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Terraces and ledges on (001 ) spinel surfaces
Surface Science 513 (2002) L402–L412 www.elsevier.com/locate/susc
Surface Science Letters
Terraces and ledges on (0 0 1) spinel surfaces Svetlana V. Yanina, C. Barry Carter
*
Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, 151 Amundson Hall, Minneapolis, MN 55455, USA Received 5 November 2001; accepted for publication 30 April 2002
Abstract The motion of steps on the (0 0 1) surface of MgAl2 O4 spinel is discussed. Atomic force microscopy observations of surface faceting and evaporation after heating to high temperatures are reported. The structural relationship between single and double-surface steps on the MgAl2 O4 (0 0 1) surface is established. Mechanisms for the formation, motion and dissociation of the double steps are proposed. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Atomic force microscopy; Evaporation and sublimation; Faceting; Step formation and bunching; Surface structure, morphology, roughness, and topography; Single crystal surfaces
1. Introduction Understanding the kinetics of step motion on vicinal surfaces is fundamental to understanding the behavior, development and properties of surfaces. While the theoretical foundations of surface kinetics are well developed [1–3], direct experimental observations only became possible with the advance of new microscopes for imaging surfaces. Techniques which have been used include transmission electron microscopy (TEM) [4–7], visible light microscopy (VLM) [8] and scanning tunneling microscopy (STM) [9]. STM has made the direct investigation of step dynamics on semiconductor and metal surfaces possible. Atomic force micros-
* Corresponding author. Tel.: +1-612-6248805; fax: +1-6126267246. E-mail address: [email protected] (C. Barry Carter).
copy (AFM), provides similar three-dimensional images of non-conductive materials, in particular ceramic oxides [10,11] and bio-minerals [12]. For practical reasons, most surface studies have concentrated on the mechanisms of crystal growth; some technologically important systems may be observed in situ [12]. For ceramic oxides it is usually impractical to study directly most hightemperature processes, such as surface reconstruction and surface evaporation, using in situ observations. However, the behavior of surfaces at high temperatures must be understood in order to explain the surface morphologies of many materials, for example thin ceramic films which are grown under non-equilibrium conditions [13]. The present paper, which discusses high-temperature step motion on the (0 0 1) surface of MgAl2 O4 spinel, is a contribution towards the better understanding of the dynamics of step motion on oxide surfaces.
0039-6028/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 9 - 6 0 2 8 ( 0 2 ) 0 1 8 2 5 - 3
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2. Background In the normal spinel structure, oxygen anions form a distorted face centered cubic (fcc) sublattice (see Fig. 1) [14–16], where Mg2þ cations occupy 1/8 of the tetrahedral interstices, and Al3þ cations occupy 1/2 of the octahedral interstices. The unit and the cell parameter of MgAl2 O4 is 8.075 A space-symmetry group is Fd3m [17]. The complex nature of the structure of spinel allows for two possible bulk-terminated arrangements of ions at its (0 0 1) surface. One arrangement may be formed by terminating the spinel crystal at a (0 0 1) plane which contains only O2 anions and octahedrally coordinated Al3þ cations; this type of (0 0 1) phase will be referred to as an (0 0 4) plane in this paper to distinguish it from an (0 0 1) plane which contains only Mg2þ cations and is referred to as an (0 0 8) plane (see Fig. 2). In the latter case, the topmost crystal plane accommodates two cations per unit-cell, which leaves the underlying O/Al(0 0 4) plane partially exposed at the surface. In MgAl2 O4 , a pair of the nearest-neighbor (0 0 8) (or (0 0 4)) planes is separated by a/4[0 0 1], throughout this paper). (which is referred to as 2 A
Fig. 1. The structure of MgAl2 O4 spinel. O2 anions are shown as large gray spheres, Mg2þ cations in tetrahedral coordination as small gray spheres, and octahedrally coordinated Al3þ cations as small black spheres. The unit-cell parameter of . MgAl2 O4 is 8.075 A
These planes have twofold symmetry; they are not equivalent with respect to the fourfold rotation
Fig. 2. Structure of {0 0 1} planes in MgAl2 O4 crystal. O2 anions are shown as large gray spheres, Al3þ cations as small black spheres, and Mg2þ cations as small gray spheres. (a) {0 0 4} plane built from O2 anions and octahedrally coordinated Al3þ cations. (b) {0 0 8} plane formed by Mg2þ cations in tetrahedral coordination, shown together with the underlying {0 0 4} plane.
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around the [0 0 1] axis. The (0 0 8) (or (0 0 4)) planes which are related by a 90° rotation around the [0 0 1] axis are separated by 2n þ 1 multiples of 2 , where n is an integer. The (0 0 8) (or the (0 0 4)) A planes which are equivalent with respect to the 90° rotation around the [0 0 1] axis are separated by 2n . multiples of 2 A The twofold symmetry of crystal planes of the (0 0 1) orientation in MgAl2 O4 originates from the fact that the cations in the spinel structure are distributed throughout the available interstices along certain directions. For the (0 0 4) planes, the Al3þ cations fill octahedral interstices along either the [1 1 0] or the [1 1 0] direction as shown in Fig. 3(a) and (b), respectively. For the (0 0 8) planes, the preferred direction is one where the edges of the tetrahedral interstices occupied by the Mg2þ cations are aligned along either [1 1 0] or [1 1 0] as
shown in Fig. 3(c) and (d), respectively. For each (0 0 4) or (0 0 8) plane, there is only one such filled/ preferred direction. While there are no available data on the atomicscale morphology of MgAl2 O4 (0 0 1), the (0 0 1) surface of magnetite (Fe3 O4 ), which has an inverse spinel structure, has been studied in detail [18]. In this study [18], the surface of Fe3 O4 (0 0 1) was found to be corrugated on the atomistic scale in the [1 1 0] and [1 1 0] directions; corrugations on the adjacent terraces were rotated through 90° with respect to each other. It was then proposed [18] that the reconstructed surface of the Fe3 O4 (0 0 1) surface consists of the Fe cations in the tetrahedral sites which reside on top of the plane containing oxygen anions and the octahedrally coordinated Fe cations; the plane of tetrahedral sites is (0 0 8) while the lower plane is (0 0 4). The
Fig. 3. Cation distribution in planes of {0 0 1} orientation in MgAl2 O4 . O2 anions are shown as large gray spheres, Al3þ cations are apart. Al3þ cations fill the upper small black spheres, and Mg2þ cations as small gray spheres. ((a) and (b)) Two {0 0 4} planes, 2 A apart. The direction plane along the [1 1 0] direction, and the lower plane along the [1 1 0] direction. ((c) and (d)) Two {0 0 8} planes, 2 A of alignment of edges of Mg2þ -filled tetrahedral interstices in the upper plane is rotated through 90° with respect to that in the lower plane.
