M K ! I DEPARTMENT OF SCIENTIFIC AND INDUSTRIAL RESEARCH i RADIO RESEARCH ' S pecial R eport N o 11 i i THERMIONIC EMISSION , ; A SURVEY OF EXISTING KNOWLEDGE WITH PARTICULAR REFERENCE TO THE FILAMENTS OF RADIO VALVES. ! i • i I .>■ PRICE2s.6d.NET "V ! f V : * /• p SV .V" i r. : .?•; ’ i :v ■ ■ ‘ -v • ■ t: .* DEPARTMENT OF SCIENTIFIC AND INDUSTRIAL RESEARCH RADIO RESEARCH S pecial R eport N o 11 THERMIONIC EMISSION A SURVEY OF EXISTING KNOWLEDGE WITH PARTICULAR REFERENCE TO THE FILAMENTS OF RADIO VALVES BY W. S. STILES, P h .D. Crown Copyright Reserved LONDON : PUBLISHED BY HIS MAJESTY ’ S STATIONERY OFFICE 1932 47 — 29 — 11 ii RADIO RESEARCH BOARD Lieut.-Col. A. G. L ee , O.B.E., M.C., M.I.E.E. (Chairman). Colonel A. S. A ngwin , D.S.O., M.C. {representing the Post Office). Professor E. V. A ppleton , D.S c ., F.R.S. N. A shbridge , Esq. Captain J. W. S. D orling , R.N. (representing the Admiralty). Professor C. L. F ortescue , O.B.E. Colonel A. C. F uller , O.B.E. (representing the War Office). Sir J oseph E. P etavel , K.B.E., D.Sc., F.R.S. G. C. S impson , Esq., C.B., C.B.E., D.Sc., LL.D., F.R.S. H. E. W imperis , Esq., C.B.E., F.R.Ae.S., M.I.E.E. (representing the Air Ministry ). COMMITTEE ON THERMIONIC VALVES E. H. R ayner , Esq., Sc.D. (Chairman). Professor E. V. A ppleton , D.S c ., F.R.S. S. B rydon , Esq., D.Sc. Professor C. L. F ortescue , O.B.E. N. H echt , Esq. Professor F. H orton , D.S c ., F.R.S. H. G. H ughes , Esq., M.Sc. G. W. C. K aye , Esq., O.B.E., D.Sc. R. A. W atson W att , Esq. Professor R. W hiddington , D.S c ., F.R.S. V, • iii PREFATORY NOTE r T T HE subject of thermionics has developed in a few years from A a method of studying the electrical properties of matter to being the basis of one of the world's widest commercial applications of physical science. The phenomena involved are fundamental, being those on which are based theories of the constitution of matter as we at present perceive it. The literature on the subject is widespread, and much of it inevitably abstruse. It was decided by the Radio Research Board on the advice of the Thermionics Committee, that for the furtherance of knowledge, for facilitating research and technical developments, a critical survey of the literature of the subject would be of very real value. The compilation of this survey was entrusted to W. S. Stiles, Ph.D., of the National Physical Laboratory. An endeavour has been made to include the most important papers up to December, 1930. It will be observed that in the Bibliography which accom panies the Survey a Decimal System of Notation has been employed, and that gaps in the numbering have been left to enable the reader to insert later references approximately in their proper position. E. H. RAYNER, Chairman, Thermionic Committee, Radio Research Board. D epartment of S cientific and I ndustrial R esearch , 16 O ld Q ueen S treet , L ondon , S.W.l. January, 1932. iv CONTENTS PAGE 1 S ection 0. General Outline 12 S ection 1. The Theory of the Temperature Emission of Electrons .. S ection 2. Variation with Temperature of Specific Electron Emission in Vacuo and Values of the Richardson Constants .. 44 59 S ection 3. Heat Effects in Thermionic Emission 65 S ection 4. The Distribution of Velocities of Thermionic Electrons .. S ection 5. Effect of Applied Electric Field at the surface of the Emitter (Schottky Effect) 70 78 S ection 6. The Photo-thermionic Effect 81 S ection 7. Thoriated Filaments and other Thin Film Emitters 97 S ection 8. Oxide-coated Filaments 107 B ibliography 114 A uthor I ndex SECTION 0 GENERAL OUTLINE PHENOMENA of a thermionic character had been observed 1 many years before the nature of the effects was realised. The systematic study of the subject may be said to commence with R ichardson ’ s paper On the Negative Radiation from Hot Platinum (0.099) in 1901, and his comprehensive memoir, The Electrical Con ductivity imparted to a Vacuum by Hot Conductors (0.100) in 1903. The attitude is here definitely adopted that the negative leak from a hot body to an auxiliary electrode in vacuo represents the simplest case of conductivity produced by matter at high tem peratures. It is assumed that electrons, normally retained in the substance by a potential discontinuity at the surface, are able, with rise of temperature and consequent increase in the velocities of thermal agitation, to escape through the surface and constitute a current between the hot body and the auxiliary electrode. If a Maxwellian distribution of velocities of the electrons within the metal be assumed, and if there is a potential discontinuity O at the surface, then the number of electrons which pass out from unit area of the surface per second is given by kT N 2^exp{-® e /AT}*, where k = gas constant for a single electron. T = absolute temperature. e = charge of an electron. m = mass of an electron. N = number of electrons per unit volume in the metal. If all the electrons which are emitted are driven across to an auxiliary electrode, the anode, by means of a sufficiently intense electric field, the saturation current between the anode and the emitter so obtained will amount to SN exp { — O e/kT}, where S is the area of the emitting surface. The experimental test and verification of the formula relating saturation current and temperature was carried out by R ichardson for platinum, carbon and sodium. He found that the conductivity * To avoid confusion between the base of natural logarithms and the electronic charge, e x is written exp (x). 