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Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus


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Volume 70, Issue 10

Issues

Phase Equilibria and Interaction Between the CsCl–PbCl2–PbO System Components

Pavel A. Arkhipov
  • Corresponding author
  • Institute of High Temperature Electrochemistry, Ural Branch of Russian Academy of Sciences Ekatherinburg, S. Kovalevskaya St., 22, 620990, Russian Federation
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/ Irina D. Zakiryanova
  • Institute of High Temperature Electrochemistry, Ural Branch of Russian Academy of Sciences Ekatherinburg, S. Kovalevskaya St., 22, 620990, Russian Federation
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/ Anna S. Kholkina
  • Institute of High Temperature Electrochemistry, Ural Branch of Russian Academy of Sciences Ekatherinburg, S. Kovalevskaya St., 22, 620990, Russian Federation
  • Ural Federal University named after the first President of Russia B. N. Yeltsin, Ekatherinburg, Russia
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/ Alexandra V. Bausheva
  • Institute of High Temperature Electrochemistry, Ural Branch of Russian Academy of Sciences Ekatherinburg, S. Kovalevskaya St., 22, 620990, Russian Federation
  • Ural Federal University named after the first President of Russia B. N. Yeltsin, Ekatherinburg, Russia
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/ Anastasia O. Khudorozhkova
  • Institute of High Temperature Electrochemistry, Ural Branch of Russian Academy of Sciences Ekatherinburg, S. Kovalevskaya St., 22, 620990, Russian Federation
  • Ural Federal University named after the first President of Russia B. N. Yeltsin, Ekatherinburg, Russia
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Published Online: 2015-08-19 | DOI: https://doi.org/10.1515/zna-2015-0273

Abstract

Thermal analysis was applied to determine liquidus temperatures in the CsCl–PbCl2–PbO system, with the PbO concentration ranging from 0 to 20 mol%. The temperature dependence of the PbO solubility in the CsCl–PbCl2 eutectic melt was studied, and the thermodynamic parameters of the PbO dissolution were calculated. The type, morphology, and composition of oxychloride ionic groupings in the melt were determined in situ using Raman spectroscopy.

Keywords: Lead Oxide; Lead Oxychloride; Liquidus Temperature; Raman Spectroscopy; Solubility; Thermal Analysis

1 Introduction

Mixtures of molten alkali metal chlorides and lead may be successfully used as electrolytes in the process of lead alloy refining [1]. The technological process of lead feed into the bath causes the formation and accumulation of lead oxide in the electrolyte that changes the physical–chemical properties of the melt (e.g. the melt electric conductivity decreases, its viscosity and density increase), and this process influences the electrochemical parameters of the electrolytic cell [2] and, therefore, the quality of the end product.

The accumulated data on phase equilibria and the interaction of components in lead(II)oxide-containing chloride systems are mostly related to the PbCl2–PbO system. The PbCl2–PbO system phase diagram presented by Podsiadlo [3] demonstrates that different ratios of components may cause the formation of several chemical compounds: Pb5Cl2O4, Pb3Cl2O2, and Pb2Cl2O.

Hacetoglu and Flengas [4] provide the results of thermodynamic calculations on the molten PbCl2–PbO system components activity and mixing enthalpy, which appeared to greatly deviate from the ideal values to the negative side. The authors consider that the following results indicate an interaction between the mixture components and suggest the formation of complex mixed oxyfluoride groupings of the (PbpOqClr)(2p–2q–2r)+ composition. The composition of such formations was observed to change based on the concentration of the mixture components and corresponds to the oxychloride compounds formed in the system [3].

Phase equilibria and component interaction in more complex chloride systems containing additional alkali metal chlorides have not been studied. There is a lack of data in the literature on the PbO interaction mechanism with chloride melts obtained using structure-sensitive methods. The structure, composition, and resistance of the groupings formed in these ionic liquids require further study.

We have previously studied phase equilibria in the ternary KCl–PbCl2–PbO system and observed that the temperature of primary crystallisation increases from 409 °C without PbO to 533 °C with 8.0 mol% of PbO [5].

This study presents results of a complex study on phase equilibria and interaction between ternary chloride CsCl–PbCl2–PbO system components, including determination of PbO dissolution in the chloride melt, liquidus temperatures, dissolution thermodynamic characteristics, and in situ Raman spectroscopy experiments on the oxide–chloride mixture component interaction.

