DIFFUSION OF CARBON THRU TUNGSTEN AND TUNGSTEN CARBIDE MARY R . ANDREWS A N D S. DUSHMAN
Introduction In a previous paper’ it was shown that when carbon diffuses into tungsten at a high temperature, a compound, Wd2, is formed, and that the cold conductance of the material decreases linearly with the carbon content until, when complete conversion to W2C has been attained, a minimum conductance of seven percent that of the tungsten is reached. Further carbonization leads to the formation of a second compound, WC, and a corresponding increase in conductance, since WC has a conductance of 40% that of tungsten. In connection with this earlier investigation, a number of observations were made on rates of carbonization and decarbonization under various conditions. A brief discussion of the mechanism of carbonization based on these preliminary observations was given in the paper referred to above. However, in view of the interest in the general subject of diffusion in metals, it seemed of importance to carry out more careful measurements on these rates, particularly since other published work on diffusion has usually been done at much lower temperatures than those used here. The present paper contains the results of this investigation.
Experimental Conditions (a) Carbonization. As was shown in the earlier paper, the rate of Carbonization of a tungsten filament heated in a hydrocarbon vapor may be limited either by the rate at which the hydrocarbon molecules reach the surface of the filament, or by the rate a t which the carbon (deposited on the surface by decomposition of the hydrocarbon) diffuses into the interior. In order to obtain data on rates of diffusion, care was taken in our carbonization experiments to have the filaments saturated at the surface with carbon. This was accomplished by first heating the filaments at about I 800°K in naphthalene vapor a t a pressure of several bars. Under these conditions, the surface of the filament became covered with carbon before diffusion into the metal had progressed appreciably. After this preliminary coating, the filament was brought quickly to the desired temperature and the rate of formation of the carbide a t constant temperatures was observed by interrupting the heating at intervals to measure the cold iesistance. During any run, the pressure of hydrocarbon was maintained above that necessary to keep the surface of the filament coated with carbon. “Production and Characteristics of the Carbides of Tungsten.” Andrew: J. Phys. Chem. 27, 270 (1923).
DIFFUSION O F CARBON
463
(b) Decarbonization. When a carbonized filament is run at a high temperature in vacuum, the W2C gradually decomposes and the carbon evaporates, leaving, if the process be carried to completion, a filament of pure tungsten of the same conductance as before carbonization. This loss of carbon in uacuum is extremely slow. We are indebted to Dr. Irving Langmuir for the suggestion that carbon would evaporate from the surface of the filament with great difficulty, and thus the rate of diffusion of carbon to the surface would be reduced. Following this reasoning, we measured the rate of loss of carbon from filaments a t known temperatures in very low pressures of oxygen. From preliminary work, it was known roughly a t what rates carbon diffused to the surface, and the pressures of gas were adjusted to cause several times as many molecules of oxygen to strike the filament as there were atoms of carbon reaching the surface. This excess of oxygen was necessary to ensure prompt removal of carbon from the surface, but it also led to the formation of oxide of tungsten, which vaporized. Increase in conductance due to loss of carbon was, therefore, partially counterbalanced by decrease of conductance due to loss of tungsten. As loss of carbon was greatest, and attack on the filament least during the first part of any run, only the initial data obtained during such a run were considered sufficiently reliable for the subsequent calculations. It is of interest to note that the product of decarbonization, even in the presence of a great excess of oxygen, is almost pure carbon monoxide, not more than a very small percentage of carbon dioxide being formed. (c) Temperature Determination.
