Structure of amorphous and liquid Zircon

Network structure of zircon (ZrSiO4) at amorphous and liquid states is investigated by molecular dynamics simulation and visualization. The short range order (SRO) and intermediate range order (IRO) characteristics are analyzed via distribution of units TOn and likages OTm (T=Zr, Si). Investigation results of network structure and size distribution of Si-O and Zr-O subnets show that the structure of zircon 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.

I. INTRODUCTION

Zirncon is one of important materials in nuclear and ceramics industries. In addition, it is a good alternative for conventional silicon oxide as a dielectric material in metal-semiconductor devices [1,2]. So, Zircon has attracted a considerable amount of interest from material scientists. Experimental and simulation rerults show that the structure of amorphous and liquid SiO2 comprises SiO4, SiO5 and SiO6 units. These units link to each other via bridging oxygens forming network of SiOx (x=4, 5, 6). At low density, most of structural units are SiO4 forming tetrahedral network. At high pressure, most of structural units are SiO6 forming octahedral network. The distribution of polyhedra (SiOx) is not uniform but forming cluster of SiO4, SiO5 and SiO6. Spattial distribution of structural units (cluster of SiOx) as well as polymerization is dependent on the density of sample. This results in the different physical properties such as the abnormaly diffusivity, dynamic heterogeneity [3-5]. For amorphous and liquid ZrO2, the structure structure is formed from ZrO5, ZrO6

and ZrO7 polyhedra (most of structural units are ZrO6 and ZrO7). These structural units connects to each other forming 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 are dominant [6,7]. The variety of large oxygen coordination and polyhedral connections with short Zr–O bond lifetimes, induced by the relatively large ionic radius of zirconium, which leads to to a reduced electronic band gap and increased delocalization in the ionic Zr–O bonding. Understanding chemical bonding and network structure as well as spattial distribution of polyhedra ZrOx help to 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 works have been coonduct to clarify the structure as well as physics properties [8,9]. In the work [10], R. Devanathan and co-workers used molecular dynamics method to produce two different amorphous states with distinct densities and structures. Result show that in the 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

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2 3 4 5 6 7

g ij(r)

3500K 300K

Si-O

Zr-O

r(Å)

3500K 300K

Fig. 1. The Si-O and Zr-O pair radial distribution functions of ZrSiO4 at 300K and 3500K.

density amorphous state, the Zr- and Si-coordination numbers are lower, and the Zr-O and Si-O bond lengths are shorter than 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. Investigation results also indicate the decomposition of ZrSiO4 into ZrO2- and SiO2-rich regions.

II. 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 is used to construct ZrSiO4 models. The potential function have form: ij=qiqj/rij + Aijexp(-Bijrij). Detail about potential parameters can be found in Ref. [9]. The software used in our calculation, analysis and visualization was written by ourselves. It was written in C language and executed on Linux operating system. Verlet algorithm is applied to integrate the equation of motion with MD step of 1.0 fs. Initial configuration of the sample is created by randomly placing all atoms in a cubic box (simulation box). To remove the effect of remembering initial configuration, the sample is heated up to 7000K. Equilibrated melt has been obtained by relaxing initial configuration for about 100 ps. After that, the sample is cooled down to the temperature of 3500K (liquid state) and 300K (amorphous state). A consequent long relaxation has been done in the NPT ensemble (constant temperature and pressure) to obtain a sample at ambient pressure. In order to improve the statistics, the measured quantities such as the coordination number, partial radial distribution function, bond-angle distributions and bond-length distributions etc... are computed by averaging over 2000 configurations separated by 50 MD steps.

III. RESULTS AND DISCUSSIONS

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Firstly, to confirm the reliability of material model we have investigated the structural characteristics such as the pair radial distribution function (PRDF), coordination number distribution. Figure 1 displays PRDFs of Si-O and Zr-O pairs. Results show that the Si-O bond lengths are about 1.60 Ǻ for model at 300K and 1.56 Ǻ for model at 3500K. It means that the Si-O bond length in liquid zircon is a little smaller than in amorphous zircon. From figure 1, it can be seen that the first peak of PRDFs gSi-O(r) and gSi-O(r) for amorphous state (at 300K) is more sharpper than for liquid state (at 3500K). It demonstrates that the structural order in amorphous zircon is higher than in liquid zircon.

Table 1. Distribution of coordination number ZSi-O, ZZr-O and ZO-T (here T is Si or Zr).

Percentage of Zij

ZSi-O 300K3500

K ZZr-O 300 K3500

K 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 66.28 285.5

3 85.56

4 27.50 26.04 6 31.20 24.37 314.2

5 12.895 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 Si is surrounded by three or four oxygens. For zircon model at 300K, the fraction of three-fold and four-fold is about 71% and 27% respectively. For model at 3500K, the fraction of three-fold and four-fold is about 69% and 26% respectively. It means that the distribution of coordination number ZSi-O in amorphous state is similar to liquid state. For Zr-O pair, most of Zr is surrounded by five or six oxygens. For model at 300K, fraction of five-fold and six-fold ia about 64% and 31% respectively. For model at 3500K, fraction of five-fold and six-fold is about 66% and 24% respectively. It means that in liquid zircon, the fraction of six-fold is smaller than in amorphous state. In contrast, the fraction of four-fold and five-fold in liquid state is higher than in amorphous state, see Table 1. The distribution of coordination number ZO-T in amorphous state is similar to in liquid state. Most of O is surrounded by two or three cations (Si or Zr). To more clarify the local enviroment of oxygens, we have investigated the distribution of all kind of linkages OT2 and OT3 (see Table 2).

