Martensitic Phase Transition Research Articles

Geometrical model for martensitic phase transitions: Understanding criticality and weak universality during microstructure growth.

A simple model for the growth of elongated domains (needle-like) during a martensitic phase transition is presented. The model is purely geometric and the only interactions are due to the sequentiality of the kinetic problem and to the excluded volume, since domains cannot retransform back to the original phase. Despite this very simple interaction, numerical simulations show that the final observed microstructure can be described as being a consequence of dipolar-like interactions. The model is analytically solved in 2D for the case in which two symmetry related domains can grow in the horizontal and vertical directions. It is remarkable that the solution is analytic both for a finite system of size L×L and in the thermodynamic limit L→∞, where the elongated domains become lines. Results prove the existence of criticality, i.e., that the domain sizes observed in the final microstructure show a power-law distribution characterized by a critical exponent. The exponent, nevertheless, depends on the relative probabilities of the different equivalent variants. The results provide a plausible explanation of the weak universality of the critical exponents measured during martensitic transformations in metallic alloys. Experimental exponents show a monotonous dependence with the number of equivalent variants that grow during the transition.

Martensitic transformation, magnetocaloric effect and phase transition strain in Ni50Mn36−xGexSn14Heusler alloys

In present work, the effect of Ge substitution for Mn on crystal structure and martensitic transformation was carefully investigated in magnetic shape memory Ni50Mn36−xGexSn14 (x = 0, 1) alloys. From X-ray diffraction (XRD) patterns, it can be found that each sample possesses cubic austenitic structure (L21) at room temperature and the main peak (220) shifts to higher degree with Ge doping, indicating that the cell volume of austenitic phase shrinks. With Ge content increasing, martensitic transformation (MT), temperature shifts to higher temperature region and the difference of magnetization between martensitic and austenitic phases (ΔM) also increases. In addition, the magnetocaloric effect (MCE) and phase transition strain (ΔL/L) were investigated in Ni50Mn35GeSn14 alloy. The maximal magnetic entropy change (ΔSm) associated with martensitic transition is 3.9 J·kg−1·K−1 with applied magnetic field change of 5 T and the maximal ΔL/L reaches 0.18% in this alloy.

High-pressure torsion driven phase transformations in Cu–Al–Ni shape memory alloys

Severe plastic deformation (SPD) frequently induces phase transformations like decomposition of supersaturated solid solution, dissolution of precipitates, amorphization, nanocrystallization etc. Such diffusive phase transitions are combined with SPD-driven accelerated mass transfer. Displacive (or martensitic) phase transitions can also take place and in combination with diffusive ones have not been investigated in depth in severely deformed materials. The goal of this work is to investigate the combination of displacive (austenite↔martensite) and diffusive (decomposition of supersaturated solid solution) phase transitions in two different Cu–Al–Ni shape memory alloys under the influence of high-pressure torsion (HPT). After homogenization in the one-phase (austenitic) β-area of Cu–Al–Ni phase diagram and quenching, the first alloy was in martensitic state (mainly β′3 martensite with a small amount of γ′3 martensite), and the second one remained austenitic (β3 phase). The HPT of these alloys led to the precipitation of α1-phase in the first case and γ1-phase in the second one (as if they were annealed at an effective temperature Teff = 620 ± 20 °C). As a result of precipitation, the matrix in the first alloy was enriched and in the second one depleted in Al. After HPT, both alloys contained mainly β′3 martensite with a certain amount of γ′3 martensite. Thus, the HPT-driven diffusive transformations (precipitation of α1-and γ1-phase) influence the followed displacive (martensitic) transformation. Simultaneously, a dramatic grain refinement is obtained and the reported results open new possibilities to investigate the superelastic and shape memory effects in nanostructured Cu–Al–Ni alloys.

