Research on the Influence of the Defects of Materials on Thermal Runaway in Microwave Hybrid Heating for Sintering Processes

Featured Application

Sintered Barium Ferrite W-type materials can be used for the manufacturing of permanent magnets for the automotive industry in order to increase the performance of electric engines. Microwave hybrid heating (MHH) is a sustainable and efficient process with a small carbon footprint that can be applied for sintering. However, the MHH process is unstable for ceramic material, with a high potential for the conversion of microwaves into heat due to the possible occurrence of the thermal runaway phenomenon.

Abstract

Thermal runaway in microwave hybrid heating of ceramics is an unwanted phenomenon which damages the sintered products. The aim of the present study is to establish to what extent the pressing forces of 100, 200 and 300 MPa used in the compaction process and the optimization of the microwave heating mechanism can reduce the occurrence of thermal runaway. Modeling and simulation of temperature distributions alongside defects created by the compaction process are performed in order to evaluate their influence on the stability of MHH. Based on CT scanning, defects with dimensions from 110 to 515 μm are studied in terms of local overheating and how the thermal runaway can lead to internal arc discharge. The results show that samples compacted at 100 MPa and exposed at 600 W injected power reach temperatures peaks around 1010 °C and are affected by major cracks and large melted areas. The samples compacted at 200 and 300 MPa present similar behavior, without arc discharge, but are also affected by cracks. Based on these findings, the MHH process can be applied to sintering processes but with a reduced injected power below 300 W for samples compacted with pressing forces higher than 300 MPa.

1. Introduction

The new generation of electrical cars produced by the automotive industry uses electrical engines that require performant permanent magnets for stators. Usually, different magnetic materials with a high coercive magnetic field are used for the fabrication of permanent magnets, but these materials are costly and the classic sintering technology takes too long a time, making them expensive products. The materials for Barium Ferrite W types are widespread as natural resources, and the industry needs sustainable technologies for magnet fabrication as well. Microwave hybrid heating (MHH) has proved to be a reliable technology for materials processing in terms of sustainability and the efficiency of the process, but it is usually unstable from a sintering process point of view. Ojo et al. reported advanced research on microwave welding using MHH technology. They reported that MHH welding is effective in producing completely fused, homogeneous, metallurgical-bonded, and crack-free weld structures. They also concluded that achieving precise control of the complex microwave heating process remains one of the major challenges of microwave welding [1]. Zhang et al. reported better heat transfer when soldering metals using SAC305 solder and the MHH process [2]. Other research has been focused on the shape and dimensions of the susceptors and their influences on the performance of MHH processes. Said et al. reported better results in terms of the strength of the joints in the case of MHH soldering [2]. Also, the efficiency of MHH has been studied by Zhang et al. They reported that MHH is an environmentally benign and cost-effective technology that may increase manufacturing product quality [3,4]. The sintering of ceramics using microwave technology has been studied by Savio et al. in order to improve the hardness of alumina. They succeeded in sintering alumina through the MHH process at 1500 °C [5].

The absorbance properties of ferrites in a microwave field have been studied by Mohapatra et al. They studied to what extent the losses in dielectrics influence the microwave absorbers’ effectiveness. They concluded that exceptional microwave absorption properties can be achieved not by a single material but by using composite-materials-based carbon. These findings support the MHH approach as a reliable technology for materials processing [6]. Also, Mudasar et al. reported the specific absorbance properties of W-type hexagonal ferrite. They concluded that W-type ferrite has a strong electromagnetic absorption ability at high frequencies [7].

