Fiveling
A fiveling, also known as a decahedral nanoparticle, a multiply-twinned particle, a pentagonal nanoparticle, a pentatwin, or a five-fold twin is a type of twinned crystal that can exist at sizes ranging from nanometers to millimetres. It contains five different single crystals arranged around a common axis. In most cases each unit has a face centered cubic arrangement of the atoms, although they are also known for other types of crystal structure.
They nucleate at quite small sizes in the nanometer range, but can be grown much larger. They have been found in mineral crystals excavated from mines such as pentagonite or native gold from Ukraine, in rods of metals grown via electrochemical processes and in nanoparticles produced by the condensation of metals either onto substrates or in inert gases. They have been investigated for their potential uses in areas such as improving the efficiency of solar cell or heterogeneous catalysis for more efficient production of chemicals. Information about them is distributed across a diverse range of scientific disciplines, mainly chemistry, materials science, mineralogy, nanomaterials and physics. Because many different names have been used, sometimes the information in the different disciplines or within any one discipline is fragmented and overlapping.
At small sizes in the nanometer range, up to millimetres in size, with fcc metals they often have a combination of and facets, a low energy shape called a Marks decahedron. Relative to a single crystal, at small sizes a fiveling can be a lower energy structure due to having more low energy surface facets. Balancing this there is an energy cost due to elastic strains to close an angular gap, which makes them higher in energy at larger sizes. They can be the most stable structure in some intermediate sizes, but they can be one among many in a population of different structures due to a combination of coexisting nanoparticles and kinetic growth factors. The temperature, gas environment and chemisorption can play an important role in both their thermodynamic stability and growth. While they are often symmetric, they can also be asymmetric with the disclination not in the center of the particle.
History
Dating back to the nineteenth century there are reports of these particles by authors such as Jacques-Louis Bournon in 1813 for marcasite, and Gustav Rose in 1831 for gold. In mineralogy and the crystal twinning literature they are referred to as a type of cyclic twin where a number of identical single crystal units are arranged in a ring-like pattern where they all join at a common point or line. The name comes from them having five members. Fivelings have also been described as a type of macle twinning. The older literature was mainly observational, with information on many materials documented by Victor Mordechai Goldschmidt in his Atlas der Kristallformen. Drawings are available showing their presence in marcasite, gold, silver, copper and diamond. New mineral forms with a fiveling structure continue to be found, for instance pentagonite, whose structure was first decoded in 1973, is named because it is often found with the five-fold twinning.Most modern analysis started with the observation of these particles by Shozo Ino and Shiro Ogawa in 1966-67, and independently but slightly later in work by John Allpress and John Veysey Sanders. In both cases these were for vacuum deposition of metal onto substrates in very clean conditions, where nanoparticle islands of size 10-50 nm were formed during thin film growth. Using transmission electron microscopy and diffraction these authors demonstrated the presence of the five single crystal units in the particles, and also the twin relationships. They also observed single crystals and a related type of icosahedral nanoparticle. They called the five-fold and icosahedral crystals multiply twinned particles. In the early work near perfect decahedron and icosahedron shapes were formed, so they were called decahedral MTPs or icosahedral MTPs, the names connecting to the decahedral and icosahedral point group symmetries. Parallel, and apparently independent there was work on larger metal whiskers which sometimes showed a very similar five-fold structure, an occurrence reported in 1877 by Gerhard vom Rath. There was fairly extensive analysis following this, particularly for the nanoparticles, both of their internal structure by some of the first electron microscopes that could image at the atomic scale, and by various continuum or atomic models as cited later.
Following this early work there was a large effort, mainly in Japan, to understand what were then called "fine particles", but would now be called nanoparticles. By heating up different elements so atoms evaporated and were then condensed in an inert argon atmosphere, fine particles of almost all the elemental solids were made and then analyzed using electron microscopes. The decahedral particles were found for all face centered cubic materials and a few others, often together with other shapes.
