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1. Simulations of multivariant Si I to Si II phase transformation in polycrystalline silicon with finite-strain scale-free phase-field approach

   https://doi.org/10.1016/j.actamat.2023.118996  

   Babaei, H ; Pratoori, R ; Levitas, V.I. ( May 2023 , Acta Materialia)

   Scale-free phase-field approach and corresponding finite element method simulations for multivariant martensitic phase transformation from cubic Si I to tetragonal Si II in a polycrystalline aggregate are presented. Important features of the model are large and very anisotropic transformation strain tensor 𝜺𝑡 = {0.1753; 0.1753; −0.447} and stress-tensor dependent athermal dissipative threshold for transformation, which produce essential challenges for computations. 3D polycrystals with stochastically oriented grains are subjected to uniaxial strain- and stress-controlled loadings under periodic boundary conditions and zero averaged lateral strains. Coupled evolution of discrete martensitic microstructure, volume fractions of martensitic variants and Si II, stress and transformation strain tensors, and texture are presented and analyzed. Macroscopic variables effectively representing multivariant transformational behavior are introduced. Macroscopic stress–strain and transformational behavior for 55 and 910 grains are close. Large transformation strains and grain boundaries lead to huge internal stresses of tens GPa, which affect microstructure evolution and macroscopic behavior. In contrast to a single crystal, the local mechanical instabilities due to phase transformation and negative local tangent modulus are stabilized at the macroscale by arresting/slowing the growth of Si II regions by the grain boundaries. This leads to increasing stress during transformation. The developed methodology can be used for studying similar phase transformations with large transformation strains and for further development by including plastic strain and strain-induced transformations. 

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2. Fifth-degree elastic energy for predictive continuum stress–strain relations and elastic instabilities under large strain and complex loading in silicon

   https://doi.org/10.1038/s41524-020-00382-8  

   Chen, Hao ; Zarkevich, Nikolai A. ; Levitas, Valery I. ; Johnson, Duane D. ; Zhang, Xiancheng ( August 2020 , npj Computational Materials)

   Materials under complex loading develop large strains and often phase transformation via an elastic instability, as observed in both simple and complex systems. Here, we represent a material (exemplified for Si I) under large Lagrangian strains within a continuum description by a 5^th-order elastic energy found by minimizing error relative to density functional theory (DFT) results. The Cauchy stress—Lagrangian strain curves for arbitrary complex loadings are in excellent correspondence with DFT results, including the elastic instability driving the Si I → II phase transformation (PT) and the shear instabilities. PT conditions for Si I → II under action of cubic axial stresses are linear in Cauchy stresses in agreement with DFT predictions. Such continuum elastic energy permits study of elastic instabilities and orientational dependence leading to different PTs, slip, twinning, or fracture, providing a fundamental basis for continuum physics simulations of crystal behavior under extreme loading.

    

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3. Nontrivial nanostructure, stress relaxation mechanisms, and crystallography for pressure-induced Si-I → Si-II phase transformation

   https://doi.org/10.1038/s41467-022-28604-1  

   Chen, Hao ; Levitas, Valery I. ; Popov, Dmitry ; Velisavljevic, Nenad ( February 2022 , Nature Communications)

   Crystallographic theory based on energy minimization suggests austenite-twinned martensite interfaces with specific orientation, which are confirmed experimentally for various materials. Pressure-induced phase transformation (PT) from semiconducting Si-I to metallic Si-II, due to very large and anisotropic transformation strain, may challenge this theory. Here, unexpected nanostructure evolution during Si-I → Si-II PT is revealed by combining molecular dynamics (MD), crystallographic theory, generalized for strained crystals, and in situ real-time Laue X-ray diffraction (XRD). Twinned Si-II, consisting of two martensitic variants, and unexpected nanobands, consisting of alternating strongly deformed and rotated residual Si-I and third variant of Si-II, form$$\{111\}$$$\left\{111\right\}$interface with Si-I and produce almost self-accommodated nanostructure despite the large transformation volumetric strain of$$-0.237$$$-0.237$. The interfacial bands arrest the$$\{111\}$$$\left\{111\right\}$interfaces, leading to repeating nucleation-growth-arrest process and to growth by propagating$$\{110\}$$$\left\{110\right\}$interface, which (as well as$$\{111\}$$$\left\{111\right\}$interface) do not appear in traditional crystallographic theory.