The thermal runaway phenomenon represents the major challenges in microwave processing technologies. Ceramics particularly suffer from a large increase in temperature in a short time, which leads to loss of process stability, initiation of arc discharge and damage to the products. Krikkis carried out a detailed multiplicity and stability analysis for microwave heating of ceramic fibers in a resonant cavity. He concluded that a stable non-uniform and asymmetric pair of temperature profiles emerges and a hot temperature front is formed at the boundary of the sample and moves along its axis, triggering a local thermal runaway at the far end while leaving the front end at a relatively low temperature [8]. Shen et al. studied the hotspot evolution in materials under various gaps and shapes. They reported that, different from the gradual decrease in the enhanced electric field, the increasing gap rapidly improves heating uniformity by nearly 30 times [9]. An effort towards the reduction of thermal runaway has been also performed by Patel et al. The research concluded that the thermal field homogeneity inside SiC materials can be reduced by using a reduced coefficient of variance, COV_T = 0.2636, which is a key indicator of temperature distribution uniformity [10]. Savu et al. studied the thermal runaway of a BaCO₃ + Fe₂O₃ homogenous mixture in a microwave field. They concluded that the peak temperatures during thermal runaway occurrence are directly connected to the grain size. Also, they reported that, above 700 °C, the temperature increases with a gradient of 350 °C/min [11]. Additional research in the field of microwave sintering of ceramics has been performed by Wang et al. as well as Hao et al. [12,13]. Other research related to microwave heating has focused mainly on process stability, rate of conversion and thermal runaway, in order to optimize the MHH process or to improve its stability [14,15,16,17,18,19].

This research aims to study the influence of materials’ internal defects as precursors for thermal runaway in Barium Ferrite W-type (based on an initial homogenous alloy of BaCO₃ + 9α-Fe₂O₃) materials in a microwave field. The study consists of modeling and simulation of the temperature distribution and microwave heating mechanism and macroscopic analysis of products processed using MHH technology.

2. Materials and Methods

Microwave hybrid heating (MHH) of Barium Ferrite W-type material requires significant control of the process mechanism in order to obtain uniform volume heating. However, the level of temperature uniformity is strongly influenced by the non-uniformity of the crude materials. In order to optimize the microwave heating mechanism, Barium Ferrite W-type samples with different defects should be modeled and simulated before processing. The simulation will provide useful information related to the specific material properties and MHH process parameters. The materials used for the simulation process and later in the microwave hybrid heating were Barium Ferrite W-type powders with an effective diameter of 49.1 μm measured using a Brookhaven particle sizer manufactured by Brookhaven Instruments Corporation (Belgium, Brussels, 2006). The crude samples were obtained through dry compaction of 4 g of Barium Ferrite W-type powders at 100 MPa, 200 MPa and 300 MPa using the LBG TC 100 universal testing machine manufactured by LBG srl (Azzano San Paolo BG, Italy, 2009). The compaction was performed using a cylindric die with the following dimensions: internal diameter = 15 mm, external diameter = 45 mm and height = 60 mm.

2.1. Non-Uniformity and Defects in Crude Sample

In order to establish non-uniformities due to the compaction procedure, or other defects caused by the inappropriate die or even by the contamination of the powders with different materials, a CT scan of the samples was performed using a computer-tomograph-type UniTOM HRScanner produced by Tescan (Brno, Czech Republic, 2023). The samples were placed one on top of the other and scanned as a whole in order to precisely determine at which pressing force the largest defects within the material are revealed. The CT scanning parameter related to the focus was microfocus dedicated to particles with dimensions greater than 1 μm and the total scanning time was 25 min. The determination of the non-uniformity factor can be performed using the ratio between the maximum dimensions of the holes obtained during compaction process and the average dimension of the particles in accordance with Equation (1) [20]:

$$k_{NU}={\displaystyle \frac{d_{max\_H}}{d_{med\_P}}}$$

(1)

where k_NU is the non-uniformity factor, d_{max_H} (μm) represents the maximum dimensions of the holes and d_{med_P} (μm) represents the average particle size of the powders.

