scholarly journals Theory of Inhomogeneous Short Range Order and Calphad Modeling. Part 4. Improved Combinatorial Factor

2019 ◽  
Author(s):  
Edward Kremer
Keyword(s):  
Low Temperatures ◽  
Short Range ◽  
Short Range Order ◽  
Range Order ◽  
Negative Entropy ◽  
Calphad Modeling ◽  
Combinatorial Factor

An improved combinatorial factor allows to reproduce the correct critical tem-peratures for the Ising lattices.As result, the accuracy of thermodynamic values calculated near the criticalpoint increases by the factor 2 - 3 for the most important lattice types.It is shown why one-particle (Bragg-Williams) and two-particle (Quasichemical)approximations cannot be adequately applied for description of important nuancesof interatomic interaction.The problem of negative entropy values manifested at low temperatures andtypical for model theories is discussed. It is being argued that this problem has tobe treated as exaggerated.

scholarly journals Theory of Inhomogeneous Short Range Order and Calphad Modeling. Part 1. Basic Formalism

2018 ◽  
Author(s):  
Edward Kremer
Keyword(s):  
Small Groups ◽  
Short Range ◽  
Short Range Order ◽  
Weighted Average ◽  
Basic Element ◽  
Range Order ◽  
Conceptual Role ◽  
Calphad Modeling ◽  
Combinatorial Factor

Conceptual role of Short Range Order in Statistical Thermodynamics of liquidalloys is discussed. It is shown why the popular model theories used by Calphadfall short in bringing this phenomenon to full usage. In contrast to this, presentedhere in details Theory of Inhomogeneous Short Range Order takes Short RangeOrder as basic element of formalism. Combinatorial factor provided by theoryexpresses the Statistical Sum of entire system as weighted average over StatisticalSums of small groups of atoms conventionally selected in the alloy. Equations ofthe theory are explicitly resolved in a parametric form.The theory in its tetrahedron approximation is applied, as introductory example,for the presentation the thermodynamic data of multiple two-component systemsdescribed previously by other authors using Redlich-Kister’ polynomials.

scholarly journals Theory of Inhomogeneous Short Range Order and Calphad Modeling. Part 6. Order-Disorder Transformations in Alloys

2020 ◽  
Author(s):  
Edward Kremer
Keyword(s):  
Long Range ◽  
Short Range ◽  
Short Range Order ◽  
Range Order ◽  
Long Range Order ◽  
Calphad Modeling ◽  
Solid Alloys

Formalism of Theory of Inhomogeneous Short Range Order (TISR) is extendedto describe Order–Disorder transformations in solid alloys. The result is a naturalintegration of Short and Long Range Order description in the framework of thesame theory.The equations of Cluster Site Approximation (CSA) are deduced directly fromthe equations of TISR. Formalism and interpretation of CSA are simplified andclarified.

scholarly journals Theory of Inhomogeneous Short Range Order and Calphad Modeling. Part 3. Association Solution Model Reconstructed

2018 ◽  
Author(s):  
Edward Kremer
Keyword(s):  
Short Range ◽  
Short Range Order ◽  
Point Of View ◽  
Range Order ◽  
Solution Model ◽  
Calphad Modeling

Internal problems of Association Solution Model are analyzed and based on this analysis a few important modifications are introduced in the formalism and in the interpretation of the model.Reconstructed model is free from the named problems and has significant advantages from the point of view of consistency and applicability. A set of comparative examples is provided.

scholarly journals Theory of Inhomogeneous Short Range Order and Calphad Modeling. Part 7. Surrounded Atom Model Reconstructed

2020 ◽  
Author(s):  
Edward Kremer
Keyword(s):  
Short Range ◽  
Short Range Order ◽  
Interatomic Interaction ◽  
Range Order ◽  
Order Effects ◽  
Atom Model ◽  
Calphad Modeling

Formalism of Theory of Inhomogeneous Short Range Order is applied to the caseof ”surrounded atoms”. It is shown that the derived equations have significantlyhigher precision in describing the Short Range Order effects than the commonlyused Surrounded Atoms Model.We argue also that the form of dependence of interatomic interaction on thecomposition, postulated by the Surrounded Atom Model, is artificial and limitsthe area of applicability of the model.

scholarly journals Theory of Inhomogeneous Short Range Order and Calphad Modeling. Part 2. Quasichemical Theory

2018 ◽  
Author(s):  
Edward Kremer
Keyword(s):  
Short Range ◽  
Short Range Order ◽  
Range Order ◽  
Quasichemical Model ◽  
Calphad Modeling

The equations of the Quasichemical Theory are deduced directly from the equations of the Theory of Inhomogeneous Short Range, establishing TISR as the rigid generalization of the Quasichemical Theory.Methodological advantages of TISR are demonstrated.The Modified Quasichemical Model is critically discussed as other generalization of the same Quasichemical Theory.Multiple comparative examples are provided.

scholarly journals Theory of Inhomogeneous Short Range Order and Calphad Modeling. Part 5. Extended Formalism

2020 ◽  
Author(s):  
Edward Kremer
Keyword(s):  
Short Range ◽  
Short Range Order ◽  
Range Order ◽  
Formal Structure ◽  
Multiple Components ◽  
Calphad Modeling

Formalism of Theory of Inhomogeneous Short Range Order is extended to in-clude systems with multiple components and multiple sublatices.The generalization is achieved in agreement with the basic formal structure ofthe theory and is in many respects seamless.The extended formalism is expected to increase significantly the area of appli-cability of theory.

Ordering in Ni4Mo by TEM and APFIM

1987 ◽  
Vol 45 ◽  
pp. 214-215
Author(s):  
E.A. Kenik ◽  
T.A. Zagula ◽  
M.K. Miller ◽  
J. Bentley
Keyword(s):  
Electron Irradiation ◽  
Low Temperatures ◽  
Short Range ◽  
Atom Probe ◽  
Range Order ◽  
Considerable Time ◽  
Probe Field ◽  
Disordered Phase ◽  
Transmission Electron ◽  
Diffraction Patterns

The state of long-range order (LRO) and short-range order (SRO) in Ni4Mo has been a topic of interest for a considerable time (see Brooks et al.). The SRO is often referred to as 1½0 order from the apparent position of the diffuse maxima in diffraction patterns, which differs from the positions of the LRO (D1a) structure. Various studies have shown that a fully disordered state cannot be retained by quenching, as the atomic arrangements responsible for the 1½0 maxima are present at temperatures above the critical ordering temperature for LRO. Over 20 studies have attempted to identify the atomic arrangements associated with this state of order. A variety of models have been proposed, but no consensus has been reached. It has also been shown that 1 MeV electron irradiation at low temperatures (∼100 K) can produce the disordered phase in Ni4Mo. Transmission electron microscopy (TEM), atom probe field ion microscopy (APFIM), and electron irradiation disordering have been applied in the current study to further the understanding of the ordering processes in Ni4Mo.

Short-range order effects in amorphous FexSi1-x/Si multilayers induced by preparation conditions

1998 ◽  
Vol 08 (PR2) ◽  
pp. Pr2-175-Pr2-178 ◽  
Author(s):  
G. T. Pérez ◽  
F. H. Salas ◽  
R. Morales ◽  
L. M. Álvarez-Prado ◽  
J. M. Alameda
Keyword(s):  
Short Range ◽  
Short Range Order ◽  
Range Order ◽  
Order Effects ◽  
Preparation Conditions
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