    

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4. Characterizing Changes in Grain Growth, Mechanical Properties, and Transformation Properties in Differently Sintered and Annealed Binder-Jet 3D Printed 14M Ni–Mn–Ga Magnetic Shape Memory Alloys

   https://doi.org/10.3390/met12050724  

   Acierno, Aaron ; Mostafaei, Amir ; Toman, Jakub ; Kimes, Katerina ; Boin, Mirko ; Wimpory, Robert C. ; Laitinen, Ville ; Saren, Andrey ; Ullakko, Kari ; Chmielus, Markus ( May 2022 , Metals)

   Ni–Mn–Ga Heusler alloys are multifunctional materials that demonstrate macroscopic strain under an externally applied magnetic field through the motion of martensite twin boundaries within the microstructure. This study sought to comprehensively characterize the microstructural, mechanical, thermal, and magnetic properties near the solidus in binder-jet 3D printed 14M Ni50Mn30Ga20. Neutron diffraction data were analyzed to identify the martensite modulation and observe the grain size evolution in samples sintered at temperatures of 1080 °C and 1090 °C. Large clusters of high neutron-count pixels in samples sintered at 1090 °C were identified, suggesting Bragg diffraction of large grains (near doubling in size) compared to 1080 °C sintered samples. The grain size was confirmed through quantitative stereology of polished surfaces for differently sintered and heat-treated samples. Nanoindentation testing revealed a greater resistance to plasticity and a larger elastic modulus in 1090 °C sintered samples (relative density ~95%) compared to the samples sintered at 1080 °C (relative density ~80%). Martensitic transformation temperatures were lower for samples sintered at 1090 °C than 1080 °C, though a further heat treatment step could be added to tailor the transformation temperature. Microstructurally, twin variants ≤10 μm in width were observed and the presence of magnetic anisotropy was confirmed through magnetic force microscopy. This study indicates that a 10 °C sintering temperature difference can largely affect the microstructure and mechanical properties (including elastic modulus and hardness) while still allowing for the presence of magnetic twin variants in the resulting modulated martensite. 

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5. Effect of a Micro-scale Dislocation Pileup on the Atomic-Scale Multi-variant Phase Transformation and Twinning

   Peng, Yipeng ; Ji, Rigelesaiyin ; Phan, Thanh ; Capolungo, Laurent ; Levitas, Valery I. ; Xiong, Liming ( August 2022 , arXivorg)

   In this paper, we perform concurrent atomistic-continuum (CAC) simulations to (i) characterize the internal stress induced by the microscale dislocation pileup at an atomically structured interface; (ii) decompose this stress into two parts, one of which is from the dislocations behind the pileup tip according to the Eshelby model and the other is from the dislocations at the pileup tip according to a super-dislocation model; and (iii) assess how such internal stresses contribute to the atomic-scale phase transformations (PTs), reverse PTs, and twinning. The main novelty of this work is to unify the atomistic description of the interface and the coarse-grained (CG) description of the lagging dislocations away from the interface within one single framework. Our major findings are: (a) the interface dynamically responds to a pileup by forming steps/ledges, the height of which is proportional to the number of dislocations arriving at the interface; (b) when the pre-sheared sample is compressed, a direct square-to-hexagonal PT occurs ahead of the pileup tip and eventually grows into a wedge shape; (c) upon a further increase of the loading, part of the newly formed hexagonal phase transforms back to the square phase. The square product phase resulting from this reverse PT forms a twin with respect to the initial square phase. All phase boundaries (PBs) and twin boundaries (TBs) are stationary and correspond to zero thermodynamic Eshelby driving forces; and (d) the stress intensity induced by a pileup consisting of 16 dislocations reduces the stress required for initiating a PT by a factor of 5.5, comparing with that in the sample containing no dislocations. This work is the first characterization of the behavior of PTs/twinning resulting from the reaction between a microscale dislocation slip and an atomically structured interface. 

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