Abstract—An extended (3 × 3) classification of polymorphic transformations is proposed with the zeroth coordination sphere added to spheres I and II according to Buerger. Thus, the transformable coordination sphere is 0 for an atom or ion, 1 for a coordination polyhedron, and 2 for the nearest surroundings of a coordination polyhedron. The other classification parameter is determined by Buerger’s energetic transformation barrier. As well as reconstructive and deformation transformations, transformations of intermediate types occur, which are characterized by disordering of structural units (atoms, molecules, and other atomic complexes). The electron transitions within an atom, the variation of atomic spin, and magnetic ordering of atoms in a crystal structure are considered as examples of polymorphic transformations with the variations in the zeroth coordination sphere. The disordering transformations are illustrated by substitution–jumps of structural units and their free or hindered rotation. The concept of “polymorphism” for chemical elements is developed.
Similar content being viewed by others
REFERENCES
Baumhauer, H., Uber die Kristalle des Carborundums. Z. Kristallogr, 1912, vol. 50, pp. 33–39.
Bokij, G.B., Kristallokhimiya (Crystal Chemistry), Moscow: Nauka, 1971.
Bridgman, P.W., The compressibility and pressure coefficient of resistance of ten elements, Proc. Am. Acad. Arts. Sci., 1927, vol. 62, no. 8, pp. 207–226.
Buerger, M.J., Crystallographic aspects of phase transformations, Phase Transformations in Solids, Smoluchowski, R., Mayer, J.E., Weyl, W.A., Eds., New-York: John Wiley and Sons, 1951, pp. 183–211.
Buerger, M.J., Phase transitions, Cristallografiya, 1971, vol. 16, pp. 1084–1096.
Dolivo-Dobrovolsky, V.V., Kristallokhimiya (Crystal Chemistry), St. Petersburg: Saint Petersburg University, 1999.
Filatov, S.K., Vysokotemperaturnaya kristallokhimiya (High-Temperature Crystal Chemistry), Leningrad: Nedra, 1990.
Filatov, S.K., Crystal chemical phenomena: systematics, controversial facts, “borderline” problems, Cryst. Rept., 1995, vol. 40, no. 1, pp. 63–69.
Filatov, S.K., General concept of increasing crystal symmetry with an increase in temperature, Cryst. Rept., 2011, vol. 56, no. 6, pp. 953–961.
Filatov, S.K., Grunin, V.S., Razumeenko, M.V., and Alekseeva, T.V., Microisomorphism and polymorphism of titanium dioxide, Kristallokhimiya i rentgenografiya mineralov (Crystal Chemistry and X-Ray of Minerals), Leningrad: Nauka, 1987, pp. 44–62.
Filatov, S.K., Polyakova, I.G., Gaikova, A.G., and Kamentsev, I.E., Thermal X-ray determination of the jump in the structural parameters of quartz during α-β transformation, Crystal. Rept., 1982, vol. 27, no. 3, pp. 624–626.
Filatov, S.K., Kotelnikova, E.N., and Chazhengina, S.Yu., New phase transition of the first kind and new polymorphic modifications of paraffins, Dokl. Akad. Nauk, 1993, vol. 330, no. 5, pp. 605–608.
Filatov, S.K., Kotelnikova, E.N., and Filippova, I.V., New mixed type rotational crystalline state of solids on an example of paraffin, Cryst. Rept., 1997, vol. 42, no. 4, pp. 608–611.
Filatov, S.K., Krivovichev, S.V., and Bubnova, R.S., Obshchaya kristallokhimiya (General Crystal Chemistry), St. Petersburg: Saint Petersburg University Press, 2018.
Frank, F.C., CII. The growth of carborundum: dislocations and polytypism, The London: Edinburgh, and Dublin Philosoph., Mag. J. Sci.: Series 7, 1951, vol. 42, no. 332, pp. 1014–1021.
Goldschmidt, V.M., Kristallchemie, Jena: Verlag von Gustav Fischer, 1934.
Grunin, V.S., Razumeenko, M.V., Patrina, I.B., Filatov, S.K., and Alekseeva, T.V., About the existence and prevalence of TiO2— rutile, anatase and brookite, Dokl. Akad. Nauk SSSR, 1983, vol. 268, no. 3, pp. 686–688.
