1、Designation: F 83 71 (Reapproved 2009)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 () indicates an editorial change since the last revision or reapproval.INTRODUCTIONCathode materials are often evaluated by an emission test which in some ways measures thetemperatur
3、e-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 t
4、emperature 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 usag
5、e 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
6、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 he
7、alth practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:3F8Recommended Practice for Testing Electron TubeMaterials Using Reference Triodes43. Terminology3.1 Definitions:3.1.1 effective work function, fthe work function ob-taine
8、d by the direct substitution of experimentally determinedvalues of emission current density and temperature into theRichardson-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)whe
9、re:J = emission current density in A/cm2measured underspecified field conditions except zero field.(J0= emission current density in A/cm2measured un-der zero field conditions.)A = the theoretical emission constant, which is calculatedfrom fundamental physical constants, with its valuegenerally taken
10、 as 120 A/cm2K2. A more exact calcu-lation (3) gives 120.17 which is used in determiningthe effective work function.T = cathode temperature, K.e = electronic charge, C.e = natural logarithmic base.k = Boltzmanns constant.f = work function, V.1This practice is under the jurisdiction of ASTM Committee
11、 F01 on Electronicsand is the direct responsibility of Subcommittee F01.03 on Metallic Materials.Current edition approved May 1, 2009. Published July 2009. Originally approvedin 1967. Last previous edition approved in 2002 as F 83 71 (2002).2The boldface numbers in parentheses refer to references at
12、 the end of thispractice.3For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.4Withdrawn.1Copyright ASTM Internati
13、onal, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.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 emittersurface. The effective work functi
14、on 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 Richardson plot, which isa plot of ln (J
15、/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 ln A 2e/k
16、T!f0(3)It can be seen (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
17、graph.However, large errors 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,
18、ftthe 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, ft, is expressed involts or sometimes as eftin elec
19、tron 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
20、 Terms4.1 Both the effective (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 o
21、f 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 temp
22、era-ture coefficient of 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 equ
23、ation(Eq 1) and considering 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
24、 that a Richardson plot 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 tempe
25、rature, is what would be 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
26、 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 a as determined hereserves the purpose of re
27、lating 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 factor
28、s 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. Key
29、words5.1 electron emitters; electron tube materials; thermionicconstants; work functionF 83 71 (2009)2APPENDIX(Nonmandatory Information)X1. EXAMPLES FOR DETERMINING THERMIONIC CONSTANTS OF CATHODESX1.1 The following examples illustrate two customarymethods for determining the thermionic constants of
30、 cathodesincluding procedures for establishing the emission current atzero field. Other methods are discussed in the literature (1, 2,3, 4).X1.1.1 Example 1The Retarding PotentialMethod (4)To determine the emission at zero field, theemission current from a cathode is measured by varying thecollectin
31、g 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 r
32、etardingfield 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 CharacteristicF 83 71 (2009)3purposes of calculation, Eq X1.1 is expressed with
33、the commonlogarithm and numerical values of the physical constants asfollows:f51.98 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 to
34、use charts (1, 5) or tables (1), from which f 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 J0o
35、btained 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
36、.2 Example 2The 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 coll
37、ecting 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 i
38、s 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=V to zero field, Fig. X1.3. Over aconsiderable voltage range, a straight-line is obtained indicat-ing the validity
39、of the Schottky equation. 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
40、 Richardson work function 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 b
41、e used for calculating the effective work function.FIG. X1.2 Temperature Dependence of Work FunctionF 83 71 (2009)4FIG. X1.3 Schottky Plot for Determining Zero Field EmissionFIG. X1.4 Richardson Plot of Emission DataF 83 71 (2009)5REFERENCES(1) Hensley, E. B., Journal of Applied Physics, Vol 32, 196
42、1, pp. 301308.(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., a
43、nd 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 pa
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45、ther 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
46、 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 serviceastm.org (e-mail); or through the ASTM website(www.astm.org).F 83 71 (2009)6
