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Beryllium diffusion in zirconium
Journal of Nuclear Materials 59 (1976) 215-220 0 North-Holland Publishing Company
BERYLLIUM DIFFUSION IN ZIRCONIUM R. TENDLER Departamento de Metalurgik, Comisidn National de Energia A tdmica. Av. de1 Libertador 8250, Buenos Aires, Argentina
and J. ABRIATA and C.F. VAROTTO Centro A tbmico Bariloche (CNEA) and Institute de Fisica ‘%A. Balseiro” (UniversidadNational de Cuyo), S.C. de Bariloche, Rio Negro, Argentina Received 23 June 1975
The diffusion coefficients of ‘Be in both OLand p phases of Zr, are reported. The temperature dependence of the diffusion coefficient in the OLphase may be expressed by D& = 0.33 exp(-31900/R7’) cm2/s. The measured values in the p hase are in agreement with previously literature reported data, which give a temperature dependence expressed by !e _- 8.33 X 10m2 exp(-3 1800/R T) cm2/s. Be diffusion in Zr, which is consistent with an interstitial-like behavior, Dp_zr is analyzed in terms of the Anthony and Turnbull conditions, and atomic size criteria. It is concluded that the latter is a very important parameter when assessing the possibility of significant interstitial-like dissolution. Les coefficients de diffusion de ‘Be dans les deux phases (Yet p du Zr sont don&. La relation entre les coefficients de diffusion en phase (2 et la temperature peut gtre exprimQ par D&, = 0,33 exp(-31900/RT) cm2/sec. Les valeurs mesure’es en phase p sont en accord avec les donnees ddjjs.citees dans la littgrature et sont reprdsentables par la relation DF& = 8,33 X lob2 exp(-31800/RQ cm2/sec. La diffusion de Be dans Zr, qui est compatible avec un comportement diffusionnel interstitiel, est analysie en termes des conditions d’Anthony et de Turnbull et des critkres de taille atomique. On en conclut que le dernier crit&re est un paramktre t&s important quand on glue la possibilitC d’une dissolution pre’f&entielle en interstitiels. Der Diffusionskoeffizient von ‘Be in LY-und fl-Zr wird angegeben. Die Temperaturabhgngigkeit des Diffusionskoeftizienten in der a-Phase betrtigt DEezr = 0,33 exp(-q/R 7’) cm2/s mit (I = 31900 cal/mol. Die Messergebnisse in der p-Phase stimmen mit den kiirzlich verGffentlichtenLiteraturwerten iiberein, deren Temperaturabhiingigkeit DFzzr = 8,33 X 10m2 exp(-q/Rn cm2 /s mit 4 = 3 1800 cal/mol lautet. Die Be-Diffusion in Zr ist mit einem zwischengitteriihnlichen Verhalten konsistent; sie wird mit Hinblick auf die Anthony- und Turnbull-Bedingung sowie das Kriterium der Atomgriisse untersucht. Daraus folgt, dass dieses Kriterium ein wichtiger Parameter bei der Beurteilung ist, ob eine zwischengitterlhnlithe LGsung msglich erscheint.
