Identification and Dissociation Energy of Gaseous HfN
273
Acknowledgments. The authors are pleased to acknowledge the support of the U. S. Atomic Energy Commission through Contract AT( 11-1)-1140 with the University of Kansas, and the Computation Center a t the University of Kansas. References and Notes (1) S.-S. Lin, Ph.D. Thesis, University of Kansas, Lawrence, Kan., 1966
(3) M. Farber, 0.M. Uy, and R. D. Srivastava, J. Chem. Phys., 56, 5312 (1972). (4) K. E. Frantseva and G. A. Seminov, High Temp. (USSR), 7, 52 (1969). (5) R. J. Ackermann and E. G. Rauh, J. Phys. Chem., 67,2596 (1963). (6) E. K. Kazenas and Yu V. Tsvetkov, Ross. J. Phys. Chem., 41, 1675 (1967). (7) I. Hargittai. M. Hargittai, V. P. Spiridonov, and E. V. Erokhin, J. Mol. StrUCt., 8,31 (1971). (8) J. G. Edwards, H. F. Franzen, and P. W. Gilles, J. Chem. Phys., 54, 545 (1971). (9) W. Rudorff and H. Kornelson, Rev. Chim. Miner., 6, 137 (1969). (IO) M. lsraelsson and L. Kihlborg, Mater. Res. Bull., 5, 19 (1970). (11) J. L. Franklin, J. G. Dillard, H. M. Rosenstock, J. T. Herron, K. Draxl, and F H. Field, Nat. Stand. Ref. Data Ser., Nat. Bur. Stand., No. 26 (1969).
(2) J. Berkowitz, W. A. Chupka, and M. G. Inghram, J. Chem. Phys., 27,87 (1957).
Identification and Dissociation Energy of Gaseous Hafnium Mononitride Fred J. Kohl* and Carl A. Stearns NASA Lewis Research Center, Cleveland, Ohio 44735 (Received September 23, 7973) Publication costs assisted by the National Aeronautics and Space Administration
The hafnium nitride molecule (HfN) has been identified by molecular beam mass spectrometry in the vapor phase at temperatures above 2800 K. The enthalpy of the reaction HfN(g) = Hf(g) + 0.5Nz(g) was determined as AH"0 = 60.5 30 kJ moly1 and combined with the dissociation energy of Nz(g) to yield the dissociation energy of HfN(g) of D O 0 = 531 30 kJ mol-I.
*
Introduction The dissociation energies of the diatomic metal nitride molecules TiN,I VN,2 ZrN,3 CeN,4 ThN,5 and UN6 have been determined in the last several years by the technique of high-temperature molecular beam mass spectrometry. Although the HfN molecule has not been observed, bond energy calculation^^^^ based on the dissociation energies of ZrN, ThN, and UN predict that it should be one of the most stable diatomic transition metal nitrides. In the present study, we have identified gaseous HfN and determined its dissociation energy by the mass spectrometric technique. Experimental Procedure and Results The experimental details and procedure used are similar to those employed in the determination of the dissociation energy of TiN.I The high-temperature Knudsen cell and double-focusing mass spectrometer system have been described in detail previously.8 In the present experiment, a sample of hafnium nitride (initial stoichiometry approximately HfW1.0) was contained in a tungsten Knudsen cell. After calibration of the system by vaporization of silver from a 0.005-mm thick foil placed in the cell, the sample was heated over a period several days to temperatures above 2800 K during which large amounts of Nz(g) were liberated. In addition to Nz+, the Hf+, HfN+, and HfO+ ions were identified. The mass spectrometer was operated a t a resolution of approximately 2000 (10% valley definition) which was sufficient to separate clearly the metal-containing peaks from any organic background peaks present at the same nomi-
*
nal m l e ratio. The ionic species were identified in the usual manner by their m l e ratio and isotopic abundance distribution. Shutter measurements established that each of the Hf-containing ions was 100% shutterable and had neutral precursors originating from the Knudsen cell. After the preliminary h a t i n g noted above, the shutterable portion of the Nz+ intensity was about 15%. The resolution of the mass spectrometer was insufficient to provide a workable separation of HfN+ from HfO+ at the same m / e peak. Therefore the HfN+ intensity was measured at m / e = 191 where the interference from HfO+ due to overlapping isotopic distributions was determined to be negligible. The m / e 191 peak of HfN+ (17?Hf 14N) represents 18.5% of the total HfN+ intensity while the m l e 191 peak of HfO+ (174Hf I7O) is less than of the total HfO+ intensity. A precise appearance potential for HfN+ was not determined because of its low intensity. A rough determination indicated that the A.P. was less than 10 eV. Ion currents, given in Table I, were measured for Nz+, Hf+, and HfN+ at 2885 and 2969 K.
