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Diffusion and trapping of oxygen in refractory metal alloys
DIFFUSION AND TRAPPING OF OXYGEN IN REFRACTORY METAL ALLOYS? R. J. LAUFf
aod C. J. ALTSFETTER$
(Received 3 Augusr 1978; in revisedform 3 January 1979)
Abstract-The diffusion coefficient of oxygen has been measured in niobium, vanadium and several dilute substitutional niobium alloys. Measurements were made over the range of 6@I-1150°C (873-1423 K) using a solid electrolytic cell technique. Oxygen diffusivity in the alloys was found to be less than in pure niobium. This is interpreted as being due to trapping of oxygen atoms by the substitutional solute atoms. The estimated substitutional-oxygen binding or ‘trap’ energies (in eV) for the solutes investigated are: Ta, 0.3 + 0.1: V, 0.55 + 0.05; Ti, 0.7 f 0.1; Zr, 0.7 f 0.05. Rksumk-Nous avons mesure le coefficient de diffusion de l’oxygene dans le niobium. le vanadium et quelques alliages substitutionnels dilub de niobium. Nous avons effectut des mesures entre 600 et 1150°C (8731423 K), par la technique de la cellule ii electrolyte solide. Nous avons trouve que la diffusivite de l’oxygene dans les alliages Ctait inferieure 1 la dilTu.sivitCde l’oxygene dans le niobium pur. Nous interprettons cette observation par un piegeage des atomes d’oxygine par les atomes du solute en substitution. L’e-stimation des energies (en eV) de liaison (ou de “piegeage”) entre un atome substitutionnel et un atome d’oxygtne donne les valeurs: Ta, 0,3 + 0.1; V, 0,55 & 0,05; Ti, 0,7 + 0.1; Zr. 0.7 f 0.05. ZusammenfassuneDer Diffusionskoefhzient von Sauerstoff wurde in Niob, Vanadium und verschiedenen verdllnnten;ubstitutionellen Nioblegierungen gemessen. Diese Messungen wurden mittels einer Technik mit fester elektrolvtischer Zelle tlber den Temneraturbereich 600-l 150°C (8731423 K) durchgefdhrt. In den Legierungen war die Sauerstoffdiffusidn geringer als in reinem Niob. Dieser Befund wird dem Einfangen von Sauerstoffatomen an substitutionell gel&ten Atomen zugeschrieben. Die daraus abgeschatxten Bindungsenergien zwischen Sauerstoff und geliistem Atom sind (in eV): Ta, 0,3 + 0.1; V. 0.55 + 0,05; Ti, 0.7 + 0.1; Zr, 47 & 405.
INTRODUCTION The mechanical properties of refractory metals are severely degraded by the presence of dissolved oxygen or massive internal oxides. Thus, the rate at which oxygen diffuses through these metals and their alloys is of considerable technological importance. Of great theoretical interest is the effect of substitutional solutes on the diffusivity of interstitial solutes. There is a wealth of literature on substitutional-interstitial (s-i) interactions in refractory metals. (See, for example, a review by Hasson and Arsenault Cl].) Unfortunately, most reported data are obtained by anelastic techniques and can not be applied directly to the determination of long-range diffusivities. Theoretical models have been proposed by McNabb and Foster [2], Koiwa (31, Oriani [4] and others, to calculate the effect of trapping on the diffusivity of interstitial solute atoms. Evaluation of these t Work submitted in partial fulfillment of the requirements for the Ph.D. in Metallurgical Engineering University of Illinois. : Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37830, U.S.A. $ Professor. Department of Metallurgy and Mining Engineering and the Materials Research Laboratory, University of Illinois, Urbana, IL 61801, U.S.A. A.W. ?7;7- u
models has been hampered by a lack of reliable data for interstitial diGion at high temperatures. Recently, a method was developed by Kirchheim et al. [5] to observe the transient diffusion of oxygen in refractory metals using a solid electrolytic cell. In the present study, this technique has been used to measure the diffusion coefficient of oxygen in niobium, vanadium and several niobium alloys. The results are used to calculate the s-i binding energy according to the Oriani model. This model assumes that solute atoms in normal interstitial sites are in equilibrium with those at trap sites, assumed here to be adjacent to substitutional solute atoms. The result, equation (l), is an effective diffusivity, D, which is different from the normal diffusivity, D,, without the trapping sites.
D=Q-[* ,:,,,3.
(1)
X, is the atom fraction of substitutional solute, and the partitioning of interstitial solute between normal and trap sites is given by
1157
K = exp
c1 AL
- k~
.
