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The stress anomaly in FeAl–Fe3Al alloys
Intermetallics 13 (2005) 1269–1274 www.elsevier.com/locate/intermet
The stress anomaly in FeAl–Fe3Al alloys D.G. Morris*, M.A. Mun˜oz-Morris Department of Physical Metallurgy, CENIM, CSIC, Avenida Gregorio del Amo 8, E-28040 Madrid, Spain Received 25 May 2004; received in revised form 3 June 2004; accepted 6 August 2004 Available online 18 April 2005
Abstract The anomalous stress peak observed near 500–600 8C in Fe–Al alloys has now been convincingly explained using a model of hardening by immobile thermal vacancies on the lower temperature side of the peak and the loss of hardening as these vacancies become mobile at higher temperatures. The large numbers of vacancies required for such hardening are associated with compositions close to stoichiometry, i.e. 40– 50%Al, raising the question of whether such a vacancy hardening model can be adopted for Fe3Al alloys, which show a similar stress peak anomaly. Examination of data on vacancy formation over the entire range of composition, Fe–Fe3Al–FeAl, shows that, indeed, a vacancy hardening model appears capable of explaining the stress anomaly for both FeAl and Fe3Al. q 2005 Elsevier Ltd. All rights reserved. Keywords: A. Iron aluminides (based on FeAl); A. Iron aluminides (based on Fe3Al); B. Mechanical properties at high temperatures; D. Defects: point defects
1. Introduction Following decades of experimental and theoretical activity on the study of the stress anomaly in Fe–Al alloys, we are now in a period of relative calm, with little present activity. This is, then, a good time to re-assess present understanding and point out areas of uncertainty in our knowledge, and where future study might be directed.
2. Stress anomaly in FeAl The stress anomaly in FeAl is a relatively new discovery [1–3] and for years it was thought that this intermetallic was different from many, such as Ni3Al, in not showing any anomalous stress peak [4–9] on mechanical testing at intermediate temperatures. It subsequently became clear that an anomalous stress peak indeed existed [1–3], at temperatures in the range 400–600 8C, and a pre-requisite was that the sample material be previously well annealed to ‘relax’ any internal structure [10–14]. * Corresponding author. Tel.: C34 91 553 8900; fax: C34 91 534 7425. E-mail address: [email protected] (D.G. Morris).
0966-9795/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.intermet.2004.08.012
Very many studies of the stress anomaly followed [15–25], both theoretical and experimental, that suggested a very wide range of mechanisms and phenomena responsible for the intermediate temperature hardening, ranging from the transition of dislocation structures from h111i superdislocations to h100i perfect dislocations [2,3,26], climb locking of h111i superdislocations [19,27], cross slip between {110}, {112} and other glide planes [28–31], relaxation of the APB structure enclosed between the partial dislocations of the h111i superdislocations [28,32], to reactions or decompositions of h111i superdislocations to create local pinning points [23,30,33,34]. More recently a vacancy hardening model has been suggested [14,35] based on the observations of large numbers of thermal vacancies at high temperatures in FeAl alloys [36–48] and the significant room temperature hardening produced by such vacancies [10,44,49,50]. This model considers that significant hardening is produced at temperatures below the anomalous stress peak, as the thermal vacancies are produced, since these are immobile, solution hardeners at such temperatures; at sufficiently high temperatures the vacancies become mobile, are able to move with whichever dislocations are present, and hence lose their hardening ability. There has been discrepancy and disagreement, over the years, between various researchers as to the important mechanisms controlling the anomalous stress peak, as reflected in the opinions of various review publications, for example [13,20,25,30]. A major reason for such
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D.G. Morris, M.A. Mun˜oz-Morris / Intermetallics 13 (2005) 1269–1274
Fig. 1. Yield strength after various up-quenching and down-quenching heat treatments (points), as compared to values measured in a standard tensile test (continuous curve). Graph taken from Ref. [14].
uncertainty is the large number of phenomena predicted and observed, and the difficulty of deciding which is the important, controlling process. At the present time, however, the results of several, critical experiments convincingly demonstrate that vacancy hardening on the lower temperature side of the anomalous stress peak, followed by loss of vacancy hardening on the higher temperature side of the peak, are the processes leading to the anomalous peak. Results of two important experiments are shown in Figs. 1 and 2, and relate to the time dependence of the anomalous stress rise [14], and to the comparison of strength at high temperatures and strength at room temperature after quenching from the same high temperatures [50]. Fig. 1 shows (continuous curve) the yield stress
Fig. 2. Variation of yield stress measured at temperature, or at room temperature after quenching from the given temperature. Graph taken from Ref. [50].
