Modelling of Epitaxial Growth of Diamond Crystals in High-Carbon Fe—Al Alloys
Standard enthalpies of formation of different K-phase unit cells are calculated and compared with formation enthalpy of modified unit cell of K-phase. Spin-polarized calculations are performed to compare electronic structure of carbon atoms in K-phase substrate, diamond, and graphite. An assumpti...
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Інститут металофізики ім. Г.В. Курдюмова НАН України
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| Zitieren: | Modelling of Epitaxial Growth of Diamond Crystals in High-Carbon Fe—Al Alloys / A.A. Mekhed, V.A. Andryushchenko // Наносистеми, наноматеріали, нанотехнології: Зб. наук. пр. — К.: РВВ ІМФ, 2013. — Т. 11, № 1. — С. 33-38. — Бібліогр.: 4 назв. — анг. |
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| author | Mekhed, A.A. Andryushchenko, V.A. |
| author_facet | Mekhed, A.A. Andryushchenko, V.A. |
| citation_txt | Modelling of Epitaxial Growth of Diamond Crystals in High-Carbon Fe—Al Alloys / A.A. Mekhed, V.A. Andryushchenko // Наносистеми, наноматеріали, нанотехнології: Зб. наук. пр. — К.: РВВ ІМФ, 2013. — Т. 11, № 1. — С. 33-38. — Бібліогр.: 4 назв. — анг. |
| collection | DSpace DC |
| container_title | Наносистеми, наноматеріали, нанотехнології |
| description | Standard enthalpies of formation of different K-phase unit cells are calculated
and compared with formation enthalpy of modified unit cell of K-phase.
Spin-polarized calculations are performed to compare electronic structure of
carbon atoms in K-phase substrate, diamond, and graphite. An assumption is
made on the epitaxial growth of the diamond crystals during the thermobaric
treatment of high-carbon Fe—Al alloys.
Розраховано стандартні ентальпії утворення різних елементарних комірок K-фази, виконано порівняння їх з ентальпією утворення модифікованої елементарної комірки. Порівняно електронні структури атомів вуглецю в K-фазі, алмазу та графіту, яких одержано спін-поляризованими розрахунками у пакеті Wien2k. Припущено епітаксіальний ріст кристалів
алмазу при термобаричному обробленні високовуглецевих стопів Fe—Al
Рассчитаны стандартные энтальпии образования разных элементарных
ячеек K-фазы, выполнено их сравнение с энтальпией образования модифицированной элементарной ячейки. Сравнены электронные структуры
атомов углерода в K-фазе, алмаза и графита, полученные в результате
спин-поляризованных расчётов в пакете Wien2k. Предположен эпитаксиальный рост кристаллов алмаза при термобарической обработке высокоуглеродистых сплавов Fe—Al.
|
| first_indexed | 2025-11-29T14:11:29Z |
| format | Article |
| fulltext |
33
PACS numbers: 71.15.Mb, 71.15.Nc,71.20.Be,81.05.uj,81.05.Zx,81.10.Aj, 82.60.Cx
Modelling of Epitaxial Growth of Diamond Crystals
in High-Carbon Fe—Al Alloys
A. A. Mekhed and V. A. Andryushchenko
G. V. Kurdyumov Institute for Metal Physics, N.A.S. of Ukraine,
Acad. Vernadsky Blvd., 36,
03680 Kyyiv-142, Ukraine
Standard enthalpies of formation of different K-phase unit cells are calculat-
ed and compared with formation enthalpy of modified unit cell of K-phase.
Spin-polarized calculations are performed to compare electronic structure of
carbon atoms in K-phase substrate, diamond, and graphite. An assumption is
made on the epitaxial growth of the diamond crystals during the thermobaric
treatment of high-carbon Fe—Al alloys.
