A previously developed unified model of a tungsten-inert gas (TIG) microarc has been extended to take into account the melting of the anode made of copper and the release of copper atoms due to its evaporation. The copper atoms enter the plasma to become excited and ionized. The presence of copper atoms and ions can strongly change the plasma parameters. The extended unified model further includes excited states of copper and collisional and radiative processes between them. Predictions of the parameters of the microarc plasma in the presence of copper species are presented and discussed

Baeva, Margarita

Methling, Ralf

Uhrlandt, Dirk

English

CTU Open Journal Systems (Czech Technical University, Prague / České vysoké učení technické v Praze)

doi:10.14311/ppt.2021.1.1Plasma Physics and Technology 8(1):1–4, 2021 © Department of Physics, FEE CTU in Prague, 2021UNIFIED MODELLING OF TIG MICROARCS WITH EVAPORATIONFROM COPPER ANODEM. Baeva∗, R.Methling, D. UhrlandtLeibniz Institute for Plasma Science and Technology, Felix-Hausdorff-Strasse 2, 17489 Greifswald, Germany∗ baeva@inp-greifswald.deAbstract. A previously developed unified model of a tungsten-inert gas (TIG) microarc has beenextended to take into account the melting of the anode made of copper and the release of copperatoms due to its evaporation. The copper atoms enter the plasma to become excited and ionized. Thepresence of copper atoms and ions can strongly change the plasma parameters. The extended unifiedmodel further includes excited states of copper and collisional and radiative processes between them.Predictions of the parameters of the microarc plasma in the presence of copper species are presentedand discussed.Keywords: unified, non-equilibrium, modelling, microarc, metal vapour.1. IntroductionMicroarcs as scaled down but still powerful heatsources can represent alternatives to electronbeams and lasers. They are applied for additive(re)manufacturing and material processing, e.g. inmicroarc welding, production of bioactive coatings.Microarcs are attractive objects for basic research,in which knowledge of the spatial structure of thearc is gained and evaluated for consideration in arcplasma models, which do not resolve the regions ofspace charge. A fluid model in atmospheric pressureargon [1] has been recently developed to provide aspatial resolution over the entire inter-electrode region,i.e. a unified non-equilibrium description of the mi-croarc. The study of the microarc plasma carried outin the work [1] has been further extended to explorethe potentials and limitations of one-dimensional incomparison to two-dimensional models [2] and thebehaviour of the microarc plasma towards a minus-cule discharge gap [3]. The present work considersthe extension of the description that takes into ac-count evaporation of the anode, which leads to thepresence of metal vapour in the microarc plasma. Weoutline the extended chemistry and present resultsshowing the influence of the metal vapour releasedfrom the melting anode on the plasma parameters.The predicted emission of metal atoms will enablecomparisons with experimental findings.2. Computational methodThe computational model considers a parallel-plateconfiguration, including an anode made of copper anda ceriated tungsten cathode with a radius of 2mmand a length of 20mm. The inter-electrode gap has alength of 400µm and contains argon at atmosphericpressure. The model is set up as one-dimensional(1D) in order to reduce the computational cost inmaking use of high level of plasma chemistry. It isbased on the equations for conservation of species andenergy, the Poisson equation for the electric potential,the heat transfer in the electrodes, and an electriccircuit used to control the current density. Detailsof the model, except for the account for evaporationand the metal vapour in the plasma, have been givenpreviously [1]. In what follows, we focus on the newfeatures related to the presence of metal vapour. Thefeatures concerning the argon species remain the sameas in reference [1].The unified model of the microarc employs a fluiddescription that involves electron, ground state atomsand ions of argon and copper, a group of excited ar-gon atoms (4s, 4p), excited levels of copper 4s2 2D5/2,4s2 2D3/2, 42P1/2, 42P3/2, and groups of excited lev-els (4P0, 4D0, 4F0), (52P1/2, 52P3/2, 42D3/2, 42D5/2)according to [4]. Doubly charged copper ions arenot included in the model, since the second ioniza-tion potential of copper of 20.29 eV lies quite abovethe first ionization potential of argon. The cross sec-tions for electron impact excitation and ionization,and rate coefficients for collisions between species ofargon and copper are taken from [4] and the refer-ences therein. 