Review
Vacancy formation and effects in FeAl
J.L. Jordan, S.C. Deevi*
Research Development and Engineering, Philip Morris USA, Richmond, VA 23112, USA Received 1 September 2002; received in revised form 7 January 2003
Abstract
Iron aluminide, FeAl, has been widely studied because of its excellent high temperature oxidation and corrosion properties. At high temperatures, FeAl generates a large number of thermal vacancies, and the vacancy concentration increases with increasing aluminum content. The mechanical properties depend on the vacancy concentration, so a thorough understanding of the generation and annihilation of vacancies is necessary. Heat treatment, temperature, and time control the vacancy concentration. Increasing vacancy concentration will increase the hardness and decrease the ductility of FeAl. The yield strength anomaly of FeAl, increasing yield strength with increasing temperature is believed to be due to vacancy hardening, and the decrease in strength above the peak temperature is attributed to the creep of FeAl. Ternary alloying elements, except boron, have little effect on the hardening at high temperature and can increase the hardness after long time anneals at low temperature. This review and analysis presents a summary of the current literature available on FeAl vacancies and their affects, including hardness, the yield strength anomaly, and the effect of ternary alloying elements.
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doi:10.1016/S0966-9795(03)00027-X
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Contents
1. Introduction ... 508
2. Defect structures ... 508
3. Determining defect structure ... 510
4. Defect concentration in triple defect structure ... 512
5. Effect of defects on material properties... 512
6. Theoretical calculations... 512
7. Vacancy measurement techniques ... 514
8. Formation and migration enthalpies of vacancies ...514
9. Vacancy concentrations... 516
10. Vacancy hardening ... 516
11. Quenching and annealing of defects... 517
* Corresponding author.
E-mail address:seetharama.c.deevi@pmusa.com (S.C. Deevi).
1. Introduction
Intermetallics, such as NiAl, Ni3Al, TiAl, Fe3Al, and FeAl, are unique materials for structural applications because of their excellent high temperature oxidation and corrosion properties. Among the iron aluminides, FeAl also possesses a high melting temperature and a B2 structure, in contrast to Fe3Al. However, it has lim- itations because of poor ductility. In addition, a B2 structure exists over a wide range of aluminum con- centrations in (36 to 50 at.% Al) FeAl alloys.
Among Fe–Al intermetallics, FeAl has the best oxi- dation resistance. Compared to steels and other com- mercial Fe-based alloys, FeAl has lower density and a better strength-to-weight ratio. In addition, FeAl exhibits high electrical resistivity (130–170 m/cm), comparable to many commercial metallic heating elements. Iron aluminide has been considered for applications as structural materials, heating elements, and as fasteners at elevated temperatures.
Interestingly, several researchers noted that consti- tutional vacancies form in aluminides. However, FeAl appears to be the only aluminide to exhibit such a high concentration of thermal vacancies. Vacancies affect the mechanical properties of materials, and a scientific understanding will allow us to industrially process iron aluminides for various engineering applications. For example, a low concentration of vacancies during forming operations will improve the formability of FeAl. However, increasing the vacancy concentration, by heat treatment, once the part is formed will improve the strength of the finished part.
While hardness and strength of iron aluminides can be increased by vacancies, vacancy hardening is detri- mental to room temperature ductility. In general, iron aluminides exhibit low room temperature ductility due to moisture-induced hydrogen embrittlement, and any further loss of ductility due to retained vacancies is detri- mental to the utilization of intermetallics in engineering applications. In addition, retained vacancies change the mode of failure from intergranular to transgranular and enhance cracking and breakage of material in room tem- perature forming operations. Therefore, it is important to understand the generation, control, and annihilation of
vacancies from a scientific and industrial point of view.
The recent literature also suggests that very few alloying elements have been effective to reduce the vacancy con- centration, as evidenced by the lowering of hardness.
Understanding the generation of vacancies and ability to control and tailor the vacancy hardening allows the material to be softened during forming and strength- ened after the completion of forming operations. The scientific and industrial interest warrants a thorough review of vacancy formation, vacancy removal, and the effect of temperature, cooling rate, and alloying elements.
In order to better understand the formation of vacan- cies in ordered alloys, research on vacancy formation in FeAl alloys started in the 1970s with Paris et al.[1], Ho and Dodd[2], Junqua, et al.[3], and Riviere[4]. The con- centration of vacancies in FeAl increases with tempera- ture and aluminum concentration[5,6]. The cooling rate also influences the vacancy concentration[7]. Vacancies influence the hardness of the material, where hardness is proportional to the square root of vacancy concen- tration[5]. Alloying additions such as Cu, Ni, Mn, Cr, V, and Ti, increase the equilibrium hardness and only slightly affect the concentration of thermal vacancies.
However, boron increases the rate of vacancy elimination [8,9]. Baker and Nagpal [10] and Liu et al. [11] have reviewed the mechanical behavior of FeAl including the effect of vacancies. Munroe [12] assessed the effects of vacancies on NiAl and FeAl with a focus on the effects of ternary alloying elements. Morris and Morris-Mun˜oz[13]
have reviewed the parameters that affect ductility in iron aluminides, including the effect of vacancies.
A comprehensive review and analysis of the literature on vacancies and their effects in FeAl has not been con- ducted. This paper will start with the fundamentals of defect formation in FeAl. It will continue with modeling that has been conducted of the material. The formation and effects of vacancies will be covered. Finally, the effects of ternary alloying additions will be discussed.
2. Defect structures
The phase diagram for Fe–Al is shown in Fig. 1 [14, also see 15]. The stoichiometric compound refers to 50
12. Vacancies and yield strength in FeAl ... 519
13. Effect of ternary additions... 523
14. Summary ... 526
Acknowledgements... 527
References ... 527
at.%. It shows the existence of sub-phases, such as a2(l), a2(h), a20, where a2is equivalent to the b or B2 phase.
The B2 phase is an ordered BCC crystal structure, pictured in Fig. 2. Thermal defects are generated in crystals at finite temperatures, since a perfect crystal exists only at absolute zero. Non-stoichiometric com- positions of FeAl (greater or less than 50 at.% Al) lead to the generation of constitutional defects. The sub- lattices of the B2 structure are defined as the a sublattice (gray atoms) containing A, or Fe atoms and the b sub- lattice (black atoms) containing B, or Al atoms. Four possible defects can be created on these sublattices, pic- tured inFig. 3: A (Fe) atoms on the b sublattice (anti-site Fe atoms), B (Al) atoms on the a sublattice (anti-site Al atoms) and vacancies on the a or b sublattice[16].
