Investigation of mechanisms of the crystal growth process (Kossel model)
DOI:
https://doi.org/10.15587/2312-8372.2018.132963Keywords:
growth mechanisms, layer-by-layer mechanism, normal mechanism, Kossel modelAbstract
The object of this research is the mechanisms of crystal growth processes. As a model of investigation, a plane-faced crystal in the form of cubes is taken. Two mechanisms of crystal growth are investigated. With the first mechanism in the process of crystal growth, the growing surface moves due to the lateral displacement of the steps, while the second one – a continuous displacement along the normal to the surface of the crystal occurs. A problematic issue when growing crystals with these mechanisms from the melt is the preservation of the purity of the metal itself, especially if it is in a molten state. It is shown that when using the «layer-by-layer» mechanism of crystal growth, the problem of the formation of two-dimensional «embryos» is a problematic moment. This process is quite sensitive to supersaturation, and the probability of its carrying out at rates below 45–50 % is quite small. In the course of the research, statistical analysis methods are used to determine the positive and negative aspects of the use of crystal growth mechanisms, analyze the results of studies to determine the dynamics of the use of a particular mechanism for growing crystals. The hypothetical-deductive method is used in the process of acquaintance with the actual material of research in the field of crystal growth, which additionally requires in-depth analysis of information sources and also a method of generalizing the results to establish the general properties and trends characteristic of the crystal growth mechanisms under study. It is justified that if the thermal conditions of the processes are not observed, it is difficult to achieve the desired orientation and configuration of the crystals. It is shown that the «normal» crystal growth mechanism is effective provided that the condition that there are enough «energetically favorable» sites for fixing the atoms on the surface, which is not always feasible.
References
- Gow, K. V., Chalmers, B. (1951). The preparation of high melting point metal single crystals and bicrystals with pre-determined crystallographic orientation. British Journal of Applied Physics, 2 (10), 300–303. doi: http://dx.doi.org/10.1088/0508-3443/2/10/305
- Hurle, D. T. J. (1966). Temperature oscillations in molten metals and their relationship to growth striae in melt-grown crystals. Philosophical Magazine, 13 (122), 305–310. doi: http://dx.doi.org/10.1080/14786436608212608
- Utech, H. P., Flemings, M. C. (1966). Elimination of Solute Banding in Indium Antimonide Crystals by Growth in a Magnetic Field. Journal of Applied Physics, 37 (5), 2021–2024. doi: http://dx.doi.org/10.1063/1.1708664
- Nacken, R., Neues, J. B. (1915). Uber das Wachstum von Kristallpolyedern in ihrem Schmelzfluß. Mineralog. Geol. Palaontol. Ref. Teil., 2, 133–164.
- Kyropoulos, S. (1926). Ein Verfahren zur Herstellung großer Kristalle. Zeitschrift Für Anorganische Und Allgemeine Chemie, 154 (1), 308–313. doi: http://dx.doi.org/10.1002/zaac.19261540129
- Czochralski, J. (1918). Ein neues Verfahren zur Messung des Kristallisationsgeschwindigkeit der Metalle. Zeitschrift für Physikalische Chemie, 92, 219.
- Sworn, C. H., Brown, T. E. (1972). The growth of dislocation-free copper crystals. Journal of Crystal Growth, 15 (3), 195–203. doi: http://dx.doi.org/10.1016/0022-0248(72)90119-4
- Howe, S., Elbaum, C. (1961). The occurrence of dislocations in crystals grown from themelt. Philosophical Magazine, 6 (70), 1227–1240. doi: http://dx.doi.org/10.1080/14786436108243373
- Hukin, D. A. (1972, 04 June). Improvements in or relating to crucibles. Available at: https://patents.google.com/patent/GB1269762A/en?oq=GB1269762A
- Carlson, O. N., Schmidt, F. A., Peterson, D. T. (1966). Electrotransport of interstitial atoms in yttrium. Journal of the Less Common Metals, 10 (1), 1–11. doi: http://dx.doi.org/10.1016/0022-5088(66)90038-5
- Schmidt, F. A., Warner, J. C. (1967). Electrotransport of carbon, nitrogen and oxygen in vanadium. Journal of the Less Common Metals, 13 (5), 493–500. doi: http://dx.doi.org/10.1016/0022-5088(67)90084-7
- Peterson, D. T., Schmidt, F. A. (1969). Electrotransport of carbon, nitrogen and oxygen in lutetium. Journal of the Less Common Metals, 18 (2), 111–116. doi: http://dx.doi.org/10.1016/0022-5088(69)90129-5
- Peterson, D. T., Schmidt, F. A. (1971). Preparation of high purity thorium and thorium single crystals. Journal of the Less Common Metals, 24 (2), 223–228. doi: http://dx.doi.org/10.1016/0022-5088(71)90099-3
- Bradley, A. J. (1925). CX. The allotropy of manganese. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 50 (299), 1018–1030. doi: http://dx.doi.org/10.1080/14786442508628546
- Mills, D., Craig, G. (1966). Etching dislocations in zirconium. Journal of Electrochemical Technology, 4, 300.
