ALLENL. BOWMAN
1596
Vol. 65
When the bending vibrations which are to be time for the bond to be formed without the immediate necessity for the orientation of the radi- changed to rotations or looser oscillations involve cals, which is characteristic of the rigid activated C-H bonds, they ill in general be in the category complex. of high frequencies discussed in Section 3. This Van der Waals forces could, of course, hold the means that, in order for the rotations to come into radicals together, and this has been suggested something resembling an equilibrium state, the several times. However, in this case the dis- zero-point energy of the bending vibrations must sociation energy would be so small and the interaction of the radicals so weak that they would be dissipated. This implies transfer of energy probably dissociate again before a normal bond betwen these degrees of freedom and other decould be formed. Especially would this be ex- grees of freedom in the molecule. Conversely, if pected to be true in the case of methyl radicals. the complex is rigid, the vibrational levels are not Tan der Waals forces betiyeen ttyo methyl radicals broadened, and the reverse association requires might be expected to be somewhat greater than matching of energy levels. This means that zerothose between two methane molecules, since the point energy must be furnished for the vibrations methyl radicals might be more polarizable. Wow- formed. The importance of this concept has alever, the difference between methyl and methane ready been pointed out.lg would have to be considerable in order for a van (18) These are vibrational levels of the activated complez, and the der Waals complex of two mcthyl radicals to be broadening which ia significant is t h a t due to interaction with the rosufficiently stable, in the light of the low boiling tations of the dissociated fragments. point of methane. (19) 0. K. Rice, J. Chsm. Phys., 4, 63 (1936).
THE V,ARI:ATION
OF LATTICE PARAMETER WITH CARBOX CONTEST OF TANTALUM CARBIDE1 BY ALLENL. BOTMAS
I,os Alamos ScientiJc Laboratory of the University of California, Los Alamos, New Mexico Received April 21, 1961
+
A lattice constant of a. = 4.4555 =t0.0003 A. has been determined for TaCo.ast * 0.00'1 at 25". The equation a0 = 4.3007 0.1563 (C/Ta) has been calculated relating composition to lattice parameter of TaC. Solution of this equation for TaCl.oo gives a lattice parameter of 4.4570 =k 0.0010 A.
Introduction TaC forms a face-centered cubic crystal lattice for which the lattice constant, ao, decreases as the crystal becomes deficient in carbon. An exact knowledge of the relationship between a0 and the TaC composition provides a possible analytical tool, and, by extrapolation, gives a value of a. for the stoichiometric composition TaCl.ooo. Lesser and Brauer, Smirnova and Ormont, Robins4 and Kempter and Nadler5 have determined the variation of lattice parameter with composition for the TaC phase, but with a notable lack of agreement. Kovalskii and UmanskiiG have measured the lattice parameter of an analyzed sample of tantalum carbide. I n addition, van Arkel,7 Becker and Ebert.,* von Schwarz and Summa,9Burgers and Basart, lo McKenna, l1 Norton ( 1 ) This work supported in part b y the U. S. Atomic Energy Commission. ( 2 ) R. Lesser and G. Brauer, Z. Metallk., 49, 622 (1958). 13) V. I. Srnirnova and B. F. Ormont, Zhur. Fiz. Khim., SO, 1327
(19%).
(4) D. A. Robins, "The Physical Chemistry of Metallic Solutions and Intermetallic Compounds," Paper 7B, Her Majesty's Stationery
Office, London, 1959. ( 5 ) C. P. Kempter a n d M. R. Nadler, J . Chem. Phys., 32, 1477 (1960). ( 6 ) A. E. Kovalskii and Ya. S. Umanskii, Zhur. Fiz. Khim., 20, 769 (1946). (7) A. E. van Arkel, Physica. 4, 286 (1924). ( 8 ) K. Becker and F. E b e r t , 2. Physilc, 31, 268 (1925). (9) M. von Schwarr and 0. Summa, Metalhirtschaft, 12, 298 (1933).
and Mowry,12 and Brownlee13have measured lattice constants of TaC. The lack of analytical data on the material studied leaves most of the reported values in question. It should be noted that in most cases the reported lattice parameters are about 4.455 A. ; thus the compositions are probably close to TaCl.oo. Experimental TaC samples were prepared by two different methods. (J) Kennametal high-purity tantalum powder and AUC. graphite powder, outgassed a t 2000°, were used as startmg materials. Spectroscopic analysis of the tantalum showed major impurities, in p.p.m., to be Nb 300, Fe 200, IT7 150, Zn 100, Mo 50. The graphite was analyzed and found to be 99.4% C. After thorough mixing the tantalumcarbon powder was loaded into a graphite crucible and heated inductively for 10 min. a t 2400" under vacuum of mm. or better. In some cases the sample was removed from the crucible, ground to a powder, and then returned for similar additional heatings. In every sample a large evolution of gas was noted at 1000" and again at 1500" as the sample was brought slowly to heating temperature. No evolution of gas was noted when a sample was heated for a second time. The sample size was about 5 g. The TaC was removed from the crucible as a firm plug with a gold or light-brown color. This color was uniform throughout when the sample had a C/Ta ratio greater than about 0.90, but with lower carbon content the gold color waa observed only on the surface, with the interior (10) W. G. Burgers a n d J. C. M. Basart, Z. onorg. allgem. Chem., 216, 209 (1934).
