Re: halogen bulbs (very long)

[David Bowman <dbowman@tiger.gtc.georgetown.ky.us>]

Regarding the discussion concerning halogen bulbs:
> > > For those of you who know about light bulbs, what's the deal with halogen?
> > > I can see why a Xenon filled bulb would be good but halogen?
> >
> > I asked the same question a few months back and was told the following...
> >
> > When a filament gets as hot as those in high intensity bulbs, some of the
> > metal from the filament vaporizes into the bulb.  The halogens react with
> > these vaporized particles from the filament and redeposits them back on
> > the filament.  This extends the life of the bulb.
>
> I'll add a little to that, but I don't have an authoritative source.
> All of what was said conforms to what I was told, and in addition I
> was told that the tungsten is redeposited preferentially at the
> hottest spots in this reaction. That seems highly counterintuitive
> to me, but my physical intuition tells me that I should not take my
> physical intuition too seriously!

My anecdotal source agrees with what Dave D. and Leigh said above.  As I
have been told the halogen in the bulb effectively acts to keep the
bulb actively repairing its own filament inhibiting the "burn out"
process and allowing significantly hotter filament temperatures, and,
hence, efficiency for the generation of visible light.

To understand what goes on in a halogen bulb it is useful to recap how
an ordinary bulb normally operates and, subsequently, burns out.  First
of all, an ordinary incandescent bulb is notoriously inefficient in
producing visible light for two primary reasons: 1. its primary spectral
band of significant emission is so broad-band (being a continuous quasi-
Planckian grayish emitter) that a small fraction of its emitted power
is confined to the visible spectrum; 2. the operating temperature of the
bulb is decidedly non-ideal for maximal emission efficiency consistent
with reason/problem 1..  Problem 1. is intrinsic to using a hot
continuous incandescent emitter and cannot be improved on very much by
changing to various other nonexistent types of emission surfaces with
high emissivity in the visible and low emissivity elsewhere.  Problem 2.
is effectively a practical problem.  For any quasi-Planckian spectrum
(intrinsically subject to problem 1.) the ideal temperature for maximal
emission efficiency (where the spectral emission peak occurs in the
middle of the visible range) is a temperature of around 6000 K --
comparable to the temperature of the surface of the sun.  Unfortunately,
this temperature is much higher than the melting (and, indeed, the
boiling) point of all known substances at feasible (near atmospheric)
pressures -- well under the multi-megabar pressures that would be needed
to keep a substance solid at such a high temperature.  This means we need
to use a conductor that is affordable and has a very high melting point,
and then operate the filament at a temperature as close to its melting
point as is feasible without causing premature failure.  The substance of
choice turns out to be tungsten.  Because of the constraint of tungsten's
melting point the filament operating temperature is confined to be about 
1/2 of the ideal temperature needed for maximum efficiency.  This means
that such a light source will emit most strongly in the near-IR, not
the visible.  The visible spectrum then falls on the high-frequency
cutoff slope of the emission spectrum causing significantly more
intensity in the red than in the blue-violet.  This gives the output (if
it is unfiltered by special bulb surface coatings) a decidedly yellow-
orange tinge that can be seen when a bulb is turned on under daylight
conditions or when it is used to expose color photographic film that has
been formulated for a daylight-type of illumination.  The bulb would
operate much more efficiently (and the light would look whiter) if its
filament temperature could be raised.  Raising the temperature would
shift the spectral peak toward the visible resulting in a higher fraction
of the emitted energy being visible, and would also result in a higher
fraction of the filament cooling mechanism being due to direct radiation
rather than via convective transport to the bulb's filler-gas.

The problem with raising the filament temperature is that doing so will
result in a *dramatically* shorter lifetime of the filament before it
burns out.  There is an intrinsic tradeoff between higher temperature
and emission efficiency on one hand, and on longer filament lifetime
on the other.  The primary means by which a filament fails is via a
catastrophic instability involving evaporation from and mobility on
the surface of the filament by surface atoms.  The evaporation rate
of atoms from the surface of tungsten is limited by the binding energy
of an atom to that surface.  The evaporation rate obeys an activated
Arrhenius-type of law with a exp(-(binding energy)/(k*T)) temperature
dependence.  The mobility of atoms on the surface also obeys such an
activated law.  As the temperature increases towards the binding
energy both the mobility of the surface atoms and their evaporation
rate increase dramatically (especially once the temperature becomes a
large fraction of the melting point).

How does this lead to bulb "burnout"?  No filament is perfectly uniform
in composition, crystalline structure, wire diameter, or geometric access
to convective and radiant cooling mechanisms.  This means that when the
filament is under normal operating conditions the surface temperature
will not be constant over the whole filament.  This means that there must
be some places where the surface is hotter than others.  Let's call these
places hot spots.  There are also places where crystal lattice defects,
i.e. crystallite grain boundaries, dislocations, surface layer steps, etc.
occur at the surface.  At such places the binding energy of an atom to its
neighbors differs from that in the more uniform surface regions.  This
causes large changes (possibly orders of magnitude larger) in the atomic
surface mobility and in the evaporation rate at these defects.  Because
there tends to be a slight excess "junction resistance" for electric
current flowing across an extended lattice defect (say, a grain boundary
for instance) this causes the filament to be preferentially heated near
such defects (heating power goes like R*I^2).   The filament thus has a
tendency to be preferentially heated to a higher temperature at just
such places where the surface mobility and evaporation rates are
anomalously high anyway.  As time goes on there is an excess of surface
atoms leaving the surface at the hot spots.  This is due to both
evaporation and due to the diffusion of mobile surface atoms from the
hot surface to the cooler regions where they slow down/stop and tend to
build up into thicker layers.  So the normal process is for the hot spots 
to thin out relative to the cooler regions (which accumulate excess atoms
from the hot spots).  Because of an electrical bottleneck effect the high
resistance thin spots are just the places where the electrical heating
effect is anomalously high (due to both the higher resistance of the
geometrically thinner wire *and* the higher resistivity of the hotter
tungsten).  Thus we have a positive feedback failure mode.  The hot spots
get thin and their increased resistance causes them to heat up even
hotter, and this causes them to further "thin out" at an ever-faster
rate.  The filament will fail when the thinnest hot spot gets so hot and
thin that the temperature exceeds the melting temperature of tungsten and
it fuses at this place.

