Radiation-induced defect's clustering and self-organization during surface modification
Defects' clustering model is applied to study of the both: helium blistering in metal lattice and a thin film islands deposition. Plasma surface modification is investigated as a first order phase transition at a fluctuation stage. Wiener stochastic processes which are associated with the clu...
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| Опубліковано в: : | Вопросы атомной науки и техники |
|---|---|
| Дата: | 2006 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2006
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Radiation-induced defect's clustering and self-organization during surface modification / A.L. Bondareva, G.I. Zmievskaya // Вопросы атомной науки и техники. — 2006. — № 5. — С. 248-253. — Бібліогр.: 21 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859749866504192000 |
|---|---|
| author | Bondareva, A.L. Zmievskaya, G.I. |
| author_facet | Bondareva, A.L. Zmievskaya, G.I. |
| citation_txt | Radiation-induced defect's clustering and self-organization during surface modification / A.L. Bondareva, G.I. Zmievskaya // Вопросы атомной науки и техники. — 2006. — № 5. — С. 248-253. — Бібліогр.: 21 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | Defects' clustering model is applied to study of the both: helium blistering in metal lattice and a thin film islands
deposition. Plasma surface modification is investigated as a first order phase transition at a fluctuation stage. Wiener
stochastic processes which are associated with the clustering evolution as well as with the defects motion are used.
Brownian motion due to a long-distance potentials of indirect interaction blisters (or islands): through acoustic
phonons and Friedel's oscillations of lattice's electronic density has been modeled. Stochastic simulation has involved
the analyse of a follows self-organization structures: vacancy-gaseous bubbles layers (or porosity) and islands
chains on the surface with roughnesses.
Модель кластеризации приложена к изучению: гелиевого блистеринга в металлах и осаждение островковых тонких пленок. Модификация поверхности плазмы исследована как фазовый переход 1-го рода на флуктуационной стадии. Исследован Винеровский стохастический процесс, который ассоциируется с эволюцией кластеризации и с движением дефектов. Промоделировано броуновское движение благодаря дальнодействующим потенциалам непрямого взаимодействия блистеров (или островов): через акустические фононы и Фриделевские осцилляции электронной плотности. Стохастическое моделирование включает анализ следующих самоорганизующихся структур: слои вакансионно-газовых пузырей (или пористость) и неупорядоченные цепочки островов на поверхности.
Модель кластерізації прикладена до вивчення: гелієвого блистерінгу у металах та осадженню
острівкових тонких плівок. Модифікація поверхні плазми досліджена як фазовий перехід 1-го роду на
флуктуаційній стадії. Досліджено Вінерівський стохастичний процес, котрий асоціюється з еволюцією
кластерізації та рухом дефектів. Промодельовано броунівський рух завдяки далекодіючим потенціалам
непрямої дії блістерів (або островів): через акустичні фонони та Фриделевські осциляції електронної
густини. Стохастичне моделювання включає аналіз наступних структур самоорганізації: шари вакансійно-
газових пузирів (або пористість) і неупорядковані ланцюги островів на поверхні.
|
| first_indexed | 2025-12-01T23:35:18Z |
| format | Article |
| fulltext |
RADIATION-INDUCED DEFECT'S CLUSTERING AND SELF-ORGANI-
ZATION DURING SURFACE MODIFICATION
A.L. Bondareva, G.I. Zmievskaya
Keldysh Institute of Applied Mathematics
Russian Academy of Sciences, Moscow, Russia
E-mail: zmi@keldysh.ru
Defects' clustering model is applied to study of the both: helium blistering in metal lattice and a thin film islands
deposition. Plasma surface modification is investigated as a first order phase transition at a fluctuation stage. Wiener
stochastic processes which are associated with the clustering evolution as well as with the defects motion are used.
Brownian motion due to a long-distance potentials of indirect interaction blisters (or islands): through acoustic
phonons and Friedel's oscillations of lattice's electronic density has been modeled. Stochastic simulation has in-
volved the analyse of a follows self-organization structures: vacancy-gaseous bubbles layers (or porosity) and is-
lands chains on the surface with roughnesses.
PACS:52.77.-j
1. INTRODUCTION
The evolution of humanity needs new materials with
specific properties and as result it, development of nan-
otechnologies. The paper deals with computer simula-
tion of properties of nano-modified materials and de-
posited thin films also as defects in materials which are
planed as thermonuclear technologies and materials.
