May, lOCil
’\~.iPUl9 A. following the effusion runs. Langmuir Expehents.-The evaporation work consisted of three rate-of-evaporation measurements on each of two samples, together with a number of auxiliary experimental heatings performed for the purpose of determining the surface and vapor compositions. Samples were heated by electron bombardment. Power was rovided by a conventional full wave rectifier power s u p p b rated to deliver 0.5 ampere d.c. a t 3000 volts maximum. Output voltage could be varied from 0 to 3000 volts by means of an autotransformer in the primary circuit of the step-up transformer. The bombarding current was maintained constant by an emission regulator which controlled the heating power to the filament.16 The rate-of-evaporation experiments were performed in the temperalure range 2641 to 2747’K. The first sample was outgamed at about 2750’K. for 1.5 hours and lost 3.5% of its original weight. The second was outgassed a t about 2825’K. for somewhat less than two hours and lost 7.7% of its original weight. Both samples adhered to their tungsten support rods so that subsequent weighings of sample plus rod were made. No eignificant error resulted from loss of tungsten since the vaporization of this metal was estimated t o have been well under 1 mg. in all runs. Areas were calculated from sample dimensions as measured with a micrometer at the beginning of each run. Indicated pressures rose to nearly 1 X 10-4 mm. during the warmup period but quickly dropped below 1 X 10-5 mm., and more slowly to about 2 X mm The auxiliary experiments involved a determination of the composition as a function of pw cent. loss of original sample weight. Thus, two samples were heated to temperatures from 2750 to 2850’K. for times such as to cause losses of 1.7 and 21$) of the original weight. Carbon contents of the samples were then determined by combustion to CO2, and the zirconium content was determined from the weight of ZrOz f0rm~d.l’ Spectroscopic analyses of samples subjected to similar treatment showed that the initial outgassing runs were effective in reducing metallic impurities to a level a t which they would exert a negligible effect on both the measured rates of evaporation and on the thermodynamic properties of the residues. A number of determinations of the crystal parameters were also made. A discussion of the results of the auxiliary experiments is most appropriately made in connection with the discussion of the Langmuir data in the following section.
ZIRCONIT34
733
C-4RBIDE
correct measured pressures for the effect of finite orifice areads peq
= (1
+ WbB/d)Pm
wb
( 7)
where P e q is the equilibrium pressure, is the Clausing orifice correction, B is the orifice area, A is the sample area, and CY, the evaporation coefficient was taken as unity. Because of the necessity of using much larger ratio of orifice area to sample area than is usual, the values of Pmwere corrected by means of equation 7 and the corrected values, P e q , thus found are given in the fifth column of Table 11. The high temperature standard free energy of formation of ZrC was obtained by combining the negative of the standard free energy change for reaction 5 with the AFo for vaporizationlo of zirconium. These values are given as AF*(f) for ZrC(s) in the sixth column of Table 11. TABLE I1 KNUDSEN EFFUSION DAT.~ Orifice area = 0.316 cm.*; orifice correction = 0.89 Temp., OK.
2730 2686 2620
Time, 8ec.
Zrloss, mg.
Prn (atm.)
2820 0 . 1 3 2.0 X .14 7 . 4 X 8220 11,460 .ll 4.1 X
Pes (atm.)
2.4 X 8.7 X 4 8 X hF026v,(f) = -38 8
AFW, kcal.
