Evan H. Copland

ATI Allvac, Monroe, North Carolina 

Nathan S. Jacobson

Glenn Research Center, Cleveland, Ohio

Measuring Thermodynamic Properties of Metals and 

Alloys With Knudsen Effusion Mass Spectrometry

NASA/TP—2010-216795

November 2010
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Evan H. Copland

ATI Allvac, Monroe, North Carolina 

Nathan S. Jacobson

Glenn Research Center, Cleveland, Ohio

Measuring Thermodynamic Properties of Metals and 

Alloys With Knudsen Effusion Mass Spectrometry

NASA/TP—2010-216795

November 2010

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

Helpful discussions about multiple-cell sampling with Christian Chatillon are very much appreciated. 

We are grateful to Gerd Rosenblatt and Andrea Ciccioli for their critical reviews of this manuscript.

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

Available electronically at http://gltrs.grc.nasa.gov

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by expert reviewer(s). 
NASA/TP—2010-216795 iii

Contents

Summary........................................................................................................................................................................1

Introduction ...................................................................................................................................................................1

Knudsen-Cell Vapor Sources and Molecular Beams....................................................................................................3

Description of Knudsen Cells From the Kinetic Theory of Gases .........................................................................3

Design of Knudsen Cells........................................................................................................................................6

Heating System/Furnace Design ............................................................................................................................7

Temperature Measurement.....................................................................................................................................8

Thermocouples.......................................................................................................................................................8

Pyrometry ...............................................................................................................................................................9

Molecular Beams..................................................................................................................................................10

Mass Spectrometric Analysis of the Molecular Beam.................................................................................................12

Instrument Description .........................................................................................................................................12

Ionizer...................................................................................................................................................................12

Mass Analyzer......................................................................................................................................................14

Detector................................................................................................................................................................15

Vacuum System and Separation of Signals From Background Gases..................................................................16

Derivation of the KEMS Equation .......................................................................................................................16

Measurement of Thermodynamic Properties of Metals and Alloys ............................................................................18

Single-Cell Techniques for Pure Materials...........................................................................................................18

Activity Measurements.........................................................................................................................................19

Single-Cell Techniques for Alloys.......................................................................................................................20

Multiple-Cell Techniques—Direct Measurement of Activities............................................................................22

Activity Calculation for Species That Cannot Be Measured Directly ..................................................................24

Checks for Correct Operation and Consistency in Measurements..............................................................................25

Consistency in Ion Intensity Measurements.........................................................................................................25

Consistency in Vapor Sampling and Temperature Measurement........................................................................25

Accuracy of Absolute Temperature Measurement ..............................................................................................26

Geometry Factor Ratio .........................................................................................................................................26

Isothermal Effusion Cells.....................................................................................................................................26

Importance of Constant Electron Energy .............................................................................................................26

Measurement Procedures.............................................................................................................................................26

Sample Exchange .................................................................................................................................................27

Instrument Setup and Configuration.....................................................................................................................27

Taking Measurements ..........................................................................................................................................27

Future Directions.........................................................................................................................................................28

Summary and Conclusions..........................................................................................................................................29

Appendix A.—Symbols...............................................................................................................................................31

Appendix B.—SIMION 8 Model of the Ion Source and Analyzer..............................................................................33

Appendix C.—Instrument-Control and Data-Acquisition System ..............................................................................39

References ...................................................................................................................................................................43
NASA/TP—2010-216795 iv
NASA/TP—2010-216795 1

Measuring Thermodynamic Properties of Metals and 

Alloys With Knudsen Effusion Mass Spectrometry

Evan H. Copland

ATI Allvac

Monroe, North Carolina 28111

Nathan S. Jacobson

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Summary

This report reviews Knudsen effusion mass spectrometry 

(KEMS) as it relates to thermodynamic measurements of 

metals and alloys. First, general aspects are reviewed, with 

emphasis on the Knudsen-cell vapor source and molecular 

beam formation, and mass spectrometry issues germane to this 

type of instrument are discussed briefly. The relationship 

between the vapor pressure inside the effusion cell and the 

measured ion intensity is the key to KEMS and is derived in 

detail. Then common methods used to determine thermodynamic quantities with KEMS are discussed. Enthalpies of 

vaporization ∆vap o HT —the fundamental measurement—are 

determined from the variation of relative partial pressure with 

temperature using the second-law method or by calculating a 

free energy of formation and subtracting the entropy contribution using the third-law method. For single-cell KEMS 

instruments, ∆vap o HT measurements can be used to determine 

the partial Gibbs free energy if the sensitivity factor remains 

constant over multiple experiments. The ion-current ratio 

method and dimer-monomer method are also viable in some 

systems. For a multiple-cell KEMS instrument, ∆vap o HT and 

activities are obtained by direct comparison with a suitable 

component reference state or a secondary standard. Internal 

checks for correct instrument operation and general procedural 

guidelines also are discussed. Finally, general comments are 

made about future directions in measuring alloy thermodynamics with KEMS.

Introduction

Accurate measurements of thermodynamic properties in 

metal and alloy systems are an important part of metallurgy.

These measurements are essential for understanding multiplecomponent solution behavior and making accurate predictions 

of the stability of a given system under a range of environments. Furthermore, advanced composites contain many 

interfaces (e.g., the fiber/matrix interface), and accurate 

prediction of potential interface reactions requires accurate 

thermodynamic data (Ref. 1). In recent years, there have been 

dramatic advances in computational thermodynamics, both 

from a fundamental basis and from a phenomenological basis 

(Ref. 2), but over the same period we have seen a decline in 

experimental thermodynamics. Basic experimentally determined thermodynamic data are still necessary, both to check 

the fundamentals-based calculations and as an input to the 

phenomenological calculations. The need for accurate thermodynamic data is recognized by a number of groups that have 

focused on improving the capabilities of the Knudsen effusion 

mass spectrometry (KEMS) technique to provide routine 

measurement of relative partial pressure and partial Gibbs 

energy in alloy systems (Refs. 3 to 5).

The KEMS technique allows the measurement of relative 

partial pressure of components, which then is used as a means 

to obtain thermodynamic property data in condensed alloy 

systems. The advantage of KEMS is that it can be applied to a 

wide range of technically important alloy systems over relevant temperature ranges. A concise description of the technique is given in the following paragraphs. 

A metal or alloy sample is placed in a small enclosure with 

a well-defined orifice known as a Knudsen cell, or effusion 

cell, as shown in Figure 1 (Ref. 6). Through careful consideration of the inner shape of the cell, effusion orifice, and surface 

area of the metallic sample, near equilibrium conditions are 

attained between the condensed phases and the vapor phase 

while the orifice continuously samples the vapor by effusion.

The distribution of the effusing vapor is defined by the shape 

of the orifice, and typically only a small solid-angle of the 

distribution is selected to form a molecule beam that is analyzed with a mass spectrometer. A critical, but often overlooked, issue is correctly defining the thermodynamic system 

that is actually measured (Refs. 7 and 8). In a Knudsen cell, 

the boundary of the thermodynamic system is the inner surface 

of the cell, and thus the alloy sample, cell material, and vapor 

are all part of the equilibrium state being measured (alloy + 

cell material + vapor). All additional components and phases 

introduced by the “container” need to be included in the 

subsequent analysis and in the use of measured data (the same 

is true for all experimental thermodynamic measurements 

made in the past and to be made in the future). In addition to 

components and phases, the temperature and chemical composition of the system need to be determined. Temperature is a 

particularly critical measurement in thermodynamics and will 

be discussed in detail. 
NASA/TP—2010-216795 2

Figure 1.—Knudsen cell showing key features; 

p, partial pressure.

Mass spectrometric analysis of a molecular beam selected 

from the effusate distribution coming from a Knudsen cell 

provides information about the identity of the vapor species in 

the cell and their flux in the beam by analysis of a representative ion beam. If one assumes that a gaseous species A forms 

an ion A+

, the relationship between its partial pressure pA in 

the effusion cell and the measured intensity in the ion beam IA

and absolute temperature T is given by

= A

A

A

I T

p S (1)

where SA is the sensitivity factor, which is derived from the 

instrument configuration and the ionization process. Ideally, 

absolute pressures can be measured if SA is accurately known.

In practice this is extremely difficult; it is typical to assume

that SA is constant and to consider relative partial pressures

(i.e., pA ∝ IAT). The variation of IAT with inverse temperature

leads to the enthalpy of vaporization ∆vap o HT , which is a central measurement in KEMS. Partial Gibbs free energy or component activities are obtained by comparing the pressure of a 

component in equilibrium with an alloy to that in equilibrium 

with the pure component at the same temperature 

(Refs. 8 to 10). The KEMS technique is well-suited for 

measuring thermodynamic activity. With a single-cell vapor

source, thermodynamic activity measurements require multiple experiments where SA must remain constant, whereas

with a multiple-cell-configured vapor source, activity is measured directly from the ion intensity ratio from samples in 

adjacent cells. Thus thermodynamic activity is determined by 

Equation (2):

= = A A

A o o

A A

p I a p I (2)

Here o

Ap and oAI are the partial pressure and ion intensity over 

the pure component, respectively.

Component activity is a direct measure of the slope of the 

Gibbs energy surfaces of the stable phases from the direction 

of the component reference state. The variation of the logarithm of activity with inverse temperature gives the partial 

molar enthalpy and entropy of mixing of the alloy component 

A, using the second-law method. A well-defined reference 

state that can be routinely measured is critical for activity 

measurements. In addition to these thermodynamic quantities, 

phase transformation temperatures can be determined from 

changes in the slopes of these plots. The extraction of the 

various thermodynamic properties from KEMS measurements 

is discussed later.

KEMS has a long history. It was first applied in 1948 

(Ref. 11) and was used quite extensively in the 1960s and 

1970s to study the vapors above pure compounds. There are a 

number of excellent reviews on this technique (Refs. 12

to 18). More recently some groups have extended this technique to multiple-component solutions, as discussed in the 

review by Kato (Ref. 3). Today there are only a small number 

of groups worldwide that utilize KEMS for both pure compound and solution thermodynamics.

This report discusses the application of KEMS to measure 

thermodynamic properties in alloy systems. The first part 

of the report describes each part of a typical magneticsector KEMS instrument (Modified Nuclide/MAAS/PATCO 

12–90–HT, shown in Fig. 2), with particular emphasis given 

to the Knudsen-cell vapor source, cell heating, temperature 

measurement, and molecular beam formation. Although a 

magnetic-sector mass spectrometer is the best choice for a 

KEMS measurement, other types of mass spectrometers have 

been shown to be suitable. The key equation relating the vapor 

pressure inside the Knudsen cell to ion intensity measured by 

the mass spectrometer (Eq. (1)) is derived together with a 

discussion of important features of the ion source design.

Actual measurements are discussed with examples of how 

to extract meaningful thermodynamic data from the collected 

data. The critical issue is maintaining constant instrument 

sensitivity. For a single-cell-configured instrument, constant 

instrument sensitivity requires a very stable ion source. Without this instrument stability, special procedures must be 

utilized such as the ion-current ratio technique or monomerdimer method in a single-cell configuration or an internal 

standard in a multiple-cell configuration. Each of these 

approaches is discussed. Then various routine checks for 

proper system operation are discussed. We conclude with 

some comments on future directions of KEMS for alloy 

thermodynamics. Additional information is provided in the 

appendixes to aid the reader. Appendix A defines the symbols 

used in the report, Appendix B provides additional information about the SIMION Version 8.0 (Scientific Instrument

Services, Inc.) model of the ion source, and Appendix C 

provides a detailed description of the instrument-control and 

data-acquisition system.
NASA/TP—2010-216795 3

Figure 2.—Knudsen effusion mass spectrometer—magnetic-sector instrument with key components indicated.

Knudsen-Cell Vapor Sources and 

Molecular Beams

Description of Knudsen Cells From the Kinetic 

Theory of Gases

Figure 1 illustrates a typical Knudsen cell. The Knudsen 

cell provides a way to probe the vapor in equilibrium with the 

condensed sample of interest plus cell material. Under the 

low-pressure conditions used (<10−4 bar) the fugacities of real 

gases are equal to their partial pressure, and the behavior of 

the vapor phase is readily described by the kinetic theory of 

gases. There are several excellent texts on this subject 

(Refs. 19 and 20). The key relationship derived from kinetic 

theory to this technique is the Hertz-Knudsen-Langmuir 

(HKL) expression, which relates the flux of a molecular 

species striking a surface, JA (mol ⋅ area−1 ⋅ s

−1

), to its equilibrium vapor pressure in a closed container:

4 2 R

   = =       π 

E

E A A A

A

A

N c p J

V M T

(3)

Here  N V A is the density of molecules in the gas, cA is the 

average molecular speed, MA is the molecular weight, T is the 

absolute temperature, and R is the gas constant. Under equilibrium conditions, the flux of molecular species striking and 

condensing on a surface is equal to the number of molecular 

species vaporizing and also relates to equilibrium vapor 

pressure. In the case where not all molecular species striking a 

surface condense, Equation (3) is extended to a condensed 

phase vaporizing into a vacuum (Ref. 21):

2 R

α

=α =

π

o E o E v A

A v A

A

p J J

M T

(4a)

Here αo

v is the vacuum vaporization coefficient, which accounts for the reduction in the observed vaporization flux 

relative to the maximum flux calculated for equilibrium 

conditions, E

Ap . In the general case where the condensed 

phase vaporizes in an unsaturated vapor phase, where pA is 

less than E

Ap , the flux is given by

( )

2 R

α − = π

E

v A A

A

A

p p J

M T (4b)

This is the general form of the HKL equation.

Vaporization coefficients vary from ~10−6 to 1, depending 

on the material system and molecular species (Ref. 22).
NASA/TP—2010-216795 4

Condensation coefficients may be similarly defined as part of 

the equilibrium vaporization-condensation process between a 

vapor and a condensed phase. Vaporization and condensation 

coefficients are important for ceramics, but for metals these 

coefficients are generally 1. Therefore in this report we use the 

HKL equation in the form of Equation (3).

Now consider a vaporizing phase in the Knudsen cell in 

Figure 1. In the cell, molecule-sample, molecule-wall, and 

molecule-molecule collisions are important. According to 

kinetic theory, after a molecule strikes a surface, it desorbs in a 

completely random direction—that is, the cosine distribution—

( ) ( ) d( ) d cos( ) 2 cos sin d 4

θ ω     = θ = θ θθ       π   T

jN N c c J V V (5)

Here dj(θ) is the element of flux at an angle θ from the normal, 

J

T is the incident flux upon the surface, dω is an element of 

solid angle ω, as shown in Figure 3(a), and dθ is an element of 

angle θ. 

A plot of dj(θ)/J

T versus θ in three dimensions yields a 

sphere, as shown in Figure 3(b). The HKL equation and flux 

distribution described by kinetic theory relate directly to the 

effusion process, which is most simply described as the loss of 

material from a cell due to the absence of a wall (i.e., the 

orifice). The type of flow through the orifice of the Knudsen 

cell defines the maximum pressure and temperature at which 

the KEMS technique can be applied. If the probability of 

molecule-molecule collisions is low over the nominal dimensions of the orifice, then the flow is characterized as “molecular flow” or “effusion” and the Knudsen cell accurately 

samples the equilibrium vapor. If the probability of moleculemolecule collisions is high, then the flow is “hydrodynamic”

and the Knudsen cell does not accurately sample the vapor 

phase. The general criterion for effusion flow through an 

orifice is a Knudsen number, Kn, greater than 8; where 

Kn = λ / 2  r and where λ

 and r are the mean free path and 

radius of the orifice. Knudsen numbers from 0.4 to 8 introduce 

a ~2.5-percent difference between calculated and measured 

fluxes, which can extend the range of the technique (Ref. 17).

The mean free path is the average distance between moleculemolecule collisions and is defined as

( ) 2

1

2 R

λ =

π



P Td (6)

where P is the total pressure and d is the molecular diameter. At 

P = 10−4 bar, d = 4×10−10 m, and T = 1273 K, the mean free path 

is 2.4×10−4 m. Thus, a 1-mm-diameter orifice in a Knudsen cell 

will accurately sample pressures up to 10−4 bar. Molecular flow 

is also important because it ensures that the vapor in equilibrium 

with the condensed phases inside the Knudsen cell does not 

react via molecule-molecule interactions in the orifice as it exits 

the cell or in the ensuing molecular beam.

