The Journal of Physical Chemisrty, Vol. 82, No.
Vaporization and Thermodynamic Studies of the La-B System
thalpies for the bent structures (see Table 111). On this basis a preferred A",Oo(CuGez) of 506.0 f 25 kJ molT1is obtained by averaging the four atomization energies corresponding to the bent structures in Table 111. The standard heat of formation, AHfoB8, for the gaseous molecule CuGez was derived as 580.0 f 28 kJ mol-l. In the calculation of the standard heat of formation of CuGez(g),the heats of vaporization (AHvosJfor germanium (374.5 f 2.1 kJ mol-l) and copper (336.8 f 1.2 kJ mol-l) were taken from Hultgren et al.7 The Pauling model of a polar bond,ll though it has shown' to be successful in predicting the atomization energies of different metal aurides, is not sensitive in predicting the atomization energy of CuGez(g). This is due to the almost equal electronegativity of both Ge and Cu, 1.8 and 1.9, respectively. Therefore, one must rely on the additivity rule of bond strength to aid in predicting the most likely structure of CuGez(g). The additivity rule predicts an atomization energy of 399 and 475 kJ mol-' for the symmetric and asymmetric structure, respectively. The values Doo(Gez)= 275.2 kJ mol-l 12913 and Doo(CuGe) = 199.5 kJ mol-' were employed. This model thus indicates the asymmetric configuration to be the more probable one, implying a higher bond order for the Ge-Ge bond. This implication comes from the use of the experimentally determined Doo(Gez),which is multiply bonded. The use of the single bond energy for Ge-Ge of
1, 1978 51
157 kJ mol-' l1would significantly decrease the calculated atomization energy. A cyclic structure, assuming three single bonds, is also a possibility when using the bond additivity concept. A final determination of the geometry of the CuGez molecule has to come from spectroscopic investigations such as IR and Raman spectroscopy.14
References and Notes (1) K. A. Gingerich, D. L. Cocke, and U. V. Choudary, Inorg. Chim. Acte, 14, L47 (1975). (2) J. E. Kingcade, M.S. Thesis, Texas A&M University, Dec 1977. (3) A. Kant and B. H. Strauss, J. Chem. Phys., 49, 3579 (1968). (4) A. Neckel and G. Sodeck, Monatsh. Chem., 103, 367 (1972). (5) K. A. Gingerich, J. Chem. Phys., 49, 14 (1968). (6) D. L. Cocke and K. A. Gingerich, J. Phys. Chem., 75, 3264 (1971). (7) R. Hultgren, P. D. Desai, D. T. Hawkins, M. Gieiser, and K. K. Kelley, "Selected Values of the Thermodynamic Properties of the Elements", American Society of Metals, Metals Park, Ohio, 1973. (8) G. Herzberg, "Molecular Spectra and Molecular Structure", Vol 111, "Electronic Spectra and Electronic Structure of Polyatomic Molecules", Van Nostrand, Princeton, N.J., 1966. (9) J. Kordis, K. A. Gingerich, and R. J. Seyse, J. Chem. R ~ y s .61, , 5114 (1974). (10) R. T. Grimiey in "Characterization of High Temperature Vapors", J. L. Margrave, Ed., Wley-Interscience, New York, N.Y., 1967 pp 195-243. (11) L. Pauiing, "The Nature of the Chemical Bond", 3d ed, Corneil University Press, Ithaca, N.Y., 1960. (12) J. Drowart, G. DeMaria, A. J. H. Boerboom, and M. G. Inghram, J . Chem. Phys., 30, 308 (1959). (13) A. Kant and H. Strauss, J. Chem. Phys., 45, 822 (1966). (14) The support of this work by the National Science Foundation under Grant CHE75-10075 is gratefully acknowledged.
Phase Relationship, Vaporization, and Thermodynamic Properties of the Lanthanum-Boron Systemt Edmund Storms" and Barbara Mueller Los Alamos Scientific Laboratory of the University of California, Los Alamos, New Mexico 87545 (Received July 18, 1977) Publication costs assisted by the Los Alamos Scientific Laboratory
The La-B system was studied between LaB4.24and LaBzg.z,and between 1400 and 2100 K to determine the phase relationship, the chemical activity of the components, the vaporization rate, and the vapor composition. A blue colored phase near LaBgwas found to exist between purple colored La& and elemental boron. Diffusion is so much slower than vaporization that large composition differences can exist between the surface and the interior which, nevertheless, produce a steady state loss rate from freely vaporizing material. The flux at 1700 K is 6 X g/cm2 s for LaB, + LaB6 and 7 X lo-'' g/cm2 s for La& + LaB9. There is an activation energy which lowers the vaporization rate of boron from La&. Freely vaporizing material will have a steady state surface composition between and La&.o.i, depending on temperature, purity, and interior composition. The free energy of formation of LaB6 is (0.0717' - 351) kJ/mol between 1700 and 2100 K.
