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GRAIN BOUNDARY STRUCTURE SIMULATION IN ORDERED Ni3Al
H. Jang, D. Farkas
To cite this version:
H. Jang, D. Farkas. GRAIN BOUNDARY STRUCTURE SIMULATION IN ORDERED Ni3Al.
Journal de Physique Colloques, 1990, 51 (C1), pp.C1-191-C1-196. �10.1051/jphyscol:1990129�. �jpa-
00230287�
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Colloque C l , supplbment au n o l , Tome 51, janvier 1990
GRAIN BOUNDARY STRUCTURE SIMULATION IN ORDERED Ni,A1
H, JANG and D. FARKAS
Materials Engineering Department, Virginia Tech, 201 Holden Hall, Blacksburg, V A 24061, U. S. A.
Resume - Nous avons btudib Ia ~nultiplicite des structures possil~les pour les joints de grains dans I'alliage ordonne Ni3AI. Nous avons etudie I'interaction des defauts ponctuels (antisites) avec ces ioints de grains, ainsi que le co~nportement dn reseal] dans la region d r ~ joint rlc grains. L'bnergie he formation des defarrts poncteels est une fonction oscillaloire de la distance a11 joint cle grains La dbpendance de I'Cnergie de joints de grains vis a vis la composition chimiqr~r est ar~ssi discr~tee.
Abstract
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The n~ultiplicity of possihle structures was slr~clied for several grain Itor~ndaries in the ordered compound Ni3Al. The interaction of lattice antisite defects ~ i t h these grain boundaries was studied a s well a s the relaxation hehavior of the lattice in the grain bonntlarg region. Several interesting features were identified, like oscillatory hehavior of defect formation energies as a function of the distance to the boundary plane. The dependence of grain 1ro1111dary energy on composition is also discussed.1 INTRODUCTION
A large hody of theoretical work has been developed in recent years in the area of grain boundary structure, particularly in ordered alloys. One of the most significant issues that arise as a result of that work is the fact that n multiplicity of different grain ltoundary structures is possihle for the same grain boundary ~nisorientation and I~o~rndary plane. This multiplicity of strt~ctures arises from possihle differences in composition atid ordering state.
The purpose of the present work is to understand the energetics of the multiplicity of structures in more detail. For this purpose we have studied the interactior. of point defects with possihle grain boundary structures.
In order to study the influences of composition we have studied the interactions of antisite dcfects wit11 grain Ooundaries We consider the addition of one antisite defect per boundary periorl in different positions in the grain Iloundary structure. By considering initial houndary structures of different compositions, further information car]
Ite ohtained on segregation hehavior to the grain houndaries. By addition of two aatisite defects of opposite kinds in the binary ordered alloy one can study the energetics of disordering processes in these honndaries. I t is interesting
to note that although disordering of the grain boundary region is inherently a high temperature process, the cnergetics of antisite defects in the grain boundary region are closely related to ordering driving forces and one can tilerefore infer general trends of the order-disorder hehavior without actually carrying out a high temperature sim~llation. The methods that can he used to study the energetics are those of molecnlar statics with embedded atom interatomic potentials.
Ni3A1 is particularly interesting due to the possihle technological applications of this material when doped with Boron to overcome its intrinsic grain honndarg hrittleness. Extensive studies have been carried out recently on various aspects of grain houndary structure in this material [l-41, a s well a s detailed studies of general planar defects in the Ll structure that are now available in the open literature [5-61. These studies include relaxation hehavior around various defects. For example, in recent work it has heen shown that oscillatory relaxation appears a s a function of the distance from a free surface [l]. This oscillations have been ohserved experimentally, a s well a s predicted by computer simnlation using local volume dependent potentials [I]. The presence of these oscillations has been analyzed fheoretically in relation to the type of interatomic potential used a s well a s the crystaIiographic plane of the free surface [S]. The oscillations have also heen obsemed in twin houndaries, antiphase houndaries and stacking faults [G].
All this work has heen carried out in Ni3AI using interaton~ic at0111 potentials developed at Los Alamos National Lab.
[7, 81. In the present work we use the same interatomic potentials and simulation technique, with the goal of 1111derstanding compositional and ordering effects. W e then compare the resrrlts and the implications for segregation a11t1 ordering hehavior to the results of other techniques, particularly the Cluster Variation Method and Monte Carlo simr~lation.
