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.