A low-melting chloride eutectic mixture PbCl2–CsCl (28.7–71.3 mol%) with an added 0.5 to 20 mol% PbO was chosen as the subject of this research and a model electrolyte to study oxychloride lead compounds, as the lead-polarising effect is greater than that of the alkali metal. The process temperatures correspond to the temperatures required in the industrial refining of designed lead alloys.

2 Experimental

2.1 Chemicals

To prepare initial salt mixtures, chemically pure CsCl and PbCl2 salts produced by Closed Joint-Stock Company “VEKTON” (St. Petersburg, Russian Federation) were used. CsCl and PbCl2 salts were preliminarily dehydrated under vacuum at continuously increasing temperature and were then remelted in argon.

The PbCl2–CsCl (28.7–71.3 mol%) eutectic mixture was formed by alloying the corresponding weight portions of the individual salts. Extra high-purity lead oxide produced by Closed Joint-Stock Company “Khimreactivsnab” (Ufa, Russian Federation), was dried under inert atmosphere at 200 °C and then melted in an alundum crucible at 940 °C and dwelled for 1 h. When the crucible cooled down, it was carefully split to form convenient portions of lead oxide to be used as additions to the chloride melt. All operations with prepared reagents and mixtures were performed in an inert-atmosphere dry box. The Pb3O2Cl2 chemical compound was additionally synthesised. A lead oxychloride of such composition was detected during a preliminary X-ray phase analysis of the frozen fusions used for experiments on lead oxide solubility in the molten chloride PbCl2–CsCl eutectics.

Pb3O2Cl2 was synthesised from the grounded mixture of the PbO and PbCl2 weight samples of the corresponding stoichiometry according to the following reaction:

2PbO(solid)+PbCl2(molten)Pb3O2Cl2(molten) (1)(1)

The mixture was heated to a temperature exceeding its melting point (695 ± 2 °C) [3] by 100 °C and dwelled at this temperature for 3 h. X-ray diffraction (XRD) analysis proved the formation of Pb3O2Cl2 phase (Fig. 1).

XRD data of the synthesised oxychloride Pb3O2Cl2.
Figure 1:

XRD data of the synthesised oxychloride Pb3O2Cl2.

The molten mixtures were yellow and lemon-coloured, or transparent without precipitation.

2.2 Measurement of Liquidus Temperature

Liquidus temperatures of the melts under study were measured by the thermal analysis method. The temperature changes of the molten mixtures were recorded as functions of time during the electrolyte cooling period.

Measurements were performed in a dry air atmosphere. The composition under study was loaded into the alundum crucible and lowered to the isometric zone of a shaft furnace with nichrome heaters. The temperature in the furnace was controlled by a microprocessing thermoregulator VARTA TP-403 and recorded by a Pt/PtRh thermocouple using a digital multimeter APPA 109N with a frequency of 1 measurement per second. Temperature changes were controlled in a real-time mode. The measurements were carried out during the period of the melt cooling down, with a rate of 2 ° per minute. The melt was reheated 70 °C higher than the temperature of the supposed primary melt crystallisation. Each melt composition was measured during several different independent experiments.

2.3 High Temperature Raman Spectra Recording Procedure

Raman spectra were recorded using a fibre optic spectrometric complex Ava-Raman (Avantes, The Netherlands), which includes a monochromatic laser (λ=532 nm, radiation power of 50 mW). The optic diffraction scheme at 180 ° was used to record spectra. The spectrometer is equipped with a notch filter that clips intensive Rayleigh scattering in the region of 150 cm−1. Two different modifications of the high-temperature optic cells were used to record spectra of crystalline (at higher temperatures) and molten samples.

A quartz glass ampule with an inner diameter of 4 mm was used as an optic cell during chloride eutectics spectra recording. An alundum crucible of 10 mm height and 12 mm diameter served as a container for chemically aggressive PbO- and Pb3O2Cl2-containing melts. The crucible was placed into the high-temperature optic attachment made in the form of duralum block with a vertically located nichrome heater and upper front quartz window for incident and scattered light (Fig. 2). The block was chilled by air blast from the outside.