2 THERMIONIC EMISSION in vacuo between an electrically-heated filament of Pt or C and a cold auxiliary electrode was, in fact, essentially unipolar, a current being obtained only when the applied potential was such as to drive electrons away from the emitter. For sodium, secondary effects gave rise to a conductivity in the opposite direction, but this never exceeded a twentieth of the " negative ” conductivity. The values of the constants in the formula Saturation current per unit area in amps./cm. 2 derived as the final results, are as follows : — ^ = AT* exp ( — b/T) A b Pt .. C .. Na .. 4-93 X 10 4 7-8 X 10 4 3-16 X 10 4 1-6 x 10 7 1-6 x 10 15 1-6 X 10 12 R ichardson points out in the same paper that the product of b and the cube root of the atomic volume is nearly a constant for these three elements. The hypothesis that the negative thermionic current is to be attributed to electrons ejected from within the substance of the emitter was almost immediately called in question by W ilson , On the Discharge of Electricity from Hot Platinum (0.110), who in an investigation of the effects of gases on the negative leak from platinum wires found that treatment of the Pt wire with nitric acid very considerably reduced the saturation current, the admission of a little hydrogen, however, bringing the current back to its former value. Although the introduction of nitrogen and water vapour gave the same current as obtained in a vacuum, provided ionisation by collision did not occur, for hydrogen a considerably larger current was obtained. W ilson drew the conclusion that the thermionic emission of platinum in vacuo is due to traces of hydrogen occluded on the surface of the platinum. W ilson further showed that a thermo-dynamic proof of the Richardson formula i = AT* exp ( — b/T) could be given, based on the analogy between the emission of negative ions by the hot body and the evaporation of molecules from a fluid. This proof did not require the electrons to come from within the metal, as assumed by R ichardson , and hence if the thermionic current were due to some surface action producing electrons, the formula relating measured saturation current and temperature would still have the form of the Richardson result. While the emission from metals occupied the attention of English physicists, a number of investigations were being carried out by W ehnelt , On the Discharge of Negative Ions by Glowing Metallic Oxides and AUied Phenomena (0.119), on the discharge of negative ions by glowing metallic oxides. The results obtained by him are summarised in a paper of 1905 (0.120). Metallic oxides were found to give a negative emission similar to that from metals, which I 3 GENERAL OUTLINE varied with temperature in the way required by Richardson's formula. W ehnelt did not give actual values of the emission constants, but for BaO and CaO R ichardson calculated them from Wehnelt ’ s results : — A b 1 • 15 x 10 8 0-72 x 10 8 A fairly extensive investigation of the current from a Nemst filament, including the variation with temperature of the negative leak in vacuum, was carried out by O wen , On the Discharge of Electricity from a Nemst Filament (0.121), in 1904, and again, R ichardson calculated the emission constants which were not given explicitly by O wen : — Nemst filament. A = 10 4 ; b = 4*62 X 10 4 The paper by R ichardson , The Emission of Negative Electricity by Hot Bodies (0.130), in 1904, summarises the state of the subject at the time and includes a table of emission constants (R ichardson , W ilson , O wen , W ehnelt ), with a critical discussion of these. At the time of this review it was still questionable whether or not the emission from oxide-coated metals consisted merely of a secondary effect due to a lowering of the exit work for the metal by the oxide layer. D eininger , Emission of Negative Ions from Glowing Metals and from Glowing Calcium Oxide (0.140), to throw light on this point, measured the emission of metal and carbon wires, and then coated the wires with calcium oxide. The emission from the coated wires was found to depend only on the oxide coating and not on the character of the underlying filament. H orton , On the Discharge of Negative Electricity from Hot Calcium and from Lime (0.141), compared the emissions from platinum, calcium on platinum, and lime on platinum, in helium at 3-24 mm. pressure and found the following values for the constants in Richardson ’ s formula : — BaO 4-49 X 10 4 4-28 X 10 4 CaO b A 6-1 X 10 4 3- 64 x 10 4 4- 79 X 10 4 1-6 x 10 6 1-7 x 10 4 6-4 x 10 4 M artyn , The Discharge of Electricity from Hot Bodies (0.142), measured the increase in the emission from a hot platinum wire due to (a) the introduction of hydrogen, (b) coating the wire with lime, and found the two effects occurred independently. J entzsch , Electron Emission of Glowing Metal Oxides (0.143), following up the work of D eininger , obtained in an extensive investigation of the emission from oxides the following values for the constants in the Richardson formula : — AT* exp ( — 6/T). Pt .. Ca on Pt .. CaO on Pt .. 