Magnetic and structural properties of the magnetic shape memory compound Ni(2)Mn(1.48)Sb(0.52)

Modulations in martensitic Heusler alloys originate from nanotwin ordering

Heusler alloys exhibiting magnetic and martensitic transitions enable applications like magnetocaloric refrigeration and actuation based on the magnetic shape memory effect. Their outstanding functional properties depend on low hysteresis losses and low actuation fields. These are only achieved if the atomic positions deviate from a tetragonal lattice by periodic displacements. The origin of the so-called modulated structures is the subject of much controversy: They are either explained by phonon softening or adaptive nanotwinning. Here we used large-scale density functional theory calculations on the Ni₂MnGa prototype system to demonstrate interaction energy between twin boundaries. Minimizing the interaction energy resulted in the experimentally observed ordered modulations at the atomic scale, it explained that a/b twin boundaries are stacking faults at the mesoscale, and contributed to the macroscopic hysteresis losses. Furthermore, we found that phonon softening paves the transformation path towards the nanotwinned martensite state. This unified both opposing concepts to explain modulated martensite.

Crystallographic features of the martensitic transformation and their impact on variant organization in the intermetallic compound Ni50Mn38Sb12 studied by SEM/EBSD

The mechanical and magnetic properties of Ni-Mn-Sb intermetallic compounds are closely related to the martensitic transformation and martensite variant organization. However, studies of these issues are very limited. Thus, a thorough crystallographic investigation of the martensitic transformation orientation relationship (OR), the transformation deformation and their impact on the variant organization of an Ni₅₀Mn₃₈Sb₁₂ alloy using scanning electron microscopy/electron backscatter diffraction (SEM/EBSD) was conducted in this work. It is shown that the martensite variants are hierarchically organized into plates, each possessing four distinct twin-related variants, and the plates into plate colonies, each containing four distinct plates delimited by compatible and incompatible plate interfaces. Such a characteristic organization is produced by the martensitic transformation. It is revealed that the transformation obeys the Pitsch relation ({0[Formula: see text]}_A // {2[Formula: see text]}_M and 〈0[Formula: see text]1〉_A // 〈[Formula: see text]2〉_M; the subscripts A and M refer to austenite and martensite, respectively). The type I twinning plane K₁ of the intra-plate variants and the compatible plate interface plane correspond to the respective orientation relationship planes {0[Formula: see text]}_A and {0[Formula: see text]}_A of austenite. The three {0[Formula: see text]}_A planes possessed by each pair of compatible plates, one corresponding to the compatible plate interface and the other two to the variants in the two plates, are interrelated by 60° and belong to a single 〈11[Formula: see text]〉_A axis zone. The {0[Formula: see text]}_A planes representing the two pairs of compatible plates in each plate colony belong to two 〈11[Formula: see text]〉_A axis zones having one {0[Formula: see text]}_A plane in common. This common plane defines the compatible plate interfaces of the two pairs of plates. The transformation strains to form the variants in the compatible plates are compatible and demonstrate an edge-to-edge character. Thus, such plates should nucleate and grow simultaneously. On the other hand, the strains to form the variants in the incompatible plates are incompatible, so they nucleate and grow separately until they meet during the transformation. The results of the present work provide comprehensive information on the martensitic transformation of Ni-Mn-Sb intermetallic compounds and its impact on martensite variant organization.

Crystal structure and crystallographic characteristics of martensite in Ni50Mn38Sb12 alloys

For Ni–Mn–Sb ferromagnetic multifunctional alloys, the crystal structures of martensite variants and the orientation relationships between them are decisive factors for their magnetic field-induced behaviours and are hence of importance. Such information has rarely been reported in the literature. In the present work, the crystal structure, microstructure and orientation relationships of Ni–Mn–Sb martensite were thoroughly investigated by X-ray diffraction (XRD) and electron backscatter diffraction (EBSD). Through XRD analyses, the crystal structure of the martensite, including the crystal system, the space group, the lattice parameters and the atomic coordinates, was fully resolved. The structure is orthorhombic and can be represented with a 4O superstructure. EBSD analyses show that the Ni–Mn–Sb martensite has a lamellar form. One martensite lamella corresponds to one orientation variant. The lamellae are organized in long plate-shaped colonies. Within each colony, four distinct orientation variants (A, B, C and D) appear repeatedly and extend in roughly the same direction. The four variants are twin related to one another, with variants A and C (or variants B and D) forming a type I twin, variants A and B (or C and D) a type II twin, and variants A and D (or B and C) a compound twin. The complete twinning elements for each twin relation were thus fully determined. The interfaces between the variants were identified to be their corresponding twinning planes. All these results provide fundamental information for Ni–Mn–Sb alloys that is useful for interpreting their magnetic and mechanical characteristics.

Constitutive modelling of magnetic shape memory alloys with discrete and continuous symmetries

A free energy-based constitutive formulation is considered for magnetic shape memory alloys. Internal state variables are introduced whose evolution describes the transition from reference state to the deformed and transformed one. We impose material symmetry restrictions on the Gibbs free energy and on the evolution equations of the internal state variables. Discrete symmetry is considered for single crystals, whereas continuous symmetry is considered for polycrystalline materials.

Atomic and magnetic order in the shape memory alloy Mn2NiGa

Magnetization and high resolution neutron powder diffraction measurements on the magnetic shape memory alloy Mn(2)NiGa have confirmed that it is ferromagnetic with a Curie temperature above 500 K. The compound undergoes a broad structural phase transformation ΔT ∼ 90 K with a mean transition temperature T(M) ∼ 270 K. The high temperature parent phase is cubic (a = 5.937 Å) and has a modified L 2(1) structure. At 500 K the ordered magnetic moment essentially all on the 4a site is 1.35 μ(B)/Mn. The low temperature martensite has space group I4/mmm and is related to the cubic phase through a Bain transformation a(tet) = (a(cub) + b(cub))/2, b(tet) = (a(cub) - b(cub)) and c(tet) = c(cub) in which the change in cell volume is < 2.6%. In this structure at 5 K the ordered moment of ≈2.3 μ(B) is again found to be confined to the sites with full Mn occupation and is aligned parallel to c. Neutron diffraction patterns obtained at 5 K suggested the presence of a weak incommensurate antiferromagnetic phase characterized by either a ((1/3)0(1/3)) or (00(1/3)) propagation vector.