Development of the KEMS Technique Nathan S. Jacobson (NASA Glenn)
The major feature of Knudsen, molecular, or rarefied gas flow is that molecule-wall collisions dominate over molecule-molecule collisions. This inturn led to the development of the Knudsen cell, which is a heated small enclosure (typically a cylinder 1 cm diameter x 1 cm length) which contains a condensed phase in equilibrium with a gas. A small orifice of well-defined geometry (typically a knife edge with a 0.5-1 mm diameter) provides a means of measuring the vapor pressure. The ratio of the areas of the effusion orifice and the vaporizing substance (if the vaporization coefficient of the substance is between 0.3 and 1) should be less than or equal to 100. In the cast of lower vaporization coefficients, the requirements for the ratio of these areas become more rigorous. Figure 1 illustrates several forms of Knudsen cells.The vapor flux, J, escaping from the orifice is converted to pressure, P, using the Hertz-Knudsen-Langmuir equation:
 Here M is the molecular weight of the escaping vapor, R is the gas constant, and T is the absolute temperature. Knudsen developed this technique and measured the vapor pressure of mercury in a classic paper (Knudsen 1915). Figure 1.Different types of Knudsen cells. Note the knife edge orifice on the top and the pyrometer sighting port on the side. (a) Basic cell (b) Cell with metal liner (c) Cell with ceramic liner (d) Cell design to minimize creep of a liquid (e) Multiple cell design for studying the reaction of the vapor generated in the bottom cell with the vapor and/or solid in the top cell (f) Multiple cell for activity measurements (g) Cell with ZrO2 base for fixing an oxygen potential (h) Cooled cell for low temperature work (Hilpert1990).
The early measurements of the quantity of material effusing from the cell orifice used target collections. Later weight losses of the cell and vapor vaporizing material were employed. Ionov(1948) first used a mass spectrometer to analyze the high temperature vapor from an inorganic substance. The vapor of alkali halides in a closed volume was studied. Mass spectrometry allowed direct identification and quantification of the species effusing from the Knudsen cell. In the 1950s, the group of Chupka and Ingraham (Chupka and Inghram 1955) developed a design for the Knudsen Effusion Mass Spectrometer which is still used today. One of the most interesting early results (Chupka and Inghram 1953; Honig 1954) was the observation of carbon polymers. These had been predicted, but not experimentally observed before. Magnetic sector, quadrupole, and time-of-flight instruments have all been used successfully for KEMS. However magnetic sector instruments are preferred as they can be designed for minimal mass discrimination effects. Electron impact ionization is most commonly used to make positive ions and today most instruments use ion counting. However, other methods of ionization have been used for KEMS.
Figure 2. Schematic of Knudsen Effusion Mass Spectrometer (Hilpert, 2001)
Beyond vapor composition, mass spectrometric signals are related to the partial pressure of the species in the effusate by the following relation:  For this illustration, assume a vapor species i, ionizes to an ion i+ with no fragmentation. Here Pi is the partial pressure of species i, k is the instrument constant, Ii is the ion intensity, T is the absolute temperature, and si is the ionization cross section. Thus the van’t Hoff expression can be used to obtain a heat of vaporization: Here Keq is the equilibrium constant, which is proportional to IiT, DvapH°Tm(i) is the heat of vaporization of species i, and R is the gas constant. This is the “second law” method and gives a heat of vaporization at the median temperature Tm, for a range of measurements. In addition the “third law” method is used in conjunction with known or estimated Gibbs energy functions (gef) to determine an enthalpy of vaporization at 298.15K for each data point.
These techniques are discussed in many excellent reviews on KEMS (Inghram and Drowart 1959; Drowart and Goldfinger 1967; Grimley 1967; Cater 1979).
A review of the literature of the literature indicates that the ‘golden age’ of KEMS was in the 1960s to 1970s. At that point there were many active groups throughout the world. The complexity of the vapor phase was initially a surprise to the physical chemistry research community and KEMS was the ideal method to probe and understand this phase. These measurements were the basis for the many of the entries in the commonly used thermochemical tables (Chekhovskoi, Ivanisov et al. 1993; Chase and National Institute of Standards and Technology (U.S.) 1998).
Initially KEMS was applied to study the vaporization behavior of various line compounds and thermodynamics of the resultant vapor species. Since partial pressures are measured with KEMS, the method lends itself to measurement of partial molar quantities such as thermodynamic activities (chemical potential) and partial molar enthalpies. The special considerations for measurement of partial molar quantities are discussed in several review papers focusing on these issues (Hilpert 1991; Kato 1993; Stolyarova and Semenov 1994; Copland and Jacobson 2010).