Again, the flux of molecules leaving the orifice is described 

by the HKL equation. For a real orifice, Equation (3) is 

modified by including the cross-sectional area of the orifice C

and the shape, or Clausing factor, WC, which is the escaping 

flux from the orifice normalized to the incident flux integrated 

over the hemisphere. The rate of molar loss of a vapor species 

is given by Equation (7), which is used to relate measured ion 

intensity to the corresponding vapor pressure (where t is time).

d

or

d 2R 2R = = π π

A CA C A

A

A A

N CW p W p j

t M T M T

(7)

The shape of a real orifice has a more complex effect than 

just reducing the transmission probability of effusion molecules as represented by WC in Equation (7). Any orifice with 

a finite length changes the angular distribution of the effusing 

molecules according to the cosine law. This deviation from 

ideal behavior can be described analytically or modeled using 

a Monte Carlo simulation. The pioneering work in the field of 

Knudsen effusion used the analytical approach (Refs. 23

to 27). The relatively simple behavior of molecular flow 

through an effusion orifice is easily modeled with a Monte 

Carlo simulation (Refs. 28 to 30). A simple code can easily be 

written, and simulations can be conducted with millions of 

molecules for adequate statistics (Ref. 31, unpublished work).

These simulations accurately model Knudsen effusion through 

an orifice or a small channel.

Monte Carlo modeling of Knudsen effusion easily yields a 

number of important results. The transmission coefficient, or 

Clausing factor, can be calculated as the number of escapes 

divided by the number of molecules entering the orifice. This is 

shown in Table I. The major advantage of the Monte Carlo 

approach over analytical approaches is that the number of wall 

collisions can be counted and averaged. Some of the molecules 

will go through the channel with no wall collisions. This fraction can also be readily obtained with the Monte Carlo simulation. As the length of the channel increases, the probability that 

molecules will pass through the orifice without any wall collisions decreases. These results are all listed in Table I. An 

understanding of this wall collision behavior is important in 

understanding Knudsen effusion because the molecule would be 

expected to thermally equilibrate with the wall after a collision.

In addition, the angle to the normal through the channel can 

be recorded for each molecule. A simple sorting routine then 

gives the angular distribution emerging from an orifice. A 

polar plot of dj(θ)/J

T is shown in Figure 3(c) for a very thin 

orifice and a channel. Note that the channel gives a more 

directed distribution. The same results are obtained from the 

analytical approach (Ref. 27). It is important to note that these 

Clausing factors are all calculated. The degree of agreement 

with the actual experiment depends on the accuracy of 

machining and measuring the actual orifice dimensions and 

attaining molecular flow conditions.
NASA/TP—2010-216795 5

Figure 3.—Molecules desorbing from a surface or emerging from an orifice.

(a) Molecule desorbing from a surface into a solid-angle element; θ, angle to 

the normal from a surface; dω, element of solid angle ω. (b) Cosine distribution for a molecule desorbing from a surface. (c) Distribution for a thin orifice 

and a channel, derived from a Monte Carlo simulation.

 

TABLE I.—CLAUSING FACTORS FOR DIFFERENT ORIFICES FROM MONTE CARLO MODELING

Length/radius, 

l/r

Clausing 

factor

Average number of wall 

collisions for returns

Average number of wall 

collisions for escapes

Fraction of escapes with no 

wall collisions

0.1 0.9523 1.0513 0.0523 0.9048

1.0 .6720 1.5870 .7136 .3821

2.0 .5144 2.2429 1.7694 .1718

4.0 .3566 3.5742 4.7624 .0557

10.0 .1910 7.5607 20.3455 .0098
NASA/TP—2010-216795 6

The Clausing factor and the distribution of effusing molecules 

have important ramifications for the accuracy of vapor sampling, 

the design of the vapor source furnace, and molecular beam 

formation. In some cases, an orifice with a high Clausing factor is 

desirable, whereas in other cases a cell with a lower Clausing 

factor is desirable. A short, or “knife-edge,” orifice has a Clausing 

factor close to unity and, thus, a near-uniform flux distribution. 

This orifice also yields the minimum number of wall collisions 

within the orifice and a large vapor flux. This type of orifice has 

traditionally been used with the Knudsen effusion weight-loss 

technique. One disadvantage of this type of orifice is that a large 

fraction of the effusing molecules are trapped inside the furnace 

heat shields, which can act as a coaxial “virtual effusion cell” and 

contaminate the effusate coming from the effusion cell. Also the 

high rate of material loss attained with a large knife-edge orifice 

can produce errors in vapor-pressure sampling. The last major 

problem with knife-edge orifices is that they promote surface 

diffusion (Ref. 16). Longer, or channel, effusion orifices have a 

lower Clausing factor and a lower probability of molecules 

leaving the cell, particularly at high angles from the normal, but 

there is a higher probability that the effusing molecules will have 

collided with the orifice wall. The lower Clausing factor helps in 

attaining solid/vapor equilibrium and accurate sampling of the 

vapor phase. Low Clausing factors at high angles from the normal 

greatly reduce the amount of effusate trapped in the furnace and 

contaminating the molecular beam. Careful selection of the 

effusate distribution close to the normal and within the orifice to 

form the molecular beam, limits the sampling of molecules that 

have collided with the orifice wall. From the authors’ perspective, 

channel orifices are ideal for the KEMS technique.

Design of Knudsen Cells

The considerations discussed thus far can be used to design a 

cell for optimum vapor sampling. A real cell is not a closed 

container, and removal of vapor means the sampled flux is not the 

same as that passing through an imaginary plane near the surface 

of the sample in a closed container. The presence of the orifice 

means that there is no condensation/revaporization flux in the 

area taken by the orifice. Thus, pressure in this region is necessarily lower than in the rest of the cell. Furthermore, not all condensed phases have vaporization and condensation coefficients 

equal to 1. Thus, the measured vapor pressure must differ from 

the equilibrium value.

This problem has been approached by several investigators 

(Refs. 15 and 32 to 35). In general, the closest approach to 

equilibrium is attained with the following conditions:

(1) A large sample surface-area to orifice-area ratio, which 

ensures that many more molecules are involved in 

vaporization and condensation than escape from the orifice (ratio values of greater than 100 are recommended 

(Ref. 16)).

(2) A large Clausing factor for vapor transport from the sample surface to the orifice.

(3) A low Clausing factor for the cell orifice (as discussed in 

the previous section).

(4) Materials being measured have vaporization and condensation coefficients that are close to unity (e.g., metals).

These factors are summarized in the Whitman-Motzfeld equation (Refs. 32 and 33):

1 1 1 2

   

= + +−         α

C e m

v D

W C

p p D W (8)

Here pe is the equilibrium pressure inside the Knudsen cell, pm is 

the measured vapor pressure, WC is the Clausing factor for the 

orifice, C is the surface area of the orifice, D is the surface area of 

the bottom of the cell cavity, αv is the vaporization coefficient, 

and WD is the Clausing factor for the cell itself. A number of 

assumptions have been made in this derivation, most notably that 

the condensation coefficient equals the vaporization coefficient. 

However, the important points about the design of a Knudsen cell 

are captured in the basic Whitman-Motzfeld equation. Our cells 

have a cavity with a diameter of 10 mm and height of 7.6 mm, 

and a typical orifice has a diameter of 1.5 mm and a length of 

4.0 mm. If tabulated Clausing factors (Ref. 27) and a vaporization coefficient of 1 are assumed, the ratio Pe/Pm has a value 

of 1.005.

The selection of an appropriate material for a Knudsen cell is a 

challenging problem. No combinations of materials are truly 

inert, considering solubility and reactivity at high temperatures. 

Selection of an appropriate material requires examining all 

possible reactions and solution formation possibilities with phase 

diagrams and thermodynamic calculations. Table II presents 

some typical cell materials for different types of samples. Typically, ceramics are used for metals and refractory metals are used 

for ceramics. Often it is best to select a cell material made of a 

stable compound in the system under investigation. For example, 

SiC in a graphite cell can be used to study carbon-saturated SiC 

(Ref. 36), Si3N4 can be used to study Si-O-N compounds 

(Ref. 37), and Al in an alumina cell can be used to study Alsaturated Al2O3 (Refs. 38 and 39).

TABLE II.—KNUDSEN-CELL MATERIALS

Material studied Knudsen-cell material Reference

SiC-C Graphite Rocabois et al. (Ref. 36)

Si3N4 Si3N4 Rocabois et al. (Ref. 37)

Al-Al2O3 Al2O3 Copland (Refs. 38 and 39)

ZrO2-Y2O3 W Stolyarova and Semenov; Belov and Semenov (Refs. 18 and 40)

SiO2 Ta with ZrO2 liners Zmbov et al. (Ref. 41)

TiC, ZrC, HfC, ThC W, Ta with graphite liners Kohl and Stearns (Ref. 42)

Ti-Al alloys Y2O3 Eckert et al. (Ref. 43)
NASA/TP—2010-216795 7

Heating System/Furnace Design

Resistance heating or electron bombardment is typically 

used to heat the Knudsen cells. Both heating methods have 

their advantages and disadvantages. Below about 1000 °C, 

resistance heating needs to be used, whereas at higher temperatures either resistance heating or electron bombardment can 

be used. Resistance heating has the advantage that no arcing or 

ion formation takes place inside the furnace. A simple passive 

control system is used and generally voltage is regulated.

Thus, temperature is set by a voltage. However, this control 

system makes temperature sensitive to any changes in resistance in the circuit, and great care needs to be taken when 

designing all electrical connections and feed-throughs. An

issue closely related to resistance heating is that power is 

proportional to current squared and that high currents are 

necessary, which means the large-diameter water-cooled 

power feed-throughs are required. Furthermore, heating 

cannot be directed to only the cell, so the entire area around 

the cell needs to be heated, resulting in more power usage. It 

is generally impractical to heat the cell in a multiple-zone 

furnace, and extra care must be taken to avoid thermal gradients.

The electron-bombardment heating method allows direct

heating of the cell alone, and it is relatively easy to apply two 

or more zones to remove thermal gradients. However, the 

circuitry is more complex than that used for resistance heating.

Also, the higher voltages of electron bombardment can lead to 

arcing and interference with spectrometer electronics.

In the authors’ KEMS instrument, resistance heating is 

used. Heating elements are made of either W or Ta and are 

illustrated as part of the entire flange assembly in Figures 4 

and 5. Ta elements can easily be formed at room temperature,

and they heat to temperatures just slightly lower than W

elements. The “hairpin” design used with the single-cell flange 

(Fig. 4) provides uniform heating and allows sighting of side 

blackbody holes for pyrometer temperature measurements. A 

25-μm-thick sheet heating element made from either W or Ta 

is used in the multiple-cell flange (Fig. 5) and provides the 

most uniform heating.

The furnace must provide an isothermal hot zone large 

enough to contain the effusion cell(s): thermal gradients 

within the Knudsen cell cannot be tolerated (Ref. 44). In most 

laboratory applications, long tube furnaces are used and 

provide a uniform heat zone in the center. This is not possible 

with KEMS. The furnace must be compact to allow placement 

of the Knudsen cell(s) as close to the ionizer as possible. An 

isothermal hot zone in such a compact furnace is achieved 

with a carefully constructed multiple-layer heat-shield pack 

that completely surrounds the cell, with a small opening for 

the molecular beam. The heat shields act as a “virtual blackbody” cavity around the Knudsen cell(s) and ensure uniform 

heating. In addition, the Knudsen cell can be placed inside a 

conductive envelope or block to further reduce thermal gradients. The use of a conductive envelope (shown in Fig. 5) is 

vital for a multiple-effusion-cell vapor source. At temperatures 

below 900 °C, heat transfer by radiation becomes less efficient, and other ways to maintain isothermal conditions need 

to be considered. Placing the effusion cell inside a heat pipe 

envelope is an option (Ref. 45).

Figure 4.—Single-cell flange used in our system. Resistance 

heating is used with the “hairpin” element.
NASA/TP—2010-216795 8

Figure 5.—Multiple-cell flange used in our system with resistance heating using a sheet 

element. The x-y position motors are computer controlled. Temperatures are measured with a pyrometer from the bottom.

As noted, the cavity created by the heat shields produces a 

“virtual Knudsen cell.” Although most of the vapor escapes 

through the hole in the heat shields, some of it remains in this 

cavity for a short time. This problem is rarely discussed, but 

these trapped vapor species would be expected to collide with 

the inner heat shield and cell block, eventually escaping from 

the hole in the heat shields. Thus, these species constitute a 

secondary vapor flux that is not representative of the cell 

interior. The secondary flux cannot be eliminated completely, 

but it may be minimized by placing the cell orifice as close to 

the heat shields as possible.

Temperature Measurement

The importance of precise temperature measurement relative to thermodynamic temperature in experimental thermodynamic measurements cannot be overstated. Perhaps the 

most difficult challenges with regard to the determination of 

heats of vaporization and other thermodynamic properties 

arise from errors in measuring the absolute temperature of the 

effusion cell. The best approach to measuring absolute temperature is to use the techniques and standards that define or

realize the International Temperature Scale (ITS–90, Refs. 46

to 50) and to calibrate the measuring instrument directly in

situ with one or more fixed points. This approach ensures that 

the measuring instrument is as close as possible to the absolute 

temperature scale and removes the costly and time-consuming 

procedure of routine calibration at a national standards laboratory. The KEMS technique is ideally suited for in situ calibration because “pure” metals can be placed inside an effusion 

cell and continuously ramped through the invariant point 

{solid + liquid + vapor + container} while both the signal 

from the temperature sensor and relative partial pressures 

in the equilibrium vapor are monitored (Ref. 51). The 

fixed points of Ag (1234.93 K), Au (1337.33 K), and Cu 

(1357.77 K) are the most practical and, together with the 

Planck radiation law ratio, define ITS–90 above 1234.93 K.

The temperature of the cell must be uniform, and the measuring device must accurately reflect the temperature within 

the cell. Two methods are commonly used for measuring 

temperatures—thermocouples and pyrometry. In alloy studies, 

pyrometry is the more reliable technique, but at temperatures 

below about 800 °C, the use of thermocouples is necessary. In 

both cases it is critical to measure the temperature as close to 

the cell as possible.

Thermocouples

Although thermocouples are generally seen as easy to set 

up and use for temperature measurement, particular care must 
NASA/TP—2010-216795 9

be taken to ensure that accurate values are obtained (Ref. 52).

The major challenges encountered when using thermocouples 

with KEMS are the quality of the junctions, incorrect use of 

lead wires (the uninterrupted thermocouple wire must extend 

all the way from the hot junction to the ice-point reference), 

use of an ice-point reference, prevention of contamination 

inside the furnace, and routine calibration. The basic thermocouple equation is

1 2 1 2 − =α − ( )   J J VV T T (9)

Here V1 – V2 is the measured potential difference, 1

J is the 

reference junction and 1

J T is its temperature, 2

J is the 

measuring junction and 2

J T is its temperature, and α is the 

Seebeck coefficient. The reference junction should be in a 

controlled 0 °C ice-point reference, thus the measured voltage 

directly indicates the temperature of 2

J .

The junctions may be formed with a variety of methods, 

including an oxyacetylene flame and spot welding. The choice 

of method depends on the oxidation resistance of the particular type of thermocouple wire used. Typically the actual 

thermocouple wires are made of high-purity, reference-grade 

material. Wires with compositional variations may generate 

secondary voltages and produce erroneous readings.

Although Pt/Pt-Rh thermocouples are widely used for hightemperature studies, we have found a number of critical 

problems that effectively preclude their use with KEMS alloy 

studies. The first is contamination of the wires. This is particularly a problem for Pt/Pt-Rh thermocouples, which are not 

recommended for use in vacuum systems and environments 

containing metal vapors, as encountered in a KEMS alloy 

study. Pt readily alloys with metals such as Al and Ag, forming intermetallic compounds. A partial solution is to use a 

ceramic thermocouple sheath to protect the thermocouple 

wires as much as possible. Frequent calibration and replacement of contaminated thermocouple wire is essential, but this 

is very time consuming and expensive. Calibration can be 

performed by comparison to a National Institute of Standards 

and Technology (NIST)-traceable standard thermocouple, but 

fixed routing in the effusion-cell vapor-source furnace makes 

this impossible. A further factor acting against the use of 

thermocouples in KEMS studies is that they are not a primary 

measurement technique used to define and maintain ITS–90.

