189:
203:
47:
35:
55:
20:
176:
structures with long range rotational but not translational periodicity, that some initially tried to explain away as icosahedral twinning. Quasicrystals generally form only when the compositional makeup (e.g. of two dissimilar metals such as titanium and manganese) serves as an antagonist to
145:
At larger sizes the energy to distort becomes larger than the gain in surface energy, and bulk materials (i.e. sufficiently large clusters) generally revert to one of the crystalline close-packing configurations. In principle they will convert to a simple
166:
Icosahedral twinning has been seen in face-centered-cubic metal nanoparticles that have nucleated: (i) by evaporation onto surfaces, (ii) out of solution, and (iii) by reduction in a polymer matrix.
87:" in the 19th century, more recently as "decahedral multiply twinned particles", "pentagonal particles" or "star particles". A variety of different methods (e.g. condensing argon, metal atoms, and
142:, an approach later extended to 3D by Yoffe. The shape is also not always that of a simple icosahedron, and there are now several software codes that make it easy to calculate the shape.
134:
for icosahedral clustering is that it cannot fill space over large distances in a way that is translationally ordered, so there is some distortion of the atomic positions, that is
676:
83:) faces having three-fold symmetry. A related, more common structure has five units similarly arranged with twinning, which were known as "
315:
281:
241:
99:
When interatom bonding does not have strong directional preferences, it is not unusual for atoms to gravitate toward a
226:
813:
747:
Pauling, Linus (1987). "So-called icosahedral and decagonal quasicrystals are twins of an 820-atom cubic crystal".
23:
158:
in diameter, but it does not always happen that the shape changes and the particles can grow to millimeter sizes.
91:) lead to the icosahedral form at size scales where surface energies are more important than those from the bulk.
808:
75:
and also nanoparticles with some thousands of atoms. These clusters are twenty-faced, with twenty interlinked
260:
Hofmeister, H. (1998). "Forty Years Study of
Fivefold Twinned Structures in Small Particles and Thin Films".
658:
803:
756:
705:
621:
554:
507:
460:
413:
347:
269:
108:
27:
335:
135:
116:
729:
379:
151:
495:
448:
780:
772:
721:
672:
639:
590:
572:
523:
476:
429:
371:
363:
311:
285:
208:
154:
shape. The size when they become less energetically stable is typically in the range of 10-30
131:
72:
318:
764:
713:
664:
629:
580:
562:
515:
468:
421:
355:
277:
216:
67:
46:
760:
709:
625:
558:
511:
464:
417:
359:
351:
273:
585:
542:
231:
194:
147:
127:
100:
694:"Structural properties of nanoclusters: Energetic, thermodynamic, and kinetic effects"
797:
693:
236:
169:
120:
112:
733:
472:
383:
188:
139:
80:
50:
Examples of digital dark field bowtie/butterfly images of an icosahedral particle.
221:
104:
76:
64:
768:
567:
717:
519:
202:
184:
776:
725:
668:
643:
576:
527:
480:
433:
367:
289:
155:
39:
784:
594:
375:
34:
401:
103:
of 12 nearest neighbors. The three most symmetric ways to do this are by
84:
634:
609:
425:
496:"Elastic strains and the energy balance for multiply twinned particles"
38:
FCC icosahedral model projected down the 5-fold on the left and 3-fold
177:
formation of one of the more common close-packed space-filling forms.
282:
10.1002/(sici)1521-4079(1998)33:1<3::aid-crat3>3.0.co;2-3
88:
54:
53:
45:
33:
18:
19:
138:. De Wit pointed out that these can be thought of in terms of
26:
of a 5-fold twinned Au nanoparticle with a shape similar to a
541:
Boukouvala, Christina; Daniel, Joshua; Ringe, Emilie (2021).
306:(ed. H. S. Nalwa, Amer. Sci. Publ., Stevenson Ranch CA) vol.
126:
Icosahedral arrangements, typically because of their smaller
302:
H. Hofmeister (2004) "Fivefold twinned nanoparticles" in
58:
Dark field analysis of dual-tetrahedron crystal pairs.
