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Solid solubility of hafnium in nickel
Journal of Alloys and Compounds 274 (1998) 185–188
L
Solid solubility of hafnium in nickel M. Hajjaji ´ Laboratoire de Chimie-Physique, Departement de Chimie, Faculte´ des Sciences Semlalia, B.P. S15, Marrakech, Morocco Received 12 January 1998
Abstract The solvus curve of the nickel-rich domain of nickel-hafnium phase diagram is determined by the parametric method based on the cell parameter measurements by X-ray diffraction. The maximum Hf solid solubility at the eutectic temperature is determined to be 1.3 at.%. On the other hand, it was found that the effect of Hf additions on the cell parameter of the Ni(Hf) solid solution is not predictable by the elastic theory. Furthermore, the determined enthalpy of Hf in Ni(Hf), containing more than 0.3 at.%, is around 113 kJ / mol. It is however about 17 kJ / mol for the Hf-lean Ni(Hf) solid solution. 1998 Elsevier Science S.A. Keywords: Phase-diagram; Ni-Hf system; Ni(Hf) solid solution; Solvus curve; Solid solubility
1. Introduction The nickel-rich region of the nickel-hafnium phasediagram (Ni content .83 at.%) exhibits a restricted solid solubility as well as a two-phase field below the eutectic temperature 11908C [1,2]. The terminal Ni(Hf) solid solution region is very limited and the solvus curve location is not well known [3]. The aim of this work is to determine the exact location of the solvus curve and to follow the effects of Hf additions on the Ni(Hf) solid solution. The adopted method for the former goal is based on the relationship between the cell parameter of Ni(Hf) and the hafnium composition in solution.
The as-cast alloys, containing up to 2 at.% Hf, were treated thermally and mechanically [4]. Specimens were annealed under vacuum (2.6310 26 torr) for 25 h at 10608C and quenched to room temperature. The investigations were carried out by means of X-ray diffraction (XRD), optical metallography, transmission electron microscopy (TEM) and microhardness testing. The accurate cell parameters of the Ni(Hf) solid solutions were determined by XRD, using a least-squares method which takes account of the major systematic errors [5].
3. Results and discussion 2. Experimental procedures Binary nickel-hafnium alloys containing up to 12 at.% Hf were prepared from pure nickel (99.99 wt.%) and pure hafnium (Van Arkel) by using an induction furnace operating under a protective helium atmosphere [4]. The main impurities associated with the hafnium are reported in Table 1. Table 1 Composition of impurities associated to hafnium Impurity
C
Cl
Nb
Si
Ta
Fe
O
N
Zr a
Amount in ppm
63
500
100
43
250
480
290
73
2.5
a
In wt.%.
0925-8388 / 98 / $19.00 1998 Elsevier Science S.A. All rights reserved. PII: S0925-8388( 98 )00356-9
The microstructure investigations done on the annealed specimens, containing less than 0.8 at.% Hf, were single phase, identified as Ni(Hf) solid solution. The monophase aspect of these samples is also shown by the graph of Fig. 1, since, the solid solution hardening is proportional to the square root of the atomic fraction solute in solution [6]. On the other hand, when the hafnium content exceeded 0.8 at.% Hf, a second phase, identified as Ni 5 Hf, occurred as intergranular precipitates and / or eutectic constituent. The cell parameter measurements performed on the annealed specimens with up to 0.65 at.% Hf revealed that the lattice parameter (a a ) of the Ni(Hf) solid solution increased linearly with Hf additions (Fig. 2, curve C) and obeys the empirical equation:
186
M. Hajjaji / Journal of Alloys and Compounds 274 (1998) 185 – 188
Fig. 1. Microhardness of Ni-X at.% Hf alloys (X ,0.8%) annealed at 10608C for 25 h. Testing weights: 27 g; 37 g.
