Научная статья на тему 'Возможные концептуальные конструкты для построения концептуальных систем химии'

Возможные концептуальные конструкты для построения концептуальных систем химии Текст научной статьи по специальности «Химические науки»

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Ключевые слова
КОНЦЕПТУАЛЬНЫЙ КОНСТРУКТ / КОНЦЕПТУАЛЬНАЯ СИСТЕМА ХИМИИ / CONCEPTUAL CONSTRUCT / CONCEPTUAL SYSTEM IN CHEMISTRY

Аннотация научной статьи по химическим наукам, автор научной работы — Иванов В. В.

Обсуждаются возможные концептуальные конструкты для построения концептуальных систем химии.

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POSSIBLE CONCEPTUAL CONSTRUCTS FOR CONSTRUCTION OF A CONCEPTUAL SYSTEMS IN CHEMISTRY

The possible conceptual constructs for construction of a conceptual systems in chemistry were discussed.

Текст научной работы на тему «Возможные концептуальные конструкты для построения концептуальных систем химии»

5. Shcherbakov I.N., Ivanov V.V., Loginov V.T., et. al. Chemical Nanoconstruction of Compositional Materials and Coatings with AntiFrictional Properties. Rostov-on-Don: «Izv. vuzov. Sev.-Kavk. Region. Tehnicheskie nauki», 2011. 132p.

6. Ivanov V.V., Balakai V.I., Ivanov A.V., Arzumanova A.V. Synergism in composite electrolytic nickel-boron-fluoroplastic coatings // Rus. J. Appl. Chem., 2006. Т.79. №4. С.610-613.

7. Ivanov V.V., Balakai V.I., Kurnakova N.Yu., et al. Synergetic effect in nickel-teflon composite electrolytic coatings // Rus. J. Appl. Chem., 2008. Т.81. № 12. С.2169-2171.

8. Balakai V.I., Ivanov V.V., Balakai I.V., Arzumanova A.V. Analysis of the phase disorder in electroplated nickel-boron coatings // Rus. J. Appl. Chem., 2009. Т.82. №.5. С.851-856.

9. Ivanov V.V., Shcherbakov I.N., Ivanov A.V. Modeling One-Stage p-Layered Structures of Ordering and Disordering Intercalated Phase by Alkaline Metals into Graphite // Izv. vuzov. Sev.-Kavk. Region. Tehnicheskie nauki. 2010. № 2. С.91-98.

10. Bespalova Zh.I., Ivanov V.V., Smirnitskaya I.V., et al. Fabrication of a titanium anode with an active coating based on mixed oxides of base metals // Rus. J. Appl. Chem., 2010. Т.83. N.2. С.242-246.

11. Ivanov V.V., Bespalova Zh.I., Smirnitskaya I.V., et al. Study of the composition of titanium anode with electrocatalytic coating based on cobalt, manganese, and nickel oxides // Rus. J. Appl. Chem., 2010. Т.83. N.5. С.831-834.

Иванов В.В.

Кандидат химических наук, доцент, Южно-Российский государственный технический университет (Новочеркасский

политехнический институт)

ВОЗМОЖНЫЕ КОНЦЕПТУАЛЬНЫЕ КОНСТРУКТЫ ДЛЯ ПОСТРОЕНИЯ КОНЦЕПТУАЛЬНЫХ СИСТЕМ

ХИМИИ

Аннотация

Обсуждаются возможные концептуальные конструкты для построения концептуальных систем химии.

Ключевые слова: концептуальный конструкт, концептуальная система химии.

Ivanov V.V.

PhD in Chemistry, associate professor, South-Russian state Еngineering University (Novocherkassk Polytechnic Institute) POSSIBLE CONCEPTUAL CONSTRUCTS FOR CONSTRUCTION OF A CONCEPTUAL SYSTEMS IN CHEMISTRY

Abstract

The possible conceptual constructs for construction of a conceptual systems in chemistry were discussed.

Keywords: conceptual construct, conceptual system in chemistry.

One or a few relations are taken as a principle of any abstract construction of a mathematical theory. These relations between elements of some multitude are the composition relation (in algebraic constructions), the ordinal relation (in order constructions), the topological relation (in topological constructions) or their possible combinations [1].