I believe the reason why light bulbs often "burn out" when they are
switched on is that at the instant of being turned on their resistance is
*much* lower than when at operating temperature (for how much lower, see
Brian W.'s posts).  This short circuit condition results in a huge initial
current pulse being sent through the filament.  The mutual magnetic forces
acting on different parts of the (coiled) filament due to the current pulse
causes a mechanical shock to the filament, flexing it.  Those places where
the filament has been already weakened by excess thinning are just the
places where the strain of this shock is concentrated.  This over-flexes
the weak spot (presumably already at some kind of extended lattice defect
or grain boundary) beyond its yield limit further damaging and cracking the
brittle metal at this weak spot so much that the resistance at this spot
becomes now so high that the cracked spot melts as soon as its
temperature rises sufficiently (nearly instantaneously) for it to happen.

Because the failure rate of a light bulb is so temperature dependent it
is possible to make a fresh bulb last nearly indefinitely by just 
operating it at a lower voltage/power/temperature than it is rated for.
The down side of this practice is that such a strategy requires using
significantly more electrical power to operate more bulbs to get the
same amount of light output due to the lower overall operating
efficiency.  OTOH, it is possible to get the bulb to give off
significantly more light for the electricity it uses by just running it
at a higher/voltage/power/temperature than it is rated for.  The down
side of this practice is that the bulb will have a *very* short life.
The rational operating temperature is determined by balancing the cost of
the electricity needed to get a certain amount of light output against
the amortized replacement costs of the failed bulbs.

Now, how does the addition of a halogen (e.g. I or Br; Joe B. mentioned
also F but I have not heard of this being confirmed elsewhere) to the
surrounding gas environment of a filament change the situation?  As I
mentioned above the halogen provides a mechanism that catalyzes an ongoing
repair process for the filament which acts to inhibit the bulb's main
failure mechanism.  It ends up that the equilibrium constant for the free
energy of formation for the appropriate tungsten halide is such that the
equilibrium fractions of halogen molecules, tungsten atoms and tungsten-
halide molecules is very temperature-dependent.  When the temperature is
relatively high the mixture prefers to exist as separate halogen molecules
and tungsten atoms.  When the temperature relatively cool the mixture
prefers to exist as enriched in tungsten-halide molecules.  Thus when
tungsten atoms evaporate off of the filament and cool down in the gas phase
away from the filament the unreacted halogen reacts with them and gobbles
them up making tungsten-halide rather than letting those tungsten atoms
deposit out on the bulb's glass interior. Also the halogen reacts directly
with the surface tungsten atoms of the filament in the regions of the
filament that are cool.  Presumably nearly all the halogen is either
bound to tungsten as a surface halide layer on the filament or as a bare
halogen on the interior of the glass bulb surface when the bulb is
turned off.  When the bulb is operating with its characteristically high
glass bulb temperature (~500 K) the halogen and the tungsten halide is
driven off of the surfaces into the gas phase.  When the tungsten-halide
molecules collide with the hot spots of the filament when it is operating
a reaction occurs at the surface which releases the metal tungsten atoms
onto the surface and lets the bare halogen escape back to the gas to go
out and scavenge for more straying tungsten atoms.  When the tungsten-
halide molecules collide with the cooler regions of the filament surface,
the glass envelope interior, each other, other gas particles, etc. they
tend to rebound remaining intact because of the lower temperatures of
these other inert collision processes.  In effect, low energy collisions
between a halogen and a tungsten atom tends to cause them to bind
together, but a high energy collision involving a tungsten-halide
molecule tends to disassociate the molecule.  The only places where
sufficiently (for disassociation) high energy collisions tend to 
preferentially take place is at the surface of the filament hot spots.
Convection processes keep the mixture of halogen halide and other gases
circulating throughout the system.

So the net effect of the presence of the halogen is that as the bulb
operates it keeps putting the tungsten atoms back on to the hot spot
surfaces, and thus prevents them from thinning out so the filament's
main failure mode is suppressed.  With the catastrophic (positive
feedback) failure mechanism suppressed it then becomes feasible to
operate the bulb at a significantly higher temperature than would
otherwise be the case, and this leads to the bulb being more efficient
as it also emits "whiter" light.  This higher operating temperature is
the main reason why halogen bulbs are brighter and "whiter" than
ordinary bulbs of the same rated power.  The reason the the glass
envelopes of halogen bulbs are so small compared to ordinary bulbs is that
in order to keep the halogen and halide from remaining on the glass
envelope interior that surface must be much hotter than the envelope 
temperature of an ordinary bulb.  Keeping the envelope small keeps it
closer to the filament heat source so the glass can remain above 200 deg C
and insure against unwanted deposition on the glass during operation.  The
use of quartz for the envelope is due to the need for a strong envelope
that doesn't mind high operating temperatures.  (Maybe quartz also has
better surface properties regarding halogen & halide depostion/sublimation
processes than ordinary glass does as well.)

David Bowman
dbowman@gtc.georgetown.ky.us