+
+
TABLE I: I o n Intensity. for t h e Nz+, Hf +, and HfN + Ions TemMultiplier anode current, A
pera-
ture, K
2885 2969
~
FNz+
1.42 X 2.31 X
leOHf+
1.01 X 2.19 X
lo-?
1B'HfN+
7.46 X 10-l2 9.59 X 10-l2
Measurements were made using 20-eV electrons at 100 FA anode current. a
The Journal of Physical Chemistry, Vol. 78. No. 3, 7974
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Fred J. Kohl and Carl A. Stearns
TABLE 11: Partial Pressures of Nz, Hf, and HfN and Third-Law Enthalpies
Temp, K
Nz
2885 2969
7.30 1.22
x
Hf
HfN
3.85 8.61
10-1
-
-A[(G'T Had/ TI,J K-1 mol-1
Log K
Pressure, N m-2
6.59 8.72
x 10-4 x 10-4
HfN(g) = Hf(g)
1.196 1.534
AH'o,
kJ mol-1
+ 0.5Nz(g)
46.71 46.95
68.7 52.2
Av 60.5
TABLE 111: Parameters for Various Ionsa Ion
Ionization crow section, a ~~~
Multiplier gain, y
Isotopic abundance, n
~~
5.44 6.50 X lo6 2.66 1 .oo x 107 7.76 (6.50 X 106) 6.40 (6.50 X lo6) k = 2.35 X 1011 N m-2 A-1 K-1 a
Intensity correction factor, E
(1.O) (2 .O) (1.O) (1.O)
0.5182
0.9927 0.3524 0 ,1845
Values in parenthesea are estimated.
Calculations and Discussion The measured ion currents I i were converted to partial pressures Pi, listed in Table 11, by use of the standard relation, Pi = kIiTEi/uiyinl, where k is the sensitivity constant determined by the silver calibration, ui is the relative maximum ionization cross section, yi is the multiplier gain, n i is the fractional isotopic abundance, and E i is a dimensionless factor to correct ion intensities measured at a particular ionizing electron energy to the maximum of the ionization efficiency curve. Relative maximum atomic ionization cross sections were taken from the work of Mann.g The cross section of Nz was obtained by multiplying Mann's value for nitrogen by the experimentally determined factor U N ~ / U N= 1.93.1° The cross section for HfN was estimated by multiplying the sum of atomic cross sections by an empirical factor of 0.7.11 It was assumed that the multiplier gains for Ag+, Hf+, and HfN+ were identical. The values of k, u, y, E, and n used are given in Table 111. From the partial pressures of Nz, Hf, and HfN the third-law enthalpy ilHo0for the reaction HfN(g) = H f k ) + 0.5Nz(g)
(1)
The AH0o of 60.5 f 30 kJ mol-l for reaction 1was combined with the dissociation energy12 of N2, DO0 = 941.4 f 8.4 kJ mol-I, to obtain the dissociation energy of gaseous HfN as DO0 = 531 f 30 kJ mol-l or DO298 = 535 f 30 kJ mol-l. The heat of formation AHOf,298 of HfN(g) was found to be 555 f 30 kJ mol-l using the heat of vaporization13 of Hf(g), AHOz98,vap = 619.2 f 4.2 kJ mol-l, and the enthalpy of reaction 1. Gingerich5q7 has employed the empirical a-parameter method of Colin and Goldfinger15 to predict a value of 0'298 [HfN(g)] = 590 f 42 kJ mol-1. This value was obtained using an average value of a = 0.5AWautomization [MN(s)]/Do298 [MN(g)] = 1.24 derived from the experimentally determined dissociation and atomization energies of solid and gaseous ZrN, ThN, and UN. By deriving an alternate value of CY = 1.32 based on the dissociation and atomization energies of only the group IV transition metal nitrides TiNl and ZrN,3 we obtain a predicted value of DO298 [HFN(g)] = 553 f 42 k J mol-l using an atomization energy5 of HfN(s) of 1461 kJ mol-l. This predicted value of 0'298 is in reasonable agreement with the experimental determination of 535 f 30 kJ mol-1 and reaffirms the usefulness of the a-parameter method to predict dissociation energies if CY is obtained from molecules of similar electronic structure.
