LOW ENERGY GRAIN BOUNDARIES IN SILVER

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LOW ENERGY GRAIN BOUNDARIES IN SILVER

W. Lojkowski, H. Gleiter

To cite this version:

W. Lojkowski, H. Gleiter. LOW ENERGY GRAIN BOUNDARIES IN SILVER. Journal de Physique Colloques, 1985, 46 (C4), pp.C4-89-C4-94. �10.1051/jphyscol:1985408�. �jpa-00224657�

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LOW ENERGY GRAIN BOUNDARIES I N S I L V E R

W. Zojkowski and H. ~ l e i t e r '

Unipress, High Pressure Research Centre, SokoZowska 29, 01 -1 ⁴²Warsaw, Po Zand

+ ~ n i v e r s i t i i t des SaarZandes, Werkstoffphysik, Bau 2, 6600 Saarbrticken, F. R. G.

~ i ? & - Les joints de grains de f a i b l e h e r g i e dms laargent ont Bte BtudiBs par l a

methcde de f r i t t a g e . On a m n t r & qu' i l s peuvent &re f o h s lorsque l a surface (1111 d'un c r i s t a l e s t mise en contact avec l a surface {ill} , {115}0u{1 1 173de l'autre c r i s t a l . Dans l a structure qui s e £ o m l e s atcmes align& dans l a direction ( 110) sont en coficidence. Les joints a i n s i £om&$ sont du type ¹= 3,5,9 ou 33c.

Abstract - ^Lowenergy grain boundaries in silver were identified a s X = 3,9,11 and 33c assymetric tilt b o w d r i e s . In one grain the boundary is parallel to the { l l l } plane. In the secord grain it i s parallel t o the {ill} ,{115} or{l 1 17)planes. Close packed rows of atoms extending along (1lO)direction.s a r e i n coincidence p s i t i o n s . Between these rows the surface of the s e c o d grain i s composed of lxm3.s parallel t o the {lOO}plane.

Introduction

For specific relative orientations of theadjoining grains, grain boundaries of low energy are observed /I/. Understanding the reasons of the l o w energy of these boundaries is crucial f o r the description of the lxiundary structure. However, no systematic study has apparently been made t o determine the c c q l e t e s e t of low energy M a r i e s existing i n a particular mtal. The purpose of the present work is t o study systematically a l l the low energy bouridaries existing i n silver and derive selection c r i t e r i a for low energy boundaries.

The expsriments were cwied out with Ag 99.999% p l r i t y by a recently developed method /2,3/. About 1 0 ~ s i n c ~ l e crystlline spheres were sintered onto the f l a t smface of single crystal plates. The plates had the surface parallel t o t h e ( l l 1 )

/specimen A/ a d ( l l 0 ) /specimen B/ plane. The spheres were abmt 50 urn i n

diameter. The specimens were sintered for 500 h. a t 1225K and 1220K , respectively.

When sintered, the spheres rotate in order t o minimise the energy of the boundary formed a t t h e i r necks. The f i n a l low energy orientations were determined from the {ill} Lextures of the specimens determined by typical X-ray techniques. The pole

figures where the textures a r e presented /J?ig.l/ consist of n m r o u s sharp maxima.

Identification of the l o w energy orientations reduces t o the deconvolution of the s e t of maxima into quartets. These quartets of maxima indicate the orientation of the 4 Ill1 7 planes of a group of equally oriented spheres. Further, the

orientation of the spheres was calculated and represented i n terr@s of misorientation of the grains o r of p a r a l l e l i t y of planes.

Results

The identified low energy misorientations are l i s t e d i n Tab.1,2,3. The experimental textures of the specimens A and B a r e ploted on Figs 1 a and b. Figs 2 a and b show the calculated positions of the maxima i f a l l the spheres rotated into orientations l i s t e d in these tables. About 70% of the m i m a could be unambiguously identified.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985408

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JOURNAL DE PHYSIQUE

Table 1

ow energy orientations of the spheres on the plates A and B E

3 9 11 33c

Table 2

Low energy orientations of the spheres on the plate A

33 ,34 very high I1 1 11 (1 1 51

31,32 high C1 1 51 C1 1 5)

91,92 11 1 5 ) G71 -71 .06)

93,94,95,96 {l 1 51 632 .45 -83)

11~12,13,14 (1 1 13689 .37 -263

15,16 (1 1 1%(.68 -68 .26)

A1 ,A2 medium (1 1 13Q64 -64 -421

orientation

34 31,32133 92,94,96 12,14,16 A2,A4,A6

Table 3

Low energy orientations of the spheres on the plate B m k e r

31,32,33,34 91,92,93,94

95,96

, ,

15,16 AI , ~ 2 , ~ 3 , ~ 4

average int-ity of the X-ray peaks very high

high medium medium medium

planes parallel t o the ( 111) or( 113 plane orientation

misorientation

planes parallel t o the (1 1 1) plane {l 1 11 11 1 51 (1 1 5 ) (1 1 17) (1 1 17)

average intensity of the X-ray peaks

angle 70.5 38.9 50.5 59.0

axis

[ oil] [ioil [Tiol [Go]

[ iio] [Tlol [i'il I ioil [Oll] [Oll]

[ 0111 10~11 [zoil [ioil [110] [110]

[ iio] [Ti01 [lei] [Tiol

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JOURNAL DE PHYSIQUE

Fig.2 a and b -Ell11 and [ I l O I p l e figures of the textures calculated with the assumption that a l l the spheres rotated into orientations listed i n Tab.1. The orientations can be identified by ccanparing the marker with the symbols i n Tab.1.

