Fivefold Twinned Nanoparticles (2004)

Twinning is widespread in crystalline materials of various origin and nature. Basic concepts and definitions of twinning are treated in many textbooks and review papers [1–3]. A description of the crystallographic fundamentals of twinning can be found in the International Tables for Crystallography, Volume D: “Physical Properties of Crystals” [4]. Twins may form as a result of erroneously attaching atoms or molecules to a growing crystal such that two crystals appear to be growing out of or into each other. Character and rule of twinning can be understood by considering the sequence of atomic layers added to a crystal during growth. Stacking of closepacked planes in face-centered cubic crystals is possible in three different positions denoted A, B, and C leading to a regular growth sequence ABCABCABCABCA. If, for example, the central A layer of this sequence is followed by a layer of misplaced atoms assuming the wrong position C, upon which a regular stacking appears again, then the following sequence will form: ABCABCACBACBA. In this way the crystal lattice is mirrored at the central layer A, which is easier to see if the central letter A is replaced by a vertical line representing a mirror or twin plane: ABCABC CBACBA. There are two general types of twin style: contact and penetration [5, 6]. The one considered here is contact twins that have a composition plane, the twin plane, that forms a boundary between the twinned subunits. Twinning often has a serious effect on the outward shape and symmetry of a crystal, in particular in the case of repeated twinning. Two types of repeated twinning are known: lamellar and cyclic. Lamellar twinning forms from parallel contact twins repeating continuously, one after another. Cyclic twinning requires nonparallel coplanar composition planes. If these twin planes enclose an angle being an integer part of 360 , then a complete circle can be formed by cyclic twinning. Some classic minerals like cassiterite (SnO2), wurtzite (ZnS), and rutile (TiO2) form cyclic twins called “trilling,” “fourling,” “sixling,” or “eightling” quite according to their twin angles of 120 , 90 , 60 , or 45 , respectively. Cyclic twinning is also found in minerals of the spinel (MgAl2O4) group whose specific rule of twinning bears its name, the spinel twin law. Here a twin plane is parallel to one of the octahedral habit planes enclosing an angle of 70.53 , which is close to 2 /5. Repeated cyclic twinning according to this twin law does not form a complete circle, but leaves a small gap. Nevertheless, it enables the formation of “fivelings” of a number of crystals. Actually, repeated twinning, also called polysynthetic twinning, or multiple twinning, is rather common in natural minerals and crystalline materials. There are also known examples of twin compounds composed of cyclicly arranged twin pairs [7]. However, it is the type of fivefold twinning on alternate coplanar twin planes in small particles, creating “fivelings” of unique morphology, for which the term “multiply twinned particles” (usually abbreviated as MTPs) was applied. The term MTP will herewith be used for such particles, otherwise, for example, for fivefold twinning in thin films, the term “fivefold twinned structures” is used. The unique morphology of MTPs and the unusual symmetry of the arrangement of building units are essential structural features, mostly at dimensions of a few nanometers, but fairly often also up to micrometer or even millimeter dimensions. Fivefold twinning in thin films and nanoparticles of nanometer dimensions is in itself a whole class of materials, the origin of widespread structures resulting from a great variety of substances and fabrication processes involved. These are introduced in this chapter together with the issues of synthesis, formation mechanisms, and stability and lattice defects. Various illustrative examples are aimed at emphasizing the importance of this phenomenon in the area of nanostructured materials. It always has attracted the attention not only of crystal growth and crystallography research,