- Field, W. G., Wagner, R. W. (1968). Thermal imaging for single crystal growth and its application to ruby. Journal of Crystal Growth, 3–4, 799–803. doi: http://dx.doi.org/10.1016/0022-0248(68)90270-4
- Drabble, J. R. (1968). The arc transfer process of crystal growth. Journal of Crystal Growth, 3–4, 804–807. doi: http://dx.doi.org/10.1016/0022-0248(68)90271-6
- Gasson, D. B., Cockayne, B. (1970). Oxide crystal growth using gas lasers. Journal of Materials Science, 5 (2), 100–104. doi: http://dx.doi.org/10.1007/bf00554627
- Precht, W., Hollox, G. E. (1968). A floating zone technique for the growth of carbide single crystals. Journal of Crystal Growth, 3–4, 818–823. doi: http://dx.doi.org/10.1016/0022-0248(68)90274-1
- Siegel, R. W., Hahn, H. (1987). Nanjphase materials. Current Trends in Physics of materials. Singapore: World Sci. Publ. Co, 403–420.
- Siegel, R. W. (1994). What do we really know about the atomic-scale structures of nanophase materials? Journal of Physics and Chemistry of Solids, 55 (10), 1097–1106. doi: http://dx.doi.org/10.1016/0022-3697(94)90127-9
- Nitevidnye kristally. (1975). Nitevidnye kristally i tonkie plenki. Voronezh: VPI, 466.
- Nitevidnye kristally dlya novoy tekhniki. (1979). Voronezh: VPI, 231.
- Part 1. Nitevidnye kristally. (1970). Nitevidnye kristally i neferromagnitnye plenki. Voronezh: VPI, 287.
- Part 2. Tonkie plenki. (1970). Nitevidnye kristally i neferromagnitnye plenki. Voronezh: VPI, 300.
- Artemev, S. R. (2015). Present concepts of non-traditional methods of growing of metal whisker crystals. Pulling of whiskers from solution. Technology Audit and Production Reserves, 3 (4 (23)), 8–12. doi: http://dx.doi.org/10.15587/2312-8372.2015.42409
- Artemev, S. R. (2015). Current concepts of non-traditional methods of cultivation metal whisker crystals. Pulling whisker pole from melt. Technology Audit and Production Reserves, 2 (4 (22)), 16–19. doi: http://dx.doi.org/10.15587/2312-8372.2015.40499
- Artemev, S. R. (2014). Study of whiskers’ mechanical properties. creep and internal friction. Technology Audit and Production Reserves, 5 (3 (19)), 16–18. doi: http://dx.doi.org/10.15587/2312-8372.2014.27909
- Artemev, S. R. (2016). Analysis of existent concepts of traditional methods of metal whiskers growing. Deposition of substance from the gas phase. Technology Audit and Production Reserves, 3 (3 (29)), 34–37. doi: http://dx.doi.org/10.15587/2312-8372.2016.70512
- Artemev, S. R. (2013). Properties of whiskers. mechanical strength test. Technology Audit and Production Reserves, 6 (1 (14)), 4–7. doi: http://dx.doi.org/10.15587/2312-8372.2013.19533
- Artemev, S. R., Andronov, V. A., Semkiv, O. M. (2013). Mechanical properties of whiskers. Technology Audit and Production Reserves, 5 (1 (13)), 42–44. doi: http://dx.doi.org/10.15587/2312-8372.2013.18393
- Artemev, S. R., Shaporev, V. P., Tsymbal, B. M. (2018). Investigation of methods of obtaining whiskers in composite material. Technology Audit and Production Reserves, 1 (3 (39)), 8–14. doi: http://dx.doi.org/10.15587/2312-8372.2018.124287
