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Theoretical and positron annihilation study of point defects in intermetallic compound Ni3Al
Acta metall, mater, Vol. 42, No. 1, pp. 195-200, 1994 Printed in Great Britain. All rights reserved
0956-7151/94 $6.00 + 0.00 Copyright © 1993 Pergamon Press Ltd
THEORETICAL A N D POSITRON ANNIHILATION STUDY OF POINT DEFECTS IN INTERMETALLIC C O M P O U N D Ni3A1 JIAN SUN and DONGLIANG LIN (T. L. LIN) Department of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200030, P. R. China (Received 16 September 1992; in revised form 4 May 1993)
Abstract--The equilibrium equation of point defects in L12 types of intermetallic compounds was established in a new simple method, which is independent of the chemical potentials. The formation energies of the relevant point defects in Ni3AI were calculated by EAM potentials and statical relaxations. The concentration of point defects at 1000 K as a function of bulk composition and the effect of temperature on them were studied for Ni3A1 alloy. The results show that the Al-antisites are the constitutional defects in hypostoichiometric Ni3A1, and the Ni-antisite defects in hyperstoichiometric Ni 3A1. The two types of vacancies belong to thermal defects. The positron annihilation technique was also conducted to measure the concentration of vacancies in Ni3A1 alloys with and without boron. Although vacancies interact with the boron dopant, the changes of vacancy concentration in Ni3A1 alloys can not be considered as the main reason in explaining the effect of stoichiometry on the segregation of boron. The effect of stoichiometry on diffusion in Ni3AI alloys was discussed additionally,
1. INTRODUCTION The intermetallic compound Ni3A1 has the LI~ ordered crystal structure. The long range ordering is responsible for its unusual high temperature mechanical properties [1, 2]. This compound has the composition range of 72.5-77 at.% Ni at room temperature, The point defects being of thermodynamic equilibrium properties, such as antisite defects, vacancies and interstitials can be introduced by thermal motion of atoms in materials. On the other hand, if the component is deviated from the stoichiometric composition, the excess atoms can also form these point defects, referred to as constitutional or stoichiometric defects. The concentration of point defects in crystals is different due to their different formation energies, and can be influenced by the temperature and the composition of Ni3Al. The properties of point defects, particularly vacancies and antisite defects, play an important role in diffusion in the bulk material, solid solution hardening effect, ordering and disordering behaviours in intermetallic compounds, Aoki and Izumi [3] first discovered that microalloying with boron suppresses intergranular fracture and improve the ductility of Ni3A1, which generated considerable interest in both grain boundary phenomena and the lattice defect in Ni3A1. The results studied by Liu et al. [4] showed that the level of boron at the grain boundaries decreases with increasing bulk aluminium above 24 at.%, with an increase of aluminium from 24 to 25.2 at.% results in a reduction of boron segregation by 45%. Since the grain boundary properties in Ni3AI are sensitive to
the boron level, the boundary remains brittle when the amount of boron segregation is insufficient. Therefore, it is very important to clarify the role of the deviation from stoichiometry in the transport of boron to the grain boundaries. Mass transport usually occurs by atomic migration via point defects, The positron annihilation study of vacancies in Ni 3A! by Dasgupta et al. [5] suggested that there exists small concentration of constitutional Ni vacancies essentially independent of composition in the stoichiometric or hyperstoichiometric alloys. The constitutional vacancies combined with the boron dopant may limit the long range transport of boron to grain boundaries. According to Dasgupta, the reason why boron segregates to grain boundaries more strongly in hypostoichiometric Ni3A1 than in either stoichiometric or hyperstoichiometric Ni3A1 can be explained. Theoretical calculation of point defects in Ni3 A1 alloys was also conducted by Foiles and Daw [6]. They calculated the formation energies and the thermal concentration of vacancies and antisites vs bulk composition. In their model, the effective formation energies of defects consist of internal energy and chemical potentials, and the latter is a function of temperature and composition of alloy calculated by Monte Carlo simulation at 1000 K. They gave the equations of the concentration of defects related to temperature and chemical potentials, but they did not calculate the detailed curves of concentration of defects vs temperature further. Therefore, the properties of constitutional defects resulting from the deviation from stoichiometry in Ni3AI is not clarified theoretically because the defects could not be identified as the constitutional defects only from the 195
196
JIAN SUN and DONGLIANG LIN (T. L. LIN): POINT DEFECTS IN Ni3A1
criteria that their formation energies are much lower than others, In the current paper, we report an extensive study on point defects in Ni3A1 alloys. The formation energies of point defects in Ni3AI, such as antisite defects, vacancies and interstitials were first calculated by embedded atom method potentials and statical relaxations. Then, the equilibrium equation of point defects in LI2 type of intermetallic compounds was established by a new simple method. The relationship of the concentration of antisites and vacancies vs bulk composition and the effect of temperature on defects were studied for Ni3A1 alloys, The concentration of vacancies in Ni3AI alloys with various AI and boron contents was also investigated by means of positron annihilation. The main purpose of this paper is to understand the effect of stoichiometry on the diffusion, in particular on the segregation of boron in Ni3A1. 2. THEORETICAL CALCULATIONS 2. I. Formation energies o f defects Computer atomistic simulation has been used to study the properties of point defects. The application of the embedded atom method potentials to the description of Ni-AI system was first presented by Foiles et al. [6]. In this calculation, the embedded atom potentials reported by Chen et al. [7] is used to calculate the formation energies of antisite defects, vacancies and interstitials with the energy gradient method. A cubic cell containing 1728 atoms with periodic boundary condition and constant pressure is
adopted. The details of the calculations are described elsewhere [8]. The calculated results listed in Table 1 show that the formation energies of vacancies and antisites are very similar to those calculated by Foiles et al. and energies of interstitials similar to those conducted by Caro et al. [9]. The formation energy of A1 vacancy is somewhat higher than Ni vacancy, and the energies of the two antisites are comparable. The formation energies of interstitials are much higher than those of vacancies and antisites, so the concentration of interstitials in Ni3AI is negligible in the later calculations. 2.2. The equilibrium equation
The equilibrium concentration of point defects can be determined in an ensemble with fixed temperature
and chemical potentials. Because the calculation of chemical potentials is very sophisticated, the chemical potentials will be replaced by the bulk composition of Ni3A1 in the present calculations. For A3B cornpounds, there are three A sites for each B site, all penetrating each other. Each lattice site will be occupied either by an atom appropriate to the sublattice, by a vacancy, or by an atom of the opposite type (an antisite defect). Assume this system in which the concentration (atomic percent) of A sublattice sites occupied by A atoms is X'AA, the concentration of B sublattice sites occupied by B atoms is XBB, the concentration of vacancies on the A sublattice sites and B sublattice sites is X v and X v, the concentration of A sublattice sites occupied by B atoms (A antisite defects) is XAB, and the concentration of B sublattice sites occupied by A atoms (B antisite defects) is XBA respectively. The concentration of atoms X^ will vary within the composition range for A3B compound, but crystal structure of the cornpound still keep unchanged. Therefore, there exist two structural constrained conditions among the concentrations of various point defects (XAA"~ XBA)/(XAA + XBA + )[BB ql_ J(AB) = XA (1) (XA~ + X ~ + XAB)I(X~B + X v + XBA)= 3.
