partial molar quantities of components can be combined to determine integral molar quantities. These can be compared to integral quantities measured using other techniques (e.g., calorimetry). The most reliable thermodynamic data are verified via several methods as well as theoretical calculations. For example, the Ti-Al system has been studied using KEMS, and the derived integral molar enthalpy compares favorably to calorimetry measurements.¹⁵⁴,¹⁵⁵ Similar favorable comparisons between KEMS and calorimetry measurements have been reported for some rare-earth oxide-silica systems.¹⁴,¹⁵⁶

### 3.2.1 | Thermochemistry of solutions: Direct measurements of thermodynamic activity of components

From Equation (42), it follows that the most direct measurement of the component activity is simply to compare the vapor pressure of a component over the alloy to the vapor pressure of the pure component:

$$a_A = \frac{p_A}{p_A^0} = \frac{l_A T S_A C_I}{l_A^0 T S_A^0 C_{II}^0} = \frac{l_A}{l_A^0} \text{GFR} \quad (48)$$

The terms $a_A$, $l_A$, and $T$ have been described previously. GFR is the geometry factor ratio from the geometry factors of the two cells, $c_I$ and $c_{II}$. Although the two cells are machined to the same dimensions, there are still microscopic orifice differences; these are accounted in the GFR. The GFR is determined by comparing ion intensity measurements in the mass spectra of the vapor for an identical substance held in each cell and should be 0.98 or better. The key parameter determining the effectiveness of the direct comparison method is the ratio of the machine constants, $\frac{S_A}{S_A^0}$. Ideally this should be constant across multiple measurements. In reality, the machine constant will change when the sample is changed due to such factors as the size and location of the ionization volume, the position of the molecular beam in the region that is sampled by the mass spectrometer, and the exact position of and heat distribution at the orifice of the Knudsen cell. Note that there is a possible surface contribution to the flux from surface diffusion through the orifice. This would depend on the alloy composition, so that one GFR may not fully correct for surface diffusion across the alloy composition range.

The general problem of varying machine constant from run to run has been circumvented in several ways. The first approach is to design the instrument for stability between runs, which includes rigidly fixing cell position for a fixed ionization volume.¹⁵⁷ A special valve between the chamber with Knudsen cell furnace⁷,⁷² also leads to enhanced stability. This has been described in Section 2.1.4. However, note that a unity value for the ratio $\frac{S_A}{S_A^0}$ cannot be strictly assumed because the ionization volume is defined by the entire device and not cell positioning alone.

Another method to limit the issue of variation in the machine constants is to use a multiple-cell system, as discussed in Section

2.1.4. A multiple-cell system involves two or more cells in a constant temperature holder within the furnace. The cells are translated to/ from the mass spectrometer sampling region via controls external to the vacuum system. The physical form of a multiple-cell system was discussed in the first part (Figure 5) of this review. Such systems have the advantage of an in situ temperature calibration and vapor pressure calibrant/standard state. The component activity is the ratio of the ion intensities, as given in Equation (48) with a GFR correction near unity. When using a restricted collimation device associated with a multiple cell, the only parameter that can lead to a different pressure reading is a different temperature. This should be minimal in a properly designed isothermal heating block.¹⁵⁸

Often, it is not possible to have the exact reference state present in an adjacent cell. An example of this is pure aluminum, which has a vapor pressure too high at the temperature necessary to study some aluminum-containing alloys. In this case, a similar metal, such as gold, would be used. Equation (48) becomes

$$a_A = \left[ \frac{p_A}{p_{Au}^0} \right]_T \left[ \frac{p_{Au}^0}{p_A^0} \right]_T = \left[ \frac{l_A}{l_A^0} \right]_T \left[ \frac{\sigma_{Au}}{\sigma_A} \right] \frac{C_I}{C_{II}^0} \left[ \frac{p_{Au}^0}{p_A^0} \right]_T \quad (49)$$

The subscript $T$ indicates that both quantities in the brackets are determined at the same temperature. In this approach, the ratio of the vapor pressure of gold to the vapor pressure of the pure component is determined from the appropriate data tables.¹⁴⁰,¹⁴¹,¹⁵⁹,¹⁶⁰ In a mass spectrometer free from mass discrimination effects in the ionizer, ion sorter, and detector, the only instrument sensitivity changes are due to the ionization cross sections, which can also be taken from tabulations and corrected for the particular electron energy used.⁸⁷,⁹¹

A third method of circumventing the problem of varying machine constants is to combine a KEMS instrument with another type of technique, for example, target collection or thermogravimetric analysis.¹⁶¹ In this case, the in situ weight loss measurement gives an independent calibration method. In situ calibration by target collection of part of the molecular beam in the mass spectrometer has been used by Drowart et al.¹⁶² for U-O, U-C, and U-N studies. Calibration via target collection or thermogravimetric measurement needs to correct for the effects of surface diffusion and vaporization from surfaces other than the effusion orifice.

### 3.2.2 | Thermodynamics of solutions: Ion current ratio method in mass spectra of a vapor over an alloy

There are several methods that circumvent this problem of nonreproducible calibration constants using a single cell. The ion current ratio technique was developed by Lyubimov,¹⁶³ Neckel and Wagner,¹⁶⁴ and Belton and Fruehan.¹⁶⁵,¹⁶⁶ Belton and Fruehan¹⁶⁶ have extended the method from binary to ternary alloys; Korobov et al.¹⁶⁷ extended the method to include intermediate line compounds. The method is based on the Gibbs-Duhem relationship. Consider a system of $n$ components:
partial molar quantities of components can be combined to determine integral molar quantities. These can be compared to integral quantities measured using other techniques (e.g., calorimetry). The most reliable thermodynamic data are verified via several methods as well as theoretical calculations. For example, the Ti-Al system has been studied using KEMS, and the derived integral molar enthalpy compares favorably to calorimetry measurements.¹⁵⁴,¹⁵⁵ Similar favorable comparisons between KEMS and calorimetry measurements have been reported for some rare-earth oxide-silica systems.¹⁴,¹⁵⁶

### 3.2.1 | Thermochemistry of solutions: Direct measurements of thermodynamic activity of components

From Equation (42), it follows that the most direct measurement of the component activity is simply to compare the vapor pressure of a component over the alloy to the vapor pressure of the pure component:

$$a_A = \frac{p_A}{p_A^0} = \frac{l_A TS_A C_I}{l_A^0 TS_A^0 C_{II}^0} = \frac{l_A}{l_A^0} \text{ GFR} \quad (48)$$

The terms $a_A$, $l_A$, and $T$ have been described previously. GFR is the geometry factor ratio from the geometry factors of the two cells, $c_I$ and $c_{II}$. Although the two cells are machined to the same dimensions, there are still microscopic orifice differences; these are accounted in the GFR. The GFR is determined by comparing ion intensity measurements in the mass spectra of the vapor for an identical substance held in each cell and should be 0.98 or better. The key parameter determining the effectiveness of the direct comparison method is the ratio of the machine constants, $\frac{S_A}{S_A^0}$. Ideally this should be constant across multiple measurements. In reality, the machine constant will change when the sample is changed due to such factors as the size and location of the ionization volume, the position of the molecular beam in the region that is sampled by the mass spectrometer, and the exact position of and heat distribution at the orifice of the Knudsen cell. Note that there is a possible surface contribution to the flux from surface diffusion through the orifice. This would depend on the alloy composition, so that one GFR may not fully correct for surface diffusion across the alloy composition range.

The general problem of varying machine constant from run to run has been circumvented in several ways. The first approach is to design the instrument for stability between runs, which includes rigidly fixing cell position for a fixed ionization volume.¹⁵⁷ A special valve between the chamber with Knudsen cell furnace⁷,⁷² also leads to enhanced stability. This has been described in Section 2.1.4. However, note that a unity value for the ratio $\frac{S_A}{S_A^0}$ cannot be strictly assumed because the ionization volume is defined by the entire device and not cell positioning alone.

Another method to limit the issue of variation in the machine constants is to use a multiple-cell system, as discussed in Section

2.1.4. A multiple-cell system involves two or more cells in a constant temperature holder within the furnace. The cells are translated to/ from the mass spectrometer sampling region via controls external to the vacuum system. The physical form of a multiple-cell system was discussed in the first part (Figure 5) of this review. Such systems have the advantage of an in situ temperature calibration and vapor pressure calibrant/standard state. The component activity is the ratio of the ion intensities, as given in Equation (48) with a GFR correction near unity. When using a restricted collimation device associated with a multiple cell, the only parameter that can lead to a different pressure reading is a different temperature. This should be minimal in a properly designed isothermal heating block.¹⁵⁸

Often, it is not possible to have the exact reference state present in an adjacent cell. An example of this is pure aluminum, which has a vapor pressure too high at the temperature necessary to study some aluminum-containing alloys. In this case, a similar metal, such as gold, would be used. Equation (48) becomes

$$a_A = \frac{[p_A]}{[p_{Au}^0]_T} \frac{[p_{Au}^0]}{[p_A^0]_T} = \frac{[l_A]}{[l_A^0]_T} \frac{[\sigma_{Au}]}{[\sigma_A]} \frac{C_I}{C_{II}^0} \frac{[p_{Au}^0]}{[p_A^0]_T} \quad (49)$$

The subscript $T$ indicates that both quantities in the brackets are determined at the same temperature. In this approach, the ratio of the vapor pressure of gold to the vapor pressure of the pure component is determined from the appropriate data tables.¹⁴⁰,¹⁴¹,¹⁵⁹,¹⁶⁰ In a mass spectrometer free from mass discrimination effects in the ionizer, ion sorter, and detector, the only instrument sensitivity changes are due to the ionization cross sections, which can also be taken from tabulations and corrected for the particular electron energy used.⁸⁷,⁹¹

A third method of circumventing the problem of varying machine constants is to combine a KEMS instrument with another type of technique, for example, target collection or thermogravimetric analysis.¹⁶¹ In this case, the in situ weight loss measurement gives an independent calibration method. In situ calibration by target collection of part of the molecular beam in the mass spectrometer has been used by Drowart et al.¹⁶² for U-O, U-C, and U-N studies. Calibration via target collection or thermogravimetric measurement needs to correct for the effects of surface diffusion and vaporization from surfaces other than the effusion orifice.

### 3.2.2 | Thermodynamics of solutions: Ion current ratio method in mass spectra of a vapor over an alloy

There are several methods that circumvent this problem of nonreproducible calibration constants using a single cell. The ion current ratio technique was developed by Lyubimov,¹⁶³ Neckel and Wagner,¹⁶⁴ and Belton and Fruehan.¹⁶⁵,¹⁶⁶ Belton and Fruehan¹⁶⁶ have extended the method from binary to ternary alloys; Korobov et al.¹⁶⁷ extended the method to include intermediate line compounds. The method is based on the Gibbs-Duhem relationship. Consider a system of $n$ components:
<figure><img src="image_33.png" /></figure>

$$0 = \sum_{i=0}^{n} x_i d\bar{G}_i \quad (50)$$

For a two-component system, this becomes

$$\begin{aligned} 0 &= x_1 d\bar{G}_1 + x_2 d\bar{G}_2 = x_1 d\ln a_1 + x_2 d\ln a_2 = x_1 d\ln a_1 + (1 - x_1) d\ln a_2 \\ &= d\ln a_2 + x_1 d\ln \frac{a_1}{a_2} = d\ln a_2 + x_1 d\ln \left( \frac{l_1}{l_2} \right) \end{aligned} \quad (51)$$

Note that the ratio of the component activities in principle cancels the ionization cross section and machine geometrical constant terms. Integrating gives the component activity and activity coefficient of that component:

$$\ln a_2 = - \int_{x_1=1}^{x_1=x_1} x_1 d\ln\left(\frac{l_1}{l_2}\right) \quad (52)$$

This can be converted to the following expression, which can be readily graphically integrated¹⁶⁵:

$$\ln \gamma_1 = - \int_{x_1=1}^{x_1=x_1} x_1 d \left[ \ln \left( \frac{l_1}{l_2} \right) - \ln \left( \frac{x_1}{x_2} \right) \right] \quad (53)$$

Analogous to Equation (43), the partial molar enthalpy of component 1 can be derived as

$$\Delta_{\text{mix}} \bar{H}_{1}^{\beta} = -R \int_{x_1=1}^{x_1=x_1} x_1 d \left[ \frac{\ln\left(\frac{l_1}{l_2}\right)}{d\left(\frac{1}{l}\right)} \right] \quad (54)$$

This method involves the preparation of a series of alloys across a composition range and then measurement of ion current ratios in the mass spectra of a vapor over an alloy as a function of temperature for each alloy. It has proven to be an accurate method, and many systems have been reported in the literature.

As noted earlier, these equations can be extended to ternary systems as well.¹⁶⁶,¹⁶⁸ The Gibbs-Duhem relation leads to two graphical integrations with expressions similar to Equation (53) for components 1 and 2, 2 and 3, and 1 and 3. Integrations are along lines of constant molar ratio of components.

### 3.2.3 | Thermodynamics of solutions: Dimer-monomer vapor species ratio method

Another single-cell method that circumvents the problem of nonconstant machine constants is the dimer-monomer vapor species ratio method. Berkowitz and Chupka¹⁶⁹ developed this method for salt mixtures; however, it applies to metallic alloys and oxide systems

as well. Many materials have a monomer-dimer equilibrium in the gaseous phase:

$$A_2(g) = 2A(g) \quad (55)$$

$$K_p = \left( \frac{P_A^2}{P_{A_2}} \right) = P_A \left( \frac{P_A}{P_{A_2}} \right) \quad (56)$$

This equilibrium can be measured for both the pure component A and an alloy containing A. The gas phase equilibrium (Equation 55) must, of course, have the same equilibrium constant for both pure A and an alloy containing A at the same temperature. The activity of component A in an alloy containing A becomes

$$a(A) = \frac{P_A^{\text{alloy}}}{P_A^0} = \frac{\left(\frac{P_A}{P_{A_2}}\right)^0}{\left(\frac{P_A}{P_{A_2}}\right)^{\text{alloy}}} = \frac{\left(\frac{l_A}{l_{A_2}}\right)^0}{\left(\frac{l_A}{l_{A_2}}\right)^{\text{alloy}}} \quad (57)$$

Note that the ionization cross sections of the vapor species and the geometrical constants all cancel, so that only the ratios of ion intensities from the mass spectra of the vapor over the alloy and pure compound are needed.

### 3.2.4 | Alloy thermodynamics via KEMS: General considerations

Many considerations must be taken into account for reliable component activity measurements of alloys. In principle, if the component under study generates a vapor pressure within the KEMS measurement range, a component activity can be measured. KEMS also has the unique advantage of permitting multiple component activities to be measured simultaneously.

Complications arise from component loss through the cell orifice. This, of course, is a bigger issue when considering narrow phase widths and line compounds. Weight, composition, and XRD measurements should be conducted before and after every run to verify that all measurements are taken in the same phase region. In this case isothermal runs are conducted, and the instantaneous composition is determined by integration of the products $I_i^+ \sqrt{t} dt$ associated with the mass loss of the sample. Pattoret et al.¹⁷⁰ have conducted such a study for the nonstoichiometric domain of $UO_{2 \pm x}$. Note the evolution of the gaseous phase yield information on the variance of the system and consequently the number of phases throughout the mass spectrometric analysis.¹⁷¹

Experiments can be modified to utilize the component activity changes with composition in the system under study. A proposed instrument with an integral hot-stage XRD system to monitor phase changes would help with this. There would obviously be many complexities in such a system, but it would also offer the advantage of monitoring vapor pressures with simultaneous identification of the phases.
$$0 = \sum_{i=0}^{n} x_i d\bar{G}_i \qquad (50)$$

For a two-component system, this becomes

$$ 
\begin{aligned}
0 = x_1 d\bar{G}_1 + x_2 d\bar{G}_2 &= x_1 d \ln a_1 + x_2 d \ln a_2 = x_1 d \ln a_1 + (1 - x_1) d \ln a_2 \\
&= d \ln a_2 + x_1 d \ln \frac{a_1}{a_2} = d \ln a_2 + x_1 d \ln \left( \frac{l_1}{l_2} \right)
\end{aligned}
\qquad (51) $$

Note that the ratio of the component activities in principle cancels the ionization cross section and machine geometrical constant terms. Integrating gives the component activity and activity coefficient of that component:

$$ \ln a_2 = - \int_{x_1=1}^{x_1=x_1} x_1 d \ln \left( \frac{l_1}{l_2} \right) \qquad (52) $$

This can be converted to the following expression, which can be readily graphically integrated¹⁶⁵:

$$ \ln \gamma_1 = - \int_{x_1=1}^{x_1=x_1} x_1 d \left[ \ln \left( \frac{l_1}{l_2} \right) - \ln \left( \frac{x_1}{x_2} \right) \right] \qquad (53) $$

Analogous to Equation (43), the partial molar enthalpy of component 1 can be derived as

$$ \Delta_{\text{mix}} \bar{H}_{1}^{\beta} = -R \int_{x_1=1}^{x_1=x_1} x_1 d \left[ \frac{\ln\left(\frac{l_1}{l_2}\right)}{d\left(\frac{1}{l}\right)} \right] \qquad (54) $$

This method involves the preparation of a series of alloys across a composition range and then measurement of ion current ratios in the mass spectra of a vapor over an alloy as a function of temperature for each alloy. It has proven to be an accurate method, and many systems have been reported in the literature.

As noted earlier, these equations can be extended to ternary systems as well.¹⁶⁶,¹⁶⁸ The Gibbs-Duhem relation leads to two graphical integrations with expressions similar to Equation (53) for components 1 and 2, 2 and 3, and 1 and 3. Integrations are along lines of constant molar ratio of components.

### 3.2.3 | Thermodynamics of solutions: Dimer-monomer vapor species ratio method

Another single-cell method that circumvents the problem of nonconstant machine constants is the dimer-monomer vapor species ratio method. Berkowitz and Chupka¹⁶⁹ developed this method for salt mixtures; however, it applies to metallic alloys and oxide systems

as well. Many materials have a monomer-dimer equilibrium in the gaseous phase:

$$ A_2(g) = 2A(g) \qquad (55) $$

$$ K_p = \left( \frac{P_A^2}{P_{A_2}} \right) = P_A \left( \frac{P_A}{P_{A_2}} \right) \qquad (56) $$

This equilibrium can be measured for both the pure component A and an alloy containing A. The gas phase equilibrium (Equation 55) must, of course, have the same equilibrium constant for both pure A and an alloy containing A at the same temperature. The activity of component A in an alloy containing A becomes

$$ a(A) = \frac{P_A^{\text{alloy}}}{P_A^0} = \frac{\left(\frac{P_A}{P_{A_2}}\right)^0}{\left(\frac{P_A}{P_{A_2}}\right)^{\text{alloy}}} = \frac{\left(\frac{l_A}{l_{A_2}}\right)^0}{\left(\frac{l_A}{l_{A_2}}\right)^{\text{alloy}}} \qquad (57) $$

Note that the ionization cross sections of the vapor species and the geometrical constants all cancel, so that only the ratios of ion intensities from the mass spectra of the vapor over the alloy and pure compound are needed.

### 3.2.4 | Alloy thermodynamics via KEMS: General considerations

Many considerations must be taken into account for reliable component activity measurements of alloys. In principle, if the component under study generates a vapor pressure within the KEMS measurement range, a component activity can be measured. KEMS also has the unique advantage of permitting multiple component activities to be measured simultaneously.

Complications arise from component loss through the cell orifice. This, of course, is a bigger issue when considering narrow phase widths and line compounds. Weight, composition, and XRD measurements should be conducted before and after every run to verify that all measurements are taken in the same phase region. In this case isothermal runs are conducted, and the instantaneous composition is determined by integration of the products $I_i^+ \sqrt{\bar{T}} dt$ associated with the mass loss of the sample. Pattoret et al.¹⁷⁰ have conducted such a study for the nonstoichiometric domain of $UO_{2 \pm x}$. Note the evolution of the gaseous phase yield information on the variance of the system and consequently the number of phases throughout the mass spectrometric analysis.¹⁷¹

Experiments can be modified to utilize the component activity changes with composition in the system under study. A proposed instrument with an integral hot-stage XRD system to monitor phase changes would help with this. There would obviously be many complexities in such a system, but it would also offer the advantage of monitoring vapor pressures with simultaneous identification of the phases.
Howard¹⁷² and Oktay¹⁷³ have developed a “valved Knudsen cell mass spectrometer.” This instrument allows alloying elements to be added to the Knudsen cell and the component activities in the resulting liquid alloy to be measured as a function of composition. This is similar to the phase changes observed by Drowart et al.¹⁷¹ over long times.

It is possible to leverage the phase rule to create a univariant system, which is easy to study. The phase rule is generally written as

$$f = c + 2 - p \qquad (58a)$$

Here, f is the degrees of freedom, c is the number components, “2” comes from the fixed pressure and temperature, and p is the number of phases, which is typically two for the solid and vapor. In a KEMS experiment the temperature is fixed, so Equation (58a) for a single phase becomes

$$f = c + 1 - p \qquad (58b)$$

Thus, a simple unary system (c = 1, p = 2) has all degrees of freedom set with a constant temperature. For a binary system, all degrees of freedom are set with two solid phases (or solid + liquid) and the vapor phase (p = 3):

$$f = 2 + 1 - 3 = 0 \qquad (58c)$$

This method has been used in the ceramic systems Y₂O₃-SiO₂¹⁴ and Yb₂O₃-SiO₂.¹⁵⁶ In these cases, there are two distinct solid phases and a gas phase. For a solid solution p = 2 and f = 1. The degrees of freedom can be reduced to zero if there is an additional relationship that links the solid and gas compositions. This is the case if a pseudo-congruent relationship fixes the pressure of each gaseous species. This relationship is known as the “effusion flow composition,” which must be the same in the pseudo-binary section as in the condensed phase.¹⁷⁴ For ternary systems, all degrees of freedom are set with three solid phases and a vapor phase (p = 4):

$$f = 3 + 1 - 4 = 0 \qquad (58d)$$

A Ni-Al-O ternary study led to highly reliable data¹⁷⁵ as a function of temperature, as long as the system remained univariant.

A wide range of metallic alloys have been studied using KEMS. For the aforementioned reasons, most of these are binary alloys, although some are ternary alloys. The techniques discussed previously have all been used to generate this range of data. The studies on nickel alloys have important applications to superalloys. Today's complex CALPHAD (calculation of phase diagrams) nickel alloy databases are built on robust assessments of the binary and ternary systems.¹⁷⁶ The Ni-Al system is interesting from both a practical point of view and a basic science point of view. The β-NiAl phase exhibits dramatic changes in activities of Ni and Al over a narrow composition range¹⁷⁷⁻¹⁸⁰ (Figure 17), and the γ' Ni₃Al phase is the basis for superalloys. Recent measurements of component activities

for complex alloys have been reported.¹⁸¹,¹⁸² These are very useful as long as the phase of the measured alloy is known.