4 THERMIONIC EMISSION He states that at the pressures worked with (about 1 mm.) the emission is independent of gas pressure. Oxide of A b <j> in volts = kb/e. Ba 141 X 10 15 x 10 15 X 10 15 X 10 10 41-6 x 10 3 44-9 x 10 3 40-3 x 10 3 39-5 x 10 3 3-5S Sr 152 3-S7 Ca 129 3-4S Mg 1-01 3-40 2-06 Be 0-31 23-9 x 10 3 36- 3 x 10 3 37- 9 x 10 3 37-3 x 10 3 36-6 x 10 3 35-6 x 10 3 X 10 3 35-1 x 10 3 56-9 x 10 3 51-2 x 10 3 30-2 x 10 3 30*2 'x 10 3 22-5 x 10 3 313 X 10 10 X 10 10 X 10 10 x 10 10 x 10 10 X 10 10 X 10 10 x 10 10 x 10 10 X 10 10 x 10 10 x 10 10 Y 5,590 3-26 206 La 3-21 •92 A1 315 3-06 1,970 Zr Th 10-5 3-20 Ce 586 37- 3-02 0-0919 Zn 3-02 Fe 1,060 8,370 1,590 4-04 Ni 4-41 2-60 Co Cd 0-112 0-00105 x 10 10 2-60 In 1-94 At this time both R ichardson , The Ionisation produced by Hot Platinum in Different Gases (0.150), and W ilson , The Effect of Hydrogen on the Discharge of Electricity from Hot Platinum (0.151), published accounts of further experiments on the effect of gases, notably hydrogen, on the negative emission from hot platinum. The general conclusion reached by these workers was that the large effects on the emission observed were to be attributed to surface actions, volume absorption being relatively unimportant. R ichard son regarded the surface action as a lowering of the exit work. We have to notice at this period a discussion which seems to have been initiated by S oddy , The Wehnelt Kathode in a High Vacuum (0.160), in 1907, and which is of particular interest as it culminated in the elucidation of the effect of space charge on the maximum current obtainable between electrodes in a thermionic tube. S oddy was unable to reconcile the assumption of specific temperature emission from Wehnelt cathodes in high vacuum, with the diminution of emission current observed on improving the vacuum conditions. Both R ichardson (0.161) and W ehnelt (0.162) answered these criticisms, but S oddy (0.163) in a further communica tion described experiments with a Wehnelt cathode which tended to show that gaseous ionisation and not specific electron emission was responsible for the conductivity produced by the glowing oxide. L ilienfield (0.164), in a reconsideration of Soddy ’ s experiments and other experiments of his own, made the suggestion that under good vacuum conditions the electrons in the space between the elec trodes will tend to inhibit the passage of the thermionic current and 5 GENERAL OUTLINE an increased anode potential will be necessary to ensure saturation. When gas and therefore positive ions are present, however, the negative space charge is largely neutralised, and for given anode potential and temperature of the emitter the thermionic current is more than under vacuum conditions. Despite difficulties in obtaining ideal conditions for thermionic emission, the use of the emission to measure temperature was considered by R ichardson , The Application of the Ionisation from Hot Bodies to Thermo-metric Work at High Temperatures (0.169), to be a promising possibility. The very consistent results obtained by D eininger were used to illustrate how this might be done and the precision which should be attained, an error of not more than about 5° at 1,500° K. being indicated. The theory put forward originally by R ichardson required that the electrons emitted by a hot body should have velocities distributed in accordance with the Maxwellian Law for the distri bution of velocities among gaseous molecules. The first experi ments made on the actual distribution of velocities among the emitted electrons were by R ichardson and B rown , The Kinetic Energy of the Negative Ions Emitted by Hot Bodies (0.170), who measured the distribution for the components normal to the emitting surface. For platinum in vacuo the Maxwellian Law was found to hold good. Confirmation of the law for the velocity components tangential to the emitting surface was subsequently obtained by R ichardson (0.171). (See Section 4 for later papers dealing with the distribution of velocities among thermionic electrons). It is of interest to note that R ichardson , On Thermionics (0.179), in a paper of 1909, first put forward the suggestion that the phenomena previously referred to as " the emission of elec tricity from hot bodies, termed “ thermionics." recognised expression in scientific literature. Richardson's