Self-organization widely known today: among them are
the processes of streamlining the particles movement in
plasma both recreated in laboratory scale plant and ob-
served in nature. This process depends on transforma-
tion of energy received from outside into heat; in that
case the groups of waves and particles intensively inter-
act in vast space, and this determines probability for for-
mation in plasma of stable large-scale structures [1,2].
The emergence (without special outside influence) of
streamlined structures and forms of movement on the
basis of the initially accidental, unregulated ones are de-
scribed as self-organization. And the fact is that the
whole system where this takes place acquires properties
that were lacking in its parts [3]. Typical of such phe-
nomena, nonlinear in there nature is of course a great
number of closely interacting independent parameters
and they always depend on energy received from out-
side. Also, in this way, it exists the fundamental prob-
lem: defects' origin in condensed matter or on the sur-
face solid body models which can be seen as a plasma-
like media evolution. It has to be associated with transi-
tions from chaos to self-organization and back: So, here
is extremely difficult to working out this problem. The
most promising way in this direction is plasma comput-
er simulation [2]. The problem of the phase transition at
inequilibrium stage kinetic description is introduced by
stochastic simulation method [3,4]. New approach is
based on the strict results of the probability analysis of
equations of mathematical physics [5]; the kinetic theo-
ry of plasma and rarefied gases [6]; the theory and prac-
tice of numerical experiment in non-linear plasma simu-
lation [2]. The progress in computer engineering allows
us to see the overall picture of initial stage of phase
transition in detail the behavior of defects origin, reten-
tion of vacancy-gaseous bubbles into lattice. The defects
(flaws) have been stratificated in lattice as defects layers
near surface. The development of this structure of de-
fects leads to following: porosity, swelling, flacking and
others harmful effects. Plasma- surface interaction is de-
picted as a plasma-like media with the adequate mathe-
matical description of various dynamic processes
brought about the construction of models taking into ac-
count the random fluctuations of the trajectories of these
processes. The large number of stochastic dynamical in-
dependent variables {x1(t),...,xN(t)} are obeyed to the
set of Ito-Stratonovich stochastic differential equations
/SDE/. The SDE system solution is connected with the
study of "forward" and "backward" Kolmogorov equa-
tions of parabolic type for distribution density of
Markov process. The relationship SDE solution to linear
parabolic partial differential equation [5,7], absolutely
stable algorithms for the given integration step size [7]
and modification of Artem'ev method for SDE with
non-linear coefficients solution [4,5,8-12] give us a
powerful tool for self-organization structures detection.
Helium ions and metal lattice would constitute a "open"
system as well as the defects interaction each others
leeds to specific form of self-organization into phase
spaces which associated with blistering problem. We
can also to observe the appearance of the fundamental
properties of loss of stability in system regarded as a
medium with large number degree of freedom. The in-
sight into the kinetic description of phase transition can
be extended by determination of distribution function of
gaseous phase in a bubbles versus the both: sizes and
coordinates. Defects appears into lattice under plasma
action on the time scale of interest when the medium
state is strongly non-equilibrium. Basic macroscopic
characteristics (the so-called moment of the distribution
function) are obtained by averaging the non-equilibrium
kinetic distribution function. The defects (flaws) have
been stratificated in lattice as defects layers near sur-
face. The development of this structure of defects leads
to following: porosity, swelling, flacking and others
harmful effects. High temperature blistering (or un-
charged defects clustering model) of He ions on a sur-
face Ni is developed in two time scales no later than 10-4
s. under follows parameters of plasma beam: energy
E=10 keV, ions flux density and dose approximately is
equal to 1016.
