DSpace at VNU: Molecular simulation of freestanding amorphous nickel thin films

TSF-32396; No of Pages 8
Thin Solid Films xxx (2013) xxx–xxx

Contents lists available at SciVerse ScienceDirect

Thin Solid Films
journal homepage: www.elsevier.com/locate/tsf

Molecular simulation of freestanding amorphous nickel thin films
T.Q. Dong a, V.V. Hoang b,⁎, G. Lauriat a
a
b

Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, UMR 8208 CNRS, 5 Boulevard Descartes, 77454 Marne-la-Vallée, Cedex 2, France
Department of Physics, Institute of Technology, National University of Ho Chi Minh City, 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City, Viet Nam

a r t i c l e

i n f o

Article history:
Received 18 September 2012
Received in revised form 19 July 2013
Accepted 19 July 2013
Available online xxxx
Keywords:
Amorphous thin films
Molecular dynamics simulations
Glass formation
Solid-like atoms

a b s t r a c t
Size effects on glass formation in freestanding Ni thin films have been studied via molecular dynamics simulation
with the n-body Gupta interatomic potential. Atomic mechanism of glass formation in the films is determined via
analysis of the spatio-temporal arrangements of solid-like atoms occurred upon cooling from the melt. Solid-like
atoms are detected via the Lindemann ratio. We find that solid-like atoms initiate and grow mainly in the interior
of the film and grow outward. Their number increases with decreasing temperature and at a glass transition
temperature they dominate in the system to form a relatively rigid glassy state of a thin film shape. We find
the existence of a mobile surface layer in both liquid and glassy states which can play an important role in various
surface properties of amorphous Ni thin films. We find that glass formation is size independent for models
containing 4000 to 108,000 atoms. Moreover, structure of amorphous Ni thin films has been studied in details
via coordination number, Honeycutt–Andersen analysis, and density profile which reveal that amorphous thin
films exhibit two different parts: interior and surface layer. The former exhibits almost the same structure like
that found for the bulk while the latter behaves a more porous structure containing a large amount of
undercoordinated sites which are the origin of various surface behaviors of the amorphous Ni or Ni-based thin
films found in practice.
© 2013 Elsevier B.V. All rights reserved.

1. Introduction
Amorphous Ni is a magnetic material which has been under intensive investigations by both experiments and computer simulations
(see [1–12] and references therein). The samples obtained in practice
are often in the form of a thin film [1,2,4] and limited information related to the structure and properties of amorphous Ni is found by experiments [1,2,4,5,7]. Experimental evidence shows that amorphous Ni
has a dense random packed structure and a typical radial distribution
function (RDF) of metallic glasses: the splitting of the second peak
[2,5]. The existence of local icosahedral order in deeply undercooled
Ni melts is also discovered experimentally, ensuring that amorphous
Ni should also contain a local icosahedral order [10]. More detailed information of structural properties of amorphous Ni at the atomic level
can be obtained via computer simulations. In literature, a limited number of simulation works have been done involving the bulk material
based on models under periodic boundary conditions (PBCs). Indeed,
molecular dynamics (MD) simulations and systematic analysis of the
local atomic structure of liquid and amorphous models containing 256

Ni atoms interacted via n-body Gupta potential have been presented
[8]. Both the RDFs of liquid and amorphous Ni are in good agreement
with the experimental data including the splitting of the second peak
in amorphous samples. The crystalline and icosahedral orders are

⁎ Corresponding author. Tel.: +84 8 38647256; fax: +84 8 38656295.
E-mail address: (V.V. Hoang).

found with almost the same proportion in the amorphous Ni [8]. Similar
properties were also observed in other study on models containing 500
Ni atoms using an embedded atom method (EAM) interatomic potential
[9]. Although the splitting of the second peak is not as strong as in the
previous work, the RDF in the liquid state is in good agreement with
the experiment [9]. Via the Honeycutt–Andersen analysis [13], local
icosahedral order in the amorphous Ni has been found together with
other ones such as fcc, hcp and bcc [9]. Recently, the equation of state
for Ni glass has been studied via MD simulations [12] and crystallization
of the amorphous Ni thin film on a singular Pd(100) surface has been
examined [11]. However, systematic simulations of structural properties of the amorphous Ni thin films have not been found in literature
yet. Thin films, systems with free surfaces, possess behaviors different
from the bulk. Therefore, understanding of structure and properties of
amorphous Ni thin films is of fundamental and technological importance since it is widely produced for practical purposes. For the simple
monatomic systems with Lennard–Jones–Gauss (LJG) interatomic potential, it is found recently that atomic mechanism of glass formation
in thin films is quite different from that of the bulk [14,15]. Hence, it
motivates us to carry out the research in this direction for Ni thin
films since the results can be generalized for a popular class of glasses,
i.e. metallic ones.
The paper is organized as follows. After the Introduction, calculation
parameters and models are introduced in Section 2. Detailed results and
discussions about the thermodynamics, structure evolution of free

standing films are given in Section 3. Finally, the last section of the
paper is dedicated to some concluding remarks.

