Some Physical and Chemical Problems of Lighting Engineering*

M. Pirani, Berlin

Beginning at the end of the eighteenth century, when, with the introduction of gas lighting, the art of obtaining light began actually to be transformed into a technology, the entire development of this field was in the hands of chemists. The triumphant path of the incandescent lamp, begun 51 years ago by the great electrical engineer Edison, also changed almost nothing in this situation; in parallel with the penetration of physical methods into chemistry, in lighting engineering physical problems are increasingly coming to the fore.

The present report is devoted to an exposition of the mutual connection between the physical and chemical problems of lighting engineering and of their significance for technical development.

1. General Principles of Excitation and Radiation

According to the conceptions of quantum theory, every act of emission of electromagnetic radiation is connected with the transition of the radiating system from one energy-rich, “excited” state to another, energy-poor, “unexcited” state.

The intensity and polarization of the emitted radiation are determined solely by the electric moment arising during the transition, in accordance with the old Maxwellian theory, preserved thanks to the so-called prin-

* Report delivered at the Society of Electric Lighting (Osram-Konzern) on April 7, 1931. ZS. f. angew. Chemie, 44, 395, 1931. Translated by V. Fabrikant.

its “right to exist” in modern quantum mechanics.

The preliminary history, i.e., the path by which the system arrived in the excited state, is entirely immaterial. The difference that exists between individual processes of radiation is caused by the difference in the influence exerted by the medium surrounding the system on the excited state, and depends on the manner in which energy is “supplied” to the system. This difference must justify the old division into “temperature” and “luminescent” radiators.

Thermal radiation arises with a thermal “supply” of energy, and luminescence with all other methods of excitation. The old view, according to which the character of radiation depends on the radiating “material,” may be rejected, since experimentally, with a high degree of obviousness, it can be shown that under appropriate conditions every substance can emit both one and the other kind of radiation.

One may imagine that excitation occurs, for example, in the following manner: let us consider a gas consisting of diatomic molecules, which may be regarded as a kind of “dumbbells,” i.e., two elastically coupled material points. An individual molecule has a number of “degrees of freedom,” namely—three degrees of freedom of displacement, in addition two degrees of freedom of oscillation of the nuclei relative to each other and, finally, two degrees of rotation of the molecule as a whole (since the nuclei are regarded as points, rotation about the line connecting them is immaterial). The molecule must be an “electric dipole”; therefore, when it rotates or when the nuclei oscillate, electromagnetic energy is radiated. Let us impart to such a gas a certain amount of thermal energy, i.e., raise its temperature. At a certain temperature the rotations and nuclear oscillations will be “excited,” and the gas will begin to radiate. It has been known since the measurements by Eucken of the specific heat of $\mathrm{H}_2$ that excitation occurs in rather sharp “steps.” (This phenomenon is made theo-

practically understandable if the nuclear vibrations and rotations are quantized.) From the laws of gas statistics it follows that, at a definite “temperature” of the gas, to each degree of freedom of the atom there corresponds an energy of no more than \(\frac{RT}{2}\), where \(R\) is the gas constant and \(T\) the absolute temperature (the principle of equipartition). The distribution within the individual degrees of freedom occurs according to the well-known Boltzmann formula:

\[ N_E = N_o e^{-\frac{E}{kT}}. \]

\(N_E\) is the number of molecules with energy \(E\), \(N_o\) their total number, \(k\) the Boltzmann constant, and \(T\) the absolute temperature. The characteristic feature of “temperature radiation” in this case is the “statistical” distribution of energy over the degrees of freedom of the system.

In “luminescence” the situation is different. We again take the above-mentioned gas, but keep its temperature so low that neither rotations nor nuclear vibrations are practically excited, and illuminate the gas with its “absorption” frequency. (Because of the quantization of rotation and of nuclear vibrations, the gas does not absorb continuously.) Owing to absorption, individuals with excited rotations and vibrations will appear; moreover, there is no rule indicating what energy a single degree of freedom must have. The distribution of energy within one degree of freedom will likewise not be according to Boltzmann. Whereas under temperature excitation a statistical distribution of energy over the degrees of freedom and among the individuals is obtained, in luminescence there exist, in addition to statistically distributed energy, certain “highly excited” individuals. Under “temperature” excitation, thermal equilibrium prevails within the gas; in luminescence it does not.*

The following may serve as a practically applicable criterion in the investigation of both cases. Under thermal equilibrium the number of collisions of the “second kind” (energy transfer

* P. Prigsheim, ZS. f. Physik, 57, 739 (1929).

of excitation into kinetic energy must be balanced by the number of impacts of the “first kind” (the conversion of kinetic energy into excitation energy), since the gas tends to preserve the “most probable” state (in other words, the entropy must remain constant). If, however, abnormally highly excited atoms exist, as in excitation by radiation, then “quenching” (the conversion of excitation energy into kinetic energy) continues until the energy distribution corresponds to thermal equilibrium. A substance in temperature equilibrium emits in each particular spectral region no more than the well-known “black body” (Fig. 1), and there is no similarity between the spectra of thermal radiators and black radiation. For example, the dipole gas considered above gives a band spectrum with a structure corresponding to nuclear vibrations and rotational (rotatory) frequencies, which is observed at least in thin layers of gas. Only in thick layers or at high pressures do the discontinuities in the spectrum disappear, so that the gas ultimately begins to act like a black body.*

Fig. 1. Energy distribution in black-body radiation as a function of absolute temperature.

