Correlation of the hardness and vacancy concentration in FeAI

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lntermetallics 1 (1993) 107-115

Correlation of the hardness and vacancy concentration in FeAI

Y. A. Changfl L. M. Pikefl 'b C. T. Liu, h A. R. Bilbrey & D. S. Stone ~

" Department of Materials Science and Engineering, University of Wisconsin, Madison, Wisconsin 53706, USA h Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA (Recieved 16 December 1992: revised version received 29 December 1992: accepted 7 January 1993)

Microhardness measurements of FeA1 containing 40 51 at.% A1 were carried out at ambient temperature on specimens which had been subjected to different heat treatments. The hardness values for specimens heat-treated at 500°C and water-quenched to ambient temperature increase slowly with composition until at about 48 at.% AI. At higher A1 concentrations the hardness values increase more rapidly. For specimens heat-treated at temperatures higher than 700°C and water quenched to ambient temperature, the hardness values increase with AI concentration with little change in slope through the entire composition range of 40-51 at.% A1. The compositional dependences of the hardness values are similar to those of the vacancy concentrations in FeA1. The vacancy concentrations as a function of A1 composition were obtained from a thermodynamic model and experimental data at the stoichiometric composition. The close resemblance of the shapes of the hardness curve and the vacancy concentration curve suggests that the hardness and thus the yield strength may be related to the presence of vacancies in the lattice. This conclusion is further supported by the evidence that the hardness of FeA1 increases with the square root of the vacancy concentration. This type of relationship agrees well with established point-defect strengthening models, based on the interaction of a moving dislocation with a point defect.

Key words." FeAI, hardness, vacancy concentration, thermodynamic model, point-defect strengthening.

I N T R O D U C T I O N

Due to their high strength, high melting point, and oxidation resistance, intermetallic compounds consisting of a transition metal and aluminum have been explored as potential high-temperature materials. In contrast to traditional solid-solution materials such as the ferrous, aluminum, nickel, and titanium alloys, our knowledge concerning the structure~roperty relationships as well as the processing science of the intermetallic compounds is scarce. One class of intermetallic compounds which offers potential for practical applications is the transition metal aluminides with a stoichiometric composition at 50 at.% AI. These compounds crys- tallize in a rather simple structure, being ordered bcc or CsC1 (B2-type). Most of these intermetallic compounds exist over a wide range of homogeneity.

Their properties may be strongly composition- dependent due to the types of point defects and their concentrations present in these compounds.

107

Recently, Nagpal and Baker 2 studied the effect of cooling rate on the hardness of two transition metal aluminides, FeA1 and NiA1. For both of these compounds, they found the hardness values to be composition-dependent, with an abrupt change in the vicinity of the stoichiometric composition. This phenomenon was reported earlier by Westbrook, 3 who moreover, indicated that vacancies may be responsible for strengthening some of these compound phases. For FeAI, Nagpal and Baker 2 also found the hardness values to be sensitive to heat treatments; this is, the samples quenched from a high temperature of 1000°C are much harder than those furnace- cooled (about 50K/h) to ambient temperature.

They attributed this behavior to the presence of different concentrations of vacancies in the lattice.

However, no attempt was made to correlate the behavior of the hardness with the concentrations of vacancies in the lattice.

The objectives of the present study are (1) to

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108 Y. A. Chang, L. M. Pike, C T. Liu, A. R. Bilbrey, D. S. Stone measure the ambient-temperature hardness of

FeA1 systematically as a function of composition and of temperature where the samples are heat- treated and quenched and (2) to correlate the compositional dependences of the hardness values with those of the vacancy concentrations. The vacancy concentrations are obtained from a statistical thermodynamic model for the B2 intermetallic phase. This model was developed on the basis of the structural defects present in these B2 phases. 1,4

2 EXPERIMENTAL METHOD AND RESULTS

2.1 Experimental procedure

Five FeA1 specimens containing 40, 45, 48, 50, and 51% A1 were prepared by arc melting in an argon atmosphere and drop casting into a copper mold, using high-purity iron and aluminum metal chips. The alloy ingots with a diameter of 2.5 cm were canned in mild-steel billets and hot extruded at 750°C at an extrusion ratio of 12 to 1. All alloys were successfully fabricated into 0.8 cm bar stocks. Cylindrical specimens of 0.7 cm diameter

× 0.5 cm height were first recrystallized for 1 h at l l00°C and then furnace-cooled to ambient temperature.

