Dr. Müllner focuses on the microstructures of crystalline materials. He has worked on the formation and characterization of microstructures, including phase transformations, defect characterization and modeling defect interaction. The objects of study included structural materials (austenitic steel) and functional materials; metals, ceramics, intermetallics, and semiconductors; materials in bulk form and thin films. He has mainly been mainly concerned with mechanical properties, more recently also with magnetic properties. While perambulating through a variety of topics (plasticity of steels, ferroelasticity of ceramics, microstructure and phase transformation of metallic thin films, magnetoplasticity of magnetic shape-memory alloys), he always liked to ponder the formation of crystallographic twins, their formation, and their description in the language of dislocations and disclinations. The magneto-mechanics of magnetic shape-memory alloys is the field of his primary interest nowadays.