Other aluminide binaries acting as the basis for currently developed or potentially useful alloys are Ti-Al, Fe-Al, and Nb-Al. Oxygen solubility is a big issue with Ti and its alloys. Copland et al.¹⁸³ have examined Ti-Al-O alloys to study the effect of oxygen concentration on the activity of Ti and Al (see Figure 18). These results provide inferences about the structure.¹⁸³

### 3.2.5 | Oxide systems: Compounds and solutions

Oxide compounds and solutions are important in a variety of metallurgical (e.g., slags in steel making), processing (e.g., glasses), and geological (e.g., magmas) applications.

KEMS can be used to obtain a component activity in an oxide mixture. Activities of components in the system under consideration are measured using methods like those discussed for alloys. For an oxide component that vaporizes congruently with the same vapor molecule as the compound, the component activity is simply the ratio of the vapor pressure of the vapor species above the solution to that above the pure oxide. For a decomposing oxide, the component activity can be determined from the equivalency of the equilibrium constants. In a multiple-cell experiment,¹⁸⁴ consider alumina, Al₂O₃, which decomposes primarily to Al(g) and O(g) at high temperatures:

$$\text{Al}_2\text{O}_3(\text{pure}) = 2\text{Al(g)} + 3\text{O(g)} \qquad K_p(T) = \frac{P_{\text{Al}}^2(\text{pure}) P_{\text{O}}^2(\text{soln})}{1} \qquad (59a)$$

$$\text{Al}_2\text{O}_3(\text{soln}) = 2\text{Al(g)} + 3\text{O(g)} \qquad K_p(T) = \frac{P_{\text{Al}}^2(\text{soln}) P_{\text{O}}^3(\text{soln})}{a(\text{Al}_2\text{O}_3)} \qquad (59b)$$

$$a(\text{Al}_2\text{O}_3) = \frac{P_{\text{Al}}^2(\text{soln}) P_{\text{O}}^3(\text{soln})}{P_{\text{Al}}^2(\text{pure}) P_{\text{O}}^3(\text{pure})} = \frac{I_{\text{Al}}^2(\text{soln}) I_{\text{O}}^3(\text{soln})}{I_{\text{Al}}^2(\text{pure}) I_{\text{O}}^3(\text{pure})} \qquad (59c)$$

Here, Kₚ(T) is the equilibrium constant for both reactions, which are equal at constant temperature; Pᵢ(pure) is the partial pressure of the species i over pure Al₂O₃; Pᵢ(soln) is the partial pressure of the species i over Al₂O₃ in solution; Iᵢ(pure) is the ion intensity of the species i over pure Al₂O₃; Iᵢ(soln) is the ion intensity of the species i over Al₂O₃ in solution; and (Al₂O₃) is the activity of Al₂O₃. In these equations, instrument sensitivities to the different species have been omitted as they are equal in the multiple-cell instrument. Note that, as with metallic alloys, component activities can be measured in complex, multicomponent oxide systems and glasses and that a convenient reference state must be selected.

Following the publication of the monograph by Stolyarova and Semenov,⁵ a number of reviews dealing with the vaporization and thermodynamic properties of oxide systems studied using KEMS at high temperatures have been completed.¹⁸⁵⁻²⁰² The general overview in this area was presented in the series of publications from decade to decade to
Howard¹⁷² and Oktay¹⁷³ have developed a “valved Knudsen cell mass spectrometer.” This instrument allows alloying elements to be added to the Knudsen cell and the component activities in the resulting liquid alloy to be measured as a function of composition. This is similar to the phase changes observed by Drowart et al.¹⁷¹ over long times.

It is possible to leverage the phase rule to create a univariant system, which is easy to study. The phase rule is generally written as

$$f = c + 2 - p \qquad (58a)$$

Here, f is the degrees of freedom, c is the number components, “2” comes from the fixed pressure and temperature, and p is the number of phases, which is typically two for the solid and vapor. In a KEMS experiment the temperature is fixed, so Equation (58a) for a single phase becomes

$$f = c + 1 - p \qquad (58b)$$

Thus, a simple unary system ($c = 1, p = 2$) has all degrees of freedom set with a constant temperature. For a binary system, all degrees of freedom are set with two solid phases (or solid + liquid) and the vapor phase ($p = 3$):

$$f = 2 + 1 - 3 = 0 \qquad (58c)$$

This method has been used in the ceramic systems Y₂O₃-SiO₂¹⁴ and Yb₂O₃-SiO₂.¹⁵⁶ In these cases, there are two distinct solid phases and a gas phase. For a solid solution $p = 2$ and $f = 1$. The degrees of freedom can be reduced to zero if there is an additional relationship that links the solid and gas compositions. This is the case if a pseudo-congruent relationship fixes the pressure of each gaseous species. This relationship is known as the “effusion flow composition,” which must be the same in the pseudo-binary section as in the condensed phase.¹⁷⁴ For ternary systems, all degrees of freedom are set with three solid phases and a vapor phase ($p = 4$):

$$f = 3 + 1 - 4 = 0 \qquad (58d)$$

A Ni-Al-O ternary study led to highly reliable data¹⁷⁵ as a function of temperature, as long as the system remained univariant.

A wide range of metallic alloys have been studied using KEMS. For the aforementioned reasons, most of these are binary alloys, although some are ternary alloys. The techniques discussed previously have all been used to generate this range of data. The studies on nickel alloys have important applications to superalloys. Today's complex CALPHAD (calculation of phase diagrams) nickel alloy databases are built on robust assessments of the binary and ternary systems.¹⁷⁶ The Ni-Al system is interesting from both a practical point of view and a basic science point of view. The β-NiAl phase exhibits dramatic changes in activities of Ni and Al over a narrow composition range¹⁷⁷⁻¹⁸⁰ (Figure 17), and the γ' Ni₃Al phase is the basis for superalloys. Recent measurements of component activities

for complex alloys have been reported.¹⁸¹,¹⁸² These are very useful as long as the phase of the measured alloy is known.

Other aluminide binaries acting as the basis for currently developed or potentially useful alloys are Ti-Al, Fe-Al, and Nb-Al. Oxygen solubility is a big issue with Ti and its alloys. Copland et al.¹⁸³ have examined Ti-Al-O alloys to study the effect of oxygen concentration on the activity of Ti and Al (see Figure 18). These results provide inferences about the structure.¹⁸³

### 3.2.5 | Oxide systems: Compounds and solutions

Oxide compounds and solutions are important in a variety of metallurgical (e.g., slags in steel making), processing (e.g., glasses), and geological (e.g., magmas) applications.

KEMS can be used to obtain a component activity in an oxide mixture. Activities of components in the system under consideration are measured using methods like those discussed for alloys. For an oxide component that vaporizes congruently with the same vapor molecule as the compound, the component activity is simply the ratio of the vapor pressure of the vapor species above the solution to that above the pure oxide. For a decomposing oxide, the component activity can be determined from the equivalency of the equilibrium constants. In a multiple-cell experiment,¹⁸⁴ consider alumina, Al₂O₃, which decomposes primarily to Al(g) and O(g) at high temperatures:

$$\text{Al}_2\text{O}_3(\text{pure}) = 2\text{Al(g)} + 3\text{O(g)} \qquad K_p(T) = \frac{P_{\text{Al}}^2(\text{pure}) P_{\text{O}}^2(\text{soln})}{1} \qquad (59a)$$

$$\text{Al}_2\text{O}_3(\text{soln}) = 2\text{Al(g)} + 3\text{O(g)} \qquad K_p(T) = \frac{P_{\text{Al}}^2(\text{soln}) P_{\text{O}}^3(\text{soln})}{a(\text{Al}_2\text{O}_3)} \qquad (59b)$$

$$a(\text{Al}_2\text{O}_3) = \frac{P_{\text{Al}}^2(\text{soln}) P_{\text{O}}^3(\text{soln})}{P_{\text{Al}}^2(\text{pure}) P_{\text{O}}^3(\text{pure})} = \frac{I_{\text{Al}}^2(\text{soln}) I_{\text{O}}^3(\text{soln})}{I_{\text{Al}}^2(\text{pure}) I_{\text{O}}^3(\text{pure})} \qquad (59c)$$

Here, $K_p(T)$ is the equilibrium constant for both reactions, which are equal at constant temperature; $P_i(\text{pure})$ is the partial pressure of the species i over pure Al₂O₃; $P_i(\text{soln})$ is the partial pressure of the species i over Al₂O₃ in solution; $I_i(\text{pure})$ is the ion intensity of the species i over pure Al₂O₃; $I_i(\text{soln})$ is the ion intensity of the species i over Al₂O₃ in solution; and (Al₂O₃) is the activity of Al₂O₃. In these equations, instrument sensitivities to the different species have been omitted as they are equal in the multiple-cell instrument. Note that, as with metallic alloys, component activities can be measured in complex, multicomponent oxide systems and glasses and that a convenient reference state must be selected.

Following the publication of the monograph by Stolyarova and Semenov,⁵ a number of reviews dealing with the vaporization and thermodynamic properties of oxide systems studied using KEMS at high temperatures have been completed.¹⁸⁵⁻²⁰² The general overview in this area was presented in the series of publications from decade to decade to
<figure><img src="image_34.png" /></figure>

<figure><img src="image_35.png" /><figcaption>**FIGURE 17** Activity as a function of composition for β-NiAl. Source: Reprinted from Bencze et al.¹⁷⁷ with permission from Springer Nature.</figcaption></figure>

decade.¹⁸⁵⁻¹⁹⁰ We can delineate them into three main groups: glass-forming oxide systems,¹⁹¹⁻¹⁹⁶ ultrahigh-refractory oxide systems mainly based on HfO₂.¹⁹⁷⁻¹⁹⁹ modeling approaches developed using the Knudsen effusion mass spectrometric thermodynamic data on oxide systems for the prediction of their high-temperature behavior,¹⁸⁹,¹⁹³⁻¹⁹⁶,²⁰⁰,²⁰¹ and comparison to thermodynamic data that may be obtained at high temperatures using KEMS and differential thermal analysis.²⁰² During the period indicated from 1994, systematic studies on the thermodynamic properties of the gaseous oxide salts or associates were successfully continued as the development of a scientific school founded by G. A. Semenov. Reviews by Lopatin and Shugurov²⁰³⁻²⁰⁹ illustrate the recent achievements in studies on thermodynamic properties and the identification of the variety of the gaseous associates in high-temperature vapor using KEMS.²⁰³⁻²⁰⁹

It should be mentioned that, although not included in the reviews discussed earlier, recent experimental data obtained using KEMS at high temperatures on oxide systems and materials for nuclear applications such as the UO₂-ZrO₂,⁶⁷,²¹⁰ Cs₂O-B₂O₃,²¹¹ Cs₂O-MoO₃,²¹² and SrO-Al₂O₃²¹³,²¹⁴ systems are available. Recent KEMS data on ceramics and glass ceramics with the special unique physicochemical properties such as the ZnO-Nb₂O₅,²¹⁵ TiO₂-Al₂O₃-SiO₂,²¹⁶,²¹⁷ and Al₂O₃-SiO₂-ZrO₂ systems²¹⁸ as well as ultrahigh refractory ceramics based on the binary and multicomponent systems containing rare-earth and hafnium oxides²¹⁹⁻²²¹ have also been

reported. It is necessary to emphasize that the thermodynamic properties obtained in all these systems were discussed within the framework of semiempirical and statistical thermodynamic approaches for modeling and prediction of thermodynamic properties of multicomponent systems based on the corresponding data on binary systems. Additionally, phase diagrams for the ZnO-Nb₂O₅²¹⁵ and the Al₂O₃-SiO₂-ZrO₂ systems²¹⁸,²²² were optimized and calculated. Examples of component isoactivity curves and Gibbs energy of formation in the Al₂O₃-SiO₂-ZrO₂ system are shown in Figure 19A-D based on experimental data and modeling provided in Stolyarova et al.²¹⁸

We next focus on the latest experimental data on the vaporization and thermodynamic properties of binary and multicomponent systems containing rare-earth and hafnium oxides.¹⁹⁷⁻¹⁹⁹,²¹⁹⁻²²⁵ In recent years, the composition of vapor, the temperature dependences of partial pressures of the vapor species, and the thermodynamic properties of vaporization of the following individual pure rare-earth oxides have been studied: Y₂O₃, La₂O₃, CeO₂, Nd₂O₃, Sm₂O₃, Gd₂O₃, Yb₂O₃, and Lu₂O₃. The study of the high-temperature behavior of Sm₂O₃ deserves special mention, as data on the composition and partial pressures of vapor species over Sm₂O₃ in a wide temperature range have not been previously published in the literature. When comparing the excess Gibbs energies at 2373 K in the La₂O₃-HfO₂, Nd₂O₃-HfO₂, Sm₂O₃-HfO₂, and Gd₂O₃-HfO₂ systems as well as in the La₂O₃-Y₂O₃, ZrO₂-Y₂O₃,
<figure><img src="image_33.png" /></figure>

<figure><img src="image_34.png" /><figcaption>**FIGURE 17** Activity as a function of composition for β-NiAl. Source: Reprinted from Bencze et al.¹⁷⁷ with permission from Springer Nature.</figcaption></figure>

decade.¹⁸⁵⁻¹⁹⁰ We can delineate them into three main groups: glass-forming oxide systems,¹⁹¹⁻¹⁹⁶ ultrahigh-refractory oxide systems mainly based on HfO₂.¹⁹⁷⁻¹⁹⁹ modeling approaches developed using the Knudsen effusion mass spectrometric thermodynamic data on oxide systems for the prediction of their high-temperature behavior,¹⁸⁹,¹⁹³⁻¹⁹⁶,²⁰⁰,²⁰¹ and comparison to thermodynamic data that may be obtained at high temperatures using KEMS and differential thermal analysis.²⁰² During the period indicated from 1994, systematic studies on the thermodynamic properties of the gaseous oxide salts or associates were successfully continued as the development of a scientific school founded by G. A. Semenov. Reviews by Lopatin and Shugurov²⁰³⁻²⁰⁹ illustrate the recent achievements in studies on thermodynamic properties and the identification of the variety of the gaseous associates in high-temperature vapor using KEMS.²⁰³⁻²⁰⁹

It should be mentioned that, although not included in the reviews discussed earlier, recent experimental data obtained using KEMS at high temperatures on oxide systems and materials for nuclear applications such as the UO₂-ZrO₂,⁶⁷,²¹⁰ Cs₂O-B₂O₃,²¹¹ Cs₂O-MoO₃,²¹² and SrO-Al₂O₃²¹³,²¹⁴ systems are available. Recent KEMS data on ceramics and glass ceramics with the special unique physicochemical properties such as the ZnO-Nb₂O₅,²¹⁵ TiO₂-Al₂O₃-SiO₂,²¹⁶,²¹⁷ and Al₂O₃-SiO₂-ZrO₂ systems²¹⁸ as well as ultrahigh refractory ceramics based on the binary and multicomponent systems containing rare-earth and hafnium oxides²¹⁹⁻²²¹ have also been

reported. It is necessary to emphasize that the thermodynamic properties obtained in all these systems were discussed within the framework of semiempirical and statistical thermodynamic approaches for modeling and prediction of thermodynamic properties of multicomponent systems based on the corresponding data on binary systems. Additionally, phase diagrams for the ZnO-Nb₂O₅²¹⁵ and the Al₂O₃-SiO₂-ZrO₂ systems²¹⁸,²²² were optimized and calculated. Examples of component isoactivity curves and Gibbs energy of formation in the Al₂O₃-SiO₂-ZrO₂ system are shown in Figure 19A-D based on experimental data and modeling provided in Stolyarova et al.²¹⁸

We next focus on the latest experimental data on the vaporization and thermodynamic properties of binary and multicomponent systems containing rare-earth and hafnium oxides.¹⁹⁷⁻¹⁹⁹,²¹⁹⁻²²⁵ In recent years, the composition of vapor, the temperature dependences of partial pressures of the vapor species, and the thermodynamic properties of vaporization of the following individual pure rare-earth oxides have been studied: Y₂O₃, La₂O₃, CeO₂, Nd₂O₃, Sm₂O₃, Gd₂O₃, Yb₂O₃, and Lu₂O₃. The study of the high-temperature behavior of Sm₂O₃ deserves special mention, as data on the composition and partial pressures of vapor species over Sm₂O₃ in a wide temperature range have not been previously published in the literature. When comparing the excess Gibbs energies at 2373 K in the La₂O₃-HfO₂, Nd₂O₃-HfO₂, Sm₂O₃-HfO₂, and Gd₂O₃-HfO₂ systems as well as in the La₂O₃-Y₂O₃, ZrO₂-Y₂O₃,
<figure><img src="image_36.png" /></figure>

**FIGURE 18** Activity as a function of composition for different [O] with constant Ti–Al ratio. (A) Activity of aluminum (B) Activity of titanium. Source: Reprinted from Copland et al.¹⁸³ with permission from Elsevier. [Color figure can be viewed at wileyonlinelibrary.com]

<figure><img src="image_37.png" /></figure>

Sm₂O₃-Y₂O₃, and Gd₂O₃-Y₂O₃ systems, it was found that there is a correlation between the electronic structure of lanthanide oxide and the degree of negative deviation from ideal behavior.

Special attention should be paid to the study of evaporation processes and thermodynamic properties in ternary systems based on hafnium and rare-earth oxides (e.g., La₂O₃-Y₂O₃-HfO₂, Gd₂O₃-Y₂O₃-HfO₂, and Y₂O₃-ZrO₂-HfO₂) using KEMS at high temperatures. In these systems, the partial pressures of the vapor species, the evaporation rates of the samples, the activities of the components, and the excess Gibbs energies were obtained for the first time. In the La₂O₃-Y₂O₃-HfO₂ and Y₂O₃-ZrO₂-HfO₂ systems, the concentration changes in the samples due to the selective evaporation of the

components at temperatures of 2337 and 2660 K, respectively, were also evaluated. Similarly, the evaporation rates and changes in the contents of components in the samples during isothermal holding in the Sm₂O₃-Y₂O₃-HfO₂, Sm₂O₃-ZrO₂-HfO₂ and Gd₂O₃-ZrO₂-HfO₂, and Gd₂O₃-ZrO₂-HfO₂ systems were compared. It is shown that at a temperature of 2373 K, the evaporation rates of samples in the Sm₂O₃-Y₂O₃-HfO₂ and Sm₂O₃-ZrO₂-HfO₂ systems are similar, and the least volatile system is Gd₂O₃-ZrO₂-HfO₂, which is consistent with the lower volatility of Gd₂O₃ compared to Sm₂O₃.

Among the modeling approaches used to calculate the thermodynamic properties of multicomponent systems, the appropriate semiempirical methods and statistical-thermodynamic
<figure><img src="image_35.png" /></figure>

**FIGURE 18** Activity as a function of composition for different [O] with constant Ti–Al ratio. (A) Activity of aluminum (B) Activity of titanium. Source: Reprinted from Copland et al.¹⁸³ with permission from Elsevier. [Color figure can be viewed at wileyonlinelibrary.com]

<figure><img src="image_36.png" /></figure>

Sm₂O₃-Y₂O₃, and Gd₂O₃-Y₂O₃ systems, it was found that there is a correlation between the electronic structure of lanthanide oxide and the degree of negative deviation from ideal behavior.

Special attention should be paid to the study of evaporation processes and thermodynamic properties in ternary systems based on hafnium and rare-earth oxides (e.g., La₂O₃-Y₂O₃-HfO₂, Gd₂O₃-Y₂O₃-HfO₂, and Y₂O₃-ZrO₂-HfO₂) using KEMS at high temperatures. In these systems, the partial pressures of the vapor species, the evaporation rates of the samples, the activities of the components, and the excess Gibbs energies were obtained for the first time. In the La₂O₃-Y₂O₃-HfO₂ and Y₂O₃-ZrO₂-HfO₂ systems, the concentration changes in the samples due to the selective evaporation of the

components at temperatures of 2337 and 2660 K, respectively, were also evaluated. Similarly, the evaporation rates and changes in the contents of components in the samples during isothermal holding in the Sm₂O₃-Y₂O₃-HfO₂, Sm₂O₃-ZrO₂-HfO₂ and Gd₂O₃-ZrO₂-HfO₂, and Gd₂O₃-ZrO₂-HfO₂ systems were compared. It is shown that at a temperature of 2373 K, the evaporation rates of samples in the Sm₂O₃-Y₂O₃-HfO₂ and Sm₂O₃-ZrO₂-HfO₂ systems are similar, and the least volatile system is Gd₂O₃-ZrO₂-HfO₂, which is consistent with the lower volatility of Gd₂O₃ compared to Sm₂O₃.

Among the modeling approaches used to calculate the thermodynamic properties of multicomponent systems, the appropriate semiempirical methods and statistical-thermodynamic
<figure><img src="image_38.png" /></figure>

<figure><img src="image_39.png" /><figcaption>**FIGURE 19** (A) The Al₂O₃ isoactivity curves in the Al₂O₃-SiO₂-ZrO₂ system calculated using Generalized Lattice Theory of Associated Solutions (GLTAS) at 2500 K.²¹⁸ (B) The SiO₂ isoactivity curves in the Al₂O₃-SiO₂-ZrO₂ system calculated using GLTAS at 2500 K. The circles indicate the sample compositions for which the experimental values were obtained.²¹⁸ (C) The ZrO₂ isoactivity curves in the Al₂O₃-SiO₂-ZrO₂ system calculated using GLTAS at 2500 K.²¹⁸ (D) The curves of constant ΔG⁵ (kJ/mol) calculated within the GLTAS approach at 2500 K using the SiO₂ activity experimental data in the Al₂O₃-SiO₂-ZrO₂ system (solid lines) and the SiO₂ and Al₂O₃ activity data for the binary SiO₂-ZrO₂ and Al₂O₃-ZrO₂ systems (dashed lines).²¹⁸</figcaption></figure>

models must be selected. A significant limitation of semiempirical methods is the inability to obtain information on the structure of the solutions for which the calculations of thermodynamic properties are carried out; additionally, it is impossible to consider the temperature dependence of thermodynamic properties if they are not available for the corresponding binary systems. Statistical-thermodynamic approaches, on the contrary, allow both modeling thermodynamic properties and relating physicochemical characteristics to structure. Among the variety of statistical and thermodynamic model approaches available, the Barker theory (generalized lattice theory of associated solutions)²²⁶ has been used to calculate the thermodynamic properties of ternary systems containing rare-earth oxides, which has been extensively studied. It should be noted that, within the framework of the Barker theory,²²⁶ it is possible to both optimize the thermodynamic description based on the available experimental data and calculate the thermodynamic quantities in solid

solutions of multicomponent systems using the data on the corresponding binary systems.

Thus, the potential of KEMS as a unique method for studying the physicochemical properties of oxides at high temperatures is shown. Obviously, a wide range of model approaches are needed to process and further use the significant array of experimental data that can be obtained using this method. These models make it possible to calculate thermodynamic properties in multicomponent systems using data from corresponding binary systems and obtain sets of mutually consistent thermodynamic quantities for the systems under study.