The grain sizes of the specimens were determined to be about 300/zm using the line intercept method. The recrystallized samples were then

annealed at temperatures ranging from 500 ° to 1000°C, followed by water quenching. These heat treatments were performed in a vertical furnace suspended over a quenching basket. At higher temperatures, a flowing argon atmosphere was used to prevent oxidation. Specimens were given the following heat treatments before quenching:

150 h/500°C, 72 h/700°C, 72 h/800°C, 24 l'ff900°C, or 5 h/1000°C. N o noticeable change of the grain size was observed after these heat treatments;

thus, all the specimens had essentially the same grain size. After quenching, the samples were mounted and polished for the hardness tests.

The microhardness was measured with a Vickers indenter, using a 500 g load and a 15 s load duration. These specimens were also characterized by X-ray diffraction.

In order to confirm the decrease in the lattice parameter values reported in the literature at A1 concentrations higher than 50%, FeA1 alloys with 49.5, 50.5, 51.5, and 52 at.% A1 were prepared for analysis in addition to the alloys mentioned earlier. Also an alloy with 55% AI was prepared, a composition chosen since it is in the two phase field of FeA1 and FeA12. These alloys were prepared by arc melting in a gettered argon environ- ment, given a homogenizing heat treatment of 16 h/1100°C in an argon atmosphere, and along with those used in the hardness measurements, crushed into a 200-mesh size powder. The powders were sealed in evacuated quartz tubing with a vacuum of ~10 -3 Torr and then given a heat treatment of either 2 h/750°C followed by 150 h/500°C or

8

3

2.910

2.905

2.900

2.895

• ' Present Sludy, quenchexl from'1000°C ' '

P I

[] Present study, quenched from 500°C A O

O Bradley and Jay, slow cooled from 750°C ~ " t a x ' ~ ta :-z tn / -

t~ Taylor and Jones, quenched from 250°C

v Lihl and Ebel, at 20°C a ¢ V J I D

o Ho and Dodd, at 20°C / J ' ~ -

I

40 45 50 55

,% AI

Fig. 1. Ambient temperature lattice parameter o f FeA1 as a function of A1 composition obtained form samples heat-treated at and quenched from 500 and 1000°C. F r o m present work and Refs 6--9.

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Correlation of the hardness and vacancy concentration in FeAl 109 5 h/1000°C. Both treatments were terminated with

a water quench. The 2 h/750°C treatment for the specimens quenched from 500°C was needed since the 150 h/500°C annealing was insufficient to elim- inate the plastic strain introduced during the crushing process. X-ray diffraction with copper- K~ radiation was then performed on the powders using a Scintag diffractometer. A scan rate of 1.4°/min and a step size of 0.02 ° were used. An ex- trapolation against the function cos20/sin 0 was used in the determination of the lattice parameter. 5

:j - \

200

2.2 Experimental results (a)

2.2.1 Lattice parameters

Figure 1 shows a comparison of the lattice parameters of FeA1 obtained in the present study with those reported in Refs 6-9. Within the scatter of the data, the results of the specimens quenched from 500°C are consistent with the literature values. The lattice parameters of the specimens quenched from 1000°C can be seen to be noticeably lower than those quenched from 500°C. This is consistent with the prediction of higher vacancy concentrations at higher temperatures. That the values from the literature agree with the 500°C data better than with the 1000°C data is quite reasonable since the literature values are from specimens annealed at a low temperature, or from slowly cooled specimens which can be expected to exhibit a defect concentration corresponding to a low temperature. It is important to note that our data confirm the decrease of the lattice parameter at A I concentrations higher than the stoichiometric composition from both specimens quenched from 500°C and from 1000°C. According to the analysis of Chang and Neumann, ~ the decrease of the lattice parameter with excess A1 over the stoichiometric composition corresponds to the formation of constitutional vacancies in the Fe sublattice. Thus, the lattice parameter data seems to confirm that FeAI is a triple-defect type phase (to be defined later) in the temperature range of 500-1000°C.

