IPa. MICROWAVE ABSORPTION THE USE OF MICROWAVES IN THE STUDY OF IONIC AND CHEMICAL EQUILIBRIA AT. HIGH TEMPERATURES BY T. M. SUGDEN Dept. of Physical Chemistry, University of Cambridge Received 1st February, 1955 An account is given of the methods available for measuring the concentration of free electrons in gases at high temperatures by the absorption of microwave radiation. The applications of these to the study of ionic and chemical equilibria in the hot gases produced by burning various combustible mixtures are described. The simplest problem dealt with is that of the thermal ionization of the alkali metals. This is modified by the inter- action of the metal and of free electrons with the free hydroxyl radicals in the hot gases to produce gaseous alkali hydroxides and negative hydroxyl ions respectively.These reactions may be elucidated and the thermochemical data characteristic of them deter- mined, Introduction of halogens into flame-gas sys tems containing traces of alkali metal gives rise to halogen ions and gaseous alkali hydroxides, whose equilibria may be studied: Brief accounts of other work, on the ionization of alkaline earths, and on the electrons liberated by carbon particles in luminous flames, are given. The purpose of this introductory paper is to outline the basis of the application of microwaves to the study of some chemical reactions in the gas phase at high temperatures. Subsequent papers in this section will deal with two particular aspects-the ionization of the alkaline earths, and the electron affinity of the hydroxyl radical.The principle of the measurements is very simple, in that the absorption of microwave radiation by free electrons is used to obtain the concentration of these electrons in gases at high temperature, and inferences made from the results concerning reactions jm which either electrons enter directly as a component, or in which one of the components also takes part in reactions involving them. Examples of these are the simple ionization of an atom of inetal A A % A+ -I- E , and the formation of the hydroxide of a inetal AOH + A + OH. In the latter case, the amount of metal available for the direct ionization is effectively reduced by removal of a proportion of it as the hydroxide. The techniques are somewhat different from those of conveiitional microwave spectro- scopy, in that careful estimates of attenuation are rcquired, whereas frequency measurements are of much less importance.Most of the work in this field has been carried out at Cambridge, where it has been especially applied to flame-gas systems, i.e. systems in which a medium for the study of thermal ionization at high temperatures is obtained by burning a combustible mixture in a suitably designed apparatus. These systeins will be described briefly, followed by an outline of the microwave methods used, and a discussion of the problems which may be studied, with some remarks on the scope of the results. 68T. M. SUGDEN 69 FLAME-GAS SYSTEMS In order that the interaction of microwaves with free electrons in hot gases (> 1500" K) may be studied in the laboratory, it is necessary to produce a zone of such gases which is reasonably extended (a few centimetres) and uniform.One very convenient method of doing this is to burn a mixture of combustible and air (or oxygen) in a M&er type of burner, in which the main reactions of combustion take place in small cones of primary reaction a few millimetres in height at the surface of the burner. Above these cones, there is an extended region of hot gases in which a marked degree of thermodynamic equilibrium obtains between the various chemical components, in contrast with the state of affairs in the primary cones. This hot gas gradually cools by entrainment of the surrounding air, although local rises of temperature at the boundaries may occur from burning of excess fuel. Even if these effects are for the moment neglected, the temperature of the burned gas is somewhat different from that calculated on the basis of thermal equilibrium determined solely by the release of heat of the various reactions of combustion involved, on account of heat losses to the burner, for the greater part.The most reliable estimate of temperature can be obtained by the method of sodium D-line reversa1,l which is now thoroughly established as suitable for burned gases at atmospheric pressure. It depends upon the establishment of thermal equilibrium between unexcited 2s atoms of sodium and atoms in the first excited (2P3p9 112) states when a trace of sodium is added to the gases. Good agreement is obtained between temperatures ob- tained by use of the resonance lines of other alkali metals, but sodium is the most convenient to use.The composition of the burned gas can then be calculated from the lmown composition of the fuel and the measured temperature. Thus, if hydrogen is used as fuel, with insufficient air for complete combustion, the burned gas consists mainly of N2, H2 and H20, with up to 0.1 % of free OH radicals and hydrogen atoms, with very minor traces of atomic oxygen and nitrogen. The amounts of