2 - SIMULATION TECHNIQUE
There have heen several studies on the detailed relaxed strncture around planar defects in Ni3AI. These include grain Itonndaries, free surfaces, antiphase boundaries, stacking faults, etc. In addition, aton~istic simulatio~~ of dislocation core structure in this material has also heen carried ont. These studies were all based on ~nolecular statics aton~istic colnpr~ter simulation resr~lts using embedded atotn potentials. The potentials were developed by Voter et a1 [7] using the en~hedded atom approach [g] and have heen used in a number of grain boundary si~nulation studies. The tecl~nique used for the simulation studies described in the present work is si~nilar to the one used in the previous str~clies. The minimization of the free energy is carried out relaxing the atomic coordinates in a conjugate gradient techniqr~e [(;1 and periodic Itor~ndarg conditions were used for the calcnlation of the grain horrndary structure. For tile calculation of the relaxed structure with the defect periodic houndary conditions were also n~aintained. That is, the
along the directions contained in t!~e grain hoandary plane was maintained, meaning that the calculations
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990129
Cl-192 COLLOQUE DE PHYSIQUE
are for the original grain houndary containing one defect per boundary period. Theretore, the calcr~lat~ons are actually for a new grain houndary structure differing from the original one in the fact that it contains one antisite defect per boundary period. In computing the grain boundary energies with the defects it was important to take into account that when the antisite defect was created, A1 was substituted for Ni or vice-versa. The su1)stitutiort involves the energy of the antisite defect plus a difference in energy related to the fact that the cohesive energy of the material is not the same per Ni atom or per A1 atom. The latter term shonld be snbtracted from the ohserved total energetic difference. This correction is not necessary when considering a pair of antisite defects illat ~naintain the composition of the hlock of atoms heing relaxed.
3
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RESULTSWe have studied in detail the antisite defect formation energies in the vicinity of a
E =
5 grain boundary of symmetrical tilt type in the 10121 plane. There are several possi1)le configurations of this honndary with different stoicl~iometries. These different configurations are obtained starting from initial configurations that have different values of the rigid hody translation of one crystal with respect to the other in the direction perpendicolar to the grain houadary plane. As a result, there are structr~ral vacancies in some of these structures that imply different cl~emical compositions. W e have cl~osen tbree of these that have different stoichiometries. All tbree configurations are ol~tained hy relaxing the structure with the initial configuration I~aving no rigid hodg translation of one crystal wit11 respect to the other in the directions parallel to the grain houndary plane. The relaxation process then yields the equilihrium values for the rigid hody translations in the three directions. The three structr~res represent local miuima in the energy functional. In the terminology of Takasugi and Izumi [9] all are fully synlmetrical boundaries. In the terminology used hy Chen et a1 [2] one is a 100-50 boundary, one is a 50-50 boundary and the other is a 100-100 houndary. These two latter boundaries have structures that contain stract~lral vacancies and have therefore different stoichiometries. The 50-50 boundary contains two Ni structural vacancies per period, whereas the 100-100 houndary contains one AI and one Ni strrlctr~ral vacancy per period. In previous studies of grain I~ouadary energies in Ni3Al Chen et a1 found that the energies of these different types of houndaries were different, with differences of up to 20%121. Furthermore, in a recent study of the energy of 2 = 3 hor~ndaries for different grain h o u ~ ~ d a r y planes it was found
that the hehavior of these two types of boundaries are different [4]. It is expected that the houndaries that are Ni-rich will behave in a way that is similar to that of pure Ni and other fcc metals, whereas the boundaries that a r e stoichiometries and AI rich are expected t o present particular features associated with the ordering in the alloy and will also he affected by factors like the different atomic sizes and bond lengths that occur in the ordered system.
Particularly, they will present AI-AI nearest neighhor honds that are not present in the hulk structure [IO].
3.1 - Relaxed grain boundary structure without defects
Fig. l shows the structure of the relaxed houndaries without defects. In this figure the houndaries are shown in a [IOfl] projection, including two consectltive planes, which are indicated a s squares and crosses, respectively. The nnmhers in the atom positions represent the different sublattices, that is, suhlattice 1 for A1 a t o n ~ s and sublattices 2, 3 and 4 for Ni atoms.
Note that the 100-50 boundary structure is symmetric with respect to the grain boundary plane [mirror plane]. In the cases of the 50-50 and 100-100 houndary this symmetry is broken due to the presence of the structural vacancies.