(11) P. M. MoKenna, Ind. Enu. Chem., 28, 767 (1936). (12) J. T. Norton and A. L. Mowry, Trans. A I M E , 186, 133 (1949). (13) L. D. Brownlee, J . Inst. Metals, 87, 58 (1958).
Sept., 196 1
V A R I A T I O S OF
LATTICEP A R A M E T E R
WJTH CARBON
of the sample gray in color. The surface was scraped off, and the remainder of the sample was pulverized in a mullite mortar. (2) Fansteel high-purity tantalum powder and spectroscopic grade Madagascar flake graphite were used as starting materials. Analysis of the tantalum showed Ta 99.870, and, in p.p.m., C 900, H 45, N 325, 0 940, K b 400, W 100, Fe 500. The melting point was 2990". T$e lattice parameter was 3.307 A. before melting and 3.304 A . after melting. The thoroughly mixed powders were heate! inductively in 25-g. batches in graphite crucibles a t 1850 , under vacuum of 10-6 mm., for six 1.5 hour periods, with material ground to a powder after each heating. As the preparation progressed, the light-brown surface coat gradually decreaoed on the samples with C/Ta less than 0.85, leaving a sample uniformly gray in color. The finished samples of C/Ta greater than 0.85 were brown in color throughout the sample. All of the samples were analyzed for tantalum and total carbon by combustion, and for free carbon by a chemical meth0d.l' 'The samples prepared by method (2) were also analyzed for nitrogen by a modified TVinkler technique. The sample is dissolved in hot H2S04-K2S04,.then made strongly alkaline with KOH, and the ammonia IS steamdistilled into boric acid, which is titrated with HC1. The samples prepared by method (2) were also analyzed for hydrogen by burning a t 1000' in a stream of oxygen and weighing the water absorbed in Mg(C10&, and for oxygen by vacuum exi raction.16 The nitrogen content ranged from 50 to 200 p.p.m., the hydrogen content from 0 to 100 p.p.m., and the oxygen content from 30 to 159 p.p.m. It should be noted t,hat the lattice parameters of the two samples with high hydrogen analysis, TaCo.ssoand Taco a01, exhibited the maximum negative deviations from the lattice parameter us. composition curve. Spectroscopic analysis of the samples (2) indicated Kb 400 p.p.m. and W 100 p.p.m. There was no iron present in the carbide samples. The absence of major impurities and the fact that in all cases the sums of the analyses of tantalum and total carbon were within 0.15% of 100% give assurance as to the high purity of the TaC samples. Repeated analyses on several samples indicated a standard deviation in the C/Ta ratio of zk0.005. The X-ray powder patterns were made in a 11.46 em. Debye-Scherrer camera using copper radiation with a nickel filter. The aa values were obtained from the back-reflection lines by applying the least-squares extrapolation of Cohen16 a8 modified by Hem'? using an IBM-704 computer. A standard deviation was calculated from each film. In addition, three films were prepared for several samples. The separate films agreed within the standard deviation in all cases.
Results The experimental data are summarized in Fig. 1 as a plot of lattice parameter, a,, a t 25 f 2 O , us. the mole ratio, C/Ta, of combined carbon in the total sample. The data are also listed in Table I. The data were fitted to a least-squares line.I* Since both 5 and y values were subject to error, a specialized weighting scheme was used.lg The function A*
Q
=
c i-1
zL',[YI
- (A
+ Bd12
was minimized. Here uil is the weight of the ith data point, y, and xi are the coordinates of the ith (14) 0 . El. liriego, Los Alamos Scientific Laboratory Report LA2306. March, 19.59.
(15) W. R. Hanseri n,ud W '. M . Rlallett, A n a l . Chem., as, 1868 (1957). (16) M . U. Cohen. Reu. Sci. Instr., 6, 68 (1938); 7 , 1955 (1936); Z. Kristallogr., 9 4 8 , 288 (1936); 948, 306 (1936). (17) J. B. Hess, Acta Cryst., 4, 209 (1951). (18) R. H. Moore and R. K. Zeigler, Los Alamos Scientific Laboratory Report LA.-2367. Oct. 1959. (19) 14'. Edwards Deming, "Statistical Adjustment of Data," John Wilev and. Sons.. Inc... New York. N. Y.., 1943.I Cham 8. _
COXTENT O F T A N T B L U M
1597
CARRIDE
4.460, I
1
I
KW
+ $ a a e a
4.410 A
W
2
4430
+ a
I
l-
-1
?
