DISLOCATION DIPOLES IN MgO

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DISLOCATION DIPOLES IN MgO

J. Washburn, Th. Cass

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C 3, suppliment au no 7-8, Tome 27, juillet-aozit 1966, page C 3-168

DISLOCATION DIPOLES IN MgO

J. WASHBURN

**C*)**

and Th. CASS (+)

Inorganic Materials Research Division, Lawrence Radiation Laboratory University of California, Berkeley California, 94 720

R6sum6.

-

On decrit des observations faites en microscopie electronique par transmission, sur des sections suivant le plan de glissement (1 10). Parmi les avantages de cette orientation des lames, on note que : 1) les forces images produisent moins de changement des sous-structures de deformation ; 2) il est possible d'observer des dislocations longues de plusieurs microns de toutes orientations ; 3) les conditions de contraste de diffraction sont relativement simples.

La formation de dipales courts ou de boucles de dislocation allongees, et de dip6les 5 longues interconnexions s'explique par un modkle simple. On remarque que les deux dislocations d'un dip6le s'annihilent, pour les dipales d'orientation vis, seulement si leur distance est inferieure a une valeur critique. On a constate, d'aprks une estimation de cette distance critique, que la force de frottement pour un glissement [l001 est 35 fois plus grande que pour un glissement [110]. L'existence de dipales de types interstitiel et lacunaire est mise en evidence de faqon indubitable par le contraste de diffraction.

Abstract.

-

Transmission electron microscopy observations on (1 10) slip plane sections of deformed magnesium oxide are described. Among the advantages of this foil orientation are :

1) less change in deformation substructure due to surface image forces; 2) the possibility of obser- ving dislocations many microns in length and of any orientation; 3) relatively simple diffraction contrast conditions.

The formation of both short terminated dipoles or elongated closed loops of dislocation and long interconnected dipoles is explained by a simple model. It is pointed out that the two dislocations of a dipole will cross-slip and annihilate when the dipole is in screw orientation only if the spacing is below a critical value. From an estimate of this critical spacing the stress for (100) glide is found to be 35 times higher than that for (110) glide. The model also explains other observed features of the dipoles such as position junctions and the correlation between length and spacing. Unambiguous diffraction contrast evidence is presented for the existence of both interstitial and vacancy type dipoles.

1. Introduction.

-

For a wide variety of materials the increase in dislocation density associated with single slip is predominantly in the form of long dipoles and small elongated closed loops rather than single dislocations o r pile-ups. Their discovery has been one of the exciting results of transmission electron microscopy. This type of deformation substructure was first clearly revealed in magnesium oxide [l].

Subsequently it has been shown that dipoles cons- titute a major part of the deformation substructure in other non-metallic crystals and, after easy glide deformation; in metals [2 to 51.

The various ways in which dipoles may be formed and terminated to give closed loops of dislocation

(*) Department of Mineral Technology, College of Enginee- ring, University of California, Berkeley, California.

(+) Presently at Universitb de Paris, Service de Physique des SoIides, Orsay 91.

have been widely discussed [5 to 91. I t is the purpose of this paper to consider how well it is now possible to account for the detailed arrangement and fine structure of dipoles in magnesium oxide as revealed by recent experiments. For these latest observations deformed magnesium oxide crystals were sectioned parallel to an active glide plane [10]. In (110) foils it was possible to follow individual dislocations and dipoles for distances of many microns without their running out a t a foil surface. The advantage of a slip plane section over any other foil orientation is some- what like the advantage of being able to see a picture as a whole rather than trying to visualize it after having been presented with thin strips cut from it a t random. For materials having the sodium chloride structure, cutting specimens parallel to (110) also minimizes the tendency for surface image forces t o change the arrangement of dislocations during thin-