An analysis of the current state of scientific knowledge indicates a need for further research into the high-temperature behavior of oxide systems containing rare-earth elements. Research by both experimental methods of high-temperature chemistry and within the framework of model approaches produces modern databases of thermodynamic data and model parameters, such as TAF-ID.²²⁷ This
<figure><img src="image_37.png" /></figure>

<figure><img src="image_38.png" /><figcaption>**FIGURE 19** (A) The Al₂O₃ isoactivity curves in the Al₂O₃-SiO₂-ZrO₂ system calculated using Generalized Lattice Theory of Associated Solutions (GLTAS) at 2500 K.²¹⁸ (B) The SiO₂ isoactivity curves in the Al₂O₃-SiO₂-ZrO₂ system calculated using GLTAS at 2500 K. The circles indicate the sample compositions for which the experimental values were obtained.²¹⁸ (C) The ZrO₂ isoactivity curves in the Al₂O₃-SiO₂-ZrO₂ system calculated using GLTAS at 2500 K.²¹⁸ (D) The curves of constant ΔG⁵ (kJ/mol) calculated within the GLTAS approach at 2500 K using the SiO₂ activity experimental data in the Al₂O₃-SiO₂-ZrO₂ system (solid lines) and the SiO₂ and Al₂O₃ activity data for the binary SiO₂-ZrO₂ and Al₂O₃-ZrO₂ systems (dashed lines).²¹⁸</figcaption></figure>

models must be selected. A significant limitation of semiempirical methods is the inability to obtain information on the structure of the solutions for which the calculations of thermodynamic properties are carried out; additionally, it is impossible to consider the temperature dependence of thermodynamic properties if they are not available for the corresponding binary systems. Statistical-thermodynamic approaches, on the contrary, allow both modeling thermodynamic properties and relating physicochemical characteristics to structure. Among the variety of statistical and thermodynamic model approaches available, the Barker theory (generalized lattice theory of associated solutions)²²⁶ has been used to calculate the thermodynamic properties of ternary systems containing rare-earth oxides, which has been extensively studied. It should be noted that, within the framework of the Barker theory,²²⁶ it is possible to both optimize the thermodynamic description based on the available experimental data and calculate the thermodynamic quantities in solid

solutions of multicomponent systems using the data on the corresponding binary systems.

Thus, the potential of KEMS as a unique method for studying the physicochemical properties of oxides at high temperatures is shown. Obviously, a wide range of model approaches are needed to process and further use the significant array of experimental data that can be obtained using this method. These models make it possible to calculate thermodynamic properties in multicomponent systems using data from corresponding binary systems and obtain sets of mutually consistent thermodynamic quantities for the systems under study.

An analysis of the current state of scientific knowledge indicates a need for further research into the high-temperature behavior of oxide systems containing rare-earth elements. Research by both experimental methods of high-temperature chemistry and within the framework of model approaches produces modern databases of thermodynamic data and model parameters, such as TAF-ID.²²⁷ This
<figure><img src="image_40.png" /></figure>

includes databases for the commonly used computational thermochemistry codes, such as FactSage or ThermoCalc, for predicting physicochemical properties and phase equilibria in oxide systems and materials.<sup>197-200,222-225</sup>

### 3.2.6 | Solution models and model parameters from KEMS

Solution behavior in metallic alloys and oxide systems is generally described using models. Although much progress has been made with first principles descriptions, models continue to be widely used for complex metallic alloys and oxide systems. These models are the primary feature of the CALPHAD method.<sup>228</sup> These models have been discussed in numerous books and review articles,<sup>226,228,229</sup> and an extensive discussion on them is outside the scope of this paper. We will summarize the key models and fitting of adjustable parameters for excess Gibbs energy of mixing with data obtained using the KEMS method. Generally, the Gibbs energy is described in terms of the constituent species, ideal Gibbs energy of mixing, and excess Gibbs energy of mixing.<sup>228</sup> For example, G<sup>φ</sup>, the Gibbs energy of phase φ, is given as<sup>230,231</sup>

$$ 
\begin{aligned}
G^{\phi} &= G_{\text{ref}} + G_{\text{mix}}^{\text{ideal}} + G_{\text{mix}}^{\text{xs}} \\
&= \sum_{i} x_i G_i^{\phi} + RT \sum_{i} x_i \ln x_i + \sum_{i=1}^{n} \sum_{j=i+1}^{n+1} \sum_{\nu=0}^{N} x_i x_j [L_{ij}^{\nu} (x_i - x_j)^{\nu}] \\
&\quad + \sum_{i=1}^{n-2} \sum_{j=i+1}^{n-1} \sum_{k=j+1}^{n} x_i x_j x_k (\nu_i L_i + \nu_j L_j + \nu_k L_k)
\end{aligned}
\quad (60) $$

Here $x_i$ is the mole fraction of the constituent i, $x_j$ is the mole fraction of the constituent j, and $L_{ij}^{\nu}$ is the interaction parameter where the superscript indicates the order and the subscripts indicate the two components of interest, namely $v_i = x_i/(x_i + x_j + x_k)$ and $L_i$ is the ternary interaction parameter. The excess Gibbs energy is described using the Redlich-Kister polynomial,<sup>232</sup> which is often used in CALPHAD calculations due to its easy manipulation to obtain thermodynamic functions.<sup>233</sup> Without the excess term we, of course, have an ideal solution. Examining only the binary interaction terms, note the first term is simply the regular solution model and the second term is the subregular solution model. The ternary interaction term may be derived from several geometric arguments—here the Muggianu approach is shown.<sup>230,231</sup> Generally, each parameter is given a linear dependence on temperature<sup>234-236</sup>:

$$ L_{ij}^{\nu} = A_{ij}^{\nu} + B_{ij}^{\nu} T \quad (61) $$

$A_{ij}^{\nu}$ and $B_{ij}^{\nu}$ are the adjustable parameters taken from experimental data, such as phase boundaries, enthalpy of mixing, and thermodynamic activity of each component. There are computer codes (e.g., PARROT for ThermoCalc<sup>116</sup> or OptiSage for FactSage<sup>115</sup>) for fitting these interaction parameters to experimental data. Accurate thermodynamic data are considered particularly desirable for setting the interaction parameters.

A wide variety of solution models have been applied to alloys, oxide systems, and other solutions. Perhaps the most common is the sublattice model, which would include two or more sublattices and equations like Equation (60) for each sublattice. Many models are based on the quasi-chemical or associates model, where the constituents in Equation (60) are not elements but rather hypothetical chemical compounds or associates. These may or may not be observable in the solution, but they allow for better modeling. There are many variations in the quasi-chemical model.<sup>226,237,238</sup> In summary, an appropriate model is selected to best describe the properties of a solution. These properties include structures, phase transformations, ordering, integral enthalpy of mixing, and thermodynamic activities of components. The parameters for a particular model are then fitted to the experimental data. KEMS can provide thermodynamic activities of components, melting enthalpies, and phase transformation temperatures, which are particularly valuable in the fitting. There are numerous examples of this in the literature. Bencze and colleagues<sup>234-236</sup> have determined binary and ternary interaction parameters from KEMS data for a number of alloys. Stolyarova and colleagues<sup>5,189,193-196,200,201</sup> have determined interaction parameters for a number of oxide systems using KEMS data.

## 4 | NOVEL APPLICATIONS OF KEMS

As discussed, the major application of KEMS has been thermodynamic measurements of both pure compounds and solutions. In this section, we discuss several novel applications of KEMS. We select a few applications that are particularly intriguing and offer promise for future studies. This list is by no means exhaustive, and there are many more novel applications of KEMS.

### 4.1 | Phase transformations

KEMS can be a valuable technique for determining phase changes, assuming, of course, an accurate temperature calibration. Gokcen et al.<sup>239</sup> have shown that the ratio of partial pressures of vapor species or ion intensities in the mass spectra of a vapor shows a discontinuity at the liquidus temperature. Consider a binary alloy with components A and B in the vapor mass spectra. The natural logarithm of the ratio of the ion intensities in the mass spectra of the vapor is given by

$$ \ln(I_A/I_B) = \frac{\Delta_{\text{vap}} \bar{G}_A^i - \Delta_{\text{vap}} \bar{G}_A^i}{RT} + \bar{C} \quad (62) $$

Here $\Delta_{\text{vap}} \bar{G}_A^i$ and $\Delta_{\text{vap}} \bar{G}_B^i$ are the partial molar Gibbs energies of vaporization of A and B from a solution i, respectively, and $\bar{C}$ is a constant. A plot of $\ln(P_A/P_B)$ versus $1/T$—similar to the component activity ratio—is linear for a homogeneous solution (i.e., monophasic domain). For a liquid, when the temperature is decreased to that of liquidus, crystals of the solid will precipitate. The partial molar
includes databases for the commonly used computational thermochemistry codes, such as FactSage or ThermoCalc, for predicting physicochemical properties and phase equilibria in oxide systems and materials.¹⁹⁷⁻²⁰⁰,²²²⁻²²⁵

### 3.2.6 | Solution models and model parameters from KEMS

Solution behavior in metallic alloys and oxide systems is generally described using models. Although much progress has been made with first principles descriptions, models continue to be widely used for complex metallic alloys and oxide systems. These models are the primary feature of the CALPHAD method.²²⁸ These models have been discussed in numerous books and review articles,²²⁶,²²⁸,²²⁹ and an extensive discussion on them is outside the scope of this paper. We will summarize the key models and fitting of adjustable parameters for excess Gibbs energy of mixing with data obtained using the KEMS method. Generally, the Gibbs energy is described in terms of the constituent species, ideal Gibbs energy of mixing, and excess Gibbs energy of mixing.²²⁸ For example, G°, the Gibbs energy of phase φ, is given as²³⁰,²³¹

$$ 
\begin{aligned}
G^{\phi} &= G_{\text{ref}} + G_{\text{mix}}^{\text{ideal}} + G_{\text{mix}}^{\text{xs}} \\
&= \sum_{i} x_{i} G_{i}^{\phi} + RT \sum_{i} x_{i} \ln x_{i} + \sum_{i=1}^{n} \sum_{j=i+1}^{n+1} \sum_{\nu=0}^{N} x_{i} x_{j} [L_{ij}^{\nu} (x_{i} - x_{j})^{\nu}] \\
&\quad + \sum_{i=1}^{n-2} \sum_{j=i+1}^{n-1} \sum_{k=j+1}^{n} x_{i} x_{j} x_{k} (\nu_{i} L_{i} + \nu_{j} L_{j} + \nu_{k} L_{k})
\end{aligned}
\quad (60) $$

Here xᵢ is the mole fraction of the constituent i, xⱼ is the mole fraction of the constituent j, and Lᵢⱼⁿ is the interaction parameter where the superscript indicates the order and the subscripts indicate the two components of interest, namely vᵢ = xᵢ/(xᵢ + xⱼ + xₖ) and Lᵢ is the ternary interaction parameter. The excess Gibbs energy is described using the Redlich-Kister polynomial,²³² which is often used in CALPHAD calculations due to its easy manipulation to obtain thermodynamic functions.²³³ Without the excess term we, of course, have an ideal solution. Examining only the binary interaction terms, note the first term is simply the regular solution model and the second term is the subregular solution model. The ternary interaction term may be derived from several geometric arguments—here the Muggianu approach is shown.²³⁰,²³¹ Generally, each parameter is given a linear dependence on temperature²³⁴⁻²³⁶:

$$ L_{ij}^{\nu} = A_{ij}^{\nu} + B_{ij}^{\nu} T \quad (61) $$

Aᵢⱼⁿ and Bᵢⱼⁿ are the adjustable parameters taken from experimental data, such as phase boundaries, enthalpy of mixing, and thermodynamic activity of each component. There are computer codes (e.g., PARROT for ThermoCalc¹¹⁶ or OptiSage for FactSage¹¹⁵) for fitting these interaction parameters to experimental data. Accurate thermodynamic data are considered particularly desirable for setting the interaction parameters.

A wide variety of solution models have been applied to alloys, oxide systems, and other solutions. Perhaps the most common is the sublattice model, which would include two or more sublattices and equations like Equation (60) for each sublattice. Many models are based on the quasi-chemical or associates model, where the constituents in Equation (60) are not elements but rather hypothetical chemical compounds or associates. These may or may not be observable in the solution, but they allow for better modeling. There are many variations in the quasi-chemical model.²²⁶,²³⁷,²³⁸ In summary, an appropriate model is selected to best describe the properties of a solution. These properties include structures, phase transformations, ordering, integral enthalpy of mixing, and thermodynamic activities of components. The parameters for a particular model are then fitted to the experimental data. KEMS can provide thermodynamic activities of components, melting enthalpies, and phase transformation temperatures, which are particularly valuable in the fitting. There are numerous examples of this in the literature. Bencze and colleagues²³⁴⁻²³⁶ have determined binary and ternary interaction parameters from KEMS data for a number of alloys. Stolyarova and colleagues⁵,¹⁸⁹,¹⁹³⁻¹⁹⁶,²⁰⁰,²⁰¹ have determined interaction parameters for a number of oxide systems using KEMS data.

## 4 | NOVEL APPLICATIONS OF KEMS

As discussed, the major application of KEMS has been thermodynamic measurements of both pure compounds and solutions. In this section, we discuss several novel applications of KEMS. We select a few applications that are particularly intriguing and offer promise for future studies. This list is by no means exhaustive, and there are many more novel applications of KEMS.

### 4.1 | Phase transformations

KEMS can be a valuable technique for determining phase changes, assuming, of course, an accurate temperature calibration. Gokcen et al.²³⁹ have shown that the ratio of partial pressures of vapor species or ion intensities in the mass spectra of a vapor shows a discontinuity at the liquidus temperature. Consider a binary alloy with components A and B in the vapor mass spectra. The natural logarithm of the ratio of the ion intensities in the mass spectra of the vapor is given by

$$ \ln(I_A/I_B) = \frac{\Delta_{\text{vap}} \bar{G}_A^i - \Delta_{\text{vap}} \bar{G}_A^i}{RT} + \bar{C} \quad (62) $$

Here ΔvapḠA and ΔvapḠB are the partial molar Gibbs energies of vaporization of A and B from a solution i, respectively, and C̄ is a constant. A plot of ln(PA/PB) versus 1/T—similar to the component activity ratio—is linear for a homogeneous solution (i.e., monophasic domain). For a liquid, when the temperature is decreased to that of liquidus, crystals of the solid will precipitate. The partial molar
quantities would change with composition of the system under study, and therefore, the plot is no longer linear. Such plots can yield quite accurate liquidus lines for a range of compositions. Nunoue and Kato²⁴⁰ have used this technique with the Fe-Ge system, and Copland has used this technique with the Ni-Al-O¹⁷⁵ system, as shown in Figure 20.

Another interesting phase change study phenomena first reported using KEMS is that of Roberts and Searcy.²⁴¹ On cooling $Ga_2S_3(s)$ between 1228 and 1203 K, they observed an increase in the partial pressure of $Ga_2S$. The vaporization of $Ga_2S_3$ is given by

$$Ga_{(2+2\epsilon)}S_{(3-\epsilon)}(s) = (1+\epsilon)Ga_2S(g) + (1-\epsilon)S_2(g) \quad (63)$$

The increase is explained by the appearance of a second phase of $Ga_2S_3$. As this second phase nucleates, the composition of the original $Ga_2S_3$ phase shifts to a higher Ga content and higher P($Ga_2S$). The appearance of a second phase has been confirmed by Jones and Edwards.²⁴² This study shows the sensitivity of the Knudsen mass spectrometric technique to small phase changes.

Chatillon and Nuta⁴² have pointed out that this phenomenon is related to the movement toward congruent vaporization in relation to continuous effusion that can modify the condensed phase composition throughout an experiment. As the specimen is cooled, it necessarily loses material to move toward a new point of congruency. This is analogous to the approach of an azeotrope in organic chemistry. Going through a two-phase region toward congruency, one of the phases loses material faster than the other. But the final P ($Ga_2S$)/P($S_2$) is lower than the starting ratio. This indicates the

importance of slow measurements and accounting for compositional differences during KEMS experiments.

## 4.2 | Ultrahigh-temperature materials

Since its inception, KEMS has been used for vapor phase analysis and determination of pressures where vaporization occurs with dissociation at very high temperatures. This is particularly useful now for materials that can withstand extreme temperatures encountered as reentry surfaces, heat engine components, and nuclear reactor components. These are termed “ultrahigh-temperature ceramics or composites” (UHTCs). Candidate UHTCs include oxides, borides, carbides, nitrides, and silicides.²⁴³ The use of an electron beam or laser heating allows attainment of temperatures in excess of 2000 K. Stolyarova and colleagues²¹⁰,²⁴⁴ have investigated numerous binary and ternary systems of the form $RE_2O_3-ZrO_2$ (RE, rare earth), $RE_2O_3-HfO_2-ZrO_2$, or $RE_2O_3-RE'_2O_3-ZrO_2$ to temperatures near 3000 K.

Other ultrahigh-temperature materials, including borides, carbides, and nitrides, have been studied using KEMS. According to Fleischer,²⁴³ there are more borides with melting points above 2273 K than any other group of inorganic compounds (i.e., carbides, nitrides, and oxides). Brewer and Haraldsen²⁴⁵ point out that thermodynamic measurements of these compounds with conventional calorimetry are challenging due to insolubility in many solvents. However, KEMS offers the possibility of obtaining accurate thermodynamic data by measuring the partial pressures of the vapor species. Storms and Mueller²⁴⁶ have studied the Mo-B system by measuring the boron partial pressures of species in compounds

<figure><img src="image_41.png" /><figcaption>**FIGURE 20** Phase changes in the Ni-Al-O system from ion current ratios. Source: Reprinted from Copland,¹⁷⁵ with permission from Elsevier.</figcaption></figure>
quantities would change with composition of the system under study, and therefore, the plot is no longer linear. Such plots can yield quite accurate liquidus lines for a range of compositions. Nunoue and Kato²⁴⁰ have used this technique with the Fe-Ge system, and Copland has used this technique with the Ni-Al-O¹⁷⁵ system, as shown in Figure 20.

Another interesting phase change study phenomena first reported using KEMS is that of Roberts and Searcy.²⁴¹ On cooling Ga₂S₃(s) between 1228 and 1203 K, they observed an increase in the partial pressure of Ga₂S. The vaporization of Ga₂S₃ is given by

$$Ga_{(2+2\epsilon)}S_{(3-\epsilon)}(s) = (1+\epsilon)Ga_2S(g) + (1-\epsilon)S_2(g) \quad (63)$$

The increase is explained by the appearance of a second phase of Ga₂S₃. As this second phase nucleates, the composition of the original Ga₂S₃ phase shifts to a higher Ga content and higher P(Ga₂S). The appearance of a second phase has been confirmed by Jones and Edwards.²⁴² This study shows the sensitivity of the Knudsen mass spectrometric technique to small phase changes.

Chatillon and Nuta⁴² have pointed out that this phenomenon is related to the movement toward congruent vaporization in relation to continuous effusion that can modify the condensed phase composition throughout an experiment. As the specimen is cooled, it necessarily loses material to move toward a new point of congruency. This is analogous to the approach of an azeotrope in organic chemistry. Going through a two-phase region toward congruency, one of the phases loses material faster than the other. But the final P (Ga₂S)/P(S₂) is lower than the starting ratio. This indicates the

importance of slow measurements and accounting for compositional differences during KEMS experiments.

## 4.2 | Ultrahigh-temperature materials

Since its inception, KEMS has been used for vapor phase analysis and determination of pressures where vaporization occurs with dissociation at very high temperatures. This is particularly useful now for materials that can withstand extreme temperatures encountered as reentry surfaces, heat engine components, and nuclear reactor components. These are termed “ultrahigh-temperature ceramics or composites” (UHTCs). Candidate UHTCs include oxides, borides, carbides, nitrides, and silicides.²⁴³ The use of an electron beam or laser heating allows attainment of temperatures in excess of 2000 K. Stolyarova and colleagues²¹⁰,²⁴⁴ have investigated numerous binary and ternary systems of the form RE₂O₃-ZrO₂ (RE, rare earth), RE₂O₃-HfO₂-ZrO₂, or RE₂O₃-RE'₂O₃-ZrO₂ to temperatures near 3000 K.

Other ultrahigh-temperature materials, including borides, carbides, and nitrides, have been studied using KEMS. According to Fleischer,²⁴³ there are more borides with melting points above 2273 K than any other group of inorganic compounds (i.e., carbides, nitrides, and oxides). Brewer and Haraldsen²⁴⁵ point out that thermodynamic measurements of these compounds with conventional calorimetry are challenging due to insolubility in many solvents. However, KEMS offers the possibility of obtaining accurate thermodynamic data by measuring the partial pressures of the vapor species. Storms and Mueller²⁴⁶ have studied the Mo-B system by measuring the boron partial pressures of species in compounds

<figure><img src="image_39.png" /><figcaption>**FIGURE 20** Phase changes in the Ni-Al-O system from ion current ratios. Source: Reprinted from Copland,¹⁷⁵ with permission from Elsevier.</figcaption></figure>
spanning the range from the boron-rich to the molybdenum-rich sides of the corresponding phase diagram. A tungsten effusion cell saturated with B vapor was used, so the cell walls were tungsten boride. Figure 21 is a plot of measured activity of boron versus Mo-B ratio in the Mo-B system. Such an activity plot in conjunction with XRD data provides phase diagram information in this system. Other metal borides have also been studied using KEMS.<sup>247,248</sup>

Refractory carbides have some of the highest melting points measured, with HfC, TaC, NbC, and ZrC melting at temperatures >3773 K.<sup>243</sup> KEMS has been successfully applied to many refractory carbides, yielding information on the vapor species as well as partial molar quantities (e.g., component activities) of metal-carbon solid solutions. Considering pure carbon, an early KEMS study by Drowart et al.<sup>249</sup> illustrated the complex behavior of this basic material. There is a large body of KEMS work on metallic carbides, primarily in the 1960s and 1970s. Much of this work has been summarized in reviews.<sup>250,251</sup> The most common high-temperature carbide is SiC, which has been studied in a number of KEMS laboratories.<sup>252-254</sup> Rocabois et al.<sup>253</sup> observed the major species: Si(g), Si<sub>2</sub>(g), Si<sub>3</sub>(g), Si<sub>2</sub>C (g), SiC<sub>2</sub>(g), Si<sub>2</sub>C<sub>2</sub>(g), and Si<sub>3</sub>C<sub>2</sub>(g). They reported enthalpies of formation at 298.15 K for each of these vapor species. Behrens and Rinehart<sup>254</sup> and Davis et al.<sup>255</sup> have used vapor pressure measurements of the Si vapor species to determine the enthalpy of formation of SiC(s) at 298.15 K.

