Abstract
Instabilities in a smooth, for example planar, crystallization front at high crystallization rates can generate cellular structures (Fig. 1). These are typical dissipative structures [1–4]. Theoretical and practical aspects of cellular structure generation have been extensively investigated (for example, [5–25]). Cellular crystals are often unsuitable for such practical uses as optics because of their inhomogeneity.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Literature Cited
P. Glansdorff and I. Prigogine, Thermodynamic Theory of Structure, Stability, and Fluctuations , Wiley-Interscience, New York (1971).
G. Nicolis and I. Prigogine, Self-organization in Nonequilibrium Systems: From Dissipative Structures to Order through Fluctuations, Wiley-Interscience, New York (1977).
H. Haken, Introduction to Synergetics. Nonequilibrium Phase Transitions and Self-Organization in Physics, Chemistry, and Biology, Springer-Verlag, New York (1977).
A M. Askhabov, “Dissipative structures in crystallogenesis,” Preprint No. 88, Komi Branch, Academy of Sciences of the USSR, Syktyvkar (1982).
G. P. Ivantsov, “Diffusion supercooling in the crystallization of a binary alloy,” DokL Akad Nauk SSSR, 81, No. 2, 179–182 (1951).
J. W. Rutter and B. Chalmers, “A prismatic substructure formed during solidification of metals,” Can. J. Phys., 31, No. 1, 15–39 (1953).
W. Tiller, K. A. Jackson, J. W. Rutter, and B. Chalmers, “The distribution of solute atoms during the solidification of metals,” Acta Metall, 1, No. 4, 428–437 (1953).
D. T. J. Hurle, “Constitutional supercooling during crystal growth from stirred melts. I. Theoretical,” Solid State Electron., 3, No. 1, 37–44 (1961).
W. W. Mullins and R. F. Sekerka, “Stability of a planar interface during solidification of a dilute binary alloy,” J. Appl Phys., 35, No. 2, 444–451 (1964).
R. F. Sekerka, “A stability function for explicit evaluation of the Mullins-Sekerka interface stability criterion,” J. Appl Phys., 36, No. 1, 264–268 (1965).
R. F. Sekerka, “Morphological stability,” J. Cryst Growth, 3/4, 71–81 (1968).
D. E. Temkin, “Stability condition of a planar solid-liquid interface during binary alloy crystallization,” DokL Akad. Nauk SSSR, 133, No. 1, 174–177 (1960).
D. T. J. Hurle, “Interface stability during the solidification of stirred binary alloy melt,” J. Cryst Growth, 5, No. 3, 162–166 (1969).
S. R. Coriell, D. T. J. Hurle, and R. F. Sekerka, “Interface stability during crystal growth: The effect of stirring,” J. Cryst Growth, 32, No. 1, 1–7 (1976).
S. R. Coriell and R. F. Sekerka, “Lateral solute segregation during unidirectional solidification of a binary alloy with a curved solid-liquid interface,” J. Cryst Growth, 46, No. 4, 479–482 (1979).
B. Caroli, C. Caroli, and B. Roulet, “On the emergence of one-dimensional front instabilities in directional solidification and fusion of binary mixtures,” J. Phys., 43, No. 12, 1767–1780 (1982).
A. A. Chernov, “Stability of a planar growth front with anisotropic surface kinetics,” in: Reports of the Fourth Ail-Union Conf. on Growth of Crystals, ’Mechanics and Kinetics of Crystal Growth,’ Tsakhkadzor, Arm. SSR, Sept. 1972, Part 2 [in Russian], Izd. Akad. Nauk Arm. SSR, Erevan (1972), pp. 168–171.
B. Billia, H. Ahdout, and L. Capella, “Stable cellular growth of a binary alloy,” J. Cryst Growth, 51, No. 1, 81–84 (1981).
A. Steinchen, B. Billia, A. Sanfeld, and L. Capella, “Criteres thermodynamiques de stabilite du front de solidification,” C. R Seances Acad Sci, Ser., 293, No. 12, 881–884 (1981).
G. V. Molev, V. E. Bozhevolnov, V. I. Korobov, and V. V. Karelin, “On the distribution of impurity Sc3+ in directed crystallization of fluorite from the melt,” J. Cryst Growth, 19, No. 2, 117–121 (1973).
