Decarbonisation of existing infrastructure systems requires a dynamic roll-out of technology at an unprecedented scale. The potential disruption in supply of critical materials could endanger such a transition to low-carbon infrastructure and, by extension, compromise energy security more broadly because low carbon technologies are reliant on these materials in a way that fossil-fuelled energy infrastructure is not. Criticality is currently defined as the combination of the potential for supply disruption and the exposure of a system of interest to that disruption. We build on this definition and develop a dynamic approach to quantifying criticality, which monitors the change in criticality during the transition towards a low-carbon infrastructure goal. This allows us to assess the relative risk of different technology pathways to reach a particular goal and reduce the probability of being 'locked in' to currently attractive but potentially future-critical technologies. To demonstrate, we apply our method to criticality of the proposed UK electricity system transition, with a focus on neodymium. We anticipate that the supply disruption potential of neodymium will decrease by almost 30% by 2050; however, our results show the criticality of low carbon electricity production increases ninefold over this period, as a result of increasing exposure to neodymium-reliant technologies. (C) 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license