For this type of measurement the vapor pressure of a particular component above the alloy is compared to the vapor pressure above the pure component: In order to apply this relationship, the calibration constant must remain constant for both the alloy and the pure material. This is an issue as breaking the vacuum to the ionizer and changing the sample very often changes the calibration constant.
There are several ways to circumvent this problem. One is the ion-current-ratio method, first developed by Lyubimov and colleagues (1958) and later independently further refined by Belton and Fruehan (1967) and Neckel and Wagner (1969). This method is based on a Gibbs-Duhem integration and requires measurements of ion current ratios over a range of composition. Consider the binary alloy AB:
Here gA is the activity coefficient for component A, xA is the mole fraction of component A, xB is the mole fraction of component B, IA is the ion intensity from the main fragment of component A and IBis the ion intensity form the main fragment of component B. Another method is the dimer-moner method developed by Berkowitz and Chupka (1960). This requires a system that has a dimmer-monomer equilibrium, which occurs with some metals and salt systems:
2A(g) = A2(g) [7]
The equilibrium ratio over the alloy is compared to that over the pure component A and the activity is given by: Various other methods have been applied to determine activities without use of a calibration constant.
A more versatile method of limiting the effects of a non-constant calibration constant is either a multi-cell KEMS system or an isolation valve so that the ion source can remain on as the sample is changed. In such cases equation [5] can be used directly. Multi-cell consists of several cells in a Knudsen cell chamber, which can be translated in and out of the sampling region. This method provides an internal standard for equation [5] and also a temperature standard. Multi-cell KEMS was first proposed by Buchler and Stauffer (1966). The major problem with this method is ‘cross talk’ between the cells or contamination of the molecular beam from one cell by the molecular beam of the other cell. The most effective method of minimizing this interference is the ‘restricted collimation’ method of Chatillon and colleagues (2002). This involves a series of apertures aligned with the cell orifice such that the ionizer only ‘sees’ inside the Knudsen cell. Several groups have successfully employed this method for multi-cell KEMS.Figures 3(a) and 3(b) illustrate a multi-cell flange and restricted collimation. The alternate method of using a valve to separate the Knudsen chamber from the ionization chamber has also been used to obtain accurate partial molar quantities (Hilpert, 1991). Such an approach allows the ionizer to always remain on and the cell to be rigidly mounted in a fixed position.
Figure 3(a). Multiple Knudsen cell configuration with furnace and translator (Copland and Jacobson, 2010).
Figure 3(b). Restricted collimation for multiple cell sampling(Copland and Jacobson, 2010).
There are many other applications of Knudsen cell mass spectrometry. The method has been used to study gas phase reactions of high temperature vapors. Gusarov and Gorokhov have developed a double oven cell for this purpose (Figure 1(e)). For example, Gokcen has suggested that ion current ratios are an accurate indicator of phase changes (1969) and Kato and colleagues (1989) have applied this method to determine liquidus lines. Chatillon has used multi-cell KEMS to measure vaporization coefficients (2005) and hence the kinetics of processes involving vapor species.Gingerich and colleagues (1980) and Ciccioli and Gigli (2009) have applied the KEMS method for fundamental studies of high temperature clusters and unusual bond types.
Since the 1970s, the number of active KEMS groups has declined significantly. There are a variety of reasons for these—decreased funding for basic sciences, the complexity of these measurements, and other priorities. Nonetheless thermodynamics and high temperature vapors remain important in many fields, such as vapor deposited coatings, fuel cells, nuclear applications, geochemistry, and general high temperature materials. KEMS is the most versatile and reliable method for experimental measurements of these important high temperature parameters.
References: Belton, G. R. and Fruehan, R. J. (1967) Determination of Activities by Mass Spectrometry. I. The Liquid Metallic SystemsIron-Nickel and Iron-Cobalt. J. Phys. Chem., 71[5], 1403–1409. Berkowitz, J. and Chupka, W. A. (1960) Composition of Vapors in Equilibrium with Salts at High Temperatures. Transactions of the New York Academy of Science, 79, 1073-1078. Buchler, A.and Stauffer, J. L.(1966) Thermodynamics, Proceedings of a Symposium, Vienna, 1965,Vol. I, International Atomic Energy Agency, Vienna, p 271. Cater, E. D. (1979) The Effusion Method at Age 69: Current State of the Art. Characterization of High Temperature Vapors and Gases. J. W. Hastie, ed. Washington, U. S. Government Printing Office: 3-38. Ciccioli, A., Gigli, G., and Meloni, G. (2009) The Si Sn Chemical Bond: An Integrated Thermochemical and Quantum Mechanical Study of the SiSn Diatomic Molecule and Small Si–Sn Clusters, Chemistry—A European Journal, 15[37],
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