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On the path dependence of the thermal vacancy concentration in stoichiometric FeAl
Intermetallics 12 (2004) 111–115 www.elsevier.com/locate/intermet
On the path dependence of the thermal vacancy concentration in stoichiometric FeAl J.H. Schneibela,*, P.R. Munroeb a
Metals and Ceramics Division, Oak Ridge National Laboratory, PO Box 2008, Oak Ridge, TN 37831, USA School of Materials Science and Engineering, University of New South Wales, Sydney, NSW 2052, Australia
b
Abstract Bulk density and dilatometer measurements were carried out for stoichiometric iron aluminide (FeAl) in order to determine the thermal vacancy concentrations as a function of time and temperature. For temperatures of 600 C and below the specimen bulk density or length were found to depend on heat treatment history, i.e., they were not unique functions of the temperature. This path dependence suggests a lack of active sources and sinks for thermal vacancies in FeAl at temperatures below 600 C. # 2003 Elsevier Ltd. All rights reserved. Keywords: A. Iron aluminides (based on FeAl); B. Thermal properties, thermodynamic properties; D. Defects: point defects, vacancies
1. Introduction It is well established that iron aluminides with the B2 structure (or ordered bcc structure) may contain significant concentrations of thermal vacancies up to several atomic per cent. For example, Kerl et al. [1] measured a value of 3.3 at.% for stoichiometric FeAl at 1178 C. Chang et al. [2] developed a thermodynamic model to predict the concentration of thermal vacancies in iron aluminides as a function of both the Al concentration and temperature. Pike et al.’s measurements of vacancy concentrations in iron aluminides [3] are in good agreement with Chang et al.’s model. One reason why thermal vacancies in iron aluminides are so important is their pronounced influence on mechanical properties. Thermal vacancies can significantly increase the strength and decrease the ductility of iron aluminides [4]. Furthermore, George et al. have convincingly shown that quenched-in thermal vacancies are the reason for an anomalous increase of the yield strength of iron-rich aluminides with temperature [5]. The interpretation of the strength of iron aluminides becomes even more complicated when Fe is partially replaced by ternary elements such as Ni [4,6–8]. Similarly, point defects such as anti-site defects, constitu* Corresponding author. Tel.: +1-865-576-4644; fax: +1-865-5747659. E-mail address: [email protected] (J.H. Schneibel). 0966-9795/$ - see front matter # 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.intermet.2003.09.004
tional vacancies and triple defects (consisting of two vacancies on the Fe sublattice and one Fe anti-site atom on the Al sublattice [2]) exist in significant concentrations, especially, in off-stoichiometric compositions. These defects also contribute to the mechanical behavior of these materials. In order to generate or remove thermal vacancies to reach the equilibrium concentration corresponding to a given temperature, holding time is an important factor. Rivie`re and Grilhe´, using electrical resistivity as a probe to measure vacancy concentration, carried out careful experiments on the kinetics of vacancy removal [9]. When the aluminum concentration is increased or the annealing temperature reduced, the rate of vacancy removal decreases [9,10] and long times are needed to ensure that the equilibrium values corresponding to a given temperature are reached. Following Nagpal and Baker’s paper on the dependence of the microhardness on annealing [11], a heat treatment of 5 days at 400 C has become almost standard in iron aluminides for removing excess thermal vacancies ahead of further experiments. However, in the current study of stoichiometric iron aluminide such a heat treatment is shown to be insufficient to completely remove excess thermal vacancies. To make matters worse, the vacancy ‘‘equilibrium’’ concentration at a temperature of 600 C or below is seen to depend on the heat treatment history. In other words, within typical experimental windows the ‘‘equilibrium’’ vacancy concentration is path dependent.
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This path dependence complicates the measurement of physical quantities that are derived from vacancy concentration measurements, such as enthalpies of formation and migration energies for vacancies.
with controlled thermal histories were examined by transmission electron microscopy (TEM) to obtain microstructural information such as dislocation densities.