1. Introduction
behavior of these impurities may be understood by a judicious use of the Anthony and Turnbull conditions [2-5 1, extent of mutual solid solubility, atomic size parameters, features of the corresponding phase diagrams and Hume-Rothery rules [6] controlling substitutional dissolution. The basic idea leading in ref. [l] to this conclusion is that a significant population of the interstitial-like states of the impurity is expected whenever the dissolution energy in a substitutional position is high enough for a very restricted
As a part of a program on the study of the transport properties of materials of nuclear interest which is under way in our laboratory, this paper will report the results of Be diffusion in both a! and 0 phases of zirconium. The trends in the diffusion behavior of several very dilute metallic impurities in Zr has been recently discussed by the same authors [ 11. It was concluded that the interstitial-like or substitutional 215
216
R. Terzdler et al. / Ber~~lliuw~ di,ffilsiotz itr zirconium
solid solubility to result. Thus, this conclusion is not affected by the real structure of the (possibly complex) fast-diffusing interstitial-like defect competing with the substitutional configuration. For the case of Zr as solvent, the proposed view of ref. [l], for the 15% Hume-Rothety size rule, leads to the conclusion that the atomic size effect is particularly important in controlling the diffusion behavior of impurities in Zr. In addition, such a size criterion has much more predictive power than the valence criterion. In effect, solute size may be known “a priori” in all cases from independent measurements, while this is not true for valences, as in the case of the transition elements. In this context, Be in Zr sets an interesting problem. Be has a normal chemical valence of 2 and, similarly to Zn and Cd in Zr, it should have from the valence criterion [ 1,141 a diffusion behavior akin to the substitutional one (if this valence value is accepted for Be in Zr). However, the atomic size of Be is small enough that solid solubility is prohibited by the 15% Hume-Rothery size rule. From this, and the size criterion advanced in ref. [ 11, Be should have diffusion behavior akill to the interstitial case, which appears to be supported by previous reported data [7] of Be diffusion in the P-phase of Zr. From the above considerations, it may be seen that Be diffusion measurements in both phases of Zr are necessary, since the influence of the 01-+ /3 Zr phase transition on the diffusion parameters may be taken as a good indication for substitutional or non-substitutional behavior. It is the aim of this paper to present Be diffusion measurements in the 01and fl phases of Zr, and from these results to show that the atomic size criterion is a more sensible parameter in deciding the type of diffusion behavior of a very dilute metallic solute in Zr than the usual valence criteria.
2. Experimental procedures The diffusion experiments were carried out on Zr polycrystals of 99.99% purity (from Leico Industries Inc, New York) with grain size greater than 2 mm. The lapping and measuring techniques were the same as indicated previously [8]. The annealing methods for the diffusion experiments in the B-Zr phase were the same as described in ref. [9] for Mn diffusion
in (3-Zr. For the cu-Zr experiments, a similar technique was employed with only a slight change: in this case the quartz tube with a Ta foil tube inside it was heated at the working temperature. Afterwards, the sliding rod with the Zr wafer, in which the tracer deposit had previously been made, was introduced into the hot zone. Heating times ranged from 1-2 minutes for the shorter diffusion annealings (30 min) to 3-5 minutes for the longer ones (40 min- 1 h). The radioactive tracer for the a-phase annealings was deposited from a 7BeC12 in HC1 sol., by the electrodeposition technique [lo]. For the P-phase experiments the tracer was deposited by the electrolytic technique for the experiment at 1148”C, and by a technique similar to the one described in ref. [7] for the experiment at 1045°C. The tracer deposit thickness was less than 500 a and its uniformity was checked by autoradiographic methods.
3. Results and discussion Be proved to be a difficult element for diffusion experiments in Zr. The tracer deposit behavior during the anneals presented a series of problems that made it difficult to determine the initial condition to which a given solution of the diffusion equation applies. Difficulties originated from surface tracer trapping in the a-phase experiments, and tracer loss to the container walls in the P-phase experiments. The penetration profiles showed, in almost all cases, an anomalous initial zone beyond which the resulting profile pointed to a “thin layer ” , “constant surface concentration” or “intermediate case solution” of the diffusion equation. In order to derive meaningful diffusion coefficients, the following procedure was employed: i) Both “thin layer” and “constant surface concentration” approximations were attempted in each experiment without considering any intermediate situation. However, only when clear “one-class” behavior was present, was the experiment accepted. It should be noticed that in those cases where at the same temperature, for different samples, the two distinct approximations were found to apply, practically the same D values resulted. This may be taken as an indication that the chosen method is correct. ii) All penetration profiles were tested for any
R. Tendler et al. / Be~l~ium diffusion in zirconium
significant gram-boundary contribution, by both Suzuoka and Fisher [I 1,121 analyses and autoradiographic techniques f131. Only if a clear absence of grain-boundary contribution was established, was the computed D bulk value accepted. Since at temperatures below 720°C some grain-boundary contribution appeared, no D bulk values below this temperatures are reported. Typical penetration profiles for both a and fl phases are shown in figs. 1 and 2. It can be seen that, after a short anomalous initial zone, good straight lines, in the corresponding approximations, were obtained . The temperature dependence of the Be bulk diffusion coefficient in both a! and 0 phases of Zr is shown in fig, 3. For the o-phase (in the temperature range studied) it may be expressed by
Dtfzr= 0.33 exp(-3 19OO/RT) cm2/s . For the fl phase, the measured diffusion coefficients are consistent with previously reported data 171,
Fig. Ji. Typical penetration profiles in the “thin layer” approximation, and 3.6 X IO3 s; (c) 1148°C and 4.2 X IO2 s.
