Fast diffusion of cobalt along stationary and moving grain boundaries in niobium

~

Acta metall, mater. Vol. 42, No. 8, pp. 2859-2868, 1994 Copyright © 1994 Elsevier ScienceLtd 0956-7151(94)E0047-K Printed in Great Britain. All rights reserved 0956-7151/94 $7.00 + 0.00

Pergamon

FAST DIFFUSION OF COBALT ALONG STATIONARY AND MOVING GRAIN BOUNDARIES IN NIOBIUM

M. K~PPERS,YU. MISHINI"andCHR.HERZIG Institut fiir Metallforschung, Universit/it Miinster, Wilhelm-Klemm-Str. 10, D-48149 Mtinster, Germany

(Received 20 September 1993) Abstraet--57Co diffusion along grain boundaries (GBs) in high-purity Nb has been studied in the temperature range 823-1471 K by the serial sectioning technique. As it was not possible to fully stabilize the grain size by any pre-diffusion annealing, part of the GBs could migrate during the diffusion anneals. Using the earlier proposed method [Z. Metallk. 84, 584 (1993)], the product P = sDoB6 Is being the GB-segregation factor, DeB the GB-diffusion (GBD) coefficient, t$ the GB width] for stationary GBs and the velocity V of moving GBs were deduced from the diffusion profiles. The P-values follow an Arrhenius dependence P = ~t4.84+599~-2.rspx 10-~3 exp[-(149.5 +_.7.2) kJ mol-l/RT] m 3 s -l and are 4-2 orders of magnitude higher in the measured temperature range than the expected P-values for GB self-diffusion in Nb. This observation is well consistent with the known fact of fast lattice diffusion of Co in Nb and provides evidence for a combined vacancy-interstitial GBD mechanism. From the temperature dependence of V an activation enthalpy of GB motion in Nb H,, ~ 182 kJ mol -t is estimated. Zusammenfassung--Es wurde die Korngrenzendiffusion yon 57Co in hochreinem polykristaUinen Nb im Temperaturbereich yon 823 bis 1471 K mit der Radiotracermethode und anschlieBender Schichtenteilung untersucht. Da es trotz verschiedener W~irmevorbehandlungen nicht mrglich war, die Kornstruktur des Nb-Materials vollst~ndig zu stabilisieren, erfolgte w~ihrend der Diffusionsgliihungen bei einem Teil der Komgrenzen eine Wanderung. In Anlehnung an die in unserer friiheren Arbeit [Z. Metallk. 84, 584 (1993)] entwickelten Methode wurden die gemessenen Diffusionsprofile in zwei Anteile beziiglich wandemder und station~irer Korngrenzen zerlegt. W/ihrend der erste Teil die Korngrenzenwanderungsgesehwindigkeit V abzuseh~itzen erlaubte, wurde aus dem zweiten Teil das Produkt P = sDoB6 berechnet Is bedeutet den Segregationsfaktor, DoB den Korngrenzendiffusionskoeffizienten, ~ die Korngrenzenbreite]. Die P-Werte folgen einer Arrheniusbeziehung: P = ~t4.84+s99~_2.6s)x 10-13 exp[-(149.5 + 7.2) kJ mol-~/RT] m 3 s-~ und sind im gemessenen Temperaturbereich 4 bis 2 Gr6~nordnungen hrher als die fiir die Komgrenzenselbstdiffusion erwarteten P-Werte. Auch unter Beriicksichtigung der Co Segregation seheint D ~ b sehr viel gr61~er als D~g/Nb zu sein. Dieser Befund ist konsistent mit der schnellen Volumendiffusion yon Co in Nb und weist auf einen kombinierten Leerstellen-Zwischengittermechanismus auch fiir die Komgrenzendiffusion in diesem System hin. Aus der Temperaturabhiingigkeit yon V kann die Aktivierungsenthalpie Hm der Korngrenzenwanderung in Nb mit Hm - 182 kJ mol -I abgesch/itzt werden. Hieraus wird gefolgert, dab H min etwa der Aktivierungsenthalpie der Korngrenzenselbstdiffusion in Nb entspricht. Das Problem der Korngrenzenwanderung bei Korngrenzendiffusionsmessungen wird diskutiert.

1. INTRODUCTION In a number of metallic systems the coefficient of impurity diffusion appears to be far too large to be explained by the standard vacancy mechanism (see e.g. [1]). By present the fast impurity diffusion has been found for several noble and late transition metals in Pb, Sn, T1, Ti, Zr and Nb. The impurity diffusion in such systems is thought to be governed by a combined mechanism involving both the vacancy exchange and the interstitial jumping of the impurity atoms. The dissociative mechanims, which is known for metal diffusion in semiconductors [2, 3], is considered as a probable candidate to account for the anomalously fast impurity transport. Recently, fast tPermanent address: Russian Institute Materials, 107005 Moscow, Russia.

of Aviation

impurity diffusion also along grain boundaries (GBs) in metals has been discovered for Ag in Pb [4], Co and Fe in ~-Zr [5, 6], Co in ct-Ti [7] and C in ~t-Fe [8]. The detailed atomic mechanism responsible for fast GBdiffusion (GBD) in metals remains also unknown, although by analogy with lattice diffusion one could think of a combined vacancy-interstitial (e.g. dissociative) or pure interstitial [8] mechanism. It is felt that progress in understanding the fast G B D phenomenon requires further accumulation of reliable and detailed experimental data. In this paper, impurity G B D of 57Co in N b has been studied over a wide temperature interval of 650 K. An advantage o f this system is that fast lattice diffusion of cobalt in niobium has been a subject of several earlier investigations and reliable values of the diffusion coefficients are available in the literature [9-12]. Moreover, the experimental observations of

2859

2860

KOPPERS

et al.:

