description 'of tungsten transport processes … bound... · description of tungsten transport...

Philips J. Res. 38, 236-247, 1983 R 1072

DESCRIPTION 'OF TUNGSTEN TRANSPORT PROCESSESIN HALOGE~ INCANDESCENT LAMPS *)

by E. SCHNEDLERPhilips GmbH Forschungslaboratorium Aachen, 5100 Aachen, Germany

AbstractIn this paper the radial separation of chemically reactive gases in halogenlamps due to concentration and thermal diffusion is treated. A numericalprocedure is described which allows to calculate the radial partial pressuredistribution including the influence of condensed phases at the filament andat the bulb. The program allows to predict the behaviour of lamps, e.g.blackening or deposition of condensed compounds. Some examples of thecalculations are reported, the W-O-CI system, the W-H-Br system andthe 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 onthe radial and axial transport in an inert gas lamp has been discussed. It wasshown that thermal diffusion is of importance for radial tungsten transports ininert gas lamps. From this result itwas concluded that thermal diffusion mightinfluence the distribution of reactive gases in halogen lamps. In the followingsections of this report the radial separation of the chemically reactive gases ina halogen lamp due to diffusion and thermal diffusion will be discussed. Anumerical procedure will be described which allows to calculate the radial par-tial pressure distribution including the influence of condensed phases at thefilament and at the bulb. The program therefore may be a tool to predict thebehaviour of lamps during operation, e.g. blackening or deposition of con-densed compounds, and the influence of getter materialon the gas composi-tion may be evaluated.

• Parts of this work have been sponsored by Bundesministerium für Forschung und Technologieunder Grant No. 03E4120A.

236 Phlllps Journol of Research Vol.38 Nos 4/5 1983

· "

q nV . ij = kAj) TI c?, - kr(j) TI c?,

1=1 I=q+l(1)

Description of tungsten transport processes in halogen incandescent lamps

As the intention of this report is to show the meaning of the different trans-port processes only a few examples of the calculations are reported, namelythe W-O-Cl-system, the W-H-Br-system and the W-Cl-system including thereactions 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 compo-sition of the chemically reacting gases at the filament has to be known. Evenfor this simple model of a radial symmetric cylinder lamp this compositionis not the same everywhere in the lamp volume. Due to different diffusionand thermal diffusion coefficients there will be a separation of the reactivegases.In halogen incandescent lamps generally the concentrations of the reactive

gases are small, c ~ 1. Therefore the heat production due to chemical re-actions is small, i.e. the heat transport by chemical reactions is negligible incomparison to thermal conduction. The temperature distribution given insec. 2.l.a of ref. 1 therefore is also applicable to the stagnant gas layer ofhalogen 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, insteadof eq. (18) of ref. 1, see2,3)

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 re-actions

(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 4/5 1983 237

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 re-

action. But these data are riot yet known for the chemical reactions, which areoccurring in incandescent lamps, nor are there any chances for their calcula-tion. The most common approximation to overcome these difficulties is toassum~ chemical equilibrium due to diffusion limited transport processes andfast 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 for-ward and backward reaction are nearly compensating and eq. (1) results in thelaw of mass action

m

Cj = Kc(T,j) . IT C?[=1

(5)

The resulting system of equations consists of eq. (3) for m atomic species inthe lamp volume, the definition eq. (4) with the N currents eq. (2), and thechemical equilibrium condition eq. (5). Together with the following boundaryconditions a and b the system has a unique solution:a) for not condensing gas phase species

I mi PI J cj(r)Vji - - -- dyer) = Nim, KB T(r)

(6)

j

Ni = number of atoms of species i,and

b) for condensed phases, the partial pressure of the gas is determined by thevapour pressure of the condensed phase.

2.2. Finite difference equations

Due to the law of mass action (5) the system of partial differential equationsis 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

(7)

238 Philips Journalof Research Vol.38 Nos 4/5 1983


For the calculation of the radial separation by diffusion and thermal diffu-sion of the different particles a finite differenceprocedure has been developed.

When assuming that the filament has a stagnant, rotational symmetric gaslayer, the radius of this layer is divided into NP-l equidistant sections. TheNP dividing points include the filament radius rl as the first and the bulbradius (resp. Langmuir radius 4» rb as the last one.