Xe(N2)2compound to 150 GPa: Reluctance to the formation of a xenon nitride

The $\mathrm{Xe}\text{\ensuremath{-}}{\mathrm{N}}_{2}$ binary phase diagram was determined at 296 K from the pressure evolution of 14 different concentrations. The properties of $\mathrm{Xe}\text{\ensuremath{-}}{\mathrm{N}}_{2}$ mixtures were characterized using visual observation, Raman spectroscopy, and powder x-ray diffraction. Above 4.9 GPa, the $\mathrm{Xe}({\mathrm{N}}_{2}{)}_{2}$ van der Waals compound is stable and adopts the $\mathrm{MgC}{\mathrm{u}}_{2}$-type Laves phase structure $(Fd\text{\ensuremath{-}}3m)$ with ${\mathrm{N}}_{2}$ molecules orientationally disordered. At 10 GPa, this cubic lattice undergoes a martensitic phase transition into a tetragonal $(I{4}_{1}/amd)$ unit cell. This transition is associated with a partial ordering of the ${\mathrm{N}}_{2}$ molecules, possibly due to the growing ${\mathrm{N}}_{2}\text{\ensuremath{-}}{\mathrm{N}}_{2}$ quadrupole-quadrupole interaction with density. No other phase transition was detected up to 154 GPa, even after heating the sample to 2000 K. Above 30 GPa, a softening of the ${\mathrm{N}}_{2}$ vibron mode with pressure reveals a weakening of the ${\mathrm{N}}_{2}$ intramolecular bond that suggests an electronic redistribution between ${\mathrm{N}}_{2}\text{\ensuremath{-}}{\mathrm{N}}_{2}$ and $\mathrm{Xe}\text{\ensuremath{-}}{\mathrm{N}}_{2}$ entities. These interactions could explain the great stability of the $\mathrm{Xe}({\mathrm{N}}_{2}{)}_{2}$ compound. However, no xenon nitride was observed.

Electronic structure and X-ray magnetic circular dichroism in the Ni-Mn-Ga Heusler alloys

The electronic structure and X-ray magnetic circular dichroism (XMCD) spectra of the Ni2MnGa and Cu doped Ni2MnGa Heusler alloys were investigated theoretically from first principles, using the fully relativistic Dirac linear MT-orbital (LMTO) band structure method. Densities of valence states, orbital and spin magnetic moments are analyzed and discussed. The electronic and magnetic structure of Ni-Mn-Ga Heusler alloys were investigated for the cubic austenitic and modulated 7M-like incommensurate martensitic phases. The X-ray absorption spectra (XAS) and XMCD at the Mn, Ni, Ga, and Cu L2,3, and Mn, Ni, and Ga K edges were investigated theoretically from first principles. The origin of the XMCD spectra in the Ni2MnGa compound is examined. The ab initio calculations reproduce well experimental XAS and XMCD spectra. The XAS at the Mn L2,3 edges remains mostly unchanged through martensitic phase transition. A fingerprint of the martensitic phase transition has been found in the Ni L2,3 XAS spectra. The experimental Ni L3 XAS has a pronounced shoulder at the L3 peak at around 853 eV. This peak is nearly suppressed in the martensitic state in comparison with the austenitic phase due to the lifting of the degeneracy in the Ni 3d related unoccupied electronic states. The XMCD of the martensitic phase is increased compared to the XMCD of the austenite phase at the Ni and Mn L2,3 edges.

Strain-rate-induced bcc-to-hcp phase transformation of Fe nanowires**Project supported by the National Natural Science Foundation of China (Grant No. 51571082) and China Postdoctoral Science Foundation (Grant No. 2015M580191).

Using molecular dynamics simulation method, the plastic deformation mechanism of Fe nanowires is studied by applying uniaxial tension along the [110] direction. The simulation result shows that the bcc-to-hcp martensitic phase transformation mechanism controls the plastic deformation of the nanowires at high strain rate or low temperature; however, the plastic deformation mechanism will transform into a dislocation nucleation mechanism at low strain rate and higher temperature. Furthermore, the underlying cause of why the bcc-to-hcp martensitic phase transition mechanism is related to high strain rate and low temperature is also carefully studied. Based on the present study, a strain rate-temperature plastic deformation map for Fe nanowires has been proposed.

Diffusion quantum Monte Carlo study of martensitic phase transition energetics: The case of phosphorene.

Recent technical advances in dealing with finite-size errors make quantum Monte Carlo methods quite appealing for treating extended systems in electronic structure calculations, especially when commonly used density functional theory (DFT) methods might not be satisfactory. We present a theoretical study of martensitic phase transition energetics of a two-dimensional phosphorene by employing diffusion Monte Carlo (DMC) approach. The DMC calculation supports DFT prediction of having a rather diffusive barrier that is characterized by having two transition states, in addition to confirming that the so-called black and blue phases of phosphorene are essentially degenerate. At the same time, the DFT calculations do not provide the quantitative accuracy in describing the energy changes for the martensitic phase transition even when hybrid exchange-correlation functional is employed. We also discuss how mechanical strain influences the stabilities of the two phases of phosphorene.

