Microwave response characteristics and influencing factors of ores based on dielectric properties of synthetic samples

Feng Lin, Xia-Ting Feng, Chengxiang Yang, Shiping Li, Jiuyu Zhang, Xiangxin Su,Tianyang Tong

Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang,110819, China

Keywords:Metal minerals Electrical conductivity Metal mineral content Synthetic ore Prediction model

ABSTRACT In order to understand the influence of different factors on the microwave response characteristics of ores, the effects of electrical conductivity, metal mineral content, compactness, metal mineral distribution,microwave frequency and temperature on the dielectric properties of synthetic ores(metal mineral and quartz) were studied.Microwave heating tests were carried out on three types of natural ores(Hongtoushan copper ore, Sishanling iron ore and Dandong gold ore) with significant differences in metal mineral contents.The test results showed that under microwave irradiation, the stronger the electrical conductivity of the metal minerals, the smaller the penetration depth in synthetic ore.For those metal minerals with lower electrical conductivity, the microwave absorption coefficient of the synthetic samples increases with increasing metal mineral content.For those metal minerals with higher electrical conductivity, the microwave absorption coefficient of the samples first increases and then decreases as the metal mineral content increases.When the metal minerals are distributed in layers,the penetration depth is much less than that given a uniform distribution.The penetration depth in the sample at microwave frequency of 915 MHz is greater than that at 2.45 GHz.The higher the electrical conductivity of metal minerals used in synthetic ores, the higher the high-temperature sensitivity of electromagnetic shielding coefficient (0 ◦C-500 ◦C).The Hongtoushan copper ore with high metal mineral content exhibits obvious size effect.The effects of ore structure and crystal particle size on the distribution characteristics of microcracks were discussed.Based on the test results, a quantitative prediction model of microwave sensitivity of ore was proposed, which provides guidance for the prediction of ore heating effect and the selection of microwave heating sequence of ore.

1.Introduction

The essence of mining to grinding is a process of breaking the ores.Mechanicalrock breaking technology isthe most commonly usedone among many rock breaking methods (Hassani, 2010); however, the hardness of metalores willleadto a seriesof difficulties inmechanical mining,crushing and grinding.In mining work, mechanical mining tool loss is significant,making it difficult to promote in metal mines(Lu et al., 2016).In grinding work, a high energy consumption is incurred and the energy utilization rate is low;meanwhile,plenty of steel loss is incurred(Jones et al.,2005;Napier,2015).Therefore,it is necessary to develop a new rock breaking method to solve the problem relating to high cost and difficulty.In the past half century,a number of new auxiliary rock breaking technologies have been developed(Graves et al.,2002;Ciccu et al.,2014;Zheng et al.,2016).Microwaves offer advantages of non-contact heating and volumeheating of materials(Song et al.,2016)and are considered for use as a potential rock-breaking technique(Hassani et al.,2016).The essence of microwave presplitting of ore and rock is the thermal stress caused by thedifferenceofmicrowave sensitivityofdifferentminerals,which leads to ore/rock fracture and even melting(Lu et al.,2019).This plays a positive role in ore mining, crushing, grinding and even mineral separation(Kingman et al.,1998).

Scholars have made preliminary exploration on the effect of microwave presplitting of ore and rock.Several studies have shown that microwave irradiation can reduce energy consumption during ore grinding (Omran et al., 2015; Batchelor et al., 2017) and promote subsequent mineral separation (Batchelor et al., 2016).Microwave pre-treatment can reduce the strengths of rocks(Nekoovaght, 2009), especially the basalt, which has great significance for future space mining (Satish, 2005).The concept of microwave-assisted tunnel boring machine (TBM) operation in tunneling operations has been proposed for a long time.The results also showed that microwave pre-treatment can improve drilling and cutting speeds in some rock types (Lindroth et al., 1993;Hartlieb et al., 2017).Experimental results have shown that metal sulfides and most metal oxides have good microwave absorbing properties (Hua et al., 1996), suggesting that most ores can react with microwave radiation.It is conceivable that microwaves have broad application prospects in mining and mineral processing.