This introduces unnecessary calibration steps and the potential 

for uncertainty in measuring absolute temperature.

Pyrometry

When the temperatures of interest are in a suitable range, 

pyrometry is the best technique for measuring the temperature 

of the Knudsen-cell vapor sources in KEMS instruments.

Some of the major advantages are that it is a noncontact 

technique, with the pyrometer placed outside the furnace and 

vacuum chamber. Also, one pyrometer can be used to measure 

temperature at multiple locations, which improves the consistency of calibration. The key advantage is that pyrometry, as 

stated in the “Temperature Measurement” section, is based on 

the Planck radiation law, which in ratio form defines ITS–90 

at all temperatures above the Ag fixed point (1234.93 K).

Thus, pyrometry is the standard method for realizing thermodynamic temperature through the use of Equation (10):

90 2 90

90 2 90

( ) exp(c ( )) 1

( ( )) exp(c ) 1

λ

λ

λ − = λ −L T T X

LT X T (10)

where Lλ(T90) and Lλ(T90(X)) are the radiances of a blackbody 

at wavelength λ, at the temperature to be determined T90 and 

the fixed point T90(X), where X can equally be Ag 

(1234.93 K), Au (1337.3 K), or Cu (1357.77 K) and where the 

second radiation constant c2 = 0.014388 mK (Ref. 46).

To ensure the correct application of pyrometry, one must 

take care to design and fabricate blackbody radiation sources 

in the effusion cell to have an emissivity that approaches 

unity. Typically, this means that the length-to-radius ratio of 

the cavity should be at least 10:1. There are a number of 

similarities in constructing a close-to-ideal blackbody cavity 

and an effusion cell that accurately samples the equilibrium 

vapor. When functioning correctly, a blackbody should emit a 

uniform flux of radiation; and when visually observed at 

steady-state conditions, it should never appear darker than the 

surrounding parts of the furnace. If the blackbody source does 

appear darker, it is likely due to reflected radiation from hotter 

surfaces like the heating element. If this occurs, radiation 

shields are needed to prevent radiation from the hotter surface 

from directly impinging on the blackbody source.

The pyrometer also needs to be carefully aligned with the 

blackbody sighting holes and chamber window so that there 

are no obstructions. An instrument that allows sighting 

through the optics of the pyrometer is invaluable and allows 

the experimenter to see the source area of the measurement 

exactly and to confirm that the proper object is being sighted.

Furthermore, it is important for the source area to lie fully 

within the opening of the blackbody and for the measured 

temperature to be independent of the location of the source 

area inside the blackbody.

After the blackbody cavities, the next critical issue is the 

window transmissivity changing with time. Even with a welldesigned vapor source to minimize the trapping of effusing 

vapors, with proper placement of the blackbody source, and 

with the use of shutters; there will inevitably be some condensation of high-temperature vapors on the window. As a result, 

the window needs to be cleaned regularly, and the transmissivity of the window needs to be measured. Window changes 

can be checked routinely using an in situ calibration technique 

where “pure” Ag, Au, or Cu are placed in an effusion cell and 

the invariant point {solid + liquid + vapor + container} is 

ramped through while both temperature and relative partial 

pressures are monitored. This procedure can be done a number 

of times during an experiment. Figure 6 illustrates an example 

of this for Au in a graphite container (Ref. 51). A clear plateau 
NASA/TP—2010-216795 10

Figure 6.—Melting point of Au in a graphite cell, showing variation of the measured 

ion intensity and temperature with time. The plateau on the measured ion intensity 

curve shows the existence of an invariant, or triple point.

is observed in relative pAu, which is characteristic of an 

invariant reaction. The changes in slope of the curve in a 

temperature-versus-time plot correspond to the start and finish 

of melting. Because the thermal mass of the sample is small in 

comparison to the whole furnace and the blackbody is not 

fully inside the metal sample, the measured temperature is not 

fixed while the invariant equilibrium exists. Thus, the invariant can only be observed on heat-up, and the first thermal 

arrest is the invariant temperature. The slower the heating rate,

the more accurate that these measurements are. The measured 

current from the photomultiplier at the invariant point is used 

to determine the window transmissivity for correcting the

measured temperature.

Traditionally disappearing filament pyrometers have been 

used, but these are subjective, with measurements varying 

from operator to operator, and are no longer used. Today, 

there are a variety of pyrometers available that use a photomultiplier tube to measure radiance at a given wavelength;

these have been shown to work very successfully. It is commonly thought that the effusion orifice and cell can be used as 

a blackbody cavity for temperature measurement. Indeed, this 

is cited as an advantage of a cross-axis ionizer, as illustrated in 

Figure 2. However, in practice this involves sighting through 

the apertures in the ionizer, and alignment becomes difficult.

The major problem with sighting the orifice is contamination 

of the window above the orifice with time. In general, the 

authors have found that precise temperature measurements are 

better made from a side or bottom port, as close to the cell 

as possible.

Molecular Beams

In KEMS only a small portion of the total distribution of 

the molecules effusing from the cell orifice form the molecular 

beam that is analyzed by the ion-source/mass spectrometer.

Thus, the portion of the distribution that is selected is critical 

to the success of KEMS in general, but it is particularly 

important for a multiple-effusion-cell-configured KEMS 

instrument. In the traditional approach, the effusion orifice and 

the larger diameter entrance orifice or slit to the ion source are 

considered to define the molecular beam. However, as shown 

in Figure 7(a), molecules can enter the ion source from a wide 

angular range (defined by holes in the heat shields and ion 

source entrance). Clearly this situation allows molecules to 

enter the molecular beam that do not originate from inside the

effusion cell and will result in erroneous results. A technique 

developed by Chatillon and coworkers (Refs. 5, 45, and 53)

can be used to solve this problem. Two small, fixed apertures 

are introduced between the effusion cell and ion source, as 

shown in the restricted collimation part of Figures 7(a) 

and (b). These apertures select a small, well-defined angular 

range that a molecule must be traveling to enter the ion source, 

form an ionization volume, and thus be analyzed. The selected 

angular range is fixed and independent of the vapor source.

For the vapor effusing from a Knudsen cell to be sampled, the 

center of the orifice needs to be moved to be concentric with 

the fixed apertures. The beam molecules must now have 

velocities aligned along the axis perpendicular to the orifice 

and minimal molecule-molecule interactions within the beam.

Thus the beam will accurately represent the vapor above the 

condensed phase in the Knudsen cell. Although a well-defined 

molecular beam is essential for Knudsen-cell mass spectrometry (Ref. 53), it has not been given adequate attention in the 

past. Our system uses two apertures above the Knudsen cell to 

define the beam (see Figs. 1 and 7). Following Morland et al. 

(Ref. 53), we refer to the fixed aperture closest to the cell as 

the “field aperture” and the aperture closest to the ion source 

as the “source aperture.”
NASA/TP—2010-216795 11

Figure 7.—Molecular beam collimation. (a) Ray diagram showing that a small field aperture limits the sampling area and allows only 

the material effusing from the cell to be sampled (adapted from Ref. 53). (b) Three-dimensional diagram of molecular beam formation and collimation, showing the beam-defining orifices, ion-beam formation, and a well-defined ionization volume.

A well-defined molecular beam strictly defines the source 

area and angular range of molecules and restricts the amount

of background vapor that reaches the ionizer. Furthermore, by 

using a small field aperture one can make the source area of 

the molecular beam smaller than the cross-sectional area of the 

cell orifice. This definition of the beam effectively removes 

the effect of the shape of the orifice on the flux distribution of 

the molecular beam and makes KEMS measurements independent of orifice shape. This effect is analogous to the 

requirements of sampling the radiation from fully within the 

blackbody when temperature is measured with a pyrometer.

The major advantage of defining the molecular beam this 

way is calibration. Consider two Knudsen cells on a multiplecell flange—one with a pure material that has a known vapor 

pressure and one with an alloy with a component that has an 

unknown vapor pressure. Ideally we can use the cell with the 

pure material to determine the calibration constant that relates 

measured ion intensity to vapor pressure. However, this determination of a calibration constant only gives a reliable value if 

the molecular beam from each cell is sampled in exactly the 

same way.

Our goal in this section is to describe the molecular beam 

mathematically. We need to understand how the intensity 

varies a function of the pressure in the cell, the Clausing factor 

of the cell orifice, the distance from the cell orifice, the area of 

the cell orifice, and the placement of defining apertures in the 
NASA/TP—2010-216795 12

molecular beam. Chatillon and his group (Refs. 5, 45, and 53)

discuss defining a molecular beam in the KEMS technique, 

and we shall follow their arguments.

Molecular beams are analogous to the transmission of 

light—a stream of photons. Many of the equations developed 

for light are readily applicable to these molecular beams. First, 

note that the flux decays as 1/a2

, where a is the distance from 

the source to the receiver. The basic equations for the flux 

received from a radiating element are derived in the paper and 

textbook by Walsh (Refs. 54 and 55). The problem germane to 

the collimation of a molecular beam in a mass spectrometer is 

the transmission of the beam from one disk source to another 

coaxial disk source. The fraction of molecules that leave the 

radiating disk and arrive at the receiving disk is given by

2 2 2 2 22 2 2

1 2 1 2 12

1 2 2

1

( ) ( )4 (, ,) 2++ − ++ − = r r a r r a rr

Fr r a

r

(11)

Here a is the distance between the two disks, r1 is the radius of 

the radiating disk, and r2 is radius of the receiving disk. This 

quantity is the unit of the solid angle that reaches the second 

aperture (Ref. 53). Thus, the flux reaching the second aperture 

can be described as

( 1 2 ) ( ) , , 2 R

  θ′ =  

π  

C A

A

A

W p j Frr a

M T (12)

Here WC(θ ́) is the Clausing factor discussed earlier in 

Equation (7), but it is for the limited angle from the normal θ ́

defined by the field and source apertures (Eq. (13)). Note also 

that the number distribution is not the same everywhere in the 

molecular beam. This is evident if a portion of the beam 

distribution is sampled as shown in Figure 3(c). If the center 

of the collimating apertures is collinear with the center of the 

distribution, then there is a symmetric number density about 

this center.

1 0

() , d

θ′   θ= θ ω ′     ∫  C

L W T r (13)

The function T is the angular distribution of a real orifice 

relative to an ideal cosine distribution, as discussed previously. We select the function for the smaller angles about the 

normal to the orifice. Equation (13) then describes the flux 

reaching the ionization chamber in terms of the critical beamdefining parameters. Figure 7(b) shows the fixed apertures that 

select a portion of the effusate distribution to form a molecular 

beam. In our system the molecular beam includes the solid 

angle about 0.76° from the normal, and the furnace is translated on an x-y plane to ensure that all cells that are sampled 

form the same angle to the normal. Such variations from cellto-cell in the multiple-cell system are accounted for in the 

experimentally determined geometry factor ratio (GFR), as 

discussed later in the “Derivation of the KEMS Equation”

section.

Mass Spectrometric Analysis of the

Molecular Beam

Although the quantitative nature of the KEMS technique 

was indicated in the introduction, it is important to reiterate it 

at the start of a discussion of the ion source, mass analysis,

and detector. The aim of this technique is to measure the 

relative partial pressure of vapor species in equilibrium with a 

condensed sample as a function of sample composition and 

absolute temperature. The pressure of each species is measured indirectly by sampling its flux in a molecular beam by 

ionization and analysis of the ion beam. Ideally, the ion-beam 

composition is representative of the molecular beam; however, 

the indirect nature of these measurements introduces a range 

of factors that affect the measured intensities in the mass 

spectra. These factors are unrelated to sample composition and 

temperature. Clearly then, the goal is to reduce the effect and 

variation of these other factors to allow the accurate study of 

vapor pressure with temperature and sample composition. The 

next section briefly discusses the aspects of mass spectrometry 

with the aim of identifying the other factors and indicating 

how their effects can be reduced to provide accurate measurement of thermodynamic activities.

Instrument Description

All mass spectrometers consist of four common elements:

(1) the ion source, (2) the mass analyzer, (3) the detector, and 

(4) the vacuum system (Ref. 56). Quadrupole, time-of-flight, 

and magnetic-sector instruments have all been used successfully to obtain thermodynamic data from metallic and alloy 

systems. It is important that the instrument introduce no massdiscrimination effects or that corrections be applied for these 

effects. Thus, in general, magnetic-sector instruments are 

preferred because they can be designed to minimize mass 

discrimination.

Ionizer

The purpose of the ion source is to produce ions representative of the sample and to accelerate and focus them through a 

static potential field to form a well-defined ion beam that is 

directed to the mass analyzer. The vapor is introduced to the 

ion source as a well-defined molecular beam that is selected 

from the material effusing out of a Knudsen-cell vapor source.

There are a variety of methods available for producing ions 

from gases (thermal ionization, vacuum discharge, ion impact, 

photo ionization, and electron impact), all of which have 

advantages for specific applications. Electron impact is the 

most versatile for high-temperature inorganic vapors and is 

generally used. The main advantages offered by electron 

impact are good sensitivity, ease of forming a controlled 
NASA/TP—2010-216795 13

electron beam, and the ability to vary the energy of the electrons over a wide range.

Ion sources used for KEMS have either (1) a mutually perpendicular arrangement of molecular, electron, and ion beams 

or (2) parallel molecular and ion beams with a perpendicular 

electron beam. As shown in Figures 1 and 7(b), our mass 

spectrometer has a mutually perpendicular arrangement.

Although this arrangement may reduce sensitivity, it has the 

advantages that collisions between ions and neutral molecules 

are reduced following ionization and that the kinetic energy 

spread of the molecules (due to the temperature of the vapor 

source) is not transferred to the ionization process and to the ion 

beam. This arrangement results in a smaller energy spread in the 

ion beam, which results in better ion-beam focusing and resolution in the mass analyzer. In a static electric field, ions with the 

same starting location, direction, and kinetic energy per unit 

charge will traverse an identical path (i.e., no mass discrimination) (Refs. 56 and 57).

Understanding ionization processes is important for interpreting measured mass spectra because it provides a method to 

identify possible “parent molecule(s)” for each ion species. The 

identification process typically involves determining the relative 

ionization potential (IP)/appearance potential (AP) of each 

parent and fragment ion and studying the shape of their ionization efficiency (IE) curves. This information allows the selection of an electron energy that will ensure that the measured ion 

intensity is not, in part, due to a fragmentation process, while 

providing the maximum instrument sensitivity. Electron impact 

ionization, ionization-efficiency curves, and ionization cross 

sections have been discussed in detail by many investigators

(Refs. 14, 56, 58, and 59). Therefore, only the basic aspects of 

the ionization process important to activity measurements are 

summarized here.

An electron with kinetic energy E collides inelastically with a 

neutral atom or molecule, some kinetic energy is absorbed, and 

the valance electron configuration of that atom takes an excited 

state. Above a threshold energy Ec, the collision results in the 

removal of a valance electron and the formation of a stable ion. 

The energy for this process is the IP.

() () 2 −+ − Ag e A g e +→ + (14)

Simple ionization of a molecule may also occur:

() () 2 −+ − AB g e AB g e +→ + (15)

where B represents another alloy component. However, many 

other processes may occur besides these simple ionization 

processes. Fragmentation may occur:

() () () 2 − + − AB g e A g B g e +→ + + (16)

Double ionization and ion-neutral molecule reactions may also 

occur. An understanding of the ionization process is important 

for correlating the correct magnitude of ion intensity with 

partial pressure in Equation (1).

One important tool in understanding ionization processes of 

high-temperature inorganic vapors is an IE curve or a plot of 

the energy of the ionizing electrons versus ion current. 

Drowart and Goldfinger (Ref. 13) and Grimley (Ref. 14) discuss 

the use of IE curves to understand fragmentation patterns. 