2.2. Simulation of the Temperature Distribution and the Local Overheating

The modeling and simulation of the temperature distribution inside materials with defects require theoretical developments that will provide information related to temperatures at different points inside the raw samples. The boundary conditions for the MHH process are as follows:

• Taking into consideration the irregular shape of the holes inside the samples, for the temperature distribution model, it is considered that holes can be approximated as spheres containing air.
• The holes in the Barium Ferrite W-type sample act as thermal concentration points where the temperature can be higher than the average values of the sample temperatures due to the reflection coefficient of microwaves and local absorption.
• The temperatures change in time and the distribution of absorbed power is uniform with a conversion rate of 60% of the microwave injected power.
• The thermal transfer in ceramic materials can be evaluated using the thermal diffusion equation presented in Equation (2) [21]:

$$\rho ·c_p·{\displaystyle \frac{dT}{dt}}=k·{\nabla }^2·∆T+P_{abs/vol}$$

(2)

where the Barium Ferrite W-type properties are as follows [22,23]: ρ = 5000 kg/m³ is the density, c_p = 800 J/kgK is the specific heat, k = 3 W/mK is the thermal conductivity, ∇ is the Laplacian, ΔT (°C) is the difference between the sample temperature and room temperature and P_abs/vol (W/m³) is the absorbed power per volume unit. Considering a uniform distribution of the microwave power, the equation can be expressed as Equation (3):

$$\rho ·c_p·{\displaystyle \frac{dT}{dt}}=P_{abs/vol}-h·{\displaystyle \frac{\left(T_h-T_c\right)}{V}}$$

(3)

where h = 20 W/m²K is the convection coefficient (usually 10–50 W/m²K for ceramic materials) [24], T_c = 25 °C is the room temperature, T_h (°C) represents the temperature in the material and V (m³) is the total volume of the samples. For the simulation process, the thermal model from SolidWorks 2016 software was used, using the 3D tetrahedral mesh recommended by application.

2.3. Modeling and Simulation of Thermal Runaway in MHH Process

Thermal runaway is an unwanted process in MHH where local overheating leads to the occurrence of microwave arc discharge or local melting of the materials. To avoid thermal runaway, the MHH process must be very well controlled by maintaining the levels of heating in safe ranges. The temperature values which can lead to the thermal runaway phenomenon can be evaluated when the absorbed microwave power P_abs (W) is higher than dissipated power P_dis (W). According to the boundary conditions, the microwave absorbed power is 60% of the total injected power in the Barium Ferrite W-type samples. The dissipated power can be evaluated using Equation (4):

$$P_{dis}=h·A·∆T$$

(4)

where A (m²) is the area of the samples P₁, P₂ and P₃. By solving Equation (4), the results show that P_abs > P_dis, which leads to the conclusion that, at the edges of the defects, the thermal runaway phenomenon will occur. In order to evaluate the thermal runaway phenomenon, it is necessary to compute the temperature on the sphere’s surfaces. The thermal transfer equation is as follows:

$$T_{ss}=T_{ext}+{\displaystyle \frac{P_{abs}}{\pi ·d_{max\_H}^2·\lambda }}·{\displaystyle \frac{1}{\left(\frac{2}{d_{max\_H}}+\frac{1}{\delta }\right)}}$$

(5)

where T_ss (°C) is the temperature on the sphere surface, T_ext (°C) is the temperature on the external surface of the sample, P_abs (W) is the effective microwave power absorbed by the Barium Ferrite W-type samples, d_{max_H} are the diameters of the defects assimilated to the shape of the sphere, λ = 3.9 W/mK [25] is the thermal conductivity of the Barium Ferrite W-type material (usually 3.9–6.3 W/mK) and δ (m) is the thickness of the Barium Ferrite W-type layer affected by heat. By solving Equation (5) and plotting the results using MATLAB 9.7 from MathWorks, the 3D thermal map can be elaborated for each case of the compaction process.

