ASTM F83-71(2018)
(Practice)Standard Practice for Definition and Determination of Thermionic Constants of Electron Emitters (Withdrawn 2023)
Standard Practice for Definition and Determination of Thermionic Constants of Electron Emitters (Withdrawn 2023)
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, health, and environmental practices and determine the applicability of regulatory limitations prior to use.
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
WITHDRAWN RATIONALE
This practice covered the definition and interpretation of the commonly used thermionic constants of electron emitters with appended standard methods of measurement.
Formerly under the jurisdiction of Committee F01 on Electronics, this practice was withdrawn in November 2023. This standard is being withdrawn without replacement because Committee F01 was disbanded.
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This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: F83 −71 (Reapproved 2018)
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 mendations issued by the World Trade Organization Technical
Barriers to Trade (TBT) Committee.
1.1 This practice covers the definition and interpretation of
the commonly used thermionic constants of electron emitters
2. Referenced Documents
(1, 2, 3), with appended standard methods of measurement.
2.1 ASTM Standards:
1.2 The values stated in SI units are to be regarded as
F8 Recommended Practice for Testing Electron Tube Mate-
standard. No other units of measurement are included in this 4
rials Using Reference Triodes
standard.
3. Terminology
1.3 This standard does not purport to address all of the
safety concerns, if any, associated with its use. It is the
3.1 Definitions:
responsibility of the user of this standard to establish appro-
3.1.1 effectiveworkfunction,φ—the work function obtained
priate safety, health, and environmental practices and deter-
by the direct substitution of experimentally determined values
mine the applicability of regulatory limitations prior to use.
of emission current density and temperature into the
1.4 This international standard was developed in accor-
Richardson-Dushman equation of electron emission of the
dance with internationally recognized principles on standard-
form:
ization established in the Decision on Principles for the
2 2eφ/kT
J 5 AT e (1)
Development of International Standards, Guides and Recom-
For direct calculation of the work function, this is conve-
niently put in the form:
This practice is under the jurisdiction ofASTM Committee F01 on Electronics φ 5 ~kT/e!ln~AT /J! (2)
and is the direct responsibility of Subcommittee F01.03 on Metallic Materials, Wire
Bonding, and Flip Chip.
Current edition approved March 1, 2018. Published April 2018. Originally For referenced ASTM standards, visit the ASTM website, www.astm.org, or
approved in 1967. Last previous edition approved in 2013 as F83 – 71 (2013). DOI: contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
10.1520/F0083-71R18. Standards volume information, refer to the standard’s Document Summary page on
The boldface numbers in parentheses refer to references at the end of this the ASTM website.
practice. Withdrawn.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
F83 − 71 (2018)
where: emission. They differ in the manner of applying the equation.
The effective work function represents a direct computation
J = emission current density in A/cm measured under
using the theoretical value of the emission constant A of the
specified field conditions except zero field. (J = emis-
equation. The Richardson work function is based on a plot of
sion current density in A/cm measured under zero field
emission data at different temperatures from which both the
conditions.)
work function and emission constant were obtained. Work
A = the theoretical emission constant, which is calculated
function varies slightly with temperature. If this variation is
from fundamental physical constants, with its value
2 2
approximately linear, it can be expressed as a simple tempera-
generally taken as 120 A/cm ·K . A more exact calcu-
ture coefficient of the work function, α, V/K. Under these
lation (3) gives 120.17 which is used in determining the
conditions, the emission data yield a straight-line Richardson
effective work function.
plot and, also, result in a straight-line plot of effective work
T = cathode temperature, K.
e = electronic charge, C.
function with temperature. These and other relations can be
e = natural logarithmic base.
seen by introducing α into the Richardson-Dushman equation
k = Boltzmann’s constant.
(Eq 1) and considering the Richardson work function as
φ = work function, V.
representing the value at 0 K. The effective work function at
temperature T is then equal to φ +αT. Substituting this into
The form of Eq 1 is a simplified form of the emission
the equation gives:
equationwhichassumeszeroreflectioncoefficientforelectrons
with energy normally sufficient for emission at the emitter 2 2 e/kT φ 1α T
~ !~ !
J 5 AT e (4)
surface. The effective work function is an empirical quantity
which can be put in the form:
and represents an average of the true work function, giving the
2eα/k 2 2eφ
0/kT
maximum information obtainable from a single measurement J 5 Ae T e (5)
~ !
of the thermionic emission.
It can be seen from Eq 5 that a Richardson plot slope would
3.1.2 Richardson work function, φ —the work function
determineφ and a value of the emission constant e−ea/ktimes
usually obtained graphically from a Richardson plot, which is
the theoretical value A. The form of Eq 4 is that used for
a plot of ln (J/T ) versus l/T using data of emission measure-
calculation of the effective work function, with φ +αT sub-
ments at various temperatures. It is the work function obtained
stitutedfortheeffectiveworkfunctionφ.Itcanbeseenthatφ ,
from Eq 1, with the value of A determined graphically, instead
the value at zero temperature, is what would be obtained from
of using the theoretical value. For better visualization of the
a straight-line Richardson plot. These observations are sum-
Richardson plot, Eq 1 may be put in the form:
marized in the following equations:
ln~J/T ! 5 lnA 2 ~e/kT!φ (3)
φ 5φ 1αT (6)
eα/k
It can be seen (Fig. X1.4) that the Richardson work func-
~TheoreticalA/RichardsonA! 5 e (7)
tion φ is obtained from the slope of the graph, and the
α k/e ln TheoreticalA/RichardsonA (8)
~ ! ~ !
emission constant A from the intercept (l/T = 0) on the ln
The above expressions are useful in equating and interpret-
(J/T ) axis. The Richardson work function is also an empiri-
ing the effective and Richardson constants. For example, if the
cal quantity. Its value is found with reasonable accuracy
thermionicconstantsofanemitterarespecifiedbytheeffective
from the graph. However, large errors in the value of Amay
work function and temperature coefficient, the equivalent
be expected (4). Considering only one factor, a slight inaccu-
Richardson work function and emission consta
...
NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: F83 − 71 (Reapproved 2018)
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. A number in parentheses indicates the year of last reapproval. A superscript
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 mendations issued by the World Trade Organization Technical
Barriers to Trade (TBT) Committee.
1.1 This practice covers the definition and interpretation of
the commonly used thermionic constants of electron emitters
2. Referenced Documents
(1, 2, 3), with appended standard methods of measurement.
2.1 ASTM Standards:
1.2 The values stated in SI units are to be regarded as
F8 Recommended Practice for Testing Electron Tube Mate-
standard. No other units of measurement are included in this 4
rials Using Reference Triodes
standard.
3. Terminology
1.3 This standard does not purport to address all of the
safety concerns, if any, associated with its use. It is the
3.1 Definitions:
responsibility of the user of this standard to establish appro-
3.1.1 effective work function, φ—the work function obtained
priate safety, health, and environmental practices and deter-
by the direct substitution of experimentally determined values
mine the applicability of regulatory limitations prior to use.
of emission current density and temperature into the
1.4 This international standard was developed in accor-
Richardson-Dushman equation of electron emission of the
dance with internationally recognized principles on standard-
form:
ization established in the Decision on Principles for the
2 2eφ/kT
J 5 AT e (1)
Development of International Standards, Guides and Recom-
For direct calculation of the work function, this is conve-
niently put in the form:
φ 5 kT/e ln AT /J (2)
This practice is under the jurisdiction of ASTM Committee F01 on Electronics ~ ! ~ !
and is the direct responsibility of Subcommittee F01.03 on Metallic Materials, Wire
Bonding, and Flip Chip.
Current edition approved March 1, 2018. Published April 2018. Originally For referenced ASTM standards, visit the ASTM website, www.astm.org, or
approved in 1967. Last previous edition approved in 2013 as F83 – 71 (2013). DOI: contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
10.1520/F0083-71R18. Standards volume information, refer to the standard’s Document Summary page on
The boldface numbers in parentheses refer to references at the end of this the ASTM website.
practice. Withdrawn.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
F83 − 71 (2018)
where: emission. They differ in the manner of applying the equation.
The effective work function represents a direct computation
J = emission current density in A/cm measured under
using the theoretical value of the emission constant A of the
specified field conditions except zero field. (J = emis-
equation. The Richardson work function is based on a plot of
sion current density in A/cm measured under zero field
emission data at different temperatures from which both the
conditions.)
work function and emission constant were obtained. Work
A = the theoretical emission constant, which is calculated
function varies slightly with temperature. If this variation is
from fundamental physical constants, with its value
2 2
approximately linear, it can be expressed as a simple tempera-
generally taken as 120 A/cm ·K . A more exact calcu-
ture coefficient of the work function, α, V/K. Under these
lation (3) gives 120.17 which is used in determining the
conditions, the emission data yield a straight-line Richardson
effective work function.
T = cathode temperature, K. plot and, also, result in a straight-line plot of effective work
e = electronic charge, C. function with temperature. These and other relations can be
e = natural logarithmic base.
seen by introducing α into the Richardson-Dushman equation
k = Boltzmann’s constant.
(Eq 1) and considering the Richardson work function as
φ = work function, V.
representing the value at 0 K. The effective work function at
temperature T is then equal to φ + αT. Substituting this into
The form of Eq 1 is a simplified form of the emission
the equation gives:
equation which assumes zero reflection coefficient for electrons
with energy normally sufficient for emission at the emitter 2 2~e/kT!~φ 1α T!
J 5 AT e (4)
surface. The effective work function is an empirical quantity
which can be put in the form:
and represents an average of the true work function, giving the
2eα/k 2 2eφ
0/kT
maximum information obtainable from a single measurement
J 5 ~Ae !T e (5)
of the thermionic emission.
It can be seen from Eq 5 that a Richardson plot slope would
3.1.2 Richardson work function, φ —the work function
determine φ and a value of the emission constant e−ea/ktimes
usually obtained graphically from a Richardson plot, which is
the theoretical value A. The form of Eq 4 is that used for
a plot of ln (J/T ) versus l/T using data of emission measure-
calculation of the effective work function, with φ + αT sub-
ments at various temperatures. It is the work function obtained
stituted for the effective work function φ. It can be seen that φ ,
from Eq 1, with the value of A determined graphically, instead
the value at zero temperature, is what would be obtained from
of using the theoretical value. For better visualization of the
a straight-line Richardson plot. These observations are sum-
Richardson plot, Eq 1 may be put in the form:
marized in the following equations:
ln J/T 5 lnA 2 e/kT φ (3)
~ ! ~ !
φ 5 φ 1αT (6)
eα/k
It can be seen (Fig. X1.4) that the Richardson work func-
TheoreticalA/RichardsonA 5 e (7)
~ !
tion φ is obtained from the slope of the graph, and the
α~k/e!ln~TheoreticalA/RichardsonA! (8)
emission constant A from the intercept (l/T = 0) on the ln
The above expressions are useful in equating and interpret-
(J/T ) axis. The Richardson work function is also an empiri-
ing the effective and Richardson constants. For example, if the
cal quantity. Its value is found with reasonable accuracy
thermionic constants of an emitter are specified by the effective
from the graph. However, large errors in the value of Amay
work function and temperature coefficient, the equivalent
be expected (4). Considering only one factor, a slight inaccu-
Richardson work function and emission constant may be
racy in the measurement of temperature introduces a large
calculated from the e
...
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