Radiation-acoustic effects at diamond-like coating deposition from the flow of hydrocarbon ions and their influence on kinetic processes
Based on the model of the nonlocal thermoelastic peak (NTP) the ion generalized to the case of the ion of polyatomic molecule, the acoustic effect of low-energy ion of a hydrocarbon molecule during plasma-ion deposition of diamond-like carbon coating is investigated. The generation of a stress wave...
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nasplib_isofts_kiev_ua-123456789-1960962025-02-23T17:49:02Z Radiation-acoustic effects at diamond-like coating deposition from the flow of hydrocarbon ions and their influence on kinetic processes Радіаційно-акустичні ефекти при осадженні алмазоподібних покриттів з потоку іонів вуглеводнів та їх вплив на кінетичні процеси Kalinichenko, O.I. Strel’nitskij, V.E. Physics of radiation and ion-plasma technologies Based on the model of the nonlocal thermoelastic peak (NTP) the ion generalized to the case of the ion of polyatomic molecule, the acoustic effect of low-energy ion of a hydrocarbon molecule during plasma-ion deposition of diamond-like carbon coating is investigated. The generation of a stress wave takes place as a result of the combined action of mechanisms associated with the rapid transfer of energy, momentum, and additional volume to the NTP volume. The magnitude, shape, and spatial dependence of the stress pulse generated by CH₄, C₂H₂, and C₆H₆ ions have been studied with absorption taken into account. The possibility of accelerating the diffusion of interstitial defects, as well as the possibility of brittle fracture of the coating at the interface with the substrate under the action of acoustic pulses from deposited hydrocarbon ions, is discussed. На основі моделі нелокального термопружного піка (НТП) іона, що була узагальнена на випадок іонів вуглеводневих молекул, досліджено акустичний ефект низькоенергетичного іона вуглеводневої молекули при плазмово-іонному осадженні алмазоподібного вуглецевого покриття. Генерація хвилі напруження має місце в результаті спільної дії механізмів, що пов’язані зі швидкою передачею енергії, імпульсу та додаткового об’єму в об’єм НТП. Досліджено величину, форму та просторову залежність імпульсу напруження, що генерується іонами CH₄, C₂H₂, C₆H₆ з врахуванням поглинання. Обговорюється можливість прискорення дифузії міжвузольних дефектів, а також можливість крихкого руйнування покриття на межі з підкладкою під дією акустичних імпульсів від НТП іонів вуглеводнів, що осаджуються. 2023 Article Radiation-acoustic effects at diamond-like coating deposition from the flow of hydrocarbon ions and their influence on kinetic processes / O.I. Kalinichenko, V.E. Strel’nitskij // Problems of Atomic Science and Technology. — 2023. — № 2. — С. 110-117. — Бібліогр.: 12 назв. — англ. 1562-6016 DOI: https://doi.org/10.46813/2023-144-110 https://nasplib.isofts.kiev.ua/handle/123456789/196096 621.793:534.1:534.2 en Problems of Atomic Science and Technology application/pdf Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Physics of radiation and ion-plasma technologies Physics of radiation and ion-plasma technologies |
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Physics of radiation and ion-plasma technologies Physics of radiation and ion-plasma technologies Kalinichenko, O.I. Strel’nitskij, V.E. Radiation-acoustic effects at diamond-like coating deposition from the flow of hydrocarbon ions and their influence on kinetic processes Problems of Atomic Science and Technology |
| description |
Based on the model of the nonlocal thermoelastic peak (NTP) the ion generalized to the case of the ion of polyatomic molecule, the acoustic effect of low-energy ion of a hydrocarbon molecule during plasma-ion deposition of diamond-like carbon coating is investigated. The generation of a stress wave takes place as a result of the combined action of mechanisms associated with the rapid transfer of energy, momentum, and additional volume to the NTP volume. The magnitude, shape, and spatial dependence of the stress pulse generated by CH₄, C₂H₂, and C₆H₆ ions have been studied with absorption taken into account. The possibility of accelerating the diffusion of interstitial defects, as well as the possibility of brittle fracture of the coating at the interface with the substrate under the action of acoustic pulses from deposited hydrocarbon ions, is discussed. |
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Article |
| author |
Kalinichenko, O.I. Strel’nitskij, V.E. |
| author_facet |
Kalinichenko, O.I. Strel’nitskij, V.E. |
| author_sort |
Kalinichenko, O.I. |
| title |
Radiation-acoustic effects at diamond-like coating deposition from the flow of hydrocarbon ions and their influence on kinetic processes |
| title_short |
Radiation-acoustic effects at diamond-like coating deposition from the flow of hydrocarbon ions and their influence on kinetic processes |
| title_full |
Radiation-acoustic effects at diamond-like coating deposition from the flow of hydrocarbon ions and their influence on kinetic processes |
| title_fullStr |
Radiation-acoustic effects at diamond-like coating deposition from the flow of hydrocarbon ions and their influence on kinetic processes |
| title_full_unstemmed |
Radiation-acoustic effects at diamond-like coating deposition from the flow of hydrocarbon ions and their influence on kinetic processes |
| title_sort |