-37.6 -39.9 -38 9 (&I 2)
For the calculation of AFo(f) to be valid, it is necessary that the composition of the carbide be that in equilibrium with graphite. That this requirement was met may be seen by noting the ready uptake of carbon during the outgassing run prior to the effusion runs, despite the extensive outgassing, and by noting that the crystal parameter of the residue, ao, following the effusion runs was equal, within experimental error, with that given by Bowman and his c o - ~ o r k e r s ’for ~ ~ the stoichiometric compound. The absence of any trend in the AFo(f) values in Table 11, which were based on successive runs with the same sample, Results and Discussion further supports the belief that the data are valid. I n the Udje of the vaporization data to calculate I n view of these observations and of the fact that partial pressures, the assumptions were made that free energy changes for reactions in which reactants the evaporatioii coefficients on zirconium car- and products are both solid do not change rapidly bide were unity, and that the percentage of molecu- with temperature, the average of the values given lar Zirconium carbide fzperies in the vapor was in the last column of Table I1 may be taken as thc negligible. That bolh of these assumptions are free energy of formation of zirconium carbide a t correct follows from the fact that the high tempera- 2675’K. as found by the Knudsen method. -4lthough zirconium carbide has been shown to ture stabilities obtained by the Knudsen and Langmuir method. are in agreement, as will be shown have a composition a t any given temperature n t which vaporization would he congruent, such below. vaporization did not orrur during the experiments The data for the Knudsen experiments are given in Table 11, where the “Zr loss” has been corrected made in this study. It is necessary therefore t o for the blank. The measured pressures, “Pm,” estimate the composition of the vapor and of the were calculated by means of the Knudsen equa- surface from which the vapor was formed. The tion.I8 Motzfeld has shown that for cells whose existence of non-congruent vaporization can be diameter is approximately equal to their height, shown, and the necessary estimates can be made as was the case liere, equation 7 may be used to with the help of the data summarized in Table 111. Under the heading “Composition,” the quantity (16) The author is indebted to Mr. Everett Rauh of Argonne Ns“C/Zr” corresponds to the subscript in the formula tional Laboratory for the circuit diagram of the regulator. ZrC,, and was calculated on the basis of the carbon (17) 0.H. Kriege. “The Analysis of Refractory Borides, Carbides, content and the zirconium-content-by-difference Nitrides and Silicides,” Los Alamos Scientific Laboratory Report No. LA 2306, August 27, 1959,PP. 25-29. because the carbon analyses are believed t o have (18) 9. Dushman, “Saientific Foundations of Vacuum Technique,” John Wiley and Sons, Inc., New York, N. Y., 1949, p. 21-22.
(19) Ketil Motzfeld, J . Phya. Chem., 69, 139 (1955).
734
B. D. POLLOCX
been more accurate than those of zirconium. The uncertainty in the crystal parameters is estimated to be 10.001K. The first entry is for stoichiometric ZrC and the second is for the powder used in the Knudsen experiments described above. The other samples are listed in order of increasing weight loss. Samples 2A and 4A are those used in the measurements of the rates of evaporation. The composition and parameter data given were obtained after the samples had undergone the indicated losses. The crystal parameters of the surface l9yer of samples 5A and 6A were found to be 4.701 A. Comparison with the values for stoichiometric ZrC13bindicates that the atomic ratio, C/Zr, in the surface layers of these two samples must have been very nearly equal to unity; that is, their composition was nearly stoichiometric. The crystal parameter at a point 0.015 inch below the surface was 4.693 A. in sample ZA, and the parameter a t oa point 0.011 inch below the surface was 4.696 A. in sample 6 4 thus indicating that the bulk of the samples had a lower C/Zr ratio than that of the surfaces. The weight losses which occurred during the evaporation rate measurements on samples 2A and 4-4 were within the range for samples 5A and 6 4 so that the surface layers of the Langmuir specimens must have also been nearly stoichiometric and there must also have been a composition inhomogeneity in these samples. Such an inhomogeneity is inconsistent with the existence of congruent vaporization. It is not likely however that diffusion of zirconium through the bulk of the samples would have been rapid enough t o have maintained the zirconium in the vapor a t a percentage much greater than that in the solid. Accordingly, the average vapor composition was estimated to have been 90% Zr and 10% C1.
Vol. 65
approximation was made that the partial pressures
Pzr and Pc, were those in equilibrium with stoichiometric ZrC and the pressures were then used to calculate the standard free energy change for the inverse of reaction 6 which could then be combined with the standard free energy changes for vaporization of the elements to Zr(g) and Cl(g) to obt’ain the free energy of formation values for ZrC(s) given in the last column of Table V. TABLE IV RATE-OF-EVAPORATION DATAFOR THE LAXGWIREXKEKIRun no.
