# Dielectric Properties of Zinc Sulfide Concentrate during the Roasting at Microwave Frequencies

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

^{3}—have been measured by using the resonance cavity perturbation technique at 915 and 2450 MHz during the roasting process for the temperature ranging from room temperature to 850 °C. The variations of dielectric constant, the dielectric loss factor, the dielectric loss tangent and the penetration depth with the temperature, frequency and apparent density have been investigated numerically. The results indicate that the dielectric constant increases as the temperature increases and temperature has a pivotal effect on the dielectric constant, while the dielectric loss factor has a complicated change and all of the temperature, frequency and apparent density have a significant impact to dielectric loss factor. Zinc sulfide concentrate is high loss material from 450 to 800 °C on the basis of theoretical analyses of dielectric loss tangent and penetration depth, its ability of absorbing microwave energy would be enhanced by increasing the apparent density as well. The experimental results also have proved that zinc sulfide concentrate is easy to be heated by microwave energy from 450 to 800 °C. In addition, the experimental date of dielectric constant and loss factor can be fitted perfectly by Boltzmann model and Gauss model, respectively.

## 1. Introduction

_{2}emission and hydrometallurgy suffers from lengthy processing times and lower recoveries. So much attention has been paid to develop the processes which are less costly, more environmentally friendly and economically acceptable, for instance, using the microwave as an energy source [2].

^{2}= −1, the relative dielectric constant (${\mathsf{\epsilon}}_{\mathrm{r}}^{\text{'}}$) measures how much energy transferred from an external electric field is stored in a material, whereas the relative dielectric loss factor (${\mathsf{\epsilon}}_{\mathrm{r}}^{"}$) measures how lossy a material is to an external electric field. ${\mathsf{\epsilon}}_{\mathrm{r}}^{\text{'}}$and ${\mathsf{\epsilon}}_{\mathrm{r}}^{"}$ are crucial parameters to the microwave absorption in materials and efficiency of microwave processing [5,6], they are effected by composition, temperature, microwave frequency, etc.

_{p}) is defined as the distance at which power density of incident wave is reduced to 1/e of its value at surface of the material [8]. It is the measure of how deep a microwave radiation can penetrate into a material and it is calculated as follows:

^{8}m/s), and f is the micorowave frequency (Hz).

_{2}emissions [10,11]. However, the kind and mass fraction of addition is dominantly based on experience analogy under the condition of no dielectric properties of zinc sulfide concentrate. Hence, it is important to know how the dielectric properties of zinc sulfide concentrate change with the temperature, microwave frequency, and apparent density.

## 2. Experimental

#### 2.1. Material and Preparation

#### 2.2. Measurement of Dielectric Properties

_{0n0}cavity, temperature control, Agilent N5230C vector network analyzer (Keysight Technologies, Penang, Malaysia), and computer with special dielectric properties computing software. The zinc sulfide concentrate powder was prepared in duplicate and filled in two quartz tube with inside diameter (ID) 28 mm, outside diameter (OD) 35 mm and length 500 mm. The two samples were formed by different external force, and their apparent densities were obtained by measuring their mass and volume. Measurement processes are as following: Ore sample is place in the induction furnace and heated to the designed temperature, then raised up quickly to the TM

_{0n0}cavity. Agilent N5230C vector network analyzer records the date changes of resonant frequency and quality factor. The testing software in the computer would calculate the parameters of dielectric properties, error date processing is considered as well. The ore sample was step-heated to 850 °C from room temperature in 50 °C steps. The two samples were measured one by one. The entire measurement process was in an air atmosphere and at atmospheric pressure.

#### 2.3. Thermogravimetric Analysis-Differential Scanning Calorimetry Analysis of Zinc Sulfide Concentrate

#### 2.4. Dielectric Properties Modeling

_{1}, A

_{2}, T

_{0}and dT are the regression coefficients. The second model is Gauss model and can also be expressed as exponential form [15,16]:

_{0}, T

_{0}and A are the regression coefficients.

