Gradients surround us in daily life and are simply defined as a change of a property over distance or time. Whether it's a slope that allows a ball to roll down a hill, or a temperature variation due to heating or cooling, the fundamental concept doesn't shift: some change is occurring over distance and time as long as the two boundaries, for instance the top of the hill and the bottom, are different. Once they are the same, the system is at rest.
In order to extract timescale information from the olivine minerals from Volcan Llaima (Fig. 2), I have been using DIPRA (Fig. 3), an open access software program created and published by Társilo Girona and Fidel Costa at the Earth Observatory of Singapore. DIPRA is a user-friendly program that allows one to model element diffusion in olivine for five different elements (Mg/Fe, Ni, Ca, Mn). By looking at the timescale information associated with different populations of crystals (ones associated with the intruding magma and ones associated with the resident magma), we are able to start to constrain the processes that occurred leading up to eruption.