In general, correct solutions to the phase-mapping problem should follow the Gibbs
phase rule, which specifies that the number of observed phases at a given chemical composition is no more than the number of chemical elements [N.sub.el]:
According to the
phase rule, when a second element is dissolved in aluminum, we have an additional degree of freedom.
All TRC developments are built upon the algebraic constraints of the Gibbs
phase rule, which specifies the number of free parameters necessary for a system to be thermodynamically well defined based on the number of chemical components and phases present.
From a thermodynamic perspective, consider Gibb's
phase rule (10) which tells us, for equilibrium conditions, the number of degrees of freedom, f, available to a system of c components when there are p coexisting phases present.
The number of ways (degrees of freedom) in which temperature, pressure, or concentration can be varied in such cases can be expressed by a simple equation, which Gibbs called the
phase rule. By the time he was through, Gibbs had left little more to do in what is now called chemical thermodynamics.