Thus the spectral distribution of black radiation always bounds from above the distribution in a band spectrum obtained under purely thermal excitation.** Experience shows that there are many substances which, even in thin layers, possess radiation,

* Pressure may in this case produce still another effect, the so-called “smearing” of the spectrum.

** R. Wood, Physical Optics, New York, 1923.

to a greater or lesser degree similar to “black” radiation, so-called “gray” radiation. The radiation of these bodies differs from the radiation of a black body only by a constant factor, the same in all parts of the spectrum. These are opaque substances and, above all, metals. Very little is known theoretically about the radiating mechanism of the lattice, especially the metal lattice; deviations from “gray” radiation have long been observed experimentally, for example the absence of red heat in copper, the line radiation of rare earths, etc.

How good, nevertheless, the approximation to the laws of black radiation is can be seen from the general applicability of such concepts as the color of incandescence, etc.

2. Temperature Radiators

The principal drawback of temperature radiators is that the materials used for this purpose, above all solid conducting substances, are selective to only a very slight degree. Therefore, according to the laws of radiation, in addition to the useful visible radiation, ultraviolet rays and infrared rays are always added as an obligatory supplement. With “gray” radiation of a body, no more than 40% can be obtained in the visible part of the spectrum. If, however, the sensitivity of the eye to different wavelengths is taken into account, we find that the visual coefficient of useful effect cannot be greater than 14% (Fig. 2).

In the figure: vertical axis — “Visual useful effect”; horizontal axis — “Temperature in °abs.”

Fig. 2. Visual useful effect of black radiation as a function of absolute temperature.

For the temperatures attained up to now, the coefficient of use-

... beneficial action is quite unsatisfactory. If substances were used that radiate selectively in the visible region, it might be possible to convert a large part of the energy into visible radiation. However, such substances are still unknown. The most convenient and rational method is the delivery of energy by the thermal radiation of conducting substances, and above all of metals and carbon. The number of refractory metals is limited. (See Table I; carbon, 3460°, is also included in it.)

TABLE I

Refractory metals

The choice from among these substances must be made from three points of view:

1) a low rate of evaporation, since it determines the service life of the incandescent filament;

2) appropriate mechanical properties: ease of processing and good strength;

3) appropriate optical properties: the substance must radiate selectively in the visible region.

Tungsten satisfies all three conditions better than the other substances; it is true that the third condition is poorly fulfilled, in general, by all solid bodies. Carbon would also be suitable in itself, but it has too high a rate of evaporation.

Besides the elements themselves, attempts are also being made in lighting engineering to use refractory compounds of these elements, on which we shall briefly dwell here. These are, above all, carbides, borides, and nitrides of the metals listed in Table I.

These compounds are usually distinguished by great hardness and strength. They possess comparatively high chemi-

...chemical stability, and only at high temperatures do water vapor, hydrochloric acid, oxygen, and other gases begin to act on them. Dissociation at high temperatures is weak. Tantalum carbide is the most stable. The methods of manufacturing filaments may be divided into several types:

1) The pressing method. From metals or from their oxides, by heating with carbon or with nitrogen to temperatures from 1700 to 2000°, finely powdered carbides or nitrides* are obtained. The powder thus obtained can, by suitable treatment, be converted into massive pieces or, with the aid of a binder, be converted by pressing into wire. In the latter case the binder (sugar, etc.) burns out.

2) The growth method.** An incandescent tungsten wire is placed in a mixture of gaseous compounds of both components of the refractory compounds, for example halogen compounds of the metals and hydrocarbons. The gaseous compounds then decompose on the surface of the wire, and refractory compounds appear on it in the form of crystals.

If the wire is a single crystal, then the crystals obtained are oriented according to its crystallographic surfaces.

3) Carburizing. A metal wire is placed in an atmosphere of hydrocarbon and heated to the temperature at which carbides form. In this process the material of the wire is converted into carbide, which proceeds from the surface inward.

Carbides*** crystallize partly in the regular, partly in the hexagonal system; nitrides**** in the regular system, borides probably in the tetragonal system. In Table II*****

* Friedrich und Sittig, Z. S. f. anorg. allg. Chem., 143, 293 [1925]; Weber, Glühfäden, 144, 169 [1925].
** K. Becker u. H. Ewest, Z. S. f. techn. Physik, 11 [1930].
*** K. Becker, F. Ebert, Z. S. f. Physik, 31, 268 [1925].
**** K. Becker, ebenda, 51, 481 [1928].
***** C. Agte u. H. Altertum, Z. S. f. techn. Physik, 11, 162 [1930]. C. Agte u. K. Moers, to appear shortly.

indicated are the melting points of simple compounds and of some mixtures. The melting points of the carbides of Zr, Hf, Nb, Ta lie above the melting points of tungsten and carbon. Several mixtures of carbides (from the carbides of tungsten, tantalum, niobium, zirconium) have also been investigated. In most cases the melting point of a mixture lies between the melting points of the components making up the mixture. Only in certain mixtures are the melting points higher than that of the most refractory constituent itself.

TABLE II

Refractory compounds

Carbides and mixtures of carbides:

Nitrides

Borides

An example of such mixtures may be a mixture of four parts tantalum carbide and one part zirconium carbide, melting at 4205°, or a mixture of four parts tantalum carbide and one part hafnium carbide, melting at 4215°. These mixtures are the most refractory of all substances found up to the present. Owing to their brittleness and the difficulty of working them, they are used very rarely, despite their rather good radiative properties.