Combine equation (1) with (2) to obtain equation (3) XAB+ (1 -- XA)XVA -- XB^ -- XA X v + XA -- ~3 = 0. (3) Thus, the concentration of various point defects and bulk composition of the compound have been linked in equation (3). For noninteracting defects, the energy of the system is E = E0 + X ' vA E vA + X avE vB + XABEAB + J(BAEBA (4) where E0 = (X'AA "~ X'Aa "3!"XV)EA + (X'BB "JI-J(BA "~ XV)EB, E 0 is the energy of the ideal lattice, E v and E v are the formation energies of vacancies on the A and B sublattice, and E m and EBA the formation energies of A antisite defects and B antisite defects respectively, which are shown in Table 1. The configuration entropy of the system is suggested by Foiles et al. 3 ? ( 4 ) ( 4 S =~ ~ XAB + f
Table 1. Formation energy of the relevant point defects in Ni3AI
Type of defect
AEf(eV)
AI vacancy
1.92
Ni vacancy
1.47
Ni antisite (Ni sublattiee occupied by AI atom)
0.56
(AI sublattice occupied by Ni atom) AI octahedral Ni octahedra!
0.59 4.53 3.78
AI antisite
(2)
v)] ~ XA +
1
~[f(4XBA)+f(4XV)]
(5)
where f ( x ) is the ideal entropy function f ( x ) = - - K [ x In(x) + (1 -- x)ln(l -- x)].
(6)
Only consider the vibration entropy introduced by tWO vacancies S v=
v v X vc v XA S f_ A --{- B~J f_B.
(7)
JIAN SUN and DONGLIANG LIN (T. L. LIN): POINT DEFECTS IN Ni3A1 The change of free energy of the system is
100 _ Ni-antisite
AF = AE - T(S + SV).
(8)
~
Al-antisite
22
_
t0 -3
197
Among four unknown concentration, XV, X v, XAB and XBA, only three are independent owing to the structural constrained condition equation (3). In the present calculation, X v, X v, and XAB or X v, X v, and XBAare chosen as the independent variables. The equilibrium state of the system at a given temperature and bulk composition corresponds to a minimum of the free energy
'--~ ~',~ 10-6 " ~, ~ 10-9 7
OAF
OAF
OAF
63j(----~n= 0,
O - ~ = 0,
0X.AB= 0
Ni content (at.%) Fig. 1. The calculated concentration of four types point defects at 1000K as a function of bulk composition.
f
OAF
\
~ k o r - - = 0). (9) 0~xI"BA The concentrations of defects can be expressed by XV=
~
A
(
+ ( X A - I)EBA)/KT] 4XBA ~xA XV = 1.,~A 1 exp [ ( - E v + XAEBA)/KT]
4XBA /
4"¥BA ) - ' exp [(--EAa- EeA)/KT ] X^e = ~ ( 1 --4-XBA 3 XA)XVA -- X A X V -{- XA -
~
(10)
when XA/> 3/4 XV=3A( 4XAB " ] ~ - X A 3------~Aa ,] exp [(--E v + ( 1 - XA)EAB)/KT ] 4XAB "~-xA XV = 14A exp [ ( - E av -J(AEAB)/KT] 3 -- 4XAB/] XeA =
3--4XAB
~S
J
VA1 10_12
72
I
I
[
I
I
1
73
74
75
76
77
78
2.3. Calculatedresults
4Xah ~ xA' I-4XBA] exp[(-EV
XBA-~-XAB"1-(1 -
VNi
exp[(--EAB--EBA)/KT] 3
XAB =,e~BA"F- (J(A - l)XV +.¥AXV-- JI"A+ ~
(11)
when XA < 3/4 where A = exp [(S~_A)/K ] = exp [(sVB)/K]. Taking the value A to be 4.5, the same as that in pure nickel [10]. The equations of defects described above are independent of chemical potentials and only have a connection with the internal energies of defects and the bulk composition of Ni3A1. Therefore, it is convenient to calculate the concentration of defects accurately at definite temperature and bulk composition. Because the equations are not the explicit functions, they can he solved by iterated method using computer. Equations (9) and (10) show that for ordered alloys, the effective vacancy energies depend on the overall composition of the alloy, but the formation energy of antisite defects does not. It is worth pointing out that the equations described above are suitable for the calculation of point defects in other A 3B type compounds,
The concentration of four types of point defects at 1000 K as a function of bulk composition has been calculated as shown in Fig. 1. It is shown that the concentration of Ni antisites are much higher than that of the other three defects in hyperstoichiometric Ni3AI, and the concentration of vacancies is also higher on Ni sublattice than on the A1 sublattice in this alloy. The concentration of four types of defects changes significantly near the stoichiometric composition. In hypostoichiometric Ni3A1, the concentration of A1 antisites is the highest one, which is the sameastheNiantisitesinhyperstoichiometricNi3A1 and less vacancies are found. The concentration of two antisites is the lowest in stoichiometric Ni3A1. However, the total concentration of two vacancies reaches the lowest in hypostoichiometric Ni3A1 with 75.9 at.% Ni content, and increases with A1 content from 24.1 to 28 at.%. The concentration of vacancies on A1 sublattice is somewhat higher than on Ni sublattice when Ni content is more than 75.9 at.%, which is reversed from the results calculated by Foiles et al. The above results may be reasonable because four types of defects have a connection with each other, which is indicated in equations (9) and (10). The effective formation energy on AI sublattice is lower than in Ni sublattice and decreases with the increase of Ni content in these alloys. In order to study the properties of the constitutional defects in Ni3A1 alloys, the relationship of the concentration of defects and temperature were calculated respectively for Ni3A1 alloys with three different bulk compositions (Ni76A124, Ni7sA125 and Ni74AI26). The calculated results are shown in Fig. 2(a-c). It can be seen in Fig. 2(a) that except AI antisites, the concentration of two types of vacancies and Ni antisites increase markedly when the temperature increases in NivrA124alloy. As is well known, the thermal concentration of defects is susceptible to temperature and increases with the increasing ternperature. In particular, at absolute zero, the concentration of thermal defects tends to zero. However, the concentration of constitutional defects reaches the
198
JIAN SUN and DONGLIANG LIN (T. L. LIN): POINT DEFECTS IN Ni3AI
highest at absolute zero, whose character can be considered the criterion to define the constitutional defects. Unlike the other three defects, the con-
Table 2. The composition of alloys AlloyNo. Composition l Ni-24at.% AI 2 3 4
10 °
Al-antisite
5
Ni-25 at.% AI Ni-26 at.% AI Ni-24 at.% AI + 700 ppmB
Ni-25 at.% AI + 700 ppmB
lO-O
N
i
-
a
n
t
i
~
6
Ni-26 at.% AI + 700 ppmB
' lO-iZ -~ ~
o o~
10 -18 10-z4
~
V^l
10_no " a , , , , , I , , , I , , , I , 400 600 800 1000 Temperature(K)
10 ° 10-6 . Vrti
~--
/
0 10-1z :~
centration of AI antisites decreases very slightly with increasing temperature. In order to maintain the stability of the LI2, structure of this alloy, the excess Ni atoms will occupy the AI sublattices, which forms AI antisites. Therefore, the A1 antisite defects are of the character of the constitutional defects resulted from the deviation from stoichiometry, but other three defects are the thermal defects introduced by the thermal motion of atoms in Ni76AI24 alloy. It can be deduced that the Ni antisites are the constitutional defects, but two types of vacancies and AI antisites are the thermal defects in Ni74A12~alloy as shown in Fig. 2(c). Four types of defects belong to thermal defects in stoichiometric Ni3AI as shown in Fig. 2(b). The calculated results show that the vacancies in Ni3A1 are simply thermal defects, not the constitutional defects.
