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Decahedral PtFe1.2 nanoparticle.[1]

A fiveling, also known as a decahedral nanoparticle, a multiply-twinned particle (MTP), 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 (fcc) 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[a] excavated from mines such as pentagonite[2] or native gold from Ukraine,[3] 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 {111} and {100} facets, a low energy shape called a Marks decahedron.[4][5] Relative to a single crystal, at small sizes a fiveling can be a lower energy structure due to having more low energy surface facets.[b] Balancing this there is an energy cost due to elastic strains to close an angular gap (disclination), 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

[edit]
Redrawn version of 1831 sketch of a gold fiveling by Rose,[6] which is a Marks Decahedron[7][8] with .

Dating back to the nineteenth century there are reports of these particles by authors such as Jacques-Louis Bournon in 1813 for marcasite,[9][10] and Gustav Rose in 1831 for gold.[6] 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.[11] The name fiveling comes from them having five members (single crystals).[12] The older literature was mainly observational, with information on many materials documented by Victor Mordechai Goldschmidt in his Atlas der Kristallformen.[13] 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.[2][14]

Most modern analysis started with the observation of these particles by Shozo Ino and Shiro Ogawa in 1966-67,[15][16] and independently but slightly later (which they acknowledged) work by John Allpress and John Veysey Sanders.[17] In both cases these were for vacuum deposition of metal onto substrates in very clean (ultra-high vacuum) 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 (MTPs). In the early work near perfect decahedron (pentagonal bipyramid) 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.[c] Parallel, and apparently independent there was work on larger metal whiskers (nanowires) which sometimes showed a very similar five-fold structure,[18][19] an occurrence reported in 1877 by Gerhard vom Rath.[20] 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,[21] 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.[22][23][24]

Calculated minimum energy decahedral structure for 75 atoms with a Lennard-Jones potential, an atomistic version of a Marks decahedron.[25]

While there was some continuing work over the following decades, it was with the National Nanotechnology Initiative[26] 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.[27] These range from colloidal solution methods[28] to different deposition approaches.[22][29] It is documented that fivelings occur frequently for diamond,[30][31] gold and silver,[32] sometimes for copper[33][34] or palladium[35][36] and less often for some of the other face-centered cubic (fcc) metals such as nickel.[4] There are also cases such as pentagonite where the crystal structure allows for five-fold twinning with minimal to no elastic strain (see later).[2] There is work where they have been observed in colloidal crystals consisting of ordered arrays of nanoparticles,[37][38] and single crystals composed on individual decahedral nanoparticles.[39] There has been extensive modeling by many different approaches such as embedded atom,[4] many body,[40] molecular dynamics,[41] tight binding approaches,[42] and density functional theory methods[43] as discussed by Francesca Baletto and Riccardo Ferrando[44] and also discussed for energy landscapes later.

Disclination strain

[edit]
Pentagonal bipyramid showing the angular gap for face-centered cubic.

These particles consist of five different (single crystal) 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 (not 360 degrees) leading to an angular gap. At small sizes this gap is closed by an elastic deformation, which Roland de Wit pointed out[45][46] could be described as a wedge disclination, a type of defect first discussed by Vito Volterra in 1907.[47] 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[48] that when intermetallics are included there is a range of different angles, some similar to fcc where there is a deficiency (positive disclination), others such as AuCu where there is an overlap (negative disclination) similar to marcasite,[9][49] while pentagonite has probably the smallest overlap at 3.5 degrees.[2]

Top view of Von Mises stress in pentagonal bipyramid and Marks decahedron.[50]

Early experimental high-resolution transmission electron microscopy data[21] supported the idea of a distributed disclination strain field in the nanoparticles, as did dark field and other imaging modes in electron microscopes.[51] In larger particles dislocations have been detected to relieve some of the strain.[52][23][53][54] The disclination deformation requires an energy which scales with the particle volume, so dislocations or grain boundaries are lower in energy for large sizes.[55]

More recently there has been detailed analysis of the atomic positions first by Craig Johnson et al,[56] followed up by a number of other authors,[57][58][59] 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.[56][60][59] 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.[61] In addition, as pointed out by Srikanth Patala, Monica Olvera de la Cruz and Marks[50] and shown in the figure, the Von Mises stress are different for (kinetic growth) pentagonal bipyramids versus the minimum energy shape.[50] 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.[56][58][59]

An alternative to the disclination strain model which was proposed by B G Bagley in 1965 for whiskers[62] is that there is a change in the atomic structure away from face-centered cubic; a hypothesis that a tetragonal crystal structure[63] 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[64] and can also be found in some of the early work of Miguel José Yacamán.[65][66] There have been measurements of the average structure using X-ray diffraction which it has been argued support this view.[67] 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,[17] Tsutomu Komoda,[21] Marks and David J. Smith[51] and more recently by high resolution imaging of details of the atomic structure.[56][57][58][59] As mentioned above, as of 2024 experimental imaging supports a disclination model with anisotropic elasticity.

Three-dimensional shape

[edit]
Decahedra for different (100) to (111) surface energies; top, down the common axis, and bottom from the side.[68]
Gold fiveling, 0.5cm tall from Miass, Siberia, Russia, a Marks decahedron with .

The three-dimensional shape depends upon how the fivelings are formed, including the environment such as gas pressure and temperature. In the very early work only pentagonal bipyramids were reported.[15][16][17] In 1970 Ino tried to model the energetics, but found that these bipyramids were higher in energy than single crystals with a Wulff construction shape. He found a lower energy form where he added {100} facets,[69] what is now commonly called the Ino decahedron. The surface energy of this form and a related icosahedral twin scale as the two-thirds power of the volume, so they can be lower in energy than a single crystal as discussed further below.

However, while Ino was able to explain the icosahedral particles, he was not able to explain the decahedral ones. Later Laurence D. Marks proposed a model using both experimental data and a theoretical analysis, which is based upon a modified Wulff construction which includes more surface facets, including Ino's {100} as well as re-entrant {111} surfaces at the twin boundaries with the possibility of others such as {110}, while retaining the decahedral point group symmetry.[7][8][55] This approach also includes the effect of gas and other environmental factors via how they change the surface energy of different facets. By combining this model with de Wit's elasticity,[46] Archibald Howie and Marks were able to rationalize the stability of the decahedral to particles.[55] Other work soon confirmed the shape reported by Marks for annealed particles.[70] This was further confirmed in detailed atomistic calculations a few years later by Charles Cleveland and Uzi Landman who coined the term Marks decahedra for these shapes,[4] this name now being widely used.[24][32][71][72]

The minimum energy or thermodynamic shape for these particles[7][8] depends upon the relative surface energies of different facets, similar to a single crystal Wulff shape; they are formed by combining segments of a conventional Wulff construction with two additional internal facets to represent the twin boundaries.[8][7] An overview of codes to calculate these shapes was published in 2021 by Christina Boukouvala et al.[73] Considering just {111} and {100} facets:[7][8]

  • The Ino decahedron occurs when the surface energy of the {100} facets is small, ;
  • Common is the Marks decahedron with {100} facets and a re-entrant surface at the twin boundaries for
  • With there is no {100} faceting, and the particles have been called nanostars.[74]
  • For very low the equilibrium shape is a long rod along the common five-fold axis.