0040-6090/$ – see front matter © 2013 Elsevier B.V. All rights reserved.
/>
Please cite this article as: T.Q. Dong, et al., Thin Solid Films (2013), />

2

T.Q. Dong et al. / Thin Solid Films xxx (2013) xxx–xxx

2. Calculations
Glass formation and thermodynamics of Ni thin films have been
studied in models containing 32,000 Ni atoms interacted via the same
n-body Gupta potential previously used in [8], which has the form:

V ¼ε

N
X
j¼1

2
4A

N
X

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3
N

h

i u
h

i
u X
exp −p r ij =r 0 −1 −t
exp −2q r ij =r 0 −1 5:

ið≠ jÞ¼1

ið≠ jÞ¼1

ð1Þ
The parameters of potential are taken as follows: A = 0.101, ε =
1.7 eV, p = 9, q = 3, r0 = 2.49 Å (see [8] and references therein).
The Verlet algorithm is employed with a time step of dt = 0.75 fs. The
cutoff is applied to the potential at rc = 3r0 [8]. Initial fcc structure
models are melted in a cube of a length L = 70.72 Å corresponding to
a real density of fcc Ni (e.g. ρ0 = 8900 kg/m3) and under PBCs at the
temperature as high as T0 = 1970 K via MD relaxation for 2 × 105
MD steps (i.e. above the experimental melting point of fcc Ni). The
melted state of model obtained at T0 = 1970 K is confirmed via
checking RDF. After that, PBCs are applied only along the x and y Cartesian directions, while along the z Cartesian direction the non-periodic
boundaries with an elastic reflection behavior are employed after
adding the empty space of a length of Δz = 2r0 at z = L. Due to using
the elastic reflection boundaries, an additional free surface will occurs
at z = 0 during further MD simulations. The systems are left to equilibrate further for 2 × 105 MD steps at T0 = 1970 K at a constant volume
of the simulation cell of the new size, i.e. NVT ensemble simulation. Then

the system is cooling down at the constant volume of the new simulation cell at the cooling rate of γ = 1013 K/s, and temperature is
decreased linearly with time as T = T0 − γ × t via the simple atomic
velocity rescaling (t is a cooling time). This means that atomic configurations of thin film shape have been under zero pressure during the
simulations. Note that if a lower cooling rate is used for simulation,
the spontaneous crystallization of Ni is observed. For comparison, the
initial liquid system containing 32,000 atoms under PBCs is quenched
at the same cooling rate under zero pressure. This system is referred

as the “bulk” one. In order to study the size effects, glass formation
and thermodynamics of models containing 4000, 11,000 and 108,000
Ni atoms have been investigated by the same procedure like that done
for models containing 32,000 atoms described above. In order to
improve statistics, we average the results over two independent runs.
3. Results and discussions
3.1. Thermodynamics
Temperature dependence of various thermodynamic quantities of
the system upon cooling from the melt can be seen in Fig. 1 which
presents the inherent intermediate scattering function, FS(Q,t), potential
energy per atom (PEA), diffusion constant D and surface energy. The
quantities such as FS(Q,t) and D at a given temperature have been
computed after relaxation of models for 5 × 105 MD steps. In the
present work, FS(Q,t) is calculated for Q = 3.1986 Å−1 which is the location of the first peak in structure factor of the bulk amorphous Ni, S(Q).
The inherent intermediate scattering function is defined as follows:

F S ðQ ; t Þ ¼

N
 h
i
1X

b exp iQ : r j ðt Þ−r j ð0Þ N
N j¼1

ð2Þ

where rj(t) is the location of the j-th atom at time t and Q is a wavevector. From Fig. 1a, one can see that FS(Q,t) is typical for the glassforming systems. At high temperature, we observe a ballistic regime at
a short time followed by a relaxation regime at a longer time. The latter
is exponential and decays to zero within 1 ps. However, at low temperature, a plateau regime is found after the ballistic one due to the caging
effects, i.e. temporary trapping of the atoms by their neighbors. On the
other hand, the long time behavior of FS(Q,t) is non-exponential, like
typical glass-forming systems (see [14,15] and references therein). This
means that glass formation has occurred in the liquid Ni models. The
influence of the free surfaces on PEA can be seen in Fig. 1b, i.e. PEA in
thin films is higher than that of the bulk due to the free surface effects.
The deviation from the linearity of a low temperature region of PEA starts

(a)

(b)

(c)

(d)

Fig. 1. (a) Inherent intermediate scattering function, FS(Q,t), from left to right for temperatures: 1970 K, 1785 K, 1600 K, 1400 K, 1220 K, 1040 K, 850 K, 660 K, 560 K, 470 K, 290 K, 100 K,
respectively and the bold line is for Tg = 560 K; (b) potential energy per atom (PEA), the straight line serves as guide for eyes; (c) inverse temperature dependence of the logarithm of
diffusion constant (ln D) in the system, the straight lines serve as guide for eyes; (d) temperature dependence of surface energy of Ni thin film. All figures of thin films are associated
with models containing 32,000 atoms.

Please cite this article as: T.Q. Dong, et al., Thin Solid Films (2013), />

T.Q. Dong et al. / Thin Solid Films xxx (2013) xxx–xxx

at the glass transition temperature, i.e. Tg = 506 K for model containing
32,000 atoms. The value Tg = 560 K for our thin film models is less than
that of the corresponding bulk (Tg − bulk = 854 K) indicating free surface
effects. Free surface enhances dynamics of atoms in the thin films leading
to the reduction of glass transition temperature, what is also observed in
LJG thin films [14]. Generally, Tg slightly increases with the cooling rate. A
much higher value Tg = 1010 K is found for the bulk Ni using EAM
interatomic potential at the same cooling rate of 1013 K/s [9]. We believe
that the discrepancy is mainly due to the use of different interatomic
potentials in the two works. Furthermore, free surfaces greatly enhance
the dynamics of atoms in the models, which can be explained from the
temperature dependence of logarithm of diffusion constant (Fig. 1c).
In addition, similar tendency like that found for FS(Q,t) can be seen
for time–temperature dependence of mean-squared displacement
(MSD) of atoms (Fig. 2): it has the ballistic regime at the beginning
followed by the plateau regime and then the diffusive one at a longer
time. One can see that glass transition temperature is a bound between
a low glassy-like dynamics and a high liquid-like one like that commonly found (see the bold line in Fig. 2). However, the MSD at low temperature of a glassy state tends to increase if the system is relaxed for a long
time unlike that of the bulk system, indicating surface effects of the thin
films [14,15]. It is clear that free surfaces can greatly enhance the
dynamics of atoms in the systems.
The diffusion coefficient of atoms in the system is calculated via the
Einstein relation:
limt→∞