4.420; 1
'
4410 IO0
0
90
00
L
.50
.60
.70
MOLE R A T I O . C/Ta,
Fig. 1.-Variation of TaC lattice parameter with composition: X, this work; 0, Lesser and Brauer; A, Smirnova and Ormont; A, Robins; - - - - Kempter and Nadler; 0 , Kovalskii and Unianslrii.
TABLE I SUMMARY OF THE DATA Com-
p o s it i o n ,
C/Ta
Error
0.994" .990 ,989" .987" .985" ,978 .978 .976 .958 .934 .932a ,927" ,898 ,877 ,833
0.005 .005 ,005 ,010 ,010 ,010 ,010 ,005 ,005 .005 ,008 ,010 ,005
Error
aa
Method of prep.
4.4555 0.0003 4.4536 ,0005 4.4552 ,0005 4.4554 .0005 4.4554 ,0005 4.4543 ,0003 4.4545 ,0005 4.4537 ,0004 4.4511 ,0010 4,4475 .0003 4.4453 ,0003 4.4440 .0010 4,4429 .0004 ,008 4.4389 .0003 .005 4.4333 ,0005 .82G ,005 4.4291 ,0004 ,801 ,005 4.4237 ,0004 .776 ,008 4.4204 .0009 .737" .005 4.4167 ,0003 ,736 .008 4.4142 ,0008 .710 .010 4.4104 ,0010 a Indicates free carbon present by analysis, but less 0.7yoby weight.
1 2 1 1 1 1 1 2 1 2 1 1 2 i 2 I
2 1
2 1 1 than
dat'a point (ao and C/Ta), A is the intercept, and B the slope of the fitted equation. The weights were taken as a function of the variance of x and y. The solutions for A and B were A = 4.3007 i 0.0032, B = 0.1563 f 0.0035. The standard deviation of the fit was 3.4 X 10-j. The quadratic form does not yield a better fit. Thus the data are fitted to the equation a0 = 4.3007
+ 0.1563X
X
=
C/Ta,
(1)
Solving this equation for X X
=
6.398~0- 27.516
(2)
A solution of equation 1 for X = 1.00 gives an
1598
ALLENL. B o w ~ a s
a. value of a. = 4.4570 f 0,0010 A. for the composition TaCl.ooo. The closest experimental approach to this composition was TaCo.994 = 0.005, with a0 = 4.4555 f 0.0003 A. Solution of equation 1 for the X-ray density yields, as a good approximation
Vol. 65
data of Kempter and Sadler were obtained by distilling carbon from pressed compacts of initial composition T a c o 955, and by heating pressed mixtures of T a c og55 plus excess graphite at about 2500'. The results from the latter preparations agree well with the present work, whereas the data from the distillation residues do not agree at all. p = 15.11 - 0.64X (3) This is most probably due to the inhomogeneity of This gives an X-ray density of 14.47 g . / ~ m for . ~ the samples. the composition TaCl ooo. The limits of homogeneity of the TaC phase vary with temperature.*O The lower limit is about Discussion TaCo.Yrat 1850' and TaCo7,a t 2400'. The upper The values reported by Lesser and Brauer limit is about Taco.$$at 2400', with a variation (open circles on Fig. I), Smirnova and Ormont toward lower carbon content at higher tempera(closed triangles) and Robins (open triangles), tures. The upper limit may reach TaCl 000 at lon-er the curve obtained by Kempter and Nadler (dashed temperatures. line), and the value of Kowalskii and Umanskii It is interesting t o note the differences betmen (closed circle) are shown for comparison. It is the lattice parameters of TaC aiid SbC. Although evident that, within experimental error, the values the atomic radii of the ommetals are essentially :he of Lesser and Brauer are in agreement with the same (Yb, a. = 3.300 AZ1;Ta, a. = 3.304 A ) , present work. The samples prepared by Lesser the lattice parameters of the stoichiometric carand Brauer were heated repeatedly until they bides are significantly dieerent (SbC, a0 = 4.470 appeared to be homogeneous and did not contain A.; TaC, a. = 4.457 A). In addition Storms any free carbon by analysis. The one value re- and E(rikorianz2 have demonstrated a distinct ported by Kon-alskii and Gmanskii is also in agree- curvature in the plot of lattice parameter us. ment with the present work after conversion from composition for NbC, as compared with the linear kX. to gngstrom units. fit for TaC. It is believed that the deviation from the present Acknowledgment.-The author gratefully acwork of the data of Smirnova and Ormont, Robins knowledges the advice of Dr. Melvin 6. Bowman, and Kempter and Sadler is due to inhomogeneity Dr. E. E(. Storms, Rlr. IT.G. Kitteman aiid Mr. of the samples. The analyses reported by Smir- Tu'. H. Krikorian during the course of this lvork. nova and Ormoiit indicate the presence of free Acknowledgment is also due to Dr. R. L. Petty carbon in almost every preparation. Such samples for computing the lattice parameter data, aiid to cannot be at equilibrium, and thus will probably Dr. R. I