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surface corrugations were attributed to the linking of the dangling (unsaturated) bonds of the topmost tetrahedrally coordinated Fe cations. Fe3 O4 (0 0 1) is not the only known surface in which the surface structure involves a 90° rotation of the direction of surface corrugations associated with stepping up or down from one terrace to another. The mechanism of reconstruction of Si(0 0 1) involves the linking of dangling bonds of tetrahedrally coordinated Si atoms to form corrugations aligned in either the [1 1 0] or the [1 1 0] direction. Being of the diamond-cubic type, the Si crystal structure possesses a center of inversion. As a result, for the adjacent terraces separated by a monatomic step, the direction of corrugation alignment is rotated through 90° [9]. Due to its poor conductivity, STM of MgAl2 O4 is not generally possible. The present paper, therefore, will be limited to the discussion of the dynamics of step motion on the MgAl2 O4 (0 0 1) surface, without a detailed analysis of surface structure on the atomic scale.
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acetone and methanol. The specimens were heat treated in a spinel crucible in vacuum (104 –105 Torr) in a Centorre furnace at 1470–2070 K for 8 h. Surface characterization was performed by AFM in air in the contact mode of operation (Nanoscope III, Digital Instruments, Santa Barbara, CA), using Si3 N4 V-shaped cantilevers (Ultralevers, Park Inst., Sunnyvale, CA) with a nominal spring constant of 0.12 N/m. Because of optical artifacts, deflection-mode images are shown for large surface areas. For deflection-mode images, the direction of scanning was from left to right. The chemical composition of the surface was monitored ex situ by X-ray energy dispersive spectroscopy (XEDS) and X-ray photoemission spectroscopy (XPS). Crystallographic orientations on spinel surfaces were determined by Laue backscattered X-ray diffraction.
4. Observations
3. Experimental
4.1. Surface rearrangement at sub-evaporation temperatures
2 2 1 mm single crystals of MgAl2 O4 (0 0 1) spinel were polished and cleaned in aqua regia,
As can be seen in Fig. 4, the polished (0 0 1) surface of MgAl2 O4 , which was heat treated at
Fig. 4. 5 5 lm height AFM images of the (0 0 1) surface of MgAl2 O4 . (a) The specimen was acid-cleaned and annealed at 1470 K. Misalignment between the polished surface and the (0 0 1) plane of the crystal is accommodated by narrow terraces with longer sides aligned along [1 1 0] direction of the crystal. (b) The specimen was annealed at 1870 K. Misalignment between the polished surface and the (0 0 1) plane is accommodated by square terraces with edges aligned along both [1 1 0] and [1 1 0] directions of the crystal.
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sub-evaporation temperatures (1470–1870 K), rearranges into a terrace-and-ledge morphology. The angle measurements show that the terraces are parallel to the (0 0 1) planes, while the ledges are aligned along the [1 1 0] and the [1 1 0] directions of the crystal. Depending on the degree and the direction of misalignment between the polished surface and the (0 0 1) crystal planes, the surface rearrangement may result in the formation of either narrow elongated (Fig. 4(a)) or wide square (Fig. 4(b)) terraces. If the polished surface is aligned with the (0 0 1) crystal planes along either the [1 1 0] or the [1 1 0] direction, the surface terraces develop preferentially along that direction and the resulting surface morphology is ‘elongated’. If the polished surface is misaligned with the (0 0 1) crystal planes along both the [1 1 0] and the [1 1 0] directions, no such preferred direction of terrace growth exists, and the ‘square’ morphology ensues. For the surfaces annealed at 1470–1670 K, the average height of the ledges is 5–10 nm. Small were also ledges of the height of multiples of 2 A observed on the surface (see Fig. 5). Here and -high ledges are called single steps, 4-A below, 2-A high ledges are called double steps. All other ledges are referred to as nanoledges. 4.2. Surface evaporation Heat treatments at 1470–1870 K generally result in the formation of many more single steps than double steps. The opposite is generally true for surfaces annealed above 2070 K, i.e., under conditions where evaporation plays an important role. On evaporated spinel surfaces the single steps can be found only at double-step intersections, or at dislocation termination sites (or other crystal defects) on the surface. As can be seen in Fig. 6, evaporation from nanoledges on the surface generates series (or trains) of double steps. Double steps formed on the (0 0 1) spinel surface upon heat treatment at 2070 K are straight and aligned along either the [1 1 0] or the [1 1 0] direction of the crystal. The average distance between the double steps appears to depend only weakly on the details of the surface morphology. Thus, far away from nanoledges and other large surface features, such as dislocation
Fig. 5. AFM image of steps on (0 0 1) surfaces of MgAl2 O4 . A 2 2 lm deflection image of the surface annealed at 1670 K. The direction of scanning was from left to right. Dark lines indicate downward steps; bright lines denote upward steps. Thick dark lines represent nanoledges; thin dark lines depict 2 (single) steps aligned along [1 1 0] direction of the crystal. A Thick bright lines denote nanoledges aligned along [1 1 0] direction. A single step is denoted by the arrow.
etch pits [19], the average step distance in a step train was measured to be 400 50 nm. The double-step lengths can be large (steps up to 100 lm in length were observed) and may be limited only by the size of the specimens. In some areas, straight double steps undergo cusping (see Fig. 7). Such cusping typically only occurs in small isolated surface areas. Double steps may undergo dissociation into pairs of single steps (see Fig. 8). Such dissociation typically affects the double steps situated between the intersecting nanoledges (see Fig. 8(a) and (b)). As can be seen in Fig. 8(a), the straight single steps on the MgAl2 O4 (0 0 1) surface tend to align along the [1 1 0] or the [1 1 0] direction of the crystal. In some cases, as shown in Fig. 8(b), the double-step dissociation results in the development of curved single steps. A pair of curved steps formed through the dissociation of a double step may recombine elsewhere on the surface into another double step. A recombined double step may be aligned in the
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direction which is orthogonal (Fig. 8(b)), or parallel (Fig. 8(c)), to the direction of the alignment of the original double step. The length of a curved single step may reach 10 lm. The average width of a curved single step is in excess of 200 nm (see Fig. 8(b)). Single steps on the MgAl2 O4 (0 0 1) surface may also outline small triangles (see Fig. 9). These triangular regions generally have irregular shapes and, when connected to straight fragments of adjacent single steps, tend to bound small triangular terraces. The observations show that the triangular steps and terraces form compact groups in certain areas of the surface.
5. Discussion Fig. 6. 5 50 lm deflection AFM image of straight doublestep trains on the (0 0 1) MgAl2 O4 surface. The direction of scanning was from left to right. Dark lines indicate downward ) steps are steps; bright lines denote upward steps. Double (4 A aligned along [1 1 0] direction of the crystal.
Fig. 7. 5 5 lm height AFM image of cusped double steps on the (0 0 1) spinel surface. Double steps exhibit wavering in the center of the image, but are straight and aligned along [1 1 0] direction of the crystal for the rest of their lengths. A black to white contrast change corresponds to a height change of 10 nm.