The data also indicate that the Al-rich phase boundary is about 51 at.% A1 at 500°C and about 53 at.% A1 at 1000°C. As shown in Fig. 1, the lattice parameters of Al-rich FeA1 samples quenched from 500°C remain constant from ~51 to 55 at.°/, AI, indicating the existence of an F e A I + FeA12 two-phase field. For the samples quenched from 1000°C, the lattice parameters of Al-rich FeA1 samples are extrapolated to ~53 at.% A1, at which composition the lattice parameter is the same as

; > ~

' :W

(b)

Fig. 2, Optical microstructures of PeAl crystallized for 1 hr at I100°C: (a) F e ~ 5 at.% AI and (b) Fe--51 at.% A1.

that present in the 55 at.% A1 sample. The 55 at.%

A1 specimens were also confirmed to be two-phase by metallographic analysis. The phase boundary values obtained are in reasonable agreement with the published phase diagram. ~°

2.2.2 Microhardness

Prior to reporting the microhardness data, let us first present the microstructures of the recrystallized specimens. Figure 2 shows a typical microstructure for the alloys with 40-51 at.% AI used in the microhardness measurements. Etch pits are visible in certain grains, but not apparent second phase particles are detected in these samples. The X-ray data are consistent with these results.

Figure 3 shows the ambient-temperature microhardness of FeA1 as a function of composition and heat-treatment temperature. Each data point reported here represents an average of six measurements. It is evident from this figure that the hardness values for FeAI samples annealed at high temperatures and quenched to ambient temperature increase monotonically with A1 composition. However, with the decrease of annealing

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110 Y. A. Chang, L. M. Pike, C. T. Liu, A. R. Bilbrey, D. S. Stone

t~

'a

.o 7 0 0 .

6 0 0 .

5 0 0 -

4 0 0 -

3 0 0 -

200 38

500°C + Water Quench (WQ) 700~C + WQ

800~C + WQ 900°C + WQ IO00°C + WQ

b '2 4'4 ' ' '

4 4 46 48 50 52

F i g . 3 .

%A1

Ambient-temperature microhardness of FeA1 as a function of AI composition from samples heat-treated at and quenched from high temperatures.

temperature, the hardness values increase more rapidly as the stoichiometric composition is approached, as the data at 500°C show.

Since the hardness o f an alloy is known to be influenced by the presence of point defects such as vacancies in the lattice, 11,12 it is desirable and in- formative to have a knowledge of the compositional dependences of the vacancy concentrations in FeAI as a function of temperature. In Section 3 we present a thermodynamic model which allows us to obtain these values.

3 T H E R M O D Y N A M I C S AND D E F E C T S T R U C T U R E O F T H E B2 P H A S E S

The B2 phases consist of two atoms, with one occupying the corners of the cube and the other the body-centered position o f the cube. Since a perfectly ordered structure may be achieved only at absolute zero, a B2 phase, even at the stoichiometric composition, must contain thermally activated structural defects at any finite temperature. In addition to thermal defects (or intrinsic defects), constitutional defects are formed at non- stoichiometric compositions. In fact, the concentrations o f the constitutional defects generated at non-stoichiometric compositions are m u c h higher than those o f thermal defects and thus dominate the total defect concentrations.

