1、Designation: F 83 71 (Reapproved 2002)Standard Practice forDefinition and Determination of Thermionic Constants ofElectron Emitters1This standard is issued under the fixed designation F 83; the number immediately following the designation indicates the year of originaladoption or, in the case of rev
2、ision, the year of last revision. A number in parentheses indicates the year of last reapproval. A superscriptepsilon (e) indicates an editorial change since the last revision or reapproval.INTRODUCTIONCathode materials are often evaluated by an emission test which in some ways measures thetemperatu
3、re-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
4、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 usa
5、ge 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.2. Referenced Documen
6、ts2.1 ASTM Standards:F 8 Practice for Testing Electron Tube Materials UsingReference Triodes33. Terminology3.1 Definitions:3.1.1 effective work function, fthe work function ob-tained by the direct substitution of experimentally determinedvalues of emission current density and temperature into theRic
7、hardson-Dushman equation of electron emission of theform:J 5 AT2e2ef/kT(1)For direct calculation of the work function, this is conve-niently put in the form:f5kT/e! ln AT2/J! (2)where:J = emission current density in A/cm2measured underspecified field conditions except zero field.(J0= emission curren
8、t density in A/cm2measured un-der zero field conditions.)A = the theoretical emission constant, which is calculatedfrom fundamental physical constants, with its valuegenerally taken as 120 A/cm2K2. A more exact calcu-lation (3) gives 120.17 which is used in determiningthe effective work function.T =
9、 cathode temperature, K.e = electronic charge, C.e = natural logarithmic base.k = Boltzmanns constant.f = work function, V.The form of Eq 1 is a simplified form of the emissionequation which assumes zero reflection coefficient for electronswith energy normally sufficient for emission at the emitters
10、urface. 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, f0the work functionusually obtained graphically from a Richard
11、son 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
12、 in the form:1This 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 March 31, 1971. Published May 1971. Originallypublished as F 83 67 T. Last previous edition F 83 67 T.2The
13、boldface numbers in parentheses refer to references at the end of thispractice.3Discontinued, see 1971 Annual Book of ASTM Standards, Part 43.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.ln J/T2! 5 ln A 2e/kT!f0(3)It can be seen (
14、Fig. X1.4) that the Richardson work functionf0is obtained from the slope of the graph, and the emissionconstant A from the intercept (l/T = 0) on the ln (J/T2) axis.The Richardson work function is also an empirical quantity. Itsvalue is found with reasonable accuracy from the graph.However, large er
15、rors in the value of Amay be expected (4).Considering only one factor, a slight inaccuracy in the mea-surement of temperature introduces a large error in the value ofA. Values of A obtained on practical emitters can range fromabout 0.1 to 200 A/cm2K2.3.1.3 true work function, ftthe difference betwee
16、n 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, ft, is expressed involts or sometimes as eftin electron volts. For a polyc
17、rystal-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 effe
18、ctive (f) and the Richardson (f0) 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 Rich
19、ardson 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
20、 the work function, a, 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 a into the Richardson-Dushman equation(Eq 1) and conside
21、ring the Richardson work function asrepresenting the value at 0 K. The effective work function attemperature T is then equal to f0+ aT. Substituting this intothe equation gives:J 5 AT2e2e/kT!f01aT!(4)which can be put in the form:J 5Ae2ea/k!T2e2ef0/kT(5)It can be seen from Eq 5 that a Richardson plot
22、 slope woulddetermine f0and a value of the emission constant eea/ktimesthe theoretical value A. The form of Eq 4 is that used forcalculation of the effective work function, with f0+ aTsubstituted for the effective work function f. It can be seen thatf0, the value at zero temperature, is what would b
23、e obtainedfrom a straight-line Richardson plot. These observations aresummarized in the following equations:f5f01aT (6)Theoretical A/Richardson A! 5 eea/k(7)ak/e! ln Theoretical A/Richardson A! (8)The above expressions are useful in equating and interpret-ing the effective and Richardson constants.
24、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 a as determined hereserves the purpose of relating the work functio
25、ns, 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
26、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 emitt
27、ers; electron tube materials; thermionicconstants; work functionAPPENDIX(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 esta
28、blishing the emission current atzero field. Other methods are discussed in the literature (1, 2,3, 4).X1.1.1 Example 1The Retarding Potential Method (4)To determine the emission at zero field, the emission currentfrom a cathode is measured by varying the collecting voltagefrom 2 or 3 V negative to 2
29、 to 5 V positive. The logarithm ofthe measured emission current is plotted as a function of theapplied voltage for a given cathode temperature (Fig. X1.1).An extrapolation of the two straight portions of the curve leadsto an intersection. At the intersection the retarding field is zeroand, hence, th
30、is point determines the zero field emission, J0.The effective work function at temperature T is obtained bysubstituting the values of J0and T in Eq 2. For purposes ofF 83 71 (2002)2calculation, Eq X1.1 is expressed with the common logarithmand numerical values of the physical constants as follows:f5
31、1.98 3 102 4T 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 f may be determinedfrom J0and T. Th
32、e 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 F 8) and confirmed by other investigators. The valuesof J0obtained in this example, although used for obtaining theeffective work functio
33、n, 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 2The Schottky Method (2, 4)An ex-trapolation to zero field emission
34、 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.)
35、 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)FIG. X1.1 Retarding Potential CharacteristicF 83 71 (2002)3where:Es= electric field at the cathode surface in volts per meterand is proportional to t
36、he 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=V to zero field, Fig. X1.3. Over aconsiderable voltage range, a straight-line is obtained indicat-ing the validity of the Schottky equ
37、ation. At lower voltagesspace charge reduces the observed current below the valuepredicted.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 line deter-mines the Richardson work fu
38、nction f0and the extrapolatedY-intercept gives the Richardson constant A. These data wereobtained from a barium dispenser cathode. The values for theemission constants are shown on Fig. X1.4. The values of zerofield emission, used in this example for the Richardson plot,can also be used for calculat
39、ing the effective work function.FIG. X1.2 Temperature Dependence of Work FunctionFIG. X1.3 Schottky Plot for Determining Zero Field EmissionF 83 71 (2002)4REFERENCES(1) Hensley, E. B., Journal of Applied Physics, Vol 32, 1961, pp. 301308.(2) Herring, C., and Nichols, M. H., Review of Modern Physics,
40、 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, Vo l 8 ,1953, p. 81.ASTM Internati
41、onal 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 thei
42、r 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 b
43、e 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 Standard
44、s, 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 serviceastm.org (e-mail); or through the ASTM website(www.astm.org).FIG. X1.4 Richardson Plot of Emission DataF 83 71 (2002)5