∂bΔr 2 ðt ÞN
¼D

6∂t

ð3Þ

where b Δr2(t) N is MSD of the atom. As found in LJG system with free
surfaces, the diffusion constant of atoms in the system with free surfaces
is higher than that of the bulk (Fig. 1c). On the other hand, surface energy of Ni thin films has been calculated via following equation:
thin film

Epot

bulk

−Epot ¼ ES =N:

ð4Þ

is a potential energy per atom in thin film, Ebulk
Here, Ethin_film
pot
pot is
potential energy per atom in the bulk, ES is the surface energy of thin
film and N is the total number of atoms in the system. As seen in
Fig. 1d, surface energy of the liquid and amorphous Ni thin film increases
with temperature, ranging from 1.0 J/m2 to 3.0 J/m2, which agrees well
with computer simulations (around 2.0 J/m2) and experiments (around
2.5 J/m2) for crystalline Ni (see [16] and references therein). We note
that at high temperature, a significant part of atoms in the models can
reach the boundary of the simulation cell. Therefore, in order to get a
true value of the surface energy of the thin films, we have shown surface

energy only for T ≤ 1200 K in Fig. 1d since in this temperature region
two free surfaces of the system are fully formed.
More details of local structure and dynamics in the systems can be
seen via the density profile, atomic displacement distribution (add)

Fig. 2. Mean-squared displacement of atoms, from top to bottom for temperatures:
1970 K, 1785 K, 1600 K, 1400 K, 1220 K, 1040 K, 850 K, 660 K, 560 K, 470 K, 290 K,
100 K, respectively and the bold line is for Tg = 560 K.

3

and PEA profile along the z direction (Figs. 3 and 4). The density, add
and PEA profiles at a given temperature are calculated by partitioning
the system along the z direction into slices of the thickness of 0.75 Å.
Note that the add corresponds to the displacement of the atoms in the
slice after a specific amount of the time (τC) at a given temperature
which is chosen appropriately. After intensive checking, we find that
τC = 2 ps is a good choice since this time is large enough for atoms to
overcome a plateau regime to diffuse if they are liquid-like (see
Fig. 2). The obtained results are insensitive to the slice thickness in the
range from 0.75 Å to 1.24 Å, the latter is an atomic radius of Ni atom.
It is clear that there is no physical meaning if one adopts a slice thickness
larger than the atomic diameter, i.e. locality of the behaviors could not
be observed due to a relatively large amount of atoms in each slice
since we have studied models containing 32,000 atoms. Statistically,
there is no physical meaning if one takes slice thickness smaller than
0.75 Å. Note that density profile along the z direction and add in models
at a given temperature have been accounted at a given moment of
relaxation time, i.e. these quantities depend on the number of atoms
in each slice of the thickness of 0.75 Å at a given moment of relaxation

time. Therefore, although in the liquid state atoms can freely move
from one slice to other during the relaxation, number of atoms in each
slice at a given moment of relaxation time can be exactly determined.
The density and add profiles presented in Fig. 3 show clearly that
amorphous Ni thin films exhibit two distinct regions: surface layer
and interior. In the latter, both the density and add almost fluctuate
around a constant value which should be close to that of the bulk. In
the former, the density decreases down to zero while the add increases
with the distance from the interior indicating the free surface effects
(Fig. 3). Some important points can be drawn as follows. We find that
density profile in the Ni thin film exhibits a layer structure of the orderly
high and low values of density. Layer structure is enhanced with
decreasing temperature like that found in liquid metals. At temperature
far below Tg, i.e. at 290 K and 190 K (see Fig. 3c and d), surface-induced
layering can be seen more clearly since the amplitude of the oscillations
of the density is greater in the outer regions and gradually decreases
inward like that found by both experiments and computer simulations
(see [17–19] and references therein).
It is speculated that occurrence of the layering structure depends on
the ratio Tm/TC (i.e. TC is a critical temperature for the system) and
monatomic LJ liquid does not exhibit a layering structure [17]. In
addition, a strong layering structure in the density profile has been suggested to be the origin of the ultra-high stability of the vapor-deposited
glasses [20]. Moreover, the layering structure has been also found for
amorphous nanoparticles of various substances [21]. Note that analysis
of the surface-induced layers of liquid Hg at 300 K reveals that the
spacing between the outer and the first inner layers (the distance between the two consecutive maxima) is equal to around 2.95 Å, whereas
for all other inner layers the spacing is slightly smaller and it is equal to
around 2.75 Å [19]. Moreover, based on the data obtained for a wide
range of simple liquid metals, a linear relationship between the
wavelength of the ionic oscillations and the radii of the associated

