R. H. Wagoner and J. P. Hirth, J. Chem. Phys. 67, 3074 (1977). 7. S. T. Lam ... 20, 653 (1958). 26. R. F. Porter and R. C. Scoonmaker, J. Chem. Phys. 29, 1070.
Journal of Materials Synthesis and Processing, Vol. 7, No. 2. 1999
Mass Spectrometric Observations of Enhanced Rates of Association Reactions: nLiF = LinFn (n = 2, 3) at LiF Single Crystal Surfaces M. F. Butman,1,3 L. S. Kudin,1 A. A. Smirnov,1 and Z. A. Munir2
A mass spectrornetric method was used to study the kinetics of lithium fluoride single-crystal sublimation. In electron impact ionization mass spectra, Li + , L i F , Li2F+, and Li3F2 ions originating from monomer (LiF), dimer (Li2F2), and trimer (Li3F3) molecular precursors were detected in the temperature range 970-1070 K. The dimer-to-monomer and trimer-to-monomer flux ratios were found to increase progressively with increasing temperature and also in comparison with those measured under equilibrium of crystalline LiF with its saturated vapor. The temperature dependence of the ion current ratio I(Li2F + )/I(Li + ) measured over the interval 916-1087 K was shown to pass reproducibly through a minimum at about 975 K. The enhancement of the rate of association reactions at LiF crystal surfaces is discussed in light of the terrace-ledge-kink model of vaporization and surface charge concept. KEY WORDS: Lithium fluoride; vaporization; mass spectrometry; surface charge.
1. INTRODUCTION
anisotropic nature of the vaporization rate from different crystalline faces [8, 9] the transient evaporation rate [5, 7], the influence of impurities [10, 11], and the fieldenhanced/retarded vaporization [12-14] have been interpreted in terms of the surface charge model. Most thoroughly this model has been developed for alkali halide crystals and its essence (see, e.g., Ref. 15) resides in the following. Because the Gibbs free energy of formation of cation vacancies is less than that for anion vacancies, the surface has an intrinsic positive charge owing to the preferential formation of cation vacancies there. However, the presence of divalent cationic impurities in alkali halide crystals of nominal purity leads to the occurrence of a negative extrinsic surface charge at sufficiently low temperatures when the concentration of extrinsic cation vacancies exceeds that of the intrinsic ones. The crossover point at which the charge vanishes is the extrinsic isoelectric temperature, Ti, and it is clearly a function of both the impurity concentration and the Gibbs energy of formation of the cation vacancies. The above model was recently used by us [15] to
Modern insight into the mechanism of vaporization of ionic solids stems from two models that are a corollary of the defect theory of surfaces, namely, the terrace-ledge-kink (TLK) model and the surface charge model. According to the TLK model [1], which is applicable to nonionic solids as well, the vaporization mechanism involves three successive stages: (1) removal of atoms, ions, or molecules from kinks and ledges; (2) diffusion and molecular association in the adsorbed layer; and (3) desorption. The surface charge, arising from differences in Gibbs free energy of formation of cation and anion vacancies, has been proposed as a contributing factor to the vaporization of ionic and semiconducting crystals [2-7]. Specifically, phenomena such as the 1
Department of Physics, State University of Chemistry and Technology, Prosp. Engelsa 7, 153460 Ivanovo, Russian Federation. 2 Department of Chemical Engineering and Materials Science, University of California, Davis. California 95616. 3 To whom correspondence should be addressed.
113 1064-7562/99/0300-0113S16.00/0 C 1999 Plenum Publishing Corporation
114 interpret the temperature dependence of the vaporization coefficients for both monomer and dimer molecules sublimated in a direction perpendicular to the (001) faces of KC1 and Nad single crystals. However, because of the relatively low fraction of dimers in the subliming fluxes, it was difficult to reveal the mechanism of surface association reactions. Among the alkali halides, lithium fluoride seems best suited for this purpose because (i) its saturated vapor contains an appreciable trimer concentration in addition to monomer and dimer concentrations that are in nearly equal proportions [16], (ii) the relative ionization cross sections of polymers have been extensively investigated [17-22], and (iii) most importantly, it was reported earlier [23] that the relative vaporization rates of dimers and trimers with respect to monomers, at the same temperature, are greater in the case of free vaporization than under equilibrium conditions. Although the relative abundance of polymers contained in fluxes from freely vaporizing surface can differ from that found in the saturated vapors, the result of the earlier work [23] needs verification through mass spectrometric examination.
