「様式３」Project No.：2076

Radiation-induced motion of liquid inclusions in crystals［１］Organization
Project Leader：
Oksana Podshyvalova, Ph.D., Prof. of “KhAI”(National Aerospace University “KharkivAviation Institute”, Ukraine)
Representative at RIE：
Toru Aoki, Ph.D., Prof. (Research Institute ofElectronics, Shizuoka University, Japan)
Participants：
Ivan Marchenko, D.Sc. (Nat. Sci. Center"Kharkov Institute for Physics & Technology" ofthe National Academy of Sciences of Ukraine,Ukraine)
Oleksandr
Kulyk,
Ph.D.,
Assoc.
Prof.
(V. N. Karazin Kharkiv National University,Ukraine)
Volodymyr Gnatyuk, Ph.D., Senior Scientist(V. E. Lashkaryov Institute of Semiconductor
Physics of the National Academy of Sciences ofUkraine, Ukraine)

They reported the achieved results, exchanged
ideas on join work in frames of the cooperative
project, and discussed further cooperation
between the partner institutions.
Apart from achieving the research results,
described in the next section, the project
participants were involved in the holding of theinternational scientific forums to discuss theresearch work concerning the project topics andgeneral cooperation issues.
Dr. O. Podshyvalova submitted the abstract
with the key research findings to the Book ofAbstracts of The Annual Meeting of 2019
Cooperative Research on Biomedical Engineering(Yokohama, Japan, 13 Mar. 2020) and Dr.
O. Kulyk presented the project-related results at
The 18th International Conference on Global
Research and Education, Inter-Academia 2019(iA-2019) in Budapest, Hungary (4-7 Sep. 2019).
Totally, 5 publications (2 articles & 3 abstracts)
related to the project results have been publishedduring the project implementation [2-5, 7].

［２］Research Progress
The project objective is to investigate themotion of liquid inclusions in alkali halide
crystals irradiated by γ-quanta and electrons.
Based on the results of experimental studies ofradiation-induced motion and transformation of
the shape of inclusions as well as thephenomenon of induced transitions of matrix
atoms into solution and back [1-5], the physicalmodel of the liquid inclusion motion is developed.
Understanding of the mechanism of spontaneous
inclusions migration is important for monitoring
the integrity of radioactive waste disposal ingeological halide sediments.
The participants of the project actively
collaborated through electronic media andface-to-face when the Ukrainian partners
O. Podshyvalova and O. Kulyk visited RIE,
Hamamatsu in January 2020 (research visits inthe frame of the 2019 Cooperative Research at
Research Center of Biomedical Engineering).

［３］Results(３－１) Research results
At gamma and electron irradiation ofdielectric single crystals structural defects and,first of all, point defects, such as color centers, areformed in them [1]. The distribution ofradiation-induced defects in a crystal depends
both on its prehistory and on exposure conditions,and is very inhomogeneous. The "matrix - colorcenters"
systemisthermodynamically
non-equilibrium and eventually relaxes into thestate of minimum free energy. For example, in thepresence of liquid inclusions in a water-soluble
crystal, their spontaneous motion is one ofrelaxation mechanisms of the system. Suchinclusion motion occurs if the characteristic size ofthe inhomogeneity of radiation defects
significantly exceeds the inclusion size and if thecrystal contains a sufficient density of screw
dislocations, which are sources of steps on the
dissolving inclusion surfaces or evaporating pore

surfaces [2-4]. As it was experimentally
determined, in a crystal with inhomogeneous
distribution of radiation defects, macroscopic
inclusions moved as a single whole with almost
unchanged shape (Fig. 1).

Fig. 2 Layout of a spherical azimuthally symmetricinclusion in the crystal matrix (the inhomogeneous
distribution of radiation defects is shown by dots).
Fig. 1. Traces of inclusions spontaneous migration in
an electron-irradiated crystal a month afterirradiation.

Well-known phenomenological theories thatare used to analyze the motion of inclusions in a
crystal describe the matrix-inclusion interaction
based on the laws of dissolution, diffusion andcrystallization flows conservation. Based on thephenomenon of induced transitions of matrix
atoms into the solution and back [5], we havedeveloped a physical model that describes thetime dependences of the main parameters ofliquid inclusions and allows us to predict thedynamics of their motion.
1. In the reference frame, where a sphericalazimuthally symmetric inclusion in a crystalline
matrix with inhomogeneous distribution of point
defects is at rest when the inclusion size does notexceed the critical size: (or moves in the negative
direction of the axis  (   ) at R  R0 ) (Fig. 2),
the matrix velocity is represented as:

U  R0   U r  R0  ;U  R0   ,(1)whereU r  R0   U r 0  U  R0  er ,U  R0   U 0  U  R0  e

2. The elementary processes of transitions ofmatrix atoms into the solution and back on thefrontal and back surfaces of the inclusion are
considered on the example of a two-level system[5]. It is obtained the system of equations for thenumber of matrix atoms in solution n1, on thefront wall n1, and solvent atoms in the inclusion N:

Un1
n
n1
 Ur0 1   0
 12  n2  n1  N ,tr R0  r (2)

Un2
nn2
 Ur0 2   0
  12  n2  n1  N ,tr R0  r U
N
N
N
Ur0
 0
  12  n2  n1  N .
tr R0  r 
3. To find solutions of equations (2) theprobability of induced transitions μ12 isrepresented in the form of a Taylor series
expansion of the small displacements along theradius r and the polar angle  :12  R0  r , 0    2
 (3)
 12  R0 ,  0  1   r ,2 n 1r 2 n 1    , n 1

whereer , e - are the unit vectors on the radial r and11
r ,2 n1 
12  R0 ,0   2n  1!

polar  axis, respectively.