The photograph of an 0.5 cm gold fiveling from Miass is a Marks decahedron with , while the sketch of Rose[6] is for . The 75 atom cluster shown above corresponds to the same shape for a small number of atoms. Experimentally, in fcc crystals fivelings with only {111} and {100} facets are common, but many other facets can be present in the Wulff construction leading to more rounded shapes,[8][71] for instance {113} facets for silicon.[75] It is known that the surface can reconstruct to a different atomic arrangement in the outermost atomic plane, for instance a dimer reconstruction for {100} facets of silicon particles[75] of a hexagonal overlayer on the {100} facets of gold decahedra.[71]

SEM image of decagonal rod of silver.[76]

What shape is present depends not just on the surface energy of the different facets, but also upon how the particles grow. The thermodynamic shape is determined by the Wulff construction, which considers the energy of each possible surface facet and yields the lowest energy shape. The original Marks decahedron was based upon a form of Wulff construction that takes into account the twin boundaries.[7][8] There is a related kinetic Wulff construction where the growth rate of different surfaces is used instead of the energies.[68][77] This type of growth matters when the formation of a new island on a flat facet limits the growth rate.[78] If the {100} surfaces of Ino grow faster, then they will not appear in the final shape, similarly for the re-entrant surfaces at the twin boundaries—this leads to the pentagonal bipyramids often observed.[68] Alternatively, if the {111} surfaces grow fast and {100} slow the kinetic shape will be a long rod along the common five-fold axis as shown in the figure.[79][80][76][81]

Fiveling (decahedral nanoparticle) showing diffusion growth at tips.[82]

Another different set of shapes can occur when diffusion of atoms to the particles dominates, a growth regime called diffusion controlled growth. In such cases surface curvature can play a major role,[83][77] for instance leading to spikes originating at the sharp corners of a pentagonal bipyramids, sometimes leading to pointy stars, as shown in the figure.[82]

Energy versus size

[edit]

The most common approach to understand the formation of these particles, first used by Ino in 1969,[69] is to look at the energy as a function of size comparing icosahedral twins, decahedral nanoparticles and single crystals. The total energy for each type of particle can be written as the sum of three terms:

for a volume , where is the surface energy, is the disclination strain energy to close the gap (or overlap for marcasite and others), and is a coupling term for the effect of the strain on the surface energy via the surface stress,[84][85][86] which can be a significant contribution.[60] The sum of these three terms is compared to the total surface energy of a single crystal (which has no strain), and to similar terms for an icosahedral particle. Because the decahedral particles have a lower total surface energy than single crystals due (approximately, in fcc) to more low energy {111} surfaces, they are lower in total energy for an intermediate size regime, with the icosahedral particles more stable at very small sizes. (The icosahedral particle have even more {111} surfaces, but also more strain.[55]) At large sizes the strain energy can become very large, so it is energetically favorable to have dislocations and/or a grain boundary instead of a distributed strain.[54] The very large mineral samples are almost certainly trapped in metastable higher energy configurations.

There is no general consensus on the exact sizes when there is a transition in which type of particle is lowest in energy, as these vary with material and also the environment such as gas and temperature; the coupling surface stress term and also the surface energies of the facets are very sensitive to these.[87][88][89] In addition, as first described by Michael Hoare and P Pal[90] and R. Stephen Berry[91][92] and analyzed for these particles by Pulickel Ajayan and Marks[93] as well as discussed by others such as Amanda Barnard,[94] David J. Wales,[40][63][95] Kristen Fichthorn[96] and Baletto and Ferrando,[44] at very small sizes there will be a statistical population of different structures so many different ones will coexist. In many cases nanoparticles are believed to grow from a very small seed without changing shape, and reflect the distribution of coexisting structures.[27]

Energy landscape for a 75 atom Leonard-Jones cluster for temperature and an order parameter.[25]

For systems where icosahedral and decahedral morphologies are both relatively low in energy, the competition between these structures has implications for structure prediction and for the global thermodynamic and kinetic properties. These result from a double funnel energy landscape[97][98] where the two families of structures are separated by a relatively high energy barrier at the temperature where they are in thermodynamic equilibrium. This situation arises for a cluster of 75 atoms with the Lennard-Jones potential, where the global potential energy minimum is decahedral, and structures based upon incomplete Mackay icosahedra[99] are also low in potential energy, but higher in entropy. The free energy barrier between these families is large compared to the available thermal energy at the temperature where they are in equilibrium. An example is shown in the figure, with probability in the lower part and energy above with axes of an order parameter and temperature . At low temperature the 75 atom decahedral cluster (Dh) is the global free energy minimum, but as the temperature increases the higher entropy of the competing structures based on incomplete icosahedra (Ic) causes the finite system analogue of a first-order phase transition; at even higher temperatures a liquid-like state is favored.[25]

There has been experiment support based upon work where single nanoparticles are imaged using electron microscopes either as they grow or as a function of time. One of the earliest works was that of Yagi et al[100] who directly observed changes in the internal structure with time during growth. More recent work has observed variations in the internal structure in liquid cells,[101] or changes between different forms due to either (or both) heating or the electron beam in an electron microscope[102][103][104] including substrate effects.[41]

Successive twinning

[edit]

Allpress and Sanders proposed an alternative approach to energy minimization to understanding these particles called "successive twinning".[17] Here one starts with a single tetrahedral unit, which then forms a twin either by accident during growth or by collision with another tetrahedron. It was proposed that this could continue to eventually have five units join.[105]

Atomistic simulation of disclination movement in decahedral particles, showing the energies relative to perfect Marks decahedra and tetrahedra.[105]

The term "successive twinning" has now come to mean a related concept: motion of the disclination either to or from a symmetric position as sketched in the atomistic simulation in the figure;[105] see also Haiqiang Zhao et al[72] for very similar experimental images.

While in many cases experimental images show symmetric structures, sometimes they are less so and the five-fold center is quite asymmetric.[106][72] There are asymmetric cases which can be metastable,[7] and asymmetry can also be a strain relief process[107] or involved in how the particle convert to single crystals or from single crystals.[100][93] During growth there may be changes, as directly observed by Katsumichi Yagi et al for growth inside an electron microscope,[100] and migration of the disclination from the outside has been observed in liquid-cell studies in electron microscopes.[101] Extensive details about the atomic processes involved in motion of the disclination have been given using molecular dynamics calculations supported by density functional theory as shown in the figure.[105]

Connections

[edit]

There are a number of related concepts and applications of decahedral particles.

Quasicrystals

[edit]

Soon after the discovery of quasicrystals it was suggested by Linus Pauling[108][109] that five-fold cyclic twins such as these were the source of the electron diffraction data observed by Dan Shechtman.[110] While there are similarities, quasicrystals are now considered to be a class of packing which is different from fivelings and the related icosahedral particles.[111][112]

Heterogeneous catalysts

[edit]

There are possible links to heterogeneous catalysis, with the decahedral particles displaying different performance.[113][114][57][115] The first study by Avery and Sanders[113] did not find them in automobile catalysts. Later work by Marks and Howie found them in silver catalysts,[114] and there have been other reports. It has been suggested that the strain at the surface can change reaction rates,[57] and since there is evidence that surface strain can change the adsorption of molecules and catalysis there is circumstantial support for this.[116][117] As of 2024, there is some experimental evidence for different catalytic reactivity.[118][115][119]

Plasmonics

[edit]

It is known that the response of the surface plasmon polaritons in nanoparticles depends upon their shape.[120] As a consequence decahedral particles have specific optical responses.[121][122] One suggested use is to improve light adsorption using their plasmonic properties by adding them to polymer solar cells.[123]

Five-fold twin at an Au tip after tensile failure.[124] The scale bar is 2 nm.

Thin films and mechanical deformation

[edit]

Most observations of fivelings have been for isolated particles. Similar structures can occur in thin films when particles merge to form a continuous coating, but do not recrystallize immediately.[125][126] They can also form during annealing of films,[127][128] which molecular dynamics simulations have indicated correlates to the motion of twin boundaries and a disclination,[129] similar to the case of isolated nanoparticles described earlier. There is experimental evidence in thin films for interactions between partial dislocations and disclinations,[130] as discussed in 1971 by de Wit.[45] They can also be formed by mechanical deformation.[124] The formation of a local fiveling structure by annealing or deformation has been attributed to a combination of stress relief and twin motion,[127][124][131] which is different from the surface energy driven formation of isolated particles described above.

