Measuring Evaporation Rates of Metal Compounds from Solid

Anal. Chem. 2007, 79, 2992-2996

Measuring Evaporation Rates of Metal Compounds from Solid Samples Christian Ludwig,*,†,‡ Jo 1 rg Wochele,† and Urs Jo 1 rimann§

Paul Scherrer Institut (ENE-LEM), CH-5232 Villigen PSI, Switzerland, School of Architecture, Civil and Environmental Engineering (ENAC-ISTE), Swiss Federal Institute of Technology at Lausanne (EPFL), Station 2, CH-1015 Lausanne, Switzerland, and Mettler-Toledo Schweiz AG, Sonnenbergstrasse 74, CH-8603 Schwerzenbach, Switzerland

A thermogravimeter (TGA, Mettler-Toledo TGA/SDTA851e) was connected to an inductively coupled plasma optical emission spectrometer (ICP-OES, Varian Liberty 110) using a condensation interface (CI), which transforms gaseous high-boiling-temperature substances into solid (or liquid) aerosols. Argon was used as the carrier gas to transfer the aerosols into the ICP-OES for on-line elemental analysis. This new analytical TGA-CI-ICP-OES device, called TGA-ICP, is the first of its kind and allows one to study the thermochemically induced evaporation behavior of high-boiling-temperature substances, such as heavy metal compounds, under different thermochemical conditions. It allows the investigation of the behavior of large solid or liquid samples (100-500 mg), which is important for applying the results to industrial processes. So far, the CI principle has allowed only semiquantitative elemental analyses of hot gases when connected to an ICPOES. In this work, we show that a direct calibration of the CI-ICP-OES device is possible in combination with a TGA. The intensities determined by ICP-OES could be directly related to gravimetrically determined evaporation rates of volatile model compounds. The results show model evaporation experiments with native CdCl2 and CdCl2 resulting from the reaction of CaCl2 with CdO. Cadmium was studied because it is a volatile toxic heavy metal and its thermal behavior is relevant in various waste-treatment and recycling processes. Understanding the volatility of inorganic high-boiling-temperature compounds is necessary for developing combustion, gasification, and metallurgical processes. Process conditions can strongly influence the chemistry and, therefore, the volatility of present compounds. To develop new and optimize existing processes, the behavior of the input materials under different thermochemical conditions must be known. In the past, most elemental analytical methods have been developed to quantify trace components in solids, at surfaces of solids, or in liquid solutions. However, studying in situ evaporation kinetics of trace components in thermochemical processes have become most * Corresponding author. Fax: 0041-(0)56-310-2199. [email protected]. † Paul Scherrer Institut (ENE-LEM). ‡ Swiss Federal Institute of Technology at Lausanne (EPFL). § Mettler-Toledo Schweiz AG.

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important in the field of separation and recycling in the past few years. Both evaporation quantities and evaporation rates under transient and steady-state conditions are of interest. Thermal separation methods could be used to remove toxic heavy metals from wastes. This would allow the recycling of residue materials for construction and heavy metals for the metallurgical industry. Process gases need to be cleaned from corrosive salts. In many cases, this would increase the service life of high-temperature process equipment. Further, clean and energy-rich gases from gasification or pyrolysis of solid fuels might be used in new applications, e.g., for power generation with hightemperature fuel cells1,2 or gas turbines or for catalytic synthesis of fuels such as methane from wood.3 The development of new environmentally friendly and more efficient high-temperature extraction processes that are economically competitive, such as chlorination, is important to exploit natural deposits4 and solid residues and wastes from human activity.5,6 Technological progress in all of the above applications depends strongly on the development of new and improved on-line diagnostic tools, especially for the analysis of alkalis and heavy metals in hot gases. A recent and comprehensive review of state-of-the-art on-line diagnostic methods for metal species in process gases is provided by Monkhouse.7 Major difficulties are encountered when sampling hot gases, because condensation phenomena can easily lead to analytical errors. In some cases, isothermal sampling of process gas is feasible by continuously sampling along a heated sample (1) Rostrupnielsen, J. R.; Christiansen, L. J. Internal steam reforming in fuel cells and alkali poisoning. Appl. Catal. A: Gen. 1995, 126 (2), 381-390. (2) Ormerod, R. M. Solid oxide fuel cells. Chem. Soc. Rev. 2003, 32 (1), 1728. (3) Seemann, S.; Biollaz, S.; Aichernig, C.; Hofbauer H.; Koch, R. Methanation of biosyngas in a bench scale reactor using a slip stream of the FICFB gasifier in Gu ¨ssing. Presented at the 2nd World Conference and Technology Exhibition on Biomass for Energy, Industry and Climate Protection, Rome, Italy, May 10-14, 2004. (4) Peek, E.; Van Weert, G. Chloride metallurgy. In Proceedings of International Conference on the Practice and Theory of Chloride/Metal Interaction; Peek, E., Van Weert, G., Eds.; Montre´al, Canada, 2002. (5) Ludwig, Chr.; Wochele, J.; Stucki, S. Recycling zinc from muncipal soild waste. In Proceedings of the International Conference R’2000, Recycling, Recovery, Re-integration; Barrage, A., Edelmann, X., Eds.; EMPA: St. Gallen, Switzerland, 2000; pp 1087-1093. (6) Ludwig, Chr., Hellweg, S., Stucki, S., Eds. Municipal Solid Waste Management; Springer-Verlag: Berlin, 2003. (7) Monkhouse, P. On-line diagnostic methods for metal species in industrial process gas. Prog. Energy Combust. Sci. 2002, 28, 331-381. 10.1021/ac0622173 CCC: $37.00

