# ASTM F83-71 (Reapproved 2013)

Designation: F83 − 71 (Reapproved 2013)Standard Practice forDefinition and Determination of Thermionic Constants ofElectron Emitters1This standard is issued under the fixed designation F83; the number immediately following the designation indicates the year of originaladoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A superscriptepsilon (´) indicates an editorial change since the last revision or reapproval.INTRODUCTIONCathode materials are often evaluated by an emission test which in some ways measures thetemperature-limited emission. A more basic approach to this problem is to relate the emission tofundamental properties of the emitter, in particular, the work function. Comparisons are convenientlymade between emitters using the thermionic constants, that is, the work function, the emissionconstant, and the temperature dependence of the work function. These quantities are independent ofgeometry and field effects when properly measured. Although referred to as “constants” thesequantities show variations under different conditions. Considerable confusion exists over thedefinition, interpretation, and usage of these terms and, hence, there is a need for at least a generalagreement on nomenclature.1. Scope1.1 This practice covers the definition and interpretation ofthe commonly used thermionic constants of electron emitters(1, 2, 3),2with appended standard methods of measurement.1.2 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.3 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:3F8 Recommended Practice for Testing Electron Tube Mate-rials Using Reference Triodes43. Terminology3.1 Definitions:3.1.1 effective work function, φ—the work function obtainedby the direct substitution of experimentally determined valuesof emission current density and temperature into theRichardson-Dushman equation of electron emission of theform:J 5 AT2e2eφ/kT(1)For direct calculation of the work function, this is conve-niently put in the form:φ 5 ~kT/e!ln~AT2/J! (2)where:J = emission current density in A/cm2measured underspecified field conditions except zero field. (J0= emis-sion current density in A/cm2measured under zero fieldconditions.)A = the theoretical emission constant, which is calculatedfrom fundamental physical constants, with its valuegenerally taken as 120 A/cm2·K2. A more exact calcu-lation (3) gives 120.17 which is used in determining theeffective work function.T = cathode temperature, K.e = electronic charge, C.e = natural logarithmic base.k = Boltzmann’s constant.φ = work function, V.The form of Eq 1 is a simplified form of the emission1This practice is under the jurisdiction of ASTM Committee F01 on Electronicsand is the direct responsibility of Subcommittee F01.03 on Metallic Materials.Current edition approved May 1, 2013. Published May 2013. Originallyapproved in 1967. Last previous edition approved in 2009 as F83 – 71 (2009). DOI:10.1520/F0083-71R13.2The boldface numbers in parentheses refer to references at the end of thispractice.3For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.4Withdrawn.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1equation which assumes zero reflection coefficient for electronswith energy normally sufficient for emission at the emittersurface. The effective work function is an empirical quantityand represents an average of the true work function, giving themaximum information obtainable from a single measurementof the thermionic emission.3.1.2 Richardson work function, φ0—the work functionusually obtained graphically from a Richardson plot, which isa plot of ln (J/T2) versus l/T using data of emission measure-ments at various temperatures. It is the work function obtainedfrom Eq 1, with the value of A determined graphically, insteadof using the theoretical value. For better visualization of theRichardson plot, Eq 1 may be put in the form:ln~J/T2! 5 lnA 2 ~e/kT!