Elastic and electronic properties of fluorite RuO₂ from first principle
The elastic, thermodynamic, and electronic properties of fluorite RuO₂ under high pressure are investigated by plane-wave pseudopotential density functional theory. The optimized lattice parameters, elastic constants, bulk modulus, and shear modulus are consistent with other theoretical values. The...
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| Zitieren: | Elastic and electronic properties of fluorite RuO₂ from first principle / Z.J. Yang, A.M. Guo, Y.D. Guo, J. Li, Z. Wang, Q. Liu, R.F. Linghu, X.D. Yang // Condensed Matter Physics. — 2012. — Т. 15, № 1. — С. 13603: 1-9. — Бібліогр.: 34 назв. — англ. |
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irk-123456789-1201532017-06-12T03:03:30Z Elastic and electronic properties of fluorite RuO₂ from first principle Yang, Z.J. Guo, A.M. Guo, Y.D. Li, J. Wang, Z. Liu, Q. Linghu, R.F. Yang, X.D. The elastic, thermodynamic, and electronic properties of fluorite RuO₂ under high pressure are investigated by plane-wave pseudopotential density functional theory. The optimized lattice parameters, elastic constants, bulk modulus, and shear modulus are consistent with other theoretical values. The phase transition from modified fluorite-type to fluorite is 88 GPa (by localized density approximation, LDA) or 115.5 GPa (by generalized gradient approximation, GGA). The Young's modulus and Lamé's coefficients are also studied under high pressure. The structure turned out to be stable for the pressure up to 120 GPa by calculating elastic constants. In addition, the thermodynamic properties, including the Debye temperature, heat capacity, thermal expansion coefficient, Grüneisen parameter, and Poisson's ratio, are investigated. A small band gap is found in the electronic structure of fluorite RuO₂ and the bandwidth increases with the pressure. Also, the present mechanical and electronic properties demonstrate that the bonding nature is a combination of covalent, ionic, and metallic contributions. Пружнi, термодинамiчнi та електричнi властивостi флюориту RuO₂ при високому тиску дослiджуються за допомогою теорiї функцiоналу густини з плоскохвильовим псевдопотенцiалом. Оптимiзованi параметри гратки, пружнi сталi, об’ємний модуль i модуль зсуву узгоджуються з iншими теоретичними значеннями. Фазовий перехiд з модифiкованого флюориту до флюориту є при 88 GPa (наближення локальної густини, LDA), чи при 115.5 GPa (узагальнене градiєнтне наближення, GGA). Також дослiджено модуль Юнга i коефiцiєнти Ламе при високих тисках. Структура є стабiльною для тискiв до 120 GPa, якщо обчислювати пружнi сталi. Крiм того, дослiджено термодинамiчнi властивостi, включаючи температуру Дебая, теплоємнiсть, коефiцiєнт теплового розширення, параметр Грюнайзена i коефiцiєнт Пуассона. В електроннiй структурi флюориту RuO₂ знайдено малу зонну щiлину i ширина зони зростає iз тиском. Також, представленi механiчнi та електроннi властивостi демонструють, що природа зв’язування є комбiнацiєю ковалентного, iонного i металiчного вкладiв. 2012 Article Elastic and electronic properties of fluorite RuO₂ from first principle / Z.J. Yang, A.M. Guo, Y.D. Guo, J. Li, Z. Wang, Q. Liu, R.F. Linghu, X.D. Yang // Condensed Matter Physics. — 2012. — Т. 15, № 1. — С. 13603: 1-9. — Бібліогр.: 34 назв. — англ. 1607-324X PACS: 63.20.dk, 71.20.-b, 62.20.D-, 65.40.-b DOI:10.5488/CMP.15.13603 arXiv:1204.5824 http://dspace.nbuv.gov.ua/handle/123456789/120153 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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The elastic, thermodynamic, and electronic properties of fluorite RuO₂ under high pressure are investigated by plane-wave pseudopotential density functional theory. The optimized lattice parameters, elastic constants, bulk modulus, and shear modulus are consistent with other theoretical values. The phase transition from modified fluorite-type to fluorite is 88 GPa (by localized density approximation, LDA) or 115.5 GPa (by generalized gradient approximation, GGA). The Young's modulus and Lamé's coefficients are also studied under high pressure. The structure turned out to be stable for the pressure up to 120 GPa by calculating elastic constants. In addition, the thermodynamic properties, including the Debye temperature, heat capacity, thermal expansion coefficient, Grüneisen parameter, and Poisson's ratio, are investigated. A small band gap is found in the electronic structure of fluorite RuO₂ and the bandwidth increases with the pressure. Also, the present mechanical and electronic properties demonstrate that the bonding nature is a combination of covalent, ionic, and metallic contributions. |