In the field of illumination engineering tungsten predominates. It therefore seems especially interesting to dwell briefly on the chemical questions connected with the use of tungsten.

Tungsten is very sensitive to hydrogen and oxygen. Water vapor decomposes on the incandescent surface of tungsten; oxygen reacts with the tungsten, and the oxide formed evaporates; hydrogen dissociates on the heated tungsten and, in atomic form, reduces the oxide, with water vapor again being formed; thus a cyclic process takes place.* Therefore even traces of these gases must be removed from the bulbs.

To a certain extent, physical means are of help here—pumping while simultaneously heating the bulb; in this way a large part of the water film on the glass and of the adsorbed gases is removed. After the lamp has been sealed off, the remaining gases can be rendered harmless only by chemical means. With phosphorus or phosphorus pentoxide it is possible to bind oxygen or water vapor.

Since, in order to remove the water film, the bulb always has to be heated strongly, the glass of which it is made must withstand this rise in temperature without softening. On the other hand, for the purposes of glass working it is precisely a large interval of softening temperatures that is required. Of great importance for the current lead-in is the thermal expansion of the glass. The coefficient of expansion of the glass must coincide with the coefficient of expansion of the fused-in metal; in this connection a coating (for example, Borax) is sometimes used for especially tight joints (in the flattened part of the stem). At present FeNi wire coated with copper is fused into Thuringian glass, and tungsten into special glasses.

Platinum, which was formerly used everywhere, now finds no application at all.

In addition to the destruction of incandescent filaments by oxidizing gases, evaporation and the phenomena associated with it play a major role. As a result of evaporation, when the luminous body is heated in a vacuum, after a comparatively short interval of time the bulbs blacken, and

* I. Langmuir, Trans. Amer. Inst. El. Eng., 31, 1921 [1913].

the transparency drops sharply, and with it—the efficiency. (Several milligrams on the surface of a bulb with a diameter of 100 mm already produce a noticeable loss of light.) By using materials with a low vapor pressure, this drawback can be partly reduced (tungsten, tantalum carbides). Many refractory materials, such as carbon, because of the high rate of their evaporation, are of little use for the manufacture of lamps and had to yield the field of activity almost completely to tungsten.

Attempts are also made to mix in substances that would form colorless compounds with the filament material and thus eliminate blackening. In doing so, halide compounds are used (NaCl, CaF₂, Na₃AlF₆, etc.). The “reactions” in this case are physical rather than chemical. These substances increase the optical transparency of the tungsten deposit in the visible part of the spectrum, i.e., they shift the absorption to another spectral region.

Finally, a radical way to reduce the transport of filament material onto the bulb walls is to fill the lamp with a neutral gas at sufficient pressure. In this case, at the same temperature, the same number of atoms will leave the surface of the wire per unit time as in vacuum, but some of the atoms will be “reflected” back and will again be deposited on the filament; moreover, of course, even small temperature differences will already play a large role.

It turns out in this case that a wire of circular cross section becomes polygonal with time, since the “reflected” atoms build up on the lattices of the crystals located in the wire and reveal their natural faces. Nitrogen, or a mixture of nitrogen with argon, is used as the filling gas. Pure argon is rarely used, in view of its easy ionizability, which entails the danger of an arc discharge. Usually the gas is used at a pressure of about one atmosphere. When filling with gas at such a high pressure, it is necessary to take into account the loss of energy due to thermal conductivity and convection in this gas; reductions of these losses are achieved by choosing gases with the lowest

thermal conductivity (the heaviest gases), and, in addition, they give a special shape to the heated filament. The filament is made in the form of a spiral of maximum density, sometimes in the form of a double spiral* (the limits here are determined by the mechanical properties of the materials). From the standpoint of convection losses, the spiral acts like a short, thick wire with a significantly reduced surface (apparently, a layer forms around the spiral through which convection cannot occur). With the spiral form of the filament the radiation “turns gray,” i.e. the advantageous optical properties of tungsten are partly lost (an increase in emissivity in the visible part of the spectrum), but this loss is more than compensated for by the possibility of a higher load. In order for these advantages to be preserved throughout the entire life of the lamp, the filament must possess mechanical properties ensuring the invariability of its original shape. If the filament sags at high temperature under the action of its own weight, this entails a lowering of the temperature and, along with it, a loss in economy.

Upon the first heating to operating temperature of the drawn tungsten filament,** its drawn structure (the fibrous arrangement of the crystals) recrystallizes, and its mechanical properties deteriorate. One can either retard recrystallization by adding, for example, thorium oxide, or try to ensure that, during recrystallization, which takes place within fractions of a second, the wire acquires a structure strong from the standpoint of shape. The most desirable is a wire made of crystals of the greatest possible length and, where possible, filling the entire cross-section of the wire, with inclined connecting surfaces (Fig. 3), since fracture occurs first of all on these surfaces.

To obtain the desired structure in drawn wire there are now two methods:***

* Geiger-Scheel, Hand. d. Physik, XIX, 370.
* F. Koref, Metallbörse, 17, 793.
* H. Altertum, E.T.Z.*, 1929, 1723.