I. Introduction This is the first in a series of papers which will show how the chemical activity and vaporization rates change as a function of temperature and composition in those systems having potential application as thermionic emitters. This information will be combined with work function studies to properly interpret the electron emission properties. Pure La& has a congruently vaporizing composition (CVC) within its single phase region which vaporizes only Work completed under the auspices of the U.S. Energy Research and Development Administration, Division of Physical Research. 0022-3654/78/2082-005 1$0 1 .OO/O
La(g) and B(g) in the same proportion as in the solid. Samples which do not have this composition will, upon vaporization, experience a change in surface composition determined by competition between diffusion and vaporization. Such samples may reach steady state so quickly as to suggest that equilibrium has been achieved. Although the surface composition will appear to be constant, it will change when the temperature is changed. In addition, different interior compositions will produce somewhat different surface compositions at the same temperature. When the diffusion rates are much less than the vaporization rate, as is the case for La& at high 0 1978 American Chemical Society
52
The Journal of Physical Chemistry, Vol. 82,
No. 1, 1978
E. Storms and B. Mueller
TABLE I: Composition, Partial Enthalpies of Vaporization, and Coefficients in the Least-Squares Equations for the Activities Based on Knudsen Measurements B/La 4.24 4.58 5.75 6.02 i 0.02c 6.07 6.12 i 0.02 6.47 6.47 6.95 8.41 8.51 8.65 9.25 15.0 19.5 29.2 LaB, t B
log aLa = A / T t B 10-4~ B
AIgLa,'
kcalimol 96.0 i 0.5b 115.3 i 0.2 124.2 i 0.4 122.7 i- 0.3 194.3 i 1.3 208.8 i 0.8 208.0 * 0.8 217 i 2 214 t 2 205.8 t 1.7 208.9 L 1.2 189.8 + 0.6 190.4 i 1.6 185.3 i 2.1 203.8 i 1.6 187.2 t 1.0 (av)
a 1 kcal/mol x 4.184 = 1 kJ/mol. based on multiple analysis.
t0.103 -0.319 -0.514 -0.481 - 2.046 - 2.362 - 2.346 - 2.547 -2.487 - 2.297 --2.366 - 1.946 - 1.961 - 1.849 - 2.254 - 1.89 - 1.989
-1.65 0.33 1.31 0.22 6.68 7.99 7.20 8.19 7.77 6.68 6.99 4.87 4.23 3.67 5.66 3.83 4.35
A%,
kcal/mol
log ag = A/T + B 10-4~ B
130.2 i. 0.9 139.9 t. 0.4
1-0.13 - 0.09
137.9 i 0.3 135.3 I 0.3 134.9 i. 0.1 131.6 * 0.2
t0.04
0.1 0.3 0.5 0.2
t 0.05 - 0.03
-0.52
+0.01 t 0.01 t 0.02
-0.14 -0.06 -0.13
133.5 i 137.4 t 135.4 i 135.7 i134.9 -I
0.2
- 0.28
- 0.63
+0.02
- 0.41 - 0.66
Standard deviation based on least-squares fit of data points.
temperatures, this behavior will be exaggerated. As a result, unexpected changes may occur in properties which are sensitive to the surface composition, such as the work function. Should a large change exist in the chemical state between the vapor and solid, an energy barrier may occur which will produce a lower vaporization rate under nonequilibrium conditions than that calculated from equilibrium measurements. The complex and tightly bound arrangement of boron atoms in LaB6 suggests the possibility of such a nonunity vaporization coefficient for boron and the need to explore this possibility. Past work has shown that the La-B system consists of two compounds, LaB4 (tetragonal) and LaBs (cubic).' LaB4 is thought to be a line compound which rapidly Converts to LaB6 as La is lost preferentially during vaporization.' Based on density measurements using quenched material, LaB6 was reported to exist between and LaB7,3,2although Russian experience, described in ref 3, gives a narrow composition range. No significant difference in lattice parameter has been observed across this range. Samples have been reported to change from purple to blue as the boron content is i n c r e a ~ e d , but ~ - ~the reason was not determined. LaB4 is said to melt peritectically at 2073 K, LaB6 melts congruently at 2990 K, and a eutectoid is believed to occur at 2623 K between LaB6 and boron.' There is very poor agreement between the published vaporization measurements. Lafferty,6 in 1951, d.emonstrated the usefulness of LaB6 as a thermionic emitter and reported three values for the vaporization rate of La from a graphite Knudsen cell containing LaB6 of unknown composition. His technique could have given too large a loss rate because of possible Lacz and L a 0 in the vapor. Nevertheless, his values were the lowest reported until our studies. Ahmed and Broers' concluded from a surface examination that LaB6 evaporates leaving no apparent residue. Thus, the CVC is in the LaB6 phase region but the exact composition is unknown. Using mass spectrometer and effusion techniques, Gordienko et al.*-lo studied a sample of LaBs,05,and found a preferential loss of La. Consequently, the CVC will have a lower vapor pressure than did their samples. Ames and McGrath,ll also using a mass spectrometer, present their Knudsen data as total free energy of formation. Unfortunately, this quantity is not useful in calculating an accurate vapor