1133
LAUF ,WQ ALTSTETTER:
DIFFUSION
The trap strength. AE,. in this model is the energy difference between a diffusing solute in a normal site and in a trap site. Solid galvanic cells have proven useful for equilibrium potential measurements for the determination of thermodynamic parameters and solubilities in metal-oxygen systems [6-S]. In applying the galvanic cell technique for kinetic measurements a metaloxygen sample is one electrode, whose potential is measured with respect to a reference electrode. The reference electrode was a V-O or Nb-0 alloy of known oxygen chemical potential in the present experiments. The specimen electrode was bonded to a block of pure zirconium, which acts as an efficient sink for oxygen. When the cell is brought to a sufficiently high temperature, the oxygen dilfuses from the sample into the zirconium. The cell EMF is a measure of the surface concentration of oxygen at the opposite face, adjacent to the electrolyte. The boundary conditions are thus established for a solution to Fick’s Law, and the diffusivity of oxygen in the alloy may be calculated, provided diffusion in the alloy is indeed the rate-limiting process. One advantage of this technique is that it eiiminates transfer of oxygen in the electrolyte and across the metal-electrolyte interfaces. Polarization reactions are also avoided. EXPERIMENTAL
PROCEDURE
The oxygen diffusion measurements were made in the electrolytic cell illustrated schematically below: Zirconium Alloy Block I Specimen I This cell was mounted in a high-vacuum furnace and heated to 1OOOC(1273 K) in approx. 2 h. The details of the experimental apparatus are published elsewhere [7,9]. The cell EMF was measured as a function of time using a high-impedence electrometer. Following the treatment of Kirchheim et al. [S], the slope of the EMF(r) curve was related to the diffusion coefficient of oxygen, D, by the following expression: dE
RTn’D
dt
SFL’
-=
AND TRAPPING
OF OXYGEN
Pure niobium was purchased in rod form from Wah Chang Albany Corp. and had a total substitutional impurity content of approximately 800ppm.t The vanadium was donated by the Bureau of Mines and had a total impurity content of approximately 40 ppm. Alloys were prepared by arc-melting in a furnace having a water-cooled copper crucible and an argon atmosphere. Each alloy ingot was turned and melted four times to insure homogeneity. The resulting ingots were swaged to 3 mm dia. and then coldrolled into strips 0.6 mm thick without intermediate anneals. Impurity levels were typically less than the starting material due to loss of silicon. aluminum and other volatile impurities. Samples were prepared by doping the metal strips with measured amounts of oxygen in a high-vacuum Sieverts apparatus. This apparatus is described in detail elsewhere [LO]. After doping. a homogenization anneal was carried out in vacuum with the specimens held at approx. 1300°C (1573 K) for 3-t h. The specimens were then slowly cooled to about IOOOC and then radiation cooled to room temperature. (The range of oxygen concentrations was 0.61.0”; after doping. A single V-6.6”. 0 alloy was also studied.) The strips were cut into segments 13 x 7 x 0.6mm. The surfaces were ground and polished through 6~ diamond paste. The zirconium blocks, which served as ‘sinks’ for oxygen, were prepared from a bar of iodide process zirconium. A 1Omm thick slice of the bar, 20mm in dia., was cold-rolled to 3 mm thick. Rectangular sections were cut from this, with dimensions slightly greater than those of the alloy samples (typically 15 x 10 x 3 mm). One face was ground and polished through 6/l diamond, and platinum leads were spot welded onto the opposite face. The electrolyte was of similar area and was 1 mm thick. It was polished through 0.25 ,u diamond paste. ’ Microhardness profiles (136’ Diamond Pyramid. 2OOg load) were made to check for changes in the oxygen distribution before and after the diffusion runs. Semiquantitative Auger analysis was also used for the same purpose. A ‘used’ specimen with its zirconium block attached was sectioned normal to the interface. It was then mounted, ground and mechanically polished.
’
where F is the Faraday constant and L is the specimen thickness. After enough time had elapsed for the EMF(r) curve to form a straight-line portion with a slope that could be accurately measured, the furnace was changed to a new temperature and dE/dt was again determined. In practice, as many as six (0, T) points could be determined from one specimen before the onset of electronic conduction in the electrolyte. (This occurs when the oxygen activity at the surface of the specimen becomes too low for normal operation of the electrolyte.) t All compositions are given on an atomic basis.
RESULTS In order to establish the applicabihry of the EMF method to the alloy systems considered in this study, oxygen diffusion coefficient measurements were made in pure niobium and pure vanadium. The results are shown in Figs. 1 and 2, respectively. The data from the literature are reviewed by Boratto and ReedHill [11-131 and by Farraro and McClellan [14]. Assigning equal weight to each measurement a least squares analysis of our data for normal diffusion of oxygen in niobium yielded the following: 0.“” = 5.3 x lo-’ exp( - 107,000 RT) m2 s-i.
(4)
LAUF A>C ALTSTEI-I’ER:
DIFFUSION
AND TRAPPING
1159
OF OXYGEN
Nb-2
IS-
7%
V
16 -
17 -
z 20 60 0.5
IO
is
Fig.
1.
2.5
20 looo/~,
30
3s
PKF
5
19-
af
19-
Diffusion of oxygen in niobium. Solid line is equation (6).
20-
21 -
20 . .
RXCV
‘si. 30 I
‘1.
Fig.
4.
Diffusion of oxygen in Nb-2.7 V. Trap energy in eV. Upper line is equation (4).
E og-
d
. Thll
work
:
oRef
I2
Similarly,
for vanadium
II.” = 6.89 x IO-’ exp( - 118,OOQ’R7) m’s_‘, j”-
,
,\_
Fig. 2. Diffusion of oxygen in vanadium. Solid line is equation (7).
I5 -
where R is in Jmol-l K-l. Data for the six substitutional alloys are shown as points in Figs. 3-8. Typical error bars for two temperatures are shown for reference. For each alloy, several values of the s-i binding (trap) ener_q, AE,. were used to calculate ‘expected’ diffusivities according to the Oriani model (4), shown as lines in
Nb-1.4%V
I5 -
I6 -
16 -
I? -
17IS
c
1
(5)
5 IS-
‘8Ci C
I9 -
20-
Nb
Fig. 3. Diffusion of oxygen in Nb-1.4V. Trap energy in eV. Upper line is equation (41.
21-
Fig. 5. Diffusion of oxygen in Nb-5.1 V. Trap energy in eV. Upper line is equation (4).
1160
LAUF
ALTSTETTER:
ANI,
DIFFUSION
AND TRAPPING
OF OXYGEN
1KxJ9a
Nb-0.9%
15-
700
r--l-+-
T
15 -
Nb-4.1%
Ta
\ 16 -
16-
17 -
17-
Is-
t “E ”
16-
19 -
d c 7
19-
3 El
d $
zo-
zo-
21 -
21 -
22L 0.5
I.5
I.0
PKl-’
NX)(Xf,
ICC01 T, (OK)-’
Fig. 6. Diffusion of oxygen in Nb-O.9Ti. Trap energy m eV. Upper line is equation (4).
Fig. 8. Diffusion of oxygen in Nb-4.1 Ta. Trap enere eV. Upper line is equation (4).
