Spatial-Energy Principles of the Processes for Complex Structure Formation 9783110935035

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Spatial-energy principles of the processes for complex structure formation

Spatial-energy principles of the processes for complex structure formation G.A. Korablev

ISBN: 90 6764 423 4

© Copyright 2005 by Koninklijke Brill NV, Leiden, The Netherlands. Koninklijke Brill NV incorporates the imprints Brill Academic Publishers, Martinus Nijhoff Publishers and VSP A C.I.P. record for this book is available from the Library of Congress All rights reserved. No part of this publication may be reproduced, translated, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior permission from the publisher. Authorization to photocopy items for internal or personal use is granted by Brill provided that the appropriate fees are paid directly to the Copyright Clearance Center, 222 Rosewood Drive, Suite 910, Danvers, MA 01923, IJSA. Fees are subject to change. PRINTED IN THE NETHERLANDS BY RIDDERPRINT B V , RJDDERKERK COVER DESIGN: ALEXANDER SILBERSTEIN

Contents

Preface

7

Introduction

10

Chapter 1. Problems of isomorphism and phase-formation

15

1.1. Theoretical studies of isomorphic replacements

15

1.2. Basic phase-formation factors

19

1.3. Some modern theories about phase-formation problems

22

Chapter 2. Spatial-energy parameter (P-parameter)

36

2.1. Dependencies between energy, charge and dimensional characteristics inside an atom

36

2.2. Principle of adding reverse values of energy parameters of oppositely charged systems. P-parameter

39

2.3. Calculations of total energy of valence electrons inside an atom using SEP method. Comparison with a statistic model

44

2.4. Calculations of electron density inside an atom via P-parameter and principle of adding reverse values of P-parameters

48

2.5. Dependence of P-parameter upon the modulus of maximum values of Yfunction radial part51 2.6. Dependence of spectral characteristics of atoms upon their spatial-energy parameters

54

2.7. Wave equation of P-parameter

55

2.8. Wave properties of P-parameter and addition principles of P-parameters

59

2.9. Some additive properties of P-parameter

62

2.10. P-parameter as an objective characteristics of electronegativity

63

Chapter 3. Experimental evidence of spatial-energy criterion of isomorphism and solubility

67

3.1. Elementary systems of Μ' - M" type

67

3.2. Estimation of isomorphic replacements in complex systems

85

3.3. Experimental check of P-parameter application taking atom coordination into account

85

3.4. Morphology of state diagrams of quasi-binary systems of vanadates of metals of II group

92

3.5. Application of effective PE-parameter

98

3.5.1. Phase-formation analysis of M0F2- M00 F2 systems

99

3.5.2. Systems based on yttrium orthovanadate

102

3.5.3. Forecasting of isomorphic miscibility of compounds with phenacite structure

106

3.5.4. Calculations of maximum solubility of binary carbides in tungsten carbide

110

Chapter 4. Temperature characteristics of solid solution expansion with the help of Pparameter (at given temperature)

119

4.1. Estimation of mutual solubility of binary system components

121

4.2. Systems of Μ Ό - M"0 type

138

4.3. Phase-formation and thermal properties in systems A1203-M203

143

4.4. Estimation of carbon solubility in metals for refractory compounds at given temperature

147

4.5. Calculations of oxygen solubility in metals

150

4.6. Method experimental check; directed search of inorganic materials

159

Chapter 5. Spatial-energy criterion of compound formation

169

5.1. P-parameter as a basic criterion of stable phase formation

169

5.2. Crystals with basic ionic bond

172

5.3. Crystals with ionic-covalence and metallic bonds. Intermetallides

175

5.4. Crystalline penetration structures

181

5.5. Estimation of ultimate carbon content value in carbide systems MCl-x .

185

Chapter 6. Other applications of P-parameter in inorganic chemistry and chemistry of solids

192

6.1. Calculations of effective ionization sections of atoms and molecules at electron shock

192

6.1.1. Free atoms

192

6.1.2. Homonuclear two-atom molecules

198

6.1.3. Ionization curve of gases

198

6.2. Shift modulus determination for metals and carbide compounds

200

6.3. Calculations of activation energy of volume diffusion and self-diffusion in solids

205

6.4. Estimation of alloy amorphization possibility

215

6.5. Solubility of components of solid solutions of system W-Co-C-O-N

223

6.6. Estimation of cluster-formation in system CaS04-H20

228

Chapter 7. Kinetics and phase-formation in fast physic-chemical processes

235

7.1. Methods for calculating P-parameters of complex organic compounds

235

7.2. Dependence of activation energy of chemical reactions upon spatial-energy characteristics of atoms

238

7.3. Basic structural interactions of components in systems OCTOGEN (OG) nitroglycerine (NG)

241

7.4. Phase-formation features of polymeric composite (PC) components.

257

Conclusion

266

General conclusions

270

References

272

Appendix I. P-parameter additive properties

302

Appendix II. Isomorphism of elementary systems

315

Appendix III. P0-parameters of valence orbitals of neutral atoms in basic state (calculated via atom ionization energy)

374

Appendix IV. P-parameters of some atoms calculated via electron bond energy according to Fischer

384

Appendix V. Calculations of P0-parameters of some atoms using electron bond energy by ESCA

405

Appendix VI. Calculations of errors when estimating solubility of components using Parameter method

Appendix VII. Methods of experiments conducted for determining the solubility boundaries of complex system components.

Appendix VIII. Analog comparisons of Lagrangian and Hamilton functions with spatial-energy parameter

UDK 541.51-541.124+546.07

Reviewer: Head of Basic-research educational center of chemical physics and mesoscopy UrD RAS, Head of the department of Chemistry and chemical engineering at Izhevsk State Technical University Doctor of chemical science, Professor

V.l. Kodolov

G.A. Korablev. Spatial-energy principles of the processes for complex structure formation, 2005, 426 p., 84 tables, 21 figures.

The methodology developed by the author and presented in this book is aimed at evaluation of formation processes for complex, multi-component systems and is based on the understanding of spatial-energy parameter (P-parameter). Such a criterion is introduced when analyzing several physical and chemical regularities,

including

Lagrangian equations and consideration of the most important atomic characteristics. Specific application of such an approach to estimate the degree and direction of structural interactions, phase-formation processes, isomorphism and solubility in numerous (over a thousand) systems, including molecular ones, is given. In particular, the distribution of phases and boundary layers in complex conglomerate of polymeric composite is analyzed. The monograph contains a lot of methodological, calculating and informative material to be used in practical material science in the process of theoretical studies and research of structural interactions in condensed systems.

7

Preface

The investigation of solid solutions and formation processes of multi-component systems is one of the key trends of physics and chemistry of condensed systems. Solid solutions have an important practical value; the problem of calculating their properties is very critical. The difficulties in predicting properties of such complex systems basically result from the lack of realistic models of solutions. Actually till now the only criterion of model adequacy has been comparison with the experiment. At the same time, the importance of electron sub-system in solutions becomes clearer. Here, the problem of picking up parameters characterizing an electron sub-system arises. G.A. Korablev developed and applied spatial-energy parameter (P-parameter) characterizing an electron sub-system and determining not only electron energy, but also the localization area of its wave function. The book contains calculation methods and multiple applications of P-parameter to predict different characteristics of solid and liquid solutions. The monograph contains a complete review of literature on phase-formation and isomorphism theory with detailed classification of existing phase-formation and maximum solubility criteria of different components in phases. As can be observed from modern state of physics and chemistry, it will be impossible to create a quantitative theory of substance condensed state based on ab initio principles in the nearest future.

Therefore, there is a necessity in phenomenological

approach such as a P-parameter method. Finally, a new approach for solving a lot of old problems in physical chemistry, chemical physics and theory of condensed substances has been formulated. Atom P-parameter is introduced and its calculation rules are postulated without sufficient analytical substantiation, but the wave equation of P-parameter obtained and corresponding numerical comparisons give the possibility to attach a definite physical sense to P-parameter. The link between P-parameter and spectral characteristics of

8 atoms, electronegativity, electron density inside an atom, and etc. is found. To explain and predict atom isomorphic interchangeability (with the help of Pparameter) the author introduces an additional hypothesis on proximity of electron densities in free atoms at the distances of orbital radius. Apparently, this hypothesis is better realized only at the condition of orbital radii proximity. The application of Pparameter for estimating mutual solubility in binary and complex systems is extremely interesting. The determination of temperature dependence of developed parameter is an important result; this defines the existing novelty of the method compared with other approaches in which analogous criteria were investigated. The book reveals other possibilities of P-parameter application in chemical physics of solid and liquid solutions: effective section of atom and molecule ionization at electron shock, metal and carbide shift modulus, diffusion activation energy, etc. All those - important and interesting characteristics of materials determining high productivity and application value of the book. Essential development of such approach is the application of P-parameter methodology for molecular and organic multi-component systems, for energy estimation of chemical reactions, for the analysis of structural interactions in 12-component conglomerate of polymeric composite. But it is necessary to underline that the contribution of electron sub-system in condensed structures is not limited only to the energy of valence electrons and localization radius of wave function. The use of only these values is a definite approximation, the possibility to reach it is practically important to solve several tasks of physics and chemistry of solids. In general, the monograph by G.A. Korablev is a useful and thorough research that allowed to interpret the data on condensed systems available in literature and form a new approach in the analysis and prognosis of substances - development and application of an effective parameter - criterion different in complex inclusion of charge, geometrical and energy factors of atoms contained in substances investigated. The book can be useful for a wide range of specialists: physicists-chemists, material

9

engineers, research institutions and other organizations dealing with the development of new materials.

Head of Department of Theoretical Physics and Mathematics ofNovgorodsky University named after Jaroslav Mudry, Doctor of physical-mathematical sciences, Professor

A. Yu. Zakharov

10 Introduction The solution of the basic problem of material science - obtaining materials with predetermined properties - can be reached only based on fundamental principles that determine the totality of physical-chemical criteria of this substance. Obviously, quantummechanical conception of physics and chemistry of solids becomes such a basis. On the other hand, it can be stated that till now a sufficient amount of experimental material on physical-chemical properties of many compounds has been accumulated. Although there are several semi-empirical models for processing this information, still there is no theoretical substantiation of research trends to solve basic problems in material science. Frequently such search is conducted intuitively using "hit or miss" method. One of the possible reasons of such discrepancy, in our opinion, is a big difficulty in conducting computations using complex quantum-mechanical apparatus to solve specific phaseformation tasks. Analogous difficulties arise during practical application (with the same purpose) of statistic atom model by Thomas-Fermi-Dirak. The problem of a priori estimation of phase-formation is one of the most important in material science and physical-chemical research. Recently, this problem has been paid much attention to by chemists, physicists and material engineers. A lot of works dedicated to the phenomenon of isomorphic replacement, arrangement of adequate model of solid solution, energy theories of replacement solid solutions have been published. But many phase-formation calculations based on using pseudo-potential, quantum-mechanical methods, statistic-thermodynamic theories are still done only for comparatively small number of systems. A lot of issues of theoretical estimation of phase-formation, solubility and character of isomorphic replacements for the majority of actual systems are still unsolved [1 ], [2]. Thus, the task to develop an effective, economical, quite reliable and simple calculating method for estimating phase-formation energy conditions, in particular isomorphic replacements and mutual solubility of compounds at the process given temperature is critical.

11 In this book the method based on the application of a new spatial-energy isomorphism criterion (P-parameter) being derived and semi-numerical characteristics of electron density inside an atom is developed. This criterion has been found and substantiated based on adding reverse values of energy components of oppositely-charged systems. P-parameter calculated for an atom following these rules gains physical sense of effective energy of valence electrons inside an atom, i.e. the energy responsible for interatomic interactions. Numerically P-parameter equals the expression of total energy in atom statistical model (taking exchange and correlative corrections into account). Since P-parameter includes basic factors characterizing the state of valence electrons inside an atom, it is possible to correlate and consequently predict many physical-chemical properties of compounds and find isomorphism energy criteria, system mutual solubility, stable phase formation, etc. with its help. P-parameter application for the analysis of many physical-chemical properties can considerably facilitate a search of new alloys, solid solutions and compounds since the calculation of P-parameter even in case of complex compounds does not cause particular difficulties. The simplicity of such calculations not requiring special computer processing not only expands the possibility of research, but also produces considerable economic effect due to decreasing time- and labor-consumption of this search. The method developed using P-parameter gives the possibility to sufficiently save raw products and materials (metals, elements, water and etc). Besides, this approach allows saving energy (electricity, fuel), human resources and etc., and also helps purposefully pick up the material of predetermined composition with the required complex of properties from a huge number of compositions. Moreover, knowing the computation solubility limits it is possible to deliberately control the alloying processes, i.e. to establish upper extreme norms of alloying additives. The establishment of spatial-energy principles of isomorphic replacements has an utmost practical importance both in elementary and complex systems for studying the kinetics of physical-chemical processes, analyzing destruction processes and forming boundary layers. All this gives the possibility to get specific recommendations to direct

12 scientific and technological researches for solving important and multilateral tasks in material science. Therefore, the application of P-parameter for directed search of new perspective materials can be useful for a wide range of specialists working in the field of physical-chemical material science. The book contains 7 chapters. The first chapter discusses general issues of physicalchemical aspects of isomorphism and phase-formation, gives literature review of several modern theories on these problems, points out the difficulty of applying these approaches for actual multi-component systems. The second chapter introduces the conception of spatial-energy parameter (Pparameter). It is shown that the effective P-parameter of valence orbitals of a neutral atom numerically equals total energy of valence electrons in statistic atom model. This chapter also contains P-parameter wave equation, establishes its direct dependence upon maximum value of wave function radial part and proves that P-parameter is a direct characteristic of radial electron density of ί-orbital in a neutral atom. Besides, the direct dependence of P-parameter upon spectral atomic characteristics is obtained, this is proved by P-parameter wave properties. The third chapter establishes the basic spatial-energy condition of isomorphism: isomorphic replacements of atomic structures can take place only in case of approximate equality of effective P-parameters of valence orbitals of interacting atoms that is estimated based on their relative difference (coefficient a). In physical sense such a condition corresponds to minimum surface-energy exchange processes of valence orbitals of atomcomponents when transferring agitations in space. These regularities were checked and confirmed based on experimental material of over a thousand simple and complex systems (solid replacement solutions, solid penetration solutions, intermetallides, oxides, etc). The fourth chapter contains methods developed based on P-parameter temperature change for predicting the estimation of system mutual solubility that was checked for several compounds following main positions of state diagrams and confirmed with solidphase synthesis of several new compounds (choice of systems is determined by the author's interests and does not have fundamental limitations).

13 In the fifth chapter P-parameter, taking atom coordinations into consideration, is considered as a main criterion of stable crystalline structure phase-formation that also corresponds to the equality condition of effective energies of valence electrons of interacting atoms (in supposition of dual inter-atomic interaction). The sixth chapter contains several examples of other possible P-parameter applications in the analysis of structural interaction processes in chemical physics and physics-chemistry of solids (calculation of effective sections of atom and molecule ionization, estimation of shift modulus for metals and carbide compounds, determination of activation energy for volume diffusion and self-diffusion in solids). It is shown that Pparameter can be used as a criterion for alloy amorphization, as well as for the estimation of complex structural interactions, for example, in systems W-Co-C-ON and CaS04-H 2 0. The seventh chapter is dedicated to kinetics and phase-formation of fast-flowing physical-chemical processes whose mechanism was estimated

via

spatial-energy

parameter. Destruction processes in system octogen-nitroglycerin and phase-formation with the assessment of boundary conditions in complex multi-component system of polymeric composite were considered following these methods. The simplicity and versatility of the proposed model allows hoping for its further practical application to solve critical tasks in material science.

Notation conventions accepted

Po - spatial-energy parameter (SEP), its dimensions Jm or EVÄ; PE - effective spatial-energy parameter, its dimensions J or EV; Ε - ionization energy, W - bond energy; Z* "nucleus effective charge; Ζ - atom nucleus charge; n* - effective main quantum number; q - effective atom nucleus charge, equal Z*/n*; η - main quantum number; rij - amount of valence electrons; R - Rydberg constant; R - atom radius; r, - orbital radius of given orbital; e- elementary charge; λ - radiation wavelenght; φ and X - dimensionless variables in Thomas-Fermi equation; V - atom total potential; U - total energy of valence electrons in atom statistic model; β - electron density of i - valence orbital at the distance r, from the nucleus D(n,l,r) - radial wave function Rr(n,l,r); X - electronegativity; a - quantitative criterion of interstructural interaction; ρ - solubility of one component in another one (at%, mol%); pmax - maximum mutual solubility of components; Tm - melting temperature (K); Κ - coordination number; ΔΗ - mixing heat.

15 Chapter one Problems of isomorphism and phase-formation 1.1. Theoretical studies of isomorphic replacements 1.1.1. Definition of isomorphism as structural conformity principle Historically, the notion of isomorphism underwent some changes. According to E. Mitsherlish [3] isomorphism - phenomenon of compliance of identically shaped crystals with analogy of their composition stehiometry. According to H. Grimm [4] isostructural substances forming solid solutions should be called isomorphic. The most modern notions of isomorphism are given in the works by E.S. Makarov [5] and V.S Urusov [6], E.S. Makarov gives the following definition of isomorphism - phenomenon of statistic inter-replacement of atoms (ions) of two or several elements, as well as two differently charged ions of one element in the given correct system of points of crystalline structure of variable composition phase. Phases with variable amount of atoms in elementary cell (i.e. solid solutions of penetration and deduction) are not considered as isomorphic mixtures of components. V.S Urusov [6] holds simple but modern crystal-chemical definition: isomorphism property of atoms of different chemical elements to replace each other in crystalline structures if the units (atoms, ions and their groups) composing the crystal have similar dimensions and character of chemical bond. It is also necessary to mention the correlation of such notions as isomorphism and solid solution of replacement. V.S Urusov shows that these terms used as synonyms reflect two approaches to understanding the phenomenon: crystal-chemical and physical-chemical and do not completely coincide with each other in content and application field. But when studying the isomorphism statics these differences are not significant and therefore both notions can be applied as synonyms (this will be used in the given research). In his work T. Penkalya [7] writes about this: "Formation of crystalline solid solutions (isomorphic mixtures) is used to be considered as the condition of isomorphism manifestation ..."