_____________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2006. № 5.
Серия: Плазменная электроника и новые методы ускорения (5), с.248-253.248
2. STOCHASTIC SIMULATION MODEL
We start simulation the phase transition by numeri-
cal approach, using the model of diffusive Markov's
process (MP) in a phase space {G} with size g of arising
bubbles as well a liquid metal thin film islands: {g(t),t≥
0}, g>2. Here the g(t=0)=g0, size g means the number of
unit volumes of "condensing" substance in the bubble
nucleus (however, it is possible also to consider the ra-
dius r of spherical bubbles or hemispheres drop of liq-
uids on the surface). The maximum of cluster size (let
us name this nucleus- cluster) is determined by condi-
tions of stability of bubble. Collisions and fluctuation
processes has produced the nuclei of new phase
(gaseous into lattice as well liquid on the lattice surface)
out of "super saturation" condition which can be de-
scribed by Ito stochastic differential equations/SDE/the
both are statistically equivalent to equations of Fokker-
Planck-Kolmogorov (FPK) and Boltzmann-like (or
Leontovich), this allows us to take the numerical solu-
tion of SDE systems is to be seen a method for the solu-
tion of Mathematical Physics Equations (MPE) for
study non-equilibrium first-kind transition processes.
The coefficients of both problems (SDE and MPE) are
related by definitions and properties of non-look-ahead
functionals of Marcov's random processes. The algo-
rithms for solution of a set of linear Ito-Stratonovich
SDE [5] by with constant coefficients have been modi-
fied for simulation and analysis of the problems with
functional-coefficients [3,7,8], in case of heterogeneous
to non-equilibrium stage of "condensation" of gaseous
particles. We assume that formation of clusters of de-
fects and evolution of their size is to be described by ki-
netic equation for f(x,y,t) of transitional probability den-
sity of a random MP {X(t),t≥0}. Here we talk about
Kolmogorov's equation (i.e., about partial differential
equations of parabolic type), which is related with
Wiener process. The kinetic equations for Brownian
particle are partial integral-differential equations [3,7]
and its have laborious methods for solving. Rate of bub-
ble/cluster growth (or degradation) and its migration
have different characteristic time scales which equal for
blistering τg ≈ 10-9, τr ≈ 10-8 s and τg ≈ 10-8, τxy ≈ 10-7 s
for film covering correspondingly. Thus, kinetic equa-
tions on a discrete time grid are solved by technique of
splitting in terms of physical processes, and every stage
is represented by its stochastic analogue. Interaction be-
tween bubbles/clusters is indirect, through lattice
phonons and electron density oscillations [9-16]. The ki-
netics equations after physical processes split look like
following, W is Wiener process. The kinetic equations
for Brownian particle are partial integral-differential
equations [3,7] and its have laborious methods for solv-
ing.
{ }
)(
),,(
),(),(
1
),(
),(
),(
αα fS
g
g
trg
tgrftggD
kT
g
g
tgrftggD
t
tgrf
+
∂
∂
∆ Φ∂
∂
+
+
∂
∂
∂
∂
=
∂
∂
,0)0,( gfgrf = ,0
2
),(
=
≤gdg
tgrdf
,02|),( =<gtgrf
,
),(),(),(
),(
),(
r
trgf
gM
trF
r
r
trgf
trrD
t
trgf
∂
∂
−
∂
∂
∂
∂
=
∂
∂
γ
,00|),( rfttrgf ==
,
right
|),(
left
|),( xxtrgfxxtrgf ===
right
|),(
left
|),( yytrgfyytrgf ===
.
Rate of bubble/cluster growth (or degradation) and its
migration have different characteristic time scales which
equal for blistering τg ≈ 10-9, τr ≈ 10-8 s and τg ≈ 10-8, τxy
≈10-7 s for film covering correspondingly. Thus, kinetic
equations on a discrete time grid are solved by tech-
nique of splitting in terms of physical processes, and ev-
ery stage is represented by its stochastic analogue. Inter-
action between bubbles/clusters is indirect, through lat-
tice phonons and electron density oscillations [9-16].
The kinetics equations after physical processes split
look like following, here is molar volume of liquid
molecules, are temperature and density of vapour
molecules. We consider single spherical nucleus with
radius of gaseous or liquid cluster r, comprising g single
droplets with molar volume. Sα is source of vapour
which generates ion with fα − maxwell ion function,
which is characterized by temperature 2500 K, g is the
number of atoms which is consisted in island-clusters,
Dg is the non-linear diffusion coefficient in the space of
cluster sizes; f(g) is the bubble size distribution function
– the probability to find the cluster with size g in inter-
val of values of g [g,g+∆g], ∆Φ is the Gibbs energy, Mg
is the cluster mass, γ is constant of friction, distribution
function f(r) is the islands space function, r is the posi-
tion of cluster mass centre in orthogonal coordinates
system: xleft = -200, xright = 200, yleft = -200, yright = 200,
)(rU
is the potential of long-range clusters interaction
between them through phonons and oscillation of elec-
tron density. The modelling 3-dimensional region is pe-
riodic across two coordinates (x and y) across the third
coordinate (axis z): on top the region contacts with plas-
ma, on bottom we have reflection from crystal lattice
layers undisturbed with vacancy and helium impurity
negligible concentration (for simplicity vacancies de-
scription here is not demonstrated). There are equations
involving partial derivatives of blister coordinate into
lattice and its size measured in number of gaseous parti-
cle without compression.