© 2007 American Chemical Society Published on Web 03/01/2007

line.8 In many cases, however, noninvasive sampling is not possible, or the transfer of process gas into an analytical device is difficult. This problem can be addressed by using a specially designed condensation interface (CI).9 In this interface, the hot gases are quenched in a controlled and efficient way. A representative fraction of the vapor remains as an aerosol in the carrier gas. Using this controlled transfer, elements in the carrier gas can be easily analyzed on-line, e.g., by an inductively coupled plasma optical emission spectrometer (ICP-OES). Investigations have been performed with samples placed in a furnace, which was connected to an ICP-OES by a CI device (CI-ICP-OES). These experiments have shown that there exists a linear relationship between the amount of heavy metals evaporated from a sample (e.g., fly ash, chemical compound) and the integrated intensities measured by ICP-OES.10 However, evaporation rates can only be determined indirectly by measuring the total evaporated elemental amount during an entire evaporation experiment by a different independent off-line method.11 Normally, digestion of both the untreated solid sample and thermally treated sample is necessary. From these results, the total evaporated amount of the element of interest can be calculated. For calculating evaporation rates from the measured ICP-OES intensities, one must further assume a linear relationship between intensities and evaporation rates. However, inhomogeneous elemental distributions can easily lead to large errors. Therefore, a direct calibration of the CI-ICP-OES method to obtain accurate on-line evaporation rates is most difficult. Together with Mettler-Toledo Ltd., the Paul Scherrer Institut has constructed a new thermogravimetric analysis-condensation interface-inductively coupled plasma optical emission spectrometry (TGA-CI-ICP-OES) instrument. In the past, TGAs have been used extensively to study the thermal behavior of various compounds. Coupling a TGA to a mass spectrometer (MS) allows one to study the thermochemically formed gaseous products. Although organics can be measured easily by TGA-MS, inorganic high-boiling-temperature substances cannot easily be detected by this method. TGA experiments are most suitable to perform with rather small homogeneous samples. “Real-world” samples often are heterogeneous, especially with respect to trace metals. Therefore, larger furnaces are needed for measuring evaporation of such samples. In this work, we show first experimental results obtained with the new prototype TGA-CI-ICP-OES instrument (denoted TGAICP for short). We show that quantitative elemental analysis of high-boiling-temperature inorganics present in the offgas of the TGA is feasible using a TGA-ICP device. As an example, we present the results of a study on the thermochemical formation and evaporation of CdCl2 (g) from CdO (s)/CaCl2 mixtures. The (8) Oikari, R.; Hayrinen, V.; Parviainen, T.; Hernberg, R. Continuous monitoring of toxic metals in gas flows using direct-current plasma excited atomic absorption spectroscopy. Appl. Spectrosc. 2001, 55 (11), 1469-1477. (9) Ludwig, Chr.; Lutz, H.; Wochele, J.; Stucki, S. Studying the evaporation behavior of heavy metals by thermo-desorption spectrometry. Fresenius’ J. Anal. Chem. 2001, 371 (8), 1057-1062. (10) Ludwig, Chr.; Schuler, A. J.; Wochele, J.; Stucki, S. Measuring heavy metals by quantitative thermal vaporization. Water Sci. Technol. 2000, 42 (7-8), 209-216. (11) Lutz, H. Detoxification of filter ashes from waste incinerators. Understanding and influencing the removal of heavy metals during a thermal treatment process. Ph.D. Thesis no. 14653, ETH Zu ¨ rich, Zu ¨ rich, Switzerland, 2002.