Each abstract construction is determines the corresponding conceptual construct:

Element - Composition - Structure (1), or ECRc;

Element - Order - Structure (2), or EpRp;

Element - Topology - Structure (3), or ETRt;

Element - Composition П Order - Structure (4), or ECHPRcp;

Element - Composition П Topology - Structure (5), or ECnTRcr;

Element - Order П Topology - Structure (6), or EpnTRpT;

Element - Composition П Order П Topology - Structure (7), or ECnPnTRcPT.

Thus, all possible conceptual constructs for conceptual systems construction were obtained [1].

The matter of all constructive elements “Structure (N)” is different. Only Structure (1) of the first conceptual construct is the structure, which completely dependence from Composition. This conceptual construct ECRc is in the best way corresponds to the second conceptual system of chemistry - the structural theories system [2]. The procedure of receipt of the conceptual construct ECRc from algebraic construction is following.

Elements

The first supposition: E = {ei} is the terminal multitude of elements, and the peP: pe1 = e2 (where e1,e2eE) is the equivalent relation, which ensures the splitting of multitude E on the classes of the similar elements Ea = {e | a(e) = a}eE,

where a is the fundamental characteristic index of the class.

The second supposition: the number of bonds ro(e) and index of bonds P(e) between elements are their characteristic. Then the structural unification of these elements into configuration is possible.

Configurations and images If assume the next:

1) a symbol C = {cij} is the multitude of configurations, where cij {ei, ej} is the combination of elements with indexes Pi(ei) and Pj(ej),

2) bond’s relation p and type of combination reR (where R is multitude of schemes of the configuration’s structures) are new,

3) relations П = <p, R> are the combinatorial rules, which determines the multitude of regular configurations or structures С(П), then the multitude of images I = {Ii} may be received upon multitude of regular structures С(П) by identification rule Id.

The images algebra may be presented in the following way:

A = <E, S, R, p, П>.

The multitude E is the composition of images and the R is the structural characteristic of the combinations, which may be formed the every image Ii.

Image-presentation and Construct

Elemental composition and configuration’s structure are the main characteristics of Image-presentation about object. The Image-presentation may be described in the following conventional construct K = <E, C, R>.

In this symbolic entry the E, C and R are denotes the Element, Composition and Structure, accordingly. If assume that Elements E are completely determines Composition of configurations C and their Structure R, then the conventional construct K is the conceptual construct ECR.

The main transformation mechanisms of a ECR-like conceptual construct and the corresponding conceptual systems

Take into consideration that the main transformation mechanisms ECR-like conceptual construct may be formed from dynamic system properties, in particular, the evolution, the homology, the furcating.

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Evolutionary transformation mechanism of the ECR conceptual construct is the possibility of crossing from one condition to another and the change of it quality. In this case the conventional construct <E, C, R> may be presented in the following way

K = <E, C, R, U, S> (or ECRUS).

The additional construct elements U and S are the possible conditions and properties of a system.

Homological transformation mechanism of the ECRUS conceptual construct is the result of manifestation of a different organization level of type

.. .super-system - system - sub-system...

Hence it follows that the one-level construct K(1) may be reorganized into following multi-level way

K(i) ^ K(n), or (ECRUS) ^ (...((ECRUS)® CRUS)(2) .. .CRUS)1®.

Furcated transformation mechanism of the K(1) conceptual construct is the possibility of the private construct Kn existence for each class of elements En of the evolutionary conceptual construct K(1). Take into account the transformation K(1) ^ Kn(1) may be presented in the following way

(ECRUS)® ^ (EEnCnRnUnSn)(1).

Thus, the main variants of a ECR-like conceptual construct were received. The corresponding variants of the conceptual systems were inferred, too.

A linear variant of the evolutionary conceptual system is

E —• C —• R —• U —• S

A homological variant of the evolutionary conceptual system is

A furcated variant of the evolutionary conceptual system is the next:

E — Ce — Re — Ue — Se

Ec — C — Rc — Uc — Sc

Er —— Cr —— R —— Ur —— Sr

Eu — Cu — Ru — U — Su

Es —— Cs —— Rs —— Us —— S

Take into account the using of the furcated variant of an evolutionary conceptual system of type (EE4C4U4S4)® [1] is fixes the following relations for property identification:

1) S(E) = S(Ec, Er, Eu, Es),

2) S(C) = S(Ce, Cr, Cu, Cs),

3) S(R) = S(Re, Rc, Ru, Rs),

4) S(U) = S(Ue, Uc, Ur, Us).

The basic forecasting principles of inorganic substances with necessary properties

The corresponding forecasting principles of an inorganic substances with necessary properties are may be formulated in the following

way.

