Introducing new technologies into infrastructure (wind turbines, electric vehicles, low-carbon materials and so on) often demands materials that are 'critical'; their supply is likely to be disrupted owing to limited reserves, geopolitical instability, environmental issues and/or increasing demand. Non-critical materials may become critical if introduced into infrastructure, owing to its gigatonne scale. This potentially poses significant risk to the development of low-carbon infrastructure. Analysis of this risk has previously overlooked the relationship between the 'local properties' that determine the selection of a technology and the overall vulnerability of the system, a global property. Treating materials or components as elements having fixed properties overlooks optima within the local-global variable space that could be exploited to minimise vulnerability while maximising performance. In this study, a framework for such analysis is presented along with a preliminary measure of relative materials criticality by way of a case study (a wind turbine generator). Although introduction of critical materials (in this case, rare earth metals) enhances technical performance by up to an order of magnitude, the associated increase in criticality may be two or three orders of magnitude. Analysis at the materials and component levels produces different results; design decisions should be based on analysis at several levels. [ABSTRACT FROM AUTHOR]