Figure 8 is a typical IE curve. The most common type of information obtained from such curves is the AP shown in the figure. The 

AP for the ionization of the molecule AB is composed of

AP IP AB AB AB = + +Σ D E (17)

Here DAB is the dissociation energy of AB, and ΣE is the sum of 

any excitation levels of the molecule. 

In the case of an atomic species, there is, of course, no dissociation term. Generally, one of two methods is used to obtain 

the AP—the linear extrapolation (LE) or the critical slope (CS) 

method. The LE method involves fitting a straight line to the 

apparently linear section of the IE curve, extrapolating back to 

the electron energy axis, and taking the intercept as the AP. This 

method is subjective, since a series of data points are approximated by the operator to be linear. Fundamentally, the IE curve 

is never linear (Ref. 60). The CS method is based on assigning 

the initial curvature of the IE at the IP to a Maxwellian energy 

distribution of the thermally emitted electrons (Refs. 56 and 58).

It should be noted that this is an approximation, since the 

energy distribution of thermally emitted electrons shows deviations from a pure Maxwellian distribution (Refs. 61 and 62). A 

plot of the logarithm of ion intensity versus electron energy 

exhibits a linear region below the AP. The slope of the linear 

region is typically independent of material. The point where this 

curve deviates from linearity is the IP for the ion. The CS 

method is generally considered to be more reliable than the 

LE method (Ref. 58). APs are generally instrument specific 

(Ref. 56) because of the spread of electron energies and the 

method of calculation. A stable and known electron energy 

across multiple experiments is critical in thermodynamic 

measurements because it ensures a consistent IE for each 

species. Figure 8 is a representative IE curve with the LE 

method used to obtain an AP for Al. To select a consistent

operating electron energy, it is essential to measure IE curves as 

part of each experiment in a thermodynamic study and to set the 

electron energy relative to the measured APs.

The probability of ionization by electron impact is put into 

a quantitative context through the concept of ionization cross

section. An ionization cross section, σA(E) (dimensions ×

area/molecule), is specific to an ionization reaction (e.g., 

() () 2 −+ − Ag e A g e +→ + ). It is defined experimentally by 

the following relation (Ref. 58):

() () ()

( ) ( ) ( )

A e eA

A

A

e eA

II E I E l E

II E

E

I El

+ −

+

−

= ρσ

σ =

ρ

(18)
NASA/TP—2010-216795 14

Figure 8.—Example of an ionization efficiency (IE) curve showing the appearance potential (AP) derived from the linear extrapolation (LE) method, where the coefficient of 

determination, R2, is 0.9634 and AP is 6.83 eV. 

where ( ) +

A II E is the ion current of the ion immediately after 

ionization and before extraction, ( ) −

eI E is the current of 

impacting electrons, ρA is the density of the vapor in the ion 

source, and le is the “collision path” of the electrons through the 

vapor in dimensions of length. An identical definition of cross 

section is used for molecular species. When multiple ionization 

processes occur, a total cross section of the neutral species is 

defined as the summation of all ion species collected in the ion 

current (Ref. 59). Although the cross-section concept is simple, 

the determination of accurate absolute values from experiments involves considerable difficulties. This description 

implies the following necessary conditions:

( ) +

A II E Ions are only produced by single-electron impact 

in the electron beam, and the fraction of ions collected to ions produced is known.

( ) −

eI E There is a total current collection of electrons 

producing ions, a uniform electron current (or 

known distribution if inhomogeneous), and no 

collection of secondary electrons.

le The electron trajectory and the shape of the ionization volume is accurately known, and therefore 

the collision path of the impacting electrons is 

known.

ρA The vapor density is uniform and known in the 

ionization region. Typically for molecular beams 

this involves knowing the temperature and pressure of the vapor source, the velocity of the 

molecules, the total beam flux, and a known distribution, if inhomogeneous.

The ionization cross section is a central quantity in the sensitivity factor in Equation (1). Difficulties in obtaining reliable, absolute cross sections result in the use of calculated 

atomic cross sections (Refs. 63 to 66) together with the additive rule for molecules species for absolute pressure calculations with KEMS. More recently, better experimental results 

have been published for absolute cross sections and for crosssection ratios for various species (Refs. 67 to 77), but there are 

still many molecular species with no data, and there is little 

agreement between reported values of commonly studied 

species (Ref. 17). The problem is clear for atoms, and it is 

even greater for molecules. For molecules, the atomic cross

sections are commonly summed and then multiplied by 0.75 

(Ref. 4). This method for molecules is an estimate, and errors 

are up to 30 percent or more. These problems suggest that the 

best approach for KEMS is to use measured cross-section 

ratios (made with the specific instrument), and this is best 

achieved with a well-designed multiple-cell configuration.

Improved calculations also lead to more reliable cross sections 

(Ref. 66).

Mass Analyzer

The resulting ion beam is sorted according to its mass-tocharge ratio by the mass analyzer. Mass spectrometers are 

generally classified according to the mass analysis method—

magnetic-sector, quadrupole, or time-of-flight. Our instrument 

is a 90° magnetic-sector instrument that uses the force exerted 

on a moving charged particle in a magnetic field to separate 

the beam according to ion momentum. For the conditions of 

equal kinetic energy and charge, these momentum spectra 

become mass-to-charge spectra. The key equation is then
NASA/TP—2010-216795 15

2 2

2 = m rBq V (19)

Here m is the mass of the ion, q is the charge, r is the radius of 

deflection, B is the magnetic field, and V is the accelerating 

voltage. Thus the mass-to-charge ratio varies as the square of 

the magnetic field and the inverse of the voltage. Generally, 

spectra are scanned by varying the magnetic field. However, 

finer scanning may be accomplished by varying the voltage.

Magnetic-sector instruments are generally preferred for 

high-temperature vapor studies because of their lack of massdiscrimination effects. The identity of an ion species is determined from the mass-to-charge ratio, whereas its relative 

abundance is determined from the intensity of its peak in the 

mass spectrum. The isotopic “fingerprint” is also useful in 

identifying peaks. Tables and computer codes are available to 

calculate isotopic abundances to check these values. The 

analyzer must sort the ions so that adjacent mass numbers are 

sufficiently separated. The resolution Res of an instrument is 

defined for two adjacent masses, M and M + ∆M (Ref. 56), in 

Equation (20):

Res = ∆

M

M (20)

The units of M and ∆M can be mass units, voltage, or magnetic field units. If the desired distance between the peaks is 

taken as the base width, then the distance between the peaks 

becomes 1. However, a 10-percent peak-overlap criterion is 

typically used. In a magnetic-sector instrument, resolution is 

set by the beam-defining slits at the exit of the ionizing chamber (electrostatic accelerator) and entrance to the multiplier.

These are vertical slits whose widths are adjustable from the 

outside of the instrument. These slits define the beam and 

resolution (Ref. 56):

Radius Res

(Source slit Detector slit) ≈ +

(21)

In our system the radius is 305 mm, the source slit is 

~0.25 mm, and the detector slit is ~0.025 mm. Thus, a resolution of ~1100 is calculated. For an inorganic species with a 

molecular weight of 100, we can separate an adjacent species 

of 100.1. We have found that this resolution is adequate for at 

least partial separation of the inorganic vapor species from 

background hydrocarbons.

Detector

The intensity of each mass-to-charge peak is measured by the 

detector—generally a Faraday cup or multiplier. Our instrument 

uses a 22-dynode electron-multiplier detector where the selected 

ions pass through a defining slit and impinge on the first 

dynode, producing secondary electrons. These electrons are 

then measured with a sensitive electrometer (ion-current measurement) or an ion counter (Refs. 56 and 78).

The output of the Faraday cup goes to a precision 2×1011-Ω

resistor, and the output of the last dynode in the multiplier 

goes to a precision 1×109

-Ω resistor. The voltage drop VA

across the resistor R is measured with an electrometer, and 

the ion current IA is simply calculated from Ohm’s law:

= 

A

A

V I

R (22)

Ion currents can be converted to counts per second, since 

1 ampere equals 6.24×1018 counts per second. Multiplier gains 

are determined from comparison of the multiplier output to the 

Faraday cup output. The major disadvantage of ion-current 

measurements is the dependence of sensitivity on mass number (Ref. 56). This problem of dependence on mass number is

introduced in the first, or conversion, dynode, where the 

number of electrons ejected from a single ion depends on the 

mass of that ion (Ref. 78). Generally, for masses greater than 

~50 amu,

γ = A A K M (23)

Here γA is the gain, K is a constant, and MA is the mass. To 

avoid these mass bias effects, we do most of our measurements with ion counting. If the system is set up so that 

>99 percent of the pulses are counted, then the efficiency of 

the first dynode does not matter and the multiplier introduces 

no mass-discrimination effects (Ref. 79).

An important aspect of detection efficiency is the “dead 

time,” τ, of the detector. This is the period of time required by 

the detector to process an event and is related to the duration 

of the pulse (Ref. 78). As the count rate increases, the time 

between events approaches τ and the probability of multiple 

events occurring during the processing time increases, resulting in possible errors. Our detector is nonextendable and 

multiple events occurring during this processing time simply 

go unnoticed and are lost. To avoid large dead-time effects, 

one should keep count rates low. However, the need for a 

large dynamic measurement range makes this difficult, and a 

correction is thus needed for high count rates. The empirical 

correction is quite simple with the true count rate RT given by

(1 ) = −τ⋅

m T

m

R R

R (24)

where Rm is the measured count rate and τ is the dead time.

The major factor determining τ is the shape of the pulse 

leaving the multiplier and how detector electronics modify this 

shape during amplification prior to counting. It is worth 

determining if the detector amplifier changes the pulse shape, 

which can be done with a representative pulse provided by 

a signal generator and oscilloscope. It is critical to avoid
NASA/TP—2010-216795 16

excessive gain and “clipping” of the amplified pulse, which 

increases pulse duration and can introduce spurious secondary 

pulses. A typical multiplier pulse has an amplitude of ~10 mV 

and is ~5 ns in duration. Provided that the amplified pulse 

remains less than 20 ns, there is very minimal dead time loss

at count rates approaching 5 MHz. If needed, τ can be determined experimentally by measuring the ion intensity of two 

isotopes over a wide range of count rates. Provided that the 

isotopic abundance KT is unaffected by the changing experimental conditions, the ratio of the measured isotopes is given 

by Equation (25), from which the dead time can be extracted.

11 2

22 1

(1 )

(1 )

−τ⋅ = = −τ⋅

Tm m

T

Tm m

RR R K

RR R (25)

To ensure good accuracy of this measurement, it is important to use an element with the largest possible isotopic 

abundance ratio (i.e., >10).

Vacuum System and Separation of Signals From 

Background Gases

A reliable, oil-free vacuum system is an essential part of a 

KEMS system. The location of the pumps on our system are 

shown in Figure 2. The vacuum system of course allows 

proper operation of the air-sensitive components such as the 

ionizer and the detector. An oil-free system minimizes background, which may block the ions formed from the molecular 

beam. Today’s oil-free turbopumps and backing pumps,

together with ion pumps, allow the construction of a true oilfree pumping system throughout.

In addition to minimizing the overall background, ions 

formed from the species in the cell can be distinguished from 

any specific background peaks by high resolution in the ion 

sorter, by the measurement of isotopes, and by use of a “shutter profile.” The shutter, which is typically a small paddle with 

a slot, can be externally scanned across the molecular beam.

The shape of the resultant profile gives some information 

about the origins of the molecular beam (Ref. 13). The intensity of the beam is thus taken as the difference between the 

maximum (peak + background) and the minimum (background). In our system, the precision movement of cells in one 

direction, in both single- and multiple-cell flanges, together 

with a small field aperture, allows a shutter profile to be 

obtained. Alternatively, in the multiple-cell flange, an empty 

cell can be used for background measurements.

Derivation of the KEMS Equation

The central KEMS equation can be derived now that the 

Knudsen-cell vapor source and mass spectrometer have been 

described. This follows directly from the vapor flux in the 

molecular beam selected from the distribution of material 

effusing from the Knudsen cell (molecular-beam flux equation) and the definition of the ionization cross section 

(Eq. (18)). However, in accordance with the aim of identifying 

factors that affect the measured ion intensity and that are 

unrelated to sample temperature and composition, it is useful 

to rewrite Equation (18) in terms of the number of ions produced per second in the elementary volume dv in the region 

defined by the intersection of the molecular and electron 

beams, ( ) +

An E (Refs. 71 and 80) (this is prior to the formation 

of the ion beam):

( )d ( ) ( )d

() () d

+ −

−

= ρσ

= σ

A e eAA

A

e eA

A

n E v I El E v

j I El E v

c

(26)

Here jA is the flux of molecular beam. The region defined by 

the intersection of the electron and molecular beams is the 

ionization volume and, provided that the electron beam is 

wider than the molecular beam, it has an approximately 

cylindrical shape (Fig. 7(b)).

Consider first an electron beam with a uniform flux. A uniform electron flux requires a specially designed electron gun 

(Refs. 81 and 82). Further consider a molecular beam with 

uniform flux across a plane perpendicular to its direction. As 

noted, the intensity of the molecular beam decreases with 1/a2

,

where a is the distance from the cell orifice to the ionization 

region. Provided that the molecular beam stays fully within 

the electron beam, this will result in a uniform rate of ion 

production across the ionization volume.

KEMS typically uses thermally generated electrons, so the 

electron beam does not have a uniform flux across a plane 

perpendicular to its direction. Furthermore, the molecular 

beam is not uniform across a plane perpendicular to its direction, as shown in Figures 3(c) and 7(b). The mathematical 

description of a molecular beam has been discussed previously 

with Equation (12). Here the differential of the molecular 

beam flux can be written as follows:

2

() 1 d

2 R

C A

A

A S

W p j s

M T a

  θ′ =  

π   ∫ (27)

where ds is an element of a surface perpendicular to the 

molecular beam. Substitution of Equation (27) into (26) with 

the assumption of a homogeneous electron beam and integrating, results in the total number of ions produced per unit 

time, ( ): + N E A

2

2

( ) ( )d

() 1 1 () dd 2 R

() 1 ( ) dd 2 R 8R

+ +

−

−

=

  θ′ =   σ

π  

  θ π ′ =   σ

π  

∫

∫∫

∫∫

A A

V

C A e e A

A A V S

C A A e e A

A V S

N E nEv

W p I l E s v

M T a c

Wp M I l E sv

M T a T

(28)
NASA/TP—2010-216795 17

Here ( ) + N E A is the total number of ions produced per unit time 

(ion intensity). The integral in Equation (28) is difficult to 

evaluate for these reasons:

(1) Coordinate systems—The molecular beam is best 

described with polar coordinates such that r is measured perpendicular to the beam. As noted, a beam of 

thermally generated electrons is difficult to describe in 

any coordinate system. If we assume that the electron 

beam apertures create a cylindrical electron beam, then 

the electron beam may be described with polar coordinates such that its radius is perpendicular to the 

direction of the electron beam. These two coordinate 

systems must be consistent for the integration.

(2) Electron beam—As noted, the mathematical description of this is not known. 

Nonetheless, the dependency of ion intensity is clearly indicated in Equation (28). The ion intensity is a function of the 

ionization volume, the electron beam flux, the vapor pressure 

in the cell, the temperature of the cell, the size of the orifice, 

the distance from the effusion orifice, and the ionization cross

section. We can easily extract the KEMS equation (Eq. (1))

from Equation (28):

2

() 1 ( ) ( ) dd 2 R 8R

k ()

+ −   θ π ′ =   σ

π  

σ =

∫∫ C A A

A e e A

A V S

A A

Wp M N E Il E sv

M T a T

p E

T

(29)

Here k is a constant incorporating all the factors in 

Equation (29).