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DISLOCATION DIPOLES I N MgO C 3 - 1 6 9

ning because dislocations can glide easily only in the plane parallel to the surfaces. The marked changes that may occur for other foil orientations, even in magnesium oxide in which dislocations are less mobile than in metals, are illustrated by the slip band shown in figure 1. The glide plane in this (100) foil is at 4 5 O to the plane of the surfaces. Where the thickness becomes small image forces have caused dipoles to slip out of the foil and all remaining dislocations have been rotated into screw orientation.

foil and the (110) plane at right angles to b gives rise to a strong 220 diffracted beam. So as to be able to take better advantage of these relatively uncomplicated diffraction conditions in deducing the detailed arrangement of dislocations from the observed images, calculated image contours were obtained [l l ] from a computer program based on the dynamical theory of Howie and Whelan [12]. Dipoles of various spacing, position, orientation, and depth in the foil were consi- dered. One result of the calculations was an estimate of the minimum separation between the two dislocations of a dipole below which there would not be sufficient diffraction contrast to make the dipole visible. It was concluded that this limit is about 6 b for a dipole that is centrally located in the foil.

2. - Description of dipole substructure in deformed magnesium oxide.

2.1 CHARACTERIZATION OF DIPOLES.

-

Necessary

parameters for the characterization of dipoles are illustrated in figure 2. The two types shown in (a)

I

I n t e r s t i t i a l I

FIG. 1. - Slip band in a MgO crystal deformed at room

temperature. As the foil becomes thinner, the observed substruc- d - Posit~on ture is less respresentative of the bulk crystal.

\

Another important advantage of (110) foils is the

7;

' t o ,

1

convenient diffraction contrast conditions : For the

r f

l

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C 3 - 1 7 0 J. WASHBURN AND TH. CASS will be called interstitial and vacancy respectively.

Orientation will be characterized by the angle, ,)I

between a tangent to the dislocation lines and the Burgers vector. Spacing, D, will be the separation between the (1 10) glide planes of the two dislocations. Position as described by the angle, 8, will refer to relative locations on the respective glide planes. For dipoles near edge orientation there are two equilibrium positions. Because the zero-stress equilibrium positions for an edge dipole are 450 and 135O the separation of the dislocations, as seen in the slip plane projection, is equal to the spacing, D. Therefore by correcting for displacement of the images from the dislocation positions an estimate of the spacing can be made if it is assumed that the dislocations are near equilibrium position. For spacings that are not too large and where the two lines are accurately parallel to each other this is probably a good assumption.

2.2 GENERAL FEATURES OF THE DIPOLE SUBSTRUC-

TURE.

-

The main features of the dipole substructure in

deformed magnesium oxide are illustrated by figure 3.

The specimen was deformed in compression at 750 OC prior to cutting parallel to an active slip plane. 750 OC represents, for MgO, the approximate upper limit for low temperature deformation behavior. Above this temperature, changes in the deformation substructure associated with non-conservative motions of dislocations begin to be increasingly important.

After low temperature deformation the dipoles that have been formed can be separated into two fairly distinct classes : (1) short terminated dipoles usually having a spacing less than 40 b and an orientation near pure edge and (2) long dipoles usually terminating only at a dipole node such as at ( ( A or running out of the foil. These long dipoles usually had a spacing greater than about 40 b and were nearly always curving. Segments in pure screw orientation were fairly common. The long dipoles and sometimes also short terminated dipoles frequently had position junctions as at (( B where there was a change from

one position of equilibrium to the other. Another feature common to most dipoles was gradual changes in spacing. Although abrupt increases or decreases

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DISLOCATION DIPOLES IN MgO C 3 - 171 in spacing were sometimes observed most changes took

place over a considerable length, the many individual steps being too small to be resolved. Dipoles of small spacing often were tapered at one or both ends, the spacing gradually becoming smaller as the end of the dipole was approached. This sometimes made it difficult to estimate the length.

