentration in zirconium also does
not change the oscillating character of the dependence δE(r) and its
correlation with the charge transfer to/from the Zr atoms (Fig. 11). In
Fig. 7. (a) The shifts of the core 3d3/2 level of zirconium atoms δE, δEdef, δEvol, δErelax in the Zr-H system with hydrogen at tetrahedral interstitial sites and (b) charge
transfer δQ, δQdef, δQvol, δQrelax to/from Zr atoms depending on the distance between the metal atoms and hydrogen.
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Computational Materials Science 153 (2018) 176–182
L.A. Svyatkin et al.
Fig. 8. The same as in Fig. 7 for the Zr-H system with hydrogen at octahedral interstitial sites.
linearized augmented plane waves. It has been shown that the vacancy
formation at the concentration of ∼6 at.% shifts the core electron level
of Zr to lower binding energies in the range from −0.06 to −0.26 eV
(depending on the coordination sphere number), the presence of helium
in the vacancy reduces these shifts by 1.1–1.8 times (from −0.03 to
−0.21 eV). The presence of vacancies or helium-in-vacancy complexes
at the concentration of 3 at.% causes practically the same core-level
shifts (in the range from −0.09 to 0.03 eV). Hydrogen dissolution
causes shifts to both lower and higher binding energies (from −0.02 to
0.07 eV at the concentration of ∼6 at.% and from −0.04 to 0.08 eV at
the concentration of ∼3 at.%). In the case of the tetrahedral coordination of hydrogen, the core electron levels are shifted mainly to
higher binding energies. It has been established that the dependence of
the core-level shift δE on the distance r between the defect and the
zirconium atoms has an intricate nonmonotonic character.
To understand the mechanism and causes of the occurrence of the
nonmonotonic dependence δE(r), the process of defect formation was
divided into three stages: (i) the occurrence of a defect in the ideal
metal lattice and, as a consequence, (ii) the change of the crystal volume (the change of the lattice parameters) and (iii) the relaxation of
atomic positions in the lattice. It has been established that the nonmonotonic character of the dependence δE(r) is formed in the first and
third stages. However, each considered stage makes a significant contribution to the formation of the core-level shift magnitude. It has been
Fig. 9. The CLS δEvol and δErelax as a function of charge transfer δQvol and
δQrelax to/from Zr atoms in Zr-vac, Zr-He-vac and Zr-H systems.
4. Conclusion
In the present paper, the core-level shifts of the of zirconium atoms
caused by the lattice defects (a vacancy, a hydrogen atom and a heliumin-vacancy complex) were calculated in the framework of the density
functional formalism, using the full-potential ab initio method of
Fig. 10. (a) Shifts of the core 3d3/2 level of zirconium atoms δE in the Zr-vac and Zr-He-vac systems and (b) charge transfer δQ to/from Zr atoms depending on the
distance between the metal atoms and the defect.
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Computational Materials Science 153 (2018) 176–182
L.A. Svyatkin et al.
Fig. 11. (a) Shifts of the core 3d3/2 level of zirconium atoms δE in the Zr-H system with hydrogen at tetrahedral or octahedral interstitial sites and (b) charge transfer
δQ to/from Zr atoms depending on the distance between the metal atoms and hydrogen.
found that at the formation of a vacancy and the placement of helium
into it the metal core-level shifts at each stage are caused by the charge
transfer from/to the zirconium atoms and in the case of hydrogen dissolution also by the formation of a Zr-H chemical bond, which significantly affects the character of the dependence of the core-level shifts
on the distance between the hydrogen and zirconium atoms. The lowering of the defect concentration in zirconium from ∼6 at.% to ∼3 at.%
does not change the intricate nonmonotonic character of the dependence δE(r) and its correlation with the charge transfer to/from the Zr
atoms.
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Data availability
The raw/processed data required to reproduce these findings cannot
be shared at this time as the data also forms part of an ongoing study.
Acknowledgments
The research was funded by the Tomsk Polytechnic University
Competitiveness Enhancement Program.
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182
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