2)( ]
max
g;
min
[
0
)
0
(
0
),(2
),(
2
1),,(
),(
1
>∈=≤≤
+
∂
∂
−
∂
∆ Φ∂
−=
tgggtgkTtt
dWtggD
g
tggD
g
trg
tggD
kTdt
dg
;
2
1),,(1
x
xD
x
zyxU
gMxH
∂
∂
−
∂
∂−=
γ
,2 xD=σ
_____________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2006. № 5.
Серия: Плазменная электроника и новые методы ускорения (5), с.248-253.249
( ) ( ) ( ) ( ) ( )( ) ++= ∫ τττττ dzyxHtxtx
t
t
x ,,,
0
0
( ) ( ) ( )( ) ( )τττττσ dWzyx
t
t
∫+
0
,,, ,
∆>∆ Φ
∆ Φ−∆ Φ++−Φ−
∆<∆ Φ
∆ Φ++−Φ−
=∆ Φ
breaktrg
ifbreakrbggca
breaktrg
ifrbggca
trg
),,(
,3/2)(
;),,(
,3/2)(
),,(
breakbrNbreak ∆=∆ Φ ,
where )( αχβχη −=Φ aa is part of Gibbs potential
connected with difference of chemical potential of phas-
es (gas in blister and metal lattice/vapour and liquid), c
is part of Gibbs potential concerned with elastic force of
lattice reaction for blister and with weight of cluster for
thin films formation, tensions on boundaries between
different phase are taken into account using, ∆Φr con-
siders bubble/cluster place in lattice/on surface, ∆Φbreak
concerns with relcases of part of connections in lattice
for blistering, Nb is number of broken bonds, ∆break is the
energy required for breaking of a single bond with lat-
tice. )( αχβχ − is difference of chemical potential of
phases
+−
=
ilmfor thin f
V
ringfor bliste
V
a
3
)
3
coscos32(
3
2
θθπ
π
η ,
− form factor, where V is atom volume of He (for blis-
tering) and evaporated material for thin films formation,
(θ-angle of contact, α is first metal vapour, β is cluster
of liquid metal on surface, S is phase of second more re-
fractory metal (substrate material).
−+−
=⋅−
=
−
filmsthinfor
blisteringforVbgb
b
SS
bl
)(sin)cos1(2
)36(),3/11(
2
3/23/1
0
3/1
0
αβα β σσθπσθπ
σπ
where SS α
σ
β
σ
α β
σ ,, are surface tension between
vapour of metal and metal liquid in island, liquid island
and substrate, vapour and substrate.
−−Ψ
−+
+−+−
=∆ Φ
filmthin
a
y
a
x
g
blisteringxk
ykxk
r
yx
zz
yyxx
))2cos()2cos(2(
))(2cos(
))(2cos())(2cos(
ππ
ϕπ
ϕπϕπ
The common form of diffusion coefficient in the
space of defects sizes is Dg=Dg0g2/3, Dg0 is calculated co-
efficient.
The long- range part of the interaction between un-
charged defects in dielectric crystals is elastic interac-
tion through the acoustic phonons. The indirect interac-
tion take place in metal lattice also via influence Friedel
oscillation in electron density, for spherical Fermi sur-
face analytically derived the dependence upon the dis-
tance between defects. Model assumption in approxima-
tion of potential: distance R between defects has been
selected as a distance between centre of mass blisters.
