Reconciling in vivo and in vitro kinetics of the polymorphic transformation in zirconia-toughened alumina for hip joints: II. Theory

In this paper, an updated analytical model for the kinetics of the tetragonal to monoclinic (t→m) polymorphic transformation in ZTA composites for hip joints is proposed and discussed. The model builds upon the so-called Mehl-Avrami-Johnson (MAJ) description of transformation kinetics, which combines two overlapping processes: nucleation of monoclinic sites, and their successive growth. Dependencies on two specific factors are introduced in the model, namely the initial fraction of monoclinic polymorph as received from the manufacturer, and the presence of different types of transition-metal stains (e.g., Ti, CoCr, and Fe) on the ZTA surface. These two factors were studied because clear indications of their potential roles on the environmental stability of implantable ZTA components were found in previous phenomenological analyses of retrievals. Nucleation and growth of monoclinic domains are two key processes whose interplay decides the actual kinetics of the overall transformation process according to two main parameters: an apparent activation energy value function of time and temperature, and a nuclei growth exponent. These parameters were clearly altered by the presence of transition metal contamination, whose effect was incorporated into the model to explain exacerbations of surface degradation. In accordance with a general analytical description of transformation kinetics for isothermal or isochronal evolutions in terms of time and temperature, the modified model of the MAJ description assesses the effect of the initial monoclinic fraction. The updated model has been validated using systematic in vitro experiments, and appears to partly reconcile in vitro and in vivo data of t→m transformation discrepancies in ZTA hip components.