radiation-acoustic effects at diamond-like coating deposition from the flow of hydrocarbon ions and their influence on kinetic processes |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2023 |
| topic_facet |
Physics of radiation and ion-plasma technologies |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/196096 |
| citation_txt |
Radiation-acoustic effects at diamond-like coating deposition from the flow of hydrocarbon ions and their influence on kinetic processes / O.I. Kalinichenko, V.E. Strel’nitskij // Problems of Atomic Science and Technology. — 2023. — № 2. — С. 110-117. — Бібліогр.: 12 назв. — англ. |
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Problems of Atomic Science and Technology |
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110 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №2(144)
https://doi.org/10.46813/2023-144-110
UDC 621.793:534.1:534.2
RADIATION-ACOUSTIC EFFECTS AT DIAMOND-LIKE COATING
DEPOSITION FROM THE FLOW OF HYDROCARBON IONS
AND THEIR INFLUENCE ON KINETIC PROCESSES
O.I. Kalinichenko, V.E. Strel’nitskij
National Science Center “Kharkov Institute of Physics and Technology”, Kharkiv, Ukraine
E-mail: aikalinichenko@kipt.kharkov.ua
Based on the model of the nonlocal thermoelastic peak (NTP) the ion generalized to the case of the ion of
polyatomic molecule, the acoustic effect of low-energy ion of a hydrocarbon molecule during plasma-ion deposition
of diamond-like carbon coating is investigated. The generation of a stress wave takes place as a result of the
combined action of mechanisms associated with the rapid transfer of energy, momentum, and additional volume to
the NTP volume. The magnitude, shape, and spatial dependence of the stress pulse generated by CH4, C2H2, and
C6H6 ions have been studied with absorption taken into account. The possibility of accelerating the diffusion of
interstitial defects, as well as the possibility of brittle fracture of the coating at the interface with the substrate under
the action of acoustic pulses from deposited hydrocarbon ions, is discussed.
INTRODUCTION
Experiments show that low-energy ions (E ~ 1 to
10 keV) bombarding the solid body surface affect the
structure and properties of the body at depths
significantly exceeding the length of the ion's path. One
of the examples of such a long-range effect is the so-
called radiation-stimulated diffusion of implanted ions
in the process of irradiation. The distribution of
introduced impurities depending on the irradiation time,
ion energy, and matrix temperature was studied in
[1–3]. The depth of impurity penetration in all
investigated cases significantly exceeded the projected
length of the ion path of such energy. Another example
of the long-range effect of ions on the target structure is
the treatment of thick (tenths of micron) opaque carbon
films with Ar
+
ions, as a result of which their
transparency increases. The thickness of the film
exceeded the length of the ion path ten times [4, 5].
The purpose of the work is to prove that acoustic
pulses excited by single hydrocarbon ions during
plasma-ion deposition of carbon coating can cause
structural rearrangement, in particular, accelerated
migration of defects and brittle fracture at a significant
distance (up to tens of nanometers) from the coating
surface. In contrast to the time-consuming methods of
molecular dynamics, the proposed macroscopic
approach allows obtaining results in analytical form,
which greatly facilitates their analysis.
In the course of theoretical studies, the concept of
the nonlocal thermoelastic peak (NTP) of the ion that
developed by us earlier for monoatomic ions [6] was
widely used. Further consideration is carried out in
relation to the ion of a hydrocarbon molecule
1n nC H ,
where n and n1 are the number of carbon and hydrogen
atoms, respectively, included in the molecule. As will
be shown below, ions of polyatomic molecules excite,
as a rule, more powerful acoustic pulses, compared to
carbon ions of the same energy, which increases their
influence on transfer and destruction processes.
MODEL OF THE NTP
OF HYDROCARBON ION
When determining the characteristics of the
thermoelastic peak generated by the ion of hydrocarbon
molecule, we take into account the fact that the
molecule, falling into the target substance, disintegrates
into its atoms, which fly with speeds equal in magnitude
and direction, and equal to the speed of the original
molecule. The kinetic energy EC of the C atom entering
the molecule is equal to
112 12CE E n n . (1)
When the condition n1 << 12n is met (that is the
most common case), the acceptable approximation of
the energy of carbon atom is EC = E/n. For energy of the
hydrogen atom, we have:
112 12
H C
E E
E E
n n n
. (2)
Each ion of the fragmented molecule forms its NTP
independently of other ions of the molecule. The
analysis shows that the size of the peaks formed from
carbon ions significantly exceeds the characteristic
distance between them, which is determined by the
lengths of the carbon-carbon bonds of the hydrocarbon
molecule. Let's introduce the parameter lCC – the
maximum distance between carbon atoms in the
molecule, which is estimated from the lengths of
carbon-carbon bonds. For CH4, C2H2, and C6H6, the lCC
parameter is 0, 0.12, and 0.46 nm, respectively. The
condition 2CC Cl R E means that there is the
almost complete spatial-temporal coincidence of carbon
peaks. Here CR E is the initial radius of the carbon
ion peak with energy EC. As a result, the thermoelastic
peak is formed, the initial radius of which is ~ CR E .
