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Nickel-enhanced grain growth in tungsten wire
Journal of Alloys and Compounds, 201 (1993) 129-137 JALCOM 738
129
Nickel-enhanced grain growth in tungsten wire In-Hyung Moon, Ki-Youl Kim, Sung-Tag Oh and Myung-Jin Suk Department of Materials Engineering, Hanyang University, Seoul 133-791 (South Korea) (Received January 18, 1993; in final form March 10, 1993)
Abstract The effect of Ni additive on recrystallization and grain growth in W wires has been investigated in order to explain the role of nickel in the activated sintering of tungsten, because the two phenomena are comparable with each other, being principally diffusion controlled and greatly influenced by the presence of Ni. The experiment was carried out in a bundle model of W wires in which the initial state of nickel could be appropriately controlled by arranging Ni-coated W wires together with non-coated wires. The recrystallization and grain growth processes were observed and analysed on the basis of the geometrical relation between the Ni source and the W wires. The development of the recrystallization front depends on the Ni diffusion path and rate. Nickel diffuses fast into the W wires through high diffusivity paths such as the surface and grain boundaries, inducing recrystallization at relatively low temperature. The apparent diffusivity of Ni in W wire, estimated by measuring the migration rate of the recrystallization front, is about 1.7 × 1 0 - 9 c m 2 S - 1 , while the surface diffusivity of Ni on W is estimated to be about 10 -5 cm 2 s-~. The role of Ni in W is further discussed.
1. Introduction
It is well known that nickel enhances the sinterability of tungsten powder compact and reduces the recrystallization temperature when added to cold-worked W metal [1-3]. This effect of nickel on the sinterability of W powder and the recrystallization of W metal suggests implicitly that the role of nickel may be similar in the sintering process of metallic powders and in the recrystallization process, because both processes are usually accepted to be diffusion controlled. Thus the role of the nickel activator in the initial stage of activated sintering might be partly explained by understanding the initial stage of Ni-induced recrystallization, which is more accessible to observation and analysis. Conversely, the role of nickel in the enhanced recrystallization of W metal might also be explained by extrapolation of the sintering data obtained from analysis of the intermediate stage of Ni-activated sintering, where the grain growth of sintered W powder compact was observed simultaneously with densification [4]. Since Vacek's discovery of the phenomenon of Niactivated sintering, many mechanisms have been suggested for it [5-10]. Several of these mechanisms are based on the possible role of nickel as a carrier phase for tungsten atom transport, i.e. the Ni-rich phase or the Ni impurity interracial layer located in W grain boundaries and on the W surface may provide a high diffusivity path for W diffusion [7, 8]. Since an en0925-8388/93/$6.00
hancement of W self-diffusion has been observed in Ni-doped W grain boundaries [11, 12], the activated sintering mechanism related to enhanced diffusivity still seems to be more plausible than the others, even though this mechanism has some difficulty in being universally accepted because of its simplification of the roles of Ni activator and W powder. According to recent work of the present authors' group, the sinterability of Ni-doped W powder compact depends not only on the physical state of the Ni activator, i.e. its geometrical relation to W (its amount, size and location), but also on its chemical state [13-15]. Ni added to W was sometimes found in visible amounts of an Ni second phase at grain boundary junctions [16], but also sometimes found as an impurity layer of a few atomic diameters at W grain boundaries, which can only be detected by modern analytical methods [17]. The presence of nickel at W grain boundaries was reported to increase the W self-diffusivity in grain boundaries [11, 12] and this enhanced W diffusivity is thought to be responsible for the activated sintering and reduced recrystallization temperature in W. In the present work, therefore, a model experiment was carried out on bundles of W wires in order to gain insight to the behaviour of Ni during the initial stage of activated sintering and recrystallization of W wires. The W wire bundle model, in which the initial location of nickel could be appropriately controlled by arranging Ni-coated W wires with non-coated wires, provides
© 1993- Elsevier Sequoia. All rights reserved
130
I.-H. Moon et aL / Ni-enhanced grain growth in W wire
geometrical simplicity for investigating both Ni-activated sintering and Ni-induced recrystallization simultaneously.
2. Experimental details The tungsten wire used for the present experiment was an undoped grade of 0.5 mm diameter with a minimum purity of 99.98% supplied by Johnson-Matthey. The impurities present in the wire are given in Table 1. The wire was first annealed in a hydrogen atmosphere at 1123 K for 1 h to reduce surface oxides. Nickel in an amount equivalent to 0.29 or 0.43 wt.% of tungsten was coated on the W wire surface by a chemical vapour deposition (CVD) method using an Ni tetracarbonyl. The amount of nickel coated was controlled by varying the deposition time at a temperature of 423 K. The chemical analysis of the deposited Ni film is given in Table 2. Only the amount of nickel in the coated layer was taken into consideration for analysis and calculation in the present study. Figure 1 is a scanning electron microscopy (SEM) image showing the uniformly coated nickel layer of 2-3/zm thickness. A cross-sectional view of the sintering model system is shown schematically in Fig. 2. Specimens were prepared in the following way. Seven W wires (one coated and six non-coated) initially in a hexagonal array were twisted into the form of a wire rope in such a way that the wires contacted each other completely. Afterwards, the central wire was discarded so as to leave the remaining six wires arranged in a ring pattern. The cross-sectional shape of each wire in the wire bundle was not circular but elliptical, as seen in subsequent microphotographs, because the wires do not intersect perpendicular to their axes. Each W wire was numbered according to its position, no. 4 designating the Nicoated W wire. TABLE 1. Impurities contained in the W wire used Element
Concentration (maximum) (ppm)
Element
Concentration (maximum) (ppm)
Aluminium Cobalt Molybdenum Oxygen Lead Silicon
> 10 5 40 10 >10 > 10
Nickel Carbon Phosphorus Chromium Iron Potassium
5 15 20 > 10 20 >5
(10) (30) (300) (30) (10) (30)
(20) (30) (50) (10) (50) (10)
C
O
0.48
2.29
Fig. 2. Schematic cross-section of W wire model specimen.
The W wire bundles were sintered in a hydrogen atmosphere for various times at 1473 and 1673 K for specimens with 0.29 and 0.43 wt.% Ni. The heating and cooling times were included in the sintering time according to their thermal effects as evaluated on the basis of diffusion data. Their contribution was determined to be 17.6 min in the present experiment. The grain size of the specimen was determined by the linear intercept method [18] using an image analyser (Leco 2001). The distance over which the recrystallization front had moved was measured on microphotographs. The microstructural development of the sintering model system was continuously observed by optical microscopy and SEM and partly further analysed by energy-dispersive spectroscopy (EDS) attached to the scanning electron microscope.
3. Experimental results
TABLE 2. Concentrations of chemical species contained in the deposited Ni film Element Concentration (wt.%)
Fig. 1. Scanning electron micrograph of Ni-coated W wire by CVD method.