aa 5 a Ni (1 1 0.51933XHf ) where a Ni is the extrapolated lattice parameter for pure Ni (0.35240 nm). This value is close to that determined experimentally (0.35238 nm). XHf is the actual hafnium content, in at.%. As can be deduced from the previous figure, the solubility limit at 10608C is 0.6560.05 at.% Hf. The variation of the cell parameter of the Ni(Hf) solid solutions, forming Ni-2 at.% Hf samples, as a function of
Fig. 2. Ni(Hf) cell parameter as a function of Hf additions. C: experimental curve; C o : Vegard’s law; C 1 : theoretical curve.
ageing temperatures (500,T ,11008C) is reported in Fig. 3. It is worth noting that measurements were not conducted below 5008C because the equilibrium state required a long ageing time (e.g. .400 h for 5008C) and under such condition, a thin layer of contamination was evolved. As shown in Fig. 3, the lattice parameter increases moderately for T below about 9608C. However, it exhibits a drastic increase for higher temperatures. As a consequence of the latter effect, it is expected that the solubility of hafnium at the eutectic temperature could not be determined with accuracy. The combination of the results reported in Fig. 2 and Fig. 3 allowed the determination of the solid solubility curve depicted in Fig. 4. The maximum Hf solubility at the eutectic temperature is estimated to be 1.3 at.% Hf. This value is slightly higher than the reported ones [3,7]. This may be due to differences in the investigation techniques and / or the amount and the nature of hafnium impurities. The increase in the lattice parameter and the strengthening of the a solid solution due to Hf additions are expected since the atomic size of the solute (R Hf 50.159 nm) is larger than that of the solvent (R Ni 50.125 nm). Based on the elastic theory [8], the lattice parameter of Ni(Hf) solid solution would change with Hf content according to the relation: R Ni 2 R Hf da ] 5 2 ]]] ? x ? dXHf a Ni R Ni
Fig. 3. Variation of the cell parameter of Ni(Hf), forming Ni-2 at.% Hf sample, as a function of the ageing temperature.
M. Hajjaji / Journal of Alloys and Compounds 274 (1998) 185 – 188
187
Fig. 5. Variation of ln XHf with reciprocal absolute temperature.
0.3 at.% Hf is around 17 kJ / mol. However, DHHf is about 113 kJ / mol for the Hf-rich solid solutions. This latter high value of DHHf is likely the result of the occurrence of a large misfit of the solute in the Ni crystal, as reported elsewhere [9].
Fig. 4. Solvus curve of Ni-Hf system.
where x is the compressibility factor:
x 5 (1 1 a ) /(KNi /KHf 1 a ), with a 5 (1 1 n ) / 2(1 2 2n ). K is the bulk modulus and n the Poisson’s ratio of the solvent. The values of the ratio KNi /KHf and n are around 2 and 1 / 3, respectively. The integration of the above equation yields to:
S
3(R Hf 2 R Ni ) aa 5 a Ni 1 1 ]]]] ? XHf 4R Ni
D
or,
4. Conclusion The results of this study show that up to about 9608C, the Hf solid solubility is accurately determined. However, there is a significant error for higher temperatures. The maximum solubility at the eutectic temperature is estimated to be 1.3 at.%. The solubility of Hf has a marked effect on the cell parameter. This fact is not governed by the elastic theory but may be caused by the presence of an electrostatic interaction phenomenon. Furthermore, for small Hf solubilities (up to about 0.3 at.%) the molar enthalpy of Hf in solution is 17 kJ / mol. Nevertheless, it is much higher (about 113 kJ / mol) for the Hf-rich solid solution. This may be due to a large misfit of Hf in the Ni crystal.
aa 5 a Ni (1 1 0.21265XHf ). This equation representing the theoretical evolution of a a as a function of Hf additions is plotted in Fig. 2 (curve C 1 ). The negative deviation from Vegard’s law (curve C o in Fig. 2) is expected since x,1. Although the elastic theory predicts an increase of a a with Hf additions it does not describe the experimental result. It seems therefore, that the atomic size is not the only factor which controls the change of Ni(Hf) lattice parameter with Hf additions. There is likely a contribution of an electrostatic phenomenon which is characterized by repulsive interactions between the unlike atoms. In order to determine the molar enthalpy of hafnium (DHHf ) in Ni(Hf) solid solution the variation of ln XHf vs. 1 /T was depicted (Fig. 5). This curve which may be decomposed into two linear branches characterizes the formation of a non-ideal solid solution. The estimated value of DHHf for dilute solid solutions containing up to
Acknowledgements This work was done at the materials science laboratory ´ of the Ecole Superieure de Chimie de Toulouse (France). I thank Professor B. Pieraggi for interesting scientific discussions.