1. Principle of fragmental construction of the substances. Crystal structure of any substance may be presented by fragments, and the composition (qualitative and quantitative), the structure, the condition and the property of their fragments are the completely set of the composition, the structure and the diagnostic property of substances.

2. Principle of the predominance of "geometric" factor into crystal structure forming. The correlation of individual elemental characteristic of the structural fragment are shapes its crystal chemical topology and the composition, and therefore, the structure condition and the property of crystal.

3. Principle of the determinate of the crystal structure by structural fragment. Crystal chemical topology and the chemical composition of the structural fragment are the completely determines the structure, the condition and the diagnostic property of crystal.

4. Principle of the determinate of the specific condition of crystal by fragment’s condition. Specific condition of the structural fragment is the result of its crystal chemical topology, the chemical composition and completely determines the structure, the condition and the diagnostic property of crystal.

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Let us notes, that their four positions are the basic forecasting and modeling principles of inorganic substances with necessary properties, in particular, ionic conductivity [1, 3-16], electrochemical activity [1, 17-23], some electric, magnetic [24-37] and anti-frictional properties [38-45].

References

1. Ivanov V.V. Combinatorial Modeling of the Probable Structures of Inorganic Substances. Rostov-on-Don: Northern-Caucasian Science Center of Higher Institute of Learning, 2003. 204p.

2. Kuznetsov V.I. Dialectic of chemistry development. From history to theory chemistry development. - M.: Nauka. 1973. 328p.

3. Shvetsov V.S., Vybornov V.F., Ivanov V.V. About Composition of Compound with High Conductivity in RbCl-CuCl System // Electrohimiya. 1982. Т.18, №7. С.986-990.

4. Shvetsov V.S., Vybornov V.F., Ivanov V.V., Kolomoets A.M. Making More Precise of the State Diagram of RbCl-CuCl System and Synthesis of the Solid Electrolyte RbCrnCb // Izv. AN SSSR. Neorg. Mater. 1984. Т.20, №8. С.1413-1415.

5. Ivanov V.V., Kolomoets A.M. Forecasting of Composition of the Solid Electrolytes Based on Copper Halides // Izv. AN SSSR. Neorg. Mater. 1987. Т.23, №3. С.501-505.

6. Ivanov V.V., Kolomoets A.M., Vybornov V.F., Shvetsov V.S. Superionic Conductor RbCrnBnb and Its Solid Solutions // Izv. AN SSSR. Neorg. Mater. 1988. Т.24, №2. С.299-302.

7. Ivanov V.V., Kolomoets A.M., Shvetsov V.S. Superionic Conductors KCrnBn+xb-x // Electrohimiya. 1990. Т.26, №2. С.183-185.

8. Ivanov V.V., Shvetsov V.S. Conductors NftCrnBn+xb-x with Fast Transfer of Copper ions // Izv. AN SSSR. Neorg. Mater. 1990. Т.26, №8. С.1734-1736.

9. Ivanov V.V. Superionic Conductor CuRb0,5K0,5Br3b // Neorg. Mater. 1992. Т.28, №1. С.220-221.

10. Ivanov V.V. Crystal Chemical Analysis of Inorganic Compounds by Geometrical □,□□-Criteria as a Semi-Empiric Prognoses Method of Cationic Conductors // Neorg. Mater. 1992. Т.28, №3. С.665-667.

11. Ivanov V.V., Skalozubov D.M. Complex Chalcogenides Na3MX4 Type as a Perspective Ionic Conductors // Izv. AN SSSR. Neorg. Mater. 1990. Т.26, №7. С.1773-1775.

12. Ivanov V.V., Skalozubov D.M. The Choice Method of Inorganic Cationic Conductors by Geometrical Criteria // Izv. AN SSSR. Neorg. Mater. 1990. Т.26, №11. С.2383-2388.

13. Ivanov V.V., Skalozubov D.M. Prognosis of Inorganic Cationic Conductors A4BX4 Type by Geometrical Criteria for A3BX4 // Izv. AN SSSR. Neorg. Mater. 1991. Т.27, №12. С. 2682-2684.

14. Ivanov V.V. Analysis of the Using Possibilities of Isomorphism for Receiving of Inorganic Cationic Conductors // Neorg. Mater. 1992. Т.28, №1. С.344-349.