57CoDIFFUSION ALONG GRAIN BOUNDARIES IN Nb

two-stage penetration profiles provide an evidence for the dissociative mechanism of Co diffusion in Nb [12]. Therefore, one has reasons to expect that GBD in this system also proceeds anomalously fast. Although niobium is an easy material to study lattice diffusion (no structural transformations, fairly low dislocation density, etc.), GBD-measurements in pure polycrystalline Nb present an extremely difficult problem. Due to high GB mobility at temperatures which are the most appropriate for GBD-measurements, it turns out to be impossible to fully stabilize the grain size by means of any pre-diffusion heat treatment. Accordingly the presence of moving GBs along with the stationary ones in the diffusion specimens strongly modifies the shape of the measured tracer penetration profiles. This in turn makes it impossible to treat the profiles in terms of the standard Fisher model [13-15], which considers only stationary GBs. Therefore in this study we had to process the obtained profiles using the recently proposed model for diffusion in polycrystals containing stationary and moving GBs [16]. The mathematical procedure based on this model allowed us to extract from the profiles the values of the GB diffusivity relating to stationary GBs. As a side result we could estimate the velocities of the moving GBs and thereby evaluate the activation enthalpy of GB migration in Nb. 2. EXPERIMENTAL Pure niobium of MARZ-quality was used for the present experiments The material was delivered by the Materials Research Corporation as a rod of 9 mm in diameter. Table 1 presents the impurity contents in this material as reported by the supplier. Cylindrical specimens with a height of about 2 mm were cut out from the rod by spark erosion and subjected to chemical etching. The initial grain size in the samples was about 10 #m. During high-temperature anneals intended to stabilize the structure the grains extensively grew and, for example, after annealing at 2000 K for 30 min reached a size of >3 ram. This grain size was inappropriate for the present GBDmeasurements since the total amount of the tracer penetrating into the specimens along the GBs was extremely small. Many attempts were made to find an optimal heat treatment which would provide a smaller grain size which at the same time remains reasonably stable in the temperature interval of sub-

sequent GBD-measurements. Finally, the following two-step regime has been chosen as optimal: 14 days at 1100 K (to provide recrystallization with a small size of new grains); 12 h at 1500 K (to reduce the dislocation density and to stabilize the grain size as much as possible). For the 1100 K anneal the specimens were wrapped with Nb foil and sealed in quartz tubes under a vacuum of 10-3 Pa. After this step one of the faces of each specimen was polished using standard metallographic techniques. At the second step the specimens were annealed at 1500K in a UHV-system ( ~ 10 -6 Pa) in a niobium container. This heat treatment resulted in a grain size of roughly 0.5 ram. Each specimen was then again wrapped with Nb foil, sealed in a quartz tube and additionally pre-annealed in conditions of the intended diffusion anneal to ensure an equilibrium GB-segregation of the spurious impurities. For the anneals at T > 1400 K the evacuated tubes were filled with purified argon under a pressure of about l atm. It was found by metallographic observations that during such pre-anneals (and therefore during the subsequent diffusion anneals) some grain growth could still occur, especially at temperatures above 1000 K. The carrier-free radioisotope 57Co (half-life 270 days) purchased from the Amersham Buchler Company as chloride in HCI solution with a specific activity of >150MBq//ag was used for diffusion experiments. A thin ( < 1 nm) layer of the tracer was evaporated in vacuum ( ~ 10-4 Pa) from a tungsten strip onto the polished surfaces of the specimens. The resultant surface activity of each specimen was about 30-40 KBq. The specimens were then wrapped with Nb foil, sealed in quartz tubes under 10 -3 Pa vacuum with (T > 1400 K) or without (T < 1400 K) argon, and subjected to diffusion anneals at temperatures from 823 to 1471 K. The temperatures were controlled and measured with calibrated NiCr-Ni or PtRh-Pt thermocouples with an accuracy of about _+ l to 2 K. After the diffusion anneals each specimen was reduced in diameter by 500-750 #m in order to eliminate the radial diffusion effect. The measurements of the diffusion penetration profiles were made by the usual radiotracer serial sectioning techcnique. Thin (2-20 #m) layers of the material parallel to the specimen surface were sequentially removed with a microtome and the sectioned chips were weighted on

Table 1. Impurity content (in wt ppm) in Nb as reported by the supplier (Materials Research Corporation, Toulouse/France) Ag 5.9

AI 3.6

Au <0.1

C 25

Ca 0.09

CI 0.65

Cr 1.8

Cu <0.1

Fe 3.4

Ga <0.1

H <1

In <0.1

K 0.18

Mg 0.45

Mo <0.1

N <5

Na 0.069

Ni 1

O 15

P <0.1

Pb <0.1

Pd <0.1

Pt <0.1

S 1.4

Si 17

Sb <0.1

Sn <0.1

Ta 2~

Ti <0.1

W <0.1

Zn 0.48

Zr <0.1

Kt3PPERS et al.: ~7CoDIFFUSION ALONG GRAIN BOUNDARIES IN Nb a microbalance with an accuracy better than _ 5 #g to calculate their thickness and the penetration depth y. To establish reproducible counting conditions, the sections were dissolved in 500 #1 of a solution 50% H20, 47% HNO3 and 3% HF (vol.%). For each section the intensity of the 122 keV y-peak of STCo was measured with a well-type intrinsic Ge-detector and the obtained count-rate was corrected for the half-life of the radioisotope and the background. From the measured count-rates and the weights of the sections the relative specific activity ~ was calculated as a function of depth y. 3. METHOD OF PROCESSING THE PROFILES

GBD is normally studied on polycrystals with stationary GBs and the measured profiles are interpreted in terms of the Fisher model [13-15]. In most of the experiments Harrison's [17] type-B kinetic regime of GBD is realized. In this regime the following conditions are fulfilled: (i) The GBs are isolated from each other, i.e. (Dvt)l/2 <
(1)

where D~ is the volume (lattice) diffusion coefficient of the solute, t the diffusion annealing time, d an average grain size in the polycrystal. (ii) Diffusion along GBs is quasi-steady, which is the case when s6 - t)l/-----2(Dr q <<1