1) The use of special mechanical-thermal treatment of the wire: a taut filament is heated to incandescence (Vergütung) and then mechanically deformed, while the stresses arising during heating to a high temperature cause recrystallization.

2) The use of special materials (tungstic acid with the addition of silicic acid) with an appropriate method of reduction directs recrystallization in the desired direction. Traces of silicic acid play an especially important role. The mechanism of this influence is unknown. It is especially interesting that the added traces of the indicated substances are almost completely removed during processing.

a                b

Fig. 3.

The finished tungsten wire contains less than \(1/100\%\) (according to spectral analysis) of impurities.

3. Chemiluminescence

The most interesting of all cases of excitation of radiation is the one in which chemical energy is converted directly into the excitation energy of an atom or molecule. The glow of glowworms or the reaction of luciferin and luciferase has long been known as “chemiluminescence.” The glow of the “nonluminous” Bunsen flame is also regarded as chemiluminescence. More recent are the so-called cold flames—reactions in which one of the participants in the reaction partially converts the energy of combination into excitation energy and emits it, or else, upon collision, excites another atom. Of such reactions, the best known are compounds in vacuum

of alkali metals with halides, in which the characteristic lines of the alkali metals are emitted. The reactions proceed in the following form:

\[ \begin{aligned} 1)\quad & \mathrm{Na} + \mathrm{Cl}_{2} = \mathrm{NaCl} + \mathrm{Cl} + 35\ \text{cal},\\ 2)\quad & \mathrm{Na}_{2} + \mathrm{Cl} = \mathrm{NaCl} + \mathrm{Na} + 73\ \text{cal}. \end{aligned} \]

For the excitation of the lines observed in the reaction of sodium vapor with chlorine, \(48.3\) cal is required. The energy liberated in process 1) proves insufficient for this, and it is converted into the kinetic energy of the participants in the reaction. Thus the excitation accompanies reaction 2). The mechanism of excitation, apparently, is as follows: NaCl absorbs the liberated energy, converting it into vibrational energy, and only upon collision with a sodium atom does it excite the latter. This may be assumed with a sufficient degree of confidence, since [[unclear: damaged text]] of greatest brightness of the \(D\) lines does not coincide with the place [[unclear: damaged text]] of greatest formation of NaCl.

For excitation of the \(D\) lines, \(2.1\) V is required; the remainder is transformed into the kinetic energy of the participants in the reaction. And indeed, the lines that arise are accompanied by a considerable Doppler effect, so that they are practically very little self-reversed.**

Because of inconveniences of a practical nature, these processes have not so far been usable in technology.

As is seen from the reaction scheme, the yield depends chiefly on the concentration of sodium molecules, and also of sodium atoms. It is necessary that, as far as possible, not a single NaCl molecule should reach the wall before, upon colliding, it has transferred its energy to a sodium atom. Therefore one should operate at a high pressure of sodium vapor. But the possibilities here are limited by the fact that even glass resistant to sodium cannot withstand without change, for a sufficient period, the action

* H. Beutler u. M. Polanyi, Z. S. f. Physik. 47, 378 [1928].
M. Polanyi, “Atomreaktionen,” Z. S. f. angew. Chemie, 44, 597, 1931.

** That is, owing to the Doppler effect the line broadens, and in self-reversal only its central part is absorbed. Translator’s note.

sodium vapors at a pressure of \(1/10\) mm Hg (350°). At 350°C the partial pressure of sodium molecules is less than \(10^{-4}\) mm Hg. However, one should not think that it is impossible to find other, more economical cases of chemiluminescence.

4. Excitation of Light in Gas Discharge

At the present stage of development, the only technically interesting method of exciting luminescence is electron impact, which occurs in electrical discharges. In view of the importance and breadth of this problem, it is necessary to dwell on it in greater detail.

A. Obtaining a Discharge; Ignition

Let us consider two electrodes of arbitrary shape to which we apply a voltage. If the medium is completely free of charge carriers, i.e., of ions and electrons, then the electric field between the electrodes does not change with time. It is determined by the potential difference between the electrodes, by their geometrical shape, and by the distance. Something different occurs if charge carriers are present in the path of the discharge. When a voltage is applied, charged particles, under the action of the field, enter into rapid motion—electrons toward the anode, and positive ions toward the cathode. As soon as the electrons attain sufficient kinetic energy, upon colliding with atoms they begin to liberate new electrons, so that positively charged ions remain. The secondary electrons arising in this process, in turn, are accelerated, can ionize again, and so on. In this way an electron avalanche is formed, moving toward the anode. Since the masses of ions \(m_i\) are approximately \(10^4\) times greater than the mass of electrons, the latter move in the same field approximately \(10^2\) times faster:

\[ \frac{v_e}{v_i} = \sqrt{\frac{m_i}{m_e}} . \]

Thus the electron velocity \(v_e\) is sufficiently great for us to be able, without gross error, to assume that the positive ions are still at the place where they were formed, while the electron avalanche has already reached the anode. Along the path of the discharge there is an excess of positively charged particles, a positive space charge, and therefore a change occurs in the voltage drop between anode and cathode. The field strength decreases at the anode and increases at the cathode (see Fig. 4).

Fig. 4.

Owing to this, the following electrons begin to ionize already at a smaller distance from the cathode, and by this the positive space charge moves still closer to the cathode, etc. The potential distribution is established gradually, as shown in Fig. 4. Finally, the positive ions from the “ionic avalanche” strike the cathode and liberate secondary electrons. At this moment ignition occurs; the discharge becomes self-sustaining.

