Hall coefficient of tantalum carbide as function of carbon conten

Dolloff, R. T.

Santoro, G. J.

English

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HALE COEFFICIENT OF TANTALUM CARBIDE 
AS FUNCTION OF CARBON CONTENT 
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NASA TN D-3135 
HALL COEFFICIENT O F  TANTALUM CARBIDE AS FUNCTION 
OFCARBONCONTENT 
By Gilbert J. Santoro and R. T. Dolloff 
Lewis Research Center 
Cleveland, Ohio 
NATIONAL AERONAUT ICs AN D SPACE ADMINISTRATION 
For sale by the Clearinghouse for Federal Scientific and Technical Information 
Springfield, Virginia 22151 - Price $1.00 
HALL COEFFICIENT OF TANTALUM CARBIDE AS FUNCTION OF CARBON CONTENT 
by Gi lbert  J. Santoro and R. T. Dolloff  
Lewis Research Center 
SUMMARY 
The Hall coefficient within the entire cubic phase region of tantalum carbide was 
investigated by a direct-current method and was  found to be negative and to increase in 
absolute magnitude with increasing carbon content, while the electrical resistivity was  
found to decrease. These results, as well as the known variation of the magnetic sus- 
ceptibility and the superconductivity transition temperature with carbon content, indicate 
that a one-carrier model is not adequate to describe the entire system. A composition 
in the ditantalum carbide phase region was also found to have a negative Hall coefficient, 
its magnitude being greater than that of any of the other samples. Magnetoresistivities 
were too small to be accurately measured. 
INTRODUCTION 
A number of investigators (refs. 1 to 4) have measured the Hal l  coefficients of the 
group IV and V transition metal carbides and nitrides and their solid solutions having 
sodium chloride type crystal structure in order to understand more fully the electronic 
binding in these materials. Their samples have been restricted either to nearly stoichio- 
metric compositions or to solid solutions of nearly stoichiometric components. The re- 
sults of these investigations have been expressed in terms of the variation of the valence 
electron concentration (VEC), that is, the valence electrons per formula with the ex- 
pressed or implied assumption that the electronic band structure is not strongly affected 
by differences in the ionic cores. A recent band structure calculation on titanium car-  
bide (ref. 5), however, implies that substitutional alloying of either the metal or the non- 
metal atom may significantly alter the density-of-states curve, even if the VEC is un- 
changed. The histograms of density of states for titanium carbide and titanium nitride 
as recently calculated by Ern and Switendick (ref. 6) clearly differ from each other not 
only with respect to the position of the Fermi level, but also with respect to the energy 
distribution of the density-of-states and to the degree of band interaction. Thus, the band 
‘k 
structure of one of these compounds cannot be universally employed for the others. 
These calculations, then, confirm the desirability of varying the VEC without resorting 
to substitutional alloying. Since these compounds exhibit rather wide single-phase re- 
gions, the VEC can be varied over a large range merely by changing the concentration of 
the nonmetal atom. Thus, in order to study more fully the effect of changes in the VEC 
on the electrical nature of tantalum carbide (TaC), room temperature Hall measurements 
were made on TaC ribbons of different carbon contents. The electrical resistivity of 
each specimen was  also determined, and attempts were made to determine magneto- 
resistivity. Measurements were also made on a sample of the hexagonal carbide, Ta2C. 
The data a r e  discussed in relation to the band structure determinations which have ap- 
peared in the literature for the group IV and group V transition metal carbides and ni- 
trides and in conjunction with other properties of nonstoichiometric tantalum carbide. 
EXPERIMENTAL PROCEDURE 
Tantalum carbide ribbons were prepared by heating pieces of tantalum foil (19 by 
0.32 by 0.0025 cm) in measured amounts of propane for 6 hours at 2000' C. The purity 
of the tantalum was at least 99.89 percent. The method is similar to that used previously 