2.4. Experimental Processing of Barium Ferrite W-Type Samples Using MHH

The microwave processing of all three Barium Ferrite W-type samples, using both direct and indirect heating, was performed in order to establish to what extent the presence of defects inside the crude compacted samples influences the uniformity, stability and overall performance of the MHH process. The initial parameters of the MHH process were as follows: P_MHH = 600 W was generated by a microwave heating installation consisting of a MW-Generator Set 6000 W and a 2450 MHz continuous-wave-containing magnetron head of type MH6000S-251BF from Muegge GmbH (Reichelsheim, Germany, 2020). The microwave generator was driven by an MW-Power Source Supply 6000 W, 2450 MHz, 3 × 400 V and a continuous-wave-type MX6000D-154KL, both manufactured by Muegge GmbH (Germany, 2020). The matching load impedance was performed using a Homer auto-tuner-type SHTH with a WR340 rectangular waveguide working at 2450 MHz and up to 6000 W from S-Team s.r.o. (Bratislava, Slovak Republic, 2008) driven by HomSoft software V5.2 produced also by S-Team s.r.o. (Slovak Republic, 2008). The temperature was measured on the surface of the sample, exposed to normal atmosphere, using an infrared pyrometer of type Sirius SI-16 manufactured by Sensortherm GmbH (Steinbach, Germany, Steinbach, 2008) with a spectral range of 1.45–1.8 μm and a temperature range of 350–1800 °C. Temperature control was performed using Sensor Tools v1.13.22 software produced by Sensortherm GmbH (Germany, 2020). The samples were positioned on the bottom of the reaction chamber for better exposure to the microwave beam. The microwave installation and auxiliary devices are presented in Figure 1.

The MHH process was maintained at constant microwave power for 600 s. Based on the input process parameters, and the conversion of the microwaves into heat, the MHH process was initially developed without a tuning process. The thermal runaway phenomenon tends to occur when spots of local overheating become more absorbent of microwaves when the temperature increases. Therefore, the first part of the MHH was performed without matching the load impedance of the microwave generator to the load. The Homer auto-tuner recorded large variations in the impedance that led to limited heating of the samples. The maximum temperatures recorded in 600 s were 515 °C for sample P₁, 475 °C for sample P₂ and 476 °C for sample P₃. An important issue reported was that the process took more than 360 s to reach 350 °C for all three samples. Therefore, matching load tuning should be applied in order to optimize the MHH process. The overall circuit impedance was calculated using a Schimdt chart, and the graphical representation can be found in Figure 2. For the P₁ sample, the microwave absorption by the Barium Ferrite W-type sample was totally uncontrolled, which justifies the low rate of conversion of microwaves into heat. More than 67% of the microwave power injected by the generator was reflected by the reaction chamber.

For samples P₂ and P₃, a microwave aggregation was reported, but the overall impedance was far from the best rate of absorption and conversion of the microwaves into heat. An average of 46% of the reflected power for P₂ and 42% for P₃ were recorded after 600 s of heating.

In order to achieve a better MHH process, matching load impedance was performed by calculating, using Equation (6), the positions of stub tuners inside the WR340 waveguide to obtain lower impedance of the overall electrical circuit:

$$d_i=-{\displaystyle \frac{\lambda }{2\pi }}·{tan}^{-1}(B_i·Z_0)$$

(6)

where d₁, d₂ and d₃ (mm) represent the length of the three stub tuners inside the WR340 waveguide, λ = 0.122 m is the wavelength of microwaves at 2450 MHz, the susceptance of stub tuners being considered is B₁ = B₂ = B₃ = 0.5 mS and Z₀ = 376.7 Ω is the air impedance.

By considering that no microwave power is dissipated in materials other than the Barium Ferrite W-type samples, the calculated lengths of the stub tuners were d₁ = 0 mm, d₂ = 16.24 mm and d₃ = 12.15 mm.

3. Results and Discussion

The results obtained after the digital reconstruction of the samples scanned using CT scanning are presented in Figure 3.