The correlations which it appear in system in conse-
quence of this indirect interaction of defects each with
another. The potential of indirect interaction, which in-
fluences on migration defects such as bubble in lattice
and clusters on surface, can be presented as
dsdd UUU += where Udd is potential of indirect inter-
action between defects of one kind (blister-blister or
cluster-cluster),
∑
≠
+=
−
−
+
−
−
−+−
−
∑
≠
++=
−
−
+
+
−
−
−+−+−
−
=
+
N
ji
nanofilmyxr
jrir
jrirrccrca
jrir
jrir
jyiyjxix
rcb
N
ji
blisterzyxr
jrir
jrirrbcrba
jrir
jrir
jzizjyiyjxix
rbb
ddU
22
3||
)(cos(
3||
4)(
4)(4)(
5
3
;222
3||
))(cos(
3||
4)(
4)(4)(4)(
5
3
Uds is potential of indirect interaction between defects of
two different kinds (between bubble and surface for
blistering and between liquid cluster of less refractory
metal on substrate surface of more refractory metal and
linear dislocation on surface or in near surface region).
___________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2006. № 5.
Серия: Плазменная электроника и новые методы ускорения (5), с.
250
∑
−
−
+
+
−
−
+−+−
−
=
d
nanofilm
drir
drirdcda
drir
drir
dzdyiydxix
db
blistering
z
surfA
dsU
3||
))(cos(
3||
4)(
4)(4)(4)(
5
3
2
brb, arb, crb, brc, arc, crc, bs, as, cs, bd, ad, cd are model coef-
ficients, z of surface is equal zero for blistering and z of
dislocation is equal dislocation depth for thin film for-
mation, if dislocation is located under surface and dislo-
cation z is equal zero if dislocation is located on sub-
strate surface.
In case of blistering (the situation of open system) is
created by a flux of inert gas atoms:
),,,(),( tzyxDtrD rr =
is the diffusion coeffi-
cient for space {R == (x, y, z)}, γ is the dissipation fac-
tor. As for coefficients of stochastic diffusion used for
modeling of bubble walk, we introduced a temperature
dependence and accounted the nonlinear coefficients by
expression:
( )20 1 z
M
eDD
g
kTE
z
m
∆+=
−
α
γ ,
D0 = 3,73⋅10-7 cm2/s, Em = 0.35 eV, x0, y0 , z0 are the ini-
tial values of coordinates x, y, z of a cluster. Diffusion
coefficient looks similar form for case of thin film for-
mation.
3. STOCHASTIC SIMULATION NUMERI-
CAL SCHEME
Kinetic equation are changed on its stochastic
analogs [3,7,11-16], stochastic differential equations
/SDE/ are solved used modified authors Artem'ev
method [17]. SDE and modifications of Artem'ev
method for these models can be found in more early pa-
pers of authors [11-16]. To solve a system of SDE with
functional-coefficients, it is required to construct a se-
ries expansion for exact solution of Cauchy problem:
.
fin
0
,0 )())((0 ))((
0
)(
Tt
t dWxt dxHxtx
≤≤
∫+∫+= ττσττ
A modified Artemiev’s method was used; it is a sec-
ond-order accuracy method, with infinite domain of sta-
bility (according to methods developed for solving of
SDEs) [17]. The modification from the original
Artemiev’s method is that the coefficients in SDE are
essentially nonlinear and depend on flaw distributions
on their sizes and coordinates. The use of Stratonovich’s
form for SDE makes possible to take a standard white
noise instead of random function ξ (t), and this simpli-
fies the calculation procedure of stochastic integral for
the Wiener process in realization of the numerical
method. As a sample, we can take the equation for cal-
culation of the bubble size. For the ith trajectory of dif-
fusive Markov’s process its values gn+1 and zn+1 at the
time moment n+1 can be calculated through these for-
mulas:
,2
2
1
2
1
∂
∂
++×
×
−
∂
∂
−+=+
ng
i
ng
g
i
ngh
ng
i
ngh
i
nhH
g
i
nHh
I
i
ng
i
ng
ξσ
σ
ξσ
( ) ( )
( )
,
,
2
1
,
,1
i
n
n
i
n
i
i
n
n
i
n
n
i
n
i
g
i
ng
g
tgD
g
tgi
tgD
kT
H
∂
∂
−
−
∂
∆ Φ∂
−=
( ).,2 n
i
n
i
ng tgiD=σ
[ ]
=
−+=
∂
∂−
∂
∂⋅=
+
∂
∂⋅−+=
−
+
−
+
i
zn
i
zn
i
n
i
nz
i
zn
zn
i
zn
i
n
i
n
i
n
i
i
n
i
zn
zn
i
zn
i
zn
i
i
znzi
n
i
n
D
zzDD
z
D
z
zyxU
gM
H
hhH
z
HhIzz
2
))(1(
2
1),,(
)(
1
2
2
10
2
1
1
1
σ
α
ξ
γ
ξσ
In this method gn, zn are the approximation of SDE sys-
tem solution at grid points by time {t}, h, hz is the time
step for size and position changes correspondingly, I is
the unit matrix, ξn is the sequence of independent ran-
dom numbers with a zero expected value and unit dis-
persion. While modeling the SDE solution on a comput-
er, the values of ξn can be calculated by formula
)2cos(log2 21 π ααξ −=n , where α1 and α2 are random
numbers uniformly distributed in the interval (0,1).
