CRYSTAL GROWTH & DESIGN
Double Parallel Twinning on Cubic Crystals†
2008 VOL. 8, NO. 2 407–411
Angel Millan* Física de la Materia Condensada, Facultad de Ciencias, ICMA, CSIC-UniVersidad de Zaragoza, Pedro Cerbuna 10, 50009 Zaragoza, Spain ReceiVed July 24, 2006; ReVised Manuscript ReceiVed July 19, 2007
ABSTRACT: Double parallel twinning on octahedral faces is a frequent phenomenon that yields tabular or even laminar shapes among cubic crystals. However, there are neither satisfactory theoretical explanations nor direct observations of this phenomenon. In this paper, we reveal that double twinning occurs simultaneously on crystal corners when the growing crystal is changing its morphology. It is caused by a change of the composition of the medium, which switches the relative stability of crystal faces. Introduction 1
Crystal twins have been known for centuries, and the laws of twinning have been long-established.2–5 However, the underlying mechanisms and causes of twinning are still elusive, mainly because there is a lack of direct observations of the phenomena. The most often made assumption is that twinning occurs on a flat growing surface when a molecule, cluster, or two-dimensional nucleus stacks in a wrong position.6,7 It would then be produced by a high supersaturation,2 a foreign substance, or other sources supplying the little extra energy needed for a twinned stacking.5 An alternative mechanism is the coalescence of crystallites through a common crystal plane.8 It would come about when an enhancement of the adherence and the probability of collision of crystallites occur.9 Twinning may also occur by mechanical deformation.10 Twin planes may already be present in the nuclei, as in the case of multiple nonparallel twinning in fine particles of a variety of fcc materials (i.e., noble metals, diamondlike materials, and semimetals).11 These theories are difficult to prove, and thus some real twinning processes have been explained in several ways without a clue as to which one works better. The phenomenon of double parallel twinning only obscures this picture. According to these theories, double twinning is the outcome of two consecutive, independently random events. However, such a process on an octahedral crystal would yield a low ratio of parallel twins, whereas parallel twins may actually rise up to 90%.12 Other features that are difficult to explain by current theories are that crystals from the same breed have a nearly equal twin plane separation, the two external twin variants usually have the same thickness,5 and they can be produced at low supersaturation, low particle density, and slow particle motion. This report reveals a mechanism based on direct observation of the phenomenon, which is consistent with these facts. We observed the process of double twinning on AgBr crystals (rock salt structure, space group Fm3m,13 ac ) 5.77475 14) by optical microscopy, thanks to a new precipitation technique15 developed by us that is especially suitable for in situ observations of crystal growth.16 The method is based on the high solubility of silver halide complexes in polar aprotic solvents. Precipitation is produced by reducing the solubility adding a poor solvent. The process has also been followed by taking samples at † Part of the special issue on the 11th International Conference on the Crystallization of Biomacromolecules, Quebec, Canada, August 16–21, 2006 (preconference August 13–16). * Phone: 34 976762461. Fax: 34 9761229. E-mail:
[email protected].
different stages during the crystal transformation, and observing these samples by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Experimental Section Silver bromide stock solutions were prepared by dissolving AgBr and KBr in dimethyl sulfoxide (DMSO). The silver concentration in stock solutions was varied from 0.01 mol/L to 3 mol/L, and the Br-/ Ag+ ratio was varied from 3:2 to 4:1. Supersaturated solutions were prepared by controlled addition of a water/DMSO mixture to 5 mL of stock solution. The water/DMSO ratio in the mixture was 1/2 for precipitation in concentrated solutions and 1/8 for diluted solutions. Drops of clear supersaturated solution were placed in between two microscope slide covers. Precipitation occurred after a few minutes. In situ observations of crystal growth were carried out on a Nikon microphot-FX microscope equipped with a video recorder. SEM observations were performed on a Jeol JSM-T300 instrument. Uultrathin slices of crystals embedded in an epoxy resin were cut with a diamond knife (Reichert Jung) and examined with a Philips EM 400 electron microscope.
Results Optical microscopy observations of AgBr crystal growth showed that early crystals are square bipyramids. After a time, which depends on the concentration of Ag+ and the Br-/Ag+ ratio in the solution, crystals suffer a dramatic change of morphology. Figure 1 shows snapshots taken under optical microscope at different times during precipitation. The crystal on column I of this figure was grown from a solution with 1 mol/L of silver and a Br/Ag ratio of 1.5. The shape of this crystal changes from square bipyramid to irregular hexagon antiprism. The first image shows that this transformation starts with the appearance of two bright layers on opposite crystal corners. The intense brightness of the layers is indicative of their smooth surface. The layer on the left corner is on top of the crystal, and that on the right is on the bottom. In the next two images, the new flat layers advance upwards and inwards, whereas the center of the crystal becomes rough. At the end of the process, the crystal is bounded by two irregular hexagonal faces on top and bottom and six trapezoidal side faces. After this event, the crystal shows accelerated lateral growth. Crystals in column II were grown from a diluted solution (0.1 mol/L silver, Br/Ag ratio of 2). This sequence of pictures shows crystals developing a tabular shape after suffering a transformation of this type. The initial crystal shape is not clear from the pictures because they are too small when transforming. However, an inspection by scanning electron microscopy (SEM) of samples of crystals grown at the same conditions showed that they are the same
10.1021/cg060481j CCC: $40.75 2008 American Chemical Society Published on Web 01/01/2008
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Figure 2. (A) Crystal bounded by incomplete {110} form. The set of (011), (01–1), (0–11), and (0–1-1) faces is missing. (B) SEM images of crystal samples at different stages of transformation into tabular crystals, bar is 10 µm.