12  R0 ,0 
1 .
12  R0 ,0 

2 n 112  R0 ,0 
r 2 n 1,.

  t , r ,   t r 2 r ,1
2U r 0

r 4 r ,34U r 0

R0 2 ,2U 0equations (2) can be converted to a simple form:

n1   n2  n1  N ,n2    n2  n1  N ,N    n2  n1  N .
(4)5. By setting the constant phase plane:  t , r ,   D,

(5)

where D is a constant, and passing into thereference system where the inclusion moves, thedependence of the inclusion velocity on its radius
has the form:

UR AxR
R, xR  .
24B  xR  CxR
R0(6)6. Based on the energy interpretation of theinclusion velocity [5], the parameters in (6) are
interpreted and their numerical values are
determined using the experimental data
presented in [6]. A comparison of theoretical
calculations with experimental data indicates anadequate description of the experimental resultsby the proposed theoretical model (Fig. 3) [7].
(３－２) Ripple effects and further developments
The proposed model of induced inclusion
motion in a crystal with inhomogeneous
distribution of radiation defects adequately
describes the non-monotonic dependence ofinclusion velocity on its size. The physical natureof non-monotonity is due to the confrontation of
two forces: the driving force, determined by agradient of radiation defects and the dissipativeforce, determined by the effective characteristicsof the viscous properties of the matrix material.
The validity of the presented physical model ofinclusions’ induced motion is confirmed forcrystals with dislocation and radiation defects
and can be applied to crystals withinhomogeneous distribution of defects of anothernature.
2.0

V – 0.08, A/s

4. Based on the type of expansion chosen in [3],by introducing in (3), the introduction of a newvariable

1.5

1.0

1.5

00

1.5

3

x–1

4.5

6

7.5

Fig. 3. Dependence of inclusions velocity V on theirdimensionless longitudinal size x. Circles areexperimental points, line is the calculation result on
the formula V - 0.08 = 5.9(x -1)/((x -1)2+1)2 [7].

［４］Achievements (List of Publications)(1) A.P. Kulik, O.V. Podshyvalova, I.G.Marchenko,
Radiation-induced motion of liquid inclusions inalkali halide crystals, Problems of Atomic Scienceand Technology 120(2) 13-19 (2019).
(2) O.P. Kulyk, V.I. Tkachenko, O.Yu. Lisina,V.O. Mikhnych, V.A. Gnatyuk, T. Aoki, Nonlinear
effects of diffusion interaction of steps onthermodynamically stable vicinal surfaces,

Physical and Technical Problems of Energy and
Their Solutions 2019, Proceedings of theInternational Scientific and Technical Conference,
P. 13, 2019 (Kharkiv, Ukraine, 19 June 2019).
(Plenary report)(3) O.P. Kulyk, L.А. Bulavin, S.F. Skoromnaya,
V.I. Tkachenko, Model of induced motion ofinclusions in the field of forces of an
inhomogeneously stressed crystal, The 18th

International Conference on Global Research andEducation in Engineering for Sustainable Future,
Inter-Academia 2019, Program and Book ofAbstracts, P. 9-10, 2019. (4-7 September 2019,
Budapest and Balatonfüred, Hungary).
(4) О.P. Kulyk, V.I. Tkachenko, O.V. Podshyvalova,V.A. Gnatyuk, T. Aoki, Nonlinear interaction ofmacrosteps on vicinal surfaces at crystal growthfrom vapour, Journal of Crystal Growth, Vol. 530,P.
125296-1-7,
Jan.
2020.
DOI:

10.1016/j.jcrysgro.2019.125296(5) O.P. Kulyk, L.А. Bulavin, S.F. Skoromnaya,V.I. Tkachenko, Model of induced motion ofinclusions in the field of forces of aninhomogeneously stressed crystal, in: A.R.

Varkonyi-Koczy (ed.) Engineering for Sustainable
Future. Inter-Academia 2019. Lecture Notes in
Networks and Systems (LNNS), Vol. 101, P.
326-3397, 2020, Cham: Springer. DOI:
10.1007/978-3-030-36841-8_32(6) V.S. Kruzhanov, O.V. Podshyvalova, Motion ofliquid inclusions in the crystal caused byradiation defects. Sov. Solid State Physics 32(2),373-378 (1990).
(7) O. Podshyvalova, V. Tkachenko, O. Kulyk,
V. Gnatyuk, T. Aoki, Radiation-induced motion ofliquid inclusions in crystals, The Annual Meetingof 2019 Cooperative Research on Biomedical
Engineering, Book of Abstracts, Abstract No 1-10,
2019, (13 March 2020, Tokyo, Japan), in press.

Page 5：１ column
Travelling Report（Mention each travel by CRP budget.）Name：Oksana Podshyvalova
Affiliation：National Aerospace University “Kharkiv Aviation Institute”, Chkalov Str. 17, Kharkiv 61070,
UkrainePeriod of time：04 January – 20 January 2020
Destination：Research Institute of Electronics, Shizuoka University
Purpose： (1) Study of the processes leading to the motion of liquid inclusions in irradiated crystals withlayer-by-layer growth/dissolution. (2) Participation in the scientific meetings at Research Institute of Electronics,
Shizuoka University during the period of stay. (3) Discussion of the research results, preparation of the publications anddevelopment of the plans of the future research.
Name of receiver：Prof. Toru Aoki

Oksana Podshyvalova
Dr., Prof.
National Aerospace University “Kharkiv Aviation Institute”,
Kharkiv, Ukraine