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

TSF-32396; No of Pages 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, 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 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 38647256; fax: +84 38656295 E-mail address: vvhoang2002@yahoo.com (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 Detailed results and discussions about the thermodynamics, structure evolution of free standing films are given in Section 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 http://dx.doi.org/10.1016/j.tsf.2013.07.055 Please cite this article as: T.Q Dong, et al., Thin Solid Films (2013), http://dx.doi.org/10.1016/j.tsf.2013.07.055 T.Q Dong et al / Thin Solid Films xxx (2013) xxx–xxx 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 4A N X vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi N h  i u h  i u X exp −p r ij =r −1 −t exp 2q r ij =r 5: i jịẳ1 i jịẳ1 1ị 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 × 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 = during further MD simulations The systems are left to equilibrate further for × 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 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 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 × 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 t ịr j 0ị N N jẳ1 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 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 (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), http://dx.doi.org/10.1016/j.tsf.2013.07.055 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 br t ịN ẳD 6t 3ị 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 ẳ ES =N: 4ị 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 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 and PEA profile along the z direction (Figs 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 = 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 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), http://dx.doi.org/10.1016/j.tsf.2013.07.055 T.Q Dong et al / Thin Solid Films xxx (2013) xxx–xxx (b) (a) (c) (d) Fig 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 (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), http://dx.doi.org/10.1016/j.tsf.2013.07.055 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 and Table One can see that RDF of the system is typical for the Table 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 (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), http://dx.doi.org/10.1016/j.tsf.2013.07.055 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 if the pair is bonded and 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]: 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 = 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 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), http://dx.doi.org/10.1016/j.tsf.2013.07.055 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 not form a pure liquid surface layer (Fig 7c and d) This means that our simulations 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) 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 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), http://dx.doi.org/10.1016/j.tsf.2013.07.055 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 (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] 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 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 (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 (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), http://dx.doi.org/10.1016/j.tsf.2013.07.055 ... 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. .. 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,... 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