We are able to present operator's scheme of comput-
er simulation as superposition of the operators A∆g, ABr,
AUD, AF, where A∆g –operator of size change; ABr –oper-
ator of lattice broken (for blistering only); AUD- operator
of space diffusion, defects interaction and interaction
between defects of two different kinds (between bubble
and surface for blistering and between liquid cluster of
less refractory metal on substrate surface of more refrac-
tory metal and linear dislocation on surface or in near
surface region); AF= AFus+ ASurf, AFus- operator of defects
fusions. The fusion of defects takes place if
fjidji aggrrr ∆++≤− /)( 3/13/1
, where 0≤ ∆f ≤a
(rd is radius of He for blistering or radius of adatom for
nanofilm, a is lattice parameter of substrate material).
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ASurf has meaning only for blistering and corresponds
with blister reflection from surface or destruction on it.
minz = 0, maxz
= 400; it is assumed that the cluster
dies on the surface if b)32( Rz ≤ (here
3
Heb grR =
is the bubble radius, rHe is the helium
radius).
4. RESULTS AND DISCUSSION
Note that blistering and thin film formation have
similar stochastic characters and are described similar
equations. Used approach allows us to receive nonequi-
librium distribution functions of bubbles/clusters con-
trasted with defect size and its space position, in terms
of its we receive evaluation of order parameter for each
problems and mathematical expectations of defects size
and others characteristics such as distance from the sur-
face, porosity evaluations of several solids layers and
the calculated tensions due to blistering, for example.
We should like to summurize results of simulation of
fluctuation stage of high-temperature blistering. In our
opinion, the most interesting results are: the self-organi-
zation of bubbles are observed, blisters form quasi-lat-
tice and blisters chains are formed athwart to incident
ions fluxes; the greatest porosity and tensions are ob-
served on depths of ∼ 0.85 Rp and ∼0.35Rp (Fig.1), Rp is
middle depth of projection run, these depths correspond
to locations of big and small blisters (Fig.2), which are
observed in laboratory experiments; the most rapid blis-
tering development is take place if temperature of sub-
strate material equals 0.47 of melting temperature. The
porosity can be considered as the order parameter of
first-kind transition for blistering. The porosity is
∑
∑
=
== N
i
i
N
i
jii
l
a
j
gfg
tzgfg
V
Vtzp
1
00
3
1
3
)(
),,(
),(
(Fig.1), where Va is total examined volume, Vl is layer
volume, N=10 is number of blister, g0 is initial blister
size in number He in blister, f(g0) is initial distribution
function from blister sizes. The fluence is 1017 ions/cm2,
energy of He ions is 10 keV, temperature is 1000 K for
presented calculation. Authors used 106 trajectory statis-
tics for kinetic distribution functions calculated. Two
maximums of porosity are good noticeable.
Fig.1. The figure 1 shows the relative porosity of differ-
ent solid layers as function from layer depth. Z is layer
depth from surface under irradiation measured in lat-
tice parameters
Fig.2. The distribution function from blister size (ab-
scissa axis, size is measured in Å) and depth (ordinate
axis, depth is measured in lattice parameter) is present-
ed by colours on this picture
The maximum located on depth approximately 0.85 Rp
(Rp is middle depth of projection run, for examined case
Rp=70 nm) is corresponded with “big” blisters. “Big”
blister can growth to 1 micrometer. The radiuses of
"big" blisters at finish of fluctuating stage are 10...14 Å
(Fig.2). The maximum located on depth approximately
0.35 Rp is conformed to “small” blisters which end sizes
can be 10-8...10-7 m. The radiuses of "small" blisters at
finish of fluctuating stage are 2...4 Å (Fig.2).
