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Dislocations at spinel surfaces
Surface Science 511 (2002) 133–146 www.elsevier.com/locate/susc
Dislocations at spinel surfaces Svetlana V. Yanina, C. Barry Carter
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Department of Chemical Engineering and Materials Science, University of Minnesota, 204 Amundson Hall, 421 Washington Ave. S.E., Minneapolis, MN 55455, USA Received 1 October 2001; accepted for publication 5 March 2002
Abstract The structure of evaporation patterns created by stationary and moving dislocations which terminate on the (0 0 1) surface of MgAl2 O4 is discussed. When the Burgers vectors of the dislocations are inclined with respect to the (0 0 1) crystal plane, these dislocations create evaporation patterns in the form of double spirals. The double evaporation -high half-ledges originating at the dislocation termispirals develop through the synergistic rotation of pairs of 2-A nation points. The dislocations, whose Burgers vectors lie in the (0 0 1) crystal plane, do not form spirals when terminating on the (0 0 1) surface, but may create kinks in the surface steps. The presence of the dislocation-related kinks causes local cusping of the surface steps. Ó 2002 Published by Elsevier Science B.V. Keywords: Evaporation and sublimation; Faceting; Step formation and bunching; Surface structure, morphology, roughness, and topography; Low index single crystal surfaces
1. Introduction The influence of crystal defects on the morphology of the developing crystal is a fundamental topic in materials science [1]. Early theoretical models of crystal growth [2,3] and evaporation [4] of crystal surfaces dealt solely with simple-cubic crystal structures. One of the consequences of this simplified approach was that only screw dislocations with Burgers vector, b, normal to the surface plane were considered as possible sources of surface ledges. In the simple-cubic structure, pure screw dislocations lying in the surface plane and any pure edge dislocations cannot cause surface
*
Corresponding author. Tel.: +612-625-8805; fax: +612-6267246. E-mail address: [email protected] (C. Barry Carter).
ledges [2]. This simplification is not valid for materials with more complex crystal structures where several possible Burgers vectors may be inclined with respect to the surface plane. Clearly, dislocations with such Burgers vectors may form a halfledge upon intersection with the surface regardless of their character. In more complex cases, dislocations with a Burgers vector which is parallel to the surface may dissociate into two or more partial dislocations the Burgers vectors of which each possess out-of-surface components. These partial dislocations may give rise to surface ledges despite the fact that the original dislocation cannot do so [5]. Spinel is one such material whose structure allows for the existence of Burgers vectors that are inclined with respect to the low-index (stable) surfaces. The widespread industrial use of spinel oxides (e.g., in computer memory devices [6] and
0039-6028/02/$ - see front matter Ó 2002 Published by Elsevier Science B.V. PII: S 0 0 3 9 - 6 0 2 8 ( 0 2 ) 0 1 5 6 1 - 3
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ferromagnetic applications [7]) prompted the present study of the interactions between the dislocations and the (0 0 1) surface of the prototypical spinel, MgAl2 O4 .
2. Background The structure of MgAl2 O4 spinel (see Fig. 1) consists of a closely packed framework of O2 anions in a distorted fcc arrangement with 1/8 of tetrahedral interstices (A-sites) and 1/2 of octahedral interstices (B-sites) filled by cations [8]. The at unit-cell parameter, a, of MgAl2 O4 , is 8.075 A 25 °C [8]. The space-symmetry group of normal spinel is Fd3m [8]; in this material, Mg2þ cations are positioned in A-sites while Al3þ cations occupy B-sites [8]. Double steps on the (0 0 1) spinel surface -high (single) may dissociate into pairs of 2-A steps of either straight or curved appearance [9]. (Throughout this paper a=4 will be approximated .) Straight single steps tend to align along as 2 A either the [1 1 0] or the [1 1 0] direction of the crystal. A straight single step will have the same direction of alignment as any other straight single (or an even multiple of 2 A ) above step lying 4 A
Fig. 1. The structure of MgAl2 O4 spinel [9]. Oxygen ions are represented as large gray spheres. Mg2þ cations in tetrahedral coordination are shown as smaller gray spheres. Octahedrally coordinated Al3þ cations are depicted as the smallest black spheres.
(or below) it. A straight single step will tend to align perpendicular to any other straight single (or an odd multiple of 2 A ) above step lying 2 A (or below) it. The height of a single step on the spinel surface is close to the distance between two nearest (0 0 4) (or (0 0 8)) planes in the bulk spinel crystal [9]. In the bulk MgAl2 O4 crystal, cations in the (0 0 1) planes are positioned along the [1 1 0] or [1 1 0] directions. It has been proposed [9] that such anisotropic cation distribution in the spinel structure is at the origins of the preferential alignment of the surface ledges on the (0 0 1) surface of MgAl2 O4 along either the [1 1 0] or [1 1 0] directions. In stoichiometric spinel, the predominant dislocation slip system is (1 1 1) [1 1 0] with the Burgers vector, b, equal to a=2[1 1 0] [10]. In nonstoichiometric spinels, a (1 1 0) [1 1 0] slip system can also be observed [10]. Two of the six possible Burgers vectors thus lie in the (0 0 1) surface plane, specifically along the [1 1 0] and [1 1 0] directions; dislocations with these Burgers vectors will be referred to as having an in-surface b. Edge dislocations and mixed dislocations with an in-surface b must terminate at the (0 0 1) surface. Dislocations with an in-surface b are not expected to create ledges at the points of emergence [2]. The remaining four Burgers vectors intersect the (0 0 1) surface at a 45° angle. Pure screw, pure edge, and most mixed dislocations with b aligned along the [0 1 1], [1 0 1], [1 0 1] or [0 1 1] directions (see Fig. 2) are inclined to the (0 0 1) plane and will be associated with half-ledges on the (0 0 1) surface. At elevated temperatures, vicinal surfaces of the MgAl2 O4 polished close to the (0 0 1) plane reconstruct into terrace-and-step morphologies with the steps aligned along the [1 1 0] and [1 1 0] directions [9]. The dynamics of step motion is high (double dominated by steps which are 4 A steps) [9]. The double steps tend to align with one another and move preferentially along either the [1 1 0] or the [1 1 0] direction of the crystal. If a (or an odd multiple of 2 A ) double step lies 2 A above (or below) another double step, the two steps are oriented perpendicular to one another [9]. (or an even multiple of 2 If a double step lies 4 A A) above (or below) another double step, such steps will be parallel to one another. The double-
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(SPM) (Nanoscope III, Digital Instruments, Santa Barbara, CA) in air using the contact mode of operation. The Si3 N4 cantilevers used were Vshaped (Ultralevers, Park Inst., Sunnyvale, CA) with a nominal spring constant of 0.12 N/m. 4. Experimental observations 4.1. Evaporation spirals Fig. 3 shows a typical evaporation pattern on the (0 0 1) spinel surface. The pattern is formed by four groups of elongated rectangular terraces and resembles a broken fourfold spiral. The terraces ledges (double steps are separated by straight 4 A
Fig. 2. Schematic illustrating the relationship between the Burgers vectors directions and the (0 0 1) planes. Two of the six possible perfect-dislocation Burgers vectors lie in the (0 0 1) plane (along the [1 1 0] and [1 1 0]). The four others lie at 45° to the (0 0 1) plane.
step height is twice the distance between the two nearest bulk (0 0 4) or (0 0 8) planes [9].
3. Experimental A single crystal of MgAl2 O4 spinel of (0 0 1) orientation was cut into 2 2 1 mm3 pieces. The samples were polished and cleaned in aqua regia, acetone and methanol. Heat treatments were performed at 1800 °C in a sintered spinel crucible at a pressure of 104 –105 Torr in a Centorre furnace for 8 h. A similar cleaning procedure has been used for the other oxides [11] and other spinel samples but the annealing temperature is much higher in the present study. Crystallographic orientations on the surfaces were determined by Laue backscattered Xray diffraction. The chemical composition of the surface was monitored ex situ by X-ray energydispersive spectroscopy (XEDS) and X-ray photoemission spectroscopy (XPS). Surface imaging was performed by scanning probe microscopy
Fig. 3. A 10 lm 10 lm height-mode SPM image of an evaporation pattern on the (0 0 1) surface of MgAl2 O4 . The high and are straight steps along the sides of the pattern are 4 A -high aligned along [1 1 0] and [1 1 0]. When steps meet, the 4-A high, as steps split into pairs of straight perpendicular steps 2 A shown schematically.