The transition metals and lanthanide metals also form useful refractory carbides. Kohl and Stearns<sup>256</sup> have examined TiC, ZrC, HfC, and ThC. They observed vapor species of the form MC(g), MC<sub>2</sub>(g), and MC<sub>4</sub>(g) at temperatures up to 3003 K. Using both the second and

<figure><img src="image_42.png" /><figcaption>**FIGURE 21** Activity as a function of composition for the Mo-B system. Source: Adapted from Storms and Mueller,<sup>246</sup> with permission from the American Chemical Society.</figcaption></figure>

third law methods of thermodynamics, they reported standard enthalpies for the following reactions:

$$M(g) + 2C(s) = MC_2(g) \quad (64a)$$

$$M(g) + 4C(s) = MC_4(g) \quad (64b)$$

For the third thermodynamic law calculations, gefs are estimated from limited structural information and analogy to monoxide species, assuming the C<sub>2</sub><sup>-2</sup> group bonding is similar to the O<sup>-2</sup> group bonding. As noted earlier, improvements in gef estimates can now be made using modern computational methods. The study of Kohl and Stearns also shows that a component activity versus composition diagram in the system under study can be constructed from the two equilibria mentioned earlier. For the first reaction without excess carbon,

$$a_c^2 = \frac{1}{K_p} \frac{P_{MC_2}}{P_M} \approx \frac{1}{K_p} \frac{l_{MC_2^+}}{l_{M^+}} \quad (65)$$

This assumes the cross sections of the M and MC<sub>2</sub> vapor species are close. Then for the second reaction, without excess carbon,

$$a_c^2 = \frac{1}{K_p} \frac{P_{MC_4}}{P_{MC_2}} \approx \frac{1}{K_p} \frac{l_{MC_4^+}}{l_{MC_2^+}} \quad (66)$$

Gupta and Gingerich<sup>257</sup> have reported bond dissociation energies for vanadium, niobium, and molybdenum carbides. They used a single cell containing a small amount of Au for calibration. At lower temperatures, the Au<sup>+</sup>/Au<sub>2</sub><sup>+</sup> ion current ratio was used to obtain a calibration constant, and then the measurements were taken in the 2600-3000 K temperature range. They used the second and third law methods of thermodynamics to report bond dissociation energies and atomization enthalpies. Gupta and Gingerich have also studied the vaporization of UC(s) and observed UC<sub>n</sub>(g) (n = 1-6) vapor species, reporting enthalpies of formation at 298 K for all these species.<sup>258</sup> Yamawaki et al.<sup>259</sup> have reported on the thermodynamics of ThC<sub>(1±x)</sub>, and Koyama and Yamawaki<sup>260</sup> have presented thermodynamic data on the mixed carbide (Th<sub>(1 - y)</sub>U<sub>x</sub>)C. In both studies dissolved oxygen plays an important role, and volatile metal oxides are observed. Nonetheless, activities of all components are reported in these systems. As shown, there is extensive research on refractory carbides using KEMS. Thus, KEMS is particularly well suited to carbides, as the generated vapor species can be analyzed, and the component activities can be measured.

Another important class of high-temperature materials is metal nitrides. These are typically less refractory than metal carbides, as they decompose into nitrogen and the metal and have somewhat lower melting points than carbides. Nonetheless, Si<sub>3</sub>N<sub>4</sub>, HfN, TaN, BN, ZrN, and TiN are all considered refractory materials. Again, KEMS is a valuable technique to study these materials, as it provides vapor composition and partial molar thermodynamic quantities. Rocabois et al.<sup>261</sup> have observed N<sub>2</sub>(g), Si(g), Si<sub>2</sub>(g), SiN(g), and Si<sub>2</sub>N(g) above Si<sub>3</sub>N<sub>4</sub>(s). They used Knudsen cells with different orifice diameters to
spanning the range from the boron-rich to the molybdenum-rich sides of the corresponding phase diagram. A tungsten effusion cell saturated with B vapor was used, so the cell walls were tungsten boride. Figure 21 is a plot of measured activity of boron versus Mo-B ratio in the Mo-B system. Such an activity plot in conjunction with XRD data provides phase diagram information in this system. Other metal borides have also been studied using KEMS.<sup>247,248</sup>

Refractory carbides have some of the highest melting points measured, with HfC, TaC, NbC, and ZrC melting at temperatures >3773 K.<sup>243</sup> KEMS has been successfully applied to many refractory carbides, yielding information on the vapor species as well as partial molar quantities (e.g., component activities) of metal-carbon solid solutions. Considering pure carbon, an early KEMS study by Drowart et al.<sup>249</sup> illustrated the complex behavior of this basic material. There is a large body of KEMS work on metallic carbides, primarily in the 1960s and 1970s. Much of this work has been summarized in reviews.<sup>250,251</sup> The most common high-temperature carbide is SiC, which has been studied in a number of KEMS laboratories.<sup>252-254</sup> Rocabois et al.<sup>253</sup> observed the major species: Si(g), Si<sub>2</sub>(g), Si<sub>3</sub>(g), Si<sub>2</sub>C (g), SiC<sub>2</sub>(g), Si<sub>2</sub>C<sub>2</sub>(g), and Si<sub>3</sub>C<sub>2</sub>(g). They reported enthalpies of formation at 298.15 K for each of these vapor species. Behrens and Rinehart<sup>254</sup> and Davis et al.<sup>255</sup> have used vapor pressure measurements of the Si vapor species to determine the enthalpy of formation of SiC(s) at 298.15 K.

The transition metals and lanthanide metals also form useful refractory carbides. Kohl and Stearns<sup>256</sup> have examined TiC, ZrC, HfC, and ThC. They observed vapor species of the form MC(g), MC<sub>2</sub>(g), and MC<sub>4</sub>(g) at temperatures up to 3003 K. Using both the second and

<figure><img src="image_40.png" /><figcaption>**FIGURE 21** Activity as a function of composition for the Mo-B system. Source: Adapted from Storms and Mueller,<sup>246</sup> with permission from the American Chemical Society.</figcaption></figure>

third law methods of thermodynamics, they reported standard enthalpies for the following reactions:

$$M(g) + 2C(s) = MC_2(g) \quad (64a)$$

$$M(g) + 4C(s) = MC_4(g) \quad (64b)$$

For the third thermodynamic law calculations, gefs are estimated from limited structural information and analogy to monoxide species, assuming the C<sub>2</sub><sup>-2</sup> group bonding is similar to the O<sup>-2</sup> group bonding. As noted earlier, improvements in gef estimates can now be made using modern computational methods. The study of Kohl and Stearns also shows that a component activity versus composition diagram in the system under study can be constructed from the two equilibria mentioned earlier. For the first reaction without excess carbon,

$$a_c^2 = \frac{1}{K_p} \frac{P_{MC_2}}{P_M} \approx \frac{1}{K_p} \frac{l_{MC_2^+}}{l_{M^+}} \quad (65)$$

This assumes the cross sections of the M and MC<sub>2</sub> vapor species are close. Then for the second reaction, without excess carbon,

$$a_c^2 = \frac{1}{K_p} \frac{P_{MC_4}}{P_{MC_2}} \approx \frac{1}{K_p} \frac{l_{MC_4^+}}{l_{MC_2^+}} \quad (66)$$

Gupta and Gingerich<sup>257</sup> have reported bond dissociation energies for vanadium, niobium, and molybdenum carbides. They used a single cell containing a small amount of Au for calibration. At lower temperatures, the Au<sup>+</sup>/Au<sub>2</sub><sup>+</sup> ion current ratio was used to obtain a calibration constant, and then the measurements were taken in the 2600-3000 K temperature range. They used the second and third law methods of thermodynamics to report bond dissociation energies and atomization enthalpies. Gupta and Gingerich have also studied the vaporization of UC(s) and observed UC<sub>n</sub>(g) (n = 1-6) vapor species, reporting enthalpies of formation at 298 K for all these species.<sup>258</sup> Yamawaki et al.<sup>259</sup> have reported on the thermodynamics of ThC<sub>(1±x)</sub>, and Koyama and Yamawaki<sup>260</sup> have presented thermodynamic data on the mixed carbide (Th<sub>(1 - y)</sub>U<sub>x</sub>)C. In both studies dissolved oxygen plays an important role, and volatile metal oxides are observed. Nonetheless, activities of all components are reported in these systems. As shown, there is extensive research on refractory carbides using KEMS. Thus, KEMS is particularly well suited to carbides, as the generated vapor species can be analyzed, and the component activities can be measured.

Another important class of high-temperature materials is metal nitrides. These are typically less refractory than metal carbides, as they decompose into nitrogen and the metal and have somewhat lower melting points than carbides. Nonetheless, Si<sub>3</sub>N<sub>4</sub>, HfN, TaN, BN, ZrN, and TiN are all considered refractory materials. Again, KEMS is a valuable technique to study these materials, as it provides vapor composition and partial molar thermodynamic quantities. Rocabois et al.<sup>261</sup> have observed N<sub>2</sub>(g), Si(g), Si<sub>2</sub>(g), SiN(g), and Si<sub>2</sub>N(g) above Si<sub>3</sub>N<sub>4</sub>(s). They used Knudsen cells with different orifice diameters to
extract a very low vaporization coefficient of the vapor, which indicated a significant kinetic barrier to decomposition. Further, Rocabois et al. showed that compounds with very low vaporization coefficients,²⁶¹ such as Si₃N₄, do not yield adequate equilibrium data to determine enthalpies of formation. They recommend using calorimetric data instead.

Kohl and Stearns²⁶² have reported that HfN decomposes primarily into Hf(g) and N₂(g) and also HfN(g). Similar results have been reported for TiN,²⁶³ ZrN,²⁶⁴ UN,²⁶⁵ and ThN.²⁶⁶ Nitrides such as BN and AlN have kinetic barriers to vaporization.⁴² Vaporization of Al or B limits the vaporization of N₂(g). In the case of TiN, N₂ loss changes the composition of the solid.²⁶⁷

Silicides have long been material candidates for very high-temperature use. MoSi₂ is commonly used as a high-temperature heating element in air, which suggests it may be useful as a structural material. Myers and coworkers have examined a number of transition metal silicides using KEMS.²⁶⁸⁻²⁷⁰ They measured the activities of the metal and silicon, from the ion intensities of the metal, Iₘ⁺, and ion current intensities of silicon, Iₗᵢ⁺, in the mass spectra of the vapor, respectively. In some cases, where the Si vapor pressure and/or silicon activity is too low to measure, they add SiO₂ to the alloy and that generates a strong SiO⁺ signal, which can be related to the activity of silicon.

## 4.3 | Measurement and fixing low oxygen potentials

In a KEMS experiment, the only source of oxygen is the residual oxygen in the vacuum system from outgassing of the construction materials. Further, oxygen-active refractory metals (W, Ta, Mo) tend to get the oxygen. Therefore, one would expect a low oxygen potential inside the cell. Note that at high temperature and low oxygen potential, the O(g) pressure becomes higher than the O₂(g) pressure. Note that O(g) must be measured at ≤17 eV to avoid O⁺ fragments in the mass spectra of the vapor from any O₂ in the ionizer. The direct measurement of oxygen is thus difficult, given the background that makes a shutterable oxygen signal less likely to be observed. However, many systems provide other species that allow indirectly an accurate determination of oxygen potential. These include the following:

$$WO_2(g) + \frac{1}{2}O_2(g) = WO_3(g) \qquad P(O_2) = \left[ \frac{P(WO_3)}{P(WO_2)K_p} \right]^2 \quad (67a)$$

$$MoO_2(g) + \frac{1}{2}O_2(g) = MoO_3(g) \qquad P(O_2) = \left[ \frac{P(MoO_3)}{P(MoO_2)K_p} \right]^2 \quad (67b)$$

$$Al_2O(g) = 2Al(g) + \frac{1}{2}O_2(g) \qquad P(O_2) = \left[ \frac{P(Al_2O)K_p}{[P(Al)]^2} \right]^2 \quad (67c)$$

Recently reaction (67c) has been used to determine the oxygen potential above Ti-Al-O alloys.¹⁸³ Such measurements are extremely

important given the high solubility of oxygen in Ti and Ti-Al alloys. Stolyarova and Semenov⁵ have shown that coupled oxide equilibria can be used to calculate the oxygen potential in an oxide system.

Related to the measurement of oxygen potential is the use of a zirconia cell to impose an oxygen potential in the cell. Detry et al. first demonstrated the use of an “electrochemical Knudsen cell” to set a sulfur potential.²⁰ More commonly, a zirconia Knudsen cell is converted into a zirconia oxygen pump, as shown in Figure 2E:

$$Pt, O_2(r) | ZrO_2 | Pt, O_2(cell) \qquad \ln\left(\frac{P(O_2)_r}{P(O_2)_{cell}}\right) = -\frac{4FE}{RT} \quad (68)$$

Here P(O₂)ₜ is the oxygen reference pressure, P(O₂)cell is the desired oxygen pressure in the cell, F is the Faraday constant, and E is the applied voltage. There are many processes that occur at low oxygen potential, for example, processes at the oxide-metal interface during the high-temperature oxidation of metals. A Knudsen cell with a controlled/known oxygen potential offers an intriguing method to probe these processes.

## 4.4 | Geological applications

There are many questions in geochemistry and cosmochemistry that can be answered using KEMS. Minerals and rocks are often complex, multicomponent solutions, which lend themselves to KEMS studies. There are some KEMS studies on complex, multicomponent rocks and minerals in the literature.¹¹⁸,²⁷¹ For example, Rammensee and Fraser have used the ion current ratio method to examine the pseudo-binaries NaAlSi₃O₈-KAlSi₃O₈,²⁷² (Na-K)AlSi₄O₁₀, and (Na-K)AlSi₅O₁₂,²⁷³

The study on magmas has always been an important topic in geology. There are several studies on magmas such as those that may have existed on earth after the giant impact that formed the moon.²⁷⁴⁻²⁷⁶ Understanding the solution behavior of lava is essential to these studies. Such behavior has been predicted from solution models.²⁷⁵⁻²⁷⁷ In the study of Fegley et al.,²⁷⁶ a magma consisting of 69 oxides was considered, and solution properties are extrapolated from a number of models. As discussed in the section on solution models, complex, multicomponent solutions can be modeled from binaries and ternary systems. KEMS can be useful in developing lower-order models for the study of geologically relevant higher-order systems and also providing a direct check for the solution properties of the actual higher-order systems.²⁷⁸,²⁷⁹

As noted, the high-resolution magnetic sector KEMS instruments can also be useful as isotope mass spectrometers. KEMS has proven useful in measuring the potassium component in K-Ar dating. In a study by Farley et al.²⁸⁰ a tracer spike enriched in ³⁹Ar and ⁴¹K was added to a lithium borate flux together with the mineral of known mass to be dated. A noble gas mass spectrometer was used to measure ⁴⁰Ar⁺/³⁹Ar, and a KEMS system was used to measure ³⁹K/⁴¹K. These two quantities are combined to calculate the age of
extract a very low vaporization coefficient of the vapor, which indicated a significant kinetic barrier to decomposition. Further, Rocabois et al. showed that compounds with very low vaporization coefficients,²⁶¹ such as Si₃N₄, do not yield adequate equilibrium data to determine enthalpies of formation. They recommend using calorimetric data instead.

Kohl and Stearns²⁶² have reported that HfN decomposes primarily into Hf(g) and N₂(g) and also HfN(g). Similar results have been reported for TiN,²⁶³ ZrN,²⁶⁴ UN,²⁶⁵ and ThN.²⁶⁶ Nitrides such as BN and AlN have kinetic barriers to vaporization.⁴² Vaporization of Al or B limits the vaporization of N₂(g). In the case of TiN, N₂ loss changes the composition of the solid.²⁶⁷

Silicides have long been material candidates for very high-temperature use. MoSi₂ is commonly used as a high-temperature heating element in air, which suggests it may be useful as a structural material. Myers and coworkers have examined a number of transition metal silicides using KEMS.²⁶⁸⁻²⁷⁰ They measured the activities of the metal and silicon, from the ion intensities of the metal, Iₘ⁺, and ion current intensities of silicon, Iₗᵢ⁺, in the mass spectra of the vapor, respectively. In some cases, where the Si vapor pressure and/or silicon activity is too low to measure, they add SiO₂ to the alloy and that generates a strong SiO⁺ signal, which can be related to the activity of silicon.

## 4.3 | Measurement and fixing low oxygen potentials

In a KEMS experiment, the only source of oxygen is the residual oxygen in the vacuum system from outgassing of the construction materials. Further, oxygen-active refractory metals (W, Ta, Mo) tend to get the oxygen. Therefore, one would expect a low oxygen potential inside the cell. Note that at high temperature and low oxygen potential, the O(g) pressure becomes higher than the O₂(g) pressure. Note that O(g) must be measured at ≤17 eV to avoid O⁺ fragments in the mass spectra of the vapor from any O₂ in the ionizer. The direct measurement of oxygen is thus difficult, given the background that makes a shutterable oxygen signal less likely to be observed. However, many systems provide other species that allow indirectly an accurate determination of oxygen potential. These include the following:

$$WO_2(g) + \frac{1}{2}O_2(g) = WO_3(g) \qquad P(O_2) = \left[ \frac{P(WO_3)}{P(WO_2)K_p} \right]^2 \quad (67a)$$

$$MoO_2(g) + \frac{1}{2}O_2(g) = MoO_3(g) \qquad P(O_2) = \left[ \frac{P(MoO_3)}{P(MoO_2)K_p} \right]^2 \quad (67b)$$

$$Al_2O(g) = 2Al(g) + \frac{1}{2}O_2(g) \qquad P(O_2) = \left[ \frac{P(Al_2O)K_p}{[P(Al)]^2} \right]^2 \quad (67c)$$

Recently reaction (67c) has been used to determine the oxygen potential above Ti-Al-O alloys.¹⁸³ Such measurements are extremely

important given the high solubility of oxygen in Ti and Ti-Al alloys. Stolyarova and Semenov⁵ have shown that coupled oxide equilibria can be used to calculate the oxygen potential in an oxide system.

Related to the measurement of oxygen potential is the use of a zirconia cell to impose an oxygen potential in the cell. Detry et al. first demonstrated the use of an “electrochemical Knudsen cell” to set a sulfur potential.²⁰ More commonly, a zirconia Knudsen cell is converted into a zirconia oxygen pump, as shown in Figure 2E:

$$Pt, O_2(r) | ZrO_2 | Pt, O_2(cell) \qquad \ln\left(\frac{P(O_2)_r}{P(O_2)_{cell}}\right) = -\frac{4FE}{RT} \quad (68)$$

Here P(O₂)ₜ is the oxygen reference pressure, P(O₂)ₜₐcell is the desired oxygen pressure in the cell, F is the Faraday constant, and E is the applied voltage. There are many processes that occur at low oxygen potential, for example, processes at the oxide-metal interface during the high-temperature oxidation of metals. A Knudsen cell with a controlled/known oxygen potential offers an intriguing method to probe these processes.

## 4.4 | Geological applications

There are many questions in geochemistry and cosmochemistry that can be answered using KEMS. Minerals and rocks are often complex, multicomponent solutions, which lend themselves to KEMS studies. There are some KEMS studies on complex, multicomponent rocks and minerals in the literature.¹¹⁸,²⁷¹ For example, Rammensee and Fraser have used the ion current ratio method to examine the pseudo-binaries NaAlSi₃O₈-KAlSi₃O₈,²⁷² (Na-K)AlSi₄O₁₀, and (Na-K)AlSi₅O₁₂,²⁷³

The study on magmas has always been an important topic in geology. There are several studies on magmas such as those that may have existed on earth after the giant impact that formed the moon.²⁷⁴⁻²⁷⁶ Understanding the solution behavior of lava is essential to these studies. Such behavior has been predicted from solution models.²⁷⁵⁻²⁷⁷ In the study of Fegley et al.,²⁷⁶ a magma consisting of 69 oxides was considered, and solution properties are extrapolated from a number of models. As discussed in the section on solution models, complex, multicomponent solutions can be modeled from binaries and ternary systems. KEMS can be useful in developing lower-order models for the study of geologically relevant higher-order systems and also providing a direct check for the solution properties of the actual higher-order systems.²⁷⁸,²⁷⁹

As noted, the high-resolution magnetic sector KEMS instruments can also be useful as isotope mass spectrometers. KEMS has proven useful in measuring the potassium component in K-Ar dating. In a study by Farley et al.²⁸⁰ a tracer spike enriched in ³⁹Ar and ⁴¹K was added to a lithium borate flux together with the mineral of known mass to be dated. A noble gas mass spectrometer was used to measure ⁴⁰Ar⁺/³⁹Ar, and a KEMS system was used to measure ³⁹K/⁴¹K. These two quantities are combined to calculate the age of
the sample. This method<sup>280</sup> was demonstrated on a basalt sample,
whose age was known from other methods.

Another intriguing application of KEMS is the study of simulated
exoplanet atmospheres.<sup>281</sup> Hot, rocky extrasolar planets such as
CoRoT-7b, Kepler-10b, and 55 CNC e are close enough to their host
suns that they may have surface temperatures from 2400 to 3000 K.
Further, they are tidally locked, meaning one side always faces the
host star.<sup>282</sup> This leads to a planet surface of magma oceans and an
atmosphere of the corresponding high-temperature vapors above
those oceans. Thus, the Knudsen cell may act as a small simulation of
the surface conditions of a hot, rocky exoplanet. In the study by Costa
et al.,<sup>281</sup> olivine and its vapor were examined using KEMS. Olivine
was selected as a test material, because it is the principal constituent
of the earth's mantle and may be a reasonable approximation to an
exoplanet surface composition. The study of exoplanets is one of the
most exciting areas in modern astrophysics, and KEMS can play an
important role in this.

4.5 | Nuclear applications

Another growth area for KEMS is its application to the nuclear field. As noted in the ultrahigh-temperature materials section, KEMS has provided excellent data on nuclear materials such as UO₂, MOX (mixed oxide, plutonium-blended uranium fuel), UC, and UN. Earlier reviews¹⁹⁰,²⁸³ have presented this work in detail. A recent reference work²⁸⁴ on fuel chemistry reports further information on KEMS studies in this field.

Recent KEMS studies in the nuclear field are heavily influenced
by events such as climate change,²⁸⁵ energy supply issues,²⁸⁶ and
decommissioned irradiation facilities for medical isotope
production.²⁸⁷ Advanced reactors such as small modular reactors,
reactors developed in GEN IV, and alternative research reactors are
drawing attention in this context. There are many ongoing advanced
reactor development efforts, funded by both the public and private
sectors.²⁸⁸ Some of these new reactor concepts need investigations
on new fuels. KEMS is the key technique for such studies. Nuclear
fuel, in its environment, under normal or accidental conditions, is a
very complex system for which the thermodynamic properties need
to be assessed before implementation in a commercial or research
reactor. KEMS has long been a key technique used to investigate
nuclear fuel behavior. KEMS investigations in this field provide unique
key data on partial vapor pressures, component activities, and
nonideal solution behavior (e.g., the behavior of fission products in
oxide fuels). These data are all essential for the safety and licensing of
a nuclear fuel. Nuclear waste is also an important domain in which
KEMS studies play a key role.

