The standard molar atomization enthalpy and the standard molar enthalpy of formation of gaseous Si2N from high-temperature mass spectrometry

O-573 J. Chem. Thermodynamics 1995, 27, 1303–1311

The standard molar atomization enthalpy and the standard molar enthalpy of formation of gaseous Si2 N from high-temperature mass spectrometry R. Viswanathan,a R. W. Schmude, Jr.,b and K. A. Gingerich c Department of Chemistry, Texas A & M University, College Station, TX 77843-3255 , U.S.A.

(Received 2 December 1994; in final form 23 May 1995) A high-temperature mass-spectrometric study of the vaporization of (silicon+boron nitride) from a boron-nitride Knudsen cell was conducted in the temperature range T = 1688 K to 1921 K. The partial pressures of Si(g), Si2(g), N2(g), and Si2 N(g) were determined. The dissociation reaction: Si2 N(g)=2Si(g)+0.5N2(g) was evaluated by using new thermal functions for Si2 N(g) calculated from the results of recent theoretical and experimental studies, and Dr H°m values: (538.0212.4) kJ·mol−1 at T :0, and (545.1212.4) kJ·mol−1 at T = 298.15 K were deduced by third-law evaluation. These values, in combination with the molar dissociation enthalpy of N2(g) yielded the molar atomization enthalpies: Dat H°m(Si2 N,g) = (1008.8 2 12.4) kJ·mol−1 at T : 0, and (1017.8 2 12.4) kJ·mol−1 at T=298.15 K, and in combination with the standard molar enthalpy of formation of Si(g) yielded: Df H°m(Si2 N, g)=(354.0214.8) kJ·mol−1 at T : 0, and (355.6214.8) kJ·mol−1 at T=298.15 K. 7 1995 Academic Press Limited.

1. Introduction Silicon-nitride thin films find a variety of applications in semiconductor devices.(1, 2) The use of chemical-vapor-deposition processes for the preparation of silicon-nitride layers as well as (silicon nitride+boron nitride) composites(3) is an incentive to conduct thermodynamic investigations on the (silicon+nitrogen) gaseous species. Zmbov and Margrave(4) were the first to obtain mass-spectrometric evidence for the existence of Si2 N. Another high-temperature mass-spectrometric study has been done by Potter.(5) Both studies involved the vaporization of elemental silicon(4, 5) or (silicon+silicon carbide) condensed-phase mixture(5) from Knudsen cells made of boron nitride. There is a significant difference in the standard molar enthalpy of formation: Df H°m(Si2 N,g,298.15 K) resulting from the two investigations: a On leave from Materials Chemistry Division, Chemical Group, Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamil Nadu 603 102, India. b Present address: Gordon College, Division of Natural Sciences and Nursing, 419 College Dr., Barnesville, GA 30204, U.S.A. c To whom correspondence should be sent.

0021–9614/95/121303+09 $12.00/0

7 1995 Academic Press Limited

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(389 2 21) kJ·mol−1 ,(4) and (352 2 25) kJ·mol−1 .(5) JANAF(6) gives Df H°m(Si2 N,g,298.15 K)=(397.5220.9) kJ·mol−1 from a third-law re-evaluation of Zmbov and Margrave’s(4) results using thermal functions based on the analogy of Si2 N(g) to C2 N(g). This discrepancy prompted us to reinvestigate (silicon+boron nitride) by Knudsen-effusion mass spectrometry.

2. Experimental Silicon powder (semiconductor grade; mass: 0.0933 g) and boron nitride powder (obtained by scrubbing a high-density boron nitride rod; mass: 0.0276 g) were placed inside a boron-nitride Knudsen cell (orifice dimensions: diameter, 1 mm; length, 2 mm). The BN cell was inserted into a graphite cell without a lid. Vaporization experiments were conducted in three sets. The details of the mass spectrometer (Nuclide Corporation) are given elsewhere.(7) Ion intensities at ratios M/z −1 (Si+ of molar mass to charge number: 28 g·mol−1 (Si+ or N+ 2 ), 56 g·mol 2 ), and −1 + 70 g·mol (Si2 N ), were measured as a function of temperature at electron-impact energies E=2.0 aJ and 2.8 aJ. In the third set, ion-intensity measurements were carried out in addition at E=3.6 aJ. The electron-energy calibration was based on the known ionization energy of Si(g).(8) The acceleration potential applied on the ions was 4.5 kV, and the entrance shield of the secondary electron-multiplier detector system was kept at a potential of −2.5 kV.