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[9]) which are aligned along either [1 1 0] or [1 1 0]. At the corners of the spiral, the double steps split -high into pairs of ledges which are straight, 2-A and lie at 90° to one another [9]; the upper ledge remains parallel to the original double step, while the lower one is rotated into the perpendicular h1 1 0i direction. Each rectangular terrace in the evaporation pattern is bound by two long double steps and four short single steps. On the (0 0 1) MgAl2 O4 surface, the width of a pattern-forming terrace is constant within a particular train of steps, but may vary from one train to another. On average, the terrace width is measured to be 300–800 nm. The dimensions of the rectangular spirals depends on the details of the surface morphology but may be as large as 50 m 50 lm. 4.2. Interacting spirals If several dislocation termination sites are situated in the close proximity, their individual evaporation patterns may coalesce. Fig. 4 shows an evaporation pattern shared by a pair of dislocations. Two small spirals originating from two separate dislocation termination sites occupy the central part of the pattern. Unlike the pattern shown in Fig. 3, these small spirals contain both straight and curved single steps. The curved single steps exhibit rough edges and cannot be assigned to any particular crystallographic direction on the surface. Like the straight single-step pairs, the pairs of curved single steps combine to form straight double steps at the corners of the pattern. The first several turns of two individual spirals in Fig. 4 are significantly wider than the first turns of the single spiral shown in Fig. 3. The outer area of the large combined pattern formed through the coalescence of two small spirals has the same topography as the pattern produced by a single dislocation (cf. the outer areas of Figs. 1 and 2). In more complex evaporation patterns, the development of one spiral may precede the formation of the others. In Fig. 5, the central spiral encountered several independent dislocation sites in the course of its evolution. One of these dislocations (A in Fig. 5) created a spiral with the same sense of rotation as the original pattern. Concerted
Fig. 4. A 5 lm 5 lm height-mode SPM image of the evaporation pattern formed when two dislocations emerge at the (0 0 1) surface of MgAl2 O4 . The straight steps at the outer edges high and are aligned along the [1 1 0] and of the pattern are 4 A [1 1 0]. Small spirals originate from the two separate dislocation -high steps termination sites. The arrangement of the curved 2-A at A and B are shown schematically in (b).
motion of the two spirals produced only minor topographic disturbances, such as cusps and dissociated double-step fragments. Another dislocation (B in Fig. 5) developed an evaporation spiral with the opposite sense of rotation with respect to that of the original spiral. As a result, step pileup occurred between the two dislocation termination sites where steps moving out from the primary spiral encountered steps moving out from the secondary spiral. On the three other sides of the
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Fig. 5. A 30 lm 30 lm deflection-mode SPM image of a complex evaporation pattern on the (0 0 1) surface of MgAl2 O4 . The direction of scanning was from left to right; dark lines indicate downward steps; bright lines denote upward steps. high and are Straight steps at the sides of the pattern are 4 A aligned along the [1 1 0] and [1 1 0] directions of the crystal. The site of emergence of a dislocation that created a spiral with the same sense of rotation as the primary (central) spiral is labeled A. The site of emergence of a dislocation that developed a spiral with the opposite sense of rotation as the central spiral is labeled B. These two step sources are shown schematically in (b).
secondary spiral, the uncoordinated motion of steps that belong to both spirals resulted in largescale cusping and dissociation of the double steps into pairs of curved single steps [9]. 4.3. Offset spirals A more complex example of an evaporation pattern is shown in Fig. 6(a). Here, a spiral
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Fig. 6. (a) A 20 lm 20 lm deflection-mode SPM image of an offset evaporation pattern on the (0 0 1) surface of MgAl2 O4 . The direction of scanning was from left to right. In the image, dark lines indicate downward steps; bright lines denote upward steps. high and are Straight steps at the sides of the pattern are 4 A aligned along [1 1 0] and [1 1 0]. The site of dislocation termination labeled B is located outside the central squares and is connected to the pattern center via a trail of cusped steps (a fault line). (b) A 5 lm 5 lm height-mode SPM image of the central part of an offset evaporation pattern on the (0 0 1) surface of MgAl2 O4 . The straight steps at the sides of the pattern are 4 A high and are aligned along [1 1 0] and [1 1 0]. The cusped step fragments gradually change the direction of their alignment from close to [1 0 0] at the top to [1 1 0] at the bottom of the spiral.
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appears to be displaced on one side. Unlike the surface structures discussed above, this evaporation pattern does not have a dislocation termination point at its center: instead, it is flat-bottomed (see Fig. 6(b)). The double steps on right side of the spiral are cusped; the cusps are aligned along a line curving from the base of the spiral to a dislocation termination site (B in Fig. 6(a)) at the outer edge of the spiral. This dislocation termination site is not enclosed by a spiral. Instead, it is attached to a straight double-step segment which is itself connected to a cusped double step and a pair of curved single steps. Remarkably, the cusped double steps shown in Fig. 6(a) are situated below the dislocation termination site while the single steps positioned directly above the dislocation termination site appear to be unaffected by the dislocation. The cusped double steps maintain the same spacing on either side of the cusp. The cusps in the upper steps appear straight and are aligned close to the [1 0 0] direction. The cusps in the lower steps originally lie along [1 0 0] but later along [1 1 0], with the location of the cusps shifting gradually to the right (see Fig. 6(b)). In some cases, an evaporation pattern may not show such displacements, but nevertheless will not contain a dislocation termination point at its center. Fig. 7(a),(b) shows a flat-bottomed evapo-high ration spiral which contains a cusped 6-A ledge amongst the regular double steps. This ledge originates at the dislocation termination point (A in Fig. 7) and dissociates into a straight single step plus a straight double step in the corner of the spiral (B in Fig. 7). The entire step-train on this side of the spiral has a narrower step spacing compared with the step spacing in the other steptrains in the pattern. The bottom of the evaporation pattern depicted in Fig. 7 is flat. In this case, the dislocation termination site does not lie outside the spiral, but is located to one side of this flat area. This particular dislocation termination site does not have an individual evaporation spiral attached to it. 4.4. Offset step-trains As illustrated in Fig. 8, a double-steptrain which is not related to a particular
Fig. 7. (a) A 10 lm 10 lm deflection-mode SPM image of flat-bottomed evaporation pattern on the (0 0 1) surface. The direction of scanning was from left to right. Dark lines indicate downward steps; bright lines denote upward steps. The straight high and are aligned steps at the sides of the pattern are 4 A along the [1 1 0] and [1 1 0] directions of the crystal. A cusped 6-high ledge originates at the dislocation termination site (A) A -high and a 2-A -high step at the and dissociates into a 4-A pattern corner (at B). (b) A 2 lm 2 lm height-mode SPM image of the cusped ledge shown in (a). At the dislocation termination site (A) the height of the narrow step changes . The 6-A -high ledge dissociates at B into abruptly from 2 to 6 A a pair of perpendicular steps. At A, the contrast at the steps is darker for the higher step.
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cusped step fragments in the lower part of Fig. 8 has dissociated into a loop of curved single steps. 4.5. Turning double steps
Fig. 8. A 10 lm 10 lm deflection-mode SPM image of an offset double-step-train which was traversed by a moving dislocation termination site. The direction of scanning was from left to right. In the image, dark lines indicate downward steps; bright lines denote upward steps. The straight steps in the train high and are aligned along the [1 1 0] direction of the are 4 A crystal. The position of the mobile dislocation termination point is labeled A. The likely initial position of the dislocation termination point is labeled B.
dislocation–termination site may still contain offset steps. Similar to the cusped steps in the evaporation pattern displayed in Fig. 6, the offset steps in this step-train are also located below the dislocation termination site (B in Fig. 8). Like the dislocation termination site shown in Fig. 6, the one in Fig. 8 is also not associated with a spiral. In Fig. 8, the steps which are situated directly above the dislocation termination site, appear not to interact with it. The cusp trail ending at the dislocation termination site originates at the edge of the first step in the train (A in Fig. 8). This trail appears to be unrelated to any other surface features situated in its vicinity. In Fig. 8, the cusps in the lower offset steps are displaced (to the lower right) with respect to the cusps in the upper steps. The upper-step cusps have rough edges, while the cusps in the middle steps have a well defined direction of alignment along [1 1 0]. One of the
A fundamentally different case of double-step cusping observed on the (0 0 1) spinel surface is shown in Fig. 9. Unlike the offset double steps discussed above, the group of double steps in Fig. 9 is cusped over a small surface region only. Here, the cusps in the steps do not align along any particular line or direction on the surface. The spacing of the steps on either sides of the cusped area are different. Local double-step cusping is usually limited to compact isolated areas of the surface. The average size of the affected regions is 0.5–3 lm. Observations show that this phenomenon is not accompanied by the presence of any other visible crystal defects in the vicinity (5–20 lm) of the cusped steps.
Fig. 9. A 10lm 10 lm deflection-mode SPM image showing curved segments in a double-step-train on the (0 0 1) surface. The direction of scanning was from left to right. On the image, dark lines indicate downward steps; bright lines denote upward high) steps on the image are aligned steps. Straight double (4 A along the [1 1 0] direction of the crystal. Cusping of the steps is limited to the central area of the image. No special surface features are visible in the vicinity of the cusps. Step segments situated in the region labeled A are more narrowly spaced than those in the region labeled B.
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5. Discussion 5.1. Dislocations with out-of-surface components of b: structure of evaporation spirals on the (0 0 1) surface of MgAl2 O4 As mentioned above, the dislocations which are expected to create half-ledges when terminating on the (0 0 1) surface of spinel may be pure screw, pure edge or mixed (such as 30°) in character. As the crystal surface evaporates, a half-ledge rotates about a dislocation emergence point, giving rise to an evaporation spiral [3]. In itself, the process of formation of the spiral-shaped evaporation pattern is not directly related to the nature of the emerging dislocation: all it requires is a half-ledge which is attached to a point on the crystal surface. Therefore, a dislocation of any character may be the origin of the evaporation spiral on the (0 0 1) surface of spinel, provided the dislocation has a component of its Burgers vector which does not lie in the (0 0 1) plane. It is not possible to identify the character of this dislocation solely on the observations of its evaporation pattern on the (0 0 1) surface; to do so requires a knowledge of the line direction. Here and below, the dislocations in spinel will be classified into those with b lying in
the (0 0 1) plane and those with b inclined to the (0 0 1) plane. Evaporation spirals found on the (0 0 1) surface of MgAl2 O4 have an uncommonly complex topography: they consist of four trains of interloped terraces (see Fig. 3). This is in contrast to the evaporation spirals observed on other ceramic materials [12], which typically consist of one large terrace spiraling up from the site of dislocation emergence. It is proposed that evaporation spirals on the MgAl2 O4 (0 0 1) surface are created through the rotation of not one but two half-ledges, each of high (see Fig. 10). Combined, the which is 2-A heights of these two half-ledges will give a value , or a=2[0 0 1], which is the component of a of 4 A perfect-dislocation Burgers vector normal to the (0 0 1) surface [10]; b lies at 45° to the (0 0 1) plane. The formation of two, instead of one, surface half-ledges at the dislocation sites on MgAl2 O4 (0 0 1) is determined by the surface structure of spinel. The (0 0 1) surface of MgAl2 O4 exists in the form of two variants, one of which tends to grow/ evaporate preferentially along the [1 1 0] direction, while the other develops preferentially along the [1 1 0] direction [9,13]. The surface terraces which belong to the different surface variants are separated by single steps, while the terraces formed by
-high (single) half-ledges emerges Fig. 10. Schematic of a double evaporation spiral on the (0 0 1) surface. A pair of perpendicular 2-A at a terminating dislocation at D. One of the half-ledges is aligned along the [1 1 0] direction, while the other one is aligned along the [1 1 0] direction. In the course of evaporation, the half-ledges rotate at the same rate but with a 90° phase-shift thus creating two -high (double) steps further from site D. The parallel segments independent spirals. The parallel segments of the spirals merge into 4-A of the half-ledge which aligns preferentially along the [1 1 0] direction (shown in gray) serve as the upper halves of the double steps aligned along the [1 1 0] direction and the lower halves of the double steps aligned in the [1 1 0] direction. The darker step behaves similarly but also rotates 90°. The progression at center of such a spiral, close to the emerging dislocation D, is shown in (b) and (c).
