metals

Article Magnetic Field Generated during -Assisted Sintering: From Health and Safety Issues to Lorentz Force Effects

Huaijiu Deng 1, Jian Dong 1, Filippo Boi 2, Theo Saunders 3, Chunfeng Hu 1 and Salvatore Grasso 1,*

1 Key Laboratory of Advanced Technologies of Materials, Ministry of Education, School of Materials Science and Engineering, Southwest Jiaotong University, Chengdu 610031, China; [email protected] (H.D.); [email protected] (J.D.); [email protected] (C.H.) 2 College of Physics, Sichuan University, Chengdu 610065, China; [email protected] 3 School of Engineering and Material Science, Queen Mary University of London, Mile End Road, London E1 4NS, UK; [email protected] * Correspondence: [email protected]; Tel.: +86-1832-8676-558

 Received: 11 November 2020; Accepted: 2 December 2020; Published: 8 December 2020 

Abstract: In the past decade, a renewed interest on electromagnetic processing of materials has motivated several investigations on the interaction between matter, electric and magnetic fields. These effects are primarily reconducted to the Joule heating and very little attention has been dedicated to the magnetic field contributions. The magnetic field generated during electric current-assisted sintering has not been widely investigated. could have significant effects on sintering as it generates significant magnetic forces, resulting in inductive electrical loads and preferential heating induced by overlapping magnetic fields (i.e., proximity effect). This work summarizes the magnetic field effects in electric current-assisted processing; it focuses on health and safety issues associated with large currents (up to 0.4 MA); using FEM simulations, it computes the self-generated magnetic field during spark plasma sintering (SPS) to consolidate materials with variable magnetic permeability; and it quantifies the Lorentz force acting at interparticle contact points. The results encourage one to pay more attention to magnetic field-related effects in order to engineer and exploit their potentials.

Keywords: magnetic field; electro-magnetic assisted processing; spark plasma sintering

1. Magnetic Field Effects in Electromagnetic Processing of Materials (EPM) In electromagnetic processing of materials (EPM) [1], research has been mostly focused on current and temperature effects, often neglecting the magnetic contribution. The purpose of this paper is to investigate the effects of self-generated magnetic fields by a current passing across the processed material. This work does not cover externally applied magnetic fields, as such a topic was extensively discussed by Guo et al. [2]. As early as 1886, Elihu Thompson developed the first resistance machine, which represented a major improvement in joining technology with a wide range of applications [3]. At that stage, it was already clear that ferromagnetic objects (both constituting the welding fixtures or the work piece) should be avoided. High current (exceeding several hundreds of Amperes) would generate a strong magnetization of these ferromagnetic materials, resulting in a decreased welding efficiency limiting the maximum output current [4]. Curiously, at that time, ferromagnetic materials in the vicinity of the welding equipment were intentionally employed to increase the resistive load on the generator.

Metals 2020, 10, 1653; doi:10.3390/met10121653 www.mdpi.com/journal/metals Metals 2020, 10, 1653 2 of 16

Electric current-assisted sintering (ECAS) techniques began their journey from the beginning of the last century. Compared with conventional sintering techniques, ECAS has the following advantages: low furnace temperature, short processing duration, direct Joule heating on the workpiece, and significantly improved material properties [2,5–8]. While magnetic field effects have been well-investigated in the case of welding, they still remain unexplored in sintering. The magnetic fields effects in ECAS, being secondary effects, are poorly discussed in the literature. Table1 summarizes magnetic-related effects in EPM. It includes several electromagnetic phenomena, their applications, physical principle and their mathematical formulation. White and Fasenfest [9] proposed a method for evaluating the discrete Biot–Savart law. Wheeler et al. [10] investigated the skin effect as early as 1942, and he also proposed a mathematical formulation for different configurations and operating . Ahmad et al. [11] analyzed the skin effect in detail by proposing computer models. The proximity effect occurring at high (>100 kHz) with applications in pipe welding was analyzed in Ref. [12]. Such an effect caused a increase in the vicinity of the strip edge zone. Zhao et al. [13] investigated the influence of the proximity effect on the welding process, including high-frequency welding of H-shaped steel and T-shaped steel. Thus far, no work has been published on the possible influence of the proximity effect on sintering. J. Trapp [14] quantified the pinch effect and its impact on the sintering of ideal spherical particles. Yurlova et al. [15] investigated the influence of the pinch effect on the sintering process, and their result suggests that magnetic forces would result in a modification of the sample shape, allowing an easy extraction out of the die. These effects became apparent under low-pressure conditions. The concept of the undesired “arc blow” effect induced by the magnetic field was analyzed by Tomoyuki et al. [16] in 2011. The experimental conditions needed for preventing arc blow were discussed by Yamaguchi et al. [17] and M. Vural [18]. Lockwood et al. [19] explained that under AC conditions, an electrical arc is more stable than in DC, and they correlated the influence of electromagnetic force with the porosity of the welded materials. With some analogies, Adamian and Shneerson [20] investigated the mechanisms of electric explosion where a strong radial compression induced by the magnetic field contributes to fragmentation of the particles. Magnetic materials subjected to an alternating electrical discharge greatly increase their , thereby reducing the welding current. The result is a direct consequence of Lenz’s law. This also explains the rationale for choosing different types of power supplies (AC/DC) for different materials. The magnetic field also generates undesired interference with the probing devices, thus affecting the readings of temperature, current, voltage. Zhang and Senkara [21] investigated how a spot welding high current affected these signals. In response to this problem, they adopted fiber-optic displacement sensors, which are insensitive to the high magnetic fields. In summary, magnetic-related effects are complex and Table1 suggests a simplification of these phenomena. This manuscript is divided into two parts. The first part provides some FEM simulations to quantify magnetic strength generated by a spark plasma sintering machine, both at the tooling level and the interparticle level for materials with different magnetic permeability (i.e., , iron, alumina, graphite). The second part of the paper provides some preliminary experimental evidence of the magnetic field effects on sintering. Metals 2020, 10, x FOR PEER REVIEW 3 of 17 MetalsMetals2020 2020, 10, 10, 1653, x FOR PEER REVIEW 3 of 17 3 of 16

