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Vacancies in Ee-Al alloys
Journal of Nuclear Materials 69 & 70 (1978) 628-632 o North-Holland Publishing Company
VACANCIES IN Fe-AI ALLOYS D. PARIS and P. LESBATS Dipart. de Mhallurgie, Ecole des Mines, Saint-Etienne, France
1. Introduction
2. Dilatometry
Iron-aluminium alloys present a B2 structure over a wide range of composition, from 23 to 52 at.% Al. These alloys have peculiar properties, mainly the ability to retain large quantities of vacancies after quenching. This behaviour has already been shown for 40 at.% Al alloys [l-4] and has been verified for higher aluminium contents, up to the limit of the B2 phase field.
Dilatometry allows the determination vacancy concentration CIJ = 3(Al/l-
of the total
Aala),
where I and a are respectively the length of the sample and the lattice parameter. When an iron-aluminium sample is annealed at a temperature close to 400°C after a high temperature quench, a contraction of the sample is observed, the
102xC
103.AL/L + 51 at% AL l 49.5 at% AL I
46 at % AL
,
1
I4
Z.’
700
800
900
1000
T OC h WI0
1,
L
Fig. 1. Vacancy concentration in an Fe-5 1 at.% Al alloy measured by: (0) the contraction during an anneal at 425°C for 24 h after quenching from the indicated temperature; (+) (Al/l&/a) measured at the indicated temperature.
700
T°C 800
900
1000
Fig. 2. AI/Zversus the quenching temperature ferent Al concentrations. 628
-4 1100
for alloys of dif-
D. Paris, P. Lesbats / Vacancies in Fe-Al
629
alloys
Table 1 Occupation of sub-lattices Al sub-lattice Fe sub-lattice _____ ____ --- -_I--_._d-x Vacancies x
+ 1000 OC 900% e 800°C
l
Al atoms
M--X +-VA
(0.5 + 6)(1000 - d) -m+x-yA
Fe atoms
(0.5%S)(lOOO-4-U
tl
Fe Al For Fe-Al
alloys only iron atoms are imaged in the so the vacant sites imaged on the Fe sublattice can be either quenched-in vacancies, fieldinduced vacancies, or Al antistructure atoms. The number of meld-induced vacancies is deduced by comparison with a sample annealed at 425’C for 24 h. The distribution between the quenched-in vacancies and the Al antistructure atoms is determined by the following method. Let y and u be the number of Al and Fe antistructure atoms in the quenched Specimen, and YA and UA the same quantities after the anneal. The occupation of the sub-lattices by vacancies, Fe and Al atoms for a total number of 1000 sites is then given in table 1. d and M represent the results of dilatometry and field ion microscopy; 6 is the degree of non sto~chiomet~ (0.5 t 6) being the total aluminium concentration of the alloy. As both sub-lattices have the same number of sites microscope;
I
30
C/
A-
35
; at % Atzt_ LO
45
Fig. 3. Al/l versus the Al concentrations temperatures.
50
55
for different quenching
magnitude of which depends on the quenching temperature; the vacancy concentration at the quenching temperature is three times this contraction (A//Z), since an anneal at 4OO’C keeps the lattice parameter constant. This method gives nearly the same results as the measurement of the dilatation obtained on increasing the temperature, corrected for the variation of the lattice parameter. Fig. 1 shows a maximum in the vacancy concentration for a temperature close to 1000°C. The temperature corresponding to this maximum does not change signi~cantly with the ~um~iurn content (fig. 2). It must be emphasized that the contraction during the anneal at 425’C increases monotonically with the aluminium concentration up to the limit of the B2 phase field (fig. 3).
3. Field ion microscopy Field ion microscopy gives information about the distribution of vacancies among both sublattices [S].
n=??r -&+yA
-6(1000-d).