These structures are the same a s reported hy Chen et al. [2].
3.2 - Formation energies for antisite defects
The energies of antisite defects in the hulk were computed and are shown in table 1. The energies reported in this table have already been corrected for the different cohesive energies attributable to AI or Ni and are therefore only the energies of having an atom in the incorrect suhlattice. The table includes vacancy formation energies for comparison. The vacancy formation energies are part of the set of properties used in the development of the interatomic potentials. As expected, the suhstitution of AI into a Ni site involves a large energy, since it introduces nearest neighbor AI-AI honds that are not present in the hulk. These nearest neighhor honds occur with bond lengths that are about 10% shorter than AI-AI honds in pure A1 or other known stable A1 compounds. On the other hand suhstitnting a Ni atom into an AI site actually involves a negative energy and is a favnred defect. This means that the present interatomic potentials actually predict that the lattice can easily accommodate extra Ni hy substituting it in A1 sites. This is also expected from the phase diagram and it is known that Ni-rich Ni3AI has better mechanical I~ehavior than the stoichiometric material and can be ductilized in its polycrystalline form by adding Boron. The energy of a pair of antisite defects refers to the interchanging of positions of a Ni and Al aton1 and is of course positive a s expected for a n ordered material. This numher is simply the sum of the energies of the two single antisite clefects, including no interaction among them. This applies to the case of the two defects heing far apart.
Fig. 2 shows the results for the energy of antisite defects a s a function of the distance from the boundary plane for the stoichiometric 100-50 houndary. The calculations are shown in the form of grain boundary energy differences for grain houndaries containing one defect per houndary period compared with the same houndary containing no defects. These values are plotted for the different sublattices, with suhlattice 1 heing occupied hy Al. Suhlattices 2, 3 and 4 are all Ni and are equivalent to each other in the bulk. Due to the presence of the Iloundary in the (012) plane they are not equivalent to each other in the results of Fig. 2a. This can he readily understood if it is noted that the environment of the different suhlattices is different in the grain boundary structure shown in Fig. l a in the vicinity of the grain houndary. Far from the grain houndary the three sublattices hecome equivalent, recovering the bulk hehavior. For the 100-50 structure one can again observe the mirror symmetry wit11 respect to the boundary plane.
These results indicate that for AI snl~stitution into Ni sites the grain houndarg will act as a strong segregation site, and all extra AI will go to the grain boundary. On the other hand this particular h o r ~ ~ ~ d a r y will not he a strongly favored site for the location of extra Ni. At high temperatures this I~oundary is expected to present AI segregation and not Ni segregation. Fig. 3 shows similar calculations for the Ni rich boundary [100- 100 houndary]. In this case the results are not symmetric with respect to grain houndary plane since the houndary contains structural two vacancies per houndary period. The same general features are observed a s in the previous case of a stoichiometric boundary. The expectation of AI segregation to this houndary is now more pronounced, due to tlie fact that the initial configuration of the houndary is now Ni rich. Fig. 4 shows the same type of calculation for an A1 rich l~oundary.
The results now show a tendency for the extra Ni to go to the 11onndar-y. This is expected since this is an originally AI rich structure.
An important feature to he noticed in the results is the oscillatory nature of the defect formation energies plotted a s a function of the distance to the grain 11oundary plane. This l~ellavior is consistent with the oscillatory I~ehavior found in the lattice relaxation displacen~ents, as analyzed in reference 161. This type of hel~avior was also found hy Farkas and Savino for the vacancy formation energy in the grain honndary region [ l I].
3.3 - Implications for Grain Boundary Ordering Behavior
111 order to study grain boundary ordering hehavior the energy of creating a pair of antisite defects per grain I~oundary period was studied a s a function of the distance from the boundary plane. As mentioned for the case of the I~olk, the energies are those of creating the pair of defects with no interaction I~etween them so as to simulate a certain amount of disorder per honndary period. The results are shown in Fig. 5 for the three different hor~ndaries considered in the present study. I t is seen that in all cases the energies decrease in the 11oundary region and disorder is expected in the vicinity of the grain boundary a t temperatures lower than in the hulk. These result can he compared to results ohtained by us nsing the cluster variation nietllod for a high temperature simulation in a two-dimensional lattice gas model system [12]. The dependence of the order-disorder parameter on the distance to the grain houndary follows a remarkably similar pattern, a s seen in the CVM results reproduced in Fig. 6. The present results are also consistent with the calculations ohtained hy Foiles 1131 using a Monte Carlo simulation with embedded atom potentials for Ni3AI. The latter author calculated the energy of formation of antisite defects in the vicinity of the grain houndary at high temperature and ohtained similar results to the ones reported in the present work reporting that the energy of formation of antisite defects is lower in the grain l~onndary region.