Wigner–Seitz spheres is found (see [19] and references therein). We
also check the spacing between consecutive maxima of the density
profile at 190 K in the outer regions and in the inner regions of the
thin films. No clear discrepancy between them is found and the mean
spacing is roughly 0.84 Å. Overall, the origin of layering structure of
liquid and amorphous materials with free surfaces is still not well
understood although some models have been proposed in order to explain the phenomenon. In particular, it is proposed that undercoordinated
sites near the surface would attempt to regain the coordination they had
in the bulk liquid, leading to an increase of atomic density in the outermost part of the liquid and consequently, it reduces the propagation of
the density oscillation into the bulk (see [19] and references therein).
Concerning the add along the z direction, it is clear that there is a
surface layer of an enhanced mobility in the amorphous Ni (Fig. 3).
Note that atomic mobility in the interior of thin film is indeed equal to

Please cite this article as: T.Q. Dong, et al., Thin Solid Films (2013), />

4

T.Q. Dong et al. / Thin Solid Films xxx (2013) xxx–xxx

(b)
(a)

(c)

(d)

Fig. 3. Density profile (normalized by ρ0 = 8900 kg/m3) and atomic displacement distribution (add, in unit of r0 = 2.49 Å) in the models containing 32,000 atoms obtained at different
temperatures.

that of the corresponding bulk at a given temperature like that thought
in the past and found recently [22]. The thickness of this layer (d) and
the discrepancy between the atomic mobility in the surface and that
in the interior of the system (h) are determined as described in
Fig. 4b. To obtain a good statistics, the quantities d and h at a given temperature have been averaged over two sides of the thin films and over
two different samples which have been obtained by two independent
runs. Important points related to the add can be described as follows:
(i) The thickness of the region of reduced density is almost the same
as the region of enhanced mobility, in contrast to the suggestion made

in Ref. [23] that the latter should be an order of magnitude larger than
that of the former (ii) The thickness of the mobile surface layer of the
amorphous Ni thin film increases with temperature, the same remarks
have been done in Ref. [24] on polystyrene (see Fig. 4c); (iii) The discrepancy between the atomic mobility in the interior and in the surface
layer also grows with temperature like that found for the amorphous
LJG thin films [14] (see Fig. 4d); (iv) The thickness of our thin film
models decreases with decreasing temperature (Fig. 3) and it should
lead to the formation of a glassy state with an enhanced density in the
interior since mean coordination number in the interior increases

(a)

(b)

(c)

(d)

Fig. 4. (a) Potential energy per atom profile in the models obtained at different temperatures (N = 32,000, color online); (b) definition of d (thickness of a mobile surface layer) and h (the
discrepancy between the atomic mobility at the surface and that in the interior), add for 850 K is used for illustration; (c) temperature dependence of thickness of a mobile surface layer;

(d) temperature dependence of the discrepancy between the atomic mobility at the surface and that in the interior.

Please cite this article as: T.Q. Dong, et al., Thin Solid Films (2013), />

T.Q. Dong et al. / Thin Solid Films xxx (2013) xxx–xxx

with decreasing temperature (Fig. 5b), similar tendency has been
observed for the freestanding thin films of the binary LJ mixture [25],
the monatomic LJ system [26] and LJG thin film [14]. Note that the diffusion constant profile in the z direction observed in Ni0.5Zr0.5 metallic
glass films [27] also has the same form as the add computed in the
present work. It is found that decrease of mobility with depth of thin
film is exponential with a smooth transition between surface and interior behavior, and a Landau analysis is applied for interpreting of the
diffusion constant profile in the z direction [27]. Our calculations show
that there is no systematic size dependence of the quantities d and h
(Fig. 4c and d). On the other hand, the discrepancy between data
observed for d and h of models of different sizes is rather small. It
seems that d and h should be size independent like that suggested for
thin films of the stable glasses [28]. In addition, the PEA profile along
the z direction also exhibits two distinct parts (surface layer and interior) like the density profile and the add indicating the tight correlation
between these three quantities, and the value of PEA in the interior
should be the same like that of the corresponding bulk at a given temperature (Fig. 4a). In the surface layer, atomic mobility increases with
the distance from the interior toward surface leading to the same tendency for PEA due to increasing of the liquid-like behaviors (both static
and dynamic ones) of the atomic configurations from slice to slice
toward surface (see Fig. 4a and b and our discussions about structure
and distribution of liquid-like atoms in the surface layer given below).
Note that PEA increases with temperature, i.e. with the increase of liquid-like content in the atomic configurations or with the corresponding
structural change from the solid-like into liquid-like in the system (see
Fig. 1b).
3.2. Evolution of structure upon cooling from the melt
The glass formation of the liquid Ni is accompanied by the evolution

of structure upon cooling from the melt and detailed analysis of evolution of structure of the system can give deeper understanding of a
glass formation in the thin films. The evolution of various quantities related to the structure of liquid and amorphous Ni thin films can be seen
in Fig. 5 and Table 1. One can see that RDF of the system is typical for the

5

Table 1
Relative fraction of the bond-pairs in the Ni thin film containing 32,000 atoms compared to
those of the bulk obtained at T = 100 K.
Materials