Temp., OK.
Time, seo.
8/17 b 8/17c 8/17d 8/26 b 8/26 c 8/26 a
2673 2671 2674 2747 2641 2647
14,900 13,200 11,880 7,100 18,600 11,600
MEXTS Area, cm.2
Wt. loss, mg.
g./cm.2-sec.
76.3 58.1 62.9 79.U 60.3 35.!1
2.04 X l o 4 1.78 2.18 4.82 1.43 1.40
2.52 2.48 2.43 2.34 2.27 2.21
Gtutal,
TABLE Tr
RESUMBOF
CALCUL.4TIoNS
FOR THE
LSKGMUIREXPERI-
MESTS
Run no.
TEmp.,
K.
Pzr
X 10’
8/17 b 2673 2 23 8/17c 2671 1 94 8/17d 2674 2 39 8/26 b 2747 5 4 8 / 2 6 ~ 2641 1 56 8/26d 2647 1 51 Av. temp. = 2676’K.
Pam
Pci
PQcl
1 40 1 38 141 2 90 1 03 1 10
6 0 6 0
1 60 1 37 1 60 3 90 1 06 1 17
X 105 X.108 x 106 (All pressures in atm.)
7 3 16 3 4 8 4 7
AFo(f) for ZrC(s), kcal.
-38 -40 -38 -39 -38 -39 h ~ . -38 (f 0
8 0 0 1
2 5 9 6)
The free energy values, AFo(f), are not very sensitive to moderate errors in compositions and Gtotd. For example, if the carbon percentage in TABLE I11 the vapor were 9% (or llgi.,) instead of lo%, the RESUMB O F DAT.4 USED TO I X F E R THE SURFACE AND VAPOR AaFo(f) values would be in error by only 0.5 kcal. COMPOSITIOM IS THE LANGMUIR EXPERIMENTS If the surfaces were ZrCo96, the free energy values Crystal paramwould be 0.6 kcal. less negative than those calLoss. as Composition eter 70of initl. culated for the stoichiometric compound. Sample wt. % ~r %c C/Zr aa, A. Reaction with oxygen in the residual gas is 1.00 4.700 Stoichiometric .. 88.37 11.63 estimated to have been no more than 570 of the ZrC powder in carbon loss at the lower temperatures. The Knudsen runs .. average of the AFo(f) values in Table V, -38.9 after outgas .. . . . 11.20 0.96 kcal., thus is taken to be the standard free energy ... 2 . 9 6 4.699 after effusion runs ... of formation of zirconium carbide at 2675’H. .95 4.701 5-4 1 . 7 88.85 11.07 as determined by the Langmuir method in good 4.693 agreement with the Knudsen result. 21ccordingly, 14 . . . 10.6 .90 21. the arerage for the two methods, -38.9 kcal., .87 18 90.1 10.25 4A will be taken as the free energy of formation as “1 8 9 . 6 10.34 .88 4.701 8 -4 determined in this study, over-all uncertainty 4.696 estimated a t f1.5 kcal. The data for the Langmuir experiments are Conclusions and Summary given in Table IV together with the total rates of The validity of the assumptions concerning evaporation, “Gtota1.” The total evaporation rates and the estimated vapor composition were used in the evaporation coefficients and the absence of calculating the partial pressures of zirconium and molecular zirconium carbide species is a consecarbon, Pzr and Pc,, giren in the third and fifth quence of the fact that the rwiiltq of the t w o columns of Table V. For comparison, the pres- nicthods are in agreement. If the eraporasures of Zr(g) and G ( g ) in equilibrium with the tion coefficients were less than unity, the calcuelements are given in columns four and six. KO lated AF’s would be more negative than the rorrect correction was made for loss of polyatomic carbon, value. Howerer. the error in the Knudsen method since the C? and Ca species could be shown to have would be smaller because of the closer approach to accounted for less than 4y0of the carbon loss. The the correct zirconium pressure. Thus, for low
May, 1961
53TRUCTURAL
DEPENDENCE O F ABSORPTION SPECTRA
