Thermodynamic Activity Measurements with Knudsen Cell Mass Spectrometry

by Evan H. Copland and Nathan S. Jacobson

oupling the Knudsen effusion method with mass spectrome- C try has proven to be one of the most useful experimental techniques for studying the equilibrium between condensed phases and complex vapors.1 The Knudsen effusion method involves placing a condensed sample in a Knudsen cell, a small enclosure, that is uniformly heated and held until equilibrium is attained between the condensed and vapor phases. The vapor is continuously sampled by effusion through a small orifice in the cell. A molecular beam is formed from the effusing vapor and directed into a mass spectrometer for identification and pressure measurement of the species in the vapor phase. Knudsen cell mass spectrometry (KCMS) has been used for nearly fifty years now and continues to be a lead- FIG. 1. Partial schematic of a Knudsen ing technique for obtaining thermody- cell mass spectrometer. (Modified Model 12-90-HT, Spectrumedix, State namic data. Indeed, much of the well- College, PA.) established vapor specie data in the 2 JANAF tables has been obtained from nique and the KCMS technique. Each lar flow is maintained as molecules pass this technique. This is due to the has specific advantages, depending on through the orifice, i.e., molecule-wall extreme versatility of the technique. material and conditions. The EMF tech- collisions dominate over molecule-mol- All classes of materials can be studied nique is suitable for lower temperature ecule collisions. As a general rule, the and all constituents of the vapor phase measurements, provided a suitable cell orifice dimensions must be kept to less can be measured over a wide range of can be constructed. KCMS is useful for then one tenth of the mean free path of -4 -11 pressures (~10 to 10 bar) and tem- higher temperature measurements in a the vapor species, over all experimental peratures (500-2800 K). The ability to system with volatile components. conditions. This, in turn, leads to an selectively measure different vapor In this paper, we briefly review the upper pressure limit of ~10-4 bar for a 1 species makes KCMS a very powerful KCMS technique and identify the major mm orifice. The lower pressure limit is tool for the measurement of compo- experimental issues that must be determined by the sensitivity of the nent activities in metallic and ceramic addressed for precise measurements. instrument and is typically ~10-11 bar. solutions. These issues include temperature mea- As we are dealing with high tempera- Today several groups are applying surement, cell material and cell design, tures and low pressures, the vapor can KCMS to measure thermodynamic and absolute pressure calibration. The be assumed to behave according to the functions in multicomponent metallic resolution of these issues is discussed kinetic theory of ideal gases. On this and ceramic systems. Thermodynamic together with some recent examples of basis, accurate predictions can be made functions, especially component measured thermodynamic data. for the effusion characteristics through activities, are extremely important in the Knudsen cell orifice.5 This allows the development of CALPHAD Basic Technique design of an optimum Knudsen cell (Calculation of Phase Diagrams) type geometry. A well-defined molecular 3 thermodynamic descriptions. These The unique feature of a Knudsen cell beam is sampled from the effusate at descriptions, in turn, are useful for mass spectrometer is the vapor genera- angles close to the normal of the orifice, modeling materials processing and tion system. This has been discussed in collimated by one or more apertures predicting reactions such as oxide for- several excellent reviews.1,4,5 Typically and directed into the ionization cham- mation and fiber/matrix interactions. a Knudsen cell is 1 cm in diameter x 1 ber of the mass spectrometer. The leading experimental methods for cm tall with an orifice of well-defined Figure 1 shows a portion of a typical measuring activities are the Galvanic geometry. The orifice is small (typically Knudsen cell mass spectrometer. The cell or electro-motive force (EMF) tech- 0.5-2 mm diameter) to ensure molecu- basic components—ionizer, accelerator,