Thin film
Interior
Surface
Bulk

Bond pairs
1321

1421

1422

1431

1541

1551

1661

0.0337
0.0627
0.0248

0.2116
0.2339
0.2555

0.0979
0.0868
0.0889

0.1727
0.1566
0.1576

0.2277
0.1844
0.2313

0.1198
0.0820
0.0782

0.0611
0.0534
0.0877

glass-forming systems [14,15,29,30] (see Fig. 5a). In the liquid state, our

RDF obtained at 1970 K agrees reasonably with that found experimentally at 1905 K [10]. Upon cooling from the melt, the height of peaks in
RDF increases like that commonly found, at T = Tg the second peak in
RDF starts to split and at T b Tg splitting of the second peak in RDF can
be seen more clearly (see Fig. 5a). Splitting of the second peak in RDF
is thought to be related to the occurrence of a local icosahedral order
in metallic glasses and serves as a signature of a glassy state of metallic
glasses [14,15,29–31]. More details of structure can be seen via coordination number distributions (Fig. 5b–d), the cutoff radius R0 = 3.10 Å
is used for calculating coordination number which is equal to the position of the first minimum after the first peak in RDF of the glassy state.
Mean coordination number profile shows a clear difference between
surface layer and interior at all temperatures studied (Fig. 5b). Surface
layer atoms have a mean coordination number much smaller than
that of the interior ones due to breaking bonds at the surface. Note
that the mean coordination number of atoms in the interior of amorphous Ni thin films fluctuates around the value slightly above Z = 12,
i.e. the coordination number of atoms in the bulk crystalline fcc Ni,
and it increases with decreasing temperature indicating the densification of the system. However, in the surface layer there is a significant
amount of atoms with coordination number less than Z = 12, i.e. the
undercoordinated sites. Undercoordinated sites can be considered as
structural defects and they mainly concentrate in the surface layer
(Fig. 5b).

(a)
(b)

(c)

(d)

Fig. 5. (a) Evolution of the radial distribution function of the models containing 32,000 atoms upon cooling from the melt, for comparison with RDF at 1970 K (the bold line) we show the
experimental data obtained at 1905 K via empty circles [10]; (b) mean coordination number profile in models containing 32,000 atoms obtained at different temperatures; (c) mean coordination number profile in the region near free surface of models containing different numbers of atoms obtained at 100 K; (d) coordination number distributions in models obtained at
100 K.

Please cite this article as: T.Q. Dong, et al., Thin Solid Films (2013), />

6

T.Q. Dong et al. / Thin Solid Films xxx (2013) xxx–xxx

Such undercoordinated sites may play an important role in various
surface activities of the amorphous metal thin films including catalytic
ones. Indeed, amorphous alloy nanomaterials have gained increasing
attention as catalytic materials since 1980; especially, the catalytic
properties of amorphous metal–metalloid alloys have been under
intensive testing for applications in practice [32]. In particular, Ni–B
amorphous nanoparticles have been mostly investigated for the use in
practice as a potential catalyst in the liquid phase hydrogenation and
modification of Ni–B alloys by other transition metals (Cu, Co, Fe, Mo
etc.) or P can enhance the catalytic activity and selectivity [32]. It is
pointed out that unique isotropic structure and high concentration of
the coordinately unsaturated sites (at the surface) of nanoscaled
amorphous materials lead to the high catalytic activity and selectivity
superior to their crystalline counterparts [21,32,33]. Therefore, our
simulations give additional understanding of the phenomenon.
In order to highlight the size effects on the structure of amorphous
Ni thin films, we also show in Figs.5c and 5d mean coordination number
along the z direction and coordination number distributions for thin
film models containing 4000 to 108,000 atoms, respectively. Some
remarks can be made as follows. Generally, size effects are not strong
on the structural properties of the amorphous models since the smallest
model contains 4000 atoms which is large enough to minimize the size
effects like that found and discussed in the past [34]. However, small difference in structural properties may lead to a dramatic difference in the

dynamical ones since we deal with the non-periodic boundary condition system [35]. On the other hand, one can see in Fig. 5c that size
effects on the structure of the surface layer are more pronounced than
that in the interior of thin films although the effects are not systematic.
This point is confirmed by a more pronounced size effect on the low coordination part of the distribution (Fig. 5d). As presented in Fig. 5c, sites
of low coordination are mainly distributed in the surface layer like that
discussed above. This means, the surface structure of the amorphous
thin films is size dependent while interior is almost size independent
like that found and discussed for the amorphous nanoparticles of various substances [21]. Other words, surface may play a key role in the
size dependence of structure and properties of the amorphous thin
films in general.
Next, the Honeycutt–Andersen analysis is used for studying of the
microstructure of amorphous Ni thin films [13]. According to the
Honeycutt–Andersen analysis, the structure is analyzed by the pairs of
atoms on which four indices are assigned: (i) First index indicates
whether or not they are near neighbors, the first index is 1 if the pair
is bonded and 2 otherwise, where we use the fixed cutoff radius Ro =
3.10 Å for determining the nearest-neighbor pairs; (ii) The second
index is equal to the number of near neighbors they have in common;
(iii) The third index is equal to the number of bonds among common
near neighbors; (iv) The fourth index denotes existence of the structure
with the same first three indices but with different arrangements.
As shown in Table 1, while the interior has a strong local icosahedral
order and its relative fraction of various bond-pairs is close to that of the
bulk, the surface layer contains a large amount of the bond-pairs characteristic for the non-close-packed atomic arrangements like that
discussed above via analyzing coordination number distributions. On
the other hand, local structure of amorphous Ni is composed mainly of
1421, 1422, 1431, 1541 and 1551 bond pairs like that found in Ref. [8].
Note that 1551 pair is a direct evidence of the existence of a local icosahedral order while 1541 pair is related to the distorted icosahedra in the
system [13], and their fractions dominate in the amorphous Ni. This
means, the energy-favored local structure of amorphous Ni is an icosahedral order which is incompatible with the global crystallographic