Figs. 3-8. The values of AE, that best describe the data are summarized in Table 1. To verify the assumption that the change in cell EMF was due to outward migration of the oxygen rather than oxide precipitation, microhardness measurements were made after the diffusion experiments for comparison with the as-doped hardness of the same alloys. Three alloys were chosen for microexamination: Nb-2.7 V-O.6 0, Nb-0.9 hardness
Ti-1.0 0 and V-6.57 0. In each case, a doped snecimen was mounted so that hardness measurements
1100900
x0
-
Nb-0.95% Zr
t5-
I6 -
DISCUSSION For both niobium and vanadium, the present technique gave dilTusivity values in agreement with Boratto and Reed-Hill’s [12, 133 equations for D to within a factor of 2, which indicates the reliability of the galvanic cell technique. In both cases of oxygen diffusion in pure metals, the Arrhenius plot is remarkably straight over the range from near room temperature to near 1900°C. Furthermore, these lines were
ie-
%
0‘ 5
l9-
ZQ-
Table 1. Trap energies for substitutional alloying elements
0.6 0.1
Element
0.8 IO
in niobium (Oriani model)
-IO+
Nb
21 -
22 05
could be taken across its thickness. Results typical of the three alloys are shown in Fig. 9. In each case, the as-doped hardness was greater than the hardness after diffusion had occurred. In each alloy, there was a general trend of decreasing hardness going toward the interface, and in the zirconium there was a decrease in hardness going away from the interface. Thus, to the alloy specimen, the interface is a sink for oxygen, while to the zirconium block, the interface is a source of oxygen. Auger analysis for oxygen [lS] confirmed this result.
\
I? -
e
in
I.5
IOCCY T, (W-’ Fig. 7. Diiusion of oxygen in Nb-O.95Zr. Trap energy in eV. Upper line is equation (4).
Ta V Ti Zr
Concentration (%) 4.1 1.4, 2.7, 5.1 0.9 0.95
Trap energy, AE, (kJ mol-‘) WI 0.3 & 0.1 0.55 & 0.05 0.7 + 0.1 0.7 + 0.05
29 53 67 67
f + f *
10 5 10 5
LAUF
AND
ALTSTETIZR:
DIFFUSION AND TRAPPING OF OXYGEN
I I
I I I I , 0
As dafmd
1 o After
diffusion
I I
0’
’
I!3
’
IO
’
5
’
0
Location,
’
5
’
IO
’
1s
’
20
(0.001”)
Fig. 9. Microhardness traverse, NbO.9 Ti-1.0 0 alloy and zirconium block. determined by quite different techniques over different parts of the temperature range. McClellan and Farraro [14] have represented the Nb-0 data by two straight line segments on an Arrhenius plot, with the break at 350°C. This is difficult to substantiate without an analysis of errors and without assessing the reliability of the various techniques. With the addition of the present data and some low temperature anelasticity results of Gibala and Wert [16] and by assuming realistic error bars a single straight line seems well justified. For all results measured and referenced in the present work (123 data points) the diffusivity of oxygen in niobium, D = 6.95 x lo-’ exp( - 1lO,OOO/RT)m* s- l,
1161
with Perkins and Padgett [lq but not with measurements of localized jumping determined anelastitally (16, 181. The diffusion data for substitutional alloys studied appear to be adequately described by the two-state Oriani model [4]. These states are taken to be ‘normal’ and ‘extraordinary’ (trapping) interstitial sites. This model gave consistent values for the O-V binding energy in three different Nb-V alloys. At the same time, substitutional species with different trap energies were easily distinguished. The model appears to be valid at least up to to 5% substitutional solute content. Following the Oriani model [4], the fraction of normal and trap sites occupied by oxygen atoms may be calculated at any temperature once the trapping energy is known. For example, for AR:, = 0.7 eV (67 kJ mol-‘) and T = lOOO’C,0.08 of the trap sites and 1.5 x 10eJ of the normal sites are occupied for a 0.5 at.% 0, 1 at.?; metal solute alloy. Of course, at temperatures usually used for internal friction measurements (530 K) essentially all of the oxygen is trapped for the the same alloy. It can be seen from Fig. 8 that the Nb-4.1 Ta alloy is not as well-described by the Oriani model as the other alloys. Figure 10 shows the result of modifying the Oriani model to allow for the trap energy to be a function of temperature E, = (0.13) (T - 1370) kJ
(8)
1370 1 i’- 2 1070K. This calculated curve fits the data rather well and emphasizes the important point that the trap energy may not necessarily be temperature-independent. It would be of great technological and scientific interest to develop a predictive model to relate the
(6)
whece R is in j mol-‘. This is nearly identical to the expression given by Boratto and Reed-Hill [13]. The best fit for all the data for oxygen diffusion in vanadium (30 points) is D = 1.56’x 10d6 exp( - 123,OOO/RT)m2 s-i,
(7)
which also agrees well with Boratto and Reed-Hill’s equation [12]. The present results for pure metals reinforce the conclusion that anelastic techniques involving localized atomic jumping can yield data that characterize long-range diffusion. This conclusion is not so well borne out by the results for oxygen diffusion in substitutional alloys, discussed below. It is noteworthy that there appears to be no dependence of D on oxygen concentration in niobium and vanadium, since data for concentrations ranging from 0.2 to 1.0% oxygen fell on the same Arrhenius lines. This is in agreement
Iooo/T.
(OK)-’
Fig. 10. Arrhenius . . plot for N+t.l Ta, allowing for variable trap energy. equation (8).