See also

[edit]
  • Chemical physics – Subdiscipline of chemistry and physics
  • Cluster (chemistry) – Collection of bound atoms or molecules
  • Cluster (physics) – Small collection of atoms or molecules
  • Crystal habit – Mineralogical term for the visible shape of a mineral
  • Crystal twinning – Two separate crystals sharing some of the same crystal lattice points in a symmetrical manner
  • Disclination – Angular defect in a material
  • Icosahedral twins – Structure found in atomic clusters and nanoparticles
  • Nanocluster – Collection of bound atoms or molecules
  • Nanomaterials – Materials whose granular size lies between 1 and 100 nm
  • Nanowire – Wire with a diameter in the nanometres
  • Nucleation – Initial step in the phase transition or molecular self-assembly of a substance
  • Surface energy – Excess energy at the surface of a material relative to its interior
  • Surface stress – Change of surface energy with strain
  • Wulff construction – Lowest energy shape of a single crystal

Notes

[edit]
  1. ^ In mineralogy millimeter sized objects are normally referred to as crystals. In other areas the terms are different. When a fiveling has only a very few atoms, for instance the smallest which is seven, it would be called a cluster. They are also sometimes called nucleii or seeds. In the size range 2-100 nm they are currently called nanoparticles, although earlier names are small particles and fine particles.
  2. ^ In the nanoparticle literature as well as physics and chemistry the term facet is common for flat external surfaces, which is how it is used herein. In the mineralogical literature the term facet is more commonly used for the external surfaces created on the surfaces of gemstones by cutting and polishing, and surface faces is used for native crystallographic surfaces such as {111}, which are also sometimes called natural facets.
  3. ^ Common usage is to connect point group names to the corresponding shapes in two dimensions, such as pentagonal with pentagon, and polyhedra in three dimensions such as decahedral for a decahedron (pentagonal bipyramid) and icosahedral for icosahedron.

