8 Ultramicroscopy 30 (1989) 8-12 North-Holland, Amsterdam

M U L T I P L E STRUCTURES IN A • ffi 27 RELATED BOUNDARY IN GERMANIUM

David A. SMITH

IBM Research Division, Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598, USA

Z. ELGAT *

Department of Materials Science and Engineering, Bard Hall, Cornell University, Ithaca, New York 14853, USA

W. KR AKOW and A.A. LEVI

IBM Research Dioision, Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598, USA

and

C.B. CARTER

Department of Materials Science and Engineering, Bard Hall, Cornell University, Ithaca, New York, 14853, USA

Received at Editorial Office 6 December 1988; presented at Symposia August 1988

An observation consistent with the occurrence of structural multiplicity has been made by high resolution transmission electron microscopy of a 29 ° (110) tilt boundary in germanium.

1. Introduction

Recent progress towards an atomistic under- standing of grain boundary structure has involved insights from computer modelling [1-3], high reso- lution transmission electron microscopy [4-7] and X-ray diffraction [8,9]. It is a limitation of all three techniques that only rather simple, relatively short period boundaries can be investigated. How- ever, for this limited class of boundaries some consensus is emerging concerning the evolution of grain boundary structure as the angle of rotation, 0, about a particular axis is increased. The key insight for the present purposes came from a seminal paper by Bishop and Chalmers [10] who noted that symmetrical tilt boundaries for low-in- dex rotation axes were comprised (before relaxa-

* Now at Luz Industries, SBIC, Bldg. B, Bar-Hotzvim, P.O. Box 7929, Jerusalem 91079, Israel.

tion) of crystals bounded by mirror-related vicinal surfaces; for example, with a rotation axis [001] all symmetrical boundaries can be built by joining mirror-related crystals bounded by surfaces of the form (hk0) . This concept was explicitly devel- oped by Sutton and Vitek [11] in the context of calculated relaxed structures to become what is now referred to as the structural unit model. In essence the structure of all boundaries belonging to a particular set can be deduced from those of a limited number of short-period "delimiting" boundaries. An example, germane to the boundary, which is the subject of this paper, follows. The pioneering work of Hornstra [12] suggested that the symmetrical tilt grain boundaries with a [110] rotation axis in diamond cubic materials might be reconstructed in such a way that all atoms re- mained tetrahedrally coordinated. With this hy- pothesis very simple structures were suggested for those boundaries with 0 ° < 0 < 38.9 °. All grain

0304-3991/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

D.A. Smith et al. / Multiple structures in ~ = 27 related boundary in germanium 9

a b c

Fig. 1. The three units designated A, B and C which are characteristic of the (110) symmetrical tilt boundaries in di-

amond cubic materials for 0 o < 0 < 38.90.

boundaries in this range of angles consist of atoms coordinated according to four patterns. These are shown in fig. 1 and are, respectively, (a) crystal coordination, A-unit, (b) a column of 5- and 7- membered puckered rings which is the core of a Lomer dislocation, B-unit and (c) an alternate configuration of 5- and 7-membered rings which is the nonius of the ~ = 9, 38.9 °, (221) boundary, C-unit. The perfect crystal, 2? = 19 (331) and Z = 9 (221), boundaries are delimiting structures from which all other [110] symmetrical tilt boundaries with 0 ° < 0 < 38.9 ° can be created. Thus a sym- metrical tilt boundary with 26.5 ° < 0 < 38.9 ° con- sists of a mixture of B and C units. The propor- tion of the two kinds of units m of type A to n of type B depends on 0, or equivalently, for the special case of symmetrical tilt boundaries, the boundary plane, and satisfies the relation m(331) + n ( 2 2 1 ) = (h, h, l) for the boundary on (h, h, 1); m and n are integers. This concept is consistent with computer modeling and observa- tions in some metals and semiconductors [3-5,7,11,13]. It should be noted that the analysis presented above only predicts the proportions of the units, not their sequence. For long period boundaries there is the possibility noted by Vitek and Sutton [11] that two or more inequivalent sequences of units can satisfy the linear combina- tion rule given above.

2. Experiment

Oriented bicrystals with a (110) rotation axis were grown from oriented seeds using a modified Czochralski technique [16,17]. TEM specimens were cut from the melt-grown bicrystals, mechard- cally ground and then ion-mined for examination

in a Siemens 102 transmission electron microscope operated at 125 kV. In a (110) orientation at opt imum defocus high resolution micrographs, in this instrument, reveal the columns of pairs of atoms associated with each lattice point as char- acteristic single bright dots. Consequently the 7-, 5- and 6-membered puckered rings which are the key features of the structures shown in fig. 1 appear as 5-, 4- and 3-sided figures in the electron microscope image.