There are two modes of defect structures in the B2 crystal: anti-structure defect structure and triple defect structure. The anti-structure defect structure results in an anti-site atom for a constitutional defect of a rich phase, and a pair of anti-structure defects for thermal defects. The triple defect structure consists of anti-site A atoms for A-rich constitutional defects and a sublattice vacancies for B-rich constitutional defects[16]. Thermal defects are generated as two a site vacancies and one anti-site A atom.
The defect structure of a material determines the number and type of defects generated in a material. It is critical to determine the defect structure of a material so that modeling and calculations of defects in the material will be accurate.
Fig. 1. Phase diagram of Fe–Al from Kubaschewski[14].
3. Determining defect structure
There are three methods for determining the defect structure of B2 phase materials[6].
1. The defect structure can be predicted from the
Hf values for a material. If the Hfvalue is less than 25–30 kJ/mol of atoms; the material has an anti-structure defect structure. Otherwise, materials with a higher Hfvalue have the triple defect structure. Table 1 shows formation enthalpies of B2 phase materials[17].
2. The defect structure can be determined by plot- ting the lattice parameter as a function of com- position. At concentrations of < 50% B, the lattice parameter will increase as anti-site A atoms are replaced by larger B atoms. At con- centrations > 50% B, the two defect structures will change differently with composition. For anti-structure defects, the lattice parameter will continue to increase due to the larger anti-site B atoms. For the triple defect structure, the lattice parameter will decrease due to the presence of a vacancies.
3. The third method for determining the defect structure is an experimental method. A comparison of the measured bulk density and the lattice para- meter density calculated assuming a certain defect structure will indicate the type of defect structure formed in the material.
The Hfvalue for FeAl is 25 to 35 kJ/mol, which puts it on the borderline for the different defect struc- tures. However, Pike [6] shows that the triple vacancy model predicts the vacancy concentration of FeAl.
The lattice parameter as a function of composition is shown in Fig. 4 [5,6]. The lattice parameter of FeAl increases with increasing atomic percent of aluminum until 50%. At greater than 50 at.%, the lattice para- meter decreases and then levels off. A comparison of the lattice parameter with variation of Al content of Chang et al.[5]for samples quenched from 500C agrees with previously reported data (upper curve in Fig. 4). The data for samples quenched from 1000 C show lower lattice parameters due to the generation of a larger number of thermal defects in these samples. However, the lattice parameter decreases with aluminum con- centrations greater than 50%, in all samples regardless
Fig. 3. Defect structures in B2 FeAl: (a) anti-site Al atom, (b) anti-site Fe atom, (c) vacancy on b (Al) sublattice, (d) vacancy on a (Fe) sublattice (gray represents iron atoms and black represents Al atoms).
Fig. 2. Crystal structure of B2 FeAl (gray represents iron atoms and black represents Al atom).
Table 1
Formation enthalpies for B2 phase materials and their related defect structure[17]
Phase Hf(KJ/g-atom) Type of defect
AgZn 6.6 9
>>
>>
>>
>>
>>
=
>>
>>
>>
>>
>>
;
Substitutional defect
AgCd 7.0
CuZn 11.1
CuBe 15.0
NiZn 16.4
AgMg 18.4
AuCd 19.2
AuZn 25.8
NiBe 41.1
FeAl 32.4 2.0 9
>>
>>
>>
=
>>
>>
>>
;
Triple defect
CoGa 36.0 5.0
NiGa 45.0 2.0
CoAl 54.1 3.0
PdIn 61.4
NiAl 69.0 2.0
PdAl 92.3
of quenching temperature, indicating the formation of constitutional vacancies in the Fe sublattice and, sub- sequently, the formation of triple defects.
However, Krachler et al. [18] have developed (and fitted the model to experimental data describing) that the point defect concentrations in FeAl using the Wagner–Schottky approximation of a hybrid (vacancies
and anti-structure atoms on both sublattices). This is in contrast to the predictions of high vacancy formation enthalpies on the Al sublattice. Data from Krachler[18]
was replotted and compared with that of Chang et al.
[5] (Fig. 5). Both sets of data show an increase in vacancy concentration across the entire range of alu- minum concentration.
Fig. 4. Lattice parameter as a function of atomic percent aluminum[5].
Fig. 5. Comparison of vacancy concentration as a function of atomic per cent aluminum for Chang et al.[5]and Krachler et al.[18].
4. Defect concentration in triple defect structure The defect concentrations in materials with the triple defect structure can be calculated using the equations:
c2vðcv2Þ ¼3 cA¼ðcv2Þ
2
where cvis the concentration of vacancies, is equal to 0.5XA or XB0.5, and is the disorder parameter given by:
ðTÞ ¼ 1
22=3exp Ht
3RT
where Ht is the energy of formation of thermal vacancies, R is the gas constant and T is the temperature [6,19,20]. Table 2 shows values of and Ht for a variety of triple defect materials. For FeAl, the value of
Htis found to be 101 kJ/mol, which is a low value for materials that form triple defects[17].
5. Effect of defects on material properties
The hardening of a material by a defect is due to the interaction between the stress field of the point defect and a moving dislocation. This occurs in two ways. The first is the elastic size effect, or dilation, which occurs because the point defect has a different atomic radius than the replaced atom. This can be correlated to the effect of the defect on the lattice parameter. The second is the elastic modulus effect where the point defect has an effect on the local elastic modulus and the elastic strain energy resulting in local ‘‘soft’’ or ‘‘hard’’ spots.
This phenomenon can be correlated to the effect of the defect on the shear modulus[6].
Hardness and strength of a B2 material are expected to vary with the square root of the concentration of the hardening defect [5,6]. For dilute alloys, the amount of hardening, , is given by:
¼ G"3=2c1=2=
where G is the shear strength, c is the solute concen- tration, is a material sensitive parameter ( 700), and
" is a weighted sum of the size ("b=d (lna)/dc) and modulus ("g=d (lnG)/dc) misfits[6].Fig. 6 [5]shows the linear relationship of hardness versus the square root of vacancy concentration for aluminum concentrations ranging from 40 to 51 atomic percent.
