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Can vacancies be the main reason of FeAl alloys hardening?

Marian Kupka

Silesian University, Institute of Materials Science, Bankowa 12, 40-007 Katowice, Poland Received 5 July 2006; received in revised form 28 November 2006; accepted 5 December 2006

Available online 19 January 2007

Abstract

The literature provides quite a lot of facts against the ‘vacancy hardening’ as the main cause of FeAl alloys hardening. The compositional dependency of the vacancy concentrations has been investigated and related to room temperature yield stress of the FeAl alloys.

Thermal point defects concentration was measured in a FeAl based alloy and applied to calculate the high temperature strengthening. The studies have shown that vacancies are not the main reason of FeAl alloys hardening.

© 2006 Elsevier B.V. All rights reserved.

Keywords: Iron aluminides (based on FeAl); Point defects; Yield strength anomaly; Vacancy hardening

1. Introduction

Heat treatments strongly affect the mechanical properties of FeAl alloys. The higher the cooling rate after annealing at elevated temperature, the higher the room temperature yield strength and hardness. As assumed, the effects arise from excess (thermal) vacancies[1].

Chang et al.[2]carried out a study of the effect of quench- ing temperature on the microhardness of FeAl alloys containing 40–51 at.%Al. The room temperature hardness of the alloys increases with both the quenching temperature and Al concen- tration. The hardness figures were correlated with the vacancy concentration through the solution hardening relationship, i.e.

the hardness is proportional to (vacancy concentration)1/2, with vacancies acting as a solute [3]. The vacancy concentration was estimated by a triple defect model developed by Neumann et al.[4].

The hardening of a material by a defect results from the inter- action between the stress field of a point defect and a moving dislocation[5]. This occurs as an elastic size effect (dilation or contraction) because the point defect has a different ‘atomic radius’ than the replaced atom. The ‘atomic radii’ are not always the adequate parameters for a size misfit. A more correct value of the size misfit may be obtained from calculations of the lattice relaxation around the defect that takes into account the electronic nature of defect—host atom interaction[6].

E-mail address:mkupka@us.edu.pl.

Over a wide range of Al content, from around 25 at.%Al, near Fe3Al with DO3order, up to about 45 at.%Al, near FeAl with B2 order, FeAl alloys show an anomalous strengthening peak at a test temperature close to 773–973 K [7]. A vacancy hardening model has been developed recently [8,9], showing that the strengthening anomaly may be produced by thermally created vacancies, leading to intermediate temperature harden- ing. Both the room temperature hardening on suitably quenched samples and the temperature strengthening anomaly has been explained as vacancy hardening using standard solute harden- ing models. A hardening H or yield strength (σ) increase is thus related to vacancy concentration CvasH = γ

Cv(or

σ = γ

Cv). The proportionality factorγ (γ) – the solution hardening rate – is a measure of vacancies hardening potency [7,10]. However, the values of proportionality factor reported in the literatureγ = G/3 and γ= G/30 (G, the shear modulus) [10] are substantially overestimated, because they have been determined directly from the relationship H = f(Cv)1/2, assum- ing a priori that the hardness increase originates from vacancies only.

Moreover, experimental values of vacancy concentration reported in the literature are usually overestimated, as FeAl alloys are susceptible to voids and cracks creation during solidi- fication[11–13]and the dominant defects in Fe-rich FeAl alloys are Fe anti-site atoms[5,10,14].

There are also quite a lot of other results of studies proving against the vacancy hardening model. Some of them have been specified below:

0925-8388/$ – see front matter © 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.jallcom.2006.12.013

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1. Chang et al.[2]used the model proposed by Neumann et al.

[4], which tries to deduce vacancy properties from thermo- dynamic activities, which were experimentally available. In the high temperature range, where the thermodynamic activ- ities were measured, their model fits well the temperature and concentration dependence in FeAl, but in the lower tem- perature part of FeAl phase diagram, vacancy concentrations have not been described sufficiently well[15].

2. Chang’s hardness data for Fe–45Al behaves anomalously starting with hardness lower than that of Morris’s Fe–39Al or Fe–43Al (Fig. 16 in Ref.[5]).

3. Kogachi and Haraguchi [16] results confirmed the rela- tion between vacancy concentration and hardness in Fe–50 at.%Al alloy, but at much higher Fe contents, where the creation of a large amount of thermal vacancies cannot be expected, rather a strong dependence of hardness on heat treatment is recognised[2,17].