A great deal of difficulty was encountered a t the beginning in maintaining a filament a t constant temperature during carbonization. Color-matching against a tungsten filament operating a t the desired temperature in vacuum, proved far from accurate. For filaments whose surfaces are pure tungsten, the most practical method is control of the watts radiated. However, the emissivity of a filament covered with a layer of carbon is obviously much greater than that of pure tungsten. It was therefore necessary to make separate observations for such filaments on the relation between watts radiated and temperature. For this purpose, measurements were made, at the same color temperature, of the watts radiated by tungsten filaments and similar filaments coated with carbon. At a color temperature corresponding to I 800'K for pure tungsten, it was observed that the carbon-coated filaments radiated 2.4 times as much as the tungsten filament, while at zooo°K the ratio was found to be 2 . 2 . It is known that a black surface must be at a somewhat higher temperature than a tungsten surface to radiate light of the same color. Since the carbon-coated filaments were blacker than those of clean tungsten, it follows that the former were photometered at a somewhat higher true temperature than the latter. The difference was slight; but, for this reason, and because the carbon coating may have increased slightly the diameter of the filament, the factor 2.2 has been used. Thus, to maintain them at any desired temperature, the
MARY R. ANDREWS AND S. DUSHMAN
464
coated filaments were run a t 2 . 2 times the watts radiated by the same-size tungsten filaments at this temperature. The cooling effect of the naphthalene vapor was regarded as negligible because of the low heat conductivity of this vapor at the pressures used (which never exceeded ten bars). I Mathematical Theory of Diffusion in a Wire During carbonization, the compound W2C forins a shell on the outside of the unaltered tungsten core, and as carbonization proceeds, the thickness of the shell increases at a rate governed by that of diffusion of carbon t h r u the carbide. During decarbonization, carbon disappeais from the outer layers of the filament, and a t any instant the latter consists of a carbide core surrounded by a tungsten shell. Thus the rate of decarbonization depends upon the rate of diffusion of carbon thru tungsten. Diffusion in both these processes is analogous to the dffusion of heat during the formation of ice on the surface of the water.’ Let us consider a tungsten filament of radius R which has been partially carbonized, leaving a residual core of metal, of radius r . (See Fig. I ) . Let C1 denote the concentration of carbon (in grams/cm3) a t the surface: That is, C1 is the solubility of carbon in W2C. We will assume that this concentration is maintained constant during carbonization. Let C z denote the concentration of carbon dissolved in the tungsten and not present as W2C. Thus C2 is the solubility of carbon in metallic tungsten. Also, let C, denote the amount of carbon required to convert unit FIG.I volume of tungsten into WZC. Assuming that the rate of formation of carbide is so rapid that the concentration gradient for carbon is linear thru the shell, the rate of penetration of carbon is given by the relation2
@
where D denotes the coefficient of diffnsion of carbon thru ITT&. The integral of equation ( T ) may be written in the form
or
Kt
=
- R2
whereK
=
(2)
II (C, - C d c o
(3)
Ingersoll and Zobel: “Mathematical Theory of Heat Conduction,” Chap. 9. For an explanation of the derivation of this equation, the reader is referred to any treatise on heat conduction, as e.g., the book by Ingersoll and Zobel. Also see I. Langmuir: Convection and Radiation of Heat-Trans. Am. Electrochem. Soc. 23, 299 (1913.) 2
DIFFUSION O F CARBON
465
and x = r/R. Integrating the right-hand side of equation (2) we get
- -Kt Rz
I
- x2 + 2x2 loge x
(4)
The simplest method of solving this equation is to plot the function y =I
- x2 + 2x2log, x and thus obtaiin graphically values of
Kt correspond-
R2
r2
ing to given values of r2/R2. The value of - is, of course, determined from
R2
conductance. r2 - S -
Since the conductivity of W2C is .07 of that of tungsten
*07 where
R2
.93
S = the ratio of the conductivity of the partially carbon-
ized filament to that of the original filament. Knowing the actual value of t corresponding to any value of r2/R2 it is possible to obtain the value of
K = D(C1- ')"
CO
Since C, is known f'rom the composition of WZC we can cel-
culate D(C1 - C,) which we shall designate the coeficient o€ penetration. The above calculations apply equally well to data obtained in decarbonization, with the single difference that concentration of carbon varies from C z to o instead of from C1 to CZ. The coefficient of penetration in this case is, therefore, DlC2,where D1corresponds to the coefficient of diffusion thru tungste11 Rates of Carbonization and Decarbonization
It is evident that the experimental observations on rates of carbonization lead only to values of the coeficient of' penetration. The methods used for the determination of C1 and C2 will be discussed in a subsequent section. Table I shows data obtained,in a typical run on the rate of carbonization, while Table I1 gives similar data for a decarbonizing run. TAI3LE 1 Penetration in a 4 mil Wire a t
Total Time of Heating
o min. 1/2
min.
