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Xiaolin Chen*, Yonghong Cheng, Xiaojrtn Xie, Hao Cui and Wutong Feng. State Key Laboratory of Electrical Insulation for Power Equipment, Xi'an Jiaotong ...
Proceedings of 2005 International Symposium on Electrical Insulating

Pl-6 1

Materials, June 5-9, 2005. Kitakyushu, Japan

Research of Dielectric Properties of Silica Based on Molecular Imitation Technique Xiaolin Chen*, Yonghong Cheng, Xiaojrtn Xie, Hao Cui and Wutong Feng State Key Laboratory of Electrical Insulation for Power Equipment, Xi’an Jiaotong University 28 West Xianning Road, Xi’an, Shanxi Province, 710049, P.R.China E-mail :[email protected]

Abstract: The material dielectric properties are obtained by means of the traditional measurement method. However, there is some inconvenience in the method, for example, the testing periods may take a long time, the testing process may be complex and may cost much. In our paper, we propose a new method to study material dielectric properties with molecular imitation technique. Firstly, the three-dimension model of material molecules is established. Based on the theories of molecular dynamics, energy band and quantum chemistry, and the micro dielectric properties can be researched in atomic level. Secondly, the macroscopic material diekectric properties can be calculated due to the interaction of crystal cells. There are many complex physical changes in the process of micro properties to macro properties, such as phase change. Finally, in order to obtain the macro dielectric properties of material, the grain boundary, phase boundary and phase change need to be considered in our imitating calculation. The material macro dielectric properties can be calculated by this imitation technique, if the molecular structure of this material is given, which is the advantage o f this method. It may be helpful in studying the dielectric properties of a new material and modifying insulation material. INTRODUCTION

The dielectric property is one of the most primary and important properties of materials. The experimental t e c h q u e and devices have been developed greatly in recent decades. And the measurement method and system are designed to detect the complex dielectric constant in high temperature. However, if the temperature is higher, the experimental technique cannot only meet the need of detecting the dielectric constant, but also obtain the relationship between the dielectric properties and the microstructure of materials, as known for us is very important for studying material dielectric regularity. We know that there are three primary methods in modem science research, i.e. theoretical analysis, experimental measurement, and computer imitating calculation. The last method has been developed greatly because of the great development of the computer

science and technology from nineties in the last century. The molecular imitation technique is an important field of the computer imitating method. It includes the imitation of molecular dynamics, quantum mechanics, and so on. It can calcuiate material microstructure and complex dielectric constant. This technique can be regarded as the complement and expansion for the experimental measurement. However, little research has been made to calculate the material dielectric property by the method of the molecular imitation technique. We present a method of studying dielectric constant of silica by molecular imitation. And the dielectric constant between O’C to 300% was obtained and the inner micro movements of molecules was imitated in OUT research.

THEORY OF MOLECULAR IMITATION The molecular imitation technique used in our research adopts the first-principles calculating arithmetic. This method doesn’t need the experimental data. It can obtain the material properties with the help of the nuclei, electrons or other structure units and their relationship. We know that the interaction of atoms is the foundation of macro formation and variation of material. The functional density theory based on the Hohenberg-Kohn rule not only supplies the method of reducing the multi-electron objects to single-electron one, but also becomes a useful tool for the calculation of electron structure and total energy of molecules. The calculation based on first principles has been developed greatly recent years, because the theory of energy bands, the calculating method of quantum chemistry and the theory of functional density develop further. Quantum mechanics provides a reliable way to calculate what electrons and atomic nuclei do in any situation. The behavior of electrons in particular governs most of the properties of materials. This is true for a single atom or for assemblies of a t o m in condensed matter, because quantum mechanics describes and explains chemical bonds. Therefore we can understand the properties of any material from first-principles, that is, based on fundamental physical laws and without using free parameters, by solving the Schrodinger equation for the electrons in that material. MOLECULAR IMITATION OF SILICA

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There are some commercial software tools that can fulfill the molecular imitation technique. The software adopted in our research is Material Studio. This software includes many different packages due to different objects. The molecular dynamics properties of silica and its structures under different temperatures were calculated with a package named DISCOVER. Then the calculating results were put into the input of another package named CASTEP. In this package, the energy bands, density of electron states, density of partial states and complex dielectric constants of silica were calculated. Moiecular Modeling