evaporation coefficients, the AF from the Knudsen experiments would be more positive than those from the Langmuir experiments. If molecular vaporization were significant, the calculated AF's would be more positive than the correct value. I n this case, the error would be greater in the Kriudsen experiments because of the suppression of Pzr by the excess graphite. Thus, departures from the two assumptions would lead to errors of opposite sign, but the results of the Knudsen experiments would be the more positive for both cases and the two effects would be cumulative Therefore agreement of the observed Knudsen and Langmuir AF values implies that both assumptions must be substantially correct. If the experimental uncertainty in the free energy determinations is taken as 1.5 kcal. a t 2675, then the lower limit for the evaporation coefficient must be 0.75 or alternatively the upper limit of the fraction of molecular zirconium in the vapor is about one-fourth P,,in the Knudsen experiments, or about 2.5 X atmosphere. The free energy values in Tables I1 and V are thermodynamically consistent in that they do not show a,ny apparent trend with temperature, as may be expected from the fact that the entropy change for reaction 2 is only about -3 e.u. A more reliable tech for significant errors may be
OF
/%DIKETONE CHELATES
735
made by use of the "Third Law" to obtain a heat of formation a t 298OK. which may then be compared with that obtained by Mah and Boyle from combustion calorimetry. Thus if AFo(f, 2675OK.) = 38.9 koal. is combined with the change of free energy function for 2675'K. from Table I, (AFOT - AH0~9e)/T = -3.3, the heat of formation a t 298OK. is found to be -47.7 kcal., in good agreement with Mah and Boyle's value -44.1 kcal. This agreement supports the validity of thi. conclusions drawn concerning the vaporizatioil processes. I n summary, zirconium carbide vaporizes at 2620 to 2747'K. predominantly by dissociation to the elements with evaporatioii coefficients equal or nearly equal to unity. Thicarbide also can vaporize congruently at compositions which are near that of the stoichiometric compound. Acknowledgments.-The author wishes to express indebtedness to Dr. R. L. lLIcKisson for his suggestions and criticism both during the work and in the preparation of the manuscript. He also wishes to thank G. W. Dollman and Ami Margrave of the Analytical Chemistry Unit for performing the necessary analyses, and Paul Romo of the Solid State Metallurgy Group for the crystal parameter measurements.
STRUCTURA.L DEPEXDESCE OF ,4BSORPTIOX SPECTRA OF o-DIKETOSE CHELATES. 11. ULTRAVIOLET' BY J. CHARETTE, G. NEIRYNCK AND PH. TEYSSI~ Departments of Physics and Chemistry, Lovanium University, Lkopoldville, Congo Received August $2, 1960
An interpretation of the absorption spectra of @-diketonechelates is presented, based on new experimental results and on previously published data. The absorption band characteristic of the T-T* transition in the ligand is found to be drpendent on the structure of the metal, of the ligand and of the solvent: these effects are discussed in terms of theories of resonance, crystal field and free electron model. The lack of significance of all the data obtained with concentrations lower than a critical value, specific of the chelate studied, is emphasized.
Introduction I n the past decade, numerous attempts have been made to correlate the molecular structure of the diketone chelates with a number of their physicochemical properties, namely magnetism, absorption spectra, X-ray diffraction, dipole moments, etc. . . . In the first part of this study,' a definite relationship was found t)etmeen the perturbed carbonyl absorption frequency and the stability of the chelate. A sirnilw relationship vias believed to he found in the ultraviolet absorption spectra by Yamasaki and Sone2s3; but a more detailed investigation revealed that other factors are determinant of the absorption frequencies, and that in many cases, their effects are inseparablc. The problem appears still more intricate orving ( 1 ) For the preceding paper, see: J. ChRrotte and P. TeyxsiB' Spectrochmm. Acta. 1 6 , 080 (1960) 12) K Yainabaki a n 1 K Sone, n'ature, 166, 998 (19fO) ( 3 ) I
