10784
J. Phys. Chem. 1996, 100, 10784-10786
Thermochemistry of BSi(g), BSi2(g), and BSi3(g) R. Viswanathan,† Richard W. Schmude, Jr.,‡ and Karl A. Gingerich* Department of Chemistry, Texas A&M UniVersity, College Station, Texas 77843 ReceiVed: January 29, 1996X
The partial pressures of Si(g), B(g), BSi(g), BSi2(g), and BSi3(g) were measured over the condensed phase mixtures silicon + silver and silicon + germanium + silicon nitride + silver, contained in boron nitride Knudsen cells. The thermal functions were calculated for the B-Si gaseous species, and the atomization enthalpies ∆atomH°m (in kJ‚mol -1) were deduced as 312 ( 12 (BSi), 767 ( 18 (BSi2), and 1199 ( 28 (BSi3) at T ) 0 K; and 317 ( 12 (BSi), 777 ( 18 (BSi2), and 1214 ( 28 (BSi3) at T ) 298.15 K. These values in combination with enthalpies of formation of Si(g) and B(g) yielded enthalpies of formation ∆fH°m (at T ) 298.15 K; in kJ‚mol -1): 698 ( 14 (BSi), 688 ( 20 (BSi2), and 701 ( 31 (BSi3).
Introduction Boron-silicon alloys are of current interest for their potential application as semiconductors.1,2 Chemical vapor deposition is one of the methods employed to prepare these alloys especially as thin films or plates.3,4 For a better understanding of such processes, thermodynamic data for not only the condensed phases but also the vapor species in the B-Si binary system are important. Thermodynamic data for silicon-containing clusters are also of fundamental interest to understand the transition from gaseous clusters to the bulk. High-temperature mass spectrometric investigations of the system B + SiC were first performed by Verhaegen et al.5 They deduced thermodynamic data for the species BSi and BSi2 by studying some pressure-independent reactions. Armas et al.6 used the Knudsen cell mass spectrometric method for measuring the activities of silicon at the boron-rich side of the B-Si phase diagram. Our mass spectrometric investigations of Si or Ge + Si contained in boron nitride Knudsen cells provided means of studying not only the silicon clusters7-9 and Ge-Si10 species but also the Si2N11 and B-Si species. In this paper, we present the results obtained in such investigations for the molecules BSi, BSi2, and BSi3. Experimental Section Measurements were carried out with a Nuclide Corp. Knudsen cell mass spectrometer described previously.12 The results presented in this paper are from three separate investigations. Boron nitride (BN) Knudsen cells were used in all experiments to contain the condensed phase mixtures: Si + Ag in series 1 and 2, and Si + Ge + Si3N4 + Ag in series 3. The electron impact energy used for ionization was 13 eV, the acceleration voltage applied on the ions was 4.5 kV, and the entrance shield of the secondary electron multiplier ion-detection system was kept at -2.5 kV. Temperatures of the Knudsen cell were measured by a calibrated optical pyrometer focused onto a black body hole at the bottom of the graphite cell, housing the BN Knudsen cell. Table 1 lists the intensities of the ions pertinent to this investigation. The ions were identified by their mass-to-charge † On leave from Materials Chemistry Division, Chemical Group, Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamil Nadu 603 102, India. ‡ Current address: Division of Nursing and Natural Science, Gordon College, 419 College Dr., Barnesville, GA 30204. X Abstract published in AdVance ACS Abstracts, May 15, 1996.