## 3. Results and Discussion

#### 3.1. Dielectric Properties of Zinc Sulfide Concentrate

^{3}at 915 and 2450 MHz frequency is shown in Figure 3. The dielectric constant of zinc sulfide concentrate at room temperature in this study is similar to that of previous study [2]. It can be seen from Figure 3a,c that the dielectric constant of zinc sulfide concentrate increases gradually as temperature increases from room temperature to 850 °C, this could be because the energy of molecules increases with temperature increases, then the relaxation time decreases, so the response to the external electric field is faster, the dielectric constant of zinc sulfide concentrate increases immediately [17]. The dielectric constant is relatively low (<5) for temperature under 450 °C because of the weak-polar nature. The dielectric constant at 2450 MHz is mostly larger than that at 915 MHz, and the difference of the dielectric constant between 2450 and 915 MHz is small, these experimental results are not in line with Debye equation [18], that’s because of the intricate characteristics of the chemical composition and phase distribution. Similar increasing trend of dielectric constant is observed for two apparent densities and the dielectric constant of 1.63 g/cm

^{3}is always bigger than that of 1.54 g/cm

^{3}. In a word, the temperature has a pivotal effect on the dielectric constant compared with frequency and apparent density.

^{3}is mostly larger than that of 1.54 g/cm

^{3}for the same temperature. Hence, the temperature, frequency and apparent density have a great effect on the dielectric loss factor.

^{3}. Properly speaking, the materials that can be heated well in an electric field have high values of $\mathrm{tan}\mathsf{\delta}$, and materials that can be heated poorly have low values of $\mathrm{tan}\mathsf{\delta}$, based on this feature, they are often referred to as “high loss” or “low loss” materials, respectively. It can be seen from Figure 4 that the zinc sulfide concentrate is medium loss material when the temperature less than about 450 °C, and zinc sulfide concentrate is high loss material because of $\mathrm{tan}\mathsf{\delta}>3\times {10}^{-2}$ when the temperature change approximately from 450 to 800 °C. The loss tangent at 915 MHz is larger than that at 2450 MHz for temperature above 400 °C, the maximum values of loss tangent are 0.232 at 2450 MHz and 0.100 at 2450 MHz, respectively. The zinc sulfide concentrate of bigger apparent density for a given temperature mostly has a higher value of dielectric loss factor, it can be concluded that the loss tangent increases and reaction process accelerates as the apparent density increases suitably, similar results for room temperature can be found in literature [24,25], so we can enhance the ability of absorbing microwave by increasing the apparent density.

#### 3.2. Effect of Temperature on Penetrate Depth of Zinc Sulfide Concentrate

^{3}. It can be found that the variation tendency of the penetration depth is same for four curves. The frequency and temperature have a more great effect on the penetrate depth rather than the apparent density. It can be concluded that zinc sulfide concentrate can be heated well from 450 to 800 °C, and 2450 MHz is beneficial to the efficient heat while 915 MHz is in favor of uniform heating.

#### 3.3. Heating Experimental Results in the Microwave Oven

^{3}was heated by 2450 MHz microwave oven at power of 1000 W. The method of microwave auxiliary heating by using silicon carbide was employed from room temperature to 450 °C, then silicon carbide was taken out quickly from the microwave cavity, later the zinc sulfide concentrate was heated directly by microwave energy. Heating experimental results show that it needs 26 min from 450 to 800 °C, heating rate is 13.85 °C /min.

#### 3.4. Modeling the Dielectric Constant

^{3}at 915 and 2450 MHz. The fitting results of regression coefficient and coefficient of determination (R

^{2}) are summarized in Table 3. It can be seen that the R

^{2}value of Boltzmann fit is 0.99 for 915 MHz and 0.97 for 2450 MHz compared to 0.97 for 915 MHz and 0.90 for 2450 MHz of Gauss fit. Since R

^{2}indicates how well the function is fitted to the experimental values, very high values of R