4
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DISCUSSIONThe first important point in the present results is that the antisite defect formation energy in the vicinity of a grain I~orrndary follows an oscillatory hel~avior a s a function of the distance to the grain houndary plane. This hehavior is similar to that found in the lattice relaxation displacements. These oscillations are connected to the fact that local volume dependent interatomic potentials were used. Ordered alloys such a s Ni3AI are particularly expected to present oscillatory relaxations that can he understood a s internal rel.wation within the four atom motif that constitntes the crystal when located at the nodes of a simple cuhic lattice.
The second important conclusion from the present results is that segregation hehavior will vary with the composition and structure of the particular boundary in question. There is a tendency for AI to segregate to the boundaries easier than Ni. This, however changes when the composition of the Iloundary is AI rich. The in~plications of the present resnlts for order-disorder hehavior are more general and indicate that the grain l~nundary appears to 11e a favored location for disorder in all cases.
Regarding the segregation of antisite defects to the grain 11011ndary region the present results indicate a tendency for segregation to grain l~oundaries, in agreement with the result of Monte Carlo Calculations [l31 and recent experimental results 1)g E. P. George et al. [14]. However, the present results indicate that this segregation I~ehavior is strongly affected hy the grain houndary composition.
REFERENCES
1. S.P. Chen, A.F. Voter and D..J. Srolovitz, Phys. Rev. letters 57, 1308 (1986).
2. S.P. Chen, A. Voter and D..J. Srolovitz, Scripta Met. 20,1389 (1987).
3. S.P. Chen, M R S Spring meeting, Reno (1988).
4. D. Farkas, M R S Fall meeting, Boston (1988).
S. E..J. Savino and D. Farkas, Phil Mag. A, 58, 227 (1988).
6. D. Farkas, E..I. Savino, P. Chidaml~aram, A.F. Voter, D..I. Srolovitz, and S.P. Chen, to appear in Phil. Mag.
7. A.F. Voter, D. Srolovitz and S.P. CIlen MRS proceedings, volume 82, 175 (1987).
8. M.S. Daw and M.I. Baskes, Phys. Rev. B29, 7443 (1984).
9. M. Takasi~gi and 0. Jzumi, Acta Met. 31, 187 (1983).
10. D. Farkas and V Rangarajan Acta Met. 35, 353 (1987).
I l. D. Farkas and E..J. Savino, to be pul~lished
12. D. Farkas and H. Jang, Phys. Rev. B 39, 11769 (1989).
13. S.M. Foiles, Mat. Res. Soc. Symp. Proc, 81, S1 (1987).
14. E.P. George, C. T. Liu and R. A. Padgett, Scripta Met. 23, 979 (1989).
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Acknowledgments
This work was supported in part by the U.S. Department of Energy, Energy Conversion and Utilization Technologies program under contract #19x-8967% with Martin Marietta Systems Inc. and was monitored hy O a k
Ridge National Laboratory. W e gratefully acknowledge A.F. Voter for tile use of the inferatomic potentials.
Tahle I
Energies of point defects in 1)11lkNi,A/ [in eV]
(a) 100/50 case
Vacancy Antisite defect Pair of antisite defects
(h) 50/50 case
1.87 [AI]
1
l.64[Ni]-.
14 [Ni ia AI site](
.46 [AI in Ni site].32
(C) 100/ 100 case
Figure I. Relaxed atomic configurations for three different
C
= 5 (012) grain Imundaries. Suhlattice 1 is occupanied by A1 and sublattices 2, 3, and 4 hy Ni atoms.Figure 2. Distribution of the defect energy by creating one anti-site defect near a 100/50 boundary. Ni (3)-AI (l) means AI atom in the sul~lattice site 1 stihstituted to tlie position of Ni at0111 in the sol)lattice site 3.
l001
I
-15 -10 -5 0 5 10 15 DISTANCE PERPENDICULAR TO G.B. (1) Figure 3. Distribution of the defect energy by creating one anti-site defect near a 100/ l00 bountlnry.Cl-196
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