2. EXPERIMENTAL The measurements were carried out with a single focusing magnetic-sector mass spectrometer, MI 1201 (200-mm radius of curvature, 90°), modified for hightemperature studies. The vacuum system consisted of three ion pumps, with rotary and sorption pumps for rough pumping. The furnace assembly area and the area of ion source were pumped differentially. A vacuum of 10~5 Pa could be maintained throughout the vaporization experiments. The furnace assembly consisted of a ceramic crystal holder, a molybdenum resistance heater, tantalum radiation shielding, a tungsten/tungsten-rhenium thermocouple held tightly between the crystal and the holder, and a movable stainless-steel shutter plate. The bottom of the furnace assembly could be moved in two perpendicular directions, thus providing the possibility of the best location. Heating was controlled to provide temperatures which could be maintained at a constant value to within ±0.5 K. The shutter plate was used to distinguish ions formed by electron bombardment of neutral species vaporized from the crystal surface from those formed by electron bombardment of residual background gas. The ions produced via electron impact were accelerated in an electrostatic
Butman, Kudin, Smirnov, and Munir field to an energy of 3 keV, mass analyzed in a variable magnetic field, and collected on the first plate of an electron multiplier. The output from the multiplier was amplified by an electrometer utilizing a 100-MQ resistor and recorded. The sensitivity of the registration system was as high as 10-17 A. To ensure the reliability of the data, ion current measurements were not made at temperatures below a value at which the noise-to-signal ratio was about 20%. In this work the samples to be vaporized were cleaved from commercial high-purity LiF single crystals (optical lens material) into 3 x 3 x 8-mm pieces which were inserted into the ceramic holder. Only (100) cleavage planes were exposed for vaporization. The samples were maintained for several hours at about 450 K under low vacuum (10-1 Pa) prior to being heated up to the test temperatures.
3. RESULTS AND DISCUSSION The shutterable ion peaks detected in the electron impact ionization mass spectrum of lithium fluoride are the isotopes of Li+, LiF+, L i 2 F , and Li3F2 ions with proper isotope ratios. The currents of Li+ and Li2F ions were measured in the temperature range 916-1087 K. The currents of LiF and Li3F2 ions, being less intense, were recorded in the narrower temperature range 970-1080 K, because a high background at the masses of interest made it difficult to distinguish small shutter effects at the temperatures lower than indicated. Two experimental runs of vaporization of two cleaved samples of an LiF single crystal were carried out. The measurements at the test temperatures were performed upon successive heating and cooling procedures during 5 h in the first run and during 11 h in the second run. The temperature dependence of the currents, /, of the most abundant isotopes of Li+ and Li2F ions is represented for both runs in Fig. 1 as lnIiT versus 1/T. The scatter of the data in Fig. 1, especially in the case of the more extended second run, is due to the fact that the intensities of ion currents were irreversibly decreasing with the time elapsed from the start of measurements, i.e., the higher current intensities are all from an earlier part of a run. This decrease may be associated with the receding of the vaporizing crystal surface at a rate of roughly about 0.2 mm per h and consequently with the decrease in the instrumental sensitivity constant. Relative intensities of ion currents pre-
115
Enhanced Rates of Association Reactions
Fig. 1. Temperature dependence of ion currents /( 7 Li*) and /( 7 Li 2 F*).