3. Experimental results and discussion 2. Experimental procedure Stoichiometric FeAl was prepared by arc-melting a mixture of 99.99 wt.% pure elemental materials in a partial pressure of argon. The resulting button was re-melted several times in order to improve homogeneity and then drop-cast into a cylindrical water-cooled copper mold with a diameter of 25 mm. During the melting and casting a small weight loss was incurred. If it is assumed that this weight loss was due only to evaporation of Al the final composition was Fe–49.83 at.% Al. The true composition is presumably somewhere between this and the stoichiometric composition. From the ingot, a 202010 mm block (for bulk density measurements) and a rod with a length of 25 mm and a diameter of 6 mm (for dilatometer experiments) were electro-discharge machined. After homogenizing for 3 days at 1000 C in air the specimens were annealed for 3 days at 700 C in air followed by oil quenching. The bulk density values were evaluated by weighing in air and in water. Prior to the measurements the water was boiled to remove any trapped air. Care was taken to remove air bubbles that formed occasionally when the block was immersed in the water. Both the temperature of the water and the air, as well as the humidity of the air, were recorded. The data was evaluated using the equations given by Bowman et al. [12]. In the equation for the density of water [Bowman et al.’s Eq. (1)] the third and fourth term correcting for air pressure and dissolved air were ignored. In the equation for the density of air [Bowman et al.’s Eq. (4)] the air pressure was set to 98.4 kPa (740 mm Hg). In order to maximize reproducibility, a single block of FeAl was used for all density experiments. The reproducibility of the density measurements was 2 parts in 10,000. The length of the FeAl rod was continuously measured in a Theta Industries Inc. dilatometer programmed to run various temperature schedules. Temperature changes were performed with linear ramps lasting 0.5 h. Because of the long-term nature of the tests, small temperature jumps occurred occasionally for unknown reasons. These jumps were small enough to allow unambiguous interpretation of the experiments—they corresponded to an error in the displacement of only 0.005%. The long-term stability of the dilatometer was better than 0.01%. Also, since the effects studied were fairly pronounced the fact that the end surfaces of the specimens were used as-machined and had a thin oxide layer from the air anneals was not considered significant for the interpretation of the experiments. Selected specimens
3.1. Kinetics of the production or removal of thermal vacancies As shown by Chang et al. [2] stoichiometric iron aluminide exhibits a rapidly increasing concentration of thermal vacancies as the temperature is increased. By quenching a specimen from high temperatures (e.g., 1000 C) into oil or water, significant concentrations of thermal vacancies are retained. When the specimen is annealed at a gradually increasing temperature, conventional thermal expansion of the lattice occurs on the one hand, and contraction due to the removal of quenched-in vacancies on the other. The contraction due to the vacancy removal can be so pronounced that the apparent coefficient of thermal expansion can be temporarily negative during heat-up (Fig. 1). The block of FeAl was annealed for 72 h at 700 C and oil-quenched. Subsequent annealing at 450 C for up to 400 h led to an increase of its density . Fig. 2 shows this increase as a function of annealing time. A fit of the form ¼ o þ Do ½1 expðt= Þ , where o is the starting value of the density and o+o its final value after long times, indicates a time constant, , of 79 h. A linear extrapolation of Rivie`re and Grilhe´ ’s [9] vacancy migration energies to an aluminum concentration of 50 at.% predicts a value of 1.8 eV. Using the time constant of 79 h at 450 C as a reference point, Table 1 shows the time constants estimated for the temperatures of interest according to: ¼ 79 h
expð1:8 eV=ðkB TÞÞ ; expð1:8 eV=ðkB 723 KÞÞ
ð1Þ
Fig. 1. Thermal expansion during heating of FeAl previously quenched from 1000 C. The solid and broken lines show the thermal expansion and temperature, respectively, as a function of time.
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Fig. 2. Density measurements showing the removal of excess thermal vacancies during annealing of a FeAl specimen that was previously annealed for 72 h at 700 C. Table 1 Estimated time constants for vacancy removal in stoichiometric FeAl using kinetic data at 450 C (Fig. 2) and a value of the migration energy of 1.8 eV obtained by linear extrapolation of Riviere and Grilhe’s data [9] Temperature ( C)
Time constant t (h)
400 450 500 550 600
626 79 (directly measured) 12.2 2.4 0.55
where kB is Boltzmann’s constant and T the temperature in K. Experimental data for 550 C indicate a value of 2.9 h (Fig. 2), which is broadly consistent with Rivie`re and Grilhe´. When the annealing time at a particular temperature is more than three times the time constant, vacancy equilibrium corresponding to that temperature is approximately reached. It is noteworthy that the time constant for 400 C is in excess of 600 h. Approximately 3 ffi 1800 h would be required at this temperature to remove the excess thermal vacancies quenched in from a 700 C anneal. This shows that a typical anneal of 120 h at 400 C is not long enough to remove all excess vacancies in stoichiometric FeAl. 3.2. Path dependence of the thermal vacancy concentration Fig. 3 shows the density as a function of time for a specimen subjected to three 550 C annealing segments, (a), (b), and (c). The heat treatments prior to each 550 C anneal are indicated in Fig. 3. They were always preceded by a ‘‘conditioning’’ anneal for 72 h at 700 C that resulted in a reproducible value of the density and presumably in the same, well-defined starting microstructure. Segment (a) in Fig. 3 shows what happens to
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Fig. 3. Dependence of the density of FeAl at 550 C on the heat treatment history.