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the same surface variant are divided by double steps [13]. From structural considerations, a dislocation terminating on the (0 0 1) spinel surface should form a double half-ledge [13]. However, removal of material from the edge of this double half-ledge will lead to its immediate dissociation into a pair of two single half-ledges [13] on the evaporating surface. The single half-ledges which are attached to the dislocation termination site will rotate until they attain their preferred directions of alignment, so that if one of these half-ledges is aligned along the [1 1 0] direction, the other single half-ledge is aligned along the [1 1 0] direction [9]. If oriented along their respective preferred directions of alignment, the two half-ledges move along the surface at the same rate, but with a 90° ‘phaseshift’ [9]. When, in the course of evaporation, the half-ledges rotate away from their preferred directions of alignment, they slow down. This 90° phase difference causes the slower half-ledge to become an obstacle to the motion of the more rapidly moving half-ledge (see Fig. 10). When the faster half-ledge catches the slower one, a double step is formed [9]. Rotation of the two half-ledges about the dislocation termination point leads to reversal in their motion. The rapid half-ledge becomes the slow, and vice versa. This causes the separation of the new fast moving half-ledge from the new slower half-ledge at the corner of the spiral. The slower half-ledge then becomes the upper half of a new double step, while the rapid ledge continues moving. It eventually becomes the lower half of the next double step, as shown in Fig. 10. After the next rotation through 90°, the faster half-ledge slows and becomes the upper half of a new double step while the second half-ledge starts to move faster. After four consecutive rotations, four double steps are formed. At the corners of the spiral, where the velocity of ledge propagation reverses, the double steps separate into pairs of perpendicular single steps. The progression at center of such a spiral is shown in Fig. 10(b) and (c). The straight dislocations move out from D. The rate of motion is always determined high step (drawn as the by the slower (upper) 2-A outer line in the schematics). The new faster moving segment in Fig. 10(c) quickly catches the
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slow moving upper step; its length is then determined by the slower moving segments. The evaporation pattern created through such a cooperative rotation of two single half-ledges is, morphologically, a double spiral (see Fig. 10). The elongated terraces in the evaporation pattern have twofold symmetry and align either parallel or perpendicular to one another. Superposition of the two perpendicular groups of parallel terraces creates a pseudo-fourfold appearance of the resulting evaporation pattern. It is proposed [9] that the existence of preferential directions of alignment/ growth of the ledges on the (0 0 1) surface of MgAl2 O4 is related to the anisotropic distribution of the cations in the (0 0 1) crystal planes in spinel structure. 5.2. Interacting spirals Interaction of a developing evaporation spiral with obstacles (such as other dislocations) may locally affect the rates of propagation of the rotating half-ledges. This effect is illustrated in Fig. 5, where the central spiral encounters another with the opposite sense of rotation (compare the central spiral in Fig. 5 with the ‘spiral’ at A). Here, in order to accommodate the motion of steps from two dislocation termination sites, the double steps surrounding the secondary spiral become cusped and dissociate. A related process is shown in Fig. 4, where two spirals with the same sense of rotation merge into a common evaporation pattern. The doubled rate of material removal from the spiral bottom leads to the widening of the lowest terraces and to the formation of two pairs of curved single steps in the opposite corners of the spiral bottom. Similar to the steps that constitute regular evaporation spirals, the double steps that make up the double spirals on the (0 0 1) surface of MgAl2 O4 maintain a steady-state inter-step distance [4]. However, upon rotation, the upper half of a double step in a double spiral becomes not the upper, but the lower half of a perpendicular double step. Therefore, the process of material removal along the edge of a given double step will not directly affect the widths of the two perpendicular double steps which are adjacent to it. This
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is in contrast to the typical evaporation spirals [14] where, from the structural standpoint, all steps are the differently oriented segments of the same halfledge. In such patterns, any changes in the step spacing which occur at one side of the spiral are typically mirrored by steps located on the other sides of the spiral. Large variations are observed in the inter-step distances for the step-trains belonging to the same evaporation spirals on a particular (0 0 1) spinel surface. In order to accommodate several independent emerging dislocations, the step-train on the lower left side of the evaporation pattern shown in Fig. 5 increases its spacing from the center of the pattern to the pattern edge. These changes, however, do not perturb inter-step spacing of the three other step-trains in the pattern. 5.3. Dislocations interacting with spirals In stoichiometric spinels, the onset of plastic deformation occurs at 1800 °C, while the deformation of non-stoichiometric spinels may take place at substantially lower temperatures [10]. The samples used in the present work were not subjected to stress intentionally; nevertheless, the possibility of the motion of dislocations in MgAl2 O4 at 1800 °C cannot be ignored. Coincidentally, the 1800 °C is the temperature chosen in this study for the observations of the ledge-wise evaporation on the (0 0 1) spinel surface. Furthermore, at temperatures below 1800 °C, the slow rate of advancement of the moving step-trains, coupled with the reduced inter-step spacing [4], make it difficult to collect data on step motion [9]. At higher (1900 °C) temperatures, the high rates of material removal from the steps cause them to roughen the step edges and destroy the ordered arrangements of the steps in the step-trains. The surface observations of the specimens that were annealed at 1800 °C, therefore, gave a unique opportunity to study interactions of moving steptrains with moving dislocations. Movement of a dislocation termination point along an evaporating surface need not correspond to motion of the dislocation itself since the dislocation may be shallowly inclined with respect to the surface: as the layer of material is removed, the dislocation termination point shifts along the
projection of the dislocation line on the evaporating surface. While such motion may be continuous throughout the heat treatment, its rate is expected to be slow. For a pure screw dislocation with b aligned along [1 0 1], the dislocation termi, as nation point will shift by a=8[0 1 0], or 1.0 A spacing) is reeach (0 0 1) crystal plane (with 2-A moved. The developing evaporation spiral may also move as the dislocation termination point shifts. As discussed below, an exception to this rule arises when the drift of the dislocation termination point is caused by the motion of the dislocation itself. The spiral shown in Fig. 6 does not have a dislocation termination point at its center. Yet, in the absence of such a point, the spiral cannot develop. The dislocation termination site at the edge of the pattern (denoted by B in Fig. 6), in contrast, does not have a spiral evaporation pattern attached to it (see A). Again, on the evaporating surface, the development of a spiral around this site appears unavoidable. In Fig. 6(a), an offset line connects the spiral-less dislocation termination site and the flat bottom of the dislocation-less spiral. This line cuts through the steps which lie below the dislocation termination site. Since the steps normally move from the spiral center, the offset steps could not have interacted with the dislocation termination site that is situated above them. On the other hand, the steps located above the dislocation termination point should have interacted with it already but there is no indication of such an interaction. It is proposed that the offset evaporation pattern in Fig. 6 developed in two stages. At the beginning of the heat treatment, the dislocation termination point (which is now situated at the outer edge of the pattern) was located in the center of the pattern. After the spiral has been developed, the evaporation of material from the vicinity of the dislocation line has removed an obstacle that was pinning the dislocation. After the dislocation was released, it moved to its final position at the edge of the pattern. The line of offsets seen in Fig. 6 shows the trajectory of motion of the dislocation termination point. It is likely that the dislocation movement continued until the end of the heat treatment, as evidenced by the fact that the final
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position of the dislocation termination point is not surrounded by a new evaporation spiral: the dislocation termination point has moved faster than the surface steps. This conclusion is supported by Fig. 6(a), which shows similar offsets in a series of double steps caused by the dislocation motion. This observation of a dislocation moving out of an etch pit is directly analogous to the classic demonstration of moving dislocations in LiF where the pits are chemical in origin and the motion of dislocations is caused by an applied stress [15]. Similar observations have been made recently on Ni3 Al using LEEM [16]. The motion of the pattern-forming steps, albeit slow if compared with that of the dislocation termination point, did not cease when the dislocation moved out of the pattern center. As Fig. 6(b) shows, the trail of the moving dislocation termination point is curved. It is expected that curving of the drift trail is the result of the shifting of the cusped fragments of the double steps along the [1 1 0] direction. For the steps close to the bottom of the spiral, the cusping occurred early on in the dislocation motion. Such steps have had more time to recover so that their cusped fragments are shifted further along the step edges. The cusped fragments in the upper steps were created later than their lower counterparts and did not move far from their original positions. The evaporation spiral shown in Fig. 6(a) is flat bottomed. Flattening of the spiral bottom may be understood if the structure of a regular evaporation spiral is recalled. At the origin of the regular evaporation spiral, there are half-ledges emerging at the point where the dislocation line intersects the surface plane (see Fig. 3). The four step-trains making up the sides of the spiral are created and augmented through the conjugated rotation of these half-ledges. In the dislocation-less spiral, there are no such half-ledges. Hence, no new steps are created and the step-trains become independent from one another in their motion. Such steptrains are expected to move in the same fashion as any other independent step-train on the surface [9]. In some cases, the movement of the dislocation termination point may cease before the heat treatment ends. As illustrated in Fig. 7, the dislocation termination point has left the center of the