4.5.1 | Molten salt fuels

Molten salt reactors (MSR) are the only reactors using liquid as fuel.
Fissile material and fission product are dissolved in the liquid, which is

also used as a coolant. A fuel treatment unit can be included in the
liquid loop to reprocess the fuel during irradiation. One reactor of this
type is the well-known Oak Ridge molten fluoride reactor built in the
1960s. Two kinds of fuels are considered for MSRs: chlorides and
fluorides. Both have different chemical and neutronic characteristics.
Depending on the function of the fuel and its composition, different
kinds of reactors can be built. With a thermal neutron spectrum,
reactors can burn <sup>235</sup>U, which represents only a fraction of the
uranium extracted, or breed <sup>233</sup>U from natural thorium, <sup>232</sup>Th, which
is more abundant in the earth's crust but requires significantly more
expensive extraction methods. Reactors with a fast neutron spectrum
can burn plutonium and other transuranium actinides, which thus
reduce nuclear waste and breed <sup>238</sup>U and <sup>232</sup>Th to form <sup>239</sup>Pu and
<sup>233</sup>U, respectively. These can then be used as fuel. The salts are also
used for pyrometallurgical processes in nuclear industry.

Many studies on these salts have been conducted using KEMS. Some examples follow. Tosolin et al.<sup>289,290</sup> have reported thermodynamic data from KEMS on the LiF-ThF<sub>4</sub>-UF<sub>4</sub> and LiF-ThF<sub>4</sub>-UF<sub>4</sub>-PuF<sub>3</sub> systems. Vozárová et al.<sup>291</sup> published KEMS-derived thermodynamic data for the CsF-ThF<sub>4</sub> system. Capelli et al.<sup>292</sup> reported data on Li<sub>x</sub>Th(1-x)F(4-3x), and Mishra<sup>293</sup> and McMurray et al.<sup>294</sup> presented data on FLiNaK. On the chloride side, Trinadh et al.<sup>108</sup> performed measurements on LiCl-KCl-UCl<sub>3</sub>. Beneš<sup>295</sup> have measured the vaporization behavior of Cs and I from fluoride melts. Taira<sup>296</sup> have studied the behavior of simulated fission products in solution for different fuel compositions. Hania<sup>297</sup> has studied irradiated molten salt fuels targeted for KEMS measurements. There is limited published information on molten chloride fuels. KEMS investigations related the development of molten chloride fast reactors as ongoing.

4.5.2 | Liquid metal coolants and metallic fuels

Liquid lead-bismuth eutectic is another important material for an advanced nuclear reactor. It is used as a primary coolant in lead-cooled fast reactors and as a fuel and coolant in accelerator-driven systems. Luongo et al.<sup>298</sup> have studied lead iodide decomposition, which is relevant for this fuel.

Metallic fuels, such as dispersion fuels, are used in research
reactors. Trinadh et al. have published KEMS studies of the U-Al
system.<sup>299,300</sup> The U-Pu-Zr system is a potential driver fuel for fast
breeder reactors. Two compositions in this ternary have also been
investigated by Trinadh et al.<sup>301</sup> Recent KEMS studies on the Gd-Al
system focus on the potential of separating actinides from the
lanthanides.<sup>302</sup>

4.5.3 | Oxide fuels

Oxides fuels are the most used in current and advanced reactors. A
large amount of literature is available and can be found in earlier
reviews, including data on highly radiotoxic oxides.<sup>77,80,303</sup> Most
<figure><img src="image_41.png" /></figure>

the sample. This method<sup>280</sup> was demonstrated on a basalt sample, whose age was known from other methods.

Another intriguing application of KEMS is the study of simulated
exoplanet atmospheres.<sup>281</sup> Hot, rocky extrasolar planets such as
CoRoT-7b, Kepler-10b, and 55 CNC e are close enough to their host
suns that they may have surface temperatures from 2400 to 3000 K.
Further, they are tidally locked, meaning one side always faces the
host star.<sup>282</sup> This leads to a planet surface of magma oceans and an
atmosphere of the corresponding high-temperature vapors above
those oceans. Thus, the Knudsen cell may act as a small simulation of
the surface conditions of a hot, rocky exoplanet. In the study by Costa
et al.,<sup>281</sup> olivine and its vapor were examined using KEMS. Olivine
was selected as a test material, because it is the principal constituent
of the earth's mantle and may be a reasonable approximation to an
exoplanet surface composition. The study of exoplanets is one of the
most exciting areas in modern astrophysics, and KEMS can play an
important role in this.

4.5 | Nuclear applications

Another growth area for KEMS is its application to the nuclear field. As noted in the ultrahigh-temperature materials section, KEMS has provided excellent data on nuclear materials such as UO₂, MOX (mixed oxide, plutonium-blended uranium fuel), UC, and UN. Earlier reviews<sup>190,283</sup> have presented this work in detail. A recent reference work<sup>284</sup> on fuel chemistry reports further information on KEMS studies in this field.

Recent KEMS studies in the nuclear field are heavily influenced
by events such as climate change,<sup>285</sup> energy supply issues,<sup>286</sup> and
decommissioned irradiation facilities for medical isotope
production.<sup>287</sup> Advanced reactors such as small modular reactors,
reactors developed in GEN IV, and alternative research reactors are
drawing attention in this context. There are many ongoing advanced
reactor development efforts, funded by both the public and private
sectors.<sup>288</sup> Some of these new reactor concepts need investigations
on new fuels. KEMS is the key technique for such studies. Nuclear
fuel, in its environment, under normal or accidental conditions, is a
very complex system for which the thermodynamic properties need
to be assessed before implementation in a commercial or research
reactor. KEMS has long been a key technique used to investigate
nuclear fuel behavior. KEMS investigations in this field provide unique
key data on partial vapor pressures, component activities, and
nonideal solution behavior (e.g., the behavior of fission products in
oxide fuels). These data are all essential for the safety and licensing of
a nuclear fuel. Nuclear waste is also an important domain in which
KEMS studies play a key role.

4.5.1 | Molten salt fuels

Molten salt reactors (MSR) are the only reactors using liquid as fuel.
Fissile material and fission product are dissolved in the liquid, which is

also used as a coolant. A fuel treatment unit can be included in the
liquid loop to reprocess the fuel during irradiation. One reactor of this
type is the well-known Oak Ridge molten fluoride reactor built in the
1960s. Two kinds of fuels are considered for MSRs: chlorides and
fluorides. Both have different chemical and neutronic characteristics.
Depending on the function of the fuel and its composition, different
kinds of reactors can be built. With a thermal neutron spectrum,
reactors can burn <sup>235</sup>U, which represents only a fraction of the
uranium extracted, or breed <sup>233</sup>U from natural thorium, <sup>232</sup>Th, which
is more abundant in the earth's crust but requires significantly more
expensive extraction methods. Reactors with a fast neutron spectrum
can burn plutonium and other transuranium actinides, which thus
reduce nuclear waste and breed <sup>238</sup>U and <sup>232</sup>Th to form <sup>239</sup>Pu and
<sup>233</sup>U, respectively. These can then be used as fuel. The salts are also
used for pyrometallurgical processes in nuclear industry.

Many studies on these salts have been conducted using KEMS. Some examples follow. Tosolin et al.<sup>289,290</sup> have reported thermodynamic data from KEMS on the LiF-ThF<sub>4</sub>-UF<sub>4</sub> and LiF-ThF<sub>4</sub>-UF<sub>4</sub>-PuF<sub>3</sub> systems. Vozárová et al.<sup>291</sup> published KEMS-derived thermodynamic data for the CsF-ThF<sub>4</sub> system. Capelli et al.<sup>292</sup> reported data on Li<sub>x</sub>Th(1-x)F<sub>4-x</sub>, and Mishra<sup>293</sup> and McMurray et al.<sup>294</sup> presented data on FLiNaK. On the chloride side, Trinadh et al.<sup>108</sup> performed measurements on LiCl-KCl-UCl<sub>3</sub>. Beneš<sup>295</sup> have measured the vaporization behavior of Cs and I from fluoride melts. Taira<sup>296</sup> have studied the behavior of simulated fission products in solution for different fuel compositions. Hania<sup>297</sup> has studied irradiated molten salt fuels targeted for KEMS measurements. There is limited published information on molten chloride fuels. KEMS investigations related the development of molten chloride fast reactors as ongoing.

4.5.2 | Liquid metal coolants and metallic fuels

Liquid lead-bismuth eutectic is another important material for an advanced nuclear reactor. It is used as a primary coolant in lead-cooled fast reactors and as a fuel and coolant in accelerator-driven systems. Luongo et al.<sup>298</sup> have studied lead iodide decomposition, which is relevant for this fuel.

Metallic fuels, such as dispersion fuels, are used in research
reactors. Trinadh et al. have published KEMS studies of the U-Al
system.<sup>299,300</sup> The U-Pu-Zr system is a potential driver fuel for fast
breeder reactors. Two compositions in this ternary have also been
investigated by Trinadh et al.<sup>301</sup> Recent KEMS studies on the Gd-Al
system focus on the potential of separating actinides from the
lanthanides.<sup>302</sup>

4.5.3 | Oxide fuels

Oxides fuels are the most used in current and advanced reactors. A
large amount of literature is available and can be found in earlier
reviews, including data on highly radiotoxic oxides.<sup>77,80,303</sup> Most
recently, in the field of fast reactors for transmutation, Smith et al. have published a thermodynamic study of the Np-O system, which included KEMS measurements and thermodynamic modeling.<sup>304</sup> Refractory ceramic oxides are also important for other nuclear issues such as nuclear waste immobilization, fuel cladding, and severe accident containment. KEMS studies on the following relevant systems have recently been reported: Sm<sub>2</sub>O<sub>3</sub>-ZrO<sub>2</sub>.<sup>67,305</sup> UO<sub>2</sub>-ZrO<sub>2</sub>.<sup>306</sup> and Sm<sub>2</sub>O<sub>3</sub>-ZrO<sub>2</sub>-HfO<sub>2</sub>.<sup>244,307</sup>

### 4.5.4 | Interacting materials, coupled diffusion/desorption, and vaporization measurements

Understanding the interaction of materials in a reactor is another area in which KEMS can play a crucial role. Regarding the interaction of fission products with their environment during severe accidents, Stolyarova and colleagues have published thermodynamic studies on the Cs<sub>2</sub>O-B<sub>2</sub>O<sub>3</sub><sup>211</sup> and Cs<sub>2</sub>O-MoO<sub>3</sub><sup>212</sup> systems. Nakajima published a KEMS study on CsBO<sub>2</sub>.<sup>308</sup> As noted earlier, the study on the thermal decomposition of lead iodide<sup>298</sup> is important in the interaction of fission products and lead-cooled reactors.

Structural materials used in the complete fuel cycle present high mechanical, thermal, and chemical constraints. A recent KEMS study reports thermodynamic measurements in structural nickel-base alloys and steel used by the fuel enrichment process.<sup>181</sup>

After the Fukushima accident in Japan, accident-tolerant fuels drew attention. Braun et al. have recently reported KEMS studies on the chemical compatibility of UO₂ fuel and an SiC coating.<sup>309</sup>

The behavior of fission products in a reactor has been discussed briefly for MSRs. For other systems, Trinadh et al. and Manikandan et al. have published studies on the Sn-Te-O and U-Sn systems, which are important for fuel safety, accident conditions, and pyro reprocessing.<sup>310,311</sup> Stolyarova et al.<sup>312</sup> have recently reported thermodynamic data and vaporization behavior of Cs, Sr, and Ba compounds relevant to nuclear safety.

Fission products or helium release behavior studies using KEMS are important to mention here. These studies address safety-relevant aspects such as radioisotope release during accidents but also fuel properties during normal operation. They combine the measurement of vaporization at equilibrium with the measurement of the release of volatile elements (or compounds) present in the material studied. This reveals interesting information on the temperature-driven diffusion processes of those volatile elements and their consequences in the material like precipitation, bubble formation, release from the matrix, the role of grain boundaries, diffusion enthalpies, and solubility. Such data are needed to understand the fuel behavior in normal and accidental operations as well as in storage conditions. Fission product release behavior from nuclear fuel has been extensively studied using KEMS. A recent example reports the comparative fission product release behavior of a homogeneous and a heterogeneous high-burn-up MOX nuclear fuel.<sup>313</sup> Other examples demonstrate the measurement using KEMS of helium solubility in stoichiometric and hyper-stoichiometric UO₂<sup>314</sup> or in La-doped UO₂ as a surrogate of

hypo-stoichiometric UO₂.<sup>315</sup> In the later study, the spent fuel storage/ disposal aspect is addressed. Diffusion and release properties of radiogenic helium need to be assessed for the prediction of material long-term behavior (spent fuel, radioisotopic thermal generator, actinide-bearing fuels). A most recent KEMS study of Luzzi et al.<sup>316</sup> reports measured helium release in the investigation of the solubility and release behavior of helium in a nuclear fuel.

### 4.5.5 | Sorption/desorption of fission products from graphite

Understanding the sorption/desorption of fission products from fuel element matrix graphite is very important in the event of an accident. Several recent publications on desorption isotherms have been obtained using a KEMS system. Hilpert et al. have studied the sorption of Sr and Cs on graphitic materials<sup>317,318</sup> using KEMS. Seelig et al.<sup>129</sup> and Walton et al.<sup>319</sup> have used KEMS to study sorption of Ag on graphitic materials. Other methods can, of course, be used to study sorption, but KEMS has proven to be very versatile for these applications given its high sensitivity. The method described in the KEMS studies<sup>129,317-319</sup> involves doping nuclear graphite with a nonradioactive isotope of the particular fission product of interest. A series of fission product loadings are examined using KEMS to derive partial pressures of vapor species as a function of temperature. The loading-dependent Sr enthalpy of vaporization,<sup>317</sup> as shown in Figure 22, indicates Sr is strongly chemisorbed on graphite. The loading dependence of partial pressures of the vapor species can be used to derive a sorption isotherm. Walton et al.<sup>319</sup> have examined Langmuir, IAEA-Freundlich, and IAEA-isotherm models for Ag desorption from NBG-17 graphite powders. For this particular case, Langmuir and IAEA-isotherm models gave the best fit.

## 4.6 | Low-volatility organics and organometallics

The lack of vapor pressure data for multifunctional condensable organic compounds formed from gas phase volatile organic carbon oxidation has led to the development of a novel KEMS device capable of performing such measurements. The design was adapted from high-temperature alloy measurements to study low-volatile organics. The challenge of such measurements is to fulfill the Knudsen conditions and to ensure equilibrium conditions in the temperature range of ~300 K. Most of the measurements comprise only a temperature range from 30 K. For this type of study, a special Knudsen cell was fabricated with a knife-edged orifice of 200-µm diameter. The cell was heated by a coaxially mounted flexible polyimide heating element. The molecular beam effusing out of the Knudsen cell was ionized by a cross-beam electron gun. The ions are separated in a quadrupole mass filter and detected by a classical secondary electron multiplier or a Faraday cup. The system consists of two vacuum chambers, one for housing the sample and Knudsen cell
<figure><img src="image_42.png" /></figure>

recently, in the field of fast reactors for transmutation, Smith et al. have published a thermodynamic study of the Np-O system, which included KEMS measurements and thermodynamic modeling.<sup>304</sup> Refractory ceramic oxides are also important for other nuclear issues such as nuclear waste immobilization, fuel cladding, and severe accident containment. KEMS studies on the following relevant systems have recently been reported: Sm<sub>2</sub>O<sub>3</sub>-ZrO<sub>2</sub><sup>67,305</sup> UO<sub>2</sub>-ZrO<sub>2</sub><sup>306</sup> and Sm<sub>2</sub>O<sub>3</sub>-ZrO<sub>2</sub>-HfO<sub>2</sub>.<sup>244,307</sup>

### 4.5.4 | Interacting materials, coupled diffusion/desorption, and vaporization measurements

Understanding the interaction of materials in a reactor is another area in which KEMS can play a crucial role. Regarding the interaction of fission products with their environment during severe accidents, Stolyarova and colleagues have published thermodynamic studies on the Cs<sub>2</sub>O-B<sub>2</sub>O<sub>3</sub><sup>211</sup> and Cs<sub>2</sub>O-MoO<sub>3</sub><sup>212</sup> systems. Nakajima published a KEMS study on CsBO<sub>2</sub>.<sup>308</sup> As noted earlier, the study on the thermal decomposition of lead iodide<sup>298</sup> is important in the interaction of fission products and lead-cooled reactors.

Structural materials used in the complete fuel cycle present high mechanical, thermal, and chemical constraints. A recent KEMS study reports thermodynamic measurements in structural nickel-base alloys and steel used by the fuel enrichment process.<sup>181</sup>

After the Fukushima accident in Japan, accident-tolerant fuels drew attention. Braun et al. have recently reported KEMS studies on the chemical compatibility of UO₂ fuel and an SiC coating.<sup>309</sup>

The behavior of fission products in a reactor has been discussed briefly for MSRs. For other systems, Trinadh et al. and Manikandan et al. have published studies on the Sn-Te-O and U-Sn systems, which are important for fuel safety, accident conditions, and pyro reprocessing.<sup>310,311</sup> Stolyarova et al.<sup>312</sup> have recently reported thermodynamic data and vaporization behavior of Cs, Sr, and Ba compounds relevant to nuclear safety.

Fission products or helium release behavior studies using KEMS are important to mention here. These studies address safety-relevant aspects such as radioisotope release during accidents but also fuel properties during normal operation. They combine the measurement of vaporization at equilibrium with the measurement of the release of volatile elements (or compounds) present in the material studied. This reveals interesting information on the temperature-driven diffusion processes of those volatile elements and their consequences in the material like precipitation, bubble formation, release from the matrix, the role of grain boundaries, diffusion enthalpies, and solubility. Such data are needed to understand the fuel behavior in normal and accidental operations as well as in storage conditions. Fission product release behavior from nuclear fuel has been extensively studied using KEMS. A recent example reports the comparative fission product release behavior of a homogeneous and a heterogeneous high-burn-up MOX nuclear fuel.<sup>313</sup> Other examples demonstrate the measurement using KEMS of helium solubility in stoichiometric and hyper-stoichiometric UO₂<sup>314</sup> or in La-doped UO₂ as a surrogate of

hypo-stoichiometric UO₂.<sup>315</sup> In the later study, the spent fuel storage/ disposal aspect is addressed. Diffusion and release properties of radiogenic helium need to be assessed for the prediction of material long-term behavior (spent fuel, radioisotopic thermal generator, actinide-bearing fuels). A most recent KEMS study of Luzzi et al.<sup>316</sup> reports measured helium release in the investigation of the solubility and release behavior of helium in a nuclear fuel.

### 4.5.5 | Sorption/desorption of fission products from graphite

Understanding the sorption/desorption of fission products from fuel element matrix graphite is very important in the event of an accident. Several recent publications on desorption isotherms have been obtained using a KEMS system. Hilpert et al. have studied the sorption of Sr and Cs on graphitic materials<sup>317,318</sup> using KEMS. Seelig et al.<sup>129</sup> and Walton et al.<sup>319</sup> have used KEMS to study sorption of Ag on graphitic materials. Other methods can, of course, be used to study sorption, but KEMS has proven to be very versatile for these applications given its high sensitivity. The method described in the KEMS studies<sup>129,317-319</sup> involves doping nuclear graphite with a nonradioactive isotope of the particular fission product of interest. A series of fission product loadings are examined using KEMS to derive partial pressures of vapor species as a function of temperature. The loading-dependent Sr enthalpy of vaporization,<sup>317</sup> as shown in Figure 22, indicates Sr is strongly chemisorbed on graphite. The loading dependence of partial pressures of the vapor species can be used to derive a sorption isotherm. Walton et al.<sup>319</sup> have examined Langmuir, IAEA-Freundlich, and IAEA-isotherm models for Ag desorption from NBG-17 graphite powders. For this particular case, Langmuir and IAEA-isotherm models gave the best fit.

## 4.6 | Low-volatility organics and organometallics

The lack of vapor pressure data for multifunctional condensable organic compounds formed from gas phase volatile organic carbon oxidation has led to the development of a novel KEMS device capable of performing such measurements. The design was adapted from high-temperature alloy measurements to study low-volatile organics. The challenge of such measurements is to fulfill the Knudsen conditions and to ensure equilibrium conditions in the temperature range of ~300 K. Most of the measurements comprise only a temperature range from 30 K. For this type of study, a special Knudsen cell was fabricated with a knife-edged orifice of 200-µm diameter. The cell was heated by a coaxially mounted flexible polyimide heating element. The molecular beam effusing out of the Knudsen cell was ionized by a cross-beam electron gun. The ions are separated in a quadrupole mass filter and detected by a classical secondary electron multiplier or a Faraday cup. The system consists of two vacuum chambers, one for housing the sample and Knudsen cell
<figure><img src="image_43.png" /></figure>

<figure><img src="image_44.png" /><figcaption>**FIGURE 22** Enthalpy of vaporization for Sr from nuclear-grade graphite. Source: Reprinted from Hilpert et al.,³¹⁸ with permission from Wiley-VCH, GmbH.</figcaption></figure>

and the other for the measurement systems. They are separated from each other by a vacuum-tight gate valve.

A further challenge for the determination of vapor pressures for organic systems is to find a suitable calibration specimen of which pressure data are well established in the literature. The following compounds have been selected: benzophenone, ferrocene, or diphenylmethane. The proof of the development of a simple KEMS system was given in 2009 by measuring the vapor pressures of dicarboxylic acid.³²⁰ The device has been built at the University of Manchester (UK) and has since been used to determine vapor pressure data for a number of organic systems. Kudin et al. have studied the thermochemistry of 5,10,15,20-tetraphenylporphyrin.³²¹ The extension of KEMS to low temperatures opens up the possibility of novel ionization methods to limit fragmentation. Booth and colleagues³²² described the use of a lithium ion attachment technique to form ions without fragmentation in mass spectra of a vapor over the compounds studied.

KEMS studies on organometallic compounds have been published at SIMaP.²¹,³²³,³²⁴ As these compounds show ignition under atmospheric pressure, the cell is fitted with a valve controlled from outside. The sample is loaded and held in a glove box before transfer to the mass spectrometer. The cell (see Figure 2F) is then opened under vacuum when starting an experiment. Thermodynamic measurements of organometallic vapor pressures require a coupling of a restricted collimation device, a liquid-nitrogen-cooled ionization

box, and a “free” shutter blade to distinguish the signal from secondary reflections in the vacuum chamber. These were described in previous sections of this review. The Knudsen cell furnace has been designed as a double envelope with a circulating liquid and temperature range of 233–473 K. Saturated pressure of the PDMAT (pentakis (dimethylamino) tantalum)—usually believed to be the same molecule as the solid or liquid compound as for organic compounds— has been determined to correspond to at least two main molecules from Ta⁴⁺ to Ta⁵⁺. Then the Knudsen is fitted with an upper cell to study high-temperature cracking of these molecules useful for the understanding of chemical vapor deposition or atomic layer deposition processes.

