Interaction between Electron and Phonon Subsystems in Hafnium Diboride
Ab initio розрахунок функцій електрон-фононного зв’язку виконано за методом ЛМТО з використанням повного потенціалу. Низьке значення усередненої константи електрон-фононної взаємодії для HfB₂ λ=0,17 свідчить, що немає підстав для виникнення надпровідного стану в цій сполуці. Вперше було розраховано...
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Інститут металофізики ім. Г.В. Курдюмова НАН України
2014
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| citation_txt | Interaction between Electron and Phonon Subsystems in Hafnium Diboride / S.M. Sichkar // Металлофизика и новейшие технологии. — 2014. — Т. 36, № 3. — С. 419-429. — Бібліогр.: 26 назв. — англ. |
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| description | Ab initio розрахунок функцій електрон-фононного зв’язку виконано за методом ЛМТО з використанням повного потенціалу. Низьке значення усередненої константи електрон-фононної взаємодії для HfB₂ λ=0,17 свідчить, що немає підстав для виникнення надпровідного стану в цій сполуці. Вперше було розраховано електричний опір і коефіцієнт анізотропії ρz/ρx=1,079 (Т=300 К) для дибориду гафнію. Було досягнуто добру узгодженість з експериментальними даними для електричного опору. У роботі виконано порівняльний аналіз результатів розрахунків фононних спектрів методами ABINIT, SIESTA, VASP та запропонованим методом ЛМТО з детальним обговоренням одержаних відмінностей.
Ab initio расчёт функций электрон-фононной связи выполнен в рамках метода ЛМТО с использованием полного потенциала. Низкое значение усреднённой константы электрон-фононного взаимодействия для HfB₂ λ=0,17 свидетельствует, что нет оснований для возникновения сверхпроводящего состояния в этом соединении. Впервые были рассчитаны электрическое сопротивление и коэффициент анизотропии ρz/ρx=1,079 (T=300 К) для диборида гафния. Было достигнуто хорошее согласие с экспериментальными данными для электрического сопротивления. В работе выполнен сравнительный анализ результатов расчётов фононных спектров методами ABINIT, Siesta, VASP и предложенным методом ЛМТО с детальным обсуждением полученных различий
Ab initio calculation of the electron—phonon coupling functions is carried out, using full potential LMTO method. Low value of the averaged electron— phonon interaction constant for HfB₂ λ=0.17 indicates that there is no evidence of superconductivity in this compound. Electrical resistivity and anisotropy factor ρz/ρx=1.079 (T=300 K) are theoretically calculated. A good agreement with experimental data of electrical resistivity is achieved. Comparative analysis of ABINIT, SIESTA, VASP, and present LMTO method for phonon spectra calculating is performed.
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419
ЭЛЕКТРОННЫЕ СТРУКТУРА И СВОЙСТВА
PACS numbers: 63.20.dk, 71.15.-m, 71.15.Mb, 71.38.-k, 72.10.Di, 72.15.Eb
Interaction between Electron and Phonon Subsystems
in Hafnium Diboride
S. M. Sichkar
G. V. Kurdyumov Institute for Metal Physics, N.A.S. of Ukraine,
36 Academician Vernadsky Blvd.,
UA-03680 Kyyiv-142, Ukraine
Ab initio calculation of the electron—phonon coupling functions is carried
out, using full potential LMTO method. Low value of the averaged electron—
phonon interaction constant for HfB2 0.17 indicates that there is no evi-
dence of superconductivity in this compound. Electrical resistivity and ani-
sotropy factor z/x 1.079 (T 300 K) are theoretically calculated. A good
agreement with experimental data of electrical resistivity is achieved. Com-
parative analysis of ABINIT, SIESTA, VASP, and present LMTO method for
phonon spectra calculating is performed.