The final stage in deriving Equation (1) is converting the 

rate of ion production to the measured ion intensity in the 

mass spectra. This involves extracting ions from the ion 

source, forming an ion beam, separating the beam according to 

mass-to-charge analysis, and measuring intensities. Therefore 

the measured ion intensity IA(E) depends on the ion-extraction 

efficiency ε(x, y, z), the transmission probability of the mass 

analyzer τion, the detection coefficient γA, and the isotopic 

abundance fA. The ion-extraction efficiency is a nonuniform 

function of the position in the ion source, which highlights the 

need for a consistent ionization volume to ensure that the ion 

beam accurately represents the rate of ion formation. The 

mutually perpendicular design of the ion source and small 

ionization volume ensure that the ions have similar starting 

positions and that their initial velocity in the ion-beam direction is negligible. Therefore, the transition probability should 

be identical for all ions:

( ) ( )(, , ) + = ε τγ I E N E xyz f A A ion A A (30)

Substitution of Equation (30) into (29) gives the KEMS 

equation:

k () ( ) (, ,)

A A

A

ion A A

p E I E

T xyz f

σ = ε τγ

(31)

Commonly, this equation is written in the following form:

k ()

( )

′ = σ

A

A

A

I ET

p E (32)

where k' is a constant relating ion intensity and temperature 

to pressure.

Much of this report has focused on our multiple-cell vaporsource flange and the use of an in situ standard. The proper 

use of a multiple-cell configuration requires that the molecular 

beam from different cells be sampled in a consistent manner.

Consistent sampling is only possible if the shape of the ionization volume is constant and the same portion of the flux 

distributions of the molecular and electron beams intersect 

(i.e., the relative positions of the beams do not change).

Consistent sampling is achieved by introducing two fixed 

apertures (the field-aperture and the source-aperture) between

the Knudsen-cell vapor source and the ion source, as discussed 

previously. These apertures fully define the shape and position 

of the molecular beam in the ion source. Also, the apertures 

limit the trajectory of molecules that can enter the ion source 

to a small, clearly defined solid angle, which removes the 

possibility of direct contamination of the molecular beam from 

adjacent effusion cells, revaporization flux from the shields, 

and general background. The ionization volume is then fixed 

by the stability of the potential surface in the ion source,

which determines electron beam shape. Part of tuning the ion 

source, therefore, involves adjusting this potential surface to 

align the maximum flux portions of the electron and molecular 

beams. The final aspect is the consistent alignment of the 

effusion orifice with the fixed apertures so that the same 

portion of the effusate distribution from each effusion cell is 

selected by the molecular beam. It is helpful to consider the 

molecular beam to be independent of the molecular species it 

samples. Alignment of the cells is very important and is 

checked visually with a camera sighting the effusion orifice 

through the molecular beam apertures (Fig. 2) and through 

scans of ion intensities with cell position.

If the conditions of consistent ionization volume, a fixed 

electron beam, and consistent alignment of the cell orifice 

with the molecular beam-defining apertures are met, the 

integration over the electron beam and the molecular beam 

shape in Equation (29) will be constant from cell to cell.

Provided that the cells are isothermal, for a comparison 

between different molecular beams, the ion ratio is given by

I

II

( ) () C

() () C

σ = ⋅⋅ σ

A A A

B B B

I E E p

IE Ep (33)

where CI and CII are constants relating only to variations in the 

flux distribution in the molecular beam because of differences 

in effusion orifice geometry. Since the true nature of the 
NASA/TP—2010-216795 18

electron and molecular beam flux distributions and the exact 

shape of the ionization volume are not known, absolute

measurements cannot be made. However, consistent sampling 

allows accurate relative measurements. When different species 

coming from one cell are compared, the GFR for a nonideal

effusate distribution is the same for both species and it 

cancels out.

From this discussion, the effect of orifice shape on the 

effusate distribution needs to be removed before the relationship between vapor pressure and sample composition and 

temperature can be studied accurately. The calibration of 

orifices is easily achieved with a multiple-cell configuration 

by putting the same material in different cells and comparing 

the rate or ion production at the one temperature. This calibration procedure is referred to as a GFR measurement:

-cell I I

-cell II II

( ) C GFR

() C = = A

A

I E

I E (34)

Measurement of Thermodynamic

Properties of Metals and Alloys

Single-Cell Techniques for Pure Materials

Most KEMS instruments use a single Knudsen-cell vapor 

source. A variety of techniques have been developed for

measuring thermodynamic quantities with a single-cell configuration (Refs. 12 to 17). First consider a pure metal. The 

determination of the heat of vaporization ∆vapHo

(A) is one of 

the most common measurements in KEMS for

( ) ( )

pA

A s A g

Keq = (35)

This is done with two related methods (Ref. 12): the 

second-law method and the third-law method. The second-law 

method is based on the van 't Hoff equation:

d ln Keq vap ( )

d(1 ) R

o H A Tm

T

∆ = − (36)

where Keq is the equilibrium constant.

As indicated by Equation (32), pA is proportional to IA(E)T. In 

most metals it has been found that the primary ionized species is 

A+ and is representative of the vapor. Thus a plot of ln(IA(E)T) 

versus 1/T gives a linear plot with slope vap ∆ H A Tm

o ( )R ,where 

Tm is the average temperature of the measurement. Figure 9 is 

an example of such a plot for Au and Ni.

Equation (36) implies that ∆vapHo

(A) is independent of temperature, but given that the heat capacities of the condensed 

and gaseous phases are different, ∆vapHo

(A) is temperature

dependent. This makes it difficult to compare measured

Figure 9.—Example of Au and Ni heat of vaporization, ∆Hv, measurement; IA, ion 

intensity in counts per second from A(g); E, energy of ionizing electrons; and T, 

absolute temperature.
NASA/TP—2010-216795 19

data taken at different temperatures. It is better to report the 

enthalpy for the reaction at the standard temperature (298 K), 

which is done with the Σ ́ method (Refs. 51, 83, and 84) using 

the free-energy functions (FEF298.15) for the condensed and 

vapor phases, which are known for the pure metals.

∆− − = + { (FEF )} ln( ) 298.15 R I T P QT A (37)

where 298.15 298.15 FEF ( = − ) o o GH T T for each phase. If the lefthand side of Equation (37) is plotted versus 1/T, the slope (Q) 

gives ∆vapHo

(A) at 298.15 K and the intercept (P) gives an 

estimate of instrument sensitivity factor for species A

(Ref. 51). The third-law method is similar but requires the 

conversion of the measured ion intensities into absolute vapor 

pressures:

[ 298.15 ] vap 298.15 ∆ − − =∆ { (FEF )} R ln( ) ( ) o T p HA A (38)

Of course, free-energy functions referenced to zero kelvin

can be used to derive a heat at zero. Basically the Gibbs free 

energy is calculated at a series of data points, and the entropy 

contribution is subtracted. This results in the heat of vaporization for each data point. The average is taken from all the data 

points, and this method can give a very accurate heat-ofvaporization measurement. However, as has been discussed, 

all the factors necessary to accurately convert ion intensities to 

vapor absolute pressures are not typically known.

Activity Measurements

Thermodynamic activities aA provide a measure of the reactivity of a component (A) in a solution phase, designated here 

as β, relative to a reference state indicated by the superscript (

o

). Activities are fundamental to understanding the 

thermodynamics of multiple-component systems (Refs. 8

to 10). Activity is defined as the ratio of a component’s 

fugacity (Ref. 8) in the solution to the reference state and also 

in terms of the change in Gibbs free energy for a mixing or 

solution reaction, which provides relative chemical potentials, 

β μ −μo A A , ( ( ) , , ,...) β β μ =∂ ∂ B A A T Pn

G N , where NA is the number of moles of A(g), as shown in Equation (39):

mix R ln R ln A β β ∆ =μ −μ = = o A AA o

f G T Ta

f (39)

The value of the activity depends on the choice of the reference state. The selection of a reference state is arbitrary, but it 

must be clearly defined and, ideally, something that can be 

routinely realized in an experiment (Refs. 9 to 10). A typical 

experimental reference state is the stable defect-free phase of 

the pure-element at the temperature of interest (Raoultian 

reference state). The mixing or solution reactions that 

represent the activity of components A and B in the binary 

solution phase AxBy

β are shown in Equations (40a) and (40b) 

(Ref. 10). The reference states for pure A and B are the 

δ-phase and ε-phase, respectively. In these reactions, the 

amounts of A and B added are so small relative to the amount 

of AxBy

β that the composition of the solution does not change:

δβ β 1

mix R ln

+

β β

+ =

∆ =μ −μ =

xy x y

o A AA A

A AB A B

G T a

(40a)

εβ β1

mix R ln

+

β β

+ =

∆ =μ −μ =

xy xy

o B BB B

B AB AB

G T a

(40b)

Each partial mixing reaction is studied directly by comparing the vaporization behavior of A from the reference and 

solution-phase equations (Eqs. (41a) and (41b)). For pure A in

the δ-phase, aA = 1 and pA = o

Ap by definition. At high temperatures and low pressures, the equilibrium vapor approaches 

ideal behavior and fugacity can be determined by measuring 

the partial pressure of a characteristic vapor species. The 

mixing reaction equation (Eq. (40a)) is obtained by subtracting 

the vaporization reactions (Eq. (41a) – (41b)), and the activity

of component A in AxBy

β is determined directly at T by comparing pA in equilibrium with the solution and reference state 

(Eq. (2)).

( )

Δ R ln vap o

A

A Ag

G Tp

δ

δ

=

= − (41a)

1 ( )

Δ R ln vap

x y xy

A A

A B AB A g

G Tp

β β +

β

= +

= − (41b)

A = A

o

A

p a p

(2)

If the composition and activity of all components in a system are measured, then the total Gibbs energy of mixing can 

be determined by Equation (42), where xi is the mole fraction.

Measuring the partial pressure of all components is not common, but in this case the temperature dependence of the 

logarithm of activity can be used to determine the partial 

molar heat of mixing as shown in Equation (43).

mix R ln ∆ = β ∑ i i

i

G T xa (42)

( )

d ln( ) mix

d1 R

β ∆ = ai Hi

T (43)

where mixHi

β ∆ is the partial molar heat of mixing. 

If partial molar heat can be obtained for each of the alloy’s 

components, then the integral heat of mixing can be calculated 
NASA/TP—2010-216795 20

and compared with that obtained from calorimetric measurements or other techniques (Ref. 43).

mix mix β β ∆ =∆ ∑ i i

i

H xH (44)

Single-Cell Techniques for Alloys

Even though thermodynamic activity is a pressure ratio or 

relative measurement, a single-cell KEMS instrument can be 

used if absolute pressures can be determined and the instrument sensitivity does not vary from run to run. Constant 

sensitivities are difficult to achieve because of changes in cell 

position and the molecular and electron beam alignment in the 

ionizer, which all lead to changes in the ionization volume.

Some investigators have a valve that isolates the ionizer in a

highly rigid cell-holding system to minimize this problem 

(Refs. 85 and 86), but this may not be possible on all instruments. Several methods have been developed to overcome the 

problem of a nonconstant sensitivity factor in a single-cell 

configuration. The ion-current-ratio technique is widely 

applied, and several groups are associated with the development of this technique (Refs. 87 to 89), which is based on the 

Gibbs-Duhem relationship (Ref. 8). For a binary alloy,

xaxa A AB B ln ln 0 + = (45a)

d ln d ln d ln   =   =  

A A

A B B

B B

a I ax x a I (45b)

1

ln d ln

A A

A

x x

A

A B

B x

I

a x

I

=

=

  = −     ∫ (45c)

1

ln d ln ln

A A

A

x x

B B

A B

A A x

I x

x

I x

=

=

   

γ =−     −

    ∫ (45d)

Here xi is the mole fraction of a component. Equation (45d) is 

equivalent to Equation (45c), where γA is the activity coefficient of component A, which is given by aA /xA. This change is 

made because Equation (45d) is readily integrated graphically.

Similar to Equation (43), the partial molar heats of mixing are 

obtained by the temperature dependence of activity or in terms 

of ion-current ratios as

( )

( ) mix

1

d ln

R d

d 1

A A

A

x x

B A

A B

x

I I

H x

T

=

β

=

 

∆ =−       ∫ (46)

It is important to recognize that the ion-current technique 

requires that measurements are taken at a series of compositions 

starting from a “pure” component at one side of the system. 

Some representative measurements from our laboratory on 

Fe-Al alloys are given in Figure 10 (Ref. 90). This is a very 

valuable technique and has been used extensively with binary 

alloys and even some ternary alloys (Refs. 3, 4, 91, and 92).

The ion-current ratio or pressure ratio is a sensitive indicator of phase changes. The ratio represents the ratio of the slope

Figure 10.—Example of activity data for the Fe-Al system at 1573 K from 

the ion-current ratio method (Ref. 90).
NASA/TP—2010-216795 21

of the Gibbs energy surface from two corners of the system, 

which can change dramatically as the phase equilibria in the

system change (Refs. 3 and 93):

( ) vap vap ln C

R

∆ −∆ = +  i i

B A

A B

G G

I I

T (47)

Here ∆vap

i GA and ∆vapi GB are the partial molar free energies 

of vaporization from a solution i of A and B, respectively, and 

C is a constant. A linear slope for ln (PA/PB) versus 1/T is 

obtained for a liquid solution over a narrow temperature range. 

When the liquidus is reached, crystals of the solid will precipitate. The partial molar quantities would change dramatically 

with composition, and hence the plot would no longer be linear. 

Such plots for a range of compositions can yield quite accurate 

solidus and liquidus lines. Nunoue and Kato (Ref. 94) have used 

this technique with the Fe-Ge system, and Copland has used this 

technique with the Ni-Al-O system (Ref. 95), as shown in 

Figures 11(a) and (b). Note the discontinuity in the activity 

ratios in Figure 11(a), which clearly establish the liquidus lines. 

The convergence at 1640 °C of five phases (not possible 

according to the phase rule) indicates the need to look in detail 

at this region. This convergence is shown in more detail in 

Figure 11(b), which indicates eutectic and peritectic points over 

a small temperature region. This phase change is further confirmed with the activity ratios of Ni-23Al and Ni-27Al, which 

show the three-phase field of γ + β + Al2O3 (Fig. 11(c)).

Another technique used to measure activity in alloys with a 

single-cell KEMS is the dimer-monomer method that was

developed by Berkowitz and Chupka (Ref. 96). This requires a 

system that has a dimer-monomer equilibrium, which is not 

common:

2A(g) = A2(g) (48)

The equilibrium ratio over the alloy is compared with that 

over the pure component A, and the activity is given by

2

2

alloy

alloy =

o A A

A o A A

I I a I I

(49)

Here alloy

AI and 2

alloy

AI are the ion intensities of the monomer 

and dimer, respectively, for the alloy, and o

AI and 2

o

AI are the 

ion intensities of the monomer and dimer, respectively, for the 

pure material. In situations where the monomer and dimer are 

measureable, this is a valuable technique for single-cell 

systems (Ref. 4).

Figure 11.—Measurement of phase boundaries in the Ni-Al-O system (from 

Ref. 95). Copyright Elsevier; used with permission. (a) Measurement of phase 

boundaries (γ, β, γ', γ' + β) using ion activities. (b) Focus on the region near 

1640 °C. (c) Activity ratios of Ni-23Al and Ni-27Al showing phase boundaries. 
NASA/TP—2010-216795 22

Figure 11.—Concluded.

Multiple-Cell Techniques—Direct Measurement 

of Activities

The critical need for a constant sensitivity factor is solved 

with a multiple-cell-configured KEMS, as shown in Figures 5 

and 7(b). Critical conditions for this method are (1) a fixed 

ionization volume that allows consistent sampling of the 

molecular flux from all cells, (2) the ability to consistently 

sample a well-defined portion of the effusate distribution from 

each cell, (3) an isothermal furnace that allows sampling from 

all cells at one temperature, and (4) the ability to accurately 

measure the absolute temperature of the samples. Once these 

conditions are achieved, the multiple-cell configuration 

provides two independent methods for determining component 
NASA/TP—2010-216795 23

activities in alloy systems. The most general method is the 

direct comparison of the measured ion intensities IA of a 

characteristic species (A) over the alloy and the pure component (°) at a single temperature (Refs. 5, 13, 97, and 98). The 

activity of A (aA) is obtained from the following equation:

o

II

I

C

C

⋅ = = ⋅=⋅ ⋅

o AA A A

A oo o

AA A A

p IT I S

a

p I TS I (50)

where SA is the instrument coefficient that has been discussed.

