DESCRIPTION 'OF TUNGSTEN TRANSPORT PROCESSES IN HALOGE~ INCANDESCENT LAMPS *)

Transcription

1 Philips J. Res. 38, , 1983 R 1072 DESCRIPTION 'OF TUNGSTEN TRANSPORT PROCESSES IN HALOGE~ INCANDESCENT LAMPS *) by E. SCHNEDLER Philips GmbH Forschungslaboratorium Aachen, 5100 Aachen, Germany Abstract In this paper the radial separation of chemically reactive gases in halogen lamps due to concentration and thermal diffusion is treated. A numerical procedure is described which allows to calculate the radial partial pressure distribution including the influence of condensed phases at the filament and at the bulb. The program allows to predict the behaviour of lamps, e.g. blackening or deposition of condensed compounds. Some examples of the calculations are reported, the W-O-CI system, the W-H-Br system and the W-CI system with the reaction of tungsten chloride with the silica bulb. 1. Introduetion In a preceding paper 1) the influence of diffusion and thermal diffusion on the radial and axial transport in an inert gas lamp has been discussed. It was shown that thermal diffusion is of importance for radial tungsten transports in inert gas lamps. From this result it was concluded that thermal diffusion might influence the distribution of reactive gases in halogen lamps. In the following sections of this report the radial separation of the chemically reactive gases in a halogen lamp due to diffusion and thermal diffusion will be discussed. A numerical procedure will be described which allows to calculate the radial partial pressure distribution including the influence of condensed phases at the filament and at the bulb. The program therefore may be a tool to predict the behaviour of lamps during operation, e.g. blackening or deposition of condensed compounds, and the influence of getter materialon the gas composition may be evaluated. Parts of this work have been sponsored by Bundesministerium under Grant No. 03E4120A. für Forschung und Technologie 236 Phlllps Journol of Research Vol.38 Nos 4/5 1983

2 " Description of tungsten transport processes in halogen incandescent lamps As the intention of this report is to show the meaning of the different transport processes only a few examples of the calculations are reported, namely the W-O-Cl-system, the W-H-Br-system and the W-Cl-system including the reactions of tungsten chloride with the silica bulb. In the following sections the notation of ref. lis used. 2. Halogen lamps 2.1. Mass transport in incandescent lamps with chemically reacting 'systems For the calculation of transport rates in incandescent lamps the composition of the chemically reacting gases at the filament has to be known. Even for this simple model of a radial symmetric cylinder lamp this composition is not the same everywhere in the lamp volume. Due to different diffusion and thermal diffusion coefficients there will be a separation of the reactive gases. In halogen incandescent lamps generally the concentrations of the reactive gases are small, c ~ 1. Therefore the heat production due to chemical reactions is small, i.e. the heat transport by chemical reactions is negligible in comparison to thermal conduction. The temperature distribution given in sec. 2.l.a of ref. 1 therefore is also applicable to the stagnant gas layer of halogen incandescent lamps. Due to the chemical reactions particles of a compound j can be generated and destroyed, we therefore have to fulfil for the current of speciesj, instead of eq. (18) of ref. 1, see 2,3) V. ij = kaj) TI c?, - kr(j) q 1=1 I=q+l n TI c?, (1) with i= 1... N (2) and v» klu), kru) number of atoms of type i in the compoundj, kinetic coefficients of-the forward respectively backward reactions (eq. (2) again neglects convection terms). The conservation of atoms in the diffusion region demands V Ij = 0, i = 1... m (3) Phllips Journalof Research Vol.38 Nos 4/