Figure 1. Scheme of TGA-CI-ICP-OES instrument (Lfurnace ) 20 mm, Ltube quench gas ) 12 mm, Ltube aerosol ) 6 mm).

simultaneous measurement of both weight loss and CI-ICP-OES signal allowed the calibration of the TGA-CI-ICP-OES equipment for measuring evaporation rates, using CdCl2 (s) as a standard material. A linear correlation over several orders of magnitude of CdCl2 evaporation rates measured by TGA and the intensities measured by CI-ICP-OES was found. In contrast to the CI-ICPOES technique,10 the TGA-CI-ICP-OES method allows a direct calibration, i.e., samples need not be analyzed for the total concentration of the element of interest. The presented experimental results illustrate the potency of this new method. EXPERIMENTAL SECTION Chemical Reagents. Cadmium evaporation experiments were performed with pure chemicals or mixtures of two compounds. All chemicals (CdO, CaCl2‚2H2O, CdCl2) were obtained from Merck (p.a. grade). TGA measurements were performed to measure the water content of the pure substances in order to calculate the molar ratio of the different anions in a mixture. The water impurity of CdO was 0.71 wt %, and the water content in CaCl2 corresponded to the formula CaCl2‚2.05H2O. The chemicals were used as obtained from the manufacturer. Homogeneous CaCl2‚2.05H2O/CdO mixtures with a Ca/Cd ratio of 2.10 were obtained by grinding the two compounds in an agate mortar. Because of the hygroscopic nature of such mixtures, a small amount of water was taken up from the air in this process. Argon gas (grade 48) was used for quenching purposes, as obtained from Sauerstoffwerk Lenzburg (Lenzburg, Switzerland). Argon gas used as a carrier gas was purified with respect to trace O2 using an in-line inert gas purifier “gaskeeper” from Aeronex (San Diego, CA). TGA-ICP Method. A thermogravimeter (TGA, MettlerToledo TGA/STDA851e) was connected to an inductively coupled plasma optical emission spectrometer (ICP-OES, Varian Liberty 110) using a purpose-designed condensation interface (CI). A scheme of the TGA-ICP instrument is shown in Figure 1. In this experimental setup, samples can be treated at temperatures ranging from room temperature to about 1100 °C. The principle Analytical Chemistry, Vol. 79, No. 7, April 1, 2007

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Figure 2. Volatilization of CdCl2. Correlation of TGA signal (mg/ min) with ICP intensity detected at two different cadmium wavelengths (left, λ ) 214.438 nm; right, λ ) 326.106 nm).

