Duality of Wave Modulation and Nanotwinning in Ni-Mn-Ga Martensite via Long-Period Commensurate States

Abstract: Understanding the crystal structure of magnetic shape memory alloys is crucial for elucidating their martensite twin boundary supermobility and related functionalities. This study analyzes and discusses the structure of martensitic single crystals of Ni50.0Mn27.7Ga22.3 and Ni50.0Mn28.1Ga21.9. Neutron and X-ray diffraction reveal an anharmonic, incommensurate five-layer modulation that evolves with temperature. This evolution gives rise to two key microstructural features: i) periodic nanodomains, identified as emerging a/b-nanotwins, and ii) long-period commensurate structures, such as the 34O, 24O, and 14O states, whose orthorhombic unit cells inherently realize a/b-nanotwins. Ab initio calculations show that these long-period structures are energetically favorable, leading to a lock-in transition. In the alloys studied, the 24O state is the locked-in phase at low temperatures, whereas literature data indicate that Ni50Mn25Ga25 (exact Ni2MnGa stoichiometry) evolves toward the 14O phase. Crucially, these results unify two seemingly contrasting structural descriptions -- wave-like modulation and discrete nanotwinning -- thereby establishing a foundation for a deeper understanding of the crystal-structure-functionality relationship in magnetic shape memory alloys.