measured for a FeAl alloy during conventional tensile testing, and (points) the yield stress after quickly upquenching or down-quenching to the stress peak temperature [14]. Of greatest importance is to note that the samples tested after very short soak times at the peak temperature (less than about 5 min) did not show anomalous hardening. These results demonstrate that (equilibrium) hardness at a given temperature is a state function—once the material reaches its equilibrium state, which requires several minutes, it acquires its equilibrium hardness. This is not consistent with hardening being a dynamically-activated process, occurring at the temperature and during deformation, as opposed to at the temperature but before deformation. It is consistent with a time-scale of the order of 5 min being necessary to create vacancies at (dislocation) sources throughout the material and migrate these vacancies through the grains to create the homogeneous, equilibrium, vacancy-hardened material. Thus, thermallyactivated processes acting on a moving dislocation, such as cross slip, climb, etc. are eliminated as being the controlling processes, and only vacancy hardening remains as a possible mechanism. Furthermore, since hardening is a state-dependent property, a similar hardness can be expected when testing at temperature or when testing a quenched sample at room temperature—apart from some slight solution softening at the high temperature. Fig. 2 shows that this is indeed the case [50], and hardening is very similar when measured on various FeAl alloys at high temperatures (during the anomalous hardening temperature range), and on the same materials at room temperature after quenching from high temperatures. Again, these observations are consistent with hardening being a material state function—dependent only on the temperature—as would be expected of vacancy hardening, but are inconsistent with any thermally-activated dislocation locking process such as cross slip, climb, APB relaxation, etc. The many other experimental observations are consistent with this vacancy hardening model, even though they were ambiguous in not defining which was the controlling hardening mechanism. One important point now clear is that it is no longer necessary for there to be a change of dislocation type (from h111i to h100i, or other) at the stress peak. Thus observations showing that such transitions may sometimes occur, but apparently do so after strains higher than those where the yield stress is determined [34], that the transition can be delayed—in strain or temperature—by higher rates of deformation [25,30], and that high-strain, high-strain-rate deformation at high temperature can lead to textural changes consistent with deformation by h111i dislocations [51], all become understandable. At the same time, it becomes understandable that the orientation dependence of critical resolved shear stress of FeAl crystals shows little change as the test temperature is increased from low temperatures (ambient) to the stress peak temperature [21,26].
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3. Stress anomaly in Fe3Al Section 2 refers to Fe–Al compositions showing only B2 order, namely with Al content of about 35–50%, with most studies carried out on alloys containing about 35–45%Al. Alloys showing DO3 order, namely those with about 25–30%Al, also show similar anomalous stress peaks, and it is of interest to examine whether the vacancy hardening model can be relevant. It is first of interest to note that the stress anomaly in the Fe3Al alloys has essentially all similar characteristics to the anomaly in the B2 FeAl alloys [19,25,29,52–58]. The peak temperature is about 500 8C, the transition of h111i superdislocations to h100i perfect dislocations has been reported as well as cross slip, APB relaxation, dislocation climb and decomposition, and strain-rate dependences of yield stresses are similar to those for FeAl above and below the stress peak. In addition, of importance, several studies with Fe3Al alloys of differing Al contents or with selected ternary additions [52,53,58] have clearly shown that the presence of DO3 order, its absence, and also the transition from DO3 order to B2 order, has no influence on the yield stress or the anomaly. Accordingly, this comparison of Fe3Al alloys and FeAl alloys seems to be justified. Counter to this implication that vacancy hardening is responsible for the stress anomaly at about 500 8C in Fe3Al alloys is the perception that vacancy concentrations are high in near-stoichiometric FeAl alloys, falling rapidly as the Al content decreases to values below 40%. For example, Fig. 3 shows values of the thermal vacancy content deduced for Fe–Al alloys with Al contents in the range about 40–50%, for temperatures near the stress anomaly and higher [49], where it is seen that very high vacancy concentrations near FeAl stoichiometry change to significantly smaller concentrations near 40%Al. It is also noteworthy that experimental measurements of high vacancy contents in Fe–Al alloys have all selected alloys with about 40–50%Al for study, e.g. [36–41,59]. Extrapolating the trend seen in Fig. 3 to
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alloys near Fe3Al stoichiometry, it is clear that very low vacancy concentrations would then be expected, seemingly insufficient to induce a stress anomaly of similar stress magnitude at similar temperature in Fe3Al as in FeAl. Indeed, this argument was earlier used to deduce that vacancy hardening could not be the important strengthening mechanism in Fe3Al alloys [25,30]. Section 4 therefore examines the available evidence on vacancy concentrations in Fe–Al alloys over a wide range of Al contents, to deduce whether the intermediate stress peak anomaly, convincingly explained by solution hardening by thermal vacancies in FeAl alloys, can also be explained by vacancy hardening in Fe3Al alloys.