6. Theoretical calculations
Fu et al.[21]have performed a local density function study of the equilibrium point defects in FeAl. They noted that vacancy formation energy increases as the distance between vacancies increases in FeAl leading to the calculation of an attractive binding energy for diva- cancies (0.57 eV). Divacancies are vacancies that are separated by one lattice parameter on Fe sites. The attractive binding energy leads to the strong tendency for vacancy clustering and results in vacancies being annealed out to open structures, such as dislocations, voids, and grains boundaries. Fu and Wang[22] calcu- lated the thermal vacancy concentration, using a ‘non- interacting model,’ to be two times lower than the experimental value, which confirms the presence of divacancies or complexes[22]. By contrast, NiAl shows a weakly repulsive binding energy and the formation of only monovacancies[22]. They also concluded that the
<111 > slip in FeAl is related to substitutional anti-site defects, which can be equilibrium point defects on both sublattices[21].
Fa¨hnle et al. [23] have used a grand canonical approach and ab-initio theoretical calculations to determine the effective formation energies, defect volume parameters and effective formation volumes in FeAl. The results of these calculations are shown in Tables 3 and 4. The effective formation energy for Al vacancies is so high that the formation of vacancies on the aluminum sublattice is very improbable. At higher
Table 2
Enthalpy of formation of triple defects, Ht, calculated from the dis- order parameter, , at temperature, T[17]
Phase T(K) Ht(kJ/mol)
FeAl 2.0 102 1173 100.9
CoGa 3.0 102 1173 89.1
NiGa 1.3 102 1173 113.5
CoAl 1.3 104 1273 269.4
PdIn 6.0 104 873 151.5
NiAl 2.0 103 1273 182.7
PdAl 3.0 104 1273 242.9 Fig. 6. Plot showing the relationship between the square root of
vacancy concentration and microhardness[5].
temperatures, they propose the formation of diva- cancies, which must be Fe–Fe due to the high formation energy for Al vacancies. They also concluded that the direct jump of Fe vacancy to the third nearest neighbor is almost impossible because of the high migration energy. Therefore, they can’t explain the experimentally observed effective jump vectors of < 110 > .
Using Ising’s model of the enthalpy of broken bonds and extending Miedema’s model of the chemical con- tribution to enthalpy, Bakker et al. [24] developed a model to describe the enthalpies of formation in B2 intermetallics. The results for FeAl are presented in
Table 5. The high formation enthalpy for a vacancy on the B (Al) sublattice agrees with the above models. For FeAl, since the enthalpies of triple defect and anti-site pairs are similar, the authors believe that at higher defect concentrations, when triple defect formation becomes more difficult, anti-site pair formation takes over.
Krachler and Ipser[25]have used a statistical thermo- dynamics approach based on the Wagner–Schottky approximation to determine the composition and tem- perature dependence of defect concentration and thermodynamic properties. Their results agree with those of Bakker et al.[24]that there is a change in the defect mechanism from triple defect to a ‘‘hybrid’’ mechanism.
They indicated that it occurs at 1100C where the con- centration of aluminum vacancies dramatically increases.
Mayer et al.[26], using abinitio calculations, agree with Krachler and Ipser[25] that there is probably a hybrid mechanism occurring. However, they predict that the aluminum vacancy concentration is of the order of 1014. Kogachi et al. [27,28] have proposed a mechanism based on the random vacancy distribution (RVD) and anti-site atom recovering process (ASAR) based on their observations of FeAl. Using in-situ neutron dif- fraction, they determined that thermal vacancies are formed on both sublattice sites and anti-structure atoms tend to return to their own sublattice sites[27].
Wolff et al.[29]have proposed a diffusion mechanism that agrees with the change in defect mechanism. At low temperatures and increasing Fe, triple defects are domi- nant and they diffuse by Fe jumping from the Fe to Al sublattice pushing the anti-site Fe atom back to the Fe sublattice, seen inFig. 7(a). At higher temperatures and
Table 3
Effective formation energy for B2-FexAl1x[23]
E~aV(eV) E~bV(eV) E~bFe(eV) E~aAl(eV)
x=0.5 1.06 3.46 0.99 0.99
x >0.5 1.56 2.96 0 1.98
Subscript V=vacancy, Fe=iron anti-site atom, Al=aluminum anti- site atom. Superscript a=Fe sublattice, b=Al sublattice.
Fig. 7. Possible diffusion processes in FeAl[29].
Table 4
Defect volume parameter (V), effective formation volume (~ ) in stoichiometric FeAl and in Fe0.52Al0.48 (numbers in parentheses) in units of 1/2 0for T=1300 K[23]
Fe vacancy Al vacancy Fe antistructure atom
Al antistructure atom
V 0.13 0.05 0.51 0.05 0.21 0.05 +0.45 0.05
~ 0.68 0.04 (0.77 0.04)
0.68 0.04 (0.59 0.04)
0.18 0.04 (0 0.04)
0.05 0.04 (0.24 0.04)
Table 5
Enthalpies of formation for FeAl defects[24]
HVa
(kJ/mol)
HVb
(kJ/mol)
H2V
(kJ/mol)
Htrchem.
Fe on b (kJ/mol)
Htrchem
Al on a (kJ/mol)
Htrtotal
Fe on b (kJ/mol)
Htrtotal
Al on a (kJ/mol)
Hpairtotal
(kJ/mol)
FeAl 63 144 208 114 364 127 377 89
Superscript a=Fe sublattice, b=Al sublattice, ‘‘chem.’’ and ‘‘total’’ indicate models used. Subscript V=vacancy, 2V=divacancy, tr=triple defect, pair=pair of anti-site defects HV=formation enthalpy of vacancy.
with increasing Al, double vacancies are formed on adjacent lattice points, Fig. 7(b), and move by double jump.
Cottrell[30]has theoretically compared the formation of vacancies in FeAl and NiAl. NiAl will form con- stitutional vacancies in the Al-rich region, where as FeAl will not. He concludes that the reason for this difference is the enthalpy of formation in FeAl, which is slightly unfavorable, compared to NiAl where it is favorable.
7. Vacancy measurement techniques
There are several methods for measuring vacancy concentrations and the properties of vacancies:
1. Change in lattice parameter versus change in bulk density—the vacancy concentration in a material is determined from the equation:
c ¼xb
b
where xis the X-ray density and b is the bulk density of the material. The X-ray density is cal- culated from the lattice parameter, assuming that all the sites are occupied[16].