16 1.1.2. Development of isomorphism theoretical conceptions Great contribution to the development of isomorphic conceptions was made by the master thesis prepared by D.I. Mendeleev [8] "Isomorphism in connection with other relations of crystalline shape to composition" (1856) and the work by V.l. Vernadsky [9] "Paragenesis of chemical elements in the earth's crust" (1910). Exceptionally important was the teaching of N.S. Kurnakov [10] on phase equilibriums. Principles of physical-chemical analysis developed by N.S. Kurnakov [10] gave the possibility to broadly investigate the homogeneity boundaries, lattice periods and properties of solid solutions of replacement [10]-[14]. V.M. Goldshmidt [15] and A.E. Fersman [16] classified the types and formulated the basic rules of isomorphism that are widely used now. Here belongs a well-known Goldshmidt's rule: isomorphic mixtures are formed in wide ranges at temperatures far from melting points if the radii of interchangeable structural units differ for less than 15%. A.E. Fersman [16] developed systems of energy contributions of single ions to crystalline lattice energy and found a series of qualitative isomorphism aspects. But such approaches did not provide with quantitative estimation of isomorphism, in particular - during the calculations of temperature dependences of isomorphic replacements. In 30-ies thermodynamic theory of quantitative description of solid solutions started to be developed. Based on recording a mixing energy R. Becker [17] derived a general equation of decay curves. Ya.I. Frenkel [18] created a general theory of crystallization, decay and regulation of solid solutions in statistic-thermodynamic approach. In researches of V.A. Kirkinsky [19] and A.A. Yaroshevsky [20] the mixing heat was considered as a basic characteristic of isomorphic mixture stability. B.F. Ormont [21] and N.N. Sirota [22] developed a theory of phases with variable composition. In 1923 H. Grimm and K. Gertsfeld [4] made the first attempt of quantitative calculation of lattice energy for solid solutions of alkali-haloid salts. In energy theories of ionic solutions presented by Wasastierna [23] and Hietala [24] the approaches based on the analysis of changes in crystalline lattice energy

17 depending upon composition were developed. But the field of applying this theory is now limited only by alkali-haloid solid solutions. Darken and Gurri [25] took into account both dimensional factor and electronegativity factor to estimate system maximum solubility, and used the diagram in coordinates "electronegativity difference -

atom diameter" to predict solubility

character. In this diagram they marked ellipsis X (with the center in the place of element location picked out as a solvent) with semi-axes approximately equal ± 0,4 units of electronegativity difference and ± 15% difference of diameters of solvent atom and component solved. Elements that got into that ellipsis as stated in [25] can form broad areas of solid solutions with a solvent, those elements that did not get inside the ellipsis produce only very limited solid solutions. The application of this method for 850 elementary systems with the data on phase solubility diagrams gave the following results. In systems for which the existence of wide regions of solid solutions had been predicted, those predictions were realized in 61.7% of experiments. The predictions regarding the existence of limited solid solutions were realized in 84.8% of experiments. Consequently, for all systems the percent of correct predictions equals 76.6. For comparison, it is necessary to mention that a criterion based only on one dimensional factor appears to be somewhat better when predicting the limited solubility (gives correct results in 90.3% of experiments), and much worse - when predicting wide solubility regions (reliability roughly 50%). Thus, the application of integrated parameter (electronegativity - atom radius) leads to a more correct prediction in most cases. "However, it is necessary to underline that after classical works by G. Jones and S.T. Konobeevsky the electron theory of metallic solid solutions has not advanced far and today general quantitative theory of solid solutions with electron approach has not been created yet. Existing theories have neither predictive force nor the possibilities of quantitative estimations of isomorphic microadmixtures. Till now, for instance, it is unclear why Cu and Au, as well as Mg and Cd form continuous solid solutions, but in analogous systems Cu - Ag and Mg - Zn rather limited solid solutions or compounds are formed" [5].

18 Further development of Wasastierna - Hietala theory are the works by V.S. Urusov [6], [26] - [29] on energy theory of isomorphism in which the degree of ionicity-covalence and experimental inter-atom distances are considered instead of ion radii taken from tables when calculating mixing heat. This theory also uses an integrated parameter of energy and dimensional characteristics of the systems. Thus, the extension of solid solutions according to energy theory of V.S. Urusov is connected with mixing heat (ΔΗ CM):

AHCM =

aA2+b(AE)2 Κ

where AR/R - dimensional factor, AE- difference in the degree of ionicity of initial compound bonds. This theory gives a good result if the value of AE is known and interatom distances in the structures of initial compounds are isotropic to a maximum extent. For example, using an integrated dimensional parameter instead of AR/ R:

XiWl+XiWl

where Vj and V2 - volumes of elementary cells of initial compounds, Xi and X2 - their molar shares in solid solutions being formed, the authors [30] calculated the maximum decay temperature for solid solutions in systems Sr3(V04)2 -Ba3(V04)2 and Mg3(V04)2Zn3(V04)2 and got the values 432K and 445.5K, respectively. In the first case the calculations are not in contradiction with the experiment [30] and unlimited solid solutions exist in the system, but in the second case the miscibility breach exists till the appearance of liquid phase. Obviously, the value AE of magnesium and zinc orthovanadates used in the calculations is wrong. Actually, to calculate AE the electronegativity values of groups and compounds can be applied [31], [32], but it is not always practicable since the information on the latter is either not available or has significant differences - as stated by several authors [33] - [38]. Therefore, V.S. Urusov [6] concludes: "...theoretical methods that can be currently applied are only the first approximation to solve a complex problem of atom chemical interactions in solid mixtures. The development of deeper approaches mainly depends on our knowledge of the theory of chemical bond in crystals, which is not accurate enough yet and does not

19 have rather simple and general ways of estimating inter-atom interaction energy even for clear crystals with non-ionic character of chemical bond. Energy model of solid solutions, in principle, is not able to overcome these difficulties and imperfectness of the theory with respect to which it is derived".

1.2. Basic phase-formation factors Despite of exceptional meaning of stable system formation under atom isomorphic inter-replacements, such processes are only phase-formation special cases in general. Actually, besides replacement solid solutions there are also deductionpenetration solid solutions the practicable importance of which cannot be overestimated. Therefore, the problems of phase stability and metastability of any material components are critical issues of material science. "Problem of phase stability in metals and metallic compounds is one of the most crucial problems of metal-physics and the whole theory of solids" [39, p. 6]. Since phase-formation nature is of universal physical-chemical basis, parameters influencing the structure stability are general both for all solid solutions (of different types) and chemical compounds. Currently several factors determining the formation of crystalline structure of the given composition are known.

1.2.1. Geometrical factors Laves [40] found out that metal structure is usually determined by several geometrical principles, the main are: 1) densest space filling, 2) highest symmetry, 3) formation of the biggest number of bonds. In Laves's model a simplified conception of atoms is used, atoms are considered as incompressible balls that is unsuitable to analyze metal structure since one of the most characteristic properties is an increased atom compressibility [40]. According to W. Pirson [39] so-called "diagrams of next-door neighbors" are more useful (especially to analyze complex structures). This method is based on the fact that effective dimensions of atoms (e.g. double phase of AxBy) can be changing till the contacts A-A, Α-B, B-B are formed. At the same time a graphic dependence of some given

20 deformation parameter upon the relation of diameters of atom-components is created, which represents a straight line. But such diagrams are built separately for each variant of narrow class of structures.

1.2.2. Factor of chemical bond One of the conditions controlling the structure stability is a factor of chemical bond. The character of isomorphic replacements depends upon the type inter-atom bond of inter-replacing components. "Two or several substances can form solid solutions only if the nature of inter-atom bond in them is identical or analogous" [5]. The availability of metallic bond in intermetallides does not usually obstacle the isomorphism of elements forming them in other systems. So, Κ and Na form Laves's phase KNa2, but, nevertheless, the perfect isomorphism of ions of these elements is observed at high temperature in silicates (feldspars) and in halogenide systems. All that complicates the issue of even qualitative influence estimation on phase-formation of inter-atom bond character.

1.2.3. Electrochemical factor (electronegativity) Apparently, there

is no single-meaning

definition of

electronegativity.

Electronegativity should be considered as a parameter expressing atom tendency to attract electrons in a specific solid [31]. According to such definition, electronegativity is a relative measure of interaction between atoms of one type with atoms of another type in given solid. If electronegativities of two components of binary compound differ considerably, there is a strong tendency to form a compound. At the same time the regions of solid solution existence and homogeneity interval of intermediary phase are very limited. Electronegativity value depends on oxidation state and changes considerably with ion valence change. At the same time, electronegativity depends very weakly upon the bond type and specific peculiarities of crystalline structure, coordination, etc. Different

21 methods of electronegativity detection (thermal, spectroscopic, quantum-mechanical, etc) give consistent results. Both factors - chemical bond and electronegativity - are connected sufficiently and have an important meaning for crystalline structure formation. But quantitative obtaining of such dependence is rather complicated and inaccurate since it is determined by the level of chemical bond theory development.

1.2.4. Dimensional factor According to W. Pirson [39] "influence exerted by relative dimensions of atomscomponents upon the compound composition, its crystalline structure (structural type) and lattice periods is meant under dimensional factor". V.M. Goldshmidt [15] found such a dimensional criterion favorable for isomorphism when ionic radii of atomscomponents differ less than 15% (to lesser radius). An analogous criterion was found by Um-Roseri [11] for metallic systems (in this case element atomic radii are compared). But this rule belongs to contradictious, but not asserting rules. This means that if 15%limit is exceeded, the existence probability of wide regions of solid solutions is very small, but if the difference of initial dimensional characteristics of atoms is under 15%, this means only the existence permissibility of vast regions of solid solutions; actually, they can be not formed.

1.2.5. Factor of electron concentration Electron concentration (e/a) is an average number of valence electrons (e), coming to one atom (a). In 1926 Um-Roseri [11] notices that electron concentration of one-type phases is the same in all systems. So, β - phases with volume-centered cubic (VCC) lattice and β - phases with a primitive lattice (CsCl type) are formed at electron concentration close to 3/2, phases of γ -brass type at e/a«21/13, and £ - phases with hexagonal densely packed (HDP) lattice - at e/a« 7,4. The explanation of these two values of electron concentration was given by Jones [12] based on the conceptions of Brillouin zones. In Brillouin zone there is a place only for a certain number of electrons at the given structure type. Additional electrons can be built into the lattice only with

22 additional energy consumption. Consequently, more advantageous and more stable is a structure of a new type with higher maximum concentration of valence electrons. After the papers by Um-Roseri and Jones were published it was found that compositions of many metallic phases show at least partial dependence upon electron concentration. But the relations between the extension of solid solutions and e/a - are not fulfilled for them. The latter circumstance shows that electron concentration factor is not a single and even not a major factor of metallic system phase-formation.

1.2.6. Factor of atom chemical indifference This criterion was introduced by E.S. Makarov [5] in 1968. If the forces of similar bonds of atoms A-A and atoms B-B exceed the forces of dissimilar bonds A-B, than neither chemical compounds nor solid solutions are formed in the system, and the components are isolated into independent crystalline phases. In this case, components A and Β are chemically inter-indifferent. E.S. Makarov thinks that "chemical indifference of atoms is a main physical-chemical condition determining a fundamental possibility of their isomorphic interchangeability during the formation of solid solution crystals". Electronegativity value is proposed as a semi-quantitative characteristic of chemical indifference [5], But electronegativity notion itself (as mentioned already) is not singlemeaning, and the application of this characteristic is not always practicable, especially for complex compounds. Besides, the fact of chemical indifference of atoms A and Β does not mean their obligatory isomorphic miscibility in elementary system Α-B, since other factors (that cannot be always estimated) can prohibit or limit this miscibility.

1.3. Some modern theories about phase-formation problems 1.3.1. Pseudopotential theory Nearly half a century passed since the first works by Um-Roseri and Jones were published. "At their time some of those theories played an important role in the development of physical metallurgy, but nowadays they considered to be chains impeding the progress. At the moment we have to regrettably underline an irresistible devotion of some leading scientists-metalphysicists and metalchemists to old views

23 having existed in physical metallurgy for nearly half a century. A significant progress that has been seen in pseudopotential theory in a few recent years makes us hope that the situation in this field will change for the better" [39, p.7]. The basis of pseudopotential method is a fact that in metals an effective potential (pseudopotential) influencing electrons in conductivity zone from the lattice of ionic skeleton is weak, to some extent. In order to describe the state of electrons in a metal the theory of disturbances by pseudopotentials can be applied. Thus, pseudopotential is an effective potential influencing the conductivity electrons and representing the function with adjusting parameters. Pseudopotential theory is based on three initial theses [41]: 1) application of self-consistent field method; 2) splitting of electron states into inner shells ("core") and states of conductivity zone, taking into account that wave functions of inner shells are greatly localized. Normally the latter circumstance significantly limits the range of metals that can be described with the help of theory presented; 3) application of disturbance theory for electrons in conductivity zone. To find a stable structure of given element the atomic volume is taken as constant and energies of different structures are compared at given atomic volume. In such a way pseudopotential theory calculates the stability and basic parameters of several structures (for sodium, magnesium, aluminum, beryllium and some transition metals and intermetallic compounds as well). For many other metals and ordered phases the calculation results do not correspond with experimental data (e.g. for lithium and zink). Such deviations are mainly connected with the necessity to choose more optimum values for pseudopotentials, as well as with the fact that during the calculations the atomic volume of any structure is taken as unchanged, but actual phase transitions are followed by considerable change in their volume. At present, method of empirical and model pseudopotential starts to be more widely applied [42], to calculate zone structure of semi-conducting solid solutions of replacement as well [43], [44], At the same time, the application of ideal crystal zone structure for solid solutions of replacement is substantiated based on pseudopotential notions. Since the difference of pseudopotentials between atoms A and Β is usually

24 much less than the pseudopotential values of atoms themselves, the influence of periodic potential part can be considered as small disturbance and, consequently, ordinary methods of disturbance theory can be used as it is done, for instance, for crystals with defects. Further, using the link between thermodynamic characteristics of solid solution and lattice parameters (αι and

ω η u ν >
0

since Α λ - — , then: mv

d2Po

, ifo

dx2

7 2

λ

h

(19)

or:

dx2

where Ek

mV1

h1

- electron kinetic energy.

Shredinger's equation for stationary state in coordinate x: d2V dx1

, 8n2m.

59 From equation (19) and Shredinger's equation for stationary state in coordinate χ it is seen that wave function numerically equals spatial-energy parameter P0, approximately: P0* ψ and in general case it is proportional to it: Ρ0~Ψ. Thus, Po-parameters, as Ψ-function, have wave properties and therefore, superposition principles and linear character of addition equations and P-parameter changes must be fulfilled.

2.8. Wave properties of P-parameter and addition principles of Pparameters Since P-parameter possesses wave properties (by analogy with Ψ'-fiinction), in the process of structural interactions the regularities on interference of corresponding waves should be mainly fulfilled as well. Interference minimum, fading-out of oscillations (in antiphase) takes place if the difference in wave motion (Δ) equals an odd number of semi-waves: Δ = (2« + 1)^ = λ|Η + 0

where η = 0, 1,2,3, ...