15. Ivanov V.V., Skalozubov D.M. Analysis of the Existence Possibilities Lithium-Containing Compounds with Cu3VS4 Structure // Izv. AN SSSR. Neorg. Mater. 1989. Т.25, №7. С.1205-1206.

16. Ivanov V.V., Skalozubov D.M. Prognosis of Inorganic Cationic Conductors AaB8-aX4 (a=2, 5, 6) and A7B4X4 Type by Geometrical Criteria for A3BX4 // Neorg. Mater. 1992. Т.28, №2. С.369-375.

17. Ezykian V.I., Ereiskaya G.P., Ivanov V.V., et. al. Study of Solid Phase Interaction Reaction between Manganese Dioxide and Lithium Hydroxide // Izv. AN SSSR. Neorg. Mater., 1989. Т.25, №5. С.795-798.

18. Khodarev O.N., Filimonov B.P., Ereiskaya G.P., Ivanov V.V. Investigation of the Reversibility of D-MnO2 Electrodes into Aprotonic Electrolytes // Electrohimiya. 1991. Т.27, №8. С.1046-1049.

19. Ivanov V.V., Ereiskaya G.P., Ezykian V.I., et. al. Electrochemical and X-Ray Investigation of Lithium-Manganese Spinel into Lithium Chemical Current Source with Aprotonic Electrolyte // Electrohimiya. 1992. Т.28, №3. С.468-471.

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20. Ivanov V.V., Ereiskaya G.P., Lutsedarskii V.A. Prognosis of the 1D Homological Series of Metal Oxides with Octahedral Structures // Izv. AN SSSR. Neorg. Mater.1990. Т.26, №4. С.781-784.

21. Ivanov V.V., Ereiskaya G.P. Structural Combinatorial Analysis of the 1D Homological Series of Transition Metal Oxides with Octahedral Structures // Izv. AN SSSR. Neorg. Mater. 1991. Т.27, №12. С. 2690-2691.

22. Bublikov E.I., Kulinich V.I., Ivanov V.V., Shcherbakova E.E. An X-Ray Diffraction Method for Determining the Amorphous Component of Electrolytic Precipitates // Industrial Laboratory, 1999. T.65, №11. C.713-715.

23. Ivanov V.V., Shcherbakov I.N., Ivanov A.V. Modeling One-Stage p-Layered Structures of Ordering and Disordering Intercalated Phase by Alkaline Metals into Graphite // Izv. vuzov. Sev.-Kavk. Region. Tehnicheskie nauki. 2010. № 2. С.91-98.

24. Ivanov V.V., Talanov V.M. Modeling of the Structure of the Ordered Spinel-Like Phases (of Tupe 2:1). // Phys. Stat. Sol. (a), 1990. V.122, №2. P.K109-112.

25. Ivanov V.V., Talanov V.M. Structural Combinatorial Modeling of Spinelloids // MOSPOQ-91, (20-24 august 1991) (Hungary). Budapest, 1991. V.1. P.37.

26. Ivanov V.V., Talanov V.M. Structural Problems of the Ordered Spinel-like Phase CuIrnS8.// Int. Conf. on Aperiodic Crystals, Les Diablerets, Switzerland, Sept. 18-22, 1994. Abstract Book. - Lausanne, Switzerland, 1994. - P.23.

27. Ivanov V.V., Talanov V.M. Spinelloid's Universe // Int. Conf. on Aperiodic Crystals, Les Diablerets, Switzerland, Sept. 18-22, 1994. Abstract Book. - Lausanne, Switzerland, 1994. - P.22.

28. Ivanov V.V., Talanov V.M., Shabel’skaya N.P. X-Ray diffraction study of the CuCnO4 - NiFe2O4 system // Inorganic Materials,

2000. Т.36, №11. С.1167-1172.

29. Ivanov V.V., Talanov V.M., Shabel’skaya N.P. Phase relations in the NiFe2O4 - NiCnO4 - CuCnO4 system // Inorganic Materials,

2001. Т.37, №8. С.839-845.

30. Ivanov V.V., Talanov V.M. Combinatorial modular design of the structures of spinel-type phases // Glass Physics and Chemistry,

2008. Т.34. №4. С.401-435.

31. Ivanov V.V., Talanov V.M. Algorithm of choice of the structural module and modular design of crystals // Russ. J. Inorg. Chem.,

2010. Т.55 № 6. С.915-924.