Similarly, the thermoelastic peak is formed from each of
the hydrogen atoms included in the original molecule.
Calculation using the SRIM2000 package [7] shows that
the peaks of hydrogen ions (ie, protons) lie inside the
combined carbon peak. Thus, if we neglect some
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №2(144) 111
inhomogeneity of the energy distribution associated
with proton peaks, it can be assumed that as a result of
implantation of the hydrocarbon molecule ion with
energy E, the thermoelastic peak with a radius R E n
and energy content E E n is formed. For simplicity
of the analysis, we assumed lCC = 0, since it does not
significantly affect the results. Here )(E is the
fraction of phonon losses of the C
+
ion with energy E.
Note that in this approximation the parameters of the
NTP of the CH4
+
ion coincide with those of the NTP of
C
+
ion.
The analysis of relaxation processes showed that
taking into account the ionization (inelastic) losses of
the implanted ion does not change the estimate of the
thermal energy density in the NTP. Using the position
of the mathematical model of the nonlocal thermoelastic
peak of monatomic ion [6], we come to the conclusion
that the initial radius of the NTP ion of hydrocarbon
molecule is determined with acceptable accuracy by the
expression 2 TR E n L E n R , where
2TR is the radius of thermal smearing of the
point heat source during the ion-ion relaxation time,
2 210 сm s is the coefficient of the thermal
conductivity of the target material (diamond-like carbon
coating), is the time of ion-ion relaxation, which is
actually the formation time of the NTP. Functions
)(E and L E were determined using SRIM2000
[7]. The presence of n thermal peaks of C
+
ions, which
coincide in space and time, leads to the revision of the
limit of applicability of the NTP model of the
hydrocarbon ion in direction of significant increase in
acceptable energies, compared to the C
+
ion. So, for
example, computer modeling showed that the NTP
model for the C6H6 ion is suitable up to energy
E = 10 keV.
The analysis of the momentum transfer process from
the primary ion to the carbon coating material was also
performed. It is shown that, despite a significant part of
the energy 1 ( )E E n contained in ionization losses
(in excited electrons), the share of momentum they
carry is negligibly small. The last circumstance is a
consequence of the insignificance of the mass of
electrons constituting ionization losses compared to
mass of hydrocarbon molecule. Thus, it is shown that
the transfer of momentum from the primary ion to the
substance in the NTP, with a sufficient degree of
accuracy, is determined by the expression 2P MnE ,
where M is the mass of the carbon atom.
ACOUSTIC IMPULSE FROM THE NTP
The generation of acoustic stresses is caused by the
pulsed change in the volume of the NTP due to thermal
expansion and introduction of additional volume by the
primary ion, as well as the transfer of momentum from
the ion to the substance of the NTP [8]. In the problem
of excitation of the acoustic pulse by the NTP of the
low-energy ion, there are three characteristic times: the
relaxation time of phonon losses = (2…5)∙10
-14
s (it is
also the relaxation time of the transmitted pulse); the
time of acoustic relaxation of NTP
ts = 2R/s ~ (1…5)·10
-13
s; and the cooling time of NTP
tT = R
2
/4 ~ 10
-11
s. Here R is the initial radius of the
NTP, s is the longitudinal sound velocity of the target
material. The evaluation of the characteristic times
shows that the relation << ts << tT is fulfilled. In view
of this, the thermal, as well as the impulse, impact on
the material of the peak can be considered as an
instantaneous load.
To find out the dependence of the amplitude of the
acoustic pulse on the NTP parameters and the target
characteristics, the task of exciting elastic oscillations
by the spherical region in the infinite homogeneous
isotropic elastic body, which acquires the energy of
phonon losses E(E/n), momentum 2P MnE , and
additional volume nV1 was considered. Accordingly,
three mechanisms of elastic oscillation generation were
considered.