28 The Electrochemical Society Interface • Summer 2001 should be at least one hundred times greater than the orifice area). This is readily done with a powder, but may require a larger cell area with a liquid. Temperature control and measurement are major sources of error in this technique. The following requirements must be met: (1) a constant temperature must be maintained; (2) temperature gradients in the cell must be eliminated; and (3) the absolute temperature must be accurately measured. Temperatures can be measured by either a pyrometer or thermocouple. These measurements must be taken at the cell, either with a black body hole drilled into the cell or a thermocouple tightly coupled to the cell. A typical calibration involves slowly varying the temperature through the melting point of a pure 2 FIG. 2. Second law heat of vaporization for copper. The tabulated value is 331.8 kJ/mol. metal (e.g., Ag, Au, Cu, etc.) and observing both the corresponding ion sorter, and detector—remain similar cross section, and k is the machine con- plateau in vapor pressure and thermal to the designs of the 1960s. However stant. The machine constant is a com- arrest. Temperature calibration must improved vacuum systems, electronics, bination of numerous factors involved be done frequently for thermocouples and data acquisition systems have led in the formation of the molecular as the vacuum and reactive vapor envi- to more reliable instruments. The major beam, the ionization process, ion col- ronment can result in rapid changes in features of a mass spectrometer for lection efficiency, transmission efficien- wire composition. analysis of high temperature vapor are cy of the analyzer, and collection effi- It is also important that the neutral summarized as follows. A small, repre- ciency of the detector. To calculate precursors for the observed ions be sentative fraction of the molecular absolute vapor pressures the values of identified. For metallic vapors this beam is ionized via impact with a σ both k and i must be known. In order identification is generally simple, e.g., focused beam of mono-energetic elec- to determine the machine constant, a the Ti vapor above Ti alloys forms Ti+ trons. An adjustable electron energy number of experimental issues must be ions. For ceramics this can be more permits precise determination of the addressed. involved as they generally form a more particular energy at which an ion complex ionization pattern, e.g., NiO appears. This measurement is very use- Critical Experimental Issues forms Ni+, NiO+, O +, and O+. ful in understanding the origin of the 2 Typically low energy ionizing elec- observed ions in the mass spectra. Once A number of requirements must be trons are used to minimize fragmenta- formed, the ions are directed into a satisfied for precise measurements. The tion and simplify the mass spectrum, high voltage accelerating region and first requirement is an inert cell. A wide but this reduces sensitivity. then into a magnetic field for selection range of refractory-metal and ceramic according to mass-to-charge ratio. Another issue related to the ion Other common techniques for ion materials have been used for Knudsen intensity measurement is the separa- selection such as quadruple filters and cells. Generally metallic alloys are stud- tion of background peaks from the peak time-of-flight instruments have been ied in refractory ceramic cells (Al2O3, of molecules emerging from the used. However the magnetic field ion ZrO2, Y2O3, etc.) and ceramics are stud- Knudsen cell. There are several selector is most desirable due to its sta- ied in refractory metal cells (W, Mo, Ir, approaches to solving this problem. bility and lack of mass discrimination. etc.). The ionizing electron energy can be Finally, the ions are directed into an Provided a suitable cell material can chosen to limit fragmentation of back- electron multiplier. Ion currents can be be identified, cell design is the next ground hydrocarbons and limit the measured by measuring the voltage issue. The size of the orifice is generally number of background peaks. A mag- drop across a precision resistor or ions determined by the maximum vapor netic sector instrument typically has a may be counted directly. The ion count- pressure over the sample in the temper- resolution of 1000 or greater, which ing technique is preferred, again, due to ature range of interest. The continuous allows separation of inorganic peaks its lack of mass discrimination and easy effusion of the vapor from the cell from any hydrocarbons. Finally a shut- adaptation to data acquisition systems. means that a pressure gradient is pre- ter, as shown in Fig. 1, can be used to The output of the mass spectrometer sent in the cell but cognizant design of interrupt the molecular beam emerging is in ion intensity, Ii. For many thermo- the cell for a given orifice can limit the from the cell so the background can be dynamic measurements this must be divergence of the measured pressure identified and subtracted. converted to partial pressure, Pi, via the from the equilibrium value to well The best test for proper operation of following equation: within the random error of the tech- a Knudsen cell instrument is a simple kI T nique. Numerous studies have consid- second law heat of vaporization of a i 5 Pi = σ (1) ered this issue. In general this is well-characterized vapor pressure stan- i achieved by a cell with a larger diameter dard. This is illustrated in Fig. 2 for Here T is the absolute temperature of than height and a sample with a large copper, where the slope of the line in a σ the vapor source, i is the ionization surface area (generally the sample area plot of ln (IiT) vs. 1/T gives a heat of