sented in Table I were recorded for a period between the second and the third hours from the beginning of crystal vaporization at the test temperatures, i.e., after the completion of intense development of surface morphology (thermal surface etching), which takes place during the first hour of vaporization at high temperatures [24]. During this development, the crystal surface, being relatively flat after cleavage, undergoes significant rough-
ening. The structural evolution begins by the formation of etch pits, nucleating at points of emergence of dislocations or impurities and growing in size until their domains overlap. At this point, the surface morphology may be considered to represent the steady-state condition. For comparison, the mass spectra obtained via Knudsen cell measurements are also listed in Table I [18-22, 25, 26]. As shown in Table I, the flux from a free-surface vaporization of lithium fluoride, like that of an equilibrium vapor of LiF, contains monomer (LiF), dimer (Li2F2), and trimer (Li3F3) molecules. However, it is clear from Table I that the relative contributions to the total flux of the different species are different in the cases of free-surface vaporization and Knudsen cell effusion. Overlapping individual mass spectra of monomers, dimers, and trimers constitute the mass spectra recorded. To obtain the ratio of the concentrations of molecular species in the vaporizing fluxes, the partial crosssection ratios, which provide a measure of the relative importance of the possible ionization paths for a given molecule, must be known. They are defined as
where Ikj is the ion intensity contribution of parent molecule j to ion k (k = 0, 1,2, and 3 apply to Li + , L i F , L i 2 F , and Li3F2 ions, respectively; j = 1, 2, and 3 apply to monomers, dimers, and trimers, respectively) and Ijj is the intensity of ion formed solely from molecule j.
Table I. Electron Impact Ionization Mass Spectra of LiF Vaporization Relative ion intensity"
T(K)
Electron energy (eV)
Li+
LiF
L i 2F
Li3F2
970 989 1013 1042 1059 1077 1060 1110 954 1100 1050 1102 1098 1078
70 70 70 70 70 70 18 75 50 80 70 Not specified 75 18
15.6 16.4 16.0 15.5 14.7 12.4 15.8 51.7 30.2 43.2 58.9 48.5 96.8 36.4
59.2 35.6 18.7 9.6 6.5 5.0 9.7 11.5 9.4 8.7 13.9 7.8 13.7 12.9
100 100 100 100 100 100 100 100 100 100 100 100 100 100
6.3 8.2 8.6 8.9 11.5 8.9 14.4 7.2 9.4 18.3 — 8.3 8.5 12.0
aCorrected
for isotopic contributions.
Free vaporization [this work] Free vaporization [this work] Free vaporization [this work] Free vaporization [this work] Free vaporization [this work] Free vaporization [this work] Free vaporization [this work] Knudsen cell measurements [25] Knudsen cell measurements [26] Knudsen cell measurements [18] Knudsen cell measurements [21] Knudsen cell measurements [19] Knudsen cell measurements [20] Knudsen cell measurements [22]
Butman, Kudin, Smirnov, and Munir
116 Thus the ion current intensities attributed to a molecular precursor of a given type can be estimated as follows:
Here I0, I1, I2, and I3 stand for the total current intensity of Li+, LiF+, Li2F+, and Li3F2 ions, respectively. The values of akj determined by different techniques [17-22] are summarized in Table II. The values of a03 and a13 are negligibly small [20] and may be disregarded. Therefore the dimer-to-monomer ( J D / J M ) and trimer-to-monomer (JT/JM) flux ratios can be calculated, respectively, as
Fig. 2. Temperature dependence of the dimer-to-monomer ratio.
and
where aM, aD, and aT are the ionization cross sections of LiF, Li2F2, and Li3F3 molecules, respectively. For our calculations, the values of akj (Table II) obtained by a double-cell distribution technique [20] was taken as the most reliable one. Relying on the results of Mohazzabi and Searcy and Grimely et al. [21, 22], these values were assumed to be temperature independent. The ratios aD/aM and aT/aM were set equal to 1.8 [20] and 2.25 [16], respectively. The values of JD/JM and jT/jM thus obtained are plotted in Figs. 2 and 3 as functions of temperature, along with those measured in the case of Knudsen effusion [16]. It can be seen from Figs. 2 and 3 that, within the errors of experiment, the values of both JD/JM and JT/JM ratios for free-surface vaporization are equal to those of equilibrium vaporization when T = 970 K. However, as the temperature increases, the frac-
Fig. 3. Temperature dependence of the trimer-to-monomer ratio.
