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1

What is Liquid? [in two dimensions]

Travis K. P., Hoover Wm. G., Hoover C. G., Hass A. B.

Computational Methods in Science and Technology

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2021

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Vol. 27, No. 1

5--23

EN

We consider the practicalities of defining, simulating, and characterizing “Liquids” from a pedagogical standpoint based on atomistic computer simulations. For simplicity and clarity we study two-dimensional systems throughout. In addition to the infinite-ranged Lennard-Jones 12/6 potential we consider two shorter-ranged families of pair potentials. At zero pressure one of them includes just nearest neighbors. The other longer-ranged family includes twelve additional neighbors. We find that these further neighbors can help stabilize the liquid phase. What about liquids? To implement Wikipedia’s definition of liquids as conforming to their container we begin by formulating and imposing smooth-container boundary conditions. To encourage conformation further we add a vertical gravitational field. Gravity helps stabilize the relatively vague liquid-gas interface. Gravity reduces the messiness associated with the curiously-named “spinodal” (tensile) portion of the phase diagram. Our simulations are mainly isothermal. We control the kinetic temperature with Nosé-Hoover thermostating, extracting or injecting heat so as to impose a mean kinetic temperature over time. Our simulations stabilizing density gradients and the temperature provide critical-point estimates fully consistent with previous efforts from free energy and Gibbs ensemble simulations. This agreement validates our approach.

2

Termodynamika układów węglowodorowych w nanoporowych strukturach złożowych

Nagy Stanisław, Siemek Jakub

Wiadomości Naftowe i Gazownicze

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2020

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R. 23, Nr 7 (261)

4--11

PL

Gaz ziemny z łupków ze złóż niskoprzepuszczalnych piaskowcowych (typu ‘tight’) i łupkowych (typu ‘shale’) jest jednym z najważniejszych paliw kopalnych uznanych jako paliwo ‘przejściowe’ w okresie transformacji energetycznej. Niniejszy artykuł opisuje złożone zjawiska związane z wpływem rozmiarów kanałów porowych, adsorpcji i kapilarnej kondensacji w strukturach nanoporowych. Zjawiska towarzyszące układom nanoporowym powodują też zmianę położenia punktu krytycznego, co wpływa zasadniczo na przesunięcie równowagi fazowej. Omówiono zmodyfikowany dwufazowy model równowagowy dwufazowy w obszarze mikro i nanoporów. Pokazano przykłady zmiany krzywych nasycenia dla wybranego składu układu gazowo-kondensatowego.

EN

Unconventional natural gas from low-permeable sandstone (tight) and shale reservoirs is one of the most important fossil fuels recognized as ‘transient’ fuels during the energy transformation. This paper describes complex phenomena related to confining conditions adsorption and capillary condensation in nanopore structures. The phenomena associated with nanopore systems also cause a critical point to shift, which essentially move the phase equilibria. Paper discusses a modified two-phase equilibrium model in micro and nanopore systems. Examples of changes in phase envelope curves are presented in the selected composition of gas-condensate systems.

3

Dissipative Particle Dynamics via Molecular Dynamics

Travis K. P.

Computational Methods in Science and Technology

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2017

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Vol. 23, No. 3

265--279

EN

We demonstrate that the main features of DPD may be obtained using molecular dynamics employing a deterministic thermostat. This apparent isomorphism holds as long as the MD pair potentials are sufficiently smooth and short ranged, which gives rise to a quadratic equation of state (pressure as a function of density). This is advantageous because it avoids the need to use stochastic forces, enabling a wider choice of integration algorithms, involves fully time reversible motion equations and offers a simpler algorithm to achieve the same objective. The isomorphism is explored and shown to hold in 2 and 3 physical dimensions as well as for binary and ternary systems for two different choices of pair potential. The mapping between DPD and Hildebrand’s regular solution theory (a consequence of the quadratic equation of state) is extended to multicomponent mixtures. The procedure for parametrization of MD (identical to that of DPD) is outlined and illustrated for a equimolar binary mixture of SnI4 and isooctane (2,2,4-trimethylpentane).