1162
LAUF AND ALTSTETTER:
DIFFUSION
AND TRAPPING
Table 1. Parameters affecting substitutional-oxygen Observed
OF OXYGEN
interactions in niobium
trap energy, AE,
Chemical afMty, .4
Element
(eV)
(eV)
mismatch, c (“b)
Ta
0.3 0.55 0.7 0.1 (0.8 - LO)*
0.13 0.13 0.52 1.39 1.68
0 - 7.7 0 + 11.2 + 10.5
V Ti Zr Hf
Size
*Predicted s-i binding energy to some easily determined properties of the substitutional element. However, before developing a model to explain the results of the present study, it is necessary to understand the significance and limitations of the parameter A&. According to a strict application of the Oriani model, AE, is the energy difference between a normal interstitial site and each of the six ‘extraordinary’ sites surrounding the substitutional solute atom. If the substitutional atom is at the center of a unit cell, the extraordinary sites are at the centers of the cube faces. The secondnearest-neighbor sites (cube edges) are considered to be normal sites. This assumption may not be valid. A recent study [19] indicated the importance of GO interactions between second and possibly third-nearest-neighbor oxygen atoms. Thus, it is not unreasonable to expect some interaction between a substitutional atom and a second-nearest-neighbor oxygen atom. Nonetheless, the question of how many sites are traps is a geometrical one, and does not affect comparisons among the present data. But, caution is indicated when attempting to compare these data to binding energies obtained by internal friction measurements. With this qualification, it is now possible to enumerate the principles on which the present, very simple model is based. 1. Chemical interaction: if the substitutional solute has a higher ‘affinity’ for oxygen than the host element, there will be a s-i attraction which will be roughly proportional to the difference in chemical affinities. A quantitative measure of oxygen affinity per se is not generally available, but a good approximation might be given by the difference of heat of formation of the oxides, expressed in eV/oxygen atom. 2. Elastic interaction: the interaction between the strain fields of the interstitial and substitutional atoms could result in an attractive or repulsive s-i interaction, depending on whether the substitutional atom is smaller or larger than the host atom [20,21]. 3. Other effects: parameters such as atomic compressibility, atom polarizability, and local or average changes in the elastic constants of the lattice are ignored. Trap saturation effects are also ignored, since saturation is not important in the ranges of temperature and oxygen concentration studied. Neglecting these effects keeps the model simple enough that possible nonlinearities in the two major modes of interac-
tion could be determined, given data for a large enough number of alloy systems. The proposed model may thus be expressed by combining affinity and elasticity effects in the following empirical formula: A& = f(A) + g(E).
(9)
The data for the four alloy systems examined in this study are presented in Table 2. along with chemical affinity and size mismatch terms for each (included are the values of these parameters for hafnium, and its ‘predicted’ trap energy) where / A = AHNm - AH/MO(eV/oxygen atom), bb EC
-
~
r'lb
h
(10)
(II)
where rx is the atomic radius of the species X in pure metal at room temperature. The o.xides used in the calculation of A were NbO, TatOs. VO, Ti02, ZrOl and Hf02. The present data are not extensive enough to determine analytical expressions forf(A) and g(e), but from the results shown in Table 2 several observations can be made. It can be seen that tantalum and vanadium are chemically similar, yet vanadium is a stronger trap, due to its smaller size. Zirconium, on the other hand, has a greater oxygen affinity than titanium, but the elastic repulsion due to its larger size partly offsets the chemical attraction, so that zirconium and titanium have about the same trap strength. It is interesting to note that Szkopiak and Smith [22] report that hafnium is a stronger trap than zirconium, which is in agreement with the prediction of the present model. The s-i interaction energies derived from these experiments, ranging up to 0.7eV. are rather higher than those estimated from internal friction measurements on similar alloys. One reason for this is that in both types of measurement, the exact nature of the trap is uncertain and may be manifested in different ways in the two types of experiments. Blanter and Khachaturyan [21] have suggested that the usual internal friction measurements would be incapable of detecting s-i binding energies approaching 1 eV.
LAUF
AND
ALTSTETTER:
DIFFUSION
CONCLUSlOSS (1) The EMF method is suitable for studying the transient diffusion of oxygen in vanadium. niobium and niobium alloys. The results are independent of the choice of reference electrode. (2) The diffusion of oxygen in several dilute substitutional- niobium alloys is slower than it is in pure niobium. This is interpreted as being due to trapping of oxygen atoms by substitutional solute atoms. (3) The effect of s-i interactions on the oxygen diffusivity can be approximately explained by theoretical models that take into account the concentration of substitutional atoms and the binding or ‘trap’ energy associated with neighboring interstitial sites. (4) The substitutional solutes examined in this stuoy are, in order of increasing trap strength Ta V, Ti and Zr. (5) The trap energy does not appear to depend on the substitutional concentration, up to about joO. It is also independent of oxygen concentration. (6) The s-i binding energy may be rationalized in terms of the sum of a chemical affinity term and an elastic term. For all of the alloy systems studied. the net chemical affinity was attractive. The elastic or ‘misfit’ energy was attractive. neutral, or repulsive, depending on the size of the particular substitutional solute atom. Ac~nor\,ler/yrmenr-This work was supported by the Materials Research Laboratory under the National Science Foundation grant DMR-76-01058.
AND TRAPPING
OF OXYGEN
1163
REFERENCES 1. D. Hasson and R. Anenault, Treatise on Marerials Science, Vol. 1. Academic Press. New York (1972). 2. A. McNabb and P. Foster, Trans. A.I.M.E. 227, 618 (1963). 3. M. Koiwa, Acra merall. 22. 1259 (1974). 4. R. Oriani, Acta merail. 18, 147 (1970). 5. R. Kirchheim. E. Albert and E. Fromm, Scripta metall. 11, 651 (1977). 6. K. Ktukkola and C. Wagner. J. elecrrochem. Sot. 104, 379 (1957). 7. G. Steckel and C. Altstetter, Acra merall. 24, 1131 (1976). 8. R. L&f and C. Altstetter, Scripta metal/. 11, 983 (1977). 9. R. Lauf. Ph.D. Thesis. University of Illinois (1978). 10. D. Potter. Ph.D. Thesis, University of Illinois (1970). 11. F. Boratto and R. Reed-Hill, MetaIl. Trans. AS. 1233 (1977). 12. F. Boratto and R. Reed-Hill, Scripta metall. 11, 1107 (1977). 13. F. Boratto and R. Reed-Hill, Scripta metal/. 11, 709 (1977). 14. K. t-arraro and R. McClellan, Marer. Sci. hgrs 33, 113 (1978). 15. G. Steckel, R. Blattner and C. Altstetter. To be published. 16. R. Gibala and C. Wert, Acra metal/. 14. 1095 (1966). 17. R. Perkins and R. Padgett, Acra merall. 25, 1221 (1977). 18. R. Powers and M. Doyle, J. appl. Phgs. 30, 51-1(1959). 19. G. Steckel and C. Altstetter. To be uublished. 20. H. Hashizume and T. Sugeno, Jap: J. appl. Phys. 6. 367 (1967). 21. M. Blanter and A. Khachaturyan, &fetal/. Trorrs. A9. 753 (1978). 7) 2. Szkopiak and J. Smith, J. Php. D. (Appl. Phys.) _-. 8, 1273 (1975).
