Evolution of structure of SiO2 nanoparticles upon cooling from the melt

Evolution of structure of spherical SiO2 nanoparticles upon cooling from the melt has been investigated via molecular-dynamics (MD) simulations under non-periodic boundary conditions (NPBC). We use the pair interatomic potentials which have weak Coulomb interaction and Morse type short-range interaction. The change in structure of SiO2 nanoparticles upon cooling process has been studied through the partial radial distribution functions (PRDFs), coordination number and bond-angle distributions at different temperatures. The core and surface structures of nanoparticles have been studied in details. Our results show significant temperature dependence of structure of nanoparticles. Moreover, temperature dependence of concentration of structural defects in nanoparticles upon cooling from the melt toward glassy state has been found and discussed. PACS Codes: 61.43.Bn; 78.55.Qr; 78.67.Bf Introduction Silica nanoparticles have potential applications in many fields including ceramics, chromatography, catalysis and chemical mechanical polishing [1]. In recent years, SiO2 nanoparticles have been investigated by means of experimental techniques such as NMR (nuclear magnetic resonance), SAXS (small angle X-ray scattering) [2], light absorption [3], FTIR (Fourier transform infrared) spectra and photoluminescence [4-7], etc. According to the diffraction data [8], liquid and amorphous silica have Zsi-O = 4 and ZO-Si = 2, i.e. the main structural element of the network is a slightly distorted SiO4 tetrahedron and the adjacent tetrahedra are linked to each other through the shared vertices. This means that Si atoms having 1, 2, 3 or 5-fold coordinations and Published: 30 October 2008 PMC Physics B 2008, 1:16 doi:10.1186/1754-0429-1-16 Received: 20 April 2008 Accepted: 30 October 2008 This article is available from: http://www.physmathcentral.com/content/1/1/16 © 2008 Nguyen et al This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/ licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Page 1 of 12 (page number not for citation purposes) PMC Physics B 2008, 1:16 http://www.physmathcentral.com/content/1/1/16 O atoms have 1 or 3-fold coordinations can be considered as structural defects in SiO2 nanoparticles, which are similar to those observed in the bulk [9,10]. Among them, the most serious defects are structural units with Zsi-O = 2, Zsi-O = 3 and Zsi-O = 1. It was found that the structural defects can play an important role in their structure and properties including photoluminescence [6], catalysis and micro-electronics [11]. In particular, the structural defects lead to the narrowing of band gap and the formation of localized states within band tail, which were experimentally measured from light-absorption study of silica nanoparticles [3]. However, very few theoretical researches have been done for SiO2 nanoparticles despite the observation of interesting properties [11-16]. Therefore, it motivates us to carry out the research on liquid and amorphous SiO2 nanoparticles by MD simulation via the microstructural analysis. Namely, we investigate the structural evolution of SiO2 nanoparticles upon cooling from the melt toward glassy state (or amorphous one). Calculation In the present study, we use interatomic potentials including weak Coulomb interactions and the Morse type potential for short-range interactions as given bellow: Where qi and qj represent the charges of ions i and j, for Si atom qSi = 1.30e and for O atom q0 = -0.65e (e is the elementary charge unit); r denotes the interatomic distance between atoms i and j; the other parameters of the Morse potentials can be found in Refs. [17-19]. MD simulations were done in a spherical SiO2 particle with three different sizes of 2 nm, 4 nm and 6 nm corresponding the real density of 2.20 g/cmfor amorphous SiO2 which have corresponding numbers of atoms of 276 (92 silicon atoms and 184 oxygen ones), 2214 (738 silicon atoms and 1476 oxygen ones) and 7479 (2493 silicon atoms and 4986 oxygen ones), respectively. We used the Verlet algorithm with the MD time step of 1.60 fs. Each model contained the number of Si and O atoms in accordance to the SiO2 stoichiometry. Firstly, N atoms are randomly placed in a sphere of fixed radius and the NPBC model has been relaxed for 5 × 10 MD steps at 7000 K in order to get a good equilibrated liquid model. We use the simple non-slip with non-elastic reflection behavior boundary (i.e. if during the relaxation atoms move out of the spherical boundary they have to be placed back to the surface and it is called NPBC). Then, the temperature of the system was decreased linearly in time as T = T0 t where  = 4.2956 × 10 K/s is the cooling rate, T0 is the initial temperature of 7000 K and t is the cooling time. This cooling process was continued until the temperature of the system was equal to 350 K. It is essential to notice that melting and evaporation points for bulk SiO2 are Tm = 1923K and Tboil = 2503K, respectively [1]. This means that the initial configuration at T = 7000K corresponds to the superheated liquid and that only due to using of NPBC it is possible to reach such a condition for SiO2 nanoparticles otherwise the evaporation occurs. Note that using potentials have been successfully used in MD simulations of U r qiq j r D r R r R ij ( ) {exp[ ( )] exp[ ( )]} = + − − − 0 1 0 2 1 2 1 0   Page 2 of 12 (page number not for citation purposes) PMC Physics B 2008, 1:16 http://www.physmathcentral.com/content/1/1/16 both structure and thermodynamic properties of silica [17-19], and in the investigation of the structure changes in cristobalite and silica glass at high temperatures [18]. These potentials reproduced well the melting temperature of cristobalite and the glass phase transition temperature of silica glass and calculated data were more accurate than those observed in other simulation works in which the traditional interatomic potentials with more strong electrostatic interaction have been used