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Ni and Ga diffusion in polycrystalline Ni3Ga
Intermetallics 10 (2002) 765–769 www.elsevier.com/locate/intermet
Ni and Ga diffusion in polycrystalline Ni3Ga Jirˇ ı´ Cˇerma´k*, Veˇra Rothova´ Institute of Physics of Materials AS CR, Zizkova 22, CZ-616 62 Brno, Czech Republic Received 25 April 2002; accepted 3 May 2002
Abstract The volume and grain boundary (GB) diffusion of 63Ni and 67Ga radiotracers in polycrystals of Ni3Ga intermetallic was studied in the vicinity of the stoichiometric composition A3B (23.5–28.3 at.% Ga). Both volume and GB diffusivity was investigated in the temperature interval 773–1373 K by the residual activity method. The obtained Ga volume diffusivity increases with increasing Ga concentration xGa; the increasing tendency of Ni volume diffusivity with increasing xGa is pronounced at lower temperatures. GB diffusivity of both Ga and Ni in Ni3Ga are close one to another and—contrary to the diffusion behavior of components in Ni3Al— they do not show any significant dependence on xGa. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: A. Intermetallics, miscellaneous; B. Diffusion
1. Introduction Intermetallic alloys show a series of very promising characteristics [1]. A number of investigations have been done in recent years that were devoted before all to their mechanical behavior. Since some of high-temperature characteristics are controlled by diffusion, it is clear that these materials are also very often a subject of diffusion studies. Due to atomic ordering of the intermetallic alloys, the study of diffusion processes is—besides its technological importance—interesting also from the theoretical viewpoint. Some sophisticated mechanisms have been proposed in recent years [1–4] that can explain diffusion coefficients measured in ordered structures. There are, however, open questions in the field and the state of art is far from being well understood. Under the wide variety of compounds, the transitionmetal aluminides attract the greatest share of both basic and applied research. One of the prominent compounds lying at the focus of interest is Ni3Al, which is a material of superior structural stability, it has very good hightemperature strength and it resists to chemical degradation. This material, however, suffers from low-temperature brittleness, which may be suppressed considerably * Corresponding author. Fax: +420-5-4121-2301. E-mail addresses: [email protected] (J. Cˇerma´k), [email protected] (V. Rothova´).
by (micro)alloying, e.g., by boron [5], nevertheless, the elimination of brittleness of Ni3Al-based alloys still remains a hot topic. It is known that the brittleness of these materials in polycrystalline form is related to grain boundaries (GB) [1]. Since GB is a site where the alloying elements may segregate (see, e.g., in [6]), it implies that the data on grain boundary chemistry and thermal changes of concentration controlled by GB diffusion may be useful for the assessment of behavior of intermetallic polycrystals with strong impact into practice. Diffusion measurements provide complete information on diffusion mechanisms only in those instances where it is possible to measure the diffusivities of both (all) chemical components. It is not the case for Ni3Al, because there is no proper radioisotope of Al for the tracer diffusion measurement. Therefore, it is inevitable to model this intermetallic by others that have radioisotopes of alloying elements and that would scale the diffusion properties of Ni3Al. One of the candidates is Ni3Ga, which has the same structure (L12—it is derived from FCC structure; the Ni atoms occupy the centers of faces, Ga atoms are in cubes corners) as Ni3Al. The aim of present study is, therefore, to measure the diffusion characteristics of both components in Ni3Ga compound to gain data that may contribute to deeper understanding of diffusion mechanism in the given class of materials.