I 2
3 4 I/2 6 8 13 23
Percent Conductance
98.5 90.3 84.5 65.0 54.1 42.2 30.7 25.0
19.1 20.5
2 I 70°K
r2/R2
.894 .831 .622 9
505
.378 .254 . I93 . I30
D(C1 - Cz) X
1010
18.6 12.6 25.4 31.0 34.8 40.8 38.0 28.8 Average = 28.8
It is worth pointing out in this connection that the mathematical theory as presented above differs greatly from that which would apply to the case in which a solid solution is formed and not a chemical compound. The equation,. applying to the former case have been put in very ronvenient form for practical use by D. H. Andrews and J. Johnston: J. Am. Chem. SOC.46, 640 (1924).
MARY R. ANDREWS AND S. DUSHMAN
466
It will be observed that the minimum conductance was considerably above seven percent. This is undoubtedly due to the formation of a shell of the second carbide, WC, a t the surface of the filament before the core was completely converted to W2C. For this reason, the last two values of D(C1 - C2) are lower than the preceding value. KO satisfactory explanation has been found for the regular increase in the first six values. It may be due to the formation of longitudinal cracks in the filament which deepen as carbonization progresses. The existence of such cracks has been shown by microscopic examination. Or, it may be that the actual temperature of the conducting tungsten core rises (since the voltage rises) as carbonization progresses. Whatever the cause for this increase, it was thought best to take an average of all the values for D(C1-Cz) in any one run. 11 Decarbonization in Low Pressure of 4 mil Filament a t 2400'11 TABLE
Total Time of Heating
Percent Conductance
r2/R2
min.
775
44.7
'
I
50.3
.710
3 8
66.7
.533 .3*3
I3
DC,XIOI"
23.3
0
1/2
0 2
86.0 85.0
36* 28 27
24
*This value is regarded as the most accurate for the reasons given in a previous section.
Solubility of Carbon in Tungsten and in, WZC To calculate the coefficient of diffusion of carbon in tungsten and in WZC, it is necessary to know the values of the terms Cz (the solubility of carbon in tungsten) and C1 (solubility in W2C). In order to determine the value of C2, the following experiment was carried out. A I 2 mil filament was first carbonized slightly and then decarbonized in excess of oxygen a t constant temperature. The resultant gases were passed over a glowing platinum filament to oxidize the CO to COZ, which was then condensed in a liquid air trap. At intervals, the run was interrupted, and the collected COZmeasured. As decarbonization neared completion, these intervals were made very short. At a certain point, the amount of COZ collected per minute began to decrease and continued to do so for some minutes, finally reaching a negligible constant value equal to the previously determined blank of the system. This blank was probably due to very small amounts of impurities in the oxygen used. It is evident that at the point a t which the evolution of carbon began to decrease rapidly, all the W2C in the filament was decomposed, and that the carbon evolved from that time on was that dissolved in the tungsten. Two such experiments were made, one at 2000°, and another a t 2 2 0 0 ~ . The values obtained at 2000' are shown in Fig. 2. From this experi-
46 7
DIFFUSION O F CARBON
ment, the concentration of carbon was calculated to be .009% of the weight of the tungsten. The value from the run made at 2 2 0 0 was .ojy’. It is hardly likely that there is such a temperature coefficient for the solubility of carbon in tungsten, but it is possible that the second value is somewhat high because some of the carbon evolved after the break in the rate of evolution of CO may have been due to traces of W2C still undecomposed. Using the weighted mean value, O.OIO%, the value of C pbecomes 0 . 0 0 2 gm/cm3. Efforts to determine the value of the solubility of carbon in W2C were unsuccessful, though several attempts were made to do so. 0 0045
7 0 0039 C
$5! 0 0033 C
5ii b%
$2 0.0027 .P
gj c
’
0 0321
900
L t
G2 :
0 0015 0 0012
2 ‘0 o.Oc1)s 0.0006
0 ’ 0 w 3 1 1 W
10
15
00
! ! 1 1 1 951 85
~
1 l 105’ I 110\ i 11’3] \ 120j ‘
1
90 LOO Time tn MlnLites
FIG.2 Rate of Decarbonization of Tungsten in Oxygen at zoooo K.