References

[edit]
  1. ^ Jang, Ji-Hoon; Lee, Eunjik; Park, Jinwoo; Kim, Gunn; Hong, Suklyun; Kwon, Young-Uk (2013). "Rational syntheses of core-shell Fex@Pt nanoparticles for the study of electrocatalytic oxygen reduction reaction". Scientific Reports. 3 (1): 2872. doi:10.1038/srep02872. ISSN 2045-2322. PMC 3791448. PMID 24096587.
  2. ^ a b c d Staples, L. W.; Evans, H. T.; Lindsay, J. R. (1973). "Cavansite and Pentagonite, New Dimorphous Calcium Vanadium Silicate Minerals from Oregon". American Mineralogist. 58 (5–6): 405–411.
  3. ^ Kvasnifsa, V. N.; Kuznetsov, Yu. A.; Latysh, I. K. (1981). "Crystal morphology of native gold from some ore regions of the Ukraine". International Geology Review. 23 (2): 227–232 Figure 5. Bibcode:1981IGRv...23..227K. doi:10.1080/00206818209467235. ISSN 0020-6814.
  4. ^ a b c d Cleveland, Charles L.; Landman, Uzi (1991). "The energetics and structure of nickel clusters: Size dependence". The Journal of Chemical Physics. 94 (11): 7376–7396. Bibcode:1991JChPh..94.7376C. doi:10.1063/1.460169. ISSN 0021-9606.
  5. ^ Doye, Jonathan (1996). "The Structure, Thermodynamics and Dynamics of Atomic Clusters". doye.chem.ox.ac.uk. Retrieved 9 May 2024.
  6. ^ a b c Rose, Gustav (1831). "Ueber die Krystallformen des Goldes und des Silbers". Annalen der Physik. 99 (10): 196–204. Bibcode:1831AnP....99..196R. doi:10.1002/andp.18310991003. ISSN 0003-3804.
  7. ^ a b c d e f g Marks, L.D. (1983). "Modified Wulff constructions for twinned particles". Journal of Crystal Growth. 61 (3): 556–566. Bibcode:1983JCrGr..61..556M. doi:10.1016/0022-0248(83)90184-7.
  8. ^ a b c d e f g Marks, L. D. (1984). "Surface structure and energetics of multiply twinned particles". Philosophical Magazine A. 49 (1): 81–93. Bibcode:1984PMagA..49...81M. doi:10.1080/01418618408233431. ISSN 0141-8610.
  9. ^ a b Comte de Bournon, Jacques-Louis (1813). Catalogue de la collection minéralogique du comte de Bournon,... faites par lui-même . Et dans lequel sont placés plusieurs observations et faits intéressants... ainsi qu'une réponse au mémoire de M. l'abbé Haüy concernant la simplicité des lois auxquelles est soumise la structure des cristaux, etc. L. Deconchy. pp. 301–308.
  10. ^ Comte de Bournon, Jacques-Louis (1813). Catalogue de la collection minéralogique du comte de Bournon,... faites par lui-même . Et dans lequel sont placés plusieurs observations et faits intéressants... ainsi qu'une réponse au mémoire de M. l'abbé Haüy concernant la simplicité des lois auxquelles est soumise la structure des cristaux, etc. L. Deconchy. pp. plates VIII and esp. IX, fig 164–168.
  11. ^ Perkins, Dexter (2022). "4.4.6: Crystal Twinning". Geosciences LibreTexts. Retrieved 27 March 2024.
  12. ^ "Definition of FIVELING". www.merriam-webster.com. Retrieved 27 March 2024.
  13. ^ Goldschmidt, Victor (1913–1923). Atlas der Krystallformen [Atlas of Crystal Forms]. Heidelberg: C. Winters.
  14. ^ White, John (2002). "Let's Get It Right: Cavansite or Pentagonite?". Rocks & Minerals. 77 (4): 274–275. Bibcode:2002RoMin..77..274W. doi:10.1080/00357529.2002.9925646. ISSN 0035-7529.
  15. ^ a b Ino, Shozo (1966). "Epitaxial Growth of Metals on Rocksalt Faces Cleaved in Vacuum. II. Orientation and Structure of Gold Particles Formed in Ultrahigh Vacuum". Journal of the Physical Society of Japan. 21 (2): 346–362. Bibcode:1966JPSJ...21..346I. doi:10.1143/JPSJ.21.346. ISSN 0031-9015.
  16. ^ a b Ino, Shozo; Ogawa, Shiro (1967). "Multiply Twinned Particles at Earlier Stages of Gold Film Formation on Alkalihalide Crystals". Journal of the Physical Society of Japan. 22 (6): 1365–1374. Bibcode:1967JPSJ...22.1365I. doi:10.1143/JPSJ.22.1365. ISSN 0031-9015.
  17. ^ a b c d Allpress, J.G.; Sanders, J.V. (1967). "The structure and orientation of crystals in deposits of metals on mica". Surface Science. 7 (1): 1–25. Bibcode:1967SurSc...7....1A. doi:10.1016/0039-6028(67)90062-3.
  18. ^ Schwoebel, Richard L. (1966). "Anomalous Growth of Gold from the Vapor Phase". Journal of Applied Physics. 37 (6): 2515–2516. Bibcode:1966JAP....37.2515S. doi:10.1063/1.1708849. ISSN 0021-8979.
  19. ^ Smit, J.; Ogburn, F.; Bechtoldt, C. J. (1968). "Multiple Twin Structures in Electrodeposited Silver Dendrites". Journal of the Electrochemical Society. 115 (4): 371. Bibcode:1968JElS..115..371S. doi:10.1149/1.2411207.
  20. ^ Rath, G. vom (1877). "Mineralogische Mittheilungen". Zeitschrift für Kristallographie - Crystalline Materials. 1 (1–6): 1–17. doi:10.1524/zkri.1877.1.1.1. ISSN 2196-7105.
  21. ^ a b c Komoda, Tsutomu (1968). "Study on the Structure of Evaporated Gold Particles by Means of a High Resolution Electron Microscope". Japanese Journal of Applied Physics. 7 (1): 27. Bibcode:1968JaJAP...7...27K. doi:10.1143/JJAP.7.27. ISSN 0021-4922.
  22. ^ a b Hayashi, Takayoshi; Ohno, Takehisa; Yatsuya, Shigeki; Uyeda, Ryozi (1977). "Formation of Ultrafine Metal Particles by Gas-Evaporation Technique. IV. Crystal Habits of Iron and Fcc Metals, Al, Co, Ni, Cu, Pd, Ag, In, Au and Pb". Japanese Journal of Applied Physics. 16 (5): 705–717. Bibcode:1977JaJAP..16..705H. doi:10.1143/JJAP.16.705. ISSN 0021-4922.
  23. ^ a b Iijima, Sumio (1987). "Fine Particles of Silicon. II. Decahedral Multiply-Twinned Particles". Japanese Journal of Applied Physics. 26 (3R): 365. Bibcode:1987JaJAP..26..365I. doi:10.1143/JJAP.26.365. ISSN 0021-4922.
  24. ^ a b Zhou, Shan; Zhao, Ming; Yang, Tung-Han; Xia, Younan (2019). "Decahedral nanocrystals of noble metals: Synthesis, characterization, and applications". Materials Today. 22: 108–131. doi:10.1016/j.mattod.2018.04.003. ISSN 1369-7021.
  25. ^ a b c Wales, David J. (2013). "Surveying a complex potential energy landscape: Overcoming broken ergodicity using basin-sampling". Chemical Physics Letters. 584: 1–9. Bibcode:2013CPL...584....1W. doi:10.1016/j.cplett.2013.07.066.
  26. ^ "Nanotechnology Timeline". nano.gov. Retrieved 5 December 2020.
  27. ^ a b Marks, L D; Peng, L (2016). "Nanoparticle shape, thermodynamics and kinetics". Journal of Physics: Condensed Matter. 28 (5): 053001. Bibcode:2016JPCM...28e3001M. doi:10.1088/0953-8984/28/5/053001. ISSN 0953-8984. PMID 26792459.
  28. ^ Jin, Rongchao; Zeng, Chenjie; Zhou, Meng; Chen, Yuxiang (2016). "Atomically Precise Colloidal Metal Nanoclusters and Nanoparticles: Fundamentals and Opportunities". Chemical Reviews. 116 (18): 10346–10413. doi:10.1021/acs.chemrev.5b00703. ISSN 0009-2665. PMID 27585252.
  29. ^ Elechiguerra, Jose Luis; Reyes-Gasga, Jose; Yacaman, Miguel Jose (2006). "The role of twinning in shape evolution of anisotropic noble metal nanostructures". Journal of Materials Chemistry. 16 (40): 3906. doi:10.1039/b607128g. ISSN 0959-9428.
