Heinz Ulbricht, Jürn Schmelzer, Reinhard Mahnke, Frank Schweitzer

Thermodynamics of Finite Systems and the
Kinetics of First-Order Phase Transitions

Leipzig: Teubner, 1988, 220 pp., 111 Figs. (ISBN 3-322-00491-0)

Phase transitions between different states of matter occur in many
equilibrium and nonequilibrium systems. The kinetics of these phase
changes are studied mainly in the case of condensation of a 
vapour in a supersaturated state via homogeneous nucleation. Based on
thermodynamic investigations of heterogeneous systems, the stochastic
and deterministic theory of nucleation and growth of the new phase is
derived.  Emphasis is put on finite-size-effects which lead to a
depletion of the vapour. The results are mainly explained in terms of
clusters (droplet model) and extended to the influence of external
fields. Numerous computer simulations are presented.


1.	Introduction						
1.1.	Types and Classification of Phase Transitions		7
1.2.	Thermodynamic and Experimental Conditions for 
	Supersaturated Vapour States				12
1.3.	Outline of Classical Nucleation Theory			19
1.3.1.	The Classical Droplet Model				19
1.3.2.	Kinetic Assumptions of Classical Nucleation Theory	23
1.3.3.	Modifications of Classical Nucleation Theory		27
1.4.	Nucleation in a Lattice Gas Model			31

2.	Thermodynamics of Heterogeneous Systems 
2.1.	Thermodynamic Premises of Classical Nucleation Theory	39
2.2.	Gibbs' Theory of Heterogeneous Systems			40
2.3.	Curvature Dependence of Surface Tension			45
2.4.	Heterogeneous Systems in Non-Equilibrium States and	
	the Principle of Inner Equilibrium			53

3.	Thermodynamics and Nucleation in Finite Systems
3.1.	The Work of Formation of Clusters			58
3.2.	Equilibriuni States and the Conditions for Stability
	of the Clusters						63
3.3.	Critical Thermodynamic Parameters for Nucleation in
	Finite Systems						67
3.4.	The Work of Formation of Critical Clusters		72
3.5.	Parameters of the Critical Cluster in Dependence on
	the System Size						76
3.6.	Formation of a Droplet Ensemble in Finite Systems	80

4.	Kinetics of Phase Transitions in Finite Systems -
	A Stochastic Approach
4.1.	Free Energy of the Cluster Distribution			86
4.2.	Kinetic Assumptions and Master Equation			92
4.3.	Results of Computer Simulations				98
4.3.1.	Stochastic Dynamics Technique				98
4.3.2.	Evolution of a Single Cluster				100
4.3.3.	Evolution of the Cluster Distribution			105
4.4.	Probability Distribution and Mean First Passage Time	111
4.5.	Mean Values for the Number of Clusters -
	Fokker-Planck Equation					117

5.	Kinetics of Growth of a New Phase - A Deterministic 
5.1.	General Scenario of First-Order Phase Transition in 
	Finite Systems						124
5.2.	Nucleation in Finite Systems - The 
	Quasi-Steady-State-Approximation			126
5.3.	Deterministic Growth Equations				128
5.3.1.	Diffusion Equation Approach				128
5.3.2.	Derivation of a General Growth Equation for 
	Clusters of a New Phase					131
5.4.	Simultaneous Description of Nucleation and Growth	133
5.5.	Curvature Dependence of Surface Tension and the
	Scenario of First-Order Phase Transitions		138
5.6.	Further Applications					140

6.	Theory of Ostwald Ripening
6.1.	Basic Equations						144
6.2.	The Lifshitz-Slyozov Theory				147
6.3.	Thermodynamic Aspects of Ostwald Ripening in Solids
	and Liquid Solutions					149
6.4.	A New Method of Kinetic Description of 
	Ostwald Ripening					152
6.5.	Ostwald Ripening and the Relations to the 
	Theory of Self-Organization				158

7.	Growth of Bubbles in Finite Systems
7.1.	The Model						168
7.2.	Thermodynamic Analysis					169
7.3.	Kinetic Description of Nucleation and 
	Growth of Bubbles					170
7.4.	Applications to Liquid-Gas Solutions and 
	Multicomponent Systems					174

8.	Nucleation and Growth in Elastic and 
	Viscoelastic Media
8.1.	Derivation of a Growth Equation for Clusters 
	in Elastic Media					176
6.2.	Models for the Calculation of Elastic Strains		176 
8.2.1.	Elastic Strains of Nabarro Type				179 
8.2.2.	Elastic Strains in Segregation Processes 
	in Elastic Media					183 
8.2.3.	The Influence of Viscous Properties of the Matrix 
	on the Development of Elastic Strains			184
8.3.	Formation and Growth of Single Clusters 
	in Elastic Media					188
8.4.	Ostwald Ripening in Elastic and Viscoelastic Media	190

References							195


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