Two sets of kinematic quantities describe the configuration of the epilayer-substrate composite: one for elastic deformation, and the other for mass transport. Imagine a curve on the surface. When some number of B-atoms cross the curve, to maintain a flat epilayer, an equal number of A-atoms must cross the curve in the opposite direction. Denote the unit vector lying in the surface normal to the curve by m. Define a vector field I in the surface (called the mass relocation), such that is the number of B-atoms across a unit length of the curve.
Mass conservation requires that the variation in the concentration relate to the variation in the mass relocation as
(6)
where L is the number of atomic sites per unit area. Similarly define a vector field J (called the mass flux), such that is the number of B-atoms across a unit length of the curve on the surface per unit time. The relation between I and Jis analogous to that between displacement and velocity. The time rate of the concentration compensates the divergence of the flux vector, namely,
is the number of B-atoms across a unit length of the curve on the surface per unit time. The relation between I and J is analogous to that between displacement and velocity. The time rate of the concentration compensates the divergence of the flux vector, namely, 
