Impact of the Samples' Surface State on the Glow Discharge Stability In

applied sciences

Article Impact of the Samples’ Surface State on the Glow Discharge Stability in the Metals’ Treatment and Welding Processes

Maksym Bolotov 1,* , Gennady Bolotov 1, Serhii Stepenko 2 and Pavlo Ihnatenko 3

1 Department of Welding Technologies and Construction, Chernihiv Polytechnic National University, 95 Shevchenko Str., 14035 Chernihiv, Ukraine; [email protected] 2 Department of Electrical Engineering and Information Measuring Technologies, Chernihiv Polytechnic National University, 95 Shevchenko Str., 14035 Chernihiv, Ukraine; [email protected] 3 Department of Machine Building and Wood Processing Technologies, Chernihiv Polytechnic National University, 95 Shevchenko Str., 14035 Chernihiv, Ukraine; [email protected] * Correspondence: [email protected]; Tel.: +380-633353906

Abstract: The low temperature plasma of glow discharge has found a widespread use as a heating source in welding and surface treatment of metals. The meticulous analysis of glow discharge’s instabilities in these processes allowed us to highlight the physicochemical characteristics of the cathode surface (the welded or treated samples) as one of the main reasons of its transition into an electric arc—as a more stable form of gas discharges. The prolonged arc action on the samples surfaces inevitably leads to the disruption of the technological process and, consequently, to undesirable overheating of samples. In this regard, the main aim of this work is to study the inﬂuence of the macro- and micro relief of the cathode on the stable glow discharge existence in the processes of metals treatment and diffusion welding. It has been analytically established and experimentally supported that the glow discharge’s stability is mainly affected by the sharp protrusions generated Citation: Bolotov, M.; Bolotov, G.; on the cathode surface because of samples pre-treatment by machining before welding. It has been Stepenko, S.; Ihnatenko, P. Impact of µ the Samples’ Surface State on the established that the rough surface pre-treatment with the Rz about 60–80 m decreases the pressure Glow Discharge Stability in the range of glow discharge sustainable existence from 1.33–13.3 kPa to 1.33–5.3 kPa compared with the Metals’ Treatment and Welding surface machining with the Rz about 10 µm. Processes. Appl. Sci. 2021, 11, 1765. https://doi.org/10.3390/app11041765 Keywords: diffusion welding; plasma; glow discharge; surface treatment; plasma techniques

Academic Editors: Alessandro Belardini and Mariusz Jasiński 1. Introduction Received: 10 December 2020 Nowadays, to obtain qualitative permanent joints of heterogeneous materials the Accepted: 10 February 2021 methods of welding in a solid state are widely used. The most prevalent of these is a Published: 17 February 2021 diffusion bonding. The wide nomenclature of compounds creates a complex of specific requirements for diffusion bonding’s energy sources. These requirements are mainly related Publisher’s Note: MDPI stays neutral to the acceptability of a wide range of materials and shapes of products, the accuracy of with regard to jurisdictional claims in the specific heat capacity control and the ability of the wide regulation of the sample’s published maps and institutional affil- iations. temperature [1]. The distributed plasma of a glow discharge burning in a rarefied gas atmosphere at a pressure of 0.1–10 kPa is widely used in processes accompanied by the direct action of charged electric particles on the treated or welded materials. Known works consider the possibility of application of gas discharges technique in the field of thin films deposition, Copyright: © 2021 by the authors. metals surfacing, treatment and modification of metals before welding [2–5]. Still, as Licensee MDPI, Basel, Switzerland. practice has shown, diffusion welding [6] and thermal and chemical-thermal surface This article is an open access article treatment [7] are the most appropriate. This is due to the high technological capabilities distributed under the terms and conditions of the Creative Commons of the glow discharge, which in these processes can serve both a processing tool and a Attribution (CC BY) license (https:// source of thermal energy for their implementation simultaneously. Additionally, a glow creativecommons.org/licenses/by/ discharge has high technical, economic, and environmental indicators, for instance, high 4.0/).

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heatingheating productivity,productivity, energy energy savings, savings, and and last last but but not not least least the the absence absence of of environmental environmental pollutionpollution [[8].8]. However,However, during during surfacesurface treatmenttreatment or or welding welding of of metals, metals, the the instabilities instabilities of of samples samples temperaturetemperature (discharge(discharge cathodecathode inin thesethese processes),processes), thethe pressurepressure ofof thethe working working gas, gas, the the voltagevoltage ofof thethe powerpower supply,supply, andand a number of other factors, can can lead lead to to the the transition transition of of a aglow glow discharge discharge into into another another form form of ofgas gas discha discharge—anrge—an electric electric arc arc [9] [(Figure9] (Figure 1).1 In). Inthis thiscase, case, the thedistributed distributed glow glow discharge discharge transforms transforms into intoa contracted a contracted form. form. Its cathode Its cathode spot spotnarrows narrows to a tovery a very small small size, size, increasing increasing the energy the energy concentration concentration dramatically. dramatically. A pro- A prolongedlonged action action of ofa concentrated a concentrated arc arc discharge discharge inevitably inevitably leads leads to to the locallocal meltingmelting andand destructiondestruction ofof samples.samples.