2. Differential dilatometry—the concentration of thermal vacancies can also be found from dila- tometric data. If the higher order terms can be ignored, the equation for thermal vacancy con- centration is:
cth¼3 l l a
a
where l/l is the change in length from the refer- ence temperature and a/a is the change in lattice parameter. However, for materials where the higher order terms cannot be ignored, such as VIII–IIIA compounds (i.e. FeAl), the following equation can be used:
cth¼ð1 þ cÞ 1 þ l l
3
1 þ a a
3
1
( )
where c is the concentration calculated from the equation above using X-ray and bulk densities[16].
3. Hardness measurements—as discussed pre- viously, hardness in FeAl samples increases with increasing vacancy concentration. Therefore, the hardness is a good indication of relative vacancy concentration[5,6].
4. Positron lifetime spectroscopy and doppler broadening [31]—the lifetime of the positron
depends on the electron density in its path. If a positron encounters a vacancy, it becomes trap- ped which greatly extends its lifetime. The life- time of a positron can be measured from the g-rays it emits as it decays, which is related to the vacancy concentration. Doppler broadening of the g-rays is also related to vacancy concentration and enthalpies of migration and formation.
5. Time-differential length change[32]—the change in length as a function of time, initial temperature and final temperature is measured [l(t, Ti, Tf)].
From the length change, pictured in Fig. 8, the energies of formation and migration and the volumes of the vacancies can be determined if absolute values of the atomic defects are available.
8. Formation and migration enthalpies of vacancies The properties of vacancies in a material can affect or determine sintering, creep, oxidation or diffusion.
Vacancies are characterized by formation enthalpy (Hf), migration enthalpy (Hm), formation volume (Vf), and the activation energy for diffusion (QD=Hf+Hm).
From the equation,
c0V¼exp SfV kB
!
exp HfV kBT
!
the effective formation enthalpy of vacancies in a mate- rial can be determined by the slope of the ln cv(T) vs.
(1/T) curve. The measurement of the vacancy concen- tration is not just a measurement of monovacancies, but can include divacancies, which makes the measurement of formation enthalpy an effective value[31].
Using differential dilatometry, Kerl et al. [33] deter- mined the effective formation enthalpy at several different
Fig. 8. Time–differential length change measurements of temperature and length profiles.
compositions. Kerl et al. [33] observed changes in the slope of the data that correspond to the sub-phases shown in the Kubaschewski[14]phase diagram (Fig. 2).
Positron lifetime spectroscopy [34–36]has been used to determine the effective formation enthalpy, effective migration enthalpy, and effective formation volume of the vacancies compared to , the mean atomic volume.
Schaefer et al. [32] measured the formation and migration energies by time differential length change measurements. Associated with these measurements is the time constant for long-range vacancy migrations which corresponds to 107jumps during the equilibra- tion process and a dislocation density of 2.2 109m2as sources or sinks. The time constant and vacancy migra- tion values measured with this method agree with pre- vious positron lifetime measurements [35,36] and confirm the validity of this method.
A complete compilation of formation and migration enthalpies, formation volumes, and diffusion activation energies is given inTable 6with the techniques used to obtain the information and the associated references.
The effective migration enthalpy is similar for DO3and
B2 phase Fe–Al, in the range of 1.3–1.5 eV for DO3
phase Fe–Al and 1.0–1.7 eV (with the exception of one measurement) for B2 phase FeAl. The effective forma- tion enthalpy ranges from 0.73 to 1.18 for DO3 phase Fe–Al and ranges from 0.3 to 1.5 for B2 FeAl. There is no correlation between atomic percent aluminum and formation enthalpy. The effective formation volume is approximately constant for both materials with a value of 0.76 for DO3 phase and 1.40 for B2 phase. The activation energy for diffusion in B2 FeAl ranges between 2.0 and 3.0 eV.
Table 7 shows comparable information for Al, Fe, TiAl, FeSi, and NiAl. Brossmann et al. [37] measured the formation of thermal vacancies in TiAl by using positron lifetime spectroscopy, and they also deter- mined the concentration of defects at the melting tem- perature to be 1.5 104. The formation enthalpy of TiAl is higher than most reported values for FeAl.
Measurement of formation enthalpy by time differential length change gave identical values for NiAl and Fe–45 at.% Al. Compared to bcc iron, which has an enthalpy of formation between 1.59 and 1.85 eV, the formation
Table 6
Vacancy formation and migration enthalpy, effective formation volume and diffusion activation energy in FeAl alloys
Al (at.%) Structure Hfeff(eV) Hmeff(eV) Vfeff() QD(eV) Method Ref.
19.9 A2 1.15 0.1 Positron annihilation [42]
23.7 DO3 1.18 1.5 2.7 [38]
24.4 DO3 1.31 0.1 Positron annihilation [42]
25 0.45 [39]
31 DO3 0.73 0.05 Positron lifetime [34]
31 DO3 0.82 0.06 0.75 0.07 (700 K) Doppler broadening [34]
31 DO30 0.80 0.09 (740 K) Doppler broadening [34]
31 B2 0.77 0.07 (790 K) Doppler broadening [34]
31 B2 0.74 0.06 (810 K) Doppler broadening [34]
36 B20 1.00 Differential dilatometry [33]
36 B2 (h) 0.49 Differential dilatometry [33]
36 A2 1.46 Differential dilatometry [33]
37 B2 1.08 0.06 1.43 0.08 (660 K) Doppler broadening [34]
37 B2 1.38 0.09 (700 K) Doppler broadening [34]
37 B2 1.41 0.20 (740 K) Doppler broadening [34]
37 B2 1.04 0.07 1.7 0.2 2.7 Positron lifetime [36]
39 B2 0.98 0.07 1.7 0.2 2.7 Positron lifetime [36]
39 B2 0.70 2.30 3.0 Hardness measurements [40]
40 B2 0.93-0.95 1.64 2.59 [41]
40 B2 0.38 Lattice parameter [2]
41/2 Cr B2 0.70 1.3 2.0 Hardness measurements [40]
43 B2 0.70 1.6 2.3 Hardness measurements [40]
43 B2 (l) 0.92 Differential dilatometry [33]
43 B2 (h) 0.51 Differential dilatometry [33]
43 A2 1.57 Differential dilatometry [33]
45 B2 1.5 0.2 1.0 0.1 Time-differential length change [32]
46 B2 0.50 [41]
50 B2 0.34 [6]
50 B2 (l) 0.85 Differential dilatometry [33]
50 B2 (h) 0.30 Differential dilatometry [33]
51 B2 0.39 [41]
Hfeff=effective formation enthalpy; Hmeff=effective migration enthalpy; Vfeff=effective formation volume; =mean atomic volume; QD=activation energy for diffusion.
enthalpy of vacancies in B2 FeAl, also BCC, is con- siderably lower. The low formation enthalpy in FeAl compared to metals gives it the unique property of forming a large concentration of vacancies at tempera- tures far from the melting point. Typically, metals don’t form noticeable quantities of vacancies until near their melting point.