aod C. J. ALTSFETTER$
(Received 3 Augusr 1978; in revisedform 3 January 1979)
Abstract-The diffusion coefficient of oxygen has been measured in niobium, vanadium and several dilute substitutional niobium alloys. Measurements were made over the range of 6@I-1150°C (873-1423 K) using a solid electrolytic cell technique. Oxygen diffusivity in the alloys was found to be less than in pure niobium. This is interpreted as being due to trapping of oxygen atoms by the substitutional solute atoms. The estimated substitutional-oxygen binding or ‘trap’ energies (in eV) for the solutes investigated are: Ta, 0.3 + 0.1: V, 0.55 + 0.05; Ti, 0.7 f 0.1; Zr, 0.7 f 0.05. Rksumk-Nous avons mesure le coefficient de diffusion de l’oxygene dans le niobium. le vanadium et quelques alliages substitutionnels dilub de niobium. Nous avons effectut des mesures entre 600 et 1150°C (8731423 K), par la technique de la cellule ii electrolyte solide. Nous avons trouve que la diffusivite de l’oxygene dans les alliages Ctait inferieure 1 la dilTu.sivitCde l’oxygene dans le niobium pur. Nous interprettons cette observation par un piegeage des atomes d’oxygine par les atomes du solute en substitution. L’e-stimation des energies (en eV) de liaison (ou de “piegeage”) entre un atome substitutionnel et un atome d’oxygtne donne les valeurs: Ta, 0,3 + 0.1; V, 0,55 & 0,05; Ti, 0,7 + 0.1; Zr. 0.7 f 0.05. ZusammenfassuneDer Diffusionskoefhzient von Sauerstoff wurde in Niob, Vanadium und verschiedenen verdllnnten;ubstitutionellen Nioblegierungen gemessen. Diese Messungen wurden mittels einer Technik mit fester elektrolvtischer Zelle tlber den Temneraturbereich 600-l 150°C (8731423 K) durchgefdhrt. In den Legierungen war die Sauerstoffdiffusidn geringer als in reinem Niob. Dieser Befund wird dem Einfangen von Sauerstoffatomen an substitutionell gel&ten Atomen zugeschrieben. Die daraus abgeschatxten Bindungsenergien zwischen Sauerstoff und geliistem Atom sind (in eV): Ta, 0,3 + 0.1; V. 0.55 + 0,05; Ti, 0.7 + 0.1; Zr, 47 & 405.
INTRODUCTION The mechanical properties of refractory metals are severely degraded by the presence of dissolved oxygen or massive internal oxides. Thus, the rate at which oxygen diffuses through these metals and their alloys is of considerable technological importance. Of great theoretical interest is the effect of substitutional solutes on the diffusivity of interstitial solutes. There is a wealth of literature on substitutional-interstitial (s-i) interactions in refractory metals. (See, for example, a review by Hasson and Arsenault Cl].) Unfortunately, most reported data are obtained by anelastic techniques and can not be applied directly to the determination of long-range diffusivities. Theoretical models have been proposed by McNabb and Foster [2], Koiwa (31, Oriani [4] and others, to calculate the effect of trapping on the diffusivity of interstitial solute atoms. Evaluation of these t Work submitted in partial fulfillment of the requirements for the Ph.D. in Metallurgical Engineering University of Illinois. : Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37830, U.S.A. $ Professor. Department of Metallurgy and Mining Engineering and the Materials Research Laboratory, University of Illinois, Urbana, IL 61801, U.S.A. A.W. ?7;7- u
models has been hampered by a lack of reliable data for interstitial diGion at high temperatures. Recently, a method was developed by Kirchheim et al. [5] to observe the transient diffusion of oxygen in refractory metals using a solid electrolytic cell. In the present study, this technique has been used to measure the diffusion coefficient of oxygen in niobium, vanadium and several niobium alloys. The results are used to calculate the s-i binding energy according to the Oriani model. This model assumes that solute atoms in normal interstitial sites are in equilibrium with those at trap sites, assumed here to be adjacent to substitutional solute atoms. The result, equation (l), is an effective diffusivity, D, which is different from the normal diffusivity, D,, without the trapping sites.
D=Q-[* ,:,,,3.
(1)
X, is the atom fraction of substitutional solute, and the partitioning of interstitial solute between normal and trap sites is given by
1157
K = exp
c1 AL
- k~
.