The mechanism of evaporation from crystal surfaces may proceed in two different modes, either through the nucleation and growth of twodimensional holes, or via the removal of material from surface nanoledges (or from crystal edges) [2]. The hole nucleation is a high-temperature process characterized by the considerable activation energies. In comparison, ledge evaporation does not require nucleation and is expected to proceed at lower temperatures. In the steady-state regime, evaporation from nanoledges results in the formation of trains of monatomic ledges which have uniform spacing and velocity of motion [2]. This expectation has been confirmed by numerous experimental observations made for evaporation from the surfaces of such materials as NaCl(1 0 0) [20], and Si(1 1 1) [21]. At 2070 K, double steps are most common while for surfaces annealed at 1470–1870 K, single steps predominate. It appears that, for the MgAl2 O4 (0 0 1), the surface rearrangement occurs through the motion of single steps, while the surface evaporation involves the rearrangement of double steps. Experimental observations show that pairs of single steps may merge into double steps (see Fig. 8(a)–(c)), which means that both the double and the single steps connect terraces of the same chemical composition and structure. Straight (both single and double) steps on the (0 0 1) spinel surface tend to align preferentially along either the
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Fig. 8. Dissociation of double-step trains into pairs of single steps on the (0 0 1) MgAl2 O4 surface. (a) 5 5 lm deflection AFM image ) steps. At the point of intersection between the step showing two nanoledges spinning off two perpendicular trains of double (4 A ) steps is formed. The direction of scanning was from left to right. On the image, trains, an array of straight perpendicular single (2 A dark lines indicate steps in the downward direction; bright lines denote the upward steps (if considered in the direction of scanning). (b) ) steps dissociating into pairs of curved single (2 A ) steps. Straight double steps are 9 9 lm height AFM image of straight double (4 A assembled into trains and aligned along the [1 1 0] and [1 1 0] directions of the crystal. A black to white contrast change corresponds to a ) steps dissociating into pairs of curved height change of 10 nm. (c) 10 10 lm deflection AFM image showing straight double (4 A ) steps. Single-step pairs subsequently recombine into straight double steps in the adjacent step train. The direction of single (2 A scanning was from left to right. Dark lines indicate downward steps direction; bright lines denote upward steps.
[1 1 0] or the [1 1 0] direction of the crystal. In principle, the difference between the surface rearrangement and the surface evaporation is that the latter removes material from the surface, while the former redistributes it across the surface. Then, the following question may be asked: why does the redistribution of material along the (0 0 1) surface
of spinel occur through the propagation of single steps, while the removal of material from the same surface generates double steps? The key to understanding this motion is that a step from plane 1 to plane 2 is fundamentally 2-A step from plane 2 to different from the parallel 2-A plane 3, even though plane 1 and 3 are identical
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Fig. 9. 10 10 lm deflection AFM image of a (0 0 1) spinel surface covered by triangular terraces. The terraces are bound ) steps. The by the alternating curved and straight single (2 A direction of scanning was from left to right. Dark lines indicate downward steps direction; bright lines denote upward steps.
different in height. The planes and are only 4 A movement of these two steps consequently occurs at different rates, one faster than the other. The result is that the motion of steps on the (0 0 1) surface of MgAl2 O4 proceeds in a highly anisotropic fashion. If a given single step is expected to move more quickly when it is aligned along the [1 1 0] direc betion, a neighboring single step, which lies 2 A low the first, will move more quickly when it is aligned along the orthogonal [1 1 0] direction (see Fig. 10(a) and (b)). In each case, the parallel step above such a fast-moving step can which lies 2 A effectively bock its motion forcing it to combine to high) step. form a double (4-A When the rapid motion of a series of lower steps aligned along the [1 1 0] direction is blocked by a series of upper steps, which moves slowly when aligned along the [1 1 0] direction, a step pileup occurs. This pileup results in the formation of a -high double step. Such double steps series of 4-A share the direction of alignment and motion with the attached upper single steps. As long as the lower step moves faster than the upper step, the
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double step they form is stable and propagates along the surface as a single entity. The observations show (see Fig. 6) that, at 2070 K, the motion of steps on the (0 0 1) surface of MgAl2 O4 proceeds fast enough for most single steps to associate into double steps. At 1470–1870 K, the motion of the steps across the surface is expected to be much slower. Thus, annealing MgAl2 O4 (0 0 1) at subevaporation temperatures results in the surface morphology which is dominated by single steps. When a train of double steps encounters another step train moving in the orthogonal direction (see Fig. 8(a) and (b)), two situations are possible: the two trains may either diverge, or come together. In the former case, the double steps dissociate into pairs of straight single steps (see Fig. 8(a)) at the point of the step train intersection (the vertex). The schematic of such dissociation is shown in Fig. 10(a). At the vertex, single steps (shown in black in Fig. 10(a)), which move rapidly in the [1 1 0] direction, encounter single steps (shown in gray in Fig. 10(a)), which move slowly in the [1 1 0] direction. The resulting pileup creates a double-step train which propagates in the [1 1 0] direction. In the orthogonal step train, the single steps (shown in black in Fig. 10(a)) which move slowly in the [1 1 0] direction are caught up by the single steps (shown in gray in Fig. 10(a)) which move rapidly in the [1 1 0] direction. Hence, a double-step train which advances in the [1 1 0] direction, is formed. Depending on its orientation, each single step may act as the lower half of a double step of the same alignment or as the upper half of a double step lying in the orthogonal direction. As shown in Fig. 10(b), two converging orthogonal double-step trains may form an array of curved single-step pairs at the point of their intersection. The mechanism of the formation of such an array is as follows. Initially, the two orthogonal nanoledges are expected to border two sides of the terrace and to join at the vertex. Once evaporation starts, the nanoledges generate two orthogonal trains of single steps. Of the two orthogonal single steps which border the topmost terrace, both tend to move rapidly along the [1 1 0] direction (and slowly in the [1 1 0] direction), but only one of them is positioned along its preferred
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Fig. 10. Schematic of step motion on the (0 0 1) surface of MgAl2 O4 . Single steps aligned along the [1 1 0] direction of the crystal are shown as gray lines. Single steps aligned along the [1 1 0] direction of the crystal are denoted in black. (a) Two diverging double-step trains are formed by straight single steps merging into straight double steps. A pattern of ‘‘interloping’’ single steps is formed at the vertex. (b) Two converging double-step trains. An array of curved single steps is formed in the terrace corner where double-step trains join. Single-steps curve when material is removed along both the [1 1 0] and [1 1 0] directions. (c) Two parallel merging double-step trains. Double steps dissociate into pairs of curved single steps at the points where they join steps from another train. Upon passing through junction points, dissociated double-step fragments recombine. (d) Formation of arrays of triangular terraces. When several double-step trains merge over a limited surface area, double steps dissociate along junction lines into pairs of curved single steps. If the number of merging step trains is large, junction lines are situated in close proximity to one another, making the surface appear as if covered with an ‘ordered’ network of triangular terraces.
direction of alignment (e.g., [1 1 0]). This step becomes the upper half of a double step which is aligned along the [1 1 0] direction. The second single step is expected to move away rapidly from the [1 1 0] direction and may become the lower half of a double step aligned in the [1 1 0] direction. At the point where the nanoledges were initially connected (the vertex), material is removed along both the [1 1 0] and the [1 1 0] directions; this results in the curving of single steps. The process repeats itself for the rest of the steps in both step trains, giving rise to surface morphologies such as those shown in Fig. 8(b).