Since identical molecular species are compared, all factors 

associated with the ion-extraction and mass-sorting processes 

are constant, and provided that the ionization volume remains 

constant, the instrument coefficient ratio reduces to the difference in effusate distribution due to the variation in the shape 

of each orifice, which is represented by the GFR: C1/CII

(Refs. 5, 13, 17, and 97 to 99). The GFRs are determined for 

each pair of cells in a separate run. A standard substance is 

placed in all cells, and provided that the cells are isothermal, 

the vapor pressures will be identical. This vapor pressure 

combined with the assumption of a constant ionization volume 

allows the GFRs to be determined by a comparison of the ion 

intensities for each pair of cells (Refs. 5, 17, 97, and 98), as 

discussed previously and described by Equation (34).

This method does not involve the determination of absolute 

pressures and requires no comparison with tabulated thermodynamic data, and therefore gives activities directly. An additional advantage is that the requirement for accurate absolute 

temperature measurement can be relaxed to some degree because 

all intensities are measured at a single temperature in an isothermal block (Ref. 5). Unfortunately, the high reactivity and high 

vapor pressures of pure components prohibit the use of direct 

measurements in some systems. The most important example is 

pure Al for Al-containing alloys. For these cases, a second 

method of determining activities is required.

The second method of determining activity is an indirect 

procedure that uses a secondary reference, for which {Au(s,l) + 

graphite} is ideal. In this method, activities are determined at 

each T by comparing the measured ratio, Au

o p p A or Auo I I A , 

to the accepted vaporization behavior Au     o oA p p of {Au(s,l) + 

graphite} and the pure-element reference, Equation (51):

Au Au II Au

o Au Au I

C

C

    = ⋅ = ⋅ ⋅⋅         

o o A i

A o o o A A i T TT T

p IS p p

a

p p IS p (51)

The ratio CI/CII is the GFR and accounts for variations in 

effusion orifices. GFRs are routinely measured to be 

1.00 ± 0.01 for a pair of cells with the field and source apertures in place (Refs. 100 to 102). The SAu/SA term is an 

instrument sensitivity (or ionization cross-section) ratio that 

relates the secondary reference, Au

o p of {Au(s,l) + graphite},

to the pure-element reference, o

Ap . These terms are 

determined in a separate experiment comparing the measured 

ratio of the vaporization behavior of A and the pure-element 

reference Au

o oA I I of {Au(s,l) + graphite}, to the accepted 

vaporization behavior Au     o o

Ap p . The SAu/SA terms must be 

independent of T; thus the accepted vaporization behavior for 

both must be correct and able to be measured routinely (Refs. 

100 to 102).

Au Au I Au

II

C

C

o o o

o o A A A T T

S I p

SI p

  = ⋅⋅ 

   (52)

Although it is more complex than the direct method 

(Eq. (50)), this procedure provides the following advantages:

(1) multiple alloys can be measured in a single experiment 

(depending on the number of effusion cells in the furnace);

(2) T measurements are calibrated with the Au melting in each 

experiment (Tmp(Au) = 1337.33 K is a fixed point defining 

ITS−90) (Ref. 46); and (3) routine measurements of 

vap ( ) ∆ 298.15 Au H o by the second- and third-law methods 

provide a systematic accuracy check (Refs. 51 and 103).

Examples of the successful use of this second indirect method 

of measuring activities are given for the Ni-Al-O system 

in Figures 11(a) and (c) and for the Ni-Al-Pt(-O) system in 

Figure 12 (Refs. 95 and 101). The data in Figure 12 show how

maintaining a constant Ni/Al ratio and varying the Pt content 

affects the activities of Ni and Al (Refs. 100 and 102).

In addition to absolute activities, the multiple-cell KEMS 

technique allows relative activities to be determined directly 

by comparing the relative partial pressure of species in equilibrium with different samples, with compositions I and II, and

in adjacent effusion cells in a single experiment, according to 

Equation (53a), where any difference in flux distribution of 

the molecular beams is again represented by the GFR. Relative activities are the most direct measure of any differences 

between the solution behavior and phase equilibrium of two 

samples. According to Equation (39), relative activities 

provide a direct measure of the difference in chemical potential between the two compositions, as in Equation (53b).

I

II

II

A I

C (I II) C

A

A

I

a

I −= ⋅ (53a)

R ln (I II) (I) (II) i i

A A A T a − =μ −μ (53b)

This method is particularly powerful for studying phase 

transformations when the compositions are chosen so that they 

are on different sides of a single phase. An example of this is 

shown in Figure 11(c), where the measurement compares

Ni-23Al and Ni-27Al, on either side of γ′-Ni3Al, in the 

{γ′ + γ + Al2O3} and {γ′ + β + Al2O3} three-phase fields. This 

result clearly shows that the γ′-Ni3Al phase decomposes prior 

to melting (Ref. 95).
NASA/TP—2010-216795 24

Figure 12.—Example of activity data for the Ni-Al-Pt system obtained using the 

multiple-cell method (adapted from Ref. 100).

Activity Calculation for Species That Cannot Be 

Measured Directly

The preceding discussion was based on the situation where 

an alloy component vaporizes or sublimates directly to characteristic species that can be measured easily. This situation is 

not the case in some reactive alloy systems because one 

component may not vaporize directly or its vapor pressure 

may be too low to measure. However, its activity can be 

calculated through an additional equilibrium between the 

components and easily measurable vapor species. Ti-Al-O is 

an important example of this type of system. Here interstitial 

O has a very high solubility in Ti-rich compositions, and 

O concentrations less than 10 at.% have O partial pressures pO

lower than about 10−20 atm at 1500 K. Clearly, these low 

partial pressures are not measurable by KEMS. Fortunately,

both Al(g) and Al2O(g) are present with significant vapor 

pressures in this highly reducing system, and they are related 

by the reaction 2Al(g) + O(g) = Al2O(g). This relation is used 

to calculate the pO in equilibrium with the atomic O in these 

alloys. The following equilibria can all be studied with a pureAl(l) + α-Al2O3 standard:

( ) ( )

Al

Al , Al

K o

sl g

p

=

= (54a)
NASA/TP—2010-216795 25

( ) ( ) ( )

2

23 2

Al O

4 3Al , 1 3 -Al O Al O

K o

s l s g

p

+α =

= (54b)

( ) ( ) 2 3 ( )

3

O

2Al , 3O -Al O

1 K

( ) o

sl g s

p

+ =α

= (54c)

The {Al + Al2O3} mixture allows the simultaneous 

determination of Au Al S S/ and Au Al O2 S S/ according to 

Equation (52), which allows aAl and Al O2 a to be determined 

above the alloy according to Equation (51). The activities of O 

and Al2O3 in an {alloy + oxide} system can be determined 

provided that both pAl and Al O2 p can be measured according to the gas-condensed phase reactions, Equations (54d) and 

(54e), and that the chemical potential of Al2O and Al2O3 can 

be defined in terms of μAl and μO (i.e., Al O Al O 2 μ = μ +μ 2 and 

Al O Al O 2 3 μ =μ +μ 2 3 ) (Ref. 9).

( ) ( )

2

2

* Al O

O 2 Al

2Al O Al O g g

a

a

a

+ =

= (54d)

( ) ( )

2

2 3

23 2

3 Al O

Al O 4 Al

4Al Al O 3Al O g g

a

a

a

+ =

= (54e)

The {Al + Al2O3} standard state defines a very stable reference state for O, and as a result, a measured aO greater than 

unity is common (Refs. 100 and 101). An interesting problem 

encountered with this procedure is the large discrepancy with 

the published data for the reactions (Eqs. (54a) and (54d)).

Clearly more accurate measurements of the vapor species in 

the Al-O system are needed (Refs. 38, 39, 95, and 100 to 102).

A similar situation exists for alloys where a component 

pressure is not measurable under the temperatures for measurable vapor pressures of other components. Examples are Hf in 

Ni-Al-Hf (Ref. 85), Cr in Mn-Cr (Ref. 104), and rare earth 

(RE) in Mg-RE alloys (Ref. 105). The latter study was based 

on a Knudsen cell without the use of a mass spectrometer.

Nonetheless the approach is applicable to a mass spectrometric study. Depending on the alloy system, several approaches 

can be taken. In some cases the effect of controlled additions 

of the low-pressure component on a fixed ratio of the measured elements is the only required information (Refs. 100 and 

102). Albers et al. (Ref. 85) and Zaitsev et al. (Ref. 104) did a 

Gibbs-Duhem integration to obtain the activities of the lowvapor-pressure component. Pahlman and Smith (Ref. 105)

assumed Raoultian behavior in the terminal RE-Mg solution 

and moved across the phase diagram to derive the activity of

the RE component in each two-phase region.

Checks for Correct Operation and 

Consistency in Measurements

Consistency in Ion Intensity Measurements

The most basic check is the reproducibility of ion intensity 

IA at each experimental measurement temperature. The typical 

cycle consists of taking six ion-intensity measurements from 

each effusion cell in turn and then repeating the process.

Therefore, 12 measurements are taken for each cell at each 

experimental temperature. Provided that the furnace maintains 

a constant temperature, IA remains consistent between the two 

measurements (typically within 1 percent) if the effusion 

orifice was consistently aligned with the fixed molecular beam 

(i.e., sampling the same portion of the effusate distribution).

Orifice alignment is checked visually by sighting through the 

ion-source and field apertures. In addition to variations in 

temperature and effusate sampling, inconsistencies in IA may 

be due to the kinetics of a phase transformation occurring in 

the effusion cell. Therefore, it is important to compare the 

behavior of all the measured ion intensities (assuming that all 

the phase changes of the in situ standard are known). If a 

similar variation is observed in both the in situ standard and 

alloy, then typically the furnace has changed temperature 

between measurements. If the furnace temperature and the 

in situ standard intensities are consistent but the alloy intensities vary, then a phase change may have occurred in the 

sample. The consistency of measured ion intensities is a check 

that equilibrium and/or steady-state conditions are achieved in 

the effusion cell.

As discussed at the beginning of this report, it is safe 

to assume that the vaporization coefficient of the common 

metals is 1. However, nonmetallic constituents of an alloy, 

such as phosphorous, may not have a vaporization coefficient 

of 1, and this needs to be considered (Ref. 106, personal 

communication).

Consistency in Vapor Sampling and 

Temperature Measurement

A good real-time check for the consistent sampling of vapor 

pressure and temperature measurements is the straight-line 

correlation of the raw data in a ln IAT versus 1/T plot. This 

works best with the in situ standard because all the phase 

changes are clearly known. A correlation that is clearly a 

straight line with a resultant heat of ±1 kJ/mol or less indicates

that there have been no systematic errors in either sampling 

the vapor pressure or measuring the temperature, as shown in 

Figure 9. That is, the electron beam and the electric fields have 

remained constant in the ion source, neither the cell orifice nor 

field aperture have clogged, there have been no discontinuities 

in the temperature measurements, the electron multiplier 

operation has remained stable, and the effusate distribution is 

being consistently sampled by aligning the orifice with the 

molecular beam. Provided that there is a clear straight-line 
NASA/TP—2010-216795 26

correlation for the in situ standard, any subsequent error 

observed for ∆vapHo is probably due to a systematic error in the 

measurement of absolute temperature.

Accuracy of Absolute Temperature 

Measurement

The most fundamental check for the accuracy of absolute 

temperature is to measure a range of thermodynamic invariant 

points that define the ITS–90 (Ref. 46). In our case the most 

applicable are the triple points of Ag, Au, and Cu. For a unary

system (or a eutectic or peritectic point in the binary system 

when the graphite container is included), this is an invariant 

point (zero degrees of freedom) that is clearly identified as a 

plateau in the measured ion intensity of a characteristic vapor 

species on heating through the triple point. Changes in the 

slope of the ion intensity versus temperature curves, corresponding to the start and finish of melting, are also clearly 

observed, as shown in Figure 6. These measurements can only 

be made on heating because the sample volume is small and 

the temperature measuring device is not embedded in the 

sample. A slower heating rate leads to more accurate measurements. A measurement of the Au invariant reaction is made 

using the in situ standard for every alloy experiment (Ref. 51).

This is also suited to measurements made with a pyrometer 

since this is the definition of temperature above the melting 

points of either Ag, Au, or Cu. Temperature measurements 

made with thermocouples are more susceptible to errors 

because of contamination and the need for calibration with a 

series of fixed points that span the whole range of measured 

temperatures. The assumption of a constant temperature offset 

over an extended temperature range cannot be made 

for thermocouples.

The measured enthalpy of vaporization ∆vapHo of the 

in situ standard is an excellent check of the accuracy of the 

temperature-pressure measurements (Ref. 51). If the difference between the measured and accepted value for ∆vapHo is 

within the experimental error, then the temperature-pressure 

measurements can be assumed to be accurate. In addition, it is 

useful to check for variation of the sensitivity factor SA with 

temperature, according to Equation (1), with a third-law-type 

method.

Geometry Factor Ratio

A major aspect of all multiple-cell measurements is the 

relative difference in the effusate distribution due to variations 

in cell orifice shape, represented by the GFR. This needs to be 

measured for each set of effusion cells in a complementary run 

with a standard substance in each cell. Typically these runs are 

done between activity measurement runs. This is a good 

opportunity to systematically check the isothermal nature of 

the effusion cells, as discussed later. With suitable field and 

source apertures, the source of the molecular beam lies fully 

within the cross section of the effusion orifice. In this case the 

flux distribution in the selected molecular beam is effectively 

independent of the variation in the effusion orifice shape.

Isothermal Effusion Cells

The condition that the cell or cells be isothermal is a fundamental requirement of both single-cell and multiple-cell 

configurations that should be continually checked. This check 

can be done in three ways, depending on the methods used to 

measure the temperature. If thermocouples are used on each 

cell, then an isothermal condition can be verified at the invariant point of the in situ standard by observing the onset of 

melting, as an arrest point in a plot of T versus time, at the 

same time in all cells during a slow ramp. If a pyrometer is 

used, an isothermal condition can be verified by repeatedly 

measuring the temperatures from all cells, which should be the 

same. The third method involves comparing the measured 

enthalpy of sublimation ∆vapHo of the in situ standard with the 

ion intensities taken from all cells but with the temperature 

measurements from one cell. If the cells are isothermal, all 

enthalpies will be identical within the experimental error.

This last method can be used with either thermocouples or 

a pyrometer.

Importance of Constant Electron Energy

Previous sections have highlighted the importance of defining an appropriate electron energy and reproducing this for all 

experiments when an in situ standard is used in activity 

measurements. A suitable electron energy is identified by 

considering the ionization-efficiency curve for all species and 

finding an energy that gives the maximum ion intensities 

without fragmentation of complex molecules. Because the 

shape of the IE curve of each species is different, any variation 

in electron energy will result in a change in the relative ion 

intensities that is unrelated to either alloy composition or 

temperature. Therefore, the electron energy must remain 

constant between runs. This is best achieved by defining the 

experimental electron energy relative to the AP and/or maximum intensity of the in situ standard, as seen in Figure 8. This

removes any calibration errors in the indicated electron 

energy. 

Measurement Procedures

This section reviews some practical procedures that outline 

an experimental run. The major points of the measurement 

procedure are presented in the following lists: (1) sample 

exchange, (2) instrument configuration, and (3) taking measurements. Since there are many types of KEMS instruments 

and cell configurations, all of which can generate excellent 

data, a detailed universal operating procedure for alloy measurements cannot be written. Rather we list some general points 

for the correct operation of a KEMS instrument. These lists

should apply to single-cell or multiple-cell configurations and 
NASA/TP—2010-216795 27

any type of mass analyzer. Thus, it is by no means allinclusive.

Sample Exchange

The procedure for exchanging samples follows:

• Have a clean set of effusion cells and fresh samples 

ready to load. The least damaging method of cleaning 

effusion cells is a high-temperature bake-out. For some 

ceramic cells, an aqua regia (HNO3:HCl-1:3) soak prior 

to bake-out will help remove bulk quantities of residual 

metals without damaging the cell.

• Weigh the metal or alloy, and load the cell about onehalf full.

• Close the high-vacuum valves, and vent the chamber 

slowly. We use a leak valve for venting.