(2)

s being the equilibrium GB-segregation factor of the solute. (iii) Lattice diffusion around GBs proceeds predominantly in the x-direction which is normal to the GB-plane. The criterion for this condition is [14] fl ~

SDGB6 3/2 I/2>> | 2D v t

(3)

where D68 is the coefficientof G B D of the solute, 6 the G B width. (iv) In radiotracer experiments the condition

(D~/)1/2 >>h

(4)

which was introduced by Suzuoka [18] (h being the initial thickness of the tracer layer), is usually realized. Under conditions (i)-(iv) the GB-related part of the tracer penetration profile 6(y) is well approximated by a simplified solution of the form [14, 15, 18] ( ~ 60 exp(--0.775w 6/5)

(5)

where 60 is the layered concentration extrapolated to the surface (y ~ 0), and w is the reduced penetration depth determined by y (4D~'~ '/4 w = ( s D c . 6 ) m \---~-,] .

(6)

2861

Based on this solution, the experimental profile is approximated by a function In 6 = In ql - q2Y 6/5

(7)

with two fitting coefficients qt and q2. The coefficient q2, which has the meaning of the slope - 0 In 6/ay 6/5, is used for the calculation of the triple product P =sDGB6 [15] P = 1.308(Dv/t)l/2q~ S/3.

(8)

The lattice diffusivity Dv is supposed to be known from independent measurements. When the GBs move during the diffusion experiment, the solute distribution becomes more complicated and the Fisher model is no longer applied. As a first step to approach this problem, a model of diffusion along a single moving GB has been recently introduced [19]. In this model the GB remains perpendicular to the specimen surface and moves with a time-independent velocity V normal to its plane (Fig. 1). The analysis based on exact analytical solutions of this model demonstrates that in time t "~ Dv/V 2 after the start of the annealing the diffusion process comes to a steady-state regime, in which the depth dependence of the layered concentration 6m (the subscript m refers to moving GBs) is described by a simplified solution 6 m "~" Cota e x p [ - y ( V / P ) l / 2 ] .

(9)

This equation is applicable when, in addition to the above conditions (i)-(iv), the following condition is met: (v) The GB displacement L -- Vt during the experiment considerably exceeds the lattice diffusion length (Dvt) la, i.e. Vt y - (Dvt)l/2>>l.

(10)

(In effect, equation (9) approximates the exact solution of the model with a practically sufficient accuracy already at ~ > 6 [19]). The tracer is diffused along the GB and left behind in the wake of the moving GB. Therefore the GB motion essentially increases the amount of the tracer absorbed by the specimen from the surface. At the same time the penetration depth of the tracer into moving GBs is considerably (by a factor of about yl/2) smaller than into stationary ones. Equation (9) suggests that the penetration profile can be approximated by a function In Cm =

In q3 - q4Y

(11)

where the fitting coefficient q4 = - 0 In 6m/Oy allows the calculation of the ratio V/P. Knowing the Pvalue for the GB, one can estimate the migration velocity V = qZ4P.

(12)

In a polycrystalline material which experiences grain growth the GB migration can be represented by

2862

KOPPERS et al.:

x I

57Co DIFFUSION ALONG GRAIN BOUNDARIES IN Nb L <
(a)

~~ionary

GB

lit Y

Under such conditions the layered concentration of the solute can be represented by a linear combination f6 m + ( 1 - f ) t ? , where ( and (m are determined by equations (5) and (9), respectively. Accordingly, the profile should be approximated by a function In t? = ln[qj e x p ( - q 2 y 6/5) + q3 e x p ( - q4Y)]

l Moving GB

Y

(c) ~l~y

4. EXPERIMENTAL RESULTS AND THEIR INTERPRETATION q2 = - ~ In ~/~y6/5

In ql

0

(1 5)

According to this model, the penetration profile should consist of two parts (Fig. 1): (1) a near-surface part with a large slope and a high level of the tracer concentration due to moving GBs, and (2) a deeply penetrating part with a smaller slope and a lower level of the tracer concentration which is caused by diffusion along stationary GBs.

In q3

4 = -~ln

(14)

with four fitting coefficients qi. Using the coefficients q2 and q4, one can calculate the P-value relating to stationary GBs from equation (8) and then estimate the migration velocity V of moving GBs from equation (12). Knowing V, one can calculate y to make sure that it was large in the experiment. Finally, the coefficients ql and q3 allow an estimation of the fraction f of moving GBs (see [16] for detail) f = [1 + 0.3205(q t/q3)Y 3/2]-1.

T

(13)

X\ \

y615

Fig. I. Schematic distribution of diffusing atoms for a stationary (a) and a moving (b) GB and expected shape of the GB-penetration profile (c) for a polycrystal containing stationary and moving GBs. The dashed area is enriched in the diffusing atoms. The coefficients q2 and q4 in equation (14) have the meaning of the slopes - d In 6/ay ~/5 and d In ?/~gy of the tail and of the near-surface part of the profile, respectively; the coefficients q~ and q3 are the activities obtained by extrapolation of these two parts of to the surface (y --*0). -

a spectrum of GB-velocities and their directions. To develop a comprehensive procedure of profile processing, a simplified model of diffusion in a polycrystal containing both stationary and moving GBs has been proposed [16]. In this model a certain fraction f of the GBs moves with the same velocity V which depends only on the temperature, whereas the rest of the GBs remain stationary. All the GBs remain perpendicular to the specimen surface. It is also assumed that the GBs are isolated from each other, for which the above condition (i) is complimented with the following one: (vi) The GB displacements are smaller than the grain size, i.e.