Ab initio розрахунок функцій електрон-фононного зв’язку виконано за
методом ЛМТО з використанням повного потенціалу. Низьке значення
усередненої константи електрон-фононної взаємодії для HfB2 0,17 сві-
дчить, що немає підстав для виникнення надпровідного стану в цій спо-
луці. Вперше було розраховано електричний опір і коефіцієнт анізотропії
z/x 1,079 (Т 300 К) для дибориду гафнію. Було досягнуто добру узго-
дженість з експериментальними даними для електричного опору. У робо-
ті виконано порівняльний аналіз результатів розрахунків фононних спе-
ктрів методами ABINIT, SIESTA, VASP та запропонованим методом
ЛМТО з детальним обговоренням одержаних відмінностей.
Ab initio расчёт функций электрон-фононной связи выполнен в рамках
метода ЛМТО с использованием полного потенциала. Низкое значение
усреднённой константы электрон-фононного взаимодействия для HfB2
0,17 свидетельствует, что нет оснований для возникновения сверхпро-
водящего состояния в этом соединении. Впервые были рассчитаны элек-
трическое сопротивление и коэффициент анизотропии z/x 1,079
(Т 300 К) для диборида гафния. Было достигнуто хорошее согласие с
экспериментальными данными для электрического сопротивления. В ра-
боте выполнен сравнительный анализ результатов расчётов фононных
спектров методами ABINIT, Siesta, VASP и предложенным методом
ЛМТО с детальным обсуждением полученных различий.
Металлофиз. новейшие технол. / Metallofiz. Noveishie Tekhnol.
2014, т. 36, № 3, сс. 419—429
Оттиски доступны непосредственно от издателя
Фотокопирование разрешено только
в соответствии с лицензией
2014 ИМФ (Институт металлофизики
им. Г. В. Курдюмова НАН Украины)
Напечатано в Украине.
420 S. M. SICHKAR
Key words: lattice dynamics, electron—phonon interaction, phonon spectrum,
thermodynamic properties, electrical resistivity, diborides.
(Received 18 November, 2013)
1. INTRODUCTION
With its high thermodynamic stability, hardness, conductivity, corro-
sion resistance, and significant melting point, ceramics based on tran-
sition metal borides is attractive material for practical application in
various fields of engineering, metallurgy, instrumentation, chemical
industry, etc. Hafnium boride (melting point 3250C, microhardness
29 5 GPa) is used as an extremely wear-resistant coating and for
production of superhard alloys. In addition, HfB2 is one of the most
refractory compounds and is used for the production of rocket jets and
some structural elements of gaseous nuclear rocket engines.
The opening of a critical transition Tc 40 K in MgB2 [1] and crea-
tion of new superconducting materials based on it (in the form of films,
ceramics, long wires and tapes) stimulated the development of work on
a detailed study of superconductivity in other diborides. Unfortunate-
ly, according to Ref. [2], no superconducting transition down to 0.42 K
has been observed in powders of diborides of transition metals (M) MB2
(M Ti, Zr, V, Ta, Cr, Mo, U). Only NbB2 is expected to be a supercon-
ductor with a rather low transition temperature ( 1 K). On the other
hand, two experimental results (superconductivity up to Tc 9.5 K in
TaB2 according to Ref. [2] and Tc 7 K in ZrB2 [3]) hold out hope to find
superconducting materials based on metal diborides.
Presently, a number of experimental studies exists dealing with the
physical properties of HfB2, such as thermal and electrical properties
[4—7], mechanical [8], and elastic properties [9].
Lawson et al. [10] studies the electronic structure and lattice proper-
ties of HfB2 in a frame of the density functional theory (DFT). Lattice
constants and elastic constants are determined. Computations of the
electronic density of states, band structure, electron localization func-
tion, etc., show the diverse bonding types that exist in these materials.
They also suggest the connection between the electronic structure and
the superior mechanical properties. Lattice dynamical effects are con-
sidered, including phonon dispersions, vibrational densities of states,
and specific heat curves. The bonding nature, elastic property and
hardness are investigated by Zhang et al. [11] for HfB2 using the first
principles total-energy plane-wave pseudopotential (PW—PP) method.