4

Thermodynamic Assessment Of The Bi-In-Zn System

Onderka B., Dębski A., Gąsior W.

Archives of Metallurgy and Materials

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2015

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Vol. 60, iss. 2A

567--575

EN

A thermodynamic description of the entire ternary Bi-In-Zn system was obtained by the CALPHAD modelling of the Gibbs energy of the liquid phase. The experimental data on the phase equilibria and the thermodynamic properties published and complemented by the authors’ own experiments were taken into account. In order to verify the phase equilibria in the Bi-In-Zn system, 15 different samples were studied in the temperature range of 300-900 K by the DTA technique during heating and cooling cycles. Coexisting phases and their composition were analyzed by the SEM and EDX techniques for 9 distinct samples after their thermal equilibration at 373 K and 473 K. Assessment and selected phase equilibrium calculations were performed with ThermoCalc and Pandat softwares, and compared with experimental data. The obtained results reproduce well the experimental data on both the phase equilibria and the thermodynamic properties in the optimized system.

PL

Z pomocą metody Calphad opracowano termodynamiczny model energii swobodnej Gibbsa fazy ciekłej w układzie fazowym Bi-In-Zn, co pozwoliło na termodynamiczny opis tego układu jako całości. Zastosowano własne i literaturowe dane eksperymentalne dotyczące równowag fazowych i właściwości termodynamicznych faz układu trójskładnikowego. W celu weryfikacji uzyskanego opisu wykonano pomiary DTA w zakresie temperatury 300-900 K dla 15 próbek stopów o różnych składach w kolejnych cyklach nagrzewania i studzenia. Równowagę fazową badano analizując technikami SEM i EDX skład fazowy i wzajemną rozpuszczalność składników wygrzewanych izotermicznie stopów w temperaturze 373 K i 473 K. Optymalizację parametrów modelowych i obliczenia termodynamiczne w układzie Bi-In-Zn wykonano za pomocą oprogramowania ThermoCalc i Pandat. Porównując obliczone równowagi fazowe i funkcje termodynamiczne z danymi doświadczalnymi stwierdzono bardzo dobrą zgodność wielkości eksperymentalnych z właściwościami topologicznymi i termodynamicznymi zoptymalizowanego układu.

5

Phase equilibria for liquefi eld natural gas (LNG) as a multicomponent mixture

Włodek T.

AGH Drilling, Oil, Gas

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2015

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Vol. 32, no. 3

539--550

EN

Liquefied natural gas (LNG) has an increasingly important role in the global natural gas market. Global demand for natural gas will grow over the coming years. LNG is transported by ships to unloading points on the storage terminals. During the LNG unloading and storage processes some part of LNG evaporates into gas phase and causes changes in the composition of stored LNG. The main component of LNG is methane, the remaining components are primarily ethane, propane, butane and nitrogen. Depending on the participation of these components the basic thermodynamic parameters of LNG can significantly change. LNG is also product sensitive to changes of temperature. In order to better prediction of changes of individual paramete rs of stored LNG caused by changes of temperature and LNG composition vapor-liquid equilibrium (VLE) calculations are performed for cryogenic conditions using equations of state.

6

Thermodynamic properties and phase equilibria in the ternary Cu-Pb-Fe system

Onderka B., Jendrzejczyk-Handzlik D, Fitzner K.

Archives of Metallurgy and Materials

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2013

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Vol. 58, iss. 2

541--548

EN

Using experimental data available in the literature, two binary systems, namely Cu-Pb and Fe-Pb were recalculated. Next, accepting Cu-Fe phase diagram assessment as given by Ansara and Jansson, the ternary Cu-Fe-Pb system was analyzed. Calculated equilibrium lines and thermodynamic functions are compared with existing experimental data. Good agreement was found between the calculated diagram and the experimental results. Having the system optimized, functional dependences of the logarithms of the activity coefficients on temperature and concentrations for Cu, Fe and Pb in the liquid solution are given.