such as BKS or TTAM potentials [20-22]. Although the potentials described above were proposed for the bulk SiO2, they also described well structural features and surface energy of amorphous SiO2 nanoparticles compared with those observed for amorphous SiO2 nanoclusters by using BKS ones [15]. Melting point of nanoparticles is size dependent in that it strongly reduces with decreasing nanoparticle size [23], and it is out of scope of the present work. In order to investigate the evolution of structure of SiO2 nanoparticles upon cooling from the melt, we saved a number of configurations at finite temperatures (i.e. at temperatures ranged from 7000 K to 350 K with the temperature interval of 700 K). and then we relaxed them for 5 × 10 MD steps before calculating static properties. In order to calculate the coordination number and bond-angle distributions in SiO2 nanoparticles, we adopted the fixed values RSi-Si = 3.30 Å, RSi-O = 2.10 Å and RO-O = 3.00 Å. Here R corresponds to the position of the minimum after the first peak in PRDFs for the amorphous state at a real density of 2.20 g/cm. In order to improve statistics, the results have been averaged over four and three independent runs for nanoparticles with the size of 2 nm and 4 nm, respectively. The single run was done for the size of 6 nm due to large number of atoms in the model. In addition, since surface structure plays an important role in the structure and properties of nanoparticles we also focus attention to the surface of SiO2 nanoparticles. Therefore, we need a criterion to decide which atoms belong to the surface and which ones belong to the core of nanoparticles. There is no common principle for such choice of surface or core of the amorphous substances. The definition of thickness of the surface in [13] is somewhat arbitrary: all atoms that were within 5 Å of the hull just touched the exterior of the droplet, and were considered to belong to the surface, atoms that had the distance between 5 Å and 8 Å from the hull belong to the transition zone and the remaining atoms belong to the interior. In contrast, no definition of surface was clearly presented for the amorphous Al2O3 thin film; they used the top 1 Å or 3 Å layer of the amorphous thin film for surface structural studies [24]. From structural point of view, it can be considered that atoms belong to the surface if they could not have full coordination for all atomic pairs in principle and in contrast, atoms belong to the core if they could have full coordination for all atomic pairs in principle like those located in the bulk. Therefore, in the present work atoms located in the outer shell of SiO2 spherical nanoparticle with thickness of 3.30 Å (i.e. the largest radius of the coordination spheres found in the system) belong to the surface of the nanoparticles and the remaining atoms belong to the core. Results and discussion The first quantity we would like to discuss here is the PRDFs, gij(r), for Si-Si, Si-O and O-O pairs at three different temperatures of 7000 K, 3500 K and 350 K. Fig. 1 shows that gij(r) of SiO2 nanPage 3 of 12 (page number not for citation purposes) PMC Physics B 2008, 1:16 http://www.physmathcentral.com/content/1/1/16 oparticles obtained at T = 350K is typical for a glassy state (or amorphous one) of the system like those found for the bulk amorphous SiO2 obtained by using different interatomic potentials or by experiment [9,10,25] since we use very high cooling rate of  = 4.2956 × 10K/s. Furthermore, Fig. 1 & Table 1 show that the peaks in PRDFs strongly depend on the temperature, i.e. they become more pronounced upon cooling in that the changes in first peaks and minima are the most remarkable. More detailed changes in structure can be found via the coordination number distributions (Tables 1 &2). One can see that when the temperature decreases, mean coordination number for all pairs, Zij, increases (Fig. 2). In particular, Zsi-O shifts from 3 to 4 (Tables 1 &2). This means that tetrahedral network structure of SiO2 nanoparticle is forming upon cooling and at the temperature of 350 K (amorphous sate), about 93.13% Si atoms are surrounded by 4 oxygen atoms. These results agree with those obtained via computer simulations for liquid and amorphous SiO2 by using BKS potentials for the system at lower temperatures (about 99%) [9] or by using the potentials which have weak Coulomb interaction and Morse type short-range interaction for the bulk (about 97.3%) [10]. Indeed, in our models at low temperature of 350 K it is also found that the mean coordination numbers ZSi-O  4 and ZO-Si  2. As mentioned in the introduction, the structural defects in SiO2 nanoparticles can play an important role in structure and properties of silica nanoparticles [6,11]. Therefore, it is interesting to study the evolution of coordination number distributions for Si-O and O-Si pairs upon cooling from the melt. Table 2 shows that the number of defects with Zsi-O = 2 and ZO-Si = 1 decreases with decreasing temperature. In contrast, the number of Si atoms having Zsi-O = 3 (3-fold coordination) decreases with decreasing temperature only after about 4200 K. The defects having 1 or 5-fold coordinations for Si atoms and 3-fold coordinations for O atoms also decrease with decreasing temperature (not shown due to small fraction). Moreover, our calculations show that the probability for the occurrence of structural defects is described well by an Arrehnius law Pij = Aij exp(-Eij/T), like those were discussed for the bulk in [9,10]. We found that Pij is described well by such law in temperature ranges such as: 2100K–4200K for SiO3(ZSi-O = 3), 2800K–7000K for SiO2 (Zsi-O = 2) and 2100K–7000K for ZO-Si = 1 (Fig. 3). Here Pij denotes the probability that an itype ion exactly has Z nearest neighbors of type j, Eij denotes activation energies. By extrapolation, we found prefactors Aij and Eij for 2 nm, 4 nm and 6 nm particles, which are shown in Table 3. Table 1: Structural characteristics of 4 nm SiO2 nanoparticle upon cooling from the melt.