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Yang, Z.J. Guo, A.M. Guo, Y.D. Li, J. Wang, Z. Liu, Q. Linghu, R.F. Yang, X.D. |
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Yang, Z.J. Guo, A.M. Guo, Y.D. Li, J. Wang, Z. Liu, Q. Linghu, R.F. Yang, X.D. Elastic and electronic properties of fluorite RuO₂ from first principle Condensed Matter Physics |
| author_facet |
Yang, Z.J. Guo, A.M. Guo, Y.D. Li, J. Wang, Z. Liu, Q. Linghu, R.F. Yang, X.D. |
| author_sort |
Yang, Z.J. |
| title |
Elastic and electronic properties of fluorite RuO₂ from first principle |
| title_short |
Elastic and electronic properties of fluorite RuO₂ from first principle |
| title_full |
Elastic and electronic properties of fluorite RuO₂ from first principle |
| title_fullStr |
Elastic and electronic properties of fluorite RuO₂ from first principle |
| title_full_unstemmed |
Elastic and electronic properties of fluorite RuO₂ from first principle |
| title_sort |
elastic and electronic properties of fluorite ruo₂ from first principle |
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Інститут фізики конденсованих систем НАН України |
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2012 |
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http://dspace.nbuv.gov.ua/handle/123456789/120153 |
| citation_txt |
Elastic and electronic properties of fluorite RuO₂ from first principle / Z.J. Yang, A.M. Guo, Y.D. Guo, J. Li, Z. Wang, Q. Liu, R.F. Linghu, X.D. Yang // Condensed Matter Physics. — 2012. — Т. 15, № 1. — С. 13603: 1-9. — Бібліогр.: 34 назв. — англ. |
| series |
Condensed Matter Physics |
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2025-07-08T17:20:13Z |
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2025-07-08T17:20:13Z |
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| fulltext |
Condensed Matter Physics, 2012, Vol. 15, No 1, 13603: 1–9
DOI: 10.5488/CMP.15.13603
http://www.icmp.lviv.ua/journal
Elastic and electronic properties of fluorite RuO2
from first principle
Z.J. Yang1∗, A.M. Guo2, Y.D. Guo3, J. Li4, Z. Wang4, Q. Liu5, R.F. Linghu6, X.D. Yang7
1 School of Science, Zhejiang University of Technology, Hangzhou 310023, China
2 Department of Physics, California State University, Northridge, California 91330–8268, USA
3 School of Physics, Neijiang Normal University, Neijiang 641112, China
4 College of Material and Chemical Engineering, Hainan Provincial Key Laboratory of Research on Utilization of
Si-Zr-Ti Resources, Hainan University, Haikou 570228, China
5 School of Physics, Chongqing University of Technology, Chongqing 400050, China
6 School of Physics, Guizhou Normal University, Guiyang 550001, China
7 Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China
Received May 2, 2011, in final form February 1, 2012
The elastic, thermodynamic, and electronic properties of fluorite RuO2 under high pressure are investigated by
plane-wave pseudopotential density functional theory. The optimized lattice parameters, elastic constants, bulk
modulus, and shear modulus are consistent with other theoretical values. The phase transition from modified
fluorite-type to fluorite is 88 GPa (by localized density approximation, LDA) or 115.5 GPa (by generalized gradient
approximation, GGA). The Young’s modulus and Lamé’s coefficients are also studied under high pressure. The
structure turned out to be stable for the pressure up to 120 GPa by calculating elastic constants. In addition,
the thermodynamic properties, including the Debye temperature, heat capacity, thermal expansion coefficient,
Grüneisen parameter, and Poisson’s ratio, are investigated. A small band gap is found in the electronic structure
of fluorite RuO2 and the bandwidth increases with the pressure. Also, the present mechanical and electronic
properties demonstrate that the bonding nature is a combination of covalent, ionic, and metallic contributions.