S0022-3654(96)00274-2 CCC: $12.00
ratio, isotopic distribution, shutter effect, and ionization efficiency curves. Appearance potentials were measured using the known ionization potentials13 of Ag and Si in series 1 and 2, and of Ag, Si, and Ge in series 3, to calibrate the electron energy scale. The values obtained (in V) are B+, 8.4 ( 0.3; BSi2+, 8.2 ( 0.6; and BSi3+, 7.6 ( 0.6. In case of the BSi+ ion, due to high noise, only an approximate value of 8 V was obtained, consistent with the value of 7.8 V, reported by Verhaegen et al.5 The ion intensities I(i+) were converted to partial pressures p(i) by the equation p(i) ) k(i)I(i+)T, where k(i) is the pressure calibration constant for the species i. The value for k(Si) at each temperature was calculated with I(Si+) and I(Si2+) (Table 1), together with the equilibrium constant for the dissociation reaction Si2(g) ) 2Si(g), from D°(Si2, g, 0 K) ) 313.3 kJ‚mol-1 9 and the free energy functions for Si(g)14 and Si2(g).9 The mean k(Si) value for each series, given in Table 1, was then used to calculate k(i) according to the relation:
k(i) ) k(Si){σ(Si)/σ(i)}{γ(Si+)/γ(i+)}{n(Si+)/n(i+)} (1) where σ, γ, and n are the ionization cross section, the relative secondary electron multiplier gain, and the isotopic abundance, respectively. The values of σ(i) for the atomic species at 13 eV were taken from Mann’s tables,15 while those for the molecular species were assumed to be 0.75∑σ(i). The relative gain of the detector, γ(i+), for atomic ions were taken from Pottie et al.;16 those for the molecular ions are the sum of the values for atomic ions divided by the total number of atoms in the molecule. Table 2 gives the values of σ, γ, and n. Thermal Functions No experimental values of molecular constants are available for BSi(g), BSi2(g), and BSi3(g). We employed predicted values and calculated the Gibbs energy functions, -(G°T - H°0)/T, and the enthalpy increments, H°T - H°0, for these molecules by using the harmonic-oscillator, rigid-rotor approximation.17 For BSi, the results by Boldyrev and Simons18 from MP2/ 6-311+G* level computations were used: ground state 4Σ-; equilibrium separation 1.905 Å; vibrational frequency 772 cm-1. The lowest lying 2Π excited state, 8000 cm-1, above the ground state was also considered. For polyatomic B-Si clusters, theoretical calculations have only been performed on positively charged BxSi+ (x ) 1-4) clusters.19 We have therefore carried out CNDO/2 calculations © 1996 American Chemical Society
Thermochemistry of BSi(g), BSi2(g), BSi3(g)
J. Phys. Chem., Vol. 100, No. 25, 1996 10785
TABLE 1: Ion Intensities (in A) Measured in Different Series of Experiments T/K
I(Si+)
I(Si2+)
I(B+)
I(BSi+)
2136 2188
6.0 × 10-8 6.5 × 10-8
1.8 × 10-9 1.5 × 10-9
2090 2132 2135
1.6 × 10-8 2.9 × 10-8 2.2 × 10-8
Series 2a:b (Si + Ag) in BN Knudsen Cell 1.3 × 10-10 3.4 × 10-10 9.7 × 10-11 1.6 × 10-12 1.9 × 10-10 7.7 × 10-11 1.6 × 10-12
2114 2134 2156 2181
8.2 × 10-9 9.5 × 10-9 1.5 × 10-8 2.0 × 10-8
5.4 × 10-11 8.4 × 10-11 1.3 × 10-10 1.9 × 10-10
1869 1896 1912
1.5 × 10-10 1.8 × 10-10 2.5 × 10-10
Series 3a: (Si + Ge + Si3N4 + Ag) in BN Knudsen Cell 4.7 × 10-12 4.0 × 10-14 6.0 × 10-12 8.6 × 10-14 6.8 × 10-12
1952 2009 1999
3.9 × 10-10 5.8 × 10-10 5.2 × 10-10
9.9 × 10-12 1.2 × 10-11 8.6 × 10-12
I(BSi2+)
Series 1:a (Si + Ag) in BN Knudsen Cell 7.9 × 10-11 1.7 × 10-10
I(BSi3+)
1.2 × 10-11 1.4 × 10-11 3.2 × 10-12 1.7 × 10-12
Series 2bc 4.0 × 10-11 6.3 × 10-11 9.1 × 10-11
8.4 × 10-13 1.3 × 10-12 2.0 × 10-12
2.0 × 10-12
d
a
Series 3be
2.0 × 10-14 2.2 × 10-14 7.5 × 10-14 1.2 × 10-13 1.2 × 10-13
6.0 × 10-14 9.0 × 10-14 3.4 × 10-14
k(Si) ) 0.83 atm A-1 K-1. b k(Si) ) 0.64 atm A-1 K-1. c k(Si) ) 1.20 atm A-1 K-1. d k(Si) ) 29.2 atm A-1 K-1. e k(Si) ) 19.0 atm A-1 K-1.