^{2}(>0.9) in two models implies that predicted value of zinc sulfide concentrate dielectric properties is very close to the experiment results. The predicted values of zinc sulfide concentrate dielectric properties will be helpful to design and simulate large size microwave system.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Gregurek, D.; Peng, Z.W.; Wenzl, C. Lead and zinc metallurgy. JOM
**2015**, 67, 1986–1987. [Google Scholar] [CrossRef] - Al-harahsheh, M.; Kingman, S.; Bradshaw, S. The reality of non-thermal effects in microwave assisted leaching systems? Hydrometallurgy
**2006**, 84, 1–13. [Google Scholar] [CrossRef] - Thostenson, E.T.; Chou, T.W. Microwave processing: Fundamentals and applications. Compos. Part A Appl. Sci. Manuf.
**1999**, 30, 1055–1071. [Google Scholar] [CrossRef] - Haque, K.E. Microwave energy for mineral treatment process—A brief review. Int. J. Miner. Process.
**1999**, 57, 1–24. [Google Scholar] [CrossRef] - Tang, J.M. Unlocking potentials of microwaves for food safety and quality. J. Food Sci.
**2015**, 80, 1776–1793. [Google Scholar] [CrossRef] [PubMed] - Peng, Z.W.; Hwang, J.Y.; Kim, B.G.; Mouris, J.; Hutcheon, R. Microwave absorption capability of high volatile bituminous coal during pyrolysis. Energy Fuels
**2012**, 26, 5146–5151. [Google Scholar] [CrossRef] - Laybourn, A.; Katrib, J.; Palade, P.A.; Easun, T.L.; Champness, N.R.; Schroder, M.; Kingman, S.W. Understanding the electromagnetic interaction of metal organic framework reactants in aqueous solution at microwave frequencies. Phys. Chem. Chem. Phys.
**2016**, 18, 5419–5431. [Google Scholar] [CrossRef] [PubMed] - Tripathi, M.; Sahu, J.N.; Ganesan, P.; Dey, T.K. Effect of temperature on dielectric properties and penetration depth of oil palm shell (OPS) and OPS char synthesized by microwave pyrolysis of OPS. Fuel
**2015**, 153, 257–266. [Google Scholar] [CrossRef] - Beatriz, G.B.; Jose, C.C.; Felipe, P.F.; Pedro, P.G.; Gabriel, L.V. In situ monitoring of materials at high temperatures through dielectric properties measurement. Materials
**2016**, 9, 349. [Google Scholar] - Chen, W.H.; Zhang, L.B.; Peng, J.H.; Yin, S.H.; Ma, A.Y.; Yang, K.; Li, S.W.; Xie, F. Effects of roasting pretreatment on zinc leaching from complicated zinc ores. Green Process. Synth.
**2016**, 5, 41–47. [Google Scholar] [CrossRef] - Yang, K.; Li, S.W.; Zhang, L.B.; Peng, J.H.; Chen, W.H.; Xie, F.; Ma, A.Y. Microwave roasting and leaching of an oxide-sulfide zinc ore. Hydrometallurgy
**2016**, 166, 243–251. [Google Scholar] [CrossRef] - Makul, N.; Rattanadecho, P.; Agrawal, D.K. Applications of microwave energy in cement and concrete—A review. Renew. Sustain. Energy Rev.
**2014**, 37, 715–733. [Google Scholar] [CrossRef] - Beberoso, D.; Albero-ortiz, A.; Monzo-cabrera, J.; Diza-morcillo, A.; Arenills, A.; Menendez, J.A. Dielectric characterization of biodegradable wastes during pyrolysis. Fuel
**2016**, 172, 146–152. [Google Scholar] [CrossRef] - Motasemi, F.; Afzal, M.T.; Salema, A.A.; Mouris, J.; Hutcheon, R.M. Microwave dielectric characterization of switchgrass for bioenergy and biofuel. Fuel
**2014**, 124, 151–157. [Google Scholar] [CrossRef] - Motasemi, F.; Afzal, M.T.; Salema, A.A. Microwave dielectric characterization of hay during pyrolysis. Ind. Crop. Prod.
**2014**, 61, 492–498. [Google Scholar] [CrossRef] - Sun, J.; Wang, W.L.; Yue, Q.Y. Review on microwave-matter interaction fundaments and efficient microwave-associated heating strategies. Materials
**2016**, 9, 231. [Google Scholar] [CrossRef] - Muley, P.D.; Boldor, D. Investigation of microwave dielectric properties of biodiesel components. Bioresour. Technol.
**2013**, 127, 165–174. [Google Scholar] [CrossRef] [PubMed] - Julrat, S.; Chongcheawchamnan, M.; Robertson, L.D. Characterization of the dielectric properties of rubber latex from 0.5 to 33 GHz. Biosyst. Eng.
**2014**, 125, 1–8. [Google Scholar] [CrossRef] - Zhang, Y.L.; Yu, X.J.; Li, X.B. Zinc recovery from franklinite by sulphation roasting. Hydrometallurgy
**2011**, 109, 211–214. [Google Scholar] [CrossRef] - Boyanov, B.; Peltekov, A.; Petkova, V. Thermal behavior of zinc sulfide concentrates with different iron content at oxidative roasting. Thermochim. Acta
**2014**, 586, 9–16. [Google Scholar] [CrossRef] - Peng, Z.W.; Hwang, J.Y. Microwave-assisted metallurgy. Int. Mater. Rev.
**2015**, 60, 30–63. [Google Scholar] [CrossRef] - Franco, A.P.; Yamamoto, L.Y.; Tadini, C.C.; Gut, J.A. Dielectric properties of green coconut water relevant to microwave processing: Effect of temperature and field frequency. J. Food Eng.
**2015**, 155, 69–78. [Google Scholar] [CrossRef] - Peng, Z.W.; Lin, X.L.; Wu, X.J.; Hwang, J.Y.; Kim, B.G.; Zhang, Y.B. Microwave absorption characteristics of anthracite during pyrolysis. Fuel Process. Technol.
**2016**, 150, 58–63. [Google Scholar] [CrossRef] - Nowak, D.; Granat, K.; Opyd, B. Examination and analysis of influence of compaction degree on dielectric properties of moulding sand components. Metalurgija
**2015**, 54, 353–356. [Google Scholar] - Zhang, L.B.; Ma, A.Y.; Liu, C.H.; Qu, W.W.; Peng, J.H.; Luo, Y.G.; Zuo, Y.G. Dielectric properties and temperature increase characteristics of zinc oxide dust from fuming furnace. Trans. Nonferr. Met. Soc. China
**2014**, 24, 4004–4011. [Google Scholar] [CrossRef]