Key words: first principle, electronic structure, elasticity, thermodynamicity
PACS: 63.20.dk, 71.20.-b, 62.20.D-, 65.40.-b
1. Introduction
Attractions to study RuO2 are due to its fundamental properties and potential superhard character-
istics [1, 2]. An extensive search for new superhard materials has been undertaken during recent years
and a new class of hard materials has been suggested: the transition-metal dioxides containing heavy
elements. Typically, the bulk modulus of modified fluorite (pyrite phase, Pa3̄) RuO2 was found to be
399 GPa [3], which is the highest value except for diamond (442 GPa) [4]. RuO2 has the rutile (P42/mnm)
structure under usual conditions [3], and can be transformed to an orthorhombic (CaCl2-type, Pnnm)
structure at about 6 GPa [5] or 11.8 GPa [6] and to a pyrite structure at about 12 GPa [2, 5]. Moreover, the
theory indicates the Pa3̄ structure can be transformed to a fluorite (Fm3̄m) structure at about 89 GPa or
97 GPa [2].
Recently, elastic properties focusing on Pa3̄ phase of RuO2 have been investigated systematically [2, 7].
Electronic structures [8–11] and optical properties [12–14] of rutile and orthorhombic [14] RuO2 have
been extensively studied. A full-potential linear muffin-tin orbital calculation on the electronic structure
and bulk modulus of fluorite RuO2 has also been performed [15]. The hardness and elasticity in cubic
RuO2 and Raman scattering of the rutile-to-CaCl2 phase transition have been probed experimentally [16].
∗E-mail: yzjscu@163.com, Tel: 86 28 85405526, Fax: 86 28 85405515
© Z.J. Yang, A.M. Guo, Y.D. Guo, J. Li, Z. Wang, Q. Liu, R.F. Linghu, X.D. Yang, 2012 13603-1
http://dx.doi.org/10.5488/CMP.15.13603
http://www.icmp.lviv.ua/journal
Z.J. Yang et al.
Previous investigations on fluorite RuO2 are not complete and some problems remain unresolved.
Many properties, such as the hardness, stabilization, elastic and thermodynamic properties etc under
high pressure, are still unknown. To reveal the superhard characteristics appropriately, a detailed theo-
retical description of the elastic and electronic properties is necessary.
2. Theoretical approaches
In thiswork, all the calculations have been performedwith CASTEP [17, 18]. In the electronic structure
calculations, we have used the non-local ultrasoft pseudopotential [19], together with the revised Perdew-
Burke-Ernzerhof (RPBE) generalized gradient approximation (GGA) exchange-correlation function [20].
Considering the computational cost, a plane-wave basis set with an energy cut-off of 600.0 eV [2] has
been applied, and the 12×12×12Monkhorst-Pack mesh has been used for the Brillouin-zone (BZ) k-point
sampling. Pseudo atomic calculations have been performed for Ru (4s24p64d75s1) and O (2s22p4), where
the self-consistent convergence of the total energy is at 5.0×10−7 eV/atom.
3. Results and discussion
In the equilibrium geometry calculations of fluorite RuO2, both the GGA and the LDA methods have
been used. The bulkmodulus (B0) and its first-order pressure derivative (B
′
0) byMurnaghan [21] equation
of state are listed in table 1.