Розраховано стандартні ентальпії утворення різних елементарних комі-
рок K-фази, виконано порівняння їх з ентальпією утворення модифікова-
ної елементарної комірки. Порівняно електронні структури атомів вугле-
цю в K-фазі, алмазу та графіту, яких одержано спін-поляризованими роз-
рахунками у пакеті Wien2k. Припущено епітаксіальний ріст кристалів
алмазу при термобаричному обробленні високовуглецевих стопів Fe—Al.
Рассчитаны стандартные энтальпии образования разных элементарных
ячеек K-фазы, выполнено их сравнение с энтальпией образования моди-
фицированной элементарной ячейки. Сравнены электронные структуры
атомов углерода в K-фазе, алмаза и графита, полученные в результате
спин-поляризованных расчётов в пакете Wien2k. Предположен эпитакси-
альный рост кристаллов алмаза при термобарической обработке высоко-
углеродистых сплавов Fe—Al.
Key words: K-phase, diamond, graphite, epitaxy, substrate, Wien2k, elec-
tron density, thermobaric treatment, standard enthalpies of formation.
(Received 8 January, 2013)
1. INTRODUCTION
The most common designation for K-phase is Fe3AlC. Type of crystal
Наносистеми, наноматеріали, нанотехнології
Nanosystems, Nanomaterials, Nanotechnologies
2013, т. 11, № 1, сс. 33—38
© 2013 ІМФ (Інститут металофізики
ім. Г. В. Курдюмова НАН України)
Надруковано в Україні.
Фотокопіювання дозволено
тільки відповідно до ліцензії
34
structure
bic face-
mann—M
eter is а ≈
are as fo
1/2 1/2 1
Howev
[2], and r
х = 0.08
chiometr
temperat
that com
bulk of c
diamond
analysis
the ratio
Fig. 1. Sc
a diamond
a
Fig. 3. Ca
ration); (c
A. A.
e of the K-p
centred cry
Mauguin sym
≈ 3.75 Å. C
ollows: 1Al
1/2 [1].
ver, actual
real chemic
to 0.66 [2,
ric compos
ture (up to
mposition o
compound,
d crystals of
has shown
of 3 to 1.
heme of epit
d on the K-p
alculated cry
c) Fe3.125Al0.8
MEKHED an
phase is des
ystal lattic
mbol of spac
oordination
l (Oh): 0 0 0
ly stoichio
cal formula
, 3]. Anoth
ition unde
2.2 K). It w
of obtained
which con
f 100—200
the presen
taxial growt
phase.
b
ystal cells: (a
825C0.5; (d) Fe
nd V. A. AND
scribed in r
ce with Sch
ace group Pm
n number М
0, 3Fe (D4h
ometric K-p
a is Fe4−уAl
her attempt
r high pre
was unsucc
K-phase w
sisted mos
micrometr
nce of Fe an
th of Fig. 2
bon is
treat
a) Fe3.5Al0.5C
e3.5Al0.5C0.5; (
DRYUSHCHE
reference li
hoenflies sy
m3m. Aver
М ≈ 5. Coor
h): 1/2 0 0;
phase has n
уCх [2], wh
t [4] was m
essure (up t
essful; exa
was Fe3AlC
tly of the K
res in size w
nd Al atoms
2. Octahedra
s deposited d
ment.
c
C, (b) Fe3.5Al
(e) Fe3AlC0.6
NKO
iterature as
ymbol Oh
1
rage unit ce
dinates of t
↓ 0.6—0.9 С
never been
ere у = 0.4—
made to ach
to 8 GPa)
mination h
C0.66. Beside
K-phase, co
were found.
s in these cr
al pore, in wh
during therm
l0.5C (distinc
6.