References [1] M.E. Kirkpatrick, W.L. Larsen, Trans. ASM. 54 (1961) 580. [2] V.N. Svechnikov, A.K. Shurin, G.P. Dimitrieva, Izvestrya Akad. Nauk. SSSR, Metall. 6 (1967) 176. [3] P. Nash, A. Nash, in: T.B. Massalski (Ed.), Binary Alloy Phase Diagrams, 2nd edition, vol. 2, ASM, 1992, p. 2094. [4] M. Hajjaji, B. Pieraggi, F. Dabosi, in: J.M.S.M. 94 Proceedings edited by Fac. Sci. Ain Chock and E.N.S.E.M. Casablanca (Morocco), vol. 1, 1994, p. 136.
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M. Hajjaji / Journal of Alloys and Compounds 274 (1998) 185 – 188
[5] B.D. Cullity, Elements of X-ray Diffraction, Addison-Wesley, 1978, p. 359. [6] M. Van Rooyen, P.F. Colijn, T.H.H. De Keijser, E.J. Mittemeijer, J. Mater. Sci. 21 (1986) 2373.
[7] R. Reinbach, Z. Metallkde. 51(5) (1960) 292. ´ ´ ´ ´ [8] J. Benard, A. Michel, J. Philibert, J. Talbot, Metallurgie Generale, Masson et Cie, 1969, p. 47. [9] R.A. Swalin, Thermodynamics of Solids, John Wiley, 1966, p. 138.
L
Solid solubility of hafnium in nickel M. Hajjaji ´ Laboratoire de Chimie-Physique, Departement de Chimie, Faculte´ des Sciences Semlalia, B.P. S15, Marrakech, Morocco Received 12 January 1998
Abstract The solvus curve of the nickel-rich domain of nickel-hafnium phase diagram is determined by the parametric method based on the cell parameter measurements by X-ray diffraction. The maximum Hf solid solubility at the eutectic temperature is determined to be 1.3 at.%. On the other hand, it was found that the effect of Hf additions on the cell parameter of the Ni(Hf) solid solution is not predictable by the elastic theory. Furthermore, the determined enthalpy of Hf in Ni(Hf), containing more than 0.3 at.%, is around 113 kJ / mol. It is however about 17 kJ / mol for the Hf-lean Ni(Hf) solid solution. 1998 Elsevier Science S.A. Keywords: Phase-diagram; Ni-Hf system; Ni(Hf) solid solution; Solvus curve; Solid solubility
1. Introduction The nickel-rich region of the nickel-hafnium phasediagram (Ni content .83 at.%) exhibits a restricted solid solubility as well as a two-phase field below the eutectic temperature 11908C [1,2]. The terminal Ni(Hf) solid solution region is very limited and the solvus curve location is not well known [3]. The aim of this work is to determine the exact location of the solvus curve and to follow the effects of Hf additions on the Ni(Hf) solid solution. The adopted method for the former goal is based on the relationship between the cell parameter of Ni(Hf) and the hafnium composition in solution.
The as-cast alloys, containing up to 2 at.% Hf, were treated thermally and mechanically [4]. Specimens were annealed under vacuum (2.6310 26 torr) for 25 h at 10608C and quenched to room temperature. The investigations were carried out by means of X-ray diffraction (XRD), optical metallography, transmission electron microscopy (TEM) and microhardness testing. The accurate cell parameters of the Ni(Hf) solid solutions were determined by XRD, using a least-squares method which takes account of the major systematic errors [5].