They also reported the elastic anisotropy, Poisson ratio, hardness, and
Debye temperature in HfB2. Deligoz et al. [12] investigate the struc-
tural parameters (the lattice constants and bond length) and phonon
dispersion relations in HfB2 and TaB2 compounds using the first-
INTERACTION BETWEEN ELECTRON AND PHONON SUBSYSTEMS 421
principles total energy calculations. Zhang et al. [13] investigated the
ideal tensile and shear strengths of TiB2, ZrB2, and HfB2 by first-
principles stress-strain calculations. Due to the nonlinearity of the
stress response at large strains, the plastic anisotropy cannot be de-
rived from elastic constants. Based on the relative stiffness of boron
hexagons, a bond length indicator is obtained to characterize the pref-
erence for basal or prismatic slip in diborides.
Authors of Ref. [4] determined the thermal conductivity, thermal
expansion, Young’s modulus, flexural strength, and brittle-plastic de-
formation transition temperature for HfB2 as well as for HfC0.98,
HfC0.76, and HfN0.92 ceramics. The thermal conductivity of HfB2 ex-
ceeds that of the other materials by a factor of 5 at room temperature
and by a factor of 2.5 at 820C. Pure HfB2 has a strength of 340 MPa in
4 point bending, which is constant from room temperature to 1600C,
while a HfB2 10% HfCx has a higher room temperature bend strength
of 440 MPa, but it drops to 200 MPa at 1600C. The results of the theo-
retical modelling suggest that HfB2 should survive the high thermal
stresses generated during the nozzle test primarily because of its supe-
rior thermal conductivity. Yang et al. [14] used in situ spectroscopic
ellipsometry to analyse HfB2 thin films. Modelling the film optical
constants with a Drude—Lorentz model, the film thickness, surface
roughness, and electrical resistivity are measured. Modelling the real-
time data in terms of film thickness and surface roughness, the film
nucleation and growth morphology are determined as a function of
substrate type, substrate temperature, and precursor pressure. Zhang
et al. [6] experimentally investigated the thermal and electrical
transport properties of various spark plasma-sintered HfB2 based pol-
ycrystalline ceramics over the 298—700 K temperature range. Meas-
urements of thermal diffusivity, electrical resistivity, and Hall coeffi-
cient are reported, as well as the derived properties of thermal conduc-
tivity, charge carrier density, and charge carrier mobility. The ther-
mal conductivity decreases with increasing temperature.
Despite a lot of publications, there are still many open questions re-
lated to the physical properties of HfB2 diboride. In recent years, the
most theoretical efforts were devoted to the lattice and mechanical
properties of HfB2. However, up to now there is no theoretical explana-
tion of the electron—phonon interaction and anisotropy of the electri-
cal resistivity in HfB2. The aim of a given work is a complex investiga-
tion of the phonon spectra, Eliashberg electron—phonon and transport
spectral functions, temperature dependence, and anisotropy of electri-
cal resistivity of the HfB2 diboride. The paper is organized as follows.
Section 2 presents the details of the calculations. Section 3 is devoted
to the phonon spectra, electron—phonon interaction, and electrical re-
sistivity in HfB2. The results are compared with available experi-
mental data. Finally, the results are summarized in Sec. 4.
422 S. M. SICHKAR
2. COMPUTATIONAL DETAILS
Most known transition-metal diborides MB2 are formed by transition
elements of III—VI group (Sc, Ti, Zr, Hf, V, Nb, and others) and have a
layered hexagonal C32 structure of the AlB2-type with the space group
symmetry P6/mmm (number 191). By choosing appropriate primitive
lattice vectors, the atoms are positioned at Hf (0, 0, 0), B (1/3, 1/6,
1/2), and B (2/3, 1/3, 1/2) in the unit cell. The distance between Hf—
Hf is equal to c. Actually, this structure is quite close packed, and can
be coped efficiently and accurately by the atomic sphere approximation
method. However, for precise calculation of the phonon spectra and
electron—phonon interaction, full potential approximation should be
used.
The Eliashberg function (the spectral function of the electron—
phonon interaction) expressed in terms of the phonon linewidths q
has the form [15]
.)(
)(2
1
)(2
v
v
v
v
FN
F
q
q
q
q
(1)
The linewidths characterize the partial contribution of each phonon:
),()(2
2
, FjFj
jj
v
jjvv g
qkk
k
q
kqkqq (2)
N(F) is the electron density of states per atom and per spin on the Fer-
mi level F , and
v
jjgq
kqk , is the electron—phonon interaction matrix ele-
ment.