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spiral but has not moved further than the side of the flat spiral bottom. Similar to the spiral in Fig. 6, the dislocation termination point shown in Fig. 7(b) is expected to have been originally pinned at the spiral center, and to start its motion only after the spiral had developed. In this case, however, the dislocation termination point became trapped at the lowest step edge so that further motion only occurred with evaporation from the step. The spiral shown in Fig. 7 has had time to recover. Thus, no line of offsets connect the center of the spiral to the final positions of the dislocation termination point on the surface, instead, this area is flat. Also, the step spacing of the train adjoining the new position of the dislocation termination point has been reduced. Fig. 7 shows that the 6-high half-ledge (along AB) is cusped which inA dicates that the new evaporation spiral started developing around the new (quasi-stationary) position of the dislocation termination point on the surface. 5.4. Moving dislocations interacting with independent step-trains The motion of a dislocation may also become evident through its interaction with an independent step-train. Such an interaction is illustrated in Fig. 8, where the moving dislocation-termination point (B in Fig. 8) passed across a step-train. It is proposed that, originally, the dislocation termination site was situated in the lower left corner of the image (in area A in Fig. 8), possibly at a nanoledge edge. In the course of evaporation, the nanoledge has spun off a step-train (see Fig. 8) which may have triggered the motion of the dislocation. As was discussed for Fig. 6(a), the cusped steps in the train in Fig. 8 which are situated below the dislocation termination site have been cut by the moving dislocation line. This observation indicates that, in this case, the velocity of the dislocation termination point exceeded the rate of advancement of the steps in the train and that the dislocation continued to move until the heat treatment was complete. The curving of the offset line and the dissociation of the cusped fragments of some of the offset steps in the lower part of Fig. 8 is
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attributed to step recovery. As before, the steps close to the current position of the dislocation termination point have had less recovery time and their cusps have remained close to their original positions. 5.5. Dislocations with in-surface b As discussed above, in spinel, a dislocation with the Burgers vector lying in the (0 0 1) plane (e.g., a=2[1 1 0] or a=2[1 1 0]) cannot create half-ledges when it emerges at a flat (0 0 1) surface. However, on a vicinal surface, such a dislocation may terminate at a surface step. Provided that its Burgers vector is not parallel to the line direction of the step, this dislocation will create a kink on the step as shown in Fig. 11. A dislocation-related kink in the step may be considered as a two half-ledges on the face of this step [2]. A dislocation with an in-surface b will create a kink when terminating at the surface, regardless of its character. It should be noted, however, that dislocations lying in, or close to, the (0 0 1) surface (e.g., near-screw dislocations with b ¼ a=2[1 1 0] or a=2[1 1 0]) are expected to move rapidly out of the crystal at elevated temperatures. Therefore it is proposed that it is mainly edge dislocations that may form kinks in the surface steps. In Fig. 9, the double steps situated above the cusped area are straight. It is proposed here that the observed step cusps are due to interactions with dislocations having an in-plane Burgers vector. It is unlikely, though not impossible, that such cusps will be caused by contaminants at these high temperatures since individual atoms would be expected to diffuse under the action of the step line tension and there is no indication of particle formation; all areas were scanned in both deflection mode and height mode. Provided the steps develop cusps only in the vicinity of the dislocation line, this indicates that the steps come in contact with the dislocation at one point only. Consequently, this implies that the dislocation line intersects the surface as opposed to lying in (or close to) the surface plane. As noted above, such dislocations with an in-surface b are likely to be predominantly edge in character. Like a dislocation-related half-ledge, the dislocation-related kink in a step must necessarily be
Fig. 11. Schematic of a [1 1 0] surface step intersected by dislocation with an in-surface direction of its Burgers vector (b ¼ a=2½1 1 0 Þ. (a) A stationary kink formed at the dislocation termination site divides the step into two segments. The dislocation causes a kink (D). At the step edge, gray arrows indicate two moving kinks of different signs which are not caused by the dislocation. (b) The dislocation-related kink can be eliminated through the advancement of kink of the opposite sign reducing the dislocation line length. The part of the step removed through the advancement of the moving kink is shown in gray. (c) The immobile dislocation-related kink hinders the advancement of kink of the same sign. A cusp in the step is formed as a result of kink pileup. In (b) and (c), the part of the step removed through the advancement of the moving kink is shown in gray.
fixed to the dislocation termination point: as it moves away from the initial dislocation termination point it will extend the dislocation line by the distance it travels along the step edge making such movement unfavorable. Such kinks may be altogether eliminated through the advance along the step edge of a kink of the opposite sign (see Fig. 11(a),(b)). At the same time, advancing kinks of the same sign cannot pass through the (stationary)
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site of the dislocation-related kink (see Fig. 11(a)– (c)). Accumulation of these kinks at the site of a terminating dislocation will result in cusping of the step. The cusp is anchored by the dislocationrelated kink and can dissipate only when enough kinks of the opposite sign reach it. The dislocation-related kink, therefore, acts as a one-way valve for the kinks moving along the step edge: it lets the kinks of one sign move through but stops kinks of the same sign. The presence of the dislocation-related kink at the step edge may, therefore, distort the steady-state regime of material removal which is established along the edge of a straight moving step [4]. This is illustrated in Fig. 9, where the straight segments of the cusped steps, situated in the upper left corner, are more narrowly spaced than their counterparts located in the lower right corner. The rate of advancement of the narrowly spaced step segments is also slower than that of the rest of the steps (as the narrow-spaced segments are situated lower in the image than their widespaced counterparts). It is expected that the oneway exchange between the left and the right step segments, which are separated by a dislocationrelated kink, is the reason for the observed discrepancy in their spacing and rates of propagation along the surface. After the step breaks away from the dislocation termination site, the dislocation-related kink is removed from the step edge and the step eventually recovers (i.e., regains its regular spacing and straight appearance, see the steps shown in the upper part of Fig. 9). As Fig. 9 shows, the dissipation of the cusp proceeds through its redistribution along the step edge.
6. Conclusions In MgAl2 O4 , dislocations with Burgers vectors intersecting the (0 0 1) crystal plane create evaporation patterns in the form of double spirals. These double evaporation spirals are actually created through the cooperative rotation of pairs of per-high, half-ledges which pendicular single, 2-A originate at the dislocation termination points on the surface. The formation of pairs of perpendicular single half-ledges at the points of dislocation
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termination on the (0 0 1) spinel surface is believed to be related to the structure of the (0 0 1) surface variants in spinel. Dislocations with b parallel to the (0 0 1) surface in MgAl2 O4 may terminate at surface steps by creating kinks. The dislocation-related kinks divide the steps into pairs of step segments that may propagate along the surface at different rates. This asymmetry leads to cusping of the steps. In the event of dislocation motion at elevated temperatures (1800 °C), the drift of the dislocation termination point along the surface typically proceeds at a significantly higher velocity than the motion of the surface steps. Such movement causes offsets in the intersected surface steps.
Acknowledgements SVY is in the Chemical Physics Program at the University of Minnesota. This research has been supported by the US Department of Energy under Grants No. DE-FG02-92ER45465 and DE-FG0201ER45883. The SPM used is part of the IT Characterization Facility at the University of Minnesota. The authors would like to acknowledge discussions with Dr. N. Ravishankar.
References [1] A.R. Verma, Crystal Growth and Dislocations, Academic Press, New York, 1953. [2] F.C. Frank, Discuss. Faraday Soc. 5 (1949) 48. [3] W.K. Burton, N. Cabrera, F.C. Frank, Philos. Trans. Roy. Soc. London A 243 (1951) 299. [4] J.P. Hirth, G.M. Pound, J. Chem. Phys. 26 (5) (1957) 1216. [5] E. Bauser, H. Strunk, Thin Solid Films 93 (1982) 185. [6] M. Naoe, N. Matsushita, K. Noma, S. Nakagawa, J. Phys. IV 7 (1) (1997) C1. [7] R. Laishram, S. Phanjoubam, H.N.K. Sarma, C. Prakash, J. Phys. D 32 (17) (1999) 2151. [8] P. Villars, L.D. Calvert, Pearson’s Handbook of Crystallographic Data for Intermetallic Phases, American Society for Metals, Metals Park, 1989. [9] S.V. Yanina, C.B. Carter, 2002, submitted. [10] T.E. Mitchell, K.P.D. Lagerl€ of, A.H. Heuer, Mater. Sci. Technol. 1 (1985) 944. [11] M.G. Norton, S.R. Summerfelt, C.B. Carter, Appl. Phys. Lett. 56 (22) (1990) 2246–2248. [12] Z.A. Munir, Metall. Trans. 22A (1991) 1305.
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[13] S.V. Yanina, C.B. Carter, Mat. Res. Soc. Symp. Proc. 620 (2001) M9.4.1–M9.4.6. [14] K.W. Keller, Metall. Trans. 22A (1991) 1299.
[15] J.P. Hirth, L. Lothe, Theory of Dislocations, Krieger Publishing, Malabar, 1982. [16] K. McCarty, Surf. Sci. 474 (2001) L165.