these minor constituents may be calculated from the data given in standard works, such as that of Lewis and von Elbe,2 for the equilibria H20 % OH + 4H2, M2% 2H, etc. It will be seen later that the hydroxyl radicals and hydrogen atoms often play important parts in reactions affecting the amount of ionization.In the earlier work in Cambridge,3~ 4 coal-gas was used as fuel, but later work has been done with hydrogen.5-9 Other workers have used acetylene and hydrogen.10 With the gas mixtures usually employed (< 2500" K), the ionization potentials of the normal constituents are too high (> 10 eV) for sensible production of free electrons to occur, and therefore for marked attenuation of microwaves, but an amount of ionization suitable for study may be obtained by the addition of traces of easily ionizable metals, or their compounds. The simplest of these are the alkali metals. They may conveniently be added as traces of fine spray of salt solutions from an atomizer operated by the supply to the burner. It has been found that in most cases all salts of a given metal used lead to the same ionization, so that the anions must be completely broken up or reacted with the bulk of the gases, the salt being merely a vehicle for conveying the metal into the flame.The additive can readily be provided in the range of 1 in 105 to 1 in 109 of the total gases. In order to circumvent the difficulties of inhomogeneity in the column of gases, various devices are used. One useful method is to surround the test flame, to which salt is added, by another flame of the same composition, but without salt. Thus, burning of excess fuel with entrained air occurs in the outer zone, without affecting the salted gases in the first few cm of height. In this way, it has been found possible to obtain columns of burned gas in the inner region in which the temperature does not vary by more than f 10" C over a height of about 12 cm, and over a cross-section of 1.5 cm diameter.Another method 5 9 9 is to surround70 IONIC A N D CHEMICAL EQUILIBRIA the salted flame with a slow stream of nitrogen, which prevents entrainment of air until a suitable height has been reached. This gives a boundary, now con- taining the additive, in which there is a rapid fall of temperature outwards, but since the amount of ionization falls rapidly with decreasing temperature, the effects introduced are not serious. Fuel-rich mixtures are used in general since it is found that these give more uniform conditions in the burned gas. THE RELATION BETWEEN ELECTRON CONCENTRATION AND CONDUCTIVITY The absorption of microwave radiation by gases containing free ions occurs because the ions acquire directed momentum by interaction with the electric field of the radiation, which is then randomized by collisions between the ions and molecules of gas.This effect, which determines the electrical conductivity Qf the gases, will be a function of three variables, the number of ions per cm3, the frequency of the radiation, and the collision frequency of the ions with molecules. Simple electromagnetic theory shows that the dielectric constant and the conductivity may be expressed in terms of these by c = 1 - - 477ne2( ~ 1 ); ( T = . - n:( - 01 ) m o2+u12 o2+w12 ’ in which n is the number of ions per cm3 of mass rn and charge e. o = 2~ (fre- quency of radiation) and w i is the collision frequency of an ion with molecules.It can be seen that the conductivity will be determined almost entirely by electrons on account of their small mass, unless there is an overwhelming preponderance of atomic and molecular ions, which is never the case in this work. These relationships are only of an approximate nature, incorrect assumptions having been made in their derivation. In particular, the effect of collisions on the ions has been replaced by a viscous force proportional to their velocity. Much more complicated formulae have been derived by Margenau 11 using accurate kinetic methods, but provided that the electrical field of the radiation is weak, so that it does not alter the Maxwellian distribution of velocities among the electrons in thermal equilibrium with the rest of the gases to an appreciable extent, the differ- ence between his more complicated formulae and the simple ones above is very slight. In particular, experimental studies of the variation of (T with the frequency of the imposed radiation w have been shown to obey a law of the form given by the simple formula.3 These studies also lead to a value for the collision frequency w I , the values obtained being of the right order of magnitude from the point of view of simple kinetic considerations.Theory is not able to provide accurate quantitative predictions of the collisional cross-section of thermal electrons with molecules of the types occurring in flame gases,12 and thus give good theoretical values of w1, but the experimental values appear to be very satisfactory.On this account, the use of measured (T as a measure of relative numbers of electrons is more accurate than its use as an absolute measure, but the latter is still probably correct within a