4. Xiao and Baker[18]observed that yield strength was increas- ing dramatically at the stoichiometric composition, where the vacancy concentration fast increased. However, a compres- sion test was performed on Fe–50 at.%Al and tensile tests on all the other alloys. In FeAl alloys an asymmetry of the flow stress with respect to the deformation direction (ten- sion or compression) is well documented to exist[14,19–21]

and results for compression are nearly twice higher than for tension.

5. A roughly linear increase was found in the yield strength (250–530 MPa) with increasing vacancy concentration (0–4× 10−3; the experimental error in Cvwas∼2 × 10−3!) in polycrystalline Fe–40 at.%Al at room temperature[11]and the lack of a further substantial increase in the yield strength with increases in vacancy concentration above∼4 × 10−3. 6. The vacancy model of anomalous temperature strengthening

assumes that dislocations moving at increasing temperature encounter an increasing number of stationary vacancies as they move [7]; but vacancies in B2 FeAl alloys start to move over atomic distances at about 470 K[22,23], i.e. at a temperature significantly lower than the yield strength peak temperature.

7. Significant amounts of thermal vacancies in FeAl alloys are created only at temperatures above 973 K and in alloys of chemical composition close to Fe–50 at.%Al [5,12,13,16]; the peak temperature is considerably lower.

For Fe–45 at.%Al, the theoretical vacancy concentration at 1300 K is of the order of 10−6[24]. Assuming the value of enthalpy of vacancies formation in Fe–40 at.%Al alloy as Heffv ≈ 1.1 eV[25], from the equationCv= exp(−Heffv/kT ) [26], e.g. for the temperature of 700 K the vacancies con- centration is obtained in the order of 10−8! Experimental Cv

value for Fe–36 at.%Al at 800 K determined by Kerl et al.[15]

amounted to approximately 2× 10−5. In situ neutron diffrac- tion studies carried out by Kogachi et al.[27]have shown that for Fe–44.8 at.%Al preliminary annealed at 773 K/120 h, the concentration of iron vacancies does not change up to 1300 K.

Taking into account that the temperature of the peak in yield stress in Fe–45Al is lower (473 K[28]) and that the energy of elastic interaction of vacancies with dislocations amounts

merely to 0.02 eV and is lower than the energy of interstitial (0.2–0.5 eV) or substitutional (0.05–0.1 eV) atoms interac- tion[26], it seems doubtful that the alloy strengthening by almost 100% may be caused by thermal vacancies.

8. For the Fe–45Al–4Cr–0.1Zr–0.02B alloy a broad yield stress maximum occurred despite the fact that the alloy prior to tests was not annealed at low temperatures to remove thermal vacancies, which remained after homogenising at a high tem- perature[29]. The fact that the presence of thermal vacancies in a homogenised alloy before the temperature tests does not

“attenuate” the temperature peak of the yield stress proves that thermal vacancies originating during mechanical tests at elevated temperatures are not the main reason of the abnormal yield stress behaviour.

9. The magnitude of the anomalous strengthening should depend on the vacancy concentration. Literature mechani- cal property data for FeAl alloys shows that the magnitude of the anomalous yield stress peak either does not change much with Al concentration [8] or falls between 300 and 75–110 MPa as the Al concentration increases from 25 at.%Al to 43–45 at.%Al[7], while it should increase. For Fe–48 at.%Al and Fe–50 at.%Al alloys, in which the largest amount of thermal vacancies is generated, the yield stress anomaly does not emerge almost at all[30,31].

The obvious question is, can the FeAl alloys strengthening at room temperature itself be due to vacancy hardening? It is also not clear, whether during studies on yield stress temperature dependence enough excess thermal vacancies are generated to cause the anomalous thermal strengthening.

This paper presents measurements of the compositional dependence of the vacancy amounts and compares to room tem- perature yield stress of the FeAl alloys. Next, this paper examines concentrations of thermal Fe-vacancies in a FeAl based alloy and applies the data to calculate the high temperature strengthening to check the vacancy model.

