Partial dislocations in the wurtzite lattice

J. Phys. Chem. Solids

Pergamon Press 1971. Vol. 32, pp. 1521-1530.

PARTIAL

DISLOCATIONS IN LATTICE

Printed in G r e a t Britain.

THE

WURTZITE

YU. A. OSIPYAN and I. S. SMIRNOVA Solid State Physics Institute of Academy of Sciences of the U.S.S.R., Chernogolovka, U.S.S.R.

(Received 14 July 1970; in revised form 12 September 1970) Abstract--The analysis has been carried out of the hypothetically possible types of partial dislocations and stacking faults in the wurtzite lattice. The models are made up of the atom arrangements in the cores of the partial dislocations both bordering the stacking fault and being formed in the process of splitting of the perfect dislocations. The possible types of the dislocation reactions are considered between the partial dislocations, as well as between the partial and perfect dislocations. INTRODUCTION

THE EXPERIMENTAL discovery of the stacking faults in the crystals having the wurtzite lattice testifies to their comparatively low energy. The investigations of the stacking faults in the wurtzite type crystals were made by different methods: the X-ray diffraction[ 1-4], the transmission electron microscopy [5-13], the moire fringes[14]. All the workers observed the stacking faults both in basal (0001) and prismatic (1120) planes. Drum[9] and Fitzgerald and Mannami[14] carried out a thorough study of the stacking fault displacement vectors and proved that in basal planes the stacking faults have the displacement vector -~[2023] and those in prismatic planes have the displacement vector 89 Chikawa[4] observed a Shockley dislocation in plane (0001) in CdS with the Burgers vector k[10T0]. Similar dislocations were also observed by Blank e t at.[8]. We found it reasonable we have made an analysis of the hypothetically possible dislocations in the wurtzite lattice, constructed models of the atom arrangements in the cores of these dislocations and considered the possible dislocation reactions. 1. THE STACKING FAULTS AND PARTIAL DISLOCATIONS

The Stacking faults in basal planes of the wurtzite are similar to the corresponding

faults in the face centered cubic f.c.c, and the close packed hexagonal structures. The difference is that in the wurtzite (as well as in the sphalerite) a stacking fault of double layers must be considered. Let a, b, c be the atoms of metals and A, B, C - r e p r e s e n t the atoms of a non-metal. Hence, the wurtzite structure can be represented by means of the symbol sequence ........

aAbBaAbBaAbBaAbB

........

which are packed normal to the [0001] direction. By the same designation, the sphalerite structure is . . . a A b B c C a A b B c C a A . . . The intrinsic stacking fault can be obtained by removing a double layer of atoms and subsequent closing up of the remaining layers. Here, a shear is to be necessarily produced by the value of~.[0223] so that a pair of layers b B will transit into c C , and layers a A into b B , i.e . . . . a A b B a A b B c C b B c C b B c C . . . It should be noted that for the wurtzite structure there are two possibilities leading to the same stacking fault, that is, removing of a double layer from distant atoms of the a A type (as it is usually done for the diamond and sphalerite lattices) and removing of a double layer from neighbouring atoms of the A b or B a types. Removing of an A a results in breaking of 3 chemical bonds per atom while removing of an A b-- in one bond per atom 1521

1522

YU. A. OSIPYAN and I. S. SMIRNOVA

only, which means that from this point of view r e m o v m g of an A b or Ba is more favourable energetically. This version is being considered now. In Fig. l(a) such a fault is shown. The sphalerite layer is given in thick lines. Evidently, such a defect, if it terminates inside the crystal, must be bordered by partial dislocations on both ends. In this case, the Burgers vector of such a dislocation does not lie in the plane of the violation and according to the established terminology this will be a F r a n k partial dislocation. It is clearly seen in the figure. Its axis lies in the [2110] direction. It is also seen that such dislocations are polar and can be of either a or/3 configurations. A similar fault, which is also bordered by a Frank partial dislocation, can be produced by means of introduction of a corresponding double l a y e r A b or Ba. In Fig. 1(b) such a fault

and a bordering F r a n k partial dislocation with the Burgers vector ~[0223] and axis, lying in the [2110] direction, are shown. If a F r a n k partial is to be produced with the axis lying in the [1010] direction, its core structure will be quite different, the dislocation is non-polar, as is seen from Fig. 2. The core structure is likely to be the same irrespectively whether the dislocation has been obtained by means of removing or introducing of a double layer.

