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COMPUTER SIMULATION OF TILT GRAIN BOUNDARY STRUCTURES IN B.C.C. METALS
V. Paidar
To cite this version:
V. Paidar. COMPUTER SIMULATION OF TILT GRAIN BOUNDARY STRUCTURES IN B.C.C. METALS. Journal de Physique Colloques, 1990, 51 (C1), pp.C1-299-C1-304.
�10.1051/jphyscol:1990147�. �jpa-00230306�
COMPUTER SIMULATION OF TILT GRAIN BOUNDARY STRUCTURES IN B.C.C. METALS
V.
PAIDARInstitute of Physics, Czechoslovak Academy of Sciences Na Slovance 2, 180 40 Praha 8, Czechoslovakia
RESUME
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l a t t i c e . W i t h t h i s p o t e n t i a l w e are a b l e %a r e p r o d u c e t h e a t o m i c s t r u c t u r e s
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990147
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o f t h e s tr'ii.ct!~.r' alr:!r~r:i t h e r-i!.ta.t i o , . ~ a:-: i s . F i n a l l y , t, h e :.i;'trsuct t.!r-es w h m - e t h e boc.!ni::lar-y p l a n e :i.s n o t a n e l e m e n t , o f ii;yrnaietry bel.trt17g t o t h e L h i r d group. 'The s i . n i u : L a t i o r i s shhawed t h a t , +;he .strc.!.~:ti.rr'&?s o f t h e f ir'?i:t t w o g i - o u ~ s c a n I:>e a n a l . y r e d ir! terrns ?of stl-i.!ctt.!t-al ! ~ r . i i 'c i n o d e l . T h e fr..!nc:Iat~tental. s%r!..!c:t r t r a l e l e m e n ' t . s w e r - e r.ieler::ted at:::ccrrr:firrg t o t h e c l . a ! s : ; i . f i c a k i o n s c h e m e i n F i g , 3. T h e s t r u r = . t c r r . a l u n i t s o f t h e i d e a l l a t , t i c : e Ft .and E: ( o r a a17d e ) c a n b e : i . i i e n t . i f i e d , f n r n ~ a l l t i 2.2 t h e !-!i-ii%zi r:!f X I b a t . i n d a r i e ? s o n the? <:li:~13. ancl <!aIt3> p l a r ~ e c ; w h i c h r S e p r . . e s e n t t h e I:~i!~..!;..!~~zir"ie f o r s % h e I.irrt:i.t,s a f iiii.s?:!i-.ienC.+~.ti,t:~~~ $3.+
@>'" artcl :l13@",~6?<5pei::t :i.ve % y. B e s i d e s t h e m i t is n e c e s s a r * # t,o intr~or:ft..tce t h e s t y u c $ t . r r * a i el.etner?.ks C , B a n d D f o r f j . l . . ' ~ t Lwo ~ L a ! ~ s i f i ~ a t , i c ! r ? l e v e l s c o i - r e s p o n d i l , g t o t h e C3 .C12:!3, 63 C:lI:l.> arid X 9 < : l 4 1 7 t i l t b o u n c f a r i e s . T h e t:)nundarqs . t y p e s r::hr:;sen f o r a!..!i- :i;ii!!i.!latior~s a r e Lis.l;ed i n T a b l e
:L
wher'e r . o t a t , i o n ar.iq:Le w i t h r~e.i;j:!er=t -kg:) t h e C:li31.7 a:.:j.s anc! C v a l u e a r e a l s o g i v e n , T h e gr-a,j.n,tiou\7dau.y!iiiti-*t.!.ct!.!r.*es a r c i:!e!:i;r:rsibecl :i.n . t h e no.t,a.i,ioc, t..!sed i n p a p E r s by Si...tc;tn~-i, Many arid
I ..!.,.tat::
.
