Metastable host–guest structure of carbon
A family of metastable host–guest structures, the prototype of which is a tetragonal tP9 structure with 9 atoms per cell has been found. It is composed of an 8-atoms tetragonal host, with atoms filling channels oriented along the c-axis. The tP9 structure has a strong analogy with the recently disco...
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Zhu, Q. Feya, O.D. Boulfelfel, S.E. Oganov, A.R. 2017-11-14T18:16:57Z 2017-11-14T18:16:57Z 2014 Metastable host–guest structure of carbon / Q. Zhu, O.D. Feya, S.E. Boulfelfel, A.R. Oganov // Сверхтвердые материалы. — 2014. — № 4. — С. 40-52. — Бібліогр.: 49 назв. — англ. 0203-3119 https://nasplib.isofts.kiev.ua/handle/123456789/126119 546.261:539.218 A family of metastable host–guest structures, the prototype of which is a tetragonal tP9 structure with 9 atoms per cell has been found. It is composed of an 8-atoms tetragonal host, with atoms filling channels oriented along the c-axis. The tP9 structure has a strong analogy with the recently discovered Ba-IV- and Rb-IV-type incommensurate structures. By considering modulations of the structure due to the variations of the host/guest ratio, it has been concluded that the most stable representative of this family of structures has a guest/host ratio of 2/3 and 26 atoms in the unit cell (space group P42/m). This structure is 0.39 eV/atom higher in energy than diamond. We predict it to have band gap 4.1 eV, bulk modulus 384 GPa, and hardness 61–71 GPa. Due to the different local environments of the host and guest atoms, we considered the possibility of replacing carbon atoms in the guest sublattice by Si atoms in the tP9 prototype and study the properties of the resulting compound SiC₈, which was found to have similarly remarkably high bulk modulus 361.2 GPa and hardness 46.2 GPa. Повідомляється про сімейство метастабільних структур господаргість, прототипом якого є тетрагональна структура tP9 з дев’ятьма атомами в комірці. Вона складається з восьми атомів тетрагонального господаря, що заповнюють канали, орієнтовані вздовж осі с. Структура tP9 аналогічна недавно відкритим Ba-IV- й Rb-IV-типам несумірних структур. Враховуючи модуляцію структури через варіацій співвідношень господар/гість, зроблено висновок, що найбільш стабільний представник цього сімейства структур має відношення гість/господар – 2/3 і 26 атомів в елементарній комірці (просторова група P42/m). Енергія цієї структури на 0,39 еВ/атом вище, ніж алмазу. Ця структура, за прогнозами, повинна мати заборонену зону – 4,1 еВ, об’ємний модуль – 384 ГПа, а твердість – 61–71 ГПа. Через різні локальні стани атомів господаря і гостя розглянуто можливість заміни атомів вуглецю гостьової підґратки атомами Si в прототипі tP9 і вивчені властивості отриманої сполуки SiC₈, які, як було виявлено, мають вельми високий об’ємний модуль пружності – 361,2 ГПа і твердість 46,2 ГПа. Сообщается о семействе метастабильных структур хозяин–гость, прототипом которого является тетрагональная структура tP9 с девятью атомами в ячейке. Она состоит из восьми атомов тетрагонального хозяина, заполняющих каналы, ориентированные вдоль оси с. Структура tP9 аналогична недавно открытым Ba-IV- и Rb-IV-типам несоразмерных структур. Учитывая модуляцию структуры из-за вариаций отношения хозяин/гость, сделан вывод, что наиболее стабильный представитель этого семейства структур имеет отношение гость/хозяин – 2/3 и 26 атомов в элементарной ячейке (пространственная группа P42/m). Энергия этой структуры на 0,39 эВ/атом выше, чем алмаза. Эта структура, по прогнозам, должна иметь запрещенную зону – 4,1 эВ, модуль объемного сжатия – 384 ГПа, а твердость – 61–71 ГПа. Из-за различных локальных состояний атомов хозяина и гостя рассмотрена возможность замены атомов углерода гостевой подрешетки атомами Si в прототипе tP9 и изучены свойства полученного соединения SiC₈, которое, как было обнаружено, имеет весьма высокий модуль объемного сжатия – 361,2 ГПа и твердость 46,2 ГПа. We thank the National Science Foundation (EAR-1114313, DMR-1231586), DARPA (Grants No. W31P4Q1310005 and No. W31P4Q1210008), and the Government (No. 14.A12.31.0003) and the Ministry of Education and Science of Russian Federation (Project No. 8512) for financial support. en Інститут надтвердих матеріалів ім. В.