In conformity with P-parameters this rule means that interaction minimum takes place if P-parameters of interacting structures are also in "antiphase". That is the interaction of either differently charged systems or heterogeneous atoms (e.g. during the formation of valence-active radicals CH, CH2, CH3, N 0 2 . . . and others) takes place. The difference in wave motion (Δ) for P-parameters can be evaluated via their Pi relative value ( γ = — ) or via the relative difference of P-parameters (coefficient a), Pi which at the interaction minimum produce an odd number:

-^HHf-

60 Table 4 Spectral regularities of multiplet transitions

Atom

Transition

C

2S 2 2P'2S'2P 2

C

2S228'2Ρ'

Ν

2S22P22S'2P 3

Ν

2S 2 2P'2S12P2

0

2S22P32S'2P 4

0 0

2S22P22S'2P 3 2S 2 2P'2S'2P 2

ΔΡ0 (nS2-nS')

λ(Α)

11,368

1335

'-I 2

323392

11,368

977

2=2 1

345054

22,954

1085

18,834

991

u 2

351527

29,210

834

2 1 4 2

355794

25,295

835

2 3

356186

Po(2P)= 11,858

20,730

790

u 2

339489

14,524Po(2P')= 9,0209=5, 5,8650 5031 14,524Po(2P')= 9,0209=5, 5,8650 5031 17,833Po(2P3)= 10,709=7, 15,830 124 Po(2P2)= 7,124 11,710 21,466Po(2P> 12,594=8, 20,338 872 Po(2P3)= 8,872 16,423 8,872

(ΣΡ) 2 λ— NK (eV2A3)

ΣΡο (eVÄ)

PoinP"1)

NH

NK

2 3

381114

Al

3S238'3Ρ'

12,253Po(3P')= 7,9149=4, 5,840 3381

10,178

1670

u 1

364004

Si

3S23S'3P'

15,7119,8716=5, 8394

12,513

1206

2=2 1

377635

Po(3P')= 6,6732

61 Pi 1 — = P\ 2

When n=0 (basic state):

It is interesting that for stationary levels of one-dimensional harmonic oscillator the energy of these levels ε = hv{^n + ^ j , i.e. in quantum oscillator, in contrast to classical, the least possible energy value does not equal zero. In given model the interaction minimum does not produce energy equal to zero corresponding to the principle of adding reverse values of P-parameters - equations (15 and 15b). Interference maximum, intensification of oscillations (in phase) takes place if the difference in wave motion equals an even number of semi-waves: λ A = 2n— = λη

or

Δ = λ(η + ΐ)

In conformity with P-parameters a maximum intensification of interactions in the phase corresponds to the interactions of similarly charged systems or systems homogeneous in their properties and functions (e.g. between fragments or blocks of complex organic structures, such as CH2 and NNO2 in octogen). Then:

γ

= Εΐ

= η + ι

( 2 0b)

Pi - in some cases (usually -

for "exchange" interactions with electron density

redistribution), or: a

= « + 11

ao (usually for kinetics of chemical reactions - see Chapter 7). Similarly, for "degenerate" systems (with similar values of functions) of twodimensional harmonic oscillator the energy of stationary states is as follows: ε = hv(n +1) In accordance with this model the principle of algebraic addition of P-parameters corresponds to interaction maximum - equations (9,10,9a). If n=0 (basic state) equation

62 (206) gives P2 = Pi, or interaction maximum of structures takes place if their Pparameters are equal. This condition will be used as a main condition of isomorphic replacements (see Chapters 3-7). Besides, it will be shown (Chapter 7) that relations of P-parameter fragments in cyclic organic structures, in accordance with equation (206) produce roughly even numbers (1,2,3,4). Similarly, while calculating the activation energy of chemical bonds ct the relation — can produce different but integral values (for given reaction). ClO

2.9. Some additive properties of P-parameter Based on initial rules Po-parameter of i orbital is found by equation (7). The resulting interaction of SEP of all atom orbitals is determined by algebraic addition rule of such Po-parameters - by equation (9a). Thus, the resulting P0-parameter of atomic structure determining the interaction of lS-orbital with all other orbitals is found by the following equation: m

P =X\Pls-aZx2Pi

(21)

i=1

Where: Xi and X2 - coefficients taking into account screening effects; Pis Po-parameter of lS-orbital; Pi - Po-parameter of each subsequent orbital; α proportionality coefficient that (as seen in the calculations) equals N, where Ν - number of orbitals starting from 2P orbital and further, i.e. Ν - number of interactions between orbitals (except for IS orbital). For all 2S- and 2P-elements of 2nd period N=l; for 3Selements of 3d period N=2; for 3P-elements of 3d period N=3, etc. Minus sign in equation (21) characterizes the interaction direction (repulsion). In all calculations the computation data from [71],[105],[106] are applied. At the same time, for four elements (P,S, CI, Ar) internal orbital radii are used as in [79]-[84]. The data obtained with the help of ESCA method are taken as bond energy value (Wj) [110]. Other initial data for orbital energy of electrons are marked in the tables with *

63 The calculations revealed [117] that if we take coefficients X\ =

X 2=—

-

and

^ , the resulting P-parameter changes from element to element taking

the values Ρ = 4,799Z. Here: Ζ - element order number; value 4,799 = PH equals Poparameter of hydrogen atom; σ - screening number. Then equation (21) will be as follows: PHZ = 4,79994Z =

Ζ

ΡλΞ

-±-Σ?-Pi Ν

(22)

Ζ

Thus, from equation (22) we can see: interaction of Po-parameter for lS-orbital and average Po-parameter of other orbitals is a number divisible by P0-parameter of hydrogen atom. The correctness of this relation is confirmed with calculations for 14 elements (Table 3, Appendix I). The computation methods are given in Table 4, Appendix I.

2.10. P-parameter as an objective characteristics of electronegativity The notion of electronegativity was introduced by Polling in 1932 as a quantitative characteristic of atom ability to attract electrons in a molecule. Currently there are many methods and several scales to calculate electronegativity. Discussions around electronegativity notion and its measuring methods have not resulted in definite answers so far, though the notion of electronegativity is widely practicable in chemical and crystal-chemical researches. Since thermal-chemical, spectroscopic and other methods provide with consistent results, this allowed S.S. Batsanov [31],[102] to develop a system of some averaged recommended values of electronegativity. Let us show that P-parameter can be successfully used as an objective characteristic of electronegativity. [118]. Based on P0-parameter physical sense we assume that electronegativity equals effective energy of one valence electron for element lowest stable oxidation state:

64

where R - atom radius (depending upon bond type - metallic or covalence), and Poparameter value is calculated via bond energy of electrons following [74] (Appendix 3). Figure 3 in denominator of equation (23) reflects the fact that probable inter-atomic interaction is considered only by bond line, i.e. on one of three spatial directions. Computations of element electronegativity by equation (23) are given in Table 1, Appendix 1. For some elements (that are characterized by the presence of both metallic and covalence bonds) computation of electronegativity (X) is made in two variants - using the values of atomic and covalence radii. Equation (23) cannot be applied for zero group elements, since, in this case, the notions of electronegativity and covalence radius for inert gases basically become senseless. The deviations from conventional values of electronegativity in calculations for equation (23) do not exceed 2-5%, in most cases. Thus, a simple relation (23) quite satisfactorily estimates electronegativity value within the limits of its values based on data by Batsanov and Poling. Vast opportunities of P-parameter for determining the electronegativity of groups and compounds, since P-parameter can be rather easily (based on initial rules) calculated both for simple and complex compounds, is the advantage of such an approach. At the same time, peculiarities of those structures can be taken into consideration, and consequently, it can be possible not only to characterize but also to predict important physical-chemical properties of those compounds (isomorphism, mutual solubility, eutectic temperature, etc). Let us show, for instance, how it is possible to determine the electronegativity of crystalline structures (XK) using P-parameter notion. In paper [119] Χκ values were obtained when averaging thermochemical and geometrical values that, in turn, were calculated by thermochemical data for crystals and with the help of covalence radii taking into account the repetition factor for bonds in crystal. With the same purpose P-parameters of all valence sublevels of atom (P'0, P"o, •• •) are considered in the approach proposed by us based on the following equation:

65 Wfi)*, 2R(nx+n2)K

(23a)

where ni and n2 - number of electrons on given valence sublevels; Κ - proportionality coefficient that is a constant value for a broad class of structures. As the calculations revealed the value of this coefficient for all elements (except for Na, K, Rb and Cs) within the limits 1.5 - 2.0. For instance, for d - elements the value Κ = 2 corresponds to the lowest, and Κ = 1,5 - highest stable oxidation state. For intermediary oxidation states interpolated values of Κ were taken. For S, p-elements Κ value was taken as equal to 2,0; 1,88; 1,75; 1,63; 1,5 for second, third, fourth, fifth and sixth periods, respectively. For S-elements Κ = 2 for all elements of the second group and for elements of 1 B-subgroup. And only for elements of 1 Α-subgroup Κ changes from 2,0 to 3,0 (from Li to Cs). The calculations by equation (23a) are given in Table 5, Appendix I, from which it is seen that Χκ values calculated are in satisfactorily accordance with corresponding values by [119], Thus, the conception of P-parameter allows to objectively evaluate the electronegativity both for neutral atoms and crystalline state.

66

Conclusions on chapter two

1. Postulated are the principle of adding reverse values of energy components of differently charged structures based on which the conception of spatial-energy parameter (P-parameter) is introduced and rules of changing P-parameters depending upon systemic character of inter-atomic interactions; it is shown that principle of adding reverse values of P-parameters is an algebraic addition of subsystem energy capacities. 2. P-parameter is physically substantiated. It is found that P-parameter is a direct characteristic of atom electron density at the distance r, from the nucleus. From the analysis of these calculations the adequacy of P-parameter (SEP) values and energy of valence electrons in atom statistic model is revealed. Therefore, the introduction of rather easily calculated SEP into the calculations can facilitate the bypass of ThomasFermi equation complexity in each specific case. 3. Calculations of electron density in atom at the distance r, from the nucleus based on atomic functions (by Clementi) are in accordance with its values calculated with the help of P-parameter. 4. Simple dependence of SEP upon the module of maximum values of ψ-function radial part is found, wave equation of P-parameter is given, its wave properties are revealed. 5. Dependence of spectral atomic characteristics upon the corresponding P-parameter values is obtained. 6. Some additive properties of P-parameter are shown. 7. It is proved that element electronegativity equals one-third of atom valence electron PE-parameter (calculated via bond energy). It is perspective to apply PE-parameter for estimating the electronegativity of crystalline structures and atomic groups and compounds. 8. P-parameter is calculated rather easily both for elementary and complex systems.

67 Chapter 3 Experimental evidence of spatial-energy criterion of isomorphism and solubility

At present a number of factors influencing isomorphic interchangeability of atoms are found: chemical indifference of atoms, dimensions of atoms, similarity of inter-atomic bond, isostructuring of crystals, etc [5],[6],[118]. However, still there is no strict quantitative measure of atom indifference, the application of dimensional factor results in many contradictions. The criterion of crystal isostructuring alone can be neither qualitative nor quantitative measure of isomorphism. For instance, metallic aluminum forms continuous solid solutions with none of numerous metals isostructural with it. The established dependence of isomorphism simultaneously upon dimensional factors and electronegativity appeared to be rather successful, though this method by Darken-Gurri gave, in the average, only 76.6% of coincidences with the experiment. In this research there is an attempt to establish a direct dependence between isomorphic replacement in crystals and spatial-energy characteristics of atom orbitals of interacting structures with the help of P-parameter.

3.1. Elementary systems of Μ' - M" type As it was already discussed in Chapter 2, P-parameter is an objective characteristic of electronegativity and directly determines the electron density (/?,) in atom at the distance r, from the nucleus. According to formula (13), SEP quite accurately (in most case with an error less than 1-2%) conveys well-known solutions [112] of Thomas-Fermi equation for interatomic potential V, of atoms at the distance r, from the nucleus. Since SEP comprises basic constants characterizing the state of atom external electrons it is possible to correlate (and consequently to predict) many physicalchemical properties of compounds with its help. When a solution is being formed, the common electron density is established in contact areas of atomic spheres. In this regard, the solubility process is followed by the

68 redistribution of electron density between atoms-components and transition of part of electrons from one atomic spheres into another, thus conditioning the system energy increase and positive solubility thermal effect (see formula of V.S. Urusov [6] of ΔΗ dependence upon electronegativity difference). Apparently, when electron densities in free atoms-components of solution are close at distances of orbital radius r, (with a little deviation from the radius of atomic sphere), the transition processes between adjacent atomic (cationic) spheres are minimal and, consequently, they contribute to the formation solid solution. Thus, the task to estimate the solubility degree, apparently, comes in many cases to a comparative estimation of electron density in free atoms (at distance r,) participating in the formation of solid solution, that can be fulfilled in the frameworks of atom statistic theory. Let us show, however, that when a rather easily evaluated SEP is introduced into the solution, it is possible to bypass the complexity of solving Thomas-Fermi equation in each specific case. For that, based on equation (14a), let us consider that the comparison of electron densities of atoms participating in solution formation comes to matching (or difference determination) of values Po/r,·. The more the difference of the latter, the more favorable is the formation of solution from energy point: in accordance with equation (20b) the interaction maximum occurs if values of P-parameters of interacting structures are equal or close. In this regard, maximum solubility estimated via relative difference of parameters Po/r, of isomorphic replacement coefficient a , is determined by the condition of minimum value of a : P'o/r

a=

-P"o/r 2 ' 100% (Fo/^+F'o/r,)/ 2

(24)

If simultaneously consider "15% difference in atomic diameters" for isomorphic replacements in elementary systems of M'-M" type, formula (24) can be simplified and brought to the following appearance: a=

PM') following equation (24a) were made using initial data for bond energy of electrons with the help of ESCA [110]. Results of such calculations that do not consider a temperature factor (for several hundreds of systems) are given in Table of Appendix 2. Since there are no ESCA data for valence orbitals of a number of elements, interpolated values were applied. The calculations by equation (24a) allow making a qualitative or semiquantitative estimation of total mutual solubility of components but it appears impossible to predict a relative contribution of each component. The application of equations (25,26) given below that empirically take into account a temperature factor, gives the possibility to obtain rather objective quantitative results to evaluate the solubility of each component. Using initial data on bond energy of electrons by [74], a maximum solubility in systems of M'-M" type were determined by the condition of minimum value of relative difference of P-parameters of atoms-components based on equations: α=

Ρτ

~ Ρ . Ε -100% (Ρτ Ρκ)'2

(25)

+

a=

Ρ τ Ρ ε

-100%

(26)

(iVP.V2

Po R in+1) f ρ =E-L r T i±10 a

(27)

(28)

where: R - atom radius; T'm and 7"m - melting temperatures of components; a = 1,1 at plus sign and a = 0,9 at minus sign in equation (28). Values of coefficient "a" are determined by the condition PT = P E at Tm = Tm • Expression (28) found empirically characterizes a temperature dependence of PE-parameter. Out of two values of α a minimum value characterizes a maximum solubility value of first component in the second, and maximum - the solubility of second component in the first. The direction of maximum solubility was determined when comparing values Q of both components, where

70 Tm/ ar;

ι ±10

N

/ r m

(28a)

Here, parameter P0 is calculated for one valence electron. If external electrons belong to two (or more) valence sub-levels (by orbital quantum number - 1) their average value is found. At the same time the direction of maximum solubility was taken as corresponding to the direction from Q maximum value - to minimum. Calculations made for several dozens of metallic systems (Table 5) allowed designing a common figure-nomogram of quantitative solubility value (p) dependence upon the values of coefficient α - Fig. 2,2b. Fig. 3 shows another option of this nomogram as a linear dependence lgC=f(a), where C - solubility in units - mols of substance to be solved per 1 mol of solvent. At the same time the following method for registering inter-atomic interactions of components was applied. First of all, the interactions of all valence electrons responsible for the manifestation of stable oxidation states of the element were considered and calculated by equations (25-28) of relative difference of corresponding P-parameters (coefficient Oy). Further, they were separately computed as additional interactions based on electrons of most external energy sublevel (if the number of energy sublevels in atom is over 1) and the value of coefficient α for such interaction was calculated. In all cases the number of valence electrons of both atoms-components taken into account was considered as either similar or equal to the value of stable oxidation state of these elements. If values of coefficient ay(34,5-38), an average value of coefficients a y and a was found for all interactions. The resulting solubility - ρ was determined based on the nomogram using this value a av . In such way the interactions between similar orbitals were calculated (by quantum number {). When dissimilar orbitals interacted, the average value for ρ for any a and a was found.

72

i5 p OH C A Λί 1ο & . M M i> m,0] w t Z 7 ω S S e.e — /-Γ

0,43250 0,47397

ο ο ω t/3 Γ-»

£ ® ο

Li-Cs

σ 00

0,65972 0,74731

\

2,815

— (Νr—1 cn 00 ι 1 CN r-H Q. Q. —

Li-Rb

A

0,6089 0,63796 0,43716 0,46947

äg.

2,063

S

0,70372 0,74731 0,67981 0,74731

Ö Ο

Li-Na

t=

orbitals

•Ό A

Prediction Solubility direction

£

— IΗ

t'Z ο'ε

ο 1 ο ο

orbitals

I ® o Si m a α sä 3 '-3 c

ο ο (π)'ι 0

s i 2 4> Ξ

Η

es

ci

α a

CN

CN CN

ΊΛ

•Β

7z> "«3 CN CN

CN CN 3,311

3,311

0,95535

CN CN

0,90154

ΊΛΊΛΊΛ

CN (Z5

CN or) τι·

CN CN CN CN « SS

οι t/3

m

u

«

t ce υ

t 00

2

CN

CI

ΪΛ

'S· r-^ OO VI 00 en Ο* "3·

3,2340

40,1

41,4

CUD

3,2340

4,792

4,792

s

3,2340

1,4349

1

13,7

+23) =9,5

1/3(2,15+3,4

0,78

0,6) =13,7

t-o"

2,8140

CN 111

J

VO o"

1,7660

PH 00 J P 0,3717

3,1631

1/3(39+1,4++

29,5

1

CN

2,1475

CN

0,90094

ΊΛ 11,8

40,7

t

81,57

J

3,924

t υ «

1,0210

ω 03

2,1421

12,2 47,0

0-0,6

'•J

2,6414

2,753

73,0

40,7

78+3= =81

•J

0,90094

CN CN 1,2066

0,84468

2,753

32,1

8,06

21,8

•«a1 CN

0,90094

3,007

ΊΛ In Ίλ CI CI

0,74731

0,74731

1,5504 2,2159

3,450

1,90 41,7

J

3,007

1,0330

0,68943

3,450

t 00

1,0256

2,634

"c/5 " « J ο ci

r—1

γ-Fe-C

3 t

1,0256

t 1,3717

bO

0,74731

u-i

0,74731

νο 0,91544

OO

2,634

OS

0,8983

ο 00

0,8983

ο s

-

Ca-Mg

υ &

r-

Li-Al

ο

-

Li-Be

41

r-

Li-Mg

Ό "cη C ω

ο

C

S C οο

'S

ο

.8 Ό

.3

J•fo 8

"W" ι

ο

C

1

υ Ο ζ

81 It should be noted that if geometrical shapes of interacting orbitals are relatively similar, for instance, system Li(ls 2 2s')-Al(3s 2 3p 1 ), minor interactions even at a > 110 should be taken into account. If for main orbitals α >110, the resulting solubility was taken as "zero" if they had dissimilar geometrical shapes (system Na - At). The results of such calculations are given in Table 8. For some systems according to [5] the type of state diagram is shown: I - splitting, II - eutectics or peritectics, III - continuous series of solid solutions, IV - broad areas of solid solutions in both components, V - broad area of solid solutions in one of the components. Solubility calculations following this method are in satisfactory accordance with experimental data [120]-[126] - deviations in most cases do not exceed 5 at.%. At the same time continuous series of solid solutions occur at a

(29) (30)

where η - number of valence electrons on i orbital.