Table I11 gives the values of DICz and D1for two wires at various temperatures. DI has been calculated on the basis of C2 = .002 and on the assumption that this solubility does not change appreciably thru the temperature range used. Values of DlC2 are shown graphically in Fig. 3. Table IV gives the values of D(Cl-C2) for a number of different wires. These are shown graphically in Fig. 4.
TABLE I11 Coefficients of Diffusion of Carbon thru Tungsten Symbol on Fig. 3.
0
A
Wire
7 mil pure tungsten
Temperature
2185’K 2355 ’’
4 mil tungsten
2070 ”
containing .5 yoT h o z
2188 ”
2300
”
2400 ”
D K z X xo10
DIX107
IO
5
20
IO
3.2 9.6 15.6 36.
I .6
4.8 7.8 I8
MARY R. ANDREWS AND S. DUSHMAN
200
100 90 80
70 60 30 40
30 20
10 9 8
7
6
5 4 3 2
1
104 T
FIG.3 Coefficients of Penetration of Carbon thru Tungsten
DIFFUSIOX O F C A R B O S
104 T
L
FIG.4 Coefficients of Penetration of Carbon thru Tungsten Carbide
469
MARY R. ANDREWS AND S. DUSHMAN
470
TABLE
Iv
Coefficients of Penetration of Carbon thru W2C Symbol on Fig. 4. 0 7
O2
A,
Wire
Temperature
7 mil pure tungsten fine grained
1975OK 2295
2 mil pure tungsten fine grained
2100
8 1/2mill
2080
2210
2190
2300
n4
4.2mill
I980
OB z.09mila 0, 2 . o '' single crystal
nP
2.gmi14
36 86 7.9 30.2 I 26 1.5
118.
215.5
10"
270
zoo; 2795 2015
X
6.2
2280
2170
2.8mi12
- C2)
16.8 28.8 103.
2075
0,
D(C1
12.8
16. 74.
I930
7.2
2040
23.6
2 000 2000
10.7 8.
2000
29.5
The coefficient of penetration thru tungsten carbide was measured for a number of wires in order to find out whether this process depends on either the quality or the grain-size of the wires. It will be observed from Fig. 4 that the values of the coefficient of penetration at any one temperature extend over a range of 300 to 400 percent, and that in general the smaller wires show the higher value. This cannot be ascribed to small grain-size in the small wires since the so-called single crystal wire and the "overlap" wire show values quite close to those found for normal wires of the same size. (The high value found for the Pintsch filament, a single-crystal thoriated wire, was probably due to error in temperature as this wire is quite variable in diameter.) Furthermore, it is evident since the diffusion takes place thru a shell of tungsten carbide or thru a shell of tungsten that has been derived from carbide, that the original Tungsten containing a fraction of a percent of thoria: fine grained. Pure tungsten with very long grains (Overlap wire) Pure tungsten, fine grained. From this wire the 2.0 mil single crystal wire was made. Pintsch wire-Large crystal wire containing a few percent of thoria.
DIFFUSIOX O F CARBON
47 1
structure of the wire cannot have any direct bearing on this process. This is confirmed by photomicrographs of various carbonized wires, which show that the grain size of the carbide formed is independent of the structure of the original filament. It is difficult to'understand, therefore, the recent observation made by W. Geiss and J. A. M.v. Liemptl, regarding the failure of a single crystal rod of tungsten to form carbide when embedded in charcoal powder and heated a t I 9ooOC. On the other hand, we have recently obtained in this laboratory very striking evidence that in such cases as the diffusion of thorium or yttrium thru tungsten, the rate is very much greater along grain boundaries than thru the lattice structure. These observations will be discussed in a subsequent paper. The most probable explanation of the differences in coefficients of penetration observed in different sizes of wire, is that the assumptions underlying the mathematical theory (on which are based the calculations of the coefficients of penetration) are not quite in accord with the actual conditions.
