Glossary of Terms for Phase Equilibria Diagrams
- Degrees of Freedom
The number of intensive variables which can be altered independently and arbitrarily without
bringing about the disappearance of a phase or the formation of a new one is called the
number of degrees of freedom of a system. Intensive variables are those which are
independent of mass, such as pressure, temperature, and composition.
The number of degrees of freedom of a system may also be defined as the "number of variable
factors, temperature, pressure, and concentration of the components, which must be arbitrarily
fixed in order that the condition of the system may be perfectly defined."
A system is termed invariant, mono-variant, bi-variant, tri-variant, and so on, according to
whether it possesses, respectively, 0, 1, 2, 3, etc., degrees of freedom.
Reference: Levin, E.M., McMurdie, H.F., and Hall, F.P., Phase Diagrams for
Ceramists: Volume 1, The American Ceramic Society, Columbus, Ohio, p. 6, 1956.
Note: The reference for the definition of Degrees of Freedom (or Variance) includes the
following additional sources.
MacDougall, F.H., Thermodynamics and Chemistry, John Wiley and Sons, New York, NY, 1939.
Findlay, A., Campbell, A.N., and Smith, N.O., The Phase Rule and Its Applications, Ninth Edition,
Dover Publications, Inc., New York, NY, 1951.
The formation of crystalline material from glass.
Reference: Levin, E.M., McMurdie, H.F., and Hall, F.P., Phase Diagrams
for Ceramists: Volume 1, The American Ceramic Society, Columbus, Ohio, p. 6, 1956.
Examples of Devitrification