Guinier, A., Bokij, G.B., Boll-Dornberger, K., Cowley, J.M., Ďurovič, S., Jagodzinski, H., Krishna, P., de Wolff, P.M., Zvyagin, B.B., Cox, D.E., Goodman, P., Hahn, Th., Kuchitsu, K., and Abrahams, S.C., Nomenclature of polytype structures. Report of the International Union of Crystallography Ad hoc Committee on the Nomenclature of Disordered, Modulated and Polytype Structures. Acta Cryst, 1984, vol. A40, pp. 399–404.
Kondo, R.-I., Mashimo, T., and Sawaoka, A., Electrical resistivity and phase transformation of hematite under shock compression, J. Geophys. Res., 1980, vol. 85, no. B2, pp. 977–982.
Kotelnikova, E.N. and Filatov, S.K., Kristallokhimiya parafinov (Crystal Chemistry of Paraffins), Leningrad: Neva, 2002, 352p.
Landau, L.D. and Lifshitz, E.M., Statistical Physics., Part 1, Oxford–New York–Toronto–Sydney–Paris–Frankfurt: Pergamon Press, 1980.
Lawson, A.W. and Ting Yuan Tang, Concerning the high pressure allotropic modification of cerium, Phys. Rev., 1949, vol. 76, pp. 301–302.
Likhter, A.I., Ryabinin, Yu.N., and Vereshchagin, L.F., The phase diagram of Cerium, Zh. Eksp. Teor. Fiz., 1957, vol. 33, no. 3 (9), pp. 610–613.
Lima-de-Faria, J., Hellner, E., Liebau, F., Makovicky, E., and Parthe, E., Report of the international union of crystallography commission on crystallographic nomenclature subcommittee on the nomenclature of inorganic structure types, Acta Cryst., 1990, Vol. A46, pp. 1–11.
Mitscherlich, E., Über die Körper, welche in zwei verschiedenen Formen kristallisieren. Abhandl, Berlin: Akad. Wissensch., aus d. Jahren 1822–1823, 1825, pp. 43–48.
Ohsumi, H. and Arima, T.-H., Novel insight into structural magnetism by polarized synchrotron X-ray scattering, Adv. Phys, 2016, vol. 1, pp. 128–145.
Poniatowskii, E.G., About the critical point on the cerium polymorphic transformation curve, Dokl. Akad. Nauk SSSR, 1958, vol. 120, no. 5, pp. 1021–1023.
Reeder, R.J., Crystal chemistry of the rhombohedral carbonates, Rev. Mineral., 1971, vol. 11, pp. 1–48.
Sanson, A., Kantor, I., Cerantola, V., Irifune, T., Carmera, A., and Pascarelli, S., Local structure and spin transition in in Fe2O3 hematite at high pressure, Phys. Rev., 2016, vol. B94, pp. 0141112-1-0141112-7.
Schuch, A.F. and Sturdivant, J.H., The structure of cerium at the temperature of liquid air, J. Chem. Phys, 1950, vol. 18, no. 1, p. 145.
Shafranovskii, I.I., Istoriya kristallografii. XIX vek (History of Crystallography, XIXth Century), Leningrad: Nauka, 1980, p. 324.
Trombe, F. and Foex, M., Domaine d’existence et propriétés des différents états allotropiques du cérium métallique, Ann. Chim., 1944, vol. 19, pp. 417–445.
Urusov, V.S., Teoreticheskaya kristallokhimiya (Theoretical Crystal Chemistry), Moscow: Moscow State University, 1987.
Verma, A. and Krishna, P., Polymorphism and polytypism in crystals, New York: John Wiley and Sons, 1966.
Voytekhovsky, Y.L., Definition, classification and matrix description of transformations of petrographic structures, Byul. Murmansk Gos. Tekhn. Univ., 2014, vol. 17, no. 2, pp. 266–270.
Weinstein, B.K., Fridkin, V.M., and Indenbom, V.L., Modern Crystallography 2. Structure of Crystals, Berlin–Heidelberg: Springer-Verlag, 2000.
Funding
This study was supported by the Russian Foundation for Basic Research, Project no. 18-29-12106.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Translated by A. Rylova
Rights and permissions
About this article
Cite this article
Filatov, S.K., Paufler, P. The Systematics of Crystal Polymorphic Transformations (Generalized on the Basis of Buerger’s Criteria). Geol. Ore Deposits 62, 690–703 (2020). https://doi.org/10.1134/S1075701520080048
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1075701520080048