Figure 1. Optical microscope images captured by a video camera during the process of transformation of bipyramidal crystals into tabular ones. In column I, a crystal growing from a solution with 1 mol/L silver. In column II, crystals growing from a solution with 0.1 mol/L silver. Bar at the bottom in column I is 20 µm. The magnification was the same for all the pictures.
kind of crystals as the one appearing in column I. The shape transformation occurs earlier and faster than in the concentrated solution, and the aspect ratio of tabular crystals is much higher. Notice that nontransforming crystals finally dissolve, except the triangular crystal on the top left that remains unchanged (it is probably a single twin crystal). To observe in detail the evolution of crystal morphology, crystals at different stages of transformation have been examined by SEM. Images of these crystals are shown in Figure 2. Figure 2A shows a crystal initiating this process. The dihedral angle between contiguous faces in this crystal are 119 and 112°, and
Figure 3. (A) Crystal bounded by incomplete {110} form. The set of (011), (01–1), (0–11), and (0–1–1) faces is missing. (B) Crystallographic scheme of the transformation of a single cubic crystal bounded by an incomplete set of {110} faces into a {111} parallel double twin.
the dihedral angle between noncontiguous faces sharing a corner are 64 and 67°. Corresponding angles in crystals before starting transformation are around 119 and 62°. These values are closer to those formed by {110} faces (120 and 60°, respectively) than to those expected for {111} octahedra (109.47 and 70.53°). However, according to the crystal symmetry, there should be 12 faces of this type and not just eight. Apparently, the crystal is bounded by the {110} form, but the set of equatorial faces is missing as shown in Figure 3A. Consequently, there are two opposite obtuse corners on the crystal, named here after v2, that are different from the other four, named v1. Crystal in
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Figure 4. Spreading of a {111} twin layer from an obtuse corner of a crystal bounded by an incomplete set of {110} faces.
Figure 2A is developing acute edges on corners v1. Smooth surfaces with a new crystallographic orientation arise from these edges and extend inward the crystal. Meanwhile, corner v2 shows the birth of an incipient layer separated from the rest of the crystal by a deep groove. The crystal in Figure 2B shows a further stage on shape transformation. Edges born on corners v1 show narrow rectangular faces on their top, whereas corner v2 shows a smooth crystal layer separated by a groove marked in the picture with an arrow. Parallel to this layer, another one is observed on the crystal bottom that is also separated by a groove. In contrast with the smoothness of the new layers, lateral faces from the original crystal are rough. The crystal in Figure 2C has already developed cap layers over its top and bottom. The angles between the long sides of these layers are 60°, which indicate that they are {111} faces. The lateral growth of these cap layers along acute edges has overshot the central part of the crystal. That leaves hollow regions underneath the long sides of the cap layers. The central part of the crystal fills in from the short sides of the cap layers, and it remains rough until it reaches the inclination of {111} faces. By then, the crystals are already flattened octahedra and they become more and more tabular as they grow on. The result of this process is an irregular hexagonal antiprism like the one shown in Figure 2D. It must be pointed out that SEM observations performed on crystals from diluted solutions were comparable to those just described for concentrated solutions. Assuming that the crystal is bounded by {110} faces, and that the set of (011), (01–1), (0–11), and (0–1–1) faces is missing, a crystallographic scheme of the transformation of crystal in Figure 1, column I, could be that depicted in Figure 3B. Figure 4 shows the spreading of a twin layer form a corner of type v2 and the formation of {111} faces on corners of type v1, and Figure 5 shows an image of a corner of type v2 developing a twin layer. Notice that dihedral angles at corners of type v1 are smaller than those formed by {111} faces. Therefore, {111} faces formed at these corners can spread inward over the existing {110} faces. On the other hand, dihedral angles at corners of type v2 are larger than those formed by {111} faces. Therefore, the development of {111} faces on this corners by normal growth can occur only by spreading along the [001] direction. However, a {111} twin crystal on this corner can easily develop a (111) face overtopping the crystal by spreading along acute edges perpendicular to the [100], [010], and [001] directions. Therefore, the creation of twin layers on corners v2 permits a rapid change from {110} to {111} morphology. Finally, the process of crystal transformation captured in Figure 1 can be represented as shown in Figure 6. Figure 6A represents the first picture in Figure 1 and corresponds to the spreading of twin layers from v2 corners in the directions indicated by the arrows. Figure 6B represents an intermediate
Figure 5. Detail of a crystal corner developing a twin layer.
