Darken's equations  In 1948, Lawrence Stamper Darken published an article entitled "Diffusion, Mobility and Their Interrelation through Free Energy in Binary Metallic Systems", in which he derived two equations describing solid-state diffusion in binary solutions. Specifically, the equations Darken created relate “binary chemical diffusion coefficient to the intrinsic and self diffusion coefficients”. The equations apply to cases when a solid solution's two interdiffusing components do not have the same coefficient of diffusion. The result of this article had a large impact on the understanding of solid state diffusion and as a result the equations have come to be known as “Darken’s equations”. Darken's first equation is Darken's first equation is used to calculate marker velocity, given here as formula_2, in respect to a binary system where the different components have their own corresponding diffusion coefficients, "D"1 and "D"2, as was discussed in the Kirkendall experiment. The marker velocity is in terms of length per unit time and the diffusion coefficients are in terms of length squared per unit time. The variables "N"1 and "N"2 represent the atom fraction of the corresponding component. In addition, the variable "x" is the distance term. It is important to note that this equation only holds in situations where the total concentration remains constant. For a binary system this is defined by "C"1 + "C"2 = "C", where "C" is the overall concentration of the system that remains constant, and "C"1 and "C"2 are the corresponding component's concentration. This is equivalent to saying that the partial molar volumes of the two components are constant and equal. In addition, the ends of the system need to be fixed in position for the equation to hold. These constraints will be further analyzed in the derivation. Darken's second equation is Darken's second equation is used to calculate the chemical diffusion coefficient (also known as the inter-diffusion coefficient), formula_4, for a binary solution. The variables "N" and "D" are the same as previously stated for Darken's first equation. In addition, the variable "a"1 is the activity coefficient for the component one. Similar to the first equation, this equation only holds in situations when the total concentration remains constant. To derive these equations Darken mainly references Kirkendall and Smigelskas’s experiment, and W. A. Johnson’s experiment, along with other findings within the metallurgical community.