2.3 EFFECT OF DEFORMATION TEMPERATURE. - The effect of deformation temperature is illustrated by figures 4 and 5. The former is from a specimen deformed at 20 OC and the latter from one deformed at 850 OC. By comparing figures 3 and 4 it can be seen that increasing the deformation temperature first tends to eliminate the short dipoles of smallest spacing. Dipoles are unstable relative to a string of circular dislocation loops enclosing the same total area [13]. Therefore when a deformed specimen is heated into a temperature range where dislocation climb becomes

possible, or when the deformation is carried out within this range, dipoles are transformed into strings of loops. The diameters and distances between loop centers for a given string are related to the original dipole spacing 1131. The effect of the gradual decrease in spacing on approaching the ends of many dipoles is clearly evident for some of the strings of loops in figure 5. As the deformation temperature is raised above 750 0C dipoles of increasingly large spacing tend to be broken up into elongated closed loops ;

fewer dipoles are formed. After deformation at 1 600 OC it is difficult to find any deformation substructure.

2.4 INTERSTITIAL VS VACANCY DIPOLES. - Previous experiments have not clearly demonstrated whether or not interstitial and vacancy dipoles are both present in approximately equal numbers. With {l 10) foils, simple diffraction contrast experiments are possible that positively identify as vacancy or interstitial any dipole that-intersects the surface and has a spacing that is not too small. Figure 6a repre- sents schematically the edge of a (110) foil where its thickness is gradually decreasing. Two dipoles are shown intersecting top and bottom surfaces respecti-

FIG. 6. - Schematic revresentation of the determination of

FIG. 5. - (110) slip plane section of a MgO crystal deformed the type of dipole in a slip plane section. a) Dipoles intersecting at 850 OC. The gradual change of loop diameter in several of the both surfaces of a thin foil. Between points A and B the contrast narrow strings of loops (see L) is evidence for non-uniform due to one of the situations in b). The expected dark-field, s = 0

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C 3

-

172 J. WASHBURN AND TH. CASS vely. Because the surface is nearly parallel to (110)

and the dislocations lie approximately on (110) the two dislocations cut the surfaces at points A and B that are widely separated compared to the spacing, D, of the dipole. Between A and B there is only one dislocation located just under the surface. It is in these regions that diffraction contrast can be unam- biguously interpreted. Figure 6b shows the local lattice rotations within the region between A and B associated with four possible cases that arise : intersection of

vacancy and interstitial dipoles with top and bottom foil surfaces. For an interstitial dipole the extra half plane of the dislocation is toward the surface while for a vacancy dipole it is on the side away from the surface. Between A and B, in a relatively thick foil, the Ashby-Brown type of strain contrast is obtained. According to their analysis [l41 a dark-field picture, taken near the exact Bragg condition can be used to identify the two types of strain : the dipole is interstitial if the black side of the black-white image is toward

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DISLOCATION DIPOLES I N MgO C 3

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173 the direction of the reciprocal lattice point correspon-

ding to the diffracted beam, figure 6c. It is of vacancy type if the opposite is true.

The four pictures in figure 7 have been taken with different diffraction conditions as marked on the prints. In each case the direction toward the reciprocal lattice point of the diffracting plane is shown by an arrow. These arrows also indicate the magnification, representing a distance on the print of 0.2 micron. The letter B or D indicates whether the image was obtained in bright or dark-field respectively and the f ,

-,

or 0 refer to positive, negative or zero devia-

tion from the exact Bragg condition. In figure 7d the black side of the strain contrast image is toward the direction of the operating reflection. Therefore, according to the Ashby-Brown criterion, this dipole is of the interstitial type. Figure 7a is the bright-field image for the same diffraction condition. Because there is no reversal of the black-white image compared to 7d the dipole must intersect the top surface of the foil [12]. Picture b and c both correspond to positive deviation from the Bragg condition but with operating reflections on opposite sides of the direct beam. This causes the dipole image to change from inside to

FIG. S.

-

( 1 10) slip plane section of a MgO crystal deformed at 750 OC. a) Bright-field ; 6-d)

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C 3

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174 J. WASHBURN AND TH. CASS outside contrast and shows that the dislocation

farthest from the surface is on the left looking from bottom to top of the photograph. Note also the position junction where contrast changes from inside to outside or vice versa along the long dipole at the right hand side of the picture.