Thermoacoustic mechanism. The rapid increase in
the volume of the NTP due to thermal expansion during
heating due to phonon losses of the ion E E n
excites thermoacoustic stresses T. The system of
equations of thermoacoustics [9], neglecting thermal
conductivity during the formation of the acoustic pulse,
leads to the single equation regarding the amplitude of
the acoustic displacement:
2
2
2
,r tu
s u
rt
, (3)
with zero initial conditions
,0 0u r ; ,0 0u r t , (4)
where ,0u r is the amplitude of the longitudinal
acoustic displacement wave excited by the NTP, t is the
time since the occurrence of the NTP, r – the radius
vector from the center of the NTP to the point of
observation, ,r t is the heat energy density in the
NTP, s, , and are the longitudinal speed of sound,
density and parameter Grüneisen coating material,
respectively. In the “wave zone”, that is, under the
condition 0r R where R is the effective radius of the
NTP, the expression was obtained for the amplitude of
the acoustic stress pulse [9]:
0
0 2
04
r ,t r x s
r ,t dy dz dx.
t ts r
(5)
The excitation of the acoustic pulse by the
instantaneously and uniformly heated spherical region
was analyzed. The expression for the amplitude of the
stress pulse in the wave zone has the form:
, 1 2T Tmy r y y y , (6)
where C Cy st r R E n R E n ; x – is the
Heaviside's “unit”;
1
2Tm CE E n R E n rV E n
,
V E – is the volume of the near-surface NTP of
carbon ion with energy E, for which the following
expression was obtained [6]:
112 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №2(144)
3
3 22 1
.
3 2 3 8
L E L E
V E R E R E
(7)
We emphasize that it is legitimate to use the initial
parameters of the NTP to determine the acoustic
stresses, since the condition 2R s is fulfilled. The
time is counted from the moment of arrival of the
leading edge of the pulse at the observation point r.
In Fig. 1 shows the universal function my ,
which specifies the shape of the stress pulse generated
by the instantaneously arising thermal field with the
uniform distribution of absorbed energy over the sphere.
In this case, the acoustic response is the spherically
symmetric bipolar stress wave that propagates from the
NTP volume with the longitudinal speed of sound s and
decreases with distance according to the law 1r .
Fig. 1. Thermoacoustic stress generated by spherical
NTP
Deformation mechanism. The rapid increase in the
volume of the NTP by the amount of the introduced
volume nV1 excites the deformation stresses D. Here,
V1 is the introduced volume of C
+
ion. In the
approximation of the uniform distribution of the
introduced volume nV1 in the volume of the NTP, it is
possible to obtain the amplitude of deformation stresses
D(r,t) from (6) after the substitution E(E/n) →
KnV1, where K is the bulk compression modulus of the
target material. As a result, we get:
, 1 2D Dmy r y y y , (8)
where
1
1 2Dm CKnV R E n rV E n
. It is clear
that the acoustic pulse excited by the deformation
mechanism coincides in shape with the thermoacoustic
pulse shown in Fig. 1, however, in this case it is
necessary to put m Dm .
Thus, the deformation pulse, like the thermoacoustic
one, is the bipolar wave that has the maximum
(compressive stress) on the leading front (y = 0) and the
equal minimum (stretching stress) on the rear front
(y = 2).
Impact (dynamic) mechanism. The generation of
the stress wave also occurs as a result of the transfer of
the ion momentum to the substance in the NTP volume
during the ion-ion relaxation time . Considering the
condition << 2R s , it can be assumed that the ion
NTP, being at rest at 0t , instantly acquires speed
2v MnE V E n at the moment 0t . This
acceleration of the spherical NTP causes wave
excitation of the elastic medium. In the hydrodynamic
approximation, the acoustic stress field in the wave zone
is given by the expression [10]:
, , , sin
4
y
I Imr y r e y
, (9)
where
1
, 2 cosIm r sR E n MnE V E n r
,
is the angle between the radius-vector r and the
momentum of the primary ion; M is the mass of the
carbon atom. The impact stress is the spherical wave
with the effective spatial length ~ 2R(E), which
diverges from the NTP at the longitudinal sound
velocity s and decreases with distance as r
-1
. Its
amplitude I is proportional to the momentum of the
primary ion and depends on the angle according to the
law ~ cosI . For the direction 0 , the amplitude
of the impact pulse is maximum. In the direction
perpendicular to the velocity vector of the incident ion,
the amplitude of the impact component is zero.
In Fig. 2 shows the universal form (time
dependence) of the impact acoustic pulse in the wave
zone in the dimensionless variables y and I Im . The
calculation is made for the case when the detection
point lies on the direction 0 .
Fig. 2. Universal function of the time dependence of the
impact pulse excited by the spherical NTP
As one can see from Fig. 2, the impact acoustic
pulse is the bipolar wave, which has the maximum
(compressive stress) at the leading front (y = 0) and the
minimum (tensile stress) at the time of y = 1.57. At the
same time, the half-waves of compression and
rarefaction are sharply asymmetric: compressive
stresses are about 5 times larger than tensile stresses, but
the half-wave of rarefaction is stretched out in time by
about the same number of times.