the density of a specimen that had been conditioned at 700 C followed by annealing at 450 C for a time long enough to reach vacancy equilibrium (i.e., 369 h). During annealing at 550 C the density decreased slightly, presumably due to the creation of additional vacancies. According to Table 1, the duration, 25 h, of the 550 C anneal was long enough to reach equilibrium. The specimen was then re-conditioned at 700 C for 72 h followed by quenching into oil. During the subsequent anneal at 550 C for 117 h its density increased because in this case thermal vacancies were removed [see segment (b) in Fig. 3]. Again, according to Table 1 the time at 550 C should have been long enough to reach the equilibrium vacancy concentration in segment (b). However, the ‘‘equilibrium’’ density is much lower than that obtained during the 550 C anneal in segment (a). Segment (c) shown in Fig. 3 is essentially a repetition of segment (a) and shows that the higher value of the ‘‘equilibrium’’ density can be reproduced. In other words, within the time scale of our experiment the vacancy ‘‘equilibrium’’ concentration at 550 C is not a unique function of the annealing temperature. It depends on the prior annealing history of the specimen. Since the results of the density measurements were unexpected, an independent set of dilatometer measurements was carried out for verification. Prior to each measurement, the specimen was conditioned in the dilatometer by annealing long enough at 700 C to reach equilibrium. Similar to the density measurements, the dilatometer data shows that the ‘‘equilibrium’’ density at 600 C depends on the temperature of the previous heat treatment (Fig. 4). As shown by segments (a) and (b), prior annealing at 700 C resulted in a higher 600 C expansion (lower ‘‘equilibrium’’ density) than prior annealing at 500 C. In order to determine the magnitude of the path dependence the bulk density values in Fig. 3 were converted into vacancy concentrations. The vacancy concentrations corresponding to 700 and 450 C determined in the companion paper [13] were used as calibration values
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Fig. 4. Dilatometer data for FeAl demonstrating the path dependence of the vacancy concentration at 600 C [segments (a) and (b)].
(Table 2). The difference in the vacancy concentrations corresponding to 450 and 700 C can be written as C ½1=ð700 CÞ 1=ð450 CÞ , where C is a proportionality factor chosen to match the difference between the vacancy concentrations at 450 and 750 C in the first two rows of Table 2. With this value of C, the vacancy concentrations corresponding to the 550 C anneals can then be interpolated from the bulk density values as 0:085% þ C ½1=ð550 CÞ 1=ð450 CÞ , where 0.085% is the value of the vacancy concentration at 450 C. The results are listed in Table 2 and plotted in Fig. 5. Clearly, depending on the path, i.e., the prior heat treatment, the ‘‘equilibrium’’ vacancy concentration at 550 C can be either lower or higher than the line connecting the 700 and 450 C data points in Fig. 5. Specimens annealed at 550 C were examined in a TEM in order to determine whether there was any difference between the microstructure of 550 C annealed specimens that were previously annealed at 700 or 450 C. It is well established for iron aluminides that dislocations form during vacancy-removal annealing at low temperatures such as 400 C [4,6,7]. The Burgers vectors of the dislocations following both heat treatments were < 001 > . This is consistent with prior studies of stoichiometric FeAl following similar heat treatments [6,14,15]. It is known that in iron-rich alloys, some dislocations with < 111 > Burgers vectors may also form during heat treatments designed to lower the vacancy
Fig. 5. Determination of the vacancy concentrations for FeAl annealed at 550 C by interpolation of bulk density values, and using independently measured values at 700 and 450 C [13]. Note that the vacancy concentration cv is in mole fractions, not at.%.