М. Бакуля НАН України Сверхтвердые материалы Получение, структура, свойства Metastable host–guest structure of carbon Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Metastable host–guest structure of carbon |
| spellingShingle |
Metastable host–guest structure of carbon Zhu, Q. Feya, O.D. Boulfelfel, S.E. Oganov, A.R. Получение, структура, свойства |
| title_short |
Metastable host–guest structure of carbon |
| title_full |
Metastable host–guest structure of carbon |
| title_fullStr |
Metastable host–guest structure of carbon |
| title_full_unstemmed |
Metastable host–guest structure of carbon |
| title_sort |
metastable host–guest structure of carbon |
| author |
Zhu, Q. Feya, O.D. Boulfelfel, S.E. Oganov, A.R. |
| author_facet |
Zhu, Q. Feya, O.D. Boulfelfel, S.E. Oganov, A.R. |
| topic |
Получение, структура, свойства |
| topic_facet |
Получение, структура, свойства |
| publishDate |
2014 |
| language |
English |
| container_title |
Сверхтвердые материалы |
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Інститут надтвердих матеріалів ім. В.М. Бакуля НАН України |
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Article |
| description |
A family of metastable host–guest structures, the prototype of which is a tetragonal tP9 structure with 9 atoms per cell has been found. It is composed of an 8-atoms tetragonal host, with atoms filling channels oriented along the c-axis. The tP9 structure has a strong analogy with the recently discovered Ba-IV- and Rb-IV-type incommensurate structures. By considering modulations of the structure due to the variations of the host/guest ratio, it has been concluded that the most stable representative of this family of structures has a guest/host ratio of 2/3 and 26 atoms in the unit cell (space group P42/m). This structure is 0.39 eV/atom higher in energy than diamond. We predict it to have band gap 4.1 eV, bulk modulus 384 GPa, and hardness 61–71 GPa. Due to the different local environments of the host and guest atoms, we considered the possibility of replacing carbon atoms in the guest sublattice by Si atoms in the tP9 prototype and study the properties of the resulting compound SiC₈, which was found to have similarly remarkably high bulk modulus 361.2 GPa and hardness 46.2 GPa.
Повідомляється про сімейство метастабільних структур господаргість, прототипом якого є тетрагональна структура tP9 з дев’ятьма атомами в комірці. Вона складається з восьми атомів тетрагонального господаря, що заповнюють канали, орієнтовані вздовж осі с. Структура tP9 аналогічна недавно відкритим Ba-IV- й Rb-IV-типам несумірних структур. Враховуючи модуляцію структури через варіацій співвідношень господар/гість, зроблено висновок, що найбільш стабільний представник цього сімейства структур має відношення гість/господар – 2/3 і 26 атомів в елементарній комірці (просторова група P42/m). Енергія цієї структури на 0,39 еВ/атом вище, ніж алмазу. Ця структура, за прогнозами, повинна мати заборонену зону – 4,1 еВ, об’ємний модуль – 384 ГПа, а твердість – 61–71 ГПа. Через різні локальні стани атомів господаря і гостя розглянуто можливість заміни атомів вуглецю гостьової підґратки атомами Si в прототипі tP9 і вивчені властивості отриманої сполуки SiC₈, які, як було виявлено, мають вельми високий об’ємний модуль пружності – 361,2 ГПа і твердість 46,2 ГПа.