in the preparation of substoichiometric tantalum carbide filaments (ref. 7). An X-ray 
diffraction pattern was made on each of the specimens with a 114.6-millimeter-diameter 
Debye-Schemer camera using copper Ka radiation. The lattice parameters, a,, were 
calculated by means of a least-square extrapolation on an IBM 7094 computer. With 
these data and an established literature curve of a. against carbon content (ref. 8) the 
Low-thermal 
switch 
Nanovoltmeter 
Figure 1. - Schematic of electrical c i rcu i t  of Hall apparatus. 
2 
composition of each sample was ascertained. 
The estimated accuracy of the carbon de- 
termination using this procedure is about 
TaCX*O. 006' 
A 1.4-centimeter length from each 
carburized ribbon was used as the Hall spec- 
imen. A direct-current method was em- 
ployed in the Hall measurements. The 
electrical circuit is shown in figure 1. All 
the vital circuit parts were electrically and 
magnetically shielded. The low thermal 
switch permitted the selection of the de- 
sired pair of leads while introducing thermal 
voltages of less than lo-' volt. All stray 
voltages could be suppressed by the bucking 
( 
Viewed from above 
1 \,--Printed c i rcu i t  board 
Figure 2. - Schematic of Hall probe. 
3 
circuit to less than lo-’ volt. The voltage signal over a 10-minute interval was stable 
to within lo-’ volt. 
A drawing of the probe head, which was 4 . 4  by 2.5 by 0.6 centimeter, is shown in 
figure 2. The printed circuit board provided a convenient way of minimizing circuit 
loops, which could otherwise produce stray voltages and fields. The leads were con- 
nected to the copper strips on the circuit board with solder that has a low thermoelectric 
effect with copper. The electrical contacts to the sample were provided by a liquid 
mercury -indium alloy to circumvent problems of wetting and generation of thermal 
stresses when other methods of soldering or welding were attempted. 
and magnetic field. 
the highest magnetic field available. The linear variation in these curves indicated 
freedom from thermal gradients caused by excessive Joule heating (proportional to the 
current squared). Then a convenient current was chosen, and the transverse voltage was 
measured as a function of the magnetic field (fig. 3(b)). This procedure indicated the 
validity of the linear variation of the Hall voltage with the magnetic field as given in the 
Hall equation 
Measurements were taken of the transverse voltage with reversal of both current 
First the voltage was measured as a function of current (fig. 3(a)) at 
RBI 10-8 E H = -  
t 
where 
12x10-7 i 
= - 8  
a- m 
m r. 
0 > -- 
2 4  
0 M 80 1 
Current, mA 
(a) Current; magnetic-field strength, 34.4 kilogauss. 
0 10 20 
Magnetic-field strength, kG 
(b) Magnetic-field strength. 
I 
Current, 
mA 
/t 
M 
40 
Figure 3. - Variation of Hall voltage with current and magnetic-field strength for various compositions. 
4 
EH Hall voltage, V 
R Hall coefficient, cc/C 
B magnetic-field strength, G 
I current, A 
t sample thickness, cm 
The existence of isothermal conditions was further verified by remeasuring a specimen 
in high-thermal-conductivity oil (high-grade transformer oil) and obtaining the same Hall 
coefficient. 
RESULTS 
The Hall coefficient was  found to be negative for all compositions tested, indicating 
electrons as the predominant carr iers .  Within the TaC phase region the Hall coefficient 
- 1; 
- 1[ 
OL o 
. I  
- -43- Electrical resistivity -u, Hal oefficient 
9 ..
Carbon'to tantalum molar ratio 
I 
7. a 8.2 a. 6 9.. 0 
Valence electrons per formula 
Figure 4. - Room-temperature variation of 
resistivity and Hall coefficient as functions 
of carbon content for cubic tantalum car- 
bide. 
became more negative with increasing carbon 
content (see fig. 4). For stoichiometric TaC a 
value of about -10X10-5 cubic centimeter per 
coulomb was found, as compared with litera- 
ture values of -llX10-5 cubic centimeter per 
coulomb (refs. 1, 3, and 4) and - 6 . 4 ~ 1 0 - ~  cubic 
centimeter per coulomb (ref. 9). The latter 
value came from poorly characterized ma- 
terials. The electrical resistivity data of the 
cubic carbide agreed with those previously re -  
ported (ref. 7), decreasing with increasing car- 
bon content (see fig. 4). The magnetoresis- 