9. Vacancy concentrations
Ho and Dodd [2] carried out the early work on vacancy concentrations. Using dilatometry, they mea- sured the change in length and lattice parameter with heat treatment and composition, shown in Fig. 9(a–e).
The divergence between length and lattice parameter measurements at temperatures greater than 700 C indicates the formation of thermal vacancies. Using this data, the vacancy concentration was calculated and is shown in Fig. 10. This plot shows a general increase in vacancy concentration with atomic percent aluminum and quench temperature, as was observed by Chang et al.[5]
and Riviere[4]. We compare inFig. 11the data of Chang et al.[5], Riviere[4], from Krachler et al.[18], and Ho and Dodd[2]. Interestingly, the data compares reasonably well.
10. Vacancy hardening
Chang et al.[5]and Pike[6]determined that there is a large change in hardness with temperature due to the large concentration of thermal defects. As a function of composition, hardness increases monotonically indicating that the hardness is controlled by vacancies on both sides of the stoichiometric value, shown inFig. 12. The calculated vacancy concentration is shown in Fig. 13.
The shapes of the curves in Figs. 12 and 13 are very similar indicating that the change in hardness is depen- dent on the vacancy concentration. In contrast to FeAl, NiAl exhibits a minimum in the vacancy concentration at the stoichiometric composition, shown inFig. 14 [44].
Morris et al.[40]found that the time required to estab- lish an equilibrium state of vacancy concentration after heating FeAl alloys (Fe–39Al, Fe–43Al, Fe–41Al–2Cr) is very short, of the order of 5 min. On quenching, the hardness increases with increasing quench temperature.
They found that there is an exponential increase from
500–900 C, with a slower increase after 900 C, as shown inFig. 15. The change in rate is due to the partial loss of vacancies during a quench from high tempera- tures resulting in dislocation of climb. During slow quenches, thermally generated vacancies will collect at sinks, which are usually < 100 > or < 111 > dislo- cations. The pre-existing dislocations will take up com- plex configurations by climb.
We compared the data from Chang et al. [5] and Morris et al. [40] in Fig. 16, showing a comparison of hardness as a function of quench temperature for water quenched samples. Hardness increases with increasing quench temperature for both sets of data. However, Chang’s [5] data for Fe–45 Al behaves anomalously, starting with a hardness less than that of Morris’s Fe–39 Al or Fe–43 Al.
Hardness decreases with annealing at low temperature ( 400C). The rate of softening during annealing is a function of the speed of vacancy migration to pre-exist- ing sinks and the number of those sinks available. Initi- ally the dislocation density is low, so the softening rate is low. As the dislocation density increases, the path length to the sinks decreases and the softening rate accelerates. With time, the dislocation density again decreases and the softening rate decreases. The hard- ening by the dislocations produced during the softening process is minimal[40].
Yoshimi et al. [45] investigated the effect of super- saturation of vacancies in FeAl single crystals. They found that, as the crystals were strengthened with super- saturation of vacancies, the critical resolved shear stress increased and the elongation decreased. They observed a cellular structure formation at 56o to [111] slip direction and the formation of numerous small dislo- cation loops in the quenched crystals. They propose that
Table 7
Vacancy formation and migration enthalpy, and diffusion activation energy in alloys similar to FeAl
Material Structure Hfeff(eV) Hmeff(eV) QD(eV) Method Ref.
Al fcc 0.67 0.03 0.61 0.03 Differential dilatometry [31]
Fe bcc (para) 1.79 0.1 1.85 0.1 [31]
Fe bcc (ferro) 1.59–1.7 [31]
g-TiAl (Ti48.5Al51.5) L10 1.41 0.06 Positron lifetime [37]
Ti66.4Al33.6 DO19 1.55 Ti 3.1 [43]
Fe75Si25 DO3 0.80 Fe 1.65 [43]
Ni75Al25 L12 1.82 Ni 3.15 [43]
NiAl B2 0.68 2.1 Ni 3.16 [43]
NiAl B2 1.5 0.25 1.8 0.1 Time differential length change [32]
these structures form by the direct interaction of dis- locations with vacancies.
Nagpal and Baker [7] have shown that the cooling rate has a dramatic effect on the hardness of FeAl, shown inFig. 17. They found that air-cooling and water quenching produce much the same effect on hardness.
Even slow cooling in a furnace will not eliminate quen- ched-in vacancies. After annealing for a long time at a low temperature, there is little change in hardness with aluminum content up to 45 at.% Al. Nagpal and Baker [7]performed similar studies on NiAl, and we compare the data of NiAl with FeAl inFig. 18. Unlike in the case of FeAl, heat treatment does not have a very pro- nounced effect on the hardness of NiAl.
Morris et al. [46] have observed that fast quenching results in single (mobile) vacancies, which significantly harden the material. However, slow quenching results in vacancy aggregates or clusters, which do not harden the material to such an extent. It is possible that some vacancies may be annealed out during slow cooling.
11. Quenching and annealing defects
Junqua et al.[3]observed the formation of loops and helices in Fe60Al40when quenched from 600 to 1200C and aged at 300–400 C. The loops were formed from inclusions in the materials and the number increased with aging time. At quench temperatures less than 800 C, they observed only helices with no dislocation loops.
Fourdeux and Lesbats [47]propose a mechanism for the elimination of vacancies in FeAl. After quenching, a few dislocations with a < 100 > Burger’s vector are ran- domly distributed throughout the sample. These dis- locations dissociate into loops that consume vacancies as they climb. The partials then recombine to grow in the remaining dislocation free region of the sample. In pure metals, clustering eliminates vacancies. However in FeAl, vacancy clustering would require vacancies to jump from one sublattice to the other, and the energy of a vacancy on the Al sublattice is too high to permit this.