Table II. Partial Cross-Section Ratios of Li2F2 and Li3F3 Molecules
T(K) 1050 1050 1100 1102 1100 1078
Electron energy (eV)
75 75 80 Not specified
75
75
a
02
0.06 0.09 0.04 0.05 0.13 0.12
a12
02.1
0.004 0.003 0.001
1.6
0
2.1
1.49
Technique Angular distribution [22] Flux gradient of a porous barrier [21] Vapor undersaturation [18] Vapor undersaturation [19] Double-cell distribution [17] Double-cell distribution [20]
117
Enhanced Rates of Association Reactions tions of dimers and trimers become progressively larger in the case of free-surface vaporization. For example, at T - 1070 K the nonequilibrium and equilibrium values of JD/JM and JT/JM differ by factors of 4.6 and 3.2, respectively. This result agrees qualitatively with the data of Rothberg et al. [23], who also reported an increase in the dimer fraction with increasing temperature from about 978 K. Such a significant increase in the polymer abundance observed in this study can be examined in light of the TLK and surface charge models. According to the vaporization mechanism, as mentioned above, the molecules break away from the steps, find their way onto the terraces, and desorb from them. It has been inferred by Dabringhaus et al. [27-30] that at the LiF surface, the polymers are formed by collisions of ion pairs at the steps but not at the terraces (mechanism I) or broken as one piece from kinks (mechanism II). At present it is not possible to decide between the two mechanisms, and therefore both are taken into consideration. In the context of the TLK model alone, it is difficult to tell why the rate of association reactions may increase significantly with increasing temperature, as is observed experimentally. Moreover, from the standpoint of this model, mechanism I must be considered unlikely since it favors the formation of polymers in the case of equilibrium vaporization when the concentration of adsorbed species at the terraces is higher because of the reverse molecular flux from the vapor phase. Therefore, further discussion is focused on the likely influence of surface charge on the association kinetics. First, the surface charge may cause the retardation of surface diffusion resulting from hindered rotation of ion pairs at the charged surface [15]. This would lead to an increase of the near-step concentration of ion pairs and, correspondingly, to the enhancement of the rate of ion pair association by mechanism I; in so doing, the enhancement is greater if the surface charge is larger. Second, the occupancy of kink sites by a surplus of ions of one sign will be accompanied by the lowering of the ledge energy, especially at high kink densities typical at high temperatures. This will enable easier disconnection of molecular associates readily from the ledges (mechanism II), on the one hand, and will increase the near-step concentration of ion pairs (mechanism I), on the other hand. Hence the significant change in the rate of vaporization of monomers and polymers may be expected to occur on going from the extrinsic temperature range (ledge charge is negative) to the intrinsic range (ledge charge is positive). In support of this interpretation Fig.
Fig. 4. Temperature dependence of the ion current ratio I(Li2F+)/ I(Li + ).
4 gives the I(Li 2 F)/I(Li + ) ion current ratio as a function of the temperature. In each heating-cooling procedure within each experimental run, this ratio, as shown in Fig. 4, passes through a minimum at T = 975 ± 15 K. Such a specific manner of variation in ion current ratio correlates well with the temperature dependence of the strength of surface charge field in the vicinity of the isoelectric temperature. This dependence is illustrated in Fig. 5 as predicted by the defect theory in the planesurface-model approximation (see, e.g., Ref. 15). In all likelihood the minimum in Fig. 4 corresponds to the isoelectric temperature of the crystal studied.
4. CONCLUSIONS In the present paper the vaporization kinetics from a lithium fluoride single-crystal surface was studied by mass spectrometry. It was established that this crystal vaporizes in the form of LiF, Li2F2, and Li3F3 molecules. In the temperature range 970-1070 K the dimerto-monomer and trimer-to-monomer flux ratios were found to increase progressively with increasing temperature and also in comparison with those measured under equilibrium of crystalline LiF with its saturated vapor.
118
Butman, Kudin, Smirnov, and Munir
REFERENCES
Fig. 5. Variation in the magnitude of the strength of the surface charge field, E, with the temperature in the vicinity of the isoelectric temperature, Ti, as predicted by defect theory for alkali halide crystals in the plane-surface-model approximation.