PL

Dwa układy podwójne Cu-Pb oraz Fe-Pb zostały powtórnie zoptymalizowane używając danych eksperymentalnych dostępnych w literaturze. Następnie, akceptując optymalizacje układu Cu-Fe opublikowana przez Ansare i Janssona, poddano analizie trójskładnikowy układ Cu-Pb-Fe. Obliczone linie równowagi faz oraz funkcje termodynamiczne zostały porównane z dostępnymi danymi eksperymentalnymi. Uzyskano dobrą zgodność pomiędzy policzonym układem a danymi eksperymentalnymi. Korzystając z wyników optymalizacji, zostały podane zalezności logarytmu współczynnika aktywności w funkcji temperatury oraz Cu, Fe i Pb w funkcji stężenia dla w roztworze ciekłym.

7

Non-linear optimization of high-pressure gas networks with respect to hydrate control

Osiadacz A. J., Uilhoorn F. E., Chaczykowski M.

Archives of Mining Sciences

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2012

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Vol. 57, no. 3

627--643

EN

In this paper, gas pipeline optimization includes constraints resulting from hydrate prevention. The key is to seek for the optimal settings of both: the compressor units and hydrate combating method at minimum fuel consumption subject to security of supply and hydrate prevention. A case study is conducted on the Polish section of the Yamal pipeline and an arbitrarily selected partial onshore and offshore pipeline. Three different configurations are investigated: (i) cooling the compressed gas, (ii) no cooling and (iii) line heating immediately after the compressor station. For each configuration, the fuel consumption of the compressors is minimized and in order to prevent hydrate formation, the outlet temperature of the line heater, allowable water vapour in the gas and methanol concentration are calculated for each pipe section. The hydrate model is based on the statistical mechanical approach of Van der Waals and Platteeuw and applicable for systems that contain water (free or dissolved in gas), methanol and mixed gases both hydrate and non-hydrate formers.

PL

W artykule omówiono zagadnienie optymalizacji gazowego systemu przesyłowego uwzględniając dodatkowo ograniczenia wynikające z warunków tworzenia się hydratów. Kryterium optymalizacji to minimum zużycia paliwa w tłoczniach gazu. Badania przeprowadzono na polskiej części gazociągu jamalskiego dla trzech przypadków pracy tłoczni: chłodzenie gazu w tłoczni, brak chłodzenia oraz podgrzewanie gazu za stacją przetłoczną. Dla każdego wariantu, zużycie paliwa przez sprężarki jest minimalizowane oraz w celu przeciwdziałania tworzenia się hydratów, temperatura wyjściowa podgrzewacza jest obliczana a także obliczana jest zawartość pary wodnej i metanolu w gazie dla każdej sekcji gazociągu. Zastosowany model hydratu jest oparty na modelu Van der Waalsa oraz Platteeuw.

8

Polyassociative Model of A2B6 Semiconductor Melt and p-T-x Phase Equilibria in Zn-Cd-Te System

Moskvin P., Antonov M., Olchowik G., Olchowik J., Zdyb A., Gulkowski S., Sadowski W.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2011

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Vol. 15, No 1

121-130

EN

This work presents a numerical analysis of p-T-x phase equilibrium in the Zn-Cd-Te ternary system in the framework of the polyassociative solution model. On the basis of the experimental data on p-T-x phase equilibrium in the ternary system, thermodynamic functions describing the formation of liquid associates were found. It was shown that the results of the mixing of components in the Zn-Cd-Te ternary melt are related to the occurrence of ZnCdTe and ZnCdTe3 associates. Dissociation parameters of these complexes were calculated and subsequently used in order to efficiently describe p-T-x phase equilibrium of the system in a wide temperature range.