TableTable 1.1. MagneticMagnetic fieldfield effectseffects inin electromagneticelectromagnetic prprocessingocessing ofof materialsmaterials (EPM).(EPM). TheThe possiblepossible implicationsimplications onon sinteringsintering areare listedlisted inin iitalics.talics. Table 1. Magnetic field effects in electromagnetic processing of materials (EPM). The possible implications on sintering are listed in italics. TypicalTypical Use,Use, ImplicationsImplications onon EffectEffect NameName Principle Principle andand MathematicalMathematical FormulationFormulation Effect Name Principle and Mathematical Formulation TypicalSinteringSintering Use, Implications on Sintering Biot–SavartBiot–Savart Law Law ThisThis formulationformulation resemblesresembles wellwell thethe magnetic-inducedmagnetic-induced This formulation resembles well the magnetic-induced ItIt cancan bebe usedused toto calculatecalculate thethe effecteffect inin usingusing DCDC currents.currents. TheThe Biot–SavartBiot–Savart LawLaw effect in using DC currents. The Biot–Savart Law quantifies magneticmagnetic fieldfield strengthstrength inin thethe quantifiesquantifies thethe magneticmagnetic fieldfield strengthstrength insideinside andand outsideoutside the magnetic field strength inside and outside the conductor. It canvicinityvicinity be used ofof to aa conductor. calculateconductor. the ItIt magneticcancan field strength in thethe conductor.conductor. ItIt refersrefers toto anan infinitelyinfinitely longlong wirewire withwith It refers to an infinitely long wire with radius r [9,22,23]. theaccuratelyaccurately vicinity of identifyidentify a conductor. thethe healthhealth It can andand accurately identify the radiusradius rr [9[9,22,23].,22,23]. safetysafetyhealth exposureexposure and safety distancedistance exposure [9,22,23].[9,22,23]. distance [9,22,23]. µ0𝜇𝜇I𝐼𝐼 Health and safety hazard for the operators and magnetization B 𝐵=𝐵== HealthHealth andand safetysafety hazardhazard forfor thethe 2π2𝜋𝑟2𝜋𝑟r0 of the electrically conductive sample under −7 operatorsoperators andand magnetizationmagnetization ofof thethe μμ00—The—The vacuumvacuum permeability,permeability, withwith valuevalue ofof 44ππ ×× 1010−7 an electrical discharge. 7 µ —The , with value of 4π 10 H/m. electricallyelectrically conductiveconductive samplesample underunder H/m.H/m.0 × − r0 is the radius of the conductor anan electricalelectrical discharge.discharge. rr00 isis thethe radiusradius ofof thethe conductorconductor

It commonly occurs in high-frequency , ItIt commonly commonly occurs occurs in in high-frequency high-frequency alternating alternating current, current, Skin effect resultingresulting inin preferentialpreferential currentcurrent flowflow withinwithin thethe skinskin Skin eeffectffect resulting in preferential current flow within the skin depth. depth.depth. s 222 ∆ =∆=∆= HeatHeat generationgeneration localizedlocalized onon thethe ωµγ𝜔𝜇𝛾𝜔𝜇𝛾 skinskin depth.depth. ThisThis effecteffect waswas Heat generation localized on the skin depth. This effect ΔΔ—(m),—(m), thethe radialradial depthdepth thatthat thethe currentcurrent cancan reachreach fromfrom commonlycommonly usedused inin inductioninduction ∆—(m), the radial depth that the current can reach from the was commonly used in of a thethe surfacesurface ofof thethe wire.wire. heating of a workpiece surface of the wire. heating workpieceof a workpiece [10,11 ,13,24]. WhereWhere 𝜔,𝜔, 𝜇, 𝜇, andand 𝛾𝛾 are are angularangular frenquency,frenquency, permeability,permeability, Where ω, µ, and γ are angular frenquency, permeability, Preferential[10,11,13,24].[10,11,13,24]. heating by skin effect. Possibility to and conductivity. andand conductivity. conductivity. PreferentialPreferentialcounterbalance heatingheating byby skinskin radiative effect.effect. heat losses. AccordingAccordingAccording to toto Lenz’s Lenz’sLenz’s law, law,law, the thethe induced inducedinduced current currentcurrent is isis always alwaysalways in inin PossibilityPossibility toto counterbalancecounterbalance the opposite direction to the imposed current, thethe oppositeopposite directiondirection toto thethe imposedimposed current,current, whichwhich radiativeradiative heatheat losses.losses. whicheventuallyeventually eventually leadsleads leadstoto thethe to currentcurrent the current inin thethe in conductorconductor the conductor tendingtending toto tending to approach the surface of the conductor [10–12,24]. approachapproach thethe surfacesurface ofof thethe conductorconductor [10–12,24].[10–12,24]. EddyEddy Eddy currents are loops of electrical current within a currentscurrents areare loopsloops ofof electricalelectrical currentcurrent withinwithin aa conductorconductor conductor resulting from a changing magnetic field [24,25]. resultingresulting fromfrom aa changingchanging magneticmagnetic fieldfield [24,25].[24,25]. ACAC resistanceresistance changechange inin thethe vicinityvicinity ofof thethe CurieCurie AnAn alternatingalternating (i.e.,(i.e., time-variable)time-variable) currentcurrent flowingflowing acrossacross aa ForFor ferromagneticferromagnetic materialsmaterials (i.e.,(i.e., temperaturetemperature ferromagneticferromagnetic conductorconductor seessees anan increaseincrease inin resistivityresistivity duedue Ni,Ni, Fe,Fe, Co),Co), thethe CurieCurie temperaturetemperature

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Table 1. Cont.