Figure 8 shows three dipoles that intersect the surfaces in the same field of view. Figure 8c which is a dark-field picture in the Bragg condition, shows that dipoles 1 and 2 are interstitial and 3 is vacancy type. Pictures 8b and 8d illustrate another method of recognizing the top and bottom surface. For a large negative deviation from the Bragg condition defects producing strain near the top surface show strong contrast in dark-field while those near the bottom surface are in weak contrast. For a positive deviation the reverse is true [l 1, 15, 161. Therefore dipoles 1 and 3 intersect the top surface and dipole 2 cuts the bottom surface.

3. - Mechanism of formation of dipoles.

3.1 JOG FORMATION. - The formation of dipoles and prismatic loops when dislocations move is clear evidence that dislocations acquire jogs during motion. One source of jogs is intersecting dislocations : some are present in the as-grown crystal and others are formed by the growth of slip bands on intersecting planes. For a number of reasons intersecting dislocations do not appear to be the major source of jogs in MgO. In typical specimens the grown-in dislocation density is very small. Some crystals are virtually free of subgrain boundaries and the density of randomly arranged dislocations is usually less than 105/cm2. The density of dipoles within glide bands after room temperature deformation is of the order of 109/cm2. Also the dipole density is insensitive to the size of the specimen and except in the immediate vicinity of glide band intersections is insensitive to the number of active slip systems. If intersecting dislocations were the primary source of jogs the number of dipoles formed should depend on both of these parameters. Even if enough jogs to account for all the dipoles could be formed at intersecting dislocations it would be difficult, if this were the only source of jogs, to account for the gradual changes in spacing in many dipoles. Figures 3, 4 and 5 have examples of dipoles that increase or decrease their spacing by as much as 50

A

within a length of one micron along their length. The grown-in dislocation density in MgO is clearly too small to account for this configuration. Another possible source of jogs is double cross-slip. As this mechanism is usually conceived it requires

that a length of dislocation in pure screw orientation leave its normal glide plane, move for some distance in another plane and then finally return to the first plane but at a different level. Two large jogs are created where the segment of dislocation on the new level is connected with the parts of the same line still on the original glide level. In the sodium chloride structure cross-slip should be difficult. The only likely cross-slip plane is

(

100

)

on which the critical stress for motion of dislocations at room temperature is known to be high. Even if double cross-slip does occasionally form a pair of long jogs it too seems incapable of explaining gradual changes in dipole spacing. If this mechanism were the primary cause of the start of dipoles they should usually occur in pairs, the two having the same spacing and one being of interstitial type while the other is vacancy type. There is no evidence that this is the case.

The observed density and fine structure of dipoles apparently requires that elementary jogs, or at least jogs short enough to be below the resolving power of the electron microscope, are frequently formed on every moving screw dislocation and that these are able to move conservatively along the dislocation, so as to collect at the cusps where the screw dislocation is attached to dipoles. If pairs of jogs are formed at random on screw segments the number of dipoles that are nucleated should be inversely related to the glide mobility of jogs. If jog mobility increases with increasing temperature, fewer dipoles of larger average spacing should be formed at high temperature as is observed.

The nucleation of a pair of jogs of opposite sense and their separation by glide is formally equivalent to double cross-slip but with the distance moved on the cross-slip plane being only one or a few intera- tomic distances. This sort of change in glide level might be promoted by impurity atom groups or even by clusters of vacancies or interstitials left by the passage of a previous dislocation.