The iron-aluminium alloy is an alloy which does not remain disordered after quenching, even at very high cooling rates [L-9]. Then it is assumed that the annealed samples have the maximum theoretical order and the quenched samples the maximum order consistent with the above experimental observations. Then YA-UA=IOOOS. A degree of order is defined by SNs=n Aol - flA@ + nBp - nBa2
where Ns is the number of sites, nA& the atoms on the cr sub-lattice, nAp, nnp and equivalent meanings (a and (3correspond to the iron and aluminium sub-lattice, A
number of A nn@ having respectively and B to Fe
& Paris, P. Lesbars / Yacancies in Fe-Al alloys
630
Table 2 Vacancies and ate-~ructore atoms --~~~~-~-~~_~__~~~__~ At.% Al 45 49.5 -~-“.-_..~__.~ VaG+ncy concentration on Fe sublattice in %O 5.5 12 Vacancy concentration lattice in %O
51
15.5
on Al sub4.5
6.5
Difference of the number of Fe atoms on Al subdattice between a sample quenched from 1000°C and an anneated sample in %O 0 2.5 --.--.l.--_-_~.~__
does not take inta account the lattice relaxation around a
7
4.5
and Al atoms), ‘The condition for this parameter to be a maximum leads to
and for a fi site
The ~s~~~bution of vacancies and antist~~Gture atoms among both sub-lattices is given in table 2.
In an alloy various types of vacancy sites mist, according to the sub-lattice on which they occur and the types of neighbouring atoms. To explain our experimental results, we tried to evaluate, by means of a simple model, the concentration af these different vacancy types. Let pAa denote the probability for an cwsite to be occupied by an A atom, and $?A@, any!, psp the equivalent quantities. Then
if the different types of vacancies with ah the possibfe con~guratians of nei~bouring atoms are taken into account, the probability for an cysite to be occupied by a vacancy is
= f(l --S) PBcu.
and for a 0 site
f (f - Cv)S - i-&y,
p~~==(l+s)t(1-cv)s-c~p, where Cv = ~~~~~ Cv, = w&k C-V@= ~v~~~, and nvs demote the total number of vacancies, and the number of vacancies on the cuand 0 sublattices, respectively. The modified vacancy energy model proposed by Cheng et al. [9] enables one to calculate the number of vacancies on both sub-lattices. However, this model.
nv, rtVa and
D, Paris, P. Lesbats / Vacancies in Fe-Al alloys
460
600
600
1000
1200
631
1%
Fig. 4. Vacancy concentration calculated for different aluminium atomic concentrations with EAV = 7850 and ebV = 5800.
101 .C 101 .C
LOO
600
600
1000
12w
Fig. 5. Fe-49.5 at.% Al alloy: total vacancy concentration distribution on both sub-lattices.
1-c
and
600
600
low
1200
TV
Fig. 6. Fe-49.5 at.% Al alloy: vacancy concentration on sublattices and distribution according to the type of vacancy. The figure indicates the number of aluminium atom nearest-neighbours of the vacancy (a) iron sub-lattice; (b) aluminium sublattice.
632
D. Paris, P. Lesbats / Vacancies in Fe-Al
and egg = 12 000 cal/g.atom are those corresponding to pure iron and pure aluminium; the energy em = 18 750 cal/g.atom is evaluated from order-disorder measurements in iron-aluminium alloys [8] using the Bragg-Williams law. The values of eAv an euv are adjusted such that-the vacancy concentrations calculated by the above equations and the Bragg-Williams law give the best fit with the experimental data (figs. 4-6). This simple model enables one to determine the overall behaviour of the variation of the vacancy concentration as a function of temperature and aluminium content, and is consistent with the fact that a large majority of the vacancies occupy the iron rather than the aluminium sub-lattice. It must be noted that the most probable vacancy at low temperatures is a vacancy on the iron sub-lattice with eight Al atoms as nearest neighbours, but that the probability to find such an environment decreases when the temperature increases. This leads to an evolution in
alloys
the distribution of the different types of vacancies, which explains the peculiar shape of the curve of vacancy concentration versus temperature in these alloys.
References [l] [2] [3] [4] [5] [6] [7] [8] [9] [lo]
J. Rieu and C. Goux, Mem. Sci. Rev. Met. 15 (1967) 1045. J. Rieu, Thesis, Paris (1968). J.P. Riviere and J. Grilhe, Acta Met. 20 (1972) 1275. N. Junqua, J.C. Desoyer and P. Moine, Phys. Status Solidi (a) 18 (1973) 387. D. Paris, P. Lesbats and J. Levy, Ser. Met. 9 (1975) 1373. J.B. Guillot, J. Levy and C. Goux, C.R. Acad. Sci. 273 (1971) 214. A. Taylor and R.M. Jones, J. Phys. Chem. Solids 6 (1958) 16. A. Silvent and G. Sainfort, Grenoble (France) Rapport CEA OM/1577/JL (1966). C.Y. Cheng, P.P. Wynblatt and J.E. Darn, Acta Met. 15 (1967) 1045. C. Kinoshita and T. Eguchi, Acta Met. 20 (1972) 45.