B. Joukoff, J. Primot, and C. Tallot, “Crystal growth and structural particularities of (BaF2)1-x(Y, LnF3)x solid solutions,” Mater. Res. Bull, 11, No. 10, 1201–1208 (1976).
A. Z. Arakelyan, K. B. Seiranyan, P. P. Fedorov, and B. P. Sobolev, “Crystallization of nonstoichiometric fluorite phases in MF2-RF3 binary systems,” in: Abstracts of Reports of the Fifth Ail-Union Conf. on Growth of Crystals [in Russian], Tbilisi, 16-19 Sept., 1977, Tbilisi (1977), pp. 135–136, 330.
M. Hoppe, K. Recker, and D. Mateika, “Untersuchung der Kristallqualitata synthetischer CaF2(Ho) und Gd3Ga5012-Einkristalle mittels lichtoptischer Methoden,” Fortschr. Mineral, 58, No. 2, 248–269 (1980).
V. A. Meleshina, E. A Krivandina, E. V. Yakovenko, and B. P. Sobolev, “Variation of composition of Ca1-xHoxF2+x and La1-ySryF3-y crystals relative to development of cellular structure,” in: Abstracts of Papers of the Sixth All-Union Conf. on Growth of Crystals, “Growth of Crystals from the Melt,” Vol. 1 [in Russian], Tsakhkadzor, Arm. SSR, Sept. 1985, Izd. Akad. Nauk Arm. SSR, Erevan (1985), pp. 239–240.
V. A. Meleshina and V. A. Smiraova, “Relation of homogeneity of crystals of YAG:Nd, CaF2:HoF3, and LaF3:SrF2 to their internal morphology,” in: Abstracts of Papers of the Ninth All-Union Scientific-Technical Conf., “Local Electron Probe Studies and Their Application”[in Russian], Ustinov (1985), p. 321.
M. A. Ol’skaya, O. N. Postinikova, P. I. Fedorov, et al, “Phase diagram of the system TlCl-TlBr and TIBr-TlI studied by thermal analysis,” in: Tr. Gos. Issled. Red. Met., Vol. 29 [in Russian], Moscow (1970), pp. 3–9.
B. P. Sobolev, Z. I. Zhmurova, V. V. Karelin, et al, “Preparation of single crystals of nonstoichiometric fluorite phases M1-xRxF2+x by the Bridgman-Stockbarger method,” in: Growth of Crystals, Vol. 16, A. A. Chernov, ed., Consultants Bureau, New York (1990).
P. I. Fedorov and P. P. Fedorov, Principles of High-Purity Substance Technology [in Russian], Moscow Inst. Chem. Eng., Moscow Inst. Chem. Technol., Moscow (1982).
T. M. Turkina, P. P. Fedorov, and B. P. Sobolev, “Stability of a planar crystallization front during growth of single crystals of solid solutions M1-xRxF2+x(where M = Ca, Sr, Ba; R = rare earth element) from the melt,” Kristallografiya, 31, No. 1, 146–152 (1986).
P. P. Fedorov and T. M. Turkina, “Relationship of the phase diagram to the planar crystallization front stability during growth of single crystals of solid solutions from the melt,” in: Abstracts of Papers of the Sixth All-Union Conf. on Growth of Crystals, “Growth of Crystals from the Melt,” Vol. 1 [in Russian], Tsakhkadzor, Arm. SSR, Sept. 1985, Izd. Akad. Nauk Arm. SSR, Erevan (1985), pp. 45–46.
P. P. Fedorov, “Transitions between eutectic and peritectic phase diagrams of binary systems,” Zh. Neorg. Khim, 31, No. 3, 759–763 (1986).
D. D. Ikrami, S. V. Petrov, P. P. Fedorov, et al, “The systems MgF2-NiF2, CaF2-NiF2, and SrF2-NiF2,” Zh. Neorg. Khim., 29, No. 4, 1062–1065 (1984).
P. P. Fedorov, A. V. Rappo, F. M. Spiridonov, and B. P. Sobolev, “Phase diagram of the system NaF-YbF3,” Zh. Neorg. Khim., 28, No. 3, 744–748 (1983).