Dislocations at spinel surfaces Svetlana V. Yanina, C. Barry Carter
*
Department of Chemical Engineering and Materials Science, University of Minnesota, 204 Amundson Hall, 421 Washington Ave. S.E., Minneapolis, MN 55455, USA Received 1 October 2001; accepted for publication 5 March 2002
Abstract The structure of evaporation patterns created by stationary and moving dislocations which terminate on the (0 0 1) surface of MgAl2 O4 is discussed. When the Burgers vectors of the dislocations are inclined with respect to the (0 0 1) crystal plane, these dislocations create evaporation patterns in the form of double spirals. The double evaporation -high half-ledges originating at the dislocation termispirals develop through the synergistic rotation of pairs of 2-A nation points. The dislocations, whose Burgers vectors lie in the (0 0 1) crystal plane, do not form spirals when terminating on the (0 0 1) surface, but may create kinks in the surface steps. The presence of the dislocation-related kinks causes local cusping of the surface steps. Ó 2002 Published by Elsevier Science B.V. Keywords: Evaporation and sublimation; Faceting; Step formation and bunching; Surface structure, morphology, roughness, and topography; Low index single crystal surfaces
1. Introduction The influence of crystal defects on the morphology of the developing crystal is a fundamental topic in materials science [1]. Early theoretical models of crystal growth [2,3] and evaporation [4] of crystal surfaces dealt solely with simple-cubic crystal structures. One of the consequences of this simplified approach was that only screw dislocations with Burgers vector, b, normal to the surface plane were considered as possible sources of surface ledges. In the simple-cubic structure, pure screw dislocations lying in the surface plane and any pure edge dislocations cannot cause surface
*
Corresponding author. Tel.: +612-625-8805; fax: +612-6267246. E-mail address: [email protected] (C. Barry Carter).
ledges [2]. This simplification is not valid for materials with more complex crystal structures where several possible Burgers vectors may be inclined with respect to the surface plane. Clearly, dislocations with such Burgers vectors may form a halfledge upon intersection with the surface regardless of their character. In more complex cases, dislocations with a Burgers vector which is parallel to the surface may dissociate into two or more partial dislocations the Burgers vectors of which each possess out-of-surface components. These partial dislocations may give rise to surface ledges despite the fact that the original dislocation cannot do so [5]. Spinel is one such material whose structure allows for the existence of Burgers vectors that are inclined with respect to the low-index (stable) surfaces. The widespread industrial use of spinel oxides (e.g., in computer memory devices [6] and
0039-6028/02/$ - see front matter Ó 2002 Published by Elsevier Science B.V. PII: S 0 0 3 9 - 6 0 2 8 ( 0 2 ) 0 1 5 6 1 - 3
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ferromagnetic applications [7]) prompted the present study of the interactions between the dislocations and the (0 0 1) surface of the prototypical spinel, MgAl2 O4 .
2. Background The structure of MgAl2 O4 spinel (see Fig. 1) consists of a closely packed framework of O2 anions in a distorted fcc arrangement with 1/8 of tetrahedral interstices (A-sites) and 1/2 of octahedral interstices (B-sites) filled by cations [8]. The at unit-cell parameter, a, of MgAl2 O4 , is 8.075 A 25 °C [8]. The space-symmetry group of normal spinel is Fd3m [8]; in this material, Mg2þ cations are positioned in A-sites while Al3þ cations occupy B-sites [8]. Double steps on the (0 0 1) spinel surface -high (single) may dissociate into pairs of 2-A steps of either straight or curved appearance [9]. (Throughout this paper a=4 will be approximated .) Straight single steps tend to align along as 2 A either the [1 1 0] or the [1 1 0] direction of the crystal. A straight single step will have the same direction of alignment as any other straight single (or an even multiple of 2 A ) above step lying 4 A
Fig. 1. The structure of MgAl2 O4 spinel [9]. Oxygen ions are represented as large gray spheres. Mg2þ cations in tetrahedral coordination are shown as smaller gray spheres. Octahedrally coordinated Al3þ cations are depicted as the smallest black spheres.
(or below) it. A straight single step will tend to align perpendicular to any other straight single (or an odd multiple of 2 A ) above step lying 2 A (or below) it. The height of a single step on the spinel surface is close to the distance between two nearest (0 0 4) (or (0 0 8)) planes in the bulk spinel crystal [9]. In the bulk MgAl2 O4 crystal, cations in the (0 0 1) planes are positioned along the [1 1 0] or [1 1 0] directions. It has been proposed [9] that such anisotropic cation distribution in the spinel structure is at the origins of the preferential alignment of the surface ledges on the (0 0 1) surface of MgAl2 O4 along either the [1 1 0] or [1 1 0] directions. In stoichiometric spinel, the predominant dislocation slip system is (1 1 1) [1 1 0] with the Burgers vector, b, equal to a=2[1 1 0] [10]. In nonstoichiometric spinels, a (1 1 0) [1 1 0] slip system can also be observed [10]. Two of the six possible Burgers vectors thus lie in the (0 0 1) surface plane, specifically along the [1 1 0] and [1 1 0] directions; dislocations with these Burgers vectors will be referred to as having an in-surface b. Edge dislocations and mixed dislocations with an in-surface b must terminate at the (0 0 1) surface. Dislocations with an in-surface b are not expected to create ledges at the points of emergence [2]. The remaining four Burgers vectors intersect the (0 0 1) surface at a 45° angle. Pure screw, pure edge, and most mixed dislocations with b aligned along the [0 1 1], [1 0 1], [1 0 1] or [0 1 1] directions (see Fig. 2) are inclined to the (0 0 1) plane and will be associated with half-ledges on the (0 0 1) surface. At elevated temperatures, vicinal surfaces of the MgAl2 O4 polished close to the (0 0 1) plane reconstruct into terrace-and-step morphologies with the steps aligned along the [1 1 0] and [1 1 0] directions [9]. The dynamics of step motion is high (double dominated by steps which are 4 A steps) [9]. The double steps tend to align with one another and move preferentially along either the [1 1 0] or the [1 1 0] direction of the crystal. If a (or an odd multiple of 2 A ) double step lies 2 A above (or below) another double step, the two steps are oriented perpendicular to one another [9]. (or an even multiple of 2 If a double step lies 4 A A) above (or below) another double step, such steps will be parallel to one another. The double-
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(SPM) (Nanoscope III, Digital Instruments, Santa Barbara, CA) in air using the contact mode of operation. The Si3 N4 cantilevers used were Vshaped (Ultralevers, Park Inst., Sunnyvale, CA) with a nominal spring constant of 0.12 N/m. 4. Experimental observations 4.1. Evaporation spirals Fig. 3 shows a typical evaporation pattern on the (0 0 1) spinel surface. The pattern is formed by four groups of elongated rectangular terraces and resembles a broken fourfold spiral. The terraces ledges (double steps are separated by straight 4 A
Fig. 2. Schematic illustrating the relationship between the Burgers vectors directions and the (0 0 1) planes. Two of the six possible perfect-dislocation Burgers vectors lie in the (0 0 1) plane (along the [1 1 0] and [1 1 0]). The four others lie at 45° to the (0 0 1) plane.
step height is twice the distance between the two nearest bulk (0 0 4) or (0 0 8) planes [9].
3. Experimental A single crystal of MgAl2 O4 spinel of (0 0 1) orientation was cut into 2 2 1 mm3 pieces. The samples were polished and cleaned in aqua regia, acetone and methanol. Heat treatments were performed at 1800 °C in a sintered spinel crucible at a pressure of 104 –105 Torr in a Centorre furnace for 8 h. A similar cleaning procedure has been used for the other oxides [11] and other spinel samples but the annealing temperature is much higher in the present study. Crystallographic orientations on the surfaces were determined by Laue backscattered Xray diffraction. The chemical composition of the surface was monitored ex situ by X-ray energydispersive spectroscopy (XEDS) and X-ray photoemission spectroscopy (XPS). Surface imaging was performed by scanning probe microscopy
Fig. 3. A 10 lm 10 lm height-mode SPM image of an evaporation pattern on the (0 0 1) surface of MgAl2 O4 . The high and are straight steps along the sides of the pattern are 4 A -high aligned along [1 1 0] and [1 1 0]. When steps meet, the 4-A high, as steps split into pairs of straight perpendicular steps 2 A shown schematically.