concentration, but such defects were not observed here [16–19]. Fig. 6 shows that the dislocation density of a specimen annealed at 550 C that was previously annealed at 450 C is approximately 10 times higher than that of a specimen previously annealed at 700 C. The average dislocation spacing is proportional to 1=2 . Assuming that the dislocations act as sources or sinks for thermal vacancies and that the diffusion distances for vacancies are proportional to the square root of the time, the time constant 2 for vacancy removal is proportional to 1=2 ¼ 1 . Based on the dislocation densities, the time constant for vacancy generation upon increasing the temperature from 450 to 550 C should then be 1=10 of that for removing vacancies upon decreasing the temperature from 700 to 550 C. Fig. 3 does not support such a large difference in the kinetics. This suggests that none or only a fraction of the observed dislocations are active sources/sinks for the thermal vacancies. It is therefore not clear what the nature of the sources and sinks for the vacancies is. Grain boundaries can be ruled out as effective sources and sinks since the grain size of the specimens was in the millimeter range and above. It is speculated that at high temperatures active dislocation sources and sinks form relatively easily and the equilibrium vacancy concentration may be reached in a relatively small amount of time, whereas this does not
Table 2 Evaluation of the vacancy concentrations at 550 C by interpolation with the measured bulk density values. The independently measured vacancy concentrations at 700 and 450 C [13] were used as calibration values Temperature of initial anneal ( C)
Annealing temperature ( C)
1000/T (1/K)
Measured bulk density (Mg/m3)
Vacancy concentration (at.%)
700 700 450 450 700
700 450 550 550 550
1.0277 1.3831 1.2151 1.2151 1.2151
5.4931 5.5194 5.5187 5.5178 5.4971
0.774—see Ref. [13] 0.085—see Ref. [13] 0.10325—interpolated 0.12673—interpolated 0.66879—interpolated
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4. Summary and conclusions In stoichiometric FeAl, the concentration of thermal vacancies was assessed by bulk density and length measurements. Within our experimental window, the vacancy concentration at 550 and 600 C depended on the annealing history. Evaluation of the dislocation densities suggests that at 600 C or below not all dislocations were active sources or sinks for thermal vacancies. It is conceivable that much longer annealing times might remove the path dependence of the vacancy concentration. The results suggest that measurements of the enthalpy of formation for stoichiometric FeAl at temperatures of 600 C and below depend on the annealing history.
Acknowledgements This research was sponsored by the Division of Materials Sciences and Engineering, US Department of Energy, under Contract DE-AC05-00OR22725 with UT-Battelle, LLC.
References
Fig. 6. TEM micrographs of FeAl specimens annealed for >55 h at 700 C followed by (a) 336 h at 450 C and 119 h at 550 C and (b) 118 h at 550 C. The dislocation density values are 1013 and 1012 m2, respectively.
hold true for relatively low temperatures such as 550 and 600 C. It is suggested that the ‘‘equilibria’’ observed at 550 C for the density measurements and at 600 C for the dilatometer experiments are not true equilibria. Instead, they are kinetically limited by the lack of active vacancy sources or sinks. It is of course possible that much longer annealing times would result in vacancy concentrations that are a unique function of temperature. Our finding casts doubts on the validity of vacancy formation enthalpy measurements for stoichiometric FeAl at temperatures at and below 600 C. Such measurements give reproducible results only when the prior annealing history is rigorously defined. Even if reproducible results are obtained they depend on the prior annealing history and their physical meaning is therefore not clear [13]. As pointed out in the introduction the situation is complicated further by the fact that stoichiometric FeAl exhibits more than one type of defect [20–22].
[1] Kerl R, Wolff J, Hehenkamp Th. Intermetallics 1999;7:301–8. [2] Chang YA, Pike LM, Liu CT, Bilbrey AR, Stone DS. Intermetallics 1993;1:107–15. [3] Pike LM, Chang YA, Liu CT. Acta Mater 1997;45:3709–19. [4] Baker I, Munroe PR. Int Mater Rev 1997;42:181–205. [5] George EP, Baker I. Philos Mag A 1998;77(3):737–50. [6] Kong CH, Munroe PR. Intermetallics 1994;2:333–41. [7] Munroe PR. In: Deevi SC, Maziasz PJ, Sikka VK, Cahn RW, editors. International symposium on nickel and iron aluminides: processing, properties, and applications. Materials Park (OH): ASM International; 1997. p. 95–113. [8] Schneibel JH. Mater Sci Eng 1998;A258:181–6. [9] Rivie`re JP, Grilhe´ J. Phys Stat Sol (a) 1974;25:429–36. [10] Wu¨rschum R, Grupp C, Schaefer H-E. Phys Rev Lett 1995; 75(1):97–100. [11] Nagpal P, Baker I. Metall Trans A 1990;21A:2281–2. [12] Bowman HA, Schoonover RM, Journal of Research of the National Bureau of Standards—C. Engineering and Instrumentation. 1967;71C(3): 179–98. [13] Schneibel JH, Pike LM, A technique for measuring thermal vacancy concentrations in stoichiometric FeAl. [submitted]. [14] Kong CH, Munroe PR. Scripta Metall Mater 1994;30:1079–83. [15] Kong CH, Munroe PR. In: Schneibel J, Crimp M, editors. Processing, properties and applications of iron aluminides. Warrendale (PA): TMS; 1994. p. 231–40. [16] Morris MA, George O, Morris DG. Mater Sci Eng 1998; A258:99–107. [17] Morris DG, Joye JC, Leboeuf M. Philos Mag 1994;69:961–80. [18] Fourdeux A, Lesbats P. Philos Mag A 1982;45:81–93. [19] Junqua N, Grilhe J. Philos Mag A 1982;46:295–305. [20] Fa¨hnle M, Meyer B, Bester G. Intermetallics 1999;7:1307–8. [21] Bester G, Meyer B, Fa¨hnle M, Fu CL. Mater Sci Eng 2002; A323:487–90. [22] Fu CL. Phys Rev B 1995;52(5):3151–8.
