Preliminary Evaluation of Thermodynamic Mixing Properties and Miscibility Limits for Cubic Dioxide (Zr, M)O2 and Zircon (Zr, M)SiO4 Solid Solutions (M = An4+, Ln4+)

1997 ◽  
Vol 506 ◽  
Author(s):  
V.A. Kurepin
Keyword(s):  
Solid Solution ◽  
Solid Solutions ◽  
Enthalpy Of Mixing ◽  
Thermodynamic Theory ◽  
Preliminary Evaluation ◽  
Interatomic Distances ◽  
Mixing Properties ◽  
Equilibrium Data ◽  
End Members ◽  
The Relationship

Cubic zirconia ZrO2 and zircon ZrSiO4 are considered as perspective crystalline form for immobilization of U, Pu and other radionuclides [1, 2]. The present study was undertaken to determine temperature dependence of solid solution limits in these compounds using thermodynamic theory of solid solutions and available equilibrium data. Thermodynamic mixing properties has been evaluated by means of the relationship between Margules parameter W and interatomic distances R in end-members AX and BX of a solid solution (A1−xBx)XW = α(ΔR/R)2where ΔR = R(BX) - R(AX), R = (1−x) R(AX) + x R(BX), α is a constant for isotypic isostructural compounds. According to the Urusov's energetic theory of enthalpy of mixing [3] such relationships exist between parameters W, AR and R of solid solutions with similar bonds between isomorphous atoms and their neighbors

scholarly journals The solid solutions of rebulite and jankovićite in the phase system Tl2S-As2S3-Sb2S3

2015 ◽  
Vol 34 (1) ◽  
pp. 125
Author(s):  
Tonci Balic-Zunic ◽  
Yves Moëlo ◽  
Ljiljana Karanović ◽  
Peter Berlepsch
Keyword(s):  
Crystal Structure ◽  
Solid Solution ◽  
Solid Solutions ◽  
Unit Cell ◽  
Phase System ◽  
Structural Topology ◽  
Coordination Polyhedra ◽  
Ideal Composition ◽  
End Members ◽  
Compositional Line

Syntheses along the Tl<sub>5</sub>(As,Sb)<sub>13</sub>S<sub>22</sub> compositional line in the Tl<sub>2</sub>S-As<sub>2</sub>S<sub>3</sub>-Sb<sub>2</sub>S<sub>3</sub> phase system showed that the compositional range of rebulite extends from  Tl<sub>5</sub>As<sub>9.5</sub>Sb<sub>3.5</sub>S<sub>22</sub> to Tl<sub>5</sub>As<sub>7.75</sub>Sb<sub>5.25</sub>S<sub>22</sub>. The Sb-rich end-member is in equilibrium with jankovićite of ideal composition Tl<sub>5</sub>Sb<sub>7.5</sub>As<sub>5.5</sub>S<sub>22</sub>. It is considered to be the As-rich end-member of the jankovićite solid solution. The crystal structure analyses of crystals from the As and Sb end-members of rebulite show that the Sb/As substitution is present in Sb3, Sb4, Sb5, As1 and As2 structural sites. Of them, Sb3 is always Sb dominated whereas other four vary from As- to Sb-dominated over the range of the solid solution. The change of the structural topology from jankovićite to rebulite, the closely related but not identical structures, is explained through necessity to accommodate the smaller volumes of the As coordination polyhedra and is accomplished through unit-cell twinning over the periodic (001)<sub>reb</sub> twin boundaries. The As end-member of the rebulite solid solution is in equilibrium with the phase of Tl<sub>2.4</sub>Sb<sub>0.68</sub>As<sub>7.18</sub>S<sub>13</sub> ideal composition, interpreted as imhofite.

True and brittle micas: composition and solid-solution series

2007 ◽  
Vol 71 (3) ◽  
pp. 285-320 ◽  
Author(s):  
G. Tischendorf ◽  
H.-J. Förster ◽  
B. Gottesmann ◽  
M. Rieder
Keyword(s):  
Solid Solution ◽  
Crystal Structures ◽  
Solid Solutions ◽  
Solid Solution Series ◽  
Octahedral Sheet ◽  
Tetrahedral Sheet ◽  
Solution Series ◽  
The Common ◽  
End Members ◽  
Graphical Presentation