φ0(3)It can be seen (Fig. X1.4) that the Richardson work func-tion φ0is obtained from the slope of the graph, and theemission constant A from the intercept (l/T = 0) on the ln(J/T2) axis. The Richardson work function is also an empiri-cal quantity. Its value is found with reasonable accuracyfrom the graph. However, large errors in the value of Amaybe expected (4). Considering only one factor, a slight inaccu-racy in the measurement of temperature introduces a largeerror in the value of A. Values of A obtained on practicalemitters can range from about 0.1 to 200 A/cm2·K2.3.1.3 true work function, φt—the difference between theFermi energy and the surface potential energy, which is themaximum potential energy of an electron at the surface of theemitter, or the energy just necessary to remove an electronfrom the emitter. The true work function, φt, is expressed involts or sometimes as eφtin electron volts. For a polycrystal-line surface, the true work function will vary with position onthe surface. It will also be a function of temperature. The truework function is primarily a theoretical concept used inanalysis involving a theoretical model of the surface.4. Interpretation and Relation of Terms4.1 Both the effective (φ) and the Richardson (φ0) workfunctions are derived from the same basic equation for electronemission. They differ in the manner of applying the equation.The effective work function represents a direct computationusing the theoretical value of the emission constant A of theequation. The Richardson work function is based on a plot ofemission data at different temperatures from which both thework function and emission constant were obtained. Workfunction varies slightly with temperature. If this variation isapproximately linear, it can be expressed as a simple tempera-ture coefficient of the work function, α, V/K. Under theseconditions, the emission data yield a straight-line Richardsonplot and, also, result in a straight-line plot of effective workfunction with temperature. These and other relations can beseen by introducing α into the Richardson-Dushman equation(Eq 1) and considering the Richardson work function asrepresenting the value at 0 K. The effective work function attemperature T is then equal to φ0+ αT. Substituting this intothe equation gives:J 5 AT2e2~e/kT!~φ01α T!(4)which can be put in the form:J 5 ~Ae2eα/k!T2e2eφ0/kT(5)It can be seen from Eq 5 that a Richardson plot slope woulddetermine φ0and a value of the emission constant e−ea/ktimesthe theoretical value A. The form of Eq 4 is that used forcalculation of the effective work function, with φ0+ αT sub-stituted for the effective work function φ. It can be seen that φ0,the value at zero temperature, is what would be obtained froma straight-line Richardson plot. These observations are sum-marized in the following equations:φ 5 φ01αT (6)~TheoreticalA/RichardsonA! 5 eeα/k(7)α~k/e!ln~TheoreticalA/RichardsonA! (8)The above expressions are useful in equating and interpret-ing the effective and Richardson constants. For example, if thethermionic constants of an emitter are specified by the effectivework function and temperature coefficient, the equivalentRichardson work function and emission constant may becalculated from the equation. Although α as determined hereserves the purpose of relating the work functions, it should notbe regarded as a true measure of the temperature coefficient.Other methods, such as the cathode cooling effect of electronemission, are available for a more valid determination (4). Thetemperature dependence of the effective work function in-volves many factors such as the presence of a reflectioncoefficient, the effects of averaging over a nonuniform surface,a temperature dependence of Fermi energy and any errors inmeasuring the temperature (including gradients) and effectivearea of the cathode; on aged cathodes interface impedance maybe a factor.5. Keywords5.1 electron emitters; electron tube materials; thermionicconstants; work functionF83 − 71 (2013)2APPENDIX(Nonmandatory Information)X1. EXAMPLES FOR DETERMINING THERMIONIC CONSTANTS OF CATHODESX1.1 The following examples illustrate two customarymethods for determining the thermionic constants of cathodesincluding procedures for establishing the emission current atzero field. Other methods are discussed in the literature (1, 2,3, 4).X1.1.1 Example 1—The Retarding PotentialMethod (4)—To determine the emission at zero field, theemission current from a cathode is measured by varying thecollecting voltage from 2 or 3 V negative to 2 to 5 V positive.The logarithm of the measured emission current is plotted as afunction of the applied voltage for a given cathode temperature(Fig. X1.1).An extrapolation of the two straight portions of thecurve leads to an intersection. At the intersection the retardingfield is zero and, hence, this point determines the zero fieldemission, J0. The effective work function at temperature T isobtained by substituting the values of J0and T in Eq 2. ForFIG. X1.1 Retarding