11 radiative transitions between copperstates are taken into account. A self-absorption forthe resonance transitions at 324.7 nm and 327.4 nmis taken into account in terms of space-independenteffective lifetimes [5]. All other transitions are treatedas optically thin.The heavy species are in equilibrium at a commontemperature T while the electrons are described as-suming a Maxwellian velocity distribution at a temper-ature Te. The unified model implies the drift-diffusionapproximation in the description of the electron trans-port. It solves the equations for conservation of speciesand energy of electrons and heavy particles, the Pois-son equation for the self-consistent electric field, theheat transfer in the electrodes. The control of thedensity of electric current is realized by considering1M. Baeva, R. Methling, D. Uhrlandt Plasma Physics and Technologyan external electric circuit with a ballast resistor anda voltage source. Gas flow and self-induced magneticfield are not considered for low currents.The boundary conditions to the microarc model con-cerning the plasma and the cathode are those reportedin [1]. While in previous works a fixed temperatureof 300K is set on the plasma edge to the anode, herewe consider the anode as a cylindrical rod made ofcopper, whose length of 100mm is much larger thanits radius of 2mm and we solve the heat transfer inthe anode body. In the case of no volume source(Joule heating is neglected since the current is low)the equation readsAsρCp∂T∂t+∇ · qs = 0. (1)In Equation (1), As is the cross section area of theanode, ρ is the mass density, and Cp is the specificheat capacity at constant pressure of the anode ma-terial. qs = −Asκ∇T is the heat flux due to heatconduction and κ is the heat conductivity of the ma-terial. Considering the model in 1D along the axis x,the boundary condition of Eq. (1) at the end, whichis not in contact with the plasma, is set as T=300K.The the boundary condition on the side with contactto the plasma is written asκdTdx = qa − LJvapmv. (2)On the r.h.s. in Eq. (2), the first term qa denotesthe heat flux from the plasma, the second term de-scribes the heat loss due to evaporation with Jvapbeing the flux of evaporated copper atoms with amass mCu. Similarly to the heat flux from the plasmato the cathode given in [1], the flux qa is written asqa = ji,Ar+(Eion,Ar −ΦCu) + ji,Cu+(Eion,Cu −ΦCu)+ 14nevth,e(2kBTe + eΦCu)− εCuσSBT4w (3)and accounts for recombination of singly charged ionsof argon and copper, a flux of electrons from theplasma and their condensation in the anode, and ablack-body radiation. ji,Ar+ and ji,Cu+ are the ioncurrent densities of respectively argon and copper ions,Eion,Ar and Eion,Cu are the corresponding ionizationpotentials, ΦCu – the work function of copper (Eion,Ar,Eion,Cu and ΦCu are expressed in units of Volt), kB –the Boltzmann constant, e is the elementary charge,σSB - the Stefan-Boltzmann constant, and εCu – theemissivity of copper.The flux Jvap is obtained applying the Langmuirequation [6]Jvap = pCu/√2πmCukBTw, (4)in which pCu denotes the equilibrium pressure of themetal vapour at temperature of the wall Tw.pCu = 133.3[Pa]T−1.27w 1013.39−17656/Tw . (5)The latent heat of evaporation L is expressed throughthe boiling Tb and critical Tc temperatures [6]:L ={L0(Tc − Tw)/(Tc − Tb) if Tw > TbL0 if Tw ≤ Tbwith L0=4.73MJ/kg, Tb=2868K, Tc=5421K.Provided the temperature for melting Tm=1356K isreached, the anode material undergoes a phase change.The latter is accounted for in solving Eq.(1) by meansof the method of apparent heat capacity. Accordingto this method, a phase transition function α(T ) isintroduced to enable a smooth transition between thesolid and liquid phases within a given interval ∆Taround the temperature of phase transition Tm. Theheat capacity of the two phases in this interval isexpressed as Cp = Cp,s(1− α) + Cp,lα. For the solidwe set α = 0 and for the liquid α = 1. The latent heatof fusion Hf is further included as an additional termto Cp, i.e. Cp readsCp = Cp,s(1− α) + Cp,lα+HfdαdT . (6)When copper vapour can be released from the anode,the mass flux Jvapmv serves as a boundary conditionfor the equation describing the transport of groundstate copper atoms, which are excited and ionized,and undergo collisions with argon species.3. Results and discussionWhen the anode is kept at constant temperature of300K, the microarc plasma contains only species ofargon. The plasma properties of a microarc with alength of 400µ m in pure argon have been analyzedin a previous work [3].Figure 1 shows