217
which gave
D&
= 8.33 X IOh exp(3 1.8001RT) cm21s .
It can be seen that high diffusivity, low activation
energy and almost no influence of the Q to /I phase transition on the diffusion parameters characterises Be diffu~on in Zr. Table 1 is a resume of the diffusion data for Be, together with the ratio values pBe = (DB$o$Tr) (at the same temperature) for OLand P Zr phases. In the case of cu-Zrit was concluded in [ 1] that when p* > lo3 the interstitial-like behavior is dominant, namely, we have a faster solute diffusion and a very slight effect of the o//3 phase transition on the impurity diffusion as compared with self-diffusion. For &Zr the present results confirm those of ref. [7] which were already discussed in ref. [ 11, concluding that in the @phase of Zr, Be is a fast-diffusing solute, similar to the interstitial-like Fe and Co. Let us now analyse Be diffusion behavior in Zr from the points of view of both valence and atomic size criteria. Be diffusion behavior in Zr satisfies
of 7Be in Zr. (a) 1045°C and 9 X 10’ S; (b) 784°C
218
ar@.
Fig. 2. Typical penetration profiles for the “constant surface concentration” approximation, of Be in Zr; (a) 1046S”Cand 9 x 10’ s; (b) 1148°Cand 4.2 X lo2 s. (3rd iteration); (c) 8465°C and 1.2 X lo3 s. (3rd iteration); (d) 833°C and 1.2 X lo3 s. (2nd iteration); (e) 740°C and 2.4 X 10’ s. (3rd iteration).
Anthony and Turnbull conditions if a low valence for this element in Zr is accepted, which differs from the normal accepted chemical valence. This is not impossible since it is well known that the effective valence of solutes in alloys does not necessarily refleet a direct relation to the normal chemical valence for the element in chemical compounds.
For the case of Zr as solvent, it has been shown [ 1,141 that a normal solute valence of 2 is high
enough that diffusion behavior akin to the substitutional one should be expected. This expectation is confirmed by the solutes Zn and Cd. Therefore, Be can be incorporated into a consistent picture under the valence scheme, only if a valence value
Table 1 Be and Zr properties and parameters of interest Element
Atomic radius (A)
Ionic radius (A)
Eiectronegativity (Pauling)
_.-Be
1.12
0.31(+2)
1.5
Zr
1.60
0.74(+2)
1.4
po =
,P=
Df$$/o~f=
Df&$=/DE#
(temp. range “C) %2X LO5 (this work)
(temp. range “C)
Maximum solubility in or-Zr at.% (temp. range “C)
Maximum solubility in /3-Zr at.% (temp. range “C)
270-300 (915-1300°C), [71
<1 (800°C) [151
<3 (965°C) [151
R. Tendler et al. / BeryNiu’m diffusion in zirconium
219 RADIUS
,
lb
0.8
RATIO I
0.9
11
P--
0
\ 14
\
\
\
\
\ \
lb
\ ‘\ \
18
\
\
\
\
Q
3 ld ATOMIC
10'
RADIUS
%I
Fig. 4. Diffusivity ratio p” = D&,p/D$‘ir for different elements in the o-phase of Zr. pa for Be, from this work. Other elements from ref. [ 11.
