The axial ising model for martensitic transformations and pseudoelasticity

A theory based on the Ising axial model for the martensitic transformation between close-packed structures in an external stress field is proposed. The quasi-spin Hamiltonian was derived for a stratified close-packed crystal which under certain limitations has the form of a Hamiltonian of the ANNNI-model wherein “the exchange integrals” are expressed in terms of the interlayer interaction potentials. The dependence of the strain on the shear stress is calculated for alloys showing the pseudoelasticity effect and it is shown that the number of steps in the deformation curve is defined by the radius of the interlayer interaction. The theory proposed is applied to the explanation of the stress-induced martensitic transformations in Cu-Al-Ni alloys.     

Ni4Ti3沉淀相对NiTi形状记忆合金相变行为的影响

采用第二近邻修正型嵌入原子势的分子动力学方法,建立了共格沉淀相与半共格沉淀相块状/柱状模型,模拟了温度诱发相变和应力诱发相变,分析了Ni₄Ti₃沉淀相对Ni Ti形状记忆合金相变行为的影响．结果表明,Ni₄Ti₃沉淀相本征应变诱发的弹性应力场对相变中马氏体变体类型、形核位置、分布等有重要影响.在温度诱发相变时,共格沉淀相促进部分马氏体变体的形核生长,能显著提高Ni Ti超弹性形状记忆合金的马氏体相变开始温度;在应力诱发相变时,Ni₄Ti₃沉淀相使马氏体早于无沉淀相区域形核,导致了相变应力降低、抑制了马氏体解孪,减小了应力-应变曲线的滞回环.     

Martensitic transformation of TiNiPd high-temperature shape memory alloys: A first-principles study

Heat of formation, elastic property and electronic structure of TiNiPd high-temperature shape memory alloys have been investigated by first-principles calculations using the pseudopotentials plane-wave method. The results show that the heat of formation difference between austenite and martensite plays an important role in the martensitic transformation. The effect of Pd content on the martensitic transformation temperature and transformation type is clarified based on the elastic constants of the B2 phases. High martensitic transformation temperature can be attributed to a low shear resistance C′. Furthermore, the mechanism of the effect of Pd addition on elastic constants is explained on the basis of the electronic structure.     

Anomalous elasticity and anelasticity of GdCu at low temperatures

The temperature dependence of the single crystal and polycrystalline elastic constants of GdCu compound have been determined between the ambient and 77 K, the interval in which the structural instability occurs. From the shear constants, C' and C₄₄ the magnitude of the elastic anisotropy was calculated, and found to be close to unity over the whole temperature range. This is in contrast with the expected behavior of the elastic anisotropy in the vicinity of martensitic transformations, where the anisotropy attains appreciable values. The large changes of the shear elastic constants, relative to the compressional constant suggests that the structural instability in GdCu is induced by a mechanism of isotropic shear. The peak in the ultrasonic attenuation is symmetric, typical of a relaxational process. The behavior of the elastic properties and ultrasonic attenuation in the temperature interval of the structural instability of GdCu is discussed.     

Martensitic transformations in some ferrous and non-ferrous alloys under magnetic field and hydrostatic pressure

Martensitic transformations are extensively influenced by external fields, such as temperature and uniaxial stress, in transformation temperatures, crystallography and amount and morphology of the product martensites. Therefore, to clarify the effect of external fields on martensitic transformations it is very important to understand the essential problems of the transformation, such as thermodynamics, kinetics and the origin of the transformation, whose information is naturally useful in technological applications using the transformation. Magnetic field and hydrostatic pressure are important in such external fields because there exist some significant differences in magnetic moment and atomic volume between the parent and martensitic states. In the present paper, therefore, we summarizz the effects of magnetic field and hydrostatic pressure on martensitic transfonnations in some ferrous and non-ferrous alloys by referring to past and recent works made by our group and many other researchers. The transformation start temperatures of all the ferrous alloys examined increase with increasing magnetic field, but those of non-ferrous alloys, such as Ti-Ni and Cu-Al-Ni shape memory alloys, are not affected. On the other hand, the transformation start temperature decreases with increasing hydrostatic pressure in some ferrous alloys, but increases in Cu-Al-Ni alloys. The magnetic field and hydrostatic pressure dependencies of the martensitic start temperature are in good agreement with those calculated by our proposed equations.