Ni 97.23
Figure 3 shows microphotographs of the sintered W model specimen which was initially composed of a 0.43 wt.% Ni-coated W wire and five pure W wires, and wires of pure W as reference. These specimens were annealed at 1673 K for 5 min (Fig. 3(a)) and 30 min (Fig. 3(b)). As seen in these photographs, the microstructure of all W wires in model specimens changed
L-H, Moon et al. / Ni-enhanced grain growth in W wire
(a)
(b) Fig. 3. Micrographs of 0.43 wt.% Ni-coated W wire (left) and pure W wire (right) sintered at 16"13 K for (a) 5 min and (b) 30 min.
drastically from the original fibrous drawn structure to the fully recrystallized grain structure after only 5 min of sintering, and the W grains were found to coarsen to an average size of about 50 tzm after 30 min of sintering. Recrystallization and grain growth progressed rapidly in all parts of the model specimen, not only in the Ni-coated W wire but also in all pure W wires. In contrast, the recrystallization in the reference was confined to the surface layer of the W wires, showing a distinct concentric circular boundary between the recrystallized zone and the non-recrystallized material, and the depth of the recrystallized surface layer increased with increasing sintering time. There was no measurable grain growth in the recrystallized zone. Thus it was confirmed once again that the presence of nickel in W wires accelerates recrystallization and grain growth in the severely deformed grain structure of cold-drawn W wires. The fact that the Ni-induced recrystallization progressed so rapidly even in non-coated W wire no. 1 located at the farthest distance from the Ni source implies that Ni has already been transferred from its original source in the coating layer on W wire no. 4 to the initially non-coated W wires. The rapid transfer of nickel atoms from the surface of coated W wire no. 4 to the non-coated W wires seems to be possible only by Ni diffusion through a high diffusivity path, either on the W surface or along grain boundaries, because Ni volume diffusion in W is not so effective at this temperature [19]. In fact, nickel is known to spread
131
very fast on W surfaces at the temperature of the present experiment [20]. In addition to the fast surface diffusion, Ni transport by evaporation and condensation through the hydrogen gas flow seems to contribute also to the rapid migration of nickel from the coated to non-coated W wires in the present system, because Ni has a high vapour pressure of 1.52 x 10-1 Pa at the sintering temperature of 1673 K [21]. Figure 4 shows the result of a simple simulation experiment which was conducted in order to verify the possible transport of nickel through the vapour phase. A couple of Ni-coated and non-coated W wires were positioned facing the direction of the gas flow. The non-coated W wire which was separated from the Ni-coated one by a distance of 220/~m was fully recrystallized, while the recrystallization in noncoated wires which were separated at distances of more than 500/zm occurred only in the outer surface layers. This phenomenon can be easily understood in the sense that the probability with which Ni vapour condenses on pure W wire decreases significantly with increasing separation distance. The eccentric ring shape of the recrystallization zone in both non-coated W wires of Fig. 4(b) demonstrates the relation between the separation distance and the Ni vapour transport. This eccentric ring-shaped zone was formed by a superposition of Ni-induced and normal strain-induced recrystallization; the latter is characterized by a concentric ring shape as shown in Fig. 3 (right) and is caused by the deformation strain due to cold drawing. Figure 5 shows a series of microphotographs of W wire models sintered at 1473 K for various times, which consisted of five non-coated W wires and one W wire coated with 0.29 wt.% Ni. The lower Ni content and lower sintering temperature were chosen in order to retard the Ni-induced recrystallization process to a measurable rate. As shown in Fig. 5(a), Ni-coated W wire no. 4, which was characterized originally by a fibrous grain structure, was recrystallized in the surface
(a) (b) Fig. 4. Ni-induced recrystallizationof pure Wwire (right) separated from Ni coated wire (left). The arrow indicates the direction of gas flow. Separation distance is (a) 220 /zm and (b) 500 /xm (1673 K in H~ atmosphere for 30 min).
132
I.-H. Moon et aL / Ni-enhanced grain growth in W wire
5oo#m ii~iiii
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
sintering time as shown in the micrographs of Figs. 5(c)-5(f). In Fig. 5(d) the front is no longer a simple arc but rather a curved line in the form of the letter "W". The recrystallization seems to progress faster in the area of a surface layer near the contact neck because of the rapid supply of Ni by surface diffusion. Thus the wavy form of the front is due to a superposition of the propagating arc front with the narrow front formed along the surface layer. However, this wavy recrystallization front changes continuously with sintering time, finally forming a negative arc as shown in Fig. 5(0. This change in the shape of the recrystallization front seems to result from the competition between surface diffusion and grain boundary diffusion of Ni atoms as well as from the change in microstructure during sintering, as will be discussed in the following section. After sintering for 16 h, even W wire no. 1 was subjected to recrystallization in a surface zone of measurable thickness as shown in Fig. 5(g). This recrystallization may be attributed to normal stress-induced recrystallization rather than to the effect of Ni, as implied by Fig. 3 and Fig. 4(b). Figure 6 shows an SEM fractograph and EDS analysis of the Ni concentration along the diameter on a fracture surface in the Ni-coated W wire shown in Fig. 5(a). As shown in Fig. 6(a), the fracture surface is divided into two distinguishable regions marked A and B; A is the recrystallized region. These two regions were also confirmed by EDS analysis of the Ni concentration in Fig. 6(b). The Ni concentration at the recrystallization front was estimated approximately by interpolating the Ni concentration curve at this boundary. It is about
Fig. 5. Micrographs of 0.29 wt.% Ni-coated W wire sintered at 1473 K for (a) 1 rain, (b) 3 rain, (c) 15 min, (d) 60 min, (e) 4 h, (f) 8 h, (g) 16 h and (h) 32 h. (a)
zone to a depth of about one-half of the radius, and the recrystallization has progressed also in the area of the contact neck between the Ni-coated and non-coated W wires even after a sintering time of only 1 min. The propagating distance of the recrystallization front from the Ni source increased with the sintering time. In the initial stage of sintering the recrystallization front in the non-coated W wires formed an arc line whose centre was in the contact neck between the non-coated and Ni-coated wires as shown in Fig. 5(b). However, the shape of this front changed slowly with increasing
o.s ~ o~ .~ aa ~, o~ front 0.1
(b)
•
20
40
~o
8o-"
100
Distance (ran)
Fig. 6. (a) Fractograph of Ni-coated W wire sintered at 1473 K for 1 min. (b) Ni concentration as a function of radial distance.
133
L-H. Moon et al. / Ni-enhanced grain growth in W wire
100 ppm, which is within the range (40-300 ppm) reported by other authors [22, 23]. Figure 7 shows a part of the microstructure given in Fig. 5(e) but at higher magnification. This microstructure deserves attention: an abnormal grain growth has occurred in the centre part of the wire and the grains are aligned perpendicular to the recrystallization front. This mode of grain growth seems to be characteristically related to the effect of Ni and to the shape of the recrystallization front developed during the sintering process.