According to Figure 1, the samples P₁, P₂ and P₃ had different lengths due to the different pressing forces used for the same quantity of powders introduced in the die. Based on the information provided by the particle sizer, the focus of the scanner was increased to 50 μm in order to detect defects, holes or local aggregations in the powders. The target area was the center of the samples and the captured images were selected from the bottom of sample P₁ to the top of P₃. The results obtained by slicing the samples are presented in

Table 1. Dimensions of defects detected for different compaction procedures.

P1 (100 MPa)		P2 (200 MPa)		P3 (300 MPa)
Defect Size (μm)	Z-Axis (mm)	Defect Size (μm)	Z-Axis (mm)	Defect Size (μm)	Z-Axis (mm)
420	1.390	488	10.050	170	19.016
489	2.165	137	11.830	188	19.620
515	5.266	376	13.090	194	20.365
503	5.170	197	15.099	110	21.496
443	7.790	198	17.797	154	22.889

. For defects detected using a compression force of 100 MPa, the standard deviation was calculated to be 40.69 μm. Similarly, for 200 MPa and 300 MPa, the standard deviations were calculated to be 147.09 μm and 33.63 μm.

According to the measurements presented in Table 1, the samples compacted at 100 MPa presented an average dimension of defects of around 474 μm, the samples compacted at 200 MPa presented an average defect dimension equal to 204 μm and the samples compacted at 300 MPa presented an average defect dimension of around 132 μm. Figure 4 presents three images obtained during the scanning process.

Analyzing the images in Figure 4, it is expected that the non-uniformity factor of the Barium Ferrite W-type sample, obtained after the compaction process, will influence the temperature distributions in the Barium Ferrite W-type material during the sintering process. It is also expected that the presence of defects will influence the uniformity of the electromagnetic field during the MHH process, taking into consideration the polarization of the edges of the holes. Considering the dimensions of the holes measured on the Z-axis using the UniTOM HRScanner and the particle size distribution measured using the Brookhaven particle sizer manufactured by Brookhaven Instruments Corporation (Belgium, Brussels, 2006), the calculated non-uniformity factor is presented in

Table 2. Dimensions of defects detected for different compaction procedures.

P1 (100 MPa)		P2 (200 MPa)		P3 (300 MPa)
dmax_H (μm)	kNU	dmax_H (μm)	kNU (mm)	dmax_H (μm)	kNU (mm)
420	8.55	488	9.94	170	3.46
489	9.96	137	2.79	188	3.83
515	10.49	376	7.66	194	3.95
503	10.24	197	4.01	110	2.24
443	9.02	198	4.03	154	3.14

.

The temperature distributions for the samples P₁, P₂ and P₃ are presented in Figure 5 and the values computed through simulation are presented in

Table 3. Temperature distributions in samples (slices on X-axis through holes).

P1 (100 MPa)		P2 (200 MPa)		P3 (300 MPa)
dmax_H (μm)	Tmax (°C)	dmax_H (μm)	Tmax (°C)	dmax_H (μm)	Tmax (°C)
420	1106	488	1212	170	1186
489	1210	137	1195	188	1121
515	1210	376	1201	194	1196
503	1211	197	1199	110	1160
443	1207	198	1200	154	1180

. The highest temperature evaluated by the simulation process is noted as T_max (°C).

According to Table 3, the temperature evolution in the sample P₁ presented the highest value of 1210 °C for the highest diameters of the holes (defects approximated as spheres with diameters of 489 and 515 μm). Similarly, the samples P₂ and P₃ presented the same behaviors, reaching 1212 °C for the sphere with a diameter of 488 μm and 1196 °C for a diameter equal to 194 μm. This behavior led to the conclusion that, during the MHH process, the risk of occurrence of the thermal runaway phenomenon is higher near to defects in the materials. The 3D thermal maps of temperatures near the defects are presented in Figure 6.