.i ( 5 . g. fS,LC3). '<W-ti.c:al b a r s d e n o t e t h e p e r . i . o d o f t h e b o u n d a r y s t r t . ! c t u i - eCl-302 COLLOQUE
DE
PHYSIQUEF i g , , 3 The c l a s s i . f i c : a . t , i n n r$c::heme f u r t h e s y m m e t r i c a l C1811 t i LZ, g r a i n hnundaries i n b. c. c. c r - y s t a l s C 1 7 3 . The i n t e r p l a r ? a . r s p a r : i n q i s p l o t t e d a s a f u n c t i o n nf t h e m i s n r i e n l . , a t i o n 8,
A B ' . \
Fig. 5 Two 1323) g r a i n b o u n d a r y c o n f i g ura t i ans.
Fig. 4 The e n e r g y o f s y m m e t r i c a l g r a i n b o u n d a r y s t r u c t u r e s
signifies that the equivalent atoms in each half-period are relatively displaced along the tilt axis by 1/2 C 1 0 1 1 . When the combination of structural elements does not contain any dot it means that the boundary structure is not centred. The description of symmetrical structu1-es of all simulated grain boundaries is summarized in Table 1.
The eneagy of symmetrical grain boundary structures as a function of misorientation is plotted in Fig. 4, where the boundary planes are also indicated. As it can be expected the most special boundary on (1213 possesses relatively very low energy. The C1113 and (1413 boundaries from the second level of classification have a lower energy than could be intel-polated from the data for the other boundaries. However, a surpl-isingly low energy was obtained for the %l1 €3233 boundary. Let as point out that the special character of this boundary does not follow from the structural unit model expressed in the classification scheme. It is apparently related directly to the potential used in our simulations.
The atamic configurations of grain boundaries are usually presented by the projection of atomic positions on the plane perpendicular to the rotation axis. To emphasize differences from the ideal lattice the atomic configurations of the €3233. boundary are displayed in Fig.5 by the net connecting the nearest neighbours in one atomic plane perpendicular to C 1 8 1 1 while the atoms from the neighbouring parallel atomic plane are denoted by standard marks (circles). Only one period of the boundary structure is shown
(in the horizontal direction). Notice that the energy of this boundary decreases with the increasing width of the boundary region differing fi-om the b.c.c. structure. The boundary atomic configuration is actually a nucleus of hexagonal structure which has the energy lower than the original b.c.c.
crystal.
4. DISCUSSION
The phase transformation of the b.c.c. to hexagonal structure, that nucleated at the €3233 grain boundary, o_ccurs according to the mechanism demonstrated in Fig. 6. The alternating (181) atomic planes with the separation of abccV2 shuffle with respect to their neighbouring parallel planes in the C 1 0 1 3 ' direction. In the case of AB' structure the shuffle direction is oriented in both crystals towards the boundary plane. The shuffling of atomic planes is accompanied by the lattice extension in C 1 0 1 1 and contraction in the C0101 perpendicular direction. Since the periodicity of the grain -boundary structure is preserved during the relaxation, the separation of (181) atomic planes cannot be changed. Similar mechanism of the b.c.c.
-
h.c.p. bulk:transformation was considered in 'C181 for the interpretation of phase transition in iron at high pressures.
The shuffling of the (18i) atomic planes in the C 1 8 1 1 direction can be described as a transversal wave with the wave vector 112 (101). The discussed instability of the b.c.c. lattice corresponds the<? to decreasing phonon frequency at the N point which lies at the centre of faces of the b.c.c.
Brillouin zone. For a monotonic shape of the <@39> branch %, connecting the centre of the Prillouin zone
r
and the point N in phonon spectra, this instability is related to a collapse of the b.c.c. lattice with respect to the homogeneous shear deformation along the C1013 plane in the (101) direction characterized by the C' elastic constant. The crystals with a tendency to such instability should exhibit a large elastic anisotropy as the anisotropy factor A (defined as the ratio of shear elastic constants c44 and C' ) increases with decreasing C'. Indeed, large values of fi are known for alkali metals which transform at low temperatures into the h.c.p. phase. Even larger values of A were measured for some binary and ternary alloys (CuZn, AuCd, CuZnNi,CuZnAl
) C 1 9 1 where martensi t ic phase transfot-mat ions play animportant role.
It should be stressed that the shuffling alone does not decrease the energy of the b.c.c. lattice. Actually, an energy increase of the b.c.c. crystal
Cl-304 COLLOQUE DE PHYSIQUE