- 1.97 - 0.28
+0.01 t 0.07
-
+0.02
Standard deviation
pressure or the composition of the CVC. In addition, their results imply a boron pressure over their sample -20 times greater than that of pure boron. Freely vaporizing single crystals have been studied by Swanson and Dickinson.12 Based on a mass spectrometric measurement at an unknown composition, the B/La atom ratio in the gas was found to change from 3 to 6 when the temperature was changed from 1700 to 2000 K. Although pressures were not measured, values of 6.3 f 0.3 eV (145 kcal/mol, 607 kJ/mol) and 6.8 f 0.3 eV (157 kcal/mol, 657 kJ/mol) were and AHB, respectively. reported for ARL~
11. Experimental Section Our work is divided into two parts: vaporization studies using Knudsen and Langmuir techniques, and phase relationship studies using melting point, thermal analysis, and metallographic techniques. Vaporization. A 60' sector, single focus mass ~pectrometerl~ was used to detect vaporization from a Knudsen cell as well as from freely vaporizing surfaces. All measurements were made at an electron energy of 20 eV to reduce fragmentati~nl~ of the oxide vapor species. Knudsen measurements were made by placing samples in a presaturated tungsten cell similar to the assembly described in ref 13. After the 13gLa+and llB+ currents were measured over a suitable temperature range, the sample was removed and pure boron was placed in the cell. This was studied in a similar manner. The activity of boron was calculated by taking the ratio of the B+ current produced by the sample to that produced by pure boron using the least-squares equations for each data set. This technique is described in greater detail in ref 14. The La activity was obtained in the following way. In a separate study, the La+ current from La metal, contained in a T a cup, was compared to B+ produced by elemental boron in consecutive measurements using the same tungsten cell. An equation for the 139La+/11B+ratio, given in Table I, was calculated from this data. This equation was combined with the equation obtained for the boron calibration for each run to give an equation describing the hypothetical behavior of La metal under the conditions of the particular run. The activity of La in the sample was obtained by combining the measured La+ least-squares equation with this hypothetical equation. Thus, the activities of La and B were measured directly without the need for uncertain values for the elemental vapor pressures, for ionization
Vaporizatlon and Thermodynamic Studies of the La-B System
iu
Flgure 1. Langmuir assembly used in the mass spectrometer.
cross sections, or for multiplier gains as the usual method requires. However, if the measured Bt/Lat ratio for the elements is converted to the pressure ratio using the conventional method, the result is too small by a factor of 2.0 compared to the pressure ratio calculated from published measurements (Table I). This difference demonstrates the possible error which may result from the conventional approach. The activities were converted to partial pressures by multiplying the activity equations by the pressure equations for the elements given in the discussion. Langmuir measurements were also made in the mass spectrometer with the sample configuration shown in Figure 1. The system was calibrated by replacing the sample with a similar piece of boron. Temperatures (IPTS-68) were measured using a photon-counting pyrometer described in ref 14. This instrument had a reproducibility of k0.2 K and an accuracy of a t least k2 K at 2000 K. Temperature gradients between the top and bottom holes in the Knudsen cell were eliminated by adjusting the relative power to the two electron bombardment filaments. In the Langmuir assembly, the temperature difference between the two holes near the evaporating surface was eliminated in a similar manner. Weight loss measurements were made in a separate apparatus using the Langmuir samples from the mass spectrometric study. Radio frequency (rf) power was used to heat the samples contained in an eddy current concentrator. The sample configuration was identical with the assembly described in ref 13. Corrections were applied for the measured weight change produced during heating by the loss of absorbed oxygen as L a 0 and various boron oxides. An NBS calibrated optical pyrometer was used to measure the temperature. Agreement between this pyrometer and the photon pyrometer was within 1.5 K between 1900 and 2000 E(. Phase Diagram. A thermal analysis study was made using the technique described by Rupert.15 The samples were contained in a presaturated tungsten crucible heated by rf. Metallographic examination was made after each study. Sample Preparation and Characterization, All borides were prepared by first arc-melting the elements together. After being broken to
