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
Network Theory and Analysis
$73.80
Shopping Cart more
0 items
Information
Shipping & Returns
Privacy Notice
Conditions of Use
Contact Us
Bestsellers
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)
Abstract:
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, http://matcalc.wkmp.tuwien.ac.at/.
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:
Version:
Special Focus Titles
01.Essays on the Philosophical Nexus between Religion and Politics. Volume 2
02.Glaciology for Glacial Geologists
03.Tropical Fruits: From Cultivation to Consumption and Health Benefits, Fruits from the Amazon
04.The Copper Garden: New Zealand Novels
05.Informed Parents, Healthy Kids: Information You Need to Know to Find the Right Mental Health Practitioner
06.An Echo of Silence: A Comprehensive Research Study on Early Child Marriage (ECM) in Iran
07.Panic Disorder: Assessment, Management and Research Insights
08.Multiple Sclerosis in Children and Adolescents
09.Parkinson’s Disease: Awareness among Young Adults
10.Cancer and Exercise
11.Psychobiological, Clinical, and Educational Aspects of Giftedness
12.Why 40%-80% of Chronic Pain Patients Are Misdiagnosed and How to Correct That

Nova Science Publishers
© Copyright 2004 - 2018

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