Physical bases of freezing point measurement using ... - Boschung

Proceedings of the 9 th SIRWEC Conference 15-17 March 1998, Luleå, Sweden 274
2.1.1 Nucleation of ice
Nine allotropic varieties of ice do exist, however only ice Ih exists under pressures
lower than 200 MPa and temperatures greater than those of liquid air. It crystallizes in the
hexagonal system (spatial group P 63/mmc) and is then the only ice that exists in the natural
state.
Ice may form either by the freezing of liquid water (producing for instance glazed frost)
or by deposition from the vapor phase (producing for instance rime). In both cases, the
initiation of the ice phase occurs by the nucleation of a small ice embryo. Under certain
conditions, water can be cooled well below 0 °C and yet remains in the liquid state. Water in
such a metastable state is said to be supercooled. If the nucleation of the ice phase occurs on
foreign particles (impurities, dust particles, gaseous bubbles, etc.), the ice is said to form by
heterogeneous nucleation. If foreign particles do not play a role in the nucleation, the ice
phase must be initiated by water molecules combining together to form an ice embryo which
can grow spontaneously. In this case, the ice is said to form by homogeneous nucleation. It is
interesting to note that vibrations also initiate the crystallization of supercooled water. The
nucleation of ice is discussed in detail in [Hobbs 1974].
2.1.2 Latent heat of fusion
The change in enthalpy dH associated with a change in phase of a material at constant
pressure p is given by :
dH = dU + pdV (1)
where dU and dV are the changes in internal energy and volume of the material respectively.
The latent heat of fusion Lf of ice is defined as the change in enthalpy when a unit mass of ice
is converted isothermally and reversibly into liquid water. In this case, the term p dV is small
compared to the other two terms in equation (1), so that Lf is equal to the change in internal
energy. The latent heat of fusion of ice at 0 °C and standard atmospheric pressure is
333.5 kJ/kg. For a discussion about this subject, see [Hobbs 1974].
To melt ice, latent heat of fusion has to be supplied (endothermic transformation), while
when water is frozen, an amount of heat equal to the latent heat of fusion is released
(exothermic transformation).
2.1.3 Scenario of the measurement
Instead of considering the cooling of pure water, let us consider first the behavior of a
saline aqueous solution during cooling from an initial temperature T0, as illustrated in the
figure 1. As pointed out by [Franks 1982], initially the solution supercools, until nucleation
takes place at the temperature Tbc and crystal growth begins. Since the latent heat cannot be
removed fast enough, the temperature rises to the melting temperature Tm. In the vicinity of
the growing ice crystals, the concentration of salt increases, reducing the local Tm, and