4. Discussion
4.1. Effect of nickel on W grain growth and on the microstructure As described in the previous section, the size and shape of the W grains in the recrystallized area are found to depend on the amount of Ni available as well as on the route of Ni transport, i.e. on the distance from the Ni source and on the location of the W grain considered. Therefore the presence of Ni can influence the kinetics of grain growth, which is generally described in the form D =kt 1/", where D is the average grain diameter, t is time, k is a temperature-dependent constant and n is the growth exponent. The exponent n is khown to have a value of more than 2 (average about 2.5) for pure materials [24]. For a composite structure like the present W-Ni system [25], similarly to the Ostwald ripening process according to the Lifshitz-Slyozov-Wagner theory [26], the value of n is 2 if the kinetics of grain growth is controlled by an interface reaction and n = 3 for the case in which the kinetics is controlled by a diffusion process in the interlayer phase. The dependence of grain growth on sintering time was determined by measuring the grain size in the
whole cross-sectional area of the Ni-coated wire (no. 4) as well as near the contact area of wire no. 5 as sketched in Fig. 8(a). A logarithmic plot of this relationship is shown in Fig. 8(b). The relation between grain size and sintering time is represented by a straight line with a slope of approximately ~. The measured growth exponent of n = 3 indicates that the grain growth kinetics in the present system is controlled by a diffusion process in the Ni interlayer phase. However, care should be taken in discussing the role of the Ni interlayer in W grain growth, because nickel is not in its equilibrium state but in a dynamic state due to the geometric characteristics of the present model system. As discussed in previous work of the present authors' group [27], the grain growth mechanism in the W-Ni system depends both on the initial W grain size and on the amount of nickel. The dependence of W grain growth on the amount of Ni is shown once again in Fig. 9, where the mean grain size is plotted for the
(a) 100:
E ::L
v
.N_ t--
10
(.9 t-¢G
~
~
Q
1/3 J ~i No4 m No5 i
1
10
....
,,,,,
100
. . . . . . . . . . . . .
1000
,,,,
10000
Time (min)
(b)
Fig. 8. (a) The part of the specimen (shaded area) where grain size measurement was conducted. (b) Logarithmic plot of the relationship between mean grain size and sintering time. 2018"
.~ Ni contact position
Fig. 7. Microstructure of wire no. 3 showing the abnormally large grains near the centre and the array of these grains perpendicular to the recrystallization front.
12-
D~ IO-
(b)
A Measured
a Position
6
Fig. 9. Mean grain size at various positions of wire no. 5 sintered at 1473 K for 32 h.
134
1.-H. Moon et aL / Ni-enhanced grain growth in 14I wire
different sites in wire no. 5 after sintering for 32 h. These sites are positioned at a fixed distance from the Ni source, i.e. the contact point with the Ni-coated W wire (no. 4) shown in Fig. 9(a). As shown in Fig. 9(b), the mean grain size at site S close to the contact area, from which Ni is supplied to the other places, is larger than at the other sites and the grain size decreases with increasing distance from the Ni source in the order from A to C. A grain size of 10/~m was obtained at site S after only 6 h of sintering, while 32 h (effective time 22 h) were required for the same grain size at site C. Such a time lag for grain growth at site C compared with site S can be attributed to the difference in Ni concentration at the two sites. In addition to the movement of the recrystallization front, a peculiar microstructure was observed in the grain growth zone just behind the recrystallization front as shown in Fig. 7. These abnormal grains were characterized by a higher aspect ratio and by their directionality; they have an aspect ratio of about 2 and are almost aligned in parallel to the Ni transport direction, i.e. in a direction perpendicular to the recrystallization front, after sintering for 4 h. Figure 10 shows quantitative data on the directionality of the abnormal grains obtained from wire no. 5 after sintering for 16 h (Fig. 10(a)) and 32 h (Fig. 10(b)). In this graph the abscissa is the angle between the longer axis of the grains and the Ni transport direction, i.e. the direction vertical to the recrystallization front. This deviation angle is divided into 22.5 ° intervals. The ordinates represent the normalized frequency of pertinent grains (left axis) and their normalized cumulative area (right axis). As shown in Fig. 10(a), the grains whose directions were not strongly different from the propagation direction of the recrystallization front (i.e. deviation angles between 22.5 ° and -22.5 °) accounted for a high proportion of about 60% of the total even after sintering for 16 h. However, after sintering for 32 h, the recrystallized grains have lost their directionality as shown in Fig. 10(b). The grains are equiaxed, with no preferred direction. The finding that the directionality of grain growth is related to the directionality of the Ni flux may manifest the role of nickel in the recrystallization and grain growth of W wire. However, a detailed explanation of the relation between the Ni flux and the directionality of recrystallized grains must await more detailed experimental study. 4.2. Estimation of apparent diffusivity of Ni in W The apparent volume diffusivity of nickel in the W model specimens can be estimated by assuming that the Ni concentration in the recrystallization front is constant, as found in the previous subsection, and by analysing the movement of the recrystallization front
6o I
/
~60
[m,roquonc, ==.re.
1/ .I50 --
5° 1......................................................................
'° 1................................................................................................................................................................................ l,o= ,r a 0
30
........................................................................................................................................................................
20 ............................................................................................................................................... 20 :~ a
1
io
z
Z -90
-45
0 45 90 -22.5 22.5 67.5 Angle (degree)
-67.5 (a) 60~
o
[60
--0~!50.......................................................................................................................................................................... ! o~o50 A
!
P
IJ..
5
.................................................................................................................................................................. 30 2o ............................................................................... i ................................................................................ 2o
:~ 1 ................L - ~ " ' L " " m " l d " l " ' ~ ' ~ -90
,
,
-45
,
,
,
,
.................100 Z ,
T
0 45 90 -22.5 22.5 67.5 Angle (degree)
-67.5 (b)
Fig. 10. Bar graphs showing the arrangement of grains grown near the centre of wire no. 5 with respect to the direction of recrystallization front movement, sintered at 1873 K for (a) 16 h and (b) 32 h.