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DISLOCATION DIPOLES IN MgO C 3

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175 fold back on the loop at the opposite side. This

results in a bending of the newly formed part of the dipole into a different orientation. If a section of screw dipole is formed in this way and if the spacing of this dipole is small enough, cross-slip will eliminate a segment of the dipole leaving a closed loop. A new dipole of the same spacing may be started at the pinning point as shown in figure 9 or, because

FIG. 9. - Dipole termination by turn of the dipole into

screw orientation.

edge dislocations move faster than screw dislocations, the forward loop may get sufficiently ahead to cause the long jog to continue to move conservatively as shown in figure 10. An edge dislocation containing

FIG. 10. - Alternate possible configuration after the cross- slip event of figure 9-2.

a long jog acquired in this way can meet another edge dislocation of opposite sign to form a dipole on which there will be an abrupt change in spacing. It is also possible that an edge loop, formed where a part of an advancing screw dislocation gets far enough ahead of neighboring parts, will run along a considerable length of the screw dislocation, terminating a number of dipoles and generating a new jog-free length of screw dislocation as shown in figure 11.

( 0 ) ( b )

FIG. 11. - Formation of long interconnected dipoles and

closed loops. a) By-passing of a segment that is held back by trailing dipoles ; and b) final configuration after screw oriented dipoles at A have annihilated by cross-slip.

When the edge part of the forward loop finally meets another forward segment the new dipole that is formed will have a spacing that includes the alge- braic sums of all those that have been terminated. When the spacing exceeds a critical value dipoles cannot be terminated by this mechanism. The force of attraction per unit length between two parallel screw dislocations is given by :

where D is the spacing. Therefore as D increases there will be a critical spacing above which F is less than the critical force necessary for glide of a dislocation in

{

100

).

If in a case like that pictured in figure 11 annihilation of screw oriented segments does not occur then a network of interconnected dipoles is formed. It seems likely that this is the explanation for the long interconnected dipoles that are observed. Figure 3 has a good example of this kind of network where several dipoles join at dipole nodes.

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C 3

-

176 3. WASHBURN AND T H . CASS

that have segments near screw orientation can be used to estimate the critical stress necessary for glide of a dislocation on the

(

100

)

cross-slip plane. For room temperature deformation the critical spacing was found to be 40 b. This corresponds to a critical stress for

{

1 0 0 ) glide 35 times greater than the critical stress for

(

110

)

glide in the same crystal. The fact that even dipoles of large spacing are usually terminated at higher temperatures of deformation is consistent with the rapid decrease with increasing temperature of the critical stress for

(

100

)

glide [17]. Also, correlation between average length of elongated loops and their spacing in a room temperature deformed crystal can be explained on the basis of the model. The smaller the spacing the shorter is the length of dislocation that must reach the screw orientation to initiate cross-slip. As a first approximation it is reasonable to assume that the shortest length that would be able to cross-slip and annihilate would be a length equal to the spacing. The result of annihilation over this length is to replace a segment of screw dipole of length D with a segment of edge dipole also of length D.

3.3 FORMATION OF POSITION JUNCTIONS. - The contrast effect illustrated at P in figures 7b and 7c, where the image position changes from outside to inside the actual dislocation positions, can be explained in two different ways : either the dipole changes a t point P from vacancy to interstitial type, the position angle remaining constant, or it changes from one position of stable equilibrium to the other ; the position angle changes from a value less than 900 on one side of P to a value greater than 900 on the other side. Although the former explanation could apply where an edge dislocation with a long jog meets another edge dislocation on a level that cuts the jog near its midpoint, it is likely that most such contrast effects correspond to the latter explanation.

The formation of position junctions is also consistent with the model. Figure 12 shows how the stable equilibrium position should vary with orientation. The curve represents the value of 0 for which the glide force between two opposite-signed parallel dislocations of orientation $, given by

cos 2 B sin2

$1

,

(1 - v)

is zero.

p is the elastic shear modulus and v is Poisson's ratio. The lateral width, X, of the dipole as a fraction of the spacing is also shown. For $

_go,

FIG. 12. - The stable position angle and lateral width of a

dipole as a function of orientation.

there is only one position of equilibrium, 0, = 900. When I/J >

$,,

there are two, at 0, and 1800 - 8,.