factor of two. It will be seen below that the very simple behaviour given by sodium in its ionization can often be used in calibration, thereby avoiding some of the difficulties. THE EXPERIMENTAL MEASUREMENT OF ELECTRICAL CONDUCTIVITY Most early work on the electrical conductivity of flame gases has been done by methods which involved the insertion of electrodes or probes in the gases (for a summary, see ref. (13)). This is unsatisfactory, on account of the disturbances introduced, and the measurement of the conductivity at microwave frequencies, where no solid object need be inserted in the gases, seems much more satisfactory, although measurements at intermediate frequencies have also been found to be useful.5 Early, but not very accurate, comparisons of the microwave and d.c.conductivity methods by Andrew, Axford and Sugden 14 in a transient flame showed compatibility between the two sets of results.T . M. SUGDEN 71 Two basic experimental methods have been adopted. The first consists of measuring the attenuation in dblcm of a beam of microwaves in passing through a known thickness of flame gases, usually from a burner of rectangular cross-section. The coefficient x of reduction of the electric field of the radiation in passing through conducting gases is given by where p is the magnetic permeability (which may be set equal to unity) and c is the velocity of light in vacuo.x is related to the attenuation of microwave power per cm /I by /I = 8.7~. At centimetric frequencies, and with the values of electron concentration and collision frequency usually encountered in flame-gas systems, the dielectric constant does not depart appreciably from unity and (4n0/w)* < 1, so that a simple binomial expansion may be performed, leading to Thus, knowing w and wl, the number of electrons cm-3 may be found from a measurement of /3 in db/cm. In a given flame p is directly proportional to n. In the experimental arrangement, microwave radiation from a klystron oscil- lator (usually in the 3 cm or 1.25 cm band) passes through an attenuator of at least 20 db to the column of flame gases, placed between suitably designed horns.It reaches a rectifying crystal via another, similar, attenuator. To facilitate amplification of the detected signal, the output of the klystron is usually modulated by a low frequency square wave. The line must be carefully tuned to eliminate standing waves. The flame gases are made attenuating by the introduction of the additive to be studied, and this attenuation measured by removing the additive, and introducing corresponding attenuation either with a calibrated rotary vane microwave attenuator, or, since the effect is practically purely a resistive one, with a calibrated resistive attenuator placed beyond the crystal. This type of system, with flames about 1 cm thick, is suitable for electron concentrations in the range of 1010 to 1012cm-3. The proportionality with attenuation does not hold for higher values, and the method is too insensitive for lower ones.Its sensitivity has been improved by at least a factor of 10 by using differential systems by Shuler and Weber,lo who employ a method of measuring the change in standing-wave ratio at a crystal fed by two beams, one of which passes through a flame, and by Page,g who has used a double-beam method in which the micro- wave power from two crystals, one of which only is affected by the flame, is balanced by a calibrated differential resistive attenuator. These modifications overcome troubles arising from long-term fluctuations in klystron output. The second method of measuring the electrical conductivity, and hence the concentration of electrons, is to measure the change in Q due to dielectric losses when a conducting column of flame gases is introduced into a cavity resonating at microwave frequencies.This method was first used by Adler 15 to study ion- ization in discharge tubes, and first applied by Sugden and Thrush 16 to a flame problem. It may readily be shown that if Qo and Ql are the values of the Q of such a cavity in the absence and presence of a column of conducting gas of conductivity o occupying part of the cavity respectively, then where g is a numerical factor determined by the dimensions of the cavity and those of the flame, and by its situation inside the cavity. In a simple disposition, such as a cylindrical flame concentric with a cylindrical cavity, this factor takes simple analytical forms.For example, in a TEo, 1,1 mode it is given for this disposition72 IONIC A N D CHEMICAL EQUILIBRIA by a2[- Jo(ka)J2(ka)J/c2([J1(kc)J2 - Jo(kc)J&c)>, where a is the radius of the cavity, c that of the column of flame gases, ka = 3.83 and J’s are Bessel functions of the first kind. For more complicated arrangements g may be estimated by graphical integration. Experimentally, a cylindrical cavity, coupled by irises to a klystron and to a waveguide system suitable for measurement of the transmitted power, is tuned by a plunger to resonate in the TEo,~, 1 or other convenient mode. The frequency of the klystron is swept by a low frequency saw-tooth voltage applied to