The Raman spectra recording set-up: 1 – block; 2 – the melt under study; 3 – alundum crucible; 4 – optic quartz window; 5 – focus object-glass; 6 – fibre optic Raman probe; 7 – laser beam and scattered light.
Figure 2:

The Raman spectra recording set-up: 1 – block; 2 – the melt under study; 3 – alundum crucible; 4 – optic quartz window; 5 – focus object-glass; 6 – fibre optic Raman probe; 7 – laser beam and scattered light.

The experiments were carried out in an air atmosphere. In addition, sample spectra demonstrated no vibrational bands, which are the characteristic of adsorbed water, hydroxyl, or carbon groupings. The X-ray phase analysis of the fusions was performed after high-temperature optic experiments. The analysis demonstrated that the products of interaction between the container material and lead oxide containing melts were not found.

This technique is successfully used to study the interaction mechanism of BaO and SiO2 with halide melts [6, 7].

3 Results and Discussion

3.1 CsCl–PbCl2–PbO System Liquidus Temperatures

The melting point of the CsCl–PbCl2 (71.3–28.7 mol%) eutectic was measured without lead oxide additions at the beginning of the studies. The temperature of the knee point is 476 ± 1 °C. The eutectic melting point detected in this study corresponds with the literature data [8].

The subsequent stage of the study was to measure the temperature of primary crystallisation of the oxychloride (CsCl–PbCl2)–PbO system. The melts cooling curves demonstrate strongly marked bends (Fig. 3).

Cooling curve of the (CsCl–PbCl2)–PbO (71.3–28.7 mol%) melt at PbO concentration of 1.5 mol%.
Figure 3:

Cooling curve of the (CsCl–PbCl2)–PbO (71.3–28.7 mol%) melt at PbO concentration of 1.5 mol%.

Figure 4 illustrates the results of liquidus temperature measurements of the oxide–chloride melt obtained by the analysis of the cooling curves.

Liquidus temperature of the (CsCl–PbCl2)–PbO (71.3–28.7 mol%) system in the PbO concentration interval of 0–20.0 mol%.
Figure 4:

Liquidus temperature of the (CsCl–PbCl2)–PbO (71.3–28.7 mol%) system in the PbO concentration interval of 0–20.0 mol%.

The lead oxide addition to the melt first slightly decreased and then increased the temperature of primary crystallisation. The minimal value of the liquidus temperature is 472 ± 1 °C. It was reached by a lead oxide addition of 1.5 mol%. This point corresponds to the pseudobinary (CsCl (71.3)–PbCl2 (28.7))–PbO system eutectics. A part of the experimental curve, which conforms to the region of molten mixture liquidus temperature increase, is approximated by the following empirical equation:

Tliqu.=485472NPbO+59700NPbO2, R2=0.99 (2)(2)

where Tliqu. is the liquidus temperature, NPbO is the PbO concentration expressed in mole fractions, and R2 is the approximation validity.

The most refractory PbO phase, or its combination with a solvent, should be the first solid phase at the melt crystallisation under conditions of (2). The PbO concentration at liquidus points corresponds to lead oxide solubility (SPbO) in this solvent mixture. The temperature dependence of the lead oxide solubility in the caesium and lead chloride eutectic mixture is presented in Figure 5 in ln(SPbO) − 1/T coordinates.

Temperature dependence of lead oxide solubility in the molten CsCl–PbCl2 (71.3–28.7 mol%) eutectics.
Figure 5:

Temperature dependence of lead oxide solubility in the molten CsCl–PbCl2 (71.3–28.7 mol%) eutectics.

The time dependence of lead oxide solubility is described by the following linear equation:

ln(SPbo)=3.094017.5/T,R2=0.93 (3)(3)

According to the thermodynamics of solutions, we calculated the partial excess free energy, chemical potential, activity and activity coefficient of PbO in the CsCl–PbCl2–PbO solution as follows. Considering the equilibrium of pure PbO solid and liquid solutions with CsCl, PbCl2, and PbO the following expression is true:

gLPbO=go,SPbO (4)(4)

where gLPbO is the molar Gibbs free energy of PbO in the liquid solution or chemical potential. go,SPbO is the molar Gibbs free energy of pure solid PbO.

The relationship between the chemical potential and chemical activity is as follows:

gLPbO=go,LPbO+RT ln(aLPbO) (5)(5)

where go,LPbO is the molar Gibbs free energy of pure liquid PbO, R is the gas constant, T is the absolute temperature, and aLPbO is the activity of PbO in the liquid solution, considering liquid as standard state.