  30. ^ Matsumoto, Seiichiro; Matsui, Yoshio (1983). "Electron microscopic observation of diamond particles grown from the vapour phase". Journal of Materials Science. 18 (6): 1785–1793. Bibcode:1983JMatS..18.1785M. doi:10.1007/BF00542075. ISSN 0022-2461.
  31. ^ Bühler, Jürgen; Prior, Yehiam (2000). "Study of morphological behavior of single diamond crystals". Journal of Crystal Growth. 209 (4): 779–788. Bibcode:2000JCrGr.209..779B. doi:10.1016/S0022-0248(99)00658-2.
  32. ^ a b Rogers, Blake; Lehr, Alexander; Velázquez-Salazar, J. Jesús; Whetten, Robert; Mendoza-Cruz, Ruben; Bazan-Diaz, Lourdes; Bahena-Uribe, Daniel; José Yacaman, Miguel (2023). "Decahedra and Icosahedra Everywhere: The Anomalous Crystallization of Au and Other Metals at the Nanoscale". Crystal Research and Technology. 58 (4). Bibcode:2023CryRT..5800259R. doi:10.1002/crat.202200259. ISSN 0232-1300.
  33. ^ Ogburn, F.; Paretzkin, B.; Peiser, H. S. (1964). "Pseudopentagonal twins in electrodeposited copper dendrites". Acta Crystallographica. 17 (6): 774–775. Bibcode:1964AcCry..17..774O. doi:10.1107/S0365110X64002006. ISSN 0365-110X.
  34. ^ Vikarchuk, A.A.; Gryzunova, N.N.; Gutkin, M.Yu.; Romanov, A.E. (2018). "Copper Pentagonal Micropyramids Grown by Mechanically Activated Electrodeposition". Reviews on Advanced Materials Science. 55 (1): 78–81. doi:10.1515/rams-2018-0030. ISSN 1605-8127.
  35. ^ Fukaya, Koji; Ino, Shozo; Ogawa, Shiro (1978). "Orientation and Structure of Palladium Particles Formed by Evaporation on Alkalihalide Crystals". Transactions of the Japan Institute of Metals. 19 (8): 445–453. doi:10.2320/matertrans1960.19.445. ISSN 0021-4434.
  36. ^ Xiong, Yujie; Cai, Honggang; Yin, Yadong; Xia, Younan (2007). "Synthesis and characterization of fivefold twinned nanorods and right bipyramids of palladium". Chemical Physics Letters. 440 (4–6): 273–278. Bibcode:2007CPL...440..273X. doi:10.1016/j.cplett.2007.04.074.
  37. ^ Rupich, Sara M.; Shevchenko, Elena V.; Bodnarchuk, Maryna I.; Lee, Byeongdu; Talapin, Dmitri V. (2010). "Size-Dependent Multiple Twinning in Nanocrystal Superlattices". Journal of the American Chemical Society. 132 (1): 289–296. doi:10.1021/ja9074425. ISSN 0002-7863. PMID 19968283.
  38. ^ Lee, Sangmin; Glotzer, Sharon C. (2022). "Entropically engineered formation of fivefold and icosahedral twinned clusters of colloidal shapes". Nature Communications. 13 (1): 7362. Bibcode:2022NatCo..13.7362L. doi:10.1038/s41467-022-34891-5. ISSN 2041-1723. PMC 9712591. PMID 36450709.
  39. ^ Song, Yongbo; Li, Yingwei; Li, Hao; Ke, Feng; Xiang, Ji; Zhou, Chuanjun; Li, Peng; Zhu, Manzhou; Jin, Rongchao (2020). "Atomically resolved Au52Cu72(SR)55 nanoalloy reveals Marks decahedron truncation and Penrose tiling surface". Nature Communications. 11 (1): 478. doi:10.1038/s41467-020-14400-2. ISSN 2041-1723. PMC 6981204. PMID 31980671.
  40. ^ a b Uppenbrink, Julia; Wales, David J. (1992). "Structure and energetics of model metal clusters". The Journal of Chemical Physics. 96 (11): 8520–8534. Bibcode:1992JChPh..96.8520U. doi:10.1063/1.462305. ISSN 0021-9606.
  41. ^ a b Ascencio, J.A.; Pérez-Alvarez, M.; Tehuacanero, S.; José-Yacamán, M. (2001). "Experimental and theoretical studies of instabilities of metal nanoparticles: a new kind of quasimelting". Applied Physics A: Materials Science & Processing. 73 (3): 295–300. Bibcode:2001ApPhA..73..295A. doi:10.1007/s003390100850. ISSN 0947-8396.
  42. ^ Gafner, Yu. Ya.; Gafner, S. L.; Chepkasov, I. V. (2010). "The effect of thermal treatment on the organization of copper and nickel nanoclusters synthesized from the gas phase". Journal of Experimental and Theoretical Physics. 111 (4): 608–618. Bibcode:2010JETP..111..608G. doi:10.1134/S1063776110100110. ISSN 1063-7761.
  43. ^ Li, Hui; Li, Lei; Pedersen, Andreas; Gao, Yi; Khetrapal, Navneet; Jónsson, Hannes; Zeng, Xiao Cheng (2015). "Magic-Number Gold Nanoclusters with Diameters from 1 to 3.5 nm: Relative Stability and Catalytic Activity for CO Oxidation". Nano Letters. 15 (1): 682–688. Bibcode:2015NanoL..15..682L. doi:10.1021/nl504192u. ISSN 1530-6984. PMID 25493586.
  44. ^ a b Mottet, C.; Goniakowski, J.; Baletto, F.; Ferrando, R.; Treglia, G. (2004). "Modeling free and supported metallic nanoclusters: structure and dynamics". Phase Transitions. 77 (1–2): 101–113. Bibcode:2004PhaTr..77..101M. doi:10.1080/1411590310001622473. ISSN 0141-1594.
  45. ^ a b de Wit, R. (1971). "Relation between Dislocations and Disclinations". Journal of Applied Physics. 42 (9): 3304–3308. Bibcode:1971JAP....42.3304D. doi:10.1063/1.1660730. ISSN 0021-8979.
  46. ^ a b Wit, R de (1972). "Partial disclinations". Journal of Physics C: Solid State Physics. 5 (5): 529–534. Bibcode:1972JPhC....5..529D. doi:10.1088/0022-3719/5/5/004. ISSN 0022-3719.
  47. ^ Volterra, Vito (1907). "Sur l'équilibre des corps élastiques multiplement connexes". Annales scientifiques de l'École normale supérieure. 24: 401–517. doi:10.24033/asens.583. ISSN 0012-9593.
  48. ^ Liang, Chao; Yu, Yi (2019). "Understanding the formation of multiply twinned structure in decahedral intermetallic nanoparticles". IUCrJ. 6 (3): 447–453. Bibcode:2019IUCrJ...6..447L. doi:10.1107/S2052252519002562. ISSN 2052-2525. PMC 6503919. PMID 31098025.
  49. ^ Arrouvel, Corinne (2021). "Surfaces, Interfaces and Crystal Growth of Marcasite FeS2". Materials Research. 24 (1). doi:10.1590/1980-5373-mr-2020-0383. ISSN 1980-5373.
  50. ^ a b c Patala, Srikanth; Marks, Laurence D.; Olvera de la Cruz, Monica (2013). "Elastic Strain Energy Effects in Faceted Decahedral Nanoparticles". The Journal of Physical Chemistry C. 117 (3): 1485–1494. doi:10.1021/jp310045g. ISSN 1932-7447.
  51. ^ a b Marks, L. D.; Smith, David J. (1983). "HREM and STEM of defects in multiply-twinned particles". Journal of Microscopy. 130 (2): 249–261. doi:10.1111/j.1365-2818.1983.tb04222.x. ISSN 0022-2720.
  52. ^ Nepijko, S.A.; Styopkin, V.I.; Hofmeister, H.; Scholtz, R. (1986). "Defects in multiply-twinned particles". Journal of Crystal Growth. 76 (2): 501–506. Bibcode:1986JCrGr..76..501N. doi:10.1016/0022-0248(86)90399-4.
  53. ^ Hofmeister, H. (1991). "Lattice defects in decahedral multiply twinned particles of palladium". Zeitschrift für Physik D: Atoms, Molecules and Clusters. 19 (1–4): 307–310. Bibcode:1991ZPhyD..19..307H. doi:10.1007/BF01448317. ISSN 0178-7683.
  54. ^ a b Romanov, Alexey E.; Vikarchuk, Anatoly A.; Kolesnikova, Anna L.; Dorogin, Leonid M.; Kink, Ilmar; Aifantis, Elias C. (2012). "Structural transformations in nano- and microobjects triggered by disclinations". Journal of Materials Research. 27 (3): 545–551. Bibcode:2012JMatR..27..545R. doi:10.1557/jmr.2011.372. ISSN 0884-2914.