To realize the industrial application of microwave presplitting technique, it is necessary to understand the microwave response characteristics and influencing factors of ores.Previous studies have shown that the power and heating time (Kingman et al.,2004), the proportion of absorbing minerals (Lu et al., 2017),the crystal size of absorbing minerals (John et al., 2015; Batchelor et al., 2015), and ore particle size (Kingman et al., 2000; Jokovic et al., 2019) affect the microwave heating of rocks.The metal mineral in ore is an important factor affecting its microwave sensitivity.Metal materials exhibit reflection, heating and discharge under microwave irradiation (Ripley et al., 2005).Bulk metals reflect microwaves, but powdered metals are readily heated (Mishra et al., 2006; Gupta et al., 2007).From the viewpoint of electrical conductivity of materials, it affects the efficacy of microwave heating.The insulator is generally microwave transparent and semiconductors are found to have a good heating effect (Uslu et al., 2004).The conductor can be heated by microwave theoretically, but it cannot be heated in practice.Therefore,it can be imagined that the content and conductivity of absorbing minerals in the ore will seriously affect the effect of microwave heating on the ore.However, there are few studies on the influences of the electrical conductivity and content of absorbing minerals on the microwave sensitivity of ores(González et al., 2018; Amini et al., 2018; Lin et al., 2021).

Dielectric properties test is an important method to characterize the microwave response of materials, which can reflect the microwave absorption, reflection and transmission properties in detail.The coefficients T, A and R represent the ratios of the transmitted, absorbed and reflected powers to the input power,respectively.These quantities can be calculated from the S-parameters(determined,for example,using a network analyzer).The full name of S-parameter is scatter parameter,which describes the frequency domain characteristics of the transmission channel.Using S-parameter, we can observe almost all the characteristics of the transmission channel, such as signal reflection and loss.The absorption coefficient A can be obtained from the relationship A = 1 R T.The closer the reflection coefficient R to 1, the stronger the reflectivity(R=1 corresponds to a perfectly reflective surface).Similarly, the closer the transmission coefficient T or absorption coefficient A to 1, the stronger the transmittance or absorbance(Li et al.,2006).The penetration depth is calculated by combining the real and imaginary parts of the dielectric constant.The greater the penetration depth, the better the microwave transmission performance.The size of the microwave absorbing material should be similar to the penetration depth to achieve the best response (Sun et al., 2016).The penetration depth Dpis calculated as follows (Peng et al., 2010):

where λ0represents the wavelength of the microwaves in free space; and ε′and μ′represent the real and imaginary parts of the complex relative permittivity,respectively;and ε′′and μ′′represent the real and imaginary parts of the permeability, respectively.

Fig.1.Bulk pure metal minerals.

Based on this, the effects of electrical conductivity, metal mineral content, compactness, metal mineral distribution, microwave frequency and temperature on the dielectric properties of synthetic ores (metal minerals mixed with quartz) were studied.In order to verify the applicability of microwave response characteristics of synthetic ore to natural ore, microwave heating tests were conducted on three types of natural ores, and the effects of ore structure and crystal particle size on the microcracks were analyzed.Finally,based on the test results,a microwave sensitivity prediction model of ores was developed.

2.Materials and methods

2.1.Sample preparation

Seven common pure metal mineral blocks (Fig.1), including sphalerite, hematite, galena, magnetite, pyrite, chalcopyrite and pyrrhotite, with a purity of more than 95%, were selected as absorbing minerals.The single mineral selected in the test can exist in the form of intact single crystal or crystal cluster in nature, and the crystal form characteristics are obvious, thus these single minerals can be directly cut off.The transparent minerals are pure quartz minerals, and the metal minerals and quartz are prepared into synthetic samples.