0966-9795/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0966-9795(02)00053-5
J. Cˇerma´k, V. Rothova´ / Intermetallics 10 (2002) 765–769
766
2. Experimental 2.1. Experimental alloys Six experimental alloys were prepared by induction melting from pure components (4N Ga and 3N7 Ni) under protective Ar atmosphere and cast into a copper mould. Ingots (cylinders of diameterlength=1280 mm) were homogenization annealed at 1000 C for 5 days. The chemical homogeneity after the annealing was checked by line X-ray chemical microanalysis at SEM/ EDAX/WEDAX. The chemical composition of alloys is shown in Table 1. The mean grain size of experimental alloys after the thermal treatment was about 200 mm. 2.2. Measurement The diffusion samples were machined from the thermally treated ingots in the form of small cylinders diameterheight=103 mm and their front planes were ground flat with metallographic papers (last grade 2400) and mechanically polished with diamond paste, so mirror-like surface smoothness was achieved. The tracer was deposited on the polished surface by vacuum-evaporation technique: An aqueous solution of gallium citrate and a solution of nickel in 0.5 M hydrochloric acid was used as a source of Ga and Ni radiotracer respectively. The respective source solution was repeatedly dropped-and-dried on the tungsten boat to form a solid plaque on the boat surface. The deposit was thermally decomposed in a vacuum chamber into a non-radioactive gaseous phase and a residual metal basis, which was afterwards evaporated from the shockheated boat onto the cold, polished samples. The thickness of the radioactive layer was of the order 102 nm. The edges of the samples were masked to prevent lateral diffusion along the sample surface. The samples were wrapped in Ni foil and sealed together with a piece of Ti foil (getter) into quartz ampoules filled with 6N Ar to about 104 Pa. This should prevent the evaporation of Ga. Diffusion anneals of sealed samples were carried out in a horizontal tube furnace with controlled temperature. Fluctuation and absolute accuracy of the chosen temperature was within 1 K. The penetration–depth Table 1 Chemical composition of experimental alloys in at.% Alloy No.
xGa
xNi
1 2 3 4 5 6
23.5 24.0 25.2 26.3 27.5 28.3
bal. bal. bal. bal. bal. bal.
curves were measured by the residual activity method [7]. The individual layers were taken-off by fine grinding and their thickness was obtained by precise weighing. Residual radioactivity of samples was measured (betarays were detected only) by an a/b/g low-level counter.
3. Results 3.1. Volume diffusion The experimental arrangement of the present diffusion measurement realizes the diffusion from a thin surface source into a half-space, described by initial– boundary conditions in one-dimensional formulation for concentration c in location x and at time t cð0; 0Þ ¼ M cðx; Ð 1 0Þ ¼ 0 0 cðx; tÞdx ¼ M:
ð1Þ
The coefficient of volume diffusion, D, can be obtained by fitting the known analytical solution of diffusion equation with the conditions (1), M x2 cðx; tÞ ¼ pffiffiffiffiffiffiffiffiffi exp ; ð2Þ 4Dt Dt to penetration curves c(x, t). Due to intensive attenuation of registered beta–rays of both diffusing isotopes, 67Ga and 63Ni, in the material of samples, the concentration c(xn,t) at the depth xn can be considered to be proportional to the measured residual activity A(xn,t) of the sample after the removing of n layers of total thickness xn: c(xn,t)=k A(xn,t). In other words, the signal from the radioactive sources—atoms 67Ga and 63Ni—under the instantaneous surface located at xn can be omitted. The proportionality constant k may be set to unity without any effect on evaluated D’s obtained from the slope of the dependence ln c vs x2—see Eq. (2). A typical example of measured concentration–depth curve c(x, t) (=A(x,t)), measured for 67Ga diffusion after the annealing 1240 K for 2 h, is illustrated in Fig. 1. It can be seen that the concentration curves can be well approximated by the known solution (2) in a certain near-surface region. At greater depth x, there is a considerable upward curvature (see dotted lines in Fig. 2) caused by the rapid diffusion along GBs. Concentration and temperature dependence of all obtained D values is shown in Figs. 2–5. 3.2. GB diffusion As it was mentioned above, obtained penetration curves have shown an upward curvature at greater
J. Cˇerma´k, V. Rothova´ / Intermetallics 10 (2002) 765–769
depth x. This makes it possible to evaluate the GB diffusivity. LeClaire [8] analyzed numerically Suzuoka’s exact solution [9] for the case defined by conditions (1) and derived simple approximate relation for evaluation of triple product P=s Db (GB diffusivity). P characterizes quantitatively the rate of diffusion transport of
767
given component along the GB. Symbols s, and Db stand for segregation factor (ratio of diffusant concentration in the GB to that in the grain next to the GB), GB width (conventionally taken to be about 0.5 nm) and diffusion coefficient in the GB, respectively. Having the dependence of average diffusant concentration c on penetration depth x, LeClaire’s theory says that—at sufficiently great x where the volume diffusion flux contributes negligibly only to overall diffusion flux—the logarithm of c is a linear function of x1.2 with relatively high numerical accuracy. The theory also gives the relation that can be used for numerical estimation of P P ¼ A " t D :
ð3Þ
Fig. 1. An example of penetration curves of 67Ga measured for the diffusion anneal carried out at 1240 K for 2 h, plotted in co-ordinates ln c vs x2. Fig. 3. Measured volume diffusion coefficients of Ni, D, in dependence on Ga concentration.