The electron—phonon interaction constant is defined as:
.)(2
12 dF (3)
It can also be expressed in terms of the phonons linewidths:
,
)(
2
v vF
v
Nq q
q
(4)
The double summation over Fermi surface in Eq. (2) is carried out on
dense mesh (793 point in the irreducible part of the Brillouin zone
(BZ)).
For the calculation of the phonon spectra and electron—phonon in-
teraction, a scalar relativistic FP-LMTO method [16] is used. In these
calculations, author used the Perdew—Wang [17] parameterization of
the exchange-correlation potential in general gradient approximation.
BZ integrations are performed using the improved tetrahedron method
[18]. Phonon spectra and electron—phonon matrix elements are calcu-
lated for 50 points in the irreducible part of the BZ, using the linear
INTERACTION BETWEEN ELECTRON AND PHONON SUBSYSTEMS 423
response scheme [16].
The 5s- and 5p-semi-core states of HfB2 are treated as valence states
in separate energy windows. Variations in charge density and potential
are expanded in spherical harmonics inside the MT-sphere as well as in
2894 plane waves in the interstitial area with 88.57 Ry cut-off energy
for HfB2. As for the area inside the MT-spheres, 3k—spd LMTO basis
set energy (0.1, 1, 2.5 Ry) is used with one-centre expansions inside
the MT-spheres performed up to lmax 6. Calculations are performed
with the experimentally observed lattice constants: a 3.141 Å and
c 3.47 Å for HfB2 [19].
3. RESULTS AND DISCUSSION
3.1. Phonon Spectra
The unit cell of HfB2 contains three atoms, which gives in general case
nine phonon branches. Figure 1 shows theoretically calculated phonon
density of state for HfB2 (full curve). The DOS for HfB2 can be separat-
ed into three distinct regions. Based on the author’s analysis of rela-
tive directions of eigenvectors for each atom in unit cell, it was shown
that the first region (with a peak in phonon DOS at 5.2 THz) is domi-
nated by the motion of Hf. This region belongs to the acoustic phonon
Fig. 1. Theoretically calculated phonon density of states (full line) F() for
HfB2. The dotted and dashed lines present the calculated phonon DOS of HfB2
by Deligoz et al. [12] and Lawson et al. [10], respectively.
424 S. M. SICHKAR
modes. The second wide region (14—20 THz) results from the coupled
motion of Hf and two B atoms in the unit cell. The E1u, A2g, B1g phonon
modes (see Table) lie in this area. The phonon DOS in the third region
extends from 22 THz to 26 THz. This is caused by the movement of bo-
ron atoms and is expected since boron is lighter than Hf. The covalent
character of the B—B bonding is also crucial for the high frequency of
phonons. The in-plane E2g mode belongs to this region. The second and
third regions represent optical phonon modes in crystals. The most
significant feature in the phonon DOS is a gap around 6—13 THz. This
gap is a consequence of the large mass difference between B (10.8 a.u.)
and Hf (178.49 a.u.), which leads to decoupling of the transition metal
and boron vibrations.
Currently, there are no data concerning the experimentally measu-
red phonon DOS in HfB2. So, author compares his results with theoret-
ically calculated phonon DOS by Deligoz et al. [12] and Lawson et al.
[10] (see Fig. 1 and Table). Calculations of Deligoz et al. [12] are based
on the density functional formalism and generalized gradient approx-
imation.
They used the Perdew—Burke—Ernzerhof functional [20] for the ex-
change-correlation energy as it is implemented in the SIESTA code
[21]. This code calculates the total energies and atomic Hellmann—
Feynman forces using a linear combination of atomic orbitals as the
basis set. The basis set consists of finite range pseudoatomic orbitals of
the Sankey—Niklewsky type [22], generalized to include multiplexing
decays.