Figure 2 demonstrates the obtained penetration profiles in the conventional coordinates log ~ vs y6/5. In spite of the use of the carrier-free radiotracer 57C0 with high activity on the sample surface and an optimal decay detection, the scatter of the data points is rather considerable, especially at larger depths. This scatter is probably caused by two reasons: (a) due to the large grain size, the statistics of the GBs as well as the total tracer amount penetrating along the GBs were very low. (b) Most of the activity was located in a near-surface region; only a limited amount of the tracer could penetrate to a larger depth to form the tail of the profile. Importantly, this depth of the high-activity zone near the surface was usually orders of magnitude larger than (Dvt) 1/2 and could therefore not be caused by direct lattice diffusion from the surface. The latter feature as well as the obvious two-step behavior of the profiles are well consistent with the presence of moving GBs in the diffusion samples (Fig. 3). As was discussed above, moving GBs very intensively absorb the tracer initially deposited on the specimen surface and spread it in a relatively shallow layer near the surface. In contrast, stationary GBs absorb a smaller amount of the tracer, but transport it to a larger depth. This behavior should obviously lead to two-step penetration profiles, where the first (near-surface) part of the profile is due to diffusion along moving GBs, whereas the second (deeply penetrating) part represents

et al.:

KOPPERS

57Co D I F F U S I O N

ALONG

GRAIN

1016

100 I

50 I

100 I

300 I

• " o o

. .~ 1012 ~

1123K 1023 K 877 K 823 K

150 I • • , t~ o

1012

200 I

2863

(c)

•

y (p.m)

(a)

IN Nb

Y (l.tm)

diffusion along stationary GBs. Following this interpretation the profiles obtained in this study were least-squares fitted by equation (14). As one can see from Fig. 2, this equation provides a good approximation of the profiles, except for the first several

1016

BOUNDARIES

1373 K 1323 K 1233 K 1095 K 874 K

~2 "~

100

\ 4

104

F

108

,

¢,,)

.aE_100 ~ 0

l

104

~ 1

, ,

I

,

2

y6/5 (105m 6Is)

Fig. 2. Tracer penetration profile for Co grain boundary diffusion in Nb. I

100

I

I

I

I

I

I

[

2

0

I

I

I

I

4

6

y6/5 ( 10Sm s/5)

y (rtm) 1O0 I

50 I

1016

150 I

200 I

(b) " v [] o

1012

1471 K 1423 K 1173K 923 K

points which were evidently affected by direct lattice or/and dislocation diffusion. The obtained fitting coefficients q~ are listed in Table 2. The calculation of P-values requires the knowledge of the volume diffusivity Dr. The Dv-values were calculated by extrapolation of the previous measurements made by different authors at temperatures 1347-2436 K using the radiotracer sectioning technique [9-12] (Fig. 4). (Note a good agreement between the results by different authors.) An Arrhenius fit through all the data in Fig. 4 gives D v -- -- ~t 3 .o•4+0-98x -0.78) X 1 0 - 6

g

[ x exp 108

.o_

104

1

100 0

I

I

I

]

1

I

I

I

I

[

I

I

I

2

y6/5 ( 105rn 6/5) Fig. 2(a,b).

I

I

3

I

1

[

(256.1+3.3)kJ/mol]m 2 -

-

RT

--

s

"

(16)

Using the coefficients q2 and the Dr-values from equation (16), P-values for stationary GBs were calculated from equation (8) (see Table 3). Table 3 demonstrates that fl in the present experiments remained sufficiently large; the lattice diffusion length (Dvt) 1/2 ranged from ~0.03#m>>h at 823K to ,~3 #m<
2864

KOPPERS et al.: 57CoDIFFUSION ALONG GRAIN BOUNDARIES IN Nb Table 2. The coefficients q~ obtained by fitting the experimental profiles by equation (14) (see Fig. 1 for detail) T (K) 823 874 877 923 1023 1095 1123 1173 1233 1323 1373 1423 1471

ql/q3

t (s) 4.493 5.622 1.949 2.855 1.834 3.392 3.294 4.980 9.800 2.358 6.600 5.530 2.650

x x × x x × x x x x x x x

106 105 10e 106 105 105 105 103 103 104 103 103 103

3.14 2.59 1.96 7.73 5.89 6.04 4.35 6.44 2.06 9.82 4.56 7.84 1.02

× x x x x x x x x x x x x

q2 ( 104 m-S/s)

q4 ( 10s m - l)

4.01 7.88 5.72 5.98 5.52 11.08 4.85 13.12 10.79 9.93 19.05 13.78 26.50

0.638 1.75 1.27 1.45 1.99 1.55 1.63 2.92 3.35 2.27 1.57 2.40 1.60

10 -2 10 -3 10 -2 10 -~ 10 -5 10 -4 10 -5 10 -5 10 -5 10 -s 10 -4 10 -s 10 -3

should be actually multiplied by the GB-segregation factor s of Co in Nb, a value which is unknown. According to the phase diagram ([20], p. 780) the solid solubility of Co in Nb in the temperature range of our measurements is about 2 at.%. From the empirical correlation between the solubility and GBsegregation [21], a value of l02 seems to be a reasonable estimation ors. With this value of s, the ~-values vary from 8 . 7 x 1 0 -3 at 1471K to 8 . 1 x l 0 -l at 823 K. At high temperatures ~ was therefore rather small in compliance with condition (ii), but for two lowest temperatures the relation (2) may look somewhat ambiguous. We have to put up with this ambiguity, taking into account the rough character of the above estimation of s and the error involved in extrapolation of the high-temperature Dr-measurements to temperatures lying ~500 K below. An alternative would be to suggest an intermediate (between type-B and type-C) diffusion regime at temperatures 823 and 874K. But in this regime the y6/5-method is known to essentially underestimate the P-values relative to the true ones [22]. However, in the Arrhenius plot (Fig. 5) the P-values for the two lowest temperatures lie (within the scatter of the data

points) on line with the other measurements, thereby confirming the assumption that all the measurements were done under type-B regime. Fitting the Arrhenius equation to the P-values in Fig. 5 yields p