F o r B2 phases, the two frequently occurring types o f defect structure are the anti-structure type and the triple-defect type. The anti-structure of defect structure occurs in phases such as CuZn, AgMg, NiZn. 1 Thermal defects in this type o f defect structure consist o f an A a t o m (normally on

the a-sublattice) occupying a/3-sublattice site, and a B atom (normally on the fl-sublattice) occupying a a-sublattice site. Constitutional defects, formed at non-stoichiometric compositions, consist of A atoms on /3-sites in A-rich compositions, and B atoms on a-sites in B-rich compositions. The triple defect o f defect structure occurs in such phases as NiA1, CoAl, FeAI. 1 Thermal defects in these phases, where the B a t o m is larger than the A atom, consist o f an A atom on the fl-sublattice, and two vacancies on the a-sublattice. This is nec- essary in order to maintain equal numbers of sites for the two sublattices. The B atoms do not go to the a-sublattice for the A atoms. At non-stoichiometric compositions, constitutional defects are formed in addition to the thermal defects. With an excess of A atoms, i.e. positive deviations of com- ponents A from the stoichiometric composition, the extra A atoms go to the fl-sublattice forming anti-structure A atoms. On the other hand, with an excess of large B atoms, which cannot go to the /3-sublattice, additional vacancies are created on the a-sublattice. It is evident that the only point defects found in triple-defect type phases are vacancies on the a-sublattice, and anti- structure A atoms on the fl-sublattice. In contrast, anti-structure type phases contain anti-structure B atoms on the a-sublattice as well as anti-structure A atoms on the fl-sublattice, but contain no vacancies on either sublattice.

F o r triple-defect type B2 phases, the lattice parameter tends to increase with the concentrations o f the B c o m p o n e n t until the stoichiometric composition is approached. At compositions higher than the stoichiometric composition, the lattice parameter decreases abruptly due to the formation

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Correlation o f the hardness and vacancy concentration in FeAI 111 of vacancies on the a-sublattice. In contrast, for

anti-structure type B2 phases, the lattice parameter increases beyond the stoichiometric compositions but with a change in slope.1

For B2 phases with the triple-defect type, Neu- m a n n et al. 4 developed a thermodynamic model taking into consideration only the first-nearest neighbour interaction for the enthalpy term. For the entropy term, the vibrational contribution is taken to be composition-independent and the configurational term consists of mixing of atoms as well as atoms and defects on the two sublattices. This model makes the assumption that the only defects present are anti-structure A atoms on /3-sublattice sites and vacancies on the a-sublattice. The basic parameter of the model is the concentration of the thermally generated vacancies at the stoichiometric composition. It is

a = ~'] = 2 (1)

, N - / x = o k N / x = o

where N0_ is the number of vacancies on the ~- sublattice; N~A is the number of A atoms on the /3-sublattice; N is the total number of atoms;

and X is the deviation from the stoichiometric composition, defined as

X = x B - 0.5 (2)

Values of ol may be determined experimentally ~ and are temperature-dependent. Alternatively, these values may be obtained by analyzing the compositional variation of the chemical potential of the c o m p o n e n t s provided that the reliable data are available. Moreover, if c~ is known at any fixed temperature, the compositional dependence of the vacancy concentration may be obtained by the following equation:

z 3 ( l + c ~ - - a 2 - - C~ 3) - - C~3(1 + Z - - Z 2 - - Z 3)

X TM 2z2(1 + ol -- c~ 2 -- ~3) (3) where z is defined as

It is worth noting that the concentration of anti- structure defects is related to the vacancy concentration. At the stoichiometric composition,

Nix=0 2

At non-stoichiometric compositions, the relation becomes

2z2 (7)

The above equation may be obtained readily from eqn (5) and the definitions of z and the concentrations of the anti-structure defects.

N e u m a n n et al. 4 analyzed the thermodynamic data of Eldridge and K o m a r e k ] 3 Gross et a/., 14 and Radcliffe et al. ~5 for FeAl, and obtained a value of a = (2 + 0.4)10 2 at 1173K. Using the model of N e u m a n n et al., 4 and the a value at 1173 K, the following relationship for the temperature dependence of a was obtained: ~

c~ = 0.63 exp [---470] (8) where T is the absolute temperature (K).