The bulk pure metal minerals and bulk quartz were crushed and ground to finer than 0.075 mm.The metal mineral powder and quartz powder were pressed and shaped in different proportions under different pressures using a small tablet press.The outer diameter of the sample is 6.97 mm, the inner diameter is 3.05 mm, and the thickness is 10 mm(the sample size is consistent with the test size of coaxial fixture of vector network analyzer).Such synthetic ore samples are shown in Fig.2.Based on the test results of seven synthetic samples, the microwave response characteristics of synthetic ores were obtained.In order to verify whether the microwave response characteristics of synthetic ores can be applied to natural ores,three typical natural ores were selected for microwave heating tests.

Three types of natural ores with obvious difference in metal mineral content, i.e.Hongtoushan copper ore (high metal mineralcontent),Sishanling iron ore(intermediate metal mineral content),and Dandong gold ore (low metal mineral content), were used in the microwave heating test.The ores were processed into cylinder samples (φ50 mm 50 mm) and different particle-sized samples(8-12.5 mm, 4-8 mm,1-3.2 mm and 0-0.4 mm) (Fig.3).

Fig.2.(a) Small tablet press and (b) powder pressed samples for synthetic ore.

Fig.3.Photos of natural ore samples.

The content of metal minerals in Hongtoushan copper ore is 60%-80%.The main minerals presented are pyrite, pyrrhotite,sphalerite and chalcopyrite.The metal minerals are mainly distributed in blocks (at up to centimeter-scale).The content of metal minerals in Sishanling iron ore is 40%-50%.The mainminerals are quartz and magnetite, and the metal minerals are mainly distributed in veins.Dandong gold ore is of quartz mica schist type.The content of metal minerals therein is 15%-20%.The main minerals presented are quartz, feldspar, mica and pyrite, and the metal minerals are mainly distributed in veins.

Fig.4.Photos of the equipment: (a) Vector network analyzer, and (b) Multi-mode cavity microwave system.

2.2.Equipment

A vector network analyzer E5063A(Fig.4a)was used to measure the dielectric properties at microwave frequency of 0.8-12 GHz,and test range of the temperature was 0◦C-500◦C.A multi-mode cavity microwave system(model CM-06S)was used for heating test(Fig.4b).The frequency of the microwave equipment is 2.45 GHz and the power is adjustable from 0 kW to 6 kW(Lu et al.,2017).An R500EX series infrared thermal imager was used for temperature measurement with a maximum temperature of 2000◦C.

2.3.Dielectric properties tests

The dielectric constant and S-parameter of the samples with different constituent proportions, pressing pressures (100 MPa,200 MPa,300 MPa and 400 MPa),and structural distributions were measured at room temperature (25◦C) and higher temperatures(25◦C-500◦C), respectively.Different structures include uniform and layered distributions.

The uniform distribution is that the metal mineral powder and quartz powder are stirred evenly and pressed into samples.The layered samples consist of two layers of minerals; one is metallic mineral powder, and the other is quartz powder.

2.4.Microwave heating tests

The microwave heating tests were conducted on Hongtoushan copper ore,Sishanling iron ore and Dandong gold ore.Each sample was placed in a quartz container, which has good microwave transmittance property and high temperature resistance, and put into the center of the microwave oven.Previous experiments showed that the heating effect of the sample was maximized in center (Lu et al., 2019).To center the specimen vertically, it was placed on a cushioning block made of mullite, a weak absorber of microwave radiation.In addition, an infrared thermometer in the center of the microwave chamber ceiling can be used to measure the surface temperature of the samples (Lin et al., 2021; Xu et al.,2021).

The microwave power was set to 4 kW, and different samples were heated for 30 s,60 s,90 s and 120 s,respectively.Considering heat dissipation and microwave leakage when heating insensitive ore,4 kW is a relatively high power that this industrial microwave oven can work for a long time.The heating time ranges from 30 s to 120 s,which includes the whole process from small cracks to large cracks.The infrared thermal imager was set in place in advance before heating was started.Immediately after heating, the microwave oven door was opened and the temperature of the sample was measured (Lin et al., 2021).