Effect Name Principle and Mathematical Formulation Typical Use, Implications on Sintering

Metals 2020AC, 10 resistance, x FOR PEER change REVIEW in the vicinity of the 4 of 17 Curie temperature to the skin effect. These effects disappear above the Curie should be considered during temperature [26,27]. heating [26,27]. Precise calibration of the temperatures and rapid drop of electrical resistance at a temperature Forgreater ferromagnetic than the Curie materials point. (i.e., Ni, Fe, Co), the Curie An alternating (i.e., time-variable) current flowing across a temperature should be considered ferromagnetic conductor sees an increase in resistivity due during heating [26,27]. to the skin effect. These effects disappear above the Curie Precise calibration of the temperatures and rapid drop of temperature [26,27]. electrical resistance at a temperature greater than the Curie point.

When using high-frequency alternating current for welding, This effect occurs under high-frequency current (100 kHz) When using high-frequency alternating current for This effect occurs under high-frequency current (100 kHz) the proximity effect should be and it was typically used to generate overheating by welding, the proximity effect and it was typically used to generate overheating by considered [11,13]. promoting an interaction between magnetic fields. Eddy should be considered [11,13]. promoting an interaction between magnetic fields. Eddy Not investigated in sintering. It is currents result in preferential current distribution Not investigated in sintering. It is expected to provide currents result in preferential current distribution [11,13,24]. expected to provide further [11,13,24]. further overheating at interparticle contact points. overheating at interparticle contact points.

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Table 1. Cont. Metals 2020, 10, x FOR PEER REVIEW 5 of 17 Metals 2020, 10, x FOR PEER REVIEW 5 of 17 Effect Name Principle and Mathematical Formulation Typical Use, Implications on Sintering Pinch effect PinchPinch effect effect The pinch effect induces a shape The pinch effect induces a shape Pinch effect refers to the compressive forces acting on the change of the sample, easing its Pinch effect refers to the compressive forces acting on the change of the sample, easing its conductivePinch effect media refers as to a the result compressive of the magnetic forces actingforces. onThe the extraction out of the die [15]. The pinch effect induces a shape change of the sample, conductiveconductive media media as as a a result result of of the the magnetic magnetic forces. forces. The extraction out of the die [15]. conductive media can be in the form of a liquid, a solid, or Might noteasing have strong its extraction implications out of the die [15]. Theconductive conductive media media can can be bein the in the form form of a of liquid, a liquid, a solid, a solid, or Might not have strong implications a plasma. These effects are particularly strong in the in pressure-assistedMight not have strong sintering. implications Pinch- in pressure-assisted ora plasma. a plasma. These These effects effects are are particularly particularly strong strong in in the the in pressure-assisted sintering. Pinch- presence of large currents as in the case of a capacitor relatedsintering. pressure Pinch-related is several orders pressure of is several orders of presencepresence of of large large currents currents as as in in the the case case of of a a capacitor capacitor related pressure is several orders of discharge [14,15,28,29]. magnitudemagnitude lower lower than than the the sintering sintering pressure ( MPa). dischargedischarge [ 14[14,15,28,29].,15,28,29]. magnitude lower than the sintering ≈ pressure (≈ MPa). pressure (≈ MPa).

An AC current is less susceptible An AC current is less susceptible This phenomenon was often encountered in the welding. to arc blowing compared to DC ThisThis phenomenonphenomenon was was often often encountered encountered in in the the welding. welding. toAn arc AC blowing current compared is less susceptible to DC to arc blowing The magnetic bias blow is caused by the unbalanced [17–19]. TheThe magnetic magnetic bias bias blow blow is is caused caused by by the the unbalanced unbalanced [17–19].compared to DC [17–19]. magnetic field around the electrical arc [17–19]. Arcing is usually seen as an magneticmagnetic fieldfield around around the the electrical electrical arc arc [ 17[17–19].–19]. ArcingArcing is usually is usually seen seen as an as undesired an effect in sintering. undesired effect in sintering. undesired effect in sintering.

Ferromagnetic materials increase Ferromagnetic materials significantly increase the Ferromagnetic materials increase Ferromagnetic materials significantly increase the the reactance, and leads to an reactance, reducing the welding or sintering current [19]. the reactance, and leads to an reactance, reducing the welding or sintering current [19]. increase in impedance, ultimately 𝑍=𝑅+𝑗𝑋 increase in impedance, ultimately Reactance dependence on duty cycle 𝑍=𝑅+𝑗𝑋 resulting in a decrease in current Reactance dependence on duty cycle where Z, R, and X are impedance, resistance, and resulting in a decrease in current where Z, R, and X are impedance, resistance, and [19]. reactance, respectively, the unit is ohm, and j is the [19]. reactance, respectively, the unit is ohm, and j is the Implications on the material selected imaginary unit. Implications on the material selected imaginary unit. as tooling. as tooling.

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Table 1. Cont.

