## 2 Materials and Methods
### 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\({}_{\text{MHH}}\) = 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-251 BF from Muegge GmbH (Reichelheim, Germany, 2020). The microwave generator was driven by an MW-Power Source Supply 6000 W, 2450 MHz, 3 \(\times\) 400 V and a continuous-wave-type MX6000D-154 KL, 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. (Brantislava, 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 \(\upmu\)m and a temperature range of 350-1800 \({}^{\circ}\)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 \({}^{\circ}\)C for sample \(P_{1}\), 475 \({}^{\circ}\)C for sample \(P_{2}\) and 476 \({}^{\circ}\)C for sample \(P_{3}\). An important issue reported was that the process took more than 360 s to reach 350 \({}^{\circ}\)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 \(P_{1}\) 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 \(P_{2}\) and \(P_{3}\), 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 \(P_{2}\) and 42% for \(P_{3}\) were recorded after 600 s of heating. Figure 1: MHH processing installation. Figure 2: Z-Schmidt charts related to matching load impedance without a tuning procedure during the MHH process: (**a**) samples compacted using 100 MPa, (**b**) samples compacted using 200 MPa, (**c**) samples compacted using 300 MPa.