was calculated according to the relation AHOo = -RT In
References and Notes K - TA[(G"T - H " o ) / T j where K = (PH~)(PN,)~/~. C. A. Stearnsand F. J. Kohl, High Temp. Sci., 2, 146'(1970). ( P H ~ N is) the - ~ equilibrium constant and A[(G'T - W O ) / (1) (2) M. Farber and R . D. Srivastava, J. Chem. Soc., Faraday Trans.
r] is the change of the Gibbs free-energy function for the reaction. The results are given in Table 11. Taking into account the estimated errors in pressure determinations and in the molecular parameters, an overall uncertainty of k30 kJ is obtained for the enthalpy of reaction 1. Values of the free-energy functions for Nz(g) were taken from the JANAF tables12 and those for Hf(g) from Hultgren's c0mpi1ation.l~The free-energy functions for HfN(g) were calculated on the basis of estimated molecular parameters. The ground state was taken as %, analogous to TiN(g).14 An internuclear distance of 1.80 A was used along with a fundamental vibrational frequency of 820 cm-l and an anharmonicity constant of 5 cm-l. The -[(GOT - Wo)/Tjvalues in J K - l mol-l calculated for HfN(g) are 285.81 at 2800 K, 287.08 at 2900 K, and 288.31 at 3000 K.
The Journal of Physical Chemistry, Vol. 78, No. 3, 1974
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69, 390 (1973). (3) K. A. Gingerlch, J. Chem. Phys., 49, 14 (1968). (4) K. A. Gingerich, J. Chem. Phys., 54, 3720 (1971). (5) K. A. Gingerich, J. Chem. Phys., 49, 19 (1968). (6) K. A. Gingerich, J. Chem. Phys., 47, 2192 (1967). (7) K. A. Gingerich, J. Cryst. Growth, 9, 31 (1971). ( 8 ) C. A. Stearns and F. J. Kohl, NASA TN D-5027 (1969); NASA TN (E7510), in press. (9) *J. B. Mann, J. Chem. Phys., 46, 1646 (1967). (10) A. C. H. Smith, E. Caplinger, R. H. Neynaber, E. W. Rothe, and S. M. Trujillo, Phys. Rev., 127, 1647 (1962). (1 1) R . F. Pottle. J. Chem. Phys., 44, 916 (1966). (12) D. R. Stuli, Ed., "JANAF Thermochemical Tables," Dow Chemical Co., Midland, Mich., dated Sept 30, 1965, for NZ(g). (13) R. Hultgren, R . L. Orr, P. D. Anderson, and K. K. Kelly, "Selected Values of Thermodynamic Properties of Metals and Alloys," University of California, Supplements dated Jan 1966 for Hf. (14) K. D. Carlson, C. R. Ciaydon, and C. Moser, J. Chem. Phys., 46, 4963 (1967). (15) R. Colin and P. Goldfinger in "Condensation and Evaporation of Solids, E. Rutner, P. Goldfinger, and J. P. Hirth, Ed., Gordon and Breach, New York, N. Y., 1964, pp 165-179.