ld
10'
10'
L
6
7
0
)
1
1’
10
11
ro'ir
OK
Fig. 3. Diffusion coefficients of .‘Be in Zr as a function of temperature, as compared to Zr self-diffusion. Symbols: a_Zr: n Be diffusion - This work, -.-.Zr self-diffusion [ 171, Zr self-diffusion fl8], - - - Zr seif-diffusion [ 191. BZr: o Be diffusion (this work), the full line passing through the points is from ref. [7], - - - Zr self-diffusion [16].
somewhere between 0 and 1 is assumed for Be in Zr. This is in agreement with the p values for Be since it has been shown that p values decreases with increasing valence [ 1,141. The size criterion as elaborated in ref. [I] is consistently satisfied by Be, as is clearly shown in fig. 4, without any recourse to the valence values. The 15% size-rule indicates that Be should not be soluble in Zrsince RBefRZr= 0.70and, accordingly, the phase
diagram shows very restricted solid solubility at both ends [ 151. As a conclusion, we confirm the idea advanced in [l] that, at least for Zr as solvent, the impurity-to-host atomic radius ratio and consequently the extent of the solid solubility, is a very important parameter to consider when assessing the possibility of significant interstitial-like dissolution.
Acknowledgements The authors are very much indebted to Sra. Susana Bermudez for assistance in the autoradiographic and metallographic analysis of the samples and to Lit. H. Mendoza, for experimental assistance.
References [l] R. Tendler, E. Santos, J. Abriata and C.F. Varotto, IAEA Symp. on Thermodynamics of Nuclear Mat. (Vienna, Oct. 1974), to be published. [ 21 B.F. Dyson, T.R. Anthony and D. Turnbull, J. Appl. Phys. 37 (1966) 2370.
I
R. Tendler et al. /Beryllium
220 [3] T.R. Anthony
[4] [5] [6]
[7] [S]
and D. Turnbull, Phys. Rev. 151 (1966) 495. T.R. Anthony, J.W. Miller and D. Turnbull, Scripta Met. 3 (1969) 183. T.R. Anthony, Vacancies and Interstitials in Metals, (North-Holland, Amsterdam, 1969) 935. A. Hume-Rothery and G.V. Raynor, The Structure of Metals and Alloys, (The Institute of Metals, London, 1954). L.V. Pavlinov, G.V. Grigoriev and G.O. Gromyko, Izv. Akad. Nauk, SSSR Metal (1969) no. 3,207. R. Tendler and C.F. Varotto, J. Nucl. Mater. 44 (1972)
[9] ?Tendler 107.
and C.F. Varotto, J. Nucl. Mater. 46 (1973)
diffusion in zirconium
[lo] [ 111 [ 121 [13]
[ 141 [ 151 [ 161 (171
[ 181 [ 191
E. Santos and F. Dyment, Plating (1973) 821. T. Suzuoka, Trans. Japan Inst. of Metals, 2 (1961) 25. J.C. Fisher, J. Appl. Phys. 22 (195 1) 74. R. Tendler and CF. Varotto, J. Nucl. Mater. 54 (1974) 212. C.M. Hood and R.J. Schultz, Acta Met. 22 (1974) 459. R.P. Elliot, Constitution of Binary Alloys, 2nd. Suppl. (McGraw Hill, New York, 1966). J.I. Federer and T.S. Lundy, Trans. Met. Sot. AIME, 227 (1963) 592. V.S. Lyaschenko, B.N. Bikov and L.V. Pavlinov, Fiz. Metall. Metallov 8 (1959) 362. F. Dyment and C.M. Libanati, J. Mat. Sci. 3 (1968) 349. P. Flubacher, EIR Bericht, No. 49 (1963).
