Electrotransport of carbon, nitrogen and oxygen in vanadium

JOURNAL OF THE LESS-COMMON METALS

ELECTROTRANSPORT VANADIUM*

F. A. SCHMIDT

OF CARBON,

493

NITROGEN

OXYGEN

IN

AND J. C. WARNER

Institute fcv Atomic Research and Department of Metallurgy, (U.S.A.) (Received

AND

Iowa State University, Ames, Iowa

May gth, 1967)

SUMMARY

The electrotransport velocities of carbon, nitrogen and oxygen in vanadium were determined at 1650”, 1735’, and 1825’C. All three solutes were found to migrate in the opposite direction from the electron flow. Diffusion coefficients and effective charges were calculated for these elements at the same temperatures. The electric mobility of nitrogen was shown to be independent of the electric field. The specific resistivity of vanadium was also determined between 950” and 1830°C.

INTRODUCTION

The migration of solutes in solid metal under the influence of a direct current has been known since 1928 when COEHN AND SPECHT~ observed hydrogen transport in palladium. Since then some 32 interstitial solute systems have been studied and critical discussions of the phenomena are available in a number of publishedreviews”-4. Most of the earlier investigators of the electrotransport phenomena considered that the electric field exerted the only force on the solute atom, which was assumed to be charged. In 1953 SEITH AND WEVER~ showed that this interpretation was incomplete and that an interaction between the moving electrons and the solute must be considered. The present interpretation of the electromigration of interstitial solutes, as reviewed by VERHOEVEN4, considers both the electrostatic force and the force resulting from moving electrons being scattered by the solute. The purpose of this investigation was to determine the migration velocities of carbon, nitrogen and oxygen in vanadium by observing the rate of movement of a discontinuity in the concentration profile. This method was used by CARLSONet al.6 and PETERSON et al.7 to determine the mobilities of interstitial solutes in yttrium and thorium metals, respectively. The specimen is treated as a pair of semi-infinite, bar-type diffusion couples and the electrotransport velocities measured by observing the displacement of the center of the concentration profile. The diffusion coefficients were calculated by the standard GRUBE methods. _____ * Work was performed in the Ames Laboratory tion No. zogo.

of the U.S. Atomic Energy Commission. Contribu-

J. Less-Common

Metals, 13 (1967) 493-500

F. A. SCHMIDT,J. C. WARNER

494 EXPERIMENTAL METHOD

The apparatus used in this investigation was identical to that described by CARLSONet al.6 in their work on yttrium. It consisted of a sample chamber which was equipped with two electrodes, a sight glass, and a flange for mounting to a vacuum base-plate. The chamber was made of stainless steel and was IO cm in diam. and 15 cm long. The base plate was equipped with two electrical “feed throughs” to which a zirconium getter wire was attached. This wire was heated by a separate electrical circuit. The vanadium specimens were threaded and screwed into tantalum “U”-shaped adapters attached to the ends of the electrodes. A d.c. current was used to heat the specimen and adapters by internal resistance and also to produce the migration of the solute atoms. It was supplied by a saturable core, step-down transformer which provided a full-wave rectified current with a 15% ripple. A standard resistance and a potentiometer were used to measure the current. The temperature of the specimens was measured with an optical pyrometer and the observed temperature corrected for the emissivity of the sample and for absorption by the viewing window. The absolute temperature measurements were accurate within +5”C. The center of the rods was about 25°C hotter than the ends at a point 0.7 cm from the adapters since some of the heat produced in the specimens was lost to the cooler adapters. The vanadium metal used to study the migration of nitrogen and oxygen was prepared by the crystal-bar process as described by CARLSONAND OWE@. This material had been electron-beam melted and contained 150 p.p.m. carbon, IO p.p.m. nitrogen and 250 p.p.m. oxygen. However, when this material was used to study the migration of carbon in vanadium, 10--20~/~ of the carbon addition was lost from the specimens at 1735” and 1825OC.This was attributed to the high oxygen content of the above material with the resultant loss of COz. To avoid this problem vanadium containing only 40 p.p.m. oxygen was used in the carbon migration experiments. This material, which was prepared by the aluminothermic reduction of VZOS~O,also contained 75 p.p.m. nitrogen and 200 p.p.m. silicon as major impurities. The specimens used in this study were rods of vanadium 6.6 cm long and 0.260 cm in diameter. One-third of the rod consisted of the host material and the remainder had a higher concentration of the solute of interest. The segments of vanadium containing approximately 500 p.p.m. of a given solute were prepared by adding the solute to the high-purity vanadium during arc-melting. Nitrogen was added to the crystal-bar vanadium by co-melting with pieces of a vanadium-7 wt.% nitrogen master alloy and oxygen was added directly as VzO5. The addition of carbon was made as amorphous graphite which contained 8 mc of 1%/g. These arc-melted alloys were then swaged into rods for use as the high-concentration ends. Sections of vanadium rod of two different solute concentrations were cut to the desired lengths and threaded at one end. These segments were electropolishedll and butt-welded together under an inert atmosphere to preserve the sharpness of the interface and to avoid contamination. In each run the specimen was positioned in the apparatus with the low concentration at the anode end. The specimen chamber was evacuated, outgassed and filled with argon to a pressure of I p.s.i. gauge. The argon atmosphere was purified by heating the zirconium getter wire to 145O’C for 20 h. A d.c. current sufficient to heat the vanadium specimen to the desired temperJ. Less-Common