3. Results and discussion 2. Experimental procedures Binary nickel-hafnium alloys containing up to 12 at.% Hf were prepared from pure nickel (99.99 wt.%) and pure hafnium (Van Arkel) by using an induction furnace operating under a protective helium atmosphere [4]. The main impurities associated with the hafnium are reported in Table 1. Table 1 Composition of impurities associated to hafnium Impurity
C
Cl
Nb
Si
Ta
Fe
O
N
Zr a
Amount in ppm
63
500
100
43
250
480
290
73
2.5
a
In wt.%.
0925-8388 / 98 / $19.00 1998 Elsevier Science S.A. All rights reserved. PII: S0925-8388( 98 )00356-9
The microstructure investigations done on the annealed specimens, containing less than 0.8 at.% Hf, were single phase, identified as Ni(Hf) solid solution. The monophase aspect of these samples is also shown by the graph of Fig. 1, since, the solid solution hardening is proportional to the square root of the atomic fraction solute in solution [6]. On the other hand, when the hafnium content exceeded 0.8 at.% Hf, a second phase, identified as Ni 5 Hf, occurred as intergranular precipitates and / or eutectic constituent. The cell parameter measurements performed on the annealed specimens with up to 0.65 at.% Hf revealed that the lattice parameter (a a ) of the Ni(Hf) solid solution increased linearly with Hf additions (Fig. 2, curve C) and obeys the empirical equation:
186
M. Hajjaji / Journal of Alloys and Compounds 274 (1998) 185 – 188
Fig. 1. Microhardness of Ni-X at.% Hf alloys (X ,0.8%) annealed at 10608C for 25 h. Testing weights: 27 g; 37 g.
aa 5 a Ni (1 1 0.51933XHf ) where a Ni is the extrapolated lattice parameter for pure Ni (0.35240 nm). This value is close to that determined experimentally (0.35238 nm). XHf is the actual hafnium content, in at.%. As can be deduced from the previous figure, the solubility limit at 10608C is 0.6560.05 at.% Hf. The variation of the cell parameter of the Ni(Hf) solid solutions, forming Ni-2 at.% Hf samples, as a function of
Fig. 2. Ni(Hf) cell parameter as a function of Hf additions. C: experimental curve; C o : Vegard’s law; C 1 : theoretical curve.
ageing temperatures (500,T ,11008C) is reported in Fig. 3. It is worth noting that measurements were not conducted below 5008C because the equilibrium state required a long ageing time (e.g. .400 h for 5008C) and under such condition, a thin layer of contamination was evolved. As shown in Fig. 3, the lattice parameter increases moderately for T below about 9608C. However, it exhibits a drastic increase for higher temperatures. As a consequence of the latter effect, it is expected that the solubility of hafnium at the eutectic temperature could not be determined with accuracy. The combination of the results reported in Fig. 2 and Fig. 3 allowed the determination of the solid solubility curve depicted in Fig. 4. The maximum Hf solubility at the eutectic temperature is estimated to be 1.3 at.% Hf. This value is slightly higher than the reported ones [3,7]. This may be due to differences in the investigation techniques and / or the amount and the nature of hafnium impurities. The increase in the lattice parameter and the strengthening of the a solid solution due to Hf additions are expected since the atomic size of the solute (R Hf 50.159 nm) is larger than that of the solvent (R Ni 50.125 nm). Based on the elastic theory [8], the lattice parameter of Ni(Hf) solid solution would change with Hf content according to the relation: R Ni 2 R Hf da ] 5 2 ]]] ? x ? dXHf a Ni R Ni
Fig. 3. Variation of the cell parameter of Ni(Hf), forming Ni-2 at.% Hf sample, as a function of the ageing temperature.
M. Hajjaji / Journal of Alloys and Compounds 274 (1998) 185 – 188
187
Fig. 5. Variation of ln XHf with reciprocal absolute temperature.