as a function of sintering time. The analysis of the diffusion coefficient was carried out on wire no. 4. The equation for diffusion in a long circular cylinder with a constant surface concentration was used for the evaluation of Ni diffusivity in wire no. 4 [28]. The boundary conditions are atr=a
C=Co
C=0
for t > 0
at 0 < r < a
for t = 0
in a cylinder of radius a (the symbols have the commonly used meanings). The corresponding solution useful for short times is C
a 1/2
Co
r 1/2 e r f c ( ~ )
+ +
a -r
(a -r)(Dta) 1;2 . a -r 4ar3/2 lerfc(~)
(9a 2 - 7r 2 - 2ar)Dt 32a3/2rs/2
i%rfc ( 2~ ( D t ) )
(1)
This solution is also valid for the Ni-coated W wire for the initial state of sintering, where r/a is not small. Since C/Co can be assumed to be constant (10 -4 ) at
L-H. M o o n et aL / Ni-enhanced grain growth in W wire
the recrystallization front under the present experimental conditions, one can calculate the diffusivity from eqn. (1) by inserting the measured values of r and t, i.e. the measured depth of the recrystallized front, x, and sintering time t as given in Table 3. The penetration depth of Ni, represented as the width of the recrystallized shell, was determined by averaging measurements at several different points. In this measurement a geometrical correction was applied to accommodate the difference between the real circular cross-sectional area of W wire and its metallographically observed elliptical area. As described previously, the effective heat treatment time during heating and cooling was included in the sintering time for the calculation of diffusivity. The Ni concentration at the recrystallization front was taken as 100 ppm in accordance with the experimental finding. The apparent diffusivity was calculated by a trial-and-error method using a computer programme. The apparent diffusion coefficient of nickel from the surface to the centre of the wire was calculated to be 1.7;< 10 -9 cm 2 s -1 at 1473 K in eqn. (1). This apparent diffusivity is an overall result of various types of diffusion: volume diffusion, grain boundary diffusion and possibly also other types of diffusion through high diffusivity paths such as dislocation and cold-working texture; these high diffusivity paths are expected to contribute sigrlificantly to the apparent diffusivity [22]. This apparent diffusivity value estimated from the present grain growth kinetics is somewhat higher than the value measured by Friedmann and Brett [22]. They reported a value of D < 1 0 - n cm 2 s -a for Ni volume diffusion in W wire during the recrystallization process. However, Kozma et al. [29] estimated a D value of 10-8-10 -11 cm 2 s -a for Ni diffusivity in grain boundaries of recrystallized W. Therefore the high apparent diffusivity obtained in the present experiment is likely to originate from a dominant contribution of grain boundary diffusion. The surface diffusivity of nickel on tungsten wire was also roughly estimated with the aid of a simple analysis method similar to the model studied by Shewmon [30]. As shown in Fig. 5, the recrystallization front of a non-
135
coated W wire was characterized by a wavy form, with the recrystallization front propagating farther near the surface layer, as represented schematically in Fig. 11(a). This diffusion couple of Ni-coated and non-coated W wires in line contact was simplified by an Ni line source on a flat surface as shown in Fig. ll(b). The Ni line source is 2b in width and the high diffusivity surface layer of W wire is of thickness & For short times the diffusion distance on the surface is not far from the source and thus the curved surface on the cylinder may be assumed to be fiat for the sake of simplicity. The present system is equivalent to the model proposed by Shewmon, except that a line source is assumed instead of a point source, so that the differential equation describing the concentration in the surface layer (Cs) can be written as
O2Cs
0C~ _D~ ~x2
J(x, t)
~t
(2)
6
where J(x, t) is the flux from the surface into the volume at any point. The surface diffusion coefficient Ds is assumed to be the same in all directions on the surface. With the same assumptions as proposed by Shewmon and taking into consideration the linear shape of the Ni source, which enables one to use the cartesian coordinate system, the Ni concentration can be expressed in the present case as follows if the volume diffusion flux directly from the source can be ignored:
C(x, z, t)=Co e x p [ - a ( x - b ) ] erfc/
z
\2(D J )
112~
]
(3)
Nicoatedlayer
No Rec
a)
all" ed
zone
No.5-W T A B L E 3. Propagation distance of recrystallization front from initial Ni source as a function of sintering time Time (s)
Propagation depth in wire no. 4 (/*m)
surface
77.7 153 213 Not available
Distance from contact point to recrystallization front on surface of wire no. 5
Not available 168 285 412
2b
~J~--
Ni-source
I x
(~.m) 1116 2292 3468 5124
--~[
z
(b) Fig. 11. Modelling of two contacting W wires for the estimation of surface diffusion: (a) diffusion couple of two contacting wires, i.e. wires no. 4 and no. 5; (b) simplified model used for calculating surface diffusivity.
136
L-H. Moon et al. / Ni-enhanced grain growth in W wire
where a2 =
By
D~8( TrDvt)l/2
(4)
where Dv is the volume diffusion coefficient. The concentration profile in the surface layer was not determined in the present experiment, but the Ni concentration at the recrystallization front in the surface layer might be assumed to be about 100 ppm as in the inner part of the specimen. Then one can estimate a and D, using appropriate argument values in eqns. (3) and (4) respectively. In the present study the following data were used for the estimation of the surface diffusivity. The effective thickness of the high diffusivity surface layer is assumed to be about the order of the effective grain boundary width, i.e. 8= 1 nm [31]. The calculated apparent volume diffusivity of 1.7 × 1 0 - 9 c m 2 s-~ was used instead of Dv because of the scarcity of data in the literature. The penetration depth z and the concentration of Ni in the W volume were taken as those of the recrystallization front, because the front was characterized by a fixed Ni concentration as described above; z was about 20 /zm after 20 min of sintering. The surface diffusivity of Ni on W, D~, is then calculated to be about 1.9×10 -5 cm s -~ at 1473 K. This value seems to be too high for surface diffusivity. Even though there are hardly any diffusion data for the W-Ni system in the literature, the data of Geguzin et al. [20], who considered Ni adatoms spreading over a W single crystal at temperatures between 1173 and 1423 K, are useful for comparison. According to their analysis, the diffusivity of Ni adatoms on the vicinal face (111) of W was 1.5×10 -5 cm 2 s -1 at 1473 K, in good agreement with our calculated value. The other data available from the literature are those reported by Flahive and Graham [32] on the diffusivity of single Ni adatoms on W ( l l l ) , giving a value of about 1 × 10 - 9 cm2 s-1. However, these data were obtained at much lower temperatures, between 375 and 425 K, and therefore cannot be compared directly with ours.
5. Conclusions The effect of nickel on the activated sintering of tungsten as well as on W grain growth was demonstrated with a W wire bundle model. As expected, Ni added to W caused low temperature recrystallization as well as low temperature sintering in the W wire bundle. The progress of the solid state reactions depends primarily on the amount of nickel available and its physical state. Nickel originally located in a restricted area on the W surface was found to be transferred very rapidly to
other sites of W wires by grain boundary as well as surface spreading. The surface diffusivity of Ni on W was estimated to be about 1.9×10 -5 cm2 s -1, while the apparent diffusivity of Ni in W was calculated to be 1.7×10 -9 c m 2 s -1.
Acknowledgments The authors gratefully acknowledge the financial support of KOSEF and ERC for Interface Science and Technology of Materials.
References 1 J. Vacek, Planseeber. Pulvermet, 7 (1959) 6. 2 T. Petrasek and J.W. Weeton, Trans. Metall. Soc. AIME, 230 (1964) 977. 3 T. Motelbano, J. Brett, L. Castleman and L. Seigle, Trans. Metall. Soc. AIME, 242 (1968) 1973. 4 Y. S. Kwon, J. S. Lee and I. H. Moon, Mod. Develop. Powder Metall., 14 (1980) 147. 5 J. H. Brophy, L. A. Shepard and J. Wulff, in W. Leszynski (ed.), Powder Metallurgy, Interscience, New York, 1961, p. 113. 6 G. V. Samsonov and V. I. Yakovlev, Soy. Powder Metall. Met. Ceram., 6 (1967) 606. 7 G. H. Gessinger and H. F. Fischmeister, Z Less-Common Met., 27 (1972) 129. 8 R. M. German and Z. A. Munir, Rev. Powder MetalL Phys. Ceram., 2 (1982) 9. 9 R. M. German, Sc£ Sinter., 15 (1983) 27. 10 W. Schatt, W. A. Kaysser, S. Rolle, A. Sibilla, E. Friedrich and G. Petzow, Powder Metall. Int., 19 (1987) (1) 14, (2) 37. 11 W. Schintlmeister and K. Richter, Planseeber. Pulvermet., 18 (1970) 3. 12 J. S. Lee, K. Klockgeter and Chr. Herzig, Z Phys. (Paris), Colloq CL 51 (1990) 569. 13 I. H. Moon, J. S. Kim and Y. L. Kim, J. Less-Common Met.,
102 (1984) 219. 14 I. H. Moon and Y. L. Kim, Scr. Metall., 20 (1986) 377. 15 I. H. Moon, Y. H. Suh and Y. L. Kim, Scr. Metall., 2l (1987) 749. 16 I. H. Moon and Y. S. Kwon, Scr. Metall., 13 (1979) 33. 17 T. G. Nieh, Scr. Metall., 18 (1984) 1279. 18 A N S I / A S T M , Annual Book of A S T M Standards, Part II, El1280, American Society for Testing and Materials, Philadelphia, PA, 1980, p. 186. 19 K. Vieregge and D. Gupta, in A. Crowson and E. S. Chen (eds.), Tungsten and Tungsten Aloys - Recent Advances, TMS, Warrendale, PA, 1991, p. 231. 20 Y. Y. Geguzin, Y. S. Kaganovsky and V. P. Strelkov, F/z. Met. Metall., 39 (1975) 992 (Engl. transl.). 21 I. Barin, Thermochemical Data of Pure Substances, VCH, Weinheim, 1989, p. 1052. 22 S. Friedmann and J. Brett, Trans. Metall. Soc. AIME, 242 (1968) 2121. 23 T. Itagaki, T. Kimura, T. Kobayashi and T. Arai, J. Iron Steel Inst. Jpn., 75 (1989) 1486. 24 M. P. Anderson, D. J. Srolovitz, G. S. Grest and P. S. Sahni, Acta Metall., 32 (1984) 783.