1133
LAUF ,WQ ALTSTETTER:
DIFFUSION
The trap strength. AE,. in this model is the energy difference between a diffusing solute in a normal site and in a trap site. Solid galvanic cells have proven useful for equilibrium potential measurements for the determination of thermodynamic parameters and solubilities in metal-oxygen systems [6-S]. In applying the galvanic cell technique for kinetic measurements a metaloxygen sample is one electrode, whose potential is measured with respect to a reference electrode. The reference electrode was a V-O or Nb-0 alloy of known oxygen chemical potential in the present experiments. The specimen electrode was bonded to a block of pure zirconium, which acts as an efficient sink for oxygen. When the cell is brought to a sufficiently high temperature, the oxygen dilfuses from the sample into the zirconium. The cell EMF is a measure of the surface concentration of oxygen at the opposite face, adjacent to the electrolyte. The boundary conditions are thus established for a solution to Fick’s Law, and the diffusivity of oxygen in the alloy may be calculated, provided diffusion in the alloy is indeed the rate-limiting process. One advantage of this technique is that it eiiminates transfer of oxygen in the electrolyte and across the metal-electrolyte interfaces. Polarization reactions are also avoided. EXPERIMENTAL
PROCEDURE
The oxygen diffusion measurements were made in the electrolytic cell illustrated schematically below: Zirconium Alloy Block I Specimen I This cell was mounted in a high-vacuum furnace and heated to 1OOOC(1273 K) in approx. 2 h. The details of the experimental apparatus are published elsewhere [7,9]. The cell EMF was measured as a function of time using a high-impedence electrometer. Following the treatment of Kirchheim et al. [S], the slope of the EMF(r) curve was related to the diffusion coefficient of oxygen, D, by the following expression: dE
RTn’D
dt
SFL’
-=
AND TRAPPING
OF OXYGEN
Pure niobium was purchased in rod form from Wah Chang Albany Corp. and had a total substitutional impurity content of approximately 800ppm.t The vanadium was donated by the Bureau of Mines and had a total impurity content of approximately 40 ppm. Alloys were prepared by arc-melting in a furnace having a water-cooled copper crucible and an argon atmosphere. Each alloy ingot was turned and melted four times to insure homogeneity. The resulting ingots were swaged to 3 mm dia. and then coldrolled into strips 0.6 mm thick without intermediate anneals. Impurity levels were typically less than the starting material due to loss of silicon. aluminum and other volatile impurities. Samples were prepared by doping the metal strips with measured amounts of oxygen in a high-vacuum Sieverts apparatus. This apparatus is described in detail elsewhere [LO]. After doping. a homogenization anneal was carried out in vacuum with the specimens held at approx. 1300°C (1573 K) for 3-t h. The specimens were then slowly cooled to about IOOOC and then radiation cooled to room temperature. (The range of oxygen concentrations was 0.61.0”; after doping. A single V-6.6”. 0 alloy was also studied.) The strips were cut into segments 13 x 7 x 0.6mm. The surfaces were ground and polished through 6~ diamond paste. The zirconium blocks, which served as ‘sinks’ for oxygen, were prepared from a bar of iodide process zirconium. A 1Omm thick slice of the bar, 20mm in dia., was cold-rolled to 3 mm thick. Rectangular sections were cut from this, with dimensions slightly greater than those of the alloy samples (typically 15 x 10 x 3 mm). One face was ground and polished through 6/l diamond, and platinum leads were spot welded onto the opposite face. The electrolyte was of similar area and was 1 mm thick. It was polished through 0.25 ,u diamond paste. ’ Microhardness profiles (136’ Diamond Pyramid. 2OOg load) were made to check for changes in the oxygen distribution before and after the diffusion runs. Semiquantitative Auger analysis was also used for the same purpose. A ‘used’ specimen with its zirconium block attached was sectioned normal to the interface. It was then mounted, ground and mechanically polished.
’
where F is the Faraday constant and L is the specimen thickness. After enough time had elapsed for the EMF(r) curve to form a straight-line portion with a slope that could be accurately measured, the furnace was changed to a new temperature and dE/dt was again determined. In practice, as many as six (0, T) points could be determined from one specimen before the onset of electronic conduction in the electrolyte. (This occurs when the oxygen activity at the surface of the specimen becomes too low for normal operation of the electrolyte.) t All compositions are given on an atomic basis.
RESULTS In order to establish the applicabihry of the EMF method to the alloy systems considered in this study, oxygen diffusion coefficient measurements were made in pure niobium and pure vanadium. The results are shown in Figs. 1 and 2, respectively. The data from the literature are reviewed by Boratto and ReedHill [11-131 and by Farraro and McClellan [14]. Assigning equal weight to each measurement a least squares analysis of our data for normal diffusion of oxygen in niobium yielded the following: 0.“” = 5.3 x lo-’ exp( - 107,000 RT) m2 s-i.
(4)
LAUF A>C ALTSTEI-I’ER:
DIFFUSION
AND TRAPPING
1159
OF OXYGEN
Nb-2
IS-
7%
V
16 -
17 -
z 20 60 0.5
IO
is
Fig.
1.
2.5
20 looo/~,
30
3s
PKF
5
19-
af
19-
Diffusion of oxygen in niobium. Solid line is equation (6).
20-
21 -
20 . .
RXCV
‘si. 30 I
‘1.
Fig.
4.
Diffusion of oxygen in Nb-2.7 V. Trap energy in eV. Upper line is equation (4).
E og-
d
. Thll
work
:
oRef
I2
Similarly,
for vanadium
II.” = 6.89 x IO-’ exp( - 118,OOQ’R7) m’s_‘, j”-
,
,\_
Fig. 2. Diffusion of oxygen in vanadium. Solid line is equation (7).
I5 -
where R is in Jmol-l K-l. Data for the six substitutional alloys are shown as points in Figs. 3-8. Typical error bars for two temperatures are shown for reference. For each alloy, several values of the s-i binding (trap) ener_q, AE,. were used to calculate ‘expected’ diffusivities according to the Oriani model (4), shown as lines in
Nb-1.4%V
I5 -
I6 -
16 -
I? -
17IS
c
1
(5)
5 IS-
‘8Ci C
I9 -
20-
Nb
Fig. 3. Diffusion of oxygen in Nb-1.4V. Trap energy in eV. Upper line is equation (41.
21-
Fig. 5. Diffusion of oxygen in Nb-5.1 V. Trap energy in eV. Upper line is equation (4).
1160
LAUF
ALTSTETTER:
ANI,
DIFFUSION
AND TRAPPING
OF OXYGEN
1KxJ9a
Nb-0.9%
15-
700
r--l-+-
T
15 -
Nb-4.1%
Ta
\ 16 -
16-
17 -
17-
Is-
t “E ”
16-
19 -
d c 7
19-
3 El
d $
zo-
zo-
21 -
21 -
22L 0.5
I.5
I.0
PKl-’
NX)(Xf,
ICC01 T, (OK)-’
Fig. 6. Diffusion of oxygen in Nb-O.9Ti. Trap energy m eV. Upper line is equation (4).
Fig. 8. Diffusion of oxygen in Nb-4.1 Ta. Trap enere eV. Upper line is equation (4).