Сообщается о семействе метастабильных структур хозяин–гость, прототипом которого является тетрагональная структура tP9 с девятью атомами в ячейке. Она состоит из восьми атомов тетрагонального хозяина, заполняющих каналы, ориентированные вдоль оси с. Структура tP9 аналогична недавно открытым Ba-IV- и Rb-IV-типам несоразмерных структур. Учитывая модуляцию структуры из-за вариаций отношения хозяин/гость, сделан вывод, что наиболее стабильный представитель этого семейства структур имеет отношение гость/хозяин – 2/3 и 26 атомов в элементарной ячейке (пространственная группа P42/m). Энергия этой структуры на 0,39 эВ/атом выше, чем алмаза. Эта структура, по прогнозам, должна иметь запрещенную зону – 4,1 эВ, модуль объемного сжатия – 384 ГПа, а твердость – 61–71 ГПа. Из-за различных локальных состояний атомов хозяина и гостя рассмотрена возможность замены атомов углерода гостевой подрешетки атомами Si в прототипе tP9 и изучены свойства полученного соединения SiC₈, которое, как было обнаружено, имеет весьма высокий модуль объемного сжатия – 361,2 ГПа и твердость 46,2 ГПа.
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0203-3119 |
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https://nasplib.isofts.kiev.ua/handle/123456789/126119 |
| citation_txt |
Metastable host–guest structure of carbon / Q. Zhu, O.D. Feya, S.E. Boulfelfel, A.R. Oganov // Сверхтвердые материалы. — 2014. — № 4. — С. 40-52. — Бібліогр.: 49 назв. — англ. |
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www.ism.kiev.ua/stm 40
UDC 546.261:539.218
Q. Zhu* (Stony Brook, NY, US)
O. D. Feya (Dolgoprudny city, Moscow Region,
Russian Federation)
S. E. Boulfelfel ( Stony Brook, NY, US)
A. R. Oganov** (Stony Brook, NY, US; Dolgoprudny city,
Moscow Region, Russian Federation; Xi’an, P. R. China)
*alecfans@gmail.com
**artem.oganov@sunysb.edu
Metastable host–guest structure of carbon
A family of metastable host–guest structures, the prototype of which
is a tetragonal tP9 structure with 9 atoms per cell has been found. It is composed of an
8-atoms tetragonal host, with atoms filling channels oriented along the c-axis. The tP9
structure has a strong analogy with the recently discovered Ba-IV- and Rb-IV-type
incommensurate structures. By considering modulations of the structure due to the
variations of the host/guest ratio, it has been concluded that the most stable
representative of this family of structures has a guest/host ratio of 2/3 and 26 atoms in
the unit cell (space group P42/m). This structure is 0.39 eV/atom higher in energy than
diamond. We predict it to have band gap 4.1 eV, bulk modulus 384 GPa, and hardness
61–71 GPa. Due to the different local environments of the host and guest atoms, we
considered the possibility of replacing carbon atoms in the guest sublattice by Si atoms
in the tP9 prototype and study the properties of the resulting compound SiC8, which
was found to have similarly remarkably high bulk modulus 361.2 GPa and hardness
46.2 GPa.
Keywords: density functional theory, evolutionary algorithm,
incommensurate crystal, silicon carbide.
INTRODUCTION
Carbon is a unique element in the sense that it adopts a wide range
of structures, from superhard insulators (diamond and lonsdaleite) to ultrasoft
semimetals (graphite, an excellent lubricant) and even superconductors
(intercalated graphite and fullerenes, doped diamond) [1–5]. Among the solid
phases, only graphite, diamond and bc8 phase (predicted to be stable at pressures
above 1 TPa) have stability fields on the phase diagram. However, the number of
all possible metastable phases is in principle infinite, and due to directional
covalent bonding, many metastable carbon phases are known, and have extremely
long (technically indefinite) lifetimes. Much work both in experiment and theory
has been done to search for novel carbon phases with special properties (such as
metallic conductivity, hardness, etc.) [6–17]. Until now, it has not been imagined
that carbon could also adopt a host–guest structure.
The nature of host–guest structures of compressed metals is still somewhat puz-
zling, given their ubiquity and complex and relatively open topologies [18]. Since
Ba-IV was first solved experimentally [19, 20], a series of complex phases with
composite host–guest structures were found for alkali, alkali earth, group 15 and 16
© Q. ZHU, O. D. FEYA, S. E. BOULFELFEL, A. R. OGANOV, 2014
ISSN 0203-3119. Сверхтвердые материалы, 2014, № 4 41
elements (e.g., [21–29]). Recently, aluminum was also predicted to adopt a similar
host–guest type structure at extremely high pressure (about 1 TPa) [30]. To the best
of our knowledge, group 14 elements have not been reported to have host–guest
structures. However, our structure searches uncovered such structures as
metastable states. Although metastable, rather than thermodynamically stable,
these are of great interest for the understanding of carbon polymorphism and of the
nature of host–guest structures. The newly found structures provide an interesting
way of constructing a host–guest network, suitable for low-coordinate atoms and
alternative to the known Ba-IV and Rb-IV host–guest structure types.