(a) (b)

FigureFigure 1. 1.The The view view of of the the glow glow discharge discharge on on the the cathode cathode surface surface in stablein stable (a) and(a) and unstable unstable (b) burning(b) burning modes modes during during the ion the ion treatment (the bright spots to the right—arc breakdowns). treatment (the bright spots to the right—arc breakdowns).

TheThe probabilityprobability of arcing increases with with the the rising rising of of the the total total and and specific specific power power of ofthe the discharge. discharge. The The energy energy characteristics characteristics of the of the ionic ionic treatment treatment processes processes are aremainly mainly de- determinedtermined by by the the magnitude magnitude of of the the discharge discharge current current and and the gas pressure inin thethe workingworking chamber.chamber. TheThe developmentdevelopment ofof processes’processes’ productivityproductivityleads leadsto tothe thenecessity necessityof of increasing increasing theirtheir values. values. That, That, in in turn, turn, entails entails rising rising of of average average current current density density (j) in(j) thein the cathode cathode spot spot of theof the discharge discharge and and the averagethe average specific specific volumetric volumetric power power (jE) in(jE) the in discharge the discharge plasma plasma [10]. However,[10]. However, with increasing with increasing of discharge of discharge energy characteristicsenergy characteristics in the interelectrode in the interelectrode gap, the short-termgap, the short-term local arc breakdowns local arc breakdowns with a duration with ofa duration one or two of half-periodsone or two ofhalf-periods the rectified of currentthe rectified can form current (Figure can2 form). (Figure 2). Appl. Sci. 2021, 11, 1765 3 of 12

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(а)

(b)

Figure 2. Oscillogram ofof thethe discharge discharge current current in in stable stable (a )(a and) and unstable unstable (b) ( mode.b) mode. (Glow (Glow discharge discharge current current 4 A. Oscillograms4 A. Oscillo- gramswere recorded were recorded from a from shunt a ofshunt 3 Ohm of 3 connected Ohm connected to the dischargeto the discharge circuit). circuit).

InIn [11,12], [11,12], the glowglow discharge’sdischarge’s instabilities instabilities are are closely closely associated associated with with its its contraction contraction(compression) (compression) and transitionand transition to a cord to forma cord of form discharge of discharge with the increasingwith the increasing of volumetric of volumetricpower (jE) accordingly.power (jE) Theaccordingly. gas in the The cord gas discharge in the heatscord updischarge extremely heats while up the extremely burning whilevoltage the decreases burning andvoltage eventually decreases the and cord eventual switcheslyinto the cord an arc switches electric. into Such an a arc mechanism electric. Suchof glow a mechanism discharge’s of instability glow discharge’s is associated instability with volumetricis associated processes with volumetric in positive processes column inof positive the discharge column plasma, of the and discharge therefore plasma, is more and characteristic therefore ofis extendedmore characteristic discharges of of ex- the tendedlaser type discharges [13], where of the the laser length type of [13], the where interelectrode the length gap of is the 0.5–1.0 interelectrode m. In the gap processes is 0.5– 1.0of ionm. treatmentIn the processes and welding of ion oftreatment metals, aand stationary welding DC of glowmetals, discharge a stationary burns DC between glow dischargethe electrodes burns with between a limited the electrodes distance of with 0.005–0.05 a limited m. distance In these of conditions, 0.005–0.05 processes m. In these in conditions,the near-electrode processes regions in the of near-electrode the discharge regions can affect of the negatively discharge its can stability. affect Thenegatively largest itsvoltage stability. drop The (100–300 largest V) voltage and the drop greatest (100–300 electric V) ﬁeldand the strength greatest accordingly electric field are observedstrength accordinglyin the cathode are region observed of the in discharge the cathode where region there of are the the discharge processes ofwhere electron there ionization are the processesand multiplication of electron which ionization determine and multiplication the glow discharge which existence.determine Thesethe glow processes discharge are existence.affected by These conditions processes both are in affected the volume by co ofnditions the cathode both layer in the and volume on the of surface the cathode of the layercathode and itself. on the They surface are quite of the fully cathode investigated itself. They and are described quite fully in [14 investigated–16]. However, and they de- scribeddo not considerin [14–16]. the impactHowever, of the they cathode do not surface consider characteristics the impact on of the the stability cathode of thesurface glow characteristicsdischarge while on surfacethe stability treatment of the and glow welding discharge of metals,while surface which treatment makes it impossible and welding to ofdetermine metals, andwhich establish makes their it impossible optimal values to determine from the pointand establish of view of their process optimal productivity values fromand dischargethe point of stability. view ofIn process this regard, productivity the aim and of thisdischarge work isstability. to study In thethis effect regard, of the aimphysicochemical of this work characteristicsis to study the ofeffect the samplesof the physicochemical surface on the stability characteristics of a glow of dischargethe sam- plesand thesurface development, on the stability on this of basis, a glow of technologicaldischarge and recommendations the development, for on the this selection basis, of technologicalvalues of the moderecommendations parameters that for ensurethe selectio the stablen of values discharge of the existence mode parameters while diffusion that ensurewelding the and stable metals discharge treatment. existence while diffusion welding and metals treatment.