Effect Name Principle and Mathematical Formulation Typical Use, Implications on Sintering Metals 2020, 10, x FOR PEER REVIEW 6 of 17 Reactance dependence on duty cycle

Ferromagnetic materials significantly increase the reactance, reducing the welding or sintering current [19]. Ferromagnetic materials increase the reactance, and leads to an increase in impedance, Z = R + jX ultimately resulting in a decrease in current [19]. where Z, R, and X are impedance, resistance, and reactance, Implications on the material selected as tooling. respectively, the unit is ohm, and j is the imaginary unit.

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In summary, magnetic-related effects are complex and Table 1 suggests a simplification of these phenomena. This manuscript is divided into two parts. The first part provides some FEM simulations to quantify magnetic strength generated by a spark plasma sintering machine, both at the tooling level and the interparticle level for materials with different magnetic permeability (i.e., copper, iron, Metalsalumina,2020 ,graphite).10, 1653 The second part of the paper provides some preliminary experimental evidence7 of 16 of the magnetic field effects on sintering.

2. The Combined Experimental/Computational Experimental/Computational Methodology The primary purpose of this paper was to developdevelop accurateaccurate simulations accounting for the magnetic fieldfield eeffects.ffects. The Multiphysics coupling was recreated using a built-in scheme using Comsol Multiphysics [30]. [30]. The The electrothermal electrothermal model model was was built built according according to to the the model model proposed proposed in in Ref. Ref. [31]. [31]. It reproducedreproduced thethe spark spark plasma plasma sintering sintering (SPS) (SPS) sample sample geometry, geometry, upper upper punch, punch, lower lower punch, punch, and and SPS die,SPS asdie, shown as shown in Figure in Figure1. 1.

Figure 1. Assumed spark plasma sintering (SPS) model’s boundary conditions for (A) electric and Figure 1. Assumed spark plasma sintering (SPS) model’s boundary conditions for (A) electric and (B) (B) thermal fields. thermal fields. The electrical and thermal boundary conditions are summarized in Figure1. Axially symmetric The electrical and thermal boundary conditions are summarized in Figure 1. Axially symmetric boundary conditions were applied along the axial axis. An electrical power input was applied to the boundary conditions were applied along the axial axis. An electrical power input was applied to the upper ram while the lower one was grounded. The lateral surfaces of graphite elements were assumed upper ram while the lower one was grounded. The lateral surfaces of graphite elements were to be electrically insulated. The initial temperature of all components was 20 ◦C, and the upper and assumed to be electrically insulated. The initial temperature of all components was 20 °C, and the lower ends were water-cooled and maintained at the preset temperature of 20 ◦C. The SPS process upper and lower ends were water-cooled and maintained at the preset temperature of 20 °C. The SPS was operated in vacuum ( 5 Pa), so convection heat transfer was ignored. The heat on the graphite process was operated in vacuum≤ (≤ 5 Pa), so convection heat transfer was ignored. The heat on the surface was mainly transferred to the environment by radiation, and the surface emissivity of graphite graphite surface was mainly transferred to the environment by radiation, and the surface emissivity elements was assumed to be equal to 0.8 [32]. of graphite elements was assumed to be equal to 0.8 [32]. FEM conditions are summarized as follows. Parameters and formula settings of electric field. FEM conditions are summarized as follows. Parameters and formula settings of electric field. No initial electric potential at all components. No initial electric potential at all components. Electric insulation boundary: n J = 0 Electric insulation boundary: 𝐧×𝐉=0× Provide the power input at this boundary (current density/electric potential): Provide the power input at this boundary (current density/electric potential): 𝑉=𝑉 V = V n J = Jn 0− × where V0 and Jn are the power supply formula in voltage and current, respectively. Metals 2020, 10, 1653 8 of 16

The electric current equation at the domain where the current passes is:

∂D J = Q J = σE + + J E = vJ = σED = ε εrE ∇ × j,v ∂t e −∇ c 0 where σ, ε0 and εr are the electric conductivity, vacuum dielectric constant, and relative .

12 ε = 8.8542 10− [F/m] 0 × Parameters and formula settings of magnetic field. Initial magnetic vector potential at all components: A = 0 Magnetic insulation boundary: n A = 0 × Coupling electric and magnetic fields:

∂A H = JB = AE = J = σE + σv B + J B = µ µrHJ = σE ∇ × ∇ × − ∂t × e 0 C where A, J, µ0 and µr are the magnetic vector potential, current density, permeability of vacuum, and relative permeability of the material.

3. Health Effects and Safe Distance for the Operators During the electric current-assisted sintering process, large current can result in a strong magnetic field, which might exceed the safety exposure limits. To the best of our knowledge, such an issue has not been discussed in the literature. To meet the safety requirements, the resulting magnetic field should be kept under control. Exposure limits are inversely proportional to the frequency accordingly to the guidelines proposed by the International Commission on Non-Ionizing Radiation Protection in 2010 [33]. In DC, a well-accepted standard for the magnetic field exposure limit is 5 Gauss (0.0005 T), whereas for AC, the exposure frequencies differ from country to country. Here, we simulated the magnetic field generated by reference SPS machines (FCT systems, Germany) operated in DC. The results are shown in Tables2 and3, and as expected, the safety distance increases with the applied current (i.e., increasing the specimen dimension). The analysis in Table2 also includes a conservative scenario where electromagnetic shielding (i.e., sintering chamber) is not employed. This assumption reflects the situation of unshielded or partially unshielded cables/conductors. The good match between simulated results and the Bio–Savart law confirms the accuracy of the simulations. The representative distribution of the magnetic field distribution is shown in Figure2.

Table 2. Safety distance test under DC conditions, for different currents assuming an exposure limit of 5 Gauss.

