121
Thermodynamics of Nanoparticles and Phase Transformations
7
7.1
Basic Considerations
The surface over volume ratio of nanoparticles is significantly larger as compared
to that of macroscopic parts (see Chapter 3). As a surface is always connected to
surface energy this large surface contributes significantly to the energy of a particle. Therefore, thermodynamic considerations must take note of this additional
factor. Furthermore, one has to realize that nanoparticles are small; therefore, all
quantities depending on the size have to be analyzed. Looking at heat capacity,
one would not expect a significant influence. However, knowing that heat capacity
is based on lattice vibrations, which depend on the atomistic nature of the particles,
one realizes that the amount and the modes of possible lattice vibrations in a small
particle are different as compared with a large particle. Similar considerations are
valid when looking at polycrystalline bodies consisting of grains in the nanometer
range. In this case, the volume fraction of grain-boundary material is significant.
As grain boundaries are less ordered as compared to well-crystallized material, one
has to expect a notable influence on the thermodynamic quantities.
7.2
Influence of the Particle Size on Thermodynamic Properties and Phase
Transformations
The free enthalpy of one particle, Gibbs enthalpy g, is defined as
g u Ts a
= − + γ .
(7.1a)
In Eq. (7.1) u is the enthalpy, T the temperature, s the entropy, γ the surface energy,
and a the surface of one particle. If the equation is related to one mole, the quantities are written in capital letters, as
G U TS A
= − + γ .
(7.1b)
The surface energy γ is independent of the quantity, however, there is a dependency on the particle size, which is often observed, but until now not really
Nanoparticles – Nanocomposites – Nanomaterials: An Introduction for Beginners, First Edition. Dieter Vollath.
© 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.
Thermodynamics of Nanoparticles and Phase Transformations
7
7.1
Basic Considerations
The surface over volume ratio of nanoparticles is significantly larger as compared
to that of macroscopic parts (see Chapter 3). As a surface is always connected to
surface energy this large surface contributes significantly to the energy of a particle. Therefore, thermodynamic considerations must take note of this additional
factor. Furthermore, one has to realize that nanoparticles are small; therefore, all
quantities depending on the size have to be analyzed. Looking at heat capacity,
one would not expect a significant influence. However, knowing that heat capacity
is based on lattice vibrations, which depend on the atomistic nature of the particles,
one realizes that the amount and the modes of possible lattice vibrations in a small
particle are different as compared with a large particle. Similar considerations are
valid when looking at polycrystalline bodies consisting of grains in the nanometer
range. In this case, the volume fraction of grain-boundary material is significant.
As grain boundaries are less ordered as compared to well-crystallized material, one
has to expect a notable influence on the thermodynamic quantities.
7.2
Influence of the Particle Size on Thermodynamic Properties and Phase
Transformations
The free enthalpy of one particle, Gibbs enthalpy g, is defined as
g u Ts a
= − + γ .
(7.1a)
In Eq. (7.1) u is the enthalpy, T the temperature, s the entropy, γ the surface energy,
and a the surface of one particle. If the equation is related to one mole, the quantities are written in capital letters, as
G U TS A
= − + γ .
(7.1b)
The surface energy γ is independent of the quantity, however, there is a dependency on the particle size, which is often observed, but until now not really
Nanoparticles – Nanocomposites – Nanomaterials: An Introduction for Beginners, First Edition. Dieter Vollath.
© 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.