tivity was too small to be measured accurately, 
an upper limit of about being typical under 
an applied field of 34.4 kilogauss. 
cient was - 1 5 . 5 ~ 1 0 - ~  cubic centimeter per 
coulomb, an order of magnitude more negative 
than any value derived from the cubic samples. 
No values have been reported in the literature 
for this ditantalum carbide. A value of 102 mi- 
crohm centimeters was found for the electrical 
resistivity of the Ta2C sample. Here again 
For the Ta2C specimen, the Hall coeffi- 
5 
the magnetoresistivity was too small to be measured accurately. 
DISCUSSION 
It has been assumed that the band structure of the IVth and Vth group transition 
metal carbides and nitrides a r e  all similar (refs. 10 and ll), and it has been reported 
that the IVth group carbides exhibit Hall values of an order of magnitude more negative 
than those for the Vth group (refs. 1 to 4). On the basis of this knowledge and with the 
previous assumption applied to the present study, the Hall coefficient of TaC would be 
predicted to become more negative with decreasing carbon content and to approach the 
value for  group IV carbides at a VEC of about 8.0, that is, at Taco. 75. The observed 
variation is opposite to this prediction; as shown in figure 4, the Hall coefficient becomes 
less negative as carbon content is decreased. The failure of this prediction casts doubt 
on the validity, even as a first approximation, of applying the band structure of any one of 
these materials to the entire group by a mere adjustment of the Fermi level in accord- 
ance with the VEC. 
The findings reported here also show that the one-carrier model cannot be utilized 
for nonstoichiometric compositions of tantalum carbide, since, based on such a model, 
the Hall coefficient for the low-carbon samples yields carrier densities which are 
greater than normal metallic carrier densities. Thus, at Taco. 75, the number of con- 
duction electrons would be about 4x10 
to about 0 . 8 ~ 1 0  
tron density for Taco. 75 corresponds to about 9 electrons per formula, whereas its 
VEC is only 8. 
The same conclusion can be reached from the following consideration: the variation 
of the magnetic susceptibility (refs. 13 and 14) and the superconductivity transition tem- 
perature (ref. 15) with carbon content in the cubic tantalum carbide phase indicates an 
increase in the density of states with increased carbon concentration. The electrical 
conductivity similarly increases. Thus, the number of conduction electrons increases, 
and this rise, on the basis of a one-carrier model, should be reflected by a decrease in 
the Hall coefficient, a prediction contrary to the variation in figure 4. 
While the one-carrier scheme has been employed to explain the data collected from 
refractory transition metal carbides and nitrides of stoichiometric composition (refs. 1 
and 3) and from their solid solutions (refs. 2 and 3), it is clear that such a scheme is 
not adequate for nonstoichiometric compositions of cubic tantalum carbide. However, 
before a unique electrical transport model can be assigned to this system, the factors 
involved in the conduction process must be ascertained. It is believed that the carbon 
vacancies greatly influence the conductivity in nonstoichiometric tantalum carbide. It 
23 per cubic centimeter as compared, for example, 
23 per cubic centimeter for silver (ref. 12) .  Furthermore, this elec- 
6 
is important, therefore, to separate this contribution to the conductivity, by means of 
low-temperature measurements, and to determine its dependence upon composition. 
CONCLUSIONS 
The room -temperature electrical transport proper ties of nonstoic hiometr ic tantalum 
carbides a r e  dominated by negative carriers throughout the entire cubic phase region. A 
one-carrier model is not adequate to explain the data, and low-temperature measure- 
ments are required before a specific model can be proposed. 
Lewis Research Center, 
National Aeronautics and Space Administration, 
Cleveland, Ohio, September 29, 1965. 
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Hall coefficient of tantalum carbide as function of carbon content

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