4. Thermal vacancy concentrations in Fe–Al alloys (over the range Fe–Fe3Al–FeAl) The work of Chang et al. [49] and others leads to the understanding that the thermal vacancy concentration at any temperature will decrease systematically as the Al content decreases, from 50 to 40%, as in these published works, and then continuing to lower Al contents. In a first stage, it is of interest to examine the influence of Al content on the extent of vacancy hardening relative to the base line, of well-annealed single-phase Fe–Al intermetallic. For this the data of Chang et al. [49] will be used, as presented in Fig. 4. Here, the upper set of curves show the Chang et al. [49] data, while the lower set of curves show the hardness difference (increase) due to the formation of thermal vacancies, as related to the samples well annealed at 500 8C and quenched. If it is considered that the 500 8C annealed–quenched samples contained the equilibrium Effect of anneals/vacancy concentration on hardness
700 600
Hardness as quenched
Microhardness (DPH)
500 1000ºC
400 900ºC 300
800ºC 700ºC
Hardness difference
200 1000ºC 900ºC 800ºC
100
700ºC
0 38
Fig. 3. Variation of thermal vacancy concentration with Al content for Fe– Al alloys at several temperatures. Graph taken from Ref. [49].
500ºC
40
42
44 46 48 Aluminium content (%)
50
52
Fig. 4. Variation of microhardness (DPH) of Fe–Al alloys as a function of Al content and after quenching from a variety of annealing temperatures. Hardness difference data are also shown, which are the differences between the hardnesses of the low temperature annealed state (500 8C) and those of materials annealed at higher temperatures. Data taken from Ref. [49].
D.G. Morris, M.A. Mun˜oz-Morris / Intermetallics 13 (2005) 1269–1274
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Effective vacancy formation enthalpy 2.5
2
Disordered A2
∆Ηt
eff
1.5
Ordered DO3, B2', B2(l)
1
0.5
Ordered B2(h)
0 0
10
20
30
40
50
Aluminium content (%) Fig. 5. Effective enthalpy of vacancy formation for Fe–Al alloys as a function of Al content, and according to the ordered state of the material. Data taken from a wide range of literature reports see text for details. (Units for enthalpy are eV/vacancy: 1 eVz96.3 kJ/mol).
vacancy concentration for this temperature, then the hardness difference lines document the increase in hardness due to the formation of thermal vacancies when materials are annealed at the high temperatures. The observation that these difference data can be connected by straight, horizontal lines indicates no Al content dependence of the vacancy hardening—relative to the 500 8C reference state. It can be concluded that either the vacancy concentration is identical for a given temperature, irrespective of the Al content, or else that any lowering of vacancy concentration at low Al contents is compensated by an increase in the specific vacancy hardening (hardness increment per unit vacancy concentration). It may be noted that the dotted lines in Fig. 5 showing constant values of hardness difference for all Al levels may alternatively be replaced by lines showing a maximum at 45%Al with a slow decrease on each side. Insufficient data are available to provide a good extrapolation to 25–30%Al, and the present hypothesis of steady hardness differences for all Al contents remains a reasonable possibility. Further information on vacancy concentration as a function of Al content can be obtained by examining vacancy formation enthalpies. (Admittedly, the thermal vacancy concentration at a given temperature depends on both formation enthalpy and entropy, but in the absence of much data on formation entropy this is assumed to be about constant.) Fig. 5 shows a summary of vacancy formation enthalpy values from very many research studies [39,40,42–44,46,48,49,60–67] as a function of Al content. Data has here been separated into three domains, following the ideas of Hehenkamp and workers [63,65], and according to the phase diagam proposed by Kubaschewski [68].
Data are shown for disordered Fe–Al alloys (A2 structure), for ordered alloys with 25–50%Al at relatively low temperatures with the DO3, B2 0 , and B2(l) structures, and for ordered alloys with 35–50%Al at relatively high temperatures with the B2(h) structure. Separating data families in this way, it becomes possible to understand how some researchers may obtain rather large values for vacancy formation enthalpy, others may obtain moderate values, and yet others small values—essentially depending on the temperatures where measurements of vacancy concentration are made, and within which phase region the alloy lies at this time. It can be seen in Fig. 5 that disordered alloys—Fe–Al alloys of very low Al content, or Fe–Al intermetallics at high temperatures—will have relatively low vacancy concentrations, corresponding to the high formation enthalpy. Of importance for the present report, Fe–Al alloys with Al contents over the full range from 25 to 50% have similar vacancy formation ethalpies at relatively low temperatures (below about 800 8C), and irrespective of whether the intermetallic adopts the DO3, B2 0 , or B2(l) structure. Accordingly, considering that the vacancy concentration will rise in a similar way for Fe3Al alloys and for FeAl alloys as the test temperature is increased towards 500– 700 8C, and considering that the hardening effect of such vacancies is similar for both families of alloys, it appears perfectly reasonable to conclude that the anomalous stress rise observed for all Fe–Al intermetallics is due to the formation of these immobile vacancies. Despite the conclusions of the previous paragraphs, it is admitted that studies carried out consistently by the same authors tend to show a decreasing thermal vacancy content as the Al content falls from 40–45%Al to 25–30%Al. Nevertheless, the enthalpy data of Fig. 5 are consistent with the present hypothesis—similar thermal vacancy content as the Al content falls. The hardness difference data of Fig. 4 are also consistent with similar thermal vacancy hardening for all Al contents (similar specific vacancy hardening and similar vacancy contents, or increasing specific vacancy hardening at lower Al levels as the vacancy content decreases). It should also be remarked that a fall in vacancy migration enthalpy at lower Al levels should imply faster vacancy movement and hence lower temperatures and stress magnitudes for the anomalous peak. Available data on migration enthalpies suggest that the effect on peak characteristics will not be significant for the 30–40%Al range, but may put in doubt the present hypothesis for Al levels of 25–30%.