**Figure 2.**Thermogravimetric Analysis (TG) and differential scanning calorimetry (DSC) curves of zinc sulfide concentrate.

**Figure 3.**The variations of dielectric properties of zinc sulfide concentrate at different temperature.

**Figure 6.**Experimental values of dielectric properties fitted with Boltzmann model and Gauss model for apparent density 1.63 g/cm

^{3}at 915 MHz and 2450 MHz.

Zn_{T} | S | Fe | Pb |
---|---|---|---|

51.16 | 32.98 | 8.26 | 1.95 |

_{T}—total zinc.

Zinc Phase | Zinc Sulfide | Zinc Carbonate | Zinc Silicate | Franklinite et al. | Zn_{T} |
---|---|---|---|---|---|

Mass fraction/% | 49.55 | 0.80 | 0.64 | 0.17 | 51.16 |

Distribution/% | 96.85 | 1.56 | 1.25 | 0.33 | 100 |

**Table 3.**Regression coefficients and R

^{2}values for Boltzmann model and Gauss model fitted to the dielectric properties experimental results.

Parameter | Model | Frequency | Regression Coefficients | R^{2} | |||
---|---|---|---|---|---|---|---|

${\mathsf{\epsilon}}_{\mathrm{r}}^{\text{'}}$ | Boltzmann model | A_{1} | A_{2} | T_{0} | dT | ||

915 MHz | 3.27 | 46,800.40 | 2108.67 | 141.71 | 0.99 | ||

2450 MHz | 4.16 | 15.79 | 760.94 | 19.47 | 0.97 | ||

${\mathsf{\epsilon}}_{\mathrm{r}}^{"}$ | Gauss model | y_{0} | T_{0} | w | A | ||

915 MHz | 0.04 | 724.12 | 228.83 | 374.52 | 0.97 | ||

2450 MHz | 0.04 | 626.37 | 225.13 | 139.98 | 0.90 |

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**MDPI and ACS Style**

He, G.; Li, S.; Yang, K.; Liu, J.; Liu, P.; Zhang, L.; Peng, J.
Dielectric Properties of Zinc Sulfide Concentrate during the Roasting at Microwave Frequencies. *Minerals* **2017**, *7*, 31.
https://doi.org/10.3390/min7020031

**AMA Style**

He G, Li S, Yang K, Liu J, Liu P, Zhang L, Peng J.
Dielectric Properties of Zinc Sulfide Concentrate during the Roasting at Microwave Frequencies. *Minerals*. 2017; 7(2):31.
https://doi.org/10.3390/min7020031

**Chicago/Turabian Style**

He, Guangjun, Shiwei Li, Kun Yang, Jian Liu, Peng Liu, Libo Zhang, and Jinhui Peng.
2017. "Dielectric Properties of Zinc Sulfide Concentrate during the Roasting at Microwave Frequencies" *Minerals* 7, no. 2: 31.
https://doi.org/10.3390/min7020031