L
-~ 10_18 t9 o
3. POSITRON ANNIHILATION STUDIES
3.1. Experimental procedure
o 1 10 -3o
b ,
J
,
,
,
I
,
,
,
,
,
400 600 800 Temperature(K)
10 ° 10
-6
Al-antisite ~ ~
~
~
10 -tz ///V m I 1
V~ -''~
/
~ 10-1a o~
, 1 i 1000
Ni-ant.isite
.o ~
,
~
0 -24
10-a°
~/ C
400
600
800
The alloys used in this study prepared by directional solidification with various aluminium and boron contents. All of them annealed at 1423 K for 50h followed by slow furnace cooling to room temperature. Their compositions are given in Table 2. Rectangular plate samples of 10 x 10 x I mm were cut off normal to the growth direction of [001], then machined and polished. All samples had very large single phase grains, approximately several mm in size, which rendered the grain boundary contribution negligible to the positron annihilation. The positron lifetime was measured by the conventional fast-fast coincidence type. The system resolution function was approximated by a guassian having a F W H M of 245 ps. A 22Na source of about 15 /tci contained in an envelope made from a thin nickel f°il was sandwiched in between two samples. More than 105 counts were accumulated in the lifetime measuring for each samples. The lifetime data for each sample were analysed using a POSITRONFIT computer program. These analyses were conducted using three-term fit without restrictions.
1000
Temperature(K)
Fig. 2. The calculated concentration of four types of point defects vs temperature,
3.2. Experimental results The lifetime spectrum for each example was represented with three lifetime components, attributable
JIAN SUN and DONGLIANG LIN (T. L. LIN): POINT DEFECTS IN Ni3AI to the bulk (Bloch state), the vacancy trapped state and the positron source respectively. The bulk lifetime of all six Ni3AI samples is very close to 116 ps found by Wang et al. [11]. The trapped state lifetime of samples is 230 ps or more in the present work, which is higher than 180 ps measured by Wang et al. The intensity of source term of all samples is very small (approx. 1%). According to the trapping model, the trapping rate for Ni3A1 alloy was calculated as a function of alloy composition shown in Fig. 3. In the positron trapping model, the trapping rate can be assumed to be K = Cv#v (12) where Cv is the concentration of vacancy, and #v is the trapping factor. Figure 3 shows that the trapping rate or concentration of two types of vacancies in Ni3A1 doped with or without boron increases with the increase of A1 content from 24 to 26at.%. The trapping rates in Ni 3A1 decrease when it is doped with boron. Because positrons are insensitive to the presence of antisite defects, the concentration of antisite defects in Ni3A1 can not be determined, 4. DISCUSSIONS The experimental results show that the positron trapping are found not only in stoichiometric and hyperstoichiometric alloys, but also in hypostoichiometric alloys with and without boron. The intensity of vacancy trapped state lifetime in pure Ni3A1 alloys in this work is higher than that in Dasgupta's. The reason is probably that the specimens were not annealed sufficiently or the cooling rate of specimens was not slow enough so that the non-equilibrium concentration of vacancies at high temperature remained at room temperature. This reason can also be used to explain why the trapped state lifetime is longer than 180 ps determined by Wang et al. [] 1] in quenched specimen of Ni3Al, which suggests that the defects may act as small vacancy clusters produced in the cooling process or vacancy boron complexes in 6• 5 i
-
Ni3AI
o Ni3AI with boron
4 -
~ •"
-
' e
~
,
* ~ 0
3 .=. e~
2
--
~
] 0
[
24
I
25
[
26
AI content (at.%) Fig. 3. The trapping rate in Ni]A1 vs A1 content,
199
the case of the alloys doped with boron. Foiles et al. found that the interaction between vacancies is weakly repulsive with the binding energies of 0.16 eV for Ni-Ni vacancy pairs and 0.18 eV for Ni-AI vacancy pairs [6]. The intensity of trapped state lifetime in boron-doped Ni 3A1 is lower than in pure Ni3A1 alloys, which suggests that a part of the vacancies are filled with boron atoms or atom clusters, and the effective concentration of vacancies is reduced. A similar result was obtained by Yang et al. [12].The capture of the vacancies by dopant to reduce the positron trapping rate was also found in iron alloy doped with carbon [13]. Positron annihilation measurements performed on Ni3A1 with various AI and boron contents by Dasgupta et al. [5] show that positron trapping was found in the stoichiometric and hyperstoichiometric Ni3A1, but no positron trapping in pure hypostoichiometric Ni3A1. The estimated vacancy concentration in pure stoichiometric and hyperstoichiometric Ni 3AI would be 2 × 10 6. Since the limitation of sensitivity of such measurements is approximately 10 7 at best for deterruination of vacancy concentration [14], the lower concentration of vacancies near or beyond the limitation can not be excluded. The results in both Dasgupta's and the present work show that the concentration of vacancies increases as the increase of A1 content in Ni3A1. However, it could not be deduced that constitutional vacancies are present in stoichiometric and hyperstoichiometric Ni3A1 alloys, but not in hypostoichiometric Ni 3A1. The calculated results apparently show that the constitutional A1 antisites exist in hypostoichiometric Ni3A1 and constitutional Ni antisites in hyperstoichiometric Ni 3A1, but not any types of constitutional vacancies in non-stoichiometric Ni3A1. The calculated equilibrium concentration of vacancies is much lower than that determined by positron annihilation at room ternperature because the calculation was conducted under the thermal equilibrium condition in which sufficiently long anneal time is needed and the defects are well separated. It also indicates that it is not easy to reach the real equilibrium state for intermetallic compounds because of difficult diffusion of atoms in compounds. On the other hand, the concentration of vacancies within overall composition of Ni3AI is significantly lower than the doped-boron concentration considered here. Although vacancies interact with the boron dopant, which may limit the long range transport of boron to grain boundary, the difference of concentration of vacancies in Ni3AI alloys with various A1 content could not be considered as the main reason in explaining the effect of stoichiometry on the segregation of boron. Computer atomistic simulation results studied by Chen et al. [15] showed that boron segregates preferentially to the grain boundary, especially to the Ni-rich grain boundary, instead of the surface and interstitial site. Furthermore, in Ni-rich grain boundary together with boron makes the grain