the predicted temperature, Ta, onthe anode end, which is in contact with the plasmaand the voltage Varc for several values of the currentdensity. Additional lines mark the levels correspond-ing to the melting (Tm) and boiling (Tb) temperatures.The Ta-values obtained for current densities between3×105 and 5.8×105 A/m2 are located between themarked levels so that copper atoms released from theanode are expected to influence the plasma parame-ters. For example, the microarc voltage Varc increasesin comparison to the case of a cooled anode (shown assolid symbols) for the Ta values presented in Fig. 1.Figure 2 shows the distribution of the gas tem-perature T and the electron temperature Te in thedischarge gap. Distance x = 0 corresponds to the posi-tion of the anode, while the cathode is at x = 400 µm.The electron temperature is presented for x from380 µm up to 400 µm (see the scale on the top ofthe graph) in order to enlarge the peak in the cath-ode space charge sheath. The results are obtained atcurrent density of about 5.8×105 A/m2. When theanode is not cooled, the gas temperature on the anodeside increases, while it decreases in the remaining partof the arc column. The electron temperature in the2vol. 8 no. 1/2021 Unified modelling of TIG microarcsFigure 1. Temperature on the anode surface Ta andarc voltage Varc versus current density. Solid symbolscorrespond to the case of cooled cathode (pure argonplasma).Figure 2. Gas temperature T (squares) and electrontemperature Te (circles) for current density 5.8×105A/m2. Solid symbols correspond to the case of cooledcathode (pure argon plasma).cathode sheath significantly increases in comparisonto pure argon plasma.Figure 3 shows the predicted number densities ofelectrons, argon and copper ions, and copper atoms ata current density of 5.8×105 A/m2. In the case of pureargon plasma (cooled anode), the electron density neis balanced by the density of argon ions nAr+ in thequasineutral bulk of the microarc. When the anode isnot cooled, the electron number density ne increasesin comparison to the value in pure argon plasma fordistances from the anode up to about 50 µm. In thisregion, the quasineutrality in the plasma bulk is pro-vided by the nCu+ number density. This effect can beexplained with the strong production of copper atomsand their low ionization potential. The number den-sity of argon ions nAr+ becomes progressively morenoticeable towards the cathode. The profile of theelectron density significantly changes in comparisonto pure argon. Its values are lower by a factor above 2in the middle of the gap. An increase of nCu in frontof the cathode is observed, which is related to therecombination of copper ions and deactivation of ex-Figure 3. Species number densities for current density5.8×105 A/m2: electrons ne (squares), ions nAr+ (cir-cles), ions nCu+ (triangles), atoms nCu (diamonds).Solid symbols correspond to the case of cooled cathode(pure argon plasma).Figure 4. Ratios of atom number densities nCu/nAr(solid symbols and scale on the left side) and ion num-ber densities nCu+/nAr+ (open symbols and scale onthe right side) for current density 5.8×105 A/m2cited atoms on the cathode. Figure 4 shows the ratiosof atom and ion densities, nCu/nAr and nCu+/nAr+ ,on the anode side of the microarc (x < 150 µm). Wenotice that nCu/nAr has a value of 0.37 at the anodeand decreases rapidly to about 0.1 within a distance of10µm from the anode. However, the number densityof copper ions exceeds that of argon ions over thesedistances by several orders of magnitude. This occursdue to the lower ionization potential of copper atoms(7.72 eV) in comparison with that of ground state ar-gon atoms (15.76 eV). In addition, the excited copperatoms at and above level 42P1/2 with an ionizationpotential below 4 eV are easier ionized than the groupof excited states of argon.Estimates of the thickness of the space-chargesheaths adjacent to the anode and the cathode areperformed according to the definition by Tonks andLangmuir. The edge between the quasineutral bulkand the space-charge sheath is defined at the positionx, where (ni − ne)/ni=0.01. This gives at a currentdensity of 5.7×105 A/m2 a thickness of the anode3M. Baeva, R. Methling, D. Uhrlandt Plasma Physics and TechnologyFigure 5. Spectral emission coefficient along the dis-tance x for spectral lines of the copper atom consideredin the model for a current density of 5.7×105 A/m2.sheath of about 2.4µm in pure argon and 1.26µmin the presence of copper species. The thickness ofthe cathode space-charge sheath slightly increases toabout 13µm in presence of copper since the main in-fluence of copper species