Electronic structure and magneto-optical Kerr effect spectra of ferromagnetic shape-memory Ni-Mn-Ga alloys: Experiment and density functional theory calculations

In this joint experimental and ab initio study, we focused on the influence of the chemical composition and martensite phase transition on the electronic, magnetic, optical, and magneto-optical properties of the ferromagnetic shape-memory Ni-Mn-Ga alloys. The polar magneto-optical Kerr effect (MOKE) spectra for the polycrystalline sample of the Ni-Mn-Ga alloy of ${\mathrm{Ni}}_{60}{\mathrm{Mn}}_{13}{\mathrm{Ga}}_{27}$ composition were measured by means of the polarization modulation method over the photon energy range $0.8\ensuremath{\le}h\ensuremath{\nu}\ensuremath{\le}5.8$ eV in magnetic field up to 1.5 T. The optical properties (refractive index $n$ and extinction coefficient $k)$ were measured directly by spectroscopic ellipsometry using the rotating analyzer method. To complement experiments, extensive first-principles calculations were made with two different first-principles approaches combining the advantages of a multiple scattering Green function method and a spin-polarized fully relativistic linear-muffin-tin-orbital method. The electronic, magnetic, and MO properties of Ni-Mn-Ga Heusler alloys were investigated for the cubic austenitic and modulated 7M-like incommensurate martensitic phases in the stoichiometric and off-stoichiometric compositions. The optical and MOKE properties of Ni-Mn-Ga systems are very sensitive to the deviation from the stoichiometry. It was shown that the ab initio calculations reproduce well experimental spectra and allow us to explain the microscopic origin of the ${\mathrm{Ni}}_{2}\mathrm{MnGa}$ optical and magneto-optical response in terms of interband transitions. The band-by-band decomposition of the ${\mathrm{Ni}}_{2}\mathrm{MnGa}$ MOKE spectra is presented and the interband transitions responsible for the prominent structures in the spectra are identified.

Hydrostatic pressure tuned magneto-structural transition and occurrence of pressure induced exchange bias effect in Mn0.85Fe0.15NiGe alloy

The magnetic and magneto-functional behavior of a Fe-doped MnNiGe alloy with nominal composition Mn0.85Fe0.15NiGe have been investigated in ambient as well as in high pressure conditions. The alloy undergoes a first order martensitic phase transition (MPT) around 200 K and also shows a large conventional magnetocaloric effect (MCE) ( J kg−1 K−1 for magnetic field (H) changing from 0–50 kOe) around the transition in ambient conditions. The application of external hydrostatic pressure (P) results in a shift in MPT towards the lower temperature and a clear decrease in the saturation moment of the alloy at 5 K. The peak value of MCE is also found to decrease with increasing external P (∼18 J kg−1 K−1 decrease in has been observed for P = 12.5 kbar). The most interesting observation is the occurrence of the exchange bias effect (EBE) on application of external P. The competing ferromagnetic and antiferromagnetic interaction in the presence of external P plays the pivotal role towards the observation of P induced EBE.

First-principles study of martensitic transformation and magnetic properties of carbon doped Ni–Mn–Sn Heusler alloys

The magnetic properties, structural stabilities and martensitic transformation of carbon doped Ni–Mn–Sn Heusler alloys are investigated by means of ab initio calculations in framework of the density functional theory. The results of calculations have shown that the martensitic transformation can be realized in all series of carbon doped Ni2Mn1.5Sn0.5−xCx alloys with tetragonal ratio of 1.34, 1.40,1.42 and 1.44, respectively for x=0.125,0.25,0.375 and 0.5. The DOS peak at the Fermi level almost disappearing in the tetragonal phase near the Fermi level is the evidence of triggering martensitic transformation which is due to the structural Jahn–Teller effect. We have also found that the difference between the austenitic and martensitic phases increases with increasing carbon content, which implies an enhancement of the martensitic phase transition temperature (TM). Besides, the electron density difference shows the enhancement of bonding between Mn and carbon atoms with the distortion taken place.

Tuning Martensitic Phase Transition by Non-Magnetic Atom Vacancy in MnCoGe Alloys and Related Giant Magnetocaloric Effect**Supported by the National Natural Science Foundation of China under Grant No 11504222.