BERYLLIUM DIFFUSION IN ZIRCONIUM R. TENDLER Departamento de Metalurgik, Comisidn National de Energia A tdmica. Av. de1 Libertador 8250, Buenos Aires, Argentina
and J. ABRIATA and C.F. VAROTTO Centro A tbmico Bariloche (CNEA) and Institute de Fisica ‘%A. Balseiro” (UniversidadNational de Cuyo), S.C. de Bariloche, Rio Negro, Argentina Received 23 June 1975
The diffusion coefficients of ‘Be in both OLand p phases of Zr, are reported. The temperature dependence of the diffusion coefficient in the OLphase may be expressed by D& = 0.33 exp(-31900/R7’) cm2/s. The measured values in the p hase are in agreement with previously literature reported data, which give a temperature dependence expressed by !e _- 8.33 X 10m2 exp(-3 1800/R T) cm2/s. Be diffusion in Zr, which is consistent with an interstitial-like behavior, Dp_zr is analyzed in terms of the Anthony and Turnbull conditions, and atomic size criteria. It is concluded that the latter is a very important parameter when assessing the possibility of significant interstitial-like dissolution. Les coefficients de diffusion de ‘Be dans les deux phases (Yet p du Zr sont don&. La relation entre les coefficients de diffusion en phase (2 et la temperature peut gtre exprimQ par D&, = 0,33 exp(-31900/RT) cm2/sec. Les valeurs mesure’es en phase p sont en accord avec les donnees ddjjs.citees dans la littgrature et sont reprdsentables par la relation DF& = 8,33 X lob2 exp(-31800/RQ cm2/sec. La diffusion de Be dans Zr, qui est compatible avec un comportement diffusionnel interstitiel, est analysie en termes des conditions d’Anthony et de Turnbull et des critkres de taille atomique. On en conclut que le dernier crit&re est un paramktre t&s important quand on glue la possibilitC d’une dissolution pre’f&entielle en interstitiels. Der Diffusionskoeffizient von ‘Be in LY-und fl-Zr wird angegeben. Die Temperaturabhgngigkeit des Diffusionskoeftizienten in der a-Phase betrtigt DEezr = 0,33 exp(-q/R 7’) cm2/s mit (I = 31900 cal/mol. Die Messergebnisse in der p-Phase stimmen mit den kiirzlich verGffentlichtenLiteraturwerten iiberein, deren Temperaturabhiingigkeit DFzzr = 8,33 X 10m2 exp(-q/Rn cm2 /s mit 4 = 3 1800 cal/mol lautet. Die Be-Diffusion in Zr ist mit einem zwischengitteriihnlichen Verhalten konsistent; sie wird mit Hinblick auf die Anthony- und Turnbull-Bedingung sowie das Kriterium der Atomgriisse untersucht. Daraus folgt, dass dieses Kriterium ein wichtiger Parameter bei der Beurteilung ist, ob eine zwischengitterlhnlithe LGsung msglich erscheint.