According to the theory of Franck–Hippel*, the principal features of which have just been set forth, the time during which breakdown takes place depends on the rate of formation of positive ions. The latter increases with increasing pressure and decreasing ionization energy. Indeed, in air at atmospheric pressure the time for establishment of the discharge is found to be from \(10^{-8}\) to \(10^{-9}\) sec, whereas in noble gases under the same conditions, or in rarefied gases, it is found to be approximately from \(10^{-3}\) to \(10^{-5}\) sec.

* A. v. Hippel und J. Franck, Z. S. f. Physik, 57 [1930].

If ignition is followed oscillographically,* it is seen that after the application of the voltage (which may occur in approximately \(10^{-9}\) sec.), there occurs a certain delay in ignition.

The reason for this is statistical: ignition takes place only when some minimal number of electrons has accumulated in front of the cathode. This is supported by the fact that, by increasing the number of electrons—by means of additional artificial ionization—one can reduce the delay time; an increase in voltage has the same effect. Neither measure has any influence on the time of ignition proper.

The number of electrons required in order for ignition to be possible is of the order of 100 per \(1\ \mathrm{cm}^{3}\). These electrons are obtained either as a result of residual ionization (owing to the radioactivity of the earth, of the building, etc., or under the action of penetrating radiation), or else artificially, by means of an auxiliary glow discharge, photoelectrically, or by heating the cathode. The auxiliary glow discharge is produced, for example, by high frequency or by additional electrodes placed close to the main ones.

The magnitude of the voltage at which breakdown occurs, the so-called ignition potential, depends: 1) on the number of initial electrons and 2) on the ionization conditions in the gas.

Let us first consider 2). To obtain a discharge, it is important that, as far as possible, all free electrons be used for ionization. This is hindered by the fact that the energy potential of ionization lies higher than the excitation potential. As soon as the electrons reach the velocities required for excitation, they excite, losing their energy in the process, and consequently for the time being are lost for ionization. Conditions are more favorable when the atoms possess metastable levels (from which the atom cannot pass to other levels by emitting radiation). Then, at sufficient gas pressure (for which usually it is enough

* Rogowski, Sommerfeld Festschrift, 1929.

pressure in tubes) part of the excited atoms passes, by collisions of the second kind or through radiation, to a metastable level and thus preserves a large part of the excitation energy for a time considerably longer than the mean lifetime of the excited term. If traces of another gas are added to such a gas (too much is unsuitable, as will be seen below from considerations of electron kinetics), the ionization potential of which is lower than the energy of the metastable term of the atoms of the other gases, then the added atoms can be ionized in collisions with long-lived metastable atoms. The energy spent on excitation is thereby partially returned back. In this way, for example, the ignition potential of argon can be lowered by 50% by adding traces of mercury, or the ignition of neon can be facilitated by adding small amounts of argon. Apparently the same effect is produced by “impurities” (Verunreinigungen), such as, for example, hydrogen. Its absorption during sputtering of the electrodes affects the “hardness” of the tube in very highly purified gases and raises the ignition potential.*

In technical tubes, owing to the connection of the “initial” electrons with charges on the walls, ignition without preliminary ionization and without an initially increased voltage occurs only very rarely. Sometimes the walls are coated with a conducting substance, a so-called “ignition strip” (Zündstich), both to eliminate charges on the walls and to create an auxiliary discharge. The reduction of the ignition potential in technical discharge tubes is of great importance, since their practical applicability depends on it. After ignition, a voltage is established on the tube which, as we shall see, depends almost not at all on the ignition process itself and which is lower than the ignition potential. The difference between the voltages at ignition and during burning must be eliminated, or intro-

* N. Pfennug, Z. S. f. Physik, 57, 723 [1929].

** H. Altertum, M. Reger, R. Seeliger, Z. S. f. techn. Physik, 9, 161 [1918].

resistance, or by some other method. It is clear that the energy lost in this case will be the greater, the greater the difference between these voltages.

With alternating current there is the possibility of “lossless” elimination of the difference between these voltages, for example by means of a choke or a capacitor. However, in a technical estimate one cannot neglect the cost of these devices. On the other hand, it should, to be sure, be noted that when tubes are replaced these devices need not be acquired anew.

Finally, when alternating current is used, the restriking potential is essential, or the potential at which the arc is ignited at the beginning of each half-period, since at the end of each half-period it goes out and must be ignited again (at the alternating-current frequencies used in practice). This potential depends strongly on the rate at which ionization disappears. It decreases with increasing frequency, i.e., with the shortening of the “dark pauses” (the phase difference between the ignition potential and the extinction potential). The use of a preliminary choke automatically shortens the “dark pauses” owing to the interaction of the characteristics of the choke and the arc. The course of the voltage on the arc becomes almost rectangular, with a maximum at the beginning of each period.