= ( 4 . 8 4 _ +5.99 2.68) X 10-13

x e x p [ - (149.5 +RT7"2) kJ/m°!7m 3sj " (17)

Table 3 also presents the values of V calculated from equation (12) using the obtained P-values. It should be emphasized that in this calculation the diffusivities of stationary and moving GBs are considered as identical, an assumption that is to be proved. Convincing experimental evidences for or T (K) 10 "s

2400 2000

I

I

1600 I • o n • A v •

10-11

1200 I

Lundy et al. (1965) Pellog (1976) AblRzer (1977) Einziger et al. (1976) Bussmann et al. (1981) Serruys et al. (1982) Wenwer et al. (1989)

10-14

g Co in Nb 10-17

Nb in Nb

10-20

Fig. 3. Typical features of GB migration in Nb. To reveal the GB positions by vacuum etching the specimen was annealed in a UHV-system in conditions simulating a diffusion anneal (1473 K, 2 h). 1--initial position, 2--final position of the triple junction. Note that the GBs A and B moved whereas the GB C remained stationary. The displacements of the GBs A and B have the same order of magnitude as expected from diffusion experiments.

10-23 L_ 3.0

4.5

6.0

7.5

9.0

10,5

T 1 (10"4/K)

Fig. 4. Arrhenius plot of Co diffusion and self-diffusion in the lattice of Nb. The measurements were made by Lundy et al. [27], PeUeg [9], Ablitzer [10], Einziger et al. [28], Bussmann et al. [29], Serruys et al. [11] and Wenwer et al. [12].

KOPPERS et al.: STCo D I F F U S I O N A L O N G G R A I N B O U N D A R I E S IN N b

2865

Table 3. Results for the grain boundary diffusivity P, velocity V, the fraction of moving GBs f and related experimental parameters T(K)

D , (11128- 1 )

=a

P (m;s -I)

//

V (ms -I)

?

L (/am)

f

823 874 877 923 1023 1095 1123 1173 1233 1323 1373 1423 1471

2.14 x 10-z2 1.90 x 10-2' 2.14 x 10-2~ 1.23 x 10-20 3.22 X 10 -19 2.33 X 10-18 4.70 x 10-~s 1.51 X 10-17 5.43 x 10-17 2.97 x 10-'6 6.94 × l0 -16 1.53 x 10 Is 3.09 x 10-Is

8.1 x 10-3 7.7 x 10-3 3.9 x 10-3 1.3 x 10-3 1.0 X 10-3 2.8 X 10-4 2.0 x 10-4 9.1 X 10-4 3.4 x 10 4 9.4 x 10-5 1.2 x l0 -4 8.6 x 10-3 8.7 x l0 -5

1.92 x 10 -22 5.24 x 10-22 5.11 x 10-22 9.39 x 10-22 2.17 X 10-2° 1.34 X 10-20 7.67 × 10 -20 2.13 X 1 0 - 1 9 3.98 x 10-19 6.89 x 10-'9 6.72 x 10-19 1.87 × 10 -18 1.29 x 10-18

107 4.2 x 106 1.8 x 106 2.0 x 10s 1.4 X 105 3.2 X 103 6.6 X 10 3 2.6 X 1 0 4 5.0 × 103 4.4 x 102 2.3 x 102 2.1 X 102 7.3 x l01

7.81 x 10-13 1.61 x 10-H 8.27 x 10-12 1.97 x 10 u 8.64 X 10-l° 3.21 X 10-m 2.04 X 10-9 1.81 x 10-s 4.47 x 10 8 3.56 x 10-a 1.66 x l0 -s 1.08 X 10 -7 3.33 x 10-~

113 278 249 300 650 122 541 329 600 317 51 205 31

3.5 9.1 1.6 x 101 5.6 x 10~ 1.6 X 102 1.1 X 102 6.7 × 102 9.0 x 101 4.4 X 102 8.4 × l02 l.l x l02 5.9 X 102 8.8 x 101

7.6 x 10-2 0.21 3.9 x 10-2 0.44 0.76 0.79 0.85 0.89 0.91 0.98 0.95 0.99 0.95

1.4 x

=Calculated with 6 = 5 x 10-t°m and s = 1

against this point are not available, but recent indirect measurements indicate that the two diffusivities are close to each other at least within an order of magnitude [23-26]. Knowing the GB-velocities at various temperatures an attempt can be made to estimate the activation enthalpy H m of GB-migration

employing the relation Voc e x p ( - H m / R T ) F. RT

(18)

the violation of relation (13) could cause additional errors in V. Finally, the fraction f of moving GBs was calculated from equation (15). The error of this calculation is rather large for the reasons that were discussed in [16]; nevertheless, f clearly exhibits a distinct temperature dependence (Fig. 7) with an abrupt increase in the temperature range T "~ 900-1100 K (0.33-0.40Tm, Tm being the melting temperature of niobium).

I f we r o u g h l y a s s u m e t h a t the a v e r a g e d r i v i n g force F o f m i g r a t i o n w a s the s a m e t h r o u g h all o u r experi m e n t s , t h e n it f o l l o w s t h a t V T o c e x p ( - H ~ / R T ) a n d H m c a n be d e t e r m i n e d f r o m the s l o p e 0 In VT/a T - ' . A n A r r h e n i u s fit to the p l o t log V T vs T-~ (Fig. 6) r e s u l t s in

VT

-- - ~5 i, . uQ= + 4 .26 1 . 7 ~] X 1 0 2

(181.9 + 13.9) k J / m o l l m . K ~-~ j--~-.

xexp-

(19)

L a r g e 7 - v a l u e s ( T a b l e 3) are c o n s i s t e n t w i t h the s t e a d y - s t a g e r e g i m e o f diffusion [cf. c o n d i t i o n (v) in S e c t i o n 3]. T h e G B d i s p l a c e m e n t L w a s <
5. D I S C U S S I O N