  55. ^ a b c d Howie, A.; Marks, L. D. (1984). "Elastic strains and the energy balance for multiply twinned particles". Philosophical Magazine A. 49 (1): 95–109. Bibcode:1984PMagA..49...95H. doi:10.1080/01418618408233432. ISSN 0141-8610.
  56. ^ a b c d Johnson, Craig L.; Snoeck, Etienne; Ezcurdia, Manex; Rodríguez-González, Benito; Pastoriza-Santos, Isabel; Liz-Marzán, Luis M.; Hÿtch, Martin J. (2008). "Effects of elastic anisotropy on strain distributions in decahedral gold nanoparticles". Nature Materials. 7 (2): 120–124. Bibcode:2008NatMa...7..120J. doi:10.1038/nmat2083. ISSN 1476-1122. PMID 18084296.
  57. ^ a b c d Walsh, Michael J.; Yoshida, Kenta; Kuwabara, Akihide; Pay, Mungo L.; Gai, Pratibha L.; Boyes, Edward D. (2012). "On the Structural Origin of the Catalytic Properties of Inherently Strained Ultrasmall Decahedral Gold Nanoparticles". Nano Letters. 12 (4): 2027–2031. arXiv:1705.05763. Bibcode:2012NanoL..12.2027W. doi:10.1021/nl300067q. ISSN 1530-6984. PMID 22385208.
  58. ^ a b c Ji, Wenhai; Qi, Weihong; Li, Xu; Zhao, Shilei; Tang, Shasha; Peng, Hongcheng; Li, Siqi (2015). "Investigation of disclinations in Marks decahedral Pd nanoparticles by aberration-corrected HRTEM". Materials Letters. 152: 283–286. Bibcode:2015MatL..152..283J. doi:10.1016/j.matlet.2015.03.137.
  59. ^ a b c d Wu, Hao; Yu, Rong; Zhu, Jing; Chen, Wei; Li, Yadong; Wang, Tao (2021). "Size-dependent strain in fivefold twins of gold". Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials. 77 (1): 93–98. doi:10.1107/S2052520620014791. ISSN 2052-5206.
  60. ^ a b Patala, Srikanth; Marks, Laurence D.; Olvera de la Cruz, Monica (2013). "Thermodynamic Analysis of Multiply Twinned Particles: Surface Stress Effects". The Journal of Physical Chemistry Letters. 4 (18): 3089–3094. doi:10.1021/jz401496d. ISSN 1948-7185.
  61. ^ Goris, Bart; De Beenhouwer, Jan; De Backer, Annick; Zanaga, Daniele; Batenburg, K. Joost; Sánchez-Iglesias, Ana; Liz-Marzán, Luis M.; Van Aert, Sandra; Bals, Sara; Sijbers, Jan; Van Tendeloo, Gustaaf (2015). "Measuring Lattice Strain in Three Dimensions through Electron Microscopy". Nano Letters. 15 (10): 6996–7001. Bibcode:2015NanoL..15.6996G. doi:10.1021/acs.nanolett.5b03008. ISSN 1530-6984. PMC 4877113. PMID 26340328.
  62. ^ Bagley, B. G. (1965). "A Dense Packing of Hard Spheres with Five-fold Symmetry". Nature. 208 (5011): 674–675. Bibcode:1965Natur.208..674B. doi:10.1038/208674a0. ISSN 0028-0836.
  63. ^ a b Wales, David J.; Doye, Jonathan P. K.; Miller, Mark A.; Mortenson, Paul N.; Walsh, Tiffany R. (2000). Prigogine, I.; Rice, Stuart A. (eds.). Energy Landscapes: From Clusters to Biomolecules. Vol. 115 (1 ed.). Wiley. pp. 39–46. doi:10.1002/9780470141748.ch1. ISBN 978-0-471-39331-3. Retrieved 1 April 2024.
  64. ^ Yang, C.Y. (1979). "Crystallography of decahedral and icosahedral particles". Journal of Crystal Growth. 47 (2): 274–282. doi:10.1016/0022-0248(79)90252-5.
  65. ^ Heinemann, K.; Yacamán, M.J.; Yang, C.Y.; Poppa, H. (1979). "The structure of small, vapor-deposited particles". Journal of Crystal Growth. 47 (2): 177–186. doi:10.1016/0022-0248(79)90240-9.
  66. ^ Yang, C.Y.; Heinemann, K.; Yacamán, M.J.; Poppa, H. (1979). "A structural analysis of small vapor-deposited "multiply twinned" gold particles". Thin Solid Films. 58 (1): 163–168. Bibcode:1979TSF....58..163Y. doi:10.1016/0040-6090(79)90231-1.
  67. ^ Sun, Yugang; Ren, Yang; Liu, Yuzi; Wen, Jianguo; Okasinski, John S.; Miller, Dean J. (2012). "Ambient-stable tetragonal phase in silver nanostructures". Nature Communications. 3 (1): 971. Bibcode:2012NatCo...3..971S. doi:10.1038/ncomms1963. ISSN 2041-1723. PMID 22828631.
  68. ^ a b c Ringe, Emilie; Van Duyne, Richard P.; Marks, Laurence D. (2013). "Kinetic and Thermodynamic Modified Wulff Constructions for Twinned Nanoparticles". The Journal of Physical Chemistry C. 117 (31): 15859–15870. doi:10.1021/jp401566m. ISSN 1932-7447.
  69. ^ a b Ino, Shozo (1969). "Stability of Multiply-Twinned Particles". Journal of the Physical Society of Japan. 27 (4): 941–953. Bibcode:1969JPSJ...27..941I. doi:10.1143/JPSJ.27.941. ISSN 0031-9015.
  70. ^ Pérez-Ramírez, J.G.; José-Yacamán, M.; Díaz-Pérez, Arturo; Berriel-Valdós, Raúl (1985). "On the equilibrium shape of multiple-twinned particles". Superlattices and Microstructures. 1 (6): 485–487. Bibcode:1985SuMi....1..485P. doi:10.1016/S0749-6036(85)80019-7.
  71. ^ a b c Casillas hi, Gilberto; Velázquez-Salazar, J. Jesús; Jose-Yacaman, Miguel (2012). "A New Mechanism of Stabilization of Large Decahedral Nanoparticles". The Journal of Physical Chemistry C. 116 (15): 8844–8848. doi:10.1021/jp3011475. ISSN 1932-7447. PMC 3353654. PMID 22609961.
  72. ^ a b c Zhao, Haiqiang; Qi, Weihong; Ji, Wenhai; Wang, Tianran; Peng, Hongcheng; Wang, Qi; Jia, Yanlin; He, Jieting (2017). "Large Marks-decahedral Pd nanoparticles synthesized by a modified hydrothermal method using a homogeneous reactor". Journal of Nanoparticle Research. 19 (5): 162. Bibcode:2017JNR....19..162Z. doi:10.1007/s11051-017-3856-0. ISSN 1388-0764.
  73. ^ Boukouvala, Christina; Daniel, Joshua; Ringe, Emilie (2021). "Approaches to modelling the shape of nanocrystals". Nano Convergence. 8 (1): 26. Bibcode:2021NanoC...8...26B. doi:10.1186/s40580-021-00275-6. ISSN 2196-5404. PMC 8429535. PMID 34499259.
  74. ^ Jin, Biao; Yan, Feng; Qi, Xin; Cai, Bin; Tao, Jinhui; Fu, Xiaofeng; Tan, Susheng; Zhang, Peijun; Pfaendtner, Jim; Naser, Nada Y.; Baneyx, François; Zhang, Xin; DeYoreo, James J.; Chen, Chun-Long (2022). "Peptoid-Directed Formation of Five-Fold Twinned Au Nanostars through Particle Attachment and Facet Stabilization". Angewandte Chemie International Edition. 61 (14): e202201980. doi:10.1002/anie.202201980. ISSN 1433-7851. PMC 9258440. PMID 35167709.
  75. ^ a b Takeguchi, Masaki; Tanaka, Miyoko; Yasuda, Hidehiro; Furuya, Kazuo (2001). "Real-time high-resolution transmission electron microscopy observation of the growth process of ( 001 ) surfaces on a nanometer-sized Si multiply twinned particle". Surface Science. 493 (1–3): 414–419. Bibcode:2001SurSc.493..414T. doi:10.1016/S0039-6028(01)01247-X.
  76. ^ a b Reyes-Gasga, J.; Elechiguerra, J.L.; Liu, C.; Camacho-Bragado, A.; Montejano-Carrizales, J.M.; Jose Yacaman, M. (2006). "On the structure of nanorods and nanowires with pentagonal cross-sections". Journal of Crystal Growth. 286 (1): 162–172. Bibcode:2006JCrGr.286..162R. doi:10.1016/j.jcrysgro.2005.09.028.
  77. ^ a b Li, B.; Lowengrub, J.; Ratz, A.; Voigt, A. (2009). "Geometric Evolution Laws for Thin Crystalline Films: Modeling and Numerics". Communications in Computational Physics. 6 (3): 433–482.
  78. ^ Combe, Nicolas; Jensen, Pablo; Pimpinelli, Alberto (2000). "Changing Shapes in the Nanoworld". Physical Review Letters. 85 (1): 110–113. arXiv:cond-mat/0005113. Bibcode:2000PhRvL..85..110C. doi:10.1103/PhysRevLett.85.110. ISSN 0031-9007. PMID 10991171.