3.3. Experimental check of P-parameter application taking atom coordination into account For crystalline compound of m-elements we introduce PK-parameter as some P0parameter value for atoms-components averaged by phase composition. The averaging

86 is carried out based on the principle of adding inverse values with the help of normalizing factor A determined by the number of heterogeneous atoms (m). The structure factor is considered via coordination numbers of surroundings (Kj) of atom of i element and quantity of the latter (N,) in elementary cell. Then the formula for computing PK-parameter will look as follows [30],[145]-[150]: A· — = ρκ N&

+

N2PZ

+

+

N'0Pq

+

NmPS

(31)

Most easily normalizing factor A can be found for extreme case when all the components are identical, i.e. P'o = P"o = ... = Po; K,= K2 =... = Km= K; N,=N2= ... =Nm=N Then formula (31) will give the following: A

1

ftiK

Ρκ

Ν Po

Since the equality PK = P 0 must take place, A=mK/N. In those cases when formula (31) is used for interacting systems with similar crystalline structures and the result is determined via relative values of PK compounds to be compared, we can take A=1 as equal for them. Then: (32) + + + Ρ' Ν Ρ" Ν Ρ" JY 1 Κ "l'o 20 m Ο Consequently, the value of PK-parameter falling at each atom of the cell will be as Ρ 1

=

JΝ

px = &

follows:

(33)

where Ζ - formula number. Let us estimate the maximum solubility in complex systems in the same way as in elementary ones by the value of relative difference of P-parameters in structures: ρ

α=

κ~ρκ

. 200(%)

(34)

Pk+PK or α = Ρχ

Ρχ

PI+P:

• 200(%)

(35)

87 where α - coefficient of isomorphic replacement. Apparently, when values of P'K and P"K calculated by equation (31) are placed into formula (34), normalizing factor A similar for isostructural compounds will automatically go down, thus being equivalent to the computation of Ρκ by formula (32) (where A = 1). The regularities obtained were checked [30],[145]-[150] based on experimental material of several dozens of oxide systems M' x MyO z - M" x M y O z . The calculations made confirmed the individuality of isomorphic replacement coefficient α for wide class of structures. Using experimental data by four quasi-binary systems of pirovanadates of metals in the second group, in which the areas of solid solutions are found, the dependence p=f(a) was arranged. In accordance with this dependence continuous solid solutions are formed at α < 3 , 8 % for systems M 2 V 2 0 7 M2V2O7, where Μ, M' - bivalent metals. The increase from 3.8 up to 26% results in the decrease of area of solid solutions (Table 7). The solubility values and composition of double pirovanadates being predicted (M:M') are given in brackets, experimental data without brackets. Polymorphous modifications of M2V2O7 are designated in abbreviated form: ß-Mg, α-Ζη, etc. Double compounds in pirovanadate systems studied are found when values of coefficient are over 38%. In the area from 38 up to 136% compounds with the relation of bivalent cations (M:M') equal to 1:1 are formed, and over 136% - with the relation (M:M') equal to 1:3 (Table 7). The prediction of the existence of double pirovanadates was selectively checked based on the criteria developed. Compounds ZnBaV 2 0 7 , and CoSrV 2 0 7 are obtained with directed synthesis. Isomorphism of orthovanadates was investigated based on systems M'V0 4 -M"V0 4 , M ^ V O ^ - M ' ^ V O ^ and 2M'V0 4 M" 3 (V0 4 ) 2 . First, Po-parameter for each atom of structure is calculated following equation (29) - Appendix 3. Further, the values of PK and P x parameters are calculated based on equations (32,33) using initial data of atom coordination in the structure [151]-[153].

Table 7 Phase-formation character in systems Μ ί Υ ^ - Μ ' ^ Ο τ Μ

Μ'

a,(%)

pmax(mol %)

Μ

M'

Ni Sr y-Mg Mn Mn

Co Ba ß-Zn ß-Zn ß-Mg

1,1 3,8 3,9 4,0

(100) 100 90 (90)

Mn Mn ß-Zn ß-Mg

7,9

(80)

Ba Sr Ba Ba Sr

Cd

ß-Mg

10,5

70

Co

α-Ζη

10,5

ß-Zn α-Ζη Μη

Cd Ni Cd

14,3 14,7 18,4

α,(%)

M:M' (1:1) (1:1) 1:1 1:1

ß-Mg

127 129 129 130 132

Ba

Cd

136

1:1

(70)

Sr

Cd

138

3:1

55-60 (50) (35)

α-Ζη Co Ni

Cd Cd Cd

120,1 126,6 129,1

(1:1) (1:1) (1:1)

1:1

89 For atoms of calcium, strontium and boron average values of coordination numbers are taken for several atoms. Computations of Ρκ and P x are given in Table 8. The coefficient of isomorphic replacement for orthovanadates is calculated and compared with experimental data obtained with X-ray phase analysis (XPA) and the results are presented in Table 9. From those comparisons it is seen that continuous solid solutions (for systems ΜΎθ4-Μ"νθ4) occur at a < 6 % , organic solid solutions - at 15%>a>6% and isomorphism is absent at a>16%. For orthovanadate systems of M'3(V04)2-M"3(V04)2 type continuous series of solid solutions are available at a< 4,0%, organic solid solutions - at 4,0%2800 Κ, limited solid solutions at T< 2800 Κ Very low solubility

WC0,875 -VC 1 > 0

2,0561

2,2097

7,20

85

Up to (85-90)%

VC0,762 -WC,,0

1,7988

2,2517

22,36

6,3-8

UptolOmol %

WC0,875 -

ZrCi,0

2,1607

2,0334

6,07

100

ZrCo,806 ~ W C i ; o

1,6363

2,2517

31,66

0,7-1,0

WC 0,875 - N b C , , o

2,1535

2,2309

3,53

100

NbC 0,766-WC 1,0

1,7242

2,2517

26,54

2-4

100% at T>2960 K, limited solid solutions at Τ (28002900), limited solid solutions - at Τ < 2800 (2-3,5)at % Zr

57 at % at T=(2700-

3100)K, Limited solid solutions - at lower Τ Low solubility is supposed

118 Conclusions on chapter three Based on many calculations and physical-chemical analyses it is established that: 1. Equality of effective spatial-energy parameters (P-parameters) of valence orbitals of interacting atoms is a main condition of isomorphism, thus corresponding to equality condition of electron densities of these orbitals. 2. Relative difference of P-parameters of interacting atoms (coefficient a) is an estimation characteristic of maximum solubility both in elementary and complex systems that is confirmed with experimental data of about one thousand systems (M1M"; M'F2-M"F2; orthovanadates, quasi-binary vanadates, compounds with phenacite structure, etc). 3. In all studied complex systems based on solid solutions of replacement continuous series of solid solutions occur at < (4-6) %, organic solid solutions - at (46)% < α < (14-20)%, absence of isomorphic replacement at a> (20-25)% . 4. Nomograms of solubility (p) dependence upon the coefficient of structural interaction and isomorphism (a) are obtained.

119 Chapter 4 Temperature characteristics of solid solution expansion with the help of P-parameter (at given temperature)

In papers

[145]-[150] there are multiple

examples

demonstrating that

isomorphism character is determined by the relative difference of P0-parameters of valence orbitals of interacting atoms (coefficient a). This regularity is most accurately fulfilled for compounds melting temperatures of which are not much different. A compound temperature change results in changing its orbital and energy characteristics

that,

finally, determines

the

changes

in P0-parameter

values.

Conventional quantum-mechanical methods for calculating these effects are rather complicated and cannot be fulfilled in all cases. Let us show, however, that these difficulties can be bypassed with the help of equations selected empirically [161]-[163]:

Ρ,,ή^ρ Here

PT

-

P-parameter

value

at

given

m temperature

(T

or

T");

Tm - melting temperature of a compound (element). Values of coefficients 0,9 and 1,1 are determined by the following condition: PT = Ρ at Τ = Tm. In this case, symbol "P" denotes one of the three P-parameters: Po, Pc, PE· At the same time, equations (39,40) can be used for recording two different temperature changes of P-parameter. 1) P-parameters of two elements (compounds) should be better compared after the P-parameter of the element with maximum melting temperature (Tm) is reduced to the second compound melting temperature (with T"m < T'm) by equation (40). Thus, a, =

P+Pt ^ • 200%

(41)

120 Coefficient α characterizes maximum solubility at process temperatures T' < T"m. To characterize maximum solubility at process temperatures T"m < Τ < T'm it is necessary to reduce P-parameter of the second component to the melting temperature of the first component by equation (39). Then: α 2 = \ Ρ ~ Ρ τ „ 1-200%

(42)

Ρ+ΡΤ

In some cases, especially in most complex systems, it is efficient to apply formula (38) instead of equations (39,40) for temperature factor. 2) With the help of equations (39,40) it is possible to calculate temperature change of P-parameter as some characteristic to equalize the electron density of interacting structures ("inflowing" and "outflowing" processes). In this case, plus sign is added to the P-parameter with least value, and minus sign - P-parameter with maximum value, but if values of P-parameters differ by less than (3-5)%, the same computation equation is applied for both P-parameters. Maximum solubility in electron density redistribution process at given temperature can be determined with total coefficient of isomorphic replacement: a 0 = a + a, 2 where

(43)

\P'T ~ PT\

a =1

;r · 200%

PT + PT

P'T and P"T - values of P-parameters at given temperature T; value α, 2 is calculated based on equations (41,42) or (38). In equation (43) coefficient α, 2 takes into account the relative difference of Pparameters at melting temperatures of one component, and coefficient α - electron density redistribution factor at process given temperature. Let us apply such an approach to particular systems.

121 4.1. Estimation of mutual solubility of binary system components Basically, temperature characteristic of mutual solubility of solid solution components is the interpretation of an important part of system state diagram, theoretical estimation of which is impeded significantly. To estimate the solubility (p) of components at the process given temperature (T) the following equations were used: α0=ατ+α>

α/-) I

χ Λ

0,8722

Η Ö

11,42

Ρ

0,8227

00 II οΓ Ο — ι I ΰ + Η

48,31

r—I

Ο νο • 1

υ .>

1>

ο 58 u Ö I οο

Ι" ω υ >

JD Ν—' £ 13

no ο" ON m

rοο 00

rs I- ~ $ m m a. μ' £ Ίλ (Ν (Ν-^

136 Table 26 Aluminum solubility estimation in magnesium 2

do =

A1(3P') P+ = 1,0210

αχ

=α τ +18

lOO/oo

400

Mg(3S ) P_ = 1,3748 0,8680

1,4015

47,01

65,01

1,54

2

450 500 550 600 650 700 750 770 800 850 900

0,9874 0,9799 1,0262 1,0671 1,1031 1,1350 1,1631 1,1734 1,1879 1,2099 1,2292

1,3573 1,3182 1,2837 1,2532 1,2263 1,2025 1,1814 1,1737 1,1628 1,1463 1,1318

37,63 29,44 22,30 16,04 10,58 5,775 1,561 0,02 2,136 5,399 8,251

55,63 47,49 40,3 34,04 38,58 23,78 19,56 18,02 20,14 23,40 26,25

1,80 2,11 2,48 2,94 3,50 4,21 5,11 5,551 4,97 4,27 3,81

2,3 2,8 3,5 4,5 5,5 7 11 13 10 8 6,4

T(K)

p - aT%

(nomog.)

ρ -aT%

(exoeriment (2) (3,5) (6,5) -

(13)

(7,8) (2)

Notes: 1) Eutectics temperature - 71 OK (experiment), temperature of maximum solubility ~ 770 Κ (calculation). 2) a =18 - a effective value obtained with the help of nomogram based on ρ average value for the following interactions: Interaction

a

ρ -ar% (by nomogram)

3S'-3P'

10,7

47

3S2-3P'

29,5

5

3S2-3S2

43,64

3

3S2-3P'3S2

78,8

1,5

average

a -effective (by nomogram)

14,1

-18

p-aT%

137 Table 26 (continued) Magnesium solubility estimation in aluminum Mg(3S 2 ) A1(3P') T(K) P. = 1,3717 P + = 1,0181

(XT

do = =ατ+15,5

p-31%

p- aT%

100/cto (nomogra m)

(experime nt)

400

0,8660

1,3975

46,96

62,46

1,60

2,1

2,7

450 500 550 600 650 700 750 765 800 850 900

0,9253 0,9777 1,0239 1,0647 1,1007 1,1324 1,1605 1,1683 1,1853 1,2071 1,2264

1,3534 1,3145 1,2801 1,2497 1,2228 1,1990 1,1780 1,1722 1,1595 1,1431 1,1285

37,57 29,39 22,24 15,99 10,51 5,713 1,497 0,334 2,201 5,446 8,315

53,07 44,89 37,74 31,49 26,01 21,21 17,00 15,83 17,70 20,95 23,82

1,88 2,23 2,65 3,18 3,84 4,71 5,88 6,32 5,65 4,77 4,20

2,5 3,0 4,0 5,0 12,5 9,8 15,5 18 14 10 7,5

3,3 4,5 6,4 9,0 12,5 16,4 (16) (15,5) (13) (6,5) (4)

Notes: 1) Eutectics temperature - 723K (experiment), temperature of maximum solubility 765 Κ (calculation) 2) a = 15,5 - α effective value obtained with the help of nomogram based on ρ average value for the following interactions: Interaction

a

ρ -aT%

3S1-3PI

10,6

47

3S 2 -3P'

29,5

5

3S 2 -3P'3S 2

78,8

1,5

ρ -aT%

average

a - effective (by nomogram)

17,8

15,5

(Interactions S 2 ,-S ] 2 or S 2 -S' - in directions Mg—>A1, Ca->Li, etc. are not taken into account).

138 4.2. Systems of M'O - M " 0 type Systems o f binary oxides were considered [163] based on systems FeO - CaO and FeO - MnO. The solubility o f the systems at any given process temperature was evaluated with the help of the following equation: «0 = U where

Ρ τ

Ρτ

Ρ τ +

Ρτ

1 1 1 _ =_ +_ ; Pc Ρκ Ρα

+

Ρ c

Pc

Ρ C +

ΐ^-200 Pc) Τ„

=

Po Fk

ρα =

(48) Ρο ^ fa

In these equations: rk and ra - radii of cation and anion (respectively); PK and PA PE-parameters o f metal and oxygen atoms (respectively). The calculation data for structural Pc-parameters are given in Tables 27 and 28. Table 29 shows that isomorphic replacement coefficient α being calculated transfers the observed maximum mutual solubility of many systems M'O - M"0 quite satisfactorily. Table 30 contains the computations of coefficients ατ, do and 100/ao, which show that changes (depending on temperature) of coefficient 100/ao are cymbate to given state diagrams by [164], Maximum solubility experimental temperature in system FeO - CaO equals, approximately, 1400 K, and calculated - about 1470 K. The computation of system FeO - MnO was carried out in three variants. Based on oxide ionic model valence 4S 2 -electrons o f metal atoms move onto valence 2P-orbitals o f oxygen atoms. Therefore, the interactions of 4S 2 -electrons o f both metals with oxygen 2P4-electrons were calculated: [(4S 2 + 2P4)i - (4S 2 + 2P 4 ) 2 ] The calculated eutectics temperature equals, approximately, 1650 K, and experimental 1700 K. 100/ao values determine solubility in the system in accordance with state diagram (Table 30).

139 Table 27 Computation of structural P c - parameters Atom

Valence orbitals

Fe' 0 Fe" Fe"' Μη' 0 Μη" Μη'" Ca Ο

4S2 2Ρ +2P2(W) 3d1 +4s' 3d1 +4s' ' 4S2 2 2P +2P2( W) 3d1 +4s' 3d1 +4s' 4S2 2 2P +2P2(W) 2

Po (eVA) 18,462 22,653 14,204 12.835 18,025 22,653 13,976 12,770 15,803 22,653

r„(A) 0,80 2,15-0,80 0,80 0,80 0,91 3,12-0,91 0,91 0,91 1,04 2,40-1,04

P3 (eV) 23,078 16,781 17,755 16,044 19,808 17,293 15,358 14,033 15,195 16,657

Pc (eV) 9,7162 8,6271 8.2020 9,2327 8,1341 7,7467 7,9462

Table 28 Computation of initial values of structural Pc- parameters Structure FeO FeO MnO MnO CaO

Metal valence orbitals 4S2 3d1 +4s' 4S2 3d1 +4s' 4S2

Pc (eV)

Coefficient α

9,7162 8,6271 9,2327 8,1341 7,9462

0,9 0,9 1,1 1,1 1,1

Pc(+) (eV)

Pc(-) (eV) 10,796 9,5857

8,3924 7,3946 7,2238

ON C*

solubility

Maximum

SO N OS

'S

s Ο

Η OH

O^· Ο Ο

Ω JT Ο NO

1

F> R- Ο "

ON © F-H

O->

r-»

Γ(N

oo

ö

Γ(Ν

NO

•η

r-

NO

oo"

cn

OO

NO

F-H

(Ν

(N

0\

NO Tf ON

f>

(Ν

NO

»-H

r^

c ο ο

·§ ο u

r

ON

ON H CU

Tf-

(N

g

o "

oo

o C

fN

Ο CS

cs

r-»

ts

fN

ΓΛ fN

fN

NO

CN ON

(Ν ON

ON ON

NO "Ψ ON

r-

m r -

m r-

NO fN NO ON

NO

CA

NO PU

Ε

Ο

P-

fN

ο (Ν

ON

00

ON

NO

r-

Ο CS ο (S

fl r·»

00

R-

CNL NO r-

r-

00

00 ο

ON.

