Nova Publishers
My Account Nova Publishers Shopping Cart
HomeBooksSeriesJournalsReference CollectionseBooksInformationSalesImprintsFor Authors
  Top » Catalog » Books » Mathematics and Statistics » Evolution Equations » My Account  |  Cart Contents  |  Checkout   
Quick Find
Use keywords to find the product you are looking for.
Advanced Search
What's New? more
The Copper Garden: New Zealand Novels
Shopping Cart more
0 items
Shipping & Returns
Privacy Notice
Conditions of Use
Contact Us
01.Evolution Equations for Grain Growth and Coarsening (pp.5-60)
Notifications more
NotificationsNotify me of updates to Evolution Equations for Grain Growth and Coarsening (pp.5-60)
Tell A Friend
Tell someone you know about this product.
Evolution Equations for Grain Growth and Coarsening (pp.5-60) $100.00
Authors:  (F.D. Fischer, J. Svoboda, Institute of Mechanics, Montanuniversitat Leoben, Leoben, Austria, and others)
A real classical topic of research for evolving systems of microstructures with grains
like metals and ceramics is grain growth and coarsening (Ostwald Ripening). Both
phenomena are driven by the decrease in total surface energy, while the chemical
composition of the individual objects remains unchanged. Only the morphology of the
system evolves and gives the impression that smaller objects are “eaten” by the larger
ones. Evolution equations for these phenomena were published in the last century mostly
as phenomenological equations. The authors show, however, that the evolution equations
can be derived from the Thermodynamic Extremal Principle (TEP). This principle, based
on the works of L. Onsager (1931, 1945) and later of H. Ziegler (1977), allows
calculation of the evolution equations of the state parameters, e.g., the effective radii of
individual grains, precipitates, etc., by maximizing the dissipation, expressed in a
quadratic form of the kinetic parameters, with the constraint that the dissipation is equal
to the negative rate of Gibbs energy in the isothermal case. Later studies have allowed
working with distribution functions of the effective radii of objects and the evolution of
those to stationary distribution functions. Also, the inverse problem has been solved, by
which the evolution equations of the grain or precipitate effective radii can be derived
from steady state distribution functions. This concept was extended from one-parameter
distribution functions to various two-parameter distribution functions. The concept of
TEP also allows successful simulations of the microstructure evolution in multicomponent
multiple particle systems. Practical applications of this concept of evolution
equations for multi-component materials are published and used in the metals processing
industry—see the program package MatCalc,
The main progress of using the TEP to derive evolution equations can be seen in a
rigorous variational approach compared to the numerous heuristic approaches to grain
growth and coarsening. 

Available Options:
Special Focus Titles
01.Chaliapin and the Jews: The Question of Chaliapin's Purported Antisemitism
02.The Humanities: Past, Present and Future
03.The Poles: Myths and Reality
04.Child-Rearing: Practices, Attitudes and Cultural Differences
05."A Home Away from Home": A Community of International and South African University Students
06.Palliative Care: Oncology Experience from Hong Kong
07.The Enigma of Autism: Genius, Disorder or Just Different?
08.The Collector Mentality: Modernization of the Hunter-Gatherer
09.Face Processing: Systems, Disorders and Cultural Differences
10.Occurrences, Structure, Biosynthesis, and Health Benefits Based on Their Evidences of Medicinal Phytochemicals in Vegetables and Fruits. Volume 8
11.Crystal Growth: Concepts, Mechanisms and Applications
12.The Economic, Social and Political Impact of Mining on Akyem Abuakwa from the Pre-Colonial Era up to 1943

Nova Science Publishers
© Copyright 2004 - 2017

Evolution Equations for Grain Growth and Coarsening (pp.5-60)