Considering that the experimental results of the synthetic samples at pressing pressure of 400 MPa will be used in the quantitative prediction model,in order to avoid the discreteness of the experimental results, three experiments were carried out on each group of synthetic samples, and then the average value was used.

3.Experimental results

3.1.Effect of metal mineral electrical conductivity

The electrical conductivity of seven metal minerals was measured with a multimeter and the average values of several measurements were calculated.As shown in Table 1, the electrical conductivity of pyrrhotite is the smallest (less than 10 Ω/cm).Chalcopyrite and pyrite have an electrical conductivity of 100-1000 Ω/cm.Magnetite and galena have an electrical conductivity of 1000-10,000 Ω/cm.The electrical conductivity of hematite and sphalerite is larger than 106Ω/cm.

Table 1Metallic pure mineral conductivity.

Seven different types of metal mineral powder were pressed into blocks, each containing 100% of the respective metal mineral and formed at a pressure of 400 MPa.The penetration depth in the pressed samples is shown in Fig.5.The higher the electrical conductivity of a metal mineral,the shallower the penetration depth in synthetic samples.For those metal minerals with intermediate or greater electrical conductivity, the penetration depth in synthetic samples is generally less than 0.5 mm at 2.45 GHz, and less than 1 mm at 915 MHz.

3.2.Effect of metal mineral content on microwave absorbing properties of samples

Each metal mineral and quartz powder sample could be pressed into synthetic samples under different pressing pressures.The absorption coefficient curves of the synthetic samples with different metal mineral contents and pressing pressures are shown in Fig.6.The larger the absorption coefficient, the stronger the microwave absorption ability of the material.For weakly conductive minerals(hematite and sphalerite), the microwave absorption coefficient ofthe synthetic samples increases with the increase in metal mineral content.For the metal minerals with intermediate or higher electrical conductivity (galena, magnetite, pyrite, chalcopyrite and pyrrhotite), the microwave absorption coefficient of the syntheticsamples first increases and then decreases with the increase in metal mineral content.

Fig.5.Penetration depth in pure mineral synthetic samples.Po - pyrrhotite; Ccp -chalcopyrite; Py - pyrite; Mag - magnetite; Gn - galena; Hem - hematite; Sp -sphalerite.

Fig.6.Microwave absorption coefficient of synthetic samples(metal minerals and quartz(Qtz)):(a)Sp-Qtz,(b)Hem-Qtz,(c)Gn-Qtz,(d)Mag-Qtz,(e)Py-Qtz,(f)Ccp-Qtz,and(g)Po-Qtz.

Fig.7.Penetration depth in synthetic samples containing two different structures: (a) Sp-Qtz, (b) Hem-Qtz, (c) Gn-Qtz, (d) Mag-Qtz, (e) Py-Qtz, (f) Ccp-Qtz, and (g) Po-Qtz.

The higher the electrical conductivity of metal minerals, the smaller the metal mineral content corresponding to the maximumabsorption coefficient of synthetic samples.Taking a pressing pressure of 400 MPa as an example, the metal mineral contents corresponding to the maximum absorption coefficient are: 40% of pyrrhotite,50%of chalcopyrite,70%of pyrite,70%of magnetite,and 80% of galena.Within the range of 100-400 MPa, the higher the pressing pressure, the smaller the metal mineral content corresponding to the maximum absorption coefficient of the synthetic samples.

There is not necessarily a positive correlation between the absorption properties and the content of absorbing minerals,and the electrical conductivity of absorbing minerals has a significant influence on this relationship.

3.3.Effect of metal mineral structure on the penetration depth in samples

The metal minerals were compressed into synthetic samples according to uniform and layered distributions, respectively.Fig.7 shows the relationship between the penetration depth in synthetic ore(at microwave frequency of 2.45 GHz)and metal mineral content under a pressure of 400 MPa.The penetration depth in synthetic samples decreases with increasing metal mineral content under the two distributions of structures analyzed here.For the weakly conductive metal minerals (sphalerite and hematite), the penetration depth in synthetic samples decreases slowly with the increase in metal mineral content.For the metal minerals with intermediate or higher electrical conductivity, the penetration depth in synthetic samples decreases with increasing metal mineral content; inflection points appear at 40% of metal mineral content,where the penetration depth decreases rapidly below 40%,and slowly thereafter.

