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Register a new userBranching of twins in shape memory alloys revisited
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We study the branching of twins appearing in shape memory alloys at the interface between austenite and martensite. In the framework of three-dimensional non-linear elasticity theory, we propose an explicit, low-energy construction of the branched microstructure, generally applicable to any shape memory material without restrictions on the symmetry class of martensite or on the geometric parameters of the interface. We show that the suggested construction follows the expected energy scaling law, i.e., that (for the surface energy of the twins being sufficiently small) the branching leads to energy reduction. Furthermore, the construction can be modified to capture different features of experimentally observed microstructures without violating this scaling law. By using a numerical procedure, we demonstrate that the proposed construction is able to predict realistically the twin width and the number of branching generations in a Cu-Al-Ni single crystal.
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We analyze generic sequences for which the geometrically linear energy [E_eta(u,chi):= eta^{-frac{2}{3}}int_{B_{0}(1)} left| e(u)- sum_{i=1}^3 chi_ie_iright|^2 d x+eta^frac{1}{3} sum_{i=1}^3 |Dchi_i|(B_{0}(1))] remains bounded in the limit $eta to 0$. Here $ e(u) :=1/2(Du + Du^T)$ is the (linearized) strain of the displacement $u$, the strains $e_i$ correspond to the martensite strains of a shape memory alloy undergoing cubic-to-tetragonal transformations and $chi_i:B_{0}(1) to {0,1}$ is the partition into phases. In this regime it is known that in addition to simple laminates also branched structures are possible, which if austenite was present would enable the alloy to form habit planes. In an ansatz-free manner we prove that the alignment of macroscopic interfaces between martensite twins is as predicted by well-known rank-one conditions. Our proof proceeds via the non-convex, non-discrete-valued differential inclusion [e(u) in bigcup_{1leq i eq jleq 3} operatorname{conv} {e_i,e_j}] satisfied by the weak limits of bounded energy sequences and of which we classify all solutions. In particular, there exist no convex integration solutions of the inclusion with complicated geometric structures.
Using a variety of thermodynamic measurements made in magnetic fields, we show evidence that the diffusionless transition (DT) in many shape-memory alloys is related to significant changes in the electronic structure. We investigate three alloys that show the shape-memory effect (In-24 at.% Tl, AuZn, and U-26 at.% Nb). We observe that the DT is significantly altered in these alloys by the application of a magnetic field. Specifically, the DT in InTl-24 at.% shows a decrease in the DT temperature with increasing magnetic field. Further investigations of AuZn were performed using an ultrasonic pulse-echo technique in magnetic fields up to 45 T. Quantum oscillations in the speed of the longitudinal sound waves propagating in the [110] direction indicated a strong acoustic de Haas-van Alphen-type effect and give information about part of the Fermi surface.
We have studied the effect of Fe addition on the structural and magnetic transitions in the magnetic shape memory alloy Ni-Mn-Ga by substituting systematically each atomic species by Fe. Calorimetric and AC susceptibility measurements have been carried out in order to study the magnetic and structural transformation properties. We find that the addition of Fe modifies the structural and magnetic transformation temperatures. Magnetic transition temperatures are displaced to higher values when Fe is substituted into Ni-Mn-Ga, while martensitic and premartensitic transformation temperatures shift to lower values. Moreover, it has been found that the electron per atom concentration essentially governs the phase stability in the quaternary system. However, the observed scaling of transition temperatures with $e/a$ differs from that reported in the related ternary system Ni-Mn-Ga.
Molecular dynamics simulations are performed to provide a detailed understanding of the functional degradation of shape memory alloys at small scale. The origin of the experimentally reported accumulation of plastic deformation and the anomalous sudden increase of the residual strain under cyclic mechanical loading are explained by detailed insights into the relevant atomic scale processes. Our work reveals that the mechanical response of shape-memory-alloy pillars under cyclic compression is significantly influenced by the presence of an amorphous-like surface region as experimentally induced by focused ion beam milling. The main factor responsible for the observed degradation of superelasticity under cyclic loading is the accumulated plastic deformation and the resultant retained martensite originating from a synergetic contribution of the amorphous and crystalline shape-memory-alloy regions. We show that the reported sudden diminishment of the stress plateaus and hysteresis under cyclic loading is caused by the increased stability of the martensite phase due to the presence of the amorphous phase. Based on the identified mechanism responsible for the degradation, we validate reported methods of recovering the superelasticity and propose a new method to prohibit the synergetic contribution of the amorphous and crystalline regions, such as to achieve a sustainable operation of shape memory alloys at small scale.
We have investigated the impact of covalent hybridization on martensitic structure and magnetic properties of Ni50Mn5+xGa35-xCu10 shape memory alloys. We found that the lattice distortion ((c-a)/a) of L10 martensite monotonously changes with the substitution of Mn for Ga atoms and shows a kink behavior at Ga(at.%)= 25 due to the weakened covalent effect between main-group and transition-metal atoms. Moreover, owing to the competition between covalence hybridization and magnetic ordering of introduced Mn atoms, the molecular magnetic moment and Curie temperature coincidently show maximums at Ga(at.%)=25 as well. These behaviors are closely associated with corresponding changes of the strength of covalent hybridization. The results therefore suggest that careful control of the concentration of main-group atoms in Heusler alloys can serve as an additional general tuning parameter for searching new multifunctional materials.
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