9

New Approach to the Determination of Phase Equilibrium in the Zn-Te System

Moskvin P., Olchowik J., Olchowik G., Zdyb A., Gulkowski S., Sadowski W.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2011

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Vol. 15, No 2

209-217

EN

The polyassociative model of the liquid phase was applied to describe the phase equilibrium in the Zn-Te system. The thermodynamic functions describing the formation of liquid associates were obtained, taking into account the experimental data on the p-T-x equilibrium in the system. The model of polyassociative solutions with the parameters obtained in this work satisfactorily describes the p-T-x diagram of the system. The numerical results of the analysis of the phase equilibrium confirmed the possibility of applying the polyassociative model to the Zn-Te system in a wide temperature range.

10

Application of the quintic equation of state to phase equilibrium model for water.volatile organic compound systems

Kozioł A., Araszkiewicz M., Wiśniewski R.

Chemical and Process Engineering

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2009

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Vol. 30, z. 4

569-578

EN

For water-volatile organic compound systems a new method of calculations of phase equilibria has been presented. The method is based on the quintic equation of state and classical mixing rules. Significant advantages of this method are: possibility of data extrapolating from the Henry's law region to the region of higher concentrations and possibility of application of the model to multicomponent systems. In addition, important thermodynamic data like liquid and vapour densities can be determined.

PL

Przedstawiono nową metodę obliczania równowag fazowych w układach lotne związki organiczne-woda opartą na opisie faz za pomocą równania stanu piątego stopnia. Najważniejsze zalety tej metody to możliwość ekstrapolacji danych równowagowych z zakresu, w jakim jest spełnione prawo Henry'ego do obszaru większych stężeń oraz możliwość zastosowania do układów wieloskładnikowych. Przedstawionej metodą można również obliczyć inne ważne wielkości fizykochemiczne obydwu faz, takie jak np. gęstości pary w fazie ciekłej i gazowej.

11

Phase equilibria in the Gd-Cr-AI system at 500°C

Verbovytsky Y., Mika T., Kotur B.

Prace Naukowe. Chemia i Ochrona Środowiska / Akademia im. Jana Długosza w Częstochowie

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2005

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Vol. 10

91--97

EN

The phase equilibria at 500°C of the Gd-Cr-AI system have been investigated in the whole concentration region. Three ternary compounds were confirmed and their homogenity regions have been investigated. The crystal structure of all compounds have been refined by Rietveld profile analysis: GdCr23-20AI19.7-20.0 (CeCr2AI20 structure type, space group Fd3m, a=1.44718(3)-1.44822(4) nm), Gd6Cr4AI43 (Ho6Mo4AI43 structure type, space group P63/mcm, a=1.09126(14) nm, c=1.7749(3) nm), GdCr4.0-28AI8.0-92 (ThMn12 structure type, space group I4/mmm, a=0.89780(18)-0.90395(15) nm, c=0.51 332(9)-0.51 253(9) nm).

12

Phase Equilibria in the Ternary System MgO-Na2O-P2O5. The Partial System Mg2P2O7-Mg6Na8(P2O7)5-NaPO3-Mg(PO)2

Podhajska-Kaźmierczak T.

Polish Journal of Chemistry

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2005

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Vol. 79 / nr 6

1033-1040

EN

The partial system Mg2P2O7-Mg6Na8(P2O7)5-NaPO3-Mg(PO3)2 in the ternary system MgO-Na2O-P2O5, have been investigated and its phase diagram has been proposed. Investigation was carried out by the differential thermal analysis (heating and cooling), X-ray diffraction methods, and microscopy in reflected light. In the composition range under investigation, five ternary phosphates: Mg6Na8(P2O7)5, Mg2Na3P5O16, MgNa(PO3)3, MgNa2(PO3)4 and MgNa4(PO3)6 appear. Two of them,Mg6Na8(P2O7)5 and MgNa4(PO3)6, congruently melt at 808 and 915°C, respectively, the remaining three melt incongruently. Phosphate Mg2Na3P5O16 melts incongruently at 675°C during heating and decomposes in a few stages. Peritectic melting point of MgNa(PO3)3 phosphate is 942°C, and that of MgNa4(PO3)6 is 785°C. For the composition range of Mg2P2O7-Mg6Na8(P2O7)5- NaPO3-Mg(PO3)2, it has been found that six quasi-binary sections, four ternary peritectics (tP 1 = 660°C, tP 2 =876°C, t P 3 = 578°C, tP 4 = 555°C) and three ternary eutectics (tE 1 = 560°C, tE 2 = 845°C, tE 3 = 540°C) occur.