5. Conclusions The present brief review has examined the characteristic features of the anomalous stress rise at intermediate temperatures in FeAl alloys and, based on the results of
D.G. Morris, M.A. Mun˜oz-Morris / Intermetallics 13 (2005) 1269–1274
several critical experiments, demonstrated that the vacancy hardening model [35] is able to explain this anomalous rise in a highly convincing manner. It has also been shown that Fe3Al alloys have anomalous peaks of very similar characteristics, even though such materials are commonly expected to have much lower vacancy contents than the exceptionally high values found in FeAl alloys. Examination of data on vacancy formation enthalpies, and on the hardening effect of such vacancies, suggests that similar numbers of hardening vacancies may indeed be found in Fe3Al alloys as in FeAl alloys, and vacancy hardening is then the single hardening mechanisms in all Fe3Al–FeAl alloys responsible for the anomalous stress rise at intermediate temperatures. It would, nevertheless, be of interest to re-examine Fe3Al alloys after quenching to confirm that high vacancy concentrations are indeed produced, that they do lead to high hardening, and their elimination leads to similar vacancy aggregates as for FeAl alloys.
6. Uncertainties of understanding, where further studies would be worthwhile The present report analyses existing experimental data to conclude that hardening by a solution of immobile thermal vacancies is responsible for the anomalous stress peak rise at intermediate temperatures in FeAl alloys. It is also suggested that similar thermal vacancies may be responsible for the anomalous stress peak in Fe3Al alloys. There are several areas where our understanding is imperfect, where additional experiments would yield useful information: (i) Fig. 3 shows a gradual decrease in vacancy content, for a given temperature, as the Al level decreases, while Fig. 5 suggests little change in DHf as long as the alloy remains ordered. A consistent re-determination of vacancy content at the moderate temperatures of relevance for the anomaly, 500–700 8C, would be valuable. (ii) In this sense, experiments on quenched and aged materials searching for vacancy clustering—as loops or voids—could be a sensitive method for detecting the consequences of small vacancy supersaturations. (iii) Fig. 4 shows decreasing absolute values of hardness as Al content decreases, but an almost steady level of hardening increment (explained here by vacancies). It would be interesting to extend this data down below 40%Al (while avoiding DO3 order). How does thermal vacancy hardening vary and how the specific hardening (per unit point defect concentration)? (iv) What is the vacancy hardening mechanism? Is this purely a solution hardening effect, of exceptionally high strength, or are there strong jog/APB tube interactions at work? Theoretical modelling and in
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situ deformation experiments would be of interest. Some work has indeed started in this area [69]. (v) Vacancy concentrations are rather small in the temperature range of the anomaly. What is the role of substitutional or interstitial elements/impurities present in similar concentrations? Some studies suggest strong interactions are possible [70,71].
Acknowledgements The authors should like to thank Drs M. Palm and G. Sauthoff, and Mr J. Konrad, of the Max-Planck-Institut fu¨r Eisenforschung, Du¨sseldorf, Germany, for the invitation to attend the highly succesful seminar on iron aluminide alloys. We should also like to thank the various referees and editor for many constructive comments that have helped to make this publication a more convincing and more readable document.