V. A. Gorbulev, P. P. Fedorov, and B. P. Sobolev, “Interaction of oxyfluorides of rare earth elements with fluorides of fluorite structure,” J. Less-Common Met, 76, No. 1/2, 55–62 (1980).
I. D. Van der Waals and F. Konstamm, Thermostatics Course, Vol. 1 [Russian translation], O.N.T.I., Moscow (1936).
M. C. Flemings, Solidification Processing of Alloys, McGraw-Hill, New York (1973).
B. P. Sobolev and P. P. Fedorov, “Phase diagrams of the CaF2-(Y, Ln)F3 systems. I. Experimental,” J. Less-Common Met, 60, No. 1, 33–46 (1978).
B. P. Sobolev and K. B. Seiranian, “Phase diagrams of systems SrF2-(Y, Ln)F3. II. Fusibility of systems and thermal behavior of phases,” J. Solid-State Chem., 39, No. 2, 17–24 (1981).
B. P. Sobolev and N. L. Tkachenko,“ Thase diagrams of BaF2-(Y, Ln)F3 systems,” J. Less-Common Met, 85, No. 2,155–170 (1982).
P. P. Fedorov and B. P. Sobolev, “Conditions for the formation of maxima on melting curves of solid solutions in salt systems,” Zh. Neorg. Khim., 24, No. 4, 1038–1040 (1979).
R. D. Shannon, “Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides,” Acta Crystallogr. Sect A: Cryst Phys., Diffr., Theor. Gen. Crystallogr., 32, No. 5, 751–767 (1976).
B. F. Dzhurinskii and T. A. Bandurkin, “Periodicity of lanthanide properties and inorganic materials,” Izv. Akad. Nauk SSSR, Neorg Mater., 15, 1024–1027 (1979).
I. O. Kulik and G. E. Zil’berman, “Controlled crystallization of melts containing impurities. II,” Kristallografiya, 4, No. 6, 898–903 (1959).
G. Graziani, M. Strani, and R. Piva, “Effect of free surface radiation in axisymmetric thermocapillary flows,” Acta Astronaut, No. 4, 231–243 (1982).
D. Schwabe and A. Scharmann, “Marangoni convection in open boat and crucible,” J. Cryst Growth, 52, No. 1, 435–449 (1981).
V. A. Batyrev and N. S. Tsikunov, “Electron microprobe x-ray spectrometry analyzer for studying zonal distribution of elements,” Zavod. Lab., 48, No. 9, 51 (1982).
H. Linde and E. Schwarth, “Untersuchungen zur Charakteristik der freien Grenzflachenkonvektion beim Stoffubergang an Fluiden Granzen,” Z Phys. Chem., 224, No. 1/2, 331–352 (1963).
S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Clarendon Press, Oxford (1961).
M. I. Greisukh, “Impurity distribution coefficient at the crystal-melt interface as a function of crystallization rate,” Izv. Akad Nauk SSSR, Neorg Mater., 9, No. 2, 309–310 (1973).
A. Jackson, “Mechanism of growth,” in: Liquid Metals and Solidification, Am. Soc. for Metals, Cleveland (1958), pp. 174–186.
G. A. Alfintsev and D. E. Ovsienko, “Characteristics of growth from the melt of crystals of substances with various entropies of fusion,” in: Growth of Crystals, Vol. 13, A. A. Chernov, ed., Consultants Bureau, New York (1985).
A. A. Frolov, “Faceting of silicide and germanide crystals during growth from the melt,” in: Growth of Crystals, Vol. 17, A. A. Chernov, ed., Consultants Bureau, New York (1990).
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Consultants Bureau, New York
About this chapter
Cite this chapter
Fedorov, P.P., Turkina, T.M., Meleshina, V.A., Sobolev, B.P. (1991). Cellular Substructures in Single Crystalline Solid Solutions of Inorganic Fluorides Having the Fluorite Structure. In: Givargizov, E.I., Grinberg, S.A. (eds) Growth of Crystals. Growth of Crystals, vol 17. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3660-4_16
Download citation
DOI: https://doi.org/10.1007/978-1-4615-3660-4_16
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6629-4
Online ISBN: 978-1-4615-3660-4
eBook Packages: Springer Book Archive