Russian Federation
In connection with the development of new methods of nanotechnology, the article discusses the features of the morphology of nanoobjects that determine the relevance of the modernization of the training of undergraduates in the study of the disciplines «Nanomaterial Science», «Nanotechnology», «Descriptive geometry, engineering and computer graphics» and «Computer modeling». Recently, the concept of «cluster» has become relevant due to the trend in the development of nanomaterials. Such nanomaterials obtained using unconventional growth mechanisms (including oriented attachment) are extremely interesting in the field of electronics, photonics and are of great interest for catalysis. The article considers homoatomic clusters constructed from identical structural units. The desire to minimize energy is expressed in the tendency to the densest arrangement of structural units in the cluster. This allows us to assert that cluster structures with the maximum number of connections per structural unit will be the most stable; that clusters tend to a quasi-spherical shape (i.e., cluster sizes along three Cartesian axes should be close if possible, while dense structures are formed, the surface of which is minimal, and the number of connections is maximum); that clusters with higher symmetry are preferable (identical structural units composing the cluster framework should strive to stay in an indistinguishable state and position from each other). The work applies the knowledge and skills laid down by students in the course of engineering and computer graphics to the study of the patterns of processes in the nanowire on the example of the principles of building nanoclusters along a tetrahedral line using three-dimensional modeling in the Autodesk 3ds Max environment. Visualization and visual representation of geometric images of nanoclusters will allow students to avoid a primitive geometric representation of nanoobjects and will serve as motivation to study other natural science subjects. The content of the article is intended for specialists working in the fields of nanotechnology, solid-state electronics, micro- and nanoelectronics, micro- and nanosystem technology, thin-film sensors.
three-dimensional modeling, nanoclusters, tetrahedral clusters
1. Bobkov A.A., Kononova I.E., Moshnikov V. A. Materialovedenie mikro- i nanosistem. Ierarhicheskie struktury pod red. V.A. Moshnikova [Material science of micro- and nanosystems. Hierarchical structures edited by V.A. Moshnikov]. SPb., Izd-vo SPbGETU «LETI» Rubl., 2017. 204 p. (in Russian)
2. Vyshnepol'skij V.I. Celi i metody obucheniya graficheskim disciplinam [Goals and methods of teaching graphic disciplines]. Geometriya i grafika [Geometry and graphics]. 2013, V. 1, I. 2, pp. 8–9. DOI: 10.12737/777. (in Russian)
3. Dubov P.L., Korol'kov D.V., Petranovskij V.P. Klastery i matrichno-izolirovannye klasternye sverhstruktury [Clusters and matrix-isolated cluster superstructures]. SPb., Izd-vo SPbGU Publ., 1995. 256 p. (in Russian)
4. Ivanov G.S. Perspektivy nachertatel'noj geometrii kak uchebnoj discipliny [Prospects for descriptive geometry as an academic discipline]. Geometriya i grafika [Geometry and graphics]. 2013, V. 1, I. 1, pp. 26–27. DOI: 10.12737/775. (in Russian)
5. Myasnichenko V.S., Kolosov A.Yu., Sokolov D.N., Sdobnyakov N.Yu. Vliyanie vneshnego davleniya na termodinamicheskuyu stabil'nost' GCK nanokristallov zolota, serebra i medi c «magicheskim» chislom atomov 147 [Effect of External Pressure on the Thermodynamic Stability of FCC Gold, Silver, and Copper Nanocrystals with the «Magic» Number of Atoms 147]. Sbornik nauchnyh trudov VI mezhdunarodnoj nauchnoj konferencii «Himicheskaya termodinamika i kinetika» pod redakciej Yu.D. Orlova [Collection of scientific papers VI of the international scientific conference «Chemical thermodynamics and kinetics» edited by Yu.D. Orlova]. Tver, Izd-vo: Tverskoj gosudarstvennyj universitet Publ., 2016, pp. 186–187. (in Russian)