Potential CharacteristicF83 − 71 (2013)3purposes of calculation, Eq X1.1 is expressed with the commonlogarithm and numerical values of the physical constants asfollows:φ 5 1.98 31024T log ~120 T2/J0! volt (X1.1)X1.1.1.1 As shown in Fig. X1.1 the procedure is repeatedfor several cathode temperatures to find the apparent variationof work function with temperature. An alternative method is touse charts (1, 5) or tables (1), from which φ may be determinedfrom J0and T. The values of work function versus temperatureare plotted in Fig. X1.2. The data were obtained on theoxide-coated cathode of a sample ASTM Reference Triode(Practice F8) and confirmed by other investigators. The valuesof J0obtained in this example, although used for obtaining theeffective work function, can also be used for a Richardson plot.X1.1.1.2 At increasing temperatures and higher emissioncurrent, the extrapolation becomes more difficult due to theeffect of space charge until this method is no longer usable.X1.1.2 Example 2—The Schottky Method (2, 4)—An ex-trapolation to zero field emission current from acceleratingfield measurements also can be made and is particularly usefulfor high current densities where space charge effects preventthe use of the retarding field method. (Common devices requirepulsed collecting voltage to avoid excessive power dissipationon the collecting element.) In an accelerating field the Schottkyeffect reduces the surface barrier at the cathode and theemission density is as followsJ 5 J0e ~0.44 =Es/T! (X1.2)where:Es= electric field at the cathode surface in volts per meterand is proportional to the applied voltage V.X1.1.2.1 The zero field emission is obtained by an extrapo-lation of the curve obtained by plotting the logarithm of themeasured currents versus=Vto zero field, Fig. X1.3. Over a considerable voltage range, astraight-line is obtained indicating the validity of theSchottky equation. At lower voltages space charge reducesthe observed current below the value predicted.X1.1.2.2 After determining the zero field emission densityfor a number of temperatures, a Richardson plot is made of thelog J0/T2versus l/T (Fig. X1.4). The slope of the linedetermines the Richardson work function φ0and the extrapo-lated Y-intercept gives the Richardson constant A. These datawere obtained from a barium dispenser cathode. The values forthe emission constants are shown on Fig. X1.4. The values ofzero field emission, used in this example for the Richardsonplot, can also be used for calculating the effective workfunction.FIG. X1.2 Temperature Dependence of Work FunctionF83 − 71 (2013)4FIG. X1.3 Schottky Plot for Determining Zero Field EmissionFIG. X1.4 Richardson Plot of Emission DataF83 − 71 (2013)5REFERENCES(1) Hensley, E. B., Journal of Applied Physics, Vol 32, 1961, pp.301–308.(2) Herring, C., and Nichols, M. H., Review of Modern Physics, Vol 21,1949, p. 185.(3) Nottingham,Handbuch Der Physik, Vol 21, Springer-Verlag, Berlin,1956, p. 1.(4) Herrman, G., and Wagener, S.,The Oxide Coated Cathode, Vol II,1951, Chapman and Hall, London.(5) Jansen, C. G., Jr., and Loosjes, R.,Philips Research Reports, Vol 8,1953, p. 81.ASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this standard are expressly advised that determination of the validity of any such patent rights, and the riskof infringement of such rights, are entirely their own responsibility.This standard is subject to revision at any time by the responsible technical committee and must be reviewed every five years andif not revised, either reapproved or withdrawn. Your comments are invited either for revision of this standard or for additional standardsand should be addressed to ASTM International Headquarters. Your comments will receive careful consideration at a meeting of theresponsible technical committee, which you may attend. If you feel that your comments have not received a fair hearing you shouldmake your views known to the ASTM Committee on Standards, at the address shown below.This standard is copyrighted by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959,United States. Individual reprints (single or multiple copies) of this standard may be obtained by contacting ASTM at the aboveaddress or at 610-832-9585 (phone), 610-832-9555 (fax), or service@astm.org (e-mail); or through the ASTM website(www.astm.org). Permission rights to photocopy the standard may also be secured from the ASTM website (www.astm.org/COPYRIGHT/).F83 − 71 (2013)6