Structure of amorphous and liquid zircon

JOURNAL OF SCIENCE OF HNUE DOI: 10.18173/2354-1059.2016-0043 Mathematical and Physical Sci., 2016, Vol. 61, No. 7, pp. 144-150 This paper is available online at STRUCTURE OF AMORPHOUS AND LIQUID ZIRCON Nguyen Viet Huy1,2, Tran Thuy Duong2, Nguyen Van Hong2 1Thai Binh College of Eduaction 2Hanoi University of Science and Technology Abstract. The network structure of zircon (ZrSiO4) in the amorphous and liquid states was investigated using molecular dynamics simulation and visualization. The short range order (SRO) and intermediate range order (IRO) characteristics were analyzed via distribution of units TOn and OTm (T=Zr, Si) linkages. The results of this investigation of the network structure and size distribution of the Si-O and Zr-O subnets shows that the zircon structure decomposes into Zr- and Si-rich regions. The micro-phase separation and structural and compositional heterogeneities of ZrSiO4 are also discussed in this work. Keywords: Oxides, molecular dynamics simulation, amorphous and liquid zircon. 1. Introduction Zircon is an important material in nuclear and ceramics industries. In addition, it is a good alternative to conventional silicon oxide as a dielectric material in metal-semiconductor devices [1-5]. Therefore, zircon has attracted a considerable amount of interest from material scientists. Experimental and simulation study results show that the structure of amorphous and liquid SiO2 is that of SiO4, SiO5 and SiO6 units. These units link to each other via bridging oxygens forming a network of SiOx (x = 4, 5, 6). At low density, most of structural units are SiO4 in a tetrahedral network. At high pressure, most of structural units are SiO6 in an octahedral network. The distribution of polyhedra (SiOx) is not uniform but it does form a cluster of SiO4, SiO5 and SiO6. The spatial distribution of structural units (cluster of SiOx) as well as polymerization is dependent on the density of the sample.This results in different physical properties such as abnormal diffusivity and dynamic heterogeneity [6-14]. For amorphous and liquid ZrO2, the structure is formed from the ZrO5, ZrO6 and ZrO7 polyhedra (most of the structural units are ZrO6 and ZrO7). These structural units connect to each other forming a network of ZrOx (x = 5, 6, 7) with a significant contribution of edge sharing of oxygen in addition to corner sharing. The coordination number of oxygen is 2, 3 and 4, however the three- and four fold predominate [15-17]. The variety of large oxygen coordination and polyhedral connections with short Zr–O bond lifetimes, induced by the relatively large ionic radius of zirconium, leads to a reduced electronic band gap and increased delocalization in the ionic Zr–O bonding. Understanding chemical bonding and network structure as well as spatial distribution of Received August 10, 2016. Accepted October 5, 2016. Contact Nguyen Viet Huy, e-mail address: nvhuy282@yahoo.com 144 Structure of amorphous and liquid Zircon polyhedra ZrOx helps clarify the extremely low viscosity of liquid ZrO2 and the absence of a first sharp diffraction peak. For amorphous and liquid ZrSiO4, many experimental and simulation studies have been done to clarify the structure as well as physical properties [16-22]. In the work [20] of R. Devanathan and co-workers a molecular dynamics method was used to produce two different amorphous states with distinct densities and structures. Results show that when in a high density state, the zircon structure is intact but the bond angle distributions are broader, and 4% of the SiO4 units are polymerized. In the low density amorphous state, the Zr- and Si-coordination numbers are lower, and the Zr-O and Si-O bond lengths are shorter than the corresponding values for the crystal state. In addition, a highly polymerized Si network is observed in the low density amorphous state. These features have all been experimentally observed in natural metamict zircon [21, 22]. Models with larger number of atoms (5400 atoms) in this investigation should help obtain more reliable results for structures at high temperature than that obtained in earlier studies. The results also indicate a decomposition of ZrSiO4 into ZrO2- and SiO2-rich regions. 