Based on the divergence theorem, we reveal that the Fickian first law relevant to the diffusion flux |J(t,x,y,z) > in the time and space is incomplete without an integral constant |J0(t) > for the integral of Fi...Based on the divergence theorem, we reveal that the Fickian first law relevant to the diffusion flux |J(t,x,y,z) > in the time and space is incomplete without an integral constant |J0(t) > for the integral of Fickian second law. The new diffusion flux (NDF) taking it into account shows that we can systematically understand the problems of one-way diffusion, impurity diffusion and self-diffusion as a special case of the interdiffusion. Applying the NDF to the interdiffusion problem between metal plates, it is clarified that the Kirkenkall effect is caused by |J0(t) > and also that the interdiffusion coefficients in alloy can be easily obtained. The interdiffusion problems are reasonably solved regardless of the intrinsic diffusion conception. Thus the NDF to replace the Fickian first law is an essential equation in physics.展开更多
The well-known Darken equation has been widely accepted in analyzing interdiffusion problems since 1948. The diffusion researchers have never conceived a doubt about the validity of Darken equation for such a long tim...The well-known Darken equation has been widely accepted in analyzing interdiffusion problems since 1948. The diffusion researchers have never conceived a doubt about the validity of Darken equation for such a long time. However, it is revealed that the Darken equation is inconsistent with the fundamental theory in mathematics. At the same time, it is clarified that the well-known intrinsic diffusion concept is an illusion. The present brief report will have a great influence on matters of the research and education relevant to diffusion problems not only in future but also in past, since the accumulated diffusivity data analyzed by the invalid Darken theory and the misjudged descriptions in existing text books should be revised or deleted as soon as possible.展开更多
文摘Based on the divergence theorem, we reveal that the Fickian first law relevant to the diffusion flux |J(t,x,y,z) > in the time and space is incomplete without an integral constant |J0(t) > for the integral of Fickian second law. The new diffusion flux (NDF) taking it into account shows that we can systematically understand the problems of one-way diffusion, impurity diffusion and self-diffusion as a special case of the interdiffusion. Applying the NDF to the interdiffusion problem between metal plates, it is clarified that the Kirkenkall effect is caused by |J0(t) > and also that the interdiffusion coefficients in alloy can be easily obtained. The interdiffusion problems are reasonably solved regardless of the intrinsic diffusion conception. Thus the NDF to replace the Fickian first law is an essential equation in physics.
文摘The well-known Darken equation has been widely accepted in analyzing interdiffusion problems since 1948. The diffusion researchers have never conceived a doubt about the validity of Darken equation for such a long time. However, it is revealed that the Darken equation is inconsistent with the fundamental theory in mathematics. At the same time, it is clarified that the well-known intrinsic diffusion concept is an illusion. The present brief report will have a great influence on matters of the research and education relevant to diffusion problems not only in future but also in past, since the accumulated diffusivity data analyzed by the invalid Darken theory and the misjudged descriptions in existing text books should be revised or deleted as soon as possible.