Standard Dimension Safety Distance Biot–Savart Max Pressing Max Current Commercialized Components without Shield (DC) Distance Force [kN] [A] SPS Types [mm] [cm] Calculation [cm] * HP D 2.5 Ø 30 25 3000 118.9 120 HP D 10 Ø 50 100 5500 217.7 200 HP D 25 Ø 80 250 8000 314.7 320 HP D 60 Ø 120 600 16,000 629.8 640 HP D 125 Ø 150 1250 24,000 956.3 960 HP D 250 Ø 300 2500 48,000/24,000 1894/1949 1920/960 * Biot–Savart calculation assumes an infinitely long conductor. Metals 2020, 10, x FOR PEER REVIEW 9 of 17 Metals 2020, 10, x FOR PEER REVIEW 9 of 17

Table 2. Safety distance test under DC conditions, for different currents assuming an exposure limit Table 2. Safety distance test under DC conditions, for different currents assuming an exposure limit of 5 Gauss. of 5 Gauss. Standard Dimension Max Safety Distance Biot–Savart Standard Dimension Max Safety Distance Biot–Savart Commercialize Components Pressing Max Current [A] Without Shield (DC) Distance Commercialize Components Pressing Max Current [A] Without Shield (DC) Distance d SPS Types [mm] Force [kN] [cm] Calculation [cm] * d SPS Types [mm] Force [kN] [cm] Calculation [cm] * HP D 2.5 Ø 30 25 3000 118.9 120 HP D 2.5 Ø 30 25 3000 118.9 120 HP D 10 Ø 50 100 5500 217.7 200 HP D 10 Ø 50 100 5500 217.7 200 HP D 25 Ø 80 250 8000 314.7 320 HP D 25 Ø 80 250 8000 314.7 320 HP D 60 Ø 120 600 16,000 629.8 640 HP D 60 Ø 120 600 16,000 629.8 640 HP D 125 Ø 150 1250 24,000 956.3 960 HP D 125 Ø 150 1250 24,000 956.3 960 HP D 250 Ø 300 2500 48,000/24,000 1894/1949 19,20/960 HP D 250 Ø 300 2500 48,000/24,000 1894/1949 19,20/960 * Biot–Savart calculation assumes an infinitely long conductor. Metals 2020, 10, 1653 * Biot–Savart calculation assumes an infinitely long conductor. 9 of 16

Table 3. Electrical conductivity and relative magnetic permeability samples considered in the Table 3. Electrical conductivity and relative magnetic permeability samples considered in the Tablesimulations 3. Electrical 20 °C. conductivity and relative magnetic permeability samples considered in the simulations 20 °C. simulations 20 ◦C. Electrical Conductivity (S Electrical Conductivity (S Relative Permeability Electrical Conductivitym) (S m) RelativeRelative Permeability Permeability m) GraphiteGraphite 8.38.3 ×10 104 4 1 1 Graphite 8.3× × 104 1 Iron 1.12 107 7 200,000 Iron 1.12 × 107 200,000 Iron 1.12× × 1012 200,000 AluminaAlumina 11 ×10 10− −12 1 1 Alumina 1× × 10−127 1 CopperCopper 5.7145.714 ×10 107 1 1 Copper 5.714× × 107 1

FigureFigure 2. 2.Simulation Simulation of of magnetic magnetic field field distribution distribution (units (units in Tesla)in Tesla) using using an alumina an alumina sample sample with 30with mm 30 Figure 2. Simulation of magnetic field distribution (units in Tesla) using an alumina sample with 30 diameter,mm diameter, and assumingand assuming a current a current of 3000 of 3000 A DC A DC and and no no sintering sintering chamber chamber (i.e., (i.e., shield). shield). The The safety safety mm diameter, and assuming a current of 3000 A DC and no sintering chamber (i.e., shield). The safety distancedistance to to meet meet the the 5 5 Gauss Gauss line line is is 119 119 cm. cm. distance to meet the 5 Gauss line is 119 cm. AA more more realistic realistic simulation simulation is instead is instead achieved achieved by considering by considering a 2 cm-thick a 2 cm-thick stainless steelstainless chamber steel A more realistic simulation is instead achieved by considering a 2 cm-thick (relativechamber permeability (relative permeability is 1.06) [34 is]. 1. The06) results[34]. The are results presented are presented in Figure3 in. The Figure magnetic 3. The fieldmagnetic strength field chamber (relative permeability is 1.06) [34]. The results are presented in Figure 3. The magnetic field onstrength the outside on the of theoutside stainless of the steel stainless is greatly steel reduced is greatly compared reduced to the compared magnetic to field thestrength magnetic on field the strength on the outside of the stainless steel is greatly reduced compared to the magnetic field inside,strength which on the shows inside, that which the stainless-steel shows that the shell stainl caness-steel effectively shell reducecan effectively the magnetic reduce field the strength,magnetic strength on the inside, which shows that the stainless-steel shell can effectively reduce the magnetic therebyfield strength, protecting thereby the safety protecting of the the operator. safety of the operator. field strength, thereby protecting the safety of the operator.

Figure 3. Magnetic field distribution when using a 30 mm sample of alumina and current of 3000 A, adding a 2 cm-thickness stainless-steel shell. The magnetic field strength at the position represented

by the green circle within the chamber is 1.94 10 3 T, while the magnetic field outside the chamber × − (red circle) is 1.218 10 7 T. The chamber can effectively shield the magnetic field down to a safe level × − for the operator.