The total amplitude of the acoustic pulse is given by
the expression:
, , , , , ,T D Iy r y r y r y r . (10)
In Fig. 3 shows the acoustic pulses that are excited
in the diamond-like coating (DLC) by the ions of
hydrocarbon molecules with energy E = 100 eV,
formally calculated for the distance r R E n from
the center of the NTP (case 0 ). To obtain the value
of the acoustic stress at the point r >> R(E/n) it is
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №2(144) 113
necessary to take into account the geometric factor and
multiply the data shown in Fig. 3, on R E n r .
Fig. 3. Acoustic pulses excited in the DLC by ions of
hydrocarbon molecules with energy
E = 100 eV ( 0 )
The effective duration of the total acoustic pulse, as
well as its components, is 13~ 2 10t R E n s s , it
decreases with the number of carbon atoms in the
hydrocarbon molecule and increases with the energy of
the ion (Fig. 4).
Fig. 4. Dependence of the effective duration of the
acoustic pulse excited by the NTP ion on the ion energy
for various ions of hydrocarbon molecules
Based on the fact that the maxima of all three
components of the acoustic pulse are reached at the
leading front (y = 0), the maximum amplitude of the
total acoustic pulse is given by the expression
, , cosm Tm Dm ImE E E E . (11)
In Fig. 5 shows the dependence of the maximum of
the total amplitude of the acoustic pulse on the ion
energy for CH4, C2H2, and C6H6 ions in DLC at 0 .
As can be seen from the presented material, the
acoustic response of the material to the bombardment of
the hydrocarbon molecule ion is the powerful pulse with
the amplitude of tens of gigapascals and subpicosecond
duration which decreases with distance according to the
law ~ 1 r . Such pulses expire quickly when passing
through the target material. However, if harmonic
oscillations sinu t are characterized by the decay
with distance according to the law
r
~ и e ,
then
for a time-limited pulse, which is a superposition of
harmonics with frequencies from the interval
0 2 Cs R E n , the decay law is determined by
the total contribution of all components and is no longer
exponential. As a result, the shape of the pulse, its
duration and the law of spatial decay also change.
When calculating the pulse passing through the
absorbing medium, the dispersion of the sound velocity
can be neglected and limited only to absorption, since
absorption leads to the disappearance of harmonics with
the large dispersion from the pulse spectrum. In this
case, taking into account the effect of the absorbing
medium on the acoustic pulse is reduced to the integral
transformation of the amplitude in the medium without
absorption and dispersion:
0
0
1
, , cos
t
r
atu r t u r e t d d
.(12)
Fig. 5. Dependence of the maximum total pulse
amplitude on the ion energy for various hydrocar
bon ions
In the most important case 2 ,
characteristic of absorption in amorphous bodies and
dielectric single crystals, we obtain the following
dependence on r for the point thermal peak [8,12]:
2 2
2
1
2
at
E E n
r
e s r
. (13)
The resulting expression describes the distance
dependence of the amplitude of the acoustic pulse also
for the non-local peak, but only for the interval
2 2, 4 ~ 3...10 nmatr r E n R E n s . At
smaller distances, the expression for the amplitude of
the acoustic pulse obtained without taking into account
absorption should be used for estimations.
Analogous considerations make it possible to obtain
approximate expressions for the deformation and impact
components of the acoustic pulse. As a result, for the
full amplitude of the acoustic pulse from the NTP of the
hydrocarbon molecule ion, we obtain the following
expression:
1
1
2 2
2 2 cos
, ,
2
2 2 cos
, .
2
at
at
at
E KnV s MnER
R r r
r V
r
E KnV s MnE
r r
e s r
(14)
Here, for brevity, we use the notations R R E n
and V V E n .
114 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №2(144)
At r ~ rat(E/n), the acoustic stress amplitude of the
passes from one asymptotic dependence to another.
Note that the limiting distance rat(E/n) increases with
the energy E of the ion and decreases with the number
of carbon atoms n in the hydrocarbon molecule.
The acoustic pulse in the interval r > rat(E/n) turns
into a bipolar antisymmetric wave, the spatial length of
which depends weakly on the radius of the NTP and
increases with the distance r according to the law
r s r . In this range of distances, absorption
leads to a power-law (not exponential) dependence on
the distance, and the pulse amplitude depends only on
the integral characteristics of the NTP: E, (E), V1, n
and does not depend on the radius of the NTP. The
independence of the pulse amplitude and duration on the
NTP size allows the use of the “point” approximation
for ions with energy E >> 1 keV, although the spherical
NTP model may no longer be applicable to them. The
relative contributions of different mechanisms to the
total acoustic pulse remain valid in this interval as well.