ο

fa ο ο

r-"

ON

oo"

cn

r-

00

fN fN

t—

ON

00

l>

NO r-

R-

m

m

CN Valence electrons

Η

System

C»

(experimental

\

Ξ

Ό cn

Ν

Vi

ts

+

Μ

~CA

ΝCA

(N CA Γ»Ί I

cn

Ν"" CA 'S·

+

Ν

CA rr 1 s

ι

T3

m

Ο υ

PH

Ο Ο G s

1 Ο 3, Jn2-2xAl2x03 that, unfortunately, cannot be currently predicted. The analysis of temperature dependence a« for systems containing transition metals reveals good correlation with their physical-chemical properties (Table 32). Thus, the computation for system Α1203-€γ203 in high-temperature region provides with low values of ao, thus corresponding to the unlimited solubility of these components found experimentally [164], [173]. When the temperature goes down, do value sharply increases, thus indicating thermodynamic instability of unlimited solid solutions Al2-2xCr2x03 at these temperatures. Thus, for instance, the authors [174] observed minor structural changes in the sample after having annealed this solution in the air at 1073K. In system A1203 - Fe2C>3 the change of do has an extremum in the temperature range of 1600 K. The availability of maximum but limited mutual solubility of oxides in the system corresponds to that [164],[173]. The analogous extremum is also available in system AI2O3 - Μη2θ3, but at about 1200 K, thus, also corresponding to maximum solubility of A1203 in Mn203 at subsolidus temperature [173]. In system A1203 - Ti 2 0 3 the availability of a very limited solid solution Α12.2χΤΪ2χθ3 is registered at 1973 K, and in system AI2O3 - V2O3 - the existence of greater mutual solubility defined only at temperature up to 1500 Κ [173],

31,222

n Tf

'—V m •o •β (S w (Z) on

£

C«"T3 ρ+'Ο,ΊΛΊΛ τοΊΛ fl Tf VO CN tN tN fNTf

υ W

Ο ΛΟ νο 00 Ό ΓΟ Ν m ΟΟ rf ^Γ Tj·" ^t —*

7,726 20,292

16,767 9,3477

6,708 11,194 7,081 6,191

f-H oo f^00" o t-

CO CO

co co

οο Ό Ό TT CO •u

υ .ν

U

β a •οΜ ce

ω %

0,450 0,414

a S

77,45 14,54

t-H — ι 1 "St Tt h «β 73 s β β ε ο

14,398

— (Ν

Ξ

υ

t/5 in

1/5 NO

ν© ιΝθ" 00

in in + Ν+ s+ Ν+ Ν+ s Ό ΓΛ

»—I NO Ο

«2 in

Ο 00 ο

cn SO

r-

ΓΊ

εο

1 ι ο

υ

σ

Υ

Ν© •/-Γ M

35,627

00

54,394

Ο

Ο*

ν© II

5,28

NO

Γ -

αο Β —

00

Η

Γ"1

Tf" in

•

>>

CO SO

CO SO •Ί-

SO CO rr

ο CO W-)

ο

co ο OS co

co Ο Os CO r—1

ro Ο OS co

co

co V)

co co 00 Ο (Ν

CO CO 00 Ο fN

co co 00 ο fN

/—Ν Β *

HH HH

r-s HH hH

U

υ

£ u

2,43

v> co τ—t

4,81

CO SO Λ) (Ν

4,34

1

fN

4,34

fN

2,17

CO

ο W

4,94

a

2,50

•β ν

tr>

SO

fN

Λ et Η

Ο

κτ,

00

Ο 00

m

m

^t

fN SO fN

fN SO fN

fN

CN

)—( 1—t ö υ

HH t—l » ω b

tfS

OS fN SO Os

OS ο ο rCO

fN OS

00

Ζ

Γ-

ο

SO SO co

so co

CS

-

co Ο fN

CO ο (Ν

I Ö

1 Ö

I Ö

>/-) CO Ο οο"

ο

00

00 ι

00

00

Co

24,418-0,14+16,250-0,86= 17,394

Solubility of first metal in second (in binary system), % (at.) 14

Co-»W

24,418-0,972+16,2500,028=24,189

2,8

W-»Co

34,476-0,14+16,250-0,86= 18,802

14

Co-»W

34,476-972+16,250-0,028=33,966

2,8

W->Co

31,934-0,14+16,250-0,86=18,446

14

Co->W

31,934-0,972+16,250-0,028=31,495

2,8

Table 70 Estimation of maximum solubility (at.%) in triple subsystems System

oc(forX 2 ), % P'E,

eV

P"E,

Calcul-

eV

X2

X, Exper-t

calc-n

12,0

9,0

n COl-XlWxi-Cx2

17,394

19,902

13,45

14,0

Wl.xiCOxi-Cx2

24,189

19,902

19,45

2,8

2,1

0,95

C0,.X,WX1-0X2

18,802

25,448

30,04

14,0

16,0

0,12

W,.x,CoxrOx2

33,966

25,448

28,67

2,8

2,1

0,18

CO,. x 1 W x 1 -NX 2

18,446

22,746

20,88

14,0

17,5

2,0

Wj.x.Cox.-N»

31,495

22,746

32,26

2,8

2,1

0,065

Calculation samples of mutual solubility of some complex carbide and nitride components of system W-Co-C-O-N are given in Tables 71 and 72. Systems, in which atoms of penetration dissolve less than by 0,1 % (at.), were not considered. The analysis of data obtained proves that the method suggested can be recommended to estimate the solubility of components of complex insufficiently studied systems and can be a rational supplement to well-known techniques [266][294],

228 Table 71 Ρε-parameters of solid solutions of penetration of double and triple components in system W-Co-C-O-N Solubility of System

Calculation of P-parameter, eV

penetration atom (calculation), %, (at.)

Coi-xiCxi

16,250-0,9925+19,902-0,0075=16,277

0,75

Wl-XiCxi

24,418-0,9945+19,902-0,0055=24,393

0,55

CO|.XI.X2WX,NX2

16,250-0,84+31,934-0,14+22,746-0,02=18,576

2

Co 1 . x l .x 2 W x l Cx 2

16,250-0,77+24,418-0,14+19,902-0,09=17,723

9

Table 71a Estimation of maximum mutual solubility of some complex components of system W-Co-C-O-N First component System

P'E, Xi

x2

CO 1 -χ 1 -X2 Wx|NX2-CO 1 -XI -X2 WX1 Cx218,576

14,0

2,0

COI.XI.X2Wx1NX2-COI.xiCXI

18,576

14,0

C0l-Xl.X2WxiNx2-WI-XICXI

18,576

14,0

eV

Second component P'E,

a, %

Calcul-d solubility %,(at.)

Xi

X2

17,723

14,0

9,0

4,7

100

2,0

16,277

0,75

-

13,2

11-13

2,0

24,393

0,55

-

27,1

0,05

eV

6.6. Estimation of cluster-formation in system CaS0 4 -H20 To estimate cluster-formation in system CaS0 4 -H 2 0 we apply the method of spatial-energy parameter (P-parameter). Initial data of P0-parameter (Appendix 3) - such tabulated numbers that can be used as the basis for calculating energy conditions of phase-formation in compounds with different molecular compositions [295]-[301]. The computation of initial values of Pparameters by equations (7,8) is given in Table 72. Structural Pc-parameter (Table 73) represents an averaged spatial-energy characteristic of a compound formed as a result of interaction (taking screening effects into account) and is found as follows:

229 1 - +

Pc

Ρ ε Ν,

— ;

+

•··

ΡεΝ2

where Νι and Ν2 - number of homogeneous atoms in the structure. When a new compound is formed from other structures in the process of isomorphous replacements and microstructural phase interactions of penetration electron density increases in the contact points of atomic spheres. When the values of electron densities of corresponding components are similar, the transfer processes are minimal, thus proving the formation of a new more stable structure. Therefore, in such cases, cluster-formation is estimated via relative difference of Pc-parameters of structures: Ν Ρ' - Ν 2 Ρ" c (N,PC'+N2Pc")/2

100%

where Ni and N2 - number of homogeneous atoms-components. That is coefficient α is a quantitative characteristic of probability of stable structure formation and quantitatively equals relative difference of effective energies of valence orbitals of interacting systems. In the system investigated water molecules are the strengthening phase that "penetrate" into interplanar spacings of "matrix" molecules and ions of anhydrous gypsum [7],[302], Similarity of energy characteristics of valence orbitals of interacting atoms-components is the main condition of such penetration. Thus, "penetration" of water molecules into interplanar spacings of gypsum crystalline structure provides a strengthening phase improving, in general, material strengthening characteristics. Quantitative estimation of such phase-formation is determined, in such case, via the value of coefficient α (Table 74). Further, percentage probability of stable structure formation via solution solidifying degree (solubility) was determined by nomogram 2 (Figure 4). In lines 1-2-3 of Table 74 there are calculations of formation probability of crystal-graphic structures of ions for bonds S-0 4 . At the same time, for ion SO42" (hexavalent sulfur) we have α = 5,43, that by nomogram gives 100% probability of stable subsystem formation.

230

Table 72 Initial P-parameters of atoms (eV)

torn

Orbi tals

Ca

4S2

O(II)

S(II)

S(IV)

S(VI)

Η

Ei, (eV)

I

6,113

1,690

17,406

6,483

II

11,871

1,690

17,406

9320

I

13,618

0,414

71380

5,225

II

35,118

0,414

71380

12,079

I

10,36

0,808

48,108

7,130

II

2335

0,808

48,108

13,552

III

34,8

0,808

48,108

17,446

2p2

3

3

ri,

lonozati onstage

p4

p4

(A)

Po q ?, (eVA) (eVA)

ΣΡ„ (eVA)

Note

*PJr,=PE

(eV)

15,803

93509

17304

41,797

20,682

25,596

20,682/0,808= =25396

59,424

73,546

38,742+20,682= =59,424 61,152/0,723= =84,809 84,809+73346= =158,355

IV

47,29

0,808

48,108

21,296

V

72,68

0,723

64,851

158355

VI

88,05

0,723

64,851

29,027 59,424+ 61,15232,125 120376

13,595 0,5295

14394

4,7985

4,7985

9,0624

2

3S

IS1

I

Table 73

Structural P-parameters (Pc) in eV NS

Structure

1 component N,

1

P'

Atoms 2 component

3 component

N2

P"Ε

N3

41,797

-

Pc

ρ 111

H2O

2

9,0624

1

2

OH

1

41,797

1

9,0624

-

-

7,447

3

CaS(VI)04 S(VI)-04

1

9,3509

1

158,355

4

41,797

8,3896

1

158355

4

41,797

5

H30

3

9,0624

1

41,797

16,471

6

H3O2

3

9,0624

2

41,797

20,516

4

-

12,642

81,334

231 Crystal-graphic data for CaS0 4 show that the formation of ions S042" - in the form of tetrahedrons "located by island principle" in crystals of distorted sodium chloride NaCl, actually corresponds to the interactions of hexavalent sulfur with oxygen. Analogously, "double layers formed by water molecules are parallel to the layers formed by Ca2+ and S042"" in dihydrate gypsum CaS0 4 -2H 2 0 [7], In Table (lines 2 and 3) the hypothetic possibility for forming ions SO/ - and SO46" in crystalline pseudostructure is considered, the unreality of which is confirmed here with great values of coefficient a, being 77,8 and 147 (respectively). Therefore, in further calculations the components of system CaS0 4 -H 2 0 with biand quadrivalent sulfur were not considered. From experimental data for dihydrate gypsum it is known that the angle between atoms H-O-H in water molecule equals 108°. This means that when analyzing clusterformation in system CaS0 4 -H 2 0 the interaction of subsystems with atom of water oxygen must be determined, i.e. such dipole-dipole interaction plays an important role in interphase interactions. In fact, coefficient α during the interaction S(VI)0 4 -20 appeared to be equal to 2,74 (line 4), this determines the stable phase with most strengthening bond in dihydrate gypsum. Analogous calculations for the interaction CaS(VI)04-2H20 (i.e. with molecules of "deformed" water) give a= 100,3 (line 5). This again confirms the aforesaid supposition on the role of oxygen atom in dipole-dipole interactions. Semiaquatic gypsum (2CaS04-H20) becomes a stable compound only at temperatures over 110°C. Therefore, calculations carried out without temperature factors give a «28, this indicates the possibility to form metastable unstable phase for semiaquatic gypsum at normal temperature mode (line 6). It is also necessary to take into account that water molecules can have cluster complexes of (H20)„ type [303]. It can be assumed that at the same time the corresponding number of molecules CaS0 4 interact with cluster formations (H20)„ in gypsum. Statistically, the number of components for stable structure formation has to be determined by spatial-energy features of crystalline lattice of initial structures. If for dihydrate gypsum these are systems of (CaS04)n-(H20)2n type, for them a=2,74% (line 4).

232 Table 74 Estimation of structural bond formation in system CaS0 4 -2H20 IlapHoe Ks

Structure

B3aHMoeeHcr-

Formation of bond

1 component 2 component α

BHe aTOMOB

p;

kOMIIOHt'HTOR

Ν,'

N2

Pc"

("penetration") Cakul ation

Experiment

1

SO42

S(VI)-04

1

158,36

4

41,797

5,43

100%

Stable phase

2

4

SO4

S(IV)-04

1

73,546

4

41,797

77,8

no

no

3

SO,6"

S(II)-04

1

25,596

4

41,797

147

no

no

S(VI)0 4 -20

1

81^34

2

41,797

2,74

100%

Stable phase

1

8,3896

2

12,642

100,3

no

2

8,3896

1

12,642

28,1

0-1%

2

81^34

1

41,797

118

no

2

8^896

1

16,471

1,85

100%

1

9^3509

1

9,0624

3,17

100%

2

8^896

1

20,516

20,04

6-8%

1

9,3509

1

7,447

22,7

2-5%

4 5 6 7 8 9

CaS(VI)042H 2 0 CaS(VI)04-

CaS(VI)04-

2H 2 0

2H 2 0

2CaS(VI)0

2CaS(VI)04-

4-H20

HJO

2CaS(VI)0 4-H2O

2S(VI)0 4 -0

2CaS(VI)0

2CaS(VI)04-

4-H3O

H3O

CaS0 4 H2O

Ca-lT

1

2CaS(VI)0

2CaS(VI)04-

0

4-H302

H3O2

1

CaS0 4 -

1

H2O

Ca-(OH)

Metastable phase

Fibrous structures

Amorphous formations

In line 8 there are computation results of interaction 2CaS(VI)0 4 -H 3 0, at the same time a=l,85, this corresponds to high solubility in accordance with nomogram, but compound H 3 0 + - is metastable. Taking the interactions of components Ca-H^ in acidic medium at pH0, Ea ->4,184(—). But values of Ea mol

(in experiment) are found for these cases [306] usually within the limits from 0 up to 4 KJ

( — ) . That is, the given equation (75) works less accurately at values a - > 0 . In Table mol

78 there are calculations of activation energy of gaseous-phase reactions with participation of halogen-hydrogen molecules, the ionic character of which was considered via coefficient γ = —t-, where μ - dipole moment of given compound; μΗα dipole moment of molecules HCl [310]. Thus, in this case equation (75) looks as follows:

241 Ea =Κγε ηα

(76)

where η = 1, 2, 3... More accurately: with participation of free atoms η = 1, 2, 3, but with participation of hydrocarbons η = 1. In Table 79 there are selective calculations of Ea for molecular reactions by equations (75 and 76) and the following equation: pl

a,,-" _

i,l

_pll r C

'

(77)

The analysis of Table 79 results in the conclusion that equation (75) works rather satisfactorily in these cases as well. The accuracy of computations is in the range of ΙΟΙ 5%, thus not exceeding the relative error in majority of experiments. In these cases η = 1, 2,3,4, 5, 6. And n=3 corresponds to main "allowed" state for threshold value of energy (activation energy) for systems containing radicals and molecules (as for reactions with free atoms). Thus, this approach gives rather rational, practicable and scientifically grounded technique for calculating activation energy of chemical reactions that is very important for calculation apparatus of chemical kinetics in nanocontainers [311].

7.3 Basic structural interactions of components in systems OCTOGEN (OG) - nitroglycerine (NG) The intensity of fast-proceeding physical-chemical processes of combustion is intensified due to the presence of components of octogen and nitroglycerine in main product [312],[313],[314], For general estimation of the character of structural interactions in this complex system let us apply the method of spatial-energy parameter (P-parameter) previously tested in many binary and more complex systems. For that we apply previously obtained values of P-parameters for free atoms (Table 75).

242 Following this technique the complex system (OG or NG) is considered as consisted of particular "blocks", each of them, in turn, represents the subsystem from a group of atoms. Thus, in octogen molecule there are 4 "blocks" of CH2 and 4 "blocks" of (N-NO2) structurally interclosed. In each separate block its P-parameter is calculated by the principle of adding reverse values of P-parameters constituting the block of atoms, and the resulting P-parameter of all the structure (OG or NG) is calculated by the principle of algebraic addition of P-parameters of "blocks" (Table 81). Then, for instance, for NG the resulting P-parameter of the "block" CH-0N0 2 is found by the algebraic addition of P-parameters of CH and 0N0 2 , each of them was previously found by the addition of reverse values of P-parameters of atoms (Equation 37). The total P-parameter of NG equals the algebraic sum of P-parameters of two "blocks" CH 2 0N0 2 and one "block" CH0N0 2 . As before [305], to estimate the main interaction character of atoms-components the relative difference of their P-parameters - coefficient α is calculated: a = , P , C ~ P \ , • 100%

{Pc + Pc)/2

(24c)

Further, the nomogram of dependence of coefficient α upon the degree of resulting interaction of components is applied (p in mol %) - Figures 3, 4. In octogen molecule consisting only of two types of "blocks" their P-parameters appeared to be equal to 30,522 eV for (N-N0 2 ) and 14,99 eV for CH2. This means that if radical (N-N0 2 ) has the surroundings consisting of two "blocks" of CH2, in such subsystem α = 2,25 % (Table 82), this proves the system stability according to the nomogram. System P-O, for which a= 6,49% is given in Table 82 for comparison. That is, at any external action (for example, friction), providing with even small increase in temperature and P-parameter for phosphorus, for this system α will be less than 6%, this determines the combustion process itself. During structural interactions in system OG-NG several stages can be distinguished.