TABLE 2: Ionization Cross Section σ (in Å2), the Relative Electron Multiplier Gain, γ, and the Isotopic Abundance, n, Employed To Convert k(Si) to k(i) i
σ(i)a
γ(i+)a
n(i+)b
Si Si2 B BSi BSi2 BSi3
2.57 3.85 0.84 2.56 4.48 6.41
0.909 0.909 0.779 0.844 0.866 0.877
0.922 0.851 0.804 0.751 0.701 0.654
a See text for how they were obtained. b Corresponds to the most abundant isotope whose ion intensity is given in Table 1. The mass numbers are 28 (Si), 56 (Si2), 11 (B), 39 (BSi), 67 (BSi2), and 95 (BSi3).
TABLE 3: Enthalpy Increments, (H°T - H°0), and Gibbs Energy Functions, -(G°T - H°0)/T for BSix(g) (x ) 1-3)a {-(G°T - H°0)/T}/ (J‚K-1‚mol-1)
(H°T - H°0)/ (kJ‚ mol-1) T/K
BSi(g)
BSi2(g)
BSi3(g)
BSi(g)
BSi2(g)
BSi3(g)
298.15 1200 1400 1600 1800 2000 2200
8.90 40.99 48.39 55.85 63.36 70.94 78.59
11.01 59.38 70.78 82.24 93.73 105.26 116.81
13.86 82.46 98.72 115.06 131.47 147.92 164.40
194.0 238.5 243.8 248.5 252.6 256.3 259.7
225.9 286.2 293.9 300.7 306.8 312.3 317.4
247.3 328.2 338.9 348.4 357.0 364.7 371.8
a
The reference pressure for all thermal functions is 1 atm.
Results and Discussion Reaction Enthalpies. From the partial pressures, the enthalpies of following reactions were evaluated:
Figure 1. Geometries selected for BSi2 and BSi3.
on BSi2 and BSi3. Schmude has shown that the CNDO/2 bond lengths for small silicon carbide clusters are 1.00 ( 0.04 times those predicted from ab initio methods.20 For BSi2 and BSi3, the linear and several nonlinear structures were considered, the nonlinear structures, shown in Figure 1, being the most stable. The predicted bond lengths are also shown in Figure 1. The Wilson GMAT/FMAT method 21,22 was used to calculate the vibrational frequencies. For this purpose, the B-Si and Si-Si stretching force constants of 2.74 and 2.16 mdyn/Å, based on the predicted vibrational frequency of 772 cm-1 for BSi18 and the experimental vibrational frequency of 511 cm-1 for Si2,9 were employed. For BSi3, the ring puckering force constant was assumed to be one-tenth of the average of the stretching force constants. The vibrational frequencies calculated for BSi2 are 839, 728, and 469 cm-1; the corresponding frequencies for BSi3 are 936, 828, 590, 437, 392, and 160 cm-1. An electronic ground state with a multiplicity of 2 was assumed for both BSi2 and BSi3 since each species has an odd number of electrons. The resulting thermal functions for BSi, BSi2, and BSi3 are listed in Table 3.
BSi(g) ) B(g) + Si(g)
(2)
BSi2(g) ) B(g) + 2Si(g)
(3)
BSi3(g) ) BSi2(g) + Si(g)
(4)
Table 4 gives the third-law enthalpies for the above reactions. Thermal functions for B(g),14 Si(g),14 and Si2(g)9 were taken from the references quoted while those for BSix (x ) 1-3) were taken from Table 3. Due to the limited number of data points, second-law evaluations of the above reactions are not expected to yield reliable values. The atomization enthalpy of BSi3 was derived by combining the enthalpy changes for reactions 3 and 4. The overall uncertainties in the atomization enthalpies of BSix (x ) 1-3) were calculated by the same procedure as described by Ran et al.23 The selected values of the atomization enthalpies are 312 ( 12 kJ‚mol-1 at T ) 0 K and 317 ( 12 kJ‚mol-1 at T ) 298.15 K for BSi(g), 767 ( 18 kJ‚mol-1 at T ) 0 K and 777 ( 18 kJ‚mol-1 at T ) 298.15 K for BSi2(g), 1199 ( 28 kJ‚mol-1 at T ) 0 K and 1214 ( 28 kJ‚mol-1 at T ) 298.15 K for BSi3(g). Comparison with Literature Data. Verhaegen et al.5 reported atomization enthalpies of BSi(g) and BSi2(g). For a meaningful comparison with our results, we subjected their
10786 J. Phys. Chem., Vol. 100, No. 25, 1996
Viswanathan et al.