its reflector so as to cover the resonance characteristic of the cavity.The change of Q on introduction of the conducting column of gases is measured from the changes in form of the characteristic. This method is more sensitive than the simple attenuation one, being able to deal with electron concentrations down to 108 cm-3. The principal experimental drawbacks are connected with introduction of hot gases into such a system. This has been done 16 by making holes of sufficient size in the two ends of the cavity, and preventing the escape of radiation from them by covering them with very coarse gauzes of thick platinum wires, spaced about 1/10 wavelength apart. The column of hot gases may be admitted inter- mittently by interrupting it with a sector disc rotating a few times a second placed between the burner and the lower gauze.This prevents overheating of the gauzes, which tends to distort them and lower Q. The whole cavity may be water-cooled, but not to a sufficient extent to cause condensation of moisture on its inner surface. Another arrangement which has been used is actually to incorporate the burner in the lower end of the cavity. Although this means that the primary cones of combustion are inside the cavity, they are in a region of low electric field where electrons have little effect on the resonant characteristics. In this case, the com- parison is made between “ clean ” (non-conducting) and “ salted ” flame gases. The results for the numbers of electrons cm-3 are usually converted for chemical purposes into concentrations expressed as atmospheres of partial pressure at the measured temperature of the gases, and are then denoted by [ E ] .THE IONIZATION OF ALKALI METALS IN FLAMES Since this problem has received a good deal of study in the past, and since many of the results which have been obtained for it using one or other of the microwave methods illustrate well the kind of information which can be derived, it will be discussed briefly. The nature of the anion of the salt of an alkali metal A having been established to be of no consequence in determining the con- centration of electrons produced, the equilibria which are considered to be im- portant in flame gases are the following : A % A+ + E ; K = [A+][e]/[A], K’= [A][OH]/[AOH], AOH % A + OH; OH- % OH + E ; K” = [OH][E]/[OH-]. To these equations must be added that for charge balance [A+] = [el + [OH-], and the mass balance for A [Ad = [A1 + [AOHI + [A+].For small ionization, which is often found below 2200” K, the last term of the last equation may be ignored. [Ao] represents the total alkali metal added (free or combined), Solution of these equations with small ionization leads to Eel2 = KCAol/(l + COHIIK’)(1 + [OHllK”), or [El2 = K[Aol/(l + + 49T. M. SUGDEN 73 in which $ = [OH]/K’ and $’= [OH]/R”. The value of [OH] will be held constant by the buffering action of the bulk of the flame gases. This law has been found to hold good over a wide range of conditions. It must be emphasized that the equilibria set out do not necessarily indicate the actual processes by which such equilibria may be reached and maintained. The actual processes must fulfil certain kinetic conditions, namely, that there shall be sufficient effective collisions for near equilibration in the time available between the burner and the measuring system.This is of the order of a few milliseconds, during which, at a pressure of one atmosphere, and at about 2000” K, a molecule will make about lO7collisions with others, and an electron about lo9 with molecules. In a bimolecular reaction between simple molecules the proportion of effective collisions is given by exp (- E/RT), where E is the energy of activation of the reaction. Thus to satisfy the required conditions, a reaction between a molecule containing one atom of alkali metal and a major constituent of the gases must have E < 50 kcal, and a correspondingly lower value of E if the flame-gas con- stituent involved is a minor one such as OH or €3.This clearly rules out the for- ward processes of all the equilibria set up above, since the ionization reaction X + A -+ X + A+ + E , in which X is any molecule present, requires E to be in the region of 100 kcal. Similar considerations apply to the decomposition of the hydroxide by X + AOH -+ X + A + OH, and also to the decomposition of OH-, if the electron affinity of the OH radical is as high as 65 kcal.9 It is possible however, to find a set of processes which fulfil the required conditions. They are X + A % X + A * A* + OH + A+ + OH- A+H20 % AOH+H OH- + H % H20 + E. The first pair of reactions is the formation and deactivation of excited atoms of alkali metal in the resonance state, involving not more than 50 kcal in the forward reaction in all cases, and which is known to be equilibrated from the consistency of line reversal measurements of temperature made on the various resonance lines.The second of these pairs involves heats of reaction in the neighbourhood of 10-20 kcal, and will involve little, if any, energy of activation in the exothermic direction, since atoms or free radicals take