The most interesting results from thin films forma-
tion are: I) three stage of cover formation during fluctua-
tion stage are discovered. The first stage lasts from 0 to 8⋅
10-7 sec, it is stage of slow development. The second
stage continues from 8⋅10-7 sec to 5⋅10-5 sec and it is
stage of quick growth of thin film. The third stage lasts
from 5⋅10-5 sec to 10-4 sec and it is notable for decelera-
tion of growth velocity; II) The study of influence of
dislocation depth on thin film formation indicates that 1)
self-organization of clusters are observed, nanofilm for-
mation begins on surface defects in particular on dislo-
cations; 2) the dislocation influence is important if its
depth is less then 5 lattice parameters;
Fig.3. The dependence of the ratio of probability of lo-
cation clusters on projection of dislocation line on sur-
face from probability of location clusters outside pro-
jection of dislocation line on surface from dislocation
depth is presented on this pictur
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ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2006. № 5.
Серия: Плазменная электроника и новые методы ускорения (5), с.
252
3) if dislocation depth is more then 5 lattice parameters
that probabilities of cluster location on dislocation line
and outside it are equal; 4) the ratio of probability of lo-
cation clusters on projection of dislocation line on sur-
face from probability of location clusters outside projec-
tion of dislocation line on surface reduces with increase
of depth and equals 1 when dislocation depth is more 5
lattice parameters of substrate material. This is non-lin-
ear function (Fig.3); 5) the projection of dislocation line
on surface can be considered as center of nanofilm for-
mation if dislocation depth is less 5 lattice parameters;
6) if dislocation locates on surface that most heavy
growth takes place on dislocation. III) The ratio of cov-
ering square at the present situation from covering
square at the initial time moment can be considered as
order parameter for problem of nanofilm formation. The
evaluation of this ratio is presented on Fig.4.
Fig.4. The ratio of total islands square at the present
situation from total islands square at initial time mo-
ment is shown. The time in τxy∼10-7 s is put off on ab-
scissa axis
The work is partially supported by grant of president
of Russia for support of young Russian scientists МК-
1120.2005.1, Russian Science Support Foundation, the
program "Nanoparticles and nanotechnology" by De-
partment of Mathematical Sciences RAS.
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КЛАСТЕРИЗАЦИЯ РАДИАЦИОННО-СТИМУЛИРОВАННЫХ ДЕФЕКТОВ И САМООРГАНИЗА-
ЦИЯ ПРИ МОДИФИКАЦИИ ПОВЕРХНОСТИ
А.Л. Бондарева, Г.И. Змиевская
Модель кластеризации приложена к изучению: гелиевого блистеринга в металлах и осаждение остров-
ковых тонких пленок. Модификация поверхности плазмы исследована как фазовый переход 1-го рода на
флуктуационной стадии. Исследован Винеровский стохастический процесс, который ассоциируется с эво-
люцией кластеризации и с движением дефектов. Промоделировано броуновское движение благодаря даль-
нодействующим потенциалам непрямого взаимодействия блистеров (или островов): через акустические фо-
ноны и Фриделевские осцилляции электронной плотности. Стохастическое моделирование включает анализ
следующих самоорганизующихся структур: слои вакансионно-газовых пузырей (или пористость) и неупоря-
доченные цепочки островов на поверхности.
КЛАСТЕРІЗАЦІЯ РАДІАЦІЙНО-СТИМУЛЬОВАНИХ ДЕФЕКТІВ І САМООРГАНІЗАЦІЯ ПРИ
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ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2006. № 5.
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МОДИФІКАЦІЇ ПОВЕРХНІ
А.Л. Бондарева, Г.І. Змієвська
Модель кластерізації прикладена до вивчення: гелієвого блистерінгу у металах та осадженню
острівкових тонких плівок. Модифікація поверхні плазми досліджена як фазовий перехід 1-го роду на
флуктуаційній стадії. Досліджено Вінерівський стохастичний процес, котрий асоціюється з еволюцією
кластерізації та рухом дефектів. Промодельовано броунівський рух завдяки далекодіючим потенціалам
непрямої дії блістерів (або островів): через акустичні фонони та Фриделевські осциляції електронної
густини. Стохастичне моделювання включає аналіз наступних структур самоорганізації: шари вакансійно-
газових пузирів (або пористість) і неупорядковані ланцюги островів на поверхні.
