Evaluation of the Excess Free Energy of Small Objects

1966 ◽  
pp. 26-32 ◽  
Author(s):  
L. M. Shcherbakov
Keyword(s):  
Free Energy ◽  
Excess Free Energy

Characterization of Textured Aluminum Lines and Modelling of Stress Voiding

1994 ◽  
Vol 343 ◽  
Author(s):  
S.C. Wardle ◽  
B.L. Adams ◽  
C.S. Nichols ◽  
D.A. Smith
Keyword(s):  
Free Energy ◽  
Excess Free Energy ◽  
Mean Field ◽  
High Energy ◽  
Polycrystalline Structure ◽  
Field Approach ◽  
Bamboo Structure ◽  
Automated Technique ◽  
Theory And Modeling

ABSTRACTIt is well known from studies of individual interfaces that grain boundaries exhibit a spectrum of properties because their structure is misorientation dependent. Usually this variability is neglected and properties are modeled using a mean field approach. The limitations inherent in this approach can be overcome, in principle, using a combination of experimental techniques, theory and modeling. The bamboo structure of an interconnect is a particularly simple polycrystalline structure that can now be readily characterized experimentally and modeled in the computer. The grain misorientations in a [111] textured aluminum line have been measured using the new automated technique of orientational imaging microscopy. By relating boundary angle to diffusivity the expected stress voiding failure processes can be predicted through the link between misorientation angle, grain boundary excess free energy and diffusivity. Consequently it can be shown that the high energy boundaries are the favored failure sites thermodynamically and kinetically.

Higher Order Conditional Probabilities and Thermodynamics of Binary Molten Alloys

1997 ◽  
Vol 11 (02n03) ◽  
pp. 93-106 ◽  
Author(s):  
O. Akinlade
Keyword(s):  
Free Energy ◽  
Experimental Evidence ◽  
Cluster Model ◽  
Excess Free Energy ◽  
Higher Order ◽  
Thermodynamic Quantities ◽  
Equiatomic Composition ◽  
Conditional Probabilities ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing

The recently introduced four atom cluster model is used to obtain higher order conditional probabilities that describe the atomic correlations in some molten binary alloys. Although the excess free energy of mixing for all the systems studied are almost symmetrical about the equiatomic composition, most other thermodynamic quantities are not and thus, the study enables us to explain the subtle differences in their physical characteristics required to describe the mechanism of the observed strong heterocoordination in Au–Zn or homocoordination in Cu–Ni within the same framework. More importantly, we obtain all calculated quantities for the whole concentration range thus complimenting experimental evidence.

scholarly journals Excess free energy of supercooled liquids at disordered walls

2014 ◽  
Vol 90 (6) ◽  
Author(s):  
Ronald Benjamin ◽  
Jürgen Horbach
Keyword(s):  
Free Energy ◽  
Excess Free Energy ◽  
Supercooled Liquids

Surfaces, Interfaces, and Changing Shapes in Multilayered Films

MRS Bulletin ◽  
1999 ◽  
Vol 24 (2) ◽  
pp. 39-43 ◽  
Author(s):  
Daniel Josell ◽  
Frans Spaepen
Keyword(s):  
Free Energy ◽  
Excess Free Energy ◽  
External Pressure ◽  
Electronic Density ◽  
Spherical Drop ◽  
Crystal Anisotropy ◽  
Fundamental Quantity ◽  
The Difference ◽  
Image Position ◽  
Work Done

It is generally recognized that the capillary forces associated with internal and external interfaces affect both the shapes of liquid-vapor surfaces and wetting of a solid by a liquid. It is less commonly understood that the same phenomenology often applies equally well to solid-solid or solid-vapor interfaces.The fundamental quantity governing capillary phenomena is the excess free energy associated with a unit area of interface. The microscopic origin of this excess free energy is often intuitively simple to understand: the atoms at a free surface have “missing bonds”; a grain boundary contains “holes” and hence does not have the optimal electronic density; an incoherent interface contains dislocations that cost strain energy; and the ordering of a liquid near a solid-liquid interface causes a lowering of the entropy and hence an increase in the free energy. In what follows we shall show how this fundamental quantity determines the shape of increasingly complex bodies: spheres, wires, thin films, and multilayers composed of liquids or solids. Crystal anisotropy is not considered here; all interfaces and surfaces are assumed isotropic.Consideration of the equilibrium of a spherical drop of radius R with surface free energy γ shows that pressure inside the droplet is higher than outside. The difference is given by the well-known Laplace equation:This result can be obtained by equating work done against internal and external pressure during an infinitesimal change of radius with the work of creating a new surface.

An efficient method for computing excess free energy of liquid

2017 ◽  
Vol 61 (1) ◽  
pp. 135-140 ◽  
Author(s):  
Jianing Song ◽  
Linqiong Qiu ◽  
John Z. H. Zhang
Keyword(s):  
Free Energy ◽  
Efficient Method ◽  
Excess Free Energy

Vapour pressures of aqueous solutions of (Ag,Tl,Cd)NO3 at 98.5 °C. II. Henry's law and excess free energy

1978 ◽  
Vol 56 (5) ◽  
pp. 635-637 ◽  
Author(s):  
Marie-Christine Abraham ◽  
Maurice Abraham ◽  
James Malcolm Sangster
Keyword(s):  
Free Energy ◽  
Activity Coefficient ◽  
Excess Free Energy ◽  
Cadmium Content ◽  
Henry's Law ◽  
Henry’S Law ◽  
Finite Concentration ◽  
Pass Through ◽  
Extremum Value ◽  
Bet Equation

Curves of the water activity coefficient γw have been obtained as a function of water mole fraction in the mixtures AgNO3 + TlNO3 + Cd(NO3)2 + H2O at 98.5 °C. It has been shown, in this study, from the BET equation itself and verified experimentally, that γw may pass through an extremum value for certain systems. The position of such an extremum near the fused salt end of the concentration scale can explain the appearance of a 'practical' Henry's law in a finite concentration range. The curves of the excess free energy of the system undergo rather unusual changes of shape as the cadmium content of the melt is varied.

Excess free energy of solid solutions of Kr-CH4mixtures at 90·67°K

1961 ◽  
Vol 4 (3) ◽  
pp. 199-203
Author(s):  
C. Lefebvre ◽  
J. Guisset
Keyword(s):  
Free Energy ◽  
Solid Solutions ◽  
Excess Free Energy
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