Fig. 2. Measured volume diffusion coefficients of Ga, D, in dependence on Ga concentration.
Fig. 4. Temperature and concentration dependence of D for volume diffusion of 67Ga. The plane—Eq. (4).
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In Eq. (3), A is the slope of great-depth linear segment of ln c vs. x1.2 curve, t, D are diffusion time and coefficient of volume diffusion respectively and constants through are known from the theory for respective diffusion kinetics [10]. In Fig. 6, one can see examples (for 67Ga diffusion in alloy 1) of measured penetration curves in co-ordinates log c vs. x1.2, which illustrate the existence of linear concentration tails.
ln D ¼ ln D0 þ BxGa
ðCxGa þ EÞ 1 R T
ð5Þ
for the Ni diffusion in Ni3Ga. Eqs. (4) and (5) were fitted to measured Ds (see planes in Figs. 4 and 5 with the result: ln Do= (18.6 1.1) (Do in m2/s), B=(0.312 0.036) (at.% Ga) 1 and Q=(236.9 5.1) kJ/mol for Ga diffusion and ln
4. Discussion 4.1. Volume diffusion As can be seen in Figs. 2 and 3, the volume diffusion coefficients show a slight increase with increasing content of Ga. As for the diffusion of Ga, this effect is in agreement with known literature data [2] and it supports the idea that the diffusion of minority component, Ga, may run by a Ga-antisite-assisted mechanism [2–4]. In the case of Ni diffusion, the slight increase in D with increasing xGa—observed especially at lower temperatures—may be due to a certain dilatation of the lattice by excess Ga concentration [11]. Comparison of present results (obtained for alloy 3 that is close to stoichiometry A3B) with literature data on both Ga and Ni volume diffusion in Ni3Ga [12,13] can be seen in Fig. 7. It is obvious that present results agree well with the literature and that there is no significant difference between the Ni and Ga diffusivity. For the concentration-temperature dependence of D we can take the simple empirical relation ln D ¼ ln D0 þ BxGa
Q1 ; RT
Fig. 6. Examples of penetration profiles plotted in co-ordinates ln c vs x1.2.
ð4Þ
for the Ga diffusion, and
Fig. 5. Temperature and concentration dependence of D for volume diffusion of 63Ni. The plane–Eq. (5).
Fig. 7. Comparison of present results with literature data on Ga and Ni volume diffusion in Ni3Ga close to stoichiometry A3B (in alloy 3). (Tm=1483 K).
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[10] for =P/(2 D1.5t 0.5) < 100). In contrast to volume diffusion, GB diffusivity P of both Ga and Ni does not depend significantly on xGa. The temperature dependence of obtained values of P is shown in Fig. 8 for the whole concentration interval studied. It can be seen that there is not any significant difference—in the frame of scatter—between values of P for Ga and Ni GB diffusion in Ni3Ga. The temperature dependence of average (Ga and Ni) GB diffusivity P can be described by Arrhenius equation 194:7 5:6 kJ=mol P ¼ 10 ð10:6þ 0:31Þ exp m3 =s RT ð6Þ It is concluded that the GB diffusivity of both components, Ga and Ni runs approximately at the same rate. This may be explain, partly at least, by a certain effective compressibility of Ga atoms at GBs [14]. Fig. 8. Temperature dependence of GB diffusivity P of Ga (full points) and Ni (crosses) in Ni4 xGax ðx xGa =25Þ.