Weber et al. [48] observed dislocation loops on the {111} plane. They propose that vacancies cluster on a
Fig. 9. Variation of lattice parameter and length for (a) Fe49Al51, (b ) Fe50Al50, (c) Fe51.5Al48.5, (d) Fe53Al47, and (e) Fe54.5Al45.5[2].
(111) plane forming a dislocation loop and an antiphase boundary (APB). A cluster of vacancies on a neighbor- ing plane forms the dendritic dislocation that sweeps out the APB. They also found that the time (t1/2) to eliminate one-half of the initial vacancy concentration increases with decreasing quench temperature below 1050 C and is not sensitive to temperatures greater than 1050 C. The time, t1/2, also increases with
decreasing annealing temperature between 300 and 400C.
Morris and Morris[49]found that the rate of vacancy annihilation, or softening, in FeAl depends on the mean free path to the vacancy sink, which is dependent on the number of vacancies and the density of sinks. This can give incorrect values of the migration enthalpy if the density of sinks depends on temperature.
Fig. 10. Variation of vacancy concentration as a function of atomic percent aluminum[2].
Fig. 11. Comparison of vacancy concentration as a function of atomic percent aluminum for Chang et al.[5], Ho and Dodd[2], and Krachler et al.[18].
12. Vacancies and yield strengthin FeAl
Yang and Baker[50]have studied the effect of vacancy concentration on the yield stress of the material. They found that the yield stress (0.2% offset stress) increases with increasing quench temperature and attributed it to the increase in vacancy concentration, shown inFig. 19.
There is an initial sharp increase in yield strength (to a vacancy concentration of approximately 4 103) fol- lowed by a slow increase in strength. They attribute the initial rise to coarse [111]slip on {110} planes. The change in slope is due to the onset of slip on the {211}
planes. They suggest that the vacancies harden FeAl by frictional strengthening, by drag on dislocations, which occurs to a greater extent on the {110} planes than the {211}. Slip on these planes produced dislocation debris, loops and pinning points on dislocations, which increased as the vacancy concentration increased.
Xiao and Baker [51] observed that yield strength increases dramatically at the stoichiometric composition and with increase of aluminum content as shown in Fig. 20.
Gaydosh et al.[52]have studied the effect of grain size and cooling rate on yield strength. They found that as the grain size increased the ductility and strength decreased, as shown by the following Hall–Petch relationship:
YS ¼342 þ 462d1=2
where d is in micrometers and YS is in MPa. They also found that yield strength decreases and ductility increa- ses with decreasing cooling rate, which agrees with
Fig. 12. Microhardness as a function of atomic percent aluminum[5].
Fig. 13. Vacancy concentration as a function of atomic percent alu- minum calculated from a thermodynamic model[5].
Fig. 14. NiAl vacancy and anti-site defect concentration[44].
Fig. 15. Variation of hardness of FeAl samples after quenching from the indicated temperature[40].
Nagpal and Baker’s [7] conclusions about the effect of cooling rate on vacancy concentration.
Morris and Morris-Mun˜oz [13] have compiled data about the effect of vacancy concentration, which is determined by heat treatment, on ductility of FeAl.
These results are presented inFigs. 21 and 22. It can be seen that a reduction of vacancy concentration greatly increases the ductility of the material.
FeAl exhibits a yield strength anomaly where the yield strength increases at intermediate temperatures
(0.35 0.45 Tm) followed by a peak in the yield strength and a subsequent decline, shown inFig. 23 [53]. There are three models that describe the anomalous increase in yield stress with temperature. Yoshimi et al. [54,55], working on single crystals of FeAl, propose the mechanism for the yield strength anomaly to be a slip transition. Below the peak temperature, the slip system is ð101Þ 111½ . However, above the peak temperature the slip system changes to a non-[111] system. The [111]
dislocations decompose to [101] and [010] dislocations just below the peak temperature.
Morris and Morris [56] propose a local climb-lock model for the yield strength anomaly where the main cause of the stress increase is the decomposition of edge
<111 > super dislocations into 12 <111 > dislocations, which become locked by climb onto non-glissile planes.
After a ‘‘nucleation’’ event, which generates climbin the dislocations, the climbforce increases until the disloca- tions are 0.7 d apart, where d is the equilibrium separa- tion of glide dislocation partials. Morris and Morris[57]
tested FeAl across the temperature range for the anom- aly and looked at the dislocation structures present at different temperatures. Detailed information of their observations is presented inTable 8.
George and Baker [53,58] propose a model that divides the yield strength versus temperature curve into different regions. They propose that the peak in the yield strength is due to a balance between two phenom- ena: (1) the presence of thermal vacancies which cause the material to harden and (2) thermal vacancies caus- ing dislocation creep (glide and climb) and therefore plastic flow to become easier.
Region I is defined by the Peierls kink mechanism typical of BCC metals given by the equation:
Fig. 16. Comparison of vacancy concentration as a function of atomic percent aluminum for Chang et al.[5]and Morris et al.[40].
Fig. 17. Microhardness as a function of atomic percent aluminum for various cooling rates in FeAl[7].
I¼0 1
kTln :
0
:
fK
8>
><
>>
:
9>
>=
>>
; 0 1=2
BB B@
1 CC CA
where :
is the strain rate, fKis the energy of formation of the kink pair and :
0 and 0are constants. The func- tional equation is given by:
I¼AIBIT1=2
Region II is the region of exhaustion of the Peierls kink region and is independent of strain rate. Region II is given by the equation:
II¼AIIBIIT
Region III, the anomalous increase in yield strength due to vacancy hardening, can be defined by:
¼ cð vÞ1=2
where b is the strength of hardening, m is the shear modulus and cvis defined as:
cv¼c0exp Ef
kT
At higher temperatures, in Region IV, vacancies become mobile and dislocation creep takes place. This region is defined by the equation:
¼
:exp Ed kT
D ’0 8>
><
>>
:
9>
>=
>>
;
1=m
Fig. 18. Microhardness as a function of atomic percent aluminum for various cooling rates in NiAl compared to FeAl[7].
Fig. 19. Yield stress as a function of experimentally determined vacancy concentration[49].