The penetration depth in synthetic samples is much smaller than that of the uniformly distributed structure when the metal minerals are distributed in layers.To compare the penetration depth difference between the two structures, the penetration depth ratio of uniform and layered distributions is given (Fig.8).This is the ratio of the penetration depth of uniform distribution to that of layered distribution at the same temperature and under the microwave frequency of 2.45 GHz and pressure of 400 MPa.The higher the electrical conductivity of a metal mineral, and the greater the penetration depth ratio,the greater the influence of the structure of the metal mineral on the microwave sensitivity of ores.When the metal mineral content is more than 40%,the penetration depth ratio decreases with the increase in metal mineral content,and the maximum penetration depth ratio occurs when the metal mineral content is 20% or 40%.

Fig.8.Penetration depth ratio between uniform and layered distributions of synthetic ores.

For weakly conductive minerals (sphalerite and hematite), the penetration depth ratio is 1-2.For those minerals with intermediate or higher electrical conductivity, the maximum penetration depth ratio of different structures of synthetic samples exceeds 5,and that of pyrrhotite synthetic samples is 46(when the content of pyrrhotite is 20%, the penetration depth in uniformly distributed synthetic samples is 69 mm,and that of the same mineral in layered distribution is 1.5 mm).

3.4.Influence of microwave frequency on penetration depth in synthetic ore

Microwave frequency also has a significant effect on the penetration depth in the ore.In this study, the synthetic sample with uniform distribution of metal minerals under pressure of 400 MPa is taken as an example(Fig.9).At microwave frequency of 915 MHz,the penetration depth in synthetic sample is greater than that at 2.45 GHz.

Fig.10 shows the penetration depth ratio of synthetic core at microwave frequencies of 915 MHz and 2.45 GHz.This is the ratio of the penetration depth at 915 MHz to that at 2.45 GHz at the same temperature.The purpose is to understand the penetration depth ratio distribution of different types of synthetic ores,and to predict the penetration depth at 915 MHz based on the penetration depth at 2.45 GHz.Within the experimental range,the penetration depth ratio changes slightly with the metal mineral content,and the ratio is 1-2.5, which has guiding significance for the selection of microwave frequency in industrial application of different types of ores.

3.5.Influence of temperature (0 ◦C-500 ◦C) on microwave transmission of synthetic ore

After high-temperature conditioning,the synthetic ore samples show obvious solidification phenomenon, in which the colors of magnetite and pyrite change after high-temperature exposure.Fig.11 shows the relationship between the electromagnetic shielding coefficient (SE) of the synthetic sample and temperature at microwave frequency of 2.45 GHz and pressing pressure of 200 MPa.The larger the SE, the worse the wave transmission performance of the sample.With the increase in temperature,the SE of synthetic sphalerite sample has no obvious change.

With the increase in temperature,the SE of synthetic magnetite samples(20%-80%of magnetite)increases first and then decreases(Fig.11d).The inflection point occurs at 300◦C,i.e.before 300◦C,SE increases gradually, and then decreases.Combined with the phenomenon observed before and after high-temperature exposure,the color of the synthetic magnetite sample changes from black to reddish brown.It can be considered that the increase of SE in magnetite samples is due to the reduction in the wave permeability caused by particle solidification,and the decrease of SE is caused by the oxidation of Fe2+in magnetite (Fe3O4) to hematite at high temperature, which leads to the enhancement of wave permeability.

With increasing temperature, the SE of pyrite samples first decreases and then increases (Fig.11e), and the inflection point therein appears at 300◦C.After high temperature, pyrite is also solidified and turns to reddish brown.It can be considered that hematite is produced in the high-temperature reaction of synthetic pyrite samples below 300◦C, which leads to the increase in wave permeability (i.e.the decrease of SE).Above 300◦C, the solidification of particles plays a leading role in reducing the wave permeability (i.e.the increase of SE).The synthetic samples of the otherfour metal minerals show that SE increases with the increase in temperature.

