Help ?

IGMIN: We're glad you're here. Please click "create a new query" if you are a new visitor to our website and need further information from us.

If you are already a member of our network and need to keep track of any developments regarding a question you have already submitted, click "take me to my Query."

Discover the nexus of Science, Technology, Engineering, and Medicine in our Multidisciplinary Open Access Journal – a platform for breakthroughs and collaborative expertise, driving knowledge and innovation. | Important Update! Building on our inaugural year's success, adjustments to article processing charges will take effect in October. More details coming soon!

Abstract at IgMin Research

Our mission is to foster interdisciplinary dialogue and accelerate the advancement of knowledge across a wide spectrum of scientific domains.

Science Group Research Article Article ID: igmin117

Homologous Series of Chemical Compounds in Three-component Systems (Aa+ – Bb+ – Cc–) and (Zn2+ - Ge4+ - P3-) in Generalized Form

Inorganic Chemistry Molecular BiologyComputational Biology Affiliation


    Ioffe Institute of the Russian Federation Academy of Sciences, Saint-Petersburg, Russia


For the first time, a method for calculating formulas of homologous series of chemical compounds of the systems (Aa+ – Bb+ – Cc–) and {Zn2+ – Ge4+ – P3–} in a generalized form is presented. The calculation is confirmed by the literature experimentally obtained compounds: thirteen compounds of the system (Na+ – Ti4+ – O2–), seven – systems (Li+ – Ti4+ – O2–), five – systems (K+ – V5a+ –  – O2–), eight – systems (Ba2+ – Cu2+ – O2*). Homological series in (Aa+ – Bb+ – Cc–) have the following generalized form: A{t – k·r + nr – r)bcBracC{t – k·r + nr)ab and AtbcB{r – k·t + nt – t}acC (r – k·t + nt)ab.
In (Zn2+ – Ge4+ – P3–) systems for the m-group the formulas of homologous series, that develops towards Ge3P4, have the following generalized form: Zn6tGe(6r – 6kt + 6n – 6t)P(8r – 8kt + 8n)  and for αm-homologous series – Zn6Ge3nP4(n + 1). A method for calculating formulas of homologous series of chemical compounds in a generalized form can be used for any system of chemical elements.