During investigations of ferrous Fe-Ni-Co-Ti shape memory alloy, we found that a magnetoelastic martensitic transformation appears and, in addition, several martensite plates grow nearly parallel to the direction of the applied magnetic field in a specimen of Fe-Ni alloy single crystal.

We further found that the isothermal process in Fe-Ni-Mn alloy changes to athermal under a magnetic field and the athermal process changes to isothermal under hydrostatic pressure. Based on these facts, a phenomenological theory has been constructed, which unifies the two transformation processes.     

Effects of Cu on the martensitic transformation and magnetic properties of Mn_(50)Ni_(40)In_(10) alloy

The structures, the martensitic transformations, and the magnetic properties are studied systematically in Mn50Ni40-xCuxIn10, Mn50-xCuxNi40In10, and Mn50Ni40In10-xCux alloys. The partial substitution of Ni by Cu reduces the martensitic transformation temperature, but has little influence on the Curie temperature of austenite. Comparatively, the martensitic transformation temperature increases and the Curie temperature of austenite decreases with the partial replacement of Mn or In by Cu. The magnetization difference between the austenite phase and the martensite phase reaches 70 emu/g in Mn50Ni39Cu1In10; a field-induced martensite-to-austenite transition is observed in this alloy.     

Temperature and pressure derivatives of elastic constants in single crystal Au-47.5 at.% Cd near martensitic phase transformation

The behavior of the elastic properties and their pressure derivatives near the martensitic transformation β→β′ was determined from sound velocity measurements at a frequency of 10 MHz, on a single crystal of Au-47.5 at.% Cd.The transformation of the β phase to the martensitic β' phase was obtained from the anisotropic elastic constants c₁₁, c₄₄ and c′, and their pressure derivatives. The behaviour of c₁₁ and c₄₄ is normal as a function of temperature, while the variation of c′ is positive with temperature. Before the β→β′ phase change the value of c′ is very small and exhibits high elastic anisotropy. The small value of c′ and the anisotropy were explained according to the crystallographic mechanism of the martensitic transformation and the Zener theory of instability of the b.c.c. structure. The pressure derivatives of c′ are negative and the variation of $\text{d}\text{c}{}_{44}\text{d}\text{P}$ with temperature is anomalous. This behavior can be explained by the influence of pressure on the transformation temperature, and by the instability of the β phase. It was found that the elastic constants c′ determine the mechanism of the transformation. From the pressure derivatives of c₁₁, c₄₄ and c′ the Grüneisen parameters for different modes of vibration were calculated. For the c′ mode the values are negative, for the c₄₄ mode the variation of the parameter with temperature is negative. This anomalous behavior can be explained as due to the anisotropic softening of the atom bonding on the (110) planes of the cubic structure, as a consequence of the phase transformation mechanism.     

Acoustic study of martensitic-phase aging in copper-based shape memory alloys

An acoustic technique was applied to study aging of the β ₁ ^′ martensitic phase in a number of copper-based shape memory alloys (Cu-Zn-Al, Cu-Al-Ni, Cu-Al-Be) characterized by various degrees of martensitic-phase stabilization. The nonlinear anelasticity of the martensitic phase was studied in wide ranges of temperature (7–300 K) and vibrational strain amplitude (2 × 10^?7 ?2 × 10^?4) at vibrational-loading frequencies of ～100 kHz. It was shown that aging effects of the martensitic phase can have homogeneous and heterogeneous components. The homogeneous component is associated with a change in the degree of atomic order in the crystal volume. The basic heterogeneous mechanisms of martensitic-phase aging are associated with the formation of atmospheres of point defects and local changes (which are greater than those in the crystal volume) in the degree of atomic order in the vicinity of partial dislocations and the boundaries between martensite variants. It is concluded that various stabilization properties of the alloys at hand result not only from the different diffusion properties of quenching point defects but also from the different influence of these defects on the degree of atomic order and the different features of their interaction with partial dislocations and intervariant boundaries.     