Fig.9.Penetration depth in synthetic samples at two microwave frequencies: (a) Sp-Qtz, (b) Hem-Qtz, (c) Gn-Qtz, (d) Mag-Qtz, (e) Py-Qtz, (f) Ccp-Qtz, and (g) Po-Qtz.

When the metal mineral content is equal to or larger than 60%,SE exhibits a marked change with temperature.For those metalminerals with intermediate or higher electrical conductivity,the SE of the synthetic samples is very large,and it is more sensitive to the high-temperature reaction.

Fig.10.Penetration depth ratio of synthetic ore at microwave frequencies of 915 MHz and 2.45 GHz.

3.6.Microwave heating test on natural ore

3.6.1.Microwave heating effect

The heating rates of three different natural ores with different particle sizes are shown in Fig.12(Lin et al.,2021).The size effect of microwave heating in Hongtoushan copper ore is significant.The heating rate of the cylindrical sample of Hongtoushan copper ore is only 0.88◦C/s,and the heating rate of the granular sample is greatly increased to 4.67◦C/s.The heating rate of Sishanling iron ore decreases linearly with the decrease in particle size and the maximum decrease is only 16.9%.The heating rate of Dandong gold ore decreases significantly with the decrease in particle size, and the maximum decrease is 71.2%.

According to the test results of the synthetic ores, it can be inferred that when metal minerals have a high electrical conductivity and account for a large proportion thereof,when they appear in the form of aggregation (>0.5 mm), this is not conducive to microwave absorption in ores.When metal minerals have a high electrical conductivity,but are presented in low amount and appear in dispersive form, it is beneficial to the absorption of microwave energy.This is consistent with the heating effect of natural ores(Batchelor et al., 2015; Lin et al., 2021).

3.6.2.Microcrack characteristics

Figs.13 and 14 show the polarizing microscope images and particle size distribution curves of the three ores after microwave irradiation, respectively.The crystal of Hongtoushan copper ore is above coarse grain grade (particle size of mineral crystal d > 0.5 mm), while that of Sishanling iron ore and Dandong gold ore is below that grade and classified as fine-grained(0.044 mm < d < 0.25 mm).

The metal minerals in Hongtoushan copper ore are mainly transgranular cracks, while the quartz feldspars mainly contain transgranular and intergranular cracks.The magnetite and quartz in Sishanling iron ore are distributed in a layered manner, with cambium bedding, and the large crack runs through along the bedding direction, and in quartz, they are mainly intergranular cracks.In Dandong gold ore, the through-cracks are mainly observed to run along the parallel and vertical bedding directions.On parallel bedding cracks, pyrite is mainly transgranular cracks,and quartz and mica experience mainly intergranular cracking.On the vertical bedding cracks,quartz and mica are mainly subjected to intergranular cracking with a few transgranular cracks also formed.

The transgranular cracks in these three ores are mainly developed in the crystalline structure of metal minerals, and gangue minerals of iron ore and gold ore (mainly quartz crystal) undergo intergranular cracking.Large cracks are preferentially generated along the bedding direction.Gangue minerals (mainly quartz crystals) in copper ore undergo transgranular and intergranular cracking.

Fig.15 illustrates the scanning electron microscopy (SEM) images of three types of ores.The shape of the cracks can be observed more clearly.The cracks are irregular, jagged and exfoliated.It can be judged that the fracture mechanism of the ore is one of tensile fracture (Zhao et al., 2018):

(1) The large particles in adjacent pyrite and pyroxene in the Hongtoushan copper ore all contain transgranular cracks,accompanied by pyroxene crystal spalling.

(2) The quartz crystals in Sishanling iron ore exhibit inlaid contact.The expansion of magnetite crystal results in transgranular cracking and the quartz crystal is squeezed,which leads to the sliding between quartz crystals accompanied by crystal spalling.