of the CI has been described earlier10,12 and is analogous to that of an aerosol-jet flow condenser for the generation of nanoparticles.13 The CI allows one to efficiently quench the hot gases that carry the high-boiling-temperature compounds. Therefore, the particles formed are very small. Typically, aerosols resulting from a CI are smaller than 200 nm, as measured using a scanning mobility particle sizer.14 The quench is established (a) by an extraordinarily steep temperature profile in the furnace and (b) by rapid mixing of the hot carrier gas with a cooling gas.15 The carrier gas and cooling gas were mixed in the quench zone at flow rates of 100 and 400 cm3/min, respectively. The gas pressure was equal to 1 atm. The quenched gas containing the aerosols formed in the CI was then transferred to the ICP-OES device for elemental analysis. The intensities were measured at λ ) 214.438, 226.502, 228.802, and 326.106 nm for Cd and at λ ) 396.847 and 317.933 nm for Ca. Typically, samples of 10-100 mg were used. Heating rates were usually set to 2 °C/min. RESULTS AND DISCUSSION Evaporation under Nonisothermal Conditions. Evaporation rates of pure inorganic compounds, such as CdCl2, can be easily measured by TGA because the derivation of the weight loss curve results directly in the evaporation rate curve. Using the TGAICP equipment, the gravimetrically determined evaporation rates can be related to the CI-ICP-OES signal. As an example, CdCl2 evaporation is presented in Figure 2. There is a linear relationship between the evaporation rates measured by TGA and the intensities obtained from CI-ICP-OES. This correlation shows that the direct calibration of the CI-ICP-OES device is feasible and will allow customization of the CI-ICP-OES for quantitative measurements in various applications. This is important not only for (12) Ludwig, Chr.; Schuler, A. J.; Wochele, J.; Stucki, S. Measuring the evaporation kinetics of heavy metals: A new method. In Proceedings of the R’99 4th World Congress Recovery, Recycling, Re-integration; Barrage, A., Edelmann, X., Eds.; EMPA: St. Gallen, Switzerland, 1999; Vol. II, pp 205210. (13) Wegner, K.; Walker, B.; Tsantilis, S.; Pratsinis, S. E. Design of metal nanoparticle synthesis by vapor flow condensation. Chem. Eng. Sci. 2002, 57 (10), 1753-1762. (14) Ramachandra, A.; Ludwig, Chr.; Mohr, M.; Schuler, A. J.; Schreiber, D. Measurement and characterization of aerosol particles formed in a jet flow condenser for analytical applications. Presented at the Particulate System Analysis Conference, Harrogate, U.K., Sep 10-12, 2003. (15) Ludwig, Chr.; Schuler, A. J. German Patent DE 19838383, 1998.

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Figure 3. TGA as a dispenser for controlled addition of heavy metals to a reference gas for calibration purposes or to a sample of process gas at a plant.

Figure 4. Volatilization of CdCl2 at constant temperatures. Correlation of TGA signal (mg/min) with Cd ICP intensities measured at λ ) 226.502 nm.

performing TGA-ICP studies, but also for calibrating ICP-OES signals from on-line sampling of process gases: Using the CI method, a TGA can be used as a dispenser for the controlled addition of high-boiling-temperature salts to a reference gas for calibration purposes (Figure 3). However, the calibration of evaporation rates using a TGA is limited by the accuracy of the gravimetrically measured evaporation rates. The detection limit of the ICP-OES for Cd allows one to measure evaporation rates as low as 0.06 µg/min, whereas for the TGA, the limit is about 2 µg/min. The limitations given by the gravimetric measurements can surely be overcome to some extent by increasing the carrier gas flow, which would allow calibration of the CI-ICP-OES at much lower concentrations. TGA-ICP measurements are then limited by the detection limits given for a particular CI-ICP-OES setup, i.e., the transfer efficiency of compounds and particles by the CI and the type and sensitivity of the ICP-OES. Evaporation under Isothermal Conditions. Experiments can last from a few minutes to several hours. To test the stability of the signal of the ICP at low evaporation rates, a set of experiments was carried out at constant evaporation rate. Constant low evaporation rates can be obtained by adjusting carrier gas flow rates, temperatures, and amounts of sample. This is shown by the gravimetrically determined rates (Figure 4, right scale) obtained during CdCl2 evaporation at different temperatures. At lower temperatures (i.e., 500 and 530 °C), a quasi-steady-state