part in the reactions. The third pair is very similar to the second in this respect. The back reaction in the last pair will be endothermic to the extent of about 50 kcal. Again, its energy of activation will not be very much larger than this, and in any case, electrons make many more collisions than molecules. Thus there is ample scope for establishment of chemical and thermal equilibrium between A, AOH, OH- and E .The predicted variation of [el2 cc [Ao] has been found in many instances (see, e.g., 5). The change of the simple atomic ionization with temperature is given by the thermodynamic equation of Saha 17 where Y is the ionization potential in electron volts, T is in OK, and K is in atm. Thus, if the effects of hydroxide and hydroxyl ion formation are slight (both I# and I#’ < l), a plot of the logarithm of the proportionality constant between [el2 and [Ao] against 1/T for a given metal in a series of flames should be a straight line of slope - 5050 V. Similarly, a plot of this logarithm against Vfor various metals in the same flame should be a straight line of slope - 5050/T. Neither of these predictions is found to be the case,6 and it has been concluded that the hydroxyl effects are important.The way in which these effects arising from the formation of alkali hydroxide and of hydroxyl ions have been worked out will74 IONIC A N D CHEMICAL EQUILIBRIA be outlined, and followed by brief accounts of the other systems to which the methods have been applied. THE STABILITY OF THE ALKALI HYDROXIDES IN THE GAS PHASE Measurements of the relative stabilities of the hydroxides can be made by studying the ionization of various alkali metals in a particular flame, which will give results independent of any hydroxyl ions formed. The ratio of electron concentrations for the same total amount of two metals added to a given flame is where $ = [OH]/K’, and K’ is the equilibrium constant of AOH % A + OH.There is sufficient thermodynamic evidence available to show that, under flame-gas conditions, NaOH is formed in negligible amounts, on account of its low heat of formation from Na and OH. Hence rpNa -0, and $ can be deduced for the other alkali metals, and therefore K’. This equilibrium constant will take the form K’ = Cexp (- AE,/RT), where C is a function of the properties of the molecules (masses, interatomic distances and frequencies of vibration) taking part in the equilibrium, and is relatively independent of temperatures, and A E ~ is the heat of reaction at 0°K. C may be estimated with fair accuracy from known data for the atom A and for OH, together with reasonable assumed properties of the gaseous molecules AOH, and thus AEo calculated from the measured K‘.This has given heats of formation for CsOH, KOH and LiOH from the corresponding atoms and OH radicals in the gas phase of 91, 86 and 102 kcal/mole respectively. These fall in the same order as the gaseous alkali fluorides and chlorides, with the same differences between the metals. On this basis, NaOH may be concluded to have a heat of formation of 81 kcal/mole, which justifies the original assumption about its instability. When &i is of the order of 10, as is usually the case, qhNa < 0.1. An important pojnt is that values of AEo obtained in this way, i.e. from absolute values of K’, and hence on the basis of the third law of thermodynamics, agree with values obtained from the variation of K’ with temperature (by com- paring various flames), this being an independent method based on the second law of thermodynamics.This consistency is regarded as a valid test of the approach adopted to problems of this type. THE ELECTRON AFFINITY OF HYDROXYL 9 As has been seen above, the electron concentration given by alkali metals in flame gases may also be influenced by the formation of hydroxyl ions. The earlier work on microwaves has suggested that this OCCU~S,~, 6 and has led to a value for the electron affinity of OH of about 62 kcal/mole. A much more elaborate study of this effect has been made by Page, and is described in a subsequent paper in this Discussion.9 It is based largely on the behaviow of sodium, whose hydroxide can be ignored, leading to [el2 = “aoll(1 + [OHIIK”), where K” is the equilibrium constant of OH- S OH + E.The main contribution made by Page has been to use various initial combustible mixtures which produce flame gases at the same temperature, but wi.th different values of [OH]. The above law is shown to be obeyed, and K” deduced at various temperatures. Consistency is obtained between electron affinities deduced from absolute K” and its variation with temperature, to give a value of 65 f 1 kcal/mole for this important thermochemical quantity. The method therefore supplies a new technique for the determination of electron affinities, in addition to those reviewed recently by Pritchard.18 It is currently being applied to other substances,T. M . SUGDEN 75 THE ELECTRON AFFINITlES OF THE HALOGENS AND THE HEATS OF FORMATION OF GASEOUS ALK,ALI HALIDES The introduction of about 0.1 % of a halogen into the flame-gas supply produces a significant reduction in the electron