4. Magnetic Field Distribution during SPS of Different Materials: Electrical Conductivity and Magnetic Permeability Effects As discussed in the introduction, the ferromagnetic material below the Curie temperature is expected to become magnetized under the application of an electrical discharge. As a representative example, Sales et al. [26] investigated the changes in electrical resistance in the vicinity of the Curie temperature of ferromagnetic materials. These effects are summarized in Table1 under the Metals 2020, 10, x FOR PEER REVIEW 10 of 17

Figure 3. Magnetic field distribution when using a 30 mm sample of alumina and current of 3000 A, adding a 2 cm-thickness stainless-steel shell. The magnetic field strength at the position represented by the green circle within the chamber is 1.94 × 10−3 T, while the magnetic field outside the chamber (red circle) is 1.218 × 10−7 T. The chamber can effectively shield the magnetic field down to a safe level for the operator.

4. Magnetic Field Distribution during SPS of Different Materials: Electrical Conductivity and Magnetic Permeability Effects As discussed in the introduction, the ferromagnetic material below the Curie temperature is Metalsexpected2020, to10, become 1653 magnetized under the application of an electrical discharge. As a representative10 of 16 example, Sales et al. [26] investigated the changes in electrical resistance in the vicinity of the Curie temperature of ferromagnetic materials. These effects are summarized in Table 1 under the section section “AC Resistance change in the vicinity of the Curie temperature.” Assuming a DC discharge, “AC Resistance change in the vicinity of the Curie temperature.” Assuming a DC discharge, magnetization effects are expected to occur depending on the electrical conductivity and magnetic magnetization effects are expected to occur depending on the electrical conductivity and magnetic permeability, as shown in Table3. permeability, as shown in Table 3. The SPS simulations were done assuming a DC voltage of 10 V DC that represents the upper The SPS simulations were done assuming a DC voltage of 10 V DC that represents the upper operating limit of the equipment. The sample diameter of the sample was 30 mm with a height of operating limit of the equipment. The sample diameter of the sample was 30 mm with a height of the the sample of 8 mm. The magnetic saturation of the 2.4 T effect for soft iron was accounted for in the sample of 8 mm. The magnetic saturation of the 2.4 T effect for soft iron was accounted for in the simulations. The resulting magnetic field distribution is shown in Figure4. simulations. The resulting magnetic field distribution is shown in Figure 4.

FigureFigure 4.4. ComparisonComparison ofof magneticmagnetic field field distribution distribution for for di differentfferent materials materials assuming assuming a voltagea voltage of 10of 10 V; (V;a) the(a) the maximum maximum recorded recorded field field strength strength within within the graphitethe graphite sample sample was was 0.053 0.053 T, (b T,) that (b) forthat iron for wasiron 1.4was T, 1.4 and T, (andc) that (c) that for alumina for alumina was was as low as low as 9.1as 9.110 × 1010−10T. T. Simulations Simulations in in ( d(d)) were were performed performed atat aa × − temperaturetemperature exceedingexceeding thethe CurieCurie point,point, reachingreaching 0.0140.014 TT withinwithin thethe ironiron sample. sample.

AccordingAccording toto FigureFigure4 4,, the the magneticmagnetic fieldfield strengthstrength dependsdepends stronglystrongly onon thethe materialsmaterials properties.properties. ForFor graphitegraphite andand alumina,alumina, thethe magneticmagnetic fieldfield distributiondistribution isis relativelyrelatively uniform.uniform. TheThe peakpeak valuevalue ofof magneticmagnetic strengthstrength isis 0.190.19 T,T, andand itit radiallyradially increases.increases. ForFor iron,iron, thethe magneticmagnetic fieldfield distributiondistribution isis didifferent,fferent, thethe peakpeak valuevalue ofof magneticmagnetic strengthstrength isis 1.41.4 TT (much(much largerlarger thanthan 0.190.19 T),T), andand thethe magneticmagnetic intensityintensity of the sample sample is is much much higher higher than than thos thosee of of the the surrounding surrounding components. components. The The intensity intensity of ofthe the magnetic magnetic field field increases increases with with the radius the radius and re andaches reaches the maximum the maximum value valueat the edge at the of edge the sample. of the sample.It needs Itto needs be pointed to be pointed out that out the that properties the properties of ferromagnetic of ferromagnetic materials materials changed changed drastically drastically when whenthe temperature the temperature exceeded exceeded the Curie the Curie point, point, due dueto the to ferromagnetic the ferromagnetic to paramagnetic to paramagnetic transition. transition. In InFigure Figure 4d,4d, the the temperature temperature of of the the iron iron sample sample exceeded exceeded the the Curie point, and thethe peakpeak valuevalue ofof thethe magneticmagnetic fieldfield strengthstrength reducedreduced fromfrom 1.41.4 toto 0.190.19 T.T. In the literature, there are some examples of sintering under the application of an externally applied magnetic field. For example, Eikeland et al. [35] investigated the externally applied magnetic field prior to sintering, resulting in an improved degree of alignment of SrFe12O19. Using a different approach, Li et al. [36] applied an external magnetic field using a coil on iron-based powders using a field strength up to 0.5 T AC 50 Hz. The results suggested an enhanced diffusion of the alloying elements resulting from the application of an external magnetic field. The implications of these magnetic fields are not well-investigated, and it is expected that any magnetic-related effect might have a radial dependence. Further work might be needed to understand and exploit these effects. Metals 2020, 10, 1653 11 of 16

5. Magnetic Field Effects at Interparticle Contacts In this section, magnetic field effects occurring at the interparticle contact point are investigated. The analysis accounts for the impact of electro-magneto-thermal effects on the sintering process. Magnetic effects are intensified by increasing the current. Selected ECAS [37] techniques are rationalized in Table4 with respect to pressure, discharge time, voltage, current, and sintered material compositions.

Table 4. Representative sintering parameters for electric current-assisted sintering (ECAS) techniques based on high current density.