According to Figure 6, the local overheating around the defects depends on the spheres’ diameters. The sample compacted at 100 MPa with a defect assimilated to a sphere having 515 μm diameter tended to suffer local overheating up to 1512 °C. The lowest temperature was 1377 °C in the case of the sample compacted at 300 MPa. For both cases, T_ss > T_ext, indicating that the thermal runaway of the Barium Ferrite W-type material will occur. The results of the thermal runaway simulation for the most relevant five temperatures higher than 1200 °C are presented in Figure 7.

According to Figure 4, the hottest spot, around 2000 °C, could be found in samples compacted at 100 MPa. However, at least one defect in the samples compacted at 200 MPa presented a peak temperature of 1985 °C. The rest of the defects for the samples compacted at 200 MPa and 300 MPa presented a similar behavior in terms of thermal runaway. The highest level of risk for thermal runaway was for the defects with temperatures higher than 1400 °C. Figure 8 shows the microwave powers absorbed by the Barium Ferrite W-type samples compacted at 100 MPa, 200 MPa and 300 MPa.

In Figure 8, the samples P₂ and P₃ present similar curves in terms of the uniformity of the absorption process and the conversion of microwaves into heat. The sample P₂ presents a stable evolution of the absorbed/reflected ratio. However, after 300 s, the absorption rate increases to above 500 W, which ensures a very good heating process, but, later, the absorption process decreases to 450 W, which is the average absorbed power for the samples compacted at 200 MPa. On the other hand, sample P₃ presents the best correlation between the stability of the process and the absorbed/reflected power ratio. Finally, the samples compacted at 100 MPa seemed to be the most unstable in terms of absorption/reflection. Even after 100 and 400 s, the absorption properties were consistent with P₂ and P₃, and the alternation between the maximum of the absorbed and reflected microwave power indicated the occurrence of the thermal runaway phenomenon.

The high rate of microwave conversion into heat followed by a cooling led to the assumption that more absorbance leads to fast heating, with temperature peaks above what was expected. A series of snapshots during the MHH processing of the P₁, P₂ and P₃ samples is presented in Figure 9 with recorded values presented in

Table 4. Thermal runaway phenomenon recorded for P₁, P₂ and P₃ samples.

Phenomenon	Local Overheating		Thermal Runaway		Arc Discharge
Sample	t (s)	Tss (°C)	t (s)	Tss (°C)	t (s)	Tss (°C)
P1	125	758	400	935	425	1010
P2	260	486	380	788	425	934
P3	360	587	390	689	425	816

, showing the occurrence of the thermal runaway phenomenon.

The MHH process suffered a thermal runaway phenomenon that was more pronounced for the samples compacted at 100 MPa. After 110 s, the local overheating occurred, raising the temperature up to 758 °C in about 15 s. The gradient of increasing temperature was recorded to be 24 °C/second, and was followed by a cooling and stabilization of the heating. The second step of the thermal runaway phenomenon was established after 400 s when an arc discharge was initiated between the sample core and the dolomite support. The temperature increased to 935 °C, followed by cooling to 612 °C. After this rapid heating/cooling cycle of the sample, the thermal runaway could not be controlled, and, after 425 s, the temperature increased up to 1010 °C and the MHH process was stopped.

The MHH process was restarted for the samples compacted at 200 and 300 MPa. According to the parameters recorded during processing, the sample P₂ suffered a local overheating after 260 s and the recorded temperature was 587 °C. After a short cooling-down period, the samples underwent thermal runaway 120 s later by increasing the temperature up to 788 °C followed by fast cooling. The process continued to be relatively unstable with a temperature gradient of 3 °C/second, but no arc discharge was reported. The most compacted sample, P₃ = 300 MPa, was also the most stable in terms of microwave heating. The temperature increased very slowly, reaching 371 °C after 75 s, 20 s later than P₁ and P₂, due to the small dimensions of the defects and lack of local overheating.