3. Results The ion-intensity ratio I +(M/z=28 g·mol−1 )/I+(M/z=29 g·mol−1 ) at an electron-impact energy of 2.0 aJ agreed well with the expected value for Si+. At higher electron-impact energies, however, this ratio (after subtraction of the background values at both ratios of molar mass to charge number) was larger and was attributed to N+ 2 arising from the ionization of the N2(g) in the equilibrium vapor. The ion Si2 N+ was identified by its isotopic distribution and its neutral precursor Si2 N by the low appearance potential (6.920.5) V. The relative intensity of Si+ 2 was measured to evaluate the dissociation equilibrium: Si2(g)=2Si(g), and obtain indirect proof for the reliability of our pressure calibration based on the assumption of unit activity of silicon in our sample: a(Si)=1. The relative intensities I(Si+)/I° and I(N+ 2 )I° were deduced from the total relative intensity I+(M/z=28 g·mol−1 )/I° by using the relations: I(Si+,x aJ)/I°={I(Si+,2.0 aJ)/I°}·s(Si,x aJ)/s(Si,2.0 aJ),

(1)

+ −1 I(N+ ,x aJ)/I°}−{I(Si+,x aJ)/I°}. 2 ,x aJ)/I°={I (M/z=28g·mol

(2)

The ionization cross sections s(Si) at the electron energies 2.0 aJ, 2.8 aJ, and 3.6 aJ were taken from Mann.(9) The usual equation: p(i )=k(i )·{I(i +)/I°}·(T/K),

(3)

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Study of Si2 N molecule

was employed to calculate the partial pressure p(i ) at temperature T, where k(i ) is the pressure constant for the species i. An average k(Si) value for each set at E=2.0 aJ was first calculated from I(Si+,2.0 aJ) and the partial pressure p°(Si) of Si(g) over elemental silicon by assuming a(Si)=1 in the sample of (silicon+boron nitride). The p°(Si) was deduced from the standard molar enthalpy of formation of Si(g): (45028) kJ·mol−1 at T=298.15 K,(6) which is the value adopted by CODATA,(10) and by JANAF,(6) and the thermal functions for Si(reference state)(6) and Si(g).(6) The p°(Si) values at T=1688 K and T=1921 K are 5.1·10−2 Pa and 1.7 Pa, respectively. The k(Si) values at E=2.8 aJ and E=3.6 aJ were subsequently deduced according to the relation: k(Si,x aJ)=k(Si,2.0 aJ)·s(Si,2.0 aJ)/s(Si,x aJ).

(4)

The pressure calibration constants for Si2 , N2 , and Si2 N were computed according to k(i )=k(Si)·{s(Si)·g(Si)·n(Si)}/{s(i )·g(i )·n(i )}.

(5)

The ionization cross-sections s(i ) for the molecules were assumed to be 0.75 times the sum of the ionization cross-sections for the constitutent atoms. The values of s for N(g) were taken from Mann.(9) The relative secondary-electron multiplier gains g for N+ and Si+ were taken from Pottie et al.(11) For molecular ions, they were assumed to be the average of those of the atomic ions constituting them. This assumption has been confirmed to be valid for N2+ from Gingerich’s(12–14) measurements of g(N2+ ) relative to g(Ag+)=0.540.(11) In equation (5), n(i ) represents the isotopic abundance of the ion. Table 1 lists the pressure calibration constants and the s, g, and n values used in the calculation of the partial pressures. TABLE 1. Pressure calibration constants k for Si, a Si2 , b N2 , c and Si2 N d E aJ