18 MeV质子辐照对TiNi形状记忆合金R相变的影响

 研究了用HZ-B串列加速器的18MeV质子辐照对TiNi形状记忆合金R相变的影响，辐照在奥氏体母相状态下进行。示差扫描量热法（DSC）表明，辐照后R相变开始温度T^s_R和逆马氏体相变结束温度T^f_A随辐照注量的增加而降低。当注量为1.53×10¹⁴/cm²时，T^sR和T^f_A分别下降6K和13K，辐照未引起R相变结束温度T^s_R和逆马氏体相变开始温度T^f_A的变化。表明辐照后母相(奥氏体相)稳定。透射电镜（TEM）分析表明辐照后没有引起合金可观察的微观组织变化。辐照对R相变开始温度T^s_{R和逆马氏体相变结束温度Af的影响可能是由于质子辐照后产生了孤立的缺陷团，形成了局部应力场，引起晶格有序度的下降所造成的。}     

Behavior of the nickel-titanium alloys with the shape memory effect under conditions of shock wave loading

The behavior of the Ti_51.1Ni_48.9 and Ti_49.4Ni_50.6 alloys with shape memory effects has been studied under submicrosecond shock wave loading in the temperature range from −80 to 160°C, which includes both the regions of the stable state of the specimens in the austenite and martensite phases and the regions of thermoelastic martensitic transformations. The grain size of the studied alloys varies from initial values 15–30 to 0.05–0.30 μm. The dependences of the dynamic elastic limit on the temperature and on the elemental composition are similar to the dependences of the yield stress of these alloys under low strain rate loading. The rarefaction shock wave formation as a consequence of the pseudoelastic behavior of the alloy during a reversible martensitic transformation has been revealed. A decrease in the grain size leads to an increase in the dynamic elastic limit and decreases the temperatures of martensitic transformations.     

热磁预处理对Ni-Mn-Ga单晶磁学和力学性能的影响

研究了预先热磁处理对Ni_503Mn_287Ga₂₁单晶的磁学和力学性能的影响.首先将样品加热到居里温度之上让其冷却,冷却方式分为两种：一种是施加一定大小的磁场从高于居里温度冷却至室温,另一种是在样品经历顺磁-铁磁相变后但还未发生奥氏体-马氏体相变前施加相同大小和方向的磁场并冷却至室温.室温时的拉伸-压缩实验结果表明单晶样品在经历前一种处理后,其可逆应变、磁化强度的变化 （ΔM）比后一种处理的相应值要小很多.在后一种热磁处理的样品中,顺磁-铁磁相变发生后形成了自发磁畴,但这种磁畴不具有择优取向.在顺磁-铁磁相变结束后施加磁场,容易导致择优的马氏体准单畴出现,从而表现出大的可逆应变和ΔM.但对于前者,我们认为样品从居里温度降到室温过程中,其中的磁畴在相同的磁场作用下获得择优生长,形成大磁畴,导致磁诱导的强各向异性.这种择优取向的大磁畴在随后马氏体相变期间影响着马氏体的自发排列方式,不利于马氏体准单畴的出现,结果导致较小的可逆应变和ΔM. 关键词： 磁和力学锻炼 Ni-Mn-Ga单晶 铁磁和马氏体相变     

Modelling of dislocation-induced martensitic transformation in anisotropic crystals