(3) The Dandong gold ore is characterized by pyrite crystal tensile fracture,and the quartz crystal is driven to reach the intercrystalline strength first, leading to intercrystalline fractures developing along the crystals.

4.Discussion

4.1.Microcrack distribution mechanism

The microcrack distribution characteristics of natural ore show that the microcrack distribution is related to bedding and crystal particle size:

(1) The effect of bedding.The crystal strength of minerals is generally greater than that between crystals (Feng et al.,2020).Intergranular cracks occur preferentially in ores under microwave irradiation.When the microwave absorbing minerals and microwave transparent minerals are layered,the absorbing and transparent minerals will produce intergranular cracks.The intergranular cracks are readily connected along the bedding direction and form large cracks.The macroscopic cracks show that the cracks are parallel to the bedding direction.

(2) The effect of crystal particle size.When the crystal particle size is small, the contact area between crystals is large and the ore has enough space to generate intergranular cracks to release energy under microwave irradiation.When the crystal particle size is large,the contact area between crystals is small,and the space available for producing intergranular cracks is limited, then the transgranular cracks will be generated to release energy.

From the application point of view, the intergranular or transgranular cracks of crystals are conducive to the crushing of the ore,thus promoting mechanical mining or grinding work.However,as a follow-up,the microcracks between crystals are more conducive to the separation of useful/useless minerals.Therefore,it is necessary to control the microwave energy output for the ore with large mineral particles, and it is not necessary to continuously increase the microwave output to produce a greater number of transgranular cracks.

Fig.11.Electromagnetic shielding coefficient of synthetic samples at different temperatures:(a)Sp-Qtz,(b)Hem-Qtz,(c)Gn-Qtz,(d)Mag-Qtz,(e)Py-Qtz,(f)Ccp-Qtz,and(g)Po-Qtz.

4.2.Sensitivity prediction model of ores

The dielectric properties test results of synthetic ores show that the microwave absorbing properties of the ores are related to the content,conductivity and structure of absorbing minerals.With the greater absorbing mineral content of the ore, the microwave heating effect is not necessarily good, and exhibits a certain size effect.Therefore, the content, conductivity and structure ofmicrowave absorbing minerals, and ore size should be considered when predicting the microwave heating effect of ores.

Fig.12.Heating rate of natural ores with different particle sizes.

To establish the prediction model of microwave sensitivity of ores, the penetration depth in ores was used as the standard to evaluate the microwave heating effect of ores.At the microwave frequency of 2.45 GHz, the penetration depth and microwave heating effect of more than ten types of ores and rocks were counted(Table 2).It can be found that when the penetration depth in the ore exceeds 100 mm, the temperature rise of the ore is extremely slow,and when the penetration depth is less than 5 mm,a significant size effect is observed.Therefore, the penetration depths of 5 mm and 100 mm are taken as critical values in microwave sensitivity criterion (Table 3).

In the industrial application of presplitting of ore and rock,microwave can be used in mining, tunneling, crushing and grinding.Therefore,according to the microwave heating sequence of an ore sample, it can be divided into two types: suitable for microwave presplitting for mining and suitable for microwave presplitting for grinding.The size of ore after fine crushing is generally less than 14 mm,and that after moderate crushing is less than 50 mm.The microwave heating effect is optimized when the size of material matches the penetration depth (Sun et al., 2016).Therefore, there are two types of presplitting for grinding: microwave presplitting after fine crushing and microwave presplitting after medium crushing.Based on this, the penetration depths in Table 4 are taken as the critical values of the criterion used for judging the microwave heating sequence of ores.

According to the effective medium theory, the dielectric constant of the mixed material can be obtained by Nelson(2012):

where εmrepresents the dielectric property of the mixture;ε1and ε2are the dielectric properties of the two components of the mixture,respectively;v1and v2are the volume fractions of the two components,respectively(v1+v2=1).It can be found that for the powder-air mixture, the higher the pressing pressure(the less the air content),the closer the dielectric constant of the powder sample to that of the solid sample.