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tJ -j

CO 30 % basically were not considered since their influence on the process is minimal, i.e. it is possible not take them into account. In general, in this research the principal possibility to estimate complex molecular-structural interactions based on basic spatial-energy characteristics of free atoms is shown [315],

255 Table 80 Structural parameters of molecules, radicals and "blocks"

Radical

P;

PI"

ΡΓ

p,

("block")

(eV)

(eV)

(eV)

(eV)

C-H

86,810

9,0624

8,2058

C-H2

86,810

2-9,0624

14,990

0-N-0 2

41,797

158,62

2- 41,797

23,701

NG

68,984

158,62

2- 41,797

30,522

OG

OH

41,797

9,0624

7,4474

C-H3

86,810

3-9,0624

20,703

N-N-O2 (III)-V-II

System

Table 81 Structural Pc-parameters of "blocks" system Pc = p'i + PI'+ P'" + -

Structure, system

Pc (eV)

P"c (eV)

ZP c ,(Pc)(eV)

(CH)-(ON02)

8,2058

23,701

31,907

(CH 2 )-(0N0 2 )

14,990

23,701

38,691

(N-N02)4-(CH2)4

4 · 30,522

4 · 14,990

182,05

octogen

[CH 2 -0N0 2 ] -2 - (CH-0N0 2 )

2 · 38,691

31,907

109,29

nitroglycerine

Notes

256 Table 82 Computation of structural interaction coefficient pll _ p . α = —f -^--100% (P^+P^/2 Structure, "blocks"

P

c (eV)

P

c (eV)

α (%)

Interaction degree - ρ mol% Forecast

(NN0 2 )2(CH2) (NN02)(0N0 2 CH 2 ) (NN02)(ONOZCH) 2(CH2) (0N0 2 CH> CH2-

(0N0 2 CH) P-0

Experiment Stable structure OG formation

Ea=Ke3a KJ mol

30,522

2· 14,99

2,25

100%

30,522

38,691

19,22

3-6%

30,522

31,907

4,44

100%

2· 14,99

31,907

6,42

91-98%

14,99

31,907

72,14

0%

-

36,4

39,169

41,797

6,49

90-98%

Combustion possibility

5,08

Mixture swelling Destruction beginning Complete destruction

4,48 7,44 4,78 5,07

257

7.4. Phase-formation features of polymeric composite (PC) components The issues of structural interactions of PC components are both of theoretical and practical interest and are discussed in many researches, for instance [314],[316], Let us consider the main structural interactions during the formation of complex mixture polymeric composite consisting of 12 components and for which octogen (OG) is the most important by its composition. The other components, except for ammonium Perchlorate (APC) - NH4CIO4, aluminum and aluminum oxide (AI2O3), iron oxide and nitroglycerine (NG) - are given as fragments Ki - C=N->0 or C2H5, K2 - (CH2CH)2OH, K3 - O-OCH3 or CH3COOCH2, K, - 2[C 2 H 5 -C(-NH)], K5 - CH2-CH-CH2, K6 - CH2-CH2-NH, K7 - NH3 or 2(CO-OH)

In this work the distribution of phases and boundary layers at initial stage of structural interaction up to 600K (in liquid-viscous layer) are investigated. The initial values of atom P-parameters were calculated before (via ionization energy - E,) by equations (7a, 8a, 36a) and are given in Table 75 and Appendix 3. Structural P-parameters of fragments (P c = Ρφ = Ρ,) were calculated by equation (37a). P-parameter of block of fragments and common P-parameters of complex structures (consisting of two and more fragments) were found by algebraic addition of corresponding Ρφ-parameters by equations (9,10). The results of such calculations are given in Table 83. It contains calculation data of P-parameters of fragments and blocks of fragments responsible for interaction active phases for all 12 components. The resulting (common) P-parameters of structures are calculated for 10 components (except for K-2 and K-5). The coefficient of structural interaction (a) between the fragments (or between the structures or between the structures and fragments) was calculated by equations (24a, 24c) and is given in Table 84. Maximum mutual solubility of components (degree of structural interaction) was found using the nomogram (Fig. 3, 4) based on coefficient α - ρ in mol% - Table 84.

258 The analysis of Table 84 shows that active structural interactions in this multicomponent system take place between separate fragments of heterogeneous structures or between a particular structure and active fragments of other structures. All that determines the metastable character of such a complex, whose stability depends upon the changes in external conditions (temperature and pressure). Summing up the data obtained, by quantitative characteristic of phase interactions (p) and taking into account the content of components, the following composition and distribution by phases and boundary layers of the whole conglomerate is proposed - Figure 21. I layer. Octogen (1) forms basic nuclei with several layers each, including: II layer. OG, NG, APC, (1, 2, 3) III layer. NG, APC, organic compounds (2, 3, 4) IV layer. Organic compounds (4) Six such nuclei located as octahedron produce a cavity inside that contains metallic phase-formations and K-7 (5, 6, 7). Octahedron variant for locating PC components, in this case, appears to be more preferable that cubic one, since the overall contact area and nearness of components is greater in octahedron than in cube, i.e. greater stability of all the macrostructure is determined. Analogously, the atomic structures of penetration are determined (see 5.4.). Each of metallic systems (Fe, Fe 2 0 3 , Al, A1 2 0 3 ) is also surrounded with surface layers containing K-7 and organic compounds, this is proved by corresponding calculations by their interaction degree (p). The organic compounds presented have high interaction degree between them (based on calculations), therefore, in Figure 21 they are all marked with only one digit (4). The second oxidizer APC (of lesser content) has a high interaction degree (p = 94-100%) with fragments OG, NG and K-4. Therefore, part of macro-formed APC is contained in the surroundings of octogen with nitroglycerine. The same particles of APC, which were used in interactions with organic compounds form separate fragments of PC composition within octahedron cavities (3,4). At the same time, mutual penetration and partial redistribution of components in the whole conglomerate space are possible since this scheme (Fig. 21) assumes the

259 initial distribution of phases that can change considerably in dynamics when external conditions are changed. As it was already mentioned, this technique allows estimating mainly the processes of exchange and penetration of atoms-components, structure fragments or structures themselves. If such process, due to several reasons, has avalanche-like, increasing, speedy character, the breaking-off of molecular bonds prevails over the exchange or penetration process itself, thus being accompanied with the destruction of macrostructures themselves (for instance, in OG). If the conditions contributing to the decrease of kinetic parameters of decay are formed, the exchange processes (and penetration processes) will prevail over the destruction processes of conglomerate macrostructure. In particular, as applicable to system OG-NG it means that the replacement process of radical N-NO2 in OG for radical CH-ONO2 in NG will take place, i.e. the destruction of OG as a macrostructure will be considerably retarded. At the same time, new structures based on OG with closed bonds will be formed, this will result in the decrease of isolation of ecologically harmful products based on HCN. Such conclusion can be very important when analyzing technological conditions for utilizing such polymeric composites.

260 Table 83 Pc-parameters of structures and their fragments Structures, structure fragments 1

Pc(eV) P'/(eV)

P"/(eV)

P"/(eV)

IP,{eV)

Basic structures

2

3

4

5

6

(N(V)H4)

158,62

4x9,0624

29,507

PCA

(C104)-

11,611

4x41,797

10,463

PCA

NH4CIO4

29,507

10,463

7,7237

PCA

A1203

2x23,939

3x41,797

34,649

FeO

15,046

41,797

11,064

Fe 2 0 3

2x23,656

3x41,797

34,347

CH

86,81

9,0624

8,2058

CH2

86,81

2x9,0624

14,99

CH3

86,81

3x9,0624

20,703

C-CH3

86,81

2x0,703

16,717

N(V)0 2

158,62

2x41,797

54,744

C-NO2

86,810

54,744

33,573

N(III)-H

68,984

9,0624

8,0101

5(CH)

5x8,2058

C-^N(III)H

86,810

- 8,0101 2

3,8285

K-4

2[C 5 H 5 -C(^NH)]

2x41,029

+3,8285x2

ΣΡ=89,715

K-4

C-(CH3-CH2)

86,810

20,703

14,99

7,9032

K-l

C-[C-N(V)0]

86,81

86,81

33,081

18,773

K-l

N(V)-0

158,62

41,797

33,081

K-l

TOH-2

3x7,9032+

2x18,773+

ΣΡ,=69,462

K-l

OH

41,797

9,0624

7,4474

K-2

(CH2CH)2-OH

2x14,99+

2x8,2058

ΣΡ,=53,839

K-2

+

41,029

7,4474

261 Table 83 (continued) 1

2

3

4

5

6

0-0-CH3

41,797

41,797

20,703

10,400

Κ-3

CH-COCH3

8,2058+

10,400

ΣΡ,=18,606

Κ-3

CO

86,810

41,797

28,213

Κ-3

CH3-C0-0-CH2

20,703+

28,213+

ΣΡ,=105,7

Κ-3

TALI

2x105,7+

18,606

ΣΡ,=230,01

Κ-3

CH2--O 2

14,99

-41,797 2

8,7289

Κ-5

CH--O 2

8,2058

-41,797 2

5,8922

CH2-CH-CH2 \ / 0

8,7289

5,8922+

N(III)H2

68,984

2x9,0624

CH2-CH2-NH

14,99+

14,99+

NH2-4R-H

14,354+

4x37,990

N(V)H3

158,62

(CH2>20-(NH3)2

2(CO-OH) (CH2)34-

41,797+14,99

ΣΡ,=29,611

Κ-5

14,354

Κ-6

8,010

ΣΡ=37,990

Κ-6

9,0624

ΣΡ=175,38

Κ-6

3x9,0624

23,209

Κ-7

20x14,99+

2x23,209

ΣΡ=364,22

Ri(K-7)

2x28,213

2x7,4474

ΣΡ=71,320

Κ-7

34x14,99

71,310

14,99

ΣΡ=580,98

R2(K-7)

364,22

580,98

33,081

216,96

Κ-7

4x14,99

4x30,522

ΣΡ= 182,05

OG

2x38,691+

31,907

8,2058

ΣΡ=109,29

NG

86,810

86,810

33,081

18,773

Κ-1

3-7,9032

2-18,773

8,2058

69,462

Κ-1

14,99

(COOH)2 R-R2 4(CH2)4(NN0 2 ) 2(CH 2 -0N0 2 )-

Κ-5

(CHONO2) C-C-NO (C-C2H5)3-(CCNO)2-CH

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EC ο u1 EC χ S^o £/ £/ υ ο

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Ο(Ν Ο

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(Ν •«t Ο 2 ν£ ζ υ

NG APC

ζ

APC 1

EC υ

7,4474 II 2x7,4474 105,70 I 10,400

CS Ο

2(OH)

OG, NG

OG

sI

53,839

29,611

(Ν

Ο

K-3

I

Ho-Sc Β Ö S W 4?

-

359

Orbital Ρ 1 2 Er-Ce A

6S2 0,408 3 6S2

6Sz+4f* 1,4888 4 5 0,320 4f*

4f» 3,142 6 24,2

6S 2 +4f" 12,810 7 öS^f*

4f 1,05

4I2 2,100 8 III

9 alloys

Er-Pr

A

6S2

6S2

0,391

4,26

6S 2 4f

III

alloys

Er-Nd

A

6S2+4f1

68 2 +4ί

1,226

19,3

6S 2 4f

III

alloys

Er-Pm

C

6S'+4f

68^+4^

1,296

13,8

6S 2 4f

?

?

Er-Sm

A

6S2

6S2

0,399

2,23

68 2 4ί"

Ill

alloys

Er-Eu

A

6S2

6S2

0,404

0,99

6S 2 4f

III

alloys

Er-Gd

A

6S2

6S2

0,407

0,25

6S24fK

III

alloys

Er-Tb

A

6S2

6S2

0,409

0,24

6sV

III

alloys

Er-Dy

A

6S2

6S2

0,407

0,25

6S 2 4f°

III

alloys

Er-Ho

A

6S2

6S2

0,410

0,49

6S z 4f"

in

alloys

Er-Tm

A

6S2

6S1

0,412

0,48

6S z 4f J

III

alloys

Er-Yb

A

6S2

6S2

0,408

0

6S 2 4f"

III

alloys

Er-Lu

A

6S2

6S2

0,422

3,37

6S 2 5d , 4f 14

III

alloys

Er-y

A

6S2

6S2

0,546

28,9

5S 2 4d'

in

alloys

Β

2

4S

2

I?

-

5S

2

I?

-

Er-Ca

6S

2

Er-Sr

Β

6S

Er-Zr

Β

6S'+4f 1

Er-Mn

C

4?

3d

Er-Sc

C

Er-Na

Β

I/2(6S2+ +4f 42 ) 6S2

4,775

168,5

4S

2 2

5,280

171

5S

7,252

132

5S24d2

II?

-

3,051

36,9

2

4S 3d

II?

-

6S2+3d2

6,551

23,0

4S23d"

III?

-

3S1

4,694

168

3S1

I?

-

5S2+4d2 2

5

Orbital

6S2

At

6 S2+4f*

6S2+4f°

4^

(4f)

Ρ

0,412

1,278

1,690

16,685

2,556

3,834

1

2

3

4

5

6

7

8

9

Tm-Ce

Β

6S2

4f*

0,320

25,1

6S24f

III

alloys

Tm-Pr

Β

6S2

6S2

0,391

5,23

6S24?

III

alloys

Tm-Nd

Β

6S2 6S2+4f*

6S2 6S 2 +4i 6S2+4f*

0,553 1,226 1,852

27,3 4,15 8.51

6S 2 4f 6S 2 4f 6S 2 4f

III III ?

alloys alloys ?

Tm -Pm C Tm-Sm

Β

6S2

6S2

0,399

3,21

6S 2 4f

Ill

alloys

Tm-Eu

Β

6S2

6S2

0,404

1,96

6S 2 4f

III

alloys

Tm-Gd

Β

6S2

6S2

0,407

1,22

6S z 4f

III

alloys

Tm-Tb

Β

6S2

6S2

0,409

0,73

6S 2 4f

III

alloys

Tm-Dy

Β

6S2

6S2

0,407

1,22

ÖSW

III

alloys

Tm-Ho

Β

2

6S

2

6S

0,410

0,49

öS^f

1

III

alloys

Tm-Er

Β

6S2

6S2

0,408

0,98

6S24f*2

III

alloys

Tm-Yb

Β

2

6S

2

6S

0,408

0,98

z

6S 4f

III

alloys

Tm-Lu

Β

6S2

6S2

0,422

2,40

ÖS^dUf 14

III

alloys

Tm-Y

Β

6S2

5S2

0,546

28,0

5S24dJ

III

alloys

Α

2

2

1?

-

1?

-

1?

-

III?

-

III?

-

11,1?

-

Tm-Ca

6S

2

4S

l

Tm-Na

Β

6S

3S

Tm-Sr

Β

6S2

5S2 2

4,775

168

4S

4

2

1

4,694

168

3S

5,280

171

5S2 2

2

Tm-Zr

Β

4?

4S

2,654

7,67

5S 4d

Tm-Sc

Β

4?

4S2

2,946

14,2

4S23d'

Β

2

2

Tm-Mn

4Ι

3d

3,051

17,66

4S'3d

i

361

OpÖHTajn.

6S

2

5P

2

Z= 70,Yb ( 6S24f*45P6) 5P2+6S2 (4f 1 +6S 2 )

4f14+6S2

4£2

Ρ 1 Υβ-Ce

2 A

0,408 3 6S2

25,94 4

26,348 5 0,320

6 24,2

7 6S24?

8 111

2,994 9 Alloys

ΥΒ-ΡΓ

A

6S2

6S2

0,391

4,26

6S 2 4f

111

Alloys

YB-Nd

A

6S2

6S2

0,553

30,2

6S 2 4f

111

Alloys

ΥΒ-ΡΠΙ

C

6S2

6SZ

0,555

30,5

6S 2 4f

Υβ-Sm

A

6S2

6S2

0,399

2,23

6S 2 4f

111

Alloys

YB-EU

A

6S2

6S2

0,404

0,99

6S 2 4f

111

Alloys

Yß-Gd

A

6S2

6S2

0,407

0,25

6S24f*

111

Alloys

YB-Tb

A

6S2

6S2

0,409

0,25

6S 2 4f

111

Alloys

Ye-Dy

A

6S2

6S2

0,407

0,25

6S24r

111

Alloys

YB-HO

A

6S2

6S2

0,410

0,49

6S"4f"

111

Alloys

ΥΒ-ΕΓ

A

6S2

6S2

0,408

0

6S24f2

111

Alloys

Ye-Tm

A

6S2

6S2

0,412

0,98

6S 2 4f"

111

Alloys

YB-LU

A

6S2

6S2

0,422

3,37

ÖS^DUF14

111

Alloys

YB-Y

A

6S2

5S2

0,546

28,9

5S 2 4d'

111

Alloys

27,493

4,25

4S2

111

Alloys

1?

-

Ye-Ca

A 5P"+6S2 4S2+3p2

YB-Na

A

Yß-Sr

Β

YB-SC

Yß-Zr

1,905

20,857

j

?

6S2

3S'

4,694

168

3S1

6S2+4?

5S2+3d2

?

?

5S24Pf,4S23d10

Β

6S2

4S2

2,946

151

4S 2 3d'

9

-

Β

6S2

5S2

2,654

147

5,2Λ2

?