Using (7) the diffusion equation (3) reads

(8)

withm

Pi = Kp(T,j)nptJI•1=1

(9)

The balance equations (8) are transformed into a set of finite difference equa-tions for the partial pressures at the NP-node points. At the boundary nodepoints rl and rb vapour pressures of the present condensed phases are insertedfor 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 ofvariables. A simultaneous solution is impossible due to the large number ofunknowns.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 viathe diffusion equations, the system has to be solved pointwise simultaneously,satisfying the law of mass action eq. (9), and iteratively satisfying the diffusioneq. (8).Assuming the same amount of chemical reactive gases, in the whole volume

as starting condition, a new partial pressure distribution is calculated for eachnode point from the pressures at the next neighbour points. This is performedby solving eq. (8) together with eq. (9) by a numerical procedure which will bedescribed elsewhere 6). This procedure takes into account any condensedphases, which may occur at the boundary node points r/and re, i.e. the proce-dure inserts the vapour pressures for the corresponding gas phases at thesepoints.The calculation of new partial pressures is performed point by point from rl

to rb and reverse until convergence appears. This method guarantees for thecorrect calculation of chemically transported species.

Philips Joumal nf Research Vnl. 38 Nns 4/5 1983 239

ra

~ v ..f Pj(r) dr = PfU)~ JI T(r) 298K'j rr

(10)

I)

'1

E. Schnedler

2.3. Filling condition and condensed phases

After some iterations, the procedure described in the preceding sectioncomes to convergence. Now we have to check whether the calculated partialpressure distribution agrees with the molar amounts of the elements enclosedin the bulb volume. This reads .

whereby rG is the real bulb radius (which is in agreement with rb, if convectionis neglected) and PfU) is the filling pressure of the atomic species i at roomtemperature.

The check of eq. (10) is out of problems for those atomic species, which arenot incorporated in any condensed phases (homogeneous constituent). Theintegration of eq. (10) can be performed e.g. by using Simpson's rule. Forthose atomic species, however, which are included in condensed phases, theremay be different or even no condition (10). This problem can be overcome bysimply taking into account the ratio of disproportionation of the condensedcompounds 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 correspondingconstituents are changed at one of the boundary nodes r» according to

(11)

wheré PeU) is the left hand side of eq. (10)

(12)

rr

Pi is the new value of the partial pressure of the constituent and u is a under-relaxation factor, which is set u = 1 for the first correction.

The calculation of the partial pressure distribution is repeated with thepartial pressures of the homogeneous constituents kept constant at ri.

After renewed convergence of the partial pressure run, the filling conditionis checked again. For further calculation the underrelaxation factor u is com-puted according to

240 Philips Journolof Research Vol.38 Nos4/S 1983

,---~-----,--,-----------~--~----""'-'--_._-----..~


(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 per-formed correction.

After some runs the filling condition will be satisfied within the desiredexactness.

2.4. Operating pressureUsing the equation of state of an ideal gas one obtains the following expres-

sion for the operating pressure

Pea·21trGPI= -------

'o

298KJ~T(r)

(14)

rr

where PI is the operating pressure, and Pea is the inert gas pressure of the lampat room temperature.

3. Results

3.1. Influence of thermal diffusion

The intension of this report is to demonstrate the consequences of the trans-port processes, which take place in the diffusion layer of incandescent lamps.For inert gas lamps it was shown analytically that thermal diffusion is an effectwhich 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 lampdue to diffusion but neglecting thermal diffusion. One finds that the stoichio-metric sum of the partial pressures

N

SP; = L Vj;Pjj=l

(15)

of the constituents chlorine, oxygen and tungsten is varying with a remarkableamount versus the temperature (resp. radius). The filling pressure of the coldlamp was chosen to 2 . 10-3 bar Cls, 2· 10-3 bar O2, and 5 bar Argon.

Phlllps Journalof Research Vol. 38 Nos 4/5 1983 241

E. Schnedler

ell

2

10-3-l---r-----r---.--.,----r----.3400 3000 2600 2200 1800 1400 1000

- T (K)0.1 0.1478 0.2035 0.2624 0.3183 0.3656 0.4

- r (cm)

Fig. 1. Separation effects due to concentration diffusion; a) = 0, filling pressures: 2 . 10-3 bar Cl-,2.10-3 bar O2, Argon.

In contrast, fig. 2 shows the stoichiometrie sum of the partial pressures ofthe same lamp with the same filling as in fig. 1, but now including thermaldiffusion effects. It is obvious that thermal diffusion is an important contribu-tion to the transport processes in incandescent lamps. Due to this effect thetotal amounts of Cb and O2 at the filament are only one fifth of the amountsat the bulb. This effect has an essential influence upon axial transports in anincandescent lamp: the smaller amounts of solved tungsten at the incan-descent wire affect the axial mass transport.

Fig. 3 shows the details of the partial pressure distribution of the lampdiscussed in fig. 2. It can be seen that the tungsten solubility at the bulb wallis maintained only by W02Cb. Even in the region near the filament tungstenis solved mainly in the form of oxygen containing high temperature com-pounds.