• Unbolt and remove the Knudsen-cell flange. It is convenient to have a flange lift or elevator so that the flange

does not need to be carried.

• Check that the orifices of the cell(s) were not obstructed 

by the holder or heat shields during the previous run.

• Check the alignment of each cell orifice with a fictitious 

molecular beam prior to removing the heat shields and 

effusion cells. This is done by installing an alignment 

fixture that contains a laser pointer mounted in the center, which represents the molecular beam. This fixture 

remains in place until the new cells have been loaded and 

the cell positions have been checked.

• Clean the condensed vapor from the bottom of the plate 

separating the furnace and ion-source chambers, and 

check the aperture for clogging.

• Take great care to avoid damaging the heating element 

when removing and replacing the heat shields, cell 

holder, and effusion cell(s).

• Load the cell(s) into the cell holder, ensuring that all orifices are unobstructed.

• Check the alignment of each orifice with the fictitious 

molecular beam; physically set the center position, and 

adjust the designated position of each cell in the stagecontrol window as required.

• Reinstall the heat shields at the standard height, and 

recheck for any obstruction of the orifices. Remove the 

alignment fixture. 

• Move the cell and cell holder into the appropriate 

position.

• Raise the flange into position, and bolt it in place.

• To ensure that the cells do not move, pump down the 

chamber slowly. We pump through a leak valve with an 

oil-free pump, taking about 2 hr to pump from atmospheric pressure to 5 torr. Below 5 torr, we close the leak 

valve and open the high-vacuum valve for the furnace 

chamber to continue pumping with a turbomolecular pump.

• Pump down the chamber overnight until the base pressures are reached.

Instrument Setup and Configuration

The procedure for setting up and configuring the instruments follows:

• Start heating about 12 hr before beginning the experiment. Use a slow heating rate to reach a temperature well 

below that of the experiment. This procedure will create 

a well-baked-out system.

• Begin experiments in the middle of the temperature 

range of interest. This will give an adequate signal for 

tuning and will allow clear observation of the cell orifice 

(if the system is so configured).

• Make sure that the cell is centered visually and is positioned for maximum signal.

• If using a pyrometer, check that there are no obstructions 

and that a reasonable temperature is measured.

• Check the electron energy calibration of the ion source 

by measuring the ionization-efficiency curve and determining the AP of several important vapor species. Set 

the electron energy for the current run relative to the 

measured APs. This will ensure that all experiments will 

take place at an identical region of the ionizationefficiency curves of the sample and reference materials 

and will allow direct comparison of the results from different runs.

• Tune the ion source to give the maximum ion intensity. It 

is important to note that this is also a function of the 

alignment of the effusion orifice with the molecular 

beam, and the position of the orifice at the maximum 

intensity should be recorded. The effusion orifices of the 

cell(s) must always be moved to this position when taking data. Generally, broad tuning maxima are preferred.

• Record the furnace temperature T, voltage V, and current 

I at each experimental temperature. Plot T versus VI and 

T versus V, and compare the results with those of previous runs. Update the furnace-control function before 

the next experiment if significant variation is observed.

(Such variations typically only occur when there has 

been a physical change in the furnace, and it is important 

to identify the cause of any observed changes.)

• Measure the melting point of a reference material (typically Au) in each experimental run. This is used for the 

thermocouple or pyrometer calibration and instrument 

sensitivity determination.

Taking Measurements

These procedures depend on the type of measurement being 

taken (e.g., multiple cell, ion-current ratio, or monomerdimer equilibria). However, we can identify these general 

procedures:

• Prior to starting an experimental run, identify a temperature range and determine a random sequence of equally 

spaced measurement temperatures that span the entire 
NASA/TP—2010-216795 28

temperature range. This will help eliminate the natural 

tendency to take a series of measurements with a continuously ramping temperature.

• The involved nature of these requirements means that the 

maximum number of data points need to be taken in each 

experimental run. Therefore, a typical run should involve 

at least 14 temperatures, which will take at least 40 hr 

over 3 days. 

• The following considerations apply to a multiple-cell

measurement:

– A relative measurement of the effusate distribution of 

each pair of cells (GFR) is needed.

– An electron-energy calibration of the ion source 

is needed.

– A known ionization cross-section ratio at a defined 

electron energy is needed.

– Accurate absolute temperature measurements are 

essential.

– An instrument sensitivity coefficient SA for the in situ 

reference material is necessary. 

– The cells must always be in the same position. For a 

given ion-source tuning, the effusion orifice of each 

cell must be returned to the same alignment used in 

the tuning procedure. This ensures that the same portion of the effusate distribution is sampled by the 

electron beam in each measurement. This must be 

visually checked for each measurement.

• To ensure that the vapor from all cells is sampled isothermally, it is essential to continually monitor the temperature of the furnace and the current supplied to the 

furnace with time.

• Typically it takes 40 to 60 min for the furnace to reach a 

steady state after the voltage is changed. The time to 

reach a steady state appears to be a function of the magnitude of the voltage change (whether the change is heating or cooling) and the temperature of the furnace.

An extended flat region (for more than 5 min) in the 

temperature-versus-time chart indicates a steady state,

and this should always be used to determine when to 

start sampling the vapor pressures.

• In addition to comparing the measurements taken at a 

uniform temperature, using a plot of ln IAT versus 1/T is 

very useful for determining the quality of the measurements. This works best with a pure reference material (A)

because any phase changes are known. If there is a 

strong straight-line correlation (typically R2 > 0.995), it 

can be assumed that there have been no physical changes 

associated with the vapor sampling processes: that is,

– The effusate distribution has been consistently 

sampled.

– The ion source (electron beam and ion accelerator 

tuning) has remained stable, and there has been a 

consistent ionization volume.

– There have been no changes to the cell orifice during 

the experiment.

– There are no obstructions to the molecular beam.

– The electron multiplier and detector have remained 

stable.

– If the preceding conditions are met, it is valid to 

assume that any subsequent difference observed 

between the measured ∆vapHo and the tabulated value 

for the pure reference material is solely due to an 

error in the measurement of the absolute temperature.

• Any thermodynamic measurement must be repeated at 

least once. The initial run should consist of evenly 

spaced data points over the widest possible temperature 

range. Regions of interest should be identified from this 

initial run. The subsequent measurements should be 

spaced between the data from the previous runs but 

should also focus on regions of interest.

Future Directions

In many ways, the application of KEMS to alloys is only in 

its infancy. As indicated, this technique offers great potential 

for accurate thermodynamic measurements on many alloys.

There are many refinements possible, particularly with current

advances in instrumentation and data acquisition.

We have devoted a large section to the derivation of the 

KEMS equation, relating ion intensity to vapor pressure. As 

noted, it would be beneficial to understand some of the 

variables in this relationship further. In particular, an independent measurement of the total vapor flux would be helpful.

This could be accomplished with an in situ weight-loss measurement or target collection system. Improved molecular beam 

definition could include better positioning of the cell, with 

more precise x, y, and z coordinates.

In regard to the ionization process, an electron gun with a 

narrow spread of electron energy would define APs better.

Although the problem of ionization cross sections can be 

partially circumvented in a multiple-cell system, better measurements and/or calculations of absolute cross sections for 

atoms and molecules would be helpful. Currently, the lower 

limit of measurement with a KEMS apparatus is ~10–10 to 

10–11 atm, and it may be possible to extend this lower limit 

with more efficient ionization processes.

In regard to the Knudsen-cell vapor source, improvement in 

micromachining techniques may give a more uniform orifice 

and the measured GFR may be closer to 1. An intriguing idea 

explored by only a few investigators is the electrochemical 

Knudsen cell (Refs. 107 and 108). In such a case, it should be 

possible to fix the activity of one component or follow 

changes in stoichiometry as the contents of the cell vaporize 

over long periods (Ref. 16).

Finally, data acquisition in mass spectrometry has come a 

very long way. Although the assignment of parent neutral 

molecules to ions for inorganic vapors over alloy systems is 

probably best done with operator judgment (utilizing the mass 

number, isotopic fingerprint, and ionization-efficiency curve 

appearance), the actual acquisition and processing of thermodynamic data is best done with a computer. Some single-cell 

systems are fully automated; our multiple-cell system is 
NASA/TP—2010-216795 29

partially automated. In principle, a multiple-cell system could 

be fully automated as well. The use of computers for acquiring 

and manipulating data will undoubtedly continue to be a 

growing area.

Summary and Conclusions

KEMS is a tremendously powerful technique for obtaining 

thermodynamic data on metals and alloys. Such information as 

heats of vaporization, thermodynamic activities of components, partial and integral molar heats of mixing, and phase 

transformation temperatures can be obtained with a high 

degree of accuracy. General experimental aspects of the 

technique have been discussed with particular emphasis on the 

Knudsen-cell vapor source. Critical considerations with the 

Knudsen cell include geometry, orifice size and shape, resultant effusate distribution, uniform heating, and temperature 

measurement. In particular, temperature measurement is one 

of the most important aspects of KEMS. It is also critical that 

the effusate from the cell form a well-defined molecular beam 

into the mass spectrometer. The basic aspects of a mass 

spectrometer, as required for these measurements, were 

discussed in this report. Generally, instruments with a magnetic ion sorter and ion-counting detection are favored to 

avoid mass-discrimination effects. A detailed derivation of the 

KEMS equation, which relates partial pressure in the cell to 

ion intensity, also was provided.

Both single-Knudsen-cell and multiple-Knudsen-cell systems 

can be used for thermodynamic measurements of metals and 

alloys. The critical consideration is the sensitivity constant SA

from Equation (1): 

= A

A

A

I T

p S (1)

where for a gaseous species A that forms an ion A+

, Equation (1) 

gives the relationship between A’s partial pressure pA in the 

effusion cell and the measured intensity in the ion beam IA and 

absolute temperature T. The constant SA is derived from the 

instrument configuration and the ionization process.

Some single-cell systems have been designed for a constant 

sensitivity factor. Other methods to circumvent this problem 

include the ion-current ratio method and the dimer-monomer 

method. The ion-current ratio is based on a Gibbs-Duhem 

integration and has been used extensively for alloys with 

similar vapor pressures. The multiple-cell technique offers 

great flexibility for studying the thermodynamics of different 

alloy systems. Thermodynamic quantities can be obtained by 

either direct comparison with a standard for the component in 

question or with a secondary standard. Internal checks for 

correct instrument operation and some general procedural 

guidelines were discussed for both single- and multiple-cell 

systems. These include guidelines on sample exchange, 

instrument setup, and actual measurements. Finally, some 

general comments were provided about future directions for 

measurements of alloy thermodynamics with the KEMS 

technique.

Glenn Research Center

National Aeronautics and Space Administration

Cleveland, Ohio, October 6, 2010
NASA/TP—2010-216795 30
NASA/TP—2010-216795 31

Appendix A.—Symbols

A, B general designations for alloy components

A+ ion of alloy element A

AxBy

β general composition of alloy AB in phase β

APAB appearance potential of gaseous molecule AB

a distance between two disks; distance from cell 

orifice to ionization region

aA thermodynamic activity of component A

ai  constants in conversion of voltage to 

temperature

B magnetic field strength

C cross-sectional area of orifice of Knudsen cell

CI, CII combined constants involved in the interaction 

between nonuniform molecular beams and

electron beams inside the ion sources for 

“identical” cells

C general constant in deriving ion current ratio 

dependence on phase changes

c2 second radiation constant

ci  constants in conversion of field to digital-toanalog controller (DAC) number

cA average molecular speed of atom A

D surface area of bottom of Knudsen cell

DAB dissociation energy of gaseous molecule AB

d diameter of molecule

di

 constants in conversion of mass to digital-toanalog controller (DAC) number

E kinetic energy of ionizing electrons

ΣE sum of excitation levels of gaseous 

molecule AB

Ec threshold energy below which no ionization 

occurs

e effective emissivity

e

− ionizing electron

F(r1, r2, a) fraction of molecules that leave radiating disk 

and arrive at receiving disk

FEF298 free-energy function referenced to 298 K

fA isotopic abundance

GT Gibbs free energy at temperature T

GFR geometry factor ratio

(g) gaseous state

298 H o enthalpy at 298 K



I detector current in pyrometer

IA ion intensity in counts per second from A(g)

alloy

AI , 2

alloy

AI ion intensities for the monomer and dimer of 

the alloy

o

AI ion intensity of A over pure component

( ) −

eI E current of impacting electrons

( ) +

A II E ion current immediately after ionization and 

before extraction

IPAB ionization potential of gaseous molecule AB

JA flux of A (mole/unit time-unit area)

E

A J flux JA related to A’s equilibrium vapor pressure in a closed container

J

T incident flux on a surface

1J reference junction

2J measuring junction

J1 to J7 focusing plates in ionizer

j(θ) flux of molecules leaving an orifice at angle θ

jA flux of A effusion from the effusion cell 

(mole/unit time-unit area)

K constant for relating multiplier gain to mass 

number

Kn Knudsen number

Keq equilibrium constant

KT isotopic abundance

k constant relating ion flux to pressure

k' constant relating ion intensity and temperature 

to pressure

Lλ(T90) radiance of blackbody at wavelength λ and 

absolute temperature (T90)

Lλ(T90(X)) radiance of blackbody at wavelength λ and a 

fixed temperature point, where X is a fixed 

point material such as Ag (1234.93 K), 

Au (1337.3 K), or Cu (1357.77 K)

(l) liquid state

le collision path of electrons through the vapor

M mass number

M + ΔM mass number of peak adjacent to peak with 

mass number M

m mass of ion

mix β ∆ G partial molar free energy of mixing

mix β ∆ Hi partial molar heat of mixing
NASA/TP—2010-216795 32

NA moles of A

( ) + N E A total number of ions produced in the ion 

source per unit time

( ) +

An E density of ions of A

nA density of A(g)

P, Q fitting parameters 

pA partial pressure of A over alloy

E

Ap equilibrium partial pressure of A in a closed 

container

o

Ap partial pressure of A over pure component

pe equilibrium pressure inside the Knudsen cell

pm measured vapor pressure

q charge of ion

R gas constant

Res resolution of mass spectrometer

Rm measured count rate

RT true count rate

R value of precision resistor in detector

r radius of orifice

rd radius of deflection

r1 radius of radiating disk

r2 radius of receiving disk

SA sensitivity factor

ds element of surface perpendicular to molecular beam

(s) solid state

T absolute temperature

1J T temperature at reference junction

2J T temperature at measuring junction

Tm average temperature of measurement

Tmp temperature at melting point

T90 absolute temperature (based on ITS−90)

T angular distribution of real orifice relative to 

ideal cosine distribution

t time

V accelerating voltage of ion source

VA voltage for signal from ion current of A

V1 voltage generated at a reference junction

V2 voltage generated at a measuring junction

V volume

vap

i ∆ GB partial molar free energies of vaporization 

from a solution i of A and B

∆vap ( ) H A o heat of vaporization of A

∆vap o HT heat of enthalpy at temperature T

WC Clausing factor

WC(θ') Clausing factor for limited angle from normal 

defined by the field and source apertures

WD Clausing factor for the Knudsen cell

x, y, z coordinates

xA, xB mole fractions of A and B

α Seebeck coefficient

αv vaporization coefficient

αo

v vacuum vaporization coefficient

β solution phase of alloy AB

γ multiplier gain

γA detection coefficient

δ phase of A in the reference state

ε phase of B in the reference state

ε(x,y,z) extraction efficiency of ion source

θ angle to the normal from a surface

λ wavelength

λ

 mean free path

, β μ μo A A relative chemical potentials

dν elementary volume

ρA density of gas in ionizing region

σA(E) ionization cross section

τ dead time

τion transmission efficiency of ion source

dω element of solid angle ω
NASA/TP—2010-216795 33

Appendix B.—SIMION 8 Model of the Ion Source and Analyzer

The ion source in our instrument was provided by the manufacturer (Nuclide/PATCO/MAAS Cross Axis Ionizer) and fitted 

with additional apertures. Figure 13 is a drawing of the ionizer 

“box” with the added apertures; Figure 14 is a drawing of the 

entire ionizer. 

