Origin of the Onset Temperature in Solid-State Ceramic Synthesis

Temperature plays a crucial role in solid-state synthesis, but there are currently no mechanistic theories to predict the optimal temperature to carry out a solid-state reaction. A variety of recent observations suggest that transient liquid intermediates provide a diffusion media for solid-state reactions at subsolidus temperatures. Here, we hypothesize that in a solid-state reaction <i>A + B </i>-&gt;<i> AB</i>, the precursors <i>A</i> and <i>B</i> first melt into a metastable liquid phase before transformation into the solid <i>AB</i> product phase. In this theory, the onset temperature of a solid-state reaction derives from the extension of liquidus curves into the metastable eutectic region of a Temperature-Composition phase diagram. We validate this theory by combining <i>in situ </i>XRD synchrotron observations with a thermal gradient heater, which produces temperature-time-transformation curves for a solid-state reaction that largely agree with the theory of a metastable liquid intermediate. To more readily predict the reaction onset temperature, we present with a strategy to combine DFT convex hulls with CALPHAD approaches to rapidly estimate the high-temperature liquidus curves of phase diagrams at minimal computational cost.