- Artemev, S. R., Belan, S. V. (2013). Properties and basic methods of receipt of threadlike crystals. Eastern-European Journal of Enterprise Technologies, 5 (1 (65)), 22–26. Available at: http://journals.uran.ua/eejet/article/view/18160
- Artemev, S. R. (2015). Existing notions of conventional breeding metal whiskers, their analysis. Eastern-European Journal of Enterprise Technologies, 1 (1 (73)), 17–23. doi: http://doi.org/10.15587/1729-4061.2015.36435
- Nomeri, M. A. Kh. (2011). Poluchenie i issledovanie opticheskikh svoystv poluprovodnikovykh oksidov ZnO2 i Zn2O3. Voronezh, 128.
- Tamman, G. (1922). Die Aggregatzustande. Leipzig, 294.
- Turnbull, D., Fisher, J. C. (1949). Rate of Nucleation in Condensed Systems. The Journal of Chemical Physics, 17 (1), 71–73. doi: http://doi.org/10.1063/1.1747055
- Honigmann, B. (1958). Gleichgewichts and Wachstumsformen von Kristallen. Dresden. doi: http://doi.org/10.1007/978-3-642-45791-3
- Reynolds, D. S.; Gillman, J. J. (Ed.). (1963). The art and Sciense of Growing Crystals. New York: Wiley, 493.
- Ewald, A. W., Tufte, O. N. (1958). Gray Tin Single Crystals. Journal of Applied Physics, 29 (7), 1007–1009. doi: http://doi.org/10.1063/1.1723351
- Weinstein, M., Mlavsky, A. I. (1964). Growth of GaP Crystals and p‐n Junctions by a Traveling Solvent Method. Journal of Applied Physics, 35 (6), 1892–1894. doi: http://doi.org/10.1063/1.1713764
- Wolff, G. A., LaBelle, H. E., Das, B. N. (1968). Solution growth of (Zn, Hg) Te and Ga (P, As) crystals. Transactions of the Metallurgical Society of AIME, 242, 436–441.
- Griffiths, L. B., Mlavsky, A. I. (1964). Growth of α-SiC Single Crystals from Chromium Solution. Journal of The Electrochemical Society, 111 (7), 805. doi: http://doi.org/10.1149/1.2426257
- Cirlin, G. E., Dubrovskii, V. G., Sibirev, N. V., Soshnikov, I. P., Samsonenko, Y. B., Tonkikh, A. A., Ustinov, V. M. (2005). The diffusion mechanism in the formation of GaAs and AlGaAs nanowhiskers during the process of molecular-beam epitaxy. Semiconductors, 39 (5), 557–564. doi: https://doi.org/10.1134/1.1923565
- Dubrovskii, V. G., Sibirev, N. V., Cirlin, G. E. (2004). Kinetic model of the growth of nanodimensional whiskers by the vapor-liquid-crystal mechanism. Technical Physics Letters, 30 (8), 682–686. doi: https://doi.org/10.1134/1.1792313
- Dubrovskii, V. G., Sibirev, N. V. (2004). Growth rate of a crystal facet of arbitrary size and growth kinetics of vertical nanowires. Physical Review E, 70 (3). doi: http://doi.org/10.1103/physreve.70.031604
- Tonkikh, A. A., Cirlin, G. E., Samsonenko, Y. B., Soshnikov, I. P., Ustinov, V. M. (2004). Properties of GaAs nanowhiskers grown on a GaAs(111)B surface using a combined technique. Semiconductors, 38 (10), 1217–1220. doi: https://doi.org/10.1134/1.1808832
- Schubert, L., Werner, P., Zakharov, N. D., Gerth, G., Kolb, F. M., Long, L. et al. (2004). Silicon nanowhiskers grown on 〈111〉Si substrates by molecular-beam epitaxy. Applied Physics Letters, 84 (24), 4968–4970. doi: http://doi.org/10.1063/1.1762701