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[9]) which are aligned along either [1 1 0] or [1 1 0]. At the corners of the spiral, the double steps split -high into pairs of ledges which are straight, 2-A and lie at 90° to one another [9]; the upper ledge remains parallel to the original double step, while the lower one is rotated into the perpendicular h1 1 0i direction. Each rectangular terrace in the evaporation pattern is bound by two long double steps and four short single steps. On the (0 0 1) MgAl2 O4 surface, the width of a pattern-forming terrace is constant within a particular train of steps, but may vary from one train to another. On average, the terrace width is measured to be 300–800 nm. The dimensions of the rectangular spirals depends on the details of the surface morphology but may be as large as 50 m 50 lm. 4.2. Interacting spirals If several dislocation termination sites are situated in the close proximity, their individual evaporation patterns may coalesce. Fig. 4 shows an evaporation pattern shared by a pair of dislocations. Two small spirals originating from two separate dislocation termination sites occupy the central part of the pattern. Unlike the pattern shown in Fig. 3, these small spirals contain both straight and curved single steps. The curved single steps exhibit rough edges and cannot be assigned to any particular crystallographic direction on the surface. Like the straight single-step pairs, the pairs of curved single steps combine to form straight double steps at the corners of the pattern. The first several turns of two individual spirals in Fig. 4 are significantly wider than the first turns of the single spiral shown in Fig. 3. The outer area of the large combined pattern formed through the coalescence of two small spirals has the same topography as the pattern produced by a single dislocation (cf. the outer areas of Figs. 1 and 2). In more complex evaporation patterns, the development of one spiral may precede the formation of the others. In Fig. 5, the central spiral encountered several independent dislocation sites in the course of its evolution. One of these dislocations (A in Fig. 5) created a spiral with the same sense of rotation as the original pattern. Concerted
Fig. 4. A 5 lm 5 lm height-mode SPM image of the evaporation pattern formed when two dislocations emerge at the (0 0 1) surface of MgAl2 O4 . The straight steps at the outer edges high and are aligned along the [1 1 0] and of the pattern are 4 A [1 1 0]. Small spirals originate from the two separate dislocation -high steps termination sites. The arrangement of the curved 2-A at A and B are shown schematically in (b).
motion of the two spirals produced only minor topographic disturbances, such as cusps and dissociated double-step fragments. Another dislocation (B in Fig. 5) developed an evaporation spiral with the opposite sense of rotation with respect to that of the original spiral. As a result, step pileup occurred between the two dislocation termination sites where steps moving out from the primary spiral encountered steps moving out from the secondary spiral. On the three other sides of the
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Fig. 5. A 30 lm 30 lm deflection-mode SPM image of a complex evaporation pattern on the (0 0 1) surface of MgAl2 O4 . The direction of scanning was from left to right; dark lines indicate downward steps; bright lines denote upward steps. high and are Straight steps at the sides of the pattern are 4 A aligned along the [1 1 0] and [1 1 0] directions of the crystal. The site of emergence of a dislocation that created a spiral with the same sense of rotation as the primary (central) spiral is labeled A. The site of emergence of a dislocation that developed a spiral with the opposite sense of rotation as the central spiral is labeled B. These two step sources are shown schematically in (b).
secondary spiral, the uncoordinated motion of steps that belong to both spirals resulted in largescale cusping and dissociation of the double steps into pairs of curved single steps [9]. 4.3. Offset spirals A more complex example of an evaporation pattern is shown in Fig. 6(a). Here, a spiral
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Fig. 6. (a) A 20 lm 20 lm deflection-mode SPM image of an offset evaporation pattern on the (0 0 1) surface of MgAl2 O4 . The direction of scanning was from left to right. In the image, dark lines indicate downward steps; bright lines denote upward steps. high and are Straight steps at the sides of the pattern are 4 A aligned along [1 1 0] and [1 1 0]. The site of dislocation termination labeled B is located outside the central squares and is connected to the pattern center via a trail of cusped steps (a fault line). (b) A 5 lm 5 lm height-mode SPM image of the central part of an offset evaporation pattern on the (0 0 1) surface of MgAl2 O4 . The straight steps at the sides of the pattern are 4 A high and are aligned along [1 1 0] and [1 1 0]. The cusped step fragments gradually change the direction of their alignment from close to [1 0 0] at the top to [1 1 0] at the bottom of the spiral.
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appears to be displaced on one side. Unlike the surface structures discussed above, this evaporation pattern does not have a dislocation termination point at its center: instead, it is flat-bottomed (see Fig. 6(b)). The double steps on right side of the spiral are cusped; the cusps are aligned along a line curving from the base of the spiral to a dislocation termination site (B in Fig. 6(a)) at the outer edge of the spiral. This dislocation termination site is not enclosed by a spiral. Instead, it is attached to a straight double-step segment which is itself connected to a cusped double step and a pair of curved single steps. Remarkably, the cusped double steps shown in Fig. 6(a) are situated below the dislocation termination site while the single steps positioned directly above the dislocation termination site appear to be unaffected by the dislocation. The cusped double steps maintain the same spacing on either side of the cusp. The cusps in the upper steps appear straight and are aligned close to the [1 0 0] direction. The cusps in the lower steps originally lie along [1 0 0] but later along [1 1 0], with the location of the cusps shifting gradually to the right (see Fig. 6(b)). In some cases, an evaporation pattern may not show such displacements, but nevertheless will not contain a dislocation termination point at its center. Fig. 7(a),(b) shows a flat-bottomed evapo-high ration spiral which contains a cusped 6-A ledge amongst the regular double steps. This ledge originates at the dislocation termination point (A in Fig. 7) and dissociates into a straight single step plus a straight double step in the corner of the spiral (B in Fig. 7). The entire step-train on this side of the spiral has a narrower step spacing compared with the step spacing in the other steptrains in the pattern. The bottom of the evaporation pattern depicted in Fig. 7 is flat. In this case, the dislocation termination site does not lie outside the spiral, but is located to one side of this flat area. This particular dislocation termination site does not have an individual evaporation spiral attached to it. 4.4. Offset step-trains As illustrated in Fig. 8, a double-steptrain which is not related to a particular
Fig. 7. (a) A 10 lm 10 lm deflection-mode SPM image of flat-bottomed evaporation pattern on the (0 0 1) surface. The direction of scanning was from left to right. Dark lines indicate downward steps; bright lines denote upward steps. The straight high and are aligned steps at the sides of the pattern are 4 A along the [1 1 0] and [1 1 0] directions of the crystal. A cusped 6-high ledge originates at the dislocation termination site (A) A -high and a 2-A -high step at the and dissociates into a 4-A pattern corner (at B). (b) A 2 lm 2 lm height-mode SPM image of the cusped ledge shown in (a). At the dislocation termination site (A) the height of the narrow step changes . The 6-A -high ledge dissociates at B into abruptly from 2 to 6 A a pair of perpendicular steps. At A, the contrast at the steps is darker for the higher step.
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cusped step fragments in the lower part of Fig. 8 has dissociated into a loop of curved single steps. 4.5. Turning double steps
Fig. 8. A 10 lm 10 lm deflection-mode SPM image of an offset double-step-train which was traversed by a moving dislocation termination site. The direction of scanning was from left to right. In the image, dark lines indicate downward steps; bright lines denote upward steps. The straight steps in the train high and are aligned along the [1 1 0] direction of the are 4 A crystal. The position of the mobile dislocation termination point is labeled A. The likely initial position of the dislocation termination point is labeled B.
dislocation–termination site may still contain offset steps. Similar to the cusped steps in the evaporation pattern displayed in Fig. 6, the offset steps in this step-train are also located below the dislocation termination site (B in Fig. 8). Like the dislocation termination site shown in Fig. 6, the one in Fig. 8 is also not associated with a spiral. In Fig. 8, the steps which are situated directly above the dislocation termination site, appear not to interact with it. The cusp trail ending at the dislocation termination site originates at the edge of the first step in the train (A in Fig. 8). This trail appears to be unrelated to any other surface features situated in its vicinity. In Fig. 8, the cusps in the lower offset steps are displaced (to the lower right) with respect to the cusps in the upper steps. The upper-step cusps have rough edges, while the cusps in the middle steps have a well defined direction of alignment along [1 1 0]. One of the
A fundamentally different case of double-step cusping observed on the (0 0 1) spinel surface is shown in Fig. 9. Unlike the offset double steps discussed above, the group of double steps in Fig. 9 is cusped over a small surface region only. Here, the cusps in the steps do not align along any particular line or direction on the surface. The spacing of the steps on either sides of the cusped area are different. Local double-step cusping is usually limited to compact isolated areas of the surface. The average size of the affected regions is 0.5–3 lm. Observations show that this phenomenon is not accompanied by the presence of any other visible crystal defects in the vicinity (5–20 lm) of the cusped steps.
Fig. 9. A 10lm 10 lm deflection-mode SPM image showing curved segments in a double-step-train on the (0 0 1) surface. The direction of scanning was from left to right. On the image, dark lines indicate downward steps; bright lines denote upward high) steps on the image are aligned steps. Straight double (4 A along the [1 1 0] direction of the crystal. Cusping of the steps is limited to the central area of the image. No special surface features are visible in the vicinity of the cusps. Step segments situated in the region labeled A are more narrowly spaced than those in the region labeled B.
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5. Discussion 5.1. Dislocations with out-of-surface components of b: structure of evaporation spirals on the (0 0 1) surface of MgAl2 O4 As mentioned above, the dislocations which are expected to create half-ledges when terminating on the (0 0 1) surface of spinel may be pure screw, pure edge or mixed (such as 30°) in character. As the crystal surface evaporates, a half-ledge rotates about a dislocation emergence point, giving rise to an evaporation spiral [3]. In itself, the process of formation of the spiral-shaped evaporation pattern is not directly related to the nature of the emerging dislocation: all it requires is a half-ledge which is attached to a point on the crystal surface. Therefore, a dislocation of any character may be the origin of the evaporation spiral on the (0 0 1) surface of spinel, provided the dislocation has a component of its Burgers vector which does not lie in the (0 0 1) plane. It is not possible to identify the character of this dislocation solely on the observations of its evaporation pattern on the (0 0 1) surface; to do so requires a knowledge of the line direction. Here and below, the dislocations in spinel will be classified into those with b lying in
the (0 0 1) plane and those with b inclined to the (0 0 1) plane. Evaporation spirals found on the (0 0 1) surface of MgAl2 O4 have an uncommonly complex topography: they consist of four trains of interloped terraces (see Fig. 3). This is in contrast to the evaporation spirals observed on other ceramic materials [12], which typically consist of one large terrace spiraling up from the site of dislocation emergence. It is proposed that evaporation spirals on the MgAl2 O4 (0 0 1) surface are created through the rotation of not one but two half-ledges, each of high (see Fig. 10). Combined, the which is 2-A heights of these two half-ledges will give a value , or a=2[0 0 1], which is the component of a of 4 A perfect-dislocation Burgers vector normal to the (0 0 1) surface [10]; b lies at 45° to the (0 0 1) plane. The formation of two, instead of one, surface half-ledges at the dislocation sites on MgAl2 O4 (0 0 1) is determined by the surface structure of spinel. The (0 0 1) surface of MgAl2 O4 exists in the form of two variants, one of which tends to grow/ evaporate preferentially along the [1 1 0] direction, while the other develops preferentially along the [1 1 0] direction [9,13]. The surface terraces which belong to the different surface variants are separated by single steps, while the terraces formed by
-high (single) half-ledges emerges Fig. 10. Schematic of a double evaporation spiral on the (0 0 1) surface. A pair of perpendicular 2-A at a terminating dislocation at D. One of the half-ledges is aligned along the [1 1 0] direction, while the other one is aligned along the [1 1 0] direction. In the course of evaporation, the half-ledges rotate at the same rate but with a 90° phase-shift thus creating two -high (double) steps further from site D. The parallel segments independent spirals. The parallel segments of the spirals merge into 4-A of the half-ledge which aligns preferentially along the [1 1 0] direction (shown in gray) serve as the upper halves of the double steps aligned along the [1 1 0] direction and the lower halves of the double steps aligned in the [1 1 0] direction. The darker step behaves similarly but also rotates 90°. The progression at center of such a spiral, close to the emerging dislocation D, is shown in (b) and (c).