L-H. Moon et al. / Ni-enhanced grain growth in W wire 25 Y. Y. Geguzin and V. I. Kibets, Fiz. Met. MetaU., 36 (1973) 1043 (Engl. transl.). 26 J. W. Martin and R. D. Doherty, Stability of Microstructure in Metallic Systems, Cambridge University Press, Cambridge, 1976, p. 173. 27 I. H. Moon, S. T. Oh and Y. L. Kim, Z Less-Common Met., 153 (1989) 275. 28 J. Crank, The Mathematics of Diffusion, Clarendon, Oxford, • 2nd edn., 1979, p. 73.
137
29 L. Kozma, E. T. Henig and R. Warren, in W. A. Kaysser and W. J. Huppmann (eds.), Horizons of Powder Metallurgy, Verlag Schmid., Freiburg, 1986, p. 1181. 30 P. G. Shewmon, J. Appl. Phys., 34 (1963) 755. 31 I. Kaur and W. Gust, Fundamentals of Grain and Interphase Boundary Diffusion, Ziegler, Stuttgart, 1988, p. 275. 32 P. G. Flahive and W. R. Graham, J. Vac. Sci. Technol., 15 (1978) 472.
129
Nickel-enhanced grain growth in tungsten wire In-Hyung Moon, Ki-Youl Kim, Sung-Tag Oh and Myung-Jin Suk Department of Materials Engineering, Hanyang University, Seoul 133-791 (South Korea) (Received January 18, 1993; in final form March 10, 1993)
Abstract The effect of Ni additive on recrystallization and grain growth in W wires has been investigated in order to explain the role of nickel in the activated sintering of tungsten, because the two phenomena are comparable with each other, being principally diffusion controlled and greatly influenced by the presence of Ni. The experiment was carried out in a bundle model of W wires in which the initial state of nickel could be appropriately controlled by arranging Ni-coated W wires together with non-coated wires. The recrystallization and grain growth processes were observed and analysed on the basis of the geometrical relation between the Ni source and the W wires. The development of the recrystallization front depends on the Ni diffusion path and rate. Nickel diffuses fast into the W wires through high diffusivity paths such as the surface and grain boundaries, inducing recrystallization at relatively low temperature. The apparent diffusivity of Ni in W wire, estimated by measuring the migration rate of the recrystallization front, is about 1.7 × 1 0 - 9 c m 2 S - 1 , while the surface diffusivity of Ni on W is estimated to be about 10 -5 cm 2 s-~. The role of Ni in W is further discussed.
1. Introduction
It is well known that nickel enhances the sinterability of tungsten powder compact and reduces the recrystallization temperature when added to cold-worked W metal [1-3]. This effect of nickel on the sinterability of W powder and the recrystallization of W metal suggests implicitly that the role of nickel may be similar in the sintering process of metallic powders and in the recrystallization process, because both processes are usually accepted to be diffusion controlled. Thus the role of the nickel activator in the initial stage of activated sintering might be partly explained by understanding the initial stage of Ni-induced recrystallization, which is more accessible to observation and analysis. Conversely, the role of nickel in the enhanced recrystallization of W metal might also be explained by extrapolation of the sintering data obtained from analysis of the intermediate stage of Ni-activated sintering, where the grain growth of sintered W powder compact was observed simultaneously with densification [4]. Since Vacek's discovery of the phenomenon of Niactivated sintering, many mechanisms have been suggested for it [5-10]. Several of these mechanisms are based on the possible role of nickel as a carrier phase for tungsten atom transport, i.e. the Ni-rich phase or the Ni impurity interracial layer located in W grain boundaries and on the W surface may provide a high diffusivity path for W diffusion [7, 8]. Since an en0925-8388/93/$6.00
hancement of W self-diffusion has been observed in Ni-doped W grain boundaries [11, 12], the activated sintering mechanism related to enhanced diffusivity still seems to be more plausible than the others, even though this mechanism has some difficulty in being universally accepted because of its simplification of the roles of Ni activator and W powder. According to recent work of the present authors' group, the sinterability of Ni-doped W powder compact depends not only on the physical state of the Ni activator, i.e. its geometrical relation to W (its amount, size and location), but also on its chemical state [13-15]. Ni added to W was sometimes found in visible amounts of an Ni second phase at grain boundary junctions [16], but also sometimes found as an impurity layer of a few atomic diameters at W grain boundaries, which can only be detected by modern analytical methods [17]. The presence of nickel at W grain boundaries was reported to increase the W self-diffusivity in grain boundaries [11, 12] and this enhanced W diffusivity is thought to be responsible for the activated sintering and reduced recrystallization temperature in W. In the present work, therefore, a model experiment was carried out on bundles of W wires in order to gain insight to the behaviour of Ni during the initial stage of activated sintering and recrystallization of W wires. The W wire bundle model, in which the initial location of nickel could be appropriately controlled by arranging Ni-coated W wires with non-coated wires, provides
© 1993- Elsevier Sequoia. All rights reserved
130
I.-H. Moon et aL / Ni-enhanced grain growth in W wire
geometrical simplicity for investigating both Ni-activated sintering and Ni-induced recrystallization simultaneously.
2. Experimental details The tungsten wire used for the present experiment was an undoped grade of 0.5 mm diameter with a minimum purity of 99.98% supplied by Johnson-Matthey. The impurities present in the wire are given in Table 1. The wire was first annealed in a hydrogen atmosphere at 1123 K for 1 h to reduce surface oxides. Nickel in an amount equivalent to 0.29 or 0.43 wt.% of tungsten was coated on the W wire surface by a chemical vapour deposition (CVD) method using an Ni tetracarbonyl. The amount of nickel coated was controlled by varying the deposition time at a temperature of 423 K. The chemical analysis of the deposited Ni film is given in Table 2. Only the amount of nickel in the coated layer was taken into consideration for analysis and calculation in the present study. Figure 1 is a scanning electron microscopy (SEM) image showing the uniformly coated nickel layer of 2-3/zm thickness. A cross-sectional view of the sintering model system is shown schematically in Fig. 2. Specimens were prepared in the following way. Seven W wires (one coated and six non-coated) initially in a hexagonal array were twisted into the form of a wire rope in such a way that the wires contacted each other completely. Afterwards, the central wire was discarded so as to leave the remaining six wires arranged in a ring pattern. The cross-sectional shape of each wire in the wire bundle was not circular but elliptical, as seen in subsequent microphotographs, because the wires do not intersect perpendicular to their axes. Each W wire was numbered according to its position, no. 4 designating the Nicoated W wire. TABLE 1. Impurities contained in the W wire used Element
Concentration (maximum) (ppm)
Element
Concentration (maximum) (ppm)
Aluminium Cobalt Molybdenum Oxygen Lead Silicon
> 10 5 40 10 >10 > 10
Nickel Carbon Phosphorus Chromium Iron Potassium
5 15 20 > 10 20 >5
(10) (30) (300) (30) (10) (30)
(20) (30) (50) (10) (50) (10)
C
O
0.48
2.29
Fig. 2. Schematic cross-section of W wire model specimen.