Metals,

13 (1967) 493-500

ELECTROTRANSPORT

OF C,

ature was passed through

Nz AND 02 IN VANADIUM

495

the rod for the specified length of time. The current density

varied from rg5o A/cm2 at 1650°C to 2260 A/cm2 at 1825’C.

After cooling, the speci-

men was cut into samples for analysis. Segments 0.5 cm long were used in the determination of the nitrogen and oxygen concentrations by vacuum-fusion analysis in a platinum concentration

bath. The accuracy of these analytical determinations was _t3%. The of carbon was traced as 14C by counting the beta activity of segments

0.15 cm in length. These samples were mounted in a self-curing acrylic resin, ground through 600 grit paper and the activity of each end counted for IO min using a Sharp LB-100 Series Lowbeta gas-proportional-measuring system. An average of the counts per minute obtained on each end of the sample was then used as the level of activity for that segment. The results from this method of analysis were also found to be accurate RESULTS

AND

within

-t3%.

DISCUSSION

PETERSON

et al.7 have shown in their

work on the migration

of interstitial

solutes in thorium that an extension of Fick’s second law may be used to express the mass transport of an interstitial atom in a unidirectional electrotransport experiment. In this treatment the mass flux without the electric field would be due solely to diffusion and it is correct provided one assumes that diffusion and electric migration are independent of one another and that the mobility, U, diffusion coefficient, D, and electric field, E, are independent of distance. These assumptions appear quite good in this investigation since the solute concentrations were well below the saturation limits, the cross section of the specimen remained constant and the temperature was constant within 10°C along the diffusion zone. Since the initial and boundary conditions for distance and time are the same in this study, the net effect of the electric field is a displacement AX, of the concentration profile of the Grube solution by an amount, AX = UEt.

(1)

Hence, this displacement of the center of the diffusion couple from the original concentration interface may be used to obtain the mobilities of carbon, nitrogen and oxygen in vanadium. Figures I, 2 and 3 show typical concentration profiles for carbon at 1825’C, nitrogen at 1735°C and oxygen at 165o’C. All three interstitial solutes were found to migrate

toward the cathode,

i.e., in the direction

opposite

to

the electron flow. The length of time selected for each electrotransport experiment was enough to allow a measurable movement to occur but not so much that the high concentration plateau disappeared into the concentration increase at the end of the specimen. The voltage drop per unit length, E, was calculated from the current density and the specific resistivity. Since the specific resistivity of vanadium was not known for the temperatures at which the migration experiments were made, this property was determined as a function of temperature using the method described by CHIOTTI~~. The specific resistivity of vanadium over the temperature range goo”-r830°C is shown in Fig. 4. The diffusion coefficients were calculated from the concentration profiles by the Grube method. The concentration data were plotted on “probability” paper so that a best-straight-line could be drawn through the points. This paper is a special type of graph paper with an error functional scale as an ordinate. J. Less-Common

Metals,

13

(1967)4g3-po

F. A. SCHMIDT, J. C. WARNER

496

When a direct current is passed through a metal, the total net force on an impurity ion in the solid can be written,

F=eEZi-

J&=eE[ZI

- $1 =eEZ*

(2)

where F is the force on the ion, e the electron charge, Zt the actual valence of the I

I

I

I 1825 “C 3 HOURS

I

I

WELD

I

INTERFACE

100 k is 5

-

fiil

.a m 50I-

5 s

DISTANCE,

Fig. I. Carbon’4

activity

of composite

Fig. 2. Nitrogen content of composite J. Less-Common

CM

sample after heating to 1825% for 3 h.

sample after heating to 1735°C for 12 h.