Inventor, Year, Reference Pressure, Discharge Time, Voltage, Current Density Sintered Material 100 MPa, 10 ms, Cremer, US1944 ≈ 2 Cu, Al, brass 5–20 V, 60 kAcm− ≈ 2 10 MPa, 1 ms, >150 kAcm− Parker, US1968 3 Ti, Fe 2000 Jcm−

The electro-magnetothermal effect is summarized in Figure5 for a copper sphere with a diameter of 100 µm and current density of 60 kA/cm2 (6 108 A/m2) under a discharge time of 50 ms. The effect × of the neck growth was investigated for contact areas of 154.94 and 754.77 µm2. The boundary conditions were similar to those for the SPS model under a significantly increased current density. The analysis of current density distribution is presented in Figure5a,b. The current flows from top to bottom following the curvature of the particles, and it was subjected to the neck constriction effect. Analysis of temperature distribution (Figure5c,d) suggests an even temperature distribution because of the high thermal diffusivity of copper; in reality, a temperature increase at the interparticle contact point should be expected because of contact resistance effects (not accounted by the proposed model). The contact resistance has an inverse dependence on the pressure. Analysis of the magnetic field strength distribution (Figure5e,f) confirms strong magnetic e ffects at the interparticle contact point. The analysis of the Lorentz force distribution is presented using the arrows in Figure5e,f. The resulting Lorentz force includes a radial compressive component and Z-axis repulsive component, which tend to repel the particles from each other. The Z-component Lorentz force plays a significant role in the molten metal ejection, and its color mapping distribution is shown in Figure5g,h. This phenomenon has some analogies with the repulsion generated in metal wire explosion. It is even more commonly seen in welding as described in Ref. [38] In welding, this effect can be reduced by controlling the welding force, preventing the formation of a molten phase. The magnetic forces are expected to be more significant for when paramagnetic copper is replaced with iron (diameter of the particles was 100 µm). The current density at the maximum cross-section through the copper powder was set at 60 and 200 kA/cm2 for iron. Figure6 shows the contribution of the Z-axis for iron, where the Lorentz force reached the peak value of 321 N/mm3, far greater than the 9.65 N/mm3 for copper. This level of force is enough to affect the shape of the particle under such high current density. The proposed model requires some experimental validation. For example, Guyot et al. [39] investigated the microscopic particle surface morphology on electrical discharge copper spheres with a diameter of 50 µm. Their results evidence the formation of molten droplets on the spheres possibly because of the Lorentz Force. In order to validate such an hypothesis, we employed 5 mm copper spheres, as shown in Figure7. Metals 2020, 10, 1653 12 of 16

Metals 2020, 10, x FOR PEER REVIEW 12 of 17

FigureFigure 5.5. ComparisonComparison ofof electro,electro, thermal,thermal, andand magneticmagnetic eeffectsffects forfor 100100µ μmm coppercopper spheresphere dischargeddischarged underunder aa currentcurrent densitydensity ofof 6060 kAkA/cm/cm22,, withwith thethe firstfirst columncolumn forfor smallsmall contactcontact areaarea andand secondsecond columncolumn forfor largelarge contact contact area area (154.94 (154.94 and and 754.77 754.77µ μmm22,, respectively).respectively). ((aa)) CurrentCurrent densitydensity distributiondistribution graphgraph forfor smallsmall contactcontact (peak(peak currentcurrent densitydensity waswas 7.597.59 ×10 101010 AA/m/m22) andand ((bb)) largelarge contactcontact areaarea (peak(peak currentcurrent × densitydensity was was 2.45 2.45 ×10 101010 A/mA/m2). The The temperature temperature distribution graph underunder ((cc)) smallsmall andand ((dd)) largelarge contactcontact × area.area. MagneticMagnetic fieldfield distributiondistribution withwith arrowsarrows indicatingindicating thethe LorentzLorentz forceforce forfor ((ee)) smallsmall contactcontact areaarea (peak(peak magnetic magnetic intensity intensity reached reached 0.13 0.13 T) andT) and for ( ffor) large (f) contactlarge contact area (peak area magnetic (peak magnetic intensity intensity reached 3 0.06reached T). Z-axis 0.06 T). component Z-axis component Lorentz forceLorentz contribution force contribution for (g) small for ( contactg) small area contact (max area of 9.65 (max N /ofmm 9.65) 3 andN/mm (h)3 for) and large (h) contactfor large area contact (max area of 1.08 (max N/ ofmm 1.08). N/mm3).

The boundary conditions were similar to those for the SPS model under a significantly increased current density. The analysis of current density distribution is presented in Figure 5a,b. The current flows from top to bottom following the curvature of the particles, and it was subjected to the neck constriction effect. Analysis of temperature distribution (Figure 5c,d) suggests an even temperature distribution because of the high thermal diffusivity of copper; in reality, a temperature increase at the interparticle contact point should be expected because of contact resistance effects (not accounted by the proposed

Metals 2020, 10, x FOR PEER REVIEW 13 of 17

model). The contact resistance has an inverse dependence on the pressure. Analysis of the magnetic field strength distribution (Figure 5e,f) confirms strong magnetic effects at the interparticle contact point. The analysis of the Lorentz force distribution is presented using the arrows in Figure 5e,f. The resulting Lorentz force includes a radial compressive component and Z-axis repulsive component, which tend to repel the particles from each other. The Z-component Lorentz force plays a significant role in the molten metal ejection, and its color mapping distribution is shown in Figure 5g,h. This phenomenon has some analogies with the repulsion generated in metal wire explosion. It is even more commonly seen in welding as described in Ref. [38] In welding, this effect can be reduced by controlling the welding force, preventing the formation of a molten phase. The magnetic forces are expected to be more significant for when paramagnetic copper is replaced with iron (diameter of the particles was 100 μm). The current density at the maximum cross- section through the copper powder was set at 60 and 200 kA/cm2 for iron. Figure 6 shows the contribution of the Z-axis for iron, where the Lorentz force reached the peak value of 321 N/mm3, far Metalsgreater2020, 10 than, 1653 the 9.65 N/mm3 for copper. This level of force is enough to affect the shape of the particle13 of 16 under such high current density.

