Second nearest-neighbor interactions in ternary regular solutions

1992 ◽  
Vol 70 (10) ◽  
pp. 2569-2573 ◽  
Author(s):  
Meguru Nagamori
Keyword(s):  
Partition Function ◽  
Present Model ◽  
Nearest Neighbor ◽  
Single Equation ◽  
Heat Of Mixing ◽  
Grand Partition Function ◽  
Regular Solutions ◽  
Third Order ◽  
Entropy Of Mixing ◽  
The Third

The concept of classical regular solutions has been expanded by considering both first and second nearest-neighbor interactions between randomly distributed molecules. While the present model requires an ideal entropy of mixing, as does the classic regularity model, its heat of mixing is expressed by a more flexible equation which attributes the second-order terms of the Margules formalism to first nearest-neighbor interactions, and the third-order terms to second nearest-neighbor interactions. The activity–composition relations have been expressed by a single equation of the grand partition function, which converges to that of the classical regularity with decreasing contributions from second nearest-neighbor molecules.

scholarly journals Theoretical investigation of mixing properties of Sb-Sn binary liquid alloy at 905K

BIBECHANA ◽  
2017 ◽  
Vol 15 ◽  
pp. 1-10
Author(s):  
H K Limbu ◽  
K K Mishra ◽  
A K Sah ◽  
I S Jha ◽  
D Adhikari
Keyword(s):  
Liquid Alloy ◽  
Nearest Neighbor ◽  
Regular Solution Model ◽  
Concentration Fluctuations ◽  
Heat Of Mixing ◽  
Entropy Of Mixing ◽  
Energy Of Mixing ◽  
Interchange Energy ◽  
Free Energy Of Mixing ◽  
Experimental Values

The thermodynamic, microscopic, surface and transport properties of Sb-Sn liquid alloy at 905K have been studied using regular solution model. In thermodynamic properties, free energy of mixing(GM) , activity(a), entropy of mixing(SM), heat of mixing (HM) have been studied. To understand structural behavior of the liquid alloys concentration fluctuations in the long wavelength limit i.e. (Scc(0)) and short range order parameter (α1) have been computed. Surface property is studied with the help of Butler’s model while transport property is computed from Moelwyn-Hughes equation. The theoretical and experimental values of thermodynamic and microscopic properties of Sb-Sn liquid alloy at 905K have been compared. In present work the value of interchange energy (w) is found to be negative suggesting that there is a tendency of unlike atoms pairing (i.e. Sb-Sn) as the nearest neighbor indicating the ordering behavior in Sb-Sn liquid alloy. The symmetric behavior of concentration fluctuations of the liquid alloy has been well explained by the model. The temperature dependence of interchange energy (w) has been found during the computation of entropy of mixing (SM) and heat of mixing (HM) of the liquid alloy.BIBECHANA 15 (2018) 1-10

A new solution of Hill's lunar problem

1966 ◽  
Vol 25 ◽  
pp. 261-265 ◽  
Author(s):  
K. Stumpff
Keyword(s):  
Differential Equation ◽  
Power Series ◽  
Fourth Order ◽  
Single Equation ◽  
Radius Vector ◽  
Third Order ◽  
Rotating System ◽  
Second Order Differential Equations ◽  
The Third ◽  
Hill's Lunar Problem

The two second order differential equations of Hill's lunar problem for rectangular co-ordinates in the rotating system are transformed into a single equation of the fourth order for the geocentric radius vector r, which can be reduced, using Jacobi's integral, to a differential equation of the third order. A discussion of this equation leads to a new exhibition of Hill's “variation orbits”. The first terms of Hill's power series, which represent these periodic solutions of the problem, are exactly confirmed by using a very simple approximative assumption about the mathematical character of the solution.

Probe size and 5th-order aberration

1987 ◽  
Vol 45 ◽  
pp. 134-135 ◽  
Author(s):  
Zhifeng Shao
Keyword(s):  
Electron Probe ◽  
Spherical Aberration ◽  
Wave Length ◽  
Cylindrical Symmetry ◽  
Electron Wave ◽  
Third Order ◽  
The Third ◽  
Probe Radius ◽  
Small Probe ◽  
Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

Children’s Recall of Approximations to English

1973 ◽  
Vol 16 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Elizabeth Carrow ◽  
Michael Mauldin
Keyword(s):  
Language Development ◽  
Fourth Order ◽  
Third Order ◽  
Memory Processes ◽  
The Third ◽  
General Index ◽  
General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

scholarly journals Ultrafast Third-Order Nonlinear Optical Response Excited by fs Laser Pulses at 1550 nm in GaN Crystals

Materials ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3194
Author(s):  
Adrian Petris ◽  
Petronela Gheorghe ◽  
Tudor Braniste ◽  
Ion Tiginyanu
Keyword(s):  
Harmonic Generation ◽  
Nonlinear Optical ◽  
Laser Pulses ◽  
Third Harmonic Generation ◽  
High Repetition Rate ◽  
Third Order ◽  
Third Harmonic ◽  
The Third ◽  
High Repetition ◽  
Gan Crystal

The ultrafast third-order optical nonlinearity of c-plane GaN crystal, excited by ultrashort (fs) high-repetition-rate laser pulses at 1550 nm, wavelength important for optical communications, is investigated for the first time by optical third-harmonic generation in non-phase-matching conditions. As the thermo-optic effect that can arise in the sample by cumulative thermal effects induced by high-repetition-rate laser pulses cannot be responsible for the third-harmonic generation, the ultrafast nonlinear optical effect of solely electronic origin is the only one involved in this process. The third-order nonlinear optical susceptibility of GaN crystal responsible for the third-harmonic generation process, an important indicative parameter for the potential use of this material in ultrafast photonic functionalities, is determined.

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

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