FRAGILE DESTRUCTION
Acoustic stresses arising near the NTP of heavy,
low-energy ions are large enough to lead to brittle
destruction of the material. Dynamic strength of metals
is d ~ 1 HPa. Such stress occurs, for example, when the
material is instantly heated to temperatures T ≥ 10
3
K,
which are characteristic of the NTP of low-energy ions.
An additional contribution to acoustic stress is made by
deformation and impact (dynamic) generation
mechanisms. It should be noted that the leading front of
the stress pulse, which has the largest value, is the
compressive stress and cannot cause brittle destruction
of the material. The possibility of destruction occurs
when the pulse reaches the boundary with a material
that has a lower acoustic rigidity and is reflected from it
with repolarization.
Let's discuss the possibility of brittle destruction in
the immediate vicinity of the near-surface NTP. In the
region of peak localization, the stress is a superposition
of the spherical bipolar wave diverging from the volume
of the peak and reflected from the free boundary of the
target, and static thermoelastic stress present in the
material near the peak. The analysis shows that the
contribution of static compressive stress leads to the fact
that compressive stresses constantly prevail near the
near-surface NTP, and, therefore, brittle fracture is
impossible here [11].
Another situation occurs near the interface of the
coating with the substrate, which is distant from the
NTP by a rather large distance of 2r R E n ~3 nm.
When an acoustic pulse normally falls on the interface
between two materials, the reflection coefficients D12
and transmission k12 are given by the expressions
12 2 2 1 1 2 2 1 1D s s s s , 12 2 2 2 2 1 12k s s s ,
where 1 2, are the densities of the materials, and
1 2,s s are the longitudinal velocities of sound. The
acoustic pulse comes from material “1” to its border
with material “2”. If the acoustic pulse from the DLC
arrives at the boundary with the substrate that has a
much lower rigidity (vacuum, polyethylene, silicon),
then 12 1D and 12 1k , i.e., the acoustic pulse is
almost completely reflected with a change in sign. If the
acoustic pulse arrives at the boundary with a material
with the close acoustic rigidity, as in the case of the
DLC on stainless steel substrate, then we have 12 1D
and 12 1k , that is, the acoustic pulse passes from the
coating to the substrate, practically without being
reflected and without changing in magnitude. Finally, if
the acoustic rigidity of the substrate exceeds that of the
coating, the pulse is reflected from the interface without
repolarization, and the coating does not break down
either.
The stress distribution in the coating near the
boundary is obtained as the sum of direct and reflected
stress pulses:
12,tot x t x st R D x st R , 0x .
(15)
Here 0x is the coordinate of the boundary, on
which the stress pulse comes from the negative half-
space; moment 0t corresponds to the arrival of the
leading front of the pulse at the interface.
In Fig. 6 shows the spatial distribution of stresses at
different time points Ct R E n y s near the
boundary of the coating with the substrate that has a
much lower rigidity, when the acoustic pulse excited by
the nonlocal elastic peak of the CH4 ion with energy of
100 eV is incident.
As can be seen from Fig. 6, the repolarization of the
pulse at the boundary and the combination of the
reflected pulse with the direct that leads to the
occurrence of significant tensile stress near the
boundary, which can lead to brittle destruction (peeling)
of the material. The maximum tensile stress is observed
at distance R E n from the boundary and is equal to
~1.2m in magnitude, where m is the maximum
compressive stress in the direct impulse. Thus, the effect
of brittle fracture must be taken into account when
depositing nanometer DLC on materials with low
stiffness, for example, on polymers.
The obtained pattern of stress distribution is correct
if the distance from the NTP to the boundary does not
exceed attr . Otherwise, it is necessary to take into
account the effect of absorption on the amplitude of the
acoustic pulse.
In Fig. 7 shows the dependence on the distance of
the maximum of the acoustic stresses generated by the
NTP of CH4
+
and C6H6
+
ions of different energies in the
DLC carbon coating. In connection with the above,
Fig. 7 also displays the maximum tensile stresses that
occur when the acoustic pulse is reflected from the
boundary with a “soft” substrate, which is distant from
the NTP by distance r.
The horizontal dash-dotted line shows the level of
critical stress that causes brittle failure of the coating
material, the vertical dashed-dotted lines mark the
distances from the NTP corresponding to the critical
stress for different ions. As can be seen from Fig. 7, the
maximum coating thickness at which brittle fracture is
possible does not exceed 10 nm for ions with energy of
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №2(144) 115
less than 1 keV. That is, such a danger exists only for
nanometer-thick films and coatings. For ions of higher
energies, this thickness, of course, increases. So, as can
be seen from Fig. 7, for C6H6
+
ions with energy of
10 keV, the limit thickness is 20 nm.
