^{1,2,a)}, Mao-Sheng Cao

^{2,a)}, Xiao-Ling Shi

^{2}, Zhi-Ling Hou

^{2}, Wei-Li Song

^{2}and Jie Yuan

^{3,a)}

### Abstract

Based on the unique geometrical structure of nanotetra-ZnO needle , we investigate the microwave responses of , including interface scattering, microcurrent attenuation, microantenna radiation, and dielectric relaxation, and build an energy attenuation model. The associated quantitative formula is deduced for calculating the microwave absorption properties of nanocomposite in the range 8–14 GHz according to the present energy attenuation model. Very good agreement between the calculated and experimental results is obtained in a wide frequency range. The maximum deviation less than 0.5 dB in the range 8–14 GHz is obtained. Using the aforementioned model, we analyze the contribution of microwave responses to the energy attenuation in the frequency range 2–18 GHz, and the results reveal that interface scattering and microcurrent attenuation make the contribution most important. In addition, we calculate the effects of the volume fraction, conductivity, permittivity, needle length of , and thickness of on the reflectivity. The results show that the microwave absorption is evidently dependent on these effect factors, and the optimal microwave absorption band and the strongest microwave absorption peak of would appear when these physical parameters are changed.

This work is supported by the National Natural Science Foundation of China under Grant Nos. 50572010, 50972014, and 50872159; the National Defense Funds of China under Grant No. A2220061080; and the National High-Technology Research and Development Program of China under Grant No. 2007AA03Z103. The authors also thank Editor J. L. Wu for revising the manuscript. X. Y. Fang, M. S. Cao, and J. Yuan contributed equally to this work.

I. INTRODUCTION

II. EXPERIMENTAL DETAILS

III. MICROWAVEATTENUATION MODEL

A. Responses of a single

1. The interface scattering response

2. The microcurrent response

3. The dielectric relaxation response

4. The microantenna response

B. Energy attenuation model of a single

C. Reflectivity calculation model of nanocomposite

IV. COMPARISON AND ANALYSIS OF FOUR RESPONSES

V. CALCULATION AND PREDICTION

VI. CONCLUSION

### Key Topics

- II-VI semiconductors
- 90.0
- Microwaves
- 40.0
- Permittivity
- 26.0
- Wave attenuation
- 22.0
- Reflectivity
- 20.0

## Figures

Schematic diagram of microwave response of . The inscribed sphere of the cube is the external sphere of . (a) , , , and are the reflected waves of the four needles of , respectively. is the resultant wave of needles 1 and 2. is the resultant wave of needles 3 and 4. and form the backscatter wave . (b) The schematic diagram of projection area of , where is the side length of the cube, is the average length of each needle of , and is the average diameter of each needle of at the root. (c) The relation between the induced field and microcurrent of each needle. (d) The schematic diagram of the induced dipole moment and microantenna radiation of each needle.

Schematic diagram of microwave response of . The inscribed sphere of the cube is the external sphere of . (a) , , , and are the reflected waves of the four needles of , respectively. is the resultant wave of needles 1 and 2. is the resultant wave of needles 3 and 4. and form the backscatter wave . (b) The schematic diagram of projection area of , where is the side length of the cube, is the average length of each needle of , and is the average diameter of each needle of at the root. (c) The relation between the induced field and microcurrent of each needle. (d) The schematic diagram of the induced dipole moment and microantenna radiation of each needle.

Schematic diagrams of (a) the nanocomposite and (b) the electromagnetic energy attenuation at the arbitrary layer.

Schematic diagrams of (a) the nanocomposite and (b) the electromagnetic energy attenuation at the arbitrary layer.

The experimental and calculated results for , , , and with and taken from Table II.

The experimental and calculated results for , , , and with and taken from Table II.

The four microwave responses dependent on the conductivity of : (a) microcurrent attenuation, (b) interface scattering, (c) microantenna radiation, and (d) dielectric relaxation response. Here , , , and with and taken from Table III.

The four microwave responses dependent on the conductivity of : (a) microcurrent attenuation, (b) interface scattering, (c) microantenna radiation, and (d) dielectric relaxation response. Here , , , and with and taken from Table III.

The four microwave responses dependent on the needle length of : (a) interface scattering, (b) microcurrent attenuation, (c) microantenna radiation, and (d) dielectric relaxation response. Here , , and with , and taken from Table III. The inset in (b) is the magnified figure of the microcurrent attenuation dependent on the needle length of .

The four microwave responses dependent on the needle length of : (a) interface scattering, (b) microcurrent attenuation, (c) microantenna radiation, and (d) dielectric relaxation response. Here , , and with , and taken from Table III. The inset in (b) is the magnified figure of the microcurrent attenuation dependent on the needle length of .

The four microwave responses dependent on the permittivity of : (a) dielectric relaxation response, (b) microantenna radiation, (c) microcurrent attenuation, and (d) interface scattering. Here , , , and with , , , , while and are taken from Table III.

The four microwave responses dependent on the permittivity of : (a) dielectric relaxation response, (b) microantenna radiation, (c) microcurrent attenuation, and (d) interface scattering. Here , , , and with , , , , while and are taken from Table III.

The comparison of four principal responses. In the calculation, , , , and , which are derived from the experimental data, while and are taken from Table III.

The comparison of four principal responses. In the calculation, , , , and , which are derived from the experimental data, while and are taken from Table III.

Frequency-dependence reflectivity of calculated at different geometrical parameters. (a) The needle lengths of are with . (b) The thicknesses of are with . Here and with and taken from Table III.

Frequency-dependence reflectivity of calculated at different geometrical parameters. (a) The needle lengths of are with . (b) The thicknesses of are with . Here and with and taken from Table III.

Frequency-dependence reflectivity of calculated with the volume fraction for , , and with and taken from Table III.

Frequency-dependence reflectivity of calculated with the volume fraction for , , and with and taken from Table III.

Frequency-dependence reflectivity of calculated at different electrical parameters (a) for the conductivity and (b) for the real parts of the dielectric constant to be , , , and with . Here , , and with and taken from Table III.

Frequency-dependence reflectivity of calculated at different electrical parameters (a) for the conductivity and (b) for the real parts of the dielectric constant to be , , , and with . Here , , and with and taken from Table III.

## Tables

Experimental results of the material parameters. Here and are the length and the heel diameter of a needle, respectively, is the density of , is the density of , is the thickness of , and is the volume fraction of (Refs. 48 and 49).

Experimental results of the material parameters. Here and are the length and the heel diameter of a needle, respectively, is the density of , is the density of , is the thickness of , and is the volume fraction of (Refs. 48 and 49).

Experimental results of the electrical parameters at different frequencies. Here and are the real part of the dielectric constant and dielectric loss tangent of , respectively, is the dielectric constant of , and and are the dielectric constant and the reflectance value of , respectively (Refs. 48 and 49).

Experimental results of the electrical parameters at different frequencies. Here and are the real part of the dielectric constant and dielectric loss tangent of , respectively, is the dielectric constant of , and and are the dielectric constant and the reflectance value of , respectively (Refs. 48 and 49).

Calculated results of the dielectric constant by the Debye equation. Here and are the optical frequency and the static dielectric constant of ZnO crystals, and the dielectric relaxation time . Due to the dielectric confinement effect, the permittivity of is larger than that of crystalline ZnO.

Calculated results of the dielectric constant by the Debye equation. Here and are the optical frequency and the static dielectric constant of ZnO crystals, and the dielectric relaxation time . Due to the dielectric confinement effect, the permittivity of is larger than that of crystalline ZnO.

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