The thermal runaway phenomenon usually occurs as a result of local overheating in materials that contain polar particles when they are activated by the microwave field. In addition to the mechanical frictions between dipoles, the empty spaces inside the materials undergo high polarizations at the edges of the holes, which usually leads to local overheating and subsequently to thermal runaway. A property of materials susceptible to microwaves is the increasing rate of conversion of the microwave into heat when the temperature increases. Therefore, the local overheating will cause better absorbance and conversion of the microwaves into heat. The result will be the occurrence of the unwanted phenomenon called thermal runaway.

The Barium Ferrite W-type materials had a similar behavior in the microwave field. The samples P₁, P₂ and P₃ were heated in a microwave field in order to establish to what extent the material defects lead to thermal runaway and to quantify this phenomenon in terms of temperature distribution and the damage suffered by the Barium Ferrite W-type samples. Figure 10 shows the temperature evolution in time for the samples heated in the microwave field. According to Figure 10, thermal runaway occurred only on P₁ and the phenomenon started from the very beginning with a peak temperature of 758 °C. The fast but brief increase in the temperature indicated that high polarization of the edges of defects led to small arc discharges inside the sample. That was the first step of the thermal runaway phenomenon, which occurred without damaging the sample.

Based on the temperature recorded on the sample surface, a determination of the hottest point can be performed using thermal conduction equations without additional internal heat sources. The temperature of the hottest point was T_{SS_P1} = 1462.66 °C. Similarly, for P₂ and P₃, the hottest points were determined to be T_{SS_P2} = 799.84 °C and T_{SS_P3} = 599.78 °C, respectively. The thermal transient was computed using the heat diffusion equation, presented in Equation (7). The simulation of the thermal transient have been performed for maximum 15 s.

$${\displaystyle \frac{\partial T}{\partial t}}=\alpha ·\left({\displaystyle \frac{1}{r}}·{\displaystyle \frac{\partial }{\partial r}}·\left(r·{\displaystyle \frac{\partial T}{\partial r}}\right)+{\displaystyle \frac{{\partial }^{2}T}{\partial z^2}}\right)$$

(7)

where α = k/ρc_p (m²/s) is the thermal diffusion, r (m) is the radial coordinate, meaning the distance to the cylinder axis, and z (m) is the axial coordinate, meaning the distance along the cylinder height. The graphical representation is presented in Figure 11.

According to Figure 11, the sample with the highest thermal load is P₁, where the heat dissipation is low in the first 5 s and becomes high when the heat reaches the surface of the sample. The temperature decrease is explained by the exposure of the external surface to the ambient temperature. On the other hand, the samples P₂ and P₃ present similar behavior in terms of the thermal transient. The heat transfer is more efficient and the temperature distributions are uniform. The case of P₃ seems to be the most stable, in terms of thermal transfer, with low temperatures and rapid cooling.

Figure 12a,b shows the top and side views of the compacted sample at 100 MPa after microwave processing. Regarding the extent to which the samples were damaged by the thermal runaway phenomenon, the sample P₁ was the most affected due to the initiation of arc discharge. According to Figure 12a,b, the Barium Ferrite W-type sample compacted at 100 MPa and heated in a microwave field presents major cracks and extended melt areas. Moreover, the thermal runaway was intense in terms of high polarization due to the electromagnetic field followed by arc discharge from inside to the surface. The high temperature of 1010 °C was recorded at the beginning of the arc discharge. Also, due to compaction, more than half of the sample suffered an exfoliation.

The sample compacted at 200 MPa had a similar behavior in the microwave field, but without the initiation of arc discharge, which led to less damage to the sample. Figure 12c,d presents top and side views of the sample compacted at 200 MPa after microwave processing. No arc discharge was reported, but the local overheating at the upper edge of the sample led to micro-melting of the surface. The highest temperature recorded was 934 °C below sintering temperature, which, for Barium Ferrite W-type materials, is usually between 1050 °C and 1200 °C. This level of heating explains the color of the sample, which, in the case of the sintered product, is typically shiny.