Metals, 13 (1967) 493-500

I

SPECIFIC

I

RESISTIVITY,

P

I

, MICROHM-CM

I

R

$ 6

P % 3

0

-

0

I

I

$

0

:

0 II VI0 OZ

OXYGEN,

I

i2

0

PPM

I

I

0

: 0

:

F. A. SCHMIDT,

498

J. C. WARNER

ion, J the current density and Q the specific resistivity. The first term is due to the electric field in the metal and the second is the result of moving electrons being scattered contained

by the ion. All of the factors influencing the scattering interaction are in dei which is called the drag friction coefficient. The effective valence

of the migrating ions in the solid, Z*, is defined by eqn. (2). By using EINSTEIN’S~~ relation between absolute mobility

B, and diffusion,

2, _=BL,

F

it is possible to determine

the magnitude

of the force on the ion and hence the effective

charge,

In these equations, k is Boltzmann’s constant, T the absolute temperature and v the velocity of the migrating species. The use of these equations assumes that the solution is ideal, that diffusion is of the activation type, and, as FRENKEL14 has shown, Fe zkT/d, where F is the total force on the ion and 6 is the ionic jump distance. Therefore, the electric field must be less than 107 V/cm if all the applied force is due to the electric field. Both conditions should apply for this work since the interstitial concentrations was less than 0.5 V/cm. TABLE THE

NITROGEN

Interstitial solute Carbon

Nitrogen

Oxygen

limits and the electric

field

I

ELECTROTRANSPORT

CARBON,

were well below the solubility

AND

VELOCITIES, OXYGEN

DIFFUSION

IN

VANADIUM

Temp. PC)

AX

t

(cm)

0)

COEFFICIENTS USING

0.260

E (V/cm)

u (Io-5

0.253 0.227 0.208

22.0

1825

0.60

1735 1650

0.55 0.60

1825 1735 1650

0.61 0.63 0.66

8 12 24

0.252 0.227 0.206

8.4 6.4 3.7

1825 1735 1650

0.64 0.47 0.47

4

0.252 0.225 0.209

17.5 8.2

3 4 7.5

;

16.9 10.7

7.8

AND

EFFECTIVE

CM DIAM.

cm21 V-set)

CHARGES,

z*,

FOR

RODS

D (IO-~ cna2/sec) I.9 I.2

0.94 0.91

0.70 0.38 2.5 I.5 I.0

z*

2.1

2.5 I.9 I.7 1.6 1.6 I.3 I.0 I.3

The electrotransport velocities, diffusion coefficients and effective charges, for carbon, nitrogen and oxygen in vanadium for the three temperatures studied are given in Table I. The data for the migration of carbon is taken from one run at each temperature while the values for nitrogen and oxygen are an average of three runs. For the nitrogen and oxygen data the average standard deviation of the diffusion coefficients and the electric mobilities was 15% while the deviation of the effective charges was 18%. The values obtained for carbon are believed to be more accurate since more data points were obtained using the tracer technique. In a separate series of experiments an effort was made to determine the specific J. Less-Common Metals,

13 (1967) 493-500

ELECTROTRANSPORT

relation

between

OF c,

electric

eqn. (4). In this study,

Nz AND 02 IN mobility,

VANADIUM

electric

499

field and temperature

since the temperature

is related

as indicated

to the current

density,

in the

thickness of the sample may be changed in order to change the electric field. Vanadium transport specimens measuring only 0.130 cm in diameter were heated to the same temperature as were the samples 0.260 cm in diameter. These thinner rods contained a similar nitrogen concentration discontinuity and the electric mobility determined. The current density used to heat these specimens varied from at 1650°C

to 3190 A/cm2 at 1825’C.

The

average

values

was again A/cm”

2800

of the electric

mobility,

diffusion coefficient and effective charge for nitrogen in vanadium using 0.130 diam. rods are given in Table II. By comparing these data with the values obtained on the larger diameter specimens (Table I), it is evident that U and D for nitrogen in vanadium are independent of the electric field. Since the effective charge, Z*, appears to be independent

of both the electric

D in eqn. (4) may be considered

TABLE THE IN

field and temperature,

to be dependent

the parameters

on temperature

U and

alone.

