Energy function for grain boundary plane orientation fundamental zone

The success of grain boundary (GB) plane orientation fundamental zone (FZ) has connected GB structures across multiple crystallographic characters with their properties in a unique insight, but quantitative understandings of the structure-property relationship therein are still lacking. Based on the well-known Read-Shockley relationship, a theoretical derivation is proposed to predict low angle GB energies as a function of FZ parameters, which forms a standard energy function that accurately captures the simulated energy trends in a simple and clear manner. The theorization presented here is therefore expected to be a starting point for modern GB energy functions.