Fig. 6. Spatial distribution of stresses created by the
acoustic pulse reaching the free boundary of the DLC
film at different time points
ACCELERATION
OF DEFECT MIGRATION
When the acoustic stress arising around the NTP
exceeds the corresponding activation thresholds, various
kinetic processes can be stimulated in the deposited
material: diffusion of defects and impurities, structural
rearrangement, and creep [12]. Thus, the equation for
the boundary of the region isr E, ,n , inside which the
acoustic pulse from the NTP activates the movement of
interstitial atoms, has the form:
, ,at is is isr E n U , (16)
where Uis is the activation migration energy of the
interstitial atom; is is its volume. Taking Uis = 0.1 eV,
is=5·10
-23
сm
3
(the volume of the interstitial atom in
carbon), we obtain i iis s sU ~ 0.3 GPa for the
stress that activates the migrants. Activation will occur
everywhere around the NTP, where the amplitude of the
acoustic wave exceeds is. The set of solutions
, ,isr r E n of equation (16) lies on the surface of
the ellipsoid of rotation extended in the direction θ = 0
due to dipole component in the amplitude at r . This
surface is the boundary of zone of interstitial activation.
r, nm0.1
1
10
100
GPa
10
0.1
1 keV
10 keVC H6 6
C H6 6
C H6 6
CH4
CH4
0.1 keV
0.1 keV
1 keV
maximum brittle fracture distance
for different ions
brittle fracture threshold
interstitial activation threshold
maximum interstitial activation
distance for different ions
1
Fig. 7. Spatial dependence of acoustic stresses excited in DLC coating at implantation of CH4
+
and C6H6
+
ions with energies of 10
2
and 10
3
eV
The limit of the area of activation of interstitial
defects in the longitudinal direction is determined using
the graph of the spatial dependence of acoustic stresses
excited in diamond-like carbon by hydrocarbon ions
(see Fig. 7). The horizontal dashed line shows the level
of the critical stress that activates the movement of
interstitial defects, the vertical dashed lines mark the
distances from the NTP corresponding to the critical
stress for different ions. As can be seen from Fig. 7, the
dimensions of the activation region, where the over-
barrier movement of migrants occurs, significantly
depend on the type and energy of the ion. Thus, for the
NTP of the CH4
+
ion with energy of 10
2
eV, the limit of
the activation region is distant from the peak by distance
of rC(10
2
) = 8 nm, while in the case of the C6H6
+
ion
with energy of 10
3
eV, the limit is moved to 20 nm.
Note that at a relatively small activation energy
Uis ≤ 0.1 eV, which is characteristic of interstitial
defects, the radius ris, which determines the limit of the
activation region, lies in the region atr r . In this
116 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №2(144)
region, it is the absorption that determines the size and
shape of the stress pulse. This also leads not to
exponential, but to a slower power-law dependence of
the stress on the distance at(r) ~ 1/r
2
. In this range, ris
increases both with energy and with the number of
carbon atoms in the hydrocarbon molecule (see Fig. 7).
In addition, in this range, the pulse amplitude depends
only on the integral characteristics of the NTP, namely
on E, E , V1, and n, and does not depend on the NTP
size. This makes it possible to estimate the amplitude of
the acoustic pulse for ions of high energies, for which
the NTP model is no longer applicable. So, in Fig. 7
shows the distance dependence of acoustic stress
excited by the C6H6
+
ion with energy of 10 keV, for
which the activation zone of the interstitial ris is shifted
to 40 nm.
It is likely that the influence of acoustic pulses
generated by NTP ions is not limited to direct activation
of defects. The well-known thermal activation of a
kinetic process can accelerate the migration of defects
by reducing the activation energy U in the stress field of
the acoustic pulse from the NTP:
, , ~ , ,ef is atU E n U r E n . (17)
Here is is the volume of the interstitial defect. The
acceleration coefficient K of the kinetic process at the
point r where the acoustic stress is currently present is
approximately equal to
0exp , ,is at BK r E n k T , (18)
where T0 is the temperature of the target, kB is the
Boltzmann constant. It can be seen from (18) that the
lower the temperature of the target T0, the greater the
relative acceleration of the kinetic process due to
acoustic activation. Estimates show that heavy ions,
including hydrocarbon ions, can significantly accelerate
the diffusion of interstitial defects at distances up to
300 nm at room temperature of the target material. Such
an effect can ensure the defect-freeness of nanometer
coatings deposited from ion flows of hydrocarbon
molecules. This conclusion agrees with the available
experimental data on the enlightenment of ~ 0.1 μm
thick carbon films by Ar
+
ions with energy of ~ 1 keV
[4, 5].