Molecular modeling is the basis of the molecular imitation. The molecular modeling method includes calling the relating database model, modeling the molecular structure through the experimental data, X-ray diffraction, nuclear magnetic resonance, and so on. Calling the relating database model is very convenient if the object is a c o m o n material. For the common material, we can also obtain the molecular model by the space group table in the database of crystals. If the material is unknown, it is necessary to deduce its crystal structure with the help of X-ray diffraction or nuclear magnetic resonance, The molecular modeling process is dynamic, because the molecular model should be modified more practically in the process of the imitating calculation. If the imitation result is far away from the experimental result, the model will be modified or rebuilt again. Fig.1 shows a typical molecular model of silica crystal. Its structure is a triclinic cell and its space group is P3121. The parameters of crystal are the following: a=b=0.4913nm, c=O.S4OSnm. Because the calculating result will be of inaccuracy if the number of the atoms is not much enough,'the model adopted in our research is a super cell containing twenty seven cells, that is 189 atoms.

Calculation of Molecular Dynamics The silica crystal model can be obtained directly in the database of software, because it is a very common material and has been researched for around a century. But there is only the crystal model under Ok in the

database. In order to calculate the dielectric properties under different temperatures, we should make the molecular dynamics calculation firstly. This caIcuIation can offer the crystal models under different temperatures and molecular dynamics properties. Based on this result, it is possible to calculate the micro properties of material. Before the process of molecdar dynamics calculation, another process that should be made is geometric optimization of the crystal model. The aim of the geometric optimization is to make the crystal energy reach the least level by the means of calculating its internal energy. We know that a structure will be stable when it has the least internal energy. The optimization adopted in our research is a comprehensive method, containing Newton's method, the conjugate gradient method and the steepest descent method. Each of the three methods has its advantages and application scope. The comprehensive method will select proper method due to the researched object and each method may be used in the process of geometric optimization. We demonstrate the optimization method using the sample shown in Fig. 1. The degree of convergence was set at O.OOlkcal/mol, the iteration number was 10000, and the number of optimization was three. Table 1 shows the variation of the lattice parameter. In this table, 1 and 2 represent before and after optimization respectively. There was slight difference between before and after optimization and the lattice of crystal expanded a little. Table1 Silica lattice parameters before and after the obtimization dnm

b/nm

c/nm

Q:

0

y

1

0.4913

0.4913

0.5405

90

90

120

2

0.4965

0.4965

0.5437

90

90

120

In order to calculate the crystal structure and molecular dynamics, an imitation method named NVT was adopted. NVT means constant temperature and constant volume. If the molecular dynamics was calculated by NVT algorithm o d y once, the internal energy curve along temperature fluctuated acutely, which could not meet the need of constant temperature. In fact, the molecular dynamics was calculated three times by NVT in our research. We found that the fluctuating amplitude would decrease after a process of calculation. The calculating result of this time was set as the input of next calculation. The energy curve along temperature would be smoother after the three calculating processes. In the NVT algorithm, Andersen hot-bath method was adopted to adjust the temperature. This method assumes that the researched object exchanges heat energy by collision with a huge hot-bath unit of constant temperature. The maximum deviation was 5000kcaVmol at each step, the molecular collision rate

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was 1.0, the step length was Ifs, and every 5000 steps

would give an output of crystal structure. According to this method, three calculating processes were made. Another important aspect in calculation was selecting the force field. Every material has its proper force field. In our calculation, a fore field named Compass was used, which was fit to the condensed materials and applied widely in molecular imitation. The existing research shows that it can be fit for silica crystal. After the molecular dynamics calculation, the crystal structures under different temperature were obtained. Fig.2 shows the silica crystal structures under O T , 100 %, 200% and 300°C. We can find out that there is great difference of silica crystal during temperature changing. This result accords with the theory of thermodynamics.