6. Myasnichenko V.S., Starostenkov M.D. Primenenie predstavleniya o strukturnyh mnogogrannikah zapolneniya koordinacionnyh sfer v ob"emnyh kristallah k probleme poiska ustojchivyh form nanoklasterov I [Application of the concept of structural polyhedra filling coordination spheres in bulk crystals to the problem of finding stable forms of nanoclusters Part I.]. Fundamental'nye problemy sovremennogo materialovedeniya [Fundamental problems of modern materials science]. 2011, V. 8, I. 2, pp. 49–52. (in Russian)
7. Myasnichenko V.S., Starostenkov M.D. Primenenie predstavleniya o strukturnyh mnogogrannikah zapolneniya koordinacionnyh sfer v ob"emnyh kristallah k probleme poiska ustojchivyh form nanoklasterov. II. [Application of the concept of structural polyhedrons filling coordination spheres in bulk crystals to the problem of finding stable forms of nanoclusters]. Fundamental'nye problemy sovremennogo materialovedeniya [Fundamental problems of modern materials science]. 2012, V. 9, I. 3, pp. 284–288. (in Russian)
8. Neorganicheskaya himiya: V 3-h t. T. 1: Fiziko-himicheskie osnovy neorganicheskoj himii: Uchebnik dlya stud. vyssh. ucheb. zavedenij. Pod red. YU.D.Tret'yakova [Inorganic chemistry: In 3 volumes. V. 1: Physical and chemical foundations of inorganic chemistry: A textbook for students of higher educational institutions. M.Ye. Tamm, Ed. Yu.D. Tretyakova]. Moscow, Izdatel'skij centr «Akademiya» Publ., 2004. 240 p. (in Russian)
9. Pleskunov I.V., Syrkov A.G. Razvitie issledovanij nizkorazmernyh metallosoderzhashchih sistem ot P.P.Vejmarna do nashih dnej [Development of research on low-dimensional metal-containing systems from P.P. Weymarn to the present day]. Zapiski Gornogo instituta [Notes of the Mining Institutez]. 2018, I. 231, R. 287. DOI: 10.25515/PMI.2018.3.287. (in Russian)
10. Polenov Yu.V., Lukin M.V., Egorova E.V. Fiziko-himicheskie osnovy nanotekhnologij: ucheb. posobie [Physical and chemical bases of nanotechnologies: textbook. allowance]. Ivanovo, Ivanovo State University of Chemical Technology Publ., 2013. 196 p. (in Russian)
11. Redel' L.V., Gafner Yu.Ya., Gafner S.L. Rol' «magicheskih» chisel pri formirovanii struktury v malyh nanoklasterah serebra [The Role of "Magic" Numbers in Structure Formation in Small Silver Nanoclusters]. Fizika tverdogo tela [Solid state physics]. 2015, V. 57, I. 10, pp. 2061–2070. (in Russian)
12. Ryzhkova D.A., Gafner S.L., Gafner YU.YA. Rol' «magicheskih» GPU chisel v ustojchivosti vnutrennego stroeniya nanoklasterov Ag89 i Ag153 [The role of “magic” hcp numbers in the stability of the internal structure of Ag89 and Ag153 nanoclusters]. Fiziko-khimicheskiye aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physicochemical aspects of studying clusters, nanostructures and nanomaterials]. 2021, I. 13, pp. 593-603. (in Russian)
13. Sal'kov N.A. Geometricheskoe modelirovanie i nachertatel'naya geometriya [Geometric modeling and descriptive geometry]. Geometriya i grafika [Geometry and graphics]. 2016, V. 4, I. 4, pp. 8–9. DOI: 10.12737/22841. (in Russian)
14. Sal'kov N.A. Kachestvo geometricheskogo obrazovaniya pri razlichnyh podhodah k metodike obucheniya [The Quality of Geometric Education with Different Approaches to Teaching Methods]. Geometriya i grafika [Geometry and graphics]. 2016, V. 8, I. 4, pp. 47–60. DOI: 10.12737/2308-4898-2021-8-4-47-60. (in Russian)