Then, combining (4) and (5), we get:

go,LPbO+RT ln(aLPbO)=go,SPbO (6)(6)

ΔgfusPbO=go,LPbOgo,SPbO=RT ln(aLPbO)  (7)(7)

where, ΔgfusPbO is the Gibbs free energy of PbO fusion.

The activity of PbO is the product of the mole fraction of PbO (XLPbO) in solution and the activity coefficient (fPbO):

aLPbO=(XLPbO) (fLPbO). (8)(8)

Then

ΔgfusPbO=RT ln(XLPbO)RT ln(fLPbO) (9)(9)

Finally, if the PbO solubility in the liquid phase (XLPbO) is experimentally obtained and the Gibbs free energy of fusion of pure PbO is provided by thermodynamic tables, then the excess free energy of PbO and the activity coefficient of PbO can be calculated as follows:

gEPbO=RT ln(fLPbO)=ΔgfusPbORT ln(XLPbO) (10)(10)

fLPbO= EXP[gEPbO/RT] (11)(11)

Thermodynamic characteristics of lead oxide dissolution in the caesium chloride and lead chloride eutectic mixtures (CsCl–PbCl2)–PbO (71.3–28.7 mol%) were calculated using literature data [9] and program HSC-7.1 Chemistry.

Table 1 demonstrates that the excess changes in Gibbs energy during overcooled liquid lead oxide and (RT ln(fPbO, solvent)) solvent mixing have small positive values. This denotes the endothermic process of interaction between lead oxide and chloride melt. The XRD analysis of the frozen fusion after the experiment on solubility detection (Fig. 6) suggests that lead oxychloride Pb3O2Cl2 is present in the caesium chloride and lead chloride mixture. We used Raman spectroscopy to detect the interaction mechanism of the oxide–chloride system components and define compositions and structures of ionic groupings, which are present in the chloride and oxide–chloride melts.

Table 1

Thermodynamic characteristics of lead oxide dissolution in (CsCl–PbCl2)–PbO (71.3–28.7 mol%).

XRD data of frozen fusion after the experiment on the lead oxide solubility in the CsCl–PbCl2 melt.
Figure 6:

XRD data of frozen fusion after the experiment on the lead oxide solubility in the CsCl–PbCl2 melt.

3.2 Raman Spectra and Structure of Crystalline Lead-containing Compounds

To obtain definitive information on the vibrational frequencies of objects under study, which is needed to interpret the experimental data, the Raman spectra of the crystalline lead-containing compounds used in this study were recorded.

An intense vibrational band was recorded in the region of 174 cm−1 in the lead oxide Raman spectrum under normal conditions, which agrees with data reported by G. A. Ozin [10]. The Raman spectrum of lead oxide (II) is illustrated in Figure 7. The location of vibrational bands (289, 385, and 414 cm−1) corresponds to an orthorhombic modification of PbO [11]. The spectrum of the PbCl2–CsCl mixture of the set eutectic composition demonstrates the intense vibrational band in the region of 199 cm−1 and wide band of low intensity in the region of 486 cm−1 conforming with a secondary spectrum, which is in accord with the literature [12, 13]. Figure 8 presents the Raman spectrum of synthesised Pb3O2Cl2. The locations of the observed vibrational bands (275, 295, 340, 435, and 474 cm−1) agree with the corresponding values in the spectrum of the natural mineral mendipite (lead oxychloride of the Pb3O2Cl2 composition) [14].

Raman spectra of PbO at 20 °C.
Figure 7:

Raman spectra of PbO at 20 °C.

Raman spectra of crystalline Pb3O2Cl2 at 20 °C.
Figure 8:

Raman spectra of crystalline Pb3O2Cl2 at 20 °C.

We further focused on the study of the crystalline Pb3O2Cl2 structure and carefully inspected vibrational bands in its spectrum, as an oxychloride of such composition was detected during XRD analysis of the frozen oxide–chloride melts under investigation.