situation was obtained within about 5 min. At high temperatures (580 °C) and very high evaporation rates (tmelt,CdCl2 ) 564 °C), quasi-steady-state evaporation was achieved within just 1 min, but a small decrease in the evaporation rate (drift) was observed. The linear range of the thermogravimetrically determined weight loss curve was used to demonstrate the quality of the CI-ICP-OES signal by overlaying the measured ICP-OES intensities (Figure 4, left scale). Both measured ICP-OES intensities and gravimetrically determined rates showed a slight and corresponding decrease for the measurements at high-temperature (580 °C). At lower temperatures (530 and 500 °C), the ICP-OES intensities and weight loss rates remained about constant. In principle, a threepoint calibration can be obtained by the three experiments. Because of the inherent instability of the ICP-OES equipment, the ICP-OES signal drifts, and therefore, between the different experiments, the ICP-OES and TGA curves do not fully overlap. To measure the drift of the ICP-OES without performing an evaporation experiment, a standard solution was nebulized into the quench gas (Figure 1). The drift was on the order of 2% per hour. However, newer ICP-OES instruments generally a smaller drift, e.g., the ICP-OES instruments of the Vista series from Varian have a high signal stability with a drift of less than 1% in 20 h, even without internal standardization or any form of drift correction.16 Our experiments were performed at moderate evaporation rates, i.e., the overall pressure in the system remained about constant (∆p e (0.5 mbar). However, strong evaporation can change the pressure and, therefore, affect the quality of the ICPOES signal. It is assumed that ICP-OES devices that have their optical pathway oriented axially with respect to the plasma flame are less sensitive to pressure changes than those with a radially oriented optical pathway. Therefore, the latter might be more suitable for TGA-ICP measurements. Studying the Thermal Behavior of Complex Mixtures. The thermal evaporation of several elements from complex homogeneous and heterogeneous samples can be monitored by ICP-OES. Thus far, no other method has been capable of monitoring several elements in one experiment. Lutz performed a detailed study on the volatilization of metals from different fly ashes.11 The volatilization strongly depends on the chemical form of Cd in the sample. Whereas CdO is hardly volatile in the temperature range 380560 °C, CdCl2 can be easily volatilized. In Figure 5, we show the Cd evaporation from a CdO/CaCl2‚2.05H2O mixture. The major weight loss in this temperature range is attributed to the release of water. This was also confirmed by independent measurements in which the water in the carrier gas was detected using a mass spectrometer. During heating, volatile CdCl2 is formed that is released from the sample. Interestingly, the onset of Cd volatilization corresponds to the DTG peak at about 515 °C, which corresponds mainly to water. This is a strong indication that the evaporation of water influences the mobilization of Cd. However, Cd volatilization does not contribute significantly to the weight loss and, therefore, does not contribute to the observed peak at 515 °C. The water loss between 500 and 560 °C corresponds to about 1.2% of the water that was originally present in the sample. This can be attributed not only to surface-adsorbed water or surface hydroxyl groups but also to traces of new compounds (16) ICP-OES Varian Vista-PRO technical specification, Varian, Inc.: Palo Alto, CA, 2004.

Figure 5. Cd evaporation during TGA of a CdO/CaCl2 2H2O mixture with a Ca/Cd ratio of 2.1. The peaks in the DTG signal result from water release. ICP measurements were performed at λ ) 228.802 nm and λ ) 317.933 nm for Cd and Ca, respectively. Ca was not detected in the carrier gas.

formed in this mixture. Most cadmium hydroxides decompose at temperatures below 400 °C.17 Cadmium hydroxychloride is more stable, and small amounts cannot be excluded even above 400 °C. However, the peak at 515 °C corresponds to a temperature that is typical for the dehydroxylation of calcium hydroxychloride.18 The interpretation of the two peaks at 453 and 474 °C remain difficult. However, at these temperatures, the dehydration of Ca(OH)2 is expected.18-20 Ca was not detected in the carrier gas, in agreement with the high melting temperatures of potentially volatile Ca compounds (CaCl2, Tmelt ) 775 °C; CaO, Tmelt ) 2900 °C). In a further example, we demonstrate the TGA-ICP sensitivity of measuring the effect of the gas composition on the evaporation rate of CdCl2 and Cd0. Elemental Cd0 has a higher vapor pressure than CdCl2, and therefore, Cd0 is more volatile than CdCl2. This can be shown by reducing CdCl2 with H2. In Figure 6, the CdCl2 evaporation rates obtained in inert (argon) and reducing atmospheres are compared. It can be seen that the evaporation rates under reducing conditions were slightly increased. As expected from thermodynamic calculations, evaporation of Cd was increased in the presence of H2. The reason for this effect is the formation of Cd0, which is more volatile than pure CdCl2. This reaction can be formulated as

CdCl2 (s) + H2 (g) T Cd0 (g) + 2HCl (g) Determination of Evaporation Rates. Evaporation rates can be obtained from ICP-OES signals in two different ways. In the state-of-the-art method, the total evaporation of a pertinent element during an entire evaporation or thermodesorption spectroscopy (17) Low, M. J. D.; Kamel, A. M. The Thermal Decomposition of Cadmium Hydroxide. J. Phys. Chem. 1965, 69 (2), 450-457. (18) Allal, K. M.; Dolignier, J. C.; Martin, G. Determination of Thermodynamical Data of Calcium Hydroxichloride. Rev. Inst. Fr. Pe´ t. 1997, 52 (3), 361368. (19) Galwey, A. K.; Laverty, G. M. A Kinetic and Mechanistic Study of Dehydroxylation of Cadmium Hydroxide. Thermochim. Acta 1993, 228, 359-378. (20) Pane, I.; Hansen, W. Investigation of blended cement hydration by isothermal calorimetry and thermal analysis. Cement Concrete Res. 2005, 35, 1155 -1164.