TABLE 4: Third-Law Enthalpies (in kJ‚mol-1) ∆rH°m at T ) 0 K for Different Reactions (Reference Pressure ) 1 atm) reaction numbera T/K
2
3
4
Series 1 761.7 766.1
2136 2188 2132 2135 2134 2156 2181
306.3 315.8
Series 2a 768.3 772.1
314.0
Series 2b 777.6 768.8 769.4 Series 3a 760.9 756.9
1869 1896
Series 3b 1952 2009 1999 meanb
312.0 ( 5.0
766.9 ( 6.3
434.5 438.9 422.3 431.9 ( 8.6
(2): BSi(g) ) B(g) + Si(g); (3): BSi2(g) ) B(g) + 2 Si(g); (4): BSi3(g) ) BSi2(g) + Si(g). b Uncertainties are standard deviations. a
TABLE 5: Third-Law Enthalpies (in kJ‚mol-1; at T ) 0 K)a for Different Reactions from Verhaegen et al.’s 5 Results reaction numberb set c
1 2d 3e
2
3
5
280 ( 14 (6) 280 ( 14 (6) 303 ( 6 (3)
734 ( 18 (4) 740 ( 19 (4) 781 ( 13 (3)
319 ( 4 (4) 285 ( 3 (4) 313 ( 1 (4)
a Mean values; uncertainties are standard deviations; the number of data points pertinent to the evaluation are given in parentheses immediately next to the enthalpy value. b (2): BSi(g) ) B(g) + Si(g); (3): BSi2(g) ) B(g) + 2Si(g); (5): Si2(g) ) 2Si(g). c Partial pressures as well as thermal functions from ref 5. d Partial pressures from ref 5; thermal functions from the present work. e I(i+)/I(Si+) derived from the partial pressures from ref 5; pressure calibration and subsequent evaluations as for the intensities measured in the present study.
partial pressures to third-law evaluations with the same thermal functions as employed in the present investigation. Atomization enthalpies smaller than those determined by us were obtained for BSi and BSi2(g) (see Table 5, set 2, reactions 1 and 3); for Si2 the value was also smaller ∼285 kJ‚mol-1. When evaluated with their own estimated thermal functions,5 the atomization enthalpies of BSi(g) and BSi2(g) remained lower (see Table 5, set 1), but D°0 (Si2) increased to a value very close to our value.9 To be uniform, we traced back the relative intensities {I(i+)/ I(Si+)} from the partial pressures and the other parameters given by Verhaegen et al., by assuming that Emax ) m‚AP (m ) any integer from 2 to 5, but the same for all the ions) and E ) 13 eV. The values were practically the same, with Emax ) 70 eV or E ) 12-15 eV. Subsequently, their intensities were treated the same way as our intensities (including pressure calibration). The resulting enthalpies are given in Table 5, set 3. We note that not only do the atomization enthalpies for BSi and BSi2 become larger but also are in better agreement with our values. Thus, the data of Verhaegen et al. and the present work are consistent except that the atomization enthalpies obtainable from the as-reported partial pressures by Verhaegen et al. are different due partly to a possible error in their pressure calibration and partly due to differences in the thermal functions. This is
