On the growth of citations of publication output of individual authors

Dependence of citations L(t) at time t on the publication duration t of 10 arbitrarily selected Polish professors is analyzed using equations based on power law and exponential growth and on progressive nucleation mechanism for overall crystallization in fixed volume. The former two approaches are well known in the bibliometric literature, but the last approach is new for the analysis of growth of citations and other related phenomena. It was found that: (1) power-law relation and exponential growth are relatively inadequate to analyze the data of all authors due to large scatter in the L(t) data of various authors, (2) in view of poor fit at low or high values of t, the exponential growth relation is worse than the power-law relation, and (3) the progressive nucleation mechanism describes the data reasonably well and gives information on the processes of sources of citations and the growth of theses citation sources.

► Time dependence of citations of publications of ten Polish professors is analyzed.
► Power law, exponential growth and progressive nucleation are used for analysis.
► Progressive nucleation mechanism is new for the analysis of growth of citations.
► We found that power law and exponential growth are inadequate to analyze the data.
► Progressive nucleation mechanism describes the data reasonably well.