AbstractMicas incorporate a wide variety of elements in their crystal structures. Elements occurring in significant concentrations in micas include: Si, IVAl, IVFe3+, B and Be in the tetrahedral sheet; Ti, VIAl, VIFe3+, Mn3+, Cr, V, Fe2+, Mn2+, Mg and Li in the octahedral sheet; K, Na, Rb, Cs, NH4, Ca and Ba in the interlayer; and O, OH, F, Cl and S as anions. Extensive substitutions within these groups of elements form compositionally varied micas as members of different solid-solution series. The most common true K micas (94% of almost 6750 mica analyses) belong to three dominant solid-solution series (phlogopite–annite, siderophyllite–polylithionite and muscovite–celadonite). Theirclassification parameters include: Mg/(Mg+Fetot) [=Mg#] formicas with VIR >2.5 a.p.f.u. and VIAl <0.5 a.p.f.u.; Fetot/(Fetot+Li) [=Fe#] formicas with VIR >2.5 a.p.f.u. and VIAl >0.5 a.p.f.u.; and VIAl/(VIAl+Fetot+Mg) [=Al#] formicas with VIR <2.5 a.p.f.u. The common true K micas plot predominantly within and between these series and have Mg6Li <0.3 a.p.f.u. Tainiolite is a mica with Mg6Li >0.7 a.p.f.u., or, fortr ansitional stages, 0.3–0.7 a.p.f.u. Some true K mica end-members, especially phlogopite, annite and muscovite, form binary solid solutions with non-K true micas and with brittle micas (6% of the micas studied). Graphical presentation of true K micas using the coordinates Mg minus Li (= mgli) and VIFetot+Mn+Ti minus VIAl (= feal) depends on theirclassification according to VIR and VIAl, complemented with the 50/50 rule.

Thermodynamic Properties of Actinide Oxide Solid Solutions

2008 ◽  
Vol 1125 ◽  
Author(s):  
Lindsay C. Shuller ◽  
Niravun Pavenayotin ◽  
Rodney C. Ewing ◽  
Udo Becker
Keyword(s):  
Solid Solution ◽  
Monte Carlo ◽  
Ab Initio ◽  
Density Functional ◽  
Configurational Entropy ◽  
Enthalpy Of Mixing ◽  
Fluorite Structure ◽  
Excess Gibbs Free Energy ◽  
Cation Ordering ◽  
End Members

ABSTRACTDensity functional theory and Monte(Carlo methods were used to investigate the solid( solution behavior of actinide dioxides (AcO2). The end(members of interest include: ZrO2, ThO2, UO2, NpO2, and PuO2; all have the isometric fluorite structure. Ab initio and subsequent Monte( Carlo simulations are used to calculate the excess enthalpy of mixing (ΔHexcess), excess Gibbs free energy of mixing (ΔGexcess), and excess configurational entropy (ΔSexcess) for the above solid(solution series. From ΔGexcess, phase diagrams are derived and miscibility gaps identified. All of the binaries of the aforementioned end(members were studied; however, this paper focuses on the U1(xZrxO2 and Np1(xUxO2 binaries. About 25 at.% Zr can be in solid solution with the UO2 matrix above 1500 K, while Np is completely miscible in the UO2 matrix. Partial cation ordering was observed at all temperatures for the U1(xZrxO2 binary. The Np1(xUxO2 binary approaches perfect cation disorder at high temperatures (2000 K). The cation ordering scheme is not identified in this study because the number of cation(cation interaction parameters was limited by the single unit cell from the ab initio calculations.

An ideal solid solution model for calculating solubility of clay minerals

Clay Minerals ◽  
1981 ◽  
Vol 16 (4) ◽  
pp. 361-373 ◽  
Author(s):  
Y. Tardy ◽  
B. Fritz
Keyword(s):  
Solid Solution ◽  
Clay Minerals ◽  
Chemical Evolution ◽  
Solid Solutions ◽  
Natural Water ◽  
Free Energies ◽  
Natural Clay ◽  
Data Set ◽  
Solubility Products ◽  
End Members

AbstractA method for estimating Gibbs free energies and stabilities of clay minerals is proposed for use with computer programs aimed at calculating the chemical evolution of natural water-rock systems. This is based on (i) a model for ideal solid solutions of a large number of end-member compositions and (ii) a data set of estimated solubility products from 36 end-members. The application of the method to the production of experimental or natural clay stabilities is discussed.

Thermodynamics of Fe3O4–Co3O4 and Fe3O4–Mn3O4 spinel solid solutions at the bulk and nanoscale

2015 ◽  
Vol 17 (34) ◽  
pp. 22286-22295 ◽  
Author(s):  
Sulata K. Sahu ◽  
Baiyu Huang ◽  
Kristina Lilova ◽  
Brian F. Woodfield ◽  
Alexandra Navrotsky
Keyword(s):  
Solid Solutions ◽  
Enthalpy Of Mixing ◽  
End Members ◽  
Spinel Solid Solutions

Enthalpy of mixing (ΔmixH) of (1 − x)Fe3O4–xMn3O4 spinel solid solutions with cubic Fe3O4 and tetragonal Mn3O4 end members.