It is useful to have a qualitative image of the shape of the electron and ion beams in this ion source and ion extraction/focusing 

region. This will aid in tuning the ion source and identifying any 

possible problems in ion-beam definition. SIMION Version 8.0 

(Scientific Instrument Services, Inc., Ref. 109) was used to model 

the electrostatic potential surfaces in both the ionizer and ionfocusing region. This important tool allowed a systematic qualitative study of how varying electrode potentials affect, in theory, 

the focusing and deflection of the electron and ions beams. The 

intent was to answer these questions about the ionizer and ionfocusing region:

(1) What ion-source variables affect the path of the electron beam?

(2) What range of deflection is expected (within usual ionsource settings), and will this result in changes to the 

interaction volume?

(3) How does varying each electrode potential in the ionfocusing plates affect the ion beam?

(4) Does the spatial range of ion generation within the 

ion source affect an ion’s transport through the ionfocusing plates?

(5) In theory, what are the best ion-focusing settings?

Modeling involved constructing an array of electrode and nonelectrode points in a three-dimensional space inside the SIMION

8.0 program. The success of such a model is predominately based 

on how accurately its dimensions and potentials match reality. 

Figure 15 shows the model of the ion source and ion accelerator 

with all parts identified. The ion accelerator is operated at 

10 000 V. The actual electronic circuit allows the range of 

voltages in Table III:

TABLE III.—RANGE OF POTENTIAL SETTINGS FOR 

ION SOURCE AND ION ACCELERATOR

Electron energya .........................................10 000 + E

Repeller, V ..................................... 10 000 + (0 to 50)

Trap, V ......................................... 10 000 + (0 to 100)

J1, V ................................................................. 10 000

J2, V .................................................... 9540 to 10 000

J3, V .................................................... 9082 to 10 000

J4, V ....................................................... 6582 to 9400

J4(a-b), V.................................................... 229 to 240

J5 .....................................................................Ground

J6, V ........................................................... 115 to 120

J7, V ........................................................... 115 to 120

Exit slit ............................................................Ground a

E, kinetic energy of electrons.

Figure 13.—Electron impact ionizer with added apertures. 
NASA/TP—2010-216795 34

Figure 14.—Ionizer and ion-extraction and focusing plates.

Figure 15.—SIMION 8.0 model of ionizer and focusing plates.
NASA/TP—2010-216795 35

The potential of J3 is a function of J2. The potential of both 

parts of J4 is also a function of J2 but is independent of J3.

The potentials identified for the split plates, J4(a-b), J6, and J7 

are the sum of both halves.

To answer the first two questions, only the ion source was 

considered and the potentials of the trap, J2, filament, and 

repeller were systematically varied from their typical range for 

a J1 potential of 10 kV. The “electrons” flown in these simulations were arbitrarily assumed to have a constant initial kinetic 

energy of 0.1 eV (due to thermal emission) with a trajectory 

toward the ionization chamber. The starting position spanned 

the width of the W filament (2 mm) where maximum electron 

emission was expected. The variables in order of decreasing 

effect on the electron beam trajectory (for any given electron 

energy) are the repeller voltage, the J2 voltage, and the trap 

voltage. The trap voltage has no apparent effect on the electron trajectory inside the chamber, but as its name suggests, it 

stops reflected electrons from reentering the chamber and 

should be set at a higher voltage (positive relative to J1) than 

the electron energy (negative relative to J1). Typically our trap 

was set to 40 V. The purpose of the repeller is to aid ion 

extraction from the source, but it must be balanced against its 

effect on the electron beam. The repeller voltage (positive 

relative to J1) always has the largest effect in attracting the

electron beam to the repeller plate. This effect decreases with 

increasing electron energy, and typically no major effect is 

observed for repeller voltages less than 2 V. (Typically operation is less than 1 V.) J2 affects the electron beam trajectory 

by leaking the accelerator potential field into the ionization 

chamber through the ion exit slit. This field leakage (negative 

relative to J1) also forces the beam toward the repeller plate.

The expected electron-beam shape for low-energy electrons 

(electron, 4 eV; repeller, 2 V; J2, 9600 V; and trap, 40 V) is 

shown in Figure 16, and a portion of the molecular beam is 

clearly missed by the ionizing electrons. However, this is not a 

great problem because it occurs below 5 eV, which is less than 

the typical ionization potential of the species being examined 

and is below the energy required for emission control of the 

electron gun.

The shape of the electron beam for typical operating conditions (electron, 25 eV; repeller, 1 V; J2, 9600 V; and trap,

40 V) together with the expected position on the molecular 

beam is shown on Figure 17, and little change is observed as 

the electron energy is increased to 70 eV. As shown in this 

figure, the electron beam flux is nonuniform and its width is 

close to that of the molecular beam, highlighting the requirements of a consistent ionization volume and fixed relationship 

between the beams. In addition, a large portion of the electron 

beam is attenuated by the apertures of the ionization chamber,

which agrees with the pattern of deposits (“electron dirt”),

Figure 16.—Undesirable shape of electron flux, where part of 

the molecular beam (red circle) is missed. This is due to a 

very low electron energy. Electron energy, 4 eV; trap, 

10 040 V; repeller, 10 002 V; J2, 9600 V.

Figure 17.—Typical operating conditions where electron beam 

correctly crosses the molecular beam (red circle). Electron 

energy, 25 eV; trap, 10 040 V; repeller, 10 002 V; J2, 

9600 V.
NASA/TP—2010-216795 36

observed on the ion source after operation. Clearly an electron 

gun design with an electrostatic lens system that confines the 

electron beam and allows accurate beam steering (Ref. 110)

would greatly improve the rate of ion production and the 

accuracy of these measurements. Note also that the ion source 

and accelerator should be shielded from all magnetic fields to 

ensure that there is no mass discrimination.

The ion beam must accurately sample the ions produced in 

the source and have the highest possible flux at the detector.

This requires the highest possible ion extraction and the 

formation of a nondivergent beam that has the highest transmission through the fixed ground potential slits at J5 and the 

beam-defining exit slit. To model the ion beam, we considered 

particles with a single atomic charge with a range of atomic 

weights. The ions were created at a range of positions that 

fully spanned the ionization volume and were assumed to have 

no initial kinetic energy. As expected, no variation was 

observed in the shape of the ion beam with atomic weight, 

indicating no mass discrimination. Ions corresponding to Au+

(196.97 amu) were used in Figures 18 to 20, which show 

representative ion-beam shapes.

The repeller voltage and the field induced by J2 are the only 

factors involved in ion extraction. The best ion-beam shape 

occurs with the repeller voltage set to zero. Increasing the 

repeller voltage increases the beam width and results in 

attenuation at the exit slit and J5. The model indicates that the 

repeller should always be set at less than 1 V. The field 

induced by J2 is the most useful force for ion extraction, and 

J2 should always be set at the lowest voltage (9540 V). The 

model also suggests that all produced ions are successfully 

extracted, and therefore the ion beam would accurately 

represent the ionization volume.

The best beam shape appears to be characterized by the 

formation of two focal points, as shown in Figures 19 and 20.

The first in the extraction slit in J1 and the second in the 

region of J2. The relative potentials of J3 and J4 determine the 

final shape of the ion beam. There appears to be two configurations that produce a nondivergent beam: (1) J4 set at its 

lowest (6582 V) and J3 set about 200 V lower than J2 

(~9400 V) and (2) J4 set at the midrange (∼8000 V) and J3 set 

to the minimum (9082 V). J4(a-b) provides the field to steer 

the beam through the aperture in J5. When J5 reaches ground 

potential, the shape of the beam is fixed. Therefore, it is 

important to adjust J4(a-b) before and after other potentials are 

changed to ensure that the beam is always centered on J5.

Following J5, limited steering of the beam is provided by 

changing the potentials of J6(y) and J7(z), which allows the 

beam to be centered on the exit slit. As with J4(a-b), J6 and J7 

should be adjusted before and after any changes are made to 

the repeller, J2, J3, and J4.

Figure 18.—Poor ion-beam shape. A large 

portion of the ions are lost by not passing 

through the ion source exit slit. Repeller, 

10 005 V; J2, 9540 V; J3, 9390 V; J4, 

8500 V.
NASA/TP—2010-216795 37

Figure 19.—Ideal thin, nondivergent ion-beam 

shape. Repeller, 10 000 V; J2, 9560 V; J3, 

9390 V; J4, 6500 V. 

Figure 20.—Ideal thin, nondivergent ion-beam 

shape. Repeller, 10 001 V; J2, 9540 V; J3, 

9090 V; J4, 8000 V.
NASA/TP—2010-216795 38
NASA/TP—2010-216795 39

Appendix C.—Instrument-Control and Data-Acquisition System

There are many approaches to controlling a KEMS instrument and acquiring data (Refs. 111 to 114). Our instrumentcontrol and data-acquisition system for KEMS was written in 

Delphi (Ref. 115) by Judith Auping of the NASA Glenn 

Research Center. Most of the functions connect to the computer via a General Purpose Interface Bus (GPIB), which 

allows a number of devices to be integrated and “daisy 

chained” together. A National Instruments NI–488.2 card is 

used together with a Dell Duo-Core Desktop Computer. The 

following devices are controlled:

(1) Magnet: The magnet current controls the magnetic field 

strength for sorting the mass-to-charge ratio—

GPIB interface.

(2) Electron energy selector: The selector controls the 

energy of ionizing electrons to determine appearance 

potential curves—GPIB interface.

(3) Furnace: The fixed and ramp voltage are set to control the temperature of the Knudsen-cell furnace—

GPIB interface.

(4) Ion counter: The output of the ion counter is monitored 

with the magnetic field strength to measure ion 

intensity—GPIB interface.

(5) Pyrometer: The output of the nano-ammeter attached 

to the pyrometer is read, and the temperature is 

calculated—GPIB interface. 

(6) Thermocouple: The thermocouple connected to the 

Agilent 34970A data acquisition/switch unit with the 

GPIB interface is read. 

(7) Stepper motors: The stepper motors on the x-y table are 

controlled to support the Knudsen-cell furnace and 

molecular beam shutter. These move the furnace and 

cells so that the molecular beam is sampled from different effusion cells. Thus, the shutter allows analysis of 

the molecular beam source. The controllers for these 

motors are “daisy chained” together via an RS485 

interface.

(8) Electrometer: A data translation DT–333 16-bit analogto-digital interface card gives the option to read the 

large dynamic range of the electrometer.

Initial parameters are read from the HTMS.ini file, shown 

in Figure 21. This gives the parameters for calibrating the 

magnetic field. We will follow the manual for the firstgeneration data system, which was supplied with the instrument (Ref. 114). The magnetic field may be scanned as either 

the mass number, field strength, or digital-to-analog controller 

(DAC) number. A DAC number of 65 535 corresponds to 

10 V to the magnet regulator, which is the maximum field 

strength. As discussed, mass is proportional in theory to the 

square of the magnetic field. A two-term equation is used:

1 2 ( )

1 2

field c c DAC

mass d exp(d ln(DAC))

= +

=

 

 

(C1)

The constants ci  and di

 are determined via experiments 

with known mass and field numbers.

Figure 21.—HTMS.ini file showing calibration values for the magnet, furnace, and pyrometer.
NASA/TP—2010-216795 40

A similar polynomial is used for the calibration of the 

heater. Here temperature is related to voltage via a simple 

cubic equation:

2 3 Va T T T =+ + + o aa a 12 3   (C2)

The constants are determined and continuously checked using 

the relationship between furnace voltage setting, measured 

current, and the temperature measured with a pyrometer. Small 

changes in the resistance in any connections in the furnace power 

system can have a significant effect on the voltage/temperature 

relationship, and this must be checked routinely.

The temperature from the pyrometer is calibrated via the 

following polynomial:

2 3

12 3

1 o a ln a ln a ln II I

a

T ee e

  

=+ + +      

    (C3)

Here the calibration constants ai  are supplied by the pyrometer manufacturer (Mikron Instruments) from a factory calibration, and e is the effective emissivity. There is an option for 

selecting either the first two terms or the full cubic. The

parameter I

 is the detector current in nanoamperes from the 

pyrometer photomultiplier tube. The value of e is determined 

by a temperature calibration, where the measured detector 

current at a fixed reference temperature is used to determine 

the effective emissivity. This effective emissivity is a combination of the emissivity of the blackbody source and the 

transmissivity of the vacuum chamber window. The transmissivity of the window can change from experiment to experiment because of condensation. This procedure is discussed in 

more detail in the main portion of this report.

The main control screen is shown in Figure 22. This shows 

each of the functions that are controlled by the computer—the 

magnet, the electron energy, the ion counter, the heater, and 

the stage position. This also displays the individual peaks as 

they are being scanned. Typically a peak is scanned as a first 

step in a measurement. Then the magnetic field might be 

moved to the center of the peak for cell-position scanning or 

ionization efficiency curve (electron energy) scanning. For 

determining the temperature dependence of ion intensity, the 

peak might be scanned and the peak height and temperature 

recorded. The flexibility of the Windows operating system 

allows these values to be easily copied to the clipboard and 

transferred to a plotting program.

Figure 22.—Main control screen.
NASA/TP—2010-216795 41

The program is written to be as flexible as possible. Nearly 

all measurements are performed by holding some parameters 

fixed and scanning another. The screen for scanning is shown 

in Figure 23, and examples are given in Table IV.

Initially there was an option to scan the shutter position, but 

the cell position movement encompasses this functionality. As

TABLE IV.—FIXED AND SCANNED PARAMETERS

Hold Scan

Temperature, electron energy, cell position Mass number

Temperature, mass number, cell position Electron energy

Mass number, cell position, electron energy Temperature

Temperature, mass number, electron energy Cell position

discussed in the body of this report, cell position is particularly 

important. Figure 24 is the screen for scanning cell position.

This controls the stepper motors on the multiple cell flange.

Signals are peaked in both the x and y directions. This should 

correspond to the view of the cell orifice with the video 

camera. These positions for maximum signal correspond to the 

proper position of each cell and are recorded as the location 

for each cell.

The program has a built-in plotting routine for the peak intensity versus mass to charge ratio, peak intensity versus electron 

energy, and peak intensity versus cell position. For a standard 

ln(IT) versus 1/T plot, measured ion intensities and temperatures 

can be “cut” from the program and “pasted” directly into various 

plotting programs for final data presentation.

Figure 23.—Scan screen.
NASA/TP—2010-216795 42

Figure 24.—Screen showing x-y table position. 
NASA/TP—2010-216795 43

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Measuring Thermodynamic Properties of Metals and Alloys With Knudsen Effusion Mass 

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13. SUPPLEMENTARY NOTES

The main part of this document will also appear in “Applied Mass Spectroscopy Handbook,” ed. M. Lee, Wiley, 2010, in press, as the 

chapter “Measuring Thermodynamic Properties of Metals and Alloys.” 

14. ABSTRACT

This report reviews Knudsen effusion mass spectrometry (KEMS) as it relates to thermodynamic measurements of metals and alloys. First, 

general aspects are reviewed, with emphasis on the Knudsen-cell vapor source and molecular beam formation, and mass spectrometry issues 

germane to this type of instrument are discussed briefly. The relationship between the vapor pressure inside the effusion cell and the 

measured ion intensity is the key to KEMS and is derived in detail. Then common methods used to determine thermodynamic quantities 

with KEMS are discussed. Enthalpies of vaporization ΔvapHo

T--the fundamental measurement--are determined from the variation of relative 

partial pressure with temperature using the second-law method or by calculating a free energy of formation and subtracting the entropy 

contribution using the third-law method. For single-cell KEMS instruments, ΔvapHo

T measurements can be used to determine the partial 

Gibbs free energy if the sensitivity factor remains constant over multiple experiments. The ion-current ratio method and dimer-monomer 

method are also viable in some systems. For a multiple-cell KEMS instrument, ΔvapHo

T and activities are obtained by direct comparison 

with a suitable component reference state or a secondary standard. Internal checks for correct instrument operation and general procedural 

guidelines also are discussed. Finally, general comments are made about future directions in measuring alloy thermodynamics with KEMS.

15. SUBJECT TERMS

Metals; Alloys; Thermodynamics; Mass spectroscopy 

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