symmetry. Note that the existence of local icosahedral order in the
supercooled and amorphous Ni has been found by both experiments
and computer simulations [8–10]. However, fraction of 1551 and 1541
bond pairs in the amorphous Ni is not as high as that found for other
metallic glasses such as LJG, Fe [14,15,31]. Maybe, this is an origin of
not high stability of a glassy state of Ni against crystallization. Indeed,

if we employ a lower cooling rate the system crystallizes. On the other
hand, fraction of 1421 bond pair in the amorphous Ni is rather high
(more than 20%) unlike that found for other metallic glasses
[14,30,31], this bond pair is related to the fcc crystalline order. A similar
high fraction of 1421 bond pair in the amorphous Ni has been found
previously [8] and it was argued that n-body Gupta potential favors
the formation of local crystalline order and at the same time reduces
the content of a local icosahedral one in the amorphous Ni models [8].
A similar situation for the bond pairs has been found for amorphous
Ni with EAM interatomic potential [9], although the fraction of 1421
one is much lower than that found in the present work or in Ref. [8].
Based on the results obtained by both experiments and computer
simulations with various interatomic potentials described above, one
can conclude that amorphous Ni contains a relatively not strong local
icosahedral order and a significant amount of fcc crystalline one.
3.3. Atomic mechanism of glass formation
The atomic mechanism of glass formation in the Ni thin films is studied via analyzing spatio-temporal arrangements of solid-like atoms
occurred and grew in the system upon cooling from the melt like that
used in the past [14,15]. Solid-like atoms are detected by using the
Lindemann-freezing criterion (origin of the Lindemann-freezing criterion can be seen in [15] and references therein). The Lindemann ratio for
the ith atom is given below [36]:
2

δi ¼ bΔr i N

1=2

=R:

ð5Þ

Here, b Δr2i N is the MSD of the ith atom and R ¼ 2:49 Å is a mean
interatomic distance of the amorphous Ni thin film. Since R does not
change much with temperature and that we fix this value for the calculations. MSD in Eq. (5) is defined after a characteristic time τC described
above, i.e. τC = 2 ps, it was proposed that τC is not larger than some
atomic vibrations in picoseconds [37]. The mean Lindemann ratio (δL)
of the system is found by the average of δi overall atoms, δL = ∑ iδi/N
and temperature dependence of the Lindemann ratio can be seen in
Fig. 6a.
One can see that in the glassy state (i.e. in the solid one), δL is almost
the same for models of different sizes since it is mainly related to the vibrations of atoms around their quasi-equilibrium positions in the glassy
matrix. However, a strong size dependence of δL can be seen in the high
temperature region in that the larger the size the smaller δL is due to
decreasing surface to volume ratio leading to the reduction of fraction
of liquid-like atoms in the models with a larger size. For convenience,
we focus attention to the models containing 32,000 atoms, i.e. the

(a)

(b)

Fig. 6. Temperature dependence of the Lindemann ratio (a) and fraction of the solid-like
atoms (b) for models containing various numbers of atoms, the arrow points out the

glass transition temperature for model containing 32,000 atoms.

Please cite this article as: T.Q. Dong, et al., Thin Solid Films (2013), />

T.Q. Dong et al. / Thin Solid Films xxx (2013) xxx–xxx

intermediate size of the size range studied. Similar to the PEA curve (see
Fig. 1b), the Lindemann ratio deviates from the linearity of a low temperature region at T = Tg. The corresponding critical value of the ratio
is δC = 0.262, i.e. the value of δL at T = Tg. Atoms with δi ≤ δC are classified as solid-like and atoms with δi N δC are classified as liquid-like.
Fig. 6b shows that solid-like atoms occur first at temperature much
higher than Tg and their number increases fast with further cooling. At
T = Tg, solid-like atoms dominate in the system and their content is
around 63%. Further cooling leads to the full solidification at around
T = 190 K. It is interesting to note that we find almost no size effects
on the curves for temperature dependence of fraction of solid-like
atoms occurred during cooling process (see Fig. 6b). This means, atomic
mechanism of glass formation obtained for Ni thin films studied should
be size independent.
More detailed information of a glass formation in the system can be
seen via the distributions of solid-like and liquid-like atoms along the z
direction during a vitrification process (Fig. 7). One can see that solidification of the system initiates and enhances in the interior and simultaneously grows outward (Fig. 7a and b). At T = Tg, although solid-like
atoms dominate in the system, a significant amount of atoms remains
liquid-like (Fig. 7c). At T ≤ Tg, liquid-like atoms have a tendency to
concentrate in the surface layer, however, they do not form a pure liquid
surface layer (Fig. 7c and d). This means that our simulations do not
support the so-called ‘glasses with liquid-like surfaces’ proposed in the
past [23] and give deeper understanding of a glass formation in the
supercooled metal thin films. On the other hand, Fig. 7c shows that at
around T = Tg or some degree below Tg, concentration of liquid-like
and solid-like atoms in the surface layer is equal each to other, i.e. we

have a mixed phase of the solid-like and liquid-like atoms with equal
concentrations. Other words, at temperature not far below Tg
amorphous thin films have a quasi-liquid surface layer which exhibits
structural, dynamical properties that are intermediate between those
of the glassy solid and normal liquid [38].
Furthermore, it is clear that a high concentration of liquid-like atoms
in the surface layer of glasses leads to the reduction of the surface rigidity which becomes weaker if temperature is closer to Tg from below due
to the increase of number of liquid-like atoms in the surface layer (see
Fig. 7c and d). This is the origin of striking experimental observation

(a)

7

done by Fakhraai and Forrest, i.e. they used atomic force microscopy
to image the filling of the nanoindentations on the polystyrene glass
surface over time at various annealing temperatures [39]. It was found
that at 20 K below Tg the process takes a few minutes; whereas at
100 K below Tg the holes fill in a few weeks due to a higher surface rigidity. Indeed, surface of glasses is not so glassy like that stated in [40] since
it contains both liquid-like and solid-like atoms as found in the present
work. Quasi-liquid surface of amorphous thin films may have important
applications for friction, lubrication, adhesion and any applications
involving surface modification by coating [39].