VACANCIES IN Fe-AI ALLOYS D. PARIS and P. LESBATS Dipart. de Mhallurgie, Ecole des Mines, Saint-Etienne, France
1. Introduction
2. Dilatometry
Iron-aluminium alloys present a B2 structure over a wide range of composition, from 23 to 52 at.% Al. These alloys have peculiar properties, mainly the ability to retain large quantities of vacancies after quenching. This behaviour has already been shown for 40 at.% Al alloys [l-4] and has been verified for higher aluminium contents, up to the limit of the B2 phase field.
Dilatometry allows the determination vacancy concentration CIJ = 3(Al/l-
of the total
Aala),
where I and a are respectively the length of the sample and the lattice parameter. When an iron-aluminium sample is annealed at a temperature close to 400°C after a high temperature quench, a contraction of the sample is observed, the
102xC
103.AL/L + 51 at% AL l 49.5 at% AL I
46 at % AL
,
1
I4
Z.’
700
800
900
1000
T OC h WI0
1,
L
Fig. 1. Vacancy concentration in an Fe-5 1 at.% Al alloy measured by: (0) the contraction during an anneal at 425°C for 24 h after quenching from the indicated temperature; (+) (Al/l&/a) measured at the indicated temperature.
700
T°C 800
900
1000
Fig. 2. AI/Zversus the quenching temperature ferent Al concentrations. 628
-4 1100
for alloys of dif-
D. Paris, P. Lesbats / Vacancies in Fe-Al
629
alloys
Table 1 Occupation of sub-lattices Al sub-lattice Fe sub-lattice _____ ____ --- -_I--_._d-x Vacancies x
+ 1000 OC 900% e 800°C
l
Al atoms
M--X +-VA
(0.5 + 6)(1000 - d) -m+x-yA
Fe atoms
(0.5%S)(lOOO-4-U
tl
Fe Al For Fe-Al
alloys only iron atoms are imaged in the so the vacant sites imaged on the Fe sublattice can be either quenched-in vacancies, fieldinduced vacancies, or Al antistructure atoms. The number of meld-induced vacancies is deduced by comparison with a sample annealed at 425’C for 24 h. The distribution between the quenched-in vacancies and the Al antistructure atoms is determined by the following method. Let y and u be the number of Al and Fe antistructure atoms in the quenched Specimen, and YA and UA the same quantities after the anneal. The occupation of the sub-lattices by vacancies, Fe and Al atoms for a total number of 1000 sites is then given in table 1. d and M represent the results of dilatometry and field ion microscopy; 6 is the degree of non sto~chiomet~ (0.5 t 6) being the total aluminium concentration of the alloy. As both sub-lattices have the same number of sites microscope;
I
30
C/
A-
35
; at % Atzt_ LO
45
Fig. 3. Al/l versus the Al concentrations temperatures.
50
55
for different quenching
magnitude of which depends on the quenching temperature; the vacancy concentration at the quenching temperature is three times this contraction (A//Z), since an anneal at 4OO’C keeps the lattice parameter constant. This method gives nearly the same results as the measurement of the dilatation obtained on increasing the temperature, corrected for the variation of the lattice parameter. Fig. 1 shows a maximum in the vacancy concentration for a temperature close to 1000°C. The temperature corresponding to this maximum does not change signi~cantly with the ~um~iurn content (fig. 2). It must be emphasized that the contraction during the anneal at 425’C increases monotonically with the aluminium concentration up to the limit of the B2 phase field (fig. 3).
3. Field ion microscopy Field ion microscopy gives information about the distribution of vacancies among both sublattices [S].
n=??r -&+yA
-6(1000-d).
The iron-aluminium alloy is an alloy which does not remain disordered after quenching, even at very high cooling rates [L-9]. Then it is assumed that the annealed samples have the maximum theoretical order and the quenched samples the maximum order consistent with the above experimental observations. Then YA-UA=IOOOS. A degree of order is defined by SNs=n Aol - flA@ + nBp - nBa2
where Ns is the number of sites, nA& the atoms on the cr sub-lattice, nAp, nnp and equivalent meanings (a and (3correspond to the iron and aluminium sub-lattice, A
number of A nn@ having respectively and B to Fe
& Paris, P. Lesbars / Yacancies in Fe-Al alloys
630
Table 2 Vacancies and ate-~ructore atoms --~~~~-~-~~_~__~~~__~ At.% Al 45 49.5 -~-“.-_..~__.~ VaG+ncy concentration on Fe sublattice in %O 5.5 12 Vacancy concentration lattice in %O
51
15.5
on Al sub4.5
6.5
Difference of the number of Fe atoms on Al subdattice between a sample quenched from 1000°C and an anneated sample in %O 0 2.5 --.--.l.--_-_~.~__
does not take inta account the lattice relaxation around a
7
4.5
and Al atoms), ‘The condition for this parameter to be a maximum leads to
and for a fi site
The ~s~~~bution of vacancies and antist~~Gture atoms among both sub-lattices is given in table 2.