Table 1. The calculated lattice constants a (Å), phase transition pressure Pt (GPa) and elastic constants
c11, c44, c12 (GPa) by LDA and GGA methods at 0 GPa and 0 K. The bulk modulus B and shear modulus G
are calculated by the elastic constants. The bulk modulus B0 (GPa) and its first-order pressure derivatives
B ′
0
are fitted by the Murnaghan equation of state.
a B0 B ′
0 Pt c11 c44 c12 B G
LDA (present) 4.7349 353 4.13 88 680.26 209.87 175.36 343.66 225.98
GGA (present) 4.8584 287 3.77 115.5 569.09 170.20 117.35 267.93 198.16
(LDA+GGA)/2 4.7967 320 3.95 102 624.68 190.04 146.36 305.79 212.07
[1, 22] 345 65
[2] 4.743 384,351 3.5,4.2 89
[2] 4.842 336,297 3.5,4.1 97 435 152 227 133
[15] 343
[23] 4.842 328 4.2 410.6 62 286.6 62
The LDA/CAPZ (embedded in CASTEP) calculations are performed using the same parameter input with GGA.
Figure 1 suggests that a significant stiffer compressibility of 82.92% is obtained using LDA at 100 GPa
as compared to GGA (80.27%). The volume compressibility (about 80%) is nearly the same as the ultra-
stiff cubic TiO2 at the same pressure [24]. The bulk modulus of the fluorite RuO2 is 353 GPa (LDA) or
287 GPa (GGA), which is slightly smaller than that of the TiO2 (282 GPa÷395 GPa). As the pressure is in-
creased to 100 GPa, the approximation value of the normalized volume of diamond, c-BN, OsO2, and OsC,
is 85%, 83%, 80%, and 84%, respectively [25–27], which is slightly larger than the current calculations. As
a comparison, figure 1 shows the Ru-O bond length contraction with increasing the pressure. Similarly,
a smaller Ru-O bond length contraction is obtained using LDA. In a word, the current Ru-O bond length
contraction, using either LDA or GGA, is much smaller than that in volume contraction.
The calculated elastic constants of fluorite RuO2 under different pressures are listed in table 2. Ac-
cording to the generalized elastic stability criteria [28] (c11 − c12 > 0, c11 + 2c12 > 0, c44 > 0) for cubic
crystals, we can demonstrate that fluorite structure is elastic stable under 120 GPa. The larger c11 and
smaller c12 indicate the inter-atomic bonding along the c-axis stronger than that along the a-axis, consis-
tent with the case of the larger bulk modulus B and the smaller shear modulus G over a wide pressure
13603-2
Elastic and electronic properties of fluorite RuO2 from first principle
Figure 1. Variation of the lattice volume (denoted by square and circle symbols) and the Ru-O bond length
(denoted by triangle symbols) with pressure. They are normalized by X /X0 , where X and X0 are the
lattice volume or Ru-O bond length at any given pressure and zero pressure at zero temperature.
range. Compared to c12 and c44, c11 varies largely by changing the pressure, meaning that it is more
difficult to obtain the same strain from the longitudinal direction than from the transverse direction.
An estimate of the zero-temperature transition pressure between the Pa3̄ and Fm3̄m structures may
be obtained from the usual condition of equal enthalpies, i.e., the pressure P, at which enthalpy H =
E +PV of both phases is the same. Our calculated Pa3̄→Fm3̄m phase transition pressure is 115.5 GPa by
GGA and 88 GPa by LDA, as shown in figure 2, in accordance with the theoretical values of 89 GPa [2] and
97 GPa [2] but is greater than the predicted 65 GPa [1, 22].
Using the calculated elastic constants at 0 K and 0 GPa, we obtain the bulk moduli B of fluorite RuO2,
with the values of 287 GPa (GGA) and 353 GPa (LDA), respectively, which is smaller than that of diamond
(442 GPa [27]), although both of them have comparable compressibility at 100 GPa. The shear constant c44
is 170.20 GPa (GGA), which is consistent with previous theoretical calculations 152 GPa [2], 140 GPa [16],
147 GPa [16], and experimental measurement 144 GPa [16], but is larger than the other theoretical value
62 GPa [23]. In general, the shear modulus of cubic materials is slightly lower than the value of c44 [16],
whereas our calculation indicates the opposite case.
There have been proposals that the shear modulus may be a better index of hardness [29]. Our calcu-
Table 2. The calculated (by GGA method) elastic constants c11 , c44, c12 (GPa), heat capacity CV
(J·mol−1
·K−1), Debye temperature Θ (K), Grüneisen parameter γ, thermal expansion coefficient α
(10−5 K−1) and Poisson’s ratio σ over a wide pressure range at zero temperature.