--4" []zTo]

t,T~o-

j [ei~o]

Fig. 2. Frank dislocation with axis [1100] and ~[2203].

[~2To]

/

/

[2iio]

' -

/

-

-

- ! , . -

[TzTo]

/

[2iTo] Fig. 1. Frank dislocation with axis [2110] and b = [2023] (a) removing of a layer (b) introducing of a layer.

b=

A fault of another type can be produced as a result of slip in a basal plane. F o r convenience, the basal plane between the distant layers will be referred to as B1, and the basal planes between the neighbouring l a y e r s as B2, the prismatic plane of the kind II is P~ (Fig. 3). F o r m e r l y considered[15] perfect

~

/

~

_

-

_

7 Bj

/ [2Tro] Fig. 3.30 ~Shockley dislocation in a basal plane Sh1B.

THE ~)~JRTZITE LATTICE

dislocations in the wurtzite lattice were obtained during slip in the basal planes of the B1 type. During slip in the basal planes B2 imperfect dislocations can be produced. The following sequence of layers is obtained during the shear along B~ into the k[10T0] vector . . . A a A b B a A b B c C a A c C a A c C If such a fault is limited inside a crystal, it must be bordered by a partial dislocation, that is a Shockley dislocation (Sh.D.). In particular, the Burgers vector of the dislocation shown in Fig. 3 is k[10T0], its direction is [21--10]. Similar to the classification of perfect dislocations, Shockley dislocations can also be distinguished by the angle between the axis and the Burgers vector. In Fig. 3 the 30 ~ Shockley dislocation is given. As is seen, its core is a homoatomic row with broken bonds and, therefore, can have a and/3 configurations. Its glide plane is B2. In Fig. 4 the Thompson's model is given with designation of the Burgers vectors of the . . . .

1523

dislocations. The vectors of the AC, DE, types are the vectors of perfect dislocations. The Shockley partials have the Ao., Bo., Co" vector types in a basal plane. The vectors of the EA type are the Burgers vectors of Frank dislocations. It can be seen by the figures that formally, the 4 types of Shockley dislocations can be produced, with the angles between the axes and the Burgers vectors of 30 ~ 90 ~ 0 ~ and 60 ~, respectively. The core structures of the dislocations that border a simple stacking fault are being considered now. The pattern of a Shockley edge partial dislocation is given in Fig. 5. Its core consists of two parallel homoatomic rows with one broken bond per atom. On the opposite side of a stacking fault (shown in heavy lines) another partial dislocation is lying having the analogous core, consisting of atoms of different type, though. The Shockley screw dislocation is shown

[i~o]

[2

Fig. 4. Thompson's model for the Burgers vectors of partial dislocations in the wurtzite lattice.

1524

YU. A. OSIPYAN and 1. S? SMIRNOVA

(a)

5 Fig. 5. Two edge Shockley dislocations with opposite signs.

in Fig. 6 (drawn in heavy lines). In the fore[b) ground is the sphalerite structure, in the background behind the dislocation, is the Fig. 7. 60 ~ Shockley dislocation in basal plane of the opposite sign. wurtzite. The dislocation axis lies in the [0110] direction, the Burgers vector is k[01]-0], of atoms of different type. Here (Fig. 7(b)) respectively. single atoms and pairs of atoms with one Naturally, the mobility of this dislocation broken bond alternate along the dislocation is limited by the faulting plane, i.e. the basal line. plane, unlike the perfect dislocations. Figs Now, let us consider the stacking fault lying 7(a) and 7(b) show the cores of the two 60 ~ in the prismatic plane of the kind I l-Pz (2110). dislocations of the opposite burgers vectors, The shear with the EF type vector is possible that limit the stacking fault on both ends. They (seeFig. 4). The defect of this type is pictured are different. One of the dislocations (7-a) in Fig. 8. It can be bordered by the Sh.D. with is a homoatomic row with three broken the 89 vector along the C axis. (Fig. 8). bonds. Evidently, the energy of such an The dislocation is non-polar. Along the [1010] atomic configuration can be considerably direction, the stacking fault in P2 can be bordecreased by means of a break-away of these dered by the Sh.D., pictured in Fig. 9. The atoms and removing them by diffusion. At the dislocation is also non-polar. opposite end of a stacking fault, the 60 ~ dislocation is located of which the core consists

b

9

[T2To]

l

~-"[6,~o] [2T/o]

Fig. 6. Screw Shockley dislocation in basal plane Sh3n.