s: L′12 cu-
and Her-
ell param-
the atoms
С (Oh) by
observed
—1.0, and
hieve stoi-
and high
has shown
es, in the
olonies of
. Spectral
rystals in
hich car-
mobaric
d
ct configu-
MODELLING OF GROWTH OF DIAMOND CRYSTALS IN HIGH-C Fe—Al ALLOYS 35
This and also the fact that the difference of lattice parameters of the
K-phase (α ≈ 3.75 nm) and diamond (3.57 nm) is about 5%, allows to
assume that epitaxial growth (or nucleation) of diamonds is possible on
the surface (or inside the volume) of K-phase (Fig. 1). Increase of pres-
sure during the thermobaric treatment will reduce the difference of
parameters even more (α ≈ 3.69 nm at 7 GPa). The most suitable sub-
strate crystal plane for epitaxial growth of diamonds on K-phase is
[200]. It contains four atoms of carbon, and it has an octahedral pore in
the middle. It is possible that undissolved carbon (K-phase can dissolve
only up to 2/3 carbon atom per cell) is deposited in this pore during the
process of thermobaric treatment (Fig. 2).
As said earlier, K-phase composition varies in a broad range, so first
we investigated different possible unit cells corresponding to different
compositions of K-phase. Linearized augmented plane wave method as
implemented in Wien2k package is used to perform spin-polarized calcu-
lations of the following crystal cells (Fig. 3): Fe3AlC, Fe3.125Al0.825C0.5,
Fe3.5Al0.5C0.5, Fe3.5Al0.5C (two configurations), Fe3Al0.66C0.66, Fe3AlC0.66.
The last one corresponds to the real K-phase in terms of composition.
Crystal cell parameter is chosen to be 0.375 nm, which corresponds to the
optimal volume of stoichiometric K-phase according to our calculations.
Generalized gradient approximation (Perdew—Burke—Ernzerhof’96) is
used as exchange-correlation potential with cut-off energy equal to −7 Ry
in all calculations. Atomic radii are chosen as follows: for Al, 2.34 a.u.;
for Fe, 1.87 a.u.; for C, 1.66 a.u.
Total energies of corresponding K-phase cells and their constituent
elements are obtained from calculations and then used to compute en-
thalpies of formation of these cells. Obtained values are listed in Table
1. Minimum of studied enthalpies of formation corresponds to the
Fe3AlC0.5 cell. Fe3AlC0.6(6) cell also has low value of enthalpy and most
probably forms when the melt is oversaturated with carbon. K-phase
cell of stoichiometric composition Fe3AlC has higher formation en-
TABLE 1. Standard enthalpies of formation of different compositions of K-
phase.
Unit cell Enthalpy of formation, eV/atom
Fe3AlC −0.03
Fe3AlC0.6(6) −0.0328
Fe3AlC0.5 −0.033
Fe3.125Al0.825C0.5 −0.0308
Fe3.5Al0.5C0.5 −0.0244
Fe3.5Al0.5C −0.0286
Fe3.5Al0.5C
* −0.0275
*Distinct atomic configuration.
36
thalpy a
sponds t
found ye
crease of
caused b
form new
rounds c
stronger
Fe—Fe an
(Fig. 4).
ture as a
As for
Fig. 4. Sp
(left) and
Fig.
A. A.
and thus pr
to experime
et. Fe3.5Al0.5
f formation
by the fact
w bonds w
carbon) an
r than prev
nd Fe—C bo
As a result
whole.
r the carbo
patial distri
Fe3.125Al0.875
5. Total elec
MEKHED an
robability
ental data:
5C has even
n enthalpie
that iron
ith iron at
nd, despite
vious bonds
onds of ato
t, this leads
on non-stoi
bution of el
5C0.5 (right).
ctron densit
nd V. A. AND
of its form
: stoichiom
n lower prob
s with decr
atoms em
toms from
this newl
s with alum
oms from o
s to decreas
ichiometry
lectron dens
ties of Fe3AlC
DRYUSHCHE
mation is l
metric K-ph
bability of
rease of alu
mbedded ins
octahedra
ly formed
minium ato
ctahedral c
se of stabili
y, one can
sities in pla
C (left) and F
NKO
lower, whi
hase has ne
formation.
uminium co
stead of al
al carcass (
bonds are
ms, the str
carcass is d
ty of K-pha
see that st
ane [200] of
Fe3AlC0.5 (ri
ich corre-
ever been
. Such in-
ontents is
luminium
(that sur-
e slightly
rength of
decreased
ase struc-
tructures
f Fe3AlC0.5
ight).