On the path dependence of the thermal vacancy concentration in stoichiometric FeAl J.H. Schneibela,*, P.R. Munroeb a
Metals and Ceramics Division, Oak Ridge National Laboratory, PO Box 2008, Oak Ridge, TN 37831, USA School of Materials Science and Engineering, University of New South Wales, Sydney, NSW 2052, Australia
b
Abstract Bulk density and dilatometer measurements were carried out for stoichiometric iron aluminide (FeAl) in order to determine the thermal vacancy concentrations as a function of time and temperature. For temperatures of 600 C and below the specimen bulk density or length were found to depend on heat treatment history, i.e., they were not unique functions of the temperature. This path dependence suggests a lack of active sources and sinks for thermal vacancies in FeAl at temperatures below 600 C. # 2003 Elsevier Ltd. All rights reserved. Keywords: A. Iron aluminides (based on FeAl); B. Thermal properties, thermodynamic properties; D. Defects: point defects, vacancies
1. Introduction It is well established that iron aluminides with the B2 structure (or ordered bcc structure) may contain significant concentrations of thermal vacancies up to several atomic per cent. For example, Kerl et al. [1] measured a value of 3.3 at.% for stoichiometric FeAl at 1178 C. Chang et al. [2] developed a thermodynamic model to predict the concentration of thermal vacancies in iron aluminides as a function of both the Al concentration and temperature. Pike et al.’s measurements of vacancy concentrations in iron aluminides [3] are in good agreement with Chang et al.’s model. One reason why thermal vacancies in iron aluminides are so important is their pronounced influence on mechanical properties. Thermal vacancies can significantly increase the strength and decrease the ductility of iron aluminides [4]. Furthermore, George et al. have convincingly shown that quenched-in thermal vacancies are the reason for an anomalous increase of the yield strength of iron-rich aluminides with temperature [5]. The interpretation of the strength of iron aluminides becomes even more complicated when Fe is partially replaced by ternary elements such as Ni [4,6–8]. Similarly, point defects such as anti-site defects, constitu* Corresponding author. Tel.: +1-865-576-4644; fax: +1-865-5747659. E-mail address: [email protected] (J.H. Schneibel). 0966-9795/$ - see front matter # 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.intermet.2003.09.004
tional vacancies and triple defects (consisting of two vacancies on the Fe sublattice and one Fe anti-site atom on the Al sublattice [2]) exist in significant concentrations, especially, in off-stoichiometric compositions. These defects also contribute to the mechanical behavior of these materials. In order to generate or remove thermal vacancies to reach the equilibrium concentration corresponding to a given temperature, holding time is an important factor. Rivie`re and Grilhe´, using electrical resistivity as a probe to measure vacancy concentration, carried out careful experiments on the kinetics of vacancy removal [9]. When the aluminum concentration is increased or the annealing temperature reduced, the rate of vacancy removal decreases [9,10] and long times are needed to ensure that the equilibrium values corresponding to a given temperature are reached. Following Nagpal and Baker’s paper on the dependence of the microhardness on annealing [11], a heat treatment of 5 days at 400 C has become almost standard in iron aluminides for removing excess thermal vacancies ahead of further experiments. However, in the current study of stoichiometric iron aluminide such a heat treatment is shown to be insufficient to completely remove excess thermal vacancies. To make matters worse, the vacancy ‘‘equilibrium’’ concentration at a temperature of 600 C or below is seen to depend on the heat treatment history. In other words, within typical experimental windows the ‘‘equilibrium’’ vacancy concentration is path dependent.