Acknowledgements Do=(13.0 4.5) (Do in m2/s), B= (0.91 0.18) (at.% Ga) 1, C= (10.5 1.8) kJ/mol/at.% Ga and E=(507 46) kJ/mol for Ni diffusion. Obtained average value of Q for Ga volume diffusion in Ni3Ga agrees well with the value 233 kJ/mol reported in [12]. Also the value of Q=244 kJ/mol calculated from Eq. (5) and xGa=25 at.% Ga for Ni volume diffusion match reasonably with literature values 259 kJ/ mol [12] and 245 kJ/mol [13]. The fact that the values of Ni and Ga volume diffusion coefficients are close one to another makes the Gaantisite-assisted mechanism [2] of gallium volume diffusion in Ni3Ga compound more likely, than the six-jump mechanism [1]. 4.2. GB diffusion GB diffusivities P were calculated from Eq. (3) using measured slopes A, Ds calculated from Eqs. (4) and (5), diffusion times t and constants =0.258, " = 1.7182, = 0.5309 and =0.4691 (values recommended in
The work was supported by projects GACR 106/01/ 0384, AS CR S2041105 and Z2041904.
References [1] Westbrook, J. H., Fleischer R. L. Intermetallic compounds, vol 2. Chichester: J.Wiley & Sons; 1995. p.17. [2] Numakura H, et al. Mater Sci Eng 2001;A312:109. [3] Athenes M, Bellon P. Philos Mag 1999;79:2243. [4] Nakajima H, et al. Mater Sci Eng 1997;A239:819. [5] Aoki K, Izumi O. Nippon Kinzoku Gakkaishi 1979;43:1190. [6] Lejcek P, Schneeweiss O. Surface Sci 2001;487:210. [7] Adda Y., Philibert J. La diffusion dans les solides, vol. 1. Saclay: Inst Nat Sci, Techn Nucleaires; 1966. p. 264. [8] LeClaire AD. Brit J Appl Phys 1963;14:351. [9] Suzuoka T. Trans Jap Inst Metals 1961;2:25. [10] Kaur I., Gust W. Fundamentals of grain and interphase boundary diffusion. Stuttgart: Ziegler Press, 1988. p. 27. [11] Yuan W, Diwald O, Mikula A, Ipser H. Z Metallkd 2000;91:448. [12] Nonaka K, et al. Defect and Diffusion Forum 1997;143–143:269. [13] Ikeda T. PhD thesis, Graduate School of Engineering, Kyoto University: Kyoto, 2000, quoted from [2]. [14] Thomson DI, et al. Acta Mater 2000;48:3623.
Ni and Ga diffusion in polycrystalline Ni3Ga Jirˇ ı´ Cˇerma´k*, Veˇra Rothova´ Institute of Physics of Materials AS CR, Zizkova 22, CZ-616 62 Brno, Czech Republic Received 25 April 2002; accepted 3 May 2002
Abstract The volume and grain boundary (GB) diffusion of 63Ni and 67Ga radiotracers in polycrystals of Ni3Ga intermetallic was studied in the vicinity of the stoichiometric composition A3B (23.5–28.3 at.% Ga). Both volume and GB diffusivity was investigated in the temperature interval 773–1373 K by the residual activity method. The obtained Ga volume diffusivity increases with increasing Ga concentration xGa; the increasing tendency of Ni volume diffusivity with increasing xGa is pronounced at lower temperatures. GB diffusivity of both Ga and Ni in Ni3Ga are close one to another and—contrary to the diffusion behavior of components in Ni3Al— they do not show any significant dependence on xGa. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: A. Intermetallics, miscellaneous; B. Diffusion
1. Introduction Intermetallic alloys show a series of very promising characteristics [1]. A number of investigations have been done in recent years that were devoted before all to their mechanical behavior. Since some of high-temperature characteristics are controlled by diffusion, it is clear that these materials are also very often a subject of diffusion studies. Due to atomic ordering of the intermetallic alloys, the study of diffusion processes is—besides its technological importance—interesting also from the theoretical viewpoint. Some sophisticated mechanisms have been proposed in recent years [1–4] that can explain diffusion coefficients measured in ordered structures. There are, however, open questions in the field and the state of art is far from being well understood. Under the wide variety of compounds, the transitionmetal aluminides attract the greatest share of both basic and applied research. One of the prominent compounds lying at the focus of interest is Ni3Al, which is a material of superior structural stability, it has very good hightemperature strength and it resists to chemical degradation. This material, however, suffers from low-temperature brittleness, which may be suppressed considerably * Corresponding author. Fax: +420-5-4121-2301. E-mail addresses: [email protected] (J. Cˇerma´k), [email protected] (V. Rothova´).