The effects of non-magnetic atom vacancy on structural, martensitic phase transitions and the corresponding magnetocaloric effect in MnCoGe1−x alloys are investigated using x-ray diffraction and magnetic measurements. The introduction of non-magnetic atom vacancy leads to the decrease of the martensitic transition temperature and realizes a temperature window where magnetic and martensitic phase transitions can be tuned together. Moreover, the giant magnetocaloric effect accompanied with the coupled magnetic-structural transition is obtained. It is observed that the peak values of magnetic entropy change of MnCoGe0.97 are about −13.9, −35.1 and −47.4 J·kg−1 K−1 for ΔH = 2, 5, 7 T, respectively.

Constitutive model for the dynamic response of a NiTi shape memory alloy

In this paper, based on irreversible thermodynamic theory, the Helmholtz free energy function, was selected to deduce both the master equations and evolution equations of the constitutive model of a NiTi alloy under high strain. The Helmholtz free energy function contains the parameters of the reflecting phase transition and plastic property. The constitutive model for a NiTi alloy was implemented using a semi-implicit stress integration algorithm. Four successive stages can be differentiated and simulated: parent phase elasticity, martensitic phase transition, martensitic elasticity, and dislocation yield. The simulation results are in good agreement with the experimental results.

Rapid Equilibration by algorithmic quenching the ringing mode in molecular dynamics

ABSTRACTLong wavelength acoustic phonons are normally weakly coupled to other vibrational modes in a crystalline system. This is particularly problematic in molecular dynamics calculations where vibrations at the system-size scale are typically excited at initiation. The equilibration time for these vibrations depends on the strength of coupling to other modes, so is typically very long. A very simple deterministic method is presented which removes this problem. Examples of equilibration in lithium and a martensitic phase transition in sodium are used to demonstrate the method.

Problem of direct martensite transformation in a thick-walled cylinder made of shape memory alloy

The axisymmetric problem on the stress-strain state of a long thick-walled circular cylinder made of shape memory alloy experiencing the direct thermoelastic martensite phase transition under the action of constant internal and external pressures and a constant axial force is solved. The problem of limit loads in such a process is also considered.

Length scales and pinning of interfaces.

The pinning of interfaces and free discontinuities by defects and heterogeneities plays an important role in a variety of phenomena, including grain growth, martensitic phase transitions, ferroelectricity, dislocations and fracture. We explore the role of length scale on the pinning of interfaces and show that the width of the interface relative to the length scale of the heterogeneity can have a profound effect on the pinning behaviour, and ultimately on hysteresis. When the heterogeneity is large, the pinning is strong and can lead to stick-slip behaviour as predicted by various models in the literature. However, when the heterogeneity is small, we find that the interface may not be pinned in a significant manner. This shows that a potential route to making materials with low hysteresis is to introduce heterogeneities at a length scale that is small compared with the width of the phase boundary. Finally, the intermediate setting where the length scale of the heterogeneity is comparable to that of the interface width is characterized by complex interactions, thereby giving rise to a non-monotone relationship between the relative heterogeneity size and the critical depinning stress.

Nanoscaled Martensitic Domains in Ferroelastic Systems: Strain Glass

Strain glass, a frozen disordered ferroelastic state characterized by randomly distributed nanoscaled, non-ergodic martensitic domains, was recently found in ferroelastic TiNi-based alloys. Point defects like anti-site defects or dopants are found essential for the formation of the strain glass, but their role has remained obscure. In this paper, phase field method is employed to simulate how point defects change a normal ferroelastic system into a strain glass and as the result to clarify the role of point defects. We found that the local symmetry-breaking caused by the anisotropic local strain field of point defects plays a central role in the formation of strain glass. Such point-defect-induced local symmetry-breaking hinders the formation of long-range strain-ordering (twinned martensite) and results in a decrease in transition temperature Tc and a reduction of ferroelastic domain size. Above a critical defect concentration, the system transforms to a frozen state of nano-sized ferroelastic domains, i.e., strain glass. In addition, our simulation shows a gradual vanishing of heat capacity peak at the transition temperature with increasing defect concentration, and it also reproduces a characteristic non-ergodic ZFC/FC behavior of the glass state, which is in good agreement with recent experimental observations. Our results also indicate that the concentration fluctuation effect of point defects cannot stabilize a strain glass to very low temperature; thus the direct interaction between the random anisotropic strain field caused by point defects and the strain order parameter of the system is crucial for the formation of strain glass. Keywords: Martensitic phase transition, nanoscaled martensite, phase field, point defect, strain glass.