32. Ivanov V.V., Talanov V.M. Principle of modular crystal structure // Crystallography Reports, 2010. Т.55. № 3. С.362-376.

33. Talanov V.M., Ivanov V.V., Shirokov V.B., Talanov M.V. Unusual orbital and atomic ordering in tetragonal phase of MgTi2O4 // Acta Cryst. A: Foundation of Crystallography, 2011. T.67. C.805.

34. Ivanov V.V., Talanov V.M., Shirokov V.B., Talanov M.V. Crystal chemistry and formation mechanism of tetragonal MgTi2O4 // Inorganic Materials. 2011. T.47. N.9. C.990-998.

35. Talanov V.M., Ivanov V.V., Shirokov V.B., Talanov M.V. Theory of structural phase transition in MgTi2O4 // Crystallography Reports, 2013. V.58. No.1. pp.89-100.

36. Ivanov V.V., Talanov V.M. A Symbolic Description of Module Packings and Crystal Structure Codes / J. of Struct. Chem., 2013. V.54. No.2. pp.408-430.

37. Ivanov V.V., Ulianov A.K., Shabel’skaya N.P. Ferrites-Chromites of Transitional Elements: Synthesis, Structure, Properties. Moscow: Izdatel’skii Dom Akademiya Estestvoznaniya, 2013. 94p.

69

38. Ivanov V.V., Balakai V.I., Ivanov A.V., Arzumanova A.V. Synergism in composite electrolytic nickel-boron-fluoroplastic coatings // Russ. J. Appl. Chem., 2006. Т.79. № 4. С.610-613.

39. Ivanov V.V., Balakai V.I., Kurnakova N.Yu., et al. Synergistic effect in nickel-teflon composite electrolytic coatings // Russ. J. Appl. Chem., 2008. Т.81. № 12. С.2169-2171.

40. Balakai V.I., Ivanov V.V., Balakai I.V., Arzumanova A.V. Analysis of the phase dosorder in electroplated nickel-boron coatings // Russ. J. Appl. Chem., 2009. Т.82. №.5. С.851-856.

41. Ivanov V.V., Talanov V.M. Combinatorial Design of Poligonal Nanostructures // Information and Structure in the Nanoworld. Conference materials: program and abstracts. 1-3 july 2009. Saint-Peterburg, Russia. 2009. P.67.

42. Bespalova Zh.I., Ivanov V.V., Smirnitskaya I.V., et al. Fabrication of a titanium anode with an active coating based on mixed oxides of base metals // Russ. J. Appl. Chem., 2010. Т.83. № 2. С.242-246.

43. Ivanov V.V., Bespalova Zh.I., Smirnitskaya I.V., et al. Study of the composition of titanium anode with electrocatalytic coat based on cobalt, manganese, and nickel oxides// Russ. J. Appl. Chem., 2010. Т.83. № 5. С.831-834.

44. Ivanov V.V., Shcherbakov I.N. Modeling of Compositional Nickel-Phosphorus Coatings with Anti-frictional Properties. Rostov-on-Don: «Izv. vuzov. Sev.-Kavk. Region. Tehnicheskie nauki», 2008. 112p.

45. Shcherbakov I.N., Ivanov V.V., Loginov V.T., et. al. Chemical Nanoconstruction of Compositional Materials and Coatings with Anti-frictional Properties. Rostov-on-Don: «Izv. vuzov. Sev.-Kavk. Region. Tehnicheskie nauki», 2011. 132p.

46. Ivanov V.V., Talanov V.M. Construction of Fractal Nanostructures Based on Kepler-Shubnikov Nets // Crystallography Reports, 2013. V.58. No.3. pp.383-392.

Иванов В.В.

Кандидат химических наук, доцент, Южно-Российский государственный технический университет (Новочеркасский

политехнический институт)

АКТИВНЫЕ АНОДЫ НА ОСНОВЕ ФАЗ С ДЕФЕКТНЫМИ ШПИНЕЛЕПОДОБНЫМИ СТРУКТУРАМИ

Аннотация

Обсуждаются составы и особенности фазовой разупорядоченности химически активных анодов, содержащих фазы структурного типа шпинели с разупорядоченностью катионов и вакансий.

Ключевые слова: дефектная шпинелеподобная структура, химическая активность, активный анод.

Ivanov V.V.