It is worth noting that values of a obtained in this manner are in agreement with the directly determined vacancy concentration by Riviere ~6 and slightly lower than those determined by H o and Dodd. 9 As pointed out by Chang and Neu- mann, ~ this is quite reasonable since vacancy concentrations determined from density measurements tend to be high due to possible voids in the samples used.

On the basis of the intrinsic vacancy concentrations according to eqn (8) and using eqn (3), the variations of the vacancy concentrations of FeA1 with composition are shown in Fig. 4 for the five temperatures used in the heat treatments of the specimens for hardness measurements.

z = ( 4 )

Equation (3) is obtained by minimizing the Gibbs energy with respect to the degree of dis- order z.

Since it is assumed that the only vacancies present are on the a sites, z is the total vacancy concentration. When ol << 1 and z < 1, eqn (3) is reduced to

.2 3 - - O~ 3

X = 2 Z 2 ( 5 )

4 D I S C U S S I O N

As shown in Fig. 4, the vacancy concentrations for Fe-rich FeA1 are relatively small, e.g. ~0.05%

at 40 at.% A1 at 500°C. They become noticeably higher at compositions above about 48 at.% A1, and thereafter increase abruptly with composition.

A comparison of Figs 3 and 4 shows that the general shapes of the hardness versus composition curves and the vacancy concentration versus compositions curves are similar. In other words, at high temperatures, both the hardness values and

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112 Y. A. Chang, L. M. Pike, C. T. Liu, A. R. Bilbrey, D. S. Stone 0.035 L

0.030'

>

0.025"

0.020"

0.015"

0.010"

T = 1 0 0 0 " C

T = 9 0 0 " C

Fig. 4.

0.005 -

0.000

T = 8 0 0 " C

T = 7 0 0 " C

T - 5 0 0 ° C

40 41 42 43 44

Vacancy concentrations of FeA1 as a

45 46 47 48 49 50 51

% AI

function of A1 composition at several temperatures.

vacancy concentrations increase smoothly with composition. This qualitative correlation between the shapes of these curves suggests that the more rapid increase in the hardness values of FeA1 beyond 48 at.% AI may be due to the corresponding changes in the vacancy concentrations.

If the presence of vacancies in FeA1 is responsible for strengthening in this intermetallic compound, it may be interesting to examine the relationship between the hardness values and the vacancy concentrations. It is well established that point defects give rise to strengthening, as a result of elastic interaction. This strengthening is related to the interaction between a moving dislocation and the point defect. This interaction can be correlated

to the size misfit of the point defect and the change in the shear modulus of the lattice due to the point defect. Analysis by Fleischer 1],12 of this dislocation-point defect interaction leads to a square root dependence of the yield strength on the defect concentration. Generalizing the results of Fleischer to the hardness test, we may postulate that

H = H 0 + 6 T ~ c 1/2 (9) where c is the defect concentration, i.e. vacancy concentration in the present case; /z is the shear modulus; y is a coefficient, and is less than unity, which depends on the strength of the interaction;

and H0 is the hardness at zero defect concentration. The factor o f 6 takes into account the

Fig. 5.

121 Fe-40AI ,0, Fe-45AI

O Fe-48AI

' A Fe-50AI 0 ~ " ~ m

[] Fe-51AI O O ~ ' ' ' ' f

A °#D

% A ~

^[]

0 , , , , I . , , i I , , , , I

0.00 0.05 0.10 0.15

(Vacancy Concentration) 1/2

0.20

Relationship between the microhardness and the square root of the vacancy concentration in FeA1.

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Correlation o f the hardness and vacancy concentration in FeAI 113 relationship between hardness and yield strength

(× 3) as well as the Taylor factor (× 2).

The hardness of FeA1 is plotted versus the square root of the vacancy concentration in Fig.

5. In making these plots, the hardness values were taken from Fig. 3 and the vacancy concentrations were obtained in the same manner as for Fig. 4.