200
JIAN SUN and DONGLIANG LIN (T. L. LIN): POINT DEFECTS IN Ni3AI
boundary stronger than the bulk. Therefore, the segregation of boron on grain boundary mainly controlled by grain boundary structure and chemistry, not by the types and distributions of point defects in NiaA1 alloys, In addition to the current interest in point defects, diffusion in ordered alloys is also of interest to study [16-18]. The measurements of tracer diffusion in Ni3AI alloys performed by Hoshino et al. [17] indicated that the effect of stoichiometry on boron segregation is not connected with the behaviour of lattice vacancies, since the diffusion behaviour of Ni is all the same on both sides of stoichiometry. If the antisite defects can be considered as a factor influencing the diffusion in ordered alloys, the calculated results may explain the reason why the diffusivity of Ni in Ni3AI shows a minimum at the stoichiometry composition below 1000 K and this trend becomes clearer with decreasing temperature. In intermetallic compounds, random vacancy jumps would disrupt the ordered arrangement of atoms on lattices. The diffusion via the Ni sublattice vacancy mechanism in the L 12 structure crystals has been established. The Ni atoms may not jump onto 4 AI sublattice sites of their 12 nearest neighbor sites, which leads to a decrease of the correlation factor from 0.7815 to 0.727. The value of 0.689 of the correlation factor for LI2 structure was further calculated by Koiwa and Ishioka [19]. Thus, if the high concentration of antisites (which corresponds to the lower long range order parameter) is introduced in crystals, the correlation factor for Ni diffusion will increase to the value between 0.7815 and 0.689. The further discussion of the detailed mechanism on the effect of antisites on the correlation factor is beyond the scope of this paper. Since constitutional antisite defects exist on both sides of stoichiometry, the diffusivity will increase with the higher concentration of antisite defects in non-stoichiometry Ni3A1. When the temperature increases, the concentration of antisite defects in stoichiometry Ni3A1 increases markedly, and is closer to a level in non-stoichiometric alloys. The diffusivity of Ni in NiaAI will be independent of bulk composition above a definite temperature which was also indicated by Hoshino. 5. CONCLUSIONS 1. The equilibrium equation of point defects in Ni 3AI can be expressed in a new simple method, which is independent of the chemical potentials. 2. The concentration of vacancies is higher on Ni sublattice than on A1 sublattice with AI content from 24.1 to 28 at.%, but the concentrations of vacancies on two sublattices are reversed when AI content is more than 24.1 at.% at 1000K.
3. In hypostoichiometric Ni3AI, the AI antisites are the constitutional defects, and the Ni antisites are the constitutional defects in hyperstoichiometric Ni3A1. Two types of vacancies simply belong to the thermal defects in NiaAI. 4. The experimental results by positron annihilation show that the concentration of vacancies increases with increasing AI content from 24 to 26 at.%. 5. Although the vacancies interact with the boron dopant, which may limit the long range transport of boron to grain boundary, the difference of vacancy concentration in Ni3A1 alloys could not be considered as the main reason in explaining the effect of stoichiometry on the segregation of boron. 6. The antisite defects have influence on the correlation factor for diffusion of Ni in Ni3A1 alloys. The effect of stoichiometry on the diffusion can be understood with the calculated results of antisite defect distribution in NiaAI alloys. REFERENCES 1. J. H. Westbrook, Trans. Am. Inst. Min. Engrs 209, 898 (1957). 2. P. H. Thornton, R. G. Davis and T. L. Johnson, Metall. Trans. 1, 207 (1970). 3. K. Aoki and O. Izumi, Nippon Kinzoku Gakkaishi 43, 1190 (1979). 4. C. T. Liu, C. L. White and J. A. Horton, Acta metall. 33, 213 (1985). 5. A. Dasgupta, L. C. Smedskjaer, D. G. Legnini and R.W. Siegel, Mater. Left. 3, 457 (1985). 6. S. M. Foils and M. S. Daw, J. Mater. Res. 2, 5 (1987). 7. A. F. Voter and S. P. Chen, in High Temperature Ordered lntermetallic Alloys (edited by C. C. Koch et al.), Vol. 39, p. 175. Mater. Res. Soc. Pittsburgh, Pa (1985). 8. T. L. Lin and Da Chen, d'. Physique, Coll. C-l, 227 (1990). 9. A. Caro, M. Victoria and R. S. Averback, J. Mater. Res. 5, 1409 (1990). 10. A. Seeger and H. Mehrer, in Vacancies and Interstitials in Metals, pp. 1-38. Horth-Holland, Amsterdam (1970). 11. T. M. Wang, M. Shimotomai and M. Doyama, J. Phys. F, Phys. 14, 37 (1984). 12. Yang Wengying, Lu Fanxiu and Zhang Shouhua, Acta metall, sinica A 4, 147 (1991). 13. P. Hantojarvi, J. Johansson, P. Morse, L. Pollanen, A. Vehanen and J. Yli-Kauppila, in Point Defects and Defect Interactions in Metals (edited by J. Takamura), p. 504 (1982). 14. P. Hantojarvi, in Positron in Solids. Springer, Berlin (1979). 15. S. P. Chen, A. F. Voter, R. C. Albers, A. M. Boring and P.J. Hay, J. Mater. Res. 5, 955 (1990). 16. G. F. Hancock, Physica status solidi(a) 7, 535 (1971). 17. K. Hoshino, S. J. Rothman and R. S. Averback, Acta metall. 36, 1271 (1988). 18. T. Ito, S. Ishioka and M. Koiwa, Phil. Mag. A 62, 499 (1990). 19. M. Koiwa and S. Ishioka, Phil. Mag. A 48, I (1983).