COMPUTATIONAL METHODS
Evolutionary structure searches were performed using the USPEX code [31–33]
in conjunction with ab initio structure relaxations using density functional theory
(DFT) [34, 35] within the Perdew-Burke-Ernzerhof (PBE) generalized gradient
approximation (GGA) [36], and the all-electron projector-augmented wave [37, 38]
(PAW) method, as implemented in the VASP code [39]. We used a PAW potential
with [1s2] core, plane wave kinetic energy cutoff of 600 eV, and Brillouin zone
sample with reciprocal space resolution of 2π×0.05 Å–1, which ensured excellent
convergence of total energies, stresses, and energy differences. These calculations
correctly yielded the ground states – graphite at normal conditions, diamond at
high pressures, and bc8 at ultrahigh pressures above 1 TPa [31].
To ensure that the obtained structures are dynamically stable, we calculated
phonon frequencies across the Brillouin zone using the frozen-phonon method as
implemented in the PHONOPY code [40]. For obtaining the electronic density of
states (DOS) of the 9-atom tP9 and SiC8 structures we used 5×5×8 grid for self-
consistent calculations, followed by a non-self-consistent calculation with a
10×10×16 k-points grid, and same-resolution grids for the 26-atom modulated
structure. Band structures were calculated using the hybrid functional HSE06 [41].
Bader analysis [42] was performed using the code [43]. We estimated hardnesses
using the Lyakhov-Oganov approach [16] and the Chen-Niu model [44]; for the
latter, bulk and shear moduli are required – these were computed within the Voigt-
Reuss-Hill averaging scheme [45–47] of the elastic constants computed by finite
strain method.
RESULTS
Host–guest structure of pure carbon
We have performed structure searches at 0, 5, 10 GPa with 3, 4, 6, 9, 12 atoms
per unit cell, respectively. Apart from the already known structures (diamond,
lonsdaleite, bc8, M-carbon, bct4, etc.), our simulations also found a tetragonal
host–guest structure. This composite structure is shown in Fig. 1, a, and consists of
a host sublattice (8 atoms in the unit cell with lattice parameters a = b = 4.560 Å
and c = 2.556 Å). The symmetry of the host sublattice is P42/m; there are two 4j
Wyckoff sites – Ch1(0.288, 0.781, 0.223) and Ch2(0.839, 0.531, 0.266). The guest
atoms occupy the sites Cg(0, 0, 0) and there is only 1 guest atom in the unit cell.
The space group of the whole host–guest structure is lowered to P4. This structure
has strong analogy with well-known Ba-IV and Rb-IV host–guest structure as
shown in Fig. 1, c, 1d. The main difference is that carbon prefers low coordination
numbers (in this structure, C atoms are in a distorted fourfold coordination), while
the average coordination number of host and guest atoms is typically 8–10 in Ba-
IV or Rb-IV type structures. tP9 is a low-coordinate host–guest structure.
www.ism.kiev.ua/stm 42
a
b
c
d
Fig. 1. Crystal structure of tP9-carbon in two projections (a, b); also shown are Ba-IV (c) and
Rb-IV (d) structures.
Bond lengths within the host sublattice vary between 1.53–1.57 Å, while the
shortest host–guest bond is 1.74 Å. Bond angles within the host sublattice are
107°90′ and 119°01′; guest-host bonds form angles 105°73′ and 124°91′. These
values are close to the ideal angles of 109°28′ and 120° for sp3- and sp2-
hybridizations.
To compute the hardness of tP9, we used the Lyakhov-Oganov [16] and Chen-
Niu [44] models – the results of these completely independent models being very
similar, 70.4 and 72.8 GPa, respectively. The bulk modulus is remarkably high,
388 GPa (for comparison, the bulk modulus of diamond computed at the same
level of theory is 431 GPa [15]). Its density is 3.37 g/cm3.