k(Si) MPa

2.0 2.8

39.2 23.3

2.0 2.8

27.7 16.5

2.0 2.8 3.6

45.4 27.0 22.6

k(Si2 ) MPa

k(N2 ) MPa

k(Si2 N) MPa

16.8 Set 2

128.7

14.8

11.9 Set 3

91.1

10.5

149.0 68.0

17.1 13.9

Set 1

19.5 16.4

a Values of s: 2.416·10−16 cm2 (at E = 2.0 aJ), 4.065·10−16 cm2 (at E = 2.8 aJ), 4.844·10−16 cm2 (at E=3.6 aJ); g=0.909; n=0.922 (for M/z=28 g·mol−1 ). b s=1.5·s(Si); g=g(Si); n=0.851 (for M/z=56 g·mol−1 ). c Values of s: 0.536·10−16 cm2 (at E=2.8 aJ), 1.175·10−16 cm2 (at E=3.6 aJ); g=g(N)=1.164; n=0.993 (for M/z=28 g·mol−1 ). d Values of s: 6.365·10−16 cm2 (at E=2.8 aJ), 7.854·10−16 cm2 (at E=3.6 aJ); g=0.994; n=0.845 (for M/z=70 g·mol−1 ).

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The principal reaction evaluated from the partial pressures was Si2 N(g)=2Si(g)+0.5N2(g).

(6)

The thermal functions for N2(g) were taken from JANAF,(6) and those for Si2 N(g) were calculated by using the harmonic-oscillator-rigid-rotor approximation(15) and the results of new experimental(16) and theoretical(17) studies for this molecule. A centrosymmetric linear Dah structure with an Si–N bond length(16) of 1.64·10−10 m was used. This yielded for the product of the moments of inertia 2.5087·10−45 kg·m2 for the molecule. The vibrational wavenumbers were taken from the ab initio study by Goldberg et al.:(17) 898 cm−1 , 613 cm−1 , 221 cm−1 , and 130 cm−1 . A 2Pg electronic ground state(16, 17) (multiplicity: 4) along with one 2A1 excited state estimated at 2000 cm−1 (multiplicity: 2) was employed in the calculations. Table 2 gives the third-law enthalpies for reaction (6) together with the ion intensities (measured or deduced) which led to these values. The thermal functions calculated for Si2 N(g) are given in table 3. The third-law entropy change Dr S°m(6) calculated from thermal functions is 170.2 J·K−1·mol−1 at T=298.15 K. The mean of 28 values at E=2.8 aJ, (538.0212.4) kJ·mol−1 , was chosen as the selected value for Dr H°m(6) at T : 0. The corresponding value at T=298.15 K is (545.1212.4) kJ·mol−1 . The standard deviation of the mean (see table 3) as well as estimated uncertainties of 22·p(N2 ), 20.4·p(Si2 N), and 23 J·K−1·mol−1 in F°m=(DT0 S°m−DT0 H°m/T ) for Si2 N(g) were taken into account for the overall uncertainty in the selected value. These values, when combined with Df H°m(Si,g,T : 0)=(44628) kJ·mol−1 ,(6) or Df H°m(Si,g,298.15 K)=(45028) kJ·mol−1 ,(6, 10) yield the standard molar enthalpy of formation of Si2 N(g): Df H°m(Si2 N,g)=(354.0220.2) kJ·mol−1 at T : 0, and (355.6220.2) kJ·mol−1 at T=298.15 K. In a recent assessment of the standard molar enthalpy of formation of Si(g), Desai(18) included additional newer experimental results that had not been considered by CODATA,(10) or JANAF.(6) He arrived at the same value (450 kJ·mol−1 at T=298.15 K) but with a smaller error bound of 24 kJ·mol−1 . Use of this value lowers the overall uncertainty in the Df H°m(Si2 N,g) to 214.8 kJ·mol−1 , which we select. From the partial pressures, an equation for the standard molar Gibbs free energy change DrG°m(6) was deduced: DrG°m(6)/(kJ·mol−1 )=(462.07240.71)−(0.124720.0225)·(T/K).

(7)

We also obtained the standard molar enthalpy of atomization of Si2 N(g): Dat H°m(Si2 N,g), by combining our selected standard molar enthalpy for reaction (6) with the standard molar enthalpy of dissociation D°m(N2 ,g,T : 0) = (941.64 2 0.60) kJ·mol−1 ,(6) or Df H°m(N,g,298.15 K) = (472.68 2 0.10) kJ·mol−1 .(6) The values of Dat H°m are (1008.8212.4) kJ·mol−1 at T :0 and (1017.8212.4) kJ·mol−1 at T=298.15 K.