paper is chiefly concerned with the calculation of the currents between emitting surfaces and collecting electrodes when the initial velocities are taken into account, the mutual repulsions of the electrons in the inter-space being, however, neglected. The cases solved are parallel planes, inclined planes, coaxial cylinders. In 1908 attention was drawn to the temperature changes which may be expected to occur in bodies emitting electrons, owing to the energy required to expel the electrons through the potential dis continuity at the surface. W ehnelt and J entzsch , Temperature Variations in the Electron Emission of Hot Bodies (0.180), Energy of Electron Emission of Hot Bodies (0.181), made measurements of the cooling effect produced in this way for lime-coated platinum wires. The measurements were complicated by heating effects due to bombardment of the filament by positive ions. At the lower temperatures the expected cooling effect was observed, but its magnitude was about ten times that calculated from the exponential the leak from hot wires, etc.," should be The term took root, and is now the >> k 6 THERMIONIC EMISSION constant in the Richardson formula. S chneider , Energy of the Electro7is emitted by Hot CaO (0.182), repeated the experiments of W ehnelt and J entzsch , and again found values for the cooling effect in excess of the calculated value. Meanwhile R ichardson and C ooke , The Heat Developed during the Absorption of Electrons by Platinum (0.183), The Heat Liberated during the Absorption of Electrons by Different Metals (0.184), The Absorption of Heat Produced by the Emission of Ions from Hot Bodies (0.185, 0.186), were engaged in a series of investigations of thermal effects in metal filaments, produced by the absorption or emission of thermionic electrons. The measured cooling effect in tungsten was found to agree very satisfactorily with the com puted value, and substantial confirmation of the theory was thereby obtained. Using Wehnelt cathodes, however, the anomalous results found by W ehnelt and J entzsch were confirmed. Later work on such cathodes by W ehnelt and L iebreich , Energy of the Electron Emission of Hot Bodies (0.187, 0.188), indicated that the emission current was subject to wide variations and these were accompanied by corresponding changes in the measured cooling effect. (See Section 3 for the further consideration of papers dealing with the thermal effects of thermionic emission.) The proof that the negative ions emitted by hot bodies in high vacua are electrons, rests on determinations of the specific charge e/m. Measurements by T homson in 1899 had established the result for carbon filaments. In 1911, B estelmeyer , Path of the Electrons Emitted by Wehnelt Cathode in a Homogeneous Magnetic Field (0.190), carried out a very careful investigation of the e/m value for the ions emitted by a Wehnelt cathode and obtained the result 1 -766 X 10 7 e.m. units, which represented probably the most accurate determination of the specific charge of an electron available at that time. It had long been known that, in addition to emitting electrons at sufficiently high temperatures, hot bodies also gave a positive ion emission which was usually of a transitory character, decaying more rapidty with time the higher the temperature. By measure ments of the ratio of charge to mass of the positive ions emitted by a large number of different substances (Pt, Pd, Ca, Ag, Ni, Os, Au, Fe, Ta, W, C, brass, steel, nichrome), R ichardson and H ulbert , The Specific Charge of the Ions Emitted by Hot Bodies (0.195), estab lished that in every case the ratio had about the same value, showing that the ions were independent of the material of the emitter and must be due to some impurity. More accurate experi ments subsequently performed by R ichardson , The Positive Ions from Hot Metals (0.196), showed that in the case of platinum, for the first hours of heating, potassium ions were emitted, followed in the final stages by an emission of sodium ions, with possibly a few ions of iron. The evidence on the nature of the positive ions was later summed up by R ichardson in his treatise (0.241). The 7 GENERAL OUTLINE conclusion reached was that the initial positive ion emission from hot metals consists of ions of the alkali metals and chiefly of potassium ions. The view that the emission of electrons from sodium, potassium, calcium and the metallic oxides arose as a secondary effect of chemical reactions, was strongly urged by F redenhagen , Emission of Negative Electrons by Heated Metals (0.200), Behaviour of Wehnelt Cathode in Different Gases (0.201), as a result of a number of investi gations. P ring and P arker , and P ring , The Ionisation Produced by Carbon at High Temperatures (0.202, 0.203), investigating the emission from carbon, found the saturation current decreased con tinuously as the pressure decreased, and with progressive purification of the carbon. They formed the conclusion that the high