112
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This path dependence complicates the measurement of physical quantities that are derived from vacancy concentration measurements, such as enthalpies of formation and migration energies for vacancies.
with controlled thermal histories were examined by transmission electron microscopy (TEM) to obtain microstructural information such as dislocation densities.
3. Experimental results and discussion 2. Experimental procedure Stoichiometric FeAl was prepared by arc-melting a mixture of 99.99 wt.% pure elemental materials in a partial pressure of argon. The resulting button was re-melted several times in order to improve homogeneity and then drop-cast into a cylindrical water-cooled copper mold with a diameter of 25 mm. During the melting and casting a small weight loss was incurred. If it is assumed that this weight loss was due only to evaporation of Al the final composition was Fe–49.83 at.% Al. The true composition is presumably somewhere between this and the stoichiometric composition. From the ingot, a 202010 mm block (for bulk density measurements) and a rod with a length of 25 mm and a diameter of 6 mm (for dilatometer experiments) were electro-discharge machined. After homogenizing for 3 days at 1000 C in air the specimens were annealed for 3 days at 700 C in air followed by oil quenching. The bulk density values were evaluated by weighing in air and in water. Prior to the measurements the water was boiled to remove any trapped air. Care was taken to remove air bubbles that formed occasionally when the block was immersed in the water. Both the temperature of the water and the air, as well as the humidity of the air, were recorded. The data was evaluated using the equations given by Bowman et al. [12]. In the equation for the density of water [Bowman et al.’s Eq. (1)] the third and fourth term correcting for air pressure and dissolved air were ignored. In the equation for the density of air [Bowman et al.’s Eq. (4)] the air pressure was set to 98.4 kPa (740 mm Hg). In order to maximize reproducibility, a single block of FeAl was used for all density experiments. The reproducibility of the density measurements was 2 parts in 10,000. The length of the FeAl rod was continuously measured in a Theta Industries Inc. dilatometer programmed to run various temperature schedules. Temperature changes were performed with linear ramps lasting 0.5 h. Because of the long-term nature of the tests, small temperature jumps occurred occasionally for unknown reasons. These jumps were small enough to allow unambiguous interpretation of the experiments—they corresponded to an error in the displacement of only 0.005%. The long-term stability of the dilatometer was better than 0.01%. Also, since the effects studied were fairly pronounced the fact that the end surfaces of the specimens were used as-machined and had a thin oxide layer from the air anneals was not considered significant for the interpretation of the experiments. Selected specimens
3.1. Kinetics of the production or removal of thermal vacancies As shown by Chang et al. [2] stoichiometric iron aluminide exhibits a rapidly increasing concentration of thermal vacancies as the temperature is increased. By quenching a specimen from high temperatures (e.g., 1000 C) into oil or water, significant concentrations of thermal vacancies are retained. When the specimen is annealed at a gradually increasing temperature, conventional thermal expansion of the lattice occurs on the one hand, and contraction due to the removal of quenched-in vacancies on the other. The contraction due to the vacancy removal can be so pronounced that the apparent coefficient of thermal expansion can be temporarily negative during heat-up (Fig. 1). The block of FeAl was annealed for 72 h at 700 C and oil-quenched. Subsequent annealing at 450 C for up to 400 h led to an increase of its density . Fig. 2 shows this increase as a function of annealing time. A fit of the form ¼ o þ Do ½1 expðt= Þ , where o is the starting value of the density and o+o its final value after long times, indicates a time constant, , of 79 h. A linear extrapolation of Rivie`re and Grilhe´ ’s [9] vacancy migration energies to an aluminum concentration of 50 at.% predicts a value of 1.8 eV. Using the time constant of 79 h at 450 C as a reference point, Table 1 shows the time constants estimated for the temperatures of interest according to: ¼ 79 h
expð1:8 eV=ðkB TÞÞ ; expð1:8 eV=ðkB 723 KÞÞ
ð1Þ
Fig. 1. Thermal expansion during heating of FeAl previously quenched from 1000 C. The solid and broken lines show the thermal expansion and temperature, respectively, as a function of time.