1. Introduction
behavior of these impurities may be understood by a judicious use of the Anthony and Turnbull conditions [2-5 1, extent of mutual solid solubility, atomic size parameters, features of the corresponding phase diagrams and Hume-Rothery rules [6] controlling substitutional dissolution. The basic idea leading in ref. [l] to this conclusion is that a significant population of the interstitial-like states of the impurity is expected whenever the dissolution energy in a substitutional position is high enough for a very restricted
As a part of a program on the study of the transport properties of materials of nuclear interest which is under way in our laboratory, this paper will report the results of Be diffusion in both a! and 0 phases of zirconium. The trends in the diffusion behavior of several very dilute metallic impurities in Zr has been recently discussed by the same authors [ 11. It was concluded that the interstitial-like or substitutional 215
216
R. Terzdler et al. / Ber~~lliuw~ di,ffilsiotz itr zirconium
solid solubility to result. Thus, this conclusion is not affected by the real structure of the (possibly complex) fast-diffusing interstitial-like defect competing with the substitutional configuration. For the case of Zr as solvent, the proposed view of ref. [l], for the 15% Hume-Rothety size rule, leads to the conclusion that the atomic size effect is particularly important in controlling the diffusion behavior of impurities in Zr. In addition, such a size criterion has much more predictive power than the valence criterion. In effect, solute size may be known “a priori” in all cases from independent measurements, while this is not true for valences, as in the case of the transition elements. In this context, Be in Zr sets an interesting problem. Be has a normal chemical valence of 2 and, similarly to Zn and Cd in Zr, it should have from the valence criterion [ 1,141 a diffusion behavior akin to the substitutional one (if this valence value is accepted for Be in Zr). However, the atomic size of Be is small enough that solid solubility is prohibited by the 15% Hume-Rothery size rule. From this, and the size criterion advanced in ref. [ 11, Be should have diffusion behavior akill to the interstitial case, which appears to be supported by previous reported data [7] of Be diffusion in the P-phase of Zr. From the above considerations, it may be seen that Be diffusion measurements in both phases of Zr are necessary, since the influence of the 01-+ /3 Zr phase transition on the diffusion parameters may be taken as a good indication for substitutional or non-substitutional behavior. It is the aim of this paper to present Be diffusion measurements in the 01and fl phases of Zr, and from these results to show that the atomic size criterion is a more sensible parameter in deciding the type of diffusion behavior of a very dilute metallic solute in Zr than the usual valence criteria.
2. Experimental procedures The diffusion experiments were carried out on Zr polycrystals of 99.99% purity (from Leico Industries Inc, New York) with grain size greater than 2 mm. The lapping and measuring techniques were the same as indicated previously [8]. The annealing methods for the diffusion experiments in the B-Zr phase were the same as described in ref. [9] for Mn diffusion
in (3-Zr. For the cu-Zr experiments, a similar technique was employed with only a slight change: in this case the quartz tube with a Ta foil tube inside it was heated at the working temperature. Afterwards, the sliding rod with the Zr wafer, in which the tracer deposit had previously been made, was introduced into the hot zone. Heating times ranged from 1-2 minutes for the shorter diffusion annealings (30 min) to 3-5 minutes for the longer ones (40 min- 1 h). The radioactive tracer for the a-phase annealings was deposited from a 7BeC12 in HC1 sol., by the electrodeposition technique [lo]. For the P-phase experiments the tracer was deposited by the electrolytic technique for the experiment at 1148”C, and by a technique similar to the one described in ref. [7] for the experiment at 1045°C. The tracer deposit thickness was less than 500 a and its uniformity was checked by autoradiographic methods.
3. Results and discussion Be proved to be a difficult element for diffusion experiments in Zr. The tracer deposit behavior during the anneals presented a series of problems that made it difficult to determine the initial condition to which a given solution of the diffusion equation applies. Difficulties originated from surface tracer trapping in the a-phase experiments, and tracer loss to the container walls in the P-phase experiments. The penetration profiles showed, in almost all cases, an anomalous initial zone beyond which the resulting profile pointed to a “thin layer ” , “constant surface concentration” or “intermediate case solution” of the diffusion equation. In order to derive meaningful diffusion coefficients, the following procedure was employed: i) Both “thin layer” and “constant surface concentration” approximations were attempted in each experiment without considering any intermediate situation. However, only when clear “one-class” behavior was present, was the experiment accepted. It should be noticed that in those cases where at the same temperature, for different samples, the two distinct approximations were found to apply, practically the same D values resulted. This may be taken as an indication that the chosen method is correct. ii) All penetration profiles were tested for any
R. Tendler et al. / Be~l~ium diffusion in zirconium
significant gram-boundary contribution, by both Suzuoka and Fisher [I 1,121 analyses and autoradiographic techniques f131. Only if a clear absence of grain-boundary contribution was established, was the computed D bulk value accepted. Since at temperatures below 720°C some grain-boundary contribution appeared, no D bulk values below this temperatures are reported. Typical penetration profiles for both a and fl phases are shown in figs. 1 and 2. It can be seen that, after a short anomalous initial zone, good straight lines, in the corresponding approximations, were obtained . The temperature dependence of the Be bulk diffusion coefficient in both a! and 0 phases of Zr is shown in fig, 3. For the o-phase (in the temperature range studied) it may be expressed by
Dtfzr= 0.33 exp(-3 19OO/RT) cm2/s . For the fl phase, the measured diffusion coefficients are consistent with previously reported data 171,
Fig. Ji. Typical penetration profiles in the “thin layer” approximation, and 3.6 X IO3 s; (c) 1148°C and 4.2 X IO2 s.