The hardness values were converted from Vickers hardness (load in kg/contact area in m m 2) to the load divided by projected area (units of GPa). A clear relationship between hardness and the square root of the vacancy concentration is seen which confirms the applicability of eqn (9). It is worth noting that for comparison to other point defect strengthening models the hardness values were also plotted versus the vacancy concentrations to the first power and the two-thirds power, respectively. ~7 No satisfactory correlation was obtained.

The correlation of the hardness in terms of the square root of the vacancy concentration, which exists on both sides of stoichiometry, suggests that the vacancies have a significantly larger effect on the hardness than the anti-structure atoms. This is especially noticeable at Fe-rich compositions where the number of anti-structure atoms significantly outnumbers the number of vacancies. This result might be relationalized on a number of grounds. First, since a vacancy has a larger size misfit than an anti-structure atom and could also be expected to affect the shear modulus more than an anti-structure atom would, vacancies would appear to be more effective strengtheners than anti-structure atoms would be. Another possibility is that the vacancies are forming some kind of defect complex, producing tetragonal-type distortions. Such distortions are known to be more effective strengtheners. ~2 Based on the slope of the data in Fig. 5, and the value for the shear modulus of FeA1 of ~100 GPa adapted from Wolfenden and Marmouche, ~ we can estimate y ~ 0.038.

This value seems to be essentially independent of composition. At 0 K, y -- 0.1 would be considered a strong interaction--comparable, for instance, to interstitial C in Fe. u A value of 0-001 or less might be expected for the weak interaction of an anti-structure atom. ~2 The high value of y from Fig. 5 relative to that of an anti-structure atom further supports the idea o f vacancies having a stronger interaction with dislocations than do anti-structure atoms. It is high enough, in fact, to lead one to suppose that some type of defect complex involving the vacancies may also be affecting the hardness.

The value of H 0 obtained by extrapolating the data in Fig. 5 to a vacancy concentration of zero is -2.6 GPA. H0 appears to be a weak function of composition.

It is interesting to compare the FeAI system to the NiAI system. NiAI has the same crystal structure as FeA1 and is also believed to be a triple-defect type phase. The hardness of NiA1 is known to have a m i n i m u m value at the stoichiometric composition. 2'3 This behavior has been associated with vacancies on the Al-rich side and anti-structure defects (Ni atoms on A1 sites) on the Ni rich side. 3 The vacancy concentration of NiAI has been determined by a number of investi- gators; for example, by Chang and N e u m a n n ~ and, more recently, by Kogachi et al. 19 The vacancy concentrations correlated well with those obtained by analyzing the variation of the chemical potential of A1 with composition in terms of the thermodynamic model, as discussed earlier.

These data indicate that vacancy concentrations in Ni-rich NiA1 are very low in comparison to Fe-rich FeA1 and that the vacancy concentration rises rapidly on the Al-rich side of stoichiometry.

This may explain why the hardness dependence on vacancy concentration in NiA1 applies only to the Al-rich side while in FeAI this dependence seems to exist on both sides of stoichiometry. Another feature of the NiA1 hardness data is that the hardness increases more rapidly on the Al-rich side of stoichiometry than it does on the Ni-rich side. 2'3 This has been attributed to vacancies being more effective strengtheners than anti-structure atoms, 2°

in agreement with our previous comments on the relative interaction strengths of vacancies and anti-structure atoms in FeA1.

In developing the thermodynamic model for FeA1, N e u m a n n et al. 4 assumed that the only defects existing in FeA1 are vacancies on the a(Fe)-sublattice and anti-structure Fe Atoms, i.e.

Fe atoms occupying the /3(A1)-sublattice. This is clearly an approximation of the actual situation.

Using similar assumptions for developing the thermodynamic model for the triple-defect type B2 phases, N e u m a n n 2~ developed a model for anti-structure type B2 phases. He found that the concentration of the anti-structure defects is a function only of the enthalpy of formation of the stoichiometric c o m p o u n d while that of the triple defects is a function of both the enthalpy of formation of the c o m p o u n d and the enthalpy of formation of vacancies. These relationships predict that less exothermic B2 phases favor the formation of the anti-structure defect type

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114 Y. A. Chang, L. M. Pike, C. T. Liu, A. R. Bilbrey, D. S. Stone phase while the more exothermic phases favor

the occurrence of the triple-defect type phase.