currents formerly observed for carbon by R ichardson were to be attributed to chemical reactions with the impurities in the carbon and with the residual gases. R ichardson , The Origin of Thermal Ionisation from Carbon (0.204), criticised Pring and Parker ’ s conclusions. The theory of a specific temperature emission of electrons was again thrown open to doubt by the work of these investigators. In a paper in 1913, however, in which L angmuir , The Effect of Space Charge and Residual Gases on Thermionic Currents in High Vacuum (0.210), records the results of investigations on the limita tion of thermionic currents by space charge and the effects of traces of residual gases on the emission, the researches of F reden hagen , P ring and P arker are reconsidered in the light of the new knowledge available, and it is shown how space charge limitation and residual gas effects may vitiate the conclusions of these writers. L angmuir emphasised the precautions necessary to obtain reliable and significant results in thermionic measurements and his paper marks the beginning of an era of exact measurements in ther- mionics. L angmuir showed that if the anode potential V be kept constant, and the temperature raised above a certain value, the current obtained is independent of temperature and is given by the expression /. V 3 ' 2 .s/w, where / is a constant depending on the dimensions and arrangement of the electrodes. A similar result was obtained by S chottky , Action of Space Charge in Thermionic Currents in High Vacua (0.211), at about the same time, and several years earlier C hild , Discharge from Hot CaO (0.212), had derived the formula in connexion with positive ion emission. The modifications necessary when the initial velocities of the electrons are taken into account (these were neglected in the theory leading to the three halves power law) are dealt with by S chottky and others. R ichardson , The Emission of Electrons from Tungsten at High Temperatures : an Experimental Proof that the Electric Current in Metals is carried by Electrons (0.213), described a further attempt 8 THERMIONIC EMISSION to provide convincing proof of the pure temperature character of the negative emission from tungsten, in a paper in 1913. The tubes used were carefully prepared in accordance with the technique found necessary by L angmuir The magnitude and persistency of the thermionic current obtained were such as to rule out the possibility of the electrons being produced by gas impacts on the surface, or by any chemical process involving consumption of the tungsten. K. K. S mith , Negative Thermionic Currents from Tungsten (0.214), continued Richardson ’ s work. D ushman , Determination of ejm from Measurements of Thermionic Currents (0.215), in the account of a series of experiments on the emission from tungsten under space charge limitation conditions, after pointing out the substantial confirmation of the law derived by C hild , L angmuir and S chottky for the maximum current for a given anode voltage, remarks : — “ The perfect definiteness of the results obtained, which are independent of vacuum conditions after a sufficiently high vacuum has once been attained, the reproducibility of the observations even after allowing gas to enter the tube and then re-exhausting, and the quantitative agreement obtained, not only in the above experi ments, but in all the experiments so far carried out in this laboratory, point to the existence of a pure electron emission per se, which is not a secondary effect due to chemical reactions, as assumed by a number of other investigators, and which is a function of the temperature only." S chottky , Influence of Structure Effects, in particular the Thomson Image Force, on the Electron Emission of Metals (0.216), dealing with the effects to be expected owing to the constitution of the thermionic emission current as a stream of electrical particles and not a continuous flow, reaches the interesting conclusion that the maximum current obtainable from a surface emitting electrons will be dependent on the electric field at the surface. This “ Schottky Effect ” was detected experimentally by S chottky and his theory confirmed. (See Section 5 for further papers dealing with the effects on the emission of an applied electric field at the surface.) In 1914, L angmuir , The Electron Emission from Tungsten Fila ments containing Thorium (Title alone published) (0.220), gave a description before the American Physical Society of an effect on the emission from a tungsten filament of a small quantity of thorium, present originally in the tungsten filament as thoria. The emission was in some cases increased by many thousand times. A number of brief references to the effect were made by L angmuir , Langmuir (0.221), The Relation between Constant Potentials and Electro-chemical Action (0.222), The Constitution and Fundamental Properties of Solids and Liquids (0.223), in the period 1914-1923, but the detailed discussion of his experiments was deferred until 1923. (See Section 7 for further papers on the emission from thoriated filaments and other thin film emitters.) 