217
which gave
D&
= 8.33 X IOh exp(3 1.8001RT) cm21s .
It can be seen that high diffusivity, low activation
energy and almost no influence of the Q to /I phase transition on the diffusion parameters characterises Be diffu~on in Zr. Table 1 is a resume of the diffusion data for Be, together with the ratio values pBe = (DB$o$Tr) (at the same temperature) for OLand P Zr phases. In the case of cu-Zrit was concluded in [ 1] that when p* > lo3 the interstitial-like behavior is dominant, namely, we have a faster solute diffusion and a very slight effect of the o//3 phase transition on the impurity diffusion as compared with self-diffusion. For &Zr the present results confirm those of ref. [7] which were already discussed in ref. [ 11, concluding that in the @phase of Zr, Be is a fast-diffusing solute, similar to the interstitial-like Fe and Co. Let us now analyse Be diffusion behavior in Zr from the points of view of both valence and atomic size criteria. Be diffusion behavior in Zr satisfies
of 7Be in Zr. (a) 1045°C and 9 X 10’ S; (b) 784°C
218
ar@.
Fig. 2. Typical penetration profiles for the “constant surface concentration” approximation, of Be in Zr; (a) 1046S”Cand 9 x 10’ s; (b) 1148°Cand 4.2 X lo2 s. (3rd iteration); (c) 8465°C and 1.2 X lo3 s. (3rd iteration); (d) 833°C and 1.2 X lo3 s. (2nd iteration); (e) 740°C and 2.4 X 10’ s. (3rd iteration).
Anthony and Turnbull conditions if a low valence for this element in Zr is accepted, which differs from the normal accepted chemical valence. This is not impossible since it is well known that the effective valence of solutes in alloys does not necessarily refleet a direct relation to the normal chemical valence for the element in chemical compounds.
For the case of Zr as solvent, it has been shown [ 1,141 that a normal solute valence of 2 is high
enough that diffusion behavior akin to the substitutional one should be expected. This expectation is confirmed by the solutes Zn and Cd. Therefore, Be can be incorporated into a consistent picture under the valence scheme, only if a valence value
Table 1 Be and Zr properties and parameters of interest Element
Atomic radius (A)
Ionic radius (A)
Eiectronegativity (Pauling)
_.-Be
1.12
0.31(+2)
1.5
Zr
1.60
0.74(+2)
1.4
po =
,P=
Df$$/o~f=
Df&$=/DE#
(temp. range “C) %2X LO5 (this work)
(temp. range “C)
Maximum solubility in or-Zr at.% (temp. range “C)
Maximum solubility in /3-Zr at.% (temp. range “C)
270-300 (915-1300°C), [71
<1 (800°C) [151
<3 (965°C) [151
R. Tendler et al. / BeryNiu’m diffusion in zirconium
219 RADIUS
,
lb
0.8
RATIO I
0.9
11
P--
0
\ 14
\
\
\
\
\ \
lb
\ ‘\ \
18
\
\
\
\
Q
3 ld ATOMIC
10'
RADIUS
%I
Fig. 4. Diffusivity ratio p” = D&,p/D$‘ir for different elements in the o-phase of Zr. pa for Be, from this work. Other elements from ref. [ 11.