P V /V0 c11 c44 c12 CV Θ γ α σ
0 1 569.0981 170.2064 117.3517 47.1572 872.0784 0.7086 4.3589 0.2124
10 0.9725 618.5525 182.6494 142.5632 42.9681 905.9000 0.6871 3.5224 0.2247
20 0.9432 672.0389 203.7597 177.3234 37.9710 948.9614 0.6643 2.7310 0.2351
30 0.9719 724.0007 214.6731 213.0271 34.9787 976.2347 0.6447 2.2390 0.2498
40 0.8957 780.0562 227.5737 254.8032 32.0164 1004.6197 0.6276 1.8230 0.2638
50 0.8759 832.5314 239.1418 287.9699 29.2934 1031.9559 0.6124 1.5240 0.2724
60 0.8583 882.1365 250.6513 326.8776 27.0493 1055.4048 0.5989 1.2880 0.2820
70 0.8426 928.6125 258.9245 359.1524 25.1941 1075.4502 0.5870 1.1170 0.2894
80 0.8278 985.5626 273.7571 401.9691 22.7703 1103.0287 0.5757 0.9278 0.2965
90 0.8153 1024.6117 279.8891 438.2222 21.7231 1115.3097 0.5663 0.8321 0.3043
100 0.8027 1066.3426 285.4165 469.7282 20.5262 1129.5911 0.5568 0.7442 0.3102
110 0.7913 1111.9641 294.8567 508.1361 19.1198 1146.9061 0.5482 0.6525 0.3159
120 0.7806 1156.7986 294.2600 540.1705 18.4615 1154.9119 0.5401 0.5986 0.3227
13603-3
Z.J. Yang et al.
lated values of G, 225.98 GPa by LDA and 198.16 GPa by GGA, aremuch greater than the theoretical values
of 133 GPa [2] and 62 GPa [23]. Even so, the current results are still incomparable with those of diamond
and c-BN, e.g., the recently calculated values for diamond are 550 GPa [30], 545 GPa [31], 518 GPa [31],
and 403 GPa for c-BN [30]. However, the current results are comparable to those of OsO2 [31] with val-
ues of 250 GPa (LDA) and 223 GPa (GGA) ([15] suggests OsO2 as a better candidate for a hard material
since their calculations confirmed that the bulk modulus of OsO2, 452 GPa, is only smaller than that of
diamond). Overall, it is reasonable to suggest that the fluorite RuO2 is a potential ultra-incompressible
material, consistent with the suggest superhard material from [2].
Figure 2. Enthalpy as a function of pressures for
the Pa3̄ and Fm3̄m phases of RuO2, (a) is the LDA
results and (b) is GGA ones.
Figure 3. Pressure dependences of mechanical
quantities (by GGA method) under different pres-
sures, X represents Bulk modulus B , Shear mod-
ulus G , Young’s modulus Y , Lamé’s coefficients λ.
In order to better understand the pressure responses of the mechanical behavior, we have studied the
bulk modulus B, shear modulus G, Young’s modulus Y, and Lamé’s coefficients λ by increasing the pres-
sure to 150 GPa. The Young’s modulus Y and Lamé’s coefficients λ are also essential for understanding the
macroscopic mechanical properties of solids and for designing hard materials. Figure 3 shows the most
significant pressure dependence of B and the least significant pressure dependence of G. In contrast to B,
the Lamé’s coefficients λ increase slowly with pressure. Compared to Lamé’s coefficients λ, the Young’s
modulus Y behaves much slower with the increase of pressure. At zero pressure, the relative magnitude
of the four mechanical parameters in descending order is: Y > B > G > λ. However, the Lamé’s coeffi-
cient λ is larger than G above nearly 30 GPa, and the B is larger than Y above nearly 150 GPa. The high Y
and B, particularly at high pressures, also suggest that fluorite RuO2 is a potential ultrahard material.