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Study of Si2 N molecule

TABLE 2. Relative ion intensities I/I° at E = 2.8 aJ and E = 3.6 aJ and the third-law standard molar enthalpies of dissociation D°m at T : 0 corresponding to the reactions Si2(g) = 2Si(g), and Si2 N(g)=2Si(g)+0.5N2(g); p°=0.101325 MPa T K

I(Si+) I°

I(Si2+ ) I°

I(N2+ ) I°

I(Si2 N+) I°

D°m(Si2 ) kJ·mol−1

D°m(Si2 N) kJ·mol−1

3.8·10−12 3.7·10−12 1.6·10−12 7.9·10−13 5.2·10−13 2.6·10−13 1.1·10−13 3.6·10−13 7.8·10−13 9.4·10−13 5.2·10−12 9.2·10−12

320.5 314.7 313.0 318.0 312.6 319.0 313.5 317.1 318.0 314.0 317.3 313.8

549.8 547.5 545.1 543.2 544.1 536.5 530.6 539.1 544.5 546.6 551.9 545.7

5.8·10−14 1.0·10−13 1.2·10−12 2.1·10−12 4.9·10−12 3.2·10−12 3.5·10−12 2.8·10−13

310.5 316.5 316.4 314.6 315.0 318.3 319.2

529.6 524.1 540.6 541.0 548.1 540.0 539.5 523.8

4.6·10−13 9.3·10−13 1.4·10−12 1.9·10−12 2.5·10−12 9.5·10−13 1.8·10−13 4.7·10−14

322.8 313.3 316.6 314.2 314.0 312.8 313.6 315.6

533.9 540.4 539.7 533.8 534.9 524.1 522.8 524.2

320.9 313.0 316.8 313.5 313.1 312.2 313.4 317.9

531.0 539.5 539.4 531.1 535.4 520.6 518.8 519.5

Set 1 (E=2.8 aJ) 1792 1818 1799 1769 1750 1719 1702 1737 1780 1792 1900 1918

−12

8.1·10 1.2·10−11 8.2·10−12 4.9·10−12 3.5·10−12 2.2·10−12 1.5·10−12 2.7·10−12 5.0·10−12 6.7·10−12 2.3·10−11 4.5·10−11

−13

4.2·10 4.5·10−13 2.4·10−13 1.7·10−13 7.4·10−14 6.8·10−14 2.7·10−14 7.2·10−14 1.6·10−13 1.9·10−13 8.4·10−13 2.2·10−12

7.9·10−12 6.2·10−12 3.3·10−12 2.5·10−12 1.8·10−12 2.1·10−12 1.9·10−12 2.6·10−12 2.8·10−12 1.5·10−12 9.9·10−12 8.4·10−12 Set 2 (E=2.8 aJ)

1688 1722 1809 1848 1886 1871 1893 1772

1.6·10−12 3.1·10−12 1.2·10−11 2.1·10−11 3.6·10−11 3.0·10−11 3.5·10−11 7.4·10−12

5.2·10−14 4.1·10−13 7.9·10−13 1.4·10−12 1.2·10−12 1.6·10−12 2.9·10−13

6.9·10−13 1.5·10−12 3.1·10−12 4.3·10−12 4.2·10−12 5.7·10−12 8.7·10−12 2.6·10−12 Set 3 (E=2.8 aJ)

1807 1861 1882 1912 1921 1862 1800 1725

7.4·10−12 1.4·10−11 1.6·10−11 2.9·10−11 3.4·10−11 2.0·10−11 7.4·10−12 2.0·10−12

4.0·10−13 3.9·10−13 5.7·10−13 1.1·10−12 1.4·10−12 7.9·10−13 2.4·10−13 5.0·10−14

1.6·10−12 1.8·10−12 4.2·10−12 5.2·10−12 5.7·10−12 3.7·10−12 7.9·10−13 4.1·10−13 Set 3 (E=3.6 aJ)

1807 1861 1882 1912 1921 1862 1800 1725

a b

8.8·10−12 1.6·10−11 2.0·10−11 3.5·10−11 4.0·10−11 2.3·10−11 8.8·10−12 2.4·10−12

4.2·10−13 3.4·10−12 4.6·10−13 4.6·10−13 4.5·10−12 1.2·10−12 6.8·10−13 6.5·10−12 1.4·10−12 1.3·10−12 1.1·10−11 2.0·10−12 1.5·10−12 7.5·10−12 2.5·10−12 9.0·10−13 5.1·10−12 7.4·10−13 2.8·10−13 2.1·10−12 1.8·10−13 7.0·10−14 1.0·10−12 4.4·10−14 D°m(Si2 )=(315.722.7) kJ·mol−1 a D°m(Si2 N)=(538.028.6) kJ·mol−1 b

Mean of 27 values at E=2.8 aJ; uncertainty is the standard deviation. Mean of 28 values at E=2.8 aJ; uncertainty is the standard deviation.