J.H. Schneibel, P.R. Munroe / Intermetallics 12 (2004) 111–115
Fig. 2. Density measurements showing the removal of excess thermal vacancies during annealing of a FeAl specimen that was previously annealed for 72 h at 700 C. Table 1 Estimated time constants for vacancy removal in stoichiometric FeAl using kinetic data at 450 C (Fig. 2) and a value of the migration energy of 1.8 eV obtained by linear extrapolation of Riviere and Grilhe’s data [9] Temperature ( C)
Time constant t (h)
400 450 500 550 600
626 79 (directly measured) 12.2 2.4 0.55
where kB is Boltzmann’s constant and T the temperature in K. Experimental data for 550 C indicate a value of 2.9 h (Fig. 2), which is broadly consistent with Rivie`re and Grilhe´. When the annealing time at a particular temperature is more than three times the time constant, vacancy equilibrium corresponding to that temperature is approximately reached. It is noteworthy that the time constant for 400 C is in excess of 600 h. Approximately 3 ffi 1800 h would be required at this temperature to remove the excess thermal vacancies quenched in from a 700 C anneal. This shows that a typical anneal of 120 h at 400 C is not long enough to remove all excess vacancies in stoichiometric FeAl. 3.2. Path dependence of the thermal vacancy concentration Fig. 3 shows the density as a function of time for a specimen subjected to three 550 C annealing segments, (a), (b), and (c). The heat treatments prior to each 550 C anneal are indicated in Fig. 3. They were always preceded by a ‘‘conditioning’’ anneal for 72 h at 700 C that resulted in a reproducible value of the density and presumably in the same, well-defined starting microstructure. Segment (a) in Fig. 3 shows what happens to
113
Fig. 3. Dependence of the density of FeAl at 550 C on the heat treatment history.
the density of a specimen that had been conditioned at 700 C followed by annealing at 450 C for a time long enough to reach vacancy equilibrium (i.e., 369 h). During annealing at 550 C the density decreased slightly, presumably due to the creation of additional vacancies. According to Table 1, the duration, 25 h, of the 550 C anneal was long enough to reach equilibrium. The specimen was then re-conditioned at 700 C for 72 h followed by quenching into oil. During the subsequent anneal at 550 C for 117 h its density increased because in this case thermal vacancies were removed [see segment (b) in Fig. 3]. Again, according to Table 1 the time at 550 C should have been long enough to reach the equilibrium vacancy concentration in segment (b). However, the ‘‘equilibrium’’ density is much lower than that obtained during the 550 C anneal in segment (a). Segment (c) shown in Fig. 3 is essentially a repetition of segment (a) and shows that the higher value of the ‘‘equilibrium’’ density can be reproduced. In other words, within the time scale of our experiment the vacancy ‘‘equilibrium’’ concentration at 550 C is not a unique function of the annealing temperature. It depends on the prior annealing history of the specimen. Since the results of the density measurements were unexpected, an independent set of dilatometer measurements was carried out for verification. Prior to each measurement, the specimen was conditioned in the dilatometer by annealing long enough at 700 C to reach equilibrium. Similar to the density measurements, the dilatometer data shows that the ‘‘equilibrium’’ density at 600 C depends on the temperature of the previous heat treatment (Fig. 4). As shown by segments (a) and (b), prior annealing at 700 C resulted in a higher 600 C expansion (lower ‘‘equilibrium’’ density) than prior annealing at 500 C. In order to determine the magnitude of the path dependence the bulk density values in Fig. 3 were converted into vacancy concentrations. The vacancy concentrations corresponding to 700 and 450 C determined in the companion paper [13] were used as calibration values
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Fig. 4. Dilatometer data for FeAl demonstrating the path dependence of the vacancy concentration at 600 C [segments (a) and (b)].
(Table 2). The difference in the vacancy concentrations corresponding to 450 and 700 C can be written as C ½1=ð700 CÞ 1=ð450 CÞ , where C is a proportionality factor chosen to match the difference between the vacancy concentrations at 450 and 750 C in the first two rows of Table 2. With this value of C, the vacancy concentrations corresponding to the 550 C anneals can then be interpolated from the bulk density values as 0:085% þ C ½1=ð550 CÞ 1=ð450 CÞ , where 0.085% is the value of the vacancy concentration at 450 C. The results are listed in Table 2 and plotted in Fig. 5. Clearly, depending on the path, i.e., the prior heat treatment, the ‘‘equilibrium’’ vacancy concentration at 550 C can be either lower or higher than the line connecting the 700 and 450 C data points in Fig. 5. Specimens annealed at 550 C were examined in a TEM in order to determine whether there was any difference between the microstructure of 550 C annealed specimens that were previously annealed at 700 or 450 C. It is well established for iron aluminides that dislocations form during vacancy-removal annealing at low temperatures such as 400 C [4,6,7]. The Burgers vectors of the dislocations following both heat treatments were < 001 > . This is consistent with prior studies of stoichiometric FeAl following similar heat treatments [6,14,15]. It is known that in iron-rich alloys, some dislocations with < 111 > Burgers vectors may also form during heat treatments designed to lower the vacancy
Fig. 5. Determination of the vacancy concentrations for FeAl annealed at 550 C by interpolation of bulk density values, and using independently measured values at 700 and 450 C [13]. Note that the vacancy concentration cv is in mole fractions, not at.%.