## 4.7 | Lithium ion battery applications

KEMS has recently been used more for the determination of low temperature and room temperature thermodynamic data. Such an approach is used in the determination of data for various lithiation states of lithium ion battery electrode materials. One example for that is the development of lighter and anode materials that also show less volume change on lithiation. Henriques and coworkers have determined thermodynamic data in the ternary alloy system Cu–Li–Sn using KEMS for the solid, solid–liquid, and liquid regions. Thermodynamic activities of components, enthalpies, and entropies of mixing were measured.³²⁵,³²⁶ This work was directly supported using CALPHAD-type modeling.²³⁶

# 5 | SUMMARY AND CONCLUSIONS

KEMS has long been a central tool in physical chemistry, and it has many applications in related fields. There are many excellent reviews on the basic concepts of this technique.¹⁻¹¹,¹⁸,⁸⁷ In this review, we focus on the current and future status of the field. The first part of the review covers instrumentation and progress in methodology. Modern simulation methods of both the neutral beam and the ionization processes can lead to many design improvements for better sensitivity, resolution, and background/noise rejection. Newer heating systems and temperature measurement devices offer better control and measurement of temperature to higher (and lower) limits. Data acquisition systems allow computer control of nearly all aspects of an experiment. Given the nonroutine nature of a KEMS experiment, it may not be possible to fully automate an experiment; nonetheless, data acquisition systems make measurements easier and more precise.

The second part of this review focuses on actual measurements and applications. We focus on current topics that show promise for the future, although the areas covered are by no means exhaustive. KEMS has always been a prime tool for analysis of vapor composition and then measurement of vapor pressures as a function of temperature and thus obtaining thermodynamic data of pure compounds and gaseous species. A key area is now coupling these
<figure><img src="image_43.png" /></figure>

<figure><img src="image_44.png" /><figcaption>**FIGURE 22** Enthalpy of vaporization for Sr from nuclear-grade graphite. Source: Reprinted from Hilpert et al.,³¹⁸ with permission from Wiley-VCH, GmbH.</figcaption></figure>

and the other for the measurement systems. They are separated from each other by a vacuum-tight gate valve.

A further challenge for the determination of vapor pressures for organic systems is to find a suitable calibration specimen of which pressure data are well established in the literature. The following compounds have been selected: benzophenone, ferrocene, or diphenylmethane. The proof of the development of a simple KEMS system was given in 2009 by measuring the vapor pressures of dicarboxylic acid.³²⁰ The device has been built at the University of Manchester (UK) and has since been used to determine vapor pressure data for a number of organic systems. Kudin et al. have studied the thermochemistry of 5,10,15,20-tetraphenylporphyrin.³²¹ The extension of KEMS to low temperatures opens up the possibility of novel ionization methods to limit fragmentation. Booth and colleagues³²² described the use of a lithium ion attachment technique to form ions without fragmentation in mass spectra of a vapor over the compounds studied.

KEMS studies on organometallic compounds have been published at SIMaP.²¹,³²³,³²⁴ As these compounds show ignition under atmospheric pressure, the cell is fitted with a valve controlled from outside. The sample is loaded and held in a glove box before transfer to the mass spectrometer. The cell (see Figure 2F) is then opened under vacuum when starting an experiment. Thermodynamic measurements of organometallic vapor pressures require a coupling of a restricted collimation device, a liquid-nitrogen-cooled ionization

box, and a “free” shutter blade to distinguish the signal from secondary reflections in the vacuum chamber. These were described in previous sections of this review. The Knudsen cell furnace has been designed as a double envelope with a circulating liquid and temperature range of 233–473 K. Saturated pressure of the PDMAT (pentakis (dimethylamino) tantalum)—usually believed to be the same molecule as the solid or liquid compound as for organic compounds— has been determined to correspond to at least two main molecules from Ta⁴⁺ to Ta⁵⁺. Then the Knudsen is fitted with an upper cell to study high-temperature cracking of these molecules useful for the understanding of chemical vapor deposition or atomic layer deposition processes.

## 4.7 | Lithium ion battery applications

KEMS has recently been used more for the determination of low temperature and room temperature thermodynamic data. Such an approach is used in the determination of data for various lithiation states of lithium ion battery electrode materials. One example for that is the development of lighter and anode materials that also show less volume change on lithiation. Henriques and coworkers have determined thermodynamic data in the ternary alloy system Cu–Li–Sn using KEMS for the solid, solid–liquid, and liquid regions. Thermodynamic activities of components, enthalpies, and entropies of mixing were measured.³²⁵,³²⁶ This work was directly supported using CALPHAD-type modeling.²³⁶

# 5 | SUMMARY AND CONCLUSIONS

KEMS has long been a central tool in physical chemistry, and it has many applications in related fields. There are many excellent reviews on the basic concepts of this technique.¹⁻¹¹,¹⁸,⁸⁷ In this review, we focus on the current and future status of the field. The first part of the review covers instrumentation and progress in methodology. Modern simulation methods of both the neutral beam and the ionization processes can lead to many design improvements for better sensitivity, resolution, and background/noise rejection. Newer heating systems and temperature measurement devices offer better control and measurement of temperature to higher (and lower) limits. Data acquisition systems allow computer control of nearly all aspects of an experiment. Given the nonroutine nature of a KEMS experiment, it may not be possible to fully automate an experiment; nonetheless, data acquisition systems make measurements easier and more precise.

The second part of this review focuses on actual measurements and applications. We focus on current topics that show promise for the future, although the areas covered are by no means exhaustive. KEMS has always been a prime tool for analysis of vapor composition and then measurement of vapor pressures as a function of temperature and thus obtaining thermodynamic data of pure compounds and gaseous species. A key area is now coupling these
<figure><img src="image_45.png" /></figure>

measurements to precision quantum chemistry calculations. These calculations can be used to generate high-fidelity gefs. It has been shown that in many cases, DFT/B3LYP is sufficient to generate these gefs. KEMS measurements of enthalpies of formation and dissociation can also be compared directly to ab intio calculations, giving them added reliability. KEMS is also well suited to the study of solutions. Although first principles can describe some solutions, model-based approaches work well for complex, multicomponent solutions. We discuss the solution thermodynamic parameters that can be fitted to model parameters. The parameters from relatively simple binary and ternary solutions can be combined to develop solution models for complex multicomponent solutions.

Finally, we select a few important applications of KEMS and likely growth areas for KEMS. These include measurement of phase transformations, measurements/control of systems with low oxygen potentials, studies on ultrahigh-temperature materials, applications to geological systems, applications to nuclear systems, and applications to organic and organometallic chemistry. As noted, this list is not exhaustive, and the number of applications of this valuable method can and should continue to grow.

## AUTHOR CONTRIBUTIONS

**Nathan S. Jacobson:** conceptualization; project administration; writing—introduction, portions of the instrumentation section, measurement section, and sections on phase transformations, ultrahigh-temperature materials, measurement and fixing of low oxygen potentials, and geological applications; figures; and overall editing and checking. **Jean-Yves Colle:** writing—section on KEMS in gloveboxes, portions of the data acquisition section, nuclear applications section; figures; and overall editing and checking. **Valentina Stolyarova:** writing—section on measurements of oxide thermodynamics; figures; and overall editing and checking. **Torsten Markus:** writing—portions of the data acquisition section, section on lithium ion battery applications; figures; and overall editing and checking. **Ioana Nuta:** writing—portions of the instrumentation section and section on low-volatility organics and organometallics; figures; and extensive editing and checking.

## ACKNOWLEDGMENTS

The authors thank the many individuals who have contributed to this review. Nathan S. Jacobson thanks his colleagues at NASA for helpful discussion—Drs. Benjamin Kowalski, Rebekah Webster, and particularly Evan Copland (now at the University of Newcastle, Australia). The authors are grateful to Prof. John H. Beynon, founder and first editor of RCM, who promoted KEMS as an important subdiscipline of general mass spectrometry. They thank Dr. Christian Chatillon for his many suggestions for this review. The authors have been fortunate to learn from the pioneers and leaders in KEMS, which include Prof. Dr. Klaus Hilpert, Prof. Alan Searcy, Dr. Donald Hildenbrand, Prof. Paul Gilles, Dr. John Hastie, Dr. Christian Chatillon, Prof. Jean Drowart, Prof. Lev Gorokhov, and Prof. G. A. Semenov. The authors dedicate this review to them.

## DATA AVAILABILITY STATEMENT

Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

## ORCID

Nathan S. Jacobson https://orcid.org/0000-0002-9177-4129

## REFERENCES

1. Inghram M, Drowart J. Mass spectrometry applied to high temperature chemistry. *High Temp Technol.* 1960;219-240.

2. Drowart J, Goldfinger P. Investigation of inorganic systems at high temperature by mass spectrometry. *Angew Chem Int Ed.* 1967;6(7): 581-648. doi:10.1002/anie.196705811

3. Cater ED. The effusion method at age 69: current state of the art. In: Hastie JW, ed. *Characterization of High Temperature Vapors and Gases*. U. S. Government Printing Office; 1979:3-38.

4. Grimley RT. Mass spectrometry. In: Margrave JL, ed. *The Characterization of High Temperature Vapors*. Wiley; 1967:195-243.

5. Stolyarova VL, Semenov GA. In: Beynon JH, ed. *Mass Spectrometric Study of the Vaporization of Oxide Systems*. Wiley; 1994.

6. Kato E. Thermodynamic studies of metallurgical systems by mass spectrometry. *J Mass Spectrom Soc Japan.* 1993;41(6):297-316. doi:10.5702/massspec.41.297

7. Hilpert K. High-temperature mass-spectrometry in materials research. *Rapid Commun Mass Spectrom.* 1991;5(4):175-187. doi:10.1002/rcm.1290050408

8. Gorokov L, Semenov G. Mass spectrometric studies in high-temperature chemistry. *Adv Mass Spectrometry*. 1971;5:349.

9. Gorokhov L. High-temperature mass spectrometry. *Adv Mass Spectrom.* 1989;11B:1064-1077.

10. Rose ME, Plante E, Haltle J. High-temperature mass spectrometric studies of inorganic systems. In: *Mass Spectrometry*. Royal Society of Chemistry; 1989:357-378. doi:10.1039/9781847556677-00357

11. Johnston G. High-temperature vaporization studies using Knudsen cell mass spectrometry—a review. *J Aust Inst Metals.* 1974;19(2): 106-115.

12. Knudsen M. Experimental determination of the vapor pressure of mercury at 0° and at higher temperatures. *Ann Phys.* 1909;29(6): 179-193. doi:10.1002/andp.19093340614

13. Santeler DJ. New concepts in molecular gas flow. *J Vac sic Technol* A. 1986;4(3):338-343. doi:10.1116/1.573923

14. Jacobson NS. Silica activity measurements in the Y₂O₃-SiO₂ system and applications to modeling of coating volatility. *J am Ceram Soc.* 2014;97(6):1959-1965. doi:10.1111/jace.12974

15. Bauschlicher CW Jr, Kowalski BA, Jacobson NS. Quantum chemical and experimental thermodynamic studies of HfO(g). *J Chem Phys.* 2022;157(15):154302. doi:10.1063/5.0120504

16. Rocabois P, Chatillon C, Bernard C. Thermodynamics of the Si-C system I. mass spectrometry studies of the condensed phases at high temperature. *High Temp-High Press.* 1995;27(1):3-23. doi:10.1068/htrt35

17. Meschi DJ, Chupka WA, Berkowitz J. Heterogeneous reactions studied by mass spectrometry. I. Reaction of B₂O₃(s) with H₂O(g). *J Chem Phys.* 1960;33(2):530-533. doi:10.1063/1.1731179

18. Copland EH, Jacobson NS. *Measuring Thermodynamic Properties of Metals and Alloys with Knudsen Effusion Mass Spectrometry*. NASA/TP--2010-216795

19. Chatillon C, Malheiros L-F, Rocabois P, Jeymond M. High-temperature mass spectrometry with the Knudsen cell: II. Technical constraints in the multiple-cell method for activity determinations. *High Temp-High Press.* 2002;34(2):213-233. doi:10.1068/htjr021
measurements to precision quantum chemistry calculations. These calculations can be used to generate high-fidelity gefs. It has been shown that in many cases, DFT/B3LYP is sufficient to generate these gefs. KEMS measurements of enthalpies of formation and dissociation can also be compared directly to ab intio calculations, giving them added reliability. KEMS is also well suited to the study of solutions. Although first principles can describe some solutions, model-based approaches work well for complex, multicomponent solutions. We discuss the solution thermodynamic parameters that can be fitted to model parameters. The parameters from relatively simple binary and ternary solutions can be combined to develop solution models for complex multicomponent solutions.

Finally, we select a few important applications of KEMS and likely growth areas for KEMS. These include measurement of phase transformations, measurements/control of systems with low oxygen potentials, studies on ultrahigh-temperature materials, applications to geological systems, applications to nuclear systems, and applications to organic and organometallic chemistry. As noted, this list is not exhaustive, and the number of applications of this valuable method can and should continue to grow.

## AUTHOR CONTRIBUTIONS

**Nathan S. Jacobson:** conceptualization; project administration; writing—introduction, portions of the instrumentation section, measurement section, and sections on phase transformations, ultrahigh-temperature materials, measurement and fixing of low oxygen potentials, and geological applications; figures; and overall editing and checking. **Jean-Yves Colle:** writing—section on KEMS in gloveboxes, portions of the data acquisition section, nuclear applications section; figures; and overall editing and checking. **Valentina Stolyarova:** writing—section on measurements of oxide thermodynamics; figures; and overall editing and checking. **Torsten Markus:** writing—portions of the data acquisition section, section on lithium ion battery applications; figures; and overall editing and checking. **Ioana Nuta:** writing—portions of the instrumentation section and section on low-volatility organics and organometallics; figures; and extensive editing and checking.

## ACKNOWLEDGMENTS

The authors thank the many individuals who have contributed to this review. Nathan S. Jacobson thanks his colleagues at NASA for helpful discussion—Drs. Benjamin Kowalski, Rebekah Webster, and particularly Evan Copland (now at the University of Newcastle, Australia). The authors are grateful to Prof. John H. Beynon, founder and first editor of RCM, who promoted KEMS as an important subdiscipline of general mass spectrometry. They thank Dr. Christian Chatillon for his many suggestions for this review. The authors have been fortunate to learn from the pioneers and leaders in KEMS, which include Prof. Dr. Klaus Hilpert, Prof. Alan Searcy, Dr. Donald Hildenbrand, Prof. Paul Gilles, Dr. John Hastie, Dr. Christian Chatillon, Prof. Jean Drowart, Prof. Lev Gorokhov, and Prof. G. A. Semenov. The authors dedicate this review to them.

## DATA AVAILABILITY STATEMENT

Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

## ORCID

Nathan S. Jacobson

<figure><img src="image_45.png" /></figure>

https://orcid.org/0000-0002-9177-4129

## REFERENCES

1. Inghram M, Drowart J. Mass spectrometry applied to high temperature chemistry. *High Temp Technol.* 1960;219-240.

2. Drowart J, Goldfinger P. Investigation of inorganic systems at high temperature by mass spectrometry. *Angew Chem Int Ed.* 1967;6(7): 581-648. doi:10.1002/anie.196705811

3. Cater ED. The effusion method at age 69: current state of the art. In: Hastie JW, ed. *Characterization of High Temperature Vapors and Gases*. U. S. Government Printing Office; 1979:3-38.

4. Grimley RT. Mass spectrometry. In: Margrave JL, ed. *The Characterization of High Temperature Vapors*. Wiley; 1967:195-243.

5. Stolyarova VL, Semenov GA. In: Beynon JH, ed. *Mass Spectrometric Study of the Vaporization of Oxide Systems*. Wiley; 1994.

6. Kato E. Thermodynamic studies of metallurgical systems by mass spectrometry. *J Mass Spectrom Soc Japan.* 1993;41(6):297-316. doi:10.5702/massspec.41.297

7. Hilpert K. High-temperature mass-spectrometry in materials research. *Rapid Commun Mass Spectrom.* 1991;5(4):175-187. doi:10.1002/rcm.1290050408

8. Gorokov L, Semenov G. Mass spectrometric studies in high-temperature chemistry. *Adv Mass Spectrometry*. 1971;5:349.

9. Gorokhov L. High-temperature mass spectrometry. *Adv Mass Spectrom.* 1989;11B:1064-1077.

10. Rose ME, Plante E, Haltle J. High-temperature mass spectrometric studies of inorganic systems. In: *Mass Spectrometry*. Royal Society of Chemistry; 1989:357-378. doi:10.1039/9781847556677-00357

11. Johnston G. High-temperature vaporization studies using Knudsen cell mass spectrometry—a review. *J Aust Inst Metals.* 1974;19(2): 106-115.

12. Knudsen M. Experimental determination of the vapor pressure of mercury at 0° and at higher temperatures. *Ann Phys.* 1909;29(6): 179-193. doi:10.1002/andp.19093340614

13. Santeler DJ. New concepts in molecular gas flow. *J Vac sic Technol* A. 1986;4(3):338-343. doi:10.1116/1.573923

14. Jacobson NS. Silica activity measurements in the Y₂O₃-SiO₂ system and applications to modeling of coating volatility. *J am Ceram Soc.* 2014;97(6):1959-1965. doi:10.1111/jace.12974

15. Bauschlicher CW Jr, Kowalski BA, Jacobson NS. Quantum chemical and experimental thermodynamic studies of HfO(g). *J Chem Phys.* 2022;157(15):154302. doi:10.1063/5.0120504

16. Rocabois P, Chatillon C, Bernard C. Thermodynamics of the Si-C system I. mass spectrometry studies of the condensed phases at high temperature. *High Temp-High Press.* 1995;27(1):3-23. doi:10.1068/htrt35

17. Meschi DJ, Chupka WA, Berkowitz J. Heterogeneous reactions studied by mass spectrometry. I. Reaction of B₂O₃(s) with H₂O(g). *J Chem Phys.* 1960;33(2):530-533. doi:10.1063/1.1731179

18. Copland EH, Jacobson NS. *Measuring Thermodynamic Properties of Metals and Alloys with Knudsen Effusion Mass Spectrometry*. NASA/TP--2010-216795

19. Chatillon C, Malheiros L-F, Rocabois P, Jeymond M. High-temperature mass spectrometry with the Knudsen cell: II. Technical constraints in the multiple-cell method for activity determinations. *High Temp-High Press.* 2002;34(2):213-233. doi:10.1068/htjr021
<figure><img src="image_46.png" /></figure>

20. Detry D, Drowart J, Goldfing P, Keller H, Rickert H. Zur Thermodynamik Von Schwefeldampf-Massenspektrometrische Untersuchungen Mit Der Elektrochemischen Knudsen-Zelle. Z Phys Chem Neue Fol. 1967;55(5-6):314-319. doi:10.1524/zpch.1967.55.5.6.314

21. Violet P, Nuta I, Artaud L, Collas H, Blanquet E, Chatillon C. A special reactor coupled with a high-temperature mass spectrometer for the investigation of the vaporization and cracking of organometallic compounds. Rapid Commun Mass Spectrom. 2009;23(6):793-800. doi:10.1002/rcm.3942

22. Colle J-Y, Capone F. Very high temperature laser heated furnace for Knudsen cell mass spectrometry. Rev Sci Instrum. 2008;79(5):055105. doi:10.1063/1.2918135

23. Shilov A. Vaporizers for KEMS: measurement errors depending on their design. ECS Transactions. 2013;46(1):187-190. doi:10.1149/04601.0187ecst

24. Cater ED. Vapor pressure measurements A. measurement of the gross equilibrium vaporization rate (Knudsen Methods). In: Rapp RA, ed. Physicochemical Methods in Metals Research. Techniques of Metals Research. IV. John Wiley & Sons, Inc.; 1970:21-94.

25. Solorio-Leyva JC, Suárez-Romero JG, Cortés-Reynoso JG, Hurtado-Ramos JB, Tepichín-Rodríguez E. Corrections of size-of-source effect and distance effect in radiometric measurements of radiance. Appl Optics. 2005;44(13):2511-2518. doi:10.1364/AO.44.002511

26. Ackermann RJ, Garg SP, Rauh EJ. High-temperature phase diagram for the system Zr-O. J am Ceram Soc. 1977;60(7-8):341-345. doi:10.1111/j.1151-2916.1977.tb15557.x

27. Bhatt Y, Venkataramani R, Garg S. Measurements of eutectic temperatures in the metal-rich regions of several MC systems. J Less-Common Met. 1987;132(2):21-24. doi:10.1016/0022-5088(87)90590-X

28. Balakrishnan S, Ananthasivan K, Kumar KH. Measurement of the solidus and liquidus in the U-Zr system by the spot-technique. J Alloys Compd. 2016;689:751-758. doi:10.1016/j.jallcom.2016.07.252

29. Preston-Thomas H. International temperature scale of 1990 (ITS-90). Metrologia. 1990;27(1):3-10. doi:10.1088/0026-1394/27/1/002

30. Yamada Y, Sakate H, Sakuma F, Ono A. High-temperature fixed points in the range 1150 C to 2500 C using metal-carbon eutectics. Metrologia. 2001;38(3):213-219. doi:10.1088/0026-1394/38/3/3

31. Hildenbrand D. Attainment of chemical equilibrium in effusive beam sources of the heterogeneous reaction type. In: Hastie J, ed. Characterization of High Temperature Vapors and Gases. U. S. Government Printing Office; 1979:171-180.

32. Whitman CI. On the measurement of vapor pressures by effusion. J Chem Phys. 1952;20(1):161-164. doi:10.1063/1.1700161

33. Motzfeldt K. The thermal decomposition of sodium carbonate by the effusion method. J Phys Chem. 1955;59(2):139-147. doi:10.1021/j150524a011

34. Paule RC, Margrave JL. Free-evaporation and effusion techniques. In: Margrave JL, ed. The Characterization of High-Temperature Vapors. John Wiley & Sons; 1967.

35. Kulkarni A, Worrell W. High-temperature thermodynamic properties of the chromium carbides determined using the torsion-effusion technique. Metall Trans A. 1972;3(9):2363-2370. doi:10.1007/BF02647039

36. Rocabois P, Chatillon C, Bernard C. Vapor-pressure and evaporation coefficient of SiO (amorphous) and SiO₂(s)+Si(s) mixtures by the multiple Knudsen cell mass-spectrometric method. Rev Int Hautes Temp. 1992;28(2):37-48.