13

Measurements of Phase Equlibria in Asymmetric Mixtures at High Pressures, Experimental setup and Introductory Measurements

Gregorowicz J., Fraś Z., Łuszczyk M.

Polish Journal of Chemistry

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2005

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Vol. 79 / nr 8

1339-1351

EN

An apparatus for measuring high-pressure phase equilibria up to 453 K and pressures up to 2000 bar is presented. The applied method of the construction of a phase diagram for a fluid mixture requires the determination of families of P-T diagrams of constant composition (isopleths). The equipment consists of a variable volume cell, a temperature stabilizing system, pressure generation system and a system that makes the loading of the cell with a gas possible. Measurements of liquid - liquid, liquid - vapour and solid - liquid equilibria were performed for two binary systems: ethylene + eicosane and carbon dioxide + squalane.

14

Study of Phase Equilibria in the System Nd2O3-Na2O-P2O5. The Partial System NdPO4-NaPO3-Nd(PO3)3

Znamierowska T., Bandrowski Sz.

Polish Journal of Chemistry

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2004

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Vol. 78 / nr 6

771-778

EN

A partial system of NdPO4-NaPO3-Nd(PO3)3 in the ternary system Nd2O3-Na2O-P2O5 was investigated and its phase diagram is proposed. Thermoanalytical methods and X-ray powder diffraction were employed. In the composition range under examination, two ternary compounds occur, which melt incongruently and have the formulae NaNd(PO3)4 (m.p. 866°C) and NaNdP2O7 (m.p. 790°C). Two quasi-binary sections, NdPO4-NaNd(PO3)4 and NaNdP2O7-NaNd(PO3)4 have been identified.

15

Database for calculation of phase equilibria in systems for lead-free solders

Kroupa A., Zemanová A., Vřeštál J.

Zeszyty Naukowe. Mechanika / Politechnika Opolska

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2003

|

z. 76

163-164

16

Discrete generation decisions simulation including market dynamic interactions

Yang W., Sheble G.B.

Systems Science

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2003

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Vol. 29, nr 4

113-123

EN

Electric market dynamics is important for market administrators to maintain market reliability, forecast problems and take remedy actions. Equilibrium analysis models have been built in the past to find market equilibrium. However, to achieve the goal of deregulation, not only should market equilibrium be identified, but also achievability of equilibrium and market transition process to equilibrium should be known. These properties cannot be got without studying interactions between market participants, which were not included in equilibrium analysis. Interactions between Generation Companies (GENCOs) are major source of market dynamics. They are particularly important for electric market and GENCOs decision making because there are few participants in electric market and current electric markets are oligopolistic. This paper models GENCOs decision making and interactions between different GENCOs from a control point of view. GENCO decisions that are evolving with time are modeled as control processes and electric markets are modeled as control systems. Corresponding market dynamics and properties are studied. An oligopolistic market is used to illustrate the ideas and numerical examples are provided for all cases. Results showed new models can provide conclusions that are difficult or impossible to get by pure equilibrium analysis.

17

Phase equilibria in the {Zr, Hf}-Ag-Al systems at 500°C and crystal structure of the ternary compounds

Kotur B. Ya., Verbovytsky Yu. V.