The samples compacted at 300 MPa presented a similar distribution to those compacted at 200 MPa in terms of temperature distributions and local overheating. No thermal runaway or arc discharge was reported, but the samples suffered from cracking and exfoliation. Figure 12e,f presents the products coded as P₃ which were heated in a microwave field. The samples presented cracks on the surface as well as local overheating in the areas where cracks were observed. In addition, around 20% of the sample suffered an exfoliation from the top of the product, which was not reported for the samples compacted at 100 and 200 MPa.

The densities of the samples could provide valuable information related to the sintering process. Following the MHH process for sintering the samples, the density of the barium ferrite cylindrical materials increased, and this increase was more significant for products compacted at higher pressures (200 MPa and 300 MPa), because the initial porosity was lower and the material was better prepared to fuse and become denser. At a pressure of 100 MPa, the final density was lower, due to a higher initial porosity.

Table 5. Measured densities before and after the MHH process for P₁, P₂ and P₃ samples.

Sample	Densities (g/cm3)
	Before MHH	After MHH
P1	2.26	2.99
P2	2.97	3.76
P3	3.09	4.12

contains the measured densities of samples before and after the MHH process.

4. Conclusions

The compaction force influences the size of defects inside materials. According to CT scanning, the defects had larger dimensions at low compaction forces. The dimensions of the defects decreased with the increase in pressing force from 515 μm for 100 MPa to 110 μm for 300 MPa. The dimensions of the defects influenced the behavior of the temperature distribution during the microwave heating process. Based on the simulation model, the hottest spot, around 1211 °C, was recorded near the largest defect, and the lowest temperature, around 1160 °C, was obtained near the smallest defect.

The local overheating, at the edge of the defects, can lead to the thermal runaway phenomenon. According to the simulation model, the level of overheating was dependent on the dimensions of the defects, with the simulation providing high temperatures of around 1512 °C with a peak of 2000 °C in the case of 100 MPa and 1377 °C for 100 MPa compaction forces. The main conclusion, after simulation of the dependency between compaction force and size of internal defect, was that the size of the defect leads to local overheating followed by thermal runaway and arc discharge.

The experimental processing of samples using MHH has shown that the process tends to be unstable and the heating time is long. Moreover, in all three cases, the temperature recorded on the top surface of the samples was below sintering temperature: 515 °C for the sample compacted at 100 MPa, 475 °C at 200 MPa and 476 °C for the sample compacted using 300 MPa. The main conclusion regarding the heating process was the need of matching the load impedance to the microwave generator.

The thermal runaway phenomenon caused damage to the samples processed in the microwave field, and the level of destruction was proportional to the compaction forces used for the crude samples. The phenomenon was more pronounced for the samples compacted at 100 MPa. After 110 s, the local overheating occurred, raising the temperature up to 758 °C in about 15 s. All three sets of samples suffered cracks due to the high temperature developed around their defects, even though the presence of the air should normally lead to a decrease in temperature. This effect is explained by the high polarization at the defects’ edges, which leads to small areas with high temperatures. However, the samples did not reach the sintering temperature, the highest temperature recorded being 1010 °C for the sample compacted using 100 MPa. For the sample compacted at 300 MPa, small cracks and exfoliation of 20% of the sample surface were observed, but this sample presented the best behavior during the MHH process.

Finally, based on previous research related to microwave hybrid heating of ceramics and the current research, three major conclusions can be extracted:

• Barium Ferrite W-type powders should be compacted at higher pressure forces in order to reduce the size of the defects in the materials.
• The MHH process can be suitable for microwave sintering if matching load impedance tuning is used. However, the level of microwave injected power should be decreased to below 300 W, taking into consideration the aggressivity of the thermal runaway phenomenon. In addition, the heating time should be increased in order to facilitate the uniform distribution of the temperature in samples by dissipating the heat from the local overheating near the defects.
• Local overheating leads to major cracks and arc discharge in the case of samples compacted at low pressure forces. It is recommended to cool the surface of the samples using compressed air in order to avoid the thermal runaway phenomenon and arc discharge.