0956-7151/94 $6.00 + 0.00 Copyright © 1993 Pergamon Press Ltd
THEORETICAL A N D POSITRON ANNIHILATION STUDY OF POINT DEFECTS IN INTERMETALLIC C O M P O U N D Ni3A1 JIAN SUN and DONGLIANG LIN (T. L. LIN) Department of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200030, P. R. China (Received 16 September 1992; in revised form 4 May 1993)
Abstract--The equilibrium equation of point defects in L12 types of intermetallic compounds was established in a new simple method, which is independent of the chemical potentials. The formation energies of the relevant point defects in Ni3AI were calculated by EAM potentials and statical relaxations. The concentration of point defects at 1000 K as a function of bulk composition and the effect of temperature on them were studied for Ni3A1 alloy. The results show that the Al-antisites are the constitutional defects in hypostoichiometric Ni3A1, and the Ni-antisite defects in hyperstoichiometric Ni 3A1. The two types of vacancies belong to thermal defects. The positron annihilation technique was also conducted to measure the concentration of vacancies in Ni3A1 alloys with and without boron. Although vacancies interact with the boron dopant, the changes of vacancy concentration in Ni3A1 alloys can not be considered as the main reason in explaining the effect of stoichiometry on the segregation of boron. The effect of stoichiometry on diffusion in Ni3AI alloys was discussed additionally,
1. INTRODUCTION The intermetallic compound Ni3A1 has the LI~ ordered crystal structure. The long range ordering is responsible for its unusual high temperature mechanical properties [1, 2]. This compound has the composition range of 72.5-77 at.% Ni at room temperature, The point defects being of thermodynamic equilibrium properties, such as antisite defects, vacancies and interstitials can be introduced by thermal motion of atoms in materials. On the other hand, if the component is deviated from the stoichiometric composition, the excess atoms can also form these point defects, referred to as constitutional or stoichiometric defects. The concentration of point defects in crystals is different due to their different formation energies, and can be influenced by the temperature and the composition of Ni3Al. The properties of point defects, particularly vacancies and antisite defects, play an important role in diffusion in the bulk material, solid solution hardening effect, ordering and disordering behaviours in intermetallic compounds, Aoki and Izumi [3] first discovered that microalloying with boron suppresses intergranular fracture and improve the ductility of Ni3A1, which generated considerable interest in both grain boundary phenomena and the lattice defect in Ni3A1. The results studied by Liu et al. [4] showed that the level of boron at the grain boundaries decreases with increasing bulk aluminium above 24 at.%, with an increase of aluminium from 24 to 25.2 at.% results in a reduction of boron segregation by 45%. Since the grain boundary properties in Ni3AI are sensitive to
the boron level, the boundary remains brittle when the amount of boron segregation is insufficient. Therefore, it is very important to clarify the role of the deviation from stoichiometry in the transport of boron to the grain boundaries. Mass transport usually occurs by atomic migration via point defects, The positron annihilation study of vacancies in Ni 3A! by Dasgupta et al. [5] suggested that there exists small concentration of constitutional Ni vacancies essentially independent of composition in the stoichiometric or hyperstoichiometric alloys. The constitutional vacancies combined with the boron dopant may limit the long range transport of boron to grain boundaries. According to Dasgupta, the reason why boron segregates to grain boundaries more strongly in hypostoichiometric Ni3A1 than in either stoichiometric or hyperstoichiometric Ni3A1 can be explained. Theoretical calculation of point defects in Ni3 A1 alloys was also conducted by Foiles and Daw [6]. They calculated the formation energies and the thermal concentration of vacancies and antisites vs bulk composition. In their model, the effective formation energies of defects consist of internal energy and chemical potentials, and the latter is a function of temperature and composition of alloy calculated by Monte Carlo simulation at 1000 K. They gave the equations of the concentration of defects related to temperature and chemical potentials, but they did not calculate the detailed curves of concentration of defects vs temperature further. Therefore, the properties of constitutional defects resulting from the deviation from stoichiometry in Ni3AI is not clarified theoretically because the defects could not be identified as the constitutional defects only from the 195
196
JIAN SUN and DONGLIANG LIN (T. L. LIN): POINT DEFECTS IN Ni3A1
criteria that their formation energies are much lower than others, In the current paper, we report an extensive study on point defects in Ni3A1 alloys. The formation energies of point defects in Ni3AI, such as antisite defects, vacancies and interstitials were first calculated by embedded atom method potentials and statical relaxations. Then, the equilibrium equation of point defects in LI2 type of intermetallic compounds was established by a new simple method. The relationship of the concentration of antisites and vacancies vs bulk composition and the effect of temperature on defects were studied for Ni3A1 alloys, The concentration of vacancies in Ni3AI alloys with various AI and boron contents was also investigated by means of positron annihilation. The main purpose of this paper is to understand the effect of stoichiometry on the diffusion, in particular on the segregation of boron in Ni3A1. 2. THEORETICAL CALCULATIONS 2. I. Formation energies o f defects Computer atomistic simulation has been used to study the properties of point defects. The application of the embedded atom method potentials to the description of Ni-AI system was first presented by Foiles et al. [6]. In this calculation, the embedded atom potentials reported by Chen et al. [7] is used to calculate the formation energies of antisite defects, vacancies and interstitials with the energy gradient method. A cubic cell containing 1728 atoms with periodic boundary condition and constant pressure is
adopted. The details of the calculations are described elsewhere [8]. The calculated results listed in Table 1 show that the formation energies of vacancies and antisites are very similar to those calculated by Foiles et al. and energies of interstitials similar to those conducted by Caro et al. [9]. The formation energy of A1 vacancy is somewhat higher than Ni vacancy, and the energies of the two antisites are comparable. The formation energies of interstitials are much higher than those of vacancies and antisites, so the concentration of interstitials in Ni3AI is negligible in the later calculations. 2.2. The equilibrium equation
The equilibrium concentration of point defects can be determined in an ensemble with fixed temperature
and chemical potentials. Because the calculation of chemical potentials is very sophisticated, the chemical potentials will be replaced by the bulk composition of Ni3A1 in the present calculations. For A3B cornpounds, there are three A sites for each B site, all penetrating each other. Each lattice site will be occupied either by an atom appropriate to the sublattice, by a vacancy, or by an atom of the opposite type (an antisite defect). Assume this system in which the concentration (atomic percent) of A sublattice sites occupied by A atoms is X'AA, the concentration of B sublattice sites occupied by B atoms is XBB, the concentration of vacancies on the A sublattice sites and B sublattice sites is X v and X v, the concentration of A sublattice sites occupied by B atoms (A antisite defects) is XAB, and the concentration of B sublattice sites occupied by A atoms (B antisite defects) is XBA respectively. The concentration of atoms X^ will vary within the composition range for A3B compound, but crystal structure of the cornpound still keep unchanged. Therefore, there exist two structural constrained conditions among the concentrations of various point defects (XAA"~ XBA)/(XAA + XBA + )[BB ql_ J(AB) = XA (1) (XA~ + X ~ + XAB)I(X~B + X v + XBA)= 3.