Prace Naukowe. Chemia / Wyższa Szkoła Pedagogiczna w Częstochowie

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2003

|

Vol. 8

7--15

EN

The phase equilibria at 500°C in the {Zr, Hf}-Ag-Al systems have been investigated in the whole concentration region. Three ternary compounds were found to occur in each of the systems: ZrAg0.32Al2.68 (AuCu3 structure type, space group Pm3m, a=0.41016(1) nm), ZrAg0.16-0.31Al1.84-1.69 (MgCu2 str. type, sp. gr. Fd3 m, a=0.75147(1)-0.75258(1) nm), Zr6Ag1.30-1.82Al5.70-5.18 (W6Fe7 str. type, sp. gr. R3 m, a=0.54017(3)-0.54072(3) nm, c=2.9021(5)-2.9055(3) nm); HfAg0.28-0.43Al1.72-1.57 (MgCu2 str. type, sp. gr. Fd 3 m, a=0.74600(2)-0.74631(3) nm), Hf6Ag0.39-1.43Al6.61-5.57 (W6Fe7 str. type, sp. gr. R3 m, a=0.53098(3)-0.53375(3) nm, c=2.9151(2)-2.9086(3) nm), Hf4Ag1.10Al1.90 (Zr4Al3str. type, sp. gr. P6, a=0.5332(1) nm, c=0.54279(7) nm). The crystal structure of these aluminides was studied using X-ray powder and single crystal diffraction data.

18

Phase Equilibria in the Ternary System MgO-Na2O-P2O5. The Partial System Mgo-Na3PO4-Na4P2O7

Podhajska-Kaźmierczak T.

Polish Journal of Chemistry

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2003

|

Vol. 77 / nr 3

295-301

EN

Apartial system of MgO-Na3PO4-Na4P2O7 in the ternary system MgO-Na2O-P2O5 was investigated and its phase diagram was obtained. Thermal analysis (heating and cooling), powder X-ray diffraction, and optical microscopy using reflected light were applied. In the composition range of interest two ternary compounds occur, which melt congruently and have the formulae MgNa4(PO4)2 (m.p. 1655°C) and MgNa6P2O9 (m.p. 1665°C). The phosphates compose a quasi-binary section with continuous solid solutions and exhibit a temperature minimum about 1520°C.

19

Phadse Equilibria in the System CePO4-Ba3(PO4)2

Szuszkiewicz W., Radomińska E., Znamierowska T., Wilk P.

Polish Journal of Chemistry

|

2002

|

Vol. 76 / nr 8

1095-1100

EN

Based on thermal investigation and X-ray powder diffraction the unknown so far phase diagram of the binary system CePO4-Ba3(PO4)2 has been elaborated. It contains an intermediate compound Ba3Ce(PO4)3, which congruently melts at about 2080 degree centigrade, is stable down to room temperature and has an eulytite structure. In the composition range given by the molar ratio of CePO4:Ba3(PO4)2 from 1:1 to 1:6 there exist solid solutions of the eulytite structure. At high temperatures there exist two binary eutectics (te1 = 1840 degree centigrade, te2 = 1600 degree centigrade).

20

Peculiarities of Components' Interaction in Rare Earth-Transition Metal-Silicon Systems in R(MxSi1-x)2-y Composition Region

Gladyshevsky E., Bodak O. I., Gorelenko Y. K., Yarovetz V. I.

Polish Journal of Chemistry

|

2001

|

Vol. 75, nr 5

617--622

EN

The explanation of ternary compounds, forming with AlB2 structure type in the rare earth metal-transition metal-silicon systems, implements on base of analysis of the dependence of the valence-electron concentration versus the kind of the transition metals in their solid solutions in the binary compounds with AlB2, _-ThSi2, and _-GdSi2 structure types appropriate to the rare earth-silicon systems. There is shown that the silicon content (as the electron donor) during formation of the ternary compounds with AlB2 structure type is dependent on the kind of transition metal and this content is decreased in the series of the compounds with Fe, Co, Ni, and Cu consecutively. The experimental data on concentrational intervals of the stability ranges of these ternary compounds are proposed to the qualitative evaluation of the effective valency of the transition metal atoms.