stage of transformation, in which top and bottom twin layers are partially covering the father crystal, and lateral faces are still rough. Figure 6C represents the final stage on crystal transformation, in which the top and bottom twin layers cover the whole crystal, and crystal sides are bounded by smooth lateral faces with a {111} orientation. The presence of parallel twins in crystals after this shape transformation was confirmed by TEM. Thin slices of crystal samples were examined by transmission electron microscopy (TEM). TEM images of a thick crystal grown from a concentrated solution and a thin crystal grown from a diluted solution are shown in images A and B in Figure 7, respectively. Both crystals show two parallel twin boundaries. The twin plane separation in the crystal grown from diluted solution is much smaller than that in the crystal grown from concentrated solution. Moreover, a comparison of twin plane separation and the size of transforming crystals suggests that double twinning occurs during this transformation. Discussion Now we examine the causes of double twinning process, taking silver halide precipitation as a model system. A key factor for the formation of {111} double twin crystals is the stability of {111} faces. In fcc crystals, {100} and {110} faces have lower surface energies than {111} faces.17 The polarity of ion stacking in the perpendicular direction contributes to the low stability of {111} faces.18 However, the dipole–dipole energy can be reduced by the covalent character of the metal–halide bond and the polarizability of the halide ions, which increases on the order Cl- < Br- < I-.19 Thus, (111) polar faces are rarely found on AgCl crystals,20 whereas {001} polar faces are
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Figure 6. Crystal drawings representing the crystal transformation shown in Figure 1.
by crystal growth itself, as we explain in the following. According to 109Ag nuclear magnetic resonance (NMR) measurements, silver in DMSO solutions is in the form of AgmBrn(n–m)– complexes.28 In concentrated solutions (1–3 M), these complexes are polynuclear and have a high bromide coordination number (n ) 4). In diluted solutions (0.1–0.4 M), the number of nuclei and the coordination of bromide ions in the complexes diminish. A similar decrease in bromide coordination number occurs when the Br/Ag ratio increases or when the size of the silver bromide counterion increases. As the AgBr crystals growth, polynuclear complexes become less stable and more free Br– is available in the solution to stabilize {111} form. Thus, both in water and DMSO systems, tabular crystal formation can be considered as a response of the system to a switch on the relative stability of crystal faces produced by an increase in the halide chemical potential in the medium. Conclusion Figure 7. TEM image of slices of tabular crystals from (A) a concentrated solution, and (B) a diluted solution. Bars are 1 µm.
found frequently in β-AgI crystals.21 Halide absorption reduces the surface energy of {111} faces in comparison to {100} and {110} faces,22 because of their capacity to accommodate a high density of halide ions on their surface. It is worthy to revise the morphology and habit of silver bromide crystals in several precipitation media. Silver bromide crystals grown from vapor,23 in water,24 or in aprotic solvents25,26 show a rich morphology. The most frequent forms in these crystals are {100}, {110}, {331}, and {111}. The combination of these forms and the occurrence of multiple twinning give rise to a large variety of crystal shapes. In vapor systems, morphology changes with the temperature difference between the source and the substrate.23 In substrates with a temperature gradient, the {100} form is found in the high-temperature region, and tabular crystals appear in the low-temperature region. In aqueous systems, morphology and twinning can be controlled by the concentration of halide in the growing medium.27 Crystal morphology changes from {100} to {111} with increasing halide concentration. In DMSO system, crystal morphology changes from {100} to {110} and then to {111} in media with increasing Br/Ag ratio.15,28 Therefore, as expected from energy considerations, {111} faces appear in the three systems studied when the bromide chemical potential in the medium is high. With respect to the process of double twinning, tabular crystals are produced in aqueous media by switching from moderate halide concentration in the nucleation stage to high halide concentration in the ripening stage. As described above, the formation of tabular crystals in DMSO solutions occurs without any external modification of the growing medium. However, there is indeed a change in the media that is produced
In conclusion, we have observed the transformation of square bipyramidal AgBr crystals bounded by an incomplete set of {110} faces into tabular hexagonal crystals bounded by {111} faces. According to SEM and TEM examinations, a double twinning process is taking place during this transformation. SEM observations also indicate that twinning events occur on two opposite corners with a crystallographic orientation different from the other four. The reason for twinning could be the incapacity of these corners to develop fast-growing acute edges by normal growth. This morphology transformation, and therefore the occurrence of twinning, is caused by variations in the medium composition during growth, switching the relative stability of crystal faces. This mechanism explains why crystals from the same breed show a regular twin plane separation and two external twin variants with a similar thickness. It also explains the high ratio of parallel twins with respect to the nonparallel usually found in silver halide precipitations. This mechanism may also apply to other systems based on cubic crystals, apart from silver halide photographic emulsions, such as semiconductors,29,30 ceramics,31 metals,32 diamond,33 and fullerenes.34 Acknowledgment. Financial support from Agfa-Gevaert is gratefully acknowledged. The author is indebted to Julio Fernández for helpful discussions.
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