MODEL
with carb
of states
thermod
Despit
and Fe3A
our furth
computa
can be a
mond an
pressure
calculati
phase (an
ties of ca
in diamo
Fig. 6. Co
densities
atom of K
lines stan
pressure o
LING OF GRO
bon non-sto
s compared
ynamically
te the expe
AlC0.66 are m
her calcula
ationally ex
substrate
nd modified
of 7 GPa)
ion shows t
nd thus, gr
arbon atom
nds.
С1
omparison o
of correspon
K-phase; C2
nd for K-ph
of 7 GPa.
OWTH OF DIA
oichiometr
d to stoich
y stable (Fig
eriment an
more therm
ations we u
xpensive. I
for a diam
d K-phase c
were calcu
that with g
radual decr
s in K-phas
of electron d
nding carbo
is on the rig
ase under n
AMOND CRYS
ry have mor
hiometric o
g. 5).
nd calculati
modynamica
used the las
n order to
mond, electr
cell (Fig. 2
ulated. The
radual incr
rease of latt
se become m
densities of
on atoms of m
ght (see Fig
no pressure,
STALS IN HIG
re evident m
one, which
ions had sh
ally prefera
st one, bec
understan
ron densiti
) (with no
ey are comp
rease in pre
tice parame
more and m
graphite/d
modified K-
. 2 for atom
, dashed lin
GH-C Fe—Al A
minimum o
h makes th
hown that
able than F
ause it is m
nd whether
ies of grap
pressure a
pared in Fi
essure appl
eter) electr
more similar
С2
iamond with
-phase. On t
m designation
es for K-ph
ALLOYS 37
of density
hem more
Fe3AlC0.5
Fe3AlC, in
much less
r K-phase
hite, dia-
and under
ig. 6. The
lied to K-
ron densi-
r to those
h electron
the left, C1
n). Dotted
hase under
38 A. A. MEKHED and V. A. ANDRYUSHCHENKO
Several cells with different number of layers of ordinary (varying
from 1 to 4) and modified K-phase were also calculated. Additional
layers of K-phase create additional splitting, but the picture mostly
remains the same. Enthalpies of formation of such unit cells are close
to 0 (varying from −0.008 to −0.01 eV/atom) and are bigger than that
of ordinary K-phase, so, these cells require special conditions to form,
e.g., abundance of the carbon.
2. CONCLUSION
We have made an assumption that K-phase, because its lattice parame-
ter (0.375 nm) is close to that of diamond (0.357 nm), can be a sub-
strate for a diamond with the substrate plane [200]. We have per-
formed electron densities calculations of K-phase unit cells with addi-
tional carbon atom in the octahedral pore of [200] plane. Calculations
have shown that with gradual increase of pressure electron densities of
carbon atoms from the substrate plane of the modified K-phase become
more and more similar to the electron densities of carbon in diamond.
We also have performed calculations of standard enthalpies of for-
mation that have shown that Fe3AlC0.5 and Fe3AlC2/3 have the lowest
enthalpies and thus have the highest probability of formation. The rea-
sons for this are provided in the article. It is worth mentioning that we
have used Fe3AlC unit cell as a basis for modified K-phase because it
has lower computational costs. Formation enthalpies of all calculated
modified K-phase unit cells are slightly higher than that of Fe3AlC,
which means that they need special conditions to form, e.g., abundance
of the carbon.
REFERENCES
1. K. J. Smittels, Metals: Handbook (Moscow: Metallurgiya: 1980) [Russian
translation].
2. V. A. Andrushenko, V. G. Gavrilyuk, and V. M. Nadutov, Fiz. Met. Metalloved.,
60, No. 4: 683 (1985) (in Russian).
