Chapter 2
Phase Transitions
2.1 Background
2.1.1 Thermodynamic Aspects
The fusion of a crystal is, together with boiling/condensation, a representative of
phenomena known as phase transitions. It is useful to summarize the terminology
and properties of phase transitions in (macroscopic) thermodynamics. Note that the
following descriptions assume thermodynamic equilibrium.
1
A phase is not only a thermodynamic concept but also a reality. A phase must be
uniform chemically and physically if viewed macroscopically, i.e., averaged over a
volume that contains a sufficiently large number of molecules. All intensive variables
(not only temperature, pressure, and density but also composition) are uniform in a
single phase. A pure substance is assumed for a while. Generally, a substance has
plural phases like gas, liquid, and solid, which are representative three phases of
matter. Although these three phases are easily distinguished from each other under
normal conditions, this is not generally true, as indicated by the gas-liquid critical
point, where gas and liquid merge to a single state.
Thermodynamics says that a phase is characterized by the Gibbs energy (G),
a thermodynamic potential relevant to the conditions where temperature (T ) and
pressure ( p) are independent variables. Now, we write the molar Gibbs energy of
phase H as μ H (T, p). Then, a surface in a (T, p, μ) space can be identified as phase
H. When a substance has two phases, H and L (Fig. 2.1), two surfaces μ H (T, p)
and μ L (T, p) generally cross with a crossing line. Since the Gibbs energy must
be minimum at thermodynamic equilibrium, the stable phase is interchanged upon
crossing the crossing line. Thus, the substance must change its form between phase H
1 We here assume a usual meaning of “equilibrium.” It is seemingly stable and steady against time
of our daily time scale. Some class of non-equilibrium and “relaxing” states is treated in Chap. 8.
© The Editor(s) (if applicable) and The Author(s), under exclusive license
to Springer Nature Singapore Pte Ltd. 2020
K. Saito, Chemical Physics of Molecular Condensed Matter,
Lecture Notes in Chemistry 104,
https://doi.org/10.1007/978-981-15-9023-8_2
31
Phase Transitions
2.1 Background
2.1.1 Thermodynamic Aspects
The fusion of a crystal is, together with boiling/condensation, a representative of
phenomena known as phase transitions. It is useful to summarize the terminology
and properties of phase transitions in (macroscopic) thermodynamics. Note that the
following descriptions assume thermodynamic equilibrium.
1
A phase is not only a thermodynamic concept but also a reality. A phase must be
uniform chemically and physically if viewed macroscopically, i.e., averaged over a
volume that contains a sufficiently large number of molecules. All intensive variables
(not only temperature, pressure, and density but also composition) are uniform in a
single phase. A pure substance is assumed for a while. Generally, a substance has
plural phases like gas, liquid, and solid, which are representative three phases of
matter. Although these three phases are easily distinguished from each other under
normal conditions, this is not generally true, as indicated by the gas-liquid critical
point, where gas and liquid merge to a single state.
Thermodynamics says that a phase is characterized by the Gibbs energy (G),
a thermodynamic potential relevant to the conditions where temperature (T ) and
pressure ( p) are independent variables. Now, we write the molar Gibbs energy of
phase H as μ H (T, p). Then, a surface in a (T, p, μ) space can be identified as phase
H. When a substance has two phases, H and L (Fig. 2.1), two surfaces μ H (T, p)
and μ L (T, p) generally cross with a crossing line. Since the Gibbs energy must
be minimum at thermodynamic equilibrium, the stable phase is interchanged upon
crossing the crossing line. Thus, the substance must change its form between phase H
1 We here assume a usual meaning of “equilibrium.” It is seemingly stable and steady against time
of our daily time scale. Some class of non-equilibrium and “relaxing” states is treated in Chap. 8.
© The Editor(s) (if applicable) and The Author(s), under exclusive license
to Springer Nature Singapore Pte Ltd. 2020
K. Saito, Chemical Physics of Molecular Condensed Matter,
Lecture Notes in Chemistry 104,
https://doi.org/10.1007/978-981-15-9023-8_2
31