/ [ooo,] /

~-

_... [o,To]

/

Fig. 8. Stacking fault in prismatic plane of the kind 11 bordered by Sh.D. with glide plane (2TT0), l-axis, bBurgers vector Sh,p...

THE WURTZITE ,LATTICE

15-25

sist of the close packed double layers 0_,4, bB, cC have some specific features associated with the fact, that glide can occur in the two types of the parallel basal planes B1 and B2 (see Fig. 3). The nucleation and motion of the perfect dislocations occur between distant layers in the planes of the BI type, while their splitting and motion of the partial dis/ / locations occur between the neighbouring J layers in the basal planes of the B2 type. As it turns out to be, the core structure of Fig. 9. Shockley dislocation with glide plane (2110), the partial dislocations, obtained by splitting axis l01]0] b = ~[0223]SH2e~. of the perfect dislocations and the structure of similar to them partial dislocations, which Unlike the basal Shockley dislocations, b o u n d the simple stacking fault, can differ these dislocations have the same glide plane " sufficiently in spite of the fact, that both their as the corresponding perfect dislocations. Burgers vectors and dislocation direction are similar. This creates the specific character of 2. SPLITTING OF PERFECT DISLOCATIONS I N the situation, connected with non-coincidence THE WURTZITE LATTICE of planes B1 and B~. This will be seen in the The perfect dislocation in the wurtzite figures below. structure, lying in the basal plane (0001) can Another cause of difference in the core split into two partial Shockley dislocations, structure of dislocations of the same type is separated by a stacking fault, for instance, that splitting of the perfect dislocation, lying according to equation in the B1 plane, can also occur in the B2 t~pe plane, that lies either lower, or above the B1 .~[ 121 O] = 89 -I- ~[01TO]. plane. In such cases different cores can also be nucleated. Here are being considered the splittings of some known types of the perfect basal dis- 2.1 Splitting of the 60 ~perfect dislocation lo~:ations (see[15]) and the types of Shockley Figure 10 pictures splitting of the 60 ~ perpartial dislocations, originating as a result fect dislocation into two Shockley partials, of this process. The wurtzite and sphalerite one is the edge, another is the 30 ~ dislocation, structures under consideration, which con- in accordance with reaction AB ~ Ao'+B~r

,~___... [o,To] [ooo~]

< <

~ 8

(b)

Shse

(d)

Shza

Sh7B

(f)

Sh, e

(a) (c)

Sh6e

(e)

Sh2B

Shee

(g)

Fig. 10. Possible version of splitting of perfect 60 ~ dislocation into partials.

Sh

Je

1526

Y U . A. O S I P Y A N

(Fig. 10(a)). Then, the two types of splitting are shown i,n schematic drawing, when the plane of splitting lies below (10(b)) and above (10(c)) the plane of the perfect dislocation location. In this connection, four versions of splitting can be realized, which are seen in Fig. 10(d). Now, the structures of the partial dislocations, nucleated during this process are being considered. If, in accordance with the drawing 10(b), the edge partial Sh2B is being split, in place of the 60 ~ perfect dislocation, the 30~ is formed. The core of this 30 ~ Shockley is different from the core of the above considered corresponding ShlB (see Fig. 3). This new formed is the ShsB. Its structure is seen in the left-hand side of Fig. 10(d). The core consists of the parallel homoatomic rows, each atom having one broken bond in one row and two broken bonds per atom in another row. If the row, having two broken bonds per atom is to be removed from the core (by diffusion, for instance) then, the atoms remaining in the core, can realize the configuration without broken bonds. The corresponding version according to the drawing 10(c) shown in Fig. 10(e). Here, the dislocation Sh2B also splits, the new 30 ~ Shockley dislocation being formed-She8. Its core consists of 3 parallel rows of atoms in two planes with one broken bond per atom. T w o homoatomic rows lie in the upper double layer, and row, consisting of atoms of different type, lies in the lower layer. By