-

-

362

2

6S 0,422

Ζ = 71, Lu ( 6S25d14f14 ) 5d' 6S2 +5d' 4,343 4,764 5 6 7 0,320 27,5

Orbital Ρ 1 2 Lu-Ce A

3 6S2

4 4f

Lu-Pr

A

6S2

6S2

0,391

7,63

Lu-Nd A

6S2

6S2

0,553

Lu-Pm C

6S2

6S2

Lu-Sm A

6S2

Lu-Eu

A

8 III

9 Alloys

6S 2 4f

III

Alloys

26,9

6S 2 4f

III

Alloys

0,555

27,2

6Sz4t

111

Alloys

6S2

0,399

5,60

6S 2 4f

III

Alloys

6S2

6S2

0,404

4,36

6S24fv

III

Alloys

Lu-Gd A

6S2

6S2

0,407

3,62

6S 2 4f

III

Alloys

A

6S2

6S2

0,409

3,13

6SV

III

Alloys

Lu-Dy A

6S2

6S2

0,407

3,62

6Sz4r

III

Alloys

Lu-Ho A

6S2

6S2

0,410

2,88

6S24f11

III

Alloys

Lu-Er

A

6S2

6S2

0,408

3,37

6S 2 4f 2

III

Alloys

Lu-Tm A

6S2

6S2

0,412

2,40

6S"4f"

III

Alloys

Lu-Yb A

6S2

6S2

0,408

3,37

6S 2 4f 4

III

Alloys

A

6S2

5S2

0,546

25,6

5S 2 4d'

III

Alloys

Lu-Na A

6S

2

1

4,694

167

3S'

1?

-

Lu-Sr

A

6S2

5S2

5,280

170

5S2

1?

-

A

2

2

2

1?

-

Lu-Tb

Lu-Y

Lu-Ca

6S

3S

4S

C 6S2+5d' 4S2+3d' 3d1 3d1 2 Lu-Zr C 6S +5d' 5S2+4d2 4d2 5d' Lu-Mn c 4d2 5d' Lu-Sc

4,775

167,5

4S

6,551 3,605 7,252 4,598 3,051

31,6 18,6 41,4 5,70 34,9

4S z 3d'

III?

-

5S24d2

III?

-

4Sz3d5

11,1?

-

363

Orbital

6S

z

5,027 1 2 Ta-Nb A

Ζ = 73, Ta (6S 2 5d 3 ) 5d 5d} 6S 2 +5d'

5d 4,556

8,867

12,929

9,583

6S2+5d3

6S2+5d2

17,956

13,894

3 5d2 6S2+5d2

4d' 5S'+4d 4

5 10,81 14,677

6 19,7 5,48

7 5S'4d 4 5S'4d 4

8 III III

9 Alloys Alloys

4

Ta-Ti

A

5d'

3d2

2,855

45,9

4S23d2

III

Alloys

Ta-Zr

A

Sd1

4d2

4,598

0,92

5S24d2

III

Alloys

5d2 6S2+5d2 5d2 6S2+5d2 5d2 6S2+5d3 5d2 6S2+5d2 6S2+5d2

5d5 5S'+4d 5 5d2 6S2+5d2 5d2 6S2+5d2 3d2 4S2+3d2 5P2+5S2

6,595 11,823 10,817 12,855 8,482 17,206 4,263 11,362 4,349

29,4 16,1 19,8 6,99 4,44 4,27 70,1 20,1 104,7

5S'4d 5 5S'4d 5 6S25d2 6S25d2 6S25d4 6S25d4 4S23d6 4S23d6 5P25S2

III III III III III III

Alloys Alloys Alloys Alloys Alloys Alloys

6S2+5d2 6S2+5d2 6S2 6S2+5d2

5d5 6S2+5d2 5S1 5S'+4d7

13,238 14,569 6,019 14,205

4,84 4,74 18,0 2,21

6S25d5 6S25d5 5S'4d' 5S'4d 7

V V IV IV

Alloys Alloys Alloys Alloys

Ta-Mo A Ta-Hf A Ta-W

A

Ta-Fe

Β

Ta-Sn

Β

Ta-Re

Β

Ta-Ru

C

Ta-Y

C

6S 2 +5d'

5S 2 +4d'

3,112

101,9

5S24d'

1

-

Ta-Cu

C

6S2+5d'

4S'+3d 2

4,798

66,5

4S'3d ,u

?

-

-

-

2

Orbital

5d

6S

Ρ

8,482

8,724

1

2

3

W-Mo A 6S'+5dl

Ζ = 74, W (6S 2 5d 4 ) 6S2+5d2 6S'+5d' 6S2+5d4

2

17,206

8,717

24,84

6S1 4,362

4

5

6

7

8

9

5S2+4d2

7,918

9,6

SS^d 5

III

Alloys

W-Mo A

6S1

5S1

5,228

18,1

SS^d 5

III

Alloys

W-Nb A

6S1 ÖS'+Sd1

5S1 5S'+4d2

3,867 8,475

12,0 11,1

5S'4d4 5S'4d4

III III

Alloys Alloys

W-Ta

A

5d2 6S2 6S2+5d2

5d2 6S2 6S2+5d3

8,867 5,027 17,956

4,44 53,8 4,27

6S25dJ 6S25d3 6S25d3

III III III

Alloys Alloys Alloys

W-Cr

A 6S'+5d' 6S1

4S1+3d5 4dl

9,309 5,16

6,57 16,8

4S13ds 4S13d5

III III

Alloys Alloys

W-V

A 6S'+5d' 6S2

4S2+3dj 4S2

8,167 5,528

6,52 44,8

4S23dJ 4S23d3

III III

Alloys Alloys

W-Ti

Β 6S'+5d' 6S2

4S2+3d2 4S2

6,547 3,692

28,4 81,1

4S23d2 4S23d2

II, IV? II

Alloys Alloys

W-Zr

Β

6S2 öS'+Sd1

5S2 5S2+4d2

2,654 7,252

107 18,3

5S24d2 5S24d2

6S2+5d2 6S2

4S2+3d3 4S2

13,232 7,099

26,1 13,2

4S23d" 4S23d6

Iln II

-

Β 6S'+5d'

5S2+5P2

4,348

40,1

5P25S2

I?

-

öS'+Sd1 6S2 W-Ag C 6S l +5d' 6S1

6S2 6S2 4d'+5S' 5S1

9,399 9,399 5,164 3,560

4,96 7,45 51,2 20,2

6S25d6 6S25d6 5S'4d lu 5S'4d10

V V I I

W-Fe

W-Sn W-Os

Β

Β

-

Alloys Alloys _

365

1

2

W-Ca C

3

4

5

6

7

8

9

6S2

4S2

4,775

35,5

4S2

1?

-

3d'+4S'

4,181

70,3

4S23S1U

1?

-

-

W-Cu C öS'+Sd1 W-Y

c

6S2+5d2

5S2+4d'

3,112

139

5S24d'

11

W-Ru

c

5d'+6S' 6S1

5SI+4d'i 5S1

8,416 6,019

3,51 31,9

5S'4dy 5S'4d7

i,v i,v

Orbital Ρ 1

6S2

2,887 8,661 2

Re-Mo A

Re-W

5d3

5d'

Ζ = 75 , Re( eS'Sd") 6S"+5d' 5d> 6S2+5d2

8,795

11,682

13,238

14,569

-

6S"+5d5

5d

22,033

5,774

3

4

5

6

7

8

9

5d2 5d'

5Sl+4d' 4d2

6,573 2,69

12,9 7,06

SS^d' 5S'4d5

V V

Alloys

6S'+5d4 ÖS'+Sd1

24,84 8,717

12,0 1,29

6S^5d4 6S25d4

V V

Alloys Alloys

A 6S2+5d5 5d3

Re-Os A

6S2

6S2

9,399

6,64

6Si4db

III

Alloys

Re-Co A

6S2

4S2

7,276

18,9

4S'3dv

III

Alloys

Re-Tc A

4d3

4d6

7,359

16,3

5S'4db

III

Alloys

Re-Ru A

4d3

4d'

8,186

5,64

5S'4dv

III

Alloys

Re-Pt

A

6S2

6S2

9,988

12,7

öS^d 8

II,IV

Alloys

Re-V

Β

5d'

3d3

2,639

8,98

4S"3d5

IV

Alloys

Re-Nb Β

5d' 5d5

4d' 5S'+4d4

2,804 14,677

2,92 10,3

5S'4d4 5S'4d4

V V

Alloys Alloys

Re-Fe

5d5

4S"+3d3

13,232

0,05

4S"3d

V

Alloys

Β

366

1

2

3

4

5

6

7

8

9

5d' 5d2

3d2 4S2+3d2

2,855 6,547

1,11 12,5

4S23d2 4S23d2

V V

Alloys Alloys

Re-Ta Β 6S2+5d5 5d5

6s"+5dJ 5d3

17,956 12,929

30,4 2,36

6S25d3 6S25d3

V V

Alloys Alloys

Re-Cr Β

5d' 5d5

3d3 4S'+3d5

2,517 10,86

13,7 12,7

4S'3d i 4S!3d5

V V

Alloys Alloys

Re-Jr

Β

6S2

6S2

9,746

10,3

6S25d7

IV

Alloys

Re-Rh Β

5d2

4d4

6,746

15,5

5S'4d8

II,IV

Alloys

Re-Pd Β

5d2

5d'

4dIÜ 4d4

5,456 2,204

5,66 26,8

ss^d 1 " 5S°4d10

II II

Alloys Alloys

3d1 6S2+5d'

3d2 3d +4S*

1,24 4,798

79,8 33,5

4S'3d lu 4S'3d10

I I

5d1

3d2 4S2 4S2+3d2

3,051 61,7 6,90 24,1 37,7 9,951

4S23d5 4S23d5 4S23d5

II II II

Re-Ti Β

Re-Cu C

Re-Mn C

2

6S 6S2+5d2

2

-

-

367 Z

Orbital

Ζ = 76 , Os ( 6S25d6) 5d 6S 0-? 4,700 4 ι 5 6 6,64 6S2 8,795

7 6S25ds

8 III

9 Alloys

1 Os-Re

2 A

6S 9,399 3 6S2

Os-Ni

Β

6S2

6S2

7,427

23,4

4S23d8

IV

Alloys

Os-Jr

Β

6S2

6S2

9,746

3,62

6S25d'

IV

Alloys

Os-Rh

Β

6S1

5S1

6,205

27,6

SS^Sd"

?

Comp.

Os-Pt*

Β

6S2

6S2

9,988

6,07

6S25d'

?

Comp.

Os-Ru

Β

6S2

5S1

6,019

43,8

5S ,4d*

?

Comp.

Os-Fe

Β

6S2

4S"

7,099

19,5

4S23d6

?

Comp.

Os-Au*

Β

6S2

6S2

2,255

123

6S25dv

?

Comp.

Os-W

Β

6S2

6S2

8,724

7,45

6S25d4

V

Alloys

Os-Co

C

6S1

4S2

7,276

43,0

4S23d7

II

-

Orbital Ρ 1 Jr-Pt*

5dJ 6S2 5d'+6S2 5d' 5d2 5d2+6S2 2,634 5,267 7,798 9,746 26,766 15,013 2 4 8 3 5 6 7 2 2 8 A 5d' 5d 2,65 0,61 6S 5d III

Jr-Rh

A

5d'

4d2

3,373

24,6

5Sl4d*

III

Alloys

Jr-Co

A

5d'

3d*

3,036

14,2

4S'3d ,u

ΠΙ

Alloys

Jr-Fe

A

5d3

3d j

6,133

23,9

4S23d

III

Alloys

Jr-Os

A

6S2

6S2

9,399

3,62

6S25d6

IV

Alloys

Jr-Au*

Β

5dl 5d'

5d' 5d2

1,887 3,774

33,0 35,5

6sJ5d® 6S'5d10

? ?

Comp. Comp.

9 Alloys

368

1

2

3

4

5

6

7

8

9

Jr-Ru Jr-Mn

Β Β

5d2 5d2

4d' 3dJ

1,229 4,537

124 14,9

5S'4d' 4S23d5

? IV

Alloys

Orbital

Z= 78, Pt* (6S 5d ) 6S 6S2+5d8

5d

5d

5d

2,65

5,29

7,94

9,988

20,568

5d

6S2+5d3

1,325

13,958

1

2

3

4

5

6

7

8

9

Pt-Pd

A

Pt-Ni

A

5d4 3d1 5d2

4d lu 4d2 3d2

5,456 1,102 2,558

3,09 18,4 3,53

5Su4dlu 5S°4d10 4S"3d8

III III III

Alloys Alloys Alloys

Pt-Rh

A

5d'

4d'

1,704

25,0

5S'4d8

III

Alloys

Pt-Jr

A

5d4

5d2

5,267

0,44

6S25dv

III

Alloys

Pt-Fe

A

5d4

3d2

4,263

21,5

4S23d6

III

Alloys

Pt-Mn A

5d2

3d2

3,051

14,1

4S23d5

III

Alloys

Pt-Mo A

5d2

4d2

2,69

1,50

5S'4d5

III

Alloys

16,1 13,3 26,4

6S25dy 6S25d9 4S23dv

III III III

Alloys Alloys Alloys

Pt-Au* A

5d2 6d2 2,255 2 8 6S +5d 6S2+5d9 17,994 2,033 5d2 3d2

Pt-Co

A

Pt-Cu

A

5d4

3d'+4S'

4,181

23,4

4S'3d1"

III

Alloys

Pt-Re

A

5d4

5d2

5,774

8,75

6S23d5

II,IV

Alloys

Pt-Zn

A

5d4

3d2

5,17

2,29

4S23dlu

IV

Alloys

Pt-Ag

A

5d'

4d2

3,184

82,5

5S'4d lu

II

Alloys

Pt-Cd

A

10,2 6,46

5S24dlu 5S24d10

V V

Alloys Alloys

4d2 8,791 5d6 2 3 6S +5d 5S2+4d2 12,954

369

1

2

3

4

5

6

7

8

Pt-W

A

5d6

5d2

8,482

6,60

6S25d4

II,IV

Alloys

Pt-Cr

A

5d6

4S'+3d'

7,556

4,96

4S13d5

II,IV

Alloys

Pt-Ru

A

5d' 5d2

4dl 4d 2

IV IV

Alloys Alloys

Orbital

5d'

6S2

Ρ

1,887

2,255

1,229 7,52 5S'4d 7 2,458 7,52 5S'4d 7 2 y Ζ = 79, Au (6S 5d ) 6S 2 +5d' 5d2 6S2+5dy 4,143

0,774

9

17,994

1

2

3

4

5

6

7

8

9

Au-Ag

A

Au-Cu

A

Au-Ni

A

5d2 3d1 6S2+5d9 6S 2 +5d' 5d2 5d2 6S2 6S2+5d9 6S 2 +5d' 5d'

5S1 4d" 5S'+4d10 3d'+4S' 4S1 3d* 4S2+3d8 4d ,u 4d4

3,560 1,604 18,498 4,181 3,558 3,817 2,558 17,354 5,456 2,204

11,7 16,2 2,76 0,91 5,89 1,13 12,6 3,62 27.4 15.5

s s W 5S'4d 10 ss^d10 4S'3d lu 4S13d10 4S23d8 4S23d8 4S23d8 5Su4dllJ 5S°4d10

III III III III III III III III III in

Alloys Alloys Alloys Alloys Alloys Alloys Alloys Alloys Alloys Alloys

3d2

Au-Pd

A

Au-Pt

A

6S2+5d9

6S2+5d8

20,568

13,3

6S25d8

III

Alloys

Au-Fe

Β

5d2 6S 2 +5d'

3d2 4S2+3d6

4,263 19,369

12,2 7,36

4S23d(> 4S23d6

II, IV II, IV

Alloys Alloys

Au-Zn

Β

6S J +5d'

3d2

5,17

22,1

4S 2 3d lu

V

Alloys

Au-Mn

Β

6S 2 +5d' 6S2+5d9 5d'

3dJ 4S2+3d5 3d1

4,537 14,335 1,539

9,08 22,6 20,3

4S23d5 4S23d5 4S23d5

V V V

Alloys Alloys Alloys

370

1

2

3

4

5

6

7

8

9

Au-Cd

Β

6S2+5d'

5S2

4,163

0,5

5S24dlu

V

Alloys

Au-Jr

C

6S2 6S2 9,746 2 9 6S +5d 6S2+5d7 26,766

125 39,2

6S25d' 6S25d7

-

-

-

-

6S2+5dy 4S2+3d2 5d' 3d2

23,3 7,45

4S23d' 4S23d7

II II

Alloys Alloys

Au-Co

C

14,236 2,033

Z= 80, Hg (6S 5d ) Orbital

6S

5dz

6S2 + 5d2

3,374

6,219

11,593

1

2

3

4

5

6

7

8

Hg-Zn

A

6S2 5d2

4S2 3d2

5,115 5,17

41,0 45,5

4S23dIU 4S23d*°

II II

Hg-Cd

A

6S2 5d2

5S2 4d2

4,163 8,791

46,8 6,73

5S24dlu 5S24d10

IV IV

Hg-Jn

A

6S2

5P'+5S2

2,339

36,2

5P'5S2

II?

Hg-Fe

Β

6S2 5d2

4S2 3d3

7,099 6,133

71,1 29.1

4S23db 4S23d6

I? I?

-

6S2 5d2

4S1 3d2

3,558 1,24

5.31 148

4S'3d10 4S'3d10

I, II? I, II?

-

Hg-Cu

Β

9 "

Alloys Alloys

Hg-As

Β

5d2 6S2

4P3 l/2(4p3)

7,57 3,79

8,22 11,6

4p34S2 4p34S2

V V

Alloys Alloys

Hg-Pb

Β

6S2 5d2

6P2 6P2+6S2

2,334 7,959

22,9 3,21

6P26S2 6P26S2

II,V II,V

Alloys Alloys

Hg-Ti

C

6S2

4S2

3,692

9,00

4S23d2

V?

