Orientation relationships between nanotwins inside type II microtwins in Ni-Mn-Ga alloy

Microstructure of the martensitic variant pairs in Ni-Mn-Ga magnetic shape memory alloys (MSMAs) underpins future research and development on the alloy with large magnetic-field-induced strain (MFIS). However, a complete description of the microstructure and crystallography of all variants pairs which have hierarchical nanotwins inside microtwins (including type I, II, and compound twins) is unavailable now, because that of the type II microtwin is still far from being thoroughly determined. By investigating a non-modulated Ni₅₄Mn₂₅Ga₂₁ alloy, this paper systematically determines the orientation relationships (ORs) between the nano-lamellae inside all three types of microtwins with a special emphasis on the type II. Inside any single variant, the nano-lamellae are {1 1 2} compound twins. Across the inter-variant interfaces of any type of microtwins, the ORs of the pair-wise nano-lamellae are classified into three crystallographic characteristics: i) identical orientation, ii) (1 1‾ 2) compound twin with its twinning plane parallel to the inter-variant interface, iii) (1 1 2) or (1‾ 1‾ 2) compound twin with its twinning plane parallel to the inner-variant nanotwin boundary. Subtle deviations from these three ORs may result as the volume fraction of the minor nano-lamellae (λ) changes. A geometric model with different values of λ and types of microtwins integrated together is established to fully understand the above hierarchically twined microstructure: its formation is accomplished by primary twinning (1 1‾ 2)[1‾ 1 1] (to form a microtwin) plus secondary conjugated twinning (1 1 2)[11 1‾] and/or (1‾ 1‾ 2)[1 1 1] (to form nanotwins). The different types of twins so formed undergo twinning/detwinning to realize deformation. With the clarified ORs and twinning systems, and the revealed formation and deformation mechanisms of all types of twin variants in a group of non-modulated martensitic plates, this paper is beneficial to further research on the MFIS improvement of MSMAs.