According to the XRD structure analysis [15], lead oxychloride of the Pb3O2Cl2 composition has a D2h16 (Pnma) symmetry space grouping and contains four formula units in elementary cell. The crystal structure of mendipite-type phases is based upon [Pb3O2]2+ double chains of edge-sharing OPb4 tetrahedra. Weak Pb–Cl bonds connect the chains with each other. R. Frost and P. Williams [14] suggest that the vibrational bands observed in the spectrum are attributed to the vibrations of the Pb–O bond in double chains, which are built up from [Pb3O2] groupings.

3.3 Raman Spectra and Structure of Lead-containing Oxide–Chloride Melts

To define the structure and composition of the ionic groupings in the oxide–chloride melt, we recorded Raman spectra of the molten PbCl2–CsCl (28.7–71.3 mol%) eutectic and of the same system with PbO addition of 12 mol%.

The intense band with a maximum at 230 cm−1 was recorded in the spectrum of PbCl2–CsCl molten mixture (Fig. 9, curve 1), which is in agreement with data reported by Dracopoulos et al. [12]. This band may be attributed to a Pb–Cl stretching frequency of C3v symmetry from the PbCl3 grouping in diluted lead chloride melts [12, 16].

A number of interesting regularities were detected when recording Raman spectra. First, the intensity of the vibrational band at 230 cm−1, which corresponds to a Pb–Cl stretching frequency from the PbCl3 grouping, decreases compared to the spectrum of the chloride melt, as the dwelling time of the chloride melt in contact with lead oxide increases. Second, wide bands of low intensity appear in the regions of 430 and 320 cm−1, and shoulders of increasing intensity were detected in the regions of 285 and 256 cm−1. The changes observed in the spectrum of the oxide–chloride melt proceed rather rapidly (over a 30-min span) and then the spectrum stabilises. Figure 9 contains the Raman spectrum of the homogeneous molten chloride mixture with PbO addition of 12 mol% (curve 2).

Vibrational bands of PbO (289, 385, and 414 cm−1) are not present in the spectrum of the frozen melt at room temperature (Fig. 9, curve 3), while vibrational bands of the Pb3O2Cl2 (270, 296, 334, 438, and 477 cm−1) phase were detected. This fact supports the XRD data of frozen fusions, conducted after experiments on the detection of lead oxide solubility. In addition, the maximum of the observed low-frequency band, which corresponds to the Pb–Cl band vibration (204 cm−1), is shifted to higher wavenumber compared to the location of the initial chloride mixture’s vibrational band (199 cm−1). Hence, the initial composition of the chloride mixture is changed.

Because the Pb3O2Cl2 oxychloride phase was detected in the frozen fusion of the oxide–chloride mixture, we found it interesting to record a spectrum of the molten chloride mixture with lead oxychloride added and to compare the spectra of lead-containing chloride melts with PbO and Pb3O2Cl2 additions. Figure 10 (curve 1) demonstrates the Raman spectrum of the PbCl2–CsCl (28.7–71.3 mol%) melt with the addition of Pb3O2Cl2 (10 mol%), where the vibrational band in the region of 230 cm−1 that corresponds to the PbCl3 chloride grouping, as well as bands that were recorded in the regions of 427 and 318 cm−1 and shoulders in the regions of 283 and 257 cm−1 that are analogous to those observed in the melt with the added lead oxide (Fig. 9, curve 2). The spectrum of the frozen PbCl2–CsCl–Pb3O2Cl2 mixture (Fig. 10, curve 2) is analogous to the spectrum of the frozen PbCl2–CsCl–PbO mixture (Fig. 9, curve 3).

Raman spectrum of the PbCl2–CsCl (28.7–71.3 mol%) melt, 510 °C – 1; Raman spectrum of the homogeneous oxide-chloride PbCl2–CsCl (28.7–71.3 mol%) melt with PbO addition of 12 mol%, 510 °C – 2; Raman spectrum of the frozen oxide–chloride mixture (20 °C) after 40-min dwelling of the oxide–chloride melt at 510 °C – 3.
Figure 9:

Raman spectrum of the PbCl2–CsCl (28.7–71.3 mol%) melt, 510 °C – 1; Raman spectrum of the homogeneous oxide-chloride PbCl2–CsCl (28.7–71.3 mol%) melt with PbO addition of 12 mol%, 510 °C – 2; Raman spectrum of the frozen oxide–chloride mixture (20 °C) after 40-min dwelling of the oxide–chloride melt at 510 °C – 3.

