text: Darken’s equations can be applied to almost any scenario involving the diffusion of two different components that have different diffusion coefficients. This holds true except in situations where there is an accompanying volume change in the material because this violates one of Darken’s critical assumptions that atomic volume is constant. More complicated equations than presented must be used in cases where there is convection. One application in which Darken’s equations play an instrumental role is in analyzing the process of diffusion bonding. Diffusion bonding is used widely in manufacturing to connect two materials without using adhesives or welding techniques. Diffusion bonding works because atoms from both materials diffuse into the other material, resulting in a bond that is formed between the two materials. The diffusion of atoms between the two materials is achieved by placing the materials in contact with each other at high pressure and temperature, while not exceeding the melting temperature of either material. Darken’s equations, particularly Darken’s second equation, come into play when determining the diffusion coefficients for the two materials in the diffusion couple. Knowing the diffusion coefficients is necessary for predicting the flux of atoms between the two materials, which can then be used in numerical models of the diffusion bonding process, as, for example, was looked at in the paper by Orhan, Aksoy, and Eroglu when creating a model to determine the amount of time required to create a diffusion bond. In a similar manner, Darken’s equations were used in a paper by Watanabe et al., on the nickel-aluminum system, to verify the interdiffusion coefficients that were calculated for nickel aluminum alloys.
  Application of Darken’s first equation has important implications for analyzing the structural integrity of materials. Darken’s first equation, , can be rewritten in terms of vacancy flux, . Use of Darken’s equation in this form has important implications for determining the flux of vacancies into a material undergoing diffusion bonding, which, due to the Kirkendall effect, could lead to porosity in the material and have an adverse effect on its strength. This is particularly important in materials such as aluminum nickel superalloys that are used in jet engines, where the structural integrity of the materials is extremely important. Porosity formation, known as Kirkendall porosity, in these nickel-aluminum superalloys have been observed when diffusion bonding has been used. It is important then to use Darken’s findings to predict this porosity formation.