B. The discharge in the stationary state and the excitation of light

In the stationary state, the voltage drop in a discharge tube is distributed among the drop at the cathode, the drop at the anode, and the positive column:

1. The drop at the cathode is caused by a layer of positive ions formed immediately in front of the cathode. Its magnitude depends strongly on the material of the cathode and on the filling gas* and, to a certain extent, does not depend on the current strength (normal cathode drop). In the stationary state of the discharge, the cathode drop serves to obtain

* Wien-Harms, Handb. d. Experimentalphysik, Bd. XIII.

necessary for maintaining the discharge. Positive ions, striking the cathode, knock out secondary electrons. If the current strength is increased above a certain value, the drop at the cathode increases sharply (anomalous cathode drop), and, correspondingly, the kinetic energy of the ions striking the cathode increases. Under the action of the increasing heating of the cathode, thermionic emission of electrons will finally begin; moreover, owing to the neutralization of positive ions by electrons, the voltage drop at the cathode will change and will acquire a definite value corresponding to equilibrium. This value is of the order of several volts. If one works from the very beginning with a heated cathode or with photoelectron emission, then under these conditions no considerable drop at the cathode is ever obtained.

1. The drop at the anode* corresponds to the negative space charge of the electrons, as is known for high-vacuum tubes. The magnitude of the drop at the anode depends mainly on the ratio between the cross sections of the anode and of the tube, and may reach such a value that the anode is heated to \(1000^\circ\) owing to bombardment by electrons.

2. The positive column arises, under the appropriate conditions, between the anode and the cathode.

It possesses a potential gradient which can accelerate electrons to the velocity necessary for excitation. As the theory of the positive column given by Schottky** shows, this occurs when ions and electrons, under the influence of some causes, are removed from the discharge (for example, by recombinations on the walls) and must be replaced. In this case the gradient increases so much that the vanished charge carriers can be replaced by the resulting ionization. In large vessels (large rectifiers), where the action of the walls is small, the gradient and, correspondingly, the electron velocities can attain only such low values that no excitation of light occurs between the anode and the cathode.

* Wien-Harms, ibid.

** W. Schottky, Z. S. f. Physik, 25, 342 and 635 [1924]; 26, 163 [1925].

Before speaking in more detail about the processes occurring in the positive column, we must pause a little over the excitation of light in an electric discharge.

In an electric discharge the energy required for the excitation of an atom or a molecule is obtained, for the most part, in an “inelastic collision” with an electron or atom. In such a collision part of the kinetic energy of the colliding partners is converted into excitation energy.

Excitation by absorption is encountered more rarely. The magnitudes of the energies needed for excitation are given by the “critical potentials” determined in the experiments of Franck and Hertz*. The probability of excitation is determined by the “excitation function” (Anregungsfunktion)**, or more precisely—the excitation yield as a function of the velocity of the electrons (Fig. 5). In general, an electron whose kinetic energy is greater than the excitation potential of an atom can excite that atom; for ions this relation will be more complicated. Concerning the atom itself, or rather its “model,” we shall say here only the following.

Fig. 5. Relative yield for the excitation of certain spectral lines as a function of electron velocity. Velocity is expressed in volts.

The energetic aspect of the phenomenon (how much is radiated) can be understood on the basis of Bohr’s model of the atom; such fine details as the time of excitation and damping, polarization,

* Frank and Jordan, Anregung von Quantensprüngen durch Stösse, 1923.

** R. Seeliger, Ann. Physik. Chem., 89, 613 [1919].

the “selection rule” are explained by adding the correspondence principle, i.e., by a far-reaching analogy with the classical oscillator.

The “energy levels” which are of primary interest to us here can be determined from optical and electrical measurements. Taking the selection rule into account, one can construct a “term diagram” of an unexcited atom, existing at a low gas or vapor pressure of the order of several millimeters Hg (Fig. 6). The vertical distance between the corresponding levels is equal to the energy released in radiation, or, equivalently, to the energy expended in excitation. We see that, for example, in sodium, as the velocity of the electrons is increased, starting from zero, first at 2.1 V the \(D\) lines appear, and then, with a further increase of the voltage, higher transitions appear. From the form of the excitation functions it follows that many terms have a probability of being excited only in a small range of electron velocities. The optimum for electron velocities usually lies between the excitation potential and twice its value.

Fig. 6. Sodium term diagram. The numbers denote the wavelength of the emitted line in Å.

Excitation of the atom in a discharge occurs first...

altogether in three spatially separated places: in the regions of the fall at the cathode, of the fall at the anode, and in the positive column.

The difference that exists between the spectra excited in these three places follows mainly from the difference in the velocities of the exciting particles. In the regions near the cathode and, in part, near the anode, the electrons have a considerable velocity, so that with some probability they can excite only the higher members of the series (spark lines). The atom’s energetically lower-lying arc lines will, for the most part, be excited by ionic impacts, since the kinetic energy of the ions in these regions is sufficient for this.

In the positive column, owing to the peculiar kinetics of the electrons, their velocity is small, so that arc lines are excited with good efficiency.

Here it should be noted that it is often erroneously asserted that the positive column somehow depends on the kind of electrodes (alkaline-earth, incandescent, iron). It is clear that this is not so: with all types of electrodes one and the same thing occurs. The motion of the electrons in the positive column differs in that, besides the stream of electrons directed from the anode to the cathode, there also exists their disordered motion, of the same order of magnitude as the directed motion.

On this basis one may consider the number of electrons in the positive column to be considerably greater than that which corresponds to the current strength. Electrons moving chaotically, with kinetic energy insufficient for excitation, will, in collisions with atoms, be reflected with a small, but by no means negligible, loss of velocity. This effect is especially noticeable in gases which, at certain electron velocities, possess abnormally large effective diameters. The electrons describe complicated zigzag trajectories, while on the average moving toward the anode with a certain definite velocity.