3.4. Size dependence of potential energy and Tg
Finally, we stop here for discussion additionally about the size effects
on glass formation in the Ni thin films and on the PEA. As shown in
Fig. 8a, the PEA exhibits clearly the size effects: at the same temperature,
if the sample size becomes larger, the PEA is lower. As expected, PEA
should be lower toward the bulk value with increasing size of thin

films like that found for liquid and amorphous nanoparticles due to reduction of surface to volume ratio [21]. On the other hand, Tg of the freestanding Ni thin films has a tendency to increase toward the bulk value
as expected (Fig. 8b). Similar tendency is found for the size dependence
of Tg of the supported and freestanding thin films of various substances
(see [41] and references therein). Glass transition in nanoscaled systems
including nanoparticles, thin films and systems in confined geometries
has been under intensive investigation. However, results obtained by
different authors are diverged. In particular, while Tg is typically lower
in a confined geometry, experiments have also found cases where Tg increases (see [41–43] and references therein). Note that the finite size effects on Tg cannot be interpreted as readily as that on the melting
temperature Tm because of the lack of a consensus on the nature of
the glass transition in general. Several attempts for interpreting the finite size dependence of Tg have been proposed. In particular, a model
of finite size effects on Tg borrowing the ideas from the theory of the
second-order phase transition has been developed and predicts a downward shift and a broadening of Tg, from finite size effects constraints on a
correlation length defined for the glass transition [44]. A recent study of

(b)

(c)
(d)

Fig. 7. Distributions of solid-like and liquid-like atoms along the z direction in models containing 32,000 atoms obtained at different temperatures (density is normalized by ρ0 = 8900 kg/m3).

Please cite this article as: T.Q. Dong, et al., Thin Solid Films (2013), />

8

T.Q. Dong et al. / Thin Solid Films xxx (2013) xxx–xxx

(a)

unlike that thought in the past [23]. This layer can be called a quasiliquid one like that suggested somewhere in the past for surface melting

of crystals [51].
Acknowledgments

(b)

One of the authors (V.V. Hoang) thanks for the financial support
from the Vietnam National Foundation for Science and Technology
Development (NAFOSTED) under Grant number 103.02-2012.17.
References
[1]
[2]
[3]
[4]
[5]

Fig. 8. (a) Temperature dependence of potential energy per atom (PEA) for models
containing different numbers of atoms; (b) size dependence of the glass transition
temperature.

finite size effects on the dynamics of supercooled liquids supports the
model [45].

[6]
[7]
[8]
[9]
[10]
[11]

4. Conclusions

In this paper, we present a detailed analysis of a glass formation in
the freestanding Ni thin films with n-body Gupta potential and some
conclusions can be made as follows. Amorphous Ni thin films contain
two distinct parts: mobile surface layer and interior. These parts of
amorphous thin films exhibit quite different structure and dynamics.
Density profile of the amorphous Ni thin films, which is normally to
the free surfaces, fluctuates very strongly near the free surfaces and
decays with the distance from the surface toward interior leading to
the formation of a strong layering structure in the region close to the
former. Layering is enhanced with decreasing temperature like that
found in the past for various liquid metals with free surfaces. Glass formation in Ni thin films exhibits a heterogeneous behavior, i.e. solid-like
atoms initiate and grow mainly in the interior and grow outward. Their
number increases upon cooling and at T = Tg they dominate in the system to form a relatively rigid glassy state. However, a full solidification
occurs at temperature much lower than Tg. We find a significant amount
of atoms remaining liquid-like in the glassy state. They may act as the
local sources of destabilization of a glassy state of the thin film, i.e. leading to the crystallization of glasses. In addition, they can perform local
atomic dynamics like the Johari–Goldstein process [46] and dynamical
heterogeneities observed below Tg [47–50]. The same atomic mechanism of a glass formation can be suggested for other metallic glasses.
Our simulations indicate clearly the dominated concentration of
undercoordinated sites in the surface layer of amorphous Ni thin films.
This is the origin of a highly catalytic performance of Ni-based amorphous catalysts observed in practice. In addition, we also find the existence of a mobile surface layer of amorphous Ni thin films obtained at
temperatures below Tg which contains both liquid-like and solid-like
atoms. This mobile surface layer can have an important role in various
surface performances of metallic glassy thin films. However, although
liquid-like atoms have a tendency to concentrate in the surface layer
to form a mobile surface they do not form a purely liquid surface layer

[12]
[13]
[14]

[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42]
[43]
[44]

[45]
[46]
[47]
[48]
[49]
[50]
[51]