by (micro)alloying, e.g., by boron [5], nevertheless, the elimination of brittleness of Ni3Al-based alloys still remains a hot topic. It is known that the brittleness of these materials in polycrystalline form is related to grain boundaries (GB) [1]. Since GB is a site where the alloying elements may segregate (see, e.g., in [6]), it implies that the data on grain boundary chemistry and thermal changes of concentration controlled by GB diffusion may be useful for the assessment of behavior of intermetallic polycrystals with strong impact into practice. Diffusion measurements provide complete information on diffusion mechanisms only in those instances where it is possible to measure the diffusivities of both (all) chemical components. It is not the case for Ni3Al, because there is no proper radioisotope of Al for the tracer diffusion measurement. Therefore, it is inevitable to model this intermetallic by others that have radioisotopes of alloying elements and that would scale the diffusion properties of Ni3Al. One of the candidates is Ni3Ga, which has the same structure (L12—it is derived from FCC structure; the Ni atoms occupy the centers of faces, Ga atoms are in cubes corners) as Ni3Al. The aim of present study is, therefore, to measure the diffusion characteristics of both components in Ni3Ga compound to gain data that may contribute to deeper understanding of diffusion mechanism in the given class of materials.
0966-9795/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0966-9795(02)00053-5
J. Cˇerma´k, V. Rothova´ / Intermetallics 10 (2002) 765–769
766
2. Experimental 2.1. Experimental alloys Six experimental alloys were prepared by induction melting from pure components (4N Ga and 3N7 Ni) under protective Ar atmosphere and cast into a copper mould. Ingots (cylinders of diameterlength=1280 mm) were homogenization annealed at 1000 C for 5 days. The chemical homogeneity after the annealing was checked by line X-ray chemical microanalysis at SEM/ EDAX/WEDAX. The chemical composition of alloys is shown in Table 1. The mean grain size of experimental alloys after the thermal treatment was about 200 mm. 2.2. Measurement The diffusion samples were machined from the thermally treated ingots in the form of small cylinders diameterheight=103 mm and their front planes were ground flat with metallographic papers (last grade 2400) and mechanically polished with diamond paste, so mirror-like surface smoothness was achieved. The tracer was deposited on the polished surface by vacuum-evaporation technique: An aqueous solution of gallium citrate and a solution of nickel in 0.5 M hydrochloric acid was used as a source of Ga and Ni radiotracer respectively. The respective source solution was repeatedly dropped-and-dried on the tungsten boat to form a solid plaque on the boat surface. The deposit was thermally decomposed in a vacuum chamber into a non-radioactive gaseous phase and a residual metal basis, which was afterwards evaporated from the shockheated boat onto the cold, polished samples. The thickness of the radioactive layer was of the order 102 nm. The edges of the samples were masked to prevent lateral diffusion along the sample surface. The samples were wrapped in Ni foil and sealed together with a piece of Ti foil (getter) into quartz ampoules filled with 6N Ar to about 104 Pa. This should prevent the evaporation of Ga. Diffusion anneals of sealed samples were carried out in a horizontal tube furnace with controlled temperature. Fluctuation and absolute accuracy of the chosen temperature was within 1 K. The penetration–depth Table 1 Chemical composition of experimental alloys in at.% Alloy No.
xGa
xNi
1 2 3 4 5 6
23.5 24.0 25.2 26.3 27.5 28.3
bal. bal. bal. bal. bal. bal.
curves were measured by the residual activity method [7]. The individual layers were taken-off by fine grinding and their thickness was obtained by precise weighing. Residual radioactivity of samples was measured (betarays were detected only) by an a/b/g low-level counter.