We have calculated the enthalpies of the host–guest structure and some other
well-known and hypothetical structures as a function of pressure (Fig. 2). Our
host–guest structure is 0.55 eV/atom higher in energy than diamond at P = 0, but
more energetically favorable than the predicted superdense allotropes [15]. At the
same time, it is dynamically stable (i.e. there are no imaginary phonon frequencies,
Fig. 3) and, once synthesized, may exist as a metastable phase. The electronic band
structure of tP9 is shown in Fig. 4. According to the HSE06 hybrid functional
(known to rather accurately estimate the band gaps of carbon allotropes), it is a
semiconductor with an indirect band gap of 3 eV at zero pressure.
The geometric difference between host and guest sublattices invites the
question of possible charge transfer (as found in γ-boron [48]). We performed
Bader analysis of the total charge density of tP9-carbon and results are presented in
Table 1. As one can see, although different carbon sites have very different local
ISSN 0203-3119. Сверхтвердые материалы, 2014, № 4 43
environments and there is a large variation of Bader volumes, charge transfer is
quite modest in this structure, and Bader charges are rather small.
0 20 40 60 80 100
Pressure, GPa
1.5
0
1.0
0.5
–1.0
E
nt
h
al
py
, r
el
at
iv
e
to
g
ra
ph
it
e,
e
V
/a
to
m
–0.5
Fig. 2. Enthalpies of various carbon structures, relative to graphite: diamond (+), lonsdaleite (×),
M-carbon ( ), bct-4 (□), tP9 (■), tP12 (○), chiral (●), hP3 (∆), tl12 (▲), graphite (�).
Γ Z M Γ A Γ X
Wavevector
15
0
10
5
F
re
qu
en
cy
, T
H
z 25
20
35
30
40
Fig. 3. Phonon dispersion curves of tP9-carbon. The absence of imaginary frequencies demon-
strates dynamical stability.
In the next section we explore an additional degree of freedom that host–guest
structures have, namely the host/guest periodicity ratio. This allows us to obtain a
more stable host–guest structure and explore its properties.
www.ism.kiev.ua/stm 44
Γ X M A Γ Z
Wavevector
–10
0
–5
5
E
n
er
gy
, e
V
10
a
–26 –22 –18 –14 –10 –6 –2 2 6 10 14
Energy, eV
0
0.5D
en
si
ty
o
f s
ta
te
s,
s
ta
te
s/
eV
⋅u
n
it
c
el
l
1.0
1.5
2.0
2.5
3.0
b
Fig. 4. Density of states (a) and band structure (b) of tP9-carbon at 0 GPa, computed with the
HSE06 hybrid functional.
Table 1. Bader charges and volumes in tP9 carbon. Space group P 4 ,
lattice parameters a = b = 4.560 Å and c = 2.556 Å
Position x y z Bader charge
Bader volume,
Å3
Cg 0.0000 0.0000 0.0000 –0.0580 6.8912
Ch1 0.2881 0.7804 0.2232 –0.0275 5.9987
Ch2 0.8394 0.5307 0.2662 +0.0423 5.4811
ISSN 0203-3119. Сверхтвердые материалы, 2014, № 4 45
Optimization of the host–guest ratio – exploring possible incommensurability
Since most host–guest structures of metals are found to be incommensurate, we
decided to explore this possibility here. To this end, we used the method of Arapan
et al. [22] and performed calculations for a set of commensurate approximants with
different Cg/Ch ratios (Cg and Ch are the numbers of guest and host cells in an
approximant supercell, respectively). Because the total energy is a continuous
function of structural parameters, after interpolating the energy as a function of
Cg/Ch, one can obtain the minimum energy and the Cg/Ch ratio corresponding to it.
If Cg/Ch is an irrational number, this would indicate an incommensurate
modulation of the structure. Fig. 5 and Fig. 6 show the calculated energies and
enthalpies of various commensurate structures; on can see that the commensurate
structure with the Cg/Ch = 2/3, containing 26 atoms in the unit cell, is energetically
optimal. Parameters of this structure are given in Table 2.