concentration, but such defects were not observed here [16–19]. Fig. 6 shows that the dislocation density of a specimen annealed at 550 C that was previously annealed at 450 C is approximately 10 times higher than that of a specimen previously annealed at 700 C. The average dislocation spacing is proportional to 1=2 . Assuming that the dislocations act as sources or sinks for thermal vacancies and that the diffusion distances for vacancies are proportional to the square root of the time, the time constant 2 for vacancy removal is proportional to 1=2 ¼ 1 . Based on the dislocation densities, the time constant for vacancy generation upon increasing the temperature from 450 to 550 C should then be 1=10 of that for removing vacancies upon decreasing the temperature from 700 to 550 C. Fig. 3 does not support such a large difference in the kinetics. This suggests that none or only a fraction of the observed dislocations are active sources/sinks for the thermal vacancies. It is therefore not clear what the nature of the sources and sinks for the vacancies is. Grain boundaries can be ruled out as effective sources and sinks since the grain size of the specimens was in the millimeter range and above. It is speculated that at high temperatures active dislocation sources and sinks form relatively easily and the equilibrium vacancy concentration may be reached in a relatively small amount of time, whereas this does not
Table 2 Evaluation of the vacancy concentrations at 550 C by interpolation with the measured bulk density values. The independently measured vacancy concentrations at 700 and 450 C [13] were used as calibration values Temperature of initial anneal ( C)
Annealing temperature ( C)
1000/T (1/K)
Measured bulk density (Mg/m3)
Vacancy concentration (at.%)
700 700 450 450 700
700 450 550 550 550
1.0277 1.3831 1.2151 1.2151 1.2151
5.4931 5.5194 5.5187 5.5178 5.4971
0.774—see Ref. [13] 0.085—see Ref. [13] 0.10325—interpolated 0.12673—interpolated 0.66879—interpolated
J.H. Schneibel, P.R. Munroe / Intermetallics 12 (2004) 111–115
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4. Summary and conclusions In stoichiometric FeAl, the concentration of thermal vacancies was assessed by bulk density and length measurements. Within our experimental window, the vacancy concentration at 550 and 600 C depended on the annealing history. Evaluation of the dislocation densities suggests that at 600 C or below not all dislocations were active sources or sinks for thermal vacancies. It is conceivable that much longer annealing times might remove the path dependence of the vacancy concentration. The results suggest that measurements of the enthalpy of formation for stoichiometric FeAl at temperatures of 600 C and below depend on the annealing history.
Acknowledgements This research was sponsored by the Division of Materials Sciences and Engineering, US Department of Energy, under Contract DE-AC05-00OR22725 with UT-Battelle, LLC.
References
Fig. 6. TEM micrographs of FeAl specimens annealed for >55 h at 700 C followed by (a) 336 h at 450 C and 119 h at 550 C and (b) 118 h at 550 C. The dislocation density values are 1013 and 1012 m2, respectively.
hold true for relatively low temperatures such as 550 and 600 C. It is suggested that the ‘‘equilibria’’ observed at 550 C for the density measurements and at 600 C for the dilatometer experiments are not true equilibria. Instead, they are kinetically limited by the lack of active vacancy sources or sinks. It is of course possible that much longer annealing times would result in vacancy concentrations that are a unique function of temperature. Our finding casts doubts on the validity of vacancy formation enthalpy measurements for stoichiometric FeAl at temperatures at and below 600 C. Such measurements give reproducible results only when the prior annealing history is rigorously defined. Even if reproducible results are obtained they depend on the prior annealing history and their physical meaning is therefore not clear [13]. As pointed out in the introduction the situation is complicated further by the fact that stoichiometric FeAl exhibits more than one type of defect [20–22].
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