APPLICATION OF CONVERGENT BEAM ELECTRON DIFFRACTION TO GRAIN BOUNDARY STRUCTURE DETERMINATION

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APPLICATION OF CONVERGENT BEAM

ELECTRON DIFFRACTION TO GRAIN BOUNDARY STRUCTURE DETERMINATION

F. Schapink, N. Blom, S. Forghany

To cite this version:

F. Schapink, N. Blom, S. Forghany. APPLICATION OF CONVERGENT BEAM ELECTRON

DIFFRACTION TO GRAIN BOUNDARY STRUCTURE DETERMINATION. Journal de Physique

Colloques, 1985, 46 (C4), pp.C4-85-C4-88. �10.1051/jphyscol:1985407�. �jpa-00224656�

APPLICATION OF CONVERGENT BEAM ELECTRON DIFFRACTION TO GRAIN BOUNDARY STRUCTURE DETERMINATION

F.W. Schapink, N.S. Blom and S.K.E. Forghany

Laboratory of MetaZZurgy, Delft University of Technology, Rotterdamseweg 137, 2628 AL Delft, The Netherlands

Rdsum6 - Nous avons utilisg la technique de la diffraction des dlectrons

faisceau convergent pour dtudier la structure des joints de grains.

L'influence de la position d'un joint de macle, situs parallglement

la sur- face de l'bchantillon, sur les cliches de diffraction, est discutde. Aussi quelques rdsultats obtenus pour un joint de macle dans le siliciurn parallsle au faisceau dlQlectrons sont rapport&.

Abstract - Convergent beam electron diffraction has been applied for

determining grain boundary structures, both for horizontal as well as vertical boundaries in thin specimens. The influence of boundary location on the CBED pattern for a horizontal twin boundary is discussed, and some preliminary experiments on the pattern symmetry of vertical twin boundaries in Si are presented.

Convergent beam electron diffraction (CBED) is a very useful tool for crystal structure determination, as has been shown by various authors /1,2/. Recently we have applied this technique to the study of bicrystal structures in specimens containing a grain boundary parallel to the specimen surface

The symmetry of CBED patterns from such bicrystals has been correlated with.the point symmetry of bicrystals, from which the latter symmetry can be deduced. Using this method information on the structure of grain boundaries can be obtained, e.g. on the existence of a rigid translation at the boundary plane. In this paper we consider two topics related to the bicrystal symmetry problem: (i) the influence of a non- ideal boundary location in a thin specimen (i.e. the boundary plane does not coincide with the specimen mid-plane) and (ii) the symmetry of CBED patterns taken from a specimen with a vertical boundary (parallel to the.incident beam).

Effect of boundary location

Previously the symmetry of CBED patterns from bicrystals has been derived from a consideration of the effect of the specimen symmetry elements seen along the incident beam zone axis. Symmetry elements that leave the incident beam on the same side of the specimen were distinguished from symmetry elements that transform the beam to the opposite side of the specimen. The latter elements enter into the diffraction group (characterizing the CBED pattern symmetry) by virtue of the

application of the reciprocity theorem in electron diffraction 111. Symmetry in the CBED pattern as a result of such symmetry elements, however, only occurs when the boundary plane is coincident with the specimen mid-plane. In practice often deviations from this idea1,boundary location occur and the influence of such deviations on the CBED pattern symmetry should be investigated.

To this end a computer simulation program of CBED patterns from bicrystals has been

set up. Briefly, such a pattern is generated from a large number of plane electron

waves incident on the specimen, each wave being diffracted according to the scheme

provided by the N-beam dynamical theory of electron diffraction 151. The program

also has the option of taking absorption into account. Fig. 1 shows a comparison

between the (000) disc of a [ill] zone-axis pattern (ZAP) taken from a twinned (111)

Au crystal and a simulated pattern from such a bicrystal, assuming zero translation

for the coherent twin boundary and a boundary location coincident with the specimen

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Fig. 1. (a) Bright-field disc (100 kV) of [ I l l ] ZAP from twinned Au crystal (negative print). (b) Simulated pattern, angle of convergence 3.5 mrad.

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Fig. 2. Simulated bright-field of [Ill]

ZAP similar to fig. Ib with boundary located at 0.6 of specimen thickness.

Fig. 3. Schematic representation of bicrystal with vertical boundary.

Incident beam is located at

boundary plane.

a satisfactory agreement between both patterns exists, considering the

approximations involved in the simulation. Upon shifting the twin boundary position in the crystal the bright-field symmetry decreases from 6 mm to 3 m as is

demonstrated in the simulated pattern in fig. 2, where the boundary is located at 0.6 of the specimen thickness. Thus, in determining bicrystal symmetry from CBED patterns the location of the boundary plane should be taken into account, and the CBED pattern symmetry classification presented previously / 3 / only holds when the boundary is located close to the specimen mid-plane.