The structural transformation caused by dislocation-induced heterogeneous nucleation in the fcc?→?bcc martensitic transformation in elastically anisotropic crystals is investigated by using the phase field microelasticity model. The three-dimensional microstructure of the dislocation-induced martensitic embryos is obtained. It is found that the embryos are not single-domain particles as is usually assumed but rather a complex self-organized assemblage of stress-accommodating twin-related microdomains. Sessile metastable martensitic embryos around the dislocation loops form in the prototype Fe–Ni alloy system above the temperatures of the martensitic transformation. A possibility that the presence of these pre-existing embryos could be responsible, at least, for a part of the elastic modulus softening with the temperature decrease observed in many martensitic systems is discussed. The effects of elastic anisotropy, the “chemical” energy barrier and structural anisotropy of the Landau free energy on the formation and growth of martensitic embryos are investigated. The assumptions of elastic isotropy and a choice of the anisotropic term in Landau polynomial do not significantly affect the microstructure of martensitic embryos but may appreciably change the undercooling that is necessary to eliminate the total nucleation barrier and start the athermal martensitic transformation.     

Ni53.2Mn22.6Ga24.2单晶的两步热弹性马氏体相变及其应力应变特性

对具有两步完全热弹性的Ni_53.2Mn_22.6Ga_24.2单晶的物性采用多种测量手段进行了表征,特别研究了不同温度下的应力-应变特性.研究表明,热诱发的中间马氏体相变应变远大于马氏体相变应变.在较低的形变温度下,沿单晶母相［001］方向的压应力诱发的是两步马氏体相变,材料表现出赝弹性;在较高的形变温度下,只能观察到一步马氏体相变,材料展现出完全超弹性特性.此外,利用热力学理论分别计算了诱发马氏体相变和中间马氏体相变的临界应力与形变温度的关系,与实验测量得到的结果相符. 关键词： 马氏体相变 形状记忆效应 应变 超弹性     

Crystalline damage growth during martensitic phase transformations

A thermomechanical model is developed within a large deformation setting in order to simulate the interactions between martensitic phase transformations and crystalline damage growth at the austenitic grain level. Subgrain information is included in the model via the crystallographic theory of martensitic transformations. The damage and transformation characteristics are dependent of the specific martensitic transformation systems activated during a loading process, which makes the model strongly anisotropic. The state of transformation for the individual transformation systems is represented by the corresponding volume fractions. The state of damage in the austenite and in the martensitic transformation systems is reflected by the corresponding damaged volume fractions. The thermodynamical forces energetically conjugated to the rate of volume fraction and the rate of damaged volume fraction are the driving forces for transformation and crystalline damage, respectively. The expressions for these driving forces follow after constructing the specific form of the Helmholtz energy for a phase-changing, damaging material. The model is used to analyze several three-dimensional boundary value problems that are representative of microstructures appearing in multiphase carbon steels containing retained austenite. The analyses show that the incorporation of damage in the model effectively limits the elastic stresses developing in the martensitic product phase, where the maximum value of the stress strongly depends on the toughness of the martensite. Furthermore, in an aggregate of randomly oriented grains of retained austenite embedded in a ferritic matrix the generation of crystalline damage delays the phase transformation process, and may arrest it if the martensitic product phase is sufficiently brittle. The response characteristics computed with the phase-changing damage model are confirmed by experimental results.     

18 MeV质子辐照对TiNi形状记忆合金R相变的影响

研究了用HZ B串列加速器的18MeV质子辐照对TiNi形状记忆合金R相变的影响,辐照在奥氏体母相状态下进行。示差扫描量热法(DSC)表明,辐照后R相变开始温度TsR和逆马氏体相变结束温度TfA随辐照注量的增加而降低。当注量为1.53×1014/cm2时,TsR和TfA分别下降6K和13K,辐照未引起R相变结束温度TfR和逆马氏体相变开始温度TsA的变化。表明辐照后母相(奥氏体相)稳定。透射电镜(TEM)分析表明辐照后没有引起合金可观察的微观组织变化。辐照对R相变开始温度TsR和逆马氏体相变结束温度Af的影响可能是由于质子辐照后产生了孤立的缺陷团,形成了局部应力场,引起晶格有序度的下降所造成的。     