0 2 4 6 8 10
Pressure, GPa
–8.8
E
n
th
al
py
,
eV
/a
to
m
–8.6
–8.4
–8.2
–8.0
–7.8
Fig. 5. Enthalpies of various commensurate analogues as a function of pressure: 1*1 (+), 1*2 (×),
2*3 ( ), 3*4 (□), 3*5 (■), 4*5 (○), 9*10 (●).
0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25
c1/c2 ratio
–8.8
E
nt
h
al
py
, e
V
/a
to
m
–8.6
–8.4
–8.2
–8.0
–7.8
Fig. 6. Total energies of various commensurate structures. Outside the range c1/c2 ∈ [0.5, 1.5]
the structure spontaneously changes into very different topologies.
www.ism.kiev.ua/stm 46
Table 2. Bader charges and volumes in the 2/3 modulated structure.
Space group P42/m, lattice parameters a = b = 4.600 Å, c = 7.499 Å
Position x y z Bader charge
Bader volume,
Å3
Cg-2a 0.0000 0.0000 0.0000 –0.0669 7.5665
Ch1-8k 0.2672 0.8027 0.0721 +0.0337 6.1236
Ch2-8k 0.8319 0.5138 0.0892 –0.0126 5.9542
Ch3-8k 0.6413 0.6073 0.2500 –0.0044 5.9274
The new 2/3 structure is more stable than tP9-carbon by 0.16 eV/atom. It is also
dynamically stable, as we can see in Fig. 7. Its lattice parameters are slightly
different from those of tP9-carbon: a = b = 4.600 Å, but c = 7.499 Å,
approximately three times the value of the c-parameter of the 1/1 structure.
Γ Z M Γ A Γ X
Wavevector
0
5
F
re
qu
en
cy
,
T
H
z
10
15
20
25
30
35
40
Fig. 7. Phonon dispersion curves of the 2/3 commensurate modulation of tP9C carbon.
The band structure of the 2/3-structure is shown in Fig. 8, and electronic densi-
ties of states computed with PBE and HSE06 are shown in Fig. 9. The computed
HSE06 band gap is 4.1 eV (much higher than 3.0 eV computed for the tP9
structure). Its hardness is computed to be 60.6 GPa using model [16] and 70.6 with
model [42], the computed bulk modulus is 383.6 GPa. The density of this phase of
carbon is 3.25 g/cm3.
SiC8 compound
We have investigated the possibility of replacing one of the sublattices with
another element. When we replaced the guest carbon atom by a larger silicon
atom, the structure remained dynamically stable (Fig. 10). Just like the host, the
guest atoms are 4-coordinate with a noticeably larger bond lengths of 1.70 Å (the
normal single C–C bond length is 1.54 Å). Thus, it is natural to place a large atom,
such as Si, in the guest sublattice, and we did it for the parent 1/1 structure. The
ISSN 0203-3119. Сверхтвердые материалы, 2014, № 4 47
structure has space group P 4 , with two independent 4h Wyckoff positions
occupied in the host sublattice by C atoms, with coordinates (0.694, 0.232, 0.241)
and (0.165, 0.477, 0.257), and the Si atom in the guest sublattice occupies the 1a
site at (0, 0, 0); the lattice parameters are a = b = 4.830 Å and c = 2.522 Å. SiC8 is
found to have interesting physical properties. Its bulk modulus is 361.2 GPa; the
hardness computed with model [16] is 46.2 GPa, i.e. the material is superhard. The
HSE06 [41] band gap is 1.8 eV. This result is interesting for absorption of solar
light – with possible applications in photocatalysis. Density of states, calculated at
different pressures using the HSE06 functional, is shown in Fig. 11. We can see
that the band gap slightly increases with pressure – opposite to the normal
tendency, but similar to diamond [49]. The density of SiC8 is 3.49 g/cm3.
Γ X M A Γ Z
Wavevector
–10
0
–5
5
E
ne
rg
y,
e
V
10
Fig. 8. HSE06 band structure of the 2/3 modulated variant of the tP9 structure.
It is interesting to compare energy of the isochemical mixture of diamond-like
Si (the ground state of Si) and diamond C with the energy of our SiC8 structure.
We find that SiC8 is 0.27 eV/atom less stable than the isochemical mixture of dia-
mond-structured Si and C. The enthalpy of formation from true ground states of the
elements, diamond-like Si and C-graphite, is 0.38 eV/atom.