The double steps in the step trains on the (0 0 1) spinel surface maintain steady-state interstep distances [2] as single entities. However, each double step consists of two single steps which are kept together only because the velocity of motion of the lower step is higher than that of its upper counterpart. If, as a result of an interaction of a double step with another surface feature, the rate of advancement of the upper double-step half abruptly increases then it may cause dissociation of this double step into a pair of separate single steps. This process is illustrated in Fig. 8(c), where several parallel double-step trains merge over a small
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surface area. The step trains shown in Fig. 8(c) may have different modes of advancement: some of them may originate from dislocation termination sites [19], while others may be spun off from nanoledges. In a dislocation-originated doublestep train, the steps may be thought of as parallel fragments of one giant spiral half-ledge emerging at the dislocation termination point on the surface [19]. The dislocation-originated step train advances through the rotation of this half-ledge [22]. Steps in a train created through the evaporation of a nanoledge are structurally disconnected from one another and may follow a straight trajectory of motion along the surface. When double steps from the different step trains merge with one another, the junction point becomes a site where the rate of advancement of the upper double-step halves may change (increase) abruptly, leading to localized step dissociation. If, for the part of the step outside the perturbed area, the rate of advancement stays constant, the dissociated step fragments are expected to undergo eventual recombination further along the step edge. An isolated dissociated double-step fragment will denote the site where the local rate of advancement of the upper double-step half did not match that of the rest of the step. In the course of step propagation, the dissociated double-step fragments (which bound the triangular terraces) are expected to drift along the step edges. If the rate of the drift is high enough, the lower single steps in the dissociated double-step fragments may not catch up with the upper single steps. Thus, the triangular terraces may become quasi-stable surface structures, decorating the junction lines between the merging step trains (see Fig. 8(c) and Fig. 10(c)). When several double-step trains (originating from separate sources) interact over a limited surface area, the dissociation/recombination of the double steps can produce ‘ordered’ arrangements of triangular terraces (see Fig. 9). As shown in Fig. 10(d), the uniform terrace size is predetermined by double-step spacing, which is approximately constant for all step trains involved in the interaction. The triangular terraces may, however, vary in shape from elongated (shown on the left-hand side of Fig. 9) to rounded (shown on the right-hand
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side of Fig. 9). An ‘ordered’ surface morphology is achieved when the step train sources (e.g., dislocation termination sites [19]) are evenly spaced, such as occurs at a dislocation pileup or at grain boundary. When step trains leave the vicinity of the array, the ordered pattern breaks up. Isolated surface areas where the double steps are cusped (see Fig. 7) are expected where dislocations having their Burgers vectors in the (0 0 1) surface plane (e.g., a/2[1 1 0]), emerge at the surface [19]. When terminating at the steps which are aligned orthogonally to the direction of their Burgers vector, such dislocations may create kinks in step edges [19]. These kinks adapt a fixed position at the point of the intersection between a step edge and a dislocation line [19], breaking up the steps into pairs of half-ledges. These half-ledges may propagate along the surface as separate entities; the rate of the advancement of one half-ledge does not then match that of its other counterpart [19]. This phenomenon is illustrated in Fig. 7, where the halfledges shown in the lower left corner move faster than those depicted in the upper right corner. When, in the course of evaporation, the step breaks away from such a dislocation termination site, the ‘fixed’ kink site is eliminated, and the step straightens out (see the steps shown in the upper half of Fig. 7). It is unlikely that such cusps will be formed by contaminants at these high temperatures since individual atoms would be expected to diffuse under the action of the step line tension. Instead, the periodic spacing of the points of dissociation in Fig. 8(b) strongly suggests that each such point is associated with a dislocation in a low-angle grain boundary which is emerging at the surface. More detailed discussion of the structure of the dislocation evaporation patterns on the (0 0 1) surface of MgAl2 O4 and the mechanisms of their formation may be found elsewhere [19].
6. Conclusions Upon annealing at 1470–2070 K, the polished (0 0 1) surface of MgAl2 O4 spinel rearranges into the terrace-and-step geometry. At sub-evaporation temperatures (1470–1870 K), the surface morphology is dominated by single steps. The single
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steps move and align preferentially along either the [1 1 0] or the [1 1 0] direction of the crystal. When evaporation dominates the surface processes (at 2070 K and above), high velocities of step motion cause the association of single steps into stable step pairs (double steps). These double steps move along the surface as single entities and, like single steps, align along either the [1 1 0] or the [1 1 0] direction. The reverse process, the dissociation of double steps, occurs when the double steps encounter obstacles in the course of their motion, such as step trains or crystal defects. Acknowledgements SVY is in the Chemical Physics Program at the University of Minnesota. This research has been supported by the U.S. Department of Energy under Grant Nos. DE-FG02-92ER45465 and DEFG02-01ER45883. The AFM used is part of the U of MN Characterization Facility. The authors would like to acknowledge discussions with Dr. N. (Ravi) Ravishankar.
References [1] W.K. Burton, N. Cabrera, F.C. Frank, Phil. Trans. Roy. Soc. A 243 (1951) 299.