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TABLE 3. Auxiliary thermodynamic quantities calculated for Si2 N(g); (F°m=DT0 S°m−DT0 H°m /T; p°=0.101325 MPa) T K

H°m(T )−H°m(0) kJ·mol−1

F°m J·K−1·mol−1

298.15 1200 1400 1600 1800 2000 2200

12.4 66.2 78.9 91.6 104.3 117.0 129.7

219.7 287.3 295.9 303.5 310.3 316.4 322.0

4. Discussion The measurements at E=3.6 aJ were carried out mainly to confirm the partial pressures derived from I+/I° at E=2.8 aJ. The partial pressures computed from the values of I+/I° given in table 2 for the third set reveal that for N2(g) they are practically identical, and for Si2 N(g), the maximum disagreement is only 125 per cent. Evaluation of the dissociation equilibrium: Si2(g)=2Si(g), from the partial pressures yielded D°m(Si2 ,g,T : 0) = (318.5 2 15.1) kJ·mol−1 (second-law) and (315.722.7) kJ·mol−1 (third-law). These are in good agreement with the value (313.327) kJ·mol−1 revised from the quoted(19) value of (31927) kJ·mol−1 in order to be consistent with the p°(Si)(6) used for pressure calibration in this work. This agreement was taken to validate our assumption that a(Si)=1 in our sample of (silicon+boron nitride). The p(Si) values reported by Potter(5) in his two experiments (one with silicon in a BN Knudsen cell, and the other with a mixture of silicon and silicon carbide in a BN Knudsen cell) differ from each other by about 0.33·p(Si). Since the p(Si) quoted for the first experiment is consistent with the p°(Si),(6) at temperatures from 1785 K to 2000 K, the lower p(Si) value in the second experiment, where the highest temperature was only 1936 K, indicating a(Si)Q1, is somewhat surprising. A closer examination of the results for the second experiment reveals that p(Si)/[{I(Si+)/I°}·(T/K)] = 2.87·10−11 MPa is very close to the mean k(Si)=(2.9220.87)·10−11 MPa, calculated from Potter’s(5) I(Si+)/I° and p°(Si) from Hultgren et al.(20) {which is about 0.33·p°(Si) lower than the JANAF(6) value at T=1800 K}. We have also evaluated the equilibrium: B(s)+0.5N2(g)=BN(s),

(8)

by assuming a(B)=1 in our sample system. The thermal functions were taken from JANAF.(6) The partial pressures of N2 reported by Zmbov and Margrave(4) and Potter(5) were also re-evaluated. The equilibrium partial pressures of N2 over BN(s) measured by Hildenbrand and Hall(21) using the torsion-effusion technique were also subjected to re-evaluation for a meaningful comparison. Table 4 compares the results with the

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Study of Si2 N molecule

TABLE 4. Comparison of the enthalpy changes for the reactions: B(s)+0.5N2(g)=BN(s), and 2Si(s,l)+BN(s)=Si2 N(g)+B(s), and of the partial pressures p(N2 ) and p(Si2 N) at T=1800 K. The partial pressures were computed by using the enthalpies and the Dr F°m s of the pertinent reactions Dr H°m(T : 0) kJ·mol−1

−248.0 −249.6 −219.7 −255.3 a −246.7 b −246.8 610.3 610.7 a 610.5 b 599.9 a b

p(i) Pa

source

B(s)+0.5N2(g)=BN(s); i=N2(g) JANAF(6) 4.2·10−1 3.4·10−1 Hildenbrand and Hall(21) 1.8·101 Zmbov and Margrave(4) 1.6·10−1 Potter(5) 5.0·10−1 Potter(5) 4.9·10−1 This work 2Si(s,l)+BN(s)=Si2 N(g)+B(s); i=Si2 N(g) 9.5·10−3 Zmbov and Margrave(4) 9.3·10−3 Potter(5) 9.4·10−3 Potter(5) 1.9·10−2 This work