5. L Co as a fast diffuser along GBs in Nb C o in N b offers a typical e x a m p l e o f fast lattice diffusion. F o r the sake o f c o m p a r i s o n , the self-diffus i o n coefficients in N b m e a s u r e d b y different a u t h o r s [10, 11, 27-29] are also s h o w n in Fig. 3, If, in spite o f a slight c u r v a t u r e at h i g h e r t e m p e r a t u r e s , the A r r h e n i u s e q u a t i o n is fitted to the w h o l e set o f the d a t a f o r N b , a n a c t i v a t i o n e n t h a l p y H vNb/Nb = ( 3 9 1 . 6 + 3 . 1 ) k J / m o l a n d a p r e e x p o n e n t i a l f a c t o r un n0vb / N b-_-

5 . ~. .+.l . 10.94ix 4~ 1 0 - S m 2 / s are o b t a i n e d . c o m p a r i s o n o n e c a n notice that:

From

this

the a c t i v a t i o n e n t h a l p y o f C o diffusion in N b , H C ° / n b = 2 5 6 k J / m o l [cf. e q u a t i o n (16)], is T (K)

T (K) 1400 I

10-17

1200 I

1000 I

800 I

o

1200

1000

I

t

I

10-2 10-4

10-19

1400

o

o

o

800 ]

o

10-6

E

10-8

n 10 -21

10-10 10-12 10-23

=

t

I 7,5

i

,

t

I

I 10.0

i

,

i

I

I 12.5

I

I

I

,

,

,

7.5

,

I

,

10.0

"1--1

,

L

t

I 12.5

(I0-4K-I)

T-1 (10-4K-1)

Fig. 5. The Arrhenius plot of the obtained P values for Co diffusion along stationary grain boundaries in Nb.

Fig. 6. Arrhenius diagram of grain boundary migration in Nb. The product VT is plotted against the inverse temperature.

2866

KOPPERS et al.: 57CoDIFFUSION ALONG GRAIN BOUNDARIES IN Nb I

I

I

I

,

1.00

/,/g

orders of magnitude slower than Co GBD in Nb. For example, at T = 1371 K = 0.5Tin pCo/Nb/pNb/Nb ,~ 104, a ratio which is anomalously large and is comparable • with D vCo/Nb ~DrNb/Nb for lattice diffusion in this system. One should keep in mind that the P-factor generally represents not only the GBD coefficients DcB but also the GB-segregation factor s, so that

f~.~.~.-%--o- bo

%

0.75

/

0.50

/

/

o/ ./

o/

/

0.25

/

/

pCo/Nb

/ o/ 0

'

,

I 750

,/,o,

i

I

i

i

i

1000

~ I

i

1250

J J

i

I

i

" 1500

T (K)

Fig. 7. Temperature dependence of the fraction f of moving grain boundaries in Nb during the diffusion anneals. considerably lower than --v~'i~Nb/Nb---- 392 kJ/mol; the diffusion coefficients of Co in Nb are much larger (e.g. by a factor of 104 at 0.5Tin) than those of Nb self-diffusion. This large difference in diffusion characteristics demonstrates that diffusion of Co in Nb is unlikely to occur by the same (i.e. vacancy) mechanism as self-diffusion in Nb [12]. In this context it would be interesting to compare the GB diffusivity of Co in Nb, measured in the present work, with GB self-diffusion in pure Nb. Unfortunately, GB self-diffusion in Nb has never been measured (see discussion of the reasons below)• Moreover, too little information is available on GB self-diffusion in b.c.c, transition metals, with which our results could be well compared. Only GB selfdiffusion in ~-Fe has been studied by the radiotracer sectioning technique (e.g. [8, 30, 31]), while for Cr, Me and W only indirect and/or estimative measurements have been made (see [32] for detail)• Based on the available results for ~-Fe, Cr and W, Gust et al. [33] have recently proposed an empirical correlation for b.c.c, transition metals: DGs6

9.2 × 10-14 exp[ L.

86.7TmJ/moll m 3

-~f

DG~Nb

(21)

p Sb/Nb = SCo/Nb/~ Nb/Nb " J~'GB

j 7

{Note that larger P-values for Ag in Pb in Fig. 8 are consistent with smaller solubility of Ag in Pb ([20], p. 53) as compared with the solubility of Co in Nb ([20], p. 780), which according to Hondros et al. [21] should lead t o SAs/Pb>>~'Co/Nb. } However, the observed large difference between Pcomb and PNb/r~bcan hardly be entirely attributed to the GB-segregation effect• From the solubility of Co in Nb, Sco/Nb is expected to be of the order of 102 (cf. Section 4). Then it follows that, e.g. at 0.5Tin, ~Ga~C°mbexceeds uGBr~Nbmbby nearly two orders of magnitude; this difference seems to be still too large to be explained by the operation of the same atomic mechanism for Co impurity- and Nb self-diffusion along the GBs. A similar behaviour, although more pronounced, was earlier found in other fast-diffusing systems: Co and Fe in ~-Zr [5, 6], Co in ~-Ti [7], Ag in Pb [4] and C in ~-Fe [8]. We can therefore suggest that Co GBD in Nb occurs by a combined vacancy-interstitial (e.g. dissociative) mechanism, the nature of which is probably similar to that of fast Co lattice diffusion in this system. Because of a large grain size and the presence of moving GBs in the specimens, the tails of the profiles relating to stationary GBs could be measured only in relatively narrow concentrational intervals and suffered from a scatter of the data points (cf. Fig. 2). This made it impossible to analyse their shape in terms of the recently proposed model of GBD by the dissociative mechanism [35]. According to this model, the shape of the profile essentially depends on the regime of lattice diffusion around GBs. Normal