2. Methods The main physicochemical characteristics of the metals surface includes its macro- and micro relief, as well as the presence of chemical compounds on it. Even after ma- Appl. Sci. 2021, 11, 1765 4 of 12

Appl. Sci. 2021, 11, x FOR PEER REVIEW2. Methods 4 of 12 The main physicochemical characteristics of the metals surface includes its macro- and chining,micro relief, the surface as well asof thethe presencevast majority of chemical of structural compounds metals on is it.covered Even afterwith machining, a thin layer the of naturalsurface ofoxide. the vastOxide majority films are of structural not ideal metalsdielectrics, is covered but they with possess a thin layer a certain of natural conductiv- oxide. ity.Oxide The films resistivity are not (ρ ideal) of most dielectrics, oxide films but they of the possess processed a certain metals conductivity. (Fe, Cu, Mo, The W, resistivity Ti, etc.) is(ρ )10 of3–10 most5 Ohm oxide m, films and ofthe the characteristic processed metals value (Fe,of the Cu, dielectric Mo, W, Ti, constant etc.) is 10is 3ε–10 ≈ 2–105 Ohm [17]. m, Therefore,and the characteristic from an electro-technical value of the dielectric point of constant view, an is εoxide≈ 2–10 film’s [17]. capacitance Therefore, fromand re- an sistanceelectro-technical are connected point ofin view,parallel. an oxideThe capaciti film’s capacitanceve properties and of resistancethe film appear are connected at times int0 −8 −6 −8 −6 ≤parallel. εε0ρ ≈ 3 The(10 capacitive–10 ) sec [18]. properties The maximum of the film electric appear field at strength times t0 due≤ εε to0ρ the≈ accumulation3 (10 –10 ) ofsec charge [18]. Theon the maximum oxide film electric over this field time strength is defined due toas the accumulation of charge on the

oxide film over this time is defined as t 1 0 E ≈≈jdt jp, (1) εε t0 1 Z0 0 E ≈ jdt ≈ jp, (1) where j—the current density at the cathodeεε0 of the discharge. 0 In a normal glow discharge, the gas pressure in the working chamber determines the currentwhere j —thedensity current in the density cathode at spot the cathodeand at the of pressures the discharge. of 1.33–13.3 kPa it can reach 102– 103 A/mIn a2. normalThus, in glow a normal discharge, DC glow the discharges gas pressure at pressures in the working characteristic chamber ofdetermines technolog- icalthe currentprocesses density of metal in thetreatment cathode and spot welding, and at thethe pressureselectric field of 1.33–13.3may not reach kPa it the can values reach of10 2the–10 electric3 A/m2 field. Thus, strength in a normal breakdown DC glow for thin discharges oxide films. at pressures As it was characteristic mentioned ofin tech-[16], thenological heating processes of the oxide of metal films treatmentto a 1200 K and leads welding, to a rapid the decrease electric fieldof its mayresistivity not reach (four the to sixvalues orders of theof magnitude). electric field Therefore, strength breakdown taking into for account thin oxide the simultaneous films. As it was heating mentioned of the filmsin [16 together], the heating with ofthe the samples oxide films and the to a noticeable 1200 K leads decline to a rapidin the decrease film resistance of its resistivity with increasing(four to sixof ordersthe temperature, of magnitude). the Therefore,emergenc takinge of arcing into accountbreakdown the simultaneous is unlikely. heatingConse- quently,of the films the presence together withof an theoxide samples film on and the thesurface noticeable of the cathode decline in(product) the film can resistance make a massivewith increasing impact ofon the the temperature, discharge’s the stability emergence but ofonly arcing on breakdownthe cold cathodes. is unlikely. With Conse- the heatingquently, of the cathode, presence this of factor an oxide becomes film on unimportant. the surface of the cathode (product) can make a massiveThe impactnext parameters on the discharge’s characterizing stability the but st onlyate of on the the cathode cold cathodes. surface With are theits heatingmacro- andof cathode, microrelief. this factorIn this becomes case, the unimportant. glow discharge’s stability can be affected with the pro- nouncedThe nextroughness parameters protrusions characterizing obtained the after state machining, of the cathode but surface not with are itsthe macro- smoothly and changingmicrorelief. surface In this waviness. case, the glow Figure discharge’s 3 shows stabilityprofile curves can be affectedof the sample’s with the surfaces pronounced ob- tainedroughness after protrusionstreatment with obtained a roughness after machining, of 60–80 µm but (Figure not with 3a) and the about smoothly 10 µm changing (Figure 3b),surface respectively. waviness. For Figure this purpose,3 shows a profile profilometer curves TR of—200 the sample’s was used. surfaces obtained af- µ µ ter treatmentThe external with view a roughness of the device of 60–80and treatemd (Figure samples3a) themselves and about are 10 shownm (Figure in Figure3b), respectively. For this purpose, a profilometer TR—200 was used. 4.