2. Content 2.1. Computational method Molecular dynamic (MD) simulation is conducted for ZrSiO4 systems (5400 atoms consist of 900 Si, 900 Zr, 3600 O atoms) at temperatures of 300 K (amorphous state) and 3500 K (liquid state). Simple pair-wise additive potential with Coulombic interaction and Born-Mayer repulsion was used to construct ZrSiO4 models. The potential functions have the form: ϕij = qiqj/rij + Aijexp(−Bijrij). Details of the potential parameters can be found in Ref. [19]. The software used for our calculations, analysis and visualization was written by ourselves. It was written in C language and executed on a Linux operating system. The Verlet algorithm was applied to integrate the equation of motion with the MD step of 1.0 fs. An initial configuration of the sample was created by randomly placing all of the atoms in a cubic box (simulation box). To remove the effect of remembered initial configuration, the sample was heated to 7000K. Equilibrated melt was obtained by relaxing the initial configuration for about 100 ps. After that, the sample was cooled to temperature of 3500 K (liquid state) and 300 K (amorphous state). A long relaxation was then done in the NPT ensemble (at constant temperature and pressure) to obtain a sample at ambient pressure. In order to improve the statistics, the measured quantities of coordination number, partial radial distribution function, bond-angle distribution and bond-length distribution were computed by averaging over 2000 configurations separated by 50 MD steps. 2.2. Results and discussions First, to confirm the reliability of the material model, we investigated the structural characteristics of pair radial distribution function (PRDF) and coordination number distribution. Figure 1 shows the PRDFs of the Si-O and Zr-O pairs. The results show that the Si-O bond lengths are about 1.60 A˚ for the model at 300 K and 1.56 A˚ for the model at 3500 K. This means that the Si-O bond length in liquid zircon is a little shorter than in it is amorphous zircon. From Figure 1, it can be seen that the first peak of PRDFs gSi−O(r) and gSi−O(r) in the amorphous state (at 300 K) is more sharper than in the liquid state (at 3500 K). This demonstrates that structural order in amorphous zircon is higher than it is in liquid zircon. 145 Nguyen Viet Huy, Tran Thuy Duong and Nguyen Van Hong Table. 1. Distribution of coordination number ZSi−O, ZZr−O and ZO−T (here T is Si or Zr) Percentage of Zij ZSi−O 300K 3500K ZZr−O 300 K 3500K ZO−T 300K 3500K 2 0.00 2.92 4 3.46 8.84 1 0.11 1.25 3 71.44 69.61 5 64.82 66.28 2 85.53 85.56 4 27.50 26.04 6 31.20 24.37 3 14.25 12.89 5 1.07 1.41 7 0.53 0.49 4 0.11 0.31 Table 1 shows the distribution of coordination number ZSi−O, ZZr−O and ZO−T (T is Si or Zr) of amorphous and liquid zircon. It can be seen that most of the Si is surrounded by three or four oxygens. For the zircon model at 300 K, the fraction which is three-fold and four-fold is about 71% and 27% respectively. For the model at 3500K, the fraction which iso three-fold and four-fold is about 69% and 26% respectively. This means that the distribution of coordination number ZSi−O in an amorphous state is similar to that in a liquid state. For the Zr-O pair, most of the Zr is surrounded by five or six oxygens. For the model at 300 K, the fraction which is five-fold and six-fold is about 64% and 31% respectively. For model at 3500 K, fraction of five-fold and six-fold is about 66% and 24% respectively. This means that for liquid zircon, the six-fold fraction is smaller than that in the amorphous state. In contrast, the four-fold and five-fold fractions in the liquid state are larger than those in the amorphous state (see Table 1). The distribution of coordination number ZO-T in the amorphous state is similar to that in the liquid state. Most of the O is surrounded by two or three cations (Si or Zr). To clarify the local environment of the oxygen, we have investigated the distribution of all kind of OT2 and OT3 linkages (see Table 2). Figure 1. Si-O and Zr-O pair radial distribution functions of ZrSiO4 at 300 K and 3500 K 146 Structure of amorphous and liquid Zircon Figure 2. Si-O, Zr-O and Zr-O-Si networks at 300 K from left to right respectively Figure 3. Cluster of SiOx with 257 atoms in model ZrSiO4 at 300 K (left) and that with 252 atoms at 3500 K (right) Table 2. Distribution of all kind of OT2 and OT3 linkages (T is Si or Zr) Linkages 300 K 3500 K Si-O-Zr 1439 1419 OT2 O-Zr2 1339 1333 O-Si2 301 328 O-Zr3 48 36 OT3 O-Si3 93 75 Si2-O-Zr 208 202 Si-O-Zr2 164 151 From Table 2, it can be seen that most of the OT2 linkages are Si-O-Zr and O-Zr2. For the model at 300 K, the number