ISSN 1063-7842, Technical Physics, 2013, Vol. 58, No. 8, pp. 1094–1099. © Pleiades Publishing, Ltd., 2013.
Original Russian Text © R.Yu. Makhmud-Akhunov, M.Yu. Tikhonchev, V.V. Svetukhin, 2013, published in Zhurnal Tekhnicheskoi Fiziki, 2013, Vol. 83, No. 8, pp. 8–13.
1094
1. INTRODUCTION
Uranium dioxide is the most widespread nuclear
fuel. Fuel elements of most power reactors are made of
uranium-dioxide tablets. In a working system, tablets
are exposed to high temperatures, pressures, irradia-
tion, and mechanical stresses. At the rated power of
the reactor, the temperature at the axis of the fuel ele-
ment can be higher than 2000 K and the pressure of
the gas products of the uranium fission inside a sealed
fuel element can be 80–100 atm [1]. Note corre-
sponding structural modifications of the tablets that
exhibit grain structure consisting of micro- and nano-
sized crystallites [2, 3].
It is known that the surface properties of a material
substantially affect its behavior in the processes that
involve cracking, swelling, sintering, melting, etc. The
instrumental study of such processes can be impossi-
ble. For example, note the study of the high-tempera-
ture processes in which nanosized crystallites take part
and the surface properties of the crystallites. Mathe-
matical simulation is a method that allows the analysis
of such processes. The widely used molecular dynam-
ics makes it possible to characterize the energy, ther-
modynamic, and structural properties of various
materials. In this work, we employ the method in the
study of the nanosized crystallites of uranium dioxide
and calculate the corresponding characteristics (in
particular, surface energy).
2. METHOD OF CALCULATION
We perform the simulation using the DL_POLY
software [4]. A cubic crystal with the fluorite structure
serves as a unit cell. Cubic nanocrystals are con-
structed using the translation of the unit cell along the
three directions. In the calculations, we employ zero
boundary conditions (free crystal in vacuum). Table 1
presents the sizes of the simulated crystals and the cor-
responding numbers of atoms.
In the calculations, the numerical integration is
performed with a step of 5 fs and the cutoff radius that
ranges from 55 to 105 Å depending on the crystallite
size is chosen in such a way that all of the particles are
located in the region of action of the potential. The
calculations in different problems are performed in a
microcanonical NVE or canonical NVT ensemble.
For the interatomic interaction, we use the Born–
Mayer potential, which employs a minimum set of
parameters. Several parameters are represented as
piecewise-linear slowly varying functions of tempera-
ture:
Molecular Dynamics Simulation of the Surface Properties
of Nanocrystalline Uranium Dioxide
R. Yu. Makhmud-Akhunov*, M. Yu. Tikhonchev, and V. V. Svetukhin
Ulyanovsk State University, ul. L’va Tolstogo 42, Ulyanovsk, 432970 Russia
*e-mail: rusmru@yandex.ru
Received October 9, 2012
Abstract—The molecular dynamics method is used to simulate the nanosized UO
2
crystals. The phase-tran-
sition temperatures are calculated for the nanosized crystals of the uranium dioxide. It is demonstrated that
the melting point and the temperature of the transition to the superionic state (melting of the anion sublat-
tice) of the crystals decrease with decreasing sizes. In particular, melting point (T
m
~ 2300 K) for the cubic
nanocrystal with a size of 3.3 nm is lower than the melting point of the single crystal by almost 1000 K. The
calculated surface energies are in agreement with the experimental results. The dependence of the surface
energy on the size of the UO
2
nanocrystals is obtained. The effect of the nanocrystal temperature on the sur-
face energy is studied. The temperature dependence of the thickness of the melt layer is obtained in the frame-
work of the model of the heterogeneous melting. The parameters and dependences can be used for the further
analysis of the microstructure properties of nuclear fuel in working systems.
DOI: 10.1134/S1063784213080197
THEORETICAL
AND MATHEMATICAL PHYSICS
Table 1. Simulated crystals
Size, unit cells 4 × 4 × 4 5 × 5 × 5 6 × 6 × 6 7 × 7 × 7 8 × 8 × 8 10 × 10 × 10
Size, Å 21.88 27.35 32.82 38.29 43.76 54.70
Number of atoms 768 1500 2592 4116 6114 12000