Figs. 3-8. The values of AE, that best describe the data are summarized in Table 1. To verify the assumption that the change in cell EMF was due to outward migration of the oxygen rather than oxide precipitation, microhardness measurements were made after the diffusion experiments for comparison with the as-doped hardness of the same alloys. Three alloys were chosen for microexamination: Nb-2.7 V-O.6 0, Nb-0.9 hardness
Ti-1.0 0 and V-6.57 0. In each case, a doped snecimen was mounted so that hardness measurements
1100900
x0
-
Nb-0.95% Zr
t5-
I6 -
DISCUSSION For both niobium and vanadium, the present technique gave dilTusivity values in agreement with Boratto and Reed-Hill’s [12, 133 equations for D to within a factor of 2, which indicates the reliability of the galvanic cell technique. In both cases of oxygen diffusion in pure metals, the Arrhenius plot is remarkably straight over the range from near room temperature to near 1900°C. Furthermore, these lines were
ie-
%
0‘ 5
l9-
ZQ-
Table 1. Trap energies for substitutional alloying elements
0.6 0.1
Element
0.8 IO
in niobium (Oriani model)
-IO+
Nb
21 -
22 05
could be taken across its thickness. Results typical of the three alloys are shown in Fig. 9. In each case, the as-doped hardness was greater than the hardness after diffusion had occurred. In each alloy, there was a general trend of decreasing hardness going toward the interface, and in the zirconium there was a decrease in hardness going away from the interface. Thus, to the alloy specimen, the interface is a sink for oxygen, while to the zirconium block, the interface is a source of oxygen. Auger analysis for oxygen [lS] confirmed this result.
\
I? -
e
in
I.5
IOCCY T, (W-’ Fig. 7. Diiusion of oxygen in Nb-O.95Zr. Trap energy in eV. Upper line is equation (4).
Ta V Ti Zr
Concentration (%) 4.1 1.4, 2.7, 5.1 0.9 0.95
Trap energy, AE, (kJ mol-‘) WI 0.3 & 0.1 0.55 & 0.05 0.7 + 0.1 0.7 + 0.05
29 53 67 67
f + f *
10 5 10 5
LAUF
AND
ALTSTETIZR:
DIFFUSION AND TRAPPING OF OXYGEN
I I
I I I I , 0
As dafmd
1 o After
diffusion
I I
0’
’
I!3
’
IO
’
5
’
0
Location,
’
5
’
IO
’
1s
’
20
(0.001”)
Fig. 9. Microhardness traverse, NbO.9 Ti-1.0 0 alloy and zirconium block. determined by quite different techniques over different parts of the temperature range. McClellan and Farraro [14] have represented the Nb-0 data by two straight line segments on an Arrhenius plot, with the break at 350°C. This is difficult to substantiate without an analysis of errors and without assessing the reliability of the various techniques. With the addition of the present data and some low temperature anelasticity results of Gibala and Wert [16] and by assuming realistic error bars a single straight line seems well justified. For all results measured and referenced in the present work (123 data points) the diffusivity of oxygen in niobium, D = 6.95 x lo-’ exp( - 1lO,OOO/RT)m* s- l,
1161
with Perkins and Padgett [lq but not with measurements of localized jumping determined anelastitally (16, 181. The diffusion data for substitutional alloys studied appear to be adequately described by the two-state Oriani model [4]. These states are taken to be ‘normal’ and ‘extraordinary’ (trapping) interstitial sites. This model gave consistent values for the O-V binding energy in three different Nb-V alloys. At the same time, substitutional species with different trap energies were easily distinguished. The model appears to be valid at least up to to 5% substitutional solute content. Following the Oriani model [4], the fraction of normal and trap sites occupied by oxygen atoms may be calculated at any temperature once the trapping energy is known. For example, for AR:, = 0.7 eV (67 kJ mol-‘) and T = lOOO’C,0.08 of the trap sites and 1.5 x 10eJ of the normal sites are occupied for a 0.5 at.% 0, 1 at.?; metal solute alloy. Of course, at temperatures usually used for internal friction measurements (530 K) essentially all of the oxygen is trapped for the the same alloy. It can be seen from Fig. 8 that the Nb-4.1 Ta alloy is not as well-described by the Oriani model as the other alloys. Figure 10 shows the result of modifying the Oriani model to allow for the trap energy to be a function of temperature E, = (0.13) (T - 1370) kJ
(8)
1370 1 i’- 2 1070K. This calculated curve fits the data rather well and emphasizes the important point that the trap energy may not necessarily be temperature-independent. It would be of great technological and scientific interest to develop a predictive model to relate the
(6)
whece R is in j mol-‘. This is nearly identical to the expression given by Boratto and Reed-Hill [13]. The best fit for all the data for oxygen diffusion in vanadium (30 points) is D = 1.56’x 10d6 exp( - 123,OOO/RT)m2 s-i,
(7)
which also agrees well with Boratto and Reed-Hill’s equation [12]. The present results for pure metals reinforce the conclusion that anelastic techniques involving localized atomic jumping can yield data that characterize long-range diffusion. This conclusion is not so well borne out by the results for oxygen diffusion in substitutional alloys, discussed below. It is noteworthy that there appears to be no dependence of D on oxygen concentration in niobium and vanadium, since data for concentrations ranging from 0.2 to 1.0% oxygen fell on the same Arrhenius lines. This is in agreement
Iooo/T.
(OK)-’
Fig. 10. Arrhenius . . plot for N+t.l Ta, allowing for variable trap energy. equation (8).