Raman spectrum of the PbCl2–CsCl (28.7–71.3 mol%) melt with the addition of Pb3O2Cl2 (10 mol%), 600 °C – 1; Raman spectrum of the frozen mixture (20 °C) after 15-min dwelling of the oxide–chloride melt at 600 °C – 2.
Figure 10:

Raman spectrum of the PbCl2–CsCl (28.7–71.3 mol%) melt with the addition of Pb3O2Cl2 (10 mol%), 600 °C – 1; Raman spectrum of the frozen mixture (20 °C) after 15-min dwelling of the oxide–chloride melt at 600 °C – 2.

Analysis of the obtained spectroscopic results pinpoints the chemical mechanism of PbO dissolution in the lead-containing chloride melts. Indeed, the intensity of the vibrational band in the 230 cm−1 region, which corresponds to the Pb–Cl bond in the PbCl3 complex anion, decreases as lead oxide is added. That is directly connected to a decrease in the amount of chloride grouping. The PbCl3 chloride groupings are destroyed in the presence of oxide anions, which have a greater ionic potential compared to chloride anions.

New vibration bands, which appear in the oxide–chloride melt spectrum in the regions of 430, 320, 285, and 256 cm−1 (Fig. 9, curve 2), are analogous to the Pb–O characteristic vibrations of dissolved lead oxychloride Pb3O2Cl2 (Fig. 10, curve 1). Such a behaviour of the vibrational bands may be explained by the presence of Pb2+ and O2−-containing groupings, which structurally is analogous to that of the Pb3O2Cl2 oxychloride crystalline lattice fragments.

According to the spectral data, complex Pb3O22+ cations, which are analogous to the components of the Pb3O2Cl2 oxychloride chain structure, are the most probable groupings forming basis. A weak counter-polarisation effect of the Cs+ cation, which is not able to form long-lived complex grouping with chlorine anions, and the relatively large charge of the complex Pb3O22+ cation results in the localisation of chloride anions around the Cs+ cation and formation of Pb3O2Cl+ ionic groupings of a complex oxide–chloride composition.

Therefore, total amount of the observed changes in the oxide–chloride melt vibrational spectrum directly indicates the chemical mechanism of interaction of lead oxide (II) with the chloride melt and demonstrates the presence of the following reaction:

[PbCl3+Cs+] (solution)+2PbO (solid)[Pb3O2Cl++Cs++2Cl] (solution) (12)(12)

The increase in the dwelling time of the chloride melt in contact with lead oxide results in the formation of a larger amount of oxychloride groupings in the melt and, thus, increases the intensity of the corresponding vibrational band.

An amount of the PbCl3 chloride groupings simultaneously decreases, which leads to a decrease in the corresponding vibrational bands’ intensity.

Oxychloride Pb3O2Cl+ groupings form double chains, which make up a solid phase–oxychloride of the Pb3O2Cl2 composition, as the melt temperature decreases. These explain the presence of Pb3O2Cl2 vibrational bands in the spectrum of the frozen melt.

4 Conclusion

The liquidus temperatures of the (CsCl–PbCl2)–PbO (71.3–28.7 mol%) system were detected in the PbO concentration region of 0–20.0 mol% by a thermal analysis method. The dissolution thermodynamic characteristics were calculated using the values of lead oxide solubility in chloride melt. In situ Raman spectroscopic analysis provided direct evidence of chemical interaction between PbO and chloride melts.

Acknowledgments

The authors are grateful to the Shared Access Centre “Composition of compounds” of the Institute of High Temperature Electrochemistry of the Ural Branch of the Russian Academy of Sciences for X-ray phase analysis. The study is financially supported by the Russian Foundation for Basic Research within the framework of scientific project No 15-03-00368a.

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About the article

Corresponding author: Pavel A. Arkhipov, Institute of High Temperature Electrochemistry, Ural Branch of Russian Academy of Sciences Ekatherinburg, S. Kovalevskaya St., 22, 620990, Russian Federation, E-mail: arh@ihte.uran.ru


Received: 2015-04-28

Accepted: 2015-07-23

Published Online: 2015-08-19

Published in Print: 2015-10-01


Citation Information: Zeitschrift für Naturforschung A, Volume 70, Issue 10, Pages 851–858, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.1515/zna-2015-0273.

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