9 GENERAL OUTLINE An investigation by S chlichter , Spontaneous Electron Emission from Glowing Metals and the Thermionic Element (0.230), of the “ spontaneous ” current between a hot emitter and a cold receiving electrode practically surrounding the emitter, as compared with the saturation current obtained by applying a potential difference across the electrodes, is of interest. For platinum the two currents were found to be nearly the same at all temperatures worked with, and the absence of any considerable reflection of electrons is indicated. A valuable review of the investigations on thermionics in the years 1905 to 1914 was published by S chottky , Review of Thermal Emission of Electrons (0.240) in 1915. In the following year R ichardson ' s treatise, The Emission of Electricity from Hot Bodies , 1st Edition (0.241), appeared. A further comprehensive account of the subject was given by R ichardson , Thermionic Electrodes (0.242) in 1917. The values of the constants A and b in the Richardson equation AT* exp { — bI T), as measured by different investigators in high vacua in the presence of gases, after various treatments of the filament, etc., were shown by R ichardson , The Influence of Gases on the Emission of Electrons and Ions from Hot Metals (0.250), to conform to a simple empirical relation, log A = a.b -f p, where a and p represent constants characteristic of the emitting substance (platinum or tungsten). A theory of the effect of gases on emission is put forward by R ichardson , which leads to the empirical equation just given. It was pointed out by C ase , New Strontium and Barium Photo electric Cells (0.270, 0.271), that the saturation current in an audion tube containing a filament coated with alkaline earth oxides is increased by illumination of the filament. Case attributes the effect to photo-electric emission from or by alkaline earth metals formed on the filament by reduction of the oxides. (See Section 6 for further papers dealing with the effect of fight on thermionic emission.) The theoretical relation between contact difference of potential and thermionic emission had been derived in the early development of the theory which led to the formula V = (klje) log i 2 li x where V is the contact potential difference between two surfaces at absolute temperature T and i x and i 2 are the thermionic saturation currents per unit area at the same temperature. An experimental proof of the result was given by R ichardson and R obertson , Contact Difference of Potential and Thermionic Emission (0.280), who determined the change in the contact difference of potential between a thoriated tungsten filament and the cold anode, on activating the filament. The shift in the current-anode voltage characteristic gives immediately the change in the contact difference 10 THERMIONIC EMISSION of potential, assuming the anode to be unaffected by the activation. The theoretical formula was satisfactorily confirmed. The effect of intense electric fields on the thermionic saturation current and other phenomena involving the potential conditions and microstructure of the emitting surface were discussed by S chottky , Cold and Hot Electron Discharges (0.290), in non- mathematical terms. The paper forms a fairly complete account of the author ’ s views on the image force and its manifestations. The introduction of caesium vapour into a thermionic tube was found by L angmuir and K ingdon , Thermionic Effects caused by Alkali Vapours in Vacuum Tubes (0.300), to modify the electron emission in a characteristic fashion. (Papers on this subject are dealt with in Section 7.) A decrease in the emission current from a tungsten filament when run at temperatures approaching the melting point was observed by J enkins , On the Emission of Positive Ions from Hot Tungsten (0.310). This is related by J enkins to the evolution of positive ions by the tungsten. This positive ion emission is of an entirely different character from that previously observed at lower temperatures, and in the presence of gases. A general account of thermionic phenomena is contained in a monograph by B loch , Thermionic Phenomena (0.320), published in 1923. Certain substances containing iron and alkali metal were investi gated by K unsman , The Thermionic Emission from Substances containing Iron and Alkali Metal (0.340), A New Source of Positive Ions (0.341), who found them to be constant sources of both positive and negative emission. The positive emission was identified as singly-charged ions of the alkali metals. Both emissions followed Richardson's equation, AT* exp { — pe/kT). Corresponding values of <f> for the positive and negative emissions in a given case were 3*41 and 4-00 volts respectively. (See 0.195, 0.196.) M itra , On the Emission of Positive Electricity from Hot Tungsten in Mullard Radio Valves (0.360), carried out a similar investigation to that of J enkins on the emission of positive ions from tungsten at high temperatures, using commercial radio valves. B rewer , Factors Influencing Thermionic Emission (0.390), The Relation between Temperature and Work Function in Thermionic Emission (0.391), observed the emission from gold and iron at atmospheric pressure of various gases, and found the positive and negative currents satisfied Richardson ’ s equation, there being a relationship between the constants of the negative and positive emissions under different conditions. An important treatise on thermionic emission appeared in 1928 as a volume of the Wien-Harms Handbuch der Experimental Physik (0.400). The work is divided into three sections, " Physics of Thermionic Emitters, ” by S chottky and R othe , “ Preparation of Thermionic Electrodes,” by S imon , and " Technical Electron 11 GENERAL OUTLINE Tubes and their Application, ” by R othe The first section includes a very comprehensive treatment of the thermo-dynamic theory of electron emission with detailed comparison with the experimental results. The effects of surface layers of other substances and the atomic and image fields at the surface are fully considered. It was observed by J ones and D uran , Electron Emission at the Surface of Platinum through which Hydrogen is Passing (0.405), that if hydrogen is passed through the walls of a hot platinum tube the emission of electrons from the exit surface far exceeds the Richardson current appropriate to platinum at the temperature concerned. The effect was complicated by surface actions similar to those originally observed by W ilson (0.110). Positive ion emission from tungsten, molybdenum, tantalum and rhodium was detected by W ahlin , The Emission of Positive Ions from Metals (0.410), when the temperature of the metal was sufficiently high for vaporisation to become appreciable. (Compare J enkins (0.310) and M itra (0.360).) An initial transitory emission of alkali metal ions occurred. S mith , The Emission of Positive Ions from Tungsten and Molybdenum (0.420), working on the same effect, used a mass spectrograph and showed that at moderate tempera tures (1,600-2,000° K.) tungsten and molybdenum emit sodium and potassium ions. Above 2,000° K. aluminium ions appear, and finally at about 2,500° (W) or 2,300° (Mo) ions of the heated metal itself are emitted. The work functions for the metal ions were determined by temperature variation measurements, as p = 6 • 55 volts (W), <j) = 6*09 volts (Mo). These values differ widely from those found by assuming the sum of the work functions of the electron and positive ion to equal the ionisation energy plus the heat of evaporation of the neutral atom. It is suggested that the ions are formed as a by-product of an irreversible recrystallisation of the metal. A brief sketch of the development of the theory and experimental measurement of thermionic emission from metal surfaces is con tained in a Dutch paper by Z wikker (0.425). The thermionic properties of tungsten in iodine vapour were examined by K aland yk , Electric Emission of Incandescent Tungsten in an Atmosphere of Iodine (0.430), who found a pronounced aug mentation of the negative emission, decreasing with rise in filament temperature, and increasing with the pressure of iodine. K alandyk attributes the extra emission to negative ions of iodine. A critical review of the whole subject of thermionic emission is contained in a monograph by D ushman , Thermionic Emission- (0.450), published in October, 1930. 12 SECTION 1 THEORY OF THE TEMPERATURE EMISSION OF ELECTRONS T he first theoretical derivation of the expected relation between the number of electrons emitted by a hot body and its temperature, was given by R ichardson , On the Electrical Conductivity Imparted to a Vacuum by Hot Conductors (1.100), on the basis of the classical electronic theory of metallic conduction. The interior of the metal is treated as a region of constant potential, within which the electrons move about in temperature motion precisely as the molecules of a perfect gas at the same temperature. An electron reaching the surface of the metal can escape only if its velocity normal to the surface is sufficient to carry it through a certain potential discontinuity at the surface O. The distribution of velocities being Maxwellian, the number escaping in unit time from unit area of the surface is given by N (£T/2 tiw )J exp (- e 0/6T) where N = number of electrons per unit volume in the metal. T = absolute temperature. k = gas constant for a single molecule (1-37x10 “ 6 c.g.s. units). e = charge on an electron (4 -77x 10 “ 10 c.g.s. e.s. units). <£ = potential discontinuity at surface in c.g.s. e.s. units. If a field is applied to collect all the electrons ejected, the thermionic current obtained is then Se N(^T/2 tcw )* exp (— e 0/&T) where S is the area of the emitting surface. This is Richardson ’ s original derivation of the thermionic emission equation. It is also pointed out in the same paper that the emitting body will lose energy owing to the emission, of amount e O + 2kT per electron. This results in a cooling of the metal (the cooling effect). (The experimental determinations of the cooling effect are dealt with in Section 3.) It is implied in Richardson ’ s analysis, although not pointed out explicitly, that the electrons after leaving the metal will have a Maxwellian distribution of velocities corresponding to the tem perature of the emitter. (See Section 4 on the distribution of velocities among the emitted electrons.) 