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D.G. Morris, M.A. Mun˜oz-Morris / Intermetallics 13 (2005) 1269–1274 George EP, Baker I. Phil Mag 1998;A77:737. Junqua N, Desoyer JC, Moine P. Phys Status Solidi 1973;A18:387. Paris D, Lesbats P, Levy J. Scripta Metall 1975;9:1373. Riviere JP. Mater Res Bull 1977;12:995. Ho K, Dodd RA. Scripta Metall 1978;12:1055. Paris D, Lesbats P. J Nucl Mater 1978;69–70:628. Fourdeux A, Lesbats P. Phil Mag 1982;A45:81. Schaefer HE, Wu¨rshum R, Sob M, Zak T, Yu WZ, Eckert W, et al. Phys Rev B 1990;41:11–869. Wu¨rschum R, Grupp C, Schaefer HE. Phys Rev Letts 1995;75:97. Pike LM, Chang YA, Liu CT. Acta Mater 1997;45:3709. Yoshimi K, Yoo MH, Hanada S. In: Baker I, Noebe RD, George EP, editors. Interstitial and substitutional solute effects in intermetallics, TMS symposium, 1998. p. 39. Jordan JL, Deevi SC. Intermetallics 2003;11:507. Haraguchi T, Yoshimi K, Kato H, Hanada S, Inoue A. Intermetallics 2003;11:707. Schneibel JH, Pike LM. Intermetallics 2004;12:85. Chang YA, Pike LM, Liu CT, Bilbrey AR, Stone DS. Intermetallics 1993;1:107. Morris DG, Liu CT, George EP. Intermetallics 1999;7:1059. Kad BK, Schoenfeld SE, Asaro RJ, McKamey CG, Sikka VK. Acta Mater 1997;45:1333. Schro¨er W, Mecking H, Hartig Ch. In: Izumi O, editor. Proceedings of the international symposium intermetallic compounds—structure and mechanical properties (JIMIS-69). Sendai: The Japan Institute of Metals; 1991. p. 567.
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The stress anomaly in FeAl–Fe3Al alloys D.G. Morris*, M.A. Mun˜oz-Morris Department of Physical Metallurgy, CENIM, CSIC, Avenida Gregorio del Amo 8, E-28040 Madrid, Spain Received 25 May 2004; received in revised form 3 June 2004; accepted 6 August 2004 Available online 18 April 2005
Abstract The anomalous stress peak observed near 500–600 8C in Fe–Al alloys has now been convincingly explained using a model of hardening by immobile thermal vacancies on the lower temperature side of the peak and the loss of hardening as these vacancies become mobile at higher temperatures. The large numbers of vacancies required for such hardening are associated with compositions close to stoichiometry, i.e. 40– 50%Al, raising the question of whether such a vacancy hardening model can be adopted for Fe3Al alloys, which show a similar stress peak anomaly. Examination of data on vacancy formation over the entire range of composition, Fe–Fe3Al–FeAl, shows that, indeed, a vacancy hardening model appears capable of explaining the stress anomaly for both FeAl and Fe3Al. q 2005 Elsevier Ltd. All rights reserved. Keywords: A. Iron aluminides (based on FeAl); A. Iron aluminides (based on Fe3Al); B. Mechanical properties at high temperatures; D. Defects: point defects
1. Introduction Following decades of experimental and theoretical activity on the study of the stress anomaly in Fe–Al alloys, we are now in a period of relative calm, with little present activity. This is, then, a good time to re-assess present understanding and point out areas of uncertainty in our knowledge, and where future study might be directed.
2. Stress anomaly in FeAl The stress anomaly in FeAl is a relatively new discovery [1–3] and for years it was thought that this intermetallic was different from many, such as Ni3Al, in not showing any anomalous stress peak [4–9] on mechanical testing at intermediate temperatures. It subsequently became clear that an anomalous stress peak indeed existed [1–3], at temperatures in the range 400–600 8C, and a pre-requisite was that the sample material be previously well annealed to ‘relax’ any internal structure [10–14]. * Corresponding author. Tel.: C34 91 553 8900; fax: C34 91 534 7425. E-mail address: [email protected] (D.G. Morris).
0966-9795/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.intermet.2004.08.012
Very many studies of the stress anomaly followed [15–25], both theoretical and experimental, that suggested a very wide range of mechanisms and phenomena responsible for the intermediate temperature hardening, ranging from the transition of dislocation structures from h111i superdislocations to h100i perfect dislocations [2,3,26], climb locking of h111i superdislocations [19,27], cross slip between {110}, {112} and other glide planes [28–31], relaxation of the APB structure enclosed between the partial dislocations of the h111i superdislocations [28,32], to reactions or decompositions of h111i superdislocations to create local pinning points [23,30,33,34]. More recently a vacancy hardening model has been suggested [14,35] based on the observations of large numbers of thermal vacancies at high temperatures in FeAl alloys [36–48] and the significant room temperature hardening produced by such vacancies [10,44,49,50]. This model considers that significant hardening is produced at temperatures below the anomalous stress peak, as the thermal vacancies are produced, since these are immobile, solution hardeners at such temperatures; at sufficiently high temperatures the vacancies become mobile, are able to move with whichever dislocations are present, and hence lose their hardening ability. There has been discrepancy and disagreement, over the years, between various researchers as to the important mechanisms controlling the anomalous stress peak, as reflected in the opinions of various review publications, for example [13,20,25,30]. A major reason for such
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D.G. Morris, M.A. Mun˜oz-Morris / Intermetallics 13 (2005) 1269–1274
Fig. 1. Yield strength after various up-quenching and down-quenching heat treatments (points), as compared to values measured in a standard tensile test (continuous curve). Graph taken from Ref. [14].