15. Sal'kov N.A. Mesto nachertatel'noj geometrii v sisteme geometricheskogo obrazovaniya tekhnicheskih vuzov [The place of descriptive geometry in the system of geometric education of technical universities]. Geometriya i grafika [Geometry and graphics]. 2016, V. 4, I. 3, pp. 53–61. DOI: 10.12737/21534. (in Russian)
16. Sal'kov N.A. Nachertatel'naya geometriya – baza dlya komp'yuternoj grafiki [Descriptive geometry – the basis for computer graphics]. Geometriya i grafika [Geometry and graphics]. 2016, V. 4, I. 2, pp. 37–47. DOI: 10.12737/19832. (in Russian)
17. Spivak L.V., Shchepina N.E. Fiziko-himicheskie osnovy processov mikro- i nanotekhnologii [Elektronnyj resurs]: ucheb. posobie: v 2 ch. [Physical and chemical foundations of micro- and nanotechnology processes Electronic resource: study guide in 2 parts]. Perm. gos. nac. issled. un-t [Perm State National Research University.]. Elektron. dan. – Perm', 2018. Part 1. http:www.psu.ru > book > uchebnie-posobiya (accessed 11 Jule 2020). (in Russian)
18. Suzdalev I.P. Nanotekhnologiya: fiziko-himiya nanoklasterov, nanostruktur i nanomaterialov [Nanotechnology: physical chemistry of nanoclusters, nanostructures and nanomaterials.]. M.: KomKniga Publ., 2006. 592 p. (in Russian)
19. Shevel'kov A. V. Himicheskie aspekty sozdaniya termoelektricheskih materialov [Chemical aspects of the creation of thermoelectric materials]. Uspekhi himii [Advances in Chemistry]. 2008, V. 77, pp. 3–21. DOI: 10.1070/RC2008v077n01ABEH003746. (in Russian)
20. Cölfen H., Antonietti M. Mesocrystals and Nonclassical Crystallization. Wiley: Chichester, UK; Hoboken, NJ, USA, 2008. 276 p. DOI: 10.1002/9780470994603.
21. Cölfen H., Antonietti M. Mesocrystals: Inorganic superstructures made by highly parallel crystallization and controlled alignment. Angew. Chem. Int. Ed. 2005, V. 44, pp. 5576–5591. DOI: 10.1002/anie.200500496.
22. Gasanly S.A., Tomaev V.V., Stoyanova T.V. The concept of the phases ratio control during the formation of composite filamentary nanocrystals xInSe-(1–x)In2O3 on glass substrates. J. Physics: Conf. Ser. 2017, V. 917, pp. 32021. DOI: 10.1088/1742-6596/917/3/032021.
23. Harbola M. K. Magic numbers for metallic clusters and the principle of maximum hardness. PNAS. 1992, V. 89 (3), P. 1036–1039. DOI: 10.1073/pnas.89.3.103.
24. Jehannin M., Rao A., Cölfen H. New horizons of nonclassical crystallization. J. Am. Chem. Soc. 2019, V. 141, pp. 10120–10136. DOI: 10.1021/jacs.9b01883.
25. Jia Yu., Yu X., Zhang H., Cheng L., Luo Zhixun Tetrahedral Pt 10−Cluster with Unique Beta Aromaticity and Superatomic Feature in Mimicking Methane // The Journal of Physical Chemistry Letters. 2021, V. 12, P. 5115–5122. DOI: 10.1021/acs.jpclett.1c01178.
26. Kaatz Forrest H., Bultheel A., Engel M., Vogel N. Magic Mathematical Relationships for Nanoclusters. Nanoscale Research Letters. 2019, V. 14, I. 150. DOI: 10.1186/s11671-019-2939-5.
27. Kononova I.E., Moshnikov V.A., Kononov P.V. Development of a model for the formation of materials with a hierarchical pore structure produced under sol–gel processing conditions. Inorganic Materials. 2018, V. 54, I. 5, P. 478–489. DOI: 10.1134/S0020168518050060.
28. Kononova I., Kononov P., Moshnikov V., Ignat’ev S. Fractal-Percolation structure architectonics in sol-gel synthesis. International Journal of Molecular Sciences. 2021, V. 22, P. 10521–10537. DOI: 10.1134/S0020168518050060.
29. Kononova I. E., Maraeva E. V., Skornikova S. A., Moshnikov V. A. Influence of Binder on Porous Structure of Zeolite Compositions and Their Catalytic Activity. Glass physics and chemistry. 2020, V. 46, I. 2, pp. 162–169. DOI: 10.1134/S1087659620020066.