The value of the Poisson’s ratio for covalent materials is small (σ= 0.1), whereas for ionic materials,
a typical value of σ is 0.25 [32]. In our cases, the value of σ for RuO2 varies from about 0.2124 to 0.3227,
as shown in table 2, indicating a higher ionic and weaker covalent contribution to intra-atomic bonding.
Besides, the typical relation between bulk and shear modulus is, respectively, G ≈ 1.1B and G ≈ 0.6B
for covalent and ionic materials. In our cases, the calculated values of G/B are in the range of 0.7396 at
0 GPa to 0.3656 at 150 GPa, indicating that the ionic bonding is dominant for fluorite RuO2. To evaluate
the material ductility or brittleness, Pugh et al. introduced the B/G ratio [33]: the material is brittle if
the ratio is less than the critical value 1.75. Therefore, fluorite RuO2 is brittle under ambient conditions
since the B/G is only 1.35. However, the brittleness decreases (or ductility increases) when the pressure
is increased and the B/G ratio rises to 2.4 when the pressure is up to 120 GPa.
The dependences of the Debye temperature Θ, heat capacity CV , Grüneisen parameter γ, thermal ex-
pansion coefficient α, and Poisson’s ratio σ on the pressure are calculated. As shown in table 2, when the
temperature keeps constant (T = 0 K),Θ and σ increase with increasing the pressure, whereasCV , γ, and
α decrease. The five thermodynamic parameters show different pressure dependences within the range
of 0÷120 GPa. It is obvious that the thermal expansion coefficient α declines most significantly, corre-
sponding to an 85% compression. The heat capacityCV and Grüneisen parameter γ, however, correspond
to smaller compressions with 60% and 25%, respectively. The other two parameters, Debye temperature
13603-4
Elastic and electronic properties of fluorite RuO2 from first principle
Θ and Poisson’s ratioσ, increase with the pressure with 32% and 52%, respectively. Moreover, all the five
parameters have shown decreased dependences with increasing the pressure, indicating anharmonicity
of the vibration. Therefore, it is necessary to further investigate the electronic energy band structure and
density of states (DOS) to better understand the physical properties. Accordingly, we have made a sys-
tematic investigation of the fluorite RuO2 at different pressures (0, 30, 60, 90 GPa) under 0 K, as shown in
figures 4, 5, and 6.
Figure 4. Energy band structure (by GGA method) along the high symmetry points in the Brillouin zone
at the pressures of 0, 90 GPa is shown in (a) and the band gap Eg as a function with the applied pressures
is shown in (b).
Figure 5. (Color online) Partial density of states (by GGA method) of O and Ru states under P = 0, 30, 60,
90 GPa.
Figure 4 presents the pressure-induced energy level shift towards higher and lower regions. We can
see that the applied pressure has a larger effect on the energy levels far away from the Fermi level than
those in the vicinity of the Fermi level, indicating a stronger effect on the core level than on the valence
level. From the energy band structure, we find that the top of the valence band occurs at W point and
the bottom of the conduction band occurs at L point (slightly lower than X point by a value of 0.02 eV),
implying that there exists an indirect gap with width of 0.5175 eV in fluorite RuO2. The calculated band
gap at zero pressure is consistent with the other theoretical value (0.5 eV) [2], but is much smaller than
those of diamond (4.15 eV) and c-BN (4.49 eV) [34]. Moreover, it is found that the band gap increases
almost linearly with the pressure.
13603-5
Z.J. Yang et al.
Figure 6. (Color online) Total density of states (by GGA method) under P = 0, 30, 60, 90 GPa near the
Fermi level.
In figures 5 and 6, we plot the calculated DOS by GGA, where the Fermi energy is taken to be zero.
From figure 5 (a), the O 2s band center is at −18.5 eV, which is consistent with those in rutile [10, 14] and
CaCl2-type [14] RuO2. The valence band width is about 4 eV, which is much larger than those in rutile [14]
(2.5 eV) and CaCl2-type [14] RuO2 (1.4 eV). In figure 5 (b), the calculated valence band width of O 2p is
about 8 eV, which is slightly larger than that in rutile RuO2 of 5.9 eV (using an extended linear augmented
plane wave potential) and 6.8 eV (using linear-muffin-tin-orbital potential) [10], but the present calcula-
tion is consistent with that in rutile [14] and CaCl2-type [14] RuO2 with the same values of about 8.1 eV.
