2
J. W. P. Schmelzer and C. Schick
Abbreviations
k B
Boltzmann constant
g(T, p) Change of the Gibbs free energy in crystallization per unit volume of
the newly evolving crystalline phase
μ i
Chemical potential of the i = 1, 2, …, k components
v
Differences of the volumes between liquid and crystal phases per unit
volume of the crystal phase
D
Diffusion coefficient
(ε)
Energy of elastic deformation caused by the formation of a crystallite of
volume V in a liquid
α p
Isobaric thermal expansion coefficient
κ T
Isothermal compressibility
τ R
Maxwell’s relaxation time
s m , h m Melting entropy and melting enthalpy per unit volume of the crystal
phase
x i
Molar fraction of the i = 1, 2, …, k components
η
Newtonian viscosity
c
Number of nucleation centers per unit volume of the liquid
n c , V c
Number of particles and volume of a critical crystal cluster
ε, ε 0
Parameters determining the elastic effects caused by crystal evolution
in the liquid (ε) and in a Hookean solid (ε 0 )
J 0
Pre-factor in the expression for the steady-steady-state nucleation rate
determined by the kinetics of crystal evolution
p, p m
Pressure, melting pressure
R, A, V
Radius, volume, and surface area of a crystal cluster
d 0
Size parameter of the particles of the liquid
c p
Specific heat per unit volume of the crystal phase
J
Steady-state nucleation rate
σ
Surface tension referred to the surface of tension
T, T m
Temperature, melting temperature
t
Time
τ ns
Time-lag in nucleation
δ
Tolman parameter
W c
Work of critical cluster formation
1 Introduction
Classical nucleation theory (CNT) is till now the major tool for the interpretation of
experimental data on nucleation in a wide spectrum of phase transformation processes
like condensation and boiling, segregation in solid and liquid solutions, melting or
crystallization [1–6]. In a variety of applications, it allows one not only a qualitative
J. W. P. Schmelzer and C. Schick
Abbreviations
k B
Boltzmann constant
g(T, p) Change of the Gibbs free energy in crystallization per unit volume of
the newly evolving crystalline phase
μ i
Chemical potential of the i = 1, 2, …, k components
v
Differences of the volumes between liquid and crystal phases per unit
volume of the crystal phase
D
Diffusion coefficient
(ε)
Energy of elastic deformation caused by the formation of a crystallite of
volume V in a liquid
α p
Isobaric thermal expansion coefficient
κ T
Isothermal compressibility
τ R
Maxwell’s relaxation time
s m , h m Melting entropy and melting enthalpy per unit volume of the crystal
phase
x i
Molar fraction of the i = 1, 2, …, k components
η
Newtonian viscosity
c
Number of nucleation centers per unit volume of the liquid
n c , V c
Number of particles and volume of a critical crystal cluster
ε, ε 0
Parameters determining the elastic effects caused by crystal evolution
in the liquid (ε) and in a Hookean solid (ε 0 )
J 0
Pre-factor in the expression for the steady-steady-state nucleation rate
determined by the kinetics of crystal evolution
p, p m
Pressure, melting pressure
R, A, V
Radius, volume, and surface area of a crystal cluster
d 0
Size parameter of the particles of the liquid
c p
Specific heat per unit volume of the crystal phase
J
Steady-state nucleation rate
σ
Surface tension referred to the surface of tension
T, T m
Temperature, melting temperature
t
Time
τ ns
Time-lag in nucleation
δ
Tolman parameter
W c
Work of critical cluster formation
1 Introduction
Classical nucleation theory (CNT) is till now the major tool for the interpretation of
experimental data on nucleation in a wide spectrum of phase transformation processes
like condensation and boiling, segregation in solid and liquid solutions, melting or
crystallization [1–6]. In a variety of applications, it allows one not only a qualitative