The Electrochemical Society Interface • Summer 2001 29 vaporization. An acceptable heat is within 2 kJ/mol of the accepted value.2 This generally indicates the above issues of proper cell material and design, temperature control and measurement, and spectra interpreta- tion are satisfied. It also indicates the vapor sampled is primarily from the cell and not condensation and re- evaporation from the heat shields. A second law heat does not require the conversion of ion intensity to absolute pressure, however, many types of measurements do require this conversion via equation.1 In order to do this precisely, a standard is needed. Reliable vapor pressure data are avail- able for most pure metals and these are excellent standards. However care must be taken to measure the standard and sample vapor pressures under FIG. 3. Data obtained for the Fe-Al system at 1573 K by the ion-current ratio technique.9 exactly the same conditions: the molecular beam must be directed to the same region in the ion source, and Clearly this approach is limited to spe- Here P and I are the partial pressure the cells used for the vapor pressure cific systems. and ion intensity, respectively. The standard and the sample must have A second approach involves taking problem is that the molecular beams matched orifices to ensure the molecu- the ion intensity ratio in a binary alloy tend to mix. There is no easy solution 12 lar beams are identical. and manipulating the Gibbs-Duhem to this problem. Chatillon has devel- In theory, one can measure the equation to cancel the calibration con- oped the restricted collimation method, 1,8 vapor pressure of a standard to obtain stant. The resultant equation for an in which a series of fixed collimating the machine constant change samples, alloy AB is: apertures physically limit the vapor entering the ion source to that which and measure the ion intensities for the xA γ ∫ + + alloy. However, maintaining an identi- ln A =- xAd[ln(I A/I B) - ln(xA/xB)] (4) originated from within the cell orifice cal machine constant from run to run xA=1 of interest. We overcome this problem γ of beam mixing by using a secondary involves using a rigidly mounted cell Here A is the activity coefficient of in-situ standard, i.e., instead of pure Al and an isolation valve between the A, xA and xB are the mole fractions of A Knudsen cell chamber and the ionizer. and B respectively, and I and I are the in the above example pure Cu or Au is A B 13 An isolation valve permits the ionizer measured ion intensities of A(g) and used. This approach requires some to remain running when a sample is B(g) over the alloy. This technique has additional corrections—so that an changed. Only a few instruments have been widely used to obtain activities expected pure Al ion intensity is these features for a reliable, constant and partial molar quantities for a num- derived from the measured Cu or Au value of k.1,6 ber of systems. It requires only mea- intensity. Such corrections are obtained For most instruments, the machine surements of the alloy—no standards from an additional run with pure Al in constant changes from run to run. are necessary. The drawback of this one cell and the Cu or Au standard in Three methods have been developed technique is the need for measurable the other. to circumvent this problem. The vapor pressures over a range of compo- Figure 4 illustrates some recent data dimer/monomer approach developed sitions for both components. An exam- on Ti-45 a/o Al. Note that both aAl and by Berkowitz and Chupka,1,7 requires ple of some data for the Fe-Al system aTi are reported. The upper limit of a system where both species are readi- obtained in our laboratory is shown in measurement is determined by both ly measurable with a well-established Fig. 3.9 Note the negative deviations the high vapor pressure and the melt- dimer/monomer equilibrium and con- from ideality, which are consistent with ing point of the alloy. The lower limit is ditions: solution models of this system.10 determined by the sensitivity of the Finally, the third approach to this instrument. The low vapor pressure of Ti gives only a narrow range for a 2A(g) = A2(g) (2) problem is the multiple cell technique, Ti which we believe to be the most versa- measurement. However aAl can be mea- Thus the activity of component A tile. This method was first discussed in sured over a wide range. We found that in the alloy, a(A), becomes the ratio of 1960 by Büchler and Stauffer;11 and fur- these data extrapolated to some aAl this equilibrium for the alloy and pure ther developed by several groups. Two or measurements taken with the EMF materials: more cells are adjacent to each other as technique and a CaF2 electrolyte at 13 o 1073 K. An important application of I (A) I(A2) shown in Fig. 1. Consider, for example, a(A) = (3) the measurement of Al activity in a Ti-Al these data is the prediction of the stable o 13 I (A2)I(A) alloy. Ideally one would have pure Al in surface oxide—TiO2 or Al2O2. Here Io(A) and Io(A ) are the ion one cell and Ti-Al in the other cell and We have illustrated some of the 2 above techniques with metallic alloy intensities measured of A(g) measured the activity, aAl , is simply: over the pure element A and I(A) and systems. It should be noted that these PAl (soln) IAl (soln) techniques are all applicable to ceramic I(A ) are the ion intensities of A(g) aAl = = (5) 2 systems as well. These systems produce measured over the alloy containing A. PAl (pure) IAl (pure)