13 TEMPERATURE EMISSION OF ELECTRONS An expression for the thermionic emission current, of the same form as Richardson ’ s, was derived by W ilson , On the Discharge of Electricity from Hot Platinum (1.101), treating the ejection of electrons as a process analogous to the evaporation of a liquid, and applying the Clapeyron equation. W ilson finds that the electron current equals AT* exp ( — Q/2T), where A is a constant independent of temperature and Q is the internal work done in evaporating one gramme molecular weight of the electrons (expressed in small calories). Use had previously been made by W ilson , On the Electrical Conductivity of Air and Salt Vapours (1.102), of thermodynamical methods, in deriving a similar formula to the above, for the current in an allied problem. A further discussion of the theory of thermal emission of electrons was given by D ebye , Theory of Electrons in Metals (1.110), who drew attention to the relation connecting the Volta difference of potential between different metals, their thermionic emission constants and their Peltier effect. The substance of Debye ’ s paper is as follows. For two different emitters in tempera ture equilibrium in an evacuated enclosure, the potentials and rj> 2 just outside the two bodies will in general be different, and the concentrations n x and n 2 in the electron atmosphere at these places will be given by w 2 /% = exp { e(p 2 — fa)/h T}. Also according to classical electron theory the concentration of electrons inside the two bodies, N x and N 2 will be related to those just outside, by the equations : n x = N x exp { — eOJ&T} n 2 = N 2 exp { — eQJkT }, where and 0 2 are the potential discontinuities at the respective surfaces. Thus n 2 (O2-O1). $2 — = kT log. N* The difference of potential <j> 2 — is identified as the Volta difference of potential between the metals, V. If these be assumed in contact another relation between N 2 and N x may be assumed, namely N P = £T log, TT: N, where P is the Peltier coefficient. Thus — V = P — ( 0 2 — OJ D ebye also discusses the nature of the forces giving rise to the exit work e O of the electrons. A well-known result of electrostatic 14 THERMIONIC EMISSION theory states that a point charge placed near a plane-conducting surface induces on the latter a charge distribution of opposite sign, such that the force between the point charge andjthe surface equals the force between the original point charge and an equal and opposite charge placed at the point where the optical image would be formed by reflection in the surface. This force is known as the Thomson image force. D ebye points out that the Thomson image force between an electron and the plane-conducting surface from which the electron originated, may be regarded as accounting for the whole of the exit work, provided the image force is assumed to act only up to a certain critical distance x 0 (depending on the substance of the emitter) from the surface. The exit work is then given by e 2 /4x 0 This conception is used to show that the Volta difference of potential is for all practical cases independent of the form of the conductors. The question of the relationship between thermionic and thermoelectric effects was taken up by R ichardson , On the Electron Theory of Contact Electro-motive Force and Thermo-electricity (1.111). Some Applications of the Electron Theory of Matter (1.112), in papers published in 1912. Debye's result is confirmed and a new relation derived connecting the Thomson specific heat of electricity <r, the work done by an electron in escaping from the metal w, and the ratio of the specific heats of electron gas at constant volume and constant pressure, y. Richardson's formula is as follows dw k — e a. 3T “ y — 1 It is obtained by consideration of a system consisting of two emitters of the same metal but at different temperatures, each in equilibrium with electron gas of appropriate pressure and temperature, and joined together by a thin wire which permits of thermal readjustment only infinitely slowly. R ichardson also discusses the possibility of thermionic emission being a type of auto-photo-electric emission brought about by the temperature radiation of the hot body. By means of a thermodynamic argument it is shown that whatever the mode of origin of the electrons (thermionic, photo-electric, etc.) the number per unit volume in eq