and I. S. S M I R N O V A

means of extra elastic displacement, one of the upper rows can be chemically closed up with the lower one, which sufficiently decreases the number of broken bonds in the core. In case of splitting the 30 ~ dislocation ShlB type, two new types of Shockley partial edge dislocations ShTB (Fig. 10(f)) and Shah (Fig. 10(g)) are to be formed (compare with Sh2B).

Whether it is possible or not to form covalent bonds between homogeneous atoms and double bonds between heterogeneous atoms, this point is important for energetic stability of the mentioned and subsequent dislocations. If there are such possibilities, sometimes with removal of the atom row off the dislocation core taken into consideration, the interlock of broken bonds can be realized, which sufficiently decreases the chemical energy of the dislocation core. This question is likely to be answered after the detailed quantum-mechanical calculations. In this connection we shall not judge by the number of broken bonds obtained, whether the splitting is advantageous or disadvantageous, but confine ourselves to listing the structures of the dislocations obtained. 2.2. Splitting o f a screw dislocation According to the vector drawing in Fig. 1 l(a), the two types of splitting of a screw perfect dislocation into two 30 ~ partials can be seen. At first approximation, the cores of both dislocations are similar (see Fig. 11 (b) the ShlB type). They somewhat differ in

B

Shje Co)

Shls (b)

Fig. 1 I. Splitting of a screw perfect dislocation.

THE WURTZITE LATTICE

character of their screw component, but this is not seen from the figure. ,Naturally, their polarity (04/3) is different. 2.3 Splitting o f 30 ~ dislocation The perfect 30 ~ dislocation in a basal plane can split into two Shockley dislocations, of which one is of a screw type, the other is the 60 ~ (Fig. 12(a)). If the shear o'B is to be produced in plane B2, the stacking fault occurs, which is bordered by an ordinary

A

(o)

Sh9e

Shloa

Shlla

(b)

(c)

(d)

1527

screw partial Shockley dislocation the Shzn type on one end, and a new 60 ~ Shockley dislocation, the ShgB type appears on the other end. Its core is shown in Fig. 12(b). Splitting of the 30 ~ perfect dislocation results in formation of four types of new partial Shockley dislocations. This happens due to the fact, that (a) splitting can be produced either above or lower the plane of location of the perfect dislocation and (b) the shear can be of trB or Ao"type. Along with the above mentioned ShgB, the 60~ Shl0n and two types of the screw Sh~IB and Sh12B are produced (Fig. 12(c, d, e), respectively). The dislocations Sh~IB and Sh12B are no longer the screw ones in the usual sense, because they have broken bonds. It should be pointed out, that during splitting of the 30 ~ dislocation into the screw and 60 ~ ones (Fig. 10(b) and (c)) the number of broken bonds do not increase. As for Fig. 12(d), here the number of broken bonds can also be decreased by means of removing of the atoms with three broken bonds and further interlock of bonds of atoms 1 and 2. :i~ 2.4 Splitting of an edge dislocation It can be realized with the formation of a stacking fault, bordered by the two 60 ~ Sh.D. As a result of this process the two new types of Shockley dislocations --ShI3B and Sh 14n (Fig. 13(b, c)) with a great number of broken bonds are produced. The atomic configurations in the core of both types are rather complex. To conclude the above said, the considered partial dislocations are given in Table 1. 3. PARTIAL DISLOCATIONS REACTIONS

3.1 Reactions between partial dislocations

Sh12 e

(e)

Fig. 12. 4 types of partial dislocation configurations, which occur during splitting of 30~ dislocation.

Figure 4 represents the totality of the Burgers vectors of the partial dislocations in the wurtzite lattice. The totality is as such: 6 vectors ___Ao" t y p e - t h e Burgers vectors of basal dislocations, the Shockley type. 6 vectors _ E C t y p e - t h e Burgers vectors of the Frank dislocations.