K. Tamura, H. Endo, Phys. Lett. A 29 (1969) 52.
T. Ichikawa, Phys. Status Solidi A 19 (1973) 707.
H.A. Davies, J. Aucote, J.B. Hull, Nat. Phys. Sci. 246 (1973) 13.
J.J. Hauser, Phys. Rev. B 17 (1978) 1908.
Y. Waseda, The Structure of Non-Crystalline Materials: Liquid and Amorphous
Solids, McGraw-Hill, New York, 1980.
Yu Koltypin, G. Katabi, X. Cao, R. Prozorov, A. Gedanken, J. Non-Cryst. Solids 201
(1996) 159.
J.M. Rojo, A. Hernando, M. El Ghannami, A. Garcia-Escorial, M.A. Gonzalez, R.
Garcia-Martinez, L. Ricciarelli, Phys. Rev. Lett. 76 (1996) 4833.
A. Posada-Amarillas, I.I. Garzon, Phys. Rev. B 53 (1996) 8363.
L. Wang, H. Liu, K. Chen, Z. Hu, Physica B 239 (1997) 267.
T. Schenk, D. Holland-Moritz, V. Simonet, R. Bellissent, D.M. Herlach, Phys. Rev. Lett.
89 (2002) 075507.
A.A. Dmitriev, A.V. Evteev, V.M. Levlev, A.T. Kosilov, Phys. Met. Metall. 100 (2005)
129, (in Russian).
S. Ozgen, L. Songur, I. Kara, Turk. J. Phys. 36 (2012) 59.
J.D. Honeycutt, H.C. Andersen, J. Phys. Chem. 91 (1987) 4950.
V.V. Hoang, T.Q. Dong, Phys. Rev. B 84 (2011) 174204.
V.V. Hoang, T. Odagaki, J. Phys. Chem. B 115 (2011) 6946.
V.M. Kutznesov, R.I. Kadyrov, G.E. Rudenskii, J. Mater. Sci. Technol. 14 (1998) 320.
E. Chacon, M. Reinaldo-Falagan, E. Velasco, P. Tarazona, Phys. Rev. Lett. 87 (2001)

166101.
H. Mo, G. Evmenenko, S. Kewalramani, K. Kim, S.N. Ehrlich, P. Dutta, Phys. Rev. Lett.
96 (2006) 096107.
L. Calderin, L.E. Gonzalez, D.J. Gonzalez, Phys. Rev. B 87 (2013) 014201.
S. Singh, J.J. de Pablo, J. Chem. Phys. 134 (2011) 194903.
V.V. Hoang, D. Ganguli, Phys. Rep. 518 (2012) 81.
V.V. Hoang, T.Q. Dong, J. Chem. Phys. 136 (2012) 104504.
R.A.L. Jones, Nat. Mater. 2 (2003) 645.
K. Paeng, S.F. Swallen, M.D. Ediger, J. Am. Chem. Soc. 133 (2011) 8444.
Z. Shi, P.G. Debenedetti, F.H. Stillinger, J. Chem. Phys. 134 (2011) 114524.
J.S. Rowlinson, B. Widom, Molecular Theory of Capillary, Dover, New York, 2002.
B. Boddeker, H. Teichler, Phys. Rev. E 59 (1999) 1948.
S.F. Swallen, K.L. Kearns, M.K. Mapes, Y.S. Kim, R.J. McMahon, M.D. Ediger, T. Wu, L.
Yu, S. Satija, Science 315 (2007) 353.
K. Nishio, J. Koga, T. Yamaguchi, F. Yonezawa, J. Phys. Soc. Jpn 73 (2004) 627.
M. Dzugutov, Phys. Rev. Lett. 70 (1993) 2924.
V.V. Hoang, N.H. Cuong, Physica B 404 (2009) 340.
Z. Wu, W. Li, M. Zhang, K. Tao, Front. Chem. Eng. Chin. 1 (2007) 87.
E.Z. Min, C. Li, Base of Science and Engineering of Green Petrochemical Technology,
Chinese Petrochem Press, Beijing, 2002.
N.T. Huff, E. Demiralp, T. Cagin, W.A. Goddard, J. Non-Cryst. Solids 253 (1999) 133.
V.V. Hoang, N.N. Linh, J. Phys. Soc. Jpn. 76 (2007) 14602.
F.A. Lindemann, Z. Phys. 11 (1910) 609.
V.N. Novikov, E. Rossler, V.K. Malinovsky, N.V. Surovtsev, Europhys. Lett. 35 (1996)
289.
E.T. Chen, R.N. Barnett, U. Landman, Phys. Rev. B 41 (1990) 439.
Z. Fakhraai, J.A. Forrest, Science 319 (2008) 600.
J.R. Dutcher, M.D. Ediger, Science 319 (2008) 577.
M. Alcoutlabi, G. McKenna, J. Phys. Condens. Matter 17 (2005) R461.
J. Schuller, Y.B. Melnichenko, R. Richert, E.W. Fisher, Phys. Rev. Lett. 73 (1994) 2224.

D.S. Fryer, P.F. Nealey, J.J. de Pablo, Macromolecules 33 (2000) 6439.
D. Sappelt, J. Jackle, J. Phys. A 26 (1993) 7325.
K. Kim, R. Yamamoto, Phys. Rev. E 61 (2000) R41.
G.P. Johari, M.J. Goldstein, Chem. Phys. 55 (1971) 4245.
W. Kob, J. Phys. Condens. Matter 11 (1999) R85.
K. Vollmayr-Lee, W. Kob, K. Binder, A. Zippelius, J. Chem. Phys. 116 (2002) 5158.
K. Vollmayr-Lee, J. Chem. Phys. 121 (2004) 4781.
K. Vollmayr-Lee, A. Zippelius, Phys. Rev. E 72 (2006) 041507.
J.G. Dash, Contemp. Phys. 30 (1989) 89.

Please cite this article as: T.Q. Dong, et al., Thin Solid Films (2013), />