3. Results 3.1. Volume diffusion The experimental arrangement of the present diffusion measurement realizes the diffusion from a thin surface source into a half-space, described by initial– boundary conditions in one-dimensional formulation for concentration c in location x and at time t cð0; 0Þ ¼ M cðx; Ð 1 0Þ ¼ 0 0 cðx; tÞdx ¼ M:
ð1Þ
The coefficient of volume diffusion, D, can be obtained by fitting the known analytical solution of diffusion equation with the conditions (1), M x2 cðx; tÞ ¼ pffiffiffiffiffiffiffiffiffi exp ; ð2Þ 4Dt Dt to penetration curves c(x, t). Due to intensive attenuation of registered beta–rays of both diffusing isotopes, 67Ga and 63Ni, in the material of samples, the concentration c(xn,t) at the depth xn can be considered to be proportional to the measured residual activity A(xn,t) of the sample after the removing of n layers of total thickness xn: c(xn,t)=k A(xn,t). In other words, the signal from the radioactive sources—atoms 67Ga and 63Ni—under the instantaneous surface located at xn can be omitted. The proportionality constant k may be set to unity without any effect on evaluated D’s obtained from the slope of the dependence ln c vs x2—see Eq. (2). A typical example of measured concentration–depth curve c(x, t) (=A(x,t)), measured for 67Ga diffusion after the annealing 1240 K for 2 h, is illustrated in Fig. 1. It can be seen that the concentration curves can be well approximated by the known solution (2) in a certain near-surface region. At greater depth x, there is a considerable upward curvature (see dotted lines in Fig. 2) caused by the rapid diffusion along GBs. Concentration and temperature dependence of all obtained D values is shown in Figs. 2–5. 3.2. GB diffusion As it was mentioned above, obtained penetration curves have shown an upward curvature at greater
J. Cˇerma´k, V. Rothova´ / Intermetallics 10 (2002) 765–769
depth x. This makes it possible to evaluate the GB diffusivity. LeClaire [8] analyzed numerically Suzuoka’s exact solution [9] for the case defined by conditions (1) and derived simple approximate relation for evaluation of triple product P=s Db (GB diffusivity). P characterizes quantitatively the rate of diffusion transport of
767
given component along the GB. Symbols s, and Db stand for segregation factor (ratio of diffusant concentration in the GB to that in the grain next to the GB), GB width (conventionally taken to be about 0.5 nm) and diffusion coefficient in the GB, respectively. Having the dependence of average diffusant concentration c on penetration depth x, LeClaire’s theory says that—at sufficiently great x where the volume diffusion flux contributes negligibly only to overall diffusion flux—the logarithm of c is a linear function of x1.2 with relatively high numerical accuracy. The theory also gives the relation that can be used for numerical estimation of P P ¼ A " t D :
ð3Þ
Fig. 1. An example of penetration curves of 67Ga measured for the diffusion anneal carried out at 1240 K for 2 h, plotted in co-ordinates ln c vs x2. Fig. 3. Measured volume diffusion coefficients of Ni, D, in dependence on Ga concentration.
Fig. 2. Measured volume diffusion coefficients of Ga, D, in dependence on Ga concentration.
Fig. 4. Temperature and concentration dependence of D for volume diffusion of 67Ga. The plane—Eq. (4).
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768
In Eq. (3), A is the slope of great-depth linear segment of ln c vs. x1.2 curve, t, D are diffusion time and coefficient of volume diffusion respectively and constants through are known from the theory for respective diffusion kinetics [10]. In Fig. 6, one can see examples (for 67Ga diffusion in alloy 1) of measured penetration curves in co-ordinates log c vs. x1.2, which illustrate the existence of linear concentration tails.
ln D ¼ ln D0 þ BxGa
ðCxGa þ EÞ 1 R T
ð5Þ
for the Ni diffusion in Ni3Ga. Eqs. (4) and (5) were fitted to measured Ds (see planes in Figs. 4 and 5 with the result: ln Do= (18.6 1.1) (Do in m2/s), B=(0.312 0.036) (at.% Ga) 1 and Q=(236.9 5.1) kJ/mol for Ga diffusion and ln
4. Discussion 4.1. Volume diffusion As can be seen in Figs. 2 and 3, the volume diffusion coefficients show a slight increase with increasing content of Ga. As for the diffusion of Ga, this effect is in agreement with known literature data [2] and it supports the idea that the diffusion of minority component, Ga, may run by a Ga-antisite-assisted mechanism [2–4]. In the case of Ni diffusion, the slight increase in D with increasing xGa—observed especially at lower temperatures—may be due to a certain dilatation of the lattice by excess Ga concentration [11]. Comparison of present results (obtained for alloy 3 that is close to stoichiometry A3B) with literature data on both Ga and Ni volume diffusion in Ni3Ga [12,13] can be seen in Fig. 7. It is obvious that present results agree well with the literature and that there is no significant difference between the Ni and Ga diffusivity. For the concentration-temperature dependence of D we can take the simple empirical relation ln D ¼ ln D0 þ BxGa
Q1 ; RT
Fig. 6. Examples of penetration profiles plotted in co-ordinates ln c vs x1.2.