3. Observations

Fig. 2 is a high resolution electron micrograph of a tilt boundary in germanium. The rotation axis is very near to [110] as evidenced by the closely similar image contrast on both sides of the boundary. The rotation angle is deduced from measurements of the angle between {111} fringes across the boundary to be 29 ° . Locally the boundary is in the symmetrical (883) orientation; however, two segments in this orientation are sep- arated by a step which is = 2 nm in height. According to t h e structural unit description the symmetrical regions of the boundary are expected to be comprised of B-units and C-units (defined above) in the ratio 2 :1 ; note 331 + 331 + 221 = 883. This expectation was realized but with the result foreshadowed earlier that the linear com- bination condition was satisfied by two different sequences of units. Detailed analysis of fig. 2 shows that in region (1) the structure may be described as . . . BBCBBC. . . and in region (2) as . . . BBBCBC. . . ; these structures have been mod- elled using a program in which the atomic interac- tions are described by a Keating potential [3,14]. Fig. 3 shows the set of three relaxed calculated structures for the {883} symmetrical tilt boundary; the differences are simply in the sequence of B and C units. The structure shown in fig. 3c in which the structural unit sequence is . . . BBBBCC .. . has not been observed but is likely to be produced during grain boundary migration. Calcu- lations show that all the structures are stable and suggest that the internal energy of the bicrystal is only weakly dependent on the sequence of units. The internal energies calculated for the structures

10 D.A. Smith et al. / Multiple structures in ~ = 27 related boundary in germanium

Fig. 2. High resolution electron micrograph of a 29 * tilt boundary in germanium. The sequence of units in regions (1) and (2) are different although their proportions are the same.

shown in figs. 3a-3c are 688, 691 and 736 mJ m -2, respectively.

4. Discussion

It is significant that the energy of the grain boundary discussed here is rather insensitive to its precise configuration and that microscopically the boundary is never planar. It is a characteristic of (110) symmetrical tilt boundaries with 26.5 ° < 0 < 38.9 ° that the boundary plane is microscopi- cally facetted [15]. One interpretation of this result is to associate a DSC lattice dislocation (i.e. a perfect grain boundary dislocation) with each C- unit and to realize that the crystallography of the ~(331) DSC dislocation imposes a step on the {331} boundary plane characteristic of the Z = 19, 26.5 o delimiting boundary. The practical point is that migration of such boundaries inevitably re- quires the formation of non-planar configurations; thus migration of the {883} symmetrical boundary can be described in terms of the glide motion of DSC dislocations and the excess energy of some of the configurations which will be produced during this process is low. Presumably the elementary processes in the twinning-like migration of the present boundary are the nucleation and propa- gation of double kinks on the DSC dislocations.

In contrast, the classical view of the migration process would be the diffusion-like propagation of steps such as that separating regions (1) and (2) in fig. 2. The expectation of this view of boundary migration, as for a diffusional phase transforma- tion, is that the step riser is disordered [16]; this does not appear to be the case in fig. 2.

There is another interesting feature of the step in fig. 2; attempts to make a single model for all of the boundary in fig. 2 fail; in essence, the regions to the left and to the right of the step are relatively displaced by ¼1110]. If it is accepted that the structure determination is correct then it is most simply concluded that there is a dislocation in the region of the step which has a Burgers vector including a component ][110]; a 60 ° lattice dislocation parallel to [110] has the required crys- tallography. In the absence of such a dislocation the conclusion is that the structures of the two segments are profoundly different. In fact, the result is to propose that in one of the two seg- ments there exists 5-coordinated germanium. This proposal has certain precedents which are dis- cussed elsewhere [17]; the question of which inter- pretation is correct cannot be decided from the present data alone, but on the basis of Occam's razor the interpretation offered in this paper is favored.

O~

J

0 2

- 1

-1

2

1

0

- 2

- 2

D.A. Smith et al. / Multiple structures in ~ = 27 related boundary in germanium 11

4. 6 a

A •

2 4 6 b

8

r 8

0 T 2 ':" 4 6 8 "r

c

Fig. 3. Three calculated relaxed structures for a 29 ° ( < 1 1 0 ) symmetrical tilt boundary in the d iamond cubic structure. The sequences of structural units in (a), Co) and (c), respectively, are .. . BBCBBC . . . . . . . BBBCBC. . . and ... CBBBBC . . . . The first two sequences were observed in fig. 2 on the left and fight of the step respectively. The numbers on the frames enclosing the structures

express the scale in units of lattice parameters.

12 D.A. Smith et al. / Multiple structures in ~, ~ 27 related boundary in germanium

4. Condusions

High resolut ion t ransmiss ion electron mi- croscopy has provided direct evidence for struct- ural multiplici ty, of the k ind proposed by Sut ton and Vitek, in a tilt b o u n d a r y in germanium.

Acknowledgement

The por t ion of this work done at Cornel l was supported by D O E unde r grant No. DE-FG-02 - 84ER45092.

References

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