Combine equation (1) with (2) to obtain equation (3) XAB+ (1 -- XA)XVA -- XB^ -- XA X v + XA -- ~3 = 0. (3) Thus, the concentration of various point defects and bulk composition of the compound have been linked in equation (3). For noninteracting defects, the energy of the system is E = E0 + X ' vA E vA + X avE vB + XABEAB + J(BAEBA (4) where E0 = (X'AA "~ X'Aa "3!"XV)EA + (X'BB "JI-J(BA "~ XV)EB, E 0 is the energy of the ideal lattice, E v and E v are the formation energies of vacancies on the A and B sublattice, and E m and EBA the formation energies of A antisite defects and B antisite defects respectively, which are shown in Table 1. The configuration entropy of the system is suggested by Foiles et al. 3 ? ( 4 ) ( 4 S =~ ~ XAB + f
Table 1. Formation energy of the relevant point defects in Ni3AI
Type of defect
AEf(eV)
AI vacancy
1.92
Ni vacancy
1.47
Ni antisite (Ni sublattiee occupied by AI atom)
0.56
(AI sublattice occupied by Ni atom) AI octahedral Ni octahedra!
0.59 4.53 3.78
AI antisite
(2)
v)] ~ XA +
1
~[f(4XBA)+f(4XV)]
(5)
where f ( x ) is the ideal entropy function f ( x ) = - - K [ x In(x) + (1 -- x)ln(l -- x)].
(6)
Only consider the vibration entropy introduced by tWO vacancies S v=
v v X vc v XA S f_ A --{- B~J f_B.
(7)
JIAN SUN and DONGLIANG LIN (T. L. LIN): POINT DEFECTS IN Ni3A1 The change of free energy of the system is
100 _ Ni-antisite
AF = AE - T(S + SV).
(8)
~
Al-antisite
22
_
t0 -3
197
Among four unknown concentration, XV, X v, XAB and XBA, only three are independent owing to the structural constrained condition equation (3). In the present calculation, X v, X v, and XAB or X v, X v, and XBAare chosen as the independent variables. The equilibrium state of the system at a given temperature and bulk composition corresponds to a minimum of the free energy
'--~ ~',~ 10-6 " ~, ~ 10-9 7
OAF
OAF
OAF
63j(----~n= 0,
O - ~ = 0,
0X.AB= 0
Ni content (at.%) Fig. 1. The calculated concentration of four types point defects at 1000K as a function of bulk composition.
f
OAF
\
~ k o r - - = 0). (9) 0~xI"BA The concentrations of defects can be expressed by XV=
~
A
(
+ ( X A - I)EBA)/KT] 4XBA ~xA XV = 1.,~A 1 exp [ ( - E v + XAEBA)/KT]
4XBA /
4"¥BA ) - ' exp [(--EAa- EeA)/KT ] X^e = ~ ( 1 --4-XBA 3 XA)XVA -- X A X V -{- XA -
~
(10)
when XA/> 3/4 XV=3A( 4XAB " ] ~ - X A 3------~Aa ,] exp [(--E v + ( 1 - XA)EAB)/KT ] 4XAB "~-xA XV = 14A exp [ ( - E av -J(AEAB)/KT] 3 -- 4XAB/] XeA =
3--4XAB
~S
J
VA1 10_12
72
I
I
[
I
I
1
73
74
75
76
77
78
2.3. Calculatedresults
4Xah ~ xA' I-4XBA] exp[(-EV
XBA-~-XAB"1-(1 -
VNi
exp[(--EAB--EBA)/KT] 3
XAB =,e~BA"F- (J(A - l)XV +.¥AXV-- JI"A+ ~
(11)
when XA < 3/4 where A = exp [(S~_A)/K ] = exp [(sVB)/K]. Taking the value A to be 4.5, the same as that in pure nickel [10]. The equations of defects described above are independent of chemical potentials and only have a connection with the internal energies of defects and the bulk composition of Ni3A1. Therefore, it is convenient to calculate the concentration of defects accurately at definite temperature and bulk composition. Because the equations are not the explicit functions, they can he solved by iterated method using computer. Equations (9) and (10) show that for ordered alloys, the effective vacancy energies depend on the overall composition of the alloy, but the formation energy of antisite defects does not. It is worth pointing out that the equations described above are suitable for the calculation of point defects in other A 3B type compounds,
The concentration of four types of point defects at 1000 K as a function of bulk composition has been calculated as shown in Fig. 1. It is shown that the concentration of Ni antisites are much higher than that of the other three defects in hyperstoichiometric Ni3AI, and the concentration of vacancies is also higher on Ni sublattice than on the A1 sublattice in this alloy. The concentration of four types of defects changes significantly near the stoichiometric composition. In hypostoichiometric Ni3A1, the concentration of A1 antisites is the highest one, which is the sameastheNiantisitesinhyperstoichiometricNi3A1 and less vacancies are found. The concentration of two antisites is the lowest in stoichiometric Ni3A1. However, the total concentration of two vacancies reaches the lowest in hypostoichiometric Ni3A1 with 75.9 at.% Ni content, and increases with A1 content from 24.1 to 28 at.%. The concentration of vacancies on A1 sublattice is somewhat higher than on Ni sublattice when Ni content is more than 75.9 at.%, which is reversed from the results calculated by Foiles et al. The above results may be reasonable because four types of defects have a connection with each other, which is indicated in equations (9) and (10). The effective formation energy on AI sublattice is lower than in Ni sublattice and decreases with the increase of Ni content in these alloys. In order to study the properties of the constitutional defects in Ni3A1 alloys, the relationship of the concentration of defects and temperature were calculated respectively for Ni3A1 alloys with three different bulk compositions (Ni76A124, Ni7sA125 and Ni74AI26). The calculated results are shown in Fig. 2(a-c). It can be seen in Fig. 2(a) that except AI antisites, the concentration of two types of vacancies and Ni antisites increase markedly when the temperature increases in NivrA124alloy. As is well known, the thermal concentration of defects is susceptible to temperature and increases with the increasing ternperature. In particular, at absolute zero, the concentration of thermal defects tends to zero. However, the concentration of constitutional defects reaches the
198
JIAN SUN and DONGLIANG LIN (T. L. LIN): POINT DEFECTS IN Ni3AI
highest at absolute zero, whose character can be considered the criterion to define the constitutional defects. Unlike the other three defects, the con-
Table 2. The composition of alloys AlloyNo. Composition l Ni-24at.% AI 2 3 4
10 °
Al-antisite
5
Ni-25 at.% AI Ni-26 at.% AI Ni-24 at.% AI + 700 ppmB
Ni-25 at.% AI + 700 ppmB
lO-O
N
i
-
a
n
t
i
~
6
Ni-26 at.% AI + 700 ppmB
' lO-iZ -~ ~
o o~
10 -18 10-z4
~
V^l
10_no " a , , , , , I , , , I , , , I , 400 600 800 1000 Temperature(K)
10 ° 10-6 . Vrti
~--
/
0 10-1z :~
centration of AI antisites decreases very slightly with increasing temperature. In order to maintain the stability of the LI2, structure of this alloy, the excess Ni atoms will occupy the AI sublattices, which forms AI antisites. Therefore, the A1 antisite defects are of the character of the constitutional defects resulted from the deviation from stoichiometry, but other three defects are the thermal defects introduced by the thermal motion of atoms in Ni76AI24 alloy. It can be deduced that the Ni antisites are the constitutional defects, but two types of vacancies and AI antisites are the thermal defects in Ni74A12~alloy as shown in Fig. 2(c). Four types of defects belong to thermal defects in stoichiometric Ni3AI as shown in Fig. 2(b). The calculated results show that the vacancies in Ni3A1 are simply thermal defects, not the constitutional defects.