The W wire bundles were sintered in a hydrogen atmosphere for various times at 1473 and 1673 K for specimens with 0.29 and 0.43 wt.% Ni. The heating and cooling times were included in the sintering time according to their thermal effects as evaluated on the basis of diffusion data. Their contribution was determined to be 17.6 min in the present experiment. The grain size of the specimen was determined by the linear intercept method [18] using an image analyser (Leco 2001). The distance over which the recrystallization front had moved was measured on microphotographs. The microstructural development of the sintering model system was continuously observed by optical microscopy and SEM and partly further analysed by energy-dispersive spectroscopy (EDS) attached to the scanning electron microscope.
3. Experimental results
TABLE 2. Concentrations of chemical species contained in the deposited Ni film Element Concentration (wt.%)
Fig. 1. Scanning electron micrograph of Ni-coated W wire by CVD method.
Ni 97.23
Figure 3 shows microphotographs of the sintered W model specimen which was initially composed of a 0.43 wt.% Ni-coated W wire and five pure W wires, and wires of pure W as reference. These specimens were annealed at 1673 K for 5 min (Fig. 3(a)) and 30 min (Fig. 3(b)). As seen in these photographs, the microstructure of all W wires in model specimens changed
L-H, Moon et al. / Ni-enhanced grain growth in W wire
(a)
(b) Fig. 3. Micrographs of 0.43 wt.% Ni-coated W wire (left) and pure W wire (right) sintered at 16"13 K for (a) 5 min and (b) 30 min.
drastically from the original fibrous drawn structure to the fully recrystallized grain structure after only 5 min of sintering, and the W grains were found to coarsen to an average size of about 50 tzm after 30 min of sintering. Recrystallization and grain growth progressed rapidly in all parts of the model specimen, not only in the Ni-coated W wire but also in all pure W wires. In contrast, the recrystallization in the reference was confined to the surface layer of the W wires, showing a distinct concentric circular boundary between the recrystallized zone and the non-recrystallized material, and the depth of the recrystallized surface layer increased with increasing sintering time. There was no measurable grain growth in the recrystallized zone. Thus it was confirmed once again that the presence of nickel in W wires accelerates recrystallization and grain growth in the severely deformed grain structure of cold-drawn W wires. The fact that the Ni-induced recrystallization progressed so rapidly even in non-coated W wire no. 1 located at the farthest distance from the Ni source implies that Ni has already been transferred from its original source in the coating layer on W wire no. 4 to the initially non-coated W wires. The rapid transfer of nickel atoms from the surface of coated W wire no. 4 to the non-coated W wires seems to be possible only by Ni diffusion through a high diffusivity path, either on the W surface or along grain boundaries, because Ni volume diffusion in W is not so effective at this temperature [19]. In fact, nickel is known to spread
131
very fast on W surfaces at the temperature of the present experiment [20]. In addition to the fast surface diffusion, Ni transport by evaporation and condensation through the hydrogen gas flow seems to contribute also to the rapid migration of nickel from the coated to non-coated W wires in the present system, because Ni has a high vapour pressure of 1.52 x 10-1 Pa at the sintering temperature of 1673 K [21]. Figure 4 shows the result of a simple simulation experiment which was conducted in order to verify the possible transport of nickel through the vapour phase. A couple of Ni-coated and non-coated W wires were positioned facing the direction of the gas flow. The non-coated W wire which was separated from the Ni-coated one by a distance of 220/~m was fully recrystallized, while the recrystallization in noncoated wires which were separated at distances of more than 500/zm occurred only in the outer surface layers. This phenomenon can be easily understood in the sense that the probability with which Ni vapour condenses on pure W wire decreases significantly with increasing separation distance. The eccentric ring shape of the recrystallization zone in both non-coated W wires of Fig. 4(b) demonstrates the relation between the separation distance and the Ni vapour transport. This eccentric ring-shaped zone was formed by a superposition of Ni-induced and normal strain-induced recrystallization; the latter is characterized by a concentric ring shape as shown in Fig. 3 (right) and is caused by the deformation strain due to cold drawing. Figure 5 shows a series of microphotographs of W wire models sintered at 1473 K for various times, which consisted of five non-coated W wires and one W wire coated with 0.29 wt.% Ni. The lower Ni content and lower sintering temperature were chosen in order to retard the Ni-induced recrystallization process to a measurable rate. As shown in Fig. 5(a), Ni-coated W wire no. 4, which was characterized originally by a fibrous grain structure, was recrystallized in the surface
(a) (b) Fig. 4. Ni-induced recrystallizationof pure Wwire (right) separated from Ni coated wire (left). The arrow indicates the direction of gas flow. Separation distance is (a) 220 /zm and (b) 500 /xm (1673 K in H~ atmosphere for 30 min).
132
I.-H. Moon et aL / Ni-enhanced grain growth in W wire
5oo#m ii~iiii
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
sintering time as shown in the micrographs of Figs. 5(c)-5(f). In Fig. 5(d) the front is no longer a simple arc but rather a curved line in the form of the letter "W". The recrystallization seems to progress faster in the area of a surface layer near the contact neck because of the rapid supply of Ni by surface diffusion. Thus the wavy form of the front is due to a superposition of the propagating arc front with the narrow front formed along the surface layer. However, this wavy recrystallization front changes continuously with sintering time, finally forming a negative arc as shown in Fig. 5(0. This change in the shape of the recrystallization front seems to result from the competition between surface diffusion and grain boundary diffusion of Ni atoms as well as from the change in microstructure during sintering, as will be discussed in the following section. After sintering for 16 h, even W wire no. 1 was subjected to recrystallization in a surface zone of measurable thickness as shown in Fig. 5(g). This recrystallization may be attributed to normal stress-induced recrystallization rather than to the effect of Ni, as implied by Fig. 3 and Fig. 4(b). Figure 6 shows an SEM fractograph and EDS analysis of the Ni concentration along the diameter on a fracture surface in the Ni-coated W wire shown in Fig. 5(a). As shown in Fig. 6(a), the fracture surface is divided into two distinguishable regions marked A and B; A is the recrystallized region. These two regions were also confirmed by EDS analysis of the Ni concentration in Fig. 6(b). The Ni concentration at the recrystallization front was estimated approximately by interpolating the Ni concentration curve at this boundary. It is about
Fig. 5. Micrographs of 0.29 wt.% Ni-coated W wire sintered at 1473 K for (a) 1 rain, (b) 3 rain, (c) 15 min, (d) 60 min, (e) 4 h, (f) 8 h, (g) 16 h and (h) 32 h. (a)
zone to a depth of about one-half of the radius, and the recrystallization has progressed also in the area of the contact neck between the Ni-coated and non-coated W wires even after a sintering time of only 1 min. The propagating distance of the recrystallization front from the Ni source increased with the sintering time. In the initial stage of sintering the recrystallization front in the non-coated W wires formed an arc line whose centre was in the contact neck between the non-coated and Ni-coated wires as shown in Fig. 5(b). However, the shape of this front changed slowly with increasing
o.s ~ o~ .~ aa ~, o~ front 0.1
(b)
•
20
40
~o
8o-"
100
Distance (ran)
Fig. 6. (a) Fractograph of Ni-coated W wire sintered at 1473 K for 1 min. (b) Ni concentration as a function of radial distance.