610:"WulffPack: A Python package for Wulff constructions"
130:, may be preferred for small clusters. However, the
16:
Structure found in atomic clusters and nanoparticles
543:"Approaches to modelling the shape of nanocrystals"
336:"Nanoparticle shape, thermodynamics and kinetics"
755:(4). American Physical Society (APS): 365–368.
692:Baletto, Francesca; Ferrando, Riccardo (2005).
657:Pimpinelli, Alberto; Villain, Jacques (1998).
304:Encyclopedia of Nanoscience and Nanotechnology
8:
663:(1 ed.). Cambridge University Press.
633:
584:
566:
453:Journal of Physics C: Solid State Physics
402:"Stability of Multiply-Twinned Particles"
406:Journal of the Physical Society of Japan
252:
79:crystals joined along triangular (e.g.
395:
393:
7:
340:Journal of Physics: Condensed Matter
329:
327:
71:is a nanostructure found in atomic
14:
494:Howie, A.; Marks, L. D. (1984).
201:
187:
614:Journal of Open Source Software
608:Rahm, J.; Erhart, Paul (2020).
262:Crystal Research and Technology
242:Self-assembly of nanoparticles
1:
360:10.1088/0953-8984/28/5/053001
334:Marks, L D; Peng, L (2016).
227:Nanomaterial based catalyst
107:clustering, by crystalline
830:
769:10.1103/physrevlett.58.365
568:10.1186/s40580-021-00275-6
718:10.1103/RevModPhys.77.371
698:Reviews of Modern Physics
660:Physics of Crystal Growth
520:10.1080/01418618408233432
473:10.1088/0022-3719/5/5/004
42:orientation on the right.
669:10.1017/cbo9780511622526
500:Philosophical Magazine A
24:Annular dark-field image
749:Physical Review Letters
449:"Partial disclinations"
59:
51:
43:
31:
57:
49:
37:
22:
115:) or hexagonal (tri-
28:pentagonal bipyramid
761:1987PhRvL..58..365P
710:2005RvMP...77..371B
635:10.21105/joss.01944
626:2020JOSS....5.1944R
559:2021NanoC...8...26B
512:1984PMagA..49...95H
465:1972JPhC....5..529D
426:10.1143/jpsj.27.941
418:1969JPSJ...27..941I
400:Ino, Shozo (1969).
352:2016JPCM...28e3001M
274:1998CryRT..33....3H
136:elastic deformation
109:face-centered-cubic
447:Wit, R de (1972).
152:Wulff construction
60:
52:
44:
32:
814:Materials science
678:978-0-521-55198-4
209:Technology portal
821:
789:
788:
744:
738:
737:
689:
683:
682:
654:
648:
647:
637:
605:
599:
598:
588:
570:
547:Nano Convergence
538:
532:
531:
491:
485:
484:
444:
438:
437:
397:
388:
387:
331:
322:
300:
294:
293:
257:
217:Crystal twinning
211:
206:
205:
197:
192:
191:
829:
828:
824:
823:
822:
820:
819:
818:
809:Crystallography
794:
793:
792:
746:
745:
741:
691:
690:
686:
679:
656:
655:
651:
607:
606:
602:
540:
539:
535:
493:
492:
488:
446:
445:
441:
399:
398:
391:
333:
332:
325:
301:
297:
259:
258:
254:
250:
207:
200:
193:
186:
183:
164:
97:
17:
12:
11:
5:
827:
825:
817:
816:
811:
806:
796:
795:
791:
790:
739:
704:(1): 371–423.
684:
677:
649:
600:
533:
486:
459:(5): 529–534.
439:
412:(4): 941–953.
389:
323:
310:, pp. 431-452
295:
251:
249:
246:
245:
244:
239:
234:
232:Nanotechnology
229:
224:
219:
213:
212:
198:
195:Science portal
182:
179:
163:
160:
148:single crystal
132:Achilles' heel
128:surface energy
117:orthobicupolar
101:kissing number
96:
93:
15:
13:
10:
9:
6:
4:
3:
2:
826:
815:
812:
810:
807:
805:
804:Nanoparticles
802:
801:
799:
786:
782:
778:
774:
770:
766:
762:
758:
754:
750:
743:
740:
735:
731:
727:
723:
719:
715:
711:
707:
703:
699:
695:
688:
685:
680:
674:
670:
666:
662:
661:
653:
650:
645:
641:
636:
631:
627:
623:
619:
615:
611:
604:
601:
596:
592:
587:
582:
578:
574:
569:
564:
560:
556:
552:
548:
544:
537:
534:
529:
525:
521:
517:
513:
509:
506:(1): 95–109.
