Solution of Some Integral Equations Occurring in the Theory of

A formula is derived for the average value of any crystal growth parameter observed uring electrochemical nucleation and growth. The formula contains a Volterra integral equation of the first kind and therefore cannot always be solved expli-citly. However, it can be solved under certain conditions, and these are discussed. The most important solutions are col-lected into tables. A large part of electrochemical nucleation theory deals with the prediction of the time evolution of the mean value properties of ensembles of crystals (1-8). The purpose of the present work is to describe some new solutions to this problem for the special case where all crystals have the same geometry, grow by the same mechanism, and are independent of each other and of electrode boundaries. Solutions are established using integral equation methods. As usual in the theory of integral equations, the Dirichlet notation y _-- f(x) is used to mean both "y is a function of x " and "f(x) is the value of the function y at a particular x. " Through-out the text, parentheses, ( ) , are reserved for this notation, square brackets, [], for multiplication, and braces, {}, for functionals. The superscript primed, as in the function f ' (x), denotes the first derivative of the function with respect o the argument x