As follows from the theory of Hertz developed by Sommermeyer*,

* G. Hertz, Dtsch. Physik. Ges., 1913; ZS. f. Physik, 32, 298 [1929].

this electron velocity tends asymptotically to a certain limiting value, owing to the fact that as the velocity increases the number of collisions grows, and consequently the compensating action of the velocity losses occurring in them is strengthened. This average velocity is constant along the entire length of the positive column. For the excitation of light it is important that the average velocity of the electrons should not be large—it may constitute a part of that which corresponds to the potential difference; but if, owing to multiple reflections, the electrons are forced to traverse a very long path (about 100 times the distance between the electrodes), then the probability of a collision with excitation will be very great.

If the tube contains a mixture of two gases, for example metallic vapors with a small excitation potential and a noble gas, then the distribution of electron velocities will be determined mainly by the excitation potential of the vapors, since the noble gas will practically not be excited. It will only increase the path of the electrons as a result of reflection in collisions and will somewhat lower the average velocity for the same reason *.

In view of the peculiar conditions prevailing in the positive column, a whole series of phenomena may be observed here. These phenomena show very clearly the influence of electric fields on light emission—in the present case, fields created by ions **.

1. The diffuse character of hydrogen-like terms due to the Stark effect. Since the fields are highly inhomogeneous, no sharp splitting or displacement is obtained, but only a “smearing” of the lines and a premature break-off of the series.

2. The appearance of lines forbidden by the “selection rule.” The number of these lines increases rapidly together with the principal quantum number. Moreover, owing to the high concentration of ions and slow electrons, a “spectrum of recombination compounds” appears—Wiedervereinigungsspektra.

* M. Pirani, ZS. f. techn. Physik, 71, 482 (1930).
** H. Krett, Neiturwiss., 19, 269 (1930).

This is a continuous spectrum adjacent to the series limit, whose intensity is proportional to the square of the current density, since the densities of both ions and electrons are proportional to the current density. This continuous spectrum has hitherto been observed only in absorption. Another consequence of recombination is a change in the course of the intensity in the series, with the higher members becoming extremely bright (normally their intensity decreases as \(1/n^3\)). Of particular interest in these phenomena is the fact that here one can clearly see how, under the action of an increasing number of external “perturbations,” owing to the increase in the number of possible combinations, the line spectrum loses its characteristic appearance and turns into a continuous one. The last members in this sequence are probably the continuous spectra of stars*.

For chemists, it is of some interest that in the positive column molecules are formed, for example compounds of metals with noble gases. Such strong dipoles as excited metal atoms polarize noble-gas atoms, and unstable compounds appear. Since the resulting molecules are very unstable, they decompose upon radiation. In the excited state, however, various degrees of excitation of nuclear vibrations are possible, which manifest themselves in the appearance of “fluctuations” in diffuse bands*.

C. Technique of Gas-Discharge Tubes

In attempting to create, on the basis of the above, rather theoretical considerations, gas-discharge tubes technically suitable for use, a whole series of problems arises****.

1. The choice of suitable atoms depending on what,

* See, for example, S. Rosseland, Astrophysik, 1930; O. Hulburt, Phys. Rev., Bd. 36.

* I. Krefft u. R. Rompe, Naturwiss. 19*, [1930].

* J. Franck, ibid. 19**, 211 [1930.]

* M. Pirani, E. T. Z.* 51, 889 [1930]; Licht u. Lampe (1931); E. и M., 49 (1931); Lichttechnik, Heft 1.

whether one wishes to obtain monochromatic or somehow colored light, ultraviolet or infrared radiation.

For example, suitable for monochromatic radiation are: Na, Mg, Tl, Ne; for ultraviolet radiation: Hg, Mg, Cd, Zr; for infrared radiation: He; for light resembling daylight: CO$_2$.

1. Convenience of operation (Schaltbarkeit); a technically impeccable tube must ignite and burn, as far as possible, at any voltage in the network. Care must be taken that the ignition and burning voltages be low and, if possible, equal. The ignition potential depends on the pressure of the corresponding gas. For small pressures it is comparatively large (about $\frac{1}{1000}$ mm Hg); at a pressure of approximately 1 mm it passes through a minimum and thereafter increases again. In tubes with a gas filling, the pressure can from the very beginning be chosen so that the ignition potential lies near its minimum. Tubes with metal vapors require, for this purpose, at least additional heating, since the vapor pressure of metals at room temperature is less than $1/1000$ mm Hg. It is possible, however, to fill such tubes with a noble gas at the corresponding pressure and, thanks to this, first ignite them.

To ensure ignition, an additional glow discharge is passed through the tube; this creates the necessary charge carriers and makes it possible to avoid an excessive increase in the ignition potential.

To reduce the burning voltage, care must be taken to eliminate the voltage drop at the cathode, using a cathode with thermal electron emission. For this purpose, cathodes of pure tungsten are used, as well as with oxides and azides. Especially simple and very effective electrodes are obtained by mixing tungsten with oxides of the alkaline-earth metals.