concentration produced by traces of alkali metals (< 0.01 %).Unpublished work of Smith and Sugden indicates that this should follow a law where K2 and K3 are the equilibrium constants of the reactions AY % A + Y, Y- % Y + E respectively, in which Y is an atom of halogen and A one of alkali metal. [YO] is the total halogen present, expressed as a concentration of atoms. The parameter 8 = [HI/&, where K4 is the equilibrium constant of the dissociation of the halogen acid HY, which may be formed in significant amounts. [q] is the electron concentration in the absence of halogen. This equation, which is found to be obeyed in form, may be applied in different ways, depending on which of the six equilibria which govern it are best known.The second term on the right-hand side is independent of the alkali metal used in a given flame. It can be seen that it offers a new way of determining the electron affinities of the halogens, and the heats of formation of the alkali halides in the gas phase. THE IONIZATION OF ALKALINE EARTHS The ionization of this group of elements in flame gases presents a much more difficult problem than do the alkali metals. The law [el2 (total concentration of added alkaline earth) is not obeyed. It is discussed in the next paper in this Discussion 8 where it is shown that positive ions such as (BaOH)-l- are likely to be very stable, and much more important than Baf.Evidence for negative ions containing alkaline earth atoms is obtained. A very peculiar feature 19 is that addition of extremely small amounts of alkaline earths to flame-gas systems containing alkali metals in reasonably larger quantities causes a marked increase in the concentration of free electrons, to values much greater than would be expected from the separate ionizations. This effect is very specific to given pairs of metals, and indicates a specific interaction between them in the gas phase. Since the alkaline earths exist overwhelmingly in the form of the diatomic oxides such as BaO in flame gases,20 it is considered that the observed effects spring from the formation of a compound positive ion such as (BaONa)+, with basically electrovalent structure Ba2+02-Na+, formed from BaO and Naf.Calculations of the energy changes of this reaction, based on the methods outlined by Rittner,zl show that this is a reasonable assumption. IONIZATION IN “ PURE ” FLAME GASES At the higher temperatures realizable with flame gases (2500-3500” I<), the number of electrons which can be provided by ionization of the normal con- stituents of the flame gases becomes increasingly significant, and has recently been studied by Shuler and Weber 10 for hydrogen flames. The great experi- mental difficulty arises from the ionization of adventitious traces of alkali metals in the gases, which make it very difficult to estimate the residual ionization, The results, however, are not inconsistent with what would be expected.A much more accessible problem is that of the free electrons produced by ionization from particles of carbon such as are present in acetylene flames. Graphite has a work function22 in the region of 4eV, which is low enough to give a measurable ‘‘vapow pressure” of electrons at ordinary flame-gas tem- peratures. This has received preliminary studies by Sugden and Thrush 16 using the cavity method, and more recently by Shuler and Weber 10 using a refined76 IONS OF ALKALINE EARTHS attenuation system. Their measurements indicate a variation of ionization with temperature requiring a rather high work function (- 8 eV). Further study of this important phenomenon is desirable, particularly with regard to the size of the particles, and to the marked increase of ionization which sets in a t the sharp boundary between luminous flames (which contain particles of carbon) and non-luminous ones, in that light might be thrown on the vexed question of how these particles are formed. 1 Gaydon and Wolfhard, Flames, Their Structure, Radiation and Temperature (Chapman 2 Lewis and von Elbe, Combustion, Flames, and Explosions of Gases (Academic Press, 3 Belcher and Sugden, Proc. Roy. SOC. A,, 1950, 201,480. 4 Belcher and Sugden, Proc. Roy. SOC. A , 1950,220, 17. 5 Smith and Sugden, Proc. Roy. SOC. A , 1952,211, 31. 6 Smith and Sugden, Proc. Roy. SOC. A , 1952,211, 58. 7 Smith and Sugden, Proc. Roy. SOC. A , 1953, 219, 204. 8 Sugden and Wheeler, this Discussion. 9 Page, this Discussion. 10 Shuler and Weber, J . Chem. Physics, 1954, 22, 491. 11 Margenau, Physic. Rev., 1945, 69, 508. 12 Mott and Massey, The Theory of Atomic Collisions (Oxford University Press, 1949). 13 Wilson, Modern Physics (Blackie and Co., London, 1944). 14 Andrew, Axford and Sugden, Trans. Faraday SOC., 1948, 44, 427. 15 Adler, J . AppI. Physics, 1949, 20, 1 125. 16 Sugden and Thrush, Nature, 1951, 168, 703. 17 Saha, Phil. Mag., 1920, 40,472. 18 Pritchard, Chem. Rev., 1953, 52, 529. 19 Sugden and Wheeler, to be published. 20 Huldt and Lagerqvist, Ark. Phys., 1950, 2, 333. 21 Rittner, J . Chem. Physics, 1951, 19, 1030. 22 Reimann, Proc. Physic. SOC., 1938, 50,496. and Hall, 1953). Inc., New York, 1951).