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Table 2. Distribution of all kind of linkages OT2 and OT3 (T is Si or Zr).

linkages 300K 3500KSi-O-Zr 1439 1419

OT2 O-Zr2 1339 1333O-Si2 301 328O-Zr3 48 36

OT3 O-Si3 93 75Si2-O-Zr 208 202Si-O-Zr2 164 151

From Table 2, it can be seen that most of linkages OT2 are Si-O-Zr and O-Zr2. For model at 300K, the number of oxygens forming linkages Si-O-Zr and O-Zr2 is 1439 and 1339 respectively. For model at 3500K, the number of oxygens forming linkages Si-O-Zr and O-Zr2 is 1419 and 1333 respectively. Most of linkages OT3 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 model at 300K and it is 202 and 151 respectively for model at 3500K. It can be seen that It also exists a significant amount of linkages O-Si2 and O-Si3 (oxygen that only links to Si) and O-Zr2 and O-Zr3 (oxygen that only links to Zr) in both models, see Table 2 and Table 3.

Table 3. Distribution of OSi (OSi means oxygens that only link to Si ), OZr (OZr

means oxygens that only link to Zr), OSi,Zr (OSi,Zr means oxygens that link to both Si and Zr), BO (BO: bridging oxygen means an oxygen links with at least two silicon atoms) and NBO (NBO: none-bridging oxygen means an oxygen links with only one silicon atom).

linkages 300K 3500KOSi 394 413OZr 1392 1405OSi,Zr 1814 1782BO 605 613NBO 1603 1573

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Table 3 shows the distribution of some kind of special linkages such as: oxygens that only link to silicon; oxygens that only link to zirconium; oxygens that link to both silicon and zircanium; bridging oxygen; none-bridging oxygen. It can be seen that the distribution of OSi, OZr, OZr,Si, BO, and NBO of zircon at 300K and 3500K is similar each other (in other word, there is not much difference). The existence of OSi, and OZr linkages with significant amount means that in model existing Si-rich regrions besides Zr-rich ones. This shows the compositional heterogeneity in ZrSiO4. This is microphase shows the network structure at 300K for: Si-O separation in multicomponent oxides. Figure 2 network where oxygens only link to silicons; Zr-O network where oxygens only link to zirconiums; Si-O-Zr network oxygens where oxygens link to both silicons and zirconiums. From figure 2, it one time again demonstrates the compositional heterogeneity in ZrSiO4. Besides, it also shows that the Si-O network is broken into subnets (clusters). The number of oxygens that only link to Zr is very much in comparison to the one that only link to Si and the Zr-O network tend to form a large network. The Si-O-Zr network forming boundary links between Si-O network and Zr-O network. Table 4 shows the size distribution of Si-O and Zr-O network at 300K and 3500K. Table 4 shows that in model ZrSiO4 at 300K, the number of SiOx-clusters with the the size less than 10 atoms is 190, the ones with the number of atoms from 10 to 29 is 60, and the ones with the number of atoms from 30 to 100 is 17. It only exists two clusters with the number of atoms more than 100 atoms.

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Fig. 2. Si-O, Zr-O and Zr-O-Si network at 300 K from left to right respectively.

Fig. 3. Cluster of SiOx with 257 atoms in model ZrSiO4 at 300K (left) and the one with 252 atoms

Figure 3 show the typical SiOx-clusters with size of 257 and 252 atoms coressponding models at 300K and 3500K.The size-distribution of SiOx clusters for model at 3500K is similar to that for model at 300K. It means that Si-O network is almost not dependent on temperature. For both models at 300K and 3500K, size-distribution of ZrOx-clusters comprises a large cluster and several ones with the number of atoms less than 10 (cluster with only one ZrOx unit).

Table 4. Size-distribution of SiOx- and ZrOx-cluster at 300K and 3500K. Nc is the number of cluster and Na is the number of atoms in one cluster.

SiOx cluster ZrOx cluster

300K 3500K300K 3500K

Nc Na Nc Na Nc Na Nc Na190 <10 201 <10 3 5 1 660 10-29 57 10-29 2 6 3 7

1730-100 18

30-100 1

4079 1 11

1 186 1 178 1 221 257 1 252 1 4046

IV. CONCLUSION

Structure of Zircon at both amorphous and liquid states mainly comprises basic structural units: SiO3, SiO4, ZrO5 and ZrO6. The Si-O bond length in liquid state is a little smaller than the one in amorphous state. Structure of zicon at amorphous state is more order than liquid state. Most of 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 linkages O-Zr2, O-Zr3 and O-Si2, O-Si3 reveals the microphase separation in amorphous and liquid zircon. The Si-O network is broken into cluster with the size from several atoms to several hundreds atoms. Network structure of zircon comprises three kinds of network: Si-O, Zr-O, and Si-O-Zr network and Si-O-Zr network have a role as the boundary between Si-O network and Zr-O one. Acknowledgement:

References6

Fig. 3. Cluster of SiOx with 257 atoms in model ZrSiO4 at 300K (left) and the one with 252 atoms

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