II

ELECTROTRANSPORT VANADIUM

USING

VELOCITY, O.IjO

CM

DIFFUSION

DIAM.

Tamp

AX

t

E

(“C)

(cm)

(h)

(Vlcm)

1825

0.51

‘735 1650

0.61

9.54

i

COEFFICIENT

EFFECTIVE

CHARGE

u (IO-5 cmZ/V-set)

D (Io-5

0.355

8.0

0.80

0.327

6.5

0.07

0.297

‘3

AND

FOR

NITROGEN

RODS

z* cm2/sec)

0.35

3.9

1.8 I.7

I.9

Equation (2) indicates that the force on a migrating ion is due both to the electric field force and the scattering interactions with electrons or electron holes. Since Z* is positive for carbon, nitrogen, and oxygen in vanadium, it can be concluded that either these solutes are positively charged ions and the electric charge is dominant, or that the interaction with the moving electrons results in a momentum transfer

toward the cathode In two recent

studies

by scattering performed

positive

holes, or both.

in this laboratory,

it was found that

the

effective charges of carbon, nitrogen, and oxygen were all negative in yttrium6 and thorium7 whereas the effective charges of these solutes were all found to be positive in the present study. It is interesting to note that the direction of migration of all three solutes is the same in a given metal. If these solutes have the same valence in the metal as they do in a chemical compound, i.e. carbon having a positive charge and oxygen and nitrogen having negative charges, the effect of valence cannot be the predominating factor in determining the direction of migration. However, if the scattering of electrons or electron holes is dominant, then these solutes could migrate in the same direction even though their valence signs are different. A second possibility is that all three solutes, carbon, nitrogen, and oxygen, take on the same valence sign depending upon the solvent metal. In this case, a dominant valence effect would produce the observed results as would also a dominant scattering effect. It has not been possible, as yet, to separate the components of Z* experimentally for interstitial alloys although a number of theoretical considerations are available4,15~16. J. Less-Common

Metals, 13 (1967) 493-500

F. A. SCHMIDT, J. C. WARNER

500 ACKNOWLEDGEMENT The authors

wish to thank

their associates,

AND J. D. VERHOEVEN for their helpful work. We also wish to acknowledge analytical

N. CARLSON, D. T. PETERSON and guidance

throughout

this

the services of the Spectrographic

Group, Health

Group I of the Ames Laboratory

for performing

Physics Group and Radio Chemistry the necessary

0.

instruction

measurements.

REFEREKCES I A. COEHN AND W. SPECHT, 2. Physik, 62 (1930) I. 2 W. JOST, Diffusion in Solids, Liquids and Gases, Academic Press, New York, 1952. 3 T. HEUMANN, The Physical Chemistry of Metallic Solutions and Intermetallic Compounds, Vol. I, Paper 2C. H.M.S.O., London, 1959. 4 J. D. VERHOEVEN, Met. Rev., 8-(;963) 311. 5 W. SEITH AND H. WEVER, 2. Electrochem., 57 (1953) 891. 6 0. N. CARLSON, F. A. SCHMIDT AND D. T. PETERSON, J. Less-Common Metals, IO (1966) I. 7 D. T. PETERSON, F. A. SCHMIDT AND J. D. VERHOEVEN, Trans. AIME, 236 (1966) 1311. 8 G. GRUBE AND A. JEDELE, Z. Elektrochem.. 38 (1932) 799. Q 0. N. CARLSON AND C. V. OWEN, J. Electrochem. Sot., 108 (1961) 88. IO 0. N. CARLSON, F. A. SCHMIDT AND W. E. KRUPP, J. Metals, 18 (1966) 320. I I E. N. HOPKINS. D. T. PETERSON AND H. H. BAKER, U.S.A.E.C. Refit. ORAL-TM-1161, February, 1966.’ 12 P. CHIOTTI, Rev. Sci. In&‘., 25 (1~54) 878. 13 A. EINSTEIN, Ann. Physik, 17 (1905) 549. 14 J. FRENKEL, Kimtic Theory of Liquids, Dover Publications, New York, 1955. 15 H. B. HUNTINGTON AND S. C. Ho, J. Phys. Sot. Jafian, 18 Suppl. II (1~63) 202. 16 M. D. SMOLIN AND I. N. FRANTSEVICH, Fiz. Tver. Tela., 3 (1961) 2115. J. Less-Common

Metals, 13 (1967) 493-500