ld
10'
10'
L
6
7
0
)
1
1’
10
11
ro'ir
OK
Fig. 3. Diffusion coefficients of .‘Be in Zr as a function of temperature, as compared to Zr self-diffusion. Symbols: a_Zr: n Be diffusion - This work, -.-.Zr self-diffusion [ 171, Zr self-diffusion fl8], - - - Zr seif-diffusion [ 191. BZr: o Be diffusion (this work), the full line passing through the points is from ref. [7], - - - Zr self-diffusion [16].
somewhere between 0 and 1 is assumed for Be in Zr. This is in agreement with the p values for Be since it has been shown that p values decreases with increasing valence [ 1,141. The size criterion as elaborated in ref. [I] is consistently satisfied by Be, as is clearly shown in fig. 4, without any recourse to the valence values. The 15% size-rule indicates that Be should not be soluble in Zrsince RBefRZr= 0.70and, accordingly, the phase
diagram shows very restricted solid solubility at both ends [ 151. As a conclusion, we confirm the idea advanced in [l] that, at least for Zr as solvent, the impurity-to-host atomic radius ratio and consequently the extent of the solid solubility, is a very important parameter to consider when assessing the possibility of significant interstitial-like dissolution.
Acknowledgements The authors are very much indebted to Sra. Susana Bermudez for assistance in the autoradiographic and metallographic analysis of the samples and to Lit. H. Mendoza, for experimental assistance.
References [l] R. Tendler, E. Santos, J. Abriata and C.F. Varotto, IAEA Symp. on Thermodynamics of Nuclear Mat. (Vienna, Oct. 1974), to be published. [ 21 B.F. Dyson, T.R. Anthony and D. Turnbull, J. Appl. Phys. 37 (1966) 2370.
I
R. Tendler et al. /Beryllium
220 [3] T.R. Anthony
[4] [5] [6]
[7] [S]
and D. Turnbull, Phys. Rev. 151 (1966) 495. T.R. Anthony, J.W. Miller and D. Turnbull, Scripta Met. 3 (1969) 183. T.R. Anthony, Vacancies and Interstitials in Metals, (North-Holland, Amsterdam, 1969) 935. A. Hume-Rothery and G.V. Raynor, The Structure of Metals and Alloys, (The Institute of Metals, London, 1954). L.V. Pavlinov, G.V. Grigoriev and G.O. Gromyko, Izv. Akad. Nauk, SSSR Metal (1969) no. 3,207. R. Tendler and C.F. Varotto, J. Nucl. Mater. 44 (1972)
[9] ?Tendler 107.
and C.F. Varotto, J. Nucl. Mater. 46 (1973)
diffusion in zirconium
[lo] [ 111 [ 121 [13]
[ 141 [ 151 [ 161 (171
[ 181 [ 191
E. Santos and F. Dyment, Plating (1973) 821. T. Suzuoka, Trans. Japan Inst. of Metals, 2 (1961) 25. J.C. Fisher, J. Appl. Phys. 22 (195 1) 74. R. Tendler and CF. Varotto, J. Nucl. Mater. 54 (1974) 212. C.M. Hood and R.J. Schultz, Acta Met. 22 (1974) 459. R.P. Elliot, Constitution of Binary Alloys, 2nd. Suppl. (McGraw Hill, New York, 1966). J.I. Federer and T.S. Lundy, Trans. Met. Sot. AIME, 227 (1963) 592. V.S. Lyaschenko, B.N. Bikov and L.V. Pavlinov, Fiz. Metall. Metallov 8 (1959) 362. F. Dyment and C.M. Libanati, J. Mat. Sci. 3 (1968) 349. P. Flubacher, EIR Bericht, No. 49 (1963).