The temperature dependence of the ion current ratio I(Li 2 F)/I(Li + ) measured over the interval 916-1087 K was shown to pass reproducibly through a minimum at about 975 K. The enhancement of the rates of association reactions at the surface of LiF was interpreted using the terrace-ledge-kink model of vaporization and the surface charge concept.
ACKNOWLEDGMENTS The authors wish to thank Dr. H. Dabringhaus (Mineralogisch-Petrologisches Institut der Universitat Bonn, Germany) for valuable comments. This work was supported by Grant 96-02-16375 from the Russian Foundation for Basic Research.
1. W. K. Burton, N. Cabrera, and F. C. Frank, Phil. Trans. R. Soc. London A243, 299 (1951). 2. D. W. Short, R. A. Rapp, and J. P. Hirth, J. Chem. Phys. 57, 1381 (1972). 3. J. E. McVicker, R. A. Rapp, and J. P. Hirth, J. Chem. Phys. 63, 2645 (1975). 4. Z. A. Munir and J. P. Hirth, J Electron. Mater. 6, 409 (1977). 5. I. V. Samarasekera and Z. A. Munir, High Temp. Sci. 10, 155 (1978). 6. R. H. Wagoner and J. P. Hirth, J. Chem. Phys. 67, 3074 (1977). 7. S. T. Lam and Z. A. Munir, J. Cryst. Growth 47, 373 (1979); J. Cryst. Growth 51, 227 (1981). 8. L. S. Seacrist and Z. A. Munir, High Temp. Sci. 3, 340 (1971). 9. R. B. Leonard and A. W. Searcy, J. Appl. Phys. 42, 4047 (1971). 10. G. A. Somorjai and J. E. Lester, J. Chem. Phys. 43, 1450 (1965). 11. J. E. Lester and G. A. Somorjai, J. Chem. Phys. 49, 2940 (1968). 12. Z. A. Munir and T. T. Nguyen, Phil. Mag. A 47, 105 (1983). 13. Z. A. Munir, Res Mechanica 11, 1 (1984). 14. Z. A. Munir and A. A. Yeh, Phil. Mag. A 56, 63 (1987). 15. M. F. Butman, A. A. Smirnov, and L. S. Kudin, Appl. Surf. Sci. 126, 185 (1998). 16. V. P. Glushko, Termodinamicheskie Svoistva Individual 'nykh Veshchestv [Thermodynamic Properties of Individual Substances], Vol. 4 (Nauka, Moscow, 1984). 17. J. Berkowitz, H. A. Tasman, and W. A. Chupka, J. Chem. Phys. 36, 2170(1962). 18. L. N. Sidorov and A. S. Alikhanyan, Zhur. Fiz. Khim. 45, 506 (1971). 19. A. S. Alikhanyan, V. B. Sholtz, and L. N. Sidorov, Vestnik Moskov. Univ. 6, 639 (1972). 20. L. N. Gorokhov, Doctor of Chemistry Thesis (Moscow University, Moscow, 1972). 21. P. Mohazzabi and A. W. Searcy, Int. J. Mass Spectrom. Ion Phys. 24,469 (1977). 22. R. T. Grimley, J. A. Forsman, and Q. G. Grindstaff, J. Phys. Chem. 82, 632 (1978). 23. G. M. Rothberg, M. Eisenstadt, and P. Kusch, J. Chem. Phys. 30, 517 (1959). 24. Z. A. Munir, J. Mater. Sci. 22, 2221 (1987). 25. J. Berkowitz and W. A. Chupka, J. Chem. Phys. 20, 653 (1958). 26. R. F. Porter and R. C. Scoonmaker, J. Chem. Phys. 29, 1070 (1958). 27. H. Dabringhaus and H. J. Meyer, J. Crystal Growth 40, 139 (1977). 28. H. Dabringhaus and H. J. Meyer, J. Crystal Growth 61, 91 (1983). 29. H. Dabringhaus and H. J. Meyer, J. Crystal Growth 61, 95 (1983). 30. R. Helmrich and H. Dabringhaus, J. Crystal Growth 169, 279 (1996).