In the Si–C system, there is a stable phase SiC. We have explored the enthalpy
of formation of SiC8 from a mixture SiC + 7C(graphite), and the resulting value is
0.44 eV/atom.
Results of Bader analysis are shown in Table 3. One can see a large positive
charge on the Si atom.
Table 3. Bader charges and in the hypothetical compound SiC8. Space
group P 4 , lattice parameters a = b = 4.830 Å and c = 2.522 Å
Position x y z Bader charge Bader volume, Å3
Si 0.0000 0.0000 0.0000 +2.3008 5.4078
Ch1 0.6944 0.2326 0.2417 –0.5854 7.5396
Ch2 0.1640 0.4769 0.2575 +0.0102 5.8274
www.ism.kiev.ua/stm 48
–22 –18 –14 –10 –6 –2 2 6 10
Energy, eV
0
2
D
en
si
ty
o
f s
ta
te
s,
s
ta
te
s/
eV
⋅u
n
it
c
el
l
4
6
8
10
12
14
a
–24 –20 –16 –12 –8 –4 0 4 8 12
Energy, eV
0
1
D
en
si
ty
o
f s
ta
te
s,
s
ta
te
s/
eV
⋅u
n
it
c
el
l
2
3
4
5
6
7
8
b
Fig. 9. Electronic density of states of the 2/3 structure computed using PBE (a) and HSE06 (b)
functionals.
CONCLUSIONS
We report a novel family of metastable host–guest structures of carbon, the
simplest prototype of which is the tetragonal tP9 structure with 9 atoms in the unit
cell. This structure consists of host (8 atoms/cell) and guest (1 atom/cell)
sublattices, the guest forming 1D-chains running along the channels of the host
structure. It shares similarities with well-known Ba-IV and Rb-IV host–guest
structures, which become stable at elevated pressures [22], and exemplifies an
extension of such structures to low-coordinate topologies. Theoretical calculations
showed that it is a semiconductor with a band gap of 3.0 eV at 0 GPa and hardness
ISSN 0203-3119. Сверхтвердые материалы, 2014, № 4 49
70–73 GPa. This structure is 0.55 eV/atom less stable than diamond at atmospheric
pressure.
Γ Z M Γ A Γ X
Wavevector
0
5
F
re
qu
en
cy
,
T
H
z
10
15
20
25
30
35
Fig. 10. Phonon dispersion curves of SiC8.
–26 –22 –18 –14 –10 –6 –2 2 6 10
Energy, eV
0
0.5
D
en
si
ty
o
f s
ta
te
s,
s
ta
te
s/
eV
⋅u
ni
t
ce
ll
1.0
1.5
2.0
2.5
0
0.5
1.0
1.5
2.0
2.5
0
0.5
1.0
1.5
2.0
2.5
0 GPa
5 GPa
100 GPa
Fig. 11. The density of states for host–guest SiC8 compound at 0, 5, 100 GPa computed using the
HSE06 hybrid functional.
www.ism.kiev.ua/stm 50
Looking at a series of modulations of this host–guest structure, it have been
found that the 2/3 modulation gives the lowest energy, lowering the energy by
0.16 eV/atom. This optimal host–guest structure contains 26 atoms in the unit cell
and is 0.52 eV/atom less stable than graphite, and 0.39 eV/atom less stable than
diamond. Its hardness is 61–71 GPa, and its band gap is 4.1 eV.
By replacing carbon atoms in the guest sublattice with Si atoms, a hypothetical
SiC8 compound has been obtained, which is 0.27 eV/atom higher in energy than
the isochemical mixture of C-diamond and diamond-type Si. This material is pre-
dicted to have interesting properties – hardness of 46 GPa and band gap of 1.8 eV.
These results show that host–guest structures may appear, at least as metastable
phases, not only in metals, but also in non-metallic elements, and may have
interesting properties. Such phases, or substitution compounds based on them, may
be synthesizable.
ACKNOWLEDGEMENTS
We thank the National Science Foundation (EAR-1114313, DMR-1231586),
DARPA (Grants No. W31P4Q1310005 and No. W31P4Q1210008), and the
Government (No. 14.A12.31.0003) and the Ministry of Education and Science of
Russian Federation (Project No. 8512) for financial support.