133
L-H. Moon et al. / Ni-enhanced grain growth in W wire
100 ppm, which is within the range (40-300 ppm) reported by other authors [22, 23]. Figure 7 shows a part of the microstructure given in Fig. 5(e) but at higher magnification. This microstructure deserves attention: an abnormal grain growth has occurred in the centre part of the wire and the grains are aligned perpendicular to the recrystallization front. This mode of grain growth seems to be characteristically related to the effect of Ni and to the shape of the recrystallization front developed during the sintering process.
4. Discussion
4.1. Effect of nickel on W grain growth and on the microstructure As described in the previous section, the size and shape of the W grains in the recrystallized area are found to depend on the amount of Ni available as well as on the route of Ni transport, i.e. on the distance from the Ni source and on the location of the W grain considered. Therefore the presence of Ni can influence the kinetics of grain growth, which is generally described in the form D =kt 1/", where D is the average grain diameter, t is time, k is a temperature-dependent constant and n is the growth exponent. The exponent n is khown to have a value of more than 2 (average about 2.5) for pure materials [24]. For a composite structure like the present W-Ni system [25], similarly to the Ostwald ripening process according to the Lifshitz-Slyozov-Wagner theory [26], the value of n is 2 if the kinetics of grain growth is controlled by an interface reaction and n = 3 for the case in which the kinetics is controlled by a diffusion process in the interlayer phase. The dependence of grain growth on sintering time was determined by measuring the grain size in the
whole cross-sectional area of the Ni-coated wire (no. 4) as well as near the contact area of wire no. 5 as sketched in Fig. 8(a). A logarithmic plot of this relationship is shown in Fig. 8(b). The relation between grain size and sintering time is represented by a straight line with a slope of approximately ~. The measured growth exponent of n = 3 indicates that the grain growth kinetics in the present system is controlled by a diffusion process in the Ni interlayer phase. However, care should be taken in discussing the role of the Ni interlayer in W grain growth, because nickel is not in its equilibrium state but in a dynamic state due to the geometric characteristics of the present model system. As discussed in previous work of the present authors' group [27], the grain growth mechanism in the W-Ni system depends both on the initial W grain size and on the amount of nickel. The dependence of W grain growth on the amount of Ni is shown once again in Fig. 9, where the mean grain size is plotted for the
(a) 100:
E ::L
v
.N_ t--
10
(.9 t-¢G
~
~
Q
1/3 J ~i No4 m No5 i
1
10
....
,,,,,
100
. . . . . . . . . . . . .
1000
,,,,
10000
Time (min)
(b)
Fig. 8. (a) The part of the specimen (shaded area) where grain size measurement was conducted. (b) Logarithmic plot of the relationship between mean grain size and sintering time. 2018"
.~ Ni contact position
Fig. 7. Microstructure of wire no. 3 showing the abnormally large grains near the centre and the array of these grains perpendicular to the recrystallization front.
12-
D~ IO-
(b)
A Measured
a Position
6
Fig. 9. Mean grain size at various positions of wire no. 5 sintered at 1473 K for 32 h.
134
1.-H. Moon et aL / Ni-enhanced grain growth in 14I wire
different sites in wire no. 5 after sintering for 32 h. These sites are positioned at a fixed distance from the Ni source, i.e. the contact point with the Ni-coated W wire (no. 4) shown in Fig. 9(a). As shown in Fig. 9(b), the mean grain size at site S close to the contact area, from which Ni is supplied to the other places, is larger than at the other sites and the grain size decreases with increasing distance from the Ni source in the order from A to C. A grain size of 10/~m was obtained at site S after only 6 h of sintering, while 32 h (effective time 22 h) were required for the same grain size at site C. Such a time lag for grain growth at site C compared with site S can be attributed to the difference in Ni concentration at the two sites. In addition to the movement of the recrystallization front, a peculiar microstructure was observed in the grain growth zone just behind the recrystallization front as shown in Fig. 7. These abnormal grains were characterized by a higher aspect ratio and by their directionality; they have an aspect ratio of about 2 and are almost aligned in parallel to the Ni transport direction, i.e. in a direction perpendicular to the recrystallization front, after sintering for 4 h. Figure 10 shows quantitative data on the directionality of the abnormal grains obtained from wire no. 5 after sintering for 16 h (Fig. 10(a)) and 32 h (Fig. 10(b)). In this graph the abscissa is the angle between the longer axis of the grains and the Ni transport direction, i.e. the direction vertical to the recrystallization front. This deviation angle is divided into 22.5 ° intervals. The ordinates represent the normalized frequency of pertinent grains (left axis) and their normalized cumulative area (right axis). As shown in Fig. 10(a), the grains whose directions were not strongly different from the propagation direction of the recrystallization front (i.e. deviation angles between 22.5 ° and -22.5 °) accounted for a high proportion of about 60% of the total even after sintering for 16 h. However, after sintering for 32 h, the recrystallized grains have lost their directionality as shown in Fig. 10(b). The grains are equiaxed, with no preferred direction. The finding that the directionality of grain growth is related to the directionality of the Ni flux may manifest the role of nickel in the recrystallization and grain growth of W wire. However, a detailed explanation of the relation between the Ni flux and the directionality of recrystallized grains must await more detailed experimental study. 4.2. Estimation of apparent diffusivity of Ni in W The apparent volume diffusivity of nickel in the W model specimens can be estimated by assuming that the Ni concentration in the recrystallization front is constant, as found in the previous subsection, and by analysing the movement of the recrystallization front
6o I
/
~60
[m,roquonc, ==.re.
1/ .I50 --
5° 1......................................................................
'° 1................................................................................................................................................................................ l,o= ,r a 0
30
........................................................................................................................................................................
20 ............................................................................................................................................... 20 :~ a
1
io
z
Z -90
-45
0 45 90 -22.5 22.5 67.5 Angle (degree)
-67.5 (a) 60~
o
[60
--0~!50.......................................................................................................................................................................... ! o~o50 A
!
P
IJ..