1162
LAUF AND ALTSTETTER:
DIFFUSION
AND TRAPPING
Table 1. Parameters affecting substitutional-oxygen Observed
OF OXYGEN
interactions in niobium
trap energy, AE,
Chemical afMty, .4
Element
(eV)
(eV)
mismatch, c (“b)
Ta
0.3 0.55 0.7 0.1 (0.8 - LO)*
0.13 0.13 0.52 1.39 1.68
0 - 7.7 0 + 11.2 + 10.5
V Ti Zr Hf
Size
*Predicted s-i binding energy to some easily determined properties of the substitutional element. However, before developing a model to explain the results of the present study, it is necessary to understand the significance and limitations of the parameter A&. According to a strict application of the Oriani model, AE, is the energy difference between a normal interstitial site and each of the six ‘extraordinary’ sites surrounding the substitutional solute atom. If the substitutional atom is at the center of a unit cell, the extraordinary sites are at the centers of the cube faces. The secondnearest-neighbor sites (cube edges) are considered to be normal sites. This assumption may not be valid. A recent study [19] indicated the importance of GO interactions between second and possibly third-nearest-neighbor oxygen atoms. Thus, it is not unreasonable to expect some interaction between a substitutional atom and a second-nearest-neighbor oxygen atom. Nonetheless, the question of how many sites are traps is a geometrical one, and does not affect comparisons among the present data. But, caution is indicated when attempting to compare these data to binding energies obtained by internal friction measurements. With this qualification, it is now possible to enumerate the principles on which the present, very simple model is based. 1. Chemical interaction: if the substitutional solute has a higher ‘affinity’ for oxygen than the host element, there will be a s-i attraction which will be roughly proportional to the difference in chemical affinities. A quantitative measure of oxygen affinity per se is not generally available, but a good approximation might be given by the difference of heat of formation of the oxides, expressed in eV/oxygen atom. 2. Elastic interaction: the interaction between the strain fields of the interstitial and substitutional atoms could result in an attractive or repulsive s-i interaction, depending on whether the substitutional atom is smaller or larger than the host atom [20,21]. 3. Other effects: parameters such as atomic compressibility, atom polarizability, and local or average changes in the elastic constants of the lattice are ignored. Trap saturation effects are also ignored, since saturation is not important in the ranges of temperature and oxygen concentration studied. Neglecting these effects keeps the model simple enough that possible nonlinearities in the two major modes of interac-
tion could be determined, given data for a large enough number of alloy systems. The proposed model may thus be expressed by combining affinity and elasticity effects in the following empirical formula: A& = f(A) + g(E).
(9)
The data for the four alloy systems examined in this study are presented in Table 2. along with chemical affinity and size mismatch terms for each (included are the values of these parameters for hafnium, and its ‘predicted’ trap energy) where / A = AHNm - AH/MO(eV/oxygen atom), bb EC
-
~
r'lb
h
(10)
(II)
where rx is the atomic radius of the species X in pure metal at room temperature. The o.xides used in the calculation of A were NbO, TatOs. VO, Ti02, ZrOl and Hf02. The present data are not extensive enough to determine analytical expressions forf(A) and g(e), but from the results shown in Table 2 several observations can be made. It can be seen that tantalum and vanadium are chemically similar, yet vanadium is a stronger trap, due to its smaller size. Zirconium, on the other hand, has a greater oxygen affinity than titanium, but the elastic repulsion due to its larger size partly offsets the chemical attraction, so that zirconium and titanium have about the same trap strength. It is interesting to note that Szkopiak and Smith [22] report that hafnium is a stronger trap than zirconium, which is in agreement with the prediction of the present model. The s-i interaction energies derived from these experiments, ranging up to 0.7eV. are rather higher than those estimated from internal friction measurements on similar alloys. One reason for this is that in both types of measurement, the exact nature of the trap is uncertain and may be manifested in different ways in the two types of experiments. Blanter and Khachaturyan [21] have suggested that the usual internal friction measurements would be incapable of detecting s-i binding energies approaching 1 eV.
LAUF
AND
ALTSTETTER:
DIFFUSION
CONCLUSlOSS (1) The EMF method is suitable for studying the transient diffusion of oxygen in vanadium. niobium and niobium alloys. The results are independent of the choice of reference electrode. (2) The diffusion of oxygen in several dilute substitutional- niobium alloys is slower than it is in pure niobium. This is interpreted as being due to trapping of oxygen atoms by substitutional solute atoms. (3) The effect of s-i interactions on the oxygen diffusivity can be approximately explained by theoretical models that take into account the concentration of substitutional atoms and the binding or ‘trap’ energy associated with neighboring interstitial sites. (4) The substitutional solutes examined in this stuoy are, in order of increasing trap strength Ta V, Ti and Zr. (5) The trap energy does not appear to depend on the substitutional concentration, up to about joO. It is also independent of oxygen concentration. (6) The s-i binding energy may be rationalized in terms of the sum of a chemical affinity term and an elastic term. For all of the alloy systems studied. the net chemical affinity was attractive. The elastic or ‘misfit’ energy was attractive. neutral, or repulsive, depending on the size of the particular substitutional solute atom. Ac~nor\,ler/yrmenr-This work was supported by the Materials Research Laboratory under the National Science Foundation grant DMR-76-01058.
AND TRAPPING
OF OXYGEN
1163
REFERENCES 1. D. Hasson and R. Anenault, Treatise on Marerials Science, Vol. 1. Academic Press. New York (1972). 2. A. McNabb and P. Foster, Trans. A.I.M.E. 227, 618 (1963). 3. M. Koiwa, Acra merall. 22. 1259 (1974). 4. R. Oriani, Acta merail. 18, 147 (1970). 5. R. Kirchheim. E. Albert and E. Fromm, Scripta metall. 11, 651 (1977). 6. K. Ktukkola and C. Wagner. J. elecrrochem. Sot. 104, 379 (1957). 7. G. Steckel and C. Altstetter, Acra merall. 24, 1131 (1976). 8. R. L&f and C. Altstetter, Scripta metal/. 11, 983 (1977). 9. R. Lauf. Ph.D. Thesis. University of Illinois (1978). 10. D. Potter. Ph.D. Thesis, University of Illinois (1970). 11. F. Boratto and R. Reed-Hill, MetaIl. Trans. AS. 1233 (1977). 12. F. Boratto and R. Reed-Hill, Scripta metall. 11, 1107 (1977). 13. F. Boratto and R. Reed-Hill, Scripta metal/. 11, 709 (1977). 14. K. t-arraro and R. McClellan, Marer. Sci. hgrs 33, 113 (1978). 15. G. Steckel, R. Blattner and C. Altstetter. To be published. 16. R. Gibala and C. Wert, Acra metal/. 14. 1095 (1966). 17. R. Perkins and R. Padgett, Acra merall. 25, 1221 (1977). 18. R. Powers and M. Doyle, J. appl. Phgs. 30, 51-1(1959). 19. G. Steckel and C. Altstetter. To be uublished. 20. H. Hashizume and T. Sugeno, Jap: J. appl. Phys. 6. 367 (1967). 21. M. Blanter and A. Khachaturyan, &fetal/. Trorrs. A9. 753 (1978). 7) 2. Szkopiak and J. Smith, J. Php. D. (Appl. Phys.) _-. 8, 1273 (1975).