(a)

Figure 3. Cont. Appl. Sci. 2021, 11, 1765 5 of 12

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(b)

Figure 3.3. TheThe proﬁleprofile curvescurves ofof thethe samplessamples surfacessurfaces obtainedobtained afterafter machiningmachining byby rotationalrotational turningturning withwith thethe roughnessroughness about 80 µm (a) and 10 µm (b): 1 - single placed; 2 - ridge-shaped protrusions. about 80 µm (a) and 10 µm (b): 1—single placed; 2—ridge-shaped(b) protrusions.

Figure 3. The profile curves of theThe samples external surf viewaces ofobtained the device after andmachining treated by samples rotational themselves turning with are the shown roughness in Figure 4. about 80 µm (a) and 10 µm (b): 1 - single placed; 2 - ridge-shaped protrusions.

(a)

(b) (b) Figure 4. The view of a profilometer TR-200 (a) which is made up of: 1- display; 2- control panel; 3- sensor (pickup) and FiguretreatedFigure 4.samples The4. The view view(b). of of a proﬁlometera profilometer TR-200 TR-200 (a ()a which) which is is made made up up of: of: 1—display; 1- display; 2- 2—control control panel; panel; 3- 3—sensor sensor (pickup) (pickup) and and treated samples (b). treated samples (b). The undergoing intense ions bombardment, the protrusions heat up much more noticeablyThe undergoing than the bulk intense of the ions electrode bombardment, (cathode). the This protrusions inevitably heat leads up to much the superheat more point’snoticeably emergence than the bulkon the of thecathode electrode surface (cathode). to temperatures This inevitably exceeding leads to the the superheat melting or point’s emergence on the cathode surface to temperatures exceeding the melting or Appl. Sci. 2021, 11, 1765 6 of 12

The undergoing intense ions bombardment, the protrusions heat up much more noticeably than the bulk of the electrode (cathode). This inevitably leads to the superheat point’s emergence on the cathode surface to temperatures exceeding the melting or boiling point of the metal. In this case, a glow discharge can transit to the local vapor arcs [19,20]. This can be observed most likely in case when the surface of the protrusions is large enough to provide heating to high temperatures, and the heat transfer to the bulk of the samples is too small.

3. The Analytical Equation of a Glow Discharge Energy Stability while Treatment and Welding of Metals Depending on Cathode Surface State Cylinders, cones or hemispheres can be taken as a model of individual micro protrusions [21]. The possibility of their heating to a boiling point is provided:

qs = qν − qT, (2)

where qs—the energy perceived by the surface of the protrusion from ions bombarding the cathode: qs = SjUct (where S—the area of the lateral surface of the protrusion, Uc—the cathodic potential drop in the discharge, t—time); qv—the heat content of the protrusion material at the boiling point: qν = VcγTboil (where V—the protrusion volume, c—the heat capacity of the metal, and γ—the density); and qT—the energy diverted from the protrusion −1 R into the sample: qT = 2πλRT[1 − er f 4at ] , (where λ—the thermal conductivity of the cathode material, R—the radius of the protrusion base, and T—the cathode surface temperature). In the processes of thermal ion treatment and diffusion welding, when the temperature of the samples is much lower than the boiling point of metal, condition (2) is feasible if qT → 0. In order to neglect the heat transfer to the samples, the value of t must be the same order as the glow discharge’s transition time into the arc t = 10−4–10−6 sec. So, then

qs = qνorSjUct = VcγTboil, (3)

In this case, for the micro relief of structural steels, it is necessary that the S/V ratio is 105–107 cm−1 (where S—the area of the lateral surface of the protrusion and V—the protrusion volume). Nevertheless, even at t = 1 sec, it is necessary that the value of S/V ≥ 102 cm−1. Such ratios of the surface and volume of the micro protrusion are possible only for thin protrusions and burrs. For real surfaces machined by turning or grinding, this ratio is much less than one, which indicates a low probability of fulfilling condition (2). Hence it follows that at the cathode’s current densities corresponding to a glow discharge (up to 103 A/m2), the probability of melting and evaporation of the roughness ridges is pretty small. This limits the possibility of thermionic emission from their vertices. At the same time, sharp protrusions on the cathode surface creates the local distortions of the electric field nearby the cathode surface. Electric field distortions near the protrusions facilitates the attraction of positive ions toward them and as a result, the active points with the increased charges concentration are formed. This, in turn, leads to dramatic increase in the electric field strength in these regions. The length of this region (dc) is determined by the cathode material as well as kind and pressure (p) of the working gas, and can be found from the ratio: pdc = c, (4) where c—a constant value for particular gas and its pressure (for a glow discharge burning in a nitrogen, c = 0.42 Pa m [22]). At a nitrogen pressure of 1.33–13.3 kPa, the average electric field strength near the discharge cathode is

Uc Eav = , (5) dc

where Uc is the cathode potential drop, which is 215 V for a glow discharge in nitrogen. Appl. Sci. 2021, 11, 1765 7 of 12