    1. Fok VA. The beginning of quantum mechanics. Science. 1976.
    2. Roothaan CCJ. Rev. Mod. Phys. 1951; 23:2; 69. DOI:10.1103/RevModPhys.23.69
    3. Slater JC. Phys. Rev. 1051; 51:3;385.
    4. Undalov YK. Russian. Inorganic Chemistry. 1998; 43:1447.
    5. Undalov YK. Russian. Inorganic Chemistry. 1999; 44:1315.
    6. Undalov YK. Russian. Inorganic Chemistry. 1999; 44:1479.
    7. Undalov YК, Terukov EI, Agafonov DV. Izvestia of St. Petersburg State Institute of Technology (Technical University). 2021; 59(85):26. DOI:10.36807/1998-9849-2021-59-85-26-36
    8. Eriemin EN. Fundamentals of chemical kinetics. Visshaia Shkola. 1976.
    9. Urusov VS. Theoreticalcrystal chemistry. Moscow State University. 1987.
    10. Kovba LM. Stoichiometry, defects in crystals and structural homology. Chemistry. 1996.
    11. Butlerov A. On the chemical structure of substances. Scientific notes of Kazan University. (Dep. Physical, mathematical and medical sciences). 1862; 1:1;1.
    12. Klinkova LA, Barkovskii NV, Fedotov VK. Physica C: Superconductivity. 2010; 470:206. https://doi.org/1016/j.physc.2010.09.013
    13. Gay PL, Rao CNR. Z Naturforsch. 1975; 30a:8;1092. https://doi.org/1515/zna-1975-0831
    14. Li Z, Guo W, Zhang NN. APL Matereals. 2020; 8:091112. DOI: 10.1063/5.0018934
    15. Drennan J, Tavares CP, Steele BCH. Mater. Res. Bull. 1982; 17:5;621. https://doi.org/1016/0025-5408(82)90044-7
    16. Savchenko VF, Lyubkina IY. Russian. Inorganic Chemistry. 1986; 2:1483.
    17. Bykova T, Dubrovinsky L, Dubrovinskaia N. Nature Communication. 2016; 10661: https://doi.org/10.1038/neomms10661
    18. Ruddbesden SN, Popper P.Acta Crystall. 1958; 11:1;54. https://doi.org/10.1107/S0365110X58000128
    19. Beznosikov VV. Structural Chem. 1991; 32:3.
    20. Magneli A, Blomberg B, Kihlborg H. Acta chem. scand. 1955; 9:8;1382. https://doi.org/10.3891/acta.chem.scand.09-1382
    21. Andersson S, Collen B, Kuylenstierna U. Acta chem. scand. 1957; 11:10; 1641. https://doi.org/10.3891/acta.chem.scand.11-1641
    22. Andersson S. Acta chem. scand. 1954; 8:9;1599. https://doi.org/10.3891/acta.chem.scand.08-1599
    23. Gado P, Holmberg B, Magneli A.Acta chem. scand. 1965; 19:8;2010. https://doi.org/10.3891/acta.chem.scand.19-2010
    24. Du MH. J Materials Chemistry C. 2019; 7:19;5710. https://doi.org/10.1039/C9TC00197B
    25. Zhang S, Xie LH, Ouyang SD. Phys. Scr. 2016; 91:015801;6. DOI: 10.1088/0031-8949/91/1/015801
    26. El-Naggar IM, Mowafy E. Adsorption. 2002; 87:3;225.
    27. Wefer K. Naturwissenschaften. 1967; 54:1:18.
    28. Bando Y, Watab=nabe M, Sekikawa Y. Acta. Cryst. 1979; B35:1541.
    29. Bamberger C, Begun G. Am. Ceram. Soc. 1987; 70:3;48. DOI: 10.1111/J.1151-2916.1987.TB04963X
    30. Clearfield A, Lehto. Solid State Chem. 1988; 73:98.
    31. Dion M, Piffard Y, Tournoux M. Inorg. Nucl.Chem. 1978; 140:917.
    32. Wadsley AD, Mumme WG. Acta. Cryst. 1968; B24:392. DOI: 10.1107/S0567740868002426
    33. Bando Y. Acta. Cryst. 1982; A38:211. DOI: 10.1107/S0567739482000473
    34. Watanabe M, Bando Y, Tsatsum M. Solid State Chem. 1979; 28:3;397. DOI: 10.1016/0022-4596(79)90091-4
    35. Kataoka K, Takahashi Y, Kijima N, Ohshima K.Mater. Res. Bull. 2009; 44: N1; 168. DOI: 10.1016/j.materresbull.2008.03.015
    36. Luchinskii GP. Chemistry of titanium. Chemistry. 1971; 472 с.
    37. Yi T, Yang Z, XieY. Mater. Chem. 2015; 3:5750. DOI: 10.1039/c4ta06882c.
    38. Hawthorne FC, Calvo C. Solid State Chem. 1977;22: N1;157.
    39. Ogihara T, Kodera T. Matereals. 2013; 6:2285. DOI: 10.1039/ma6062285
    40. Fotiev АА, Slobodin BV, Hodos M.Ya. Vanadatiy. Nauka. 1988; 267s.
    41. An JN, Xu Y, Zhen L, Yuang YD. Ceram. International. 2010; 36:6; 1825. DOI: 10.1016/J.CERAMINT.2010.03.031
    42. Poulus EF, Miehe G, Fuess H, Yehia I. Solid State Chem. 1991; 90:1;17. DOI: 10.1016/0022-4596(91)90166-F
    43. Jiang XP,Huang JG, Yu Y. Supercond. Sci. Technol. 1988; 1:2;102. DOI: 10.1088/0953-2048/1/2/012
    44. Maeda M, Kadoi M, Ikeda T. Jpn. J. Appl. Phys. 1989; 28:8;1417. DOI:10.1143/JJAP.28.1417
    45. Zandbergen HW, Jansen J, Svetchnikov VL. Physica C: Superconductivity and its applications. 1999; 328:3-4;211. https://doi.org/10.1016/S021-4534(99)00537-7

Similar Articles

Dimensioning of Splices Using the Magnetic System
Ryszard Błażej, Leszek Jurdziak, Agata Kirjanów-Błażej, Paweł Kostrzewa and Aleksandra Rzeszowska
Solar Energy Resource Potentials of the City of Arkadag
Penjiyev Ahmet Myradovich and Orazov Parahat Orazmuhamedovich
The Influence of Low Pesticide Doses on Fusarium Molds
Mihaela UrsanOana-Alina Boiu-Sicuia, Ioana Irina Crăinescu and Călina Petruța Cornea
Peritoneal Carcinomatosis from Ovarian Cancer: A Case Report
Andrea González De Godos, Enrique Asensio Diaz, Pilar Pinto Fuentes, Baltasar Pérez Saborido and David Pacheco Sánchez