5
.................................................................................................................................................................. 30 2o ............................................................................... i ................................................................................ 2o
:~ 1 ................L - ~ " ' L " " m " l d " l " ' ~ ' ~ -90
,
,
-45
,
,
,
,
.................100 Z ,
T
0 45 90 -22.5 22.5 67.5 Angle (degree)
-67.5 (b)
Fig. 10. Bar graphs showing the arrangement of grains grown near the centre of wire no. 5 with respect to the direction of recrystallization front movement, sintered at 1873 K for (a) 16 h and (b) 32 h.
as a function of sintering time. The analysis of the diffusion coefficient was carried out on wire no. 4. The equation for diffusion in a long circular cylinder with a constant surface concentration was used for the evaluation of Ni diffusivity in wire no. 4 [28]. The boundary conditions are atr=a
C=Co
C=0
for t > 0
at 0 < r < a
for t = 0
in a cylinder of radius a (the symbols have the commonly used meanings). The corresponding solution useful for short times is C
a 1/2
Co
r 1/2 e r f c ( ~ )
+ +
a -r
(a -r)(Dta) 1;2 . a -r 4ar3/2 lerfc(~)
(9a 2 - 7r 2 - 2ar)Dt 32a3/2rs/2
i%rfc ( 2~ ( D t ) )
(1)
This solution is also valid for the Ni-coated W wire for the initial state of sintering, where r/a is not small. Since C/Co can be assumed to be constant (10 -4 ) at
L-H. M o o n et aL / Ni-enhanced grain growth in W wire
the recrystallization front under the present experimental conditions, one can calculate the diffusivity from eqn. (1) by inserting the measured values of r and t, i.e. the measured depth of the recrystallized front, x, and sintering time t as given in Table 3. The penetration depth of Ni, represented as the width of the recrystallized shell, was determined by averaging measurements at several different points. In this measurement a geometrical correction was applied to accommodate the difference between the real circular cross-sectional area of W wire and its metallographically observed elliptical area. As described previously, the effective heat treatment time during heating and cooling was included in the sintering time for the calculation of diffusivity. The Ni concentration at the recrystallization front was taken as 100 ppm in accordance with the experimental finding. The apparent diffusivity was calculated by a trial-and-error method using a computer programme. The apparent diffusion coefficient of nickel from the surface to the centre of the wire was calculated to be 1.7;< 10 -9 cm 2 s -1 at 1473 K in eqn. (1). This apparent diffusivity is an overall result of various types of diffusion: volume diffusion, grain boundary diffusion and possibly also other types of diffusion through high diffusivity paths such as dislocation and cold-working texture; these high diffusivity paths are expected to contribute sigrlificantly to the apparent diffusivity [22]. This apparent diffusivity value estimated from the present grain growth kinetics is somewhat higher than the value measured by Friedmann and Brett [22]. They reported a value of D < 1 0 - n cm 2 s -a for Ni volume diffusion in W wire during the recrystallization process. However, Kozma et al. [29] estimated a D value of 10-8-10 -11 cm 2 s -a for Ni diffusivity in grain boundaries of recrystallized W. Therefore the high apparent diffusivity obtained in the present experiment is likely to originate from a dominant contribution of grain boundary diffusion. The surface diffusivity of nickel on tungsten wire was also roughly estimated with the aid of a simple analysis method similar to the model studied by Shewmon [30]. As shown in Fig. 5, the recrystallization front of a non-
135
coated W wire was characterized by a wavy form, with the recrystallization front propagating farther near the surface layer, as represented schematically in Fig. 11(a). This diffusion couple of Ni-coated and non-coated W wires in line contact was simplified by an Ni line source on a flat surface as shown in Fig. ll(b). The Ni line source is 2b in width and the high diffusivity surface layer of W wire is of thickness & For short times the diffusion distance on the surface is not far from the source and thus the curved surface on the cylinder may be assumed to be fiat for the sake of simplicity. The present system is equivalent to the model proposed by Shewmon, except that a line source is assumed instead of a point source, so that the differential equation describing the concentration in the surface layer (Cs) can be written as
O2Cs
0C~ _D~ ~x2
J(x, t)
~t
(2)
6
where J(x, t) is the flux from the surface into the volume at any point. The surface diffusion coefficient Ds is assumed to be the same in all directions on the surface. With the same assumptions as proposed by Shewmon and taking into consideration the linear shape of the Ni source, which enables one to use the cartesian coordinate system, the Ni concentration can be expressed in the present case as follows if the volume diffusion flux directly from the source can be ignored:
C(x, z, t)=Co e x p [ - a ( x - b ) ] erfc/
z
\2(D J )
112~
]
(3)
Nicoatedlayer
No Rec
a)
all" ed
zone
No.5-W T A B L E 3. Propagation distance of recrystallization front from initial Ni source as a function of sintering time Time (s)
Propagation depth in wire no. 4 (/*m)
surface
77.7 153 213 Not available
Distance from contact point to recrystallization front on surface of wire no. 5
Not available 168 285 412
2b
~J~--
Ni-source
I x
(~.m) 1116 2292 3468 5124
--~[
z
(b) Fig. 11. Modelling of two contacting W wires for the estimation of surface diffusion: (a) diffusion couple of two contacting wires, i.e. wires no. 4 and no. 5; (b) simplified model used for calculating surface diffusivity.
136
L-H. Moon et al. / Ni-enhanced grain growth in W wire
where a2 =
By
D~8( TrDvt)l/2
(4)
where Dv is the volume diffusion coefficient. The concentration profile in the surface layer was not determined in the present experiment, but the Ni concentration at the recrystallization front in the surface layer might be assumed to be about 100 ppm as in the inner part of the specimen. Then one can estimate a and D, using appropriate argument values in eqns. (3) and (4) respectively. In the present study the following data were used for the estimation of the surface diffusivity. The effective thickness of the high diffusivity surface layer is assumed to be about the order of the effective grain boundary width, i.e. 8= 1 nm [31]. The calculated apparent volume diffusivity of 1.7 × 1 0 - 9 c m 2 s-~ was used instead of Dv because of the scarcity of data in the literature. The penetration depth z and the concentration of Ni in the W volume were taken as those of the recrystallization front, because the front was characterized by a fixed Ni concentration as described above; z was about 20 /zm after 20 min of sintering. The surface diffusivity of Ni on W, D~, is then calculated to be about 1.9×10 -5 cm s -~ at 1473 K. This value seems to be too high for surface diffusivity. Even though there are hardly any diffusion data for the W-Ni system in the literature, the data of Geguzin et al. [20], who considered Ni adatoms spreading over a W single crystal at temperatures between 1173 and 1423 K, are useful for comparison. According to their analysis, the diffusivity of Ni adatoms on the vicinal face (111) of W was 1.5×10 -5 cm 2 s -1 at 1473 K, in good agreement with our calculated value. The other data available from the literature are those reported by Flahive and Graham [32] on the diffusivity of single Ni adatoms on W ( l l l ) , giving a value of about 1 × 10 - 9 cm2 s-1. However, these data were obtained at much lower temperatures, between 375 and 425 K, and therefore cannot be compared directly with ours.
5. Conclusions The effect of nickel on the activated sintering of tungsten as well as on W grain growth was demonstrated with a W wire bundle model. As expected, Ni added to W caused low temperature recrystallization as well as low temperature sintering in the W wire bundle. The progress of the solid state reactions depends primarily on the amount of nickel available and its physical state. Nickel originally located in a restricted area on the W surface was found to be transferred very rapidly to
other sites of W wires by grain boundary as well as surface spreading. The surface diffusivity of Ni on W was estimated to be about 1.9×10 -5 cm2 s -1, while the apparent diffusivity of Ni in W was calculated to be 1.7×10 -9 c m 2 s -1.
Acknowledgments The authors gratefully acknowledge the financial support of KOSEF and ERC for Interface Science and Technology of Materials.
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