30. Krasnyy V.A. The use of nanomaterials to improve the wear resistance of machine parts under fretting corrosion conditions. In IOP Conference Series: Materials Science and Engineering; IOP Publishing: 2019, V. 560, pp. 1–5. DOI: 10.1088/1757-899x/560/1/012186.
31. Madison A.E., Madison P.A. Looking for alternatives to the superspace description of icosahedral quasicrystals. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2019, V. 475, pp. 20180667. DOI: 10.1098/rspa.2018.0667.
32. Madison A.E., Madison P.A. Structure of icosahedral quasicrystals within the multiple cell approach. Structural Chemistry. 2020, V. 31, I. 1, pp. 485–505. DOI: 10.1007/s11224-019-01430-w.
33. Madison A.E. Substitution rules for icosahedral quasicrystals. RSC Adv. 2015, V. 5, pp. 5745–5753. DOI: 10.1039/C4RA09524C.
34. Niederberger M., Cölfen H. Oriented attachment and mesocrystals: Non-classical crystallization mechanisms based on nanoparticle assembly. Phys. Chem. Chem. Phys. 2006, V. 8, pp. 3271–3287. DOI: 10.1039/B604589H.
35. Reimann S. M., Koskinen M., Ha¨kkinen H., Lindelof P. E., Manninen M. Magic triangular and tetrahedral clusters. Physical review B. 1997, V. 56, I. 19, P. 1247–1250. DOI: 10.1103/PhysRevB.56.12147.
36. Salikhov K.M., Stoyanov N.D., Stoyanova T.V. Using Optical Activation to Create Hydrogen and Hydrogen-Containing Gas Sensors. Key Eng. Mater. 2020, V. 854, pp.87–93. DOI: 10.4028/www.scientific.net/kem.854.87.
37. Smerdov R., Spivak Y., Bizyaev I., Somov P., Gerasimov V., Mustafaev A., Moshnikov V. Advances in Novel Low-Macroscopic Field Emission Electrode Design Based on Fullerene-Doped Porous Silicon. Electronics. 2020, V. 10, pp. 42. DOI: 10.3390/electronics10010042.
38. Smerdov, R.; Mustafaev, A.; Spivak, Y.; Moshnikov, V. Functionalized nanostructured materials for novel plasma energy systems. In Topical Issues of Rational Use of Natural Resources 2019. CRC Press. 2019, pp. 434–441. DOI: 10.1201/9781003014577-55.
39. Spivak Yu. M., Kononova I. E., Kononov P. V., V. A. Moshnikov, S. A. Ignat’ev. The architectonics features of heterostructures for ir range detectors based on polycrystalline layers of lead chalcogenides. Crystals. 2021, V. 11, P. 1143–1159. DOI: 10.3390/cryst11091143.
40. Sturm E.V., Colfen H. Mesocrystals: Past, Presence, Future. Crystals. 2017, V. 7, pp. 207. DOI: 10.3390/cryst7070207.
41. Syrkov A.G. On the priority of Saint-Petersburg Mining University in the field of nanotechnology science and nanomaterials. J. Min. Inst. 2016, V. 221, pp. 730–736. DOI: 10.1088/1742-6596/917/3/032021.
42. Tomaev V.V., Levine K.L., Stoyanova, Sirkov A.G. T.V. Formation of nanocomposite film (polypirrol)/(aluminum) oxide on aluminum surface. In AIP Conference Proceedings, AIP Publishing LLC. 2019, V. 2064, I. 030016. DOI: 10.1063/1.5087678.
43. Tomaev V., Levine, K., Stoyanova T.; Syrkov, A.G. Synthesis and Study of a Polypyrrole–Aluminum Oxide Nanocomposite Film on an Aluminum Surface. Glas. Phys. Chem. 2019, V. 45, pp. 291–297. DOI: 10.1134/s1087659619040126.
44. Wang J., Mbah C. F., Przybilla T., Zubiri B. A., Spiecker E. Magic number colloidal clusters as minimum free energy structures. Nature communications. 2018, V. 9, I. 5259. DOI: 10.1038/s41467-018-07600-4.