___________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2006. № 5.
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254
|
| id | nasplib_isofts_kiev_ua-123456789-81276 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-01T23:35:18Z |
| publishDate | 2006 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Bondareva, A.L. Zmievskaya, G.I. 2015-05-13T19:51:19Z 2015-05-13T19:51:19Z 2006 Radiation-induced defect's clustering and self-organization during surface modification / A.L. Bondareva, G.I. Zmievskaya // Вопросы атомной науки и техники. — 2006. — № 5. — С. 248-253. — Бібліогр.: 21 назв. — англ. 1562-6016 PACS:52.77.-j https://nasplib.isofts.kiev.ua/handle/123456789/81276 Defects' clustering model is applied to study of the both: helium blistering in metal lattice and a thin film islands deposition. Plasma surface modification is investigated as a first order phase transition at a fluctuation stage. Wiener stochastic processes which are associated with the clustering evolution as well as with the defects motion are used. Brownian motion due to a long-distance potentials of indirect interaction blisters (or islands): through acoustic phonons and Friedel's oscillations of lattice's electronic density has been modeled. Stochastic simulation has involved the analyse of a follows self-organization structures: vacancy-gaseous bubbles layers (or porosity) and islands chains on the surface with roughnesses. Модель кластеризации приложена к изучению: гелиевого блистеринга в металлах и осаждение островковых тонких пленок. Модификация поверхности плазмы исследована как фазовый переход 1-го рода на флуктуационной стадии. Исследован Винеровский стохастический процесс, который ассоциируется с эволюцией кластеризации и с движением дефектов. Промоделировано броуновское движение благодаря дальнодействующим потенциалам непрямого взаимодействия блистеров (или островов): через акустические фононы и Фриделевские осцилляции электронной плотности. Стохастическое моделирование включает анализ следующих самоорганизующихся структур: слои вакансионно-газовых пузырей (или пористость) и неупорядоченные цепочки островов на поверхности. Модель кластерізації прикладена до вивчення: гелієвого блистерінгу у металах та осадженню острівкових тонких плівок. Модифікація поверхні плазми досліджена як фазовий перехід 1-го роду на флуктуаційній стадії. Досліджено Вінерівський стохастичний процес, котрий асоціюється з еволюцією кластерізації та рухом дефектів. Промодельовано броунівський рух завдяки далекодіючим потенціалам непрямої дії блістерів (або островів): через акустичні фонони та Фриделевські осциляції електронної густини. Стохастичне моделювання включає аналіз наступних структур самоорганізації: шари вакансійно- газових пузирів (або пористість) і неупорядковані ланцюги островів на поверхні. The work is partially supported by grant of president of Russia for support of young Russian scientists МК- 1120.2005.1, Russian Science Support Foundation, the program "Nanoparticles and nanotechnology" by Department of Mathematical Sciences RAS. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Приложения и технологии Radiation-induced defect's clustering and self-organization during surface modification Кластеризация радиационно-стимулированных дефектов и самоорганизация при модификации поверхности Кластерізація радіаційно-стимульованих дефектів і самоорганізація при модифікації поверхні Article published earlier |
| spellingShingle | Radiation-induced defect's clustering and self-organization during surface modification Bondareva, A.L. Zmievskaya, G.I. Приложения и технологии |
| title | Radiation-induced defect's clustering and self-organization during surface modification |
| title_alt | Кластеризация радиационно-стимулированных дефектов и самоорганизация при модификации поверхности Кластерізація радіаційно-стимульованих дефектів і самоорганізація при модифікації поверхні |
| title_full | Radiation-induced defect's clustering and self-organization during surface modification |
| title_fullStr | Radiation-induced defect's clustering and self-organization during surface modification |
| title_full_unstemmed | Radiation-induced defect's clustering and self-organization during surface modification |
| title_short | Radiation-induced defect's clustering and self-organization during surface modification |
| title_sort | radiation-induced defect's clustering and self-organization during surface modification |
| topic | Приложения и технологии |
| topic_facet | Приложения и технологии |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/81276 |
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