37. WC DM. The Problem of Knudsen Flow. Part I. General Theory. Oak Ridge Gaseous Diffusion Plant (K-25); 1956.

38. DeMarcus WC, Hopper E. Knudsen flow through a circular capillary. J Chem Phys. 1955;23(7):1344. doi:10.1063/1.1742272

39. Davis DH. Monte Carlo calculation of molecular flow rates through a cylindrical elbow and pipes of other shapes. J Appl Phys. 1960;31(7):1169-1176. doi:10.1063/1.1735797

40. Rosenblatt GM. Evaporation from Solids. In: Hannay NB, ed. Treatise on Solid State Chemistry. Springer; US, 1976:165-240. doi:10.1007/978-1-4613-4313-4_3

41. Rosenblatt GM. Effect of restrictions to molecular flow upon measurements of vaporization rate and vapor pressure. J Phys Chem. 1967;71(5):1327-1333. doi:10.1021/j100864a022

42. Chatillon C, Nuta I. Mass spectrometric studies of non-equilibrium vaporizations in Knudsen cells: a way to the determination of the nature of kinetic processes. ECS Transactions. 2013;46(1):1-22. doi:10.1149/04601.0001ecst

43. Jacobson N, Lee K, Fox D. Reactions of silicon carbide and silicon (IV) oxide at elevated temperatures. J am Ceram Soc. 1992;75(6):1603-1611. doi:10.1111/j.1151-2916.1992.tb04232.x

44. Heyrman M, Chatillon C. Evaporation/condensation coefficients as determined by the multiple Knudsen effusion cell method. J Phys Chem Solid. 2005;66(2-4):494-497. doi:10.1016/j.jpcs.2004.06.025

45. Rosenblatt GM. Interpretation of Knudsen vapor-pressure measurements on porous solids. J Electrochem Soc. 1963;110(6):563. doi:10.1149/1.2425815

46. Golden DM, Spokes GN, Benson SW. Very low-pressure pyrolysis (VLPP); a versatile kinetic tool. Angew Chem Int Ed. 1973;12(7):534-546. doi:10.1002/anie.197305341

47. Abbasi M, Evans J, Abramson I. Diffusion of gases in porous solids: Monte Carlo simulations in the Knudsen and ordinary diffusion regimes. AIChE J. 1983;29(4):617-624. doi:10.1002/aic.690290415

48. Gorokhov L, Milushin M, Emelyanov A. Knudsen effusion mass spectrometric determination of metal hydroxide stabilities. In: Hastie JW, ed. Materials Chemistry at High Temperatures. Vol.1. Humana Press; 1990:395-403. doi:10.1007/978-1-4612-0481-7_29

49. Heyrman M, Chatillon C, Collas H, Chemin JL. Improvements and new capabilities for the multiple Knudsen cell device used in high-temperature mass spectrometry. Rapid Commun Mass Spectrom. 2004;18(2):163-174. doi:10.1002/rcm.1298

50. Chatillon C, Senillou C, Allibert M, Pattoret A. High-temperature thermodynamical studies by a mass spectrometry device for measurements using multiple effusion cells. Rev Sci Instrum. 1976;47(3):334-340. doi:10.1063/1.1134618

51. Heyrman M, Chatillon C. Methodological improvements in the multiple Knudsen cell mass spectrometry. J Phys Chem Solid. 2005;66(2-4):376-378. doi:10.1016/j.jpcs.2004.06.076

52. Johnston G, Burley N. Quad-cell mass spectrometry: vaporization studies up to 2300 K using a rotatable, multiple Knudsen Cell ('QUAD-CELL'). In: Czairliyan A, ed. Proceedings of the Seventh Symposium on Thermophysical Properties. American Society of Mechanical Engineers, New York; 1977:222-230.

53. Hilpert K, Ruthardt K. Determination of the dissociation-energy of the Cr₂ molecule. Ber Bunsen Phys Chem. 1987;91(7):724-731. doi:10.1002/bbpc.19870910707

54. Wahlbeck P. Effusion. VII. The failure of isotropy of a gas in an effusion cell and the transition region. J Chem Phys. 1971;55(4):1709-1715. doi:10.1063/1.1676300

55. Demarcus WC. The Problem of Knudsen Flow. Part II. Solution of Integral Equation with Probability Kernels. Oak Ridge Gaseous Diffusion Plant (K-25); 1956.

56. Grimley RT, Wagner LC, Castle PM. Angular-distributions of molecular species effusing from near-ideal orifices. J Phys Chem. 1975;79(4):302-308. doi:10.1021/j100571a003

57. Ward JW, Fraser MV. Some of the parameters affecting Knudsen effusion. IV Monte Carlo calculations of effusion probabilities and flux gradients for Knudsen cells. J Chem Phys. 1968;49(9):3743-3750. doi:10.1063/1.1670674
<figure><img src="image_46.png" /></figure>

20. Detry D, Drowart J, Goldfing P, Keller H, Rickert H. Zur Thermodynamik Von Schwefeldampf-Massenspektrometrische Untersuchungen Mit Der Elektrochemischen Knudsen-Zelle. Z Phys Chem Neue Fol. 1967;55(5-6):314-319. doi:10.1524/zpch.1967.55.5.6.314

21. Violet P, Nuta I, Artaud L, Collas H, Blanquet E, Chatillon C. A special reactor coupled with a high-temperature mass spectrometer for the investigation of the vaporization and cracking of organometallic compounds. Rapid Commun Mass Spectrom. 2009;23(6):793-800. doi:10.1002/rcm.3942

22. Colle J-Y, Capone F. Very high temperature laser heated furnace for Knudsen cell mass spectrometry. Rev Sci Instrum. 2008;79(5):055105. doi:10.1063/1.2918135

23. Shilov A. Vaporizers for KEMS: measurement errors depending on their design. ECS Transactions. 2013;46(1):187-190. doi:10.1149/04601.0187ecst

24. Cater ED. Vapor pressure measurements A. measurement of the gross equilibrium vaporization rate (Knudsen Methods). In: Rapp RA, ed. Physicochemical Methods in Metals Research. Techniques of Metals Research. IV. John Wiley & Sons, Inc.; 1970:21-94.

25. Solorio-Leyva JC, Suárez-Romero JG, Cortés-Reynoso JG, Hurtado-Ramos JB, Tepichín-Rodríguez E. Corrections of size-of-source effect and distance effect in radiometric measurements of radiance. Appl Optics. 2005;44(13):2511-2518. doi:10.1364/AO.44.002511

26. Ackermann RJ, Garg SP, Rauh EJ. High-temperature phase diagram for the system Zr-O. J am Ceram Soc. 1977;60(7-8):341-345. doi:10.1111/j.1151-2916.1977.tb15557.x

27. Bhatt Y, Venkataramani R, Garg S. Measurements of eutectic temperatures in the metal-rich regions of several MC systems. J Less-Common Met. 1987;132(2):21-24. doi:10.1016/0022-5088(87)90590-X

28. Balakrishnan S, Ananthasivan K, Kumar KH. Measurement of the solidus and liquidus in the U-Zr system by the spot-technique. J Alloys Compd. 2016;689:751-758. doi:10.1016/j.jallcom.2016.07.252

29. Preston-Thomas H. International temperature scale of 1990 (ITS-90). Metrologia. 1990;27(1):3-10. doi:10.1088/0026-1394/27/1/002

30. Yamada Y, Sakate H, Sakuma F, Ono A. High-temperature fixed points in the range 1150 C to 2500 C using metal-carbon eutectics. Metrologia. 2001;38(3):213-219. doi:10.1088/0026-1394/38/3/3

31. Hildenbrand D. Attainment of chemical equilibrium in effusive beam sources of the heterogeneous reaction type. In: Hastie J, ed. Characterization of High Temperature Vapors and Gases. U. S. Government Printing Office; 1979:171-180.

32. Whitman CI. On the measurement of vapor pressures by effusion. J Chem Phys. 1952;20(1):161-164. doi:10.1063/1.1700161

33. Motzfeldt K. The thermal decomposition of sodium carbonate by the effusion method. J Phys Chem. 1955;59(2):139-147. doi:10.1021/j150524a011

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<figure><img src="image_47.png" /></figure>

58. Ward JW, Fraser MV. Study of some of the parameters affecting Knudsen effusion. VI. Monte Carlo analyses of channel orifices. *J Chem Phys.* 1969;50(4):1877-1882. doi:10.1063/1.1671283

59. Ward JW, Bivins RL, Fraser MV. Monte-Carlo simulation of specular and surface diffusional perturbations to flow from Knudsen cells. *J Vac Sci Technol A.* 1970;7(1):206-210. doi:10.1116/1.1315797

60. Ward JW, Bivins RL, Fraser MV. Monte-Carlo analysis of behavior of divergent conical effusion orifices. *J Vac Sci Technol A.* 1972;9(3): 1056-1061. doi:10.1116/1.1316990

61. Radke MJ, Jacobson NS, Copland EH. Monte Carlo simulation of a Knudsen effusion mass spectrometer sampling system. *Rapid Commun Mass Spectrom.* 2017;31(12):1041-1046. doi:10.1002/rcm.7873

62. Margrave JL. *The Characterization of High-Temperature Vapors*. Wiley; 1967.

63. Froment A, Chatillon C, Colin M. Determination of B and C activities in the non-stoichiometric $B_4-xC$ compound by the multiple Knudsen-cell mass spectrometric method. *Rev Int Hautes Temp.* 1991;27(4): 141-158.

64. Morland P, Chatillon C, Rocabois P. High-temperature mass spectrometry using the Knudsen effusion cell I-optimization of sampling constraints on the molecular beam. *High Temp Mat Sci.* 1997;37(3):167-187.

65. Nuta I, Chatillon C. Knudsen cell mass spectrometry using restricted molecular beam collimation. I. Optimization of the beam from the vaporizing surface. *Rapid Commun Mass Spectrom.* 2015;29(1):10-18. doi:10.1002/rcm.7071

66. Benigni P, Berche A, Mikaelian G, Rogez J. Transformation of a double focusing BE mass spectrometer for multiple-cell Knudsen effusion-part I: scientific concepts. *ECS Transactions.* 2013;46(1): 127-141. doi:10.1149/04601.0127ecst

67. Baïchi M, Chatillon C, Guéneau C, Chatain S. Mass spectrometric study of $UO_2-ZrO_2$ pseudo-binary system. *J Nucl Mater.* 2001;294 (1-2):84-87. doi:10.1016/S0022-3115(01)00477-9

68. Walsh JW. Radiation from a perfectly diffusing circular disc (Part I). *P Phys Soc Lond.* 1919;32(1):59-71. doi:10.1088/1478-7814/32/1/308

69. Walsh JW. *Photometry*. Constable & Co. Ltd; 1958.

70. Nuta I, Chatillon C. Erratum to: Knudsen cell mass spectrometry using restricted molecular beam collimation. I. Optimization of the beam from the vaporizing surface. *Rapid Commun Mass Spectrom.* 2017;31(12):1077-1078. doi:10.1002/rcm.7870

71. Chatillon C, Nuta I. Spurious molecular beams in Knudsen effusion mass spectrometry. CAL. 2019;65:8-15. doi:10.1016/j.calphad.2019.01.009

72. Trinadh V, Manikandan P, Bera S, et al. Vaporisation studies over Sn-Te-O system. In: *Proceedings of the Thirty First ISMAS Symposium on Mass Spectrometry*; 2017.

73. Murad E. Mass spectrometric techniques. In: *Spectrometric Techniques*. Academic Press; 1985:181-251. doi:10.1016/B978-0-12-710404-1.50009-7

74. Dunaev A, Kudin L, Motalov V, Ivanov D, Butman M, Krämer K. Mass spectrometric study of molecular and ionic sublimation of lanthanum triiodide. *Thermochim Acta.* 2015;622:82-87. doi:10.1016/j.tca.2015.09.008

75. Motalov V, Dunaev A, Kudin L, Butman M, Krämer K. Molecular and ionic sublimation of neodymium, dysprosium, holmium, and erbium triiodides and thermochemistry of molecules and ions. *Int J Mass Spectrom.* 2020;457:116431. doi:10.1016/j.ijms.2020.116431

76. Klemperer O, Barnett ME. *Electron Optics*. Cambridge University Press; 1971.

77. Gotcu-Freis P, Colle J-Y, Hiernaut J-P, Konings RJM. The vaporisation behaviour of americium dioxide by use of mass spectrometry. *J Nucl Mater.* 2011;409(3):194-198. doi:10.1016/j.jnucmat.2010.12.024

78. Ivanov D, Bourdon B. Numerical simulations of magnetic electron-impact ion source. *Int J Mass Spectrom.* 2019;442:35-43. doi:10.1016/j.ijms.2019.05.005

79. Dahl DA. SIMION for the personal computer in reflection. *InterJ Mass Spectrom.* 2000;200(1-3):3-25. doi:10.1016/S1387-3806(00)00305-5

80. Capone F, Colle Y, Hiernaut JP, Ronchi C. Mass spectrometric measurement of the ionization energies and cross sections of uranium and plutonium oxide vapors. *J Phys Chem A.* 1999;103(50): 10899-10906. doi:10.1021/jp992405f

81. Levin RD, Lias SG, Ionization Potential and Appearance Potential Measurements, 1971-1981. : U.S. Dept. of Commerce, National Bureau of Standards; 1982 Available from: http://purl.access.gpo.gov/GPO/LPS113176. Accessed January 12, 2024.

82. Rosenstock HM, Draxl K, Steiner B, Herron J-T. *Energetics of Gaseous Ions*. National Standard Reference Data System; 1977.

83. Banon S, Chatillon C, Allibert M. High temperature mass spectrometric study of ionization and fragmentation of TiO and $TiO_2$ gas under electron impact. *High Temp Sci.* 1982;15(1):17-40.

84. Speight JG. *Lange's Handbook of Chemistry*. McGraw-Hill Education; 2017.

85. Knutsen GF, Searcy AW. Characterization of the gaseous and solid products of aluminum sulfate decomposition. *J Electrochem Soc.* 1978;125(2):327-330. doi:10.1149/1.2131439

86. Brittain RD, Hildenbrand DL. Catalytic effects in the decomposition behavior of metal sulfates. *J Electrochem Soc.* 1983;130(3):C104-C.

87. Drowart J, Chatillon C, Hastie J, Bonnell D. High-temperature mass spectrometry: instrumental techniques, ionization cross-sections, pressure measurements, and thermodynamic data—(IUPAC technical report). *Pure Appl Chem.* 2005;77(4):683-737. doi:10.1351/pac200577040683

88. Chatillon C, Allibert M, Pattoret A. Thermodynamic and physicochemical behavior of the interactions between Knudsen-effusion cells and the systems under investigation: analysis by high temperature mass spectrometry. In: *Characterization of High Temperature Vapors and Gases*. Vol.1. U. S. Government Printing Office; 1979:181-210.

89. Otvos JW, Stevenson DP. Cross-sections of molecules for ionization by electrons. *J Am Chem Soc.* 1956;78(3):546-551. doi:10.1021/ja01584a009

90. Mann JB. Ionization cross sections of elements calculated from mean-square radii of atomic orbitals. *J Chem Phys.* 1967;46(5):1646-1651. doi:10.1063/1.1840917

91. Mann JB. Ionization cross sections of elements. Recent development in mass-spectroscopy. In: *Proceedings of International Conference on Mass Spectroscopy*; 1969.

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94. Bell K, Gilbody H, Hughes J, Kingston A, Smith F. Recommended data on the electron impact ionization of light atoms and ions. *J Phys Chem Ref Data Monogr.* 1983;12(4):891-916. doi:10.1063/1.555700

95. Colle J-Y. *Knudsen Effusion Mass Spectrometry (KEMS-Online)* https://sites.google.com/site/kemsonline/home?authuser=0. Accessed January 12, 2024.

96. Freund RS, Wetzel RC, Shul RJ, Hayes TR. Cross-section measurements for electron-impact ionization of atoms. *Phys Rev A.* 1990;41(7):3575-3595. doi:10.1103/PhysRevA.41.3575

97. Younés C, Nguyen L, Pattoret A. Studies of the thermodynamic systems UO, Ce-O, U-Ce-O, U-La-O, Ce-La-O, and Ce-La-YO by mass spectrometry: improved assessment of uncertainties in derived thermodynamic data. *High Temp-High Press.* 1981;13(1).
<figure><img src="image_47.png" /></figure>

58. Ward JW, Fraser MV. Study of some of the parameters affecting Knudsen effusion. VI. Monte Carlo analyses of channel orifices. *J Chem Phys.* 1969;50(4):1877-1882. doi:10.1063/1.1671283

59. Ward JW, Bivins RL, Fraser MV. Monte-Carlo simulation of specular and surface diffusional perturbations to flow from Knudsen cells. *J Vac Sci Technol A.* 1970;7(1):206-210. doi:10.1116/1.1315797

60. Ward JW, Bivins RL, Fraser MV. Monte-Carlo analysis of behavior of divergent conical effusion orifices. *J Vac Sci Technol A.* 1972;9(3): 1056-1061. doi:10.1116/1.1316990

61. Radke MJ, Jacobson NS, Copland EH. Monte Carlo simulation of a Knudsen effusion mass spectrometer sampling system. *Rapid Commun Mass Spectrom.* 2017;31(12):1041-1046. doi:10.1002/rcm.7873

62. Margrave JL. *The Characterization of High-Temperature Vapors*. Wiley; 1967.

63. Froment A, Chatillon C, Colin M. Determination of B and C activities in the non-stoichiometric $B_4-xC$ compound by the multiple Knudsen-cell mass spectrometric method. *Rev Int Hautes Temp.* 1991;27(4): 141-158.

64. Morland P, Chatillon C, Rocabois P. High-temperature mass spectrometry using the Knudsen effusion cell I-optimization of sampling constraints on the molecular beam. *High Temp Mat Sci.* 1997;37(3):167-187.

65. Nuta I, Chatillon C. Knudsen cell mass spectrometry using restricted molecular beam collimation. I. Optimization of the beam from the vaporizing surface. *Rapid Commun Mass Spectrom.* 2015;29(1):10-18. doi:10.1002/rcm.7071

66. Benigni P, Berche A, Mikaelian G, Rogez J. Transformation of a double focusing BE mass spectrometer for multiple-cell Knudsen effusion-part I: scientific concepts. *ECS Transactions.* 2013;46(1): 127-141. doi:10.1149/04601.0127ecst

67. Baïchi M, Chatillon C, Guéneau C, Chatain S. Mass spectrometric study of $UO_2-ZrO_2$ pseudo-binary system. *J Nucl Mater.* 2001;294 (1-2):84-87. doi:10.1016/S0022-3115(01)00477-9

68. Walsh JW. Radiation from a perfectly diffusing circular disc (Part I). *P Phys Soc Lond.* 1919;32(1):59-71. doi:10.1088/1478-7814/32/ 1/308

69. Walsh JW. *Photometry*. Constable & Co. Ltd; 1958.

70. Nuta I, Chatillon C. Erratum to: Knudsen cell mass spectrometry using restricted molecular beam collimation. I. Optimization of the beam from the vaporizing surface. *Rapid Commun Mass Spectrom.* 2017;31(12):1077-1078. doi:10.1002/rcm.7870

71. Chatillon C, Nuta I. Spurious molecular beams in Knudsen effusion mass spectrometry. CAL. 2019;65:8-15. doi:10.1016/j.calphad.2019. 01.009

72. Trinadh V, Manikandan P, Bera S, et al. Vaporisation studies over Sn-Te-O system. In: *Proceedings of the Thirty First ISMAS Symposium on Mass Spectrometry*; 2017.

73. Murad E. Mass spectrometric techniques. In: *Spectrometric Techniques*. Academic Press; 1985:181-251. doi:10.1016/B978-0- 12-710404-1.50009-7

74. Dunaev A, Kudin L, Motalov V, Ivanov D, Butman M, Krämer K. Mass spectrometric study of molecular and ionic sublimation of lanthanum triiodide. *Thermochim Acta.* 2015;622:82-87. doi:10. 1016/j.tca.2015.09.008

75. Motalov V, Dunaev A, Kudin L, Butman M, Krämer K. Molecular and ionic sublimation of neodymium, dysprosium, holmium, and erbium triiodides and thermochemistry of molecules and ions. *Int J Mass Spectrom.* 2020;457:116431. doi:10.1016/j.ijms.2020.116431

76. Klemperer O, Barnett ME. *Electron Optics*. Cambridge University Press; 1971.

77. Gotcu-Freis P, Colle J-Y, Hiernaut J-P, Konings RJM. The vaporisation behaviour of americium dioxide by use of mass spectrometry. *J Nucl Mater.* 2011;409(3):194-198. doi:10.1016/j. jnucmat.2010.12.024

78. Ivanov D, Bourdon B. Numerical simulations of magnetic electron-impact ion source. *Int J Mass Spectrom.* 2019;442:35-43. doi:10. 1016/j.ijms.2019.05.005

79. Dahl DA. SIMION for the personal computer in reflection. *InterJ Mass Spectrom.* 2000;200(1-3):3-25. doi:10.1016/S1387-3806(00) 00305-5

80. Capone F, Colle Y, Hiernaut JP, Ronchi C. Mass spectrometric measurement of the ionization energies and cross sections of uranium and plutonium oxide vapors. *J Phys Chem A.* 1999;103(50): 10899-10906. doi:10.1021/jp992405f

81. Levin RD, Lias SG, Ionization Potential and Appearance Potential Measurements, 1971-1981. : U.S. Dept. of Commerce, National Bureau of Standards; 1982 Available from: http://purl.access.gpo. gov/GPO/LPS113176. Accessed January 12, 2024.

82. Rosenstock HM, Draxl K, Steiner B, Herron J-T. *Energetics of Gaseous Ions*. National Standard Reference Data System; 1977.

83. Banon S, Chatillon C, Allibert M. High temperature mass spectrometric study of ionization and fragmentation of TiO and $TiO_2$ gas under electron impact. *High Temp Sci.* 1982;15(1):17-40.

84. Speight JG. *Lange's Handbook of Chemistry*. McGraw-Hill Education; 2017.

85. Knutsen GF, Searcy AW. Characterization of the gaseous and solid products of aluminum sulfate decomposition. *J Electrochem Soc.* 1978;125(2):327-330. doi:10.1149/1.2131439

86. Brittain RD, Hildenbrand DL. Catalytic effects in the decomposition behavior of metal sulfates. *J Electrochem Soc.* 1983;130(3):C104-C.

87. Drowart J, Chatillon C, Hastie J, Bonnell D. High-temperature mass spectrometry: instrumental techniques, ionization cross-sections, pressure measurements, and thermodynamic data—(IUPAC technical report). *Pure Appl Chem.* 2005;77(4):683-737. doi:10.1351/ pac200577040683

88. Chatillon C, Allibert M, Pattoret A. Thermodynamic and physicochemical behavior of the interactions between Knudsen-effusion cells and the systems under investigation: analysis by high temperature mass spectrometry. In: *Characterization of High Temperature Vapors and Gases*. Vol.1. U. S. Government Printing Office; 1979:181-210.

89. Otvos JW, Stevenson DP. Cross-sections of molecules for ionization by electrons. *J Am Chem Soc.* 1956;78(3):546-551. doi:10.1021/ ja01584a009

90. Mann JB. Ionization cross sections of elements calculated from mean-square radii of atomic orbitals. *J Chem Phys.* 1967;46(5):1646- 1651. doi:10.1063/1.1840917

91. Mann JB. Ionization cross sections of elements. Recent development in mass-spectroscopy. In: *Proceedings of International Conference on Mass Spectroscopy*; 1969.