Indeed, experimental data for numerous B2 phases support the prediction o f the simple model.

For instance, NiA1 with an enthalpy o f formation of - 6 9 kJ/mol of atoms exhibits the triple-defect type ~'2~ while C u Z n with a value o f -11.1 kJ/mol of atoms exhibits the anti-structure defect type.

However, for some B2 phases whose enthalpy of formation values fall in-between the extreme values, the model predicts a hybrid behavior. In other words, the defects present in these B2 phases may consist o f both the triple-defect type and the anti-structure defect type. FeAI was pointed out to be one such phase. Although the lattice parameters in Fig. 1 indicate the existence on vacancies in FeA1, it is probable that a consider- able a m o u n t of A1 atoms also occupy the a(Fe)- sublattice. Recent first principle calculations o f

F u 22 indicate the existence o f vacancies mainly on the Fe-sublattices but anti-structure atoms on both sublattices. Moreover, his calculations also suggest the formation o f vacancy clusters. The results o f his preliminary calculation are not in- consistent with the semi-empirical thermodynamic arguments o f N e u m a n n . 2~ In view of the complex defect structure in FeA1, the calculated vacancy concentrations in FeAI presented in Fig. 4 must be considered qualitatively correct. More rigorous theoretical calculations and more careful and systematic experimental investigations are needed before definitive conclusions can be reached. Never- theless, the resemblance between the shapes o f the hardness and vacancy concentration curves of FeAI, and the apparent agreement o f the dependence o f hardness on the vacancy concentration with that p r e d i c t e d by dislocation-point defect interactions, indicate that the hardness o f FeA1 is related to the vacancy concentrations in the lattice t h r o u g h o u t the entire range o f homogeneity.

C O N C L U S I O N S

The ambient-temperature hardness values of FeA1 annealed at 500°C and quenched to ambient temperature show abrupt increase as the stoichiometric composition is approached. However, the hardness values for FeA1 annealed above 700°C and higher and quenched to ambient temperature increase smoothly with AI composition, even at the stoichiometric composition.

The lattice parameters obtained supported the data reported in the literature in that they

decrease at 50 at.% A1 and higher. These data indicate that the triple-defect structure exists in FeAI although the anti-structure defect type may also be present. The existence of the anti-structure defects is based on theoretical arguments. Never- theless, the vacancy concentrations were calculated from a thermodynamic model developed on the assumption of the triple-defect type. The shapes o f the calculated vacancy c o n c e n t r a t i o n - - composition curves at 500°C, as well as at 700°C and higher, show close resemblance to those of the hardness curves. In addition, the hardness appears to increase with the square root of the vacancy concentration. This relationship is in agreement with point defect strengthening models based on the interaction of a moving dislocation with a point defect. For these reasons it seems plausible to conclude that the hardness of FeA1 is related to the vacancy concentration t h r o u g h o u t the range of 40-51 at.% A l - - t h a t is, on both sides of stoichiometry.

ACKNOWLEDGEMENT

This research was sponsored by the Division o f Materials Sciences of the Basic Energy Sciences, U.S. D e p a r t m e n t o f Energy, under Contract DE- AC-05-840R-21400 with Martin Marietta Energy Systems Inc. and Subcontract No. SJ403-19 from Martin Marietta Energy Systems Inc. to the Uni- versity o f Wisconsin-Madison.

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Correlation o f the hardness and vacancy concentration in FeAI 115

15. Radcliffe, S. V., Averbach, B. L. & Cohen, M., Acta Met- all., 9 (1961) 169.

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20. Lawley, A., in Intermetallic Compounds ed. J. H. West- brook. John Wiley, New York, 1967, p. 413.

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