is on the anode side of themicroarc. However, the magnitude of the cathode fallincreases by about 15V if the anode is not cooled.This gives rise to the increase of the electron temper-ature (see Fig. 2). The anode fall becomes -2.55V inthe presence of copper instead of -4.3V in pure argon.Figure 5 presents the axial dependence of the spec-tral emission coefficient for spectral lines originatingfrom excited states of Cu atoms considered in themodel. The spectral emission coefficient is given asε(λij , x) =14πhcλijAijni(x), (7)where h is the Plank constant, c is the speed of light,Aij is the probability of the radiative transition atwavelength λij from level i to level j, and ni(x) is thenumber density of species on level i. The radiationfrom copper atoms occurs mostly close to the anodesurface, where the electron density and copper atomdensity are largest (see Fig. 3). Then, the reaction ratefor excitation of copper atoms, which is proportional totheir product, becomes largest. A secondary increaseappears in front of the cathode, which is related tothe peak of the electron temperature (see Fig. 4).Since the 1D model presumes that uniform plasmain radial direction, the values at a given distance xare proportional to the radial radiance that can becompared with results from "side-on" measurements.Such comparison has been done in a recent studyon plasma between copper electrodes [7], where agood agreement of the model predictions and theexperimental findings has been found.The large length of the anode considered in thepresent model is beneficial for reaching temperaturesbeyond the melting point of copper and the release ofcopper metal vapour. In the practice, the thicknessof the anode, whose back surface is kept at 300K bywater-cooling, and the temperature on the plasmaside are related. The maximum temperature reachedon the plasma side increases with the anode thicknessdue to decrease of the temperature gradient. Modelpredictions can therefore be useful to obtain the onsetof melting.4. ConclusionsThe thermal regime of the anode influences the param-eters of the microarc plasma. The model presentedpredicts that a copper anode with a length of 100mmand a radius of 2mm melts for a current density be-yond 3×105 A/m2. The release of copper vapour intothe plasma leads to a shift and an increase of themaximum electron and ion densities towards the an-ode. The evaporation of copper atoms progressivelyincreases with the current density. For temperaturesclose to the boiling point, a noticeable amount of cop-per atoms and ions is predicted. Their influence isrestricted to a distance from the anode, which is lessthan the half length of the gap.AcknowledgementsThe work was funded by the Deutsche Forschungsgemein-schaft (DFG, German Research Foundation) - projectnumber 390828847.References[1] M. Baeva, D. Loffhagen, and D. Uhrlandt. Unifiednon-equilibrium modelling of tungsten-inert gasmicroarcs in atmospheric pressure argon. Plasma Chem.Plasma Process., 39:949–968, 2019.doi:10.1007/s11090-019-10020-x.[2] M. Baeva, D. Loffhagen, and D. Uhrlandt. Unifiedmodelling of non-equilibrium microarcs in atmosphericpressure argon: potentials and limitations of one-dimensional models in comparison to two-dimensionalmodels. Japanese Journal of Applied Physics,59:SHHC05, 2020. doi:10.35848/1347-4065/ab71da.[3] M. Baeva, D. Loffhagen, M. M. Becker, E. Siewert, andD. Uhrlandt. Plasma parameters of microarcs towardsminuscule discharge gap. Contrib. Plasma Phys.,60:e202000033, 2020. doi:10.1002/ctpp.202000033.[4] A. Bogaerts, R. Gijbels, and R. Carman. Collisional -radiative model for the sputtered copper atoms and ionsin a direct current argon glow discharge. SpectrochimicaActa Part B, 53:1679–1703, 1998.doi:10.1016/S0584-8547(98)00201-8.[5] Y. Golubovskii, S. Gorchakov, D. Loffhagen, andD. Uhrlandt. Influence of the resonance radiationtransport on plasma parameters. Eur. Phys. J. Appl.Phys., 37:101–104, 2007. doi:10.1051/epjap:2006150.[6] M. S. Benilov, S. Jacobsson, A. Kadani, and Z. S.Vaporization of a solid surface in an ambient gas. J.Phys. D: Appl. Phys., 34:1993–1999, 2001.doi:10.1088/0022-3727/34/13/310.[7] M. Baeva, V. F. Boretskij, D. Gonzalez, R. Methling,O. Murmantsev, D. Uhrlandt, and A. Veklich. Unifiedmodelling of low-current short-length arcs betweencopper electrodes. J. Phys. D: Appl. Phys., 54:025203,2021. doi:10.1088/1361-6463/abba5d.4

Unified modelling of TIG microarcs with evaporation from copper anode

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Unified modelling of TIG microarcs with evaporation from copper anode

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