92. McFarland RH. Gryziński electron-impact ionization cross-section computations for the alkali metals. *Phys Ther Rev.* 1965;139(1A): A40-A42. doi:10.1103/PhysRev.139.A40

93. Bethe H. Zur theorie des durchgangs schneller korpuskularstrahlen durch materie. *Ann Phys.* 1930;397(3):325-400. doi:10.1002/andp. 19303970303

94. Bell K, Gilbody H, Hughes J, Kingston A, Smith F. Recommended data on the electron impact ionization of light atoms and ions. *J Phys Chem Ref Data Monogr.* 1983;12(4):891-916. doi:10.1063/1.555700

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96. Freund RS, Wetzel RC, Shul RJ, Hayes TR. Cross-section measurements for electron-impact ionization of atoms. *Phys Rev A.* 1990;41(7):3575-3595. doi:10.1103/PhysRevA.41.3575

97. Younés C, Nguyen L, Pattoret A. Studies of the thermodynamic systems UO, Ce-O, U-Ce-O, U-La-O, Ce-La-O, and Ce-La-YO by mass spectrometry: improved assessment of uncertainties in derived thermodynamic data. *High Temp-High Press.* 1981;13(1).
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126. Souček P, Beneš O, Claux B, et al. Synthesis of UF₄ and ThF₄ by HF gas fluorination and re-determination of the UF₄ melting point. *J Fluorine Chem*. 2017;200:33-40. doi:10.1016/j.jfluchem.2017.05.011

127. Colle J-Y, Rautio J, Freis D. A modular LabVIEW application frame for Knudsen effusion mass spectrometry instrument control. *SoftwareX*. 2021;16:100875. doi:10.1016/j.softx.2021.100875

128. Dunaev A, Kryuchkov A, Kudin L, Butman M. Automated complex for high-temperature researches on base of mass-spectrometer MI1201. *Izvestiya Vysshikh Uchebnykh Zavedenii Seriya Khimiya I Khimicheskaya Tekhnologiya*. 2011;54(8).

129. Seelig J, Ghosh T, Jacobson N, et al. Sorption of Ag and its vaporization from graphite at high temperatures. *J Nucl Mater*. 2017;493:132-146. doi:10.1016/j.jnucmat.2017.06.002

130. Lewis GN, Randall M. Revised by: Pitzer KS, Brewer L, eds. *Thermodynamics*. 2nd ed., McGraw Hill, 1961.

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132. Jacobson NS, Myers DL. High-temperature vaporization of B₂O₃ under reducing conditions. *J Phys Chem B*. 2011;115(45):13253-13260. doi:10.1021/jp206480d

133. Hildenbrand DL, Lau KH. Thermochemistry of gaseous manganese oxides and hydroxides. *J Chem Phys*. 1994;100(11):8377-8380. doi:10.1063/1.466783

134. Hildenbrand DL, Lau KH. Thermochemistry of gaseous SiO (OH), SiO (OH)₂, and SiO₂. *J Chem Phys*. 1994;101(7):6076-6079. doi:10.1063/1.467322

135. Nguyen QN, Bauschlicher C Jr, Myers DL, Jacobson NS, Opila EJ. Computational and experimental study of thermodynamics of the reaction of titania and water at high temperatures. *J Phys Chem A*. 2017;121(49):9508-9517. doi:10.1021/acs.jpca.7b08614
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124. Huang J, Furukawa T, Aoto K. Thermodynamic study of sodium-iron oxides: part I. Mass spectrometric study of Na-Fe oxides. *Thermochim Acta*. 2003;405(1):61-66. doi:10.1016/S0040-6031(03)00136-9

125. Raj DDA, Viswanathan R, Manikandan P. The design, construction, and testing of a Knudsen effusion mass spectrometric system suitable for studies of nuclear fuel materials. *ECS Transactions*. 2013; 46(1):77-97. doi:10.1149/04601.0077ecst

126. Souček P, Beneš O, Claux B, et al. Synthesis of UF₄ and ThF₄ by HF gas fluorination and re-determination of the UF₄ melting point. *J Fluorine Chem*. 2017;200:33-40. doi:10.1016/j.jfluchem.2017.05.011

127. Colle J-Y, Rautio J, Freis D. A modular LabVIEW application frame for Knudsen effusion mass spectrometry instrument control. *SoftwareX*. 2021;16:100875. doi:10.1016/j.softx.2021.100875

128. Dunaev A, Kryuchkov A, Kudin L, Butman M. Automated complex for high-temperature researches on base of mass-spectrometer MI1201. *Izvestiya Vysshikh Uchebnykh Zavedenii Seriya Khimiya I Khimicheskaya Tekhnologiya*. 2011;54(8).

129. Seelig J, Ghosh T, Jacobson N, et al. Sorption of Ag and its vaporization from graphite at high temperatures. *J Nucl Mater*. 2017;493:132-146. doi:10.1016/j.jnucmat.2017.06.002

130. Lewis GN, Randall M. Revised by: Pitzer KS, Brewer L, eds. *Thermodynamics*. 2nd ed., McGraw Hill, 1961.

131. Cubicciotti D. A new sigma-plot treatment of equilibrium data and its application to vaporization of bismuth chloride. *J Phys Chem*. 1966;70(7):2410-2413. doi:10.1021/j100879a504

132. Jacobson NS, Myers DL. High-temperature vaporization of B₂O₃ under reducing conditions. *J Phys Chem B*. 2011;115(45):13253-13260. doi:10.1021/jp206480d

133. Hildenbrand DL, Lau KH. Thermochemistry of gaseous manganese oxides and hydroxides. *J Chem Phys*. 1994;100(11):8377-8380. doi:10.1063/1.466783

134. Hildenbrand DL, Lau KH. Thermochemistry of gaseous SiO (OH), SiO (OH)₂, and SiO₂. *J Chem Phys*. 1994;101(7):6076-6079. doi:10.1063/1.467322

135. Nguyen QN, Bauschlicher C Jr, Myers DL, Jacobson NS, Opila EJ. Computational and experimental study of thermodynamics of the reaction of titania and water at high temperatures. *J Phys Chem A*. 2017;121(49):9508-9517. doi:10.1021/acs.jpca.7b08614
<figure><img src="image_48.png" /></figure>

136. Dunning TH Jr. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. *J Chem Phys.* 1989;90(2):1007-1023. doi:10.1063/1.456153

137. Kendall RA, Dunning TH Jr, Harrison RJ. Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions. *J Chem Phys.* 1992;96(9):6796-6806. doi:10.1063/1.462569

138. Balabanov NB, Peterson KA. Systematically convergent basis sets for transition metals. I. All-electron correlation consistent basis sets for the 3 d elements Sc-Zn. *J Chem Phys.* 2005;123(6):064107. doi:10.1063/1.1998907

139. Bauschlicher CW Jr, Jacobson NS, Myers DL, Opila EJ. Computational chemistry derivation of Cr, Mn, and La hydroxide and oxyhydroxide thermodynamics. *J Phys Chem A.* 2022;126(9): 1551-1561. doi:10.1021/acs.jpc.a2c00764

140. Chase MW. NIST-JANAF Thermochemical Tables. 4thed. American Chemical Society; American Institute of Physics for the National Institute of Standards and Technology; 1998.

141. Barin I. Thermochemical Data of Pure Substances. Thirded. VCH; 1995. doi:10.1002/9783527619825

142. Drowart J, Honig R. A mass spectrometric method for the determination of dissociation energies of diatomic molecules. *J Phys Chem.* 1957;61(7):980-985. doi:10.1021/j150553a032

143. Gingerich K. Mass-spectrometric determination of bond energies of high-temperature molecules. *Chimia*. 1972;26(12):619-623.

144. Gingerich KA. Mass spectrometric determination of atomization energies of inorganic molecules and their correlation by empirical models of bonding. In: Hastie JW, ed. Characterization of High Temperature Vapors and Gases. Vol.1(561). U. S. Government Printing Office; 1979:289-300.

145. Smoes S, Drowart J, Verhaegen G. Mass-spectrometric study of gaseous oxides and suboxides of scandium, yttrium, and lanthanum. *J Chem Phys.* 1965;43(2):732-736. doi:10.1063/1.1696798

146. Hilpert K, Gingerich KA. Atomization enthalpies of the molecules Cu-3, Ag-3, and Au-3. *Ber Bunsen Phys Chem.* 1980;84(8):739-745. doi:10.1002/bbpc.19800840810

147. Gingerich KA. Experimental and predicted stability of diatomic metals and metallic clusters. In: Faraday Symposia of the Chemical Society Royal Society of Chemistry. Vol.14; 1980:109-125. doi:10.1039/fs9801400109

148. Gingerich KA, Shim I, Gupta S, Kingcade J Jr. Bond energies of small metal clusters. *Surf Sci.* 1985;156:495-503. doi:10.1016/0039-6028 (85)90611-9

149. Shim I, Gingerich KA. Ab initio HF-Cl calculations of the electronic "band structure" in the Fe₂ molecule. *J Chem Phys.* 1982;77(5): 2490-2497. doi:10.1063/1.444120

150. Roki F-Z, Ohnet M-N, Fillet S, Chatillon C, Nuta I. Critical assessment of thermodynamic properties of Csl solid, liquid and gas phases. *J Chem Thermodyn.* 2014;70:46-72. doi:10.1016/j.jct.2013.09.038

151. Moore R, Robinson D, Argent B. The use of high resolution mass spectrometry in the measurement of thermodynamic properties of metallic systems. *J Phys E Sci Instrum.* 1975;8(8):641-648. doi:10.1088/0022-3735/8/8/010

152. Chatillon C, Pattoret A, Drowart J. Thermodynamic studies of condensed phases by high temperature mass spectrometry. *High Temper-High Press.* 1975;7(2):119-148.

153. Lupis CH. Chemical Thermodynamics of Materials. Elsevier Science Publishing Co, Inc; 1983:581.

154. Eckert M, Bencze L, Kath D, Nickel H, Hilpert K. Thermodynamic activities in the alloys of the Ti-Al system. *Ber Bunsen Phys Chem.* 1996;100(4):418-424.

155. Jacobson NS, Brady MP, Mehrotra GM. Thermodynamics of selected Ti-Al and Ti-Al-Cr alloys. *Oxid Met.* 1999;52(5-6):537-556. doi:10.1023/A:1018820401533

156. Costa GC, Jacobson NS. Mass spectrometric measurements of the silica activity in the Yb₂O₃-SiO₂ system and implications to assess the degradation of silicate-based coatings in combustion environments. *J Eur Ceram Soc.* 2015;35(15):4259-4267. doi:10.1016/j.jeurceramsoc.2015.07.019

157. Lee MY, Adams A. A combination compact Knudsen cell-mass spectrometer apparatus for alloy studies. *High Temp Sci.* 1988;25(2): 103-116.

158. Chatillon C, Allibert M, Moracchioli R, Pattoret A. Etudes thermochimiques à haute température par spectrométrie de masse: emploi de dispositifs à caloducs pour le maintien isotherme de cellules d'effusion [Rapport de recherche]. *LTPCM*. 1974;21. hal-01364059

159. Gurvich LV, Veyts IV, Alcock CB. Thermodynamic Properties of Individual Substances. In: *Institut vysokikh temperatur (akademiia nauk SSSR), and gosudarstvennyi institut prikladnoi khimii (Soviet Union)*. 4th ed. Hemisphere Pub. Corp.; 1989.

160. Hultgren R, Desai PD, Hawkins DT, Gleiser M, Kelley KK, Wagman DD. *Selected Values of the Thermodynamic Properties of the Elements*. American Society for Metals; 1973.

161. Schiffman R. Thermodynamics of the ytterbium-lead system by simultaneous weight-loss-mass-spectrometry Knudsen effusion. *J Phys Chem.* 1982;86(19):3855-3861. doi:10.1021/j100216a030

162. Drowart J, Pattoret A, Smoes S. The heat of sublimation of uranium and the consistency of the thermodynamic data for uranium compounds. *J Nucl Mater.* 1964;12(3):319-322. doi:10.1016/0022-3115(64)90086-8

163. Lyubimov A, Zobens VY, Rakhovskii V. A mass spectrometric determination of the thermodynamic characteristics of binary metallic systems. *Zhur Fiz Khim*. 1958;32.

164. Neckel A, Wagner S. Massenspektrometrische Bestimmung thermodynamischer Aktivitäten. I. Das system gold-Kupfer. *Berich Bunsen Gesell.* 1969;73(2):210-217. doi:10.1002/bbpc.19690730221

165. Belton GR, Fruehan RJ. Determination of activities by mass spectrometry. I. The liquid metallic systems iron-nickel and iron-cobalt. *J Phys Chem.* 1967;71(5):1403-1409. doi:10.1021/j100864a034

166. Belton GR, Fruehan RJ. The determination of activities by mass-spectrometry—some additional methods. *Metall Trans A.* 1971;2(1): 291-296. doi:10.1007/BF02662673

167. Korobov M, McCreary J, Kematick R, Myers C. The ion-current-ratio method in Knudsen-cell mass spectrometry: binary mixtures with stoichiometric intermediate phases. *J Chem Thermodyn.* 1992;24 (12):1275-1279. doi:10.1016/S0021-9614(05)08267-8

168. Neckel A, Wagner S. Massenspektrometrische Bestimmung thermodynamischer Aktivitäten in Dreistoffsystemen. *Monatsh Chem.* 1969;100(2):664-670. doi:10.1007/BF00904114

169. Berkowitz J, Chupka W. Composition of vapors in equilibrium with salts at high temperatures. *Ann N Y Acad Sci.* 1960;79(11):1073-1078. doi:10.1111/j.1749-6632.1960.tb42773.x

170. Pattoret A, Drowart J, Smoes S. Mass spectrometric determination of heat of sublimation of uranium. *T Faraday Soc.* 1969;65:98-112. doi:10.1039/tf9696500098

171. Drowart J, Pattoret A, Smoes S. Concerning the influence of oxygen on the vapor pressure of uranium. *J Chem Phys.* 1965;42(7):2629-2630. doi:10.1063/1.1696358

172. Howard SM. Direct activity measurements in liquid Ag-Cu alloys using a valved Knudsen cell-mass spectrometer system. *Metall Mater Trans B.* 1989;20(6):845-852. doi:10.1007/BF02670189

173. Oktay E. The thermodynamic activities of silver in liquid silver-copper-geranium alloys/Thermodynamische Aktivitäten von Ag in flüssigen Ag-Cu-Ge-Legierungen. *Inter J Mater Res.* 1994;85(12): 824-827. doi:10.1515/ijmr-1994-851204
<figure><img src="image_48.png" /></figure>

136. Dunning TH Jr. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. *J Chem Phys.* 1989;90(2):1007-1023. doi:10.1063/1.456153

137. Kendall RA, Dunning TH Jr, Harrison RJ. Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions. *J Chem Phys.* 1992;96(9):6796-6806. doi:10.1063/1.462569

138. Balabanov NB, Peterson KA. Systematically convergent basis sets for transition metals. I. All-electron correlation consistent basis sets for the 3 d elements Sc-Zn. *J Chem Phys.* 2005;123(6):064107. doi:10.1063/1.1998907

139. Bauschlicher CW Jr, Jacobson NS, Myers DL, Opila EJ. Computational chemistry derivation of Cr, Mn, and La hydroxide and oxyhydroxide thermodynamics. *J Phys Chem A.* 2022;126(9): 1551-1561. doi:10.1021/acs.jpca.2c00764

140. Chase MW. NIST-JANAF Thermochemical Tables. 4thed. American Chemical Society; American Institute of Physics for the National Institute of Standards and Technology; 1998.

141. Barin I. Thermochemical Data of Pure Substances. Thirded. VCH; 1995. doi:10.1002/9783527619825

142. Drowart J, Honig R. A mass spectrometric method for the determination of dissociation energies of diatomic molecules. *J Phys Chem.* 1957;61(7):980-985. doi:10.1021/j150553a032

143. Gingerich K. Mass-spectrometric determination of bond energies of high-temperature molecules. *Chimia*. 1972;26(12):619-623.

144. Gingerich KA. Mass spectrometric determination of atomization energies of inorganic molecules and their correlation by empirical models of bonding. In: Hastie JW, ed. Characterization of High Temperature Vapors and Gases. Vol.1(561). U. S. Government Printing Office; 1979:289-300.

145. Smoes S, Drowart J, Verhaegen G. Mass-spectrometric study of gaseous oxides and suboxides of scandium, yttrium, and lanthanum. *J Chem Phys.* 1965;43(2):732-736. doi:10.1063/1.1696798

146. Hilpert K, Gingerich KA. Atomization enthalpies of the molecules Cu-3, Ag-3, and Au-3. *Ber Bunsen Phys Chem.* 1980;84(8):739-745. doi:10.1002/bbpc.19800840810

147. Gingerich KA. Experimental and predicted stability of diatomic metals and metallic clusters. In: Faraday Symposia of the Chemical Society Royal Society of Chemistry. Vol.14; 1980:109-125. doi:10.1039/fs9801400109

148. Gingerich KA, Shim I, Gupta S, Kingcade J Jr. Bond energies of small metal clusters. *Surf Sci.* 1985;156:495-503. doi:10.1016/0039-6028 (85)90611-9

149. Shim I, Gingerich KA. Ab initio HF-Cl calculations of the electronic "band structure" in the Fe₂ molecule. *J Chem Phys.* 1982;77(5): 2490-2497. doi:10.1063/1.444120

150. Roki F-Z, Ohnet M-N, Fillet S, Chatillon C, Nuta I. Critical assessment of thermodynamic properties of Csl solid, liquid and gas phases. *J Chem Thermodyn.* 2014;70:46-72. doi:10.1016/j.jct.2013.09.038

151. Moore R, Robinson D, Argent B. The use of high resolution mass spectrometry in the measurement of thermodynamic properties of metallic systems. *J Phys E Sci Instrum.* 1975;8(8):641-648. doi:10.1088/0022-3735/8/8/010

152. Chatillon C, Pattoret A, Drowart J. Thermodynamic studies of condensed phases by high temperature mass spectrometry. *High Temper-High Press.* 1975;7(2):119-148.

153. Lupis CH. Chemical Thermodynamics of Materials. Elsevier Science Publishing Co, Inc; 1983:581.

154. Eckert M, Bencze L, Kath D, Nickel H, Hilpert K. Thermodynamic activities in the alloys of the Ti-Al system. *Ber Bunsen Phys Chem.* 1996;100(4):418-424.

155. Jacobson NS, Brady MP, Mehrotra GM. Thermodynamics of selected Ti-Al and Ti-Al-Cr alloys. *Oxid Met.* 1999;52(5-6):537-556. doi:10.1023/A:1018820401533

156. Costa GC, Jacobson NS. Mass spectrometric measurements of the silica activity in the Yb₂O₃-SiO₂ system and implications to assess the degradation of silicate-based coatings in combustion environments. *J Eur Ceram Soc.* 2015;35(15):4259-4267. doi:10.1016/j.jeurceramsoc.2015.07.019

157. Lee MY, Adams A. A combination compact Knudsen cell-mass spectrometer apparatus for alloy studies. *High Temp Sci.* 1988;25(2): 103-116.

158. Chatillon C, Allibert M, Moracchioli R, Pattoret A. Etudes thermochimiques à haute température par spectrométrie de masse: emploi de dispositifs à caloducs pour le maintien isotherme de cellules d'effusion [Rapport de recherche]. *LTPCM*. 1974;21. hal-01364059

159. Gurvich LV, Veyts IV, Alcock CB. Thermodynamic Properties of Individual Substances. In: *Institut vysokikh temperatur (akademiia nauk SSSR), and gosudarstvennyi institut prikladnoi khimii (Soviet Union)*. 4th ed. Hemisphere Pub. Corp.; 1989.

160. Hultgren R, Desai PD, Hawkins DT, Gleiser M, Kelley KK, Wagman DD. *Selected Values of the Thermodynamic Properties of the Elements*. American Society for Metals; 1973.

161. Schiffman R. Thermodynamics of the ytterbium-lead system by simultaneous weight-loss-mass-spectrometry Knudsen effusion. *J Phys Chem.* 1982;86(19):3855-3861. doi:10.1021/j100216a030

162. Drowart J, Pattoret A, Smoes S. The heat of sublimation of uranium and the consistency of the thermodynamic data for uranium compounds. *J Nucl Mater.* 1964;12(3):319-322. doi:10.1016/0022-3115(64)90086-8

163. Lyubimov A, Zobens VY, Rakhovskii V. A mass spectrometric determination of the thermodynamic characteristics of binary metallic systems. *Zhur Fiz Khim*. 1958;32.

164. Neckel A, Wagner S. Massenspektrometrische Bestimmung thermodynamischer Aktivitäten. I. Das system gold-Kupfer. *Berich Bunsen Gesell.* 1969;73(2):210-217. doi:10.1002/bbpc.19690730221

165. Belton GR, Fruehan RJ. Determination of activities by mass spectrometry. I. The liquid metallic systems iron-nickel and iron-cobalt. *J Phys Chem.* 1967;71(5):1403-1409. doi:10.1021/j100864a034

166. Belton GR, Fruehan RJ. The determination of activities by mass-spectrometry—some additional methods. *Metall Trans A.* 1971;2(1): 291-296. doi:10.1007/BF02662673

167. Korobov M, McCreary J, Kematick R, Myers C. The ion-current-ratio method in Knudsen-cell mass spectrometry: binary mixtures with stoichiometric intermediate phases. *J Chem Thermodyn.* 1992;24 (12):1275-1279. doi:10.1016/S0021-9614(05)08267-8

168. Neckel A, Wagner S. Massenspektrometrische Bestimmung thermodynamischer Aktivitäten in Dreistoffsystemen. *Monatsh Chem.* 1969;100(2):664-670. doi:10.1007/BF00904114

169. Berkowitz J, Chupka W. Composition of vapors in equilibrium with salts at high temperatures. *Ann N Y Acad Sci.* 1960;79(11):1073-1078. doi:10.1111/j.1749-6632.1960.tb42773.x

170. Pattoret A, Drowart J, Smoes S. Mass spectrometric determination of heat of sublimation of uranium. *T Faraday Soc.* 1969;65:98-112. doi:10.1039/tf9696500098

171. Drowart J, Pattoret A, Smoes S. Concerning the influence of oxygen on the vapor pressure of uranium. *J Chem Phys.* 1965;42(7):2629-2630. doi:10.1063/1.1696358

172. Howard SM. Direct activity measurements in liquid Ag-Cu alloys using a valved Knudsen cell-mass spectrometer system. *Metall Mater Trans B.* 1989;20(6):845-852. doi:10.1007/BF02670189

173. Oktay E. The thermodynamic activities of silver in liquid silver-copper-geranium alloys/Thermodynamische Aktivitäten von Ag in flüssigen Ag-Cu-Ge-Legierungen. *Inter J Mater Res.* 1994;85(12): 824-827. doi:10.1515/ijmr-1994-851204