Alloys

371

1

2

3

4

5

6

7

8

9

Hg-Ga

C

6S2 6S2+5d2

4S2 4S 2 +4P'

4,875 6,085

36,4 62,3

4P'4S 2 4P ! 4S 2

I I

-

5d2 6S2

6P3 6S2

9,275 13,216

1,47 118,6

6P36S2 6P36S2

II II

-

5d2

6S2+5d2

6,029

30,7

6S2+5dy

V

Alloys

Hg-Bi

C

Hg-Au*

Β

Z=82, Pb CöP'öS") 2 6P2 + 6S 6P1

Orbital

6P

6S

Ρ

2,338

5,831

7,959

1,169

1

2

3

4

5

6

7

8

9

Pb-Jn

Β

6Ρ2

5P'+5S 2

2,339

0,04

5P'5S 2

IV

Alloys

Pb-Bi

A

6P2+6S2

6P>

9.275

15,3

6P36S2

II,V

Alloys

Pb-Cd Β

6Ρ2

5S2

4,163

56,1

5S 2 4d lu

II

-

Pb-Co Β

6Ρ2

3d2

2,033

14,0

4S24dIÜ

I

-

Pb-Ag Β

6Ρ1 6Ρ2

4d2 5S1

3,185 3,560

92,6

5S'4d ,u 5S'4d 10

IIE

•

HE

Pb-Zn Β

6S2

5S2

5,115

9,60

4S 2 3d lu

Ι,ιι

Pb-Ca Β

6Ρ2

4S2

4,775

68,5

4S2

Pb-Na Β

6Ρ1

3S1

4,694

120,2

3S1

Comp.

Phase

Pb-K

Β

6Ρ1

4S1

5,06

124,9

4S1

Comp.

-

Pb-Sr

Β

6Ρ2

5S2

5,280

77,2

5S2

Pb-Hg Β

6Ρ2

6S2 5d2

3,374 8,219

36,3 3,21

6S25dIU 6S25d10

II II

Alloys Alloys

5S2 5P2+5S2

1,991 4,348

95,5 58,7

5P25S2 5P25S2

IIB IIB

Alloys Alloys

2

6P +6S Pb-Sn

Β

2

6S2 6P2+6S2

-

-

-

372

1

2

Pb-Si

Β

4

5

6

7

8

6P2 3P2 2 2 6P +6S 3P2+3S2

6,271 16,781

91,4 71,3

SP^S 2 3P23S2

I I

6P2 4P2 2 2 6P +6S 4P2+4S 2

5,647 8,284

82,9 4,00

4P24S 2 4P 2 4S 2

HE

Pb-Mn Β

6P2 3d2 2 2 6P +6S 4S2+3d2

3,651 9,951

26,5 23,2

4S23d5 4S23d5

I I

Pb-Fe

Β

6P2 3d2 2 2 6P +6S 4S2+3d2

4,263 11,362

58,3 35,2

4S23db 4S23d6

I I

Pb-Al

C 6P2+6S2 3P'+3S2

3,644

74,4

3P'3S2

I

-

Pb-Ga

C 6P2+6S2 4P'+4S2

6,085

26,7

4P'4S2

I

-

Pb-As

C

6P2 4P3 2 2 3 6P +6S 4P + 4S2

7,57 20,837

4P34S2 4P34S2

II II

6P2 5P3 2 2 6P +6S 5P3+5S2

6, 198 17,746

76,1

5P35S2 5P35S2

II II

C

6P1 3d2 2 2 6P +6S 4S2+3d2

1,685 8,394

36,2 97,3

4S13d5 4S'3d5

1,11 1,11

Pb-Mo C

6P1 4d2 2 2 6P +6S 5S' + 4d'

2,69 6,573

78,8 19,1

SSUd* 5S'4d5

I? I?

Pb-Ni

C

6P2 3d2 2 2 2 6P +6S 4S + 3d2

2,558 9,985

8,99 22,6

4S23d5 4S23d5

I, II 1,11

Pb-Eu

C

0,4035

141,1

6S 2 (4f)

?

Pb-Ge

Pb-Sb

Pb-Cr

Β

C

3

6P2

6S2

-

89,4 -

HE

9 -

Alloys Alloys -

-

-

-

-

-

-

-

3

Orbital

6P

Ρ

9,275

6S

2

13,216

Z=83, Bi (6P36S2) 6P3 + 6S2 22,491

1

2

3

4

5

6

7

8

9

Bi-Sb

A

6P3 6P3+6S2

5P3 5P3+5S2

6,198 17,746

39,8 23,6

5P j 5S 2 5P35S2

III III

Alloys Alloys

Bi-Pb

A

6P3 6P3

6P2 6P2+6S2

2,338 7,959

15,3

6P^6S2 6P26S2

V

6P3 6P3

4d3 4d 3 +5S'

6,393 9,953

36,8 7,05

5S'4d 10 5S'4d 10

II II

Comp. Comp.

6S 2 +5d'

4,142

138

6S24dy

II

Comp.

Bi-Ag

Β

Bi-Au*

Β 6P3+6S"

Bi-Fe

Β

6P3

3d3

6,133

40,8

4S23db

I

-

Bi-Cd

C

6P3

5S2

4,163

76,1

5S 2 4d lu

II

-

Bi-Hg

C

6P3

6S2

3,374

93,3

6S 2 5d lu

II

-

Bi-Sn

C

6P3 6P3

5P2 5P 2 +5S 2

2,357 4,348

72,3

5Ρ"582 5P25S2

II II

-

6P3 6P3

4S1 4S ! +3d 2

3,558 4,798

89,1 63,6

4S'3d lu 4S'3d10

II II

-

6P3 6P3+6S2

3d3 3d3+4S2

4S537 11,437

68,6 65,2

4S23d5 4S23d5

II II

-

6P3 6P3+6S2

3P2 3P4+3S2

10,19 33,87

40,4

3P43S2 3P43S2

Bi-Cu

Bi-Mn

Bi-S

C

C

C

-

374 APPENDIX 3 Po-parameters of valence orbitals of neutral atoms in basic state (calculated via atom ionization energy) Electrons of valence orbitals 2

Ei (eV)

(A)

(eVÄ)

Po (eVÄ)

ΣΡ0 (eVÄ)

3

4

5

6

7

IS1 2S1 2S1 2S1 2P1 2S1 2S1 2P1 2P1 2S1 2S1

13,595 5,390 9,323 18,211 8,296 25,155 37,92 11,260 24,383 47,86 64,48

0,5295 1,586 1,040 1,040 0,776 0,769 0,769 0,596 0,596 0,620 0,620

14,394 5,890 13,159 13,158 21,105 23,890 23,890 35,395 35,395 37,243 37,243

4,7985 3,487 5,583 7,764 4,933 10,688 13,132 5,641 10,302 16,515 19,281

4,7985 3,487

2P1 2P1 2P1

14,54 29,60 47,426

0,488 0,487 0,487

52,912 52,912 52,912

6,257 11,329 16,078

2P1 2P1

13,618 35,118

0,414 0,414

71,380 71,380

5,225 12,079

17,304

2P2

7,0 (W)

0,413

71,380

5,349

22,653

F(I)

2P1

17,423

0,360

94,641

5,882

5,882

F(I)

2S1

17,423

0,396

94,641

6,432

Na

3S1

5,138

1,713

10,058

4,694

4,694

Mg

3S1 3S1

7,469 15,035

1,279 1,279

17,501 17,501

6,274 9,162

15,436

Atom 1 Η Li Be Β

C

N(III)

0

Ti

13,347 28,753

51,739

33,664

375 APPENDIX 3 (continued) 1

2

3

4

5

6

7

Al

5,986 18,829 28,44

1,312 1,044 1,044

26,443 27,119 27,119

6,055 11,396 14,173

31,624

Si

3P1 3S1 3S1 3pi

8,152 16,342 33,46 45,13

1,068 1,068 0,904 0,904

29,377 29,377 38,462 38,462

6,716 10,948 16,932 19,799

P(III)

3P1 3S1 3S1 3pi

10,487 19,73 30,16

0,919 0,916 0,916

38,199 38,199 38,199

7,696 12,268 16,038

0,808 0,808 0,808 0,808

48,108 48,108 48,108 48,108

7,130 13,552 17,446 21,296

20,682

3pi

10,360 23,35 34,8 47,29

C1(I)

3P1

12,268

0,728

59,842

8,125

8,125

Κ

4S1

4,339

2,162

10,993

5,062

5,062

Ca

4S1 4S1 4Sl 4S1 4d'

6,113 11,871 6,56 12,89 24,75

1,690 1,690 1,57 1,57 0,539

17,406 17,406 19,311 19,311 81,099

6,483 9,320 6,717 9,882 11,456

15,803

Ti(II)

4S1 4S1

6,82 13,58

1,477 1,477

20,879 20,879

6,795 10,231

17,026

Ti(ni)

3d1

28,14

0,489

106,04

12,184

29,210

Ti(IV)

3d1

43,24

0,489

106,04

17,629

46,839

V(II)

4Sl 4S1 3d1

6,74 14,21 29,699

1,401 1,401 0,449

22,328 22,328 129,09

6,6362 10,525 12,097

17,162

3P1 3pi S(II) S(IV)

Sc

V(III)

3pi 3pi 3 pl

54,394

35,996

59,424

28,055

29,249

376 APPENDIX 3 (continued) 1

2

3

4

5

6

7

V(V)

3d1 3d1

48,0 65,2

0,449 0,449

129,09 129,09

18,468 23,863

71,579

Cr(III) 4S'3d5

4S1 3d1 3d1

6,765 16,498 31,00

1,453 0,427 0,426

23,712 152,29 152,29

6,949 6,734 12,152

Cr(V) 4S'3d5

3d1 3d1

(51) 73

0,426 0,426

152,29 152,29

19,014 25,825

Cr(III) 4S23d4

4S1 4S1 3d1

6,765 16,498 31,00

1,453 1,453 0,426

23,712 23,712 152,29

6,949 11,920 12,152

Cr(V)

3d1 3d1

(51) 73

0,426 0,426

152,29 152,29

19,014 25,825

(75,860)

Mn(II)

4S1 4S1

7,435 154640

1,278 1,278

25, 118 25, 118

6,895 11,130

18,025

Mn(III)

3d1

33,69

0,3885

177,33

12,200

30,225

Mn(V)

3d1 3d1

(53) (76)

0,389 0,389

177,33 177,33

18,478 25,340

(74,043)

Fe(II)

4S1 4S1 3d1

7,893 16,183 30,64

1,227 1,227 0,365

26,57 26,57 199,95

7,098 11,364 10,564

18,462

4S1 4S1 3d1

7,866 17,057 33,49

1,181 1,181 0,343

27,983 27,983 224,85

6,973 11,714 10,929

Ni(III)

4S1 4S1 3d1

7,635 18,153 36,16

1,139 1,139 0,324

29,348 29,348 251,16

6,708 12,130 11,194

30,032

Ni(IV)

3d1

(56)

0,324

251,16

16,922

46,954

Fe(III) Co(II) Co(III) Ni(II)

25,835

(70,674)

31,048

29,026 18,687 29,615 18,838

377 APPENDIX 3 (continued) 1

2

3

4

5

6

7

Cu(I) 4S'3d , ° Cu(II) 4S'3d 10 Zn'

4S1

7,726

1,191

30,717

7,081

7,081

3d'

20,922

0,312

278,78

6,191

13,272

4S1 4S1

9,394 17,964

1,065 1,065

32,02 32,02

7,623 11,976

19,599

Zn"

4S' 3d1

9,394 17,964

1,065 0,293

32,02 308,13

7,623 5,175

12,798

Ga

4P' 4S1 4S1

6,00 20,51 30,70

1,254 0,960 0,960

34,833 44,940 44,940

6,188 13,691 17,799

Ge(III)

4 pl 4P1

7,900 15,935

1,090 1,090

41,372 41,372

7,128 12,233

19,361

Ge(IV)

4S1 4S1

34,21 45,7

0,886 0,886

58,223 58,223

19,933 23,882

61,176

As (III)

4P1 4P1 4P1

9,815 18,62 28,3

1,001 0,982 0,982

49,936 49,936 42,936

8,210 13,384 17,854

As(V)

4S1 4S1

50,1 62,9

0,826 0,826

71,987 71,987

26,277 30,176

95,901

Se(II)

4P1 4P1

9,752 21,19

0,918 0,918

61,803 61,803

7,819 14,795

22,614

Br(I)

4P1

11,84

0,851

73,346

8,859

8,859

Rb

5S1

4,176

2,287

14,309

5,7275

5,7275

Sr

5S1 5S1

5,694 11,030

1,836 1,836

21,223 21,223

7,004 10,363

17,367

37,678

39,448

378 APPENDIX 3 (continued) 1

2

3

4

5

6

7

y

5S1 5S1 4d'

6,38 12, 23 20,5

1,693 1,693 0,856

22,540 22,540 229,18

7,302 10,792 16,640

34,554

Zr(II)

5S1 5S1

6,835 12,92

1,593 1,593

23,926 23,926

7,483 11,064

18,547

Zr(IV)

4d' 4d'

24,8 33,97

0,790 0,790

153,76 153,76

17,378 22,848

58,773

Nb(III) 5S'4d 4

5S1 4d' 4d'

6,882 14,320 28,1

1,589 0,747 0,747

20,191 113,64 113,64

7,093 9,776 17,718

Nb(IV) 5S'4d 4

4d' 4d'

38,3 50

0,747 0,747

113,64 113,64

22,855 28,113

Nb(III) 5S24d

5S1 4d' 4d'

6,882 14,320 28,10

1,589 1,589 0,747

25,822 25,822 136,55

7,682 12,095 18,191

Nb(V) 5S24d3

4d' 4d*

38,3 50

136,55 136,55

23,653 29,329

90,950

17,475

0,7 47

34,587

85,555

37,968

0,7 47 Mo(II) 5S'4d5 Mo(III) 5S'4d 5 Mo(VI) 5S'4d 5 Mo(II) 5S24d4 Mo(III) 5S24d4

1

5S 4dl 4d'

7,10 16,155 29,6

1,520 0,702 0,696

21,472 110,79 110,79

7,182 10,293 13,373

4d' 4d' 4d' 5S1 5S1 4d'

46,4 61,2 67 7,10 16,155 29,6

0,696 0,696 0,696 1,520 1,520 0,696

110,79 110,79 110,79 28,027 28,027 139,352

25,006 30,767 32,819 7,792 13,088 17,949

30,848

123,44 20,872 38,82

379 APPENDIX 3 (continued) 1

2

3

4

5

6

7

Mo(III) 5S24d4 Mo(VI) 5S24d4

4d'

29,6

0,696

139,352

17,949

38,82

4d' 4dJ 4d'

46,4 61,2 67

0,696 0,696 0,696

139,352 139,362 139,352

26,218 32,623 34,940

132,61

Te(III) 5S'4d 6

5S1 4dJ 4d'

7,23 14,87 31,9

1,391 0,648 0,648

30,076 149,33 149,33

7,537 9,052 18,158

Te(V) 5S'4d6

4d' 4d'

(43) (59)

0,648 0,648

149,33 149,33

23,482 30,439

88,668

Ru(II) 5S'4d7

5S1 4d'

7,36 16,60

1,410 0,515

24,217 147,7

7,265 8,081

15,346

30,3

0,515

147,73

14,114

29,46

(47)

0,515

147,73

20,797

50,257

Ru(III) 5S'4d 7 Ru(IV) 5S'4d 7

34,747

Ru(V) Ru(VI)

4d' 4d'

(63) (81)

0,515 0,515

147,73 147,73

26,602 32,530

76,859 109,39

Rh(III) 5S'4d 8

5S1 4d* 4d'

7,46 15,92 32,8

1,364 0,589 0,589

25,388 162,61 162,61

7,264 8,866 17,266

33,396

Rh(IV)

4d'

(46)

0,589

162,61

23,224

56,620

380 APPENDIX 3 (continued) 1

2

3

4

5

6

7

Pd (II) 5S°4d10

4d' 4d'

8,33 19,42

0,567 0,567

166,87 166,87

4,593 10,329

14,922

Pd (IV) 5S°4d10

4d' 4d'

(33) (49)

0,567 0,567

166,87 166,87

16,825 23,818

55,565

Ag(I) 5S*4d Ag(II) 5S 4d10

5S1

7,576

1,286

26,283

7,108

7,108

4d'

21,487

0,536

196,12

10,936

18,044

Ag(I) 5S 4d9

5S1

7,576

1,286

37,122

7,717

7,717

Ag(II) 5S24d9 Cd(II)

5S1

21,487

1,286

37,122

15,841

23,558

5S1 5S1

8,994 16,909

1,184 1,184

38,65 38,65

8,349 13,188

30,298

Cd(II)

55' 4d'

8,994 16,909

1,184 0,508

38,65 266,84

8,349 8,322

16,671

Jn

5P1 5S1 5S1

5,785 13,86 28,0

1,382 1,093 1,093

41,318 52,103 52,103

6,699 14,770 19,280

Sn(II)

5P1 5P1

7,332 14,6

1,240 1,240

47,714 47,714

7,637 13,124

20,761

Sn(IV)

5S1 5S1

30,7 46,4

1,027 1,027

65,022 65,022

21,237 27,507

69,505

Sb(III)

5P1 5P1 5P1

8,64 16,5 24,8

1,193 1,140 1,140

57,529 57,529 57,529

8,742 14,175 18,956

40,749

41,870

381 APPENDIX 3 (continued) 1

2

3

4

5

6

7

Sb(V)

5S' 5S1

44,1 63,8

0,969 0,969

77,644 77,644

27,563 34,418

103,85

Te(II)

5P1 5P1

9,010 18,6

1,111 1,111

67,282 67,282

8,792 15,809

24,601

Te(IV)

5P1 5P1

31 38

1,111 1,111

67,282 67,282

22,780 25,941

50,542

J(I)

5P1

10,451

1,044

77,65

9,567

9,567

Cs

6S1

3,893

2,518

16,193

6,106

6,100

Ba

6S1 6S1

5,211 20,608

2,060 2,060

22,950 22,950

7,314 10,858

18,172

Ce(II) ÖS^f 2

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