1528

YU. A. OSIPYAN and I. S. S M I R N O V A

Table 1. N

A

(a)

Shl3 ~'

8

$hl4 B

(b) Fig. 13. 2 types of partial dislocation configurations+ which arise at splitting of edge perfect dislocation.

12 vectors _+EF type-- the Burgers vectors of the Shockley dislocations, lying in the prismatic planes of the 11 kind. At such a set of the burgers vectors, 465 geometrical combinations prove to be possible, which reflect interactions of the dislocations under consideration. In Table 2 are summed up the most interesting reactions, advantageous from the view point of energetic balance. The reaction type (I) means interaction of the two Shockley dislocations, of which, the Burgers vectors form a sharp angle. As a result, a new Sh.D. occurs. The reactions types (2) and (3) describe interactions of Frank and Shockley dislocations. As a result, a new sessile dislocation is formed, with a Frank defect on one end and a Shockiey defect on the Other end.

I. 2. 3. 4. 5. 6. 7. 8. 9. 10. II. 12. 13. 14. 15. 16. 17. 18.

Dislocation

Axis

Frank (2]70) Frank (IT00) Shockley-30 ~ (21~-0) Shockley-90 ~ (21-1-0) Shockley-O~ (10T0) Shockley-60 ~ (1100) ShockleyShockley Shockley-30~ Shockley-30~ Shockley-90~ Shockley-90 ~ Shockley-60 ~ Shockley-60 ~ Shockley-O~ Shockley-0 ~ Shockley-60 ~ Shockley-60 ~

(1To0) (0001) (0110) (21--[0) (21-]-0) (21~-0) (21--]0) (1]-00) (1i-00) (10T0) (1010)

(ITO0) (1100)

Burgers vector

Type

Fig.

~(0223) ~(2203) 89 .~(01T0) :~(10T0) .~(01T0)

F, F2 Shjn Shz, Sh:,:~ Sh4.,3

la, b 2 3 5 6 7a

Sh4u Ship.. Shzt,= k(1T00) Sh~t~ 89 Sh6, 89 Shrn ](01T0) Shsn 89 Sh,,a 89 Shl0.,~ 89 ShHu .~(10]-0) Sh~...,j ~(01]0) Sh~a8 :~(01T0) Sh,4A

"(oTIO) 89 89

7b 8 9 10d 10i 10f 10g 12b 12c 12d 12e 13b 13c

The third group of the reactions deal with interaction of Frank defects. These reactions are likely to be interpreted this way: as a result of growth there can occur complex configurations from Frank defects, with different burgers vectors. In between, sessile dislocations will be lying, with the Burgers vectors, pointed out in reactions [4-6]. The fourth group of the reactions describe interactions of the basal Sh.D. and Sh.D., which lie in the prismatic plane of the II kind. The reactions (7), (8) result in formation of a dihedron of stacking faults, between the (1210) type and (0001) basal plane. Along the vertex of this z/ngle there forms a stair rod dislocation with the (01T0) type axis and the Burgers vector ~[T103] in case of reaction (7) and [1323] in case of reaction (8). The group 5 corresponds to interaction of Frank defects, lying in a basal plane and defects, lying in prismatic planes. Exactly such dihedrons have been repeatedly observed in the experiments. In particular, Drum[9] observed a stair rod dislocation, corresponding to reaction ( I 0). The group 6 deals with interaction of the

THE WURTZITE LATTICE

1529

Table 2. Reactions between partial dislocations Group

N

Type reactions

I

1

.~[OlTO] +k[TOlO] =. 89

ii

2

~,[0-523]+ 89

Phys. sense of reactions Formation o f a n e w dislocation

3 4 111

5 ~:6

IV V VI

7 8 9 10 11 12 13 14

Formation of a sessile disloc. /,[0_523] +.k[10T0] = ~[2_503] Formationofa sessile disloc. ~[0223] + 88 = 89 Formation of a sessile disloc. /,[022~3-]+/,[02_53] = ~-[01]-0] Formation of a sessile disloc. ~/,[0223] +/,[9-5023] = ..-}[TI00] Formation of a sessile disloc. 89 ] + ~[ I]-00] =/,[]-103] Stair rod disloc. 89 ] + ~[ 10]-0] =/,[1323] Stair rod disloc. .4[]-101] +/,[0223] = ~[3120] Stair rod disloc. 89 +~[2203] = ~[]-100] Stair rod disloc. ~}[]-101]+~[2023] =/,[5320] Stair rod disloc. 89 +89 = [0001 ] Perfect dislocat. 89 +89 I1 = 89 Y~b,= 0 89 ] +89 10I-]-] -----89 Stair rod disloc.