30 The Electrochemical Society Interface • Summer 2001 11. A. Buchler and J. L. Stauffer, Thermodynamics, Vol. 1, IAEA (Vienna), 271 (1966). 12. C. Chatillon, in High Temperature Materials Chemistry IX, K. Spear, Editor, PV 97-39, The Electrochemical Society, Proceedings Series, Pennington, NJ (1997). 13. N. S. Jacobson, M. P. Brady, and G. M. Mehrotra, Oxid. Met., 52, 537 (1999). 14. V. L. Stolyarova, Rapid. Comm. Mass Spec., 7, 1022 (1993).

About the Authors

Evan H. Copland is a National Research Council Post-doctoral Fellow at the NASA Glenn Research Center. He received his PhD from the University of South Whales, Sydney, Australia. His interests include thermodynamics and kinetics of solid-state chemical

FIG. 4. Data for the Ti-45Al system obtained by the double cell technique.13 reactions and computational thermodynamics.

Nathan S. Jacobson is a 2 3 P Al P O Materials Scientist at the NASA Al O (pure) = 2Al(g) + 3O(g) K= Glenn Research Center. He received 2 3 1 his PhD from the University of of 2 3 California at Berkeley. His research P Al(soln) P O(soln) Al2O3(soln) = 2Al(g-soln) + 3O (g-soln) K= interests include high temperature aAl O 2 3 chemistry, high temperature mass 2 3 2 3 spectrometry and corrosion/oxida- P Al(soln) P O(soln) I Al(soln) I O(soln) a = = Al2O3 2 3 2 3 tion of ceramics. P AlP O I AlI O (6) mass spectra that are much more com- References Memories plex and the activities must be derived accordingly. Consider a solution with 1. K. Hilpert, Rapid Comm. Mass Spec., 5, 175 alumina as a constituent12 (see scheme (1991). Wanted 6 above). 2. M. W. Chase, Jr., NIST-JANAF Thermochemical Tables, Fourth Edition, Several groups are actively using the Journal of Physical and Chemical necdotes, photographs, and KCMS technique to measure the prop- Reference Data Monograph 9, American items of interest about ECS for 1,12,14 erties of complex oxide solutions. Institute of Physics, Woodbury, NY (1998). ause in Centennial Celebration This type of data are used to develop 3. N. Saunders and A. P. Miodownik, Calphad publications and exhibits. oxide solution models. Calculation of Phase Diagrams, A Humorous and/or historical Comprehensive Guide, Pergamon, Oxford, interest a must; age and Conclusions England (1998). 4. J. Drowart and P. Goldfinger, Angewandte eccentricity a plus. Chemie, International Ed., 6, 581 (1967). One of the oldest and most useful Photos will be returned. 5. E. D. Cater, in Characterization of High techniques in fundamental high tem- Temperature Vapors and Gases, Volume 1, perature science is Knudsen cell mass ed. by J. W. Hastie, National Bureau of spectrometry. A large amount of well- Standards Publication 561/2, Washington, established data on pure compounds DC (1979). has been determined from this tech- 6. M. C. Y. Lee and A. Adams, High Temp. Sci., 25, 103 (1988). nique. The extreme versatility of this 7. J. Berkowitz and W. A. Chupka, Ann. N. Y. technique continues to make it a lead- Acad. Sci., 79, 1073 (1960). ing experimental approach for funda- 8. G. R. Belton and R. J. Fruehan, J. Phys. Please contact mental thermodynamic data. Today, Chem., 71, 1403 (1967). Mary Yess the emphasis is more on solutions and 9. N. S. Jacobson and G. M. Mehrotra, Met. ECS Director of Publications the KCMS technique is particular suited Trans., 24B, 481 (1993). 65 South Main Street 10. U. Kattner and B. P. Burton, in Phase to measurement of activities in multi- Pennington, NJ 08534-2839 USA Diagrams of Binary Iron Alloys, H. Okamoto tel. 609.737.1902, ext. 119 component solutions. The primary Editor, p. 12, ASM International, Materials e-mail [email protected] experimental issues are discussed for Park, Oh, (1993). these types of studies.

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