Heats of Diffusion It will be observed from Fig. 4 that in general, the values of the coefficients of penetration for any one wire lie on a straight line whose slope obviously is a measure of the heat of diffusion of carbon thru tungsten carbide. The slopes obtained for different wires are practically the same within the limits of experimental error. Applying the modified van? Hoff equation dln(D C) - - -Q d R
(+)
it is found that the heat of diffusion of carbon thru W2C is about 108,000 cal/ mol. Similarly from the slope of the line in Fig. 3, the heat of diffusion of carbon thru tungsten is found to be 7 2 , 0 0 0 cal/mol. It is of interest to observe that this value of the heat of diffusion for carbon thru tungsten is somewhat less, but of the same order of magnitude as that observed by Langmuir2 for the heat of diffusion of thorium thru tungsten, 94,000 calories. On the basis of certain semi-theoretical considerations Langmuir and Dushman3 have derived an equation of the form D = K,", where : and No = number of atoms of the diffusing substance per unit area. The other symbols have their usual significance. Metalkunde, 1'01. 16, p. 37 (1924). 22, 357 (1923). 3 Phys. Rev. 20, July (1922)
* Phys. Rev.
MARY R. ANDREWS AND S . DUSHMAN
472
This equation, then, gives the relation between the heat of diffusion and the absolute value of the diffusion constant at any temperature. By means of this equation, it is possible to calculate the absolute value of the diffusion constant a t any temperature from the observed value of &, the heat of diffusion. Table V gives values of D and D, calculated in this manner for different temperatures. For comparison, the values of D1 as derived directly from the decarbonization data and values of Cz, and values of D(Cl-C2)are shown in columns 4 and 5 respectively.
TABLE T.' Diffusion Constants calculated from the Heats of Diffusion D1 Di D D(Ci- Cd from Q'
20ooO
from experiment 4.4 XIO-~ 9 XIO-~
220oO
2.3
Temp.
2400'
XIO-' 4.5X10-' . 88 X I o - ~ I . 8 X I o - ~
from Q
from experiment
7.5x10-l~ ( 3 t o 1 2 ) X 1 0 - ~ ~ I . Xro-l1 (3.6to12)X10-~ 7 . 3 X I o-ll (3.oto 8) X I 0-'
It will be observed that the two methods of determining D1 yield results that agree quite satisfactorily, in fact within the limits of the possible errors in the value of Cz used in deriving D1 from experiment. The values for D, however, are of an entirely different order of magnitude from any that are to be expected. Using these calculated values of D and the observed values of D(Cl-C2) the values of C1-C2are found to be altogether too large. This may be because the conditions of diffusion thru a compound such as tungsten carbide are undoubtedly far more complex than those for diffusion thru the simple metallic lattice of tungsten. X-ray spectro-grams taken in this laboratory by Dr. W. P. Davey show that W2C has a rhombohedral structure with the side of the unit triangle equal to 4.66"A an.d an axial ratio of I .42. He calculates that the tungsten atoms are arranged in a similar manner to the calcium and carbon atoms in calcite, and that their nearest approach to each other is I .42A.I This gives a complex structure already containing carbon, thru which carbon must diffuse, and the mechanism of this diffusion is probably different from that of carbon thru tungsten. Moreover, there may be a n appreciable temperature coefficient to the solubility gradient (C,-C,). If this were the case, the value of Q, as calculated from the slope of the values of D(Cl-Cz)would be too great. It is hardly conceivable, however, that this temperature coefficient of solubility could be sufficiently large to reduce Q to the value corresponding to values of D a thousand or ten thousand fold larger. 1
This work will be published later in more detail by Dr. Davey.