PhD in Chemistry, associate professor, South-Russian state Еngineering University (Novocherkassk Polytechnic Institute) ACTIVE ANODES BASED ON PHASES WITH DEFECT SPINEL-LIKE STRUCTURES

Abstract

Compositions and phase disordering peculiarities of the chemic active anodes including the spinel type structure phases with cations and vacancies disordering were discussed.

Keywords: defect spinel-like structure, chemic activity, active anode.

Оксидные системы на основе неблагородных металлов используются в качестве электродных материалов для ряда электрохимических процессов [1-3]. Известно, что для процессов восстановления кислорода и электролиза хлоридных растворов считается перспективным оксид кобальта [4,5]. По сравнению с оксидами других металлов ^304^^^ обладают сравнительно низким перенапряжением выделения хлора, высокой селективностью к реакции разряда хлорид-ионов и удовлетворительной коррозионной стойкостью. Однако, аноды, приготовленные только из Co3O4, по основным указанным выше характеристикам, за исключением селективности по отношению к хлорной реакции, уступают анодам на основе оксидов рутения и титана со структурой рутила.

Структуры 2-3 шпинелей Co3O4, MrnO4 и CoMrnO4 (Fd3m, z = 8) соответствуют структурной формуле нормальной шпинели AnBnI2X4 (где A и B - тетраэдрически и октаэдрически координированные катионы, структурная разупорядоченность в катионных подрешетках отсутствует). В отличие от представителей других структурных типов разупорядоченность в шпинели определяется двумя причинами: явлением обращенности (атомной разупорядоченностью в катионной подрешетке) и изовалентным или гетеровалентным изоморфизмом, когда в катионной подрешетке образуются атомные вакансии, приводящие к повышенной поверхностной или объемной активности дефектной шпинелеподобной фазы [7 - 17]. Формально допускается существование дефектной шпинели за счет протекающих обменных квазихимических процессов:

An ^ (2/3)AIn + (1/3) - в подрешетке тетраэдрических катионов,

BIn ^ (3/4)BIV + (1/4) - в подрешетке октаэдрических катионов.

Дефектную шпинель можно представить и как результат проявления изоморфизма в соответствующих системах MenMenI2O4 -Men2O3 и MenMenI2O4 - MeIVO2 (Me - Co, Mn), который в общем случае сопровождается образованием разупорядоченных твердых растворов [17].

Для определения состава фаз в поверхностных слоях покрытия использовали следующие данные о концентрации элементов: O - 60,0; Ti - 1,0; Mn - 27,5; Co - 11, % (ат.) [5]. Составы упорядоченных фаз со структурой дефектной шпинели вида (Co,Mn)3-xO4 при возможных минимальных и максимальных значениях степени дефектности приведены в табл. 1.

Таблица 1. Составы шпинелеподобных (Co,Mn)3-xO4 и рутилоподобных (Mn,Ti)O2 фаз и их содержание в поверхностных слоях

покрытия титанового анода

Тип упорядоченного твердого раствора Степень дефектности структуры, x Фазовый состав покрытия, % моль, и химический состав фаз

AA’B4X4X’4 0,02 0,31 95 (Co0,38Mn0,62)2,98O4 + 5 TiO2 80 (Co0,30Mn0,70)2,69O4 + 20 (Mn0,81Ti0,19)O2

ABB’X2X’2 A2BB’3X2X’6 0 0,33 76 (Co0,38Mn0,62)3O4 + 24 (Mn0,90Ti0,10)O2 70 (Co0,31Mn0,69)2,75O4 + 30 (Mn0,70Ti0,30)O2

Ниже с учетом наиболее вероятного распределения катионов кобальта и марганца по тетраэдрическим и октаэдрическим узлам кристаллической решетки шпинели для возможных типов упорядоченных фаз приведены соответствующие кристаллохимические формулы и варианты остаточной разупорядоченности.

1. Упорядоченные типа 1:1 фазы вида AA’B4X4X’4 (0,02 < х < 0,31):

а) х = 0,02, формула Co2+0,94Co3+0,040,02)[Co3+0,15Mn3+1,85]04,

(I) A = Co2+; A’ = 0,88Co2+ + 0,08Co3+ + 0,04 ;

(II) A = 0,96Co2+ + 0,04 ; A’ = 0,92Co2+ + 0,08Co3+.

б) х = 0,31, формула (Co2+0,07Co3+0,680,31)[Co3+0,13Mn3+1,87]O4,.

(I) A = 0,14Co2+ + 0,86Co3+; A’ = 0,38Co3+ + 0,62 ;

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