CONCLUSIONS
1. The acoustic effect of the single low-energy ion
of hydrocarbon molecule falling on the diamond-like
carbon coating was studied. The analysis showed that
the generation of the stress wave occurs in the NTP i. e.,
in the nanometer region, where the energy and
momentum transferred from the ion to the target
particles are contained. The NTP model for the
monatomic ion, which was developed earlier, was
generalized to the case of hydrocarbon molecule ions
when determining the space-time and energy parameters
of the NTP.
2. The generation takes place as a result of the joint
action of the following mechanisms: (a) thermoacoustic,
associated with rapid heating of matter in the NTP;
(b) deformation caused by the rapid introduction of the
introduced volume of the ion into the volume of the
NTP; (c) impact, associated with the transfer of the ion
momentum into the volume of the NTP.
In the linear acoustic approximation, the total
amplitude of the stress pulse excited by the spherical
NTP was found. The size and shape of the stress pulse
generated by CH4, C2H2, C6H6 ions were investigated.
It was established that sound absorption affects the
size and shape of the stress pulse at distances r > rat.
The extinction length rat lies in the interval from 3 to
10 nm for the considered ions CH4, C2H2, C6H6 with
energy from 100 eV to 1 keV. For a realistic quadratic
dependence of the absorption coefficient on the
frequency, the spatial attenuation of the stress amplitude
is given by a power-law dependence 2
at r instead
of the exponential that which is typical for harmonic
oscillations. This relatively slower spatial decrease of
the amplitude of the stress pulse expands the role of
acoustic effects in the kinetic processes occurring in the
material under ion radiation.
3. The spatial dependence of acoustic stresses
generated by CH4, C2H2, C6H6 ions in DLC coating was
studied in order to determine the influence on the
processes of transport and destruction. Acceleration of
the migration of interstitial defects takes place in the
zone where the acoustic stress exceeds the limiting
stress of defect activation is = 0.3 GPa. The maximum
depth of acoustic activation is from 8 to 40 nm,
increasing with energy and the number of carbon atoms
in the incident ion. The activation zone has the shape of
the ellipsoid of rotation, elongated in the direction
0 due to the impact component in the amplitude of
the stress pulse.
The possibility of the defects migration accelerating
outside the activation zone by reducing the effective
activation energy in the field of the acoustic wave
excited by the NTP ion is discussed. Estimates show
that hydrocarbon ions can significantly accelerate the
diffusion of interstitial defects at distances up to 300 nm
at room temperature in a diamond-like target. Such an
effect can ensure defect-free nanometer coatings
deposited from flows of hydrocarbon ions.
The possibility of destruction of the coating occurs
when the acoustic pulse from the NTP reaches the
boundary with a substrate with lower acoustic rigidity.
The combination of direct and reflected pulses leads to
the occurrence of significant tensile stresses near the
boundary, which can lead to brittle fracture (to peeling)
of the material. The maximum thickness of the coating,
at which brittle failure at the boundary with the
substrate is possible, lies in the range of 3 to 10 nm for
ions CH4, C2H2, C6H6 with energy less than 1 keV, and
the maximum thickness increases with increasing ion
energy. This effect can be manifested when DLC are
deposited on materials with relatively low rigidity, for
example, on polymers.
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Article received 27.01.2023
РАДІАЦІЙНО-АКУСТИЧНІ ЕФЕКТИ ПРИ ОСАДЖЕННІ АЛМАЗОПОДІБНИХ
ПОКРИТТІВ З ПОТОКУ ІОНІВ ВУГЛЕВОДНІВ
ТА ЇХ ВПЛИВ НА КІНЕТИЧНІ ПРОЦЕСИ
О.І. Калініченко, В.Є. Стрельницький
На основі моделі нелокального термопружного піка (НТП) іона, що була узагальнена на випадок іонів
вуглеводневих молекул, досліджено акустичний ефект низькоенергетичного іона вуглеводневої молекули
при плазмово-іонному осадженні алмазоподібного вуглецевого покриття. Генерація хвилі напруження має
місце в результаті спільної дії механізмів, що пов’язані зі швидкою передачею енергії, імпульсу та
додаткового об’єму в об’єм НТП. Досліджено величину, форму та просторову залежність імпульсу
напруження, що генерується іонами CH4, C2H2, C6H6 з врахуванням поглинання. Обговорюється можливість
прискорення дифузії міжвузольних дефектів, а також можливість крихкого руйнування покриття на межі з
підкладкою під дією акустичних імпульсів від НТП іонів вуглеводнів, що осаджуються.
http://dx.doi.org/10.1016/S0257-8972(03)00684-4
https://doi.org/10.1016/j.surfcoat.2004.04.049
https://doi.org/10.1016/j.diamond.2005.10.022
https://doi.org/10.1016/j.nimb.2010.04.001
https://doi.org/10.1016/j.surfcoat.2006.08.127
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