ABSTRACT
Phase transitions in materials have been characterized as either first or "higher" order. Formally, if the Gibbs free energy function is discontinuous at the transformation temperature, it is a first order transformation; if not, it is of higher order. Examples of a first order phase transformation would be boiling, sublimation, and solidification. Most solid-state polymorphic transformations are also first order transitions. The quartz to trydimite (or crystobalite) reconstructive transformation requires the breaking of bonds to form a new crystal structure. Transformations such as this show an activated barrier associated with the breaking of bonds and the diffusion of atoms, and thus occur sluggishly at lower temperatures. The significant kinetic barrier to these transformations permits metastable presence of the high temperature phases at pressures and temperatures where they are not thermodynamically stable. For example, crystobalite may be permanently formed at room temperature by rapid quenching from elevated temperature. Displasive (martensitic13) transformations such as a-j3 quartz require only shifts in bond angle and occur quite rapidly. Quenching-in of the high temperature forms of these materials is more difficult, and sometimes cannot be accomplished without the introduction of impurity atoms into the high-temperature structure. The latent heats, and thus the DTA/DSC peak intensities of first order phase transitions, increase with increasing severity of structural change via the transformation. For example, the latent heat of the a to j3 quartz displasive transformation in silica is 0.63 kJ /mol. For the fusion of aluminum, the latent heat is 2.57 kJ /mol, and for the boiling of aluminum the latent
heat is 67.9 kJjmol [7]. Higher order transitions show little or no structural alter-
ation. Second order and "lambda" transitions both fit in this category. An example of a second order transformation is the nonsuperconducting to superconducting transformation at cryogenic temperatures (e.g. lead at -265.96°C). An example of a lambda transformation is the Curie temperature in ferromagnetic materials. Below this temperature, the material can be made into a permanent magnet, while above this temperature it cannot (paramagnetic). In the ferromagnetic state, an applied magnetic field can bring the dipole moments of neighboring atoms into mutual parallelism, and they will remain that way even after the magnetic field is removed. As the Curie temperature is approached, the increasing disorder due to random thermal agitation of electrons diminishes the parallelism. The Curie temperature represents the point at which the last of the mutual parallelism disappears.