FigureFigure 6. Lorentz 6. Lorentz force force z-axis z-axis contribution contribution ( a(,ab,b)) and andmagnetic magnetic fieldfield distribution (c (c,d,d) )in in the the case case of of 2 2 coppercopper (60 kA(60/ kA/cmcm ) in2) thein the first first column column and and iron iron in in the the second second columncolumn (200 kA/cm kA/cm2).). Metals 2020, 10, x FOR PEER REVIEW 14 of 17

The proposed model requires some experimental validation. For example, Guyot et al. [39] investigated the microscopic particle surface morphology on electrical discharge copper spheres with a diameter of 50 μm. Their results evidence the formation of molten droplets on the spheres possibly because of the Lorentz Force. In order to validate such an hypothesis, we employed 5 mm copper spheres, as shown in Figure 7.

Figure 7. (a) Surface morphology of as-received 5 mm copper spheres. (b,c) Overall appearance Figure 7. (a) Surface morphology of as-received 5 mm copper spheres. (b,c) Overall appearance with optical microscope and SEM after application of a current of 15 kA/cm2 for 0.4 s. (d) Local appearance with optical microscope at a current 7.5 kA/cm2 for 0.6 s. (e,f) The Lorentz force contribution Z- component and the magnetic field strength distribution were simulated using a current of 15 kA/cm2 for 0.4 s, the Lorentz force peak value was 15.7 N/mm3, and the peak magnetic field strength was 1.16 T.

Figure 7a shows the surface of the copper ball before application of an electric current, and the surface was smooth. Figure 7b,c show the overall morphology of bonded particles after application of a 15 kA/cm2 discharge for 0.4 s. The two copper balls were bonded together well at the contact position. Surprisingly, there are many protrusions on the surface of the copper ball that might originate by the molten material being ejected due to the Lorentz force. Figure 7d shows a similar observation when using a current of 7.5 kA/cm2 for 0.6 s. Figure 7e,f map the Lorentz force and magnetic distribution, and the peak value was iron at 15.7 N/mm3, which is sufficient to promote molten metal ejection under a high current density [40]. The Joule heat generated by the high current softens or even partially melts the copper spheres at their interparticle contact. At the same time, the high current produces strong magnetic effects, and the liquid copper is ejected from the neck under the action of the repulsive Lorentz force, resulting in the formation of molten droplets, which reprecipitated on the spheres.

Metals 2020, 10, 1653 14 of 16

with optical microscope and SEM after application of a current of 15 kA/cm2 for 0.4 s. (d) Local appearance with optical microscope at a current 7.5 kA/cm2 for 0.6 s. (e,f) The Lorentz force contribution Z-component and the magnetic field strength distribution were simulated using a current of 15 kA/cm2 for 0.4 s, the Lorentz force peak value was 15.7 N/mm3, and the peak magnetic field strength was 1.16 T. Figure7a shows the surface of the copper ball before application of an electric current, and the surface was smooth. Figure7b,c show the overall morphology of bonded particles after application of a 15 kA/cm2 discharge for 0.4 s. The two copper balls were bonded together well at the contact position. Surprisingly, there are many protrusions on the surface of the copper ball that might originate by the molten material being ejected due to the Lorentz force. Figure7d shows a similar observation when using a current of 7.5 kA/cm2 for 0.6 s. Figure7e,f map the Lorentz force and magnetic distribution, and the peak value was iron at 15.7 N/mm3, which is sufficient to promote molten metal ejection under a high current density [40]. The Joule heat generated by the high current softens or even partially melts the copper spheres at their interparticle contact. At the same time, the high current produces strong magnetic effects, and the liquid copper is ejected from the neck under the action of the repulsive Lorentz force, resulting in the formation of molten droplets, which reprecipitated on the spheres.

6. Conclusions This article analyzed the possible role of magnetic fields on electric current-assisted processing. The first section surveyed these effects considering the Biot–Savart Law, skin effect, AC resistance change in the vicinity of the Curie temperature, proximity effect, pinch effect, and reactance dependence on duty cycle. By using finite element simulation, we could determine the safe distance (i.e., exclusion zone from the current conductor) for the operator. The second section simulates the magnetic field distribution at the tooling level (punch/die/sample assembly) during spark plasma sintering of the materials with variable electrical conductivity and different magnetic permeability. The same analysis was carried out at the interparticle level in the case of copper and iron spherical particles. The model was experimentally validated using 15 kA/cm2 for 0.4 s, where the molten droplet ejection was correlated with the strong repulsive Lorentz force acting on the molten copper. The results suggest that magnetic-related effects cannot be neglected when using ferromagnetic materials, when using extremely large currents. Further investigation should be dedicated to pulsing and frequency-related effects and how to exploit magnetic-related effects.

Author Contributions: S.G. contributed to the conception of the study. H.D. and S.G. performed the data analyses and wrote the manuscript. J.D., F.B. and T.S. contributed significantly to analysis and manuscript preparation. C.H. helped perform the analysis with constructive discussions. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: This work was supported by the Thousand Talents Program of China and Sichuan Province. Conflicts of Interest: The authors declare no conflict of interest.

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