3 E. Schnedler with (4) j=l the index i defines the atomic constituents of a chemical system. Eq. (1) contains the kinetic coefficients of the forward and backward reaction. But these data are riot yet known for the chemical reactions, which are occurring in incandescent lamps, nor are there any chances for their calculation. The most common approximation to overcome these difficulties is to assum~ chemical equilibrium due to diffusion limited transport processes and fast chemical reactions, Le. it is assumed that both right hand terms of eq. (1) are very large as compared with the left hand side diffusion term. Then forward and backward reaction are nearly compensating and eq. (1) results in the law of mass action m Cj = Kc(T,j). IT C? [=1 The resulting system of equations consists of eq. (3) for m atomic species in the lamp volume, the definition eq. (4) with the N currents eq. (2), and the chemical equilibrium condition eq. (5). Together with the following boundary conditions a and b the system has a unique solution: a) for not condensing gas phase species I mi PI J cj(r) Vji dyer) = Ni (6) m, KB T(r) j Ni = number of atoms of species i, and b) for condensed phases, the partial pressure of the gas is determined by the vapour pressure of the condensed phase Finite difference equations Due to the law of mass action (5) the system of partial differential equations is highly non linear. Thus a numerical solution procedure has to be developed. For numerical calculations it seems to be more convenient to use partial pressures instead of concentrations (5) (7) 238 Philips Journalof Research Vol.38 Nos 4/5 1983

4 Description of tungsten transport processes in halogen incandescent lamps For the calculation of the radial separation by diffusion and thermal diffusion of the different particles a finite differenceprocedure has been developed. When assuming that the filament has a stagnant, rotational symmetric gas layer, the radius of this layer is divided into NP-l equidistant sections. The NP dividing points include the filament radius rl as the first and the bulb radius (resp. Langmuir radius 4» rb as the last one. Using (7) the diffusion equation (3) reads (8) with m Pi = K p(t,j)npt JI 1=1 (9) The balance equations (8) are transformed into a set of finite difference equations for the partial pressures at the NP-node points. At the boundary node points rl and rb vapour pressures of the present condensed phases are inserted for the partial pressures of the corresponding gas phase compounds.. The resulting systemof equations which has to be solved by application of eq. (9) represents a system of nonlinear equations with a high number of variables. A simultaneous solution is impossible due to the large number of unknowns. As the coupling of the variables via the law of mass action at one point is much stronger than the coupling with the variables at neighbouring points via the diffusion equations, the system has to be solved pointwise simultaneously, satisfying the law of mass action eq. (9), and iteratively satisfying the diffusion eq. (8). Assuming the same amount of chemical reactive gases, in the whole volume as starting condition, a new partial pressure distribution is calculated for each node point from the pressures at the next neighbour points. This is performed by solving eq. (8) together with eq. (9) by a numerical procedure which will be described elsewhere 6). This procedure takes into account any condensed phases, which may occur at the boundary node points r/and re, i.e. the procedure inserts the vapour pressures for the corresponding gas phases at these points. The calculation of new partial pressures is performed point by point from rl to rb and reverse until convergence appears. This method guarantees for the correct calculation of chemically transported species. Philips Joumal nf Research Vnl. 38 Nns 4/

5 I ) '1 E. Schnedler 2.3. Filling condition and condensed phases After some iterations, the procedure described in the preceding section comes to convergence. Now we have to check whether the calculated partial pressure distribution agrees with the molar amounts of the elements enclosed in the bulb volume. This reads. ra ~ v..f Pj(r) dr = PfU) ~ JI T(r) 298K' j rr (10) whereby rg is the real bulb radius (which is in agreement with rb, if convection is neglected) and PfU) is the filling pressure of the atomic species i at room temperature. The check of eq. (10) is out of problems for those atomic species, which are not incorporated in any condensed phases (homogeneous constituent). The integration of eq. (10) can be performed e.g. by using Simpson's rule. For those atomic species, however, which are included in condensed phases, there may be different or even no condition (10). This problem can be overcome by simply taking into account the ratio of disproportionation of the condensed compounds besides eq. (10) (see ref. 5). If any of the homogeneous constituents does not fulfil eq. (10), a correction procedure is applied. The value of the partial pressures of the corresponding constituents are changed at one of the boundary nodes r» according to wheré PeU) is the left hand side of eq. (10) (11) rr (12) Pi is the new value of the partial pressure of the constituent and u is a underrelaxation factor, which is set u = 1 for the first correction. The calculation of the partial pressure distribution is repeated with the partial pressures of the homogeneous constituents kept constant at ri. After renewed convergence of the partial pressure run, the filling condition is checked again. For further calculation the underrelaxation factor u is computed according to 240 Philips Journolof Research Vol.38 Nos4/S 1983