A first-principles study on the structural and elastic properties and the equation of state of wurtzite-type cadmium selenide under pressure

A first-principles investigation on the crystal structural and elastic properties and the equation of state of wurtzite-type cadmium selenide (w-CdSe) has been conducted using the plane-wave pseudo-potential density functional theory and the quasi-harmonic Debye model. The elastic constants, the aggregate elastic moduli, the elastic anisotropy, and Poisson's ratio under pressure have been investigated. Our calculated equilibrium lattice constants, the elastic constants, and the aggregate elastic moduli at zero pressure are in good agreement with the experimental data and other theoretical results. The variations in the compressional and shear elastic wave velocities with pressure at zero temperature up to pressure 2.7 GPa have been studied; the computed Debye temperature at zero pressure and zero temperature is in reasonable agreement with the result of Bonello et al., In addition, the equation of state of w-CdSe in the pressure range of 0–2.7 GPa and up to a temperature of 900 K has also been obtained.     

Ultrasonic measurement of the elastic properties of benzoyl glycine single crystals

Certain organic crystals are found to possess high non-linear optical coefficients, often one to two orders of magnitude higher than those of the well-known inorganic non-linear optical materials. Benzoyl glycine is one such crystal whose optical second-harmonic generation efficiency is much higher than that of potassium dihydrogen phosphate. Single crystals of benzoyl glycine are grown by solvent evaporation technique usingN, N-dimethyl formamide as the solvent. All the nine second-order elastic stiffness constants of this orthorhombic crystal are determined from ultrasonic wave velocity measurements employing the pulse echo overlap technique. The anisotropy of elastic wave propagation in this crystal is demonstrated by plotting the phase velocity, slowness, Young’s modulus and linear compressibility surfaces along symmetry planes. The volume compressibility, bulk modulus and relevant Poisson’s ratios are also determined. Variation of the diagonal elastic stiffness constants with temperature over a limited range are measured and reported.     

Effect of gallium alloying on the structure,the phase composition,and the thermoelastic martensitic transformations in ternary Ni–Mn–Ga alloys

The effect of gallium alloying on the structure, the phase composition, and the properties of quasibinary Ni₅₀Mn_50–zGa_z (0 ? z ? 25 at %) alloys is studied over a wide temperature range. The influence of the alloy composition on the type of crystal structure in high-temperature austenite and martensite and the critical martensitic transformation temperatures is analyzed. A general phase diagram of the magnetic and structural transformations in the alloys is plotted. The temperature–concentration boundaries of the B2 and L2₁ superstructures in the austenite field, the tetragonal L1₀ (2M) martensite, and the 10M and 14M martensite phases with complex multilayer crystal lattices are found. The predominant morphology of martensite is shown to be determined by the hierarchy of the packets of thin coherent lamellae of nano- and submicrocrystalline crystals with planar habit plane boundaries close to {011}_B2. Martensite crystals are twinned along one of the 24 \(24\left\{ {011} \right\}{\left\langle {01\bar 1} \right\rangle _{B2}}\) “soft” twinning shear systems, which provides coherent accommodation of the martensitic transformation–induced elastic stresses.     

Magneto-optical spectroscopy of the martensitic transition in Fe48Mn24Ga28 Heusler alloys

Magneto-optical spectra of polycrystalline samples of the Fe₄₈Mn₂₄Ga₂₈ Heusler alloy undergoing martensitic transformation from the high-temperature paramagnetic austenitic to ferromagnetic martensitic phase have been studied at 50–320 K in the transversal Kerr effect geometry. A comparison of magnetooptical spectra with data obtained in magnetic measurements has demonstrated that the martensitic transition on the surface of a sample and in its bulk takes place in the same temperature interval. Magnetic anisotropy has been found in the martensitic phase driven by large multidomain inclusions of martensite in austenite. The magneto-optical signal of Fe₄₈Mn₂₄Ga₂₈ differs strongly in spectral shape from that measured in Ni-Mn-Ga.