(20) One should have in mind, however, that this equation is very uncertain because of a little number of the data points involved in its derivation. The normalized Arrhenius diagram in Fig. 8 compares our results for Co in Nb with the correlation line determined by equation (20). The results for Pb GB self-diffusion (P0eb/Pb = 6.1 x 10 -15 m3/s, HP~Pb = 44.33 kJ/mol [34]) and fast Ag GBD in Pb ( P0As/Pb = 1•58 x 10 -l° m3/s, H A ~ Pb = 41.12 IO/mol [4]) are also included for better comparison• Lead is the only f.c.c, metal for which both self- and fast impurity diffusion have been measured both in the lattice and along the GBs. This diagram demonstrates that the system Co/Nb exhibits a similar behaviour as Ag/Pb [4]. If we assume that equation (20) represents GB self-diffusion in Nb, then the latter is several

I l l l l r l l l [ r l r l l l J F I l l l l r 10-14

" - - •in P b 10-17

g

10 20

ft. 1 0 -23

B.C.C. "'-.. transition ,,,

10-26 1.0

I,,,

1.5

,m~ta,ls,

"..

, , t ....

2.0

2.5

f , , ,

3.0

3.5

wr Fig. 8. The normalized Arrhenius plot of grain boundary diffusion of Co in Nb (this work) and of Ag in Pb [4]. The data for grain boundary self-diffusion in Pb [34] and the empirical correlation for b.c.c, transition metals [33] are shown for comparison.

KOPPERS et al.: STCoDIFFUSION ALONG GRAIN BOUNDARIES IN Nb Fisher-type profiles are expected when the lattice diffusion is interstitial-controlled, which occurs when a sufficient amount of vacancy sources are available in the bulk. If, on the contrary, the bulk is nearly free of dislocations and other vacancy sources (a sitution more typical for semiconductors), the diffusion of the solute from the GBs to the bulk is limited by diffusion of new vacancies which are generated by the GBs. In this vacancy-controlled regime the profiles are predicted to exhibit a downward curvature; special methods of profile processing should be then applied to extract the GB diffusivity. The model allows to verify the hypothesis of the dissociative mechanism of fast impurity diffusion; for this, however, specially performed GBD experiments are required in the future. 5.2. GB migration in Nb

In our experiments part of the GBs could move during the diffusion anneals (see Fig. 3). According to the procedure that we used for processing the depth profiles, they were decomposed into two parts relating to moving and stationary GBs, respectively. From the first, near-surface part of the profiles we could roughly estimate the GB-velocities V at various temperatures. In spite of the scatter of the obtained V-values, the product VT obeys the Arrenhius law with an estimated enthalpy of GB-migration of Hm ~- 182 kJ/mol. The same kind of procedure has been recently applied in the investigation of GB self-diffusion in ,t-Hf, where also some fraction of GBs moved during the diffusion experiments [16]. The obtained value of H m ~- 195 kJ/mol was comparable with the directly measured activation enthalpy of GB self-diffusion in ~-Hf, HGs "" 202 kJ/mol. This agreement was interpreted as an experimental support to the idea that the activation barrier and the mechanism of atomic transport across the GBs during their migration are probably the same as for the self-diffusion along the GBs. If this idea is true and can be extended to other pure metals, then one can expect that the activation enthalpy for GB selfdiffusion in Nb is also close to Hm, so that HGa = 182 kJ/mol. This hypothesis does not seem to be unreasonable. Indeed, with this value of HoB the ratio HGa/Hv = 182/392 ~- 0.46 is consistent with the vacancy mechanism of GB self-diffusion in pure Nb. Also, the normalized activation enthalpy HGB/RTm ~-8.0 is comparable with this quantity for Pb (8.9) and with the empirical correlation [33] according to which HGB/RTm in b.c.c, transition metals ranges from 7.5 to 14.5 with a mean value of 10.4 [cf. equation (20)]. Of course this indirect estimation can by no means remove the problem of direct GB self-diffusion measurements in Nb. In our view an important if not the main obstacle to such measurements consists in significant GB migration in pure material at temperatures that are appropriate for GBD experiments. Both in ~t-Hf [16] and in Nb no pre-diffusion heat

2867

treatment could guarantee stable grain size in the working temperature range. At relatively low temperatures, when the GB displacements were smaller than the grain size, the tracer penetration profiles could be treated using the model of Ref. [16]. However, at higher temperatures (e.g. > 1500 K for Nb) the grain growth was so extensive that the tails relating to stationary GBs could no longer be distinguished and any reasonable interpretation of the profiles was not possible. The measurements of the present paper were therefore made at relatively low (compared with Tm) temperatures and were eased by the anomalously high Co diffusivity in Nb. With self-diffusion in pure polycrystalline Nb, however, the situation could be much more difficult. This reasoning evidently also applies to the refractory metals like Cr, Mo and W and explains, at least partly, the lack of reliable experimental data on their GB selfdiffusion. A solution of this problem could consist in using bicrystalline specimens with a single plane GB; this practically excludes GB motion and thus allows to extend the measurements towards higher temperatures, but on the other hand the activities to be measured during profiling become very small. In appropriate experimental conditions GBD-measurements on bicrystals are, however, possible [36, 37]. Also fast impurity GBD can be better studied on bicrystals; due to the elimination of GB motion one can more carefully examine the shape of the profiles in order to compare it with the above discussed dissociative model [35]. 6. CONCLUSIONS 1. GB diffusion of 57Co in high-purity polycrystalline Nb has been studied in the temperature range 823-1471 K using the radiotracer serial sectioning technique. 2. No regime of pre-diffusion heat treatment could be found to fully stabilize the grain size in the material in the temperature range of GBD measurements. As a consequence, a certain fraction of GBs in the specimens experienced migration in the course of the diffusion anneals. The obtained concentrationdepth profiles were therefore interpreted in terms of the recently proposed model of diffusion in polycrystals containing both stationary and moving GBs [16]. Following this model, the profiles were decomposed into two parts: (a) a long-penetrating tail caused by stationary GBs, from which the product P = SDGB~ was calculated; (b) a near-surface part due to moving GBs, from which the GB velocity V was estimated assuming the same value of P for stationary and moving GBs. 3. An activation enthalpy of ~Co/Nb_ 149.5kJ/mol and a pre-exponential factor of pCo°/Nb=4.84× 10-J3m3/s are obtained. The P values for Co in Nb are 2-4 orders of magnitude larger than expected P-values for GB self-diffusion in Nb. Even taking into account the segregation effect 4.