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6 7 In these conditions, the Eav reaches up to 10 –10 V/m. A further increase in the electric field. A noticeable field emission current, sufficient for the existence of an arc electric field strength inevitably leads to the appearance of a current of field electron discharge, appears at the electric field strength of about 109 V/m. In this regard, it is ad- emission from the tip of the protrusion due to the ejection of electrons from the surface by visable to assess the degree of influence of the protrusions surface roughness on a local a strong electric field. A noticeable field emission current, sufficient for the existence of an increase in the electricarc field discharge, strength appears at the atcathode the electric of a glow field strengthdischarge. of Meanwhile, about 109 V/m. the In this regard, it is magnitude of the fieldadvisable strength to assessdoes not the depe degreend ofon influence the number of the of protrusionsprotrusions, surface but on roughness on a local their size and shape.increase in the electric field strength at the cathode of a glow discharge. Meanwhile, the In mechanical magnitudeengineering, of thethe fieldsurface strength machining does not of depend samples on of the the number third—sixth of protrusions, but on their class of cleanliness issize widely and shape. used. In this case, the maximum height of the surface protrusions varies, respectively,In mechanical from Rz = engineering, 40–80 to 6–10 the µm. surface Since machining the height of of samples the micro of the third—sixth class protrusion is much ofless cleanliness than the interelectrode is widely used. gap In (of this 0.01 case, m theor more), maximum for calculation height of the of surface protrusions electric field of suchvaries, protrusion respectively, the electr fromostatics Rz = 40–80 task tohas 6–10 beingµm. solved Since theabout height the ofcon- the micro protrusion is ductive ellipsoid in muchan external less than field the parallel interelectrode to one of gap the (of main 0.01 axes m or of more), the ellipsoid for calculation [23]. of electric field of This is an equivalentsuch to a protrusion semi-ellipsoidal the electrostatics protrusion task on one has beingof the solvedflat electrodes, about the or conductive to ellipsoid in the gap between twoan electrodes external field parallel parallel to ea toch one other of the (Figure main axes5) which of the exceeds ellipsoid protru- [23]. This is an equivalent sion height. If the x tois the a semi-ellipsoidal axis of the protrusi protrusionon in the on form one of of a the semi-ellipsoid flat electrodes, of rotation or to the gap between two perpendicular to theelectrodes electrode, parallelwhere x to= 0, each then other the field (Figure strength5) which on the exceeds extension protrusion of this height. If the x is axis when x is greaterthe than axis the of theheight protrusion of the protrusion in the form h is of [22]: a semi-ellipsoid of rotation perpendicular to the electrode, where x = 0, then the field strength on the extension of this axis when x is greater cc− than the height ofarth the protrusion h is [22]: =−xx + 1 Ex() Eav  (1 ) , (6) cc" ccx2 x # arth − −−c − c ()(1)arth arth x 2 x 1 E(x)hh = Eav (1 − hhc) + c , (6) arth c − c ( c − c )( x2 − ) x h h arth h h c2 1 c where Еav is the average electric field strength created in the cathode region of a glow discharge by a cathodicwhere potentialEav is thedrop; average c—half electric the distance field strength between createdthe ellipsoid in the focuses cathode region of a glow discharge by a cathodic potential drop; c—half the distance between the ellipsoid focuses located on the x axis (Figure 5), determined, according to [24], as = –. √ located on the x axis (Figure5), determined, according to [24], as c = a2–b2.

Figure 5. Scheme of a Figuresemi-elliptical 5. Scheme protrusion of a semi-elliptical on the surface protrusion of a flat on cathode: the surface a, b ofare a flatthe cathode:semi a, b are the semi axes axes of the ellipsoid; h—the height of the protrusion; dc—the length of the cathodic potential drop of the ellipsoid; h—the height of the protrusion; dc—the length of the cathodic potential drop region. region. The term in square brackets in this expression describes the field strength increasing The term in squaredue tobrackets the presence in this ofexpression a protrusion. describes Denote the it field by β Estrength, then the increasing expression (6) can be written due to the presence asof Ea (protrusion.x) = Eav βE. Denote The term it by in β parenthesesЕ, then the expression of expression (6) can (6) isbe always written less than one and on as Е(х) = Еav βЕ. The theterm surface in parentheses of the protrusion of expression at x = h(6)vanishes. is always Therefore, less than theone main and ison the second term, the the surface of the protrusionvalue of whichat x = h is vanishes maximum. Therefore, at minimum the main x, i.e., isat thex =secondh and term, at the thex = dc simultaneously. value of which is maximumFigure4 shows at minimum the dependence x, i.e., at x of = theh and field at enhancementthe x = dc simultaneously.βE on the ratio h/dc. Expression Figure 4 shows the dependence(6) describes of an the increase field enhancement in the field strength βЕ on the on ratio a flat h/d smoothс. Expression cathode from a protrusion (6) describes an increasehaving in athe smooth field strength peak with on a a considerable flat smooth radius.cathode For from a hemisphericala protrusion protrusion having having a smooth peakthe with same a semiconsiderable axes a = b,ra thedius. field For enhancement a hemispherical is β Eprotrusion≈ 3 [25]. The having results of calculating βE the same semi axes afrom = b, expressionthe field enhancement (6) for surface is β protrusionsЕ ≈ 3 [25]. The in theresults form of of calculating semi-ellipsoidal βE extended along from expression (6) thefor surface x-axis are protrusions shown in in Figure the form6. The of graphsemi-ellipsoidal also shows extended that, depending along on the degree of the x-axis are shownprotrusions in Figure 6. elongation, The graph the also electric shows field that, enhancement depending on at the their degree apex canof reach up to 10–30. protrusions elongation, the electric field enhancement at their apex can reach up to 10–30. Appl. Sci. 2021, 11, x FOR PEER REVIEW 8 of 12