2. Experimental procedure

Investigations at room temperature were carried out on FeAl alloys with var- ious aluminium contents (40, 45 and 50 at.%Al). For the temperature tests the Fe–40Al based alloy was chosen. The alloys were melted in a Balzers VSG-02 induction vacuum furnace and cast to sand and graphite moulds. The melting practice was described by Barcik et al.[32]. All alloys were re-melted several times to improve their homogeneity. Bulk samples to be used for room temper- ature measurements were not subject to heat treatment. The other samples were homogenised at 1273 K for 72 h and then annealed at 673 K for 120 h to remove the retained vacancies.

Compression tests of Ø6 mm× 9 mm specimens were performed at room temperature on an INSTRON 1195 testing machine at an initial strain rate of

∼1 × 10−4s−1. Yield stress R0.2cat 0.2% strain was determined. Button-head tensile specimens with a gauge section 29 mm in length and∼4 mm in diam- eter were machined from the cast rods. Specimens were first electropolished to reduce surface irregularities and then heat-treated. Tensile tests were per- formed at temperatures ranging from the room temperature to 1073 K, under an argon atmosphere, at strain rate of∼0.5 × 10−4s−1. Yield strength R0.2was determined using the 0.2% offset method.

Vacancy concentration indicator, W, at room temperature was determined using the Doppler broadening technique. In these measurements, the momentum component p2of the positron–electron pair annihilation in the direction of the

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semiconductor detector is measured. Momentum p2is related to the Doppler shiftE by the equation p2= 2E/c, where c is the velocity of light. The shape of a positron annihilation peak consists of a Gaussian part, reflecting annihilation with core electrons and of a parabolic part caused by annihilation with valence electrons. Positrons get trapped by vacancies because of their negative charge in reference to the bulk lattice. The first approximation of annihilation peak shape is Gaussian and vacancy trapped positrons contribute to the central part of the peak. Parameter W, which is an accurate measure of the vacancy concentration, is the ratio of the central to total area of Doppler broadened annihilation peak.

When parameter W is larger, the average volume of trapped sites (the vacancy concentration) increases.

The same method of vacancy concentration determination in FeAl alloys was applied in papers[33,34]. A conventional22Na source sealed by kapton films was used as a positron source. For the Doppler broadening measurements, a Ge semiconductor detector with an energy resolution of 581 eV for 122 keV

␥-line of57Co was used to monitor the energy spectrum of␥-ray annihilation lines. The numerical analysis of the Doppler broadening spectra was performed and the statistical error determinedW = ±0.002, at the ratio of counts 106for every positron annihilation curve.

Concentrations of thermal vacancies [CvFe] at yield strength peak tempera- ture were estimated based on a precise combination of dilatometry and lattice parameter measurements[15,35]:

[CvFe]= 3L

Lo a ao



(1)

whereL/Lois the change in sample length from the reference temperature (673 K) anda/aois the change in the lattice parameter. Changes in sample length were recorded by means of a precise dilatometer head with resolu- tion of±0.057 ␮m. The lattice parameter was measured in ˚A with accuracy to the fifth place after the decimal point. The experimental error inCvFe was

∼±0.14 × 10−3.

The concentration of antistructure atoms [FeAl] can be determined by mag- netic susceptibility measurements using a magnetic balance[35–37].

The concentration of thermal antistructure atoms [FeAl] was determined by the following formula:

[FeAl]=3kB(C1− C2) 2eff

(2)

where N and kBare the Avogadro number and the Boltzmann constant, respec- tively,μeffthe effective magnetic moment equal to 7.8Band C1and C2are the Curie constants corresponding to the first heating (after specimen’s fast cooling from the yield strength peak temperature) and to the second heating—after slow cooling of the same specimen down to room temperature.

3. Results and discussion

3.1. Room temperature strengthening

Fe–40, Fe–45 and Fe–50 at.%Al alloys were cast to sand moulds. Large-grained alloys with the same average grain size D ∼ 490 ␮m (Table 1) were used to avoid the influence of¯ grain-boundary strengthening. Apart from the grain size,Table 1 presents values of the yield stress R0.2c (determined in a com- pression test) and parameter W characterising the vacancies concentration in tested alloys. With increasing aluminium con-

Table 1

The yield strength, R0.2c(compression tests), vacancy concentration parameter, W, and average grain size,D, of FeAl alloys

Alloy R0.2c(MPa) W D (␮m)

Fe–40 at.%Al 500 0.485± 0.002 490

Fe–45 at.%Al 1000 0.485± 0.002 490

Fe–50 at.%Al 1310 0.513± 0.002 495

tent in FeAl alloys a clear gradual increase in the yield stress is observed from 500 MPa for the Fe–40Al alloy to 1310 MPa in the case of the stoichiometric alloy.