While there was some continuing work over the following decades, it was with the National Nanotechnology Initiative that substantial interest was reignited. At the same time terms such as pentagonal nanoparticle, pentatwin, or five-fold twin became common in the literature, together with the earlier names. A large number of different methods have now been published for fabricating fivelings, sometimes with a high yield but often as part of a larger population of different shapes. These range from colloidal solution methods to different deposition approaches. It is documented that fivelings occur frequently for diamond, gold and silver, sometimes for copper or palladium and less often for some of the other face-centered cubic metals such as nickel. There are also cases such as pentagonite where the crystal structure allows for five-fold twinning with minimal to no elastic strain . There is work where they have been observed in colloidal crystals consisting of ordered arrays of nanoparticles, and single crystals composed on individual decahedral nanoparticles. There has been extensive modeling by many different approaches such as embedded atom, many body, molecular dynamics, tight binding approaches, and density functional theory methods as discussed by Francesca Baletto and Riccardo Ferrando and also discussed for [|energy landscapes] later.
Disclination strain
These particles consist of five different units which are joined together by twin boundaries. The simplest form shown in the figure has five tetrahedral crystals which most commonly have a face centered cubic structure, but there are other possibilities such as diamond cubic and a few others as well as more complex shapes. The angle between two twin planes is approximately 70.5 degrees in fcc, so five of these sums to 352.5 degrees leading to an angular gap. At small sizes this gap is closed by an elastic deformation, which Roland de Wit pointed out could be described as a wedge disclination, a type of defect first discussed by Vito Volterra in 1907. With a disclination the strains to close the gap vary radially and are distributed throughout the particle.With other structures the angle can be different; marcasite has a twin angle of 74.6 degrees, so instead of closing a missing wedge, one of angle 13 degrees has to be opened, which would be termed a negative disclination of 13 degrees. It has been pointed out by Chao Liang and Yi Yu that when intermetallics are included there is a range of different angles, some similar to fcc where there is a deficiency, others such as AuCu where there is an overlap similar to marcasite, while pentagonite has probably the smallest overlap at 3.5 degrees.
Early experimental high-resolution transmission electron microscopy data supported the idea of a distributed disclination strain field in the nanoparticles, as did dark field and other imaging modes in electron microscopes. In larger particles dislocations have been detected to relieve some of the strain. The disclination deformation requires an energy which scales with the particle volume, so dislocations or grain boundaries are lower in energy for large sizes.
More recently there has been detailed analysis of the atomic positions first by Craig Johnson et al, followed up by a number of other authors, providing more information on the strains and showing how they are distributed in the particles. While the classic disclination strain field is a reasonable first approximation model, there are differences when more complete elastic models are used such as finite element methods, particularly as pointed out by Johnson et al, anisotropic elasticity needs to be used. One further complication is that the strain field is three dimensional, and more complex approaches are needed to measure the full details as detailed by Bart Goris et al, who also mention issues with strain from the support film. In addition, as pointed out by Srikanth Patala, Monica Olvera de la Cruz and Marks and shown in the figure, the Von Mises stress are different for pentagonal bipyramids versus the minimum energy shape. As of 2024 the strains are consistent with finite element calculations and a disclination strain field, with the possible addition of a shear component at the twin boundaries to accommodate some of the strains.
An alternative to the disclination strain model which was proposed by B. G. Bagley in 1965 for whiskers is that there is a change in the atomic structure away from face-centered cubic; a hypothesis that a tetragonal crystal structure is lower in energy than fcc, and a lower energy atomic structure leads to the decahedral particles. This view was expanded upon by Cary Y. Yang and can also be found in some of the early work of Miguel José Yacamán. There have been measurements of the average structure using X-ray diffraction which it has been argued support this view. However, these x-ray measurements only see the average which necessarily shows a tetragonal arrangement, and there is extensive evidence for inhomogeneous deformations dating back to the early work of Allpress and Sanders, Tsutomu Komoda, Marks and David J. Smith and more recently by high resolution imaging of details of the atomic structure. As mentioned [|above], as of 2024 experimental imaging supports a disclination model with anisotropic elasticity.