The interactions between electrons and core ions are simulated with
the separable Troullier—Martins [23] normconserving pseudopoten-
tials. In other words, they used the so-called ‘frozen phonon’ technique
and built an optimized rhombohedral supercell with 36 atoms. This
method is inconvenient for calculating phonon spectra for small q-
points as well as for compounds with large number of atoms per unit
cell. Lawson et al. [10] used two different codes to calculate the phonon
spectra. VASP, the supercell method, based on the projected augment-
ed wave potentials. Second method, ABINIT, uses Fritz Haber Insti-
TABLE. Theoretically calculated phonon frequencies (in THz) in the sym-
metry point for HfB2 and calculated phonon frequencies by Deligoz et al. Ref.
[12] and Lawson et al. Ref. [10].
Reference E1u A2g B1g E2g
Present work 13.76 15.03 17.12 25.17
SIESTA [12] 14.10 15.19 15.87 24.49
VASP [10] 13.34 14.00 16.40 24.16
ABINIT [10] 12.92 13.85 16.01 23.59
INTERACTION BETWEEN ELECTRON AND PHONON SUBSYSTEMS 425
tute pseudopotentials in the Troulliers—Martin form. VASP results of
Lawson et al. [10] is slightly closer to our calculation with respect to
ABINIT data. There is a good agreement between author’s calculations
and the results of Deligoz et al. [12] in a shape and energy position of
the second peak in the phonon DOS. There is an energy shift towards
smaller energies of the first, second and third peaks of the Lawson et
al. [10] calculations in comparison with the Deligoz et al. [12] data.
The difference between third peaks in VASP and SIESTA data reaches
2.2 THz. Results presented here lie between these two calculations.
In next section, it will be shown how the shift of the third peak of
matrix element at 2.1 THz with respect to the third peak of phonon
DOS can dramatically decrease value of averaged electron—phonon
coupling. So, SIESTA and VASP codes do not provide phonon spectra
with sufficient accuracy for precise calculation of critical supercon-
ductivity temperature.
3.2. Electron—Phonon Interaction
Figure 2 shows theoretically calculated Eliashberg functions for HfB2
as well as electron—phonon prefactor 2() (definition of this function
is merely ratio (2()F()/F())); 2() has strongly varying character.
Therefore, matrix element of electron—phonon interaction cannot be
presented in form 2() const and hence well-known McMillan ap-
Fig. 2. Theoretically calculated Eliashberg function 2F() of HfB2 (full line)
and electron—phonon prefactor 2() (dashed line).
426 S. M. SICHKAR
proximation [24] is not valid for HfB2. The electron—phonon coupling
cannot be factorized into independent electronic and phonon parts.
There is no difference between main peaks positions of phonon spec-
tra and electron—phonon coupling function. Electron—phonon prefac-
tor has three peaks: 5.2 THz, 17.1 THz, and 21.3 THz (the correspond-
ing peaks in the phonon DOS and Eliashberg function are situated at
the 5.2 THz, 17.1 THz, and 23.4 THz frequencies). The difference in
the positions of the third peaks in electron—phonon prefactor and in
phonon DOS can explain the suppression of high-energy peak in Eli-
ashberg function (23.4 THz). The third peak of matrix element of elec-
tron—phonon interaction (2()) lies between two main peaks of phonon
DOS (in region with low phonon DOS). This fact strongly influences on
the decreasing of the value of averaged electron—phonon coupling.
By integrating the Eliashberg function according to Formula (3),
the averaged electron—phonon constant is calculated, 0.17. The
constant of the electron—phonon interaction also can be roughly esti-
mated by comparison of the theoretically calculated DOS at the Fermi
level and the electron specific heat coefficient . Cp T, where 1.0
mJmole
1K2
for HfB2 [25]. HfB2 possesses quite small value of the
DOS at the Fermi level of 0.4 states/(celleV). It gives the theoretically
calculated b 0.8 mJmole
1K2
and h 0.2 in qualitative agreement
with 0.17.
To calculate the superconductivity transition temperature Tc for
HfB2, McMillan formula modified by Allen—Dynes [26] is used:
,
)62.01(
)1(04.1
exp
2.1
*
log
c
T (5)
where log–the effective logarithmically averaged phonon frequency,
*–the screening Coulomb pseudopotential. As a result, Tc is less than
0.01 K (*
0.10, log 459.25 K).