Furthermore, the calculated conduction band width is 4 eV, which is far smaller than that of valence
conduction.
The Ru s semi-core band, centered at −73.3 eV, displays larger relative intensity (3.6) and smaller
width (1.2 eV) with respect to those in the conduction band with smaller relative intensity (1.9) and larger
width (2.2 eV). The other Ru s electrons distribute mainly in the ranges of −21 eV÷−18 eV, −8.6 eV÷
−1.6 eV, −1.5 eV÷0.5 eV, have formed very weak peak with intensities less than 0.1, and thus could be
ignored as compared with the peak far away from the Fermi level. In figure 5 (d), the Ru p state locates at
−43.5 eV in the valence bandwith width of 1.3 eV and distributes in the energy range of 6.3÷27.5 eV in the
conduction band (corresponding to two sharp peaks centered at around 10 eV and 16 eV, respectively).
The relative intensity of Ru p state in the valence band is far greater than that in conduction band, and
the DOS distributed in the energy range−20÷5 eV is ignored due to their subtle relative intensities (below
0.12). The Ru 4d state, shown in figure 5 (e), is distributed at −18.8 eV and around the Fermi level with
widths of 2.3 eV and 12.0 eV, respectively. Moreover, the relative intensity of the inner valence band is
considerably smaller than that in the outer valence band and in the conduction band.
The four sharp peaks of the total DOS within −7.5÷5 eV originate from the strong hybridization be-
tween Ru 4d and O 2p, as seen in figure 6. The complete overlap of the Ru 4d and O 2p states from −8 eV
to 4 eV indicates a strong covalent interaction between them, whereas the nonzero DOS value at Fermi
level indicates a moderate metallic feature in its bonding state. Although there is a large hybridization
between Ru 4d and O 2p states, the charge transfer from Ru to O is possible in the present case. By ana-
lyzing the Mulliken population results, it is found that the charge transfer from Ru to O is as numerous
as about 1.01 electrons. Therefore, the bonding behavior between Ru-O has ionic contributions owing to
charge transfer. In a word, the bonding behavior between the Ru-O is a combination of covalent, metallic
and ionic contributions.
To emphasize the pressure dependence of the DOS, we have investigated the DOS under different
pressures (30, 60, 90 GPa), as shown in figures 5 and 6. It is clearly seen that the applied pressure causes
the energy levels shifting towards both sides of the Fermi level and thus the energy band is broadened.
Under a higher pressure, the energy level shift is decreased, implying the strong repulsion among the
13603-6
Elastic and electronic properties of fluorite RuO2 from first principle
core electrons. Meanwhile, in general, the relative intensity decreases with increasing the pressure. Ac-
cordingly, the relative shift in the lower energy space is always larger than those in the higher energy
space, implying different bonding strength. The change of the DOS can be attributed to the charge trans-
fer during lattice distortion. With the increase of pressure, a higher overlap of the wavefunction results
in a stronger delocalization of electrons. Electrons transfer from the majority to minority spin band and
form broader bands. The center changes and electrons become more localized when lattice distortion
changes from negative to positive. The majority and minority bands move with respect to the Fermi
level, which affects both the spin polarization ratio and magnetic properties. The current investigations
reveal that the relative intensity of O s and p states decrease with the pressure both in the valence and
conduction bands. However, the relative intensity of Ru s state keeps almost unchanged in the semi-core
band and the main peak in the conduction band has been split into two peaks with the pressure. By
analyzing Ru p state, we find that the relative intensity decreases slightly with the pressure in the whole
valence band and in the higher-energy range from 12.5 eV to 25 eV, but increases with the pressure within
7.5 eV÷12.5 eV. Interestingly, there is observed an increase of the relative intensity of Ru d state with the
pressure in the deeper-lying valence band, whereas the relative intensity of the other Ru d state decreases
with the pressure, presenting opposite variation tendencies. The different intensity variation trends have
unambiguously demonstrated that the applied pressure has induced various charge transfer tendencies.