0.3 at.% Hf is around 17 kJ / mol. However, DHHf is about 113 kJ / mol for the Hf-rich solid solutions. This latter high value of DHHf is likely the result of the occurrence of a large misfit of the solute in the Ni crystal, as reported elsewhere [9].
Fig. 4. Solvus curve of Ni-Hf system.
where x is the compressibility factor:
x 5 (1 1 a ) /(KNi /KHf 1 a ), with a 5 (1 1 n ) / 2(1 2 2n ). K is the bulk modulus and n the Poisson’s ratio of the solvent. The values of the ratio KNi /KHf and n are around 2 and 1 / 3, respectively. The integration of the above equation yields to:
S
3(R Hf 2 R Ni ) aa 5 a Ni 1 1 ]]]] ? XHf 4R Ni
D
or,
4. Conclusion The results of this study show that up to about 9608C, the Hf solid solubility is accurately determined. However, there is a significant error for higher temperatures. The maximum solubility at the eutectic temperature is estimated to be 1.3 at.%. The solubility of Hf has a marked effect on the cell parameter. This fact is not governed by the elastic theory but may be caused by the presence of an electrostatic interaction phenomenon. Furthermore, for small Hf solubilities (up to about 0.3 at.%) the molar enthalpy of Hf in solution is 17 kJ / mol. Nevertheless, it is much higher (about 113 kJ / mol) for the Hf-rich solid solution. This may be due to a large misfit of Hf in the Ni crystal.
aa 5 a Ni (1 1 0.21265XHf ). This equation representing the theoretical evolution of a a as a function of Hf additions is plotted in Fig. 2 (curve C 1 ). The negative deviation from Vegard’s law (curve C o in Fig. 2) is expected since x,1. Although the elastic theory predicts an increase of a a with Hf additions it does not describe the experimental result. It seems therefore, that the atomic size is not the only factor which controls the change of Ni(Hf) lattice parameter with Hf additions. There is likely a contribution of an electrostatic phenomenon which is characterized by repulsive interactions between the unlike atoms. In order to determine the molar enthalpy of hafnium (DHHf ) in Ni(Hf) solid solution the variation of ln XHf vs. 1 /T was depicted (Fig. 5). This curve which may be decomposed into two linear branches characterizes the formation of a non-ideal solid solution. The estimated value of DHHf for dilute solid solutions containing up to
Acknowledgements This work was done at the materials science laboratory ´ of the Ecole Superieure de Chimie de Toulouse (France). I thank Professor B. Pieraggi for interesting scientific discussions.
References [1] M.E. Kirkpatrick, W.L. Larsen, Trans. ASM. 54 (1961) 580. [2] V.N. Svechnikov, A.K. Shurin, G.P. Dimitrieva, Izvestrya Akad. Nauk. SSSR, Metall. 6 (1967) 176. [3] P. Nash, A. Nash, in: T.B. Massalski (Ed.), Binary Alloy Phase Diagrams, 2nd edition, vol. 2, ASM, 1992, p. 2094. [4] M. Hajjaji, B. Pieraggi, F. Dabosi, in: J.M.S.M. 94 Proceedings edited by Fac. Sci. Ain Chock and E.N.S.E.M. Casablanca (Morocco), vol. 1, 1994, p. 136.
188
M. Hajjaji / Journal of Alloys and Compounds 274 (1998) 185 – 188
[5] B.D. Cullity, Elements of X-ray Diffraction, Addison-Wesley, 1978, p. 359. [6] M. Van Rooyen, P.F. Colijn, T.H.H. De Keijser, E.J. Mittemeijer, J. Mater. Sci. 21 (1986) 2373.
[7] R. Reinbach, Z. Metallkde. 51(5) (1960) 292. ´ ´ ´ ´ [8] J. Benard, A. Michel, J. Philibert, J. Talbot, Metallurgie Generale, Masson et Cie, 1969, p. 47. [9] R.A. Swalin, Thermodynamics of Solids, John Wiley, 1966, p. 138.