In practice, after machining protrusions are formed on the surface, having an acute-angled shape, with a radius at the apex within the unit fractions of micrometers (Figure 3). The acute-angled protrusions contribute dramatically to a more intense electric field distortions and an additional increase in its intensity nearby the protrusion. Such an increase in electric field strength can be estimated by the coefficient [21]: h μ = , (7) r Appl. Sci. 2021, 11, 1765 8 of 12 where h—the height of the protrusion; r—the curvature radius on the peak of the protrusion.

Figure 6. The dependenceFigure 6. The of the dependence field enhancement of the field on the enhancement cathode surface on the on cathodethe ratio surfaceof the pro- on the ratio of the trusion’s heightprotrusion’s and the length height of the and cathodic the length potent of theial drop cathodic region: potential 1- ratio drop a/b = region: 4; 2- ratio 1—ratio a/b = a/b2. = 4; 2—ratio a/b = 2. For protrusions with a height of 20–40 µm or more with a radius of vertex curvature from fractions to unitsIn practice, of micrometers after machining (Figure protrusions3), the value are of formedµ can reach on the up surface, to µ ≥ having10. an acute- Then the fieldangled strength shape, near withthe vertices a radius of at such the apexprotrusions within thewill unit be fractions of micrometers (Figure3 ). The acute-angled protrusions contribute= βμ dramatically to a more intense electric field distor- Ex() Eav E , (8) tions and an additional increase in its intensity nearby the protrusion. Such an increase in Under conditionselectric field of increased strength cangas bepressure, estimated the by boundary the coefficient of the [21region]: of cathodic potential drop declines sharply and approaches the vertices of micro protrusions h roughness x = dc ≈ h. As a result, the local field strengthµ near= , the vertices of such protru- (7) sions can reach E(x) ≥ 109 V/m. Such values of the local electricr field strength provide for a current densitywhere of fieldh—the emission height from of the the protrusion; peak of ther—the protrusions curvature of radius jfe ≥ 10 on7 theA/m peak2, suffi- of the protrusion. cient for an arc breakdownsFor protrusions exciting with in athe height interelectrode of 20–40 µ gapm or [26]. more The with latter a radius is in many of vertex curvature orders higherfrom than fractionsthe current to unitsdensity of micrometersin the cathode (Figure spot 3of), thethe valueglow ofdischarge.µ can reach It is up to µ ≥ 10. suggested thatThen in these the field conditions strength the near Joule’ thes vertices heating of and such evaporation protrusions of will the bevertices of the protrusions entail the arc breakdowns [27]. In this case, condition (2) can already be fulfilled, i.e., the probability of melting and evaporationE(x) = E ofav βprotrusionsEµ, increases dra- (8) matically. In turn, the latter contributes to the development of thermionic emission from these areas with theUnder arc formation conditions on of the increased surface of gas the pressure, cathode the spot boundary of an arc of discharge. the region of cathodic As was mentionedpotential above drop the declines long-term sharply action and of approachesa stable arc thedischarge vertices on of a micro surface protrusions of the roughness x = d ≈ h. As a result, the local field strength near the vertices of such protrusions can reach samples can lead toc their melting and destruction. E(x) ≥ 109 V/m. Such values of the local electric field strength provide for a current density Hence, for the prevention of a glow discharge transition into an electric arc, the of field emission from the peak of the protrusions of j ≥ 107 A/m2, sufficient for an arc length of the cathodic potential drop must exceed the maximum heightfe of the roughness breakdowns exciting in the interelectrode gap [26]. The latter is in many orders higher protrusions. The cleanliness class of the samples surface treatment determines this. than the current density in the cathode spot of the glow discharge. It is suggested that The adequacy of this assumption has been checked under conditions of ion treat- in these conditions the Joule’s heating and evaporation of the vertices of the protrusions ment in a glow discharge in a nitrogen. The cylindrical c with dimensions of 20 × 60 mm entail the arc breakdowns [27]. In this case, condition (2) can already be fulfilled, i.e., the made of steel A 659 CS Type 1020 (cathode of discharge simultaneously) were used. The probability of melting and evaporation of protrusions increases dramatically. In turn, the glow discharge was powered from a controlled full-wave rectifier with an output voltage latter contributes to the development of thermionic emission from these areas with the arc of 0–1000 V through a ballast resistor of 80 Ohm. The discharge current was of 4 A. A flat formation on the surface of the cathode spot of an arc discharge. As was mentioned above annular anode located at a distance of 0.008 m from the cathode surface was used as the the long-term action of a stable arc discharge on a surface of the samples can lead to their second dischargemelting electrode and destruction. (Figure 7). Hence, for the prevention of a glow discharge transition into an electric arc, the length of the cathodic potential drop must exceed the maximum height of the roughness protrusions. The cleanliness class of the samples surface treatment determines this. The adequacy of this assumption has been checked under conditions of ion treatment in a glow discharge in a nitrogen. The cylindrical c with dimensions of 20 × 60 mm made of steel A 659 CS Type 1020 (cathode of discharge simultaneously) were used. The glow discharge was powered from a controlled full-wave rectifier with an output voltage of 0–1000 V through a ballast resistor of 80 Ohm. The discharge current was of 4 A. A flat Appl. Sci. 2021, 11, 1765 9 of 12