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Figure 6. Evaporation rates of CdCl2 in inert (Ar) and reducing (Ar/ H2) atmospheres. Simultaneous measurements with ICP-OES and TGA connect ICP intensities (left, λ ) 228.802 nm) with TGA rates (right).

Figure 7. Comparison of the three different methods (A-C, see text) that were used to measure evaporation rates.

(TDS) experiment has to be known. Under the assumption that the integrated ICP-OES signal is proportional to the total evaporated mass, the evaporation rates can be calibrated (ICP integraltotal loss method). For the calculation of the total evaporated mass of a particular element, its amounts in the untreated sample and in the residue have to be analyzed. This is most inconvenient, as the samples might be heterogeneous or might need to be digested for analysis. In particular, the digestion of residues from thermally treated materials is known to be a difficult and tedious task. The opportunity to use TGA to calibrate CI-ICP-OES can be most beneficial for the investigation of hot process gases. The calibration gained from previous TGA-ICP experiments, e.g., Figure 2, can be directly used to determine evaporation rates. For illustration, in Figure 7, the CdCl2 evaporation rates determined by three different methods are compared. The evaporation rates were determined (A) by the ICP integral-total loss method, (B) by the TGA-ICP calibration method (Figure 2), and (C) by direct TGA measurements. There is a satisfactory agreement among all of the methods. The rate curve of method A crosses the original TGA curve (C) (mean error 5.5%), whereas method B underestimates method C

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for all rate values with a mean error of 7.1%. New ICP-OES instruments generally show a smaller drift and high signal stability, and it is assumed that the agreement of the three methods would be much better. For the weight loss curve, the results are much better, i.e., showing mean errors of 0.05% and 0.1% for methods A and B, respectively. For more complicated systems, weight losses can be caused by a variety of species, and therefore, method C is not applicable. The above examples with TGA and CI-ICP clearly show the potential of the method for studying the thermochemical behavior of solid samples. Quantitative measurements of real-world materials (e.g., fuels, wastes, ashes, residues, etc.) can become a difficult task if matrix effects falsify the ICP measurements. A way to cope with these problems is to increase the flow of quench gas or to further dilute the gas probed with the ICP. However, this will reduce the detection limits of all elements. CONCLUSIONS The principle of the condensation interface, which was developed at PSI and has been used in various fields in the past, has been successfully applied, together with Mettler-Toledo Ltd., to construct and test a TGA-ICP device, the first of its kind. The ICP-OES is a multi-element analyzer and state-of-the-art instrument that allows the simultaneous detection of different elements. Therefore, the TGA-ICP instrument is not limited to studying only the volatilization of Cd. Cadmium was merely chosen as an example. The new opportunity for on-line measurement of the elemental composition of hot producer gases adds important information to TGA curves. The use of the CI allows one to connect a thermal reactor with almost any commercially available ICP or other elemental detector. This flexibility is most advantageous for application in various fields such as waste treatment, recycling, and materials testing. For the investigation of industrial flue gases, the TGA-CI equipment could be used for calibration purposes. In real flue gases, matrix effects cannot be excluded. The TGA-CI instrument could be used to add controlled amounts of high-boiling-temperature compounds, thus allowing the calibration of measurements using the standard addition method. However, this is only possible as long as constant operation, i.e., constant gas composition, can be obtained during the sampling period, i.e., for about 10-20 min. ACKNOWLEDGMENT We thank Albert Schuler for performing the TGA-ICP experiments, as well as Markus Schubnell (Mettler-Toledo AG) and Alexander Wokaun, Otto Haas, Samuel Stucki, Rudolf Struis, Arvind Ramachandra, and Harald Lutz (all Paul Scherrer Institut) for fruitful discussions. This project was financially supported as GRS-058/00 by Gebert Ru¨f Foundation. Received for review November 23, 2006. Accepted January 22, 2007. AC0622173