6 ,---~-----,--, ~--~----""'-'--_._ ~ Description of tungsten transport processes in halogen incandescent lamps (13) where the values designed with an asterisk are those from the previous run, and g is an empirical constant. Thus u is a measure for the action of the performed correction. After some runs the filling condition will be satisfied within the desired exactness Operating pressure Using the equation of state of an ideal gas one obtains the following expression for the operating pressure Pea 21trG PI= 'o 298KJ~ rr T(r) (14) where PI is the operating pressure, and Pea is the inert gas pressure of the lamp at room temperature. 3. Results 3.1. Influence of thermal diffusion The intension of this report is to demonstrate the consequences of the transport processes, which take place in the diffusion layer of incandescent lamps. For inert gas lamps it was shown analytically that thermal diffusion is an effect which may not be neglected in transport calculations. A similar result is derived for halogen lamps, as figs 1 and 2 demonstrate. Fig. 1 shows the separation of the reactive gases in a radial symmetric lamp due to diffusion but neglecting thermal diffusion. One finds that the stoichiometric sum of the partial pressures N SP; = L Vj;Pj j=l (15) of the constituents chlorine, oxygen and tungsten is varying with a remarkable amount versus the temperature (resp. radius). The filling pressure of the cold lamp was chosen to bar Cls, bar O2, and 5 bar Argon. Phlllps Journalof Research Vol. 38 Nos 4/

7 E. Schnedler ell l---r-----r ,----r T (K) r (cm) Fig. 1. Separation effects due to concentration bar O 2, Argon. diffusion; a) = 0, filling pressures: bar Cl-, In contrast, fig. 2 shows the stoichiometrie sum of the partial pressures of the same lamp with the same filling as in fig. 1, but now including thermal diffusion effects. It is obvious that thermal diffusion is an important contribution to the transport processes in incandescent lamps. Due to this effect the total amounts of Cb and O2 at the filament are only one fifth of the amounts at the bulb. This effect has an essential influence upon axial transports in an incandescent lamp: the smaller amounts of solved tungsten at the incandescent wire affect the axial mass transport. Fig. 3 shows the details of the partial pressure distribution of the lamp discussed in fig. 2. It can be seen that the tungsten solubility at the bulb wall is maintained only by W02Cb. Even in the region near the filament tungsten is solved mainly in the form of oxygen containing high temperature compounds. 242 Phillps Journal uf Research Vul.38 Nus 4/5 1983

8 Description of tungsten transport processes in halogen incandescent lamps ,----, _--, T(K) Q Q r (cm) Fig. 2. Separation effects due to concentration ci., bar O2, Argon. and thermal diffusion, filling pressures: bar 3.2. Infiuence of oxygen on tungsten transports As another example fig. 4 shows the stoichiometrie sum of the partial pressures of an incandescent lamp filled with bar HBr, and Krypton. One finds that especially H2 is enriched in the bulb region, which may lead to an increased reduction of tungsten bromides. The details of the corresponding partial pressure distribution are given in fig. 5. One finds that the partial pressures of the tungsten bromides are below 10-5 bar at the bulb. The addition of 10-5 bar O 2 increases the partial pressures of the tungsten compounds about a factor 7 in the bulb region. This result is demonstrated in fig. 6, it shows that very small amounts of oxygen have a major effect on the tungsten solubility, which will result in a higher tungsten transport rate along the axis of the filament of a real lamp. Phllips Journalof Research Vol. 38 Nos 4/