4. Conclusions
The current investigations revealed that the fluorite RuO2 is a potential ultrahardmaterial. The elastic
stability criteria show that the fluorite RuO2 is elastic stable up to 120 GPa. The calculated Poisson’s ratio
and Debye temperature increase monotonously with the pressure. However, the heat capacity, Grüneisen
parameter, and thermal expansion coefficient decrease with the pressure. An analysis based on Poisson’s
ratio, G/B , and DOS reveals that the bonding nature in RuO2 is a combination of ionic, covalent and
metallic contributions, which contributes to the hardness and fundamental properties. The energy band
investigations found an energy gap between the top of the valence band and the bottom of the conduction
band, and the gap seems to increase monotonously with the pressure. Moreover, the different intensity
variation trends of DOS have unambiguously demonstrated that the applied pressure has caused various
charge transfer tendencies.
Acknowledgements
We are thankful for financial support from the National Natural Science Foundation of China
(Grant Nos: 10974139, 10964002, 11104247) and the Provincial Natural Science Foundation of Guizhou
(Grant Nos: [2009]2066 and TZJF–2008–42), Hainan (Grant No: 110001), Chong Qing (Grant
No: CSTCcstc2011jja90002) and Zhejiang (Grant No: Y201121807).
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Elastic and electronic properties of fluorite RuO2 from first principle
Пружнi та електроннi властивостi флюориту RuO2
з перших принципiв
З.Дж. Янг1, А.M. Гуо2, Й.Д. Гуо3, Дж. Лi4, З. Ванг4, К. Лiу5, Р.Ф. Лiнгха6, X.Д. Янг7
1 Природничий факультет, Технологiчний унiверситет Чжецзяну, 310023 Ханчжоу, КНР
2 Фiзичний факультет, Калiфорнiйський державний унiверситет, Нортрiдж, Калiфорнiя 91330–8268, США
3 Фiзичний факультет, Педагогiчний унiверситет Нейцзяню, Нейцзян 641112, КНР
4 Коледж матерiалознавства i хiмiчної iнженерiї, Xайнанська центральна регiональна дослiдна
лабораторiя з питань утилiзацiї Si-Zr-Ti, Xайнанський унiверситет, Хайкоу 570228, КНР
5 Фiзичний факультет, Чунцинський технологiчний унiверситет, Чунцин 400050, КНР
6 Фiзичний факультет, Педагогiчний унiверситет Гуйчжоу, Гуйян 550001, КНР
7 Iнститут атомної i молекулярної фiзики, Сичуанський унiверситет, Ченду 610065, КНР
Пружнi, термодинамiчнi та електричнi властивостi флюориту RuO2 при високому тиску дослiджуються за
допомогою теорiї функцiоналу густини з плоскохвильовим псевдопотенцiалом. Оптимiзованi параметри
гратки, пружнi сталi, об’ємний модуль i модуль зсуву узгоджуються з iншими теоретичними значеннями.
Фазовий перехiд з модифiкованого флюориту до флюориту є при 88 GPa (наближення локальної густини,
LDA), чи при 115.5 GPa (узагальнене градiєнтне наближення, GGA). Також дослiджено модуль Юнга i коефi-
цiєнти Ламе при високих тисках. Структура є стабiльною для тискiв до 120 GPa, якщо обчислювати пружнi
сталi. Крiм того, дослiджено термодинамiчнi властивостi, включаючи температуру Дебая, теплоємнiсть,
коефiцiєнт теплового розширення, параметр Грюнайзена i коефiцiєнт Пуассона. В електроннiй структурi
флюориту RuO2 знайдено малу зонну щiлину i ширина зони зростає iз тиском. Також, представленi ме-
ханiчнi та електроннi властивостi демонструють, що природа зв’язування є комбiнацiєю ковалентного,
iонного i металiчного вкладiв.
Ключовi слова: першi принципи, електронна структура, пружнiсть, термодинамiчнiсть
13603-9
Introduction
Theoretical approaches
Results and discussion
Conclusions
|