Enthalpies of formation of CdSxSe1–x solid solutions

2009 ◽  
Vol 24 (4) ◽  
pp. 1368-1374 ◽  
Author(s):  
Fen Xu ◽  
Xuchu Ma ◽  
Susan M. Kauzlarich ◽  
Alexandra Navrotsky
Keyword(s):  
Solid Solution ◽  
Thermodynamic Properties ◽  
Molar Volume ◽  
Solid Solutions ◽  
Calorimetric Method ◽  
Molar Ratio ◽  
Enthalpies Of Formation ◽  
Size Difference ◽  
Experimental Errors ◽  
End Members

The enthalpies of oxidative drop solution (ΔHds) for a series of CdSxSe1–x samples were obtained by calorimetry in molten 3Na2O·4MoO3 at 975 K. They become more exothermic linearly with increasing S content. The enthalpies of formation from the elements (ΔHf,el) depend linearly on molar ratio of S/(S + Se). This is the first report of thermodynamic properties of CdSxSe1–x solid solutions measured by any direct calorimetric method. The enthalpies of formation at 298 K from the binary chalcogenide end-members (ΔHf,CdM) (M = S, Se) for wurtzite CdSxSe1–x are found to be zero within experimental errors. These results strongly suggest that wurtzite CdS and CdSe form an ideal solid solution, despite a substantial difference in molar volume and anion radius. This implies that size difference affects thermodynamics less strongly when larger and more polarizable anions are mixed in chalcogenides than when cations are mixed in oxides.

Monazite end members and solid solutions: synthesis, unit-cell characteristics, and utilization as microprobe standards

1989 ◽  
Vol 53 (369) ◽  
pp. 120-123 ◽  
Author(s):  
J. M. Montel ◽  
F. Lhote ◽  
J. M. Claude
Keyword(s):  
Solid Solution ◽  
Experimental Study ◽  
Solid Solutions ◽  
Unit Cell ◽  
Solid Solution Series ◽  
Solution Series ◽  
End Members ◽  
Characteristics And Utilization

The synthesis of monazite was first reported by Radominsky (1875). Since then various methods have been used to synthesize various end members of the monazite solid solution series, mainly CePO4 and LaPO4 (e.g. Anthony, 1957, 1965). As part of an experimental study dealing with the solubility of monazite in granitic melts (Montel, 1986, 1987, and in prep.), the synthesis of some of the end members, as well as solid solutions, was achieved.

scholarly journals Synthesis of Ce1−xPdxO2−δ Solid Solution in Molten Nitrate

Catalysts ◽  
2020 ◽  
Vol 10 (6) ◽  
pp. 640
Author(s):  
Hideaki Sasaki ◽  
Keisuke Sakamoto ◽  
Masami Mori ◽  
Tatsuaki Sakamoto
Keyword(s):  
Electron Microscopy ◽  
Solid Solution ◽  
Solid Solutions ◽  
Photoelectron Spectroscopy ◽  
Synthesis Method ◽  
X Ray Diffraction ◽  
X Ray ◽  
Transmission Electron ◽  
Co Precipitation ◽  
Ionic States

CeO2-based solid solutions in which Pd partially substitutes for Ce attract considerable attention, owing to their high catalytic performances. In this study, the solid solution (Ce1−xPdxO2−δ) with a high Pd content (x ~ 0.2) was synthesized through co-precipitation under oxidative conditions using molten nitrate, and its structure and thermal decomposition were examined. The characteristics of the solid solution, such as the change in a lattice constant, inhibition of sintering, and ionic states, were examined using X-ray diffraction (XRD), scanning electron microscopy–energy-dispersive X-ray spectroscopy (SEM−EDS), transmission electron microscopy (TEM)−EDS, and X-ray photoelectron spectroscopy (XPS). The synthesis method proposed in this study appears suitable for the easy preparation of CeO2 solid solutions with a high Pd content.

Electron microprobe study of turquoise-group solid solutions in the Neyshabour and Meydook mines, northeast and southern Iran

2020 ◽  
Vol 58 (1) ◽  
pp. 71-83
Author(s):  
Elahe Mansouri Gandomani ◽  
Nematollah Rashidnejad-Omran ◽  
Amir Emamjomeh ◽  
Pietro Vignola ◽  
Tahereh Hashemzadeh
Keyword(s):  
Solid Solution ◽  
Solid Solutions ◽  
Electron Microprobe ◽  
Electron Probe Microanalysis ◽  
Electron Probe ◽  
Major Elements ◽  
Point Of View ◽  
Chemical Compositions ◽  
Light Blue ◽  
Quaternary Solid Solution

ABSTRACT Turquoise, CuAl6(PO4)4(OH)8·4H2O, belongs to the turquoise group, which consists of turquoise, chalcosiderite, aheylite, faustite, planerite, and UM1981-32-PO:FeH. In order to study turquoise-group solid solutions in samples from the Neyshabour and Meydook mines, 17 samples were selected and investigated using electron probe microanalysis. In addition, their major elements were compared in order to evaluate the feasibility of distinguishing the provenance of Persian turquoises. The electron microprobe data show that the studied samples are not constituted of pure turquoise (or any other pure endmember) and belong, from the chemical point of view, to turquoise-group solid solutions. In a turquoise–planerite–chalcosiderite–unknown mineral quaternary solid solution diagram, the chemical compositions of the analyzed samples lie along the turquoise–planerite line with minor involvement of chalcosiderite and the unknown mineral. Among light blue samples with varying hues and saturations from both studied areas, planerite is more abundant among samples from Meydook compared with samples from Neyshabour. Nevertheless, not all the light blue samples are planerite. This study demonstrates that distinguishing the deposit of origin for isochromatic blue and green turquoises, based on electron probe microanalysis method and constitutive major elements, is not possible.

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