The evaluation of vacancies concentration has shown that the amount of such defects in Fe–40Al and Fe–45Al alloys is similar and at the same time much lower as compared to the alloy of stoichiometric composition.

The obtained results are interesting because of a high value of the yield stress for the Fe–45Al alloy (R0.2c= 1000 MPa), at R0.2c= 500 MPa for the Fe–40Al alloy, despite the same concen- tration of vacancies in both alloys.

Similar results of studies at ambient temperature were obtained by Gialanella et al. [33] for Fe–40 at.%Al alloy quenched from 773 and 1073 K. Hardness increased from 425 to 600 HV despite the fact that the vacancy concentration indi- cator, W, determined by positron annihilation, changed slightly, from 0.474 to 0.478 (atW = ±0.002).

The presented results clearly show that strength parameters of FeAl alloys (R0.2and HV) may substantially increase, despite the same (or close) vacancies concentration. This contradicts the statement of Xiao and Baker[18]about a decisive influence of vacancies on mechanical properties of FeAl alloys. An alterna- tive – to vacancy hardening – reason of hardness increase in FeAl alloys quenched from high temperatures may be for example a specific substructure observed after fast cooling.

Examinations of the structure of Fe–40Al based alloy, quenched in water from 1273 K, carried out using a HREM have shown the existence of extremely small (2–3 nm) antiphase domains (Fig. 1a). In the case of slow cooling with the fur- nace, during which the alloy gets entirely ordered, no antiphase domains have been observed in the structure (Fig. 1b).

As the alloy gets ordered via diffusion and requires a specific time, at fast cooling from a high temperature the disorder–order transformation does not proceed entirely and a large number of small ordered areas (domains) are created, separated by antiphase boundaries. Domains’ boundaries constitute resis- tance to a dislocation slip resulting in an increase in strength parameters. Such effect was obtained by Ardley for ordered Cu3Au at a similar domains’ size (2 nm) [38]. Such domains presence was also found in an intermetallic Ni3Al compound [39].

3.2. High temperature strengthening

Temperature changes of the yield strength, R0.2(determined in a tensile test), of the Fe–40Al based alloy are presented in Fig. 2. A distinct maximum may be seen at 823 K. The thermal strengtheningR0.2amounts to∼95 MPa.

Numerous methods for adding the effects of multiple harden- ing sources have been suggested[40]. One of these is the ‘mean square law’. This assumption suggests that the square of total increase in the yield strength is equal to the sum of squares of the changes in the yield strength if a few defects were considered separately:

σ =



(γ1c11/2)2+ (γ2c12/2)2+ · · · + (γnc1n/2)2 (3)

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Fig. 1. HREM image of Fe–40Al based alloy structure after Fourier filtration: (a) heated at 1273 K and then quenched—antiphase domains present and (b) heated at 1273 K and slowly cooled with the furnace—no antiphase domains.

where γn and cn are the solution hardening rate and defect concentration, respectively, of the n-type defect.

The defects structure in B2 FeAl alloys may be described using the Bradley–Taylor method, according to which in Fe-rich alloys there are only antistructure iron atoms in the aluminium sublattice (FeAl), while during temperature rising vacancies in the iron sublattice originate (VFe) apart from those defects[41].

These two types of defects existing in a binary FeAl alloy are retained also in a ternary FeAl–Me alloy[42].

The assessment of strengthening of the tested Fe–40Al based alloy was carried out assuming that the increase in the yield stress results from a solution hardening originating from VFe

vacancies and antistructure FeAlatoms.

The vacancy concentrationCVFe was determined using Eq.