  79. ^ Ni, Chaoying; Hassan, Puthusserickal A.; Kaler, Eric W. (2005). "Structural Characteristics and Growth of Pentagonal Silver Nanorods Prepared by a Surfactant Method". Langmuir. 21 (8): 3334–3337. doi:10.1021/la046807c. ISSN 0743-7463. PMID 15807571.
  80. ^ Wang, Jen-Hung; Yang, Tze-Hsien; Wu, Wen-Wei; Chen, Lih-Juann; Chen, Chih-Hung; Chu, Cheng-Jie (2006). "Synthesis and growth mechanism of pentagonal Cu nanobats with field emission characteristics". Nanotechnology. 17 (3): 719–722. Bibcode:2006Nanot..17..719W. doi:10.1088/0957-4484/17/3/017. ISSN 0957-4484.
  81. ^ Qi, Xin; Chen, Zihao; Yan, Tianyu; Fichthorn, Kristen A. (2019). "Growth Mechanism of Five-Fold Twinned Ag Nanowires from Multiscale Theory and Simulations". ACS Nano. 13 (4): 4647–4656. doi:10.1021/acsnano.9b00820. ISSN 1936-0851. OSTI 1594111. PMID 30869861.
  82. ^ a b Bazán-Díaz, Lourdes; Mendoza-Cruz, Rubén; Velázquez-Salazar, J. Jesús; Plascencia-Villa, Germán; Romeu, David; Reyes-Gasga, José; Herrera-Becerra, Raúl; José-Yacamán, Miguel; Guisbiers, Grégory (2015). "Gold–copper nanostars as photo-thermal agents: synthesis and advanced electron microscopy characterization". Nanoscale. 7 (48): 20734–20742. Bibcode:2015Nanos...720734B. doi:10.1039/C5NR06491K. ISSN 2040-3364. PMID 26602429.
  83. ^ Ball, R. C.; Blunt, M. J.; Rath Spivack, O. (1989). "Diffusion-controlled growth". Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences. 423 (1864): 123–132. Bibcode:1989RSPSA.423..123B. doi:10.1098/rspa.1989.0045. ISSN 0080-4630.
  84. ^ Vermaak, J.S.; Mays, C.W.; Kuhlmann-Wilsdorf, D. (1968). "On surface stress and surface tension". Surface Science. 12 (2): 128–133. doi:10.1016/0039-6028(68)90118-0.
  85. ^ Mays, C.W.; Vermaak, J.S.; Kuhlmann-Wilsdorf, D. (1968). "On surface stress and surface tension". Surface Science. 12 (2): 134–140. Bibcode:1968SurSc..12..134M. doi:10.1016/0039-6028(68)90119-2.
  86. ^ Müller, Pierre; Saùl, Andres; Leroy, Frédéric (2013). "Simple views on surface stress and surface energy concepts". Advances in Natural Sciences: Nanoscience and Nanotechnology. 5 (1): 013002. doi:10.1088/2043-6262/5/1/013002. ISSN 2043-6262.
  87. ^ Feibelman, Peter J. (1997). "First-principles calculations of stress induced by gas adsorption on Pt(111)". Physical Review B. 56 (4): 2175–2182. Bibcode:1997PhRvB..56.2175F. doi:10.1103/PhysRevB.56.2175. ISSN 0163-1829.
  88. ^ Graoui, H.; Giorgio, S.; Henry, C.R. (1998). "Shape variations of Pd particles under oxygen adsorption". Surface Science. 417 (2–3): 350–360. Bibcode:1998SurSc.417..350G. doi:10.1016/S0039-6028(98)00688-8.
  89. ^ Wynblatt, P.; Chatain, D. (2009). "Surface segregation anisotropy and the equilibrium crystal shape of alloy crystals". Reviews on Advanced Materials Science. 21: 44–56. S2CID 137869647.
  90. ^ Hoare, M.R.; Pal, P. (1971). "Physical cluster mechanics: Statics and energy surfaces for monatomic systems". Advances in Physics. 20 (84): 161–196. Bibcode:1971AdPhy..20..161H. doi:10.1080/00018737100101231. ISSN 0001-8732.
  91. ^ Berry, R. Stephen; Jellinek, Julius; Natanson, Grigory (1984). "Melting of clusters and melting". Physical Review A. 30 (2): 919–931. Bibcode:1984PhRvA..30..919B. doi:10.1103/PhysRevA.30.919. ISSN 0556-2791.
  92. ^ Berry, R. Stephen. (1993). "Potential surfaces and dynamics: what clusters tell us". Chemical Reviews. 93 (7): 2379–2394. doi:10.1021/cr00023a003. ISSN 0009-2665.
  93. ^ a b Ajayan, P. M.; Marks, L. D. (1988). "Quasimelting and phases of small particles". Physical Review Letters. 60 (7): 585–587. Bibcode:1988PhRvL..60..585A. doi:10.1103/PhysRevLett.60.585. ISSN 0031-9007. PMID 10038590.
  94. ^ Barnard, Amanda S.; Young, Neil P.; Kirkland, Angus I.; van Huis, Marijn A.; Xu, Huifang (2009). "Nanogold: A Quantitative Phase Map". ACS Nano. 3 (6): 1431–1436. doi:10.1021/nn900220k. ISSN 1936-0851. PMID 19489558.
  95. ^ Wales, David J. (2018). "Exploring Energy Landscapes". Annual Review of Physical Chemistry. 69 (1): 401–425. Bibcode:2018ARPC...69..401W. doi:10.1146/annurev-physchem-050317-021219. ISSN 0066-426X. PMID 29677468.
  96. ^ Zhang, Huaizhong; Khan, Mohd Ahmed; Yan, Tianyu; Fichthorn, Kristen A. (2024). "Size and temperature dependent shapes of copper nanocrystals using parallel tempering molecular dynamics". Nanoscale. 16 (23): 11146–11155. doi:10.1039/D4NR00317A. ISSN 2040-3364. PMID 38506642.
  97. ^ Wales, David (2001). Energy Landscapes: Applications to Clusters, Biomolecules and Glasses (1 ed.). Cambridge University Press. p. 4590479. doi:10.1017/cbo9780511721724. ISBN 978-0-521-81415-7.
  98. ^ Wales, David J.; Miller, Mark A.; Walsh, Tiffany R. (1998). "Archetypal energy landscapes". Nature. 394 (6695): 758–760. Bibcode:1998Natur.394..758W. doi:10.1038/29487. ISSN 0028-0836.
  99. ^ Mackay, A. L. (1962). "A dense non-crystallographic packing of equal spheres". Acta Crystallographica. 15 (9): 916–918. Bibcode:1962AcCry..15..916M. doi:10.1107/S0365110X6200239X. ISSN 0365-110X.
  100. ^ a b c Yagi, K.; Takayanagi, K.; Kobayashi, K.; Honjo, G. (1975). "In-situ observations of growth processes of multiply twinned particles". Journal of Crystal Growth. 28 (1): 117–124. Bibcode:1975JCrGr..28..117Y. doi:10.1016/0022-0248(75)90033-0.
  101. ^ a b Ma, Xiaoming; Lin, Fang; Chen, Xin; Jin, Chuanhong (25 August 2020). "Unveiling Growth Pathways of Multiply Twinned Gold Nanoparticles by In Situ Liquid Cell Transmission Electron Microscopy". ACS Nano. 14 (8): 9594–9604. doi:10.1021/acsnano.9b10173. ISSN 1936-0851. PMID 32806061.
  102. ^ Iijima, Sumio; Ichihashi, Toshinari (1986). "Structural instability of ultrafine particles of metals". Physical Review Letters. 56 (6): 616–619. Bibcode:1986PhRvL..56..616I. doi:10.1103/PhysRevLett.56.616. ISSN 0031-9007. PMID 10033240.
  103. ^ Smith, David J.; Petford-Long, Amanda K.; Wallenberg, L. R.; Bovin, J.-O. (1986). "Dynamic Atomic-Level Rearrangements in Small Gold Particles". Science. 233 (4766): 872–875. Bibcode:1986Sci...233..872S. doi:10.1126/science.233.4766.872. ISSN 0036-8075. PMID 17752214.
  104. ^ Young, N.P.; van Huis, M.A.; Zandbergen, H.W.; Xu, H.; Kirkland, A.I. (2010). "Transformations of gold nanoparticles investigated using variable temperature high-resolution transmission electron microscopy". Ultramicroscopy. 110 (5): 506–516. doi:10.1016/j.ultramic.2009.12.010. PMID 20083353.
  105. ^ a b c d El Koraychy, El Yakout; Roncaglia, Cesare; Nelli, Diana; Cerbelaud, Manuella; Ferrando, Riccardo (2022). "Growth mechanisms from tetrahedral seeds to multiply twinned Au nanoparticles revealed by atomistic simulations". Nanoscale Horizons. 7 (8): 883–889. Bibcode:2022NanoH...7..883E. doi:10.1039/D1NH00599E. ISSN 2055-6756. PMID 35722927.