Si in BN Knudsen cell. (Silicon+silicon carbide) in BN Knudsen cell.

calorimetric value of the standard molar enthalpy of formation of BN(s) reported by Wise et al.,(22) which has been adopted by JANAF.(6) In terms of p(N2 ) at T=1800 K, as deduced from the value of the mean molar enthalpy given in table 4, the vapor-pressure measurements yield results that are 10.2·p(N2 ) lower (Hildenbrand and Hall); 10.62·p(N2 ) lower, and 10.19·p(N2 ) higher (Potter, two experiments); and 10.17·p(N2 ) higher (this work) than the calorimetric measurement. Zmbov and Margrave’s results are, however, 144·p(N2 ) higher. Good agreement between the p(N2 ) reported by Hildenbrand and Hall, who extrapolated the observed pressures to zero orifice diameter to compute the equilibrium pressures, and the results by Potter and the present work indicates that Si(l) acted as a vaporization catalyst(24) that caused an effective vaporization coefficient of 1 for N2 . The low vaporization coefficients for N2 from BN(s), reported by Hildenbrand and Hall(21) as well as by Dreger et al. (Langmuir vaporization study),(23) may be explained by the theory proposed by Brewer and Kane:(24) the non-existence of N2 units in the lattice of BN. Due to lack of information, the reason for the very high p(N2 ) obtained by Zmbov and Margrave(4) could not be ascertained, especially since the p(Si) obtained by these authors using calibration on the basis of p°(Ag) is only 130 per cent higher than the p°(Si) used by us as well as by Potter for pressure calibration. One possible explanation is that Zmbov and Margrave might have divided the p(N2 ) which they actually measured by the vaporization coefficient with values ranging from 6.6·10−3 to 9.8·10−3 reported by Dreger et al.(23) An analysis of Potter’s results for I(Si+), I(N2+ ), p(Si), and p(N2 ) indicates that he also (like us) did not use the vaporization coefficient in calculating the p(N2 ), although his statement that p(N2 ) was in excellent agreement with that reported by Hildenbrand and Hall(21) when the low vaporization coefficient for BN was taken into account raises a doubt as to whether his measured p(N2 ) values were much lower. Such a doubt is

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not alleviated on reading his comment on the p(N2 ) values reported by Zmbov and Margrave:(4) ‘‘since BN has a low vaporization coefficient, it would be expected that the observed nitrogen pressures would be only a small fraction of the equilibrium pressure’’. Neither Zmbov and Margrave(4) nor Potter(5) mentioned how they deduced the I(N2+ )/I° whether from the total relative ion intensity at M/z=28 g·mol−1 (as we did in the present study) or by mass-separating the peaks 28Si+ and 28N2+ . In order to compare the p(Si2 N) values, the reaction: 2Si(s,l)+BN(s)=Si2 N(g)+B(s),

(9)

was evaluated once again by assuming a=1 for all the condensed-phase participants. The results of Potter(5) and Zmbov and Margrave(4) agree, but are both 10.5·p(Si2 N) lower than our value at T=1800 K. Zmbov and Margrave did not give details, but the differences between the s and g values used by us and by Potter account for a discrepancy of 0.33·p(Si2 N). Re-evaluation of Potter’s(5) results yielded Df H°m(Si2 N,g)=354.2 kJ·mol−1 at T : 0, and 355.8 kJ·mol−1 at T=298.15 K (experiment 1) and 351.8 kJ·mol−1 at T : 0, and 353.4 kJ·mol−1 at T=298.15 K (experiment 2), in very good agreement with our values of (354.0214.8) kJ·mol−1 at T : 0, and (355.6214.8) kJ·mol−1 at T=298.15 K. As expected, due to the high p(N2 ) obtained by them, Zmbov and Margrave’s(4) re-evaluated results indicate lower stability: 399.0 kJ·mol−1 at T : 0, and 400.6 kJ·mol−1 at T=298.15 K. The as-reported Df H°m(Si2 N,g,298.15 K) values are somewhat lower: (389.1220.9) kJ·mol−1 (Zmbov and Margrave),(4) and (351.5225.1) kJ·mol−1 (Potter).(5) The authors wish to acknowledge the financial support from the National Science Foundation under Grant No. CHE-9117752 and from the Robert A. Welch Foundation under Grant No. A-0387. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

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