3. H. G. Goldshmidt, Interstitial Alloys (London: Butterworths: 1967).
4. V. A. Andryushchenko et al., Metallofiz. Noveishie Tekhnol., 31, No. 9: 1257
(2009) (in Russian).
|
| id | nasplib_isofts_kiev_ua-123456789-75896 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1816-5230 |
| language | English |
| last_indexed | 2025-11-29T14:11:29Z |
| publishDate | 2013 |
| publisher | Інститут металофізики ім. Г.В. Курдюмова НАН України |
| record_format | dspace |
| spelling | Mekhed, A.A. Andryushchenko, V.A. 2015-02-05T17:37:26Z 2015-02-05T17:37:26Z 2013 Modelling of Epitaxial Growth of Diamond Crystals in High-Carbon Fe—Al Alloys / A.A. Mekhed, V.A. Andryushchenko // Наносистеми, наноматеріали, нанотехнології: Зб. наук. пр. — К.: РВВ ІМФ, 2013. — Т. 11, № 1. — С. 33-38. — Бібліогр.: 4 назв. — анг. 1816-5230 PACSnumbers:71.15.Mb,71.15.Nc,71.20.Be,81.05.uj,81.05.Zx,81.10.Aj,82.60.Cx https://nasplib.isofts.kiev.ua/handle/123456789/75896 Standard enthalpies of formation of different K-phase unit cells are calculated and compared with formation enthalpy of modified unit cell of K-phase. Spin-polarized calculations are performed to compare electronic structure of carbon atoms in K-phase substrate, diamond, and graphite. An assumption is made on the epitaxial growth of the diamond crystals during the thermobaric treatment of high-carbon Fe—Al alloys. Розраховано стандартні ентальпії утворення різних елементарних комірок K-фази, виконано порівняння їх з ентальпією утворення модифікованої елементарної комірки. Порівняно електронні структури атомів вуглецю в K-фазі, алмазу та графіту, яких одержано спін-поляризованими розрахунками у пакеті Wien2k. Припущено епітаксіальний ріст кристалів алмазу при термобаричному обробленні високовуглецевих стопів Fe—Al Рассчитаны стандартные энтальпии образования разных элементарных ячеек K-фазы, выполнено их сравнение с энтальпией образования модифицированной элементарной ячейки. Сравнены электронные структуры атомов углерода в K-фазе, алмаза и графита, полученные в результате спин-поляризованных расчётов в пакете Wien2k. Предположен эпитаксиальный рост кристаллов алмаза при термобарической обработке высокоуглеродистых сплавов Fe—Al. en Інститут металофізики ім. Г.В. Курдюмова НАН України Наносистеми, наноматеріали, нанотехнології Modelling of Epitaxial Growth of Diamond Crystals in High-Carbon Fe—Al Alloys Article published earlier |
| spellingShingle | Modelling of Epitaxial Growth of Diamond Crystals in High-Carbon Fe—Al Alloys Mekhed, A.A. Andryushchenko, V.A. |
| title | Modelling of Epitaxial Growth of Diamond Crystals in High-Carbon Fe—Al Alloys |
| title_full | Modelling of Epitaxial Growth of Diamond Crystals in High-Carbon Fe—Al Alloys |
| title_fullStr | Modelling of Epitaxial Growth of Diamond Crystals in High-Carbon Fe—Al Alloys |
| title_full_unstemmed | Modelling of Epitaxial Growth of Diamond Crystals in High-Carbon Fe—Al Alloys |
| title_short | Modelling of Epitaxial Growth of Diamond Crystals in High-Carbon Fe—Al Alloys |
| title_sort | modelling of epitaxial growth of diamond crystals in high-carbon fe—al alloys |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/75896 |
| work_keys_str_mv | AT mekhedaa modellingofepitaxialgrowthofdiamondcrystalsinhighcarbonfealalloys AT andryushchenkova modellingofepitaxialgrowthofdiamondcrystalsinhighcarbonfealalloys |