First-principles calculations provide information on the strain evolution of (a) the overall energy of the system and (b) the c/a lattice parameter ratio. High-resolution transmission electron microscopy (HRTEM) reveals the presence of two phases (c) a highly distorted monoclinic version of a tetragonal structure and a monoclinic version of the bulk rhombohedral phase (d). These complex phase boundaries manifest themselves on the surface of the sample as imaged via (e) atomic force microscopy and these features correspond to dramatic surface height changes as shown from (f) the line trace. (g) HRTEM imaging of boundaries shows a smooth transition between phases.^[41]