505:
501:
497:
490:
487:
482:
478:
474:
470:
466:
462:
458:
454:
450:
443:
440:
435:
431:
427:
423:
419:
415:
411:
407:
403:
396:
394:
390:
385:
381:
377:
373:
369:
365:
361:
357:
353:
349:
346:(5): 053001.
345:
341:
337:
330:
328:
324:
320:
317:
316:1-58883-059-4
313:
309:
305:
299:
296:
291:
287:
283:
279:
275:
271:
267:
263:
256:
253:
247:
243:
240:
238:
237:Quasicrystals
235:
233:
230:
228:
225:
223:
220:
218:
215:
214:
210:
204:
199:
196:
190:
185:
180:
178:
175:
171:
170:Quasicrystals
167:
161:
159:
157:
153:
149:
143:
141:
140:disclinations
137:
133:
129:
124:
122:
121:close packing
118:
114:
113:cuboctahedral
110:
106:
102:
94:
92:
90:
89:virus capsids
86:
82:
78:
74:
70:
69:
66:
56:
48:
41:
36:
29:
25:
21:
752:
748:
742:
701:
697:
687:
659:
652:
620:(45): 1944.
617:
613:
603:
550:
546:
536:
503:
499:
489:
456:
452:
442:
409:
405:
343:
339:
307:
303:
298:
265:
261:
255:
173:
168:
165:
144:
125:
98:
63:
61:
268:(1): 3–25.
222:Icosahedron
105:icosahedral
81:cubic-(111)
77:tetrahedral
65:icosahedral
798:Categories
248:References
174:un-twinned
156:nanometers
777:0031-9007
726:0034-6861
644:2475-9066
577:2196-5404
553:(1): 26.
528:0141-8610
481:0022-3719
434:0031-9015
368:0953-8984
290:0232-1300
85:fivelings
40:zone axis
785:10034915
734:54700637
595:34499259
384:12503859
376:26792459
181:See also
162:Ubiquity
73:clusters
757:Bibcode
706:Bibcode
622:Bibcode
586:8429535
555:Bibcode
508:Bibcode
461:Bibcode
414:Bibcode
348:Bibcode
270:Bibcode
150:with a
783:
775:
732:
724:
675:
642:
593:
583:
575:
526:
479:
432:
382:
374:
366:
314:
288:
95:Causes
730:S2CID
380:S2CID
781:PMID
773:ISSN
722:ISSN
673:ISBN
640:ISSN
591:PMID
573:ISSN
524:ISSN
477:ISSN
430:ISSN
372:PMID
364:ISSN
312:ISBN
286:ISSN
172:are
68:twin
765:doi
714:doi
665:doi
630:doi
581:PMC
563:doi
516:doi
469:doi
422:doi
356:doi
319:pdf
278:doi
62:An
800::
779:.
771:.
763:.
753:58
751:.
728:.
720:.
712:.
702:77
700:.
696:.
671:.
638:.
628:.
616:.
612:.
589:.
579:.
571:.
561:.
549:.
545:.
522:.
514:.
504:49
502:.
498:.
475:.
467:.
455:.
451:.
428:.
420:.
410:27
408:.
404:.
392:^
378:.
370:.
362:.
354:.
344:28
342:.
338:.
326:^
284:.
276:.
266:33
264:.
123:.
119:)
787:.
767::
759::
736:.
716::
708::
681:.
667::
646:.
632::
624::
618:5
597:.
565::
557::
551:8
530:.
518::
510::
483:.
471::
463::
457:5
436:.
424::
416::
386:.
358::
350::
321:.
308:3
292:.
280::
272::
111:(
30:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