242 Phillps Journal uf Research Vul.38 Nus 4/5 1983

Phllips Journalof Research Vol. 38 Nos 4/5 1983 243


2

2

10-3-1----,----,----.---.--_--, __ --.3400 3000 2600 2200 1800 14.00 1000

- T(K)0.1 0.1478 Q2035 0.2624 Q3183 0.3656 0.4

- r (cm)

Fig. 2. Separation effects due to concentration and thermal diffusion, filling pressures: 2· 10-3 barci., 2.10-3 bar O2, Argon.

3.2. Infiuence of oxygen on tungsten transports

As another example fig. 4 shows the stoichiometrie sum of the partial pres-sures of an incandescent lamp filled with 1.5.10-3 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 below10-5 bar at the bulb. The addition of 10-5 bar O2 increases the partial pres-sures of the tungsten compounds about a factor 7 in the bulb region. Thisresult is demonstrated in fig. 6, it shows that very small amounts of oxygenhave a major effect on the tungsten solubility, which will result in a highertungsten transport rate along the axis of the filament of a real lamp.

E. Schnedler

\10-5'~~~-.--~--.-~~-.------r------r------r--3400 3000 2600 2200 1800 1400 1000

- T(K)

Fig. 3. Partial pressure distribution corresponding to fig. 2, filling pressures: 2·10"-3 bar Cb,2.10-3 bar O2, Argon.

3100 2700 2300 1900 1500 1100 700- T(K)

Fig. 4. Separation effects due to concentration and thermal diffusion, filling pressures: 1.5· 10-3

bar HBr, Krypton.

244 Phlllps Journolof Research Vol.38 Nos 4/5 1983

10-2

Brl HBr-- _-------..'-0.Q.._o:_....

10-3 -r- - - - -_

i /,/ H2/

-_ --/ ,/

,/ // /

10-4./ /

// //

/

10-53100 2700 2300 1900 1500 1100 700- T (K)


Fig. 5. Partial pressure distribution corresponding to fig. 4, filling pressures: 1.5.10-3 bar HBr,Krypton.

,// .

/ // /./ ./ //

_.-._._. HBr»>: --._

/~-/./ - - - _ _ _ H2

- ---

1O-5+----<r__,_----..----.-..__..c::::.--.------'---..----.-3100 2700 2300 1900 1500 1100 700

-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 4/5 1983 245

10-'..------,------,--------,

Cl

E. Schnedler

-------"'"~ 10~+-----~----~'~~--~I...o~Cl.

/\

/ \t 10-3+-----!----!--+---_\_---1

//

0.2 0.3- r {cm}

0.4

Fig. 7. Partial pressure distribution without the tungsten halide-silica reaction. filling pressures:5.10-3 bar Ch. Krypton.

3.3. Attack of silica at the bulb wal!

Another feature of this program is that it is possible to consider condensedphases at the bulb radius as well as at the filament radius. This allows to cal-culate the influence of condensed compounds, such as bulb silica, and gettersupon the chemical transport reactions. As example the influence of the bulbsilica upon the W-CI system shall be demonstrated. Fig. 7 shows the partialpressure distribution in a radial symmetric lamp neglecting reactions with thebulb silica, filled with 5 bar Kr and 5 . 10-3 bar Cl-. The partial pressures ofthe 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 bulbwall region.This result clearly demonstrates that the tungsten solubility cannot be

246 Phillps JournnI of Research Vol.38 Nos4/S 1983

Phillps Journalof Research Vol. 38 Nos 4/5 1983 247


10-'.,------,------,-------,

CI2~ ------.............. "..-----,g 1O-2.J------If------+':>.if/:...._---l

';;, I \\

I 10~+-----~---/~-4~--\-~

// \/ \

10-4+------I-f-----t-------\-j\

Cl

SiCI4................................... M M ..

10-6..j-..l..,L_~_,,_--I-~"---___:'---t--...t<....---~0.1 0.2 0.3

_ r (cm)0.4

Fig. 8. Partial pressure distribution with the tungsten halide-silica reaction, filling pressures:5.10-3 bar C12, Krypton.

remarkably increased by the reaction of tungsten chlorides with the silicabulb. Especially in the high temperature region near the filament no oxygencontaining tungsten compounds can be detected which would increase thetungsten transport along the filament of a real lamp.

Due to the results of this report one might guess that also axial separationeffects are of importance for halogen incandescent lamps. This is subject offurther research and the results will be reported elsewhere.

REFERENCES1) E. Schnedler, preceding paper in this volume.2) L. D. Landau and E. M. Lifshitz, Lehrbuch der Theoretischen Physik, Bd. VI, Akademie-

Verlag Berlin, 1974.3) S. R. de Groot and P. Mazur, Non-Equilibrium Thermodynamics, North Holland Publishing

Co., Amsterdam, 1962.4) W. Elenbaas, Philips Res. Repts. 18, 147, 1963.5) E. Schnedler, The Calculation of Complex Chemical Equilibria, to be prepared.

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