[2] J.P. Hirth, G.M. Pound, J. Chem. Phys. 26 (5) (1957) 1216. [3] W.W. Mullins, Phil. Mag. 6 (1961) 1313. [4] H. H€ oche, H. Bethge, J. Cryst. Growth 42 (1977) 110. [5] K. Reichelt, B. Lampert, Vacuum 30 (10) (1980) 383. [6] K.W. Keller, J. Cryst. Growth 74 (1986) 161. [7] Z.A. Munir, Met. Trans. 22A (1991) 1305. [8] A.R. Verma, Crystal Growth and Dislocations, Academic Press, New York, 1953. [9] R.J. Hamers, U.K. K€ ohler, J.E. Demuth, Ultramicroscopy 31 (1989) 10. [10] J. Giocondi, G.S. Rohrer, M. Skowronski, V. Balakrishna, G. Augustine, H.M. Hobgood, R.H. Hopkins, J. Cryst. Growth 181 (4) (1997) 351. [11] J.R. Heffelfinger, M.W. Bench, C.B. Carter, Surf. Sci. 370 (1997) L168. [12] H.H. Teng, P.M. Dove, C.A. Orme, J.J. De Yoreo, Science 282 (1998) 724. [13] R. Ramesh, K. Luther, B. Wilkens, D.L. Hart, E. Wang, J.M. Tarascon, A. Inam, X.D. Wu, T. Vencatesan, Appl. Phys. Lett. 57 (1990) 1505. [14] P.M. Raccah, R.J. Bouchard, A. Wolf, J. Appl. Phys. 37 (3) (1966) 1436. [15] G. Bacon, Acta Cryst. 5 (1952) 684. [16] U. Schmocker, F. Waldner, J. Phys. C 9 (1976) L235. [17] P. Villars, L.D. Calvert, Pearson’s Handbook of Crystallographic Data for Intermetallic Phases, American Society for Metals, Metals Park, OH, 1989. [18] G. Tarrach, D. B€ urgler, T. Schaub, R. Weisendanger, H.-J. G€ unterodt, Surf. Sci. 285 (1993) 1. [19] S. Yanina, C.B. Carter, Ph.D. Thesis, University of Minnesota, 2001. [20] H. H€ oche, H. Bethge, J. Cryst. Growth 52 (1981) 27. [21] A. Masson, R. Kern, J. Cryst. Growth 2 (1968) 227. [22] F.C. Frank, Disc. Farad. Soc. 5 (1949) 48.
Surface Science Letters
Terraces and ledges on (0 0 1) spinel surfaces Svetlana V. Yanina, C. Barry Carter
*
Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, 151 Amundson Hall, Minneapolis, MN 55455, USA Received 5 November 2001; accepted for publication 30 April 2002
Abstract The motion of steps on the (0 0 1) surface of MgAl2 O4 spinel is discussed. Atomic force microscopy observations of surface faceting and evaporation after heating to high temperatures are reported. The structural relationship between single and double-surface steps on the MgAl2 O4 (0 0 1) surface is established. Mechanisms for the formation, motion and dissociation of the double steps are proposed. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Atomic force microscopy; Evaporation and sublimation; Faceting; Step formation and bunching; Surface structure, morphology, roughness, and topography; Single crystal surfaces
1. Introduction Understanding the kinetics of step motion on vicinal surfaces is fundamental to understanding the behavior, development and properties of surfaces. While the theoretical foundations of surface kinetics are well developed [1–3], direct experimental observations only became possible with the advance of new microscopes for imaging surfaces. Techniques which have been used include transmission electron microscopy (TEM) [4–7], visible light microscopy (VLM) [8] and scanning tunneling microscopy (STM) [9]. STM has made the direct investigation of step dynamics on semiconductor and metal surfaces possible. Atomic force micros-
* Corresponding author. Tel.: +1-612-6248805; fax: +1-6126267246. E-mail address: [email protected] (C. Barry Carter).
copy (AFM), provides similar three-dimensional images of non-conductive materials, in particular ceramic oxides [10,11] and bio-minerals [12]. For practical reasons, most surface studies have concentrated on the mechanisms of crystal growth; some technologically important systems may be observed in situ [12]. For ceramic oxides it is usually impractical to study directly most hightemperature processes, such as surface reconstruction and surface evaporation, using in situ observations. However, the behavior of surfaces at high temperatures must be understood in order to explain the surface morphologies of many materials, for example thin ceramic films which are grown under non-equilibrium conditions [13]. The present paper, which discusses high-temperature step motion on the (0 0 1) surface of MgAl2 O4 spinel, is a contribution towards the better understanding of the dynamics of step motion on oxide surfaces.
0039-6028/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 9 - 6 0 2 8 ( 0 2 ) 0 1 8 2 5 - 3
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2. Background In the normal spinel structure, oxygen anions form a distorted face centered cubic (fcc) sublattice (see Fig. 1) [14–16], where Mg2þ cations occupy 1/8 of the tetrahedral interstices, and Al3þ cations occupy 1/2 of the octahedral interstices. The unit and the cell parameter of MgAl2 O4 is 8.075 A space-symmetry group is Fd3m [17]. The complex nature of the structure of spinel allows for two possible bulk-terminated arrangements of ions at its (0 0 1) surface. One arrangement may be formed by terminating the spinel crystal at a (0 0 1) plane which contains only O2 anions and octahedrally coordinated Al3þ cations; this type of (0 0 1) phase will be referred to as an (0 0 4) plane in this paper to distinguish it from an (0 0 1) plane which contains only Mg2þ cations and is referred to as an (0 0 8) plane (see Fig. 2). In the latter case, the topmost crystal plane accommodates two cations per unit-cell, which leaves the underlying O/Al(0 0 4) plane partially exposed at the surface. In MgAl2 O4 , a pair of the nearest-neighbor (0 0 8) (or (0 0 4)) planes is separated by a/4[0 0 1], throughout this paper). (which is referred to as 2 A
Fig. 1. The structure of MgAl2 O4 spinel. O2 anions are shown as large gray spheres, Mg2þ cations in tetrahedral coordination as small gray spheres, and octahedrally coordinated Al3þ cations as small black spheres. The unit-cell parameter of . MgAl2 O4 is 8.075 A
These planes have twofold symmetry; they are not equivalent with respect to the fourfold rotation
Fig. 2. Structure of {0 0 1} planes in MgAl2 O4 crystal. O2 anions are shown as large gray spheres, Al3þ cations as small black spheres, and Mg2þ cations as small gray spheres. (a) {0 0 4} plane built from O2 anions and octahedrally coordinated Al3þ cations. (b) {0 0 8} plane formed by Mg2þ cations in tetrahedral coordination, shown together with the underlying {0 0 4} plane.
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around the [0 0 1] axis. The (0 0 8) (or (0 0 4)) planes which are related by a 90° rotation around the [0 0 1] axis are separated by 2n þ 1 multiples of 2 , where n is an integer. The (0 0 8) (or the (0 0 4)) A planes which are equivalent with respect to the 90° rotation around the [0 0 1] axis are separated by 2n . multiples of 2 A The twofold symmetry of crystal planes of the (0 0 1) orientation in MgAl2 O4 originates from the fact that the cations in the spinel structure are distributed throughout the available interstices along certain directions. For the (0 0 4) planes, the Al3þ cations fill octahedral interstices along either the [1 1 0] or the [1 1 0] direction as shown in Fig. 3(a) and (b), respectively. For the (0 0 8) planes, the preferred direction is one where the edges of the tetrahedral interstices occupied by the Mg2þ cations are aligned along either [1 1 0] or [1 1 0] as
shown in Fig. 3(c) and (d), respectively. For each (0 0 4) or (0 0 8) plane, there is only one such filled/ preferred direction. While there are no available data on the atomicscale morphology of MgAl2 O4 (0 0 1), the (0 0 1) surface of magnetite (Fe3 O4 ), which has an inverse spinel structure, has been studied in detail [18]. In this study [18], the surface of Fe3 O4 (0 0 1) was found to be corrugated on the atomistic scale in the [1 1 0] and [1 1 0] directions; corrugations on the adjacent terraces were rotated through 90° with respect to each other. It was then proposed [18] that the reconstructed surface of the Fe3 O4 (0 0 1) surface consists of the Fe cations in the tetrahedral sites which reside on top of the plane containing oxygen anions and the octahedrally coordinated Fe cations; the plane of tetrahedral sites is (0 0 8) while the lower plane is (0 0 4). The
Fig. 3. Cation distribution in planes of {0 0 1} orientation in MgAl2 O4 . O2 anions are shown as large gray spheres, Al3þ cations are apart. Al3þ cations fill the upper small black spheres, and Mg2þ cations as small gray spheres. ((a) and (b)) Two {0 0 4} planes, 2 A apart. The direction plane along the [1 1 0] direction, and the lower plane along the [1 1 0] direction. ((c) and (d)) Two {0 0 8} planes, 2 A of alignment of edges of Mg2þ -filled tetrahedral interstices in the upper plane is rotated through 90° with respect to that in the lower plane.