Magnetic nature of the austenite–martensite phase transition and spin glass behaviour in nanostructured Mn2Ni1.6Sn0.4 melt-spun ribbons

Nanocrystalline ribbons of inverse Heusler alloy Mn2Ni1.6Sn0.4 have been synthesised by melt spinning of the arc-melted bulk precursor. The single-phase ribbons crystallize into a cubic structure and exhibit very fine crystallite size of <2 nm. Temperature-dependent magnetization (M–T) measurements reveal ferromagnetic–austenite (FM-A)–antiferromagnetic–martensite (AFM-M) phase transition that begins at MS ≈ 249 K and finishes at Mf ≈ 224 K. During warming, the reverse AFM-M to FM-A transitions begins at As ≈ 240 K and finishes at Af ≈ 261 K. A re-entrant FM transition is observed in the M-phase at \(T_{\text{CM}}\) ≈ 145 K. These transitions are also confirmed by temperature-dependent resistivity (ρ–T) measurements. The hysteretic behaviour of M–T and ρ–T in the temperature regime spanned by the A-M transition is a manifestation of the first-order phase transition. M–T and ρ–T data also provide unambiguous evidence in favour of spin glass at \(T < T_{\text{CM}}\). The scaling of the glass freezing temperature (Tf) with frequency, extracted from the frequency-dependent AC susceptibility measurements, confirms the existence of canonical spin glass at \(T < T_{\text{CM}}\) ≈ 145 K. The occurrence of canonical spin glass has been explained in terms of the nanostructuring modified interactions between the coexisting FM and AFM correlations in the martensitic phase.

Simulation of Control System for Shape Memory Nanotweezers

Thermoelastic martensitic phase transition in Ni-Ti based shape memory alloys enables designing micro- and nanotools that are controlled by small changes in temperature (~10°С). This makes it feasible creating a new generation of complex microrobotical systems for manipulation and treatment of various nanoobjects in nanoindustry, medicine, nanoelectronics, etc. This work deals with the development of a physical and mathematical model for the micro manipulation system. The system under investigation pertains to shape memory composite nanotweezers with the composition Ti2NiCu/Pt located at the tip of a tungsten microneedle. The activation and control of the nanotweezers is done by heating them by the passage of an electric current flowing through a microdiode located in the needle. The microdiode serves the twin purpose of Joule heating and temperature sensing/measurement so as to close the feedback loop of the control system. The prototype of the control system was manufactured and tested. The data from the simulation were compared with those from the preliminary experiments.

Multiple magnetic transitions and associated room temperature magneto-functionality in Ni2.048Mn1.312In0.64

Present work reports on the observation of multiple magnetic transitions in a Ni-excess ferromagnetic shape memory alloy with nominal composition Ni2.048Mn1.312In0.64. The magnetization data reveal two distinct thermal hystereses associated with two different phase transitions at different temperature regions. The high temperature magnetic hysteresis is due to the martensitic phase transition whereas the low temperature hysteresis occurs around the magnetic anomaly signifying the transition from a paramagnetic-like state to the ferromagnetic ground state within the martensite. Clear thermal hysteresis along with the sign of the curvatures of Arrott plot curves confirm the first-order nature of both the transitions. In addition, the studied alloy is found to be functionally rich with the observation of large magnetoresistance (−45% and −4% at 80 kOe) and magnetocaloric effect (+16.7 Jkg−1K−1 and −2.25 Jkg−1K−1 at 50kOe) around these two hysteresis regions (300K and 195K respectively).

Phase Transition and Magnetocaloric Properties of Ni50Mn35–xIn15Cux Bulk Alloys and Ribbons

The martensitic and magnetic phase transitions are investigated in Ni50Mn35– x In15Cu x ( $x = 0$ , 1, 2, 3, 4, and 5) ferromagnetic shape memory alloys using X-ray diffraction, differential thermal analysis, and magnetization measurements. Ascribed to the increase of valence electron concentration, the martensitic transformation temperatures increase to over room temperature with the increase of Cu-substitution, both in bulks and ribbons. Curie temperature of martensitic phase, however, decreases with Cu-substitution. Thermomagnetic curves show that the magnetic and structural transitions are coupled from $x = 0$ to 3. Cu-substitution improves magnetocaloric effect (MCE). The comparison between bulks and ribbons shows that the martensitic transformation temperatures and the MCE of ribbons are slightly lower than those of the bulks, and are suggested to be related to Mn-volatilization in annealed bulks, small and inhomogeneous grain sizes in ribbons.