supported by our observation that the reported5 p(B) yielded an activity of boron ranging from 1.5 to 2.2 while the reevaluated p(B) gave an activity of boron ranging from 0.6 to 1. Enthalpies of Formation. We deduced the enthalpies of formation for BSix by combining our selected atomization enthalpies with the enthalpies of formation of B(g)24 (565 ( 5 kJ‚mol-1 at T ) 298.15 K; 560 ( 5 kJ‚mol-1 at T ) 0 K), and of Si(g)25 (450 ( 4 kJ‚mol-1 at T ) 298.15 K; 446 ( 4 kJ‚mol-1 at T ) 0 K). The values are 698 ( 14 kJ‚mol-1 at T ) 298.15 K; 694 ( 14 kJ mol-1 at T ) 0 K for BSi(g), 688 ( 20 kJ‚mol-1 at T ) 298.15 K; 685 ( 20 kJ‚mol-1 at T ) 0 K for BSi2(g), and 701 ( 31 kJ‚mol-1 at T ) 298.15 K; 699 ( 31 kJ‚mol-1 at T ) 0 K for BSi3. Acknowledgment. We acknowledge the Robert A. Welch Foundation under Grant No. A-0387 and the National Science Foundation under Grant No. CHE-9117752 for financial support in carrying out this work. References and Notes (1) Li, X.-H.; Carlsson, J. R. A.; Johansson, M.; Ekstro¨m, B.; Gong, S. F.; Hentzell, H. T. G. Appl. Phys. Lett. 1992, 61, 1316. (2) Carlsson, J. R. A.; Li, X. -H.; Gong, S. F.; Hentzell, H. T. G. J. Appl. Phys. 1993, 74, 891. (3) Ong, C. W.; Chik, K. P.; Wong, H. K. J. Appl. Phys. 1993, 74, 6094. (4) Mukaida, M.; Goto, T.; Hirai, T. J. Mater. Sci. 1992, 27, 255. (5) Verhaegen, G.; Stafford, F. E.; Drowart, J. J. Chem. Phys. 1964, 40, 1622. (6) Armas, B.; Male, G.; Salanoubat, D.; Chatillon, C.; Allibert, M. J. Less-Common Met. 1981, 82, 245. (7) Schmude, Jr., R. W.; Ran, Q.; Gingerich, K. A. J. Chem. Phys. 1993, 99, 7998. (8) Ran, Q.; Schmude, Jr. R. W.; Miller, M.; Gingerich, K. A. Chem. Phys. Lett. 1994, 230, 337. (9) Schmude, Jr. R. W.; Ran, Q.; Gingerich, K. A.; Kingcade, Jr., J. E. J. Chem. Phys. 1995, 102, 2574. (D°0 (Si2) ) 313.3 kJ‚mol-1, when based on ∆fH°m(Si, g, 298.15 K) ) 450 kJ‚mol-1 24,25). (10) Viswanathan, R.; Schmude, Jr., R. W.; Gingerich, K. A. J. Chem. Thermodyn. 1995, 27, 763. (11) Viswanathan, R.; Schmude, Jr., R. W.; Gingerich, K. A. J. Chem. Thermodyn. 1995, 27, 1303. (12) Gingerich, K. A. J. Chem. Phys. 1968, 49, 14. (13) Moore, C. E. “Ionization Potentials and Ionization Limits Derived from the Analyses of Optical Spectra”; Natl. Bur. Stand. U.S. NSRDSNBS 34, 1970. (14) Chase, M. W., Jr.; Davies, C. A.; Downey, J. R.; Frurip, D. J.; Mc Donald, R. A.; Syverud, A. N. JANAF Thermochemical Tables, 3rd ed.; J. Phys. Chem. Ref. Data 1985, 14, Suppl. No. 1. (15) Mann, J. B. In Recent DeVelopments in Mass Spectrometry; Proc. Int. Conf. Mass Spectrom.; Ogata, K., Hayakawa, T., Eds.; University of Tokyo Press: Tokyo, 1970; p 814 (ionization cross-section tables obtained on request). (16) Pottie, R. F.; Cocke, D. L.; Gingerich, K. A. Int. J. Mass Spectrom. Ion Phys. 1973, 11, 41. (17) Stull, D. R.; Prophet, H. In Characterization of High Temperature Vapors; Margrave, J. L., Ed. Wiley Interscience: New York, 1971; p 359. (18) Boldyrev, A. I.; Simons, J. J. Phys. Chem. 1993, 97, 1526. (19) Bernardo, D. N.; Morrison, G. H. Surf. Sci. 1989, 223, L913. (20) Schmude, Jr., R. W. Ph.D. Dissertation, Texas A&M University, College Station, TX 77843, 1994. (21) Wilson, Jr., E. B.; Decius, J. C; Cross, P. C. Molecular Vibrations; McGraw Hill: New York, 1955. (22) Schachtchneider, J. H; Snyder, R. G. Spectrochim. Acta 1963, 19, 117. (23) Ran, Q.; Schmude, Jr., R. W.; Gingerich, K. A.; Wilhite, D. W.; Kingcade, Jr., J. E. J. Phys. Chem. 1993, 97, 8535. (24) CODATA Key Values for Thermodynamics; Cox, J. D., Wagman, D. D., Medvedev, V. A., Eds.; Hemisphere Publishing Corp.: New York, 1989. (25) Desai, P. D. J. Phys. Chem. Ref. Data 1986, 15, 967.
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