L
-~ 10_18 t9 o
3. POSITRON ANNIHILATION STUDIES
3.1. Experimental procedure
o 1 10 -3o
b ,
J
,
,
,
I
,
,
,
,
,
400 600 800 Temperature(K)
10 ° 10
-6
Al-antisite ~ ~
~
~
10 -tz ///V m I 1
V~ -''~
/
~ 10-1a o~
, 1 i 1000
Ni-ant.isite
.o ~
,
~
0 -24
10-a°
~/ C
400
600
800
The alloys used in this study prepared by directional solidification with various aluminium and boron contents. All of them annealed at 1423 K for 50h followed by slow furnace cooling to room temperature. Their compositions are given in Table 2. Rectangular plate samples of 10 x 10 x I mm were cut off normal to the growth direction of [001], then machined and polished. All samples had very large single phase grains, approximately several mm in size, which rendered the grain boundary contribution negligible to the positron annihilation. The positron lifetime was measured by the conventional fast-fast coincidence type. The system resolution function was approximated by a guassian having a F W H M of 245 ps. A 22Na source of about 15 /tci contained in an envelope made from a thin nickel f°il was sandwiched in between two samples. More than 105 counts were accumulated in the lifetime measuring for each samples. The lifetime data for each sample were analysed using a POSITRONFIT computer program. These analyses were conducted using three-term fit without restrictions.
1000
Temperature(K)
Fig. 2. The calculated concentration of four types of point defects vs temperature,
3.2. Experimental results The lifetime spectrum for each example was represented with three lifetime components, attributable
JIAN SUN and DONGLIANG LIN (T. L. LIN): POINT DEFECTS IN Ni3AI to the bulk (Bloch state), the vacancy trapped state and the positron source respectively. The bulk lifetime of all six Ni3AI samples is very close to 116 ps found by Wang et al. [11]. The trapped state lifetime of samples is 230 ps or more in the present work, which is higher than 180 ps measured by Wang et al. The intensity of source term of all samples is very small (approx. 1%). According to the trapping model, the trapping rate for Ni3A1 alloy was calculated as a function of alloy composition shown in Fig. 3. In the positron trapping model, the trapping rate can be assumed to be K = Cv#v (12) where Cv is the concentration of vacancy, and #v is the trapping factor. Figure 3 shows that the trapping rate or concentration of two types of vacancies in Ni3A1 doped with or without boron increases with the increase of A1 content from 24 to 26at.%. The trapping rates in Ni 3A1 decrease when it is doped with boron. Because positrons are insensitive to the presence of antisite defects, the concentration of antisite defects in Ni3A1 can not be determined, 4. DISCUSSIONS The experimental results show that the positron trapping are found not only in stoichiometric and hyperstoichiometric alloys, but also in hypostoichiometric alloys with and without boron. The intensity of vacancy trapped state lifetime in pure Ni3A1 alloys in this work is higher than that in Dasgupta's. The reason is probably that the specimens were not annealed sufficiently or the cooling rate of specimens was not slow enough so that the non-equilibrium concentration of vacancies at high temperature remained at room temperature. This reason can also be used to explain why the trapped state lifetime is longer than 180 ps determined by Wang et al. [] 1] in quenched specimen of Ni3Al, which suggests that the defects may act as small vacancy clusters produced in the cooling process or vacancy boron complexes in 6• 5 i
-
Ni3AI
o Ni3AI with boron
4 -
~ •"
-
' e
~
,
* ~ 0
3 .=. e~
2
--
~
] 0
[
24
I
25
[
26
AI content (at.%) Fig. 3. The trapping rate in Ni]A1 vs A1 content,
199
the case of the alloys doped with boron. Foiles et al. found that the interaction between vacancies is weakly repulsive with the binding energies of 0.16 eV for Ni-Ni vacancy pairs and 0.18 eV for Ni-AI vacancy pairs [6]. The intensity of trapped state lifetime in boron-doped Ni 3A1 is lower than in pure Ni3A1 alloys, which suggests that a part of the vacancies are filled with boron atoms or atom clusters, and the effective concentration of vacancies is reduced. A similar result was obtained by Yang et al. [12].The capture of the vacancies by dopant to reduce the positron trapping rate was also found in iron alloy doped with carbon [13]. Positron annihilation measurements performed on Ni3A1 with various AI and boron contents by Dasgupta et al. [5] show that positron trapping was found in the stoichiometric and hyperstoichiometric Ni3A1, but no positron trapping in pure hypostoichiometric Ni3A1. The estimated vacancy concentration in pure stoichiometric and hyperstoichiometric Ni 3AI would be 2 × 10 6. Since the limitation of sensitivity of such measurements is approximately 10 7 at best for deterruination of vacancy concentration [14], the lower concentration of vacancies near or beyond the limitation can not be excluded. The results in both Dasgupta's and the present work show that the concentration of vacancies increases as the increase of A1 content in Ni3A1. However, it could not be deduced that constitutional vacancies are present in stoichiometric and hyperstoichiometric Ni3A1 alloys, but not in hypostoichiometric Ni 3A1. The calculated results apparently show that the constitutional A1 antisites exist in hypostoichiometric Ni3A1 and constitutional Ni antisites in hyperstoichiometric Ni 3A1, but not any types of constitutional vacancies in non-stoichiometric Ni3A1. The calculated equilibrium concentration of vacancies is much lower than that determined by positron annihilation at room ternperature because the calculation was conducted under the thermal equilibrium condition in which sufficiently long anneal time is needed and the defects are well separated. It also indicates that it is not easy to reach the real equilibrium state for intermetallic compounds because of difficult diffusion of atoms in compounds. On the other hand, the concentration of vacancies within overall composition of Ni3AI is significantly lower than the doped-boron concentration considered here. Although vacancies interact with the boron dopant, which may limit the long range transport of boron to grain boundary, the difference of concentration of vacancies in Ni3AI alloys with various A1 content could not be considered as the main reason in explaining the effect of stoichiometry on the segregation of boron. Computer atomistic simulation results studied by Chen et al. [15] showed that boron segregates preferentially to the grain boundary, especially to the Ni-rich grain boundary, instead of the surface and interstitial site. Furthermore, in Ni-rich grain boundary together with boron makes the grain