ð4Þ
for the Ga diffusion, and
Fig. 5. Temperature and concentration dependence of D for volume diffusion of 63Ni. The plane–Eq. (5).
Fig. 7. Comparison of present results with literature data on Ga and Ni volume diffusion in Ni3Ga close to stoichiometry A3B (in alloy 3). (Tm=1483 K).
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[10] for =P/(2 D1.5t 0.5) < 100). In contrast to volume diffusion, GB diffusivity P of both Ga and Ni does not depend significantly on xGa. The temperature dependence of obtained values of P is shown in Fig. 8 for the whole concentration interval studied. It can be seen that there is not any significant difference—in the frame of scatter—between values of P for Ga and Ni GB diffusion in Ni3Ga. The temperature dependence of average (Ga and Ni) GB diffusivity P can be described by Arrhenius equation 194:7 5:6 kJ=mol P ¼ 10 ð10:6þ 0:31Þ exp m3 =s RT ð6Þ It is concluded that the GB diffusivity of both components, Ga and Ni runs approximately at the same rate. This may be explain, partly at least, by a certain effective compressibility of Ga atoms at GBs [14]. Fig. 8. Temperature dependence of GB diffusivity P of Ga (full points) and Ni (crosses) in Ni4 xGax ðx xGa =25Þ.
Acknowledgements Do=(13.0 4.5) (Do in m2/s), B= (0.91 0.18) (at.% Ga) 1, C= (10.5 1.8) kJ/mol/at.% Ga and E=(507 46) kJ/mol for Ni diffusion. Obtained average value of Q for Ga volume diffusion in Ni3Ga agrees well with the value 233 kJ/mol reported in [12]. Also the value of Q=244 kJ/mol calculated from Eq. (5) and xGa=25 at.% Ga for Ni volume diffusion match reasonably with literature values 259 kJ/ mol [12] and 245 kJ/mol [13]. The fact that the values of Ni and Ga volume diffusion coefficients are close one to another makes the Gaantisite-assisted mechanism [2] of gallium volume diffusion in Ni3Ga compound more likely, than the six-jump mechanism [1]. 4.2. GB diffusion GB diffusivities P were calculated from Eq. (3) using measured slopes A, Ds calculated from Eqs. (4) and (5), diffusion times t and constants =0.258, " = 1.7182, = 0.5309 and =0.4691 (values recommended in
The work was supported by projects GACR 106/01/ 0384, AS CR S2041105 and Z2041904.
References [1] Westbrook, J. H., Fleischer R. L. Intermetallic compounds, vol 2. Chichester: J.Wiley & Sons; 1995. p.17. [2] Numakura H, et al. Mater Sci Eng 2001;A312:109. [3] Athenes M, Bellon P. Philos Mag 1999;79:2243. [4] Nakajima H, et al. Mater Sci Eng 1997;A239:819. [5] Aoki K, Izumi O. Nippon Kinzoku Gakkaishi 1979;43:1190. [6] Lejcek P, Schneeweiss O. Surface Sci 2001;487:210. [7] Adda Y., Philibert J. La diffusion dans les solides, vol. 1. Saclay: Inst Nat Sci, Techn Nucleaires; 1966. p. 264. [8] LeClaire AD. Brit J Appl Phys 1963;14:351. [9] Suzuoka T. Trans Jap Inst Metals 1961;2:25. [10] Kaur I., Gust W. Fundamentals of grain and interphase boundary diffusion. Stuttgart: Ziegler Press, 1988. p. 27. [11] Yuan W, Diwald O, Mikula A, Ipser H. Z Metallkd 2000;91:448. [12] Nonaka K, et al. Defect and Diffusion Forum 1997;143–143:269. [13] Ikeda T. PhD thesis, Graduate School of Engineering, Kyoto University: Kyoto, 2000, quoted from [2]. [14] Thomson DI, et al. Acta Mater 2000;48:3623.