Shockley dislocations l,ymg in the prismatic planes of the kind II. Reaction (12) corresponds to interaction of the two Sh.D., lying in the same plane. As a result of this interaction, a sessile dislocation is being formed, with the Burgers vector [0001] stacking faults with different displacement vectors lying on both ends of this dislocation. It should be noted that as a result .of the reaction of the two Sh.D. the Sh2p2 type, an edge dislocation is formed while a screw type dislocation occurs in case of the dislocations the Ship2 type. Reactions (13) and (14) describe the two types of stair rod dislocations as a result of formation of a dehedron of stacking faults Reaction (13) results in formation of a dislocation with the [0001] axis and the Burgers vector b = 89 reaction ( 14)-the [0001] axis and b = 89 respectively.

= 89

of the Burgers vectors is being considered: 6vectors• i = 1,2,3 2 vectors • e type 6 vectors • type 12 vectors • AE type 12 vectors • EF type. In Table 3; the 240 physically non-equivalent combinations are given, which are advantageous fiom the view point of energetic balance. From the view point of the elastic energy decrease, reaction (I) is energetically advantageous. It can reflect the following process. The perfect dislocation with the Burgers vector the type (Fig. 4) AB splits into two Shockley partials AB ~ Ao'+o'B, then, one of the new-formed dislocationsjannihilate with the other Sh.D. of the opposite Burgers vector, which participates in the initial reaction. As a result, one Sho~ckley partial remains, All + Bo = Ao" + o'B + Bo" --~ Ao'.

3.2 Reactions o f partial and pelfect dis-

locations Below, the following totality of totality

It should be noted that only basal perfect dislocations can participate in such a reaction,

1530

YU. A. OS1PYAN and I. S. S M I R N O V A

Table 3. Reactions o f partial and perfect 9 dislocations N 1

Reactions 89

+ { [ 1 0 ] 0 ] = ~[T100]

2

~-[2110]+~[2023]=~t[2203]

3

[0001] +-~[022-3] = ~t[0223]

4 5

89

+ 89

[0001] + 89

= 411123] = 89

Phys. sense of reactions Splitting with annihilatibn of partials of different signs. Formation of a sessile dislocation. Splitting with annihilation of partials of different signs. Formation of a sessile dislocation. Formationofa sessile dislocation.

(a)

(b)

because the dislocations, lying in the prismatic plane of the kind 1 --P1, and having the Burgers vector cannot split with violation of a stacking parallel to the basal plane. Reaction (2) describes the interaction of a perfect dislocation with the Burgers vector a~ and a Frank defect. As a result of this reaction, a new sessile is formed. Reaction (3) deals with the interaction of a Frank defect and the perfect dislocation, lying in the prismatic plane of the kind I or the kind II, during its interaction with the basal plane. A sessile is formed. Reaction (4) is of major interest. It describes energetically advantageous formation of a sessile dislocation. In particular, it can occur between the 30 ~ basal perfect dislocation and a Shockley partial the Sh2e2 type. Another example of this reaction is interaction of a perfect dislocation with the C axis and the Burgers vector a~, in the prismatic plane of the kind I - P 1 (Fig. 14a) and a partial Shlp~ type. As a result of this reaction, on one end of the stacking fault a sessile is formed of which, the pattern is given in Fig. 14(b). Its axis lies in the C direction, the Burgers vector is ~[1123]. On the other end of the stacking fault, a routine partial Shle~ lies. Reaction (5) similarly to reaction (2) results in formation of a sessile dislocation.

$h

~P2

Fig. 14. Sessile, which occured after splitting of edge dislocation with violation of stacking non-parallel to the glide plane.

Acknowledgement-The authors Malygyn for help in drawing.

are grateful to G.

REFERENCES

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