uncertainty is the large number of phenomena predicted and observed, and the difficulty of deciding which is the important, controlling process. At the present time, however, the results of several, critical experiments convincingly demonstrate that vacancy hardening on the lower temperature side of the anomalous stress peak, followed by loss of vacancy hardening on the higher temperature side of the peak, are the processes leading to the anomalous peak. Results of two important experiments are shown in Figs. 1 and 2, and relate to the time dependence of the anomalous stress rise [14], and to the comparison of strength at high temperatures and strength at room temperature after quenching from the same high temperatures [50]. Fig. 1 shows (continuous curve) the yield stress
Fig. 2. Variation of yield stress measured at temperature, or at room temperature after quenching from the given temperature. Graph taken from Ref. [50].
measured for a FeAl alloy during conventional tensile testing, and (points) the yield stress after quickly upquenching or down-quenching to the stress peak temperature [14]. Of greatest importance is to note that the samples tested after very short soak times at the peak temperature (less than about 5 min) did not show anomalous hardening. These results demonstrate that (equilibrium) hardness at a given temperature is a state function—once the material reaches its equilibrium state, which requires several minutes, it acquires its equilibrium hardness. This is not consistent with hardening being a dynamically-activated process, occurring at the temperature and during deformation, as opposed to at the temperature but before deformation. It is consistent with a time-scale of the order of 5 min being necessary to create vacancies at (dislocation) sources throughout the material and migrate these vacancies through the grains to create the homogeneous, equilibrium, vacancy-hardened material. Thus, thermallyactivated processes acting on a moving dislocation, such as cross slip, climb, etc. are eliminated as being the controlling processes, and only vacancy hardening remains as a possible mechanism. Furthermore, since hardening is a state-dependent property, a similar hardness can be expected when testing at temperature or when testing a quenched sample at room temperature—apart from some slight solution softening at the high temperature. Fig. 2 shows that this is indeed the case [50], and hardening is very similar when measured on various FeAl alloys at high temperatures (during the anomalous hardening temperature range), and on the same materials at room temperature after quenching from high temperatures. Again, these observations are consistent with hardening being a material state function—dependent only on the temperature—as would be expected of vacancy hardening, but are inconsistent with any thermally-activated dislocation locking process such as cross slip, climb, APB relaxation, etc. The many other experimental observations are consistent with this vacancy hardening model, even though they were ambiguous in not defining which was the controlling hardening mechanism. One important point now clear is that it is no longer necessary for there to be a change of dislocation type (from h111i to h100i, or other) at the stress peak. Thus observations showing that such transitions may sometimes occur, but apparently do so after strains higher than those where the yield stress is determined [34], that the transition can be delayed—in strain or temperature—by higher rates of deformation [25,30], and that high-strain, high-strain-rate deformation at high temperature can lead to textural changes consistent with deformation by h111i dislocations [51], all become understandable. At the same time, it becomes understandable that the orientation dependence of critical resolved shear stress of FeAl crystals shows little change as the test temperature is increased from low temperatures (ambient) to the stress peak temperature [21,26].
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3. Stress anomaly in Fe3Al Section 2 refers to Fe–Al compositions showing only B2 order, namely with Al content of about 35–50%, with most studies carried out on alloys containing about 35–45%Al. Alloys showing DO3 order, namely those with about 25–30%Al, also show similar anomalous stress peaks, and it is of interest to examine whether the vacancy hardening model can be relevant. It is first of interest to note that the stress anomaly in the Fe3Al alloys has essentially all similar characteristics to the anomaly in the B2 FeAl alloys [19,25,29,52–58]. The peak temperature is about 500 8C, the transition of h111i superdislocations to h100i perfect dislocations has been reported as well as cross slip, APB relaxation, dislocation climb and decomposition, and strain-rate dependences of yield stresses are similar to those for FeAl above and below the stress peak. In addition, of importance, several studies with Fe3Al alloys of differing Al contents or with selected ternary additions [52,53,58] have clearly shown that the presence of DO3 order, its absence, and also the transition from DO3 order to B2 order, has no influence on the yield stress or the anomaly. Accordingly, this comparison of Fe3Al alloys and FeAl alloys seems to be justified. Counter to this implication that vacancy hardening is responsible for the stress anomaly at about 500 8C in Fe3Al alloys is the perception that vacancy concentrations are high in near-stoichiometric FeAl alloys, falling rapidly as the Al content decreases to values below 40%. For example, Fig. 3 shows values of the thermal vacancy content deduced for Fe–Al alloys with Al contents in the range about 40–50%, for temperatures near the stress anomaly and higher [49], where it is seen that very high vacancy concentrations near FeAl stoichiometry change to significantly smaller concentrations near 40%Al. It is also noteworthy that experimental measurements of high vacancy contents in Fe–Al alloys have all selected alloys with about 40–50%Al for study, e.g. [36–41,59]. Extrapolating the trend seen in Fig. 3 to
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alloys near Fe3Al stoichiometry, it is clear that very low vacancy concentrations would then be expected, seemingly insufficient to induce a stress anomaly of similar stress magnitude at similar temperature in Fe3Al as in FeAl. Indeed, this argument was earlier used to deduce that vacancy hardening could not be the important strengthening mechanism in Fe3Al alloys [25,30]. Section 4 therefore examines the available evidence on vacancy concentrations in Fe–Al alloys over a wide range of Al contents, to deduce whether the intermediate stress peak anomaly, convincingly explained by solution hardening by thermal vacancies in FeAl alloys, can also be explained by vacancy hardening in Fe3Al alloys.