3.3. Electrical Resistivity
In the pure metals (excluding low-temperature region), the electron—
phonon interaction is the dominant factor governing electrical conduc-
tivity of the substance. Using the lowest-order variational approxima-
tion, the solution for the Boltzmann equation gives the following for-
mula for the temperature dependence of I(T):
),(
sinh)(
)(
2
tr
0
2
2
2
I
cell
I
F
d
N
Tk
T
F
B (6)
where the subscript I specifies the direction of the electrical current.
In this work, two directions: [0001] (c-axis or z direction) and ]0110[
INTERACTION BETWEEN ELECTRON AND PHONON SUBSYSTEMS 427
(a-axis or x direction) are investigated; 2
I is the average square of
the I component of the Fermi velocity, /(2kBTI).
Mathematically, the transport function )(
2
tr F differs from 2F()
only by an additional factor
2
I I I
[1 ( ) ( )/ ]v v k k , which preferen-
tially weights the backscattering processes.
Formula (6) remains valid in the range tr 5 T 2tr [16], where:
2 1/2
tr tr
, (7)
,)(
2
0
2
tr
tr
tr
2
dF (8)
.)(2
0
2
tr
1
tr
dF (9)
The low-temperature electrical resistivity is the result of electron-
electron interaction, size effects, scattering on impurities, etc.; how-
ever, for high temperatures, it is necessarily to take into account the
effects of anharmonicity and the temperature smearing of the Fermi
surface. In present calculations, tr 654.4 K for c-axis, and 679.9 K
for a-axis for HfB2.
Figure 3 represents the theoretically calculated temperature de-
pendence of electrical resistivity of HfB2 for the [0001] direction (full
curve) and the basal ]0110[ direction (dashed curve) and experimental
Fig. 3. Theoretically calculated for the [0001] direction (full curve) and the
basal ]0110[ direction (dashed curve), and experimentally measured tem-
perature dependence of electrical resistivity of HfB2 [6] (open circles).
428 S. M. SICHKAR
measurements for polycrystalline HfB2 [6] (open circles). Specimen of
HB2 ceramics is produced by spark plasma sintering method and has
good ratio of experimental and theoretically calculated density
exp/th 98.1% Theoretical results are in a good agreement with the
experiment. The small discrepancy does not exceed accuracy of calcu-
lation. Anisotropy ratio of electrical resistivity at T 300 K:
z/x 1.079. Actually, this fact indicates that for HfB2 anisotropy is
not clearly expressed.
4. SUMMARY
The phonon subsystem as well as the electron—phonon interaction of
HfB2 is studied using full potential linear muffin-tin orbital methods.
The calculated phonon spectra and phonon DOS for HfB2 show that
different theoretical approaches to the calculation may give sufficient
discrepancies, especially in high-energy region. Therefore, it is very
important to use accurate shape of the crystalline potential in self-
consistent calculation.
There are no regions in k-space with high electron—phonon interac-
tion or phonon dispersion curves with soft modes in HfB2. The aver-
aged electron—phonon interaction constant for HfB2 is rather small
0.17. This clearly indicates that there is no evidence of supercon-
ductivity in this compound. Of course, this conclusion matches to di-
rect calculation of transition temperature according Formula (5).
The temperature dependence of the electrical resistivity in HfB2 is
calculated in the lowest-order variational approximation of the Boltz-
mann equation. These results are in good agreement with the experi-
ment. Anisotropic behaviour of the electrical resistivity in hafnium
diboride is rather small.
