ASTM F83-71(2013)
(Practice)Standard Practice for Definition and Determination of Thermionic Constants of Electron Emitters
Standard Practice for Definition and Determination of Thermionic Constants of Electron Emitters
ABSTRACT
This practice covers the definition and interpretation of the commonly used thermionic constants of electron emitters with appended standard methods of measurement. Cathode materials shall alternatively be evaluated by relating the temperature-limited emission to fundamental properties of the emitter, particularly the work function. Comparisons are made between emitters using the thermionic constants such as the work function, emission constant, and the temperature dependence of the work function. These thermionic constants are geometry and field effects-independent, but exhibit variations under different conditions. The pertinent equations the Richardson-Dushman equation of electron emission to evaluate the effective work function, which in turn, shall be used to find the Richardson work function and the true work function. Sample computations are also detailed.
SCOPE
1.1 This practice covers the definition and interpretation of the commonly used thermionic constants of electron emitters (1, 2, 3),2 with appended standard methods of measurement.
1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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Designation:F83 −71 (Reapproved 2013)
Standard Practice for
Definition and Determination of Thermionic Constants of
Electron Emitters
This standard is issued under the fixed designation F83; the number immediately following the designation indicates the year of original
adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.Asuperscript
epsilon (´) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
Cathode materials are often evaluated by an emission test which in some ways measures the
temperature-limited emission. A more basic approach to this problem is to relate the emission to
fundamental properties of the emitter, in particular, the work function. Comparisons are conveniently
made between emitters using the thermionic constants, that is, the work function, the emission
constant, and the temperature dependence of the work function. These quantities are independent of
geometry and field effects when properly measured. Although referred to as “constants” these
quantities show variations under different conditions. Considerable confusion exists over the
definition, interpretation, and usage of these terms and, hence, there is a need for at least a general
agreement on nomenclature.
1. Scope 3. Terminology
1.1 This practice covers the definition and interpretation of
3.1 Definitions:
the commonly used thermionic constants of electron emitters
3.1.1 effectiveworkfunction,φ—the work function obtained
(1, 2, 3), with appended standard methods of measurement.
by the direct substitution of experimentally determined values
1.2 The values stated in SI units are to be regarded as of emission current density and temperature into the
standard. No other units of measurement are included in this
Richardson-Dushman equation of electron emission of the
standard.
form:
2 2eφ/kT
1.3 This standard does not purport to address all of the
J 5 AT e (1)
safety concerns, if any, associated with its use. It is the
For direct calculation of the work function, this is conve-
responsibility of the user of this standard to establish appro-
niently put in the form:
priate safety and health practices and determine the applica-
bility of regulatory limitations prior to use.
φ 5 ~kT/e!ln~AT /J! (2)
where:
2. Referenced Documents
J = emission current density in A/cm measured under
2.1 ASTM Standards:
specified field conditions except zero field. (J = emis-
F8 Recommended Practice for Testing Electron Tube Mate-
sion current density in A/cm measured under zero field
rials Using Reference Triodes
conditions.)
A = the theoretical emission constant, which is calculated
from fundamental physical constants, with its value
2 2
This practice is under the jurisdiction ofASTM Committee F01 on Electronics
generally taken as 120 A/cm ·K . A more exact calcu-
and is the direct responsibility of Subcommittee F01.03 on Metallic Materials.
lation (3) gives 120.17 which is used in determining the
Current edition approved May 1, 2013. Published May 2013. Originally
approved in 1967. Last previous edition approved in 2009 as F83 – 71 (2009). DOI: effective work function.
10.1520/F0083-71R13.
T = cathode temperature, K.
The boldface numbers in parentheses refer to references at the end of this
e = electronic charge, C.
practice.
e = natural logarithmic base.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
k = Boltzmann’s constant.
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
φ = work function, V.
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website.
The form of Eq 1 is a simplified form of the emission
Withdrawn.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
F83−71 (2013)
equationwhichassumeszeroreflectioncoefficientforelectrons ture coefficient of the work function, α, V/K. Under these
with energy normally sufficient for emission at the emitter conditions, the emission data yield a straight-line Richardson
surface. The effective work function is an empirical quantity plot and, also, result in a straight-line plot of effective work
and represents an average of the true work function, giving the function with temperature. These and other relations can be
maximum information obtainable from a single measurement seen by introducing α into the Richardson-Dushman equation
of the thermionic emission. (Eq 1) and considering the Richardson work function as
representing the value at 0 K. The effective work function at
3.1.2 Richardson work function, φ —the work function
temperature T is then equal to φ +αT. Substituting this into
usually obtained graphically from a Richardson plot, which is
the equation gives:
a plot of ln (J/T ) versus l/T using data of emission measure-
2 2 e/kT φ 1α T
~ !~ !
ments at various temperatures. It is the work function obtained J 5 AT e (4)
from Eq 1, with the value of A determined graphically, instead
which can be put in the form:
of using the theoretical value. For better visualization of the
2eα/k 2 2eφ
0/kT
J 5 ~Ae !T e (5)
Richardson plot, Eq 1 may be put in the form:
ln J/T 5 lnA 2 e/kT φ (3)
~ ! ~ ! It can be seen from Eq 5 that a Richardson plot slope would
determineφ and a value of the emission constant e−ea/ktimes
It can be seen (Fig. X1.4) that the Richardson work func-
the theoretical value A. The form of Eq 4 is that used for
tion φ is obtained from the slope of the graph, and the
calculation of the effective work function, with φ +αT sub-
emission constant A from the intercept (l/T = 0) on the ln
stitutedfortheeffectiveworkfunctionφ.Itcanbeseenthatφ ,
(J/T ) axis. The Richardson work function is also an empiri-
the value at zero temperature, is what would be obtained from
cal quantity. Its value is found with reasonable accuracy
a straight-line Richardson plot. These observations are sum-
from the graph. However, large errors in the value of Amay
marized in the following equations:
be expected (4). Considering only one factor, a slight inaccu-
φ 5φ 1αT (6)
racy in the measurement of temperature introduces a large 0
eα/k
error in the value of A. Values of A obtained on practical
~TheoreticalA/RichardsonA! 5 e (7)
2 2
emitters can range from about 0.1 to 200 A/cm ·K .
α~k/e!ln~TheoreticalA/RichardsonA! (8)
3.1.3 true work function, φ—the difference between the
t
The above expressions are useful in equating and interpret-
Fermi energy and the surface potential energy, which is the
ing the effective and Richardson constants. For example, if the
maximum potential energy of an electron at the surface of the
thermionicconstantsofanemitterarespecifiedbytheeffective
emitter, or the energy just necessary to remove an electron
work function and temperature coefficient, the equivalent
from the emitter. The true work function, φ, is expressed in
t
Richardson work function and emission constant may be
volts or sometimes as eφ in electron volts. For a polycrystal-
t
calculated from the equation. Although α as determined here
line surface, the true work function will vary with position on
serves the purpose of relating the work functi
...
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