CBED patterns from vertical boundaries

Frequently boundaries in thin specimens are oriented (nearly) perpendicular to the surface, hence it is important to analyse CBED patterns for this boundary

orientation, see fig. 3 . In order to correlate the effect of various symmetry elements on the symmetry present in the CBED pattern, one has to consider separately those symmetry elements that leave the bicrystal invariant and the symetry elements that transform z into -z (fig. 3). The detailed consideration of these effects, from which the correlation between the diffraction groups and the bicrystal point

symmetry for a vertical boundary emerges, will be presented elsewhere. Here we will discuss one example, that of a vertical coherent twin boundary in a silicof! specimen with a [I101 surface normal. When the incident beam is along the common [I101 zone axis of the bicrystal, the point symmetry of the bicrystal specimen seen down this axis is mm2 when there is no translation at the vertical boundary. One mirror plane is produced by the (111) boundary plane, which is a mirror plane itself relating matrix ancj twin in the bicrystal, whereas the second mirror originates from the common (110) planes parallel to the surface in the bicrystal. A rigid translation of the crystals parallel to [ I l l ] would not change this symmetry, since such a translation does not destroy the-mirrorplanes considered here. Fig. 4 shows the bright-field of a large angle [I101 ZAP taken in the conventional TEM mode 161, with the vertical boundary running through the centre of the pattern. It can be seen that this boundary is a mirror line in the pattern. However, from the mm2 bicrystal symmetry indicated above the symmetry of the bright-field ZAP is expected to be 2mm which is not found experimentally.

Different reasons may exist for the origin of the difference between theoretically expected and observed symmetries for the vertical twin boundary. First of all, it is unlikely that the lower symmetry is caused by a tilt of the specimen, since the surface normal was only a few degrees away from the [I101 zone axis. It is thought that the major cause is the following. In the derivation of the interrelation between bicrystal symmetry and CBED pattern symmetry an idealized geometry for the incident convergent beam has been assumed, i.e. essentially zero beam diameter.

However, in practice a relatively large beam diameter (say, of the order of 10 vm) occurs, especially in a large-angle ZAP. For a vertical boundary, with the incident beam centred as indicated in fig. 5, this means that the M and T crystals meeting at the boundary are illuminated by different sections of the incident beam cone, i.e.

these regions see different incident beam directions. Consequently, horizontal synmetry elements existing in a bicrystal specimen (such as the (110) mirror planes for the vertical twin boundary) will disappear in the pattern, since the application of the reciprocity theorem followed by the symmetry operation of the horizontal symmetry element correlates different incident beam directions on the same ^{side of}

the bicrystal specimen (e.g. the M side in fig. 5).

Finally fig. 6 shows a [ I ~ o ] ZAP-similar to fig. 4, for a faceted twin boundary in Si,-the facets consisting of (112) and (111) segments. It appears that for some (112) segments the intensity distribution across the boundary is not continuous;

whether this phenomenon is related to a rigid translation existing at these facets remains a subject of further investigation.

Conclusions~

CBED has been shown to be a very valuable tool for the determination of bicrystal

symmetry, and hence of grain boundary structure. For a horizontal boundary, the

effect of boundary location in the specimen should be taken into account. In the

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case of a vertical boundary several aspects of the patterns obtained so far have to be further elucidated.

Acknowledgement

This work is part of the research program of the Dutch Foundation for Chemical Research (SON) and has'been made ~ossible by financial support from the Netherlands Organixation for the Advancement of Pure Research (ZWO). Thanks are due to

Dr. Y.S. Oei for providing the Si specimen.

References

1. BUXTON B.F. et al., Phil. Trans. Roy. Soc., London, A281 (1976) 171.

2. GOODMAN P., Acta Cryst. A31 (1975) 804.

3. SCHAPINK F.W., FORGHANY S.K.E. and BUXTON B.F., Acta Cryst. A39 (1983) 805.

4. BUXTON B.F., FORGHANY S.K.E. and SCRAPINK F.W., Inst. of Phys. Conf. Ser. No. 68 (1984) 59.

5. HUMPHREYS C.J., Rep. Progr. Phys. 42 (1979) 1825.

6. FUNG K.K., Ultramicroscopy 12 (1984) 243.

1 7

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, -

Fig. 5. Schematic illustration

of large-angleconvergent beam on specimen with vertical twin boundary.

m indicates mirrorplane.

J _r

Fig. 4. Bright field large-angle [ I ~ o ] ZAP of Si crystal with vertical twin boundary.

Arrows indicate trace of ( I l l ) boundary plane.

Fig. 6. Bright-field [ I ~ o ] ZAP, similar to fig. 4, from faceted twin boundary.

Frame identifies facets.