GB

--

2868

KOPPERS et al.: 57Co DIFFUSION ALONG GRAIN BOUNDARIES IN Nb

the diffusion coefficient *"GBI"tC°/Nbis still much higher than "-'~arbNb/Nb"The system C o / N b exhibits a similar diffusion behaviour as Co and Fe in ~t-Zr [5, 6], Co in ~t-Ti [7] and especially Ag in Pb [4], where fast solute diffusion both in the lattice and along the GBs has been found. It is concluded that Co G B D in N b probably occurs by a type of combined vacancy-interstitial mechanism. 4. F r o m the temperature dependence of GB velocities, an activation enthalpy of GB-migration in N b is estimated as Hm "" 182 kJ/mol. By analogy with an earlier study of G B self-diffusion and GB-migration in ~ - H f [16], it is suggested that the activation enthalpy of GB self-diffusion in N b is comparable with Hm. 5. GB self-diffusion in N b has not yet been directly measured. This work demonstrates that GB migration presents a serious obstacle to measurements of GB self-diffusion in pure polycrystalline Nb, as well as in other pure high-melting b.c.c, transition metals. A possible solution could probably consist in making diffusion measurements in individual GBs in bicrystals. ,4cknowledgements--The work was partly supported by funds of a NATO linkage grant. One of us (Y. M.) is also grateful to the Alexander von Humboldt Foundation for financial support.

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(199o). 7. Chr. Herzig, R. Willecke and K. Vieregge, Phil. Mag. .4 63, 949 (1991). 8. E. Budke, Chr. Herzig and H. Wever, Physica status solidi (a) 127, 87 (1991).

9. J. Pelleg, Phil. Mag. A 33, 165 (1976). 10. D. Ablitzer, Phil. Mag. ,4 35, 1239 (1977). 11. Y. Sermys and G. Breb6c, in Diffusion in Metals and Alloys DIMET,4 82 (edited by F. J. Kedves and D. L. Beke), Trans. Tech., Diffusion and Defect Monogr. Ser., Vol. 7, p. 351 (1983). 12. F. Wenwer, N. Stolwijk and H, Mehrer, Z. Metallk. 80, 205 (1989). 13. J. C. Fisher, J. appl. Phys. 22, 74 0951). 14. A. D. Le Clarie, Br. J. appl. Phys. 14, 351 (1963). 15. I. Kaur and W. Gust, Fundamentals of Grain and Interphase Boundary Diffusion. Ziegler, Stuttgart (1988). 16. F. Giithoff, Yu. Mishin and Chr. Herzig, Z. Metallk. 84, 584 (1993). 17. L. G. Harrison, Trans. Faraday Soc. 57, 1191 (1961). 18. T. Suzuoka, Trans. Japan. Inst. Metals 2, 25 (1961). 19. Yu. M. Mishin and I. M. Razumovskii, ,4eta metall. mater. 40, 839 (1992). 20. Binary Alloy Phase Diagrams (editor-in-chief T. B. Massalski), Vol. 1. Am. Soc. Metals, Metals Park, Ohio (1986). 21. E. D. Hondros and M. P. Seah, Int. metall. Rev. 222, 262 (1977). 22. A. Atkinson and R. I. Taylor, Phil. Mag. A 43, 979 (1981). 23. W. Gust, M. B. Hintz, A. Lodding, H. Odelius and B. Predel, ,4cta metall. 30, 75 (1982). 24. W. Gust, A. Lodding, H. Odelius, B. Predel and U. Roll, Scripta metall. 18, 1149 (1984). 25. W. Gust, J. Beuers, J. Steffen, S. Stiltz and B. Predel, Acta metall. 34, 1671 (1986). 26. P. Neuhaus, Chr. Herzig and W. Gust, ,4cta metall. 37, 587 (1989). 27. T. S. Lundy, F. R. Winslow, R. E. Pawel and C. J. McHargue, Trans. Am. Inst. Min. Engrs 233, 1533 (1965). 28. R. E. Einziger, J. N. Mundy and H. A. Hoff, Phys. Rev. B 17, 440 (1978). 29. W. Bussmann, Chr. Herzig, H. A. Hoff and J. N. Mundy, Phys. Rev. B 23, 6216 (1981). 30. J. lkmardini, P. Gas, E. D. Hondros and M. P. Seah, Proc. R. Soc. ,4 379, 159 (1982). 31. H. H/insel, L. Stratmann, H. Keller and E. J. Grabke, Aeta metall. 33, 659 (1985). 32. I. Kaur, W. Gust and L. Kozma, Handbook of Grain and Interphase Boundary Diffusion Data. Ziegler, Stuttgart (1989). 33. W. Gust, S. Mayer, A. B6gel and B. Predel, J. Physique 46, C4-537 (1985). 34. D. Gupta and K. K. Kim, J. appl. Phys. 51, 2066 (1980). 35. Yu. M. Mishin and Chr. Herzig, J. appl. Phys. 73, 8206 (1993). 36. J. Sommer, Chr. Herzig, S. Mayer and W. Gust, Defect Diffusion Forum 66-69, 843 (1989). 37. J. Sommer, Chr. Herzig, T. Muschik and W. Gust, Mater. Sci. Forum 126-129, 329 (1993).