For industrial application, the form of the alternating-current curve is important, and for two reasons:

1) as was indicated above, in order to reduce the losses arising from the difference between the ignition and burning potentials. The ideal current source would be one that supplied a voltage corresponding to the variable resistance of the consumer—in the present case, the gas-discharge tube. With alternating current this can be approximately achieved, namely by means of a special transformer or a series choke of suitable design, since in this case the voltage differences are eliminated without loss;

2) as was indicated above, it is best, if possible, to supply the tube with a rectangular alternating current. This shortens the “dark pauses,” which is especially noticeable in tubes with high pressure. However, for some purposes another form of curve may also be suitable.

A most interesting technical, as well as physical, problem in the development of gas-light tubes is the increase of efficiency. The energy introduced into the tube is equal to the current multiplied by the burning voltage and by the phase coefficient (about 0.95), and is distributed as follows:

1. Heating of the cathode by positive ions accelerated in the region of the cathode voltage drop.

2. Heating of the anode by electrons accelerated in the region of the anode voltage drop.

3. Losses to convection and thermal conduction as a result of heating of the glass vessel.

4. Radiation outside the desired spectral region, which includes the infrared radiation of the heated glass.

5. Radiation in the desired part of the spectrum. Since, in order to obtain low burning voltages, the voltage drop at the cathode is eliminated, the losses almost completely disappear as well. When alternating current is used, the anode drop (which amounts to up to 10% of the total voltage) can be made to heat the anode to such an extent that during the second half-period, when it is the cathode, it would have sufficient emission. Items 3 and 4

have partly identical causes: heating of the glass vessel, which may occur in various ways; either owing to absorption by the glass of the gas radiation (thus, for example, ordinary glass absorbs all radiation lying outside the spectral interval from 15,000 to 3500 Å), or owing to the energy released in the recombination of ions and electrons. On the other hand, there is heating from the gas, which is itself heated either owing to pure absorption (i.e., “quenching” of excited atoms), or owing to elastic losses when electrons are reflected from gas atoms. According to Sommermeyer’s theory, despite the fact that at each collision the loss of velocity is very small, the elastic losses are, on the whole, of the same order as the losses in the tube in general. Losses due to quenching of radiation can also reach a considerable magnitude, especially when an ultraviolet resonance line of the noble gases is involved (in this case 15–20% is released in a single quenching collision).

The direct heating of the gas itself proceeds differently from case to case. In gases with strong radiation in the far ultraviolet, such as helium and ozone, absorption of these lines can yield a portion of the energy that is converted into heat in the glass. This is clearly shown by the following experiment: if one measures with a thermopile, first, all the radiation emitted by the tube, and, second, only the radiation of the glass heated to the same temperature, then for the ratio of the glass radiation to the total radiation one obtains the value 10:12. If the same experiment is repeated with exactly the same lamp made of glass that transmits ultraviolet, then, for example, with mercury a smaller portion will be absorbed by the glass. With the same supplied energy, and also with constant total radiation, the value obtained for the aforementioned ratio is 9:12; that is, the glass absorbs less and, correspondingly, emits less.

From a number of experimental facts it is evident that losses upon reflection must play an extremely important role in the energy balance of gas-discharge tubes. For example, when heavier basic gases are used, the losses

on reflection, and at the same time the heating of the glass vessel is less than with lighter ones, which is in agreement with Sommermeyer’s calculations.

For technical discharge tubes the energy balance turns out to be such that, of the total supplied energy, 70% is expended through thermal conduction and radiation of the glass, approximately 10% is spent on heating the electrodes, and the remaining 20% falls on the radiation transmitted by the glass. Depending on the spectral composition of the radiation transmitted by the glass, these 20% are distributed over various spectral regions. In sodium, for example, chiefly the resonance lines around 5900 Å and two infrared lines around 8200 and 11,000 Å are emitted. The ratio of the \(D\) line to both infrared lines is approximately \(3:1\), so that of the 20% of radiated energy approximately 15% lies in the visible region. With neon one can obtain an efficiency of radiation of 17%, since its infrared radiation is very weak. Sodium differs from neon also in that sodium has weak ultraviolet radiation. If one takes care that the losses of electrons upon reflection are small, i.e., uses heavy rare gases, for example krypton, then the amount of energy converted in the glass into heat is small. Thus the efficiency of radiation is high; moreover, no radiation is absorbed by the gas. However, it is then necessary somehow to take care of a sufficient pressure of sodium vapor, amounting to \(1/1000\) mm Hg. For example, the tube may be heated from the outside. Indeed, in experiments of this kind, when not only the tube but also the electrodes were heated from the outside, an output of the \(D\) line of about 370 Lm/Watt was achieved. Since the luminous equivalent* for the \(D\) line is 530 Lm/Watt, the output achieved is therefore above 60%, which, together

* The luminous equivalent is the number of lumens corresponding to 1 watt of radiant energy. Clearly, the luminous equivalent depends on the curve of the spectral sensitivity of the eye. The luminous equivalent has its greatest value for green monochromatic light—624 Lm/Watt. For radiation corresponding in its spectral composition to white light, the luminous equivalent is 248 Lm/Watt. Translator’s note.

with infrared lines makes it possible to convert the supplied energy into radiation with an efficiency of 80%.

Unfortunately, this high economy cannot be used technically, since neither the tube nor the electrodes should be heated externally. To obtain the necessary sodium-vapor pressure, the tube has to be heated at the expense of losses.

In any case, the experiments have shown that the possibility is not excluded of significantly raising the existing limits of luminous efficacy (for example, 15% for sodium lamps). The technical development of the measures required for this will be a task for the coming years.