  106. ^ Uppenbrink, J.; Wales, D. J.; Kirkland, A. I.; Jefferson, D. A.; Urban, J. (1992). "Structure and energetics of model symmetric and asymmetric decahedra". Philosophical Magazine B. 65 (5): 1079–1096. Bibcode:1992PMagB..65.1079U. doi:10.1080/13642819208217922. ISSN 1364-2812.
  107. ^ Dundurs, J.; Marks, L. D.; Ajayan, P. M. (1988). "Structural fluctuations in small particles". Philosophical Magazine A. 57 (4): 605–620. Bibcode:1988PMagA..57..605D. doi:10.1080/01418618808214410. ISSN 0141-8610.
  108. ^ Pauling, Linus (1985). "Apparent icosahedral symmetry is due to directed multiple twinning of cubic crystals". Nature. 317 (6037): 512–514. Bibcode:1985Natur.317..512P. doi:10.1038/317512a0. ISSN 0028-0836.
  109. ^ Pauling, Linus (1987). "So-called icosahedral and decagonal quasicrystals are twins of an 820-atom cubic crystal". Physical Review Letters. 58 (4): 365–368. Bibcode:1987PhRvL..58..365P. doi:10.1103/PhysRevLett.58.365. PMID 10034915.
  110. ^ Shechtman, D.; Blech, I.; Gratias, D.; Cahn, J. W. (1984). "Metallic Phase with Long-Range Orientational Order and No Translational Symmetry". Physical Review Letters. 53 (20): 1951–1953. Bibcode:1984PhRvL..53.1951S. doi:10.1103/PhysRevLett.53.1951. ISSN 0031-9007.
  111. ^ "NIST and the Nobel (September 30, 2016, Updated November 17, 2019) The Nobel Moment: Dan Shechtman". NIST. 30 September 2016.
  112. ^ "Quasicrystal - Online Dictionary of Crystallography". dictionary.iucr.org. Retrieved 4 April 2024.
  113. ^ a b Avery, N; Sanders, J V (1970). "The structure of metallic particles in dispersed catalysts". Journal of Catalysis. 18 (2): 129–132. doi:10.1016/0021-9517(70)90171-5.
  114. ^ a b Marks, L. D.; Howie, A. (1979). "Multiply-twinned particles in silver catalysts". Nature. 282 (5735): 196–198. Bibcode:1979Natur.282..196M. doi:10.1038/282196a0. ISSN 0028-0836.
  115. ^ a b Zhou, Yuheng; Zhu, Yihan; Wang, Zhi-Qiang; Zou, Shihui; Ma, Guicen; Xia, Ming; Kong, Xueqian; Xiao, Liping; Gong, Xue-Qing; Fan, Jie (2017). "Catalytic Activity Control via Crossover between Two Different Microstructures". Journal of the American Chemical Society. 139 (39): 13740–13748. doi:10.1021/jacs.7b05476. hdl:10754/625450. ISSN 0002-7863. PMID 28885842.
  116. ^ Grabow, Lars; Xu, Ye; Mavrikakis, Manos (2006). "Lattice strain effects on CO oxidation on Pt(111)". Physical Chemistry Chemical Physics. 8 (29): 3369–3374. Bibcode:2006PCCP....8.3369G. doi:10.1039/b606131a. ISSN 1463-9076. PMID 16855712.
  117. ^ Liu, Fuzhu; Wu, Chao; Yang, Guang; Yang, Shengchun (2015). "CO Oxidation over Strained Pt(100) Surface: A DFT Study". The Journal of Physical Chemistry C. 119 (27): 15500–15505. doi:10.1021/acs.jpcc.5b04511. ISSN 1932-7447.
  118. ^ Wang, Qiyu; Cui, Xiaoqiang; Guan, Weiming; Zhang, Lei; Fan, Xiaofeng; Shi, Zhan; Zheng, Weitao (2014). "Shape-dependent catalytic activity of oxygen reduction reaction (ORR) on silver nanodecahedra and nanocubes". Journal of Power Sources. 269: 152–157. Bibcode:2014JPS...269..152W. doi:10.1016/j.jpowsour.2014.06.160.
  119. ^ Choi, Chungseok; Cheng, Tao; Flores Espinosa, Michelle; Fei, Huilong; Duan, Xiangfeng; Goddard, William A.; Huang, Yu (2019). "A Highly Active Star Decahedron Cu Nanocatalyst for Hydrocarbon Production at Low Overpotentials". Advanced Materials. 31 (6): e1805405. Bibcode:2019AdM....3105405C. doi:10.1002/adma.201805405. ISSN 0935-9648. PMID 30549121.
  120. ^ Eustis, Susie; El-Sayed, Mostafa A. (2006). "Why gold nanoparticles are more precious than pretty gold: Noble metal surface plasmon resonance and its enhancement of the radiative and nonradiative properties of nanocrystals of different shapes". Chem. Soc. Rev. 35 (3): 209–217. doi:10.1039/B514191E. ISSN 0306-0012. PMID 16505915.
  121. ^ Rodríguez-Fernández, Jessica; Novo, Carolina; Myroshnychenko, Viktor; Funston, Alison M.; Sánchez-Iglesias, Ana; Pastoriza-Santos, Isabel; Pérez-Juste, Jorge; García de Abajo, F. Javier; Liz-Marzán, Luis M.; Mulvaney, Paul (2009). "Spectroscopy, Imaging, and Modeling of Individual Gold Decahedra". The Journal of Physical Chemistry C. 113 (43): 18623–18631. doi:10.1021/jp907646d. ISSN 1932-7447.
  122. ^ Pietrobon, Brendan; McEachran, Matthew; Kitaev, Vladimir (2009). "Synthesis of Size-Controlled Faceted Pentagonal Silver Nanorods with Tunable Plasmonic Properties and Self-Assembly of These Nanorods". ACS Nano. 3 (1): 21–26. doi:10.1021/nn800591y. ISSN 1936-0851. PMID 19206244.
  123. ^ Jheng, Jhih-Yuan; Sah, Pai-Tao; Chang, Wei-Che; Chen, Jhe-Han; Chan, Li-Hsin (2017). "Decahedral gold nanoparticles for enhancing performance of polymer solar cells". Dyes and Pigments. 138: 83–89. doi:10.1016/j.dyepig.2016.11.027.
  124. ^ a b c Wang, Xiang; Zheng, Sixue; Deng, Chuang; Weinberger, Christopher R.; Wang, Guofeng; Mao, Scott X. (2023). "In Situ Atomic-Scale Observation of 5-Fold Twin Formation in Nanoscale Crystal under Mechanical Loading". Nano Letters. 23 (2): 514–522. Bibcode:2023NanoL..23..514W. doi:10.1021/acs.nanolett.2c03852. ISSN 1530-6984. PMC 10032584. PMID 36633548.
  125. ^ Marks, L.D. (1986). "Solid-like growth". Thin Solid Films. 136 (2): 309–315. Bibcode:1986TSF...136..309M. doi:10.1016/0040-6090(86)90290-7.
  126. ^ Bikmukhametov, Ilias; Tucker, Garritt J.; Thompson, Gregory B. (2024). "Five-fold twin structures in sputter-deposited nickel alloy films". Scripta Materialia. 241: 115866. doi:10.1016/j.scriptamat.2023.115866. ISSN 1359-6462.
  127. ^ a b Huang, P.; Dai, G. Q.; Wang, F.; Xu, K. W.; Li, Y. H. (2009). "Fivefold annealing twin in nanocrystalline Cu". Applied Physics Letters. 95 (20). Bibcode:2009ApPhL..95t3101H. doi:10.1063/1.3263948. ISSN 0003-6951.
  128. ^ Parajuli, Prakash; Mendoza-Cruz, Ruben; Velazquez-Salazar, J. Jesus; Yacaman, Miguel Jose; Ponce, Arturo (2019). "Fivefold annealing twin in nanocrystalline Au/Pd film". Materials Letters. 244: 88–91. Bibcode:2019MatL..244...88P. doi:10.1016/j.matlet.2019.02.060. ISSN 0167-577X.
  129. ^ Bringa, E; Farkas, D; Caro, A; Wang, Y; Mcnaney, J; Smith, R (2008). "Fivefold twin formation during annealing of nanocrystalline Cu". Scripta Materialia. 59 (12): 1267–1270. doi:10.1016/j.scriptamat.2008.08.041. OSTI 966234.
  130. ^ Chen, Yingbin; Huang, Qishan; Zhao, Shuchun; Zhou, Haofei; Wang, Jiangwei (2021). "Interactions between Dislocations and Penta-Twins in Metallic Nanocrystals". Metals. 11 (11): 1775. doi:10.3390/met11111775. ISSN 2075-4701.
  131. ^ Thomas, Spencer L.; King, Alexander H.; Srolovitz, David J. (2016). "When twins collide: Twin junctions in nanocrystalline nickel". Acta Materialia. 113: 301–310. Bibcode:2016AcMat.113..301T. doi:10.1016/j.actamat.2016.04.030.
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