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Fig.3~-r(l 1 5), "33" ; Fig.M-(1 1 5) , "92" ; Fig.3e-(1 1 17), "16" ; Fig.3£-(17 12, "A2" ;

Fig.3q-(1 0 0 ) e f a c e ; Fig.3h- surface of a sphere on plate A i f it rot+& into the r 9 -38 - 9 ( 1 1 0) misorientation; Fig .3i- ideem for the t 11, -50.5 ( 1 1 0) misorientation.

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JOURNAL DE PHYSIQUE

Discussion

The low energy boundaries found in the present experiment form a s l ~ l l e r s e t than that generated basing on the coincidence /4,5/, plane matching / 6 / 1 or boundary periodicity /7/ rrodels. In fact, the a b v e c r i t e r i a are fulfilled by boundaries with a (100) or(l1UmLsorientation axis. In the present expriment only boundaries with a (110) misorientation axis were found t o be of l o w energy. These exprhm-ital results can be understood by examining the structure of the low energy bour.daries on the plate A.

The structure of the boundary i s determined by the structure of the surfaces of the crystals meeting a t the boundary. For the plate A the (1ll)surface meets the surfaces parallel to the planes listed i n Tab.2. These surfaces are puttedon Fig.3 a-f. The surface of the plate A i s c~nposed of close packed rows of at- extending along the three.

<

110) directions. Between these r m s of atoms there are parallel rows of holes. I n the rows of holes perfectly lock-in the edges of the steps on the surfaces ploted on Fig.3 b-f

.

The edges are parallel to the close packed (1lO)directions a s well. Atcans a t the edges of the steps p s s e s perfect l a t t i c e coordinates i n both grains. The structure of the surfaces plottedon Fig.3 c-f between the rows of atoms in coincidence positions i s identical t o that of the surface parallel to the (100)plane /Fig.3g/. Fig.3b show the surface of the boundary i f a sphere is i n coherent twin orientation. In that case each row of atoms i s i n coincidence. On the other h a d , even i f there are close packed rows of atoms in coincidence /Fig.3h-i/ but between these rows the surface of the second grain is not of the ~ ~ 1 0 0 ) t y p , the b o w is not found expxinaentally as low energy.

The low energy orientations for the plate B can be described according to the s m s c h e as above under the additional-condition that its surface is faceted into facets parallel t o the (111) or (111) planes. They can be interpreted a s a sumn of t w sets of orientations , each of thePn lent to the s e t of l o w energy

orientations of the plate A.

From the above described structure of low energy boundaries conclusions can be drawn for the factors controlling the grain bundary energy. It seems that it can be divided into t m terms. One is of "geamtrical" nature and i s related to the atomic mismatch a t the border of grains. Such a m i m t c h creates long range strain fields around the bmndary. It i s minimised when close packed rows of atoms are parallel. The second factor i s of "chemical" nature and depends on the interatomic interactions. The results obtained are consistent with the idea that the energy of an atom i n the boundary depends on its coordination n*, or i n other mrds, on the n* of "broken bonds"

.

Atams on the close packed { 111 1 and h00) surfaces have the lowest n m k r of broken bonds than on any other surface. Joining together such surfaces doesnot, howver, result in a l o w energy boundary. A Ebrther decrease of the energy is p s s i b l e by t i l t i n g the grain with the hoolplane parallel to the boundary so that steps are formed. The atoms on the edges of the steps gain additional bonds i f they perfectly lock-in i n appropiate holes i n the surface of the second grain. I n fact, forming a step mansbreakingtm bonds but lock-in in a hole i n the (1111 surface means a gain of three bonds.

Acknowledgnwt

The experbzntal part of the mrk was acconplished a t the University of Saarbrlicken.

One of the autors is very grateful1 t o the Alexander von Hmbldtfoundation for the ftmncial s u p p r t of h i s stay i n Saarbrlicken.

References

1.P.H.-hey, in: "Grain boundary Structure and Properties", G.A.Chadwick, D.A.Smith eds., Academic Press 1976, p.139

2 .H.Sauter, H-Gleiter, G.Wo, Acta Met. 3,467,1977 3.G.H.Henmmn1 H.Gleiter, G.E&m, Acta Met. 2,353,1976 B.M.L.Kronberg, F.H.Wilson, Trans.AIME 185, 501, 1949

5. W.Bo1Imnt-1, "Crystal Defects and crystal Interfaces", Springer, Berlin, 1970 6.P.H.Fmphey, Scripta Met.g,107,1972

7.H.Gleiter1 phys.st.s01.~,9,1971