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the same surface variant are divided by double steps [13]. From structural considerations, a dislocation terminating on the (0 0 1) spinel surface should form a double half-ledge [13]. However, removal of material from the edge of this double half-ledge will lead to its immediate dissociation into a pair of two single half-ledges [13] on the evaporating surface. The single half-ledges which are attached to the dislocation termination site will rotate until they attain their preferred directions of alignment, so that if one of these half-ledges is aligned along the [1 1 0] direction, the other single half-ledge is aligned along the [1 1 0] direction [9]. If oriented along their respective preferred directions of alignment, the two half-ledges move along the surface at the same rate, but with a 90° ‘phaseshift’ [9]. When, in the course of evaporation, the half-ledges rotate away from their preferred directions of alignment, they slow down. This 90° phase difference causes the slower half-ledge to become an obstacle to the motion of the more rapidly moving half-ledge (see Fig. 10). When the faster half-ledge catches the slower one, a double step is formed [9]. Rotation of the two half-ledges about the dislocation termination point leads to reversal in their motion. The rapid half-ledge becomes the slow, and vice versa. This causes the separation of the new fast moving half-ledge from the new slower half-ledge at the corner of the spiral. The slower half-ledge then becomes the upper half of a new double step, while the rapid ledge continues moving. It eventually becomes the lower half of the next double step, as shown in Fig. 10. After the next rotation through 90°, the faster half-ledge slows and becomes the upper half of a new double step while the second half-ledge starts to move faster. After four consecutive rotations, four double steps are formed. At the corners of the spiral, where the velocity of ledge propagation reverses, the double steps separate into pairs of perpendicular single steps. The progression at center of such a spiral is shown in Fig. 10(b) and (c). The straight dislocations move out from D. The rate of motion is always determined high step (drawn as the by the slower (upper) 2-A outer line in the schematics). The new faster moving segment in Fig. 10(c) quickly catches the
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slow moving upper step; its length is then determined by the slower moving segments. The evaporation pattern created through such a cooperative rotation of two single half-ledges is, morphologically, a double spiral (see Fig. 10). The elongated terraces in the evaporation pattern have twofold symmetry and align either parallel or perpendicular to one another. Superposition of the two perpendicular groups of parallel terraces creates a pseudo-fourfold appearance of the resulting evaporation pattern. It is proposed [9] that the existence of preferential directions of alignment/ growth of the ledges on the (0 0 1) surface of MgAl2 O4 is related to the anisotropic distribution of the cations in the (0 0 1) crystal planes in spinel structure. 5.2. Interacting spirals Interaction of a developing evaporation spiral with obstacles (such as other dislocations) may locally affect the rates of propagation of the rotating half-ledges. This effect is illustrated in Fig. 5, where the central spiral encounters another with the opposite sense of rotation (compare the central spiral in Fig. 5 with the ‘spiral’ at A). Here, in order to accommodate the motion of steps from two dislocation termination sites, the double steps surrounding the secondary spiral become cusped and dissociate. A related process is shown in Fig. 4, where two spirals with the same sense of rotation merge into a common evaporation pattern. The doubled rate of material removal from the spiral bottom leads to the widening of the lowest terraces and to the formation of two pairs of curved single steps in the opposite corners of the spiral bottom. Similar to the steps that constitute regular evaporation spirals, the double steps that make up the double spirals on the (0 0 1) surface of MgAl2 O4 maintain a steady-state inter-step distance [4]. However, upon rotation, the upper half of a double step in a double spiral becomes not the upper, but the lower half of a perpendicular double step. Therefore, the process of material removal along the edge of a given double step will not directly affect the widths of the two perpendicular double steps which are adjacent to it. This
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is in contrast to the typical evaporation spirals [14] where, from the structural standpoint, all steps are the differently oriented segments of the same halfledge. In such patterns, any changes in the step spacing which occur at one side of the spiral are typically mirrored by steps located on the other sides of the spiral. Large variations are observed in the inter-step distances for the step-trains belonging to the same evaporation spirals on a particular (0 0 1) spinel surface. In order to accommodate several independent emerging dislocations, the step-train on the lower left side of the evaporation pattern shown in Fig. 5 increases its spacing from the center of the pattern to the pattern edge. These changes, however, do not perturb inter-step spacing of the three other step-trains in the pattern. 5.3. Dislocations interacting with spirals In stoichiometric spinels, the onset of plastic deformation occurs at 1800 °C, while the deformation of non-stoichiometric spinels may take place at substantially lower temperatures [10]. The samples used in the present work were not subjected to stress intentionally; nevertheless, the possibility of the motion of dislocations in MgAl2 O4 at 1800 °C cannot be ignored. Coincidentally, the 1800 °C is the temperature chosen in this study for the observations of the ledge-wise evaporation on the (0 0 1) spinel surface. Furthermore, at temperatures below 1800 °C, the slow rate of advancement of the moving step-trains, coupled with the reduced inter-step spacing [4], make it difficult to collect data on step motion [9]. At higher (1900 °C) temperatures, the high rates of material removal from the steps cause them to roughen the step edges and destroy the ordered arrangements of the steps in the step-trains. The surface observations of the specimens that were annealed at 1800 °C, therefore, gave a unique opportunity to study interactions of moving steptrains with moving dislocations. Movement of a dislocation termination point along an evaporating surface need not correspond to motion of the dislocation itself since the dislocation may be shallowly inclined with respect to the surface: as the layer of material is removed, the dislocation termination point shifts along the
projection of the dislocation line on the evaporating surface. While such motion may be continuous throughout the heat treatment, its rate is expected to be slow. For a pure screw dislocation with b aligned along [1 0 1], the dislocation termi, as nation point will shift by a=8[0 1 0], or 1.0 A spacing) is reeach (0 0 1) crystal plane (with 2-A moved. The developing evaporation spiral may also move as the dislocation termination point shifts. As discussed below, an exception to this rule arises when the drift of the dislocation termination point is caused by the motion of the dislocation itself. The spiral shown in Fig. 6 does not have a dislocation termination point at its center. Yet, in the absence of such a point, the spiral cannot develop. The dislocation termination site at the edge of the pattern (denoted by B in Fig. 6), in contrast, does not have a spiral evaporation pattern attached to it (see A). Again, on the evaporating surface, the development of a spiral around this site appears unavoidable. In Fig. 6(a), an offset line connects the spiral-less dislocation termination site and the flat bottom of the dislocation-less spiral. This line cuts through the steps which lie below the dislocation termination site. Since the steps normally move from the spiral center, the offset steps could not have interacted with the dislocation termination site that is situated above them. On the other hand, the steps located above the dislocation termination point should have interacted with it already but there is no indication of such an interaction. It is proposed that the offset evaporation pattern in Fig. 6 developed in two stages. At the beginning of the heat treatment, the dislocation termination point (which is now situated at the outer edge of the pattern) was located in the center of the pattern. After the spiral has been developed, the evaporation of material from the vicinity of the dislocation line has removed an obstacle that was pinning the dislocation. After the dislocation was released, it moved to its final position at the edge of the pattern. The line of offsets seen in Fig. 6 shows the trajectory of motion of the dislocation termination point. It is likely that the dislocation movement continued until the end of the heat treatment, as evidenced by the fact that the final
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position of the dislocation termination point is not surrounded by a new evaporation spiral: the dislocation termination point has moved faster than the surface steps. This conclusion is supported by Fig. 6(a), which shows similar offsets in a series of double steps caused by the dislocation motion. This observation of a dislocation moving out of an etch pit is directly analogous to the classic demonstration of moving dislocations in LiF where the pits are chemical in origin and the motion of dislocations is caused by an applied stress [15]. Similar observations have been made recently on Ni3 Al using LEEM [16]. The motion of the pattern-forming steps, albeit slow if compared with that of the dislocation termination point, did not cease when the dislocation moved out of the pattern center. As Fig. 6(b) shows, the trail of the moving dislocation termination point is curved. It is expected that curving of the drift trail is the result of the shifting of the cusped fragments of the double steps along the [1 1 0] direction. For the steps close to the bottom of the spiral, the cusping occurred early on in the dislocation motion. Such steps have had more time to recover so that their cusped fragments are shifted further along the step edges. The cusped fragments in the upper steps were created later than their lower counterparts and did not move far from their original positions. The evaporation spiral shown in Fig. 6(a) is flat bottomed. Flattening of the spiral bottom may be understood if the structure of a regular evaporation spiral is recalled. At the origin of the regular evaporation spiral, there are half-ledges emerging at the point where the dislocation line intersects the surface plane (see Fig. 3). The four step-trains making up the sides of the spiral are created and augmented through the conjugated rotation of these half-ledges. In the dislocation-less spiral, there are no such half-ledges. Hence, no new steps are created and the step-trains become independent from one another in their motion. Such steptrains are expected to move in the same fashion as any other independent step-train on the surface [9]. In some cases, the movement of the dislocation termination point may cease before the heat treatment ends. As illustrated in Fig. 7, the dislocation termination point has left the center of the