annular anode located at a distance of 0.008 m from the cathode surface was used as the Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 12 Appl. Sci. 2021, 11, x FOR PEER REVIEW second discharge electrode (Figure7). 9 of 12

Figure 7. The schematic view of experiments: 1- treated samples (cathode); 2- anode ring; 3- plasma Figure 7. The schematic view of experiments: 1- treated samples (cathode); 2- anode ring; 3- plasma ofFigure glow 7.discharge;The schematic dc- the viewlength of of experiments: the cathode potential 1—treated drop. samples (cathode); 2—anode ring; 3— of glow discharge; dc- the length of the cathode potential drop. plasma of glow discharge; dc—the length of the cathode potential drop. The steel samples obtained by rough, semi-finishing and finishing had the height of The steel samples obtainedthe surfaceThe by steel rough,roughness samples semi-f protrusions obtainedinishing byand of rough, finishing60–80, semi-finishing 30–40, had theand height 10–15 and of finishingµm accordingly. had the During height the surface roughness protrusionstreatment,of the surface a ofgradual roughness60–80, increase 30–40, protrusions andin gas 10–15 pressure of 60–80,µm accordingly.in 30–40, the working and During 10–15 chamberµ m accordingly. was performed. During treatment, a gradual increasetreatment,As in gasthe a pressure gradualcriteria increaseofin theglow working in discharge gas pressure chamber stability, in was the performed. workingthe limiting chamber pressure was performed.at which the As the criteria of short-termglowAs discharge the arcs criteria at thestability, of interelectrode glow the discharge limiting gap stability, emerpressurege thedeveloping, at limiting which pressure apparentlythe at whichfrom the the tops short- of short-term arcs at the interelectrodetheterm highest arcs at or thegap most interelectrodeemer sharpge developing, protrusions gap emerge apparently was developing,chos en.from A thefurther apparently tops rising of fromof a gas the topspressure of the is the highest or most sharpaccompaniedhighest protrusions or most by was sharpan chosincrease protrusionsen. A in further the frequenc was rising chosen. yof of a gasmicroarc A furtherpressure discharges rising is of aformation gas pressure until isa accompanied by an increasestableaccompanied inelectric the frequenc arc by is an established increasey of microarc in in the the discharges frequency discharge offormationgap. microarc The cathode until discharges a (products) formation temperature until a stable electric arc is establishedwhilestable electrictreatment in the disc arc was isharge established 700–1000 gap. The inK. cathode the The discharge cathod (products)e’s gap. temperature temperature The cathode was (products) measured temperature with the while treatment was 700–1000whilechromel-alumel treatment K. The thermocouplecathod was 700–1000e’s temperature at K. three The differen cathode’swas measuredt points temperature in with the axialthe was direction measured and withthen the chromel-alumel thermocoupleresultschromel-alumel atwas three averaged. differen thermocouple Thet points view atin of threethe treatment axial different direction by points stable and in glowthen the axial thedischarge direction and and in thenthe mo- the results was averaged. Thementsresults view of was arcingof averaged.treatment breakdowns The by viewstable (blurred of glow treatment by discharge flar bye and stable and multitude glowin the discharge mo-of micro-arcs) and in are the shown moments in ments of arcing breakdownsFigureof arcing (blurred 8. breakdowns by flare (blurredand multitude by flare of and micro-arcs) multitude are of micro-arcs)shown in are shown in Figure8. Figure 8.

(a) (b) (a) (b) Figure 8.8. The visualized scheme of treatment in a stable (a)) andand disturbeddisturbed (b) byby aa multiplemultiple micro-arcsmicro-arcs breakdownbreakdown glow Figure 8. The visualized scheme of treatment in a stable (a) and disturbed (b) by a multiple micro-arcs breakdown glow discharge. discharge. The experimental results are shown in Figure 9 in the form of a curve corresponding The experimental resultsto the averagedare shown over in Figure the results 9 in the of forma number of a curve of measurements, corresponding the limiting values of gas to the averaged over thepressure results ofdepending a number on of themeasurements, parameters ofthe th limitinge surface values relief. of Here gas along with the dimen- pressure depending on the parameters of the surface relief. Here along with the dimen- Appl. Sci. 2021, 11, x FOR PEER REVIEW 10 of 12

Appl. Sci. 2021, 11, 1765 sions of the roughness protrusions, the values of the extent of the cathodic potential10 ofdrop 12 region corresponding to the gas pressures are given. The obtained results indicate that the glow discharge’s instabilities really begin to appear when the boundary of the cathodic potential drop region (dc) approaches the The experimental results are shown in Figure9 in the form of a curve corresponding vertices of the micro protrusions. A glow discharge remains stable at gas pressures below to the averaged over the results of a number of measurements, the limiting values of gas the obtained experimental curve. Knowing the samples surface characteristics in the form pressure depending on the parameters of the surface relief. Here along with the dimensions of the Rz = Rmax quantity, enables to determine the gas pressure boundary values for the of the roughness protrusions, the values of the extent of the cathodic potential drop region various technological processes of ion treatment or diffusion bonding, as well, in ad- corresponding to the gas pressures are given. vance.

