Influence of deviations of the equilibrium interatomic distances from the vegard rule on the heats of formation of inorganic solid solutions

1969 ◽  
Vol 18 (12) ◽  
pp. 2509-2513
Author(s):  
V. S. Urusov
Keyword(s):  
Solid Solutions ◽  
Heats Of Formation ◽  
Interatomic Distances

scholarly journals The apparent sizes of atoms in metallic crystals with special reference to aluminium and indium, and the electronic state of magnesium

1940 ◽  
Vol 177 (968) ◽  
pp. 27-37 ◽  
Keyword(s):  
Experimental Data ◽  
Special Reference ◽  
Solid Solutions ◽  
Brillouin Zone ◽  
Abrupt Change ◽  
Atomic Radius ◽  
Previous Suggestion ◽  
Interatomic Distances ◽  
The Face ◽  
Metallic Aluminium

The interatomic distances in crystals of alloys cannot be accounted for by assigning a fixed atomic radius to each kind of atom, and the causes of this variation are discussed with special references to the Brillouin zone characteristics of different structures. According to the theory of Jones, the effect of an overlap across the side of a Brillouin zone is to compress the zone at right angles to the face concerned, and so to expand the crystal lattice in the same direction. This expansion is not a property of an atom which can be transferred to any of its alloys, but is a characteristic of a structure with sufficient electrons to produce an overlap. The lattice spacings of alloys of aluminium and indium with copper, silver, gold, and magnesium are examined, and the apparent sizes of the aluminium and indium atoms are discussed, and are shown to be in agreement with the theory. The previous suggestion, that in metallic aluminium the atoms exist in an incompletely ionized state, is improbable, and is no longer required in order to explain the facts. New experimental data for the lattice spacings of solid solutions of aluminium and indium are presented, and these show that, whilst the curves connecting the a parameter with the composition are smooth and continuous, the corresponding curves for the c parameter show an abrupt change in direction at about 0.75 atomic % of indium or aluminium. This is taken to imply that, although in metallic magnesium with two electrons per atom, the overlap of the first Brillouin zone is in the a direction only, the structure is so near to the stage at which the c overlap sets in that the addition of less than one electron per hundred atoms causes the c overlap to take place.

Heats of Formation of Some Solid Solutions of Alkali Halide

1958 ◽  
Vol 62 (2) ◽  
pp. 145-150 ◽  
Author(s):  
M. W. Lister ◽  
N. F. Meyers
Keyword(s):  
Solid Solutions ◽  
Alkali Halide ◽  
Heats Of Formation

Prediction of Solid + Liquid Equilibrium Diagrams for Binary Mixtures Forming Solid Solutions with an Extremum

1982 ◽  
Vol 19 ◽  
Author(s):  
Witold Brostow ◽  
M. Antonieta Macip
Keyword(s):  
Binary Mixtures ◽  
Solid Solutions ◽  
Intermolecular Potentials ◽  
Gibbs Function ◽  
Liquid Equilibrium ◽  
Regular Solutions ◽  
Interatomic Distances ◽  
Organic Mixtures ◽  
Coexisting Phases ◽  
Solid Liquid

ABSTRACTConvenient methods of correlation and prediction of S+L diagrams exist only for systems forming eutectics. To deal with solid solutions, we have adopted the model of strictly regular solutions of Guggenheim [3–5]. Our key assumption is that values of the Gibbs function of interchange w are different in the two coexisting phases: wS and wL. The assumption is based on the fact that the average interatomic distances R are also different, and this affects the averages of the interatomic (or intermolecular) potentials. The input parameters are enthalpies and temperatures of melting of pure components and any pair of experimental points on the diagram. For a number of binary alloy systems the agreement with the experiment is good. Since we believe in the basic unity of materials (see Chap. 1 in [7]), calcuations have also been made for organic mixtures, again with good results.

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 Structural characterization and colour of Ni3−xCuxP2O8 (0 ≤ x ≤ 3) materials

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
M. A. Tena ◽  
Rafael Mendoza ◽  
Camino Trobajo ◽  
José R. García ◽  
Santiago García-Granda
Keyword(s):  
Solid Solutions ◽  
Structural Characterization ◽  
Structural Changes ◽  
Ceramic Pigments ◽  
Gradual Change ◽  
Unit Cell Parameters ◽  
Interatomic Distances ◽  
Cell Parameters ◽  
Colour Parameters

AbstractThe structural characterization of Ni3−xCuxP2O8 (0.0 ≤ x ≤ 3.0) compositions was performed and the colour parameters of these materials measured. Solid solutions with Ni3P2O8, Ni2CuP2O8 and Cu3P2O8 structures were obtained and the compositional range in which they are formed was established. Structural distortion was detected in these solid solutions when x increases from the variation in the unit cell parameters and that of the interatomic distances. Solid solutions with Ni3P2O8 structure are stable at 1200 °C and may be used as ceramic pigments. Changes in the colour of these materials were related to the structural changes. Yellow materials are obtained from Ni3−xCuxP2O8 solid solutions with a Ni3P2O8 or Ni2CuP2O8 structure and a gradual change from yellow to brown is obtained with the introduction of Cu(II) in the Ni3P2O8 structure, 0.0 ≤ x ≤ 0.7 at 1200 °C.

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