(a) 0°C

arising by the non-uniform electron gas. While GGA assumes that there is gradient in electron distribution, taking the effect of non-uniform electron density into account. Compared these two approximation, it was found that GGA was fit for silica crystal. So, it was adopted to calculate the exchanging correlation density. The selection of pseudopotential methods was crucial in this calculating process. In first principles, the comnion pseudopotential methods include norm constant pseudopotential method and soft pseudopotential method. The former makes the calculation from the atom potential, inducing no experimental parameters and adopting the expansion of plane wave to represent the ekctronic state. However, if the 2p orbit or 3d orbit of electron cloud in atom is uncompleted, the pseudopotential will be very hard, which increases the calculating quantity. The latter can reduce it by reducing the basic function o f plane wave. Using the soft pseudopotential method in CASTEP package, the energy band, density of states, and other properties can be calculated rapidly. The first principles calculation by CASTEP needs the crystal structure of molecular dynamics under a certain temperature. The molecular dynamics results contain many frame fiIes storing the crystal structures under a temperature, so the statistical calculation was adopted in order to obtain more accurate result. The calculation result can offer the information of the energy band, density of electron states, density of partial states and complex dielectric constants. The same calculation process was carried out under different temperatures, therefore the above properties along the temperatures can be obtained.

(bi 100%

(b)300'C Fig2 silica crystal structures under O"C, loo%, 200% and 300°C ( c ) 200%

Calculation of First Principles

After the crystal structures under different temperatures were obtained, the calculation based on first principles was made by CASTEP package to calculate the energy band, density of electron states, density of partial states and complex dielectric constants under the corresponding temperature, The algorithm basis of CASTEP package is the first principles of density functional method. The density functional theory has an important composition named exchanging correlation density functional. In CASTEP package, the exchanging correlation density functional is fulfilled by LDA (Locaf Density Approximation) or GGA (Global Gradient Approximation). In LDA, the uniform electron gas replaces the non-uniform one, ignoring the effect of electron exchanging energy

In our research, all the caIcuIation was made in reciprocal space. The space symmetry of models followed the lowest symmetry that was P1, and the cutting off energy of plane wave was 300.0eV. During calculating the energy band and density of states, the pseudopotential function was GGA, the exchanging correlation potential hnction was PBE (Perdew Burke Emerhof), and the tolerance was 1E-5eV. The calculation results were compared with the experimental results, and then the calculating parameters were adjusted if the difference was great. According to this method, the dielectric properties under high temperatures codd be deduced. Fig.3-Fig.6 show respectively the energy band, density of electron states, density of partial statss and complex dielectric constants. From Fig,3 and Fig.4, it could be seen that the density of electron states was key component. Fig8 shows directly the variation of the complex dielectric constant along temperatures and the abnormal dispersion in optical range was obtained, which agreed with dielectric theory.

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temperature, the dielectric constant along temperatures can be obtained. The researched object described in this paper is silica crystal under 300’C. We will research other material under high temperature in our further

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Fig.3 CASTEP band structure of silica under 300°C Enww IwW

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[ I ] M D Segall, Philip J D Lindan, M J Probert, et al.. “First-principles simulation: ideas, illustrations and the CASTEP code”, JOURNAL OF PHYSICS: CONDENSED MATTER, 2002, NO.14, P2717-2744 (21 I.Morrison, I.-C.Li, %Jenkins, et al., “Ab-Initio Total Energy Studies of the Static and Dynamical Properties of Ice Ih”, J.Phys.Chem.B 1997,lOI P6 146-61SO. 131 V.Milman, B.Winkler, J.A.White, et al., “Electronic Structure, Properties, and Phase Stability of Inorganic Crystals: A Pseudopotential Plane-Wave Study”, Intemational Journal of Quantum Chemishy, vo1.77,2000, P895-910.

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0

1

2

3

*

5

0

7

D

9

1

0

1

1

I

P

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Fig.4 Density of electron states of silica under 300°C

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6 I 2

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Fig.5 Density of partial states of silica under 300°C

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Fig.6 Complex dielectric function of silica under 300% CONCLUSION AND DISCUSSION

We propose a method to study the dielectric properties of silica crystal by molecular imitation technique. a s technique can also calculate other dielectric crystal. Using this technique, the dielectric properties can be calculated. Moreover, the microstructure of crystal can be obtained at the same time. It may be helpful to research the relationship between the macro properties such as dieIectric constant and the microstructure of crystal. By the means of combing the molecular dynamics and the first principles, the complex dielectric constant under different temperature can be calculated rapidly. After calculating the parameter under different

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