4. Thermal vacancy concentrations in Fe–Al alloys (over the range Fe–Fe3Al–FeAl) The work of Chang et al. [49] and others leads to the understanding that the thermal vacancy concentration at any temperature will decrease systematically as the Al content decreases, from 50 to 40%, as in these published works, and then continuing to lower Al contents. In a first stage, it is of interest to examine the influence of Al content on the extent of vacancy hardening relative to the base line, of well-annealed single-phase Fe–Al intermetallic. For this the data of Chang et al. [49] will be used, as presented in Fig. 4. Here, the upper set of curves show the Chang et al. [49] data, while the lower set of curves show the hardness difference (increase) due to the formation of thermal vacancies, as related to the samples well annealed at 500 8C and quenched. If it is considered that the 500 8C annealed–quenched samples contained the equilibrium Effect of anneals/vacancy concentration on hardness
700 600
Hardness as quenched
Microhardness (DPH)
500 1000ºC
400 900ºC 300
800ºC 700ºC
Hardness difference
200 1000ºC 900ºC 800ºC
100
700ºC
0 38
Fig. 3. Variation of thermal vacancy concentration with Al content for Fe– Al alloys at several temperatures. Graph taken from Ref. [49].
500ºC
40
42
44 46 48 Aluminium content (%)
50
52
Fig. 4. Variation of microhardness (DPH) of Fe–Al alloys as a function of Al content and after quenching from a variety of annealing temperatures. Hardness difference data are also shown, which are the differences between the hardnesses of the low temperature annealed state (500 8C) and those of materials annealed at higher temperatures. Data taken from Ref. [49].
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Effective vacancy formation enthalpy 2.5
2
Disordered A2
∆Ηt
eff
1.5
Ordered DO3, B2', B2(l)
1
0.5
Ordered B2(h)
0 0
10
20
30
40
50
Aluminium content (%) Fig. 5. Effective enthalpy of vacancy formation for Fe–Al alloys as a function of Al content, and according to the ordered state of the material. Data taken from a wide range of literature reports see text for details. (Units for enthalpy are eV/vacancy: 1 eVz96.3 kJ/mol).
vacancy concentration for this temperature, then the hardness difference lines document the increase in hardness due to the formation of thermal vacancies when materials are annealed at the high temperatures. The observation that these difference data can be connected by straight, horizontal lines indicates no Al content dependence of the vacancy hardening—relative to the 500 8C reference state. It can be concluded that either the vacancy concentration is identical for a given temperature, irrespective of the Al content, or else that any lowering of vacancy concentration at low Al contents is compensated by an increase in the specific vacancy hardening (hardness increment per unit vacancy concentration). It may be noted that the dotted lines in Fig. 5 showing constant values of hardness difference for all Al levels may alternatively be replaced by lines showing a maximum at 45%Al with a slow decrease on each side. Insufficient data are available to provide a good extrapolation to 25–30%Al, and the present hypothesis of steady hardness differences for all Al contents remains a reasonable possibility. Further information on vacancy concentration as a function of Al content can be obtained by examining vacancy formation enthalpies. (Admittedly, the thermal vacancy concentration at a given temperature depends on both formation enthalpy and entropy, but in the absence of much data on formation entropy this is assumed to be about constant.) Fig. 5 shows a summary of vacancy formation enthalpy values from very many research studies [39,40,42–44,46,48,49,60–67] as a function of Al content. Data has here been separated into three domains, following the ideas of Hehenkamp and workers [63,65], and according to the phase diagam proposed by Kubaschewski [68].