Fig. 20. Yield stress as a function of atomic percent aluminum[50].
where Ed is the activation enthalpy for vacancy diffu- sion, :
is the strain rate, and m is a material constant.
The dependence of the yield stress as given by the George and Baker model[53]confirms the dependence of the anomaly on vacancies. If some time is required to generate vacancies and the anomaly is dependant on the generation of vacancies, then the anomaly will not be present in samples that have not been heated for suffi- cient time to generate the vacancies. In this experiment, the samples have been immediately heated to tempera- ture and held at the temperature for 1 s, 30 s, 5 min, or 30 min at a higher temperature and 5 s at the test tem- perature, compared to a standard tensile test. Increasing the time at temperature increased the yield strength to a saturation value. Heating the sample to a higher tem- perature and holding it for 30 min then down quenching to the test temperature resulted in values higher than the standard test values, possibly due to the higher equili- brium value of vacancies at the higher temperature. This larger concentration of vacancies is not annealed out before the test temperature. Both the up-quenching and down-quenching experiments verify the dependence of the yield strength anomaly on vacancy concentration.
Baker and Yang[59]have measured the yield strength as a function of temperature and strain rate, shown in Fig. 24. At low strain rates, the yield stress exhibits a gradual decline as opposed to the increase at inter- mediate temperatures. Using both strain rates a change from < 111 > to < 110 > slip was observed.
There are two strong supports for the vacancy solu- tion strengthening theory—(1) the dependence of the anomaly on time at temperature, which indicates that the process is not a thermally-activated dislocation locking process and (2) the appearance of the same trend in yield strength versus temperature in Fe–40 Al quenched from high temperature and the material tested at different temperatures (Fig. 25 [59]). Morris et al.[60]
in an effort to distinguish which theory is most likely in control studied the dislocations present after deformation
Fig. 23. Yield strength anomaly in FeAl[53].
Fig. 21. Influence of heat treatments to reduce the retained vacancy concentration on the ductility of Fe–45 Al alloys, with or without 400 ppm boron[13].
Fig. 22. Influence of heat treatments on yield stress and tensile ductility of Fe–40 Al containing 0.6% carbon. The filled data points show the softening and ductilising effect of aging material extruded (at 1000C) at low temperature (400–500C). The open symbol data points show aging data for material well quenched from high temperature (1000C), when the grain size has increased somewhat. The sequence of arrows shows an example of the variation of yield stress and ductility on progressively aging a quenched material at one aging temperature (500C). Data for other aging temperatures (400C for strong-brittle materials and 650C for softer-ductile materials) sow similar stress–ductility trends[13].
Fig. 24. Yield stress anomaly as a function of temperature and strain rate[54].
of Fe–40 Al samples quenched from temperature. They found that there was no significant pinning of disloca- tions, other than jogs created from the intersection of glissile dislocations with forest dislocations, which leads to the conclusion of the presence of weak obstacles, namely single vacancies as opposed to vacancy aggre- gates such as di- and tri- vacancy aggregates.
13. Effect of ternary additions
Munroe[61]has studied the effects of Ni on FeAl in the composition (Fe55xNix) Al45 where x is equal to 0.1, 0.3, 1.0, 3.0, or 10.0 (all given in at.%). He found that Ni affects the softening behavior of FeAl alloys by increasing the equilibrium hardness after a low tem- perature (400 C, 120 h) anneal. At a Ni concentration of 10%, a small number of < 001 > dislocations were
formed. However, at lower concentrations of Ni, the concentration of < 001 > dislocations decreased and the concentration of cuboidal voids increased. Munroe[61]
proposes a method of void formation: the vacancies are attracted to the Ni on the Fe lattice (Ni has a slightly larger atomic radius). Divacancies are then formed pre- ferentially near Ni because of the strong tendency of FeAl to form divacancies. The divacancies associated with Ni attract and trap mobile divacancies, which can lead to the formation of cuboidal arrays of vacancies and the formation of cuboidal voids in the material.
Schneibel [62] confirmed the increase in equilibrium vacancy concentration by the addition of nickel. He found that nickel concentrations of 2 vol.% can cause softening in FeAl at high temperature anneals by redu- cing the vacancy hardening. He proposed two mechan- isms for this: (1) the formation of nickel/vacancy complexes and (2) the presence of small voids in FeAl with Ni. The presence of voids agrees with the method proposed by Munroe.
Kong and Munroe [63] studied the materials Fe49Al50X1where X equals Cu, Ni, Co, Mn, Cr, V, or Ti and Fe45Al50X5where X equals Cu, Ni, Co, or Cr.
The materials were heated to high temperature to induce vacancies and, then, aged at 400C for 120 h to annihilate the vacancies. In the samples with 5% alloy- ing additions, an increase in equilibrium hardness and a reduced susceptibility to vacancy hardening were observed. The increase in equilibrium hardness is higher than expected for solid solution strengthening from the alloying additions. The additions may inhibit divacancy formation, for which FeAl has a strong tendency, which inhibits the vacancy removal during aging and reduces the sensitivity of the mechanical properties to heat treatment. All the samples exhibited a high density of
<001 > dislocations, but the samples with V or Co
Table 8
Summary of flow stress variation and dislocation structures observed on testing FeAl across the temperature of the stress peak[56]
Temperature (C) Flow stress variations Dislocation Configurations
20–500 Flow stress is constant Glissile < 111 > superdislocations, typically on edges {110}
500–525 Rising flow stress Mostly < 111 > glissile superdislocations, typically on edges {110}.
Reactions < 111 > + < 111 > giving < 100 > junctions, straight along
<010 > , on {001} planes. < 111 > decomposition to < 100 > + < 011 >
when uperdislocation is 45oedge (near < 010 > ), not when -45oedge (near < 101 > )
20–512 Few large, quenched-in prismatic < 100 > loops on {110}. Little interaction
with < 111 > dislocations
512 Fine debris in matrix. Short dipoles on < 111 > dislocations. Fine cross-slip
activity
525 Stress maximum No large prismatic loops. No fine debris. Very few < 111 > superdislocations—
still glissile < 100 > and < 110 > dislocations on {001} - {011} and {110}
planes, respectively
550 and above Falling flow stress Gradual evolution from fixture of < 100 > and < 110 > to < 100 > only
Fig. 25. Variation of flow stress for materials tested at temperature and materials tested quenched from temperature[59].
additions also exhibited a small number of < 111 > dis- locations. These < 111 > dislocations are formed as dipoles from < 001 > dislocations pinned by quenched in vacancies. It was unclear why only V or Co samples formed < 111 > dislocations.