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surface corrugations were attributed to the linking of the dangling (unsaturated) bonds of the topmost tetrahedrally coordinated Fe cations. Fe3 O4 (0 0 1) is not the only known surface in which the surface structure involves a 90° rotation of the direction of surface corrugations associated with stepping up or down from one terrace to another. The mechanism of reconstruction of Si(0 0 1) involves the linking of dangling bonds of tetrahedrally coordinated Si atoms to form corrugations aligned in either the [1 1 0] or the [1 1 0] direction. Being of the diamond-cubic type, the Si crystal structure possesses a center of inversion. As a result, for the adjacent terraces separated by a monatomic step, the direction of corrugation alignment is rotated through 90° [9]. Due to its poor conductivity, STM of MgAl2 O4 is not generally possible. The present paper, therefore, will be limited to the discussion of the dynamics of step motion on the MgAl2 O4 (0 0 1) surface, without a detailed analysis of surface structure on the atomic scale.
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acetone and methanol. The specimens were heat treated in a spinel crucible in vacuum (104 –105 Torr) in a Centorre furnace at 1470–2070 K for 8 h. Surface characterization was performed by AFM in air in the contact mode of operation (Nanoscope III, Digital Instruments, Santa Barbara, CA), using Si3 N4 V-shaped cantilevers (Ultralevers, Park Inst., Sunnyvale, CA) with a nominal spring constant of 0.12 N/m. Because of optical artifacts, deflection-mode images are shown for large surface areas. For deflection-mode images, the direction of scanning was from left to right. The chemical composition of the surface was monitored ex situ by X-ray energy dispersive spectroscopy (XEDS) and X-ray photoemission spectroscopy (XPS). Crystallographic orientations on spinel surfaces were determined by Laue backscattered X-ray diffraction.
4. Observations
3. Experimental
4.1. Surface rearrangement at sub-evaporation temperatures
2 2 1 mm single crystals of MgAl2 O4 (0 0 1) spinel were polished and cleaned in aqua regia,
As can be seen in Fig. 4, the polished (0 0 1) surface of MgAl2 O4 , which was heat treated at
Fig. 4. 5 5 lm height AFM images of the (0 0 1) surface of MgAl2 O4 . (a) The specimen was acid-cleaned and annealed at 1470 K. Misalignment between the polished surface and the (0 0 1) plane of the crystal is accommodated by narrow terraces with longer sides aligned along [1 1 0] direction of the crystal. (b) The specimen was annealed at 1870 K. Misalignment between the polished surface and the (0 0 1) plane is accommodated by square terraces with edges aligned along both [1 1 0] and [1 1 0] directions of the crystal.
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sub-evaporation temperatures (1470–1870 K), rearranges into a terrace-and-ledge morphology. The angle measurements show that the terraces are parallel to the (0 0 1) planes, while the ledges are aligned along the [1 1 0] and the [1 1 0] directions of the crystal. Depending on the degree and the direction of misalignment between the polished surface and the (0 0 1) crystal planes, the surface rearrangement may result in the formation of either narrow elongated (Fig. 4(a)) or wide square (Fig. 4(b)) terraces. If the polished surface is aligned with the (0 0 1) crystal planes along either the [1 1 0] or the [1 1 0] direction, the surface terraces develop preferentially along that direction and the resulting surface morphology is ‘elongated’. If the polished surface is misaligned with the (0 0 1) crystal planes along both the [1 1 0] and the [1 1 0] directions, no such preferred direction of terrace growth exists, and the ‘square’ morphology ensues. For the surfaces annealed at 1470–1670 K, the average height of the ledges is 5–10 nm. Small were also ledges of the height of multiples of 2 A observed on the surface (see Fig. 5). Here and -high ledges are called single steps, 4-A below, 2-A high ledges are called double steps. All other ledges are referred to as nanoledges. 4.2. Surface evaporation Heat treatments at 1470–1870 K generally result in the formation of many more single steps than double steps. The opposite is generally true for surfaces annealed above 2070 K, i.e., under conditions where evaporation plays an important role. On evaporated spinel surfaces the single steps can be found only at double-step intersections, or at dislocation termination sites (or other crystal defects) on the surface. As can be seen in Fig. 6, evaporation from nanoledges on the surface generates series (or trains) of double steps. Double steps formed on the (0 0 1) spinel surface upon heat treatment at 2070 K are straight and aligned along either the [1 1 0] or the [1 1 0] direction of the crystal. The average distance between the double steps appears to depend only weakly on the details of the surface morphology. Thus, far away from nanoledges and other large surface features, such as dislocation
Fig. 5. AFM image of steps on (0 0 1) surfaces of MgAl2 O4 . A 2 2 lm deflection image of the surface annealed at 1670 K. The direction of scanning was from left to right. Dark lines indicate downward steps; bright lines denote upward steps. Thick dark lines represent nanoledges; thin dark lines depict 2 (single) steps aligned along [1 1 0] direction of the crystal. A Thick bright lines denote nanoledges aligned along [1 1 0] direction. A single step is denoted by the arrow.
etch pits [19], the average step distance in a step train was measured to be 400 50 nm. The double-step lengths can be large (steps up to 100 lm in length were observed) and may be limited only by the size of the specimens. In some areas, straight double steps undergo cusping (see Fig. 7). Such cusping typically only occurs in small isolated surface areas. Double steps may undergo dissociation into pairs of single steps (see Fig. 8). Such dissociation typically affects the double steps situated between the intersecting nanoledges (see Fig. 8(a) and (b)). As can be seen in Fig. 8(a), the straight single steps on the MgAl2 O4 (0 0 1) surface tend to align along the [1 1 0] or the [1 1 0] direction of the crystal. In some cases, as shown in Fig. 8(b), the double-step dissociation results in the development of curved single steps. A pair of curved steps formed through the dissociation of a double step may recombine elsewhere on the surface into another double step. A recombined double step may be aligned in the
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direction which is orthogonal (Fig. 8(b)), or parallel (Fig. 8(c)), to the direction of the alignment of the original double step. The length of a curved single step may reach 10 lm. The average width of a curved single step is in excess of 200 nm (see Fig. 8(b)). Single steps on the MgAl2 O4 (0 0 1) surface may also outline small triangles (see Fig. 9). These triangular regions generally have irregular shapes and, when connected to straight fragments of adjacent single steps, tend to bound small triangular terraces. The observations show that the triangular steps and terraces form compact groups in certain areas of the surface.