FigureFigure 9. 9.The The experimentalexperimental dependencedependence ofof thethe workingworking gas pressure ((P)P) on the surface roughness roughness parameters (Rz) according to the conditions of glow discharge stability: (dc—cathodic potential parameters (Rz) according to the conditions of glow discharge stability: (dc—cathodic potential drop drop region). region).

4. ConclusionsThe obtained results indicate that the glow discharge’s instabilities really begin to appearIt whenis shown the that boundary the low of temperature the cathodic plasma potential of DC drop glow region discharge (dc) approaches which burns the in verticesthe active ofthe or microinert gases protrusions. at the Amedium glow discharge pressures remains is the perspective stable at gas source pressures of surface below theheating obtained in the experimental processes of curve. diffusion Knowing bonding the samples and ion surfacetreatment characteristics of metals. At in thethe formsame oftime, the Rza number = Rmax of quantity, factors on enables the cathode to determine surface the can gas emerge, pressure which boundary leads to values the transition for the variousof a glow technological discharge processesinto an electric of ion arc treatment as a more or diffusion stable form bonding, of gas as discharges. well, in advance. In this study, the impact of macro and micro relief of the samples on the stability of a glow 4.discharge Conclusions while diffusion bonding and treatment of metal has been analyzed and ana- lyticalIt is equation shown that of a the glow low discharge temperature energy plasma stability of DC glowboundary discharge has been which obtained. burns in theThe activemain orconclusions inert gases of at this the study medium can pressuresbe summarized, is the perspective as follows: source of surface heating in the processes of diffusion bonding and ion treatment of metals. At the same time, a 1. The emergence of oxide films on the surfaces of specimens during welding or metals number of factors on the cathode surface can emerge, which leads to the transition of a treatment does not lead to a significant disruption of a glow discharge stability as glow discharge into an electric arc as a more stable form of gas discharges. In this study, long as electrical field strength does not exceed the breakdown values. the impact of macro and micro relief of the samples on the stability of a glow discharge

while2. On diffusion the other bonding hand, and the treatment roughness of of metal a cathode’s has been surface analyzed affects and analyticalthe glow equationdischarge of a glowstability discharge at the energy working stability gas pressures boundary when has beenthe height obtained. of the The protrusions main conclusions roughness of this studybecomes can becomparable summarized, to the as length follows: of the cathode potential drop region dc. 3. The direct dependence of the dc length on the gas pressure allows to determine the 1. The emergence of oxide films on the surfaces of specimens during welding or metals limit values of the latter based on the given characteristics of the samples surface treatment does not lead to a significant disruption of a glow discharge stability as microrelief which ensures the stable glow discharge existence during ion treatment long as electrical field strength does not exceed the breakdown values. and welding of metals. In our experiments the increase of the cathode surface 2. On the other hand, the roughness of a cathode’s surface affects the glow discharge roughness from 10–15 µm to 60–80 µm led to a rapid decrease of the region of the stability at the working gas pressures when the height of the protrusions roughness limiting pressure of the stable glow discharge existence from 1.33–13.3 kPa to a 1.33– becomes comparable to the length of the cathode potential drop region d . 5.3 kPa, respectively. c 3. The direct dependence of the dc length on the gas pressure allows to determine the limit values of the latter based on the given characteristics of the samples surface Author Contributions: G.B.: conceptualization and methodology.; M.G.: experiments, results val- idation,microrelief formal analysis, which ensureswriting—original the stable draft glow preparation; discharge existenceS.S.: literature during review, ion treatmentmain glow discharge’sand welding instabilities of metals. related In with our surface experiments state of the cathode, increase writing—review of the cathode and surface editing; rough- P.I.: ness from 10–15 µm to 60–80 µm led to a rapid decrease of the region of the limiting Appl. Sci. 2021, 11, 1765 11 of 12

pressure of the stable glow discharge existence from 1.33–13.3 kPa to a 1.33–5.3 kPa, respectively.

Author Contributions: G.B.: conceptualization and methodology; M.B.: experiments, results val- idation, formal analysis, writing—original draft preparation; S.S.: literature review, main glow discharge’s instabilities related with surface state of cathode, writing—review and editing; P.I.: in- vestigation, data curation, getting profilograms. All authors have read and agreed to the published version of the manuscript. Funding: This research is supported by the Ministry of Education and Science of Ukraine (Grant 0117U007259 “New high-tech energy-efficient heating source for precision welding, brazing and surface treatment of metals”). Conflicts of Interest: The authors declare no conflict of interest.

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