Data are shown for disordered Fe–Al alloys (A2 structure), for ordered alloys with 25–50%Al at relatively low temperatures with the DO3, B2 0 , and B2(l) structures, and for ordered alloys with 35–50%Al at relatively high temperatures with the B2(h) structure. Separating data families in this way, it becomes possible to understand how some researchers may obtain rather large values for vacancy formation enthalpy, others may obtain moderate values, and yet others small values—essentially depending on the temperatures where measurements of vacancy concentration are made, and within which phase region the alloy lies at this time. It can be seen in Fig. 5 that disordered alloys—Fe–Al alloys of very low Al content, or Fe–Al intermetallics at high temperatures—will have relatively low vacancy concentrations, corresponding to the high formation enthalpy. Of importance for the present report, Fe–Al alloys with Al contents over the full range from 25 to 50% have similar vacancy formation ethalpies at relatively low temperatures (below about 800 8C), and irrespective of whether the intermetallic adopts the DO3, B2 0 , or B2(l) structure. Accordingly, considering that the vacancy concentration will rise in a similar way for Fe3Al alloys and for FeAl alloys as the test temperature is increased towards 500– 700 8C, and considering that the hardening effect of such vacancies is similar for both families of alloys, it appears perfectly reasonable to conclude that the anomalous stress rise observed for all Fe–Al intermetallics is due to the formation of these immobile vacancies. Despite the conclusions of the previous paragraphs, it is admitted that studies carried out consistently by the same authors tend to show a decreasing thermal vacancy content as the Al content falls from 40–45%Al to 25–30%Al. Nevertheless, the enthalpy data of Fig. 5 are consistent with the present hypothesis—similar thermal vacancy content as the Al content falls. The hardness difference data of Fig. 4 are also consistent with similar thermal vacancy hardening for all Al contents (similar specific vacancy hardening and similar vacancy contents, or increasing specific vacancy hardening at lower Al levels as the vacancy content decreases). It should also be remarked that a fall in vacancy migration enthalpy at lower Al levels should imply faster vacancy movement and hence lower temperatures and stress magnitudes for the anomalous peak. Available data on migration enthalpies suggest that the effect on peak characteristics will not be significant for the 30–40%Al range, but may put in doubt the present hypothesis for Al levels of 25–30%.
5. Conclusions The present brief review has examined the characteristic features of the anomalous stress rise at intermediate temperatures in FeAl alloys and, based on the results of
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several critical experiments, demonstrated that the vacancy hardening model [35] is able to explain this anomalous rise in a highly convincing manner. It has also been shown that Fe3Al alloys have anomalous peaks of very similar characteristics, even though such materials are commonly expected to have much lower vacancy contents than the exceptionally high values found in FeAl alloys. Examination of data on vacancy formation enthalpies, and on the hardening effect of such vacancies, suggests that similar numbers of hardening vacancies may indeed be found in Fe3Al alloys as in FeAl alloys, and vacancy hardening is then the single hardening mechanisms in all Fe3Al–FeAl alloys responsible for the anomalous stress rise at intermediate temperatures. It would, nevertheless, be of interest to re-examine Fe3Al alloys after quenching to confirm that high vacancy concentrations are indeed produced, that they do lead to high hardening, and their elimination leads to similar vacancy aggregates as for FeAl alloys.
6. Uncertainties of understanding, where further studies would be worthwhile The present report analyses existing experimental data to conclude that hardening by a solution of immobile thermal vacancies is responsible for the anomalous stress peak rise at intermediate temperatures in FeAl alloys. It is also suggested that similar thermal vacancies may be responsible for the anomalous stress peak in Fe3Al alloys. There are several areas where our understanding is imperfect, where additional experiments would yield useful information: (i) Fig. 3 shows a gradual decrease in vacancy content, for a given temperature, as the Al level decreases, while Fig. 5 suggests little change in DHf as long as the alloy remains ordered. A consistent re-determination of vacancy content at the moderate temperatures of relevance for the anomaly, 500–700 8C, would be valuable. (ii) In this sense, experiments on quenched and aged materials searching for vacancy clustering—as loops or voids—could be a sensitive method for detecting the consequences of small vacancy supersaturations. (iii) Fig. 4 shows decreasing absolute values of hardness as Al content decreases, but an almost steady level of hardening increment (explained here by vacancies). It would be interesting to extend this data down below 40%Al (while avoiding DO3 order). How does thermal vacancy hardening vary and how the specific hardening (per unit point defect concentration)? (iv) What is the vacancy hardening mechanism? Is this purely a solution hardening effect, of exceptionally high strength, or are there strong jog/APB tube interactions at work? Theoretical modelling and in
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situ deformation experiments would be of interest. Some work has indeed started in this area [69]. (v) Vacancy concentrations are rather small in the temperature range of the anomaly. What is the role of substitutional or interstitial elements/impurities present in similar concentrations? Some studies suggest strong interactions are possible [70,71].
Acknowledgements The authors should like to thank Drs M. Palm and G. Sauthoff, and Mr J. Konrad, of the Max-Planck-Institut fu¨r Eisenforschung, Du¨sseldorf, Germany, for the invitation to attend the highly succesful seminar on iron aluminide alloys. We should also like to thank the various referees and editor for many constructive comments that have helped to make this publication a more convincing and more readable document.
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