of oxygens forming Si-O-Zr and O-Zr2 linkages is 1439 and 1339 respectively. For the model at 3500 K, the number of oxygens forming Si-O-Zr and O-Zr2 linkages is 1419 and 1333 respectively. Most of the OT3 linkages are Si2-O-Zr and Si-O-Zr2. The number of oxygens forming Si2-O-Zr and Si-O-Zr2 are 208 and 164 respectively for the model at 300 K and it is 202 and 151 respectively for the model at 3500 K. It can be seen that there exists a significant 147 Nguyen Viet Huy, Tran Thuy Duong and Nguyen Van Hong amount of O-Si2 and O-Si3 (oxygen that only links to Si) and O-Zr2 and O-Zrv (oxygen that only links to Zr) linkage in both models (see Tables 2 and 3). Table 3. Distribution of OSi, OZr, OSi,Zr, BO and NBO Linkages 300 K 3500 K OSi 394 413 OZr 1392 1405 OSi,Zr 1814 1782 BO 605 613 NBO 1603 1573 (OSi being oxygen that links only to Si, OZr means oxygens that only link to Zr, OSi,Zr being oxygen that links only to both Si and Zr, BO: bridging oxygen is an oxygen that links with at least two silicon atoms, NBO: none-bridging oxygen is an oxygen that links with only one silicon atom) Table 3 shows the distribution of special linkages such as oxygen that links only to silicon, oxygen that links only to zirconium, oxygen that links to both silicon and zirconium, bridging oxygen, and non-bridging oxygen. It can be seen that the distribution of OSi, OZr, OZr,Si, BO, and NBO of zircon at 300 K and 3500 K is similar (in other word, there is not much difference). The existence of OSi, and OZr linkages of significant amount means that in model existing Si-rich regions besides those which are Zr-rich. This shows a compositional heterogeneity in ZrSiO4. This is a microphase separation in the multicomponent oxides. Figure 2 shows the network structure at 300 K for the Si-O network where oxygen links only to silicon, the Zr-O network where oxygen links only to zirconium, and the Si-O-Zr network where oxygen links to both silicon and zirconium. Figure 2, again demonstrates the compositional heterogeneity of ZrSiO4. Table 4. Size-distribution of SiOx- and ZrOx-clusters at 300 K and 3500 K SiOx clusters ZrOx cluster 300 K 3500 K 300 K 3500 K Nc Na Nc Na Nc Na Nc Na 190 <10 201 <10 3 5 1 6 60 10-29 57 10-29 2 6 3 7 17 30-100 18 30-100 1 4079 1 11 1 186 1 178 1 22 1 257 1 252 1 4046 Nc is the number of cluster and Na is the number of atoms in one cluster In addition, it also shows that the Si-O network is broken into subnets (clusters). The number of oxygens that link only to Zr compares to that which links only to Si and the Zr-O network and tends to form a large network. The Si-O-Zr network forms a boundary links between the Si-O network and the Zr-O network. Table 4 shows the size distribution of the Si-O and Zr-O networks at 300 K and 3500 K. Table 4 shows that in the ZrSiO4 model at 300 K, the number of SiOx clusters with less than 10 atoms is 190; those with 10-29 atoms is 60; Those with 30 to 100 atoms is 17. There exist only two clusters with more than 100 atoms. Figure 3 show typical SiOx-clusters with a 148 Structure of amorphous and liquid Zircon size of 257 and 252 atoms which correspond to models at 300 K and 3500 K. The size-distribution of SiOx clusters for the model at 3500 K is similar to that for the model at 300 K. This means that the Si-O network is almost not dependent on temperature. For both models at 300 K and 3500 K, the size-distribution of the ZrOx-clusters is that of a large cluster plus several with less than 10 atoms (a cluster with only one ZrOx unit). 3. Conclusion The structure of zircon in both the amorphous and liquid state consists mainly of the basic structural units SiO3, SiO4, ZrO5 and ZrO6. The Si-O bond length in the liquid state is a little smaller than that in the amorphous state. The structure of zicon in the amorphous state is more orderly than that in the liquid state. Most of the O is surrounded by two or three cations (Si or Zr) forming linkages O-Si2, Zr-O-Si, O-Zr2, O-Si3, Zr-O-Si2, Si-O-Zr2 and O-Zr3. The existence of the O-Zr2, O-Zr3 and O-Si2, O-Si3 linkages reveals a microphase separation in the amorphous and liquid zircon. The Si-O network is broken into clusters with a size of several to several hundred atoms. The network structure of zircon consists of three kinds of networks and the Si-O, Zr-O, Si-O-Zr and Si-O-Zr networks, with the later two serving as a boundary between Si-O and Zr-O networks. 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