(1). The obtained increase in thermal vacancies concentration

Cv= 6× 10−4 at Fe–40Al based alloy temperature raising from 673 to 823 K (yield stress peak temperature,Fig. 2) is lower than the value obtained by Yang and Baker (Cv≈ 1 × 10−3) [11]. However, the present result is more precise, because the experimental error of vacancies concentration measurement by those authors was equal to 2× 10−3, while in this paper it amounted to 0.14× 10−3. For Fe–39 at.%Al alloy, Schaefer obtained a similar, to obtain in this paper, concentration of vacan- cies at 830 K (Cv≈ 10−4)[43]. The lattice parameter is shown as a function of quenching temperature inTable 2. A decrease in the lattice parameter after quenching from a temperature above

Fig. 2. Graph of yield strength vs. temperature for Fe–40Al based alloy deformed under tension.

973 K is evident. Yang and Baker attribute this effect to a higher vacancy concentration[11].

The concentration of antistructure FeAliron atoms was cal- culated from the formula(2). Parameters, which have been used in determination of the strengthening have been specified in Table 3. The calculated amount of point defects corresponds to their concentration increase at temperature raising from the reference temperature (673 K) to the temperature at which the maximum of yield stress occurred (823 K). Experimental yield stress increase in the same temperature range (Fig. 2) amounts toR0.2exp= 95 MPa.

The magnitude of strengthening was calculated from the for- mula(3). Because of similar values of elastic interaction energy of substitutional atoms and vacancies with dislocations[26]and similar lattice deformations (of spherical symmetry)[44], the value of solution strengthening rate of FeAlatoms was assumed for vacancies (γ = G/120[45]; G = 75 GPa[45]). The value of anomalous increase in the yield stress calculated on the basis of solution strengthening theory was equal to 36 MPa.

It shall be clearly emphasised that if the strengthening originating from vacancies only was considered separately then only 15 MPa would be obtained, while that from antistructure iron atoms—33 MPa. So it shows that the contribution of FeAl atoms in thermal strengthening of the studied alloy is twice as large as that of VFe. Despite considering an addi- tional strengthening originating from antistructure iron atoms (not comprised by the vacancy model), this value is clearly

Table 2

The lattice parameter of Fe–40Al based alloy as a function of quenching temperature

Temperature (K) a ( ˚A) a ( ˚A)

673 2.89264 5.2E− 5

773 2.89514 4.2E− 5

823 2.89551 5.7E− 5

873 2.89654 3.7E− 5

923 2.89778 2.6E− 5

973 2.89668 3.8E− 5

1073 2.89627 1.8E− 5

1173 2.89404 3.8E− 5

1273 2.89344 3.1E− 5

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Table 3

The length sample change,L/Lo; lattice parameter change,a/ao; Curie constants difference, C1− C2; defects concentrations,CvFeandCFeAlof the Fe–40Al based alloy

Yield stress peak temperature (K) L/Lo× 103 a/ao× 103 (C1− C2)× 103(emu g−1K) CvFe(%) CFeAl(%)

823 1.192 0.992 1.04 0.06 0.28

Lo, ao—the length and lattice parameter after annealing at 673 K/120 h.

lower than the experimentally determined increase in the yield stress (R0.2exp= 95 MPa). It is also much smaller than the temperature strengthening of binary Fe–45 at.%Al alloy (R0.2≈ 260 MPa) obtained by Reimann and Sauthoff[28].

The above results show that the anomaly in the yield stress of the FeAl alloy is not caused mainly by strengthening originating from thermal vacancies.

A clear dependence of the yield stress temperature changes on the long-range order parameter for the alloy based on B2 FeAl phase was obtained for the first time in paper[36].

4. Summary

Both the room temperature hardening on appropriately quenched samples and the temperature strengthening anomaly of FeAl alloys were often explained in the literature by the vacancy hardening, using standard solute hardening models.

Results of other authors raise doubts (described in this paper) regarding the rightness of the ‘vacancy model’. From those and from tests and calculations presented in this paper (carried out based on solid-solution hardening model as well as experi- mentally determined point defect concentrations), it results that thermal vacancies cannot be the main reason of strengthening of substoichiometric (Fe-rich) FeAl alloys. This was confirmed by precise measurements of lattice parameters, which have shown that an increased amount of thermal vacancies originates only at a temperature much higher than the maximum strengthening temperature.

The reason for FeAl alloys strengthening at room temperature may be, e.g. small antiphase domains, which existence in the substructure of quenched Fe–40Al alloy was found in this paper.

However, temperature anomaly in FeAl alloys yield stress may be caused by changes in long-range order of the FeAl phase observed in paper[36].

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References

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