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| id | nasplib_isofts_kiev_ua-123456789-106903 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1024-1809 |
| language | English |
| last_indexed | 2025-12-07T17:26:19Z |
| publishDate | 2014 |
| publisher | Інститут металофізики ім. Г.В. Курдюмова НАН України |
| record_format | dspace |
| spelling | Sichkar, S.M. 2016-10-08T19:07:58Z 2016-10-08T19:07:58Z 2014 Interaction between Electron and Phonon Subsystems in Hafnium Diboride / S.M. Sichkar // Металлофизика и новейшие технологии. — 2014. — Т. 36, № 3. — С. 419-429. — Бібліогр.: 26 назв. — англ. 1024-1809 PACS: 63.20.dk, 71.15.-m, 71.15.Mb, 71.38.-k, 72.10.Di, 72.15.Eb DOI: http://dx.doi.org/10.15407/mfint.36.03.0419 https://nasplib.isofts.kiev.ua/handle/123456789/106903 Ab initio розрахунок функцій електрон-фононного зв’язку виконано за методом ЛМТО з використанням повного потенціалу. Низьке значення усередненої константи електрон-фононної взаємодії для HfB₂ λ=0,17 свідчить, що немає підстав для виникнення надпровідного стану в цій сполуці. Вперше було розраховано електричний опір і коефіцієнт анізотропії ρz/ρx=1,079 (Т=300 К) для дибориду гафнію. Було досягнуто добру узгодженість з експериментальними даними для електричного опору. У роботі виконано порівняльний аналіз результатів розрахунків фононних спектрів методами ABINIT, SIESTA, VASP та запропонованим методом ЛМТО з детальним обговоренням одержаних відмінностей. Ab initio расчёт функций электрон-фононной связи выполнен в рамках метода ЛМТО с использованием полного потенциала. Низкое значение усреднённой константы электрон-фононного взаимодействия для HfB₂ λ=0,17 свидетельствует, что нет оснований для возникновения сверхпроводящего состояния в этом соединении. Впервые были рассчитаны электрическое сопротивление и коэффициент анизотропии ρz/ρx=1,079 (T=300 К) для диборида гафния. Было достигнуто хорошее согласие с экспериментальными данными для электрического сопротивления. В работе выполнен сравнительный анализ результатов расчётов фононных спектров методами ABINIT, Siesta, VASP и предложенным методом ЛМТО с детальным обсуждением полученных различий Ab initio calculation of the electron—phonon coupling functions is carried out, using full potential LMTO method. Low value of the averaged electron— phonon interaction constant for HfB₂ λ=0.17 indicates that there is no evidence of superconductivity in this compound. Electrical resistivity and anisotropy factor ρz/ρx=1.079 (T=300 K) are theoretically calculated. A good agreement with experimental data of electrical resistivity is achieved. Comparative analysis of ABINIT, SIESTA, VASP, and present LMTO method for phonon spectra calculating is performed. en Інститут металофізики ім. Г.В. Курдюмова НАН України Металлофизика и новейшие технологии Электронные структура и свойства Interaction between Electron and Phonon Subsystems in Hafnium Diboride Взаємодія між електронними і фононними підсистемами в дибориді гафнію Взаимодействие между электронными и фононными подсистемами в дибориде гафния Article published earlier |
| spellingShingle | Interaction between Electron and Phonon Subsystems in Hafnium Diboride Sichkar, S.M. Электронные структура и свойства |
| title | Interaction between Electron and Phonon Subsystems in Hafnium Diboride |
| title_alt | Взаємодія між електронними і фононними підсистемами в дибориді гафнію Взаимодействие между электронными и фононными подсистемами в дибориде гафния |
| title_full | Interaction between Electron and Phonon Subsystems in Hafnium Diboride |
| title_fullStr | Interaction between Electron and Phonon Subsystems in Hafnium Diboride |
| title_full_unstemmed | Interaction between Electron and Phonon Subsystems in Hafnium Diboride |
| title_short | Interaction between Electron and Phonon Subsystems in Hafnium Diboride |
| title_sort | interaction between electron and phonon subsystems in hafnium diboride |
| topic | Электронные структура и свойства |
| topic_facet | Электронные структура и свойства |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/106903 |
| work_keys_str_mv | AT sichkarsm interactionbetweenelectronandphononsubsystemsinhafniumdiboride AT sichkarsm vzaêmodíâmíželektronnimiífononnimipídsistemamivdiboridígafníû AT sichkarsm vzaimodeistviemežduélektronnymiifononnymipodsistemamivdiboridegafniâ |