In an alloy various types of vacancy sites mist, according to the sub-lattice on which they occur and the types of neighbouring atoms. To explain our experimental results, we tried to evaluate, by means of a simple model, the concentration af these different vacancy types. Let pAa denote the probability for an cwsite to be occupied by an A atom, and $?A@, any!, psp the equivalent quantities. Then
if the different types of vacancies with ah the possibfe con~guratians of nei~bouring atoms are taken into account, the probability for an cysite to be occupied by a vacancy is
= f(l --S) PBcu.
and for a 0 site
f (f - Cv)S - i-&y,
p~~==(l+s)t(1-cv)s-c~p, where Cv = ~~~~~ Cv, = w&k C-V@= ~v~~~, and nvs demote the total number of vacancies, and the number of vacancies on the cuand 0 sublattices, respectively. The modified vacancy energy model proposed by Cheng et al. [9] enables one to calculate the number of vacancies on both sub-lattices. However, this model.
nv, rtVa and
D, Paris, P. Lesbats / Vacancies in Fe-Al alloys
460
600
600
1000
1200
631
1%
Fig. 4. Vacancy concentration calculated for different aluminium atomic concentrations with EAV = 7850 and ebV = 5800.
101 .C 101 .C
LOO
600
600
1000
12w
Fig. 5. Fe-49.5 at.% Al alloy: total vacancy concentration distribution on both sub-lattices.
1-c
and
600
600
low
1200
TV
Fig. 6. Fe-49.5 at.% Al alloy: vacancy concentration on sublattices and distribution according to the type of vacancy. The figure indicates the number of aluminium atom nearest-neighbours of the vacancy (a) iron sub-lattice; (b) aluminium sublattice.
632
D. Paris, P. Lesbats / Vacancies in Fe-Al
and egg = 12 000 cal/g.atom are those corresponding to pure iron and pure aluminium; the energy em = 18 750 cal/g.atom is evaluated from order-disorder measurements in iron-aluminium alloys [8] using the Bragg-Williams law. The values of eAv an euv are adjusted such that-the vacancy concentrations calculated by the above equations and the Bragg-Williams law give the best fit with the experimental data (figs. 4-6). This simple model enables one to determine the overall behaviour of the variation of the vacancy concentration as a function of temperature and aluminium content, and is consistent with the fact that a large majority of the vacancies occupy the iron rather than the aluminium sub-lattice. It must be noted that the most probable vacancy at low temperatures is a vacancy on the iron sub-lattice with eight Al atoms as nearest neighbours, but that the probability to find such an environment decreases when the temperature increases. This leads to an evolution in
alloys
the distribution of the different types of vacancies, which explains the peculiar shape of the curve of vacancy concentration versus temperature in these alloys.
References [l] [2] [3] [4] [5] [6] [7] [8] [9] [lo]
J. Rieu and C. Goux, Mem. Sci. Rev. Met. 15 (1967) 1045. J. Rieu, Thesis, Paris (1968). J.P. Riviere and J. Grilhe, Acta Met. 20 (1972) 1275. N. Junqua, J.C. Desoyer and P. Moine, Phys. Status Solidi (a) 18 (1973) 387. D. Paris, P. Lesbats and J. Levy, Ser. Met. 9 (1975) 1373. J.B. Guillot, J. Levy and C. Goux, C.R. Acad. Sci. 273 (1971) 214. A. Taylor and R.M. Jones, J. Phys. Chem. Solids 6 (1958) 16. A. Silvent and G. Sainfort, Grenoble (France) Rapport CEA OM/1577/JL (1966). C.Y. Cheng, P.P. Wynblatt and J.E. Darn, Acta Met. 15 (1967) 1045. C. Kinoshita and T. Eguchi, Acta Met. 20 (1972) 45.