1. An exhaustive study of diffusion in a concentration gradient emphasising the atomistic approach is given by J. R. Manning in his book “Diffusion Kinetics for Atoms in Crystals”, D. van Nostrand Co. Inc. (1968) Chapter 5.
2. A concise treatment of the Boltzmann–Matano method is given in W. Jost, “Diffusion in Solids, Liquids and Gases”, Academic Press, (1960) p. 75–77 and also in “Solid State Reactions”, p. 87–89, by H. Schmalzried, Verlag Chemie (1981). A more complete discussion including the relation between the chemical and tracer diffusion coefficients can be found in “Physical Chemistry of Metals”, by L. S. Darkin and R. W. Gurry, McGraw-Hill (1953) p. 450–464.