Повідомляється про сімейство метастабільних структур господар–
гість, прототипом якого є тетрагональна структура tP9 з дев’ятьма атомами в
комірці. Вона складається з восьми атомів тетрагонального господаря, що заповнюють
канали, орієнтовані вздовж осі с. Структура tP9 аналогічна недавно відкритим Ba-IV- й
Rb-IV-типам несумірних структур. Враховуючи модуляцію структури через варіацій
співвідношень господар/гість, зроблено висновок, що найбільш стабільний представник
цього сімейства структур має відношення гість/господар – 2/3 і 26 атомів в
елементарній комірці (просторова група P42/m). Енергія цієї структури на 0,39 еВ/атом
вище, ніж алмазу. Ця структура, за прогнозами, повинна мати заборонену зону – 4,1 еВ,
об’ємний модуль – 384 ГПа, а твердість – 61–71 ГПа. Через різні локальні стани атомів
господаря і гостя розглянуто можливість заміни атомів вуглецю гостьової підґратки
атомами Si в прототипі tP9 і вивчені властивості отриманої сполуки SiC8, які, як було
виявлено, мають вельми високий об’ємний модуль пружності – 361,2 ГПа і твердість
46,2 ГПа.
Ключові слова: теорія функціонала щільності, еволюційний алгоритм,
несумірний кристал, карбід кремнію.
Сообщается о семействе метастабильных структур хозяин–гость,
прототипом которого является тетрагональная структура tP9 с девятью атомами в
ячейке. Она состоит из восьми атомов тетрагонального хозяина, заполняющих каналы,
ориентированные вдоль оси с. Структура tP9 аналогична недавно открытым Ba-IV- и Rb-
IV-типам несоразмерных структур. Учитывая модуляцию структуры из-за вариаций
отношения хозяин/гость, сделан вывод, что наиболее стабильный представитель этого
семейства структур имеет отношение гость/хозяин – 2/3 и 26 атомов в элементарной
ячейке (пространственная группа P42/m). Энергия этой структуры на 0,39 эВ/атом вы-
ше, чем алмаза. Эта структура, по прогнозам, должна иметь запрещенную зону – 4,1 эВ,
модуль объемного сжатия – 384 ГПа, а твердость – 61–71 ГПа. Из-за различных локаль-
ных состояний атомов хозяина и гостя рассмотрена возможность замены атомов угле-
рода гостевой подрешетки атомами Si в прототипе tP9 и изучены свойства полученного
соединения SiC8, которое, как было обнаружено, имеет весьма высокий модуль объемного
сжатия – 361,2 ГПа и твердость 46,2 ГПа.
Ключевые слова: теория функционала плотности, эволюционный алго-
ритм, несоразмерной кристалл, карбид кремния.
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Department of Geosciences, Received 15.03.14
State University of New York
Center for Materials by Design,
Institute for Advanced Computational Science,
State University of New York
Moscow Institute of Physics and Technology
Northwestern Polytechnical University, Xi’an, P. R. China
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/KOR <FEFFc7740020c124c815c7440020c0acc6a9d558c5ec0020b370c2a4d06cd0d10020d504b9b0d1300020bc0f0020ad50c815ae30c5d0c11c0020ace0d488c9c8b85c0020c778c1c4d560002000410064006f0062006500200050004400460020bb38c11cb97c0020c791c131d569b2c8b2e4002e0020c774b807ac8c0020c791c131b41c00200050004400460020bb38c11cb2940020004100630072006f0062006100740020bc0f002000410064006f00620065002000520065006100640065007200200035002e00300020c774c0c1c5d0c11c0020c5f40020c2180020c788c2b5b2c8b2e4002e>
/NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken voor kwaliteitsafdrukken op desktopprinters en proofers. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.)
/NOR <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>
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/SVE <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>
/ENU (Use these settings to create Adobe PDF documents for quality printing on desktop printers and proofers. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
/RUS ()
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
/FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
(Adobe)
(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /NoConversion
/DestinationProfileName ()
/DestinationProfileSelector /NA
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure true
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles true
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /NA
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /LeaveUntagged
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|