Fig.13.Microcrack characteristics of ore samples: (a) Copper, (b) Iron, and (c) Gold.

Fig.14.Particle size distribution of mineral crystals.

The dielectric constant of synthetic sample at pressure of 400 MPa is used as a reference to obtain the content of absorbing minerals corresponding to the critical penetration depth(the tests with 2% and 5% metal mineral contents were also supplemented).Here, any material with size greater than 14 mm is defined as“bulk”, and that less than 14 mm is defined as “granular”.The results in Section 3.1 show that the penetration depth of absorbing minerals with good electrical conductivity is generally less than 0.5 mm, thus the size of absorbing mineral particles or aggregates with good electrical conductivity should match the penetration depth(<0.5 mm)to obtain the best heating effect.Considering the size, structure, content and conductivity of the absorbing mineral,as well as the size of the ore,the microwave sensitivity prediction model (Table 5) and heating sequence prediction model of ores(Table 6) are given.

Table 2Penetration depth and microwave heating effect of ores and rocks.

Table 3Criterion for determining microwave sensitivity of ores.

Table 4Criteria for determining microwave heating order of ores.

Table 5Prediction model of microwave sensitivity of ores.

Table 6Prediction model of microwave heating sequence of ores.

The microwave heating effects of three types of natural ores used in this test are consistent with the prediction model proposed.Batchelor et al.(2015) conducted the microwave heating tests on more than ten types of natural ores, and the critical content (40%)and the size(0.5 mm)of absorbing minerals were also similar to the results of our sensitivity prediction model, which further verified the accuracy of the model.At the same time, the model complements the prediction of microwave sensitivity based on electrical conductivity and size of ores.The above prediction models provide guidance for the prediction of microwave sensitivity of ores and the selection of microwave heating sequence.

5.Conclusions

In this paper,taking synthetic ores(metal minerals mixed with quartz) as the research object, the effects of various factors on the dielectric properties of synthetic ores are studied.In order to verify the applicability of microwave response characteristics of synthetic ore to natural ore, microwave heating tests were conducted on three types of natural ores, and the effects of ore structure and crystal particle size on the microcracks were analyzed.Finally, a microwave sensitivity prediction model of the ores was developed.The main conclusions are drawn as follows:

(1) The stronger the electrical conductivity of a metal mineral,the smaller the penetration depth in a synthetic ore.For metal minerals of low electrical conductivity,the absorptioncoefficient of synthetic ores increases with increasing metal mineral content.For those metal minerals with good electrical conductivity, the absorption coefficient of synthetic ores first increases and then decreases as the metal mineral content increases.

Fig.15.SEM images of natural ores: (a) Copper, (b) Iron, and (c) Gold.

(2) When the metal minerals are distributed in layers, the penetration depth in synthetic ores is much less than that in samples containing a uniform distribution.The penetration depth in a synthetic ore is greater at microwave frequency of 915 MHz than that at 2.45 GHz,and the ratio of penetration depth at 915 MHz to that at 2.45 GHz is 1-2.5.The higher the electrical conductivity of metal minerals used in synthetic ores, the higher the high-temperature sensitivity of electromagnetic shielding coefficient (0◦C-500◦C).

(3) The Hongtoushan copper ore with high metal mineral content exhibits obvious size effect, and the ore structure and crystal particle size have a significant influence on the distribution of microcracks in samples.

(4) The quantitative prediction model of microwave sensitivity of ores is proposed, which provides guidance for the prediction of microwave heating effect and the selection of microwave heating sequence.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

We gratefully acknowledge financial support from the National Natural Science Foundation of China (Grant No.41827806) and supported by Liaoning Revitalization Talents Program (Grant No.XLYC1801002).The authors are also grateful to Mr.Jun Zhao and Mr.Mengfei Jiang at Northeastern University, China, for their valuable academic discussions and generous assistance with the laboratory tests.The authors would also like to thank the journal editor and anonymous reviewers for their valuable suggestions.