5. Discussion Fig. 6. 5 50 lm deflection AFM image of straight doublestep trains on the (0 0 1) MgAl2 O4 surface. The direction of scanning was from left to right. Dark lines indicate downward ) steps are steps; bright lines denote upward steps. Double (4 A aligned along [1 1 0] direction of the crystal.
Fig. 7. 5 5 lm height AFM image of cusped double steps on the (0 0 1) spinel surface. Double steps exhibit wavering in the center of the image, but are straight and aligned along [1 1 0] direction of the crystal for the rest of their lengths. A black to white contrast change corresponds to a height change of 10 nm.
The mechanism of evaporation from crystal surfaces may proceed in two different modes, either through the nucleation and growth of twodimensional holes, or via the removal of material from surface nanoledges (or from crystal edges) [2]. The hole nucleation is a high-temperature process characterized by the considerable activation energies. In comparison, ledge evaporation does not require nucleation and is expected to proceed at lower temperatures. In the steady-state regime, evaporation from nanoledges results in the formation of trains of monatomic ledges which have uniform spacing and velocity of motion [2]. This expectation has been confirmed by numerous experimental observations made for evaporation from the surfaces of such materials as NaCl(1 0 0) [20], and Si(1 1 1) [21]. At 2070 K, double steps are most common while for surfaces annealed at 1470–1870 K, single steps predominate. It appears that, for the MgAl2 O4 (0 0 1), the surface rearrangement occurs through the motion of single steps, while the surface evaporation involves the rearrangement of double steps. Experimental observations show that pairs of single steps may merge into double steps (see Fig. 8(a)–(c)), which means that both the double and the single steps connect terraces of the same chemical composition and structure. Straight (both single and double) steps on the (0 0 1) spinel surface tend to align preferentially along either the
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Fig. 8. Dissociation of double-step trains into pairs of single steps on the (0 0 1) MgAl2 O4 surface. (a) 5 5 lm deflection AFM image ) steps. At the point of intersection between the step showing two nanoledges spinning off two perpendicular trains of double (4 A ) steps is formed. The direction of scanning was from left to right. On the image, trains, an array of straight perpendicular single (2 A dark lines indicate steps in the downward direction; bright lines denote the upward steps (if considered in the direction of scanning). (b) ) steps dissociating into pairs of curved single (2 A ) steps. Straight double steps are 9 9 lm height AFM image of straight double (4 A assembled into trains and aligned along the [1 1 0] and [1 1 0] directions of the crystal. A black to white contrast change corresponds to a ) steps dissociating into pairs of curved height change of 10 nm. (c) 10 10 lm deflection AFM image showing straight double (4 A ) steps. Single-step pairs subsequently recombine into straight double steps in the adjacent step train. The direction of single (2 A scanning was from left to right. Dark lines indicate downward steps direction; bright lines denote upward steps.
[1 1 0] or the [1 1 0] direction of the crystal. In principle, the difference between the surface rearrangement and the surface evaporation is that the latter removes material from the surface, while the former redistributes it across the surface. Then, the following question may be asked: why does the redistribution of material along the (0 0 1) surface
of spinel occur through the propagation of single steps, while the removal of material from the same surface generates double steps? The key to understanding this motion is that a step from plane 1 to plane 2 is fundamentally 2-A step from plane 2 to different from the parallel 2-A plane 3, even though plane 1 and 3 are identical
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Fig. 9. 10 10 lm deflection AFM image of a (0 0 1) spinel surface covered by triangular terraces. The terraces are bound ) steps. The by the alternating curved and straight single (2 A direction of scanning was from left to right. Dark lines indicate downward steps direction; bright lines denote upward steps.
different in height. The planes and are only 4 A movement of these two steps consequently occurs at different rates, one faster than the other. The result is that the motion of steps on the (0 0 1) surface of MgAl2 O4 proceeds in a highly anisotropic fashion. If a given single step is expected to move more quickly when it is aligned along the [1 1 0] direc betion, a neighboring single step, which lies 2 A low the first, will move more quickly when it is aligned along the orthogonal [1 1 0] direction (see Fig. 10(a) and (b)). In each case, the parallel step above such a fast-moving step can which lies 2 A effectively bock its motion forcing it to combine to high) step. form a double (4-A When the rapid motion of a series of lower steps aligned along the [1 1 0] direction is blocked by a series of upper steps, which moves slowly when aligned along the [1 1 0] direction, a step pileup occurs. This pileup results in the formation of a -high double step. Such double steps series of 4-A share the direction of alignment and motion with the attached upper single steps. As long as the lower step moves faster than the upper step, the
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double step they form is stable and propagates along the surface as a single entity. The observations show (see Fig. 6) that, at 2070 K, the motion of steps on the (0 0 1) surface of MgAl2 O4 proceeds fast enough for most single steps to associate into double steps. At 1470–1870 K, the motion of the steps across the surface is expected to be much slower. Thus, annealing MgAl2 O4 (0 0 1) at subevaporation temperatures results in the surface morphology which is dominated by single steps. When a train of double steps encounters another step train moving in the orthogonal direction (see Fig. 8(a) and (b)), two situations are possible: the two trains may either diverge, or come together. In the former case, the double steps dissociate into pairs of straight single steps (see Fig. 8(a)) at the point of the step train intersection (the vertex). The schematic of such dissociation is shown in Fig. 10(a). At the vertex, single steps (shown in black in Fig. 10(a)), which move rapidly in the [1 1 0] direction, encounter single steps (shown in gray in Fig. 10(a)), which move slowly in the [1 1 0] direction. The resulting pileup creates a double-step train which propagates in the [1 1 0] direction. In the orthogonal step train, the single steps (shown in black in Fig. 10(a)) which move slowly in the [1 1 0] direction are caught up by the single steps (shown in gray in Fig. 10(a)) which move rapidly in the [1 1 0] direction. Hence, a double-step train which advances in the [1 1 0] direction, is formed. Depending on its orientation, each single step may act as the lower half of a double step of the same alignment or as the upper half of a double step lying in the orthogonal direction. As shown in Fig. 10(b), two converging orthogonal double-step trains may form an array of curved single-step pairs at the point of their intersection. The mechanism of the formation of such an array is as follows. Initially, the two orthogonal nanoledges are expected to border two sides of the terrace and to join at the vertex. Once evaporation starts, the nanoledges generate two orthogonal trains of single steps. Of the two orthogonal single steps which border the topmost terrace, both tend to move rapidly along the [1 1 0] direction (and slowly in the [1 1 0] direction), but only one of them is positioned along its preferred
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Fig. 10. Schematic of step motion on the (0 0 1) surface of MgAl2 O4 . Single steps aligned along the [1 1 0] direction of the crystal are shown as gray lines. Single steps aligned along the [1 1 0] direction of the crystal are denoted in black. (a) Two diverging double-step trains are formed by straight single steps merging into straight double steps. A pattern of ‘‘interloping’’ single steps is formed at the vertex. (b) Two converging double-step trains. An array of curved single steps is formed in the terrace corner where double-step trains join. Single-steps curve when material is removed along both the [1 1 0] and [1 1 0] directions. (c) Two parallel merging double-step trains. Double steps dissociate into pairs of curved single steps at the points where they join steps from another train. Upon passing through junction points, dissociated double-step fragments recombine. (d) Formation of arrays of triangular terraces. When several double-step trains merge over a limited surface area, double steps dissociate along junction lines into pairs of curved single steps. If the number of merging step trains is large, junction lines are situated in close proximity to one another, making the surface appear as if covered with an ‘ordered’ network of triangular terraces.