200
JIAN SUN and DONGLIANG LIN (T. L. LIN): POINT DEFECTS IN Ni3AI
boundary stronger than the bulk. Therefore, the segregation of boron on grain boundary mainly controlled by grain boundary structure and chemistry, not by the types and distributions of point defects in NiaA1 alloys, In addition to the current interest in point defects, diffusion in ordered alloys is also of interest to study [16-18]. The measurements of tracer diffusion in Ni3AI alloys performed by Hoshino et al. [17] indicated that the effect of stoichiometry on boron segregation is not connected with the behaviour of lattice vacancies, since the diffusion behaviour of Ni is all the same on both sides of stoichiometry. If the antisite defects can be considered as a factor influencing the diffusion in ordered alloys, the calculated results may explain the reason why the diffusivity of Ni in Ni3AI shows a minimum at the stoichiometry composition below 1000 K and this trend becomes clearer with decreasing temperature. In intermetallic compounds, random vacancy jumps would disrupt the ordered arrangement of atoms on lattices. The diffusion via the Ni sublattice vacancy mechanism in the L 12 structure crystals has been established. The Ni atoms may not jump onto 4 AI sublattice sites of their 12 nearest neighbor sites, which leads to a decrease of the correlation factor from 0.7815 to 0.727. The value of 0.689 of the correlation factor for LI2 structure was further calculated by Koiwa and Ishioka [19]. Thus, if the high concentration of antisites (which corresponds to the lower long range order parameter) is introduced in crystals, the correlation factor for Ni diffusion will increase to the value between 0.7815 and 0.689. The further discussion of the detailed mechanism on the effect of antisites on the correlation factor is beyond the scope of this paper. Since constitutional antisite defects exist on both sides of stoichiometry, the diffusivity will increase with the higher concentration of antisite defects in non-stoichiometry Ni3A1. When the temperature increases, the concentration of antisite defects in stoichiometry Ni3A1 increases markedly, and is closer to a level in non-stoichiometric alloys. The diffusivity of Ni in NiaAI will be independent of bulk composition above a definite temperature which was also indicated by Hoshino. 5. CONCLUSIONS 1. The equilibrium equation of point defects in Ni 3AI can be expressed in a new simple method, which is independent of the chemical potentials. 2. The concentration of vacancies is higher on Ni sublattice than on A1 sublattice with AI content from 24.1 to 28 at.%, but the concentrations of vacancies on two sublattices are reversed when AI content is more than 24.1 at.% at 1000K.
3. In hypostoichiometric Ni3AI, the AI antisites are the constitutional defects, and the Ni antisites are the constitutional defects in hyperstoichiometric Ni3A1. Two types of vacancies simply belong to the thermal defects in NiaAI. 4. The experimental results by positron annihilation show that the concentration of vacancies increases with increasing AI content from 24 to 26 at.%. 5. Although the vacancies interact with the boron dopant, which may limit the long range transport of boron to grain boundary, the difference of vacancy concentration in Ni3A1 alloys could not be considered as the main reason in explaining the effect of stoichiometry on the segregation of boron. 6. The antisite defects have influence on the correlation factor for diffusion of Ni in Ni3A1 alloys. The effect of stoichiometry on the diffusion can be understood with the calculated results of antisite defect distribution in NiaAI alloys. REFERENCES 1. J. H. Westbrook, Trans. Am. Inst. Min. Engrs 209, 898 (1957). 2. P. H. Thornton, R. G. Davis and T. L. Johnson, Metall. Trans. 1, 207 (1970). 3. K. Aoki and O. Izumi, Nippon Kinzoku Gakkaishi 43, 1190 (1979). 4. C. T. Liu, C. L. White and J. A. Horton, Acta metall. 33, 213 (1985). 5. A. Dasgupta, L. C. Smedskjaer, D. G. Legnini and R.W. Siegel, Mater. Left. 3, 457 (1985). 6. S. M. Foils and M. S. Daw, J. Mater. Res. 2, 5 (1987). 7. A. F. Voter and S. P. Chen, in High Temperature Ordered lntermetallic Alloys (edited by C. C. Koch et al.), Vol. 39, p. 175. Mater. Res. Soc. Pittsburgh, Pa (1985). 8. T. L. Lin and Da Chen, d'. Physique, Coll. C-l, 227 (1990). 9. A. Caro, M. Victoria and R. S. Averback, J. Mater. Res. 5, 1409 (1990). 10. A. Seeger and H. Mehrer, in Vacancies and Interstitials in Metals, pp. 1-38. Horth-Holland, Amsterdam (1970). 11. T. M. Wang, M. Shimotomai and M. Doyama, J. Phys. F, Phys. 14, 37 (1984). 12. Yang Wengying, Lu Fanxiu and Zhang Shouhua, Acta metall, sinica A 4, 147 (1991). 13. P. Hantojarvi, J. Johansson, P. Morse, L. Pollanen, A. Vehanen and J. Yli-Kauppila, in Point Defects and Defect Interactions in Metals (edited by J. Takamura), p. 504 (1982). 14. P. Hantojarvi, in Positron in Solids. Springer, Berlin (1979). 15. S. P. Chen, A. F. Voter, R. C. Albers, A. M. Boring and P.J. Hay, J. Mater. Res. 5, 955 (1990). 16. G. F. Hancock, Physica status solidi(a) 7, 535 (1971). 17. K. Hoshino, S. J. Rothman and R. S. Averback, Acta metall. 36, 1271 (1988). 18. T. Ito, S. Ishioka and M. Koiwa, Phil. Mag. A 62, 499 (1990). 19. M. Koiwa and S. Ishioka, Phil. Mag. A 48, I (1983).