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spiral but has not moved further than the side of the flat spiral bottom. Similar to the spiral in Fig. 6, the dislocation termination point shown in Fig. 7(b) is expected to have been originally pinned at the spiral center, and to start its motion only after the spiral had developed. In this case, however, the dislocation termination point became trapped at the lowest step edge so that further motion only occurred with evaporation from the step. The spiral shown in Fig. 7 has had time to recover. Thus, no line of offsets connect the center of the spiral to the final positions of the dislocation termination point on the surface, instead, this area is flat. Also, the step spacing of the train adjoining the new position of the dislocation termination point has been reduced. Fig. 7 shows that the 6-high half-ledge (along AB) is cusped which inA dicates that the new evaporation spiral started developing around the new (quasi-stationary) position of the dislocation termination point on the surface. 5.4. Moving dislocations interacting with independent step-trains The motion of a dislocation may also become evident through its interaction with an independent step-train. Such an interaction is illustrated in Fig. 8, where the moving dislocation-termination point (B in Fig. 8) passed across a step-train. It is proposed that, originally, the dislocation termination site was situated in the lower left corner of the image (in area A in Fig. 8), possibly at a nanoledge edge. In the course of evaporation, the nanoledge has spun off a step-train (see Fig. 8) which may have triggered the motion of the dislocation. As was discussed for Fig. 6(a), the cusped steps in the train in Fig. 8 which are situated below the dislocation termination site have been cut by the moving dislocation line. This observation indicates that, in this case, the velocity of the dislocation termination point exceeded the rate of advancement of the steps in the train and that the dislocation continued to move until the heat treatment was complete. The curving of the offset line and the dissociation of the cusped fragments of some of the offset steps in the lower part of Fig. 8 is
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attributed to step recovery. As before, the steps close to the current position of the dislocation termination point have had less recovery time and their cusps have remained close to their original positions. 5.5. Dislocations with in-surface b As discussed above, in spinel, a dislocation with the Burgers vector lying in the (0 0 1) plane (e.g., a=2[1 1 0] or a=2[1 1 0]) cannot create half-ledges when it emerges at a flat (0 0 1) surface. However, on a vicinal surface, such a dislocation may terminate at a surface step. Provided that its Burgers vector is not parallel to the line direction of the step, this dislocation will create a kink on the step as shown in Fig. 11. A dislocation-related kink in the step may be considered as a two half-ledges on the face of this step [2]. A dislocation with an in-surface b will create a kink when terminating at the surface, regardless of its character. It should be noted, however, that dislocations lying in, or close to, the (0 0 1) surface (e.g., near-screw dislocations with b ¼ a=2[1 1 0] or a=2[1 1 0]) are expected to move rapidly out of the crystal at elevated temperatures. Therefore it is proposed that it is mainly edge dislocations that may form kinks in the surface steps. In Fig. 9, the double steps situated above the cusped area are straight. It is proposed here that the observed step cusps are due to interactions with dislocations having an in-plane Burgers vector. It is unlikely, though not impossible, that such cusps will be caused by contaminants at these high temperatures since individual atoms would be expected to diffuse under the action of the step line tension and there is no indication of particle formation; all areas were scanned in both deflection mode and height mode. Provided the steps develop cusps only in the vicinity of the dislocation line, this indicates that the steps come in contact with the dislocation at one point only. Consequently, this implies that the dislocation line intersects the surface as opposed to lying in (or close to) the surface plane. As noted above, such dislocations with an in-surface b are likely to be predominantly edge in character. Like a dislocation-related half-ledge, the dislocation-related kink in a step must necessarily be
Fig. 11. Schematic of a [1 1 0] surface step intersected by dislocation with an in-surface direction of its Burgers vector (b ¼ a=2½1 1 0 Þ. (a) A stationary kink formed at the dislocation termination site divides the step into two segments. The dislocation causes a kink (D). At the step edge, gray arrows indicate two moving kinks of different signs which are not caused by the dislocation. (b) The dislocation-related kink can be eliminated through the advancement of kink of the opposite sign reducing the dislocation line length. The part of the step removed through the advancement of the moving kink is shown in gray. (c) The immobile dislocation-related kink hinders the advancement of kink of the same sign. A cusp in the step is formed as a result of kink pileup. In (b) and (c), the part of the step removed through the advancement of the moving kink is shown in gray.
fixed to the dislocation termination point: as it moves away from the initial dislocation termination point it will extend the dislocation line by the distance it travels along the step edge making such movement unfavorable. Such kinks may be altogether eliminated through the advance along the step edge of a kink of the opposite sign (see Fig. 11(a),(b)). At the same time, advancing kinks of the same sign cannot pass through the (stationary)
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site of the dislocation-related kink (see Fig. 11(a)– (c)). Accumulation of these kinks at the site of a terminating dislocation will result in cusping of the step. The cusp is anchored by the dislocationrelated kink and can dissipate only when enough kinks of the opposite sign reach it. The dislocation-related kink, therefore, acts as a one-way valve for the kinks moving along the step edge: it lets the kinks of one sign move through but stops kinks of the same sign. The presence of the dislocation-related kink at the step edge may, therefore, distort the steady-state regime of material removal which is established along the edge of a straight moving step [4]. This is illustrated in Fig. 9, where the straight segments of the cusped steps, situated in the upper left corner, are more narrowly spaced than their counterparts located in the lower right corner. The rate of advancement of the narrowly spaced step segments is also slower than that of the rest of the steps (as the narrow-spaced segments are situated lower in the image than their widespaced counterparts). It is expected that the oneway exchange between the left and the right step segments, which are separated by a dislocationrelated kink, is the reason for the observed discrepancy in their spacing and rates of propagation along the surface. After the step breaks away from the dislocation termination site, the dislocation-related kink is removed from the step edge and the step eventually recovers (i.e., regains its regular spacing and straight appearance, see the steps shown in the upper part of Fig. 9). As Fig. 9 shows, the dissipation of the cusp proceeds through its redistribution along the step edge.
6. Conclusions In MgAl2 O4 , dislocations with Burgers vectors intersecting the (0 0 1) crystal plane create evaporation patterns in the form of double spirals. These double evaporation spirals are actually created through the cooperative rotation of pairs of per-high, half-ledges which pendicular single, 2-A originate at the dislocation termination points on the surface. The formation of pairs of perpendicular single half-ledges at the points of dislocation
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termination on the (0 0 1) spinel surface is believed to be related to the structure of the (0 0 1) surface variants in spinel. Dislocations with b parallel to the (0 0 1) surface in MgAl2 O4 may terminate at surface steps by creating kinks. The dislocation-related kinks divide the steps into pairs of step segments that may propagate along the surface at different rates. This asymmetry leads to cusping of the steps. In the event of dislocation motion at elevated temperatures (1800 °C), the drift of the dislocation termination point along the surface typically proceeds at a significantly higher velocity than the motion of the surface steps. Such movement causes offsets in the intersected surface steps.
Acknowledgements SVY is in the Chemical Physics Program at the University of Minnesota. This research has been supported by the US Department of Energy under Grants No. DE-FG02-92ER45465 and DE-FG0201ER45883. The SPM used is part of the IT Characterization Facility at the University of Minnesota. The authors would like to acknowledge discussions with Dr. N. Ravishankar.
References [1] A.R. Verma, Crystal Growth and Dislocations, Academic Press, New York, 1953. [2] F.C. Frank, Discuss. Faraday Soc. 5 (1949) 48. [3] W.K. Burton, N. Cabrera, F.C. Frank, Philos. Trans. Roy. Soc. London A 243 (1951) 299. [4] J.P. Hirth, G.M. Pound, J. Chem. Phys. 26 (5) (1957) 1216. [5] E. Bauser, H. Strunk, Thin Solid Films 93 (1982) 185. [6] M. Naoe, N. Matsushita, K. Noma, S. Nakagawa, J. Phys. IV 7 (1) (1997) C1. [7] R. Laishram, S. Phanjoubam, H.N.K. Sarma, C. Prakash, J. Phys. D 32 (17) (1999) 2151. [8] P. Villars, L.D. Calvert, Pearson’s Handbook of Crystallographic Data for Intermetallic Phases, American Society for Metals, Metals Park, 1989. [9] S.V. Yanina, C.B. Carter, 2002, submitted. [10] T.E. Mitchell, K.P.D. Lagerl€ of, A.H. Heuer, Mater. Sci. Technol. 1 (1985) 944. [11] M.G. Norton, S.R. Summerfelt, C.B. Carter, Appl. Phys. Lett. 56 (22) (1990) 2246–2248. [12] Z.A. Munir, Metall. Trans. 22A (1991) 1305.
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[13] S.V. Yanina, C.B. Carter, Mat. Res. Soc. Symp. Proc. 620 (2001) M9.4.1–M9.4.6. [14] K.W. Keller, Metall. Trans. 22A (1991) 1299.
[15] J.P. Hirth, L. Lothe, Theory of Dislocations, Krieger Publishing, Malabar, 1982. [16] K. McCarty, Surf. Sci. 474 (2001) L165.