Pike et al.[64]have also studied the effect of nickel on vacancy concentration in FeAl. They annealed samples with varying degrees of Al concentration and Ni con- centration at 700 and 1000C. The samples annealed at 700 C showed significantly lower vacancy concen- trations (Fig. 26), which they believe indicates that nickel does not prevent the removal of vacancies, which disagrees with Monroe’s observation. However, usual anneals for vacancy removal are at 400 C. They also confirmed that the hardness follows the square root of vacancy concentration (Fig. 27) as in pure FeAl. The authors compare the data of Pike et al.[64]and Monroe [61] as Fig. 28. The hardness, and therefore vacancy
concentration, of Fe–45Al–xNi increases with increas- ing temperature and nickel concentration, except for an initial decrease at low nickel concentrations for the 700 and 950C samples. A comparison of the data confirms the general trend with temperature and Ni content.
Boron is used in FeAl to reinforce the grain bound- aries and change the fracture mode to a less brittle intergranular mode. Deevi, et al.[65] studied the effect of boron content on Fe–45 at.% Al and found that boron increased the room temperature yield and ulti- mate tensile strengths (probably) due to the grain boundary strengthening of boron. Interestingly, the room temperature tensile strengths of boron-doped FeAl alloys are almost 100% higher than the binary Fe–45 at.% Al alloy. The boron-doped alloys retained their high strength and exhibited high tensile elongations even after a vacancy-annealing treatment of 400C for 120 h. Interestingly, the binary and boron-doped Fe–45 at.% Al alloys exhibited similar trends in hardness values with four different heat treatments and at five different boron concentrations suggesting that boron had little influence in either enhancing or reducing the vacancies. Boron addition resulted in precipitates, and the grain size reduced from 300 mm in binary Fe–45 at.% Al to 25 mm with 4 at.% B, respectively. Pike and Liu[66]noted that binary and boron doped Fe–40 at.%
Al alloys exhibited environmental softening of yield strength when tested in air vs. vacuum after a vacancy annealing treatment. They also noted that samples with a large amount of quenched-in vacancies exhibited no change in yield strength between air and vacuum. Their yield strength data [66] suggests that binary and 500 ppm boron (by weight) containing Fe–40 at.% Al alloys exhibited similar strengths when tested under similar conditions. A comparison of Deevi et al’s[65]with Pike
Fig. 26. Vacancy concentration of Ni-doped FeAl alloys[62].
Fig. 27. Hardness of Ni-doped FeAl alloys versus the square root of vacancy concentration[63].
and Liu [66] suggests that boron is not as effective at lower Al contents as in the case of Fe–45 at.% Al.
Fraczkiewicz et al.[8]determined that boron accelerates the vacancy elimination kinetics, as shown inFig. 29 (a–c) for varying aluminum concentrations. A dislocation cell
structure is formed during the elimination and dis- appears after a long anneal. During the quench from high temperatures and the initial stages of the anneal, a non-equilibrium process is occurring for the fast migra- tion of the vacancy-boron complexes [9]. After time at
Fig. 28. Comparison of hardness versus atomic percent Ni in Fe–45Al–xNi alloys from Pike et al.[64]and Kong and Munroe[61].
Fig. 29. Kinetics of quenched-in vacancy elimination during an isothermal annealing at 380C: (a) dilatometric study of Fe–40Al alloys, pure or boron doped; (b) dilatometric study of Fe–46Al alloys, pure or boron doped; (c) dilatometric study of Fe–50Al alloys, pure or boron doped[8].
the low temperature anneal, boron will migrate back to its equilibrium positions in the matrix, however an equilibrium concentration will remain at the grain boundaries for reinforcement[9].
The authors compare data from Deevi et al.[65]and Munroe[60]for similar additions of boron or nickel in Fig. 30. Hardness values are consistently higher for samples containing nickel than for samples containing boron.
Oca et al.[67,68]carried out a study of the influence of carbon on the formation of vacancies and its influ- ence on the evolution of hardening and softening of the FeAl intermetallic sheet produced by roll compaction and cold rolling of water atomized FeAl particles [69–
73]. A very high vacancy concentration is retained in this material after a rapid quench from high tempera- tures, which leads to a strong increase of hardness with the quench temperature. At the highest annealing tem- perature, 430C, Oca et al.[66]observed a rapid initial softening as a function of the annealing time and then a hardness stabilization. For lower temperatures, 380–
340 C, an initial softening was followed by age hard- ening response. They interpreted the softening to the loss of vacancies, and the age hardening behavior to the precipitation of carbon-rich phases, either of stable structure of meta-stable structure.
14. Summary
This review and analysis has covered the funda- mentals of defects and defect structures in B2 FeAl, the
results of modeling FeAl, the formation and effects of vacancies, and the effect of ternary alloying additions on the vacancy formation and annihilation in FeAl.
Although there is some disagreement, in the Fe–Al B2 crystal structure, defects are formed as triple defects—
anti-site Fe atoms for iron-rich compositions, Fe vacancies for aluminum-rich compositions, and two Fe vacancies and one Fe anti-site atom for thermal defects.
Vacancy formation and migration enthalpies have been measured in B2 FeAl and are found to be in the ranges of 0.3–1.5 eV and 1.0–1.7 eV, respectively. In summary, increasing aluminum content in FeAl will increase vacancy concentration, which will increase hardness and yield strength and decrease ductility. The following general trends can be identified from the available sci- entific data:
1. Vacancy concentration in FeAl is controlled by heat treatment. Higher temperatures will result in higher vacancy concentrations. A low tempera- ture (400 C) anneal will greatly reduce the vacancy concentration.
2. Reducing the vacancy concentration will reduce the hardness and increase the ductility of FeAl, which will increase the formability.
3. FeAl exhibits a yield stress anomaly—an increase in yield strength at intermediate temperatures—
which is believed to be due to thermal vacancy formation in the alloy.
4. Ternary alloying additions have little effect on vacancy concentrations at high temperature, and they can increase the equilibrium hardness.
Fig. 30. Comparison of hardness versus atomic percent Ni in Fe–45Al–x (B or Ni) alloys from Deevi[64]and Munroe[61].