Thus, two edge dislocations on closely spaced parallel planes that meet will stop a t the first equilibrium position. In the slip plane projection, they do not pass each other. However, as screw dislocations or dislocations near screw orientation have only one stable position, they superimpose in the slip plane projection.

This situation is illustrated schematically in figure 13a where the dislocations have stopped in the 8

>

900 position. If a stress is applied, figure 13b,

0 is decreased for all positions of equilibrium. There- fore the screw dislocations will be driven past one another as seen in the slip plane projection. Where the dipole curves away from screw orientation, on both sides, the dipole will prefer to take up the second

(8, < 900) position rather than the first. The position

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DISLOCATION DIPOLES IN MgO C 3

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177

FIG. 13.

-

Formation of position junctions on a mixed orientation dipole ; a) zero applied stress ; b) with a stress applied two position junctions have been nucleated ; c) further stressing causes the junctions to be driven to the edge-oriented portions of the dipole; d ) one position junction has been driven off the dipole end, causing the dipole to take up the second equilibrium position.

pictured in figure 2 b. Finally, if the end of the dipole is free to rotate, the entire dipole may be flipped to the second position, figure 13d.

It can be shown, by considering the energy of a mixed orientation dipole, that position junctions will readily be formed if, for any part of a dipole, the orientation angle is less than $,. For dipoles oriented near

+,,

an applied stress will easily displace the dislocations from their equilibrium positions by distances that are significant fractions of the dipole spacing.

Acknowledgments. - Support of this work by the United States Atomic Energy Commission through the Inorganic Materials Division of the Lawrence

Radiation Laboratory is gratefully acknowledged. One of us (T. C.) would also like to thank the National Science Foundation for the award of a Post-Doctoral Fellowship. We are also grateful to MM. J.-M. Du- pouy and Y. Adda, Section de Recherches de M6tal- lurgie Physique, Centre #Etudes Nuclkaires de Saclay, for use of their laboratory facilities.

[l] WASHBURN (J.), GROVES (G. W.), KELLY (A.), and WILLIAMSON (G. K.), Phil. Mug., 1960, 5 , 991. [2] ALEXANDER (H.), and MADER (S.), Acta Met.,1962,

10,887.

[3] STEEDS (J.) and HIRSCH (P. B.), Conference on the Relation between Structure and Strength of Metals and Alloys, National Physical Laboratory, Teddington (H. M. S. O.), 1963, p. 39.

[4] KEH (A. S.) and WEISSMAN (S.), Electroiz Micvascopy and the Strength of Crystals, Interscience, New York, 1963, p. 231.

[5] FOVRIE (J. T.), Phil. Mug., 1964, 10, 1027.

[6] JOHNSTON (W. G.) and GILMAN (J. J.), J. Appl. Phys., 1960, 31, 632.

[7] WASHBURN (J.), Electron Microscopy and the Strength of Crystals, Interscience, New York, 1963, p. 301. [8] FOURIE (J. T.), and WILSDORF (H. G. F.), J. Appl.

Phys., 1960, 31, 2219.

[9] TETELMAN (A. S.), Acta Met., 1962, 10,813.

[l01 CASS (T. R.), and WASHBURN (J.), Proc. Brit. Ceuam. Soc. 1966, 6,239.

[l l] CASS (T. R.), Ph. D. Thesis, University of California, Berkeley, 1965, UCRL-11996.

[l21 HOWIE (A.), and WHELAN (M. J.), Proc. Roy. SOC., 1961, A 263,217 ; Ibid, 1962, A 267,206.

[l31 GROVES (G. W.), and KELLY (A.), J. Appl. Phys., 1962, 33 Supplement, 456.

[l41 ASHBY (M. G.), and BROWN (L. M.), Phil. Mug., 1963, 8, 1083 ; Ibid, 1963, 8, 1649.

[l51 WILKENS (M.), Phys. Stat. Sol., 1964, 6,939.

[l61 BELL (W.), and THOMAS (G.), Phys. Stat. Sol., 1965, 12, 843.