direction of alignment (e.g., [1 1 0]). This step becomes the upper half of a double step which is aligned along the [1 1 0] direction. The second single step is expected to move away rapidly from the [1 1 0] direction and may become the lower half of a double step aligned in the [1 1 0] direction. At the point where the nanoledges were initially connected (the vertex), material is removed along both the [1 1 0] and the [1 1 0] directions; this results in the curving of single steps. The process repeats itself for the rest of the steps in both step trains, giving rise to surface morphologies such as those shown in Fig. 8(b).
The double steps in the step trains on the (0 0 1) spinel surface maintain steady-state interstep distances [2] as single entities. However, each double step consists of two single steps which are kept together only because the velocity of motion of the lower step is higher than that of its upper counterpart. If, as a result of an interaction of a double step with another surface feature, the rate of advancement of the upper double-step half abruptly increases then it may cause dissociation of this double step into a pair of separate single steps. This process is illustrated in Fig. 8(c), where several parallel double-step trains merge over a small
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surface area. The step trains shown in Fig. 8(c) may have different modes of advancement: some of them may originate from dislocation termination sites [19], while others may be spun off from nanoledges. In a dislocation-originated doublestep train, the steps may be thought of as parallel fragments of one giant spiral half-ledge emerging at the dislocation termination point on the surface [19]. The dislocation-originated step train advances through the rotation of this half-ledge [22]. Steps in a train created through the evaporation of a nanoledge are structurally disconnected from one another and may follow a straight trajectory of motion along the surface. When double steps from the different step trains merge with one another, the junction point becomes a site where the rate of advancement of the upper double-step halves may change (increase) abruptly, leading to localized step dissociation. If, for the part of the step outside the perturbed area, the rate of advancement stays constant, the dissociated step fragments are expected to undergo eventual recombination further along the step edge. An isolated dissociated double-step fragment will denote the site where the local rate of advancement of the upper double-step half did not match that of the rest of the step. In the course of step propagation, the dissociated double-step fragments (which bound the triangular terraces) are expected to drift along the step edges. If the rate of the drift is high enough, the lower single steps in the dissociated double-step fragments may not catch up with the upper single steps. Thus, the triangular terraces may become quasi-stable surface structures, decorating the junction lines between the merging step trains (see Fig. 8(c) and Fig. 10(c)). When several double-step trains (originating from separate sources) interact over a limited surface area, the dissociation/recombination of the double steps can produce ‘ordered’ arrangements of triangular terraces (see Fig. 9). As shown in Fig. 10(d), the uniform terrace size is predetermined by double-step spacing, which is approximately constant for all step trains involved in the interaction. The triangular terraces may, however, vary in shape from elongated (shown on the left-hand side of Fig. 9) to rounded (shown on the right-hand
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side of Fig. 9). An ‘ordered’ surface morphology is achieved when the step train sources (e.g., dislocation termination sites [19]) are evenly spaced, such as occurs at a dislocation pileup or at grain boundary. When step trains leave the vicinity of the array, the ordered pattern breaks up. Isolated surface areas where the double steps are cusped (see Fig. 7) are expected where dislocations having their Burgers vectors in the (0 0 1) surface plane (e.g., a/2[1 1 0]), emerge at the surface [19]. When terminating at the steps which are aligned orthogonally to the direction of their Burgers vector, such dislocations may create kinks in step edges [19]. These kinks adapt a fixed position at the point of the intersection between a step edge and a dislocation line [19], breaking up the steps into pairs of half-ledges. These half-ledges may propagate along the surface as separate entities; the rate of the advancement of one half-ledge does not then match that of its other counterpart [19]. This phenomenon is illustrated in Fig. 7, where the halfledges shown in the lower left corner move faster than those depicted in the upper right corner. When, in the course of evaporation, the step breaks away from such a dislocation termination site, the ‘fixed’ kink site is eliminated, and the step straightens out (see the steps shown in the upper half of Fig. 7). It is unlikely that such cusps will be formed by contaminants at these high temperatures since individual atoms would be expected to diffuse under the action of the step line tension. Instead, the periodic spacing of the points of dissociation in Fig. 8(b) strongly suggests that each such point is associated with a dislocation in a low-angle grain boundary which is emerging at the surface. More detailed discussion of the structure of the dislocation evaporation patterns on the (0 0 1) surface of MgAl2 O4 and the mechanisms of their formation may be found elsewhere [19].
6. Conclusions Upon annealing at 1470–2070 K, the polished (0 0 1) surface of MgAl2 O4 spinel rearranges into the terrace-and-step geometry. At sub-evaporation temperatures (1470–1870 K), the surface morphology is dominated by single steps. The single
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steps move and align preferentially along either the [1 1 0] or the [1 1 0] direction of the crystal. When evaporation dominates the surface processes (at 2070 K and above), high velocities of step motion cause the association of single steps into stable step pairs (double steps). These double steps move along the surface as single entities and, like single steps, align along either the [1 1 0] or the [1 1 0] direction. The reverse process, the dissociation of double steps, occurs when the double steps encounter obstacles in the course of their motion, such as step trains or crystal defects. Acknowledgements SVY is in the Chemical Physics Program at the University of Minnesota. This research has been supported by the U.S. Department of Energy under Grant Nos. DE-FG02-92ER45465 and DEFG02-01ER45883. The AFM used is part of the U of MN Characterization Facility. The authors would like to acknowledge discussions with Dr. N. (Ravi) Ravishankar.
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