9 E. Schnedler \ 10-5'~~~-.--~--.-~~ r------r------r T(K) Fig. 3. Partial pressure distribution corresponding to fig. 2, filling pressures: 2 10"-3 bar Cb, bar O 2, Argon T(K) Fig. 4. Separation effects due to concentration and thermal diffusion, filling pressures: bar HBr, Krypton. 244 Phlllps Journolof Research Vol.38 Nos 4/5 1983

10 Description of tungsten transport processes in halogen incandescent lamps -.. '- 0.Q.._ o:_... i 10-2 Brl -- _ r _ /,/ H2 -_ -- / /,/ 10-4.,/ / / / / / / / / / / HBr T (K) Fig. 5. Partial pressure distribution corresponding to fig. 4, filling pressures: bar HBr, Krypton. _.-._._. HBr»>: --._,/ /. / / / /. /. / / / /~- /./ _ H O <r,_ c:::: ' T(K) Fig. 6. Partial pressure distribution, filling pressures: 1.5 IO- s bar HBr, 10-6 bar 02, Krypton. Philips Journni of Research Vnl.38 Nns 4/

11 E. Schnedler 10-' ,------, , "'" ~ 10~+-----~----~'~~--~ I... o /\ ~ Cl. Cl / \ t !----!--+---_\_---1 // r {cm} 0.4 Fig. 7. Partial pressure distribution without the tungsten halide-silica reaction. filling pressures: bar Ch. Krypton Attack of silica at the bulb wal! Another feature of this program is that it is possible to consider condensed phases at the bulb radius as well as at the filament radius. This allows to calculate the influence of condensed compounds, such as bulb silica, and getters upon the chemical transport reactions. As example the influence of the bulb silica upon the W-CI system shall be demonstrated. Fig. 7 shows the partial pressure distribution in a radial symmetric lamp neglecting reactions with the bulb silica, filled with 5 bar Kr and bar Cl-. The partial pressures of the tungsten halides are about 10-5 bar. This calculation has been repeated taking into account the reactions of the tungsten halides with the silica of the bulb. The results are given in fig. 8. Additional gaseous compounds, as SiCl4 and W02Cb, appear in the bulb wall region. This result clearly demonstrates that the tungsten solubility cannot be 246 Phillps JournnI of Research Vol.38 Nos4/S 1983

12 ... M M.. Description of tungsten transport processes in halogen incandescent lamps 10-'.,------,------, , ~ " ,g 1O- 2.J------If ':>.if/:..._---l ';;, I \\ I 10~+-----~---/~-4~--\-~ // \ / \ I-f-----t \-j \ Cl SiCI4 CI j-..l..,L_~_,,_--I-~"--- :'---t--...t<...---~ _ r (cm) Fig. 8. Partial pressure distribution with the tungsten halide-silica reaction, filling pressures: bar C1 2, Krypton. remarkably increased by the reaction of tungsten chlorides with the silica bulb. Especially in the high temperature region near the filament no oxygen containing tungsten compounds can be detected which would increase the tungsten transport along the filament of a real lamp. Due to the results of this report one might guess that also axial separation effects are of importance for halogen incandescent lamps. This is subject of further research and the results will be reported elsewhere. REFERENCES 1) E. Schnedler, preceding paper in this volume. 2) L. D. Landau and E. M. Lifshitz, Lehrbuch der Theoretischen Physik, Bd. VI, Akademie- Verlag Berlin, ) S. R. de Groot and P. Mazur, Non-Equilibrium Thermodynamics, North Holland Publishing Co., Amsterdam, ) W. Elenbaas, Philips Res. Repts. 18, 147, ) E. Schnedler, The Calculation of Complex Chemical Equilibria, to be prepared. Phillps Journalof Research Vol. 38 Nos 4/