- Tretyakov, Y. D., Goodilin, E. A., Peryshkov, D. V., Itkis, D. M. (2004). Structural and microstructural features of functional materials based on cuprates and manganites. Russian Chemical Reviews, 73 (9), 881–898. doi: https://doi.org/10.1070/rc2004v073n09abeh000920
- Grigorieva, A. V., Goodilin, E. A., Givargizov, E. I., Tretyakov, Y. D. (2004). Crystallization of amino acids on substrates with superficial chiral reliefs. Mendeleev Communications, 14 (4), 150–152. doi: http://doi.org/10.1070/mc2004v014n04abeh001961
- Peryshkov, D. V., Grigorieva, A. V., Semenenko, D. A., Gudilin, E. A., Volkov, V. V., Dembo, K. A. et al. (2006). Vliyanie predystorii polucheniya na uporyadochenie strukturnykh elementov kserogeley pentoksida vanadiya. DAN Khimiya, 406 (2), 203–208.
- Goodilin, E. A., Pomerantseva, E. A., Krivetsky, V. V., Itkis, D. M., Hester, J., Tretyakov, Y. D. (2005). A simple method of growth and lithiation of Ba6Mn24O48 whiskers. Journal of Materials Chemistry, 15 (16), 1614. doi: http://doi.org/10.1039/b416512h
- Shaporev, V. P., Sebko, V. V., Shestopalov, A. V. (2014). Tekhnologicheskie zakonomernosti protsessov, kotorye lezhat v osnove massovogo proizvodstva viskerov neorganicheskikh tugoplavkikh soedineniy. Vestnik NTU «KhPI». Seriya: khimiya, khimicheskaya tekhnologiya i ekologiya, 27, 114–142.
- Shaporev, V. P., Pitak, I. V., Shestopalov, A. V. (2014). Tekhnologicheskie zakonomernosti protsessov obrazovaniya i rosta nitevidnykh kristallov neorganicheskikh soedineniy iz rastvor-rasplavov. Vestnik Kremenchugskogo natsional'nogo universiteta imeni M. Ostrogradskogo, 3, 25–29.
- Shaporev, V. P., Pitak, I. V., Shestopalov, A. V. (2015). K voprosu ob organizatsii potochnogo proizvodstva nitevidnykh kristallov tugoplavkikh neorganicheskikh soedineniy metodom kristallizatsii iz rastvor-rasplavov na osnove galoidov shhelochnykh metallov. Zhurnal integrirovannykh tekhnologiy i energosberezheniya, 1, 47–60. Available at: http://repository.kpi.kharkov.ua/bitstream/KhPI-Press/28545/1/ITE_2015_1_Shaporev_K_voprosu.pdf
- Givargizov, E. I. (1976). Rost nitevidnykh i plastinchatykh kristallov iz para. Moscow: Gosizdat, 192.
- Givargizov, E. I. (1981). Teoriya rosta i metody vyrashhivaniya kristallov. Moscow: Mir, 220.
- Spiridonov, E. M. (1995). Geneticheskaya mineralogiya. Ontogeniya. Rost kristallov. MGU im. M. Lomonosova. NII Mekhaniki, 166.
- Falckenberg, R. (1975). Growth of Mg-Al spinel crystals of large diameter using a modified flame fusion technique. Journal of Crystal Growth, 29 (2), 195–202. doi: http://doi.org/10.1016/0022-0248(75)90224-9
- Nigh, H. E. (1963). A Method for Growing Rare‐Earth Single Crystals. Journal of Applied Physics, 34 (11), 